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Consulting Engineer
Sv <&/*, tr\^
MM. 3T3.,
,
Consulting Engineer
The Publishers and the Author will be grateful to
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their attention to any errors of omission or of commis-
sion that they may find therein. It is intended to make
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rarely happens that the early editions of works of any
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by the kindly criticism of his readers.
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WORKS OF WILLIAM KENT
PUBLISHED BY
JOHN WILEY & SONS.
The Mechanical Engineers' Pocket-Book.
A Reference Book of Rules, Tables, Data, and
Formulae, for the Use of Engineers, Mechanics,
and Students, xxxii-f- noo pages, i6mo, morocco,
$5.00.
Steam-Boiler Economy.
A Treatise on the Theory and Practice of Fuel
Economy in the Operation of Steam-Boilers.
xiv + 458 PaSes> T36 figures, 8vo, cloth, $4.00.
THE
MECHANICAL ENGINEER'S
POCKET-BOOK
A REFERENCE-BOOK OF RULES, TABLES, DATA,
AND FORMULAE, FOR THE USE OF
ENGINEERS, MECHANICS,
AND STUDENTS.
BY
WILLIAM KENT, A.M., M.E.,
Dean and Professor of Mechanical Engineering in the L. C. Smith
College of Applied Science, Syracuse University,
Member Amer. Soc'y Mechl Engrs. and Amer. Inst. Mining Engrs.
SEVENTH EDITION, REVISED AND ENLARGED
TEXTH THOUSAND.
TOTAL ISSTO FORTY-FIVE THOUSAND.
NEW YORK :
JOHN WILEY & SONS.
LONDON: CHAPMAN & HALL, LIMITED.
1906.
COPYRIGHT, 1895, 1902,
BY
WILLIAM KENT.
PRESS OF
BRAUNWORTH & CO.
BOOKBINDERS AND PRINTERS
BROOKLYN. N. Y.
PREFACE.
MORE than twenty years ago the author began to follow
the advice given by Nystrom : " Every engineeer should
make his own pocket-book, as he proceeds in study and
practice, to suit his particular business." The manuscript
pocket-book thus begun, however, soon gave place to more
modern means for disposing of the accumulation of engi-
neering facts and figures, viz., the index rerum, the scrap-
book, the collection of indexed envelopes, portfolios and
boxes, the card catalogue, etc. Four years ago, at the re-
quest of the publishers, the labor was begun of selecting
from this accumulated mass such matter as pertained to
mechanical engineering, and of condensing, digesting, and
arranging it in form for publication. In addition to "this, a
careful examination was made of the transactions of engi-
neering societies, and of the most important recent works
on mechanical engineering, in order to fill gaps that might
be left in the original collection, and insure that no impor-
tant facts had been overlooked.
Some ideas have been kept in mind during the prepara-
tion of the Pocket-book that will, it is believed, cause it to
differ from other works of its class. In the first place it
was considered that the field of mechanical engineering was
so great, and the literature of the subject so vast, that as
little space as possible should be given to subjects which
especially belong to civil engineering. While the mechan-
ical engineer must continually deal with problems which
belong properly to civil engineering, this latter branch is
so well covered by Trautwine's " Civil Engineer's Pocket-
book " that any attempt to treat it exhaustively would not
only fill no "long-felt want," but would occupy space
which should be given to mechanical engineering.
Another idea prominently kept in view by the author has
been that he would not assume the position of an "au-
thority " in giving rules and formulae for designing, but
only that of compiler, giving not only the name of the
originator of the rule, where it was known, but also the
volume and page from which it was taken, so that its
lii
288901
17 PREFACE.
derivation may be traced when desired. When different
formulae for the same problem have been found they have
been given in contrast, and in many cases examples have
been calculated by each to show the difference between
them. In some cases these differences are quite remark-
able, as will be seen under Safety-valves and Crank-pins.
Occasionally the study of these differences has led to the
author's devising a new ^formula, in which case the deriva
tion of the formula is given.
Much attention has been paid to the abstracting' of data
of experiments from recent periodical literature, and numer-
ous references to other data are given. In this respect
the present work will be found to differ from other Pocket-
books.
The author desires to express his obligation to the many
persons who have assisted him in the preparation of the
work, to manufacturers who have furnished their cata-
logues and given permission for the use of their tables,
and to many engineers who have contributed original data
and tables. The names of these persons are mentioned in
their proper places in the text, and in all cases it has been
endeavored to give credit to whom credit is due. The
thanks of the author are also due to the following gentle-
men who have given assistance in revising manuscript or
proofs of the sections named : Prof. De Volson Wood,
mechanics and turbines ; Mr. Frank Richards, compressed
air ; Mr. Alfred R. Wolff, windmills ; Mr. Alex. C.
Humphreys, illuminating gas ; Mr. Albert E. Mitchell,
locomotives ; Prof. James E. Denton, refrigerating-ma*
chinery ; Messrs. Joseph Wetzler and Thomas W. Varley,
electrical engineering ; and Mr. Walter S. Dix, for valuable
contributions on several subjects, and suggestions as to their
treatment. WILLIAM KENT.
PASSAIC, N. JM April^ 1895.
FIFTH EDITION, MARCH, 1900.
Some typographical and other errors discovered in the fourth
edition have been corrected. New tables and some additions
have been made under the head of Compressed Air. The new
(1899) code of the Boiler Test Committee of the American
Society of Mechanical Engineers has been substituted for the
old (1885) code. W. K.
PREFACE TO FOURTH EDITION.
IN this edition many extensive alterations have been made.
Much obsolete matter has been cut out and fresh matter substi-
tuted. In the first 170 pages but few changes have been found
necessary, but a few typographical and other minor errors have
been corrected. The tables of sizes, weight, and strength of
materials (pages 172 to 282) have been thoroughly revised, many
entirely new tables, kindly furnished by manufacturers, having
been substituted. Especial attention is called to the new matter
on Cast-iron Columns (pages 250 to 253). In the remainder of
the book changes of importance have been made in more than 100
pages, and all typographical errors reported to date have been
corrected. Manufacturers' tables have been revised by reference
to their latest catalogues or from tables furnished by the manufac-
turers especially for this work. Much new matter is inserted
under the heads of Fans and Blowers, Flow of Air in Pipes, and
Compressed Air. The chapter on Wire-rope Transmission (pages
917 to 922) has been entirely rewritten. The chapter on Electrical
Engineering has been improved by the omission of some matter
that has become out of date and the insertion of some new matter.
It has been found necessary to place much of the new matter of
this edition in an Appendix, as space could not conveniently be
made for it in the body of the book. It has not been found possi-
ble to make in the body of the book many of the cross-references
which should be made to the items in the Appendix. Users of the
book may find it advisable to write in the margin such cross-refer-
ences as they may desire.
The Index has been thoroughly revised and greatly enlarged.
The author is under continued obligation to many manufacturers
who have furnished new tables and data, and to many individual
engineers who have furnished new matter, pointed out errors in
the earlier editions, and offered helpful suggestions. He will be
glad to receive similar aid, which will assist in the further
improvement of the book in future editions.
WILLIAM KENT.
PASSAIC, N. J., September^ 1898.
SIXTH EDITION. DECEMBER, 1902.
THE chapter on Electrical Engineering has been thoroughly
revised, much of the old matter cut out and new matter sub-
stituted. Fourteen new pages have been devoted to the sub-
ject of Alternating Currents. The chapter on Locomotives has
been revised. Some new matter has been added under Cast
Iron, Specifications for Steel, Springs, Steam-engines, and
Friction and Lubrication. Slight changes and corrections in
the text have been made in nearly a hundred pages.
IV& PBEFACE.
SEVENTH EDITION, OCTOBER 1904.
AN entirely new index has been made, with about twice as
many titles as the former index. The electrical engineering
chapter has been further revised and some new matter added.
Four pages on Coal Handling Machinery have been inserted
at page 911, .and numerous minor changes have been made.
W. K.
SYRACUSE, N. Y.
CONTENTS.
(For Alphabetical Index see page 1093.)
MATHEMATICS.
Arithmetic.
PAGE
Arithmetical and Algebraical Signs 1
Greatest Common Divisor 2
Least Common Multiple 2
Fractions 2
Decimals 3
Table. Decimal Equivalents of Fractions of One Inch 3
Table. Products of Fractions expressed in Decimals 4
Compound or Denominate Numbers 5
Reduction Descending and Ascending 5
Ratio and Proportion 5
Involution, or Powers of Numbers 6
Table. First Nine Powers of the First Nine Numbers 7
Table. First Forty Powers of 2 7
Evolution. Square Root 7
CubeRoot 8
Alligation. 10
Permutation 10
Combination < 10
Arithmetical Progression 11
Geometrical Progression 11
Interest 13
Discount 13
Compound Interest 14
Compound Interest Table, 3, 4, 5, and 6 per cent 14
Equation of Payments 14
Partial Payments 15
Annuities 16
Tables of Amount, Present Values, etc., of Annuities 16
Weights and Measures.
Long Measure 17
Old Land Measure 17
Nautical Measure 17
Square Measure 18
Solid or Cubic Measure 18
Liquid Measure 18
The Miners' Inch 18
Apothecaries' Fluid Measure 18
Dry Measure * 18
Shipping Measure 19
Avoirdupois Weight 19
Troy Weight 19
Apothecaries' Weight 19
To Weigh Correctly on an Incorrect Balance 19
Circular Measure 20
Measure of time , 20
V
y: CONTENTS.
Board and Timber Measure ] 20
Table. Contents in Feet of Joists, Scantlings, and Timber 20
French or Metric Measures 21
British and French Equivalents 21
Metric Conversion Tables 23
Compound Units.
of Pressure and Weight 27
of Water, Weight, and Bulk f 27
of Work, Power, and Duty P 27
of Velocity « 27
of Pressure per unit area 27
Wire and Sheet Metal Gauges , 28
Twist-drill and Steel-wire Gauges 28
Music- wire Gauge 29
Circular- mil Wire Gauge 30
NewU. S. Standard Wire and Sheet Gauge, 1893 30
Decimal Gauge 32
Algebra.
Addition, Multiplication, etc 33
Powers of Numbers 33
Parentheses, Division 34
Simple Equations and Problems 34
Equations containing two or more Unknown Quantities 35
Elimination 35
Quadratic Equations 35
Theory of Exponents.. 36
Binomial Theorem.... 36
Geometrical Problems of Construction 37
of Straight Lines 37
of Angles 38
of Circles , 39
of Triangles 41
of Squares and Polygons 42
oftheEllipse 45
of the Parabola , 48
of the Hyperbola 49
of the Cycloid... 49
of the Tractrix or Schiele Anti-friction Curve 50
oftheSpiral 50
of the Catenary . 51
of the Involute 52
Geometrical Propositions 53
' Mensuration, Plane Surfaces.
Quadrilateral, Parallelogram, etc 54
Trapezium and Trapezoid c . . .. 54
Triangles 54
Polygons. Table of Polygons. . 55
Irregular Figures 55
Properties of the Circle 57
Values of ir and its Multiples, etc 57
Relations of arc, chord, etc 58
Relations of circle to inscribed square, etc 58
Sectors and Segments 59
Circular Ring 59
The Ellipse 59
The Helix 60
TheSpiral 60
Mensuration, Solid Bodies.
Prism ... 60
Pyramid 60
Wedge , 61
The Prismoidal Formula > €
Rectangular Prismoid. 61
Cylinder 61
Cone * •• »> >» > *1
CONTENTS. Vll
PAGE
Sphere 61
Spherical Triangle J
Spherical Polygon • • • • « j
Spherical Zone "2
Spherical Segment 62
Spheroid or Ellipsoid
Polyedron 62
Cylindrical Ring 62
Solids of Revolution 62
Spindles J
Frustrum of a Spheroid "
Parabolic Conoid t
Volume of a Cask 64
Irregular Solids 64
Plane Trigonometry.
Solution of Plane Triangles 65
Sine, Tangent, Secant, etc t
Signs of the Trigonometric Functions t
Trigonometrical Formulae ,. C
Solution of Plane Right-angled Triangles C
Solution of Oblique-angled Triangles 68
Analytical Geometry.
Ordinates and Abscissas 69
Equations of a Straight Line, In tersections, etc C
Equations of the Circle 70
Equations of the Ellipse . 70
Equations of the Parabola 70
Equations of the Hyperbola 70
Logarithmic Curves • . 71
Differential Calculus.
Definitions 72
Differentials of Algebraic Functions 72
Formulae for Differentiating 73
Partial Differentials 73
Integrals.. . . 73
Formulae for Integration 74
Integration between Limits 74
Quadrature of a Plane Surface 74
Quadrature of Surfaces of Revolution 75
Cubature of Volumes of Revolution 75
Second, Third, etc., Differentials , 75
Maclaurin's and Taylor's Theorems 76
Maxima and Minima.. 76
Differential of an Exponential Function 77
Logarithms.. 77
Differential Forms which have Known Integrals 78
Exponential Functions 78
Circular Functions 78
The Cycloid 79
Integral Calculus 79
Mathematical Tables.
Reciprocals of Numbers 1 to 2000 80
Squares, Cubes, Square Roots, and Cube Roots from 0.1 to 1600 86
Squares and Cubes of Decimals 101
Fifth Roots and Fifth Powers 102
Circumferences and Areas of Circles, Diameters 1 to 1000 103
Circumferences and Areas of Circles, Advancing by Eighths from ^ to
100 108
Decimals of a Foot Equivalent to Inches and Fractions of an Inch 112
Circumferences of Circles in Feet and Inches, from 1 inch to 32 feet 11
inches in diameter 113
Lengths of Circular Arcs, Degrees Given 114
Lengths of Circular Arcs, Height of Arc Given . 115
Areas of the Segments of a Circle 116
viii CONTENTS.
PAGE
Spheres 118
Contents of Pipes and Cylinders, Cubic Feet and Gallons 120
Cylindrical Vessels, Tanks, Cisterns, etc 121
Gallons in a Number of Cubic Feet 122
Cubic Feet in a Number of Gallons 122
Square Feet in Plates 3 to 32 feet long and 1 inch wide 123
Capacities of Rectangular Tanks in Gallons 125
Number of Barrels in Cylindrical Cisterns and Tanks 126
Logarithms 127
Table of Logarithms 129
Hyperbolic Logarithms 156
Natural Trigonometrical Functions 159
logarithmic Trigonometrical Functions 162
MATEKIAL.S.
Chemical Elements 165
Specific Gravity and Weight of Materials 163
Metals, Properties of 164
The Hydrometer 165
Aluminum 166
Antimony 166
Bismuth 166
Cadmium 167
Copper 167
Gold .- 167
Iridium 167
Iron 167
Lead 167
Magnesium 168
Manganese 168
Mercury 1 68
Nickel 168
Platinum 168
Silver 168
Tin 168
Zinc 168
Miscellaneous Materials.
Order of Malleability, etc., of Metals 169
Formulae and Table for Calculating Weight of Rods, Plates, etc 169
Measures and Weights of Various Materials 169
Commercial Sizes of Iron Bars 170
Weights of Iron Bars 171
of Flat Rolled Iron 172
of Iron and Steel Sheets 174
of Plate Iron 175
of Steel Blooms 176
of Structural Shapes 177
Sizes and Weights of Carnegie Deck Beams 177
" Steel Channels 178
" " ZBars 178
" " Pencoyd Steel Angles 179
*• " " Tees... 180
•• '« Channels 1«0
" •• Roofing Materials 181
" •* Terra-cotta 181
" *« Tiles 181
" " Tin Plates ...181
" •• Slates 183
" " PineShingles 183
'• " Sky-light Glass . 184
Weights of Various Ropf-coverings 184
Cast-iron Pipes or Columns 185
" " " 12- ft. lengths 186
*• " Pipe-fittings 187
" " Water and Gas-pipe 188
and thickness of Cast-iron Pipes 189
Safe Pressures on Cast Iron Pipe 189
CONTENTS. IX
PAGE
Sheet-iron Hydraulic Pipe.. 191
Standard Pipe Flanges 192
Pipe Flanges and Cast-iron Pipe 193
Standard Sizes of W rough t-iron Pipe 194
Wrought-iron Welded Tubes ... 196
Riveted Iron Pipes 197
Weight of Iron for Riveted Pipe , 197
Spiral Riveted Pipe 198
Seamless Brass Tubing 198, 199
Coiled Pipes 199
Brass, Copper, and Zinc Tubing 200
Lead and Tin-lined Lead Pipe , 201
Weight of Copper and Brass Wire and Plates 202
Round Bolt Copper 203
44 Sheet and Bar Brass 203
Composition of Rolled Brass 203
Sizesof Shot 204
Screw-thread, U. S. Standard 204
Limit-gauges for Screw-threads 205
Size of Iron for Standard Bolts 206
Sizes of Screw-threads for Bolts and Taps 207
Set Screws and Tap Screws 208
Standard Machine Screws 209
Sizes and Weights of Nuts 209
Weight of Bolts with Heads 210
Track Bolts 210
Weights of Nuts and Bolt-heads 211
Rivets 211
Sizes of Turnbuckles 211
Washers 212
Track Spikes 212
Railway Spikes 212
Boat Spikes 212
Wrought Spikes 213
Wire Spikes ... 213
Cut Nails 213
Wire Nails , 214, 215
Iron Wire, Size, Strength, etc 216
Galvanized Iron Telegraph Wire 217
Tests of Telegraph Wire 217
Copper Wire Table, B. W. Gauge 218
" Edison or Circular Mil Gauge.... 219
" 4t B.&S.Gauge 220
Insulated Wire 221
Copper Telegraph Wire 221
Electric Cables 221,222
Galvanized Steel-wire Strand 223
Steel-wire Cables for Vessels 223
Specifications for Galvanized Iron Wire 224
Strength of Piano Wire 224
Plough-steel Wire 224
Wires of different metals 225
Specifications for Copper Wire 225
Cable-traction Ropes 226
Wire Ropes 226, 227
Plough-steel Ropes 227, 228
Galvanized Iron Wire Rope 228
Steel Hawsers 223, 229
Flat Wire Ropes 2*9
Galvanized Steel Cables ... 230
Strength of Chains and Ropes 230
Notes on use of Wire Rope 231
' Locked Wire Rope 231
Crane Chains 232
Weights of Logs, Lumber, etc 232
Sizes of Fire Brick 233
Fire Clay, Analysis 234
Magnesia Bricks 235
Asbestos 235
X CONTENTS.
Strength of Materials.
_ , . _. PAQK
Stress and Strain 236
ElasticLimit . 236
Yield Point 237
Modulus of Elasticity 237
Resilience 238
Elastic Limit and Ultimate Stress 238
Repeated Stresses 238
Repeated Shocks 240
Stresses due to Sudden Shocks 241
Increasing Tensile Strength of Bars by Twisting 241
Tensile Strength 242
Measurement of Elongation 243
Shapes of Test Specimens 243
Coinpressive Strength 244
Columns, Pillars, or Struts 246
Hodgkinson's Formula 246
Gordon's Formula. 247
Moment of Inertia 247
Radius of Gyration — 247
Elements of Usual Sections 248
Strength of Cast-iron Columns 250
Transverse Strength of Cast iron Water-pipe 251
Safe Load on Cast-iron Columns 252
Strength of Brackets on Cast-iron Columns 252
Eccentric Loading of Columns 254
Wrought-iron Columns 255
Built Columns . . . . 256
Phoenix Columns 257
Working Formulae for Struts 259
Merriman's Formula for Columns 2GC
Working Strains in Bridge Members 263
Working Stresses for Steel 263
Resistance of Hollow Cylinders to Collapse 264
Collapsing Pressure of Tubes or Flues 265
Formula for Corrugated Furnaces 266
Transverse Strength 266
Formulae for Flexure of Beams 267
Safe Loads on Steel Beams 269
Elastic Resilience 270
Beams of Uniform Strength 271
Properties of Rolled Structural Shapes 272
" SteellBeams 273
Spacing of Steel I Beams 276
Properties of Steel Channels 277
" T Shapes 278
** •' Angles 279a
" Zbars 280
Size of Beams for Floors 280
Flooring Material.. 281
Tie Rods for Brick Arches 281
Torsional Strength 281
Elastic Resistance to Torsion 282
Combined Stresses , 282
Stress due to Temperature 283
Strength of Flat Plates 283
Strength of Unstayed Flat Surfaces 284
Unbraced Heads of Boilers 285
Thickness of Flat Cast-iron Plates ... 286
Strength of Stayed Surfaces 286
Spherical Shells and Domed Heads 286
Stresses in Steel Plating under Water Pressure 287
Thick Hollow Cylinders under Tension 287
Thin Cylinders under Tension 289
Hollow Copper Balls 289
Holding Power of Nails, Spikes, Bolts, and Screws 289
Cut versus Wire Nails 29(1
Strength of Wrought-iron Bolts.: 293
CONTENTS. xi
PAGE
Initial Strain on Bolts 292
Stand Pipes and their Design , 292
Riveted Steel Water-pipes 295
Mannesmann Tubes 296
Kirkaldy's Tests of Materials 296
Cast Iron 296
Iron Castings 297
Iron Bars, Forgings, etc 297
Steel Rails and Tires 298
Steel Axles, Shafts, Spring Steel 299
Riveted Joints 299
Welds 300
Copper, Brass, Bronze, etc 300
Wire, Wire-rope , 301
Ropes, Hemp, and Cotton 301
Belting, Canvas 302
Stones, Brick, Cement * 302
Tensile Strength of Wire 303
Watertown Testing-machine Tests 303
Riveted Joints 303
Wrought-iron Bars, Compression Tests 304
Steel Eye-bars ^ 304
Wrought-iron Columns ... 305
Cold Drawn Steel 305
American Woods 306
Shearing Strength of Iron and Steel 306
Holding Power of Boiler-tubes 307
Chains, Weight, Proof Test, etc 307
Wrought-iron Chain Cables , 308
Strength of Glass 308
Copper at High Temperatures 309
Strength of Timber 309
Expansion of Timber 311
Shearing Strength of Woods 312
Strength of Brick, Stone, etc . ... 312
" Flagging 313
" ** Lime and Cement Mortar 313
Moduli of Elasticity of Various Materials 314
Factors of Safety 314
Properties of Cork 316
Vulcanized India-rubber 316
XylolithorWoodstone 316
Aluminum, Properties and Uses 317
Alloys.
Alloys of Copper and Tin, Bronze 319
Copper and Zinc, Brass 321
Variation in Strength of Bronze 321
Copper-tin-zinc Alloys.
Liquation or Separation of Metals.
Alloys used in Brs
Jrass, Foundries 325
Copper-nickel Alloys 326
Copper-zinc-iron Alloys 326
Tobin Bronze 326
Phosphor Bronze 327
Aluminum Bronze 328
Aluminum Brass 329
Caution as to Strength of Alloys 329
Aluminum hardened 330
Alloys of Aluminum, Silicon, andiron 330
Tungsten-aluminum Alloys 331
Aluminum-tin Alloys 331
Manganese Alloys 331
Manganese Bronze 331
German Silver , 332
Alloys of Bismuth 332
Fusible Alloys , 333
bearing Metal Alloys , , ,,...,.., 333
Xll CONTENTS.
PAGE
Alloys containing Antimony 03 336
White-metal Alloys 336
Type-metal 336
Babbitt metals 336
Solders 338
Ropes and Chains.
Strength of Hemp, Iron, and Steel Ropes , 333
FlatRopes t 339
Working Load of Ropes and Chains ... 339
Strength of Ropes and Chain Cables 340
Rope for Hoisting or Transmission 340
Cordage, Technical terms of 341
Splicing of Ropes 341
Coal Hoisting 343
Manila Cordage, Weight, etc 344
Knots, how to make ., 344
Splicing Wire Ropes 346
Springs.
Laminated Steel Springs 847
Helical Steel Springs- 347
Carrying Capacity of Springs 349
Elliptical Springs .. 352
Phosphor-bronze Springs 352
Springs to Resist Torsional Force 352
Helical Springs for Cars, etc .1 353
Riveted Joints.
Fairbairn's Experiments 354
Loss of Strength by Punching .'. 354
Strength of Perforated Plates 354
Hand vs. Hydraulic Riveting 355
Formulae for Pitch of Rivets 357
Proportions of Joints 358
Efficiencies of Join ts 359
Diameter of Rivets 360
Strength of Riveted Joints 361
Riveting Pressures 362
Shearing Resistance of Rivet Iron 363
Iron and Steel.
Classification of Iron and Steel 364
Grading of Pig Iron 365
Influence of Silicon Sulphur, Phos. and Mn on Cast Iron 365
Tests of Cast Iron 369
Chemistry of Foundry Iron • 370
Analyses of Castings , 373
Strength of Cast Iron 374
Specifications for Cast Iron 374
Mixture of Cast Iron with Steel 375
Bessemerized Cast Iron 375
Bad Cast Iron , 375
Malleable Cast Iron 375
Wrought Iron ; 377
Chemistry of Wrought Iron 377
Influence of Rolling on Wrought Iron 377
Specifications for Wrought Iron 378
Stay-bolt Iron 378
Formulae for Unit Strains in Structures 379
Permissible Stresses in Structures 381
Proportioning Materials in Memphis Bridge 382
Tenacity of Iron at High Temperatures 382
Effect of Cold on Strength of Iron 383
Expansion of Iron by Heat 385
Durability of Cast Iron 885
Corrosion of Iron and Steel 386
Preservative Coatings ; Paints, etc 387
CONTENTS Xlll
PAGE
Non-oxidizing Process of Annealing 387
Manganese Plating of Iron 389
Steel.
Relation between Chemical and Physical Properties 389
Variation in Strength 391
Open-hearth 392
Bessemer 392
Hardening Soft Steel 393
Effect of Cold Rolling 393
Comparison of Full-sized and Small Pieces 393
Treatment of Structural Steel 394
Influence of Annealing upon Magnetic Capacity 396
Specifications for Steel 397
Chemical Requirements 397
Kinds of Steel used for Different Purposes 397
Castings, Axles, Forgings 397
Tires, Rails, Splice-bars, Structural Steel 398
Boiler-plate and Rivet Steel 399
May Carbon be Burned out of Steel ? 402
Recalescerice of Steel 402
Effect of Nicking r. Bar 402
Electric Conductivity 403
Specific Gravity 403
Occasional Failures 403
Segregation in Ingots 404
Earliest Uses for Structures 405
Steel Castings 405
Manganese Steel 407
Nickel Steel 407
Aluminum Steel 409
Chrome Steel 409
Tungsten Steel 409
Compressed Steel 410
Crucible Steel 410
Effect of Heat on Grain 412
1 ' Hammering, etc 412
Heating and Forging 412
Tempering Steel 413
MECHANICS.
Force, Unit of Force 415
Inertia 415
Newton's Laws of Motion 415
Resolution of Forces 415
Parallelogram of Forces 416
Moment of a Force 416
Statical Moment, Stability 417
Stability of a Dam 417
Parallel Forces 417
Couples 418
Equilibrium of Forces 418
Centre of Gravity 418
Moment of Inertia 419
Centre of Gyration 420
Radius of Gyration 420
Centre of Oscillation 421
Centre of Percussion 422
The Pendulum 422
Conical Pendulum 423
Centrifugal Force 423
Acceleration 423
Falling Bodies 424
Value of g 424
Angular Velocity 425
Height due to Velocity 425
Parallelogram of Velocities 426
Mass 427
XIV CONTENTS.
PAGE
Force of Acceleration, 427
Motion on Inclined Planes : 428
Momentum 428
Vis Viva 428
Work, Foot-pound 428
Power, Horse-power 429
Energy 429
Work of Acceleration ....... 430
Force of a Blow . . „ , , 430
Impact of Bodies . . . . „ . . .... 431
Energy of Recoil of Guns 431
Conservation of Energy 432
Perpetual Motion 432
Efficiency of a Machine 432
Animal-power, Man-power 433
Work of aHorse . ... 434
Man-wheel 434
Horse-gin 434
Resistance of Vehicles 435
Elements of Machines,
The Lever 435
The Bent Lever 436
The Moving Strut 436
The Toggle-joint 436
The Inclined Plane 437
The Wedge 437
The Screw 437
The Cam 438
The Pulley 438
Differential Pulley 439
Differential Windlass 439
Differential Screw 439
Wheel and Axle 439
Toothed-wheel Gearing 439
Endless Screw , 440
Stresses in Framed Structures.
Cranes and Derricks 440
Shear Poles and Guys 442
King Post Truss or Bridge 442
Queen Post Truss 442
Burr Truss 443
Pratt or Whip pie Truss 443
Howe Truss 445
Warren Girder . 445
Roof Truss 446
HEAT.
Thermometers and Pyrometers 448
Centigrade and Fahrenheit degrees compared 449
Copper-ball Pyrometer 451
Thermo-electric Pyrometer 451
Temperatures in Furnaces 451
Wiborgh Air Pyrometer , 453
Seeger's Fire-clay Pyrometer , 453
Mesur6 and Nouel's Pyrometer 453
Uehling and Steinbart's Pyrometer 453
Air-thermometer 454
High Temperatures judged by Color.... 454
Boiling-points of Substances 455
Melting-points 455
Unit of Heat 455
Mechanical Equivalent of Heat 456
Heat of Combustion 456
Specific Heat 457
Latent Heat of Fusion 459, 461
Expansion by Heat 460
Absolute Temperature 461
Absolute Zero ; 461
CONTENTS. XY
PAGE
Latent Heat 461
Latent Heat of Evaporation 462
Total Heat of Evaporation 462
Evaporation and Drying 462
Evaporation from Reservoirs 463
Evaporation by the Multiple System 463
Resistance to Boiling 463
Manufacture of Salt 464
Solubility of Salt and Sulphate of Lime 464
Salt Contents of Brines 464
Concentration of Sugar Solutions 465
Evaporating by Exhaust Steam 465
Drying in Vacuum 466
Radiation of Heat 467
Conduction and Convection of Heat 468
Rate of External Conduction 469
Steam-pipe Coverings . . 470
Transmission through Plates 471
•• in Condenser Tubes 473
»* ** Cast-iron Plates 474
** from Air or Gases to Water 474
•' from Steam or Hot Water to Air 475
'• through Walls of Buildings 478
Thermodynamics 478
PHYSICAL PROPERTIES OF GASES.
Expansion of Gases 479
Boyle and Marriotte's Law.... 479
Law of Charles, Avogadro's Law 479
Saturation Point of Vapors 480
Law of Gaseous Pressure , 480
Flow of Gases 480
Absorption by Liquids 480
AIR.
Properties of Air 481
Air-manometer 481
Pressure at Different Altitudes 481
Barometric Pressures .... 482
Levelling by the Barometer and by Boiling Water 482
To find Difference in Altitude 483
Moisture in Atmosphere 483
Weight of Air and Mixtures of Air and Vapor 484
Specific Heat of Air 484
Flow of Air.
Flow of Air through Orifices 484
Flow of Air in Pipes 485
Effect of Bends in Pipe 488
Flow of Compressed Air 488
Tables of Flow of Air 489
Anemometer Measurements 491
Equalization of Pipes 491
Loss of Pressure in Pipes 493
Wind.
Force of the Wind 493
Wind Pressure in Storms 495
Windmills 495
Capacity of Windmills 497
Economy of Windmills 498
Electric Power from Windmills 499
Compressed Air.
Heating of Air by Compression 499
Loss of Energy in Compressed Air 499
Volumes and Pressures...., , 500
CONTENTS.
Loss due to Excess of Pressure *».... 501
Horse-power Required for Compression 501
Table for Adiabatic Compression 502
Mean Effective Pressures 502
Mean and Terminal Pressures 503
Air-compressors. 503
Practical Results 505
Efficiency of Compressed-air Engines 506
Requirements of Rock-drills , 506
Popp Compressed-air System 507
Small Compressed-air Motors 507
Efficiency of Air-heating Stoves 507
Efficiency of Compressed-air Transmission 508
Shops Operated by Compressed Air „ 509
Pneumatic Postal Transmission t 509
Mekarski Compressed-air Tramways 510
Compressed Air Working Pumps in Mines 511
Fans and Blowers.
Centrifugal Fans 511
Best Proportions of Fans 512
Pressure due to Velocity 513
Experiments with Blowers 514
Quantity of Air Delivered 514
Efficiency of Fans and Positive Blowers 516
Capacity of Fans and Blowers 517
Table of Centrifugal Fans 518
Engines, Fans, and Steam-coils for the Blower System of Heating 519
Sturtevant Steel Pressure-blower 519
Diameter of Blast-pipes 519
Efficiency of Fans 520
Centrifugal Ventilators for Mines 521
Experiments on Mine Ventilators 522
Disk Fans 524
Air Removed by Exhaust Wheel , 525
Efficiency of Disk Fans 525
Positive Rotary Blowers 526
Blowing Engines . . . . 0 0 0 526
Steam-jet Blowers „<> 527
Steam -jet for Ventilation 527
HEATING AND VENTILATION.
Ventilation 528
Quantity of Air Discharged through a Ventilating Duct 530
Artificial Cooling of Air , 531
Mine-ventilation 531
Friction of Air in Underground Passages 531
Equivalent Orifices 533
Relative Efficiency of Fans and Heated Chimneys 533
Heating and Ventilating of Large Buildings 534
Rules for Computing Radiating Surfaces *. 536
Overhead Steam-pipes 537
Indirect Heating-surface 537
Boiler Heating-surface Required 538
Proportion of Grate-surface to Radiator-surface 538
Steam-consumption in Car-heating 538
Diameters of Steam Supply Mains 539
Registers and Cold-air Ducts 539
Physical Properties of Steam and Condensed Water 540
Size of Steam-pipes for Heating 540
Heating a Greenhouse by Steam 541
Heating a Greenhouse by Hot Water 542
Hot- water Heating , 542
Law of Velocity of Flow 542
Proportions of Radiating Surfaces to Cubic Capacities 543
Diameter of Main and Branch Pipes 543
Rules for Hot-water Heating w 544
Arrangements of Mains ,..,..,.... tt .,.,,..,.,..•.... 544
CONTENTS. XVll
PAGE
Blower System of Heating and Ventilating 6;u« 545
Experiments with Radiators . . , 545
Heating a Building to 70° F. ., 545
Heating by Electricity 546
WATER.
Expansion of Water .... 547
Weight of Water at different temperatures 547
Pressure of Water due to its Weight 549
Head Corresponding to Pressures , 549
Buoyancy 550
Boiling-point 550
Freezing-point 550
Sea-water 549,550
Ice and Snow 550
Specific Heat of Water 550
Compressibility of Water 551
Impurities of Water 551
Causes of Incrustation 551
Means for Preventing Incrustation 552
Analyses of Boiler-scale 552
Hardness of Water 553
Purifying Feed-water 554
Softening Hard Water 555
Hydraulics. Flow of Water.
Fomulae for Discharge through Orifices 555
Flow of Water from Orifices 555
Flow in Open and Closed Channels 557
General Formulae for Flow , . 557
Table Fall ofFeet per mile, etc 558
Values of Vr for Circular Pipes 559
Kutter's Formula 559
Molesworth's Formula 562
Bazin's Formula ... 563
IV Arcy's Formula 563
Older Formulae 564
Velocity of Water in Open Channels 564
Mean, Surface and Bottom Velocities 564
Safe Bottom and Mean Velocities 565
Resistance of Soil to Erosion 565
Abrading and Transporting Power of Water 565
Grade of Sewers 566
Relations of Diameter of Pipe to Quantity discharged 566
Flow of Water in a 20-inch Pipe 566
Velocities in Smooth Cast-iron Water-pipes 567
Table of Flow of Water in Circular Pipes 568-573
Loss of Head . . 573
Flow of Water in Riveted Pipes 574
Fractional Heads at given rates of discharge 577
Effect of Bend and Curves •• 578
Hydraulic Grade-line 578
Flow of Water in House-service Pipes 578
Air-bound Pipes 579
VerticalJets 579
Water Delivered through Meters 579
Fire Streams 579
Friction Losses in Hose 580
Head and Pressure Losses by Friction , 580
Loss of Pressure in smooth 2^-inch Hose 580
Rated capacity of Steam Fire-engines 580
Pressures required to throw water through Nozzles 581
The Siphon 581
Measurement of Flowing Water 582
Piezometer 582
Pitot Tube Gauge ... . 583
The Venturi Meter... 583
Measurement of Discharge by means of Nozzles 584
XV111 CONTENTS.
PAGE
Flow through Rectangular Orifices ....................... . ...... t ........ 584
Measurement of an Open Stream ......................................... 584
Miners' Inch Measurements ..... ............ ............................ 585
Flow of Water over Weirs .............................................. 586
Francis's Formula for Weirs ............................................. 586
Weir Table ............................................................... 587
Bazin's Experiments .................... .. ............................... 587
Water-power*
Power of a Fall of Water .................................................. 588
Horse-power of a Running Stream ..... ., > ............................... 589
Current Motors. ... .................... » ...... . ....................... 589
Horse-power of Water Flowing in a Tube...7 . .......................... 589
Maximum Efficiency of a Long Conduit .................. ............... 589
Mill-power ............. . ............................................. ,.,.. 689
Value of Water-power ........................... , ..................... , . 590
The Power of Ocean Waves ................. ...... ....................... 599
Utilization of Tidal Power ............................................... 600
Turbine Wheels.
Proportions of Turbines ..... ........................................ ..... 591
Tests of Turbines ............... .......................................... 596
Dimensions of Turbines ......... ....................................... 597
The Pelton Water-wheel .................................................. 597
Pumps.
Theoretical capacity of a pump ....... . ................................. 601
Depth of Suction .......... ............................................... 602
Amount oi Water raised by a Single-acting Lift-pump ................... 602
Proportioning the Steam-cylinder of a Direct-acting Pump .............. 602
Speed of Water through Pipes and Pump -passages .................... 602
Sizes of Direct-acting Pumps ................... ................... ----- 603
The Deane Pump .............................. .......................... 603
Efficiency of Small Pumps .............................. ....... .. ..... 603
The Worthington Duplex Pump .......................................... 604
Speed of Piston ............... ,. ......................................... 605
Speed of Water through Valves. ........... . .......................... .. 605
Boiler-feed Pumps ............... . ....................................... 605
Pump Valves ........... ................................................. 606
Centrifugal Pumps ............ ....................... .................. 606
Lawrence Centrifugal Pumps .......................................... 607
Efficiency of Centrifugal and Reciprocating Pumps ...................... 608
Vanes of Centrifugal Pumps ............................................. 609
The Centrifugal Pump used as a Suction Dredge ........................ 609
Duty Trials of Pumping Engines... ............................... • 609
Leakage Tests of Pumps ............................................... 611
Vacuum Pnmps .... ............ . ....................................... 612
The Pulsometer... ...................................... ................ 612
TheJetPump ........................ .................................. 614
The Injector ................................................ . .............. 614
Air-lift Pump ................................................ .............. 6i4
The Hydraulic Ram ............................ .......................... 614
Quantity of Water Delivered by the Hydraulic Ram . ............ , ........ 615
Hydraulic Pressure Transmission.
Energy of Water under Pressure .......................... . ............ 616
Efficiency of Apparatus .................................................. 616
Hydraulic Presses -------- ................... ........................... 617
Hydraulic Power in London ............. ..... .......................... 617
Hydraulic Riveting Machines ............................................. 618
Hydraulic Forging ................. . . . ............ ....................... 618
The Aiken Intensifler ......... , .......................... ................ 619
Hydraulic Engine ..................................... ................... 61S
FUEL.
Theory of Combustion
Total Heat of Combustion
CONTENTS. XIX
PACK
Analyses of Gases of Combustion 622
Temperature of the Fire 622
Classification of Solid Fuel 623
Classification of Coals 624
Analyses of Coals 624
Western Lignites 631
Analyses of Foreign Coals 631
Nixon's Navigation Coal 632
Sampling Coal for Analyses 632
.Relative Value of Fine Sizes 632
Pressed Fuel... 632
Relative Value of Steam Coals , ... 633
Approximate Heating Value of Coals 634
Kind of Furnace Adapted for Different Coals 635
Downward-draught Furnaces 635
Calorimetric Tests of American Coals 636
E vaporati ve Power of Bituminous Coals 636
Weathering of Coal , 637
Coke 637
Experiments in Coking 637
Coal Washing 633
Recovery of By-products in Coke manufacture 638
Making Hard Coke 638
Generation of Steam from the Waste Heat and Gases from Coke-ovens. 638
Products of the Distillation of Coal 639
Wood as Fuel 639
Heating Value of Wood 639
Composition of Wood 640
Charcoal 640
Yield of Charcoal from a Cord of Wood 641
Consumption of Charcoal in Blast Furnaces 641
Absorption of Water and of Gases by Charcoal 641
Composition of Charcoals 642
Miscellaneous Solid Fuels 642
Dust-fuel— Dust Explosions 642
Peat or Turf 643
Sawdust as Fuel 643
Horse-manure as Fuel 643
Wet Tan-bark as Fuel.... 643
Straw as Fuel 643
Bagasse as Fuel in Sugar Manufacture 643
Petroleum.
Products of Distillation 645
Lima Petroleum 645
Value of Petroleum as Fuel 645
Oil vs. Coal as Fuel 646
Fuel Gas*
Carbon Gas 646
Anthracite Gas , 647
Bituminous Gas 647
Water Gas 64&
Producer-gas from One Ton of Coal 649
Natural Gas in Ohio and Indiana 649
Combustion of Producer-gas 650
Use of Steam in Producers 650
Gas Fuel for Small Furnaces *. 651
Illuminating Gas,
Coal-gas 651
Water-gas 652
Analyses of Water-gas and Coal gas 653
Calorific Equivalents of Constituents 654
Efficiency of a Water-gas Plant 654
Space Required for a Water-gas Plant 656
Ruel-value of Illuminating-gas 666
XX CONTENTS.
PAGE
Flow of Gas in Pipes 657
Service for Lamps • 658
STEAM.
Temperature and Pressure > » 659
Total Heat « 659
Latent Heat of Steam 659
Latent Heatof Volume 660
Specific Heat of Saturated Steam 660
Density andVolume 660
Superheated Steam 661
Regnault's Experiments 661
Table of the Properties of Steam .- 662
Flow of Steam.
Napier's Approximate Rule «.... 669
Flow of Steam in Pipes , 669
Loss of Pressure Due to Radiation 671
Resistance to Flow by Bends 672
Sizes of Steam-pipes for Stationary Engines 673
Sizes of Steam-pipes for Marine Engines 674
Steam Pipes.
Bursting-tests of Copper Steam-pipes 674
Thickness of Copper Steam-pipes.. , 675
Reinforcing Steam-pipes , 675
Wire-wound Steam- pipes 675
Riveted Steel Steam-pipes.. 675
Valves in Steam-pipes 675
Failure of a Copper Steam-pipe 676
The Steam Looj> 676
Loss from an Uncovered Steam-pipe , 676
THE STEAM BOILER.
The Horse-power of a Steam -boiler .... — 677
Measures for Comparing the Duty of Boilers 678
Steam-boiler Proportions 678
Heating-surface 678
Horse-power, Builders' Rating 679
Grate-surface 680
AreasofFlues 680
Air-passages Through Grate-bars 681
Performance of Boilers , ,...., 681
Conditions which Secure Economy , 682
Efficiency of a Boiler .. ...683
Tests of Steam-boilers 685
Boilers at the Centennial Exhibition 685
Tests of Tubulous Boilers 686
High Rates of Evaporation , 687
Economy Effected by Heating the Air..., 687
Results of Tests with Different Coals 688
Maximum Boiler Efficiency with Cumberland Coal . , 689
Boilers Using Waste Gases • 689
Boilers for Blast Furnaces » — 689
Rules for Conducting Boiler Tests , 690
Table of Factors of Evaporation 695
Strength of Steam-boilers.
Rules for Construction... 700
Shell-plate Formulae 701
Rules for Flat Plates 701
Furnace Formulae 702
Material for Stays 703
Loads allowed on Stays 703
Girders 703
Rules for Construction of Boilers in Merchant Vessels iu U. 8 705
CONTENTS. Xxi
PAGB
U. S. Rule for Allowable Pressures 706
Safe-working Pressures • 707
Rules Governing Inspection of Boilers in Philadelphia 708
Flues and Tubes for Steam Boilers 709
Flat-stayed Surfaces 4. 709
Diameter of Stay-bolts. 710
Strength of Stays 710
Stay-bolts in Curved Surfaces . 710
Boiler Attachments, Furnaces, etc*
Fusible Plugs 710
Steam Domes 711
Height of Furnace. 711
Mechanical Stokers 711
The Hawley Down-draught Furnace 712
Under-feed Stokers 712
Smoke Prevention 712
Gas-fired Steam-boilers 714
Forced Combustion .....i 714
Fuel Economizers. 715
Incrustation and Scale 716
Boiler-scale Compounds.. 717
Removal of Hard Scale 718
Corrosion in Marine Boilers 719
TJseofZinc 720
Effect of Deposit on Flues 720
Dangerous Boilers 720
Safety Valves.
Rules for Area of Safety-valves ..... 721
Spring-loaded Safety-valves 724
The Injector.
Equation of the In jector 725
Performance of Injectors ............. 726
Boiler-feeding Pumps 726
Feed-water Heaters.
Strains Caused by Cold Feed-water 727
Steam Separators*
Efficiency of Steam Separators 728
Determination of Moisture in Steam*
Coil Calorimeter. 729
Throttling Calorimeters 729
Separating Calorimeters 730
Identification of Dry Steam 730
Usual Amount of Moisture in Steam 731
Chimneys*
Chimney Draught Theory 731
Force or Intensity of Draught. . 732
Rate of Combustion Due to Height of Chimney 733
High Chimneys not Necessary 734
Heights of Chimneys Required for Different Fuels 734
Table of Size of Chimneys 734
Protection of Chimney from Lightning 736
Some Tall Brick Chimneys 737
Stability of Chimneys . 738
Weak Chimneys 739
Steel Chimneys 740
Sheet-iron Chimneys 741
THE STEAM ENGINE*
Expansion of Steam , 742
Mean and Terminal Absolute Pressures 743
CONTENTS.
•Condensers, Air-pumps, Circulating-pumps, etc.
PAGE
The Jet Condenser 839
Ejector Condensers 840
The Surface Condenser 840
Condenser Tubes 840
Tube-plates 841
Spacing of Tubes 841
Quantity of Cooling Water 841
Air-pump 841
Area through Valve-seats 842
Circulating-pump. . . . 843
Feed-pumps for Marine Engines 843
An Evaporative Surface Condenser 844
Continuous Use of Condensing Water 844
Increase of Power by Condensers 846
Evaporators and Distillers 817
GAS, PETROLEUM, AND 1IOT-AIU ENGINES.
Gas-engines 847
Efficiency of the Gas-engine 848
Tests of the Simplex Gas-engine 848
A 320-H.P. Gas-engine 848
Test of an Otto Gas-engine 849
Temperatures and Pressures Developed 849
Test of the Clerk Gas-engine 849
Combustion of the Gas in the Otto Engine 849
Use of Carburetted Air in Gas-engines 849
The Otto Gasoline-engine . 850
The Priestman Petroleum-engine 850
Test of a 5-H.P. Priestman Petroleum-engine 850
Naphtha-engines 851
Hot-air or Caloric Engines 851
Test of a Hot-air Engine 851
LOCOMOTIVES.
Resistance of Trains 851
Inertia and Resistance at Increasing Speeds 853
Efficiency of the Mechanism of a Locomotive 854
Size of Locomotive Cylinders 855
Size of Locomotive Boilers 855
Qualities Essential for a Free-steaming Locomotive 855
Wootten's Locomotive 855
Grate -surf ace, Smokestacks, and Exhaust-nozzles for Locomotives .... 856
Exhaust Nozzles 856
Fire-brick Arches 857
Size. Weight, Tractive Power, etc 857
Leading American Types 858
Steam Distribution for High Speed 858
Speed of Railway Trains 859
Formulae for Curves 859a
Performance of a High-speed Locomotive 859a
Locomotive Link-motion 859a
Dimensions of Some American Locomotives 859-862
Indicated Water Consumption 862
Locomotive Testing Apparatus 863
Waste of Fuel in Locomotives 863
Advantages of Compounding 863
Counterbalancing Locomotives 864
Maximum Safe Load on Steel Rails 865
Narrow-gauge Railways 865
Petroleum -burning Locomotives 865
Fireless Locomotives 866
SHAFTING.
Diameters to Resist Torsional Strain 867
Deflection of Shafting 868
Horse-power Transmitted by Shafting 869
Table for Laying Out Shafting » 871
CONTEXTS. XXV
PULLETS.
PAGE
Proportions of Pulleys 873
Convexity of Pulleys 874
Cone or Step Pulleys 874
BELTING.
Theory of Belts and Bands 876
Centrifugal Tension 876
Belting Practice, Formulae for Belting 877
Horse-power of a Belt one mch wide 878
A. F. Nagle's Formula : 878
Width of Belt for Given Horse-power 879
Taylor's Rules for Belting 880
Notes on Belting 882
Lacing of Belts 883
Setting a Belt on Quarter-twist 883
To Find the Length of Belt 884
To Find the Angle of the Arc of Contact 884
To Find the Length of Belt when Closely Rolled 884
To Find the Approximate Weight of Belts 884
Relations of the Size and Speeds of Driving and Driven Pulleys 884
Evils of Tight Belts 885
Sag of Belts 885
Arrangements of Belts and Pulleys 885
Care of Belts 886
Strength of Belting 886
Adhesion, Independent of Diameter 886
Endless Belts 886
Belt Data 886
Belt Dressing 887
Cement for Cloth or Leather 887
Rubber Belting 887
GEARING.
Pitch, Pitch-circle, etc 887
Diametral and Circular Pitch 888
Chordal Pitch 889
Diameter of Pitch-line of Wheels from 10 to 100 Teeth 889
Proportions of Teeth 889
Proportion of Gear-wheels 891
Width of Teeth 891
Rules for Calculating the Speed of Gears and Pulleys 891
Milling Cutters for Interchangeable Gears 892
Forms of the Teeth.
The Cycloidal Tooth 892
The Involute Tooth 894
Approximation by Circular Arcs 896
Stepped Gears 897
Twisted Teeth 897
Spiral Gears 897
Worm Gearing 897
Teeth of Bevel-wheels. 898
Annular and Differential Gearing 898
Efficiency of Gearing 899
Strength of Gear Teeth.
Various Formulas for Strength 900
Comparison of Formulae 903
Maximum Speed of Gearing 905
A Heavy Machine-cut Spur-gear 905
Fractional Gearing 905
Frictional Grooved Gearing 906
HOISTING.
Weight and Strength of Cordage 906
Working Strength of Blocks 906
XXVI CONTENTS.
PAGE
Efficiency of Chain-blocks 907
Proportions of Hooks 907
Power of Hoisting Engines. 908
Effect of Slack Rope on Strain in Hoisting 908
Limit of Depth for Hoisting ' 908
Large Hoisting Records 908
Pneumatic Hoisting 909
Counterbalancing of Winding-engines 909
Cranes.
Classification of Cranes .•"••-.• 911
Position of the Inclined Brace in a Jib Crane 912
A Large Travelling-crane ; 912
A 150-ton Pillar Crane 912
Compressed-air Travelling Cranes .' 912
Coal-handling Machinery.
Weight of Overhead Bins 912a
Supply-pipes from Bins 912a
Types of Coal Elevators 912a
Combined Elevators and Conveyors ; 912a
Coal Conveyors 912a
Weight of Chain 9126
Weight of Flights 912c
Horse-power of Conveyors 912c
Bucket Conveyors 912c
Screw Conveyors 912d
Belt Conveyors Ql2d
Capacity of Belt Conveyors 9l2d
Wire-rope Haulage.
Self-acting Inclined Plane 913
Simple Engine Plane 913
Tail-rope System 913
Endless Rope System 914
Wire-rope Tramways ^ 914
Suspension Cableways and Cable Hoists 915
Stress in Hoisting-ropes on Inclined Planes 915
Tension Required to Prevent Wire Slipping on Drums 916
Taper Ropes of Uniform Tensile Strength 916
Effect of Various Sized Drums on the Life of Wire Ropes 917
WIRE-ROPE TRANSMISSION.
Elastic Limit of Wire Ropes 917
Bending Stresses of Wire Ropes - 918
Horse-power Transmitted 919
Diameters of Minimum Sheaves 919
Deflections of the Rope 920
Long-distance Transmission 921
ROPE DRIVING.
Formulae for Rope Driving 922
Horse-power of Transmission at Various Speeds 924
Sag of the Rope Between Pulleys 925
Tension on the Slack Part of the Rope 925
Miscellaneous Notes on Rope-driving 926
FRICTION AND LUBRICATION.
Coefficient of Friction 928
Rolling Friction 928
Friction of Solids 928
Friction of Rest . . 928
Laws of Unlubricated Friction 928
Friction of Sliding Steel Tires 928
Coefficient of Rolling Friction 929
Laws of Fluid Friction 929
Angles of Repose 929
CONTENTS. XXV11
PAGE
Friction of Motion 929
Coefficient of Friction of Journal 930
Experiments on Friction of a Journal 931
Coefficients of Friction of Journal with Oil Bath 932
Coefficients of Friction of Motion and of Rest 932
Value of Anti-friction Metals 932
Cast-iron for Bearings 933
Friction of Metal Under Steam-pressure • 933
Morin's Laws of Friction . . . 933
Laws of Friction of well-lubricated Journals 934
Allowable Pressures on Bearing-surface 935
Oil-pressure in a Bearing 937
Friction of Car-journal Brasses 937
Experiments on Overheating of Bearings 938
Moment of Friction and Work of Friction 938
Pivot Bearings 939
The Schiele Curve. ^ 939
Friction of a Flat Pivot-bearing 939
Mercury-bath Pivot 940
Ball Bearings 940
Friction Rollers. . . 940
Bearings for Very High Rotative Speed 941
Friction of Steam-engines 941
Distribution of the Friction of Engines 941
Lubrication.
Durability of Lubricants. 942
Qualifications of Lubricants 943
Amount of Oil to run an Engine 943
Examination of Oils 943
Penna. R. R. Specifications 944
Soda Mixture for Machine Tools 945
Solid Lubricants , 945
Graphite, Soapstone, Fibre-graphite, Metaline 945
THE FOUNDRY.
Cupola Practice 946
Charging a Cupola > 948
Charges in Stove Foundries 949
Results of Increased Driving 949
Pressure Blowers 950
Loss of Iron in Melting 950
Use of Softeners. . 950
Shrinkage of Castings 951
Weight of Castings from Weight of Pattern 952
Moulding Sand 952
Foundry Ladles 952
THE MACHINE SHOP.
Speed of Cutting Tools 953
Table of Cutting Speeds 954
Speed of Turret Lathes 954
Forms of Cutting Tools 955
Rule for Gearing Lathes -. 955
Change-gears for Lathes 956
Metric Screw-threads 956
Setting the Taper in a Lathe 956
Speed of Drilling Holes 956
Speed of Twist-drills 957
Milling Cutters 957
Speed of Cutters 958
Results with Milling-machines 959
Milling with or Against Feed 960
Milling-machine vs. Planer 960
Power Required for Machine Tools 960
Heavy Work on a Planer 960
Horse-power to run Lathes 961
XXX CONTENTS.
Electrical Resistance.
Laws of Electrical Resistance 1027
Electrical Conductivity of Different Metals and Alloys 1028
Conductors and Insulators 1028
Resistance Varies with Temperature 1028
Annealing 1029
Standard of Resistance of Copper Wire 1029
Direct Electric Currents.
Ohm's Law 1029
Series and Parallel or Multiple Circuits 1030
Resistance of Conductors in Series and Parallel 1030
Internal Resistance 1031
Electrical, Indicated, and Brake Horse-power 1031
Power of the Circuit 1031
Heat Generated by a Current 1031
Heating of Conductors 1032
Fusion of Wires 1032
Heating of Coils 1032
Allowable Carrying Capacity of Copper Wires 1033
Underwriters' Insulation 1033
Copper-wire Table 1034, 1035
Electric Transmission, Direct Currents.
Section of Wire Required for a Given Current 1033
Weight of Copper for a Given Power 1036
Short-circuiting 1036
Economy of Electric Transmission 1036
Wire Table for 110, 220, 500, 1000, and 2000 volt Circuits 1037
Efficiency of Long-distance Transmission 1038
Table of Electrical Horse-powers 1039
Cost of Copper for Long-distance Transmission 1040
Systems of Electrical Distribution 1041
Electric Lighting.
Arc Lights 1042
Incandescent Lamps 1042
Variation in Candle-power and Life 1042
Specifications for Lamps 1043
Special Lamps 1043
Nernst Lamp 1043
Electric Welding 1044
Electric Heaters 1044
Electric Accumulators or Storage-batteries.
Description of Storage-batteries 1045
Sizes and Weights of Storage-batteries 1048
General Rules for Storage-cells 1048
Electrolysis 1048
Electro-chemical Equivalents 1049
Efficiency of a Storage-cell 1048
Electro-magnets.
Units of Electro-magnetic Measurements 1050
Lines of Loops of Force 1050
The magnetic Circuit 1051
Permeability 1052
Tractive or Lifting Force of a Magnet 1053
Magnet Windings 1053
Determining the Polarity of Electro-magnets 1054
Determining the Direction of a Current 1054
Dynamo-electric Machines.
Kinds of Dynamo-electric Machines as regards Manner of Winding. . . 1055
Moving Force of a Dynamo-electric Machine 1055
Torque of an Armature : • • •. 1056
Electro-motive Force of the Armature Circuit 1056
Strength of the Magnetic Field 1057
Dynamo Design 1058
COKTEOTS.
Alternating Currents.
PAGE
Maximum, Average, and Effective Values 1061
Frequency 1061
Inductance, Capacity, Power Factor 1062
Reactance, Impedance, Admittance 1063
Skin Effect Factors 1063
Ohm's Law Applied to Alternating Currents 1064
Impedance Polygons 1066
Capacity of Conductors 1066
Self-inductance of Lines and Circuits 1066
Capacity of Conductors 1067
Single-phase and Polyphase Currents 1068
Measurement of Power in Polyphase Circuits 1069
Alternating-current Generators 1070
Transformers, Converters, etc 1070
Synchronous Motors 1071
Induction Motors 1072
Calculation of Alternating-current Circuits 1072
Weight of Copper Required in Different Systems. .' 1074
Electrical Machinery.
Direct-current Generators and Motors 1074-1076
Alternating-current Generators 1077
Induction Motors 1077
Symbols Used in Electrical Diagrams 1078
APPENDIX.
Strength of Timber.
Safe Load on White-oak Beams 1079
Mathematics.
Formula for Interpolation 1080
Maxima and Minima without the Calculus 1080
Riveted Joints.
Pressure Required to Drive Hot Rivets 1080
Heating and Ventilation.
Capacities for Hot-blast or Plenum Heating with Fans and Blowers. . 1081
Water-wheels.
Water-power Plants Operating under High Pressure 1G81
Formulae for Power of Jet Water-wheels 1082
Gas Fuel.
Composition Energy, etc., of Various Gases 1082
Steam-boilers.
Rules for Steam-boiler Construction 1083
Boiler Feeding 1083
Feed-water Heaters 1083
The Steam-engine.
Current Practice in Engine Proportions 1084
Work of Steam-turbines 1085
Relative Cost of Different Sizes of Engines 1085
Gearing:.
Efficiency of Worm Gearing 1086
Hydraulic Formulae.
Flow of Water from Orifices, etc 1087
Tin and Terne Plate.
Penna. R. R. Co.'s Specifications 1088
LIST OF AUTHORITIES 1089
NAMES AND ABBREVIATIONS OF PERIODICALS
AND TEXT-BOOKS FREQUENTLY REFERRED TO
IN THIS WORK.
Am. Mach. American Machinist.
App. Cyl. Mech. Appleton's Cyclopaedia of Mechanics, Vols. I and n.
Bull. I. & S. A. Bulletin of the American Iron and Steel Association
(Philadelphia).
Burr's Elasticity and Resistance of Materials.
Clark, E. T. D. D. K. Clark's Rules, Tables, and Data for Mechanical En-
gineers.
Clark, S. E. D. K. Clark's Treatise on the Steam-engine.
Col. Coll. Qly. Columbia College Quarterly.
Eugg. Engineering (London).
Eng. News. Engineering News.
Engr. The Engineer (London).
Fairbairn's Useful Information for Engineers.
Flynn's Irrigation Canals and Flow of Water.
Jour. A. C. I. W. Journal of American Charcoal Iron Workers' Association.
Jour. F. I. Journal of the Franklin Institute.
Kapp's Electric Transmission of Energy.
Lanza's Applied Mechanics.
Merriman's Strength of Materials.
Modern Mechanism. Supplementary volume of Appleton's Cyclopaedia of
Mechanics.
Proc. Inst. C. E. Proceedings Institution of Civil Engineers (London).
Proc. Inst. M. E. Proceedings Institution of Mechanical Engineers (Lon-
don).
Peabody's Thermodynamics.
Proceedings Engineers' Club of Philadelphia.
Rankine, S. E. Rankine's The Steam Engine and other Prime Movers.
Rankine's Machinery and Millwork.
Rankine, R. T. D. Rankine's Rules, Tables, and Data.
Reports of U. S. Test Board.
Reports of U. S. Testing Machine at Watertown, Massachusetts.
Rontgen's Thermodynamics,
Seaton's Manual of Marine Engineering.
Hamilton Smith, Jr.'s Hydraulics.
The Stevens Indicator.
Thompson's Dynamo-electric Machinery.
Thurston's Manual of the Steam Engine.
Thurstou's Materials of Engineering.
Trans. A. I. E. E. Transactions American Institute of Electrical Engineers.
Trans. A. I. M. E. Transactions American Institute of Mining Engineers.
Trans. A. S. C. E. Transactions American Society of Civil Engineers.
Trans. A. S. M. E. Transactions American Soc'ty of Mechanical Engineers
Trautwine's Civil Engineer's Pocket Book.
The Locomotive (Hartford, Connecticut).
Unwin's Elements of Machine Design.
Weisbach's Mechanics of Engineering.
Wood's Resistance of Materials.
Wood's Thermodynamics.
xxzii
MATHEMATICS.
a Alpha
/3 Beta
y Gamma
6 Delta
e Epsilon
£ Zeta
H
0
I
K
A
M
Eta
0 Theta
Iota
Kappa
Lambda
Mu
N v
H f
O -o
n TT
p p
2 <r *
Nu
Xi
Omicron
Pi
Rho
Sigma
T
Y
*
X
*
n
T
V
X
w
Tau
Upsilon
P&
Chi
Psi
Omega
Greek Letters.
B
r
A
E
Z
Arithmetical and Algebraical Signs and Abbreviation*.
£ angle.
L right angle.
± perpendicular to.
sin., sine,
cos., cosine,
tang., or tan., tangent,
sec., secant,
versin., versed sine,
cot., cotangent.
cosec., cosecant,
covers., co- versed sine.
In Algebra, the first letters of the
alphabet, a, 6, c, d, etc., are gener-
ally used to denote known quantities,
and the last letters, w, x, y, z, etc.,
imknown quantities.
Abbreviations and Symbols com-
monly used.
d, differential (in calculus).
/, integral (in calculus).
J *, integral between limits a and 6.
A, delta, difference.
2. sigma, sign of summation.
IT, pi, ratio of circumference of circle
to diameter = 3.14159.
g, acceleration due to gravity = 32.16
ft. per sec. per sec.
Abbreviations frequently used in
this Book.
L., 1., length in feet and inches.
B., b., breadth in feet and inches.
D., d., depth or diameter.
H., h., height, feet and inches.
T., t., thickness or temperature.
V.,v., velocity.
F., force, or factor of safety.
f., coefficient of friction.
EM coefficient of elasticity.
R., r., radius.
W., w., weight.
P., p., pressure or load.
H.P., horse-power.
I.H.P., indicated horse-power.
B.H.P., brake horse-power,
h. p., hif1-
4- plus (addition).
4- positive.
- minus (subtraction).
— negative.
i: plus or minus.
=F minus or plus.
z= equals.
x multiplied by.
ab or a.b = a x b.
^- divided by
/ divided by.
£- = a/6 = a -f- b. 15-16 = — •
.2 = — , .002 =^.
V* square root.
V cube root.
V 4th root.
: is to, :: so is, : to (proportion).
2 : 4 x 3 : 6, as 2 is to 4 so is 3 to 6.
: ratio; divided by.
2 : 4, ratio of 2 to 4 = 2/4.
/. therefore.
> greater than.
< less than,
n square.
O round.
0 degrees, arc or thermometer.
' minutes or feet.
11 seconds or inches.
' " '" accents to distinguish letters, as
a', a", a'".
«i» «2< «3< «;,' <V r®ad a sub 1, a sub 6,
etc.
( ) C ] { } vincula, denoting
that the numbers enclosed are
to be taken together ; as,
(a -f 6)c = 4 + 3 x 5 = 35.
a8, a8, a squared, a cubed.
an, a raised to the_nth power.
a3 = |/«2? af = |/a3.
a-* = -,a-2 = -L
a aa
10» = 10 to the 9th power = 1,000 000 -
000.
sin. a = the sine of a.
sin.— Ja= the arc whose sine is a.
sin. a-* = -;
sin. a.
log. = logarithm.
log. or hyp. log. = hyperbolic loga-
rithm.
.
. p., high pressure.
. p., intermediate
pressure.
1. p., low pressure.
A.W. G., American Wire Gauge
(Brown & Sharpe).
B.W.G., Birmingham Wire Gauge.
r. p. m., or revs, permin., revolutions
per minute.
MATHEMATICS.
ARITHMETIC.
The user of this book is supposed to have had a training in arithmetic as
well as in elementary algebra. Only those rules are given here which are
apt to be easily forgotten.
GREATEST COMMON MEASURE. OR GREATEST
COMMON DIVISOR OF TWO NUMBERS.
Rule.— Divide the greater number by the less ; then divide the divisor
by the remainder, and so on, dividing always the last divisor by the last
remainder, until there is no remainder, and the last divisor is the greatest
common measure required.
LEAST COMMON MULTIPLE OF TWO OR MORE
NUMBERS.
Rule. — Divide the given numbers by any number that will divide the
greatest number of them without a remainder, and set the quotients with
the undivided numbers in a line beneath.
Divide the second line as before, and so on, until there are no two numbers
that can be divided ; then the continued product of the divisors and last
quotients will give the multiple required.
FRACTIONS.
To reduce a common fraction to its lowest terms.— Divide
both terms by their greatest common divisor: 39/52 = 3/4.
To change an improper fraction to a mixed number.—
Divide the numerator by the denominator; the quotient is the whole number,
and the remainder placed over the denominator is the fraction: 39/4 = 9%.
To change a mixed number to an improper fraction.—
Multiply the whole number by the denominator of the fraction; to the prod-
uct add the numerator; place the sum over the denominator: 1% = 15/8.
To express a whole number in the form of a fraction
with a given denominator. — Multiply the whole number by the
given denominator, and place the product over that denominator: 13 = 39/3.
To reduce, a compound to a simple fraction, also to
multiply fractions.— Multiply the numerators together for a new
numerator and the denominators together for a new denominator:
To reduce a complex to a simple fraction.— The numerator
and denominator must each first be given the form of a simple fraction;
then multiply the numerator of the upper fraction by the denominator of
the lower for the new numerator, and the denominator of the upper by the
numerator of the lower for the new denominator:
To divide fractions. — Reduce both to the form of simple fractions,
invert the divisor, and proceed as in multication:
3 3 5 3 v 4 12 3
_^1M=_4._=_X_=_==_.
Cancellation of fractions. — In compound or multiplied fractions,
divide any numerator and any denominator by any number which will
divide them both without remainder, striking out the numbers thus divided
and setting down the quotients in their stead.
To reduce fractions to a common denominator. — Reduce
each fraction to the form of a simple fraction ; then multiply each numera-
DECIMALS.
tor by all the denominators except its own for the new numerators, and all
the denominators together for the common denominator:
1 1 3_21 14 18
2' 3' 7 " 42' 42' 42*
To add fractions.— Reduce them to a common denominator, then
add the numerators and place their sum over the common denominator:
_
2 ,3 ' 7
__
42 ~ 42 ~~
To subtract fractions.— Reduce them to a common denominator,
subtract the numerators and place the difference over the common denomi-
nator:
1 3_7-6_ 1
2 7~ 14 ~14*
DECIMALS.
To add decimals.— Set down the figures so that the decimal points
are one above the other, then proceed as in simple addition: 18.75+ .012 =
18.762.
To subtract decimals.— Set down the figures so that the decimal
points are one above the other, then proceed as in simple subtraction: 18.75
- .012 = 18.738.
To multiply decimals.— Multiply as in multiplication of whole
numbers, then point off as many decimal places as there are in multiplier
and multiplicand taken together: 1.5 X .02 = .030 = .03.
To divide decimals.— Divide as in whole numbers, and point off in
the quotient as many decimal places as those in the dividend exceed those
in the divisor. Ciphers must be added to the dividend to make its decimal
places at least equal those in the divisor, and as many more as it is desired
to have in the quotient: 1.5 -*- .25 = 6. 0.1 -f- 0.3 = 0.10000 •*- 0.3 = 0.3333 -f-
Decimal Equivalents of Fractions of One Incb.
1-64
.015625
17-64
.265625
33-64
.515625
49-64
.765625
1-32
.03125
9-32
.28125
17-32
.53125
25-32
.78125
3-64
.046875
19-64
.296875
35-84
.546875
51-64
.796875
1-16
.0625
5-16
.3125
9-16
.5625
13-16
.8125
5-64
.078125
21-64
.328125
37-64
.578125
53-64
.828125
3-32
.09375
11-32
.34375
19-32
.59375
27-32
.84375
7-64
.109375
23-64
.359375
39-64
.609375
55-64
.859375
1-8
.125
3-8
.375
5-8
.625
7-8
.875
9-64
.140625
25-64
.390625
41-64
.640625
57-64
.890625
5-32
.15625
13-32
.40625
21-32
.65625
29-32
.90625
11-64
3-16
.171875
.1875
27-64
7-16
.421875
.4375
43-64
11-16
.671875
.6875
59-64
15-16
.921875
.9375
13-64
.203125
29-64
.453125
45-64
.703125
61-64
.953125
7-32
.21875
15-32
.46875
23-32
.71875
31-32
.96875
15-64
.234375
31-64
.484375
47-64
.734375
63-64
.984375
1-4
.25
1-2
.50
3-4
.75
1
1.
To convert a common fraction into a decimal.— Divide the
numerator by the denominator, adding to che numerator as many ciphers
prefixed by a decimal point as are necessary to give the number of' decimal
places desired in the result: % = 1.0000 -=-3 = 0.3333 -f.
To convert a decimal into a common fraction.— Set down
the decimal as a numerator, and place as the denominator 1 with as many
ciphers annexed as there are decimal places in the numerator; erase the
0*0
•fe
«joo
ARITHMETIC.
TH O T-»
1> £~ GO
g §
CO t- i-i
s s
C» CO CO
to 10 rf<
CO CO
CO -^1
8 g g §
O O O O
CO 00
COMPOUKD NUMBERS. 5
decimal point in the numerator, and reduce the fraction thus formed to It*
lowest terms:
To reduce a recurring decimal to a common fraction.—
Subtract the decimal figures that do not recur from the whole decimal in-
cluding one set of recurring figures; set down the remainder as the numer-
ator of the fraction, and as many nines as there are recurring figures, fol-
lowed by as many ciphers as there are non-recurring figures, in the denom-
inator. Thus:
.79054054, the recurring figures being 054.
Subtract 79
J17
= (reduced to its lowest terms) ^
COMPOUND OR DENOMINATE NUMBERS.
Reduction descending.— To reduce a compound number to a lower
denomination. Multiply the number by as many units of the lower denomi-
nation as makes one of the higher.
3 yards to inches: 3 X 36 = 108 inches.
.04 square feet to square inches: .04 X 144 = 5.76 sq. in.
If the given number is in more than one denomination proceed in steps
from the highest denomination to the next lower, and so on to the lowest,
adding in the units of each denomination as the operation proceeds.
3 yds. 1 ft. 7 in. to inches: 3x3 = 9, -f 1 = 10, 10 X 12 = 120, -f 7 = 127 in.
Reduction ascending*— To express a number of a lower denomi-
nation in terms of a higher, divide the number by the numb r of units of
the lower denomination contained in one of the next higher; the quotient is
in the higher denomination, and the remainder, if any, in the lower.
127 inches to higher denomination.
127 -*- 12 = 10 feet + 7 inches ; 10 feet -*- 3 = 3 yards + 1 foot.
Ans. 3 yds. 1 ft. 7 in.
To express the result in decimals of the higher denomination, divide the
given number by the number of units of the given denomination contained
in one of the required denomination, carrying the result to as many places
of decimals as may be desired.
127 inches to yards: 127 -*- 36 = 3£f = 3.5277 -f yards.
RATIO AND PROPORTION.
Ratio is the relation of one number to another, as obtained by dividing
one by the other.
Ratio of 2 to 4, or 2 : 4 = 2/4 = 1/2.
Ratio of 4 to 2, or 4 : 2 = 2.
Proportion is the equality of two ratios. Ratio of 2 to 4 equals ratio
of 3 to 6, 2/4 = 3/6; expressed thus, 2 : 4 : : 3 : 6; read, 2 is to 4 as 3 is to 6.
The first and fourth terms are called the extremes or outer terms, the
second and third the means or inner terms.
The product of the means equals the product of the extremes:
2 : 4 : : 3 : 6; 2 X 6 = 12; 3 X 4 = 12.
Hence, given the first three terms to find the fourth, multiply the second
and third terms together and divide by the first.
4 v 3
2 : 4 : : 3 : what number ? Ans, — = 6,
6 ARITHMETIC.
Algebraic expression of proportion.— a : b : : c : d; =- = %;ad
be . be . ad ad
= be; from which a — — ; d — — ; & = — ; c = -=— .
d a c b
Mean proportional between two given numbers, 1st and 2d, is such
a number that the ratio which the first bears to it equals the ratio which it
bears to the second. Thus, 2 : 4 : : 4 : 8; 4 is a mean proportional between
2 and 8. To find the mean proportional between two numbers, extract the
square root of their product.
Mean proportional of 2 and 8 = V% x 8 = 4.
Single Rule of Three ; or, finding the fourth term of a proportion
when three terms are given.— Rule, as above, when the terms are stated in
their proper order, multiply the second by the third and divide by the first.
The difficulty is to state the terms in their proper order. The term which is
of the same kind as the required or fourth term is made the third; the first
and second must be like each other in kind and denomination. To deter-
mine which is to be made second and which first requires a little reasoning.
If an inspection of the problem shows that the answer should be greater
than the third term, then the greater of the other two given terms should
be made the second term — otherwise the first. Thus, 3 men remove 54 cubic
feet of rock in a day; how many men will remove in the same time 10 cubic
yards ? The answer is to be men— make men third term; the answer is to
be more than three men, therefore make the greater quantity, 10 cubic
yards, the second term ; but as it is not the same denomination as the other
term it must be reduced, = 270 cubic feet. The proportion is then stated:
3 X 270
54 : 270 : : 3 : x (the required number) ; x = — — — = 15 men.
The problem is more complicated if we increase the number of given
terms. Thus, in the above question, substitute for the words " in the same
time " the words " in 3 days." First solve it as above, as if the work were
to be done in the same time; then make another proportion, stating it thus:
If 15 men do it in the same time, it will take fewer men to do it in 3 days;
make 1 day the 2d term and 3 days the first term 3:1 : : 15 men : 5 men.
Compound Proportion, or Double Rule of Three.— By this
rule are solved questions like the one just given, in which two or more stat-
ings are required by the single rule of three. In it as in the single rule,
there is one third term, which is of the same kind and denomination as the
fourth or required term, but there may be two or more first and second
terms. Set down the third term, take each pair of terms of the same kind
separately, and arrange them as first and second by the same reasoning as
is adopted in the single rule of three, making the greater of the pair the
second if this pair considered alone should require the answer to be
greater.
Set down all the first terms one under the other, and likewise all the
second terms. Multiply all the first terms together and all the second terms
together. Multiply the product of all the second terms by the third term . and
divide this product by the product of all the first terms. Example: If 3 men
remove 4 cubic yards in one day, working 12 hours a day, how many men
working 10 hours a day will remove 20 cubic yards in 3 days ?
Yards 4
Days 3
Hours 10
Products 120
20
1 : : 3 men.
12
240 : : 3 : 6 men. Ans.
To abbreviate by cancellation, any one of the first terms may cancel
either the third or any of the second terms; thus, 3 in first cancels 3 in third,
making it 1, 10 cancels into 20 making the latter 2, which into 4 makes it 2,
which into 12 makes it 6, and the figures remaining are only 1 : 6 : : 1 : 6.
INVOLUTION, OR POWERS OF NUMBERS.
Involution is the continued multiplication of a number by itself a
given number of times. The number is called the root, or first power, and
the products are called powers. The second power is called the square and
POWERS OF HUMBERS.
the third power the cube. The operation may be indicated without being
performed by writing a small figure called the index or exponent to the
right of and a, little above the root; thus, 33 = cube of 3, = 27.
To multiply two or more powers of the same number, add their exponents;
thus, 22 x 23' = 25, or 4 X 8 = 32 = 25.
To divide two powers of the same number, subtract their exponents; thus,
23 -r- 22 = 21 = 2; 22 -f- 24 = 2~2 = — = -. The exponent may thus be nega-
tive 23 -t- 23 = 2° = 1, whence the zero power of any number = 1. The
first power of a number is the number itself. The exponent may be frac-
tional, as 2*, 23, which means that the root is to be raised to a power whose
exponent is the numerator of the fraction, and the root whose sign is the
denominator is to be extracted (see Evolution). The exponent may be a
deeimal, as 2°'5, 21*6; read, two to the five-tenths power, two to the one and
five-tenths power. These powers are solved by means of Logarithms (which
see).
First Nine Powers of the First Nine Numbers.
1st
3d
3d
4th
5th
6th
7th
8th
9th
Pow'r
Pow'r
Power.
Power.
Power.
Power.
Power.
Power.
Power.
1
1
1
j
1
1
1
1
1
2
4
8
16
32
64
128
256
512
3
9
27
81
243
729
2187
6561
19683.
4
16
64
256
1024
4096
16384
65536
262144
5
25
125
625
3125
15625
78125
390625
1953125
6
36
216
1296
7776
46656
279936
1679616
10077696
7
49
343
2401
16807
117649
823543
5764801
40353607
8
64
512
4096
32768
262144
2097152
16777216
134217728
9
81
729
6561
59049
531441
4782969
43046721
387420489
The First Forty Powers of 2.
0
h
o
L*
c
L
»
L
oJ
"3
1
o
"3
i
1
o
1
o
1
>
fi
p.
>
PH
>
PH
l
9
512
18
262144
27
134217728
36
68719476736
2
10
1024
19
524288
28
268435456
37
137438953472
4
11
2048
20
1048576
29
536870912
38
274877906944
8
12
4096
21
2097152
30
1073741824
39
549755813888
16
13
8192
22
4194304
31
2147483048
40
1099511627776
32
14
16384
23
8388608
32
4294967296
64
15
32768
24
16777216
33
8589934592
128
16
65536
25
33554432
34
17179869184
256
17
131072
26
67108864
35
34350738368
EVOLUTION.
Evolution is the finding of the root (or extracting the root) of any
number the power of which is given.
I/ V
* the
The sign tf indicates that the square root is to be extracted :
cube root, 4th root, ?ith root.
A fractional exponent with 1 for the numerator of the fraction is also
used to indicate that the operation of extracting the root is to be performed;
thus, 2*, 2* = V2, Vs.
When the power of a number is indicated, the involution not being per-
formed, the extraction of any root of that power may also be indicated by
8 ARITHMETIC.
dividing the index of the power by the index of the root, indicating the
division by a fraction. Thus, extract the square root of the 6th power of 2:
|/2« = 2$ _ 2f _ g3 _ 8<
The 6th power of 2, as in the table above, is 64 ; |/64 ss 8.
Difficult problems in evolution are performed by logarithms, but the
square root and the cube root may be extracted directly according to the
rules given below. The 4th root is the square root of the square root. The
6th root is the cube root of the square root, or the square root of the cube
root ; the 9th root is the cube root of the cube root • etc.
To Extract tlie Square Root.— Point off the given number into
periods of two places each, beginning with units. If there are decimals,
point these off likewise, beginning at the decimal point, and supplying
as many ciphers as may be needed. Find the greatest number whose
square is less than the first left-hand period, and place it as the first
figure in the quotient. Subtract its square from the left-hand period,
and to the remainder annex the two figures of the second period for
a dividend. Double the first figure of the quotient for a partial divisor ;
find how many times the latter is contained in the dividend exclusive
of the right-hand figure, and set the figure representing that number of
times as the second figure in the quotient, and annex it to the right of
the partial divisor, forming the complete divisor. Multiply this divisor by
the second figure in the quotient and subtract the product from the divi-
dend. To the remainder bring down the next period and proceed as before,
in each case doubling the figures in the root already found to obtain the
trial divisor. Should the product of the second figure in the root by the
completed divisor be greater than the dividend, erase the second figure both
from the quotient and from the divisor, and substitute the next smaller
figure, or one small enough to make the product of the second figure by the
divisor less than or equal to the dividend.
3.141 5926536 1 [1.77245 -f
27T274
34712515
1 2489
3542 8692
7084
35444 160865
1141776
354485 1908936
1772425
To extract the square root of a fraction, extract the root of numerator
/4 2
and denominator separately. \/ - — -, or first convert the fraction into a
p 9 3
decimal, j/|= 4/.4444 + = .6666 + .
T 9
To Kxtract the Cube Root.— Point off the number into periods of
3 figures each, beginning at the right hand, or unit's place. Point off deci-
mals in periods of 3 figures from the decimal point. Find the greatest cube
that does not exceed the left-hand period ; write its root as the first figure
in the required root, Subtract the cube from the left-hand period, and to
the remainder bring down the next period for a dividend.
Square the first figure of the root; multiply by 300, and divide the product
into the dividend for a trial divisor ; write the quotient after the first figure
of the root as a trial second figure.
Complete the divisor by adding to 3CO times the square of the first figure,
30 times the product of the first by the second figure, and the square of the
second figure. Multiply this divisor by the second figure; subtract the
product from the remainder. (Should the product be greater than the
remainder, the last figure of the root and the complete divisor are too large ;
CUBE ROOT.
substitute for the last figure the next smaller number, and correct the trial
divisor accordingly.)
To the remainder bring down the next period, and proceed as before to
find the third figure of the root— that is, square the two figures of the root
already found; multiply by 300 for a trial divisor, etc.
If at any time the trial divisor is greater than the dividend, bring down an-
other period of 3 figures, and place 0 in the root and proceed.
The cube root of a number will contain as many figures as there are
periods of 3 in the number.
Shorter Methods of Extracting the Cube Root,- 1, From
Went worth's Algebra:
300 x
30x
x 2 =
1,881, 365,963,625 1 12345
1
300 881
728
64 153365
300 x
30 x
122 =
12 x 3 =
43200
1080
300 x
30 x
123 x 4 =
4,2 =
442891 132867
1089 J 20498963
4538700 1
14760*
16|
4553476 )• 18213904
_ I4!7!! 25J85059625
300 x 12342 = 456826800
30 x 1234 x 5 = 185100
52= 25
457011925 2285059625
After the first two figures of the root are found the next trial divisor is
found by bringing down the sum of the 60 and 4 obtained in completing the
preceding divisor; then adding the three lines connected by the brace, and
annexing two ciphers. This method shortens the work in long examples, as
is seen in the case of the last two trial divisors, saving the labor of squaring
123 and 1234. A further shortening of the work is made by obtaining the
last two figures of the root by division, the divisor employed being three
times the square of the part of the root already found ; thus, after finding
the first three figures:
3 x 123» =
45387|20498963|45.1-f
—181548 ~
234416
226935
74813
The error due to the remainder is not sufficient to change the fifth figure of
the root.
2. By Prof. H. A. Wood (Stevens Indicator, July, 1890):
I. Having separated the number into periods of three figures each, count-
ing from the right, divide by the square of the nearest root of the first
period, or first two periods ; the nearest root is the trial root.
II. To the quotient obtained add twice the trial root, and divide by 3.
This gives the root, or first approximation.
III. By using the first approximate root as a new trial root, and proceed-
ing as before, a nearer approximation is obtained, which process may be
repeated until the root has been extracted, or the approximation carried as
far as desired.
10 ARITHMETIC.
EXAMPLE.— Required the cube root of 20. The nearest cube to 20 is 3*.
32 = 9)20.0
2.2
6_
3)871
2.7 IstT. R.
7.29)20.000
3)8.143
2.714, 1st ap. cube root,
2.7142 = 7.365796)20.0000000
2.7152534
5.428
3)8.1432534
2.7144178 2d ap. cube root.
REMARK. — In the example it will be observed that the second term, or
first two figures of the root, were obtained by using for trial root the root of
the first period. Using, in like manner, these two terms for trial root, we
obtained four terms of the root ; and these four terms for trial root gave
seven figures of the root correct. In that example the last figure should be
7. Should we take these eight figures for trial root we should obtain at least
fifteen figures of the root correct.
To Extract a Higher Root than the Cube,— The fourth root is
the square root of the square root ; the sixth root is the cube root of the
square root or the square root of the cube root. Other roots are most con-
veniently found by the use of logarithms.
ALLIGATION
shows the value of a mixture of different ingredients when the quantity
and value of each is known.
Let the ingredients be a, 6, c, d, etc., and their respective values per unit
w>> x, y, z, etc.
A = the sum of the quantities = a-\-b-\-c-}-d, etc.
P — mean value or price per unit of A.
AP = aw -f bx -f- cy + dz, etc.
_ aw -\-bx-\-cy-\-dz
A
PERMUTATION
shows in how many positions any number of things may be arranged in a
vrow; thus, the letters a, b, c may be arranged in six positions, viz. abc, acb,
'cab, cba, bac, bca.
Rule.— Multiply together all the numbers used in counting the things; thus,
permutations of 1, 2, and 3 = 1X2X3 = 6. In how many positions can 9
things in a row be placed ?
1X2X3X4X5X6X7X8X9 = 362880.
COMBINATION
shows how many arrangements of a few things may be made out of a
greater number. Rule : Set down that figure which indicates the greater
number, and after it a series of figures diminishing by 1, until as many are
set down as the number of the few things to be taken in each combination.
Then beginning under the last one set down said number of few things ;
then going backward set down a series diminishing by 1 until arriving under
the first of the upper numbers. Multiply together all the upper numbers to
form one product, and all the lower numbers to form another; divide the
upper product by the lower one.
GEOMETRICAL PROGRESSION. 11
How many combinations of 9 things can be made, taking 3 in each com-
bination ?
9X8X7 _ 504 _ 84
1X2X3" 6
ARITHMETICAL PROGRESSION,
in a series of numbers, is a progressive increase or decrease in each succes-
sive number by the addition or subtraction of the same amount at each step,
as 1, 2, 3, 4, 5, etc., or 15, 12, 9, 6, etc. The numbers are called terms, and the
equal increase or decrease the difference. Examples in arithmetical pro-
gression may be solved by the following formulae :
Let a = first term, I = last term, d = common difference, n = number of
terms, s = sum of the terms:
I = a -f (u — l)d,
_2s _
~~ n ~ '
= d + a) ,
- d)» + Sds
OE01TIKTRICAI, PROGRESSION,
in a series of numbers, is a progressive increase or decrease in each sue.
cessive number by the same multiplier or divisor at each step, as 1, 2, 4, 8,
16. etc., or 243, 81, 27, 9, etc. The common multiplier is called the ratio.
Let a = first term, I = last term, r — ratio or constant multiplier, n =:
number of terms, m = any term, as 1st, 2d, etc., s = sum of the terms:
' a -r- (r - I)« _ (r-l)sr~ - l
l = ar*-l> -p- -7n—r~
iog Z = log a + (n - 1) log r, f(£ - l)n ~ x - a(« - a)n - J = 0.
m = af"* - a* log w = log a -f- (m - 1) log r.
n - 1 /— n — 1/~~^
yjn - yan
= n-l- n-l.- '
ARITHMETIC.
=: o.
log I - log a 1
logr "
log I — log a
'' log (s - a) - log (* - 0 "
log a = log I - (n — 1) log r.
log I — log a
logr = n__!
. l°g [ft + (r — l)s] — log a
log r
log Z - log [?•/• - (r - l)s]
log r
Population of the United States.
(A problem in geometrical progression.^
Tear.
1860
1870
1880
1890
1900
1905
1910
Population.
81,443,821
39,818,449*
50,155,783
62,622,250
76,295,220
Est. 83,577,000
" 91554,000
Increase in 10 Annual Increase,
Years, per cent. per cent.
26.63
25.96
24.86
21.834
2.39
2.33
2.25
1.994
Est. 1.840
44 1.840
Est. 20.0
Estimated Population in Each Year from 1870 to 1909.
(Based on the above rates of increase, in even thousands.)
1870. . . .
39,818
1880.. .
50,156
1890..
62,622
1900. ..
76,295
1871 ....
40,748
1881.. .
51,281
1891.
63,871
1901. ..
77,699
1872. ..
41,699
1882 . .
52,433
1892. .
65,145
1902. ..
79,129
1873....
42,673
1883.. .
53,610
1893. .
66,444
1903. ..
80,585
1874....
43,670
1884.. .
54,813
1894.
67,770
1904. ..
82,067
1875...
44,690
1885..
56,043
1895.
69,122
1905. ..
83,577
1876....
45,373
1886.. .
57,301
1896.
70,500
1906. ..
85,115
1877....
46,800
1887.. .
58,588
1897.
71,906
1907. ..
86,681
1878 ..
47,893
1888.. .
59,903
1898.
73,341
1908. ..
88,276
1879....
49,011
1889.. .
61,247
1899.
74,803
1909. ..
89,900
The above table has been calculated by logarithms as follows :
log r = log I - log a -*- (n - 1), log m = log a -f- (w* — 1) loS r
Pop. 1900. . . . 76,295,2-20 log = 7.8824988 = log I
" 1890 . . . 62,022,250 log = 7.7967285 = log a
cliff. = .0857703
n = 11, n - 1 = 10; diff. •*• 10 = .00857703 = log r,
add log for 1890 7.7967285 = log a
log for 1891 = 7.80530553 No. = 63,871 . . .
add again .00857703
log for 1892 7.81388256 No. = 65,145 . . .
Compound interest is a form of geometrical progression ; the ratio be-
ing 1 plus the percentage.
* Corrected by addition of 1,260,078, estimated error of the census of 1870,
Census Bulletin No, 16, Dec, 12, 1890,
DISCOUNT. 13
INTEREST AND DISCOUNT.
Interest is money paid for the use of money for a given time; the fao
tors are :
p, the sum loaned, or the principal:
t, the time in years;
r, the rate of interest;
t, the amount of interest for the given rate and time;
a = p + * = the amount of the principal with interest
at the end of the time.
Formulae :
i = interest = principal X time X rate per cent = i = ^~;
a = amount = principal -f- interest = p -{- ^55;
_ 100*
- pt>
, ,. 100*
t = time = .
pr
If the rate is expressed decimally as a per cent,— thus, 6 per cent = .06,—
the formulae become
pt1 pr7 tr
Rules for finding Interest.— Multiply the principal by ;the rate
per annum divided by 100, and by the time in yc *i ; and fractions of a year.
If the time is given in days, interest = Principal X rate X no. of days
oo5 X 100
In banks interest is sometimes calculated on the basis of 360 days to a
year, or 12 months of 30 days each.
Short rules for interest at 6 per cent, when 360 days are taken as 1 year:
Multiply the principal by number of days.and divide by 6000.
Multiply the principal by number of months and divide by 200.
The interest of 1 dollar for one month is ^ cent.
Interest of 100 Dollars for Different Times and Rates.
Time. 2# 3# 4# 6# 6£ 8£ 10*
lyear $2.00 $3.00 $4.00 $5.00 $6.00 $8.00 $10.00
1 month .16f .25 .33$ .41f .50 .66| .83$
1 day = 3$s year .0055f .0083$ .0111$ .0138| .0166§ .0222* .0277$
1 day = 3$5 year .005479 .008219 .010959 .013699 .016438 .0219178 .0273973
Discount is interest deducted for payment of money before it is due.
True discount is the difference between the amount of a debt pay-
able at a future date without interest and its present worth. The present
worth is that sum which put at interest at the legal rate will amount to the
debt when it is due.
To find the present worth of an amount due at future date, divide the
amount by the amount of $1 placed at interest for the given time. The dis-
count equals the amount minus the present worth.
What discount should be allowed on $103 paid six months before it is due,
interest being 6 per cent per annum ?
103
T = $100 present worth, discount = 8.00.
1 + 1 X .06 X |
Bank discount is the amount deducted by a bank as interest on
money loaned on promissory notes. It is interest calculated not on the act-
ual sum loaned, but on the gross amount of the note, from which the dis-
count is deducted in advance. It is also calculated on the basis of 360 days
in the year, and for 3 (in some banks 4) days more than the time specified "in
the note. These are called days of grace, and the note is not payable till
tfce last of these days. In some States days of grace have been abolished.
14
ARITHMETIC.
What discount will be deducted by a bank in discounting a note for $108
payable 6 months hence ? Six months = 182 days, add 3 days grace = 185
days
,103 X 185
6000
= $3.176.
Compound Interest.— In compound interest the interest is added to
the principal at the end of each year, (or shorter period if agreed upon).
Let p = the principal, r = the rate expressed decimal^, n = no of years,
and a the amount :
a = amount = p (1 + r)n ; r = rate =
p = principal =
no. ot years _ n =
Compound Interest Table.
(Talue of one dollar at compound interest, compounded yearly, at
3, 4, 5, and 6 per cent, from 1 to 50 years.)
£
3#
4*
6*
w
05
1
F
3*
W
5*
w
i
1.03
3.04
1.05
1.06
16
1.6047
1.8730
2.1829
2.5403
2
1.0609
1.0816
1.1025
1.1236
17
1.6528
1.9479
2.2920
2.6928
3
1.0927
1.1249
1.1576
1.1910
18
1.7024
2.0258
2.4066
2.8543
4
.1255
1.1699
1.2155
1.2625
19
1.7535
2.1068
2.5269
3.0256
5
.1593
1.2166
1.2763
1.3382
20
1.8061
2.1911
2.6533
3.2071
6
.1941
1.2653
1.3401
1.4185
21
1.8603
2.2787
2.7859
3.3995
7
.2299
1.3159
.4071
1.5036
22
1.9161
2.3699
2.9252
3.6035
8
.2668
1.3686
.4774
1.5938
23
1.9736
24647
3.0715
3.8197
9
.3048
.4233
.5513
1.6895
24
2.0328
2.5633
3.2251
40487
10
.3439
.4802
.6289
1.7908
25
2.0937
2.6658
3.3863
4.2919
11
1.3842
.5394
.7103
1.8983
30
2.4272
3.2433
4.3219
5.7435
12
1.4258
.6010
.7958
2.0122
35
2.8138
3.9460
5.5159
7.6862
13
1.4685
.6651
.8856
2.1329
40
3.2620
4.8009
7.0398
10.2858
14
1.5126
.7317
.9799
2.2609
45
3.7815
5.8410
8.9847
13.7648
15
1.5580
1.8009
2.0789
2.3965
50
4.3838
7.1064
11.4670
18.4204
At compound interest at 3 per cent money will double itself in 23J^ years,
at 4 per cent in 17% years, at 5 per cent in 14.2 years, and at 6 per cent in
11. 9 years.
EQUATION OF PAYMENTS.
By equation of payments we find the equivalent or average time in which
one payment should be made to cancel a number of obligations due at dif-
ferent dates ; also the number of days upon which to calculate interest or
discount upon a gross sum which is composed of several smaller sums pay-
able at different dates.
Rule.— Multiply each item by the time of its maturity in days from a
fixed date, taken as a standard, and divide the sum of the products by the
sum of the items: the result is the average time in days from the standard
date.
A owes B $100 due in 30 days, $200 due in 60 days, and $300 due in 90 days.
In how many days may the whole be paid in one sum of $600 ?
100 x 30 -f- 200 x 60 -f 300 x 90 = 42,000 ; 42,000 -f- 600 = 70 days, ana.
A owes B $100, $200, and $300, which amounts are overdue respectively 30,
60, and 90 days. If he now pays the whole amount, $600, how many days'
interest should he pay on that sum ? Ans. 70 days.
ANNUITIES.
15
PARTIAL PAYMENTS.
To compute Interest on notes and bonds when partial payments have been
made:
United States Rule.— Find the amount of the principal to the time
of the first payment, and, subtracting the payment from it, find the amount
of the remainder as a new principal to the time of the next payment.
If the payment is less than the interest, find the amount of the principal
to the time when the sum of the payments equals or exceeds the interest
due, and subtract the sum of the payments from this amount.
Proceed in this manner till the time of settlement.
Note.— The principles upon which the preceding rule is founded are:
1st. That payments must be applied first to discharge accrued interest,
and then the remainder, if any, toward the discharge of the principal.
26. That only unpaid principal can draw interest.
Mercantile Method.— When partial payments are made on short
notes or interest accounts, business men commonly employ the following
method :
Find the amount of the whole debt to the time of settlement ; also find
the amount of each payment from the time it was made to the time of set-
tlement. Subtract the amount of payments from the amount of the debt;
the remainder will be the balance due.
ANNUITIES.
An Annuity is a fixed sum of money paid yearly, or at other equal times
agreed upon. The values of annuities are calculated by the principles of
compound interest.
1. Let i denote interest on $1 for a year, then at the end of a year the
amount will be 1 + i. At the end of n years it will be (1 + i)».
2. The sum which in n years will amount to 1 is n or (l + i)~ w, or the
present value of 1 due in n years.
(1 I i)n — 1
3. The amount of an annuity of 1 in any number of years n is v ~ . - .
4. The present value of an annuity of 1 for any number of years n is
5. The annuity which 1 will purchase for any number of years n is
6. The annuity which would amount to 1 in n years is -
Amounts, Present Values, etc., at 5% Interest.
Years
(1)
(2)
(3)
(4)
(5)
(6)
(l+i)n
(l_f i)-n
(1 4- i)n - 1
l-(l+9-»
i
i
i
i
i-d+9-"
(1 + 9" -1
1
1.05
.952381
1.
.952381
1.05
1.
2
1.1025
.907029
2.05
1.859410
.537805
.487805
3
1.157625
.863838
3.1525
2.723248
.367209
.317209
4
1.215506
.822702
4.310125
3.545951
.282012
.232012
5
1.276282
.783526
5.525631
4.329477
.230975
.180975
6...
.340096
.746215
6.801913
5.075692
.197017
.147018
7
.407100
.710681
8.142008
5.786373
.172820
.122820
8
.477455
.676839
9.549109
6.463213
.154722
.104722
9
1. 5513">8
.644609
11.026564
7.107822
.140690
.090690
10
.628895
.613913
12.577893
7.721735
.129505
.078505
16
ARITHMETIC.
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-
WEIGHTS AND MEASUBES.
TABLES FOR CALCULATING SIN It ING -FUNDS AND
PRESENT VALUES.
Engineers and others connected with municipal work an d*indus trial enter-
prises often find it necessary to calculate payments to sinking-funds which
will provide a sum of money sufficient to pay off a bond issue or other debt
at the end of a given period, or to determine the present value of certain
annual charges. The accompanying tables were computed by Mr. John W.
Hill, of Cincinnati, Eng'g News, Jan. 25, 1894.
Table I (opposite page) shows the annual sum at various rates of interest
required to net $1000 in from 2 to 50 years, and Table II shows the present
value at various rates of interest of an annual charge of $1000 for from 5 to
50 years, at five-year intervals and for 100 years.
Table II.— Capitalization of Annuity of $1000 for
from 5 to 1OO Years.
5
10
15
20
25
Rate of Interest, per cent.
w
3
SM
4
«*
5
6*
6
4,645 88
8,752.17
12,381.41
15,589.215
18,424.67
4,579.60
8,530.13
11,937.80
14,877.27
17,413.01
4,514.92
8,316.45
11,517.23
14,212.12
16,481.28
4,451.68
8,110.74
11,118.06
13,590.21
15,621.93
4,389.91
7,912.67
10,739.42
13,007.88
14,828.12
4,329.45
7,721.73
10,379.53
12,462.13
14,093.86
4,268.09
7,537.54
10,037.48
11,950.26
13,413.82
4,212.40
7,860.19
9,712.30
11,469.96
12,783.38
30
35
40
45
50
100
20,930.59
23,145.31
25,103.53
26,833.15
28,362.48
36,614.21
19,600.21
21,487.04
23,114.36
24,518.49
25,729.58
31,598.81
18,391.8517,291.86
20,000.43 18,664.37
21,354.8319,792.65
22,495.2320,719.89
23,455.21i21,482.08
27,655.3624,504.96
16,288.77
17,460.89
18,401.49
19,156.24
19,761.93
21,949.21
15,372.36
16,374.36
17,159.01
17,773.99
18,255.86
19,847.90
14,533.63
15,390.48
16,044.92
16,547.65
16,931.97
18,095.83
13,764.85
14,488.65
15,046.31
15,455.85
15,761.87
16,612.64
WEIGHTS AND MEASURES.
Long Measure.— Measures of Length.
12 inches = 1 foot.
3 feet = 1 yard.
1760 yards, or 5280 feet = 1 mile.
Additional measures of length in occasional use : 1000 mils = 1 inch ;
4 inches = 1 hand; 9 inches = 1 span; 2*4 feet = 1 military pace; 2 yards =
1 fathom; 5V£ yards, or 16^> feet = 1 rod (formerly also called pole or perch).
Old Land Measure.— 7.92 inches = 1 link; 100 links, or 66 feet, or 4
rods =i 1 chain; 10 chains, or 220 yards = 1 furlong; 8 furlongs = 1 mile;
10 square chains = 1 acre.
Nautieal Measure*
6°8°ut6efmllesr 1>15156 Stat" \ = 1 nautical mile, or knot.*
3 nautical miles = 1 league.
60 Ta'tuTe milll' °P 69'168 [ = 1 degree (at the ecluator)-
360 degrees = circumference of the earth at the equator.
*The British Admiralty takes the round figure of 6080 ft. which is the
length of the *' measured mile1' used in trials of vessels. The value varies
from 6080.26 to 6088.44 ft. according to different measures of the earth's di-
ameter. There is a difference of opinion among writers as to the use of the
word " knot" to mean length or-a distance— some holding that it should be
used only to denote a rate of speed. The length between knots on the log
line is 1/120 of a nautical mile, or 50.7 ft., when a half-minute glass is used;
so that a speed of 10 knots is equal to 10 nautical miles per hour.
18 ARITHMETIC.
Square Measure.— Measures of Surface.
144 square incites, or 183.35 circular \ _ ^ square foot.
9 square feet = 1 square yard .
30]4 square yards, or 272>£ square feet = 1 square rod.
10 sq. chains, or 160 sq. rods, or 4840 sq. | *
yards, or 43560 sq. feet, f - -1 e<
640 acres ' = 1 square mile.
An acre equals a square whose side is 208.71 feet.
Circular Inch; Circular Mil.— A circular inch is the area of a
circle 1 inch in diameter = 0.7854 square inch.
I square inch = 1.2732 circular inches.
A circular mil is the area of a circle 1 mil, or .001 inch in diameter.
10002 or 1,000,000 circular mils = 1 circular inch.
1 square inch = 1,273,239 circular mils.
The mil and circular mil are used in electrical calculations involving
the diameter and area of wires.
Solid or Cubic Measure.— Measures of Volume.
1728 cubic inches = 1 cubic foot.
27 cubic feet = 1 cubic yard.
1 cord of wood = a pile, 4x4x8 feet = 128 cubic feet.
1 perch of masonry = 16^X 1MX1 foot =24^ cubic feet.
Liquid Measure.
4 gills = 1 pint.
2 pints = 1 quart.
„ j U. S. 231 cubic inches.
4 quarts = 1 gallon J Eng 2?7 274 cubic inchegi
31 K gallons = 1 barrel.
42 gallons = 1 tierce.
2 barrels, or 63 gallons = 1 hogshead.
84 gallons, or 2 tierces = 1 puncheon.
2 hogsheads, or 126 gallons = 1 pipe or butt.
2 pipes, or 3 puncheons = 1 tun.
A gallon of water at 62° F. weighs 8.3356 Ibs.
The U. S. gallon contains 281 cubic inches; 7.4805 gallons = 1 cubic foot.
A cylinder 7 in. diam. and 6 in. high contains 1 gallon, very nearly, or 230.9
cubic inches. The British Imperial gallon contains 277.274 cubic inches
= 1.20032 U. S. gallon, or 10 Ibs. of water at 62° F.
Tlie Miner's Inch.— (Western U. S. for measuring flow of a stream
of water).
The term Miner's Inch is more or less indefinite, for the reason that Cali-
f ornip, water companies do not all use the same head above the centre of
the aperture, and the inch varies from 1.36 to 1.73 cubic feet per minute
each; but the most common measurement is through an aperture 2 inches
high and whatever length is required, and through a plank 1£ inches thick.
The lower edge of the aperture should be 2 inches above the bottom of the
measuring-box, and the plank 5 inches high above the aperture, thus mak-
ing a 6-inch head above the centre of the stream. Each square inch of this
opening represents a miners inch, which is equal to a flow of H cubic feet
per minute.
Apothecaries' Fluid Measure.
60 minims = 1 fluid drachm. 8 drachms = 1 fluid ounce.
In the U. S. a fluid ounce is the 128th part of a U. S. gallon, or 1 805 cu. ins.
It contains 456.3 grains of water at 39° F, In Great Britain the fluid ounce
is 1.732 cu. ins. and contains i ounce avoirdupois, or 437.5 grains of water at
62° F.
Dry Measure, U. S.
2 pints = 1 quart. 8 quarts = 1 peck. 4 pecks = 1 bushel.
The standard U. S. bushel is the Winchester bushel, which is in cylinder
WEIGHTS AND MEASURES. 19
form, 18>3 inches diameter and 8 inches deep, and contains 3150.42 cubic
inches.
A struck bushel contains 2150.42 cubic inches = 1.2445 cu. ft.; 1 cubic foot
- 0.80356 struck bushel. A heaped bushel is a cylinder 18^ inches diam-
eter and 8 inches deep, with a heaped cone not less than 6 inches high.
It is equal to 1^ struck bushels.
The British Imperial bushel is based on the Imperial gallon, and contains
8 such gallons, or 2218.192 cubic inches = 1.2837 cubic feet. The English
quarter = 8 Imperial bushels.
Capacity of a cylinder in U. S. gallons = square of diameter, in inches X
height in inches X .0034. (Accurate within 1 part in 100,000.)
Capacity of a cylinder in U. S. bushels = square of diameter in inches X
height in inches X .0003652.
Shipping Measure*
Register Ton.— For register tonnage or for measurement of the entire
internal capacity of a vessel :
100 cubic feet = 1 register ton.
This number is arbitrarily assumed to facilitate computation.
Shipping Ton.— For the measurement of cargo :
1 U. S. shipping ton.
40 cubic feet =
42 cubic feet =
31. 16 Imp. bushels.
32.143 U. S. "
1 British shipping ton.
32.719 Imp. bushels.
33.75 U. S.
Carpenter's Rule.— Weight a vessel will carry = length of keel X breadth
at main beam X depth of hold in feet -4-95 (the cubic feet allowed for a ton).
The result will be the tonnage. For a double-decker instead of the depth
of the hold take half the breadth of the beam.
Measures of Weight.— Avoirdupois, or Commercial
Weight.
16 drachms, or 437.5 grains = 1 ounce, oz.
16 ounces, or 7000 grains = 1 pound, Ib.
28 pounds =1 quarter, qr.
4 quarters = 1 hundredweight, cwt. = 112 Ibs.
20 hundred weight = 1 ton of 2240 pounds, or long ton.
2000 pounds = 1 net, or short ton.
2204.6 pounds = 1 metric ton.
1 stone = 14 pounds ; 1 quintal = 100 pounds.
The drachm, quarter, hundredweight, stone, and quintal are now seldom
used in the United States.
Tr*y Weight.
24 grains = 1 pennyweight, dwt.
20 pennyweights = 1 ounce, oz. = 480 grains.
12 ounces = 1 pound, Ib. = 5760 grains.
Troy weight is used for weighing gold and silver. The grain is the same
in Avoirdupois, Troy, and Apothecaries' weights. A carat, used in weighing
diamonds = 3.168 grains = .205 gramme.
Apothecaries9 Weight.
20 grains = 1 scruple, 3
3 scruples = 1 drachm, 3 = 60 grains.
8 drachms = 1 ounce, § = 480 grains.
12 ounces = 1 pound, Ib. = 5760 grains.
To determine whether a balance has unequal arms.—
After weighing an article and obtaining equilibrium, transpose the article
and the weights. If the balance is true, it will remain in equilibrium ; if
untrue, the pan suspended from the longer arm will descend.
To weigh correctly on an incorrect balance.— First, by
substitution. Put the article to be weighed in one pan of the balance and
20 ARITHMETIC.
counterpoise it by any convenient heavy articles placed on the other pan.
Remove the article to be weighed and substitute for it standard weights
until equipoise is again established. The amount of these weights is the
weight of the article.
Second, by transposition. Determine the apparent weight of the article
as usual, then its apparent weight after transposing the article and the
weights. If the difference is small, add half the difference to the smaller
of the apparent weights to obtain the true weight. If the difference is 2
per cent the error of this method is 1 part in 10,000. For larger differences,
or to obtain a perfectly accurate result, multiply the two apparent weights
together and extract the square root of the product.
Circular Measure*
60 seconds, " = 1 minute, '.
60 minutes, ' • = 1 degree, °.
90 degrees = 1 quadrant.
360 " = circumference.
Time.
60 seconds = 1 minute.
60 minutes = 1 hour.
24 hours = 1 day.
7 days = 1 week.
365 days, 5 hours, 48 minutes, 48 seconds = 1 year.
By the Gregorian Calendar every year whose number is divisible by 4 is a
leap year, and contains 366 days, the other years containing 365 days, ex-
cept that the centesimal years are leap years only when the number of the
year is divisible by 400.
The comparative values of mean solar and sidereal time are shown by the
following relations according to Bessel :
365.24222 mean solar days = 366.24222 sidereal days, whence
1 mean solar day = 1.00273791 sidereal days;
1 sidereal day = 0 99726957 mean solar day;
24 hours mean solar time = 24h 3m 568.555 sidereal time;
24 hours sidereal time = 23h 56m 48.091 mean solar time,
whence 1 mean solar day is 3m 558.91 longer than a sidereal day, reckoned in
mean solar time.
BOARD AND TIMBER MEASURE.
Board Measure.
In board measure boards are assumed to be one inch in thickness. To
obtain the number of feet board measure (B. M.) of a board or stick of
square timber, multiply together the length in feet, the breadth in feet, and
the thickness in inches.
To compute the measure or surface in square feet.— When
all dimensions are in feet, multiply the length by the breadth, and the pro-
duct will give the surface required.
When either of the dimensions are in inches, multiply as above and divide
the product by 12.
When all dimensions are in inches, multiply as before and divide product
by 144.
Timber Measure.
To compute the vol ume of round timber.— When all dimen-
sions are in feet, multiply the length by one quarter of the product of the
mean girth and diameter, and the product will give the measurement in
cubic feet. When length is given in feet and girth and diameter in inches,
divide the product by 144 ; when all the dimensions are in inches, divide by
1728.
To compute the volume of square timber.— When all dimen-
sions are in feet, multiply together the length, breadth, and depth; the
product will be the volume in cubic feet. When one dimension is given in
inches, divide by 12; when two dimensions are in inches, divide by 144; when
all three dimensions are iu inches, divide by 1728.
WEIGHTS AKD MEASURES.
Contents in Feet of Joists, Scantling, and Timber.
Length in Feet.
Size.
12
14
16
18
20
22
24
26
28
30
Feet Board Measure.
2X 4
8
9
11
12
13
15
16
17
19
20
2X6
12
14
16
18
20
22
24
26
28
30
2X8
16
19
21
24
27
29
32
35
37
40
2 X 10
20
23
27
30
33
37
40
43
47
50
2 X 12
24
28
32
36
40
44
48
52
56
60
2 X 14
28
33
37
42
47
51
56
61
65
70
3X8
24
28
32
36
40
44
48
52
56
60
3 X 10
30
35
40
45
50
55
60
65
70
75
3 X 12
36
42
48
54
60
66
72
78
84
90
3X14
42
49
56
63
70
77
84
91
98
105
4X4
16
19
21
24
27
29
32
35
37
40
4X6
24
28
32
36
40
44
48
52
56
60
4X8
32
37
43
48
53
59
64
69
75
80
4 X 10
40
47
53
60
67
73
80
87
93
100
4 X 12
48
56
64
72
80
88
96
104
112
120
4 X 14
56
65
75
84
93
103
112
121
131
140
6X6
36
42
48
54
60
66
72
78
84
90
6X8
48
56
64
72
80
88
96
104
112
120
6 X 10
60
70
80
90
100
110
120
130
140
150
6X 12
72
84
96
108
120
132
144
156
168
180
6X 14
84
98
112
126
140
154
168
182
196
210
8X* 8
64
75
85
96
107
117
128
139
149
160
8 X 10
80
93
107
120
133
147
160
173
187
200
8 X 12
96
112
128
144
160
176
192
208
224
240
8 X 14
112
131
149
168
187
205
224
243
261
280
10 X 10
100
117
133
150
167
183
200
217
233
250
10 X 12
120
140
160
180
200
2^0
240
260
280
300
10 X 14
140
J63
187
210
233
257
280
303
327
350
12 X 12
144
168
192
216
240
264
288
312
336
360
12 X 14
168
196
224
252
280
308
336
364
392
420
14 X 14
196
229
261
294
327
359
392
425
457
490
FRENCH OR METRIC MEASURES.
The metric unit of length is the metre = 39.37 inches.
The metric unit of weight is the gram = 15.432 grains.
The following prefixes are used for subdivisions and multiples; Milli = T0^
Centi = Tfo, Deci = j^, Deca = 10, Hecto = 100, Kilo = 1000, Myria = 10,000.
FRENCH AND BRITISH (AND AMERICAN)
EQUIVALENT MEASURES.
Measures of Length.
FRENCH. BRITISH and U. S.
1 metre = 39.37 inches, or 3.28083 feet, or 1.09361 yards.
.8048 metre = 1 foot.
1 centimetre = .3937 inch.
£54 centimetres = 1 inch.
1 milimetre = .03937 inch, or 1/25 inch, nearly.
25.4 millimetres = 1 inch.
1 kilometre = 1093.61 yards, or 0.62137 mile.
22 ARITHMETIC.
Measures of Surface.
FRENCH. BRITISH and U. S.
isquaremetre = j '°;
.836 square metre = 1 square yard.
.0929 square metre = 1 square foot.
1 square centimetre = .155 square inch.
6.452 square centimetres = 1 square inch.
1 square millimetre = .00155 sq. in. = 1973.5 circ. mils.
645.2 square millimetres = 1 square inch.
1 centiare = 1 sq. metre = 10.764 square feet.
1 are = 1 sq. decametre = 1076.41 " 4*
1 hectare = 100 ares = 107641 " " = 2.4711 acres.
1 sq. kilometre = .386109 sq. miles = 247.11 "
1 sq. myriametre =38.6109" "
Of Volume.
FRENCH. BRITISH and U. S.
1 onbip metre - 4 35'314 cubic feet«
- 1 1.308 cubic yards.
.7645 cubic metre = 1 cubic yard.
.02832 cubic metre = 1 cubic foot.
1 cubic decimetre = {«;<«, ^ic inches,
28.32 cubic decimetres = 1 cubic foot.
1 cubic centimetre = .061 cubic inch.
16.387 cubic centimetres = 1 cubic inch.
1 cubic centimetre = 1 millilitre = .061 cubic inch.
1 centilitre = = .610 " "
1 decilitre = = 6.102 "
1 litre = 1 cubic decimetre = 61.023 " " = 1.05671 quarts, U. S.
1 hectolitre or decistere = 3.5314 cubic feet = 2.8375 bushels, "
1 stere, kilolitre, or cubic metre = 1.308 cubic yards = 28.37 bushels, "
Of Capacity.
FRENCH. BRITISH and U. S. »
f 61. 023 cubic inches,
(— 1 niihin rlppimpfr^ - J -08531 Cubic foot,
1 .2642 gallon (American),
[2.202 pounds of water at 62° F.
28.317 litres = 1 cubic foot.
4.543 litres = 1 gallon (British).
3.785 litres = 1 gallon (American).
Of Weight.
FRENCH. BRITISH and U. S.
1 gramme = 15.432 grains.
.0648 gramme = 1 grain.
28.35 gramme = 1 ounce avoirdupois.
1 kilogramme = 2.2046 pounds.
.4536 kilogramme = 1 pound.
1 tonne or metric ton = j -
1000 kilogrammes = 1
Mr. O. H. Titmann, in Bulletin No. 9 of the U. S. Coast and Geodetic Sur-
vey, discusses the work of various authorities who have compared the yard
and the metre, and by referring all the observations to a common standard
has succeeded in reconciling the discrepancies within very narrow limits.
The following are his results for the number of inches in a metre according
to the eomparisc/zis of the authorities named:
1817. Hassler ......................... 39.36994 inches.
1818. Kater ........................... 39.36990 "
1835. Baily ........................... 39.36973 "
1866. Clarke .......................... 39.36970 "
1885. Comstock ...................... 39.36984 "
The mean of these is ......... ... 39.36982 "
METKIC WEIGHTS AND MEASURES. 23
METRIC CONVERSION TABLES.
The following tables, with the subjoined memoranda, were published in
1890 by the United States Coast and Geodetic Survey, office of standard
weights and measures, T. C. Mendenhall, Superintendent.
Tables for Converting U. S. Weights and Pleasures—
Customary to Metric.
LINEAR.
Inches to Milli-
metres.
Feet to Metres.
Yards to Metres.
Miles to Kilo-
metres.
J _
25.4001
0.304801
0.914402
1.60935
2 =
50.8001
0.609601
1.828804
3.21869
O
76.2002
0.914402
2.743205
4.82804
4 =
101.6002
1.219202
3.657607
6.43739
5 =
127.0003
1.524003
4.572009
8.04674
6 =
152.4003
1.828804
5.486411
9.65608
7 =
177.8004
2.133604
6.400813
11.26543
8 =
203.2004
2.438405
7.315215
12.87478
9 =
228.6005
2.743205
8.229616
14.48412
SQUARE.
Square Inches to
Square Centi-
metres.
Square Feet to
Square Deci-
metres.
Square Yards to
Square Metres.
Acres to
Hectares.
1
6.452
9 290
0.836
0.4047
2 =
12.903
1&581
1.672
0.8094
3 =
19.355
27.871
2.508
1.2141
4 =
25.807
37.161
3.344
1.6187
5 =
32.258
46.452
4.181
2.0234
6 =
38.710
55.742
5.017
2.4281
7 =
45.161
65.032
5.853
2.8328
8 =
51.613
74.323
6.689
3 2375
9 =
58.065
83.613
7.525
3.6422
CUBIC.
Cubic Inches to
Cubic Centi-
metres.
Cubic Feet to
Cubic Metres.
Cubic Yards to
Cubic Metres.
Bushels to
Hectolitres.
1 =
16.387
0.02832
0.765
0.35242
2 =
32.774
0.05663
1.529
0.70485
o
49.161
0.08495
2.294
1.05727
4 =
65.549
0.11327
3.058
1.40969
5 =
81.936
0.14158
3.823
1.76211
6 =
98.323
0.16990
4.587
2.11454
7 =
114.710
0.19822
5.352
2.46696
8 =
131 097
0.22654
6.116
2.81938
9 =
147.484
0.25485
6.881
3.17181
ARITHMETIC.
CAPACITY.
Fluid Drachms
to Millilitres or
Fluid Ounces to
Quarts to Litres.
Gallons to Litres.
Cubic Centi-
Millilitres.
metres.
1 =
3.70
29.57
0.94636
3.78544
2 =
7.39
59.15
1.89272
7.57088
3 =
11.09
88.72
2.83908
11.35632
4 =
14.79
118.30
3.78544
15.14176
5 =
18.48
147.87
4.73180
18.92720
6 =
22.18
177.44
5.67816
22.71264
7 =
25.88
207.02
6.62452
26.49808
8 =
29.57
236.59
7.57088
30.28352
9 =
33.38
266.16
8.51724
34.06896
WEIGHT.
Grains to Milli-
grammes.
Avoirdupois
Ounces to
Grammes.
Avoirdupois
Pounds to Kilo-
grammes.
Troy Ounces to
Grammes.
1 =
64.7989
28.3495
0.45359
31.10348
2 =
129.5978
56.6991
0.90719
62.20696
3 =
194.3968
85.0486
1.36078
93.31044
4 =
259.1957
113.3981
1.81*37
124.41392
5 =
323.9946
141.7476
2.26796
155.51740
6 =
388.7935
170.0972
2.72156
186.62089
7 =
453.5924
198.4467
3.17515
217.72437
—
518.3914
226.7962
3.62874
248.82785
9 =
583.1903
255.1457
4.08233
279.93133
1 chain = 20.1169 metres.
1 square mile — 259 hectares.
1 fathom = 1.829 metres.
1 nautical mile = 1853.27 metres.
1 foot = 0.304801 metre.
1 avoir, pound = 453.5924277 gram.
15432.35639 grains = 1 kilogramme.
Tables for Converting 17. S. Weights and Measures
Metric to Customary.
LINEAR.
1 =
2 =
3 =
4 =
5 =
Metres to
Inches.
Metres to
Feet.
Metres to
Yards.
Kilometres to
Miles.
39.3700
78.7400
118.1100
157.4800
196.8500
3.28083
6.56167
9.84250
13.12333
16.40417
1.093611
2.187222
3.280833
4.374444
5.468056
0.62137
1.24274
1.86411
2.48548
3.10685
II II II II
«0i>ooca 1
236.2200
275.5900
314.9600
354.3300
19.68500
22.96583
26.24667
29.52750
6.561667
7.655278
8.748889
9.842500
3.72822
4.34959
4.97096
5.59233
METRIC CONVERSION TABLES.
SQUARE.
Square Centi-
metres to
Square Inches.
Square Metres
to Square Feet.
Square Metres
to Square Yards.
Hectares to
Acres.
1 =
0.1550
10.764
1.196
2.471
2 —
0.3100
21.528
2.392
4.942
3 =
0.4650
32.292
3.588
7.413
4 =
0.6200
43.055
4.784
9.884
5 =
0.7750
53.819
5.980
12.355
6 =
0.9300
64.583
7.176
14.826
7 =
1.0850
75.347
8.372
17.297
8 =
1.2400
86.111
9.568
19.768
9 =
1.3950
96.874
10.764
22.239
CUBIC.
Cubic Centi-
metres to Cubic
Inches.
Cubic Deci-
metres to Cubic
Inches.
Cubic Metres to
Cubic Feet.
Cubic Metres to
Cubic Yards.
1==
0.0610
61.023
35.314
1.308
2 =
0.12^0
122.047
70.629
2.616
3 =
0.1831
183.070
105.943
3.924
4 =
0.2441
244.093
141.258
5.232
5 =
0.3051
305.117
• 176.572
6.540
6 =
0.3661
366.140
211.887
7.848
7 =
. 0.4272
427.163
247.201
9.156
8 =
0.4882
488.187
282.516
10.464
9 =
0.5492
549.210
317.830
11.771
CAPACITY.
Millilitres or
Cubic Centi-
litres to Fluid
Drachms.
Centilitres
to Fluid
Ounces.
Litres to
Quarts.
Dekalitres
to
Gallons.
Hektolitres
to
Bushels.
1 =
0.27
0.338
1.0567
2.6417
2.8375
2 —
0.54
0.676
2.1134
5.2834
5.6750
3 =
0.81
1.014
3.1700
7.9251
8.5125
4 =
1.08
1.352
4.2267
10.5668
11.3500
5 =
1.35
1.691
5.2834
13.2085
14.1875
6 =
1.62
2.029
6.3401
15.8502
17.0250
7 —
1.89
2.368
7.3968
18.4919
i 19.8625
8 =
*.16
2.706
8.4534
21.1336
! 22.7000
9 =
2.43
3.043
9.5101
23.7753
25.5375
26
ARITHMETIC.
WEIGHT.
1 =
2 =
3 =
4 =
5 =
Milligrammes
to Grains.
Kilogrammes
to Grains.
Hectogrammes
(100 grammes)
to Ounces Av.
Kilogrammes
to Pounds
Avoirdupois.
0.01543
0.03086
0.04630
0.06173
0.07716
15432.36
30864.71
46297.07
61729.43
77161.78
3.5274
7.0548
10.5822
14.1096
17.6370
2.20462
4.40924
6.61386
8.81849
11.02311
6 =
8 =
9 =
0.09259
0.10803
0.12346
0.13889
92594.14
108026.49
123458.85
138891 .21
21.1644
24.6918
28.2192
31.7466
13.22773
15.43235
17.63697
19.84159
WEIGHT— (Continued).
Quintals to
Pounds Av.
Milliers or Tonnes to
Pounds Av.
Grammes to Ounces,
Troy.
W^CdO*-*
II II II II II
220.46
440.92
661.38
881.84
1102.30
2204 6
4409.2
6613.8
8818.4
11023.0
0.03215
0.06430
0.09645
0.12860
0.16075
6 =
7 =
8 =
9 =
1322.76
1543.22
1763.68
1984.14
13227.6
15432.2
17636.8
19841.4
0.19290
0.22505
0.25721
0.28936
i
The only authorized material standard of customary length is the
Troughton scale belonging to this office, whose length at 59°.62 Fahr. con-
forms to the British standard. The yard in use in the United States is there-
fore equal to the British yard.
The only authorized material standard of customary weight is the Troy
pound of the mint. It is of brass of unknown density, and therefore not
suitable for a standard of mass. It was derived from the British standard
Troy pound of 1758 by direct comparison. The British Avoirdupois pound
was also derived from the latter, and contains 7000 grains Troy.
The grain Troy is therefore the same as the grain Avoirdupois, and the
pound Avoirdupois in use in the United States is equal to the British pound
Avoirdupois.
The metric system was legalized in the United States in 1866.
By the concurrent action of the principal governments of the world an
International Bureau of Weights and Measures has been established near
The International Standard Metre is derived from the Metre des Archives,
and its length is defined by the distance between two lines at 0° Centigrade,
on a platinum-iridium bar deposited at the International Bureau.
The International Standard Kilogramme is a mass of platinum-iridium
deposited at the same place, and its weight in vacua is the same as that of
the Kilogramme des Archives.
Copies of these international standards are deposited in the office of
standard weights and measures of the U. S. Coast and Geodetic Survey.
The litre is equal to a cubic decimetre of water, and it is measured by the
quantity of distilled water which, at its maximum density, will counterpoise
the standard kilogramme in a vacuum; the volume of such a quantity of
water being, as nearly as has been ascertained, equal to a cubic decimetre.
WEIGHTS AND MEASURES — COMPOUND UNITS. 27
COMPOUND UNITS.
Measures of Pressure and Weight.
f 144 Ibs. per square foot.
2.0355 ins. of mercury at 32* F.
1 Ib. per square inch. = i 2.0416 " " " " 62° F.
2.309 ft. of water at 62° F.
[ 27.71 ins. " " " 62° F.
1 ounce per sq. In. = {
f 2116.3 Ibs. per square foot.
I 33.947 ft. of water at 62° F.
1 atmosphere (14.7 Ibs. per sq. in.) = -j 30 ins. of mercury at 62° F.
-
29.922 ins. of mercury at 32° F.
1.76
. . .
.760 millimetres of mercury at 32° F.
.03609 Ib. or .5774 oz. per sq. in.
1 inch of water at 62° F. =•< 5.196 Ibs. per square foot.
.0736 in. of mercury at 62° F.
1
•<
(
j
1 foot of water at «• F. = \
1 inch of water at 38° F. = 5;gg}^.I?r
( .491 Ib. or 7.86 oz. per sq. in.
1 inch of mercury at 62° F. t=4 1.132ft. of water at 62° F.
f 13. 58 ins. " " •* 62° F.
Weight of One Cubic Foot of Pure Water.
At 32° F. (freezing-point) ............................ 62.418 Ibs.
" 39.1° F. (maximum density) .......... . ............ 62.425 "
" 62° F. (standard temperature) ....... ............... 62.355 "
u 212° F. (boiling-point, under 1 atmosphere) ........ 59.76 *
American gallon = 231 cubic ins. of water at 62° F. = 8.3356 Ibs.
British •• = 277.274 " " " " " " =10 Ibs.
Measures of Work, Power, and Duty.
Work.— /The sustained exertion of pressure through space.
Unit of work.— One foot-pound, i.e., a pressure of one pound exerted
through a space of one foot.
Horse-power.— The rate of work. Unit of horse- power = 33,000 ft.-
Ibs. per minute, or 550 ft. -Ibs. per second = 1,980,000 ft. -Ibs. per hour.
Heat unit = heat required to raise 1 Ib. of water 1° F. (from 39° to 40°).
33000
Horse-power expressed in heat units = ~^g~ = 42.416 heat units per min-
ute = .707 heat unit per second = 2545 heat units per hour.
1 Ib. of f ue! per H. P. per hour=
1,000,000 ft.-lbs. per Ib. of fuel = 1.98 Ibs. of fuel per H. P. per hour.
5280 22
Velocity.— Feet per second = ^^ = 15 x miles per hour.
Gross tons per mile = ^ = — Ibs. per yard (single rail.)
French and British Equivalents of Compound Units.
FRENCH. BRITISH.
ramme per square millimetre = 1.422 Jbs. per square inch.
*'
1 g
1 ki
.
ilogramme per square *' = 1422.32
1 •• " J* centimetre = 14.223 •• " * " j
1.0335 kg. per sq. cm. — 1 atmosphere = 14.7
0.070308 kilogramme per square centimetre = 1 Ib. per square inch.
1 gramme per litre = 0.062428 Ib. per cubic foot.
1 kilogrammetre = 7.2330 foot-pounds.
28
ARITHMETIC.
WIRE AND SHEET-METAL, GAUGES COMPARED.
Number of
Gauge.
Birmingham
(or Stubs' Iron)
Wire Gauge.
American or
Brown and
Sharpe Gauge.
Roebling's and
Washburn
& Moen's
Gauge.
2|
4> <M
fit!
QQ &0 <S
CQ ®
British Imperial
Standard
Wire Gauge.
(Legal Standard
in Great Britain
since
March 1, 1884.)
U. S. Standard
Gauge for
Sheet and Plate
Iron and Steel.
(Legal Standard
since July 1, 1893.)
Number of
Gauge.
inch.
inch.
inch.
inch.
inch.
millim.
inch.
0000000
.49
.500
12.7
.5
7/0
000000
.46
.464
11.78
.469
6/0
00000
.43
.432
10.97
.438
5/0
0000
.454
.46
.393
.4
10.16
.406
4/0
000
.425
.40964
.362
.372
9.45
.375
3/0
00
.38
.3648
.331
.348
8.84
.344
2/0
0
.34
.32486
.307
.324
8.23
.313
0
1
.3
.2893
.283
.227
.3
7.62
.281
1
2
.284
.25763
.263
.219
.276
7.01
.266
2
3
.259
.22942
.244
.212
.252
6.4
.25
3
4
.238
.20431
.225
.207
.232
5.89
.234
4
5
.22
.18194
.207
.204
.212
5.38
.219
5
6
.203
.16202
.192
.201
.192
4.88
.203
6
7
.18
.14428
.177
.199
.176
4.47
.188
7
8
.165
.12849
.162
.197
.16
4.06
.172
8
9
.148
.11443
.148
.194
.144
3.66
.156
9
10
.134
.10189
.135
.191
.128
3.25
.141
10
11
.12
.09074
.12
.188
.116
2.95
.125
11
12
.109
.08081
.105
.185
.104
2.64
.109
12
13
.095
.07196
.092
.182
.092
2.34
.094
13
14
.083
.06408
.08
.180
.08
2.03
.078
14
15
.072
.05707
.072
.178
.072
1.83
.07
15
16
.065
.05082
.063
.175
.064
1.63
.0625
16
17
.058
.04526
.054
.172
.056
1.42
.0563
17
18
.049
.0403
.047
.168
.048
1 . 22
.05
18
19
.042
.03589
.041
.164
.04
1,02
.0438
19
20
.035
.03196
.035
.161
.036
.91
.0375
20
21
.032
.02846
.032
.157
.032
.81
.0344
21
22
.028
.02535
.028
.155
.028
.71
.0313
22
23
.025
.02257
.025
.153
.024
.61
.0281
23
24
.022
.0201
.023
.151
.022
.56
.025
24
25
.02
.0179
.02
.148
.02
.51
.0219
25
26
.018
.01594
.018
.146
.018
.46
.0188
26
27
.016
.01419
.017
.143
.0164
.42
.0172
27
28
.014
.01264
.016
.139
.0148
.38
.0156
28
29
.013
.01126
.015
.134
.0136
.35
.0141
29
30
.012
.01002
.014
.127
.0124
.31
.0125
30
31
.01
.00893
.0135
.120
.0116
.29
.0109
31
32
.009
.00795
.013
.115
.0108
.27
.0101
32
33
.008
.00708
.011
.112
.01
.25
.0094
33
34
.007
.0063
.01
.110
.0092
.23
.0086
34
35
.005
.00561
.0095
.108
.0084
.21
.0078
35
36
004
.005
.009
.106
.0076
.19
.007
36
37
.00445
.0085
.103
.0068
.17
.0066
37
38
.00390
.008
.101
.006
.15
.0063
38
39
.00353
.0075
.099
.0052
.13
39
40
.00314
.007
.097
.0048
.12
40
41
.095
.0044
.11
41
42
.092
.004
.10
42
43
.088
.0036
.09
43
44
.085
.0032
.08
44
45
.081
.0028
.07
45
46
.079
.0024
.06
46
47
.077
.002
.05
47
48
.075
.0016
.04
48
49
.072
.0012
.03
49
50
.069
.001
.025
50
WIRE GAUGE TABLES.
EDISON, OR CIRCULAR ftllL GAUGE, FOR ELEC-
TRICAL WIRES.
Gauge
Num-
ber.
Circular
Mils.
Diam-
eter
in Mils.
Gauge
Num-
ber.
Circular
Mils.
Diam-
eter
in Mils.
Gauge
Num-
ber.
Circular
Mils.
Diam-
eter
in Mils.
3
3,000
54.78
70
70,000
264.58
190
190,000
435.89
5
5,000
70.72
75
75,000
273.87
200
200.000
447.22
8
8,000
89.45
80
80,000
282.85
220
220,000
469.05
12
12,000
109.55
85
85,000
291.55
240
240,000
489.90
15
15,000
122.48
90
90,000
300.00
260
260,000
509.91
20
20,000
141.43
95
95,000
308.23
280
280,000
529.16
25
25,000
158.1?
100
100,000
316.23
300
300,000
547.73
30
30,000
173.21
110
110,000
331.67
320
320,000
565.69
35
35,000
187.09
120
120,000
346.42
340
340,000
583.10
40
40,000
200.00
130
130,000
360.56
360
360,000
600.00
45
45,000
212.14
140
140,000
374.17
50
50,000
223.61
150
150,000
387.30
55
55,000
234.53
160
160,000
400.00
60
60,000
244.95
17'0
170,000
412.32
65
65,000
254.96
180-
180,000
424.27
TWIST DRILL AND STEEL WIRE GAUGE.
(Morse Twist Drill aud Machine Co.)
No.
Size.
No.
Size.
No.
Size.
No.
Size.
No.
Size.
No.
Size.
inch.
inch
inch.
inch.
inch.
inch.
1
.2280
11
.1910
21
.1590
31
.1200
41
.0960
51
.0670
y
.2210
12
.1890
22
.1570
32
.1160
42
.0935
52
.0635
3
.2130
13
.1850
23
.1540
33
.1130
43
.0890
53
.0595
4
.2090
14
.1620
24
.1520
34
.1110
44
.0860
54
.0550
5
.2055
15
.1800
25
.1495
35
.1100
45
.0820
55
.0520
6
.2040
16
.1770
26
.1470
36
.1065
46
.0810
56
.0465
7
.2010
17
.1730
27
.1440
37
.1040
47
.0785
57
.0430
8
.199J
18
.1695
28
.1405
38
.1015
48
.0760
58
.0420
9
.1960
19
.1660
29
.1360
39
.0995
49
.0730
59
.0410
10
.1935
20
.1610
30
.1285
40
.0980
50
.0700
60
.0400
STUBS' STEEL WIRE GAUGE.
(For Nos. 1 to 50 see table on page 28.)
No.
Size.
No.
Size.
No.
Size.
No.
Size.
No.
Size.
No.
Size.
inch.
inch.
inch.
inch.
inch.
inch.
Z
.413
P
.323
F
.257
51
.066
61
.038
71
.026
Y
.404
O
.316
E
.250
52
.063
62
.037
72
.024
X
.397
N
.302
D
.246
53
.058
63
.036
73
.023
W
.386
M
295
C
.242
54
.055
64
.035
74
.022
V
.377
L
!&o
B
.238
55
.050
65
.033
75
.020
U
.368
K
.281
A
.234
56
.045
66
.032
76
.018
T
.358
J
.277
1
(See
57
.042
67
.031
77
.016
S
.348
I
.272
to
1 page
58
.041
68
.030
78
.015
K
.339
H
.266
50
( 28
59
.040
69
.029
79
*.014
Q
.332
G
.261
60
.039
70
.027
80
.013
The Stubs' Steel Wire Gauge is used in measuring drawn steel wire or
drill rods of Stubs' make, and is also used by many makers of American
drill rods,
30 AKITHMETIC.
THE: EDISON OR CIRCULAR MIL, WIRE GAUGE.
(For table of copper wires by this'gauge, giving weights, electrical resist
ances, etc., see Copper Wire.)
Mr. C. J. Field (Stevens Indicator, July, 1887) thus describes the origin of
the Edison gauge:
The Edison company experienced inconvenience and loss by not having a
wide ^nough range nor sufficient number of sizes in the existing gauges.
This was felt more particularly in the central-station work in making
electrical determinations for the street system. They were compelled to
make use of two of the existing gauges at least, thereby introducing a
complication that was liable to lead to mistakes by the contractors and
linemen.
In the incandescent system an even distribution throughout the entire
system and a uniform pressure at the point of delivery are obtained by cal-
culating for a given maximum percentage of loss from the potential as
delivered from the dynamo. In carrying this out, on account of lack of
regular sizes, it was often necessary to use larger sizes than the occasion
demanded, and even to assume new sizes for large underground conductors.
It was also found that nearly all manufacturers based their calculation for
the conductivity of their wire on a variety of units, and that not one used
the latest unit as adopted by the British Association and determined from
Dr. Matthiesseif s experiments ; and as this was the unit employed in the
manufacture of the Edison lamps, there was a further reason for construct-
ing a new gauge. The engineering department of the Edison company,
knowing the requirements, have designed a gauge that has the widest
range obtainable and a large number of sizes which increase in a regular
and uniform manner. The basis of the graduation is the sectional area, and
the number of the wire corresponds. A wire of 100,000 circular mils area ts
No. 100 ; a wire of one half the size will be No. 50 ; twice the size No. .200.
In the older gauges, as the number increased the size decreased. With
this gauge, however, the number increases with the wire, and the number
multiplied by 1000 will ^ive the circular mils.
The wreight per mil-foot, 0.00000302705 pounds, agrees with a specific
gravity of 8.889, which is the latest figure given for copper. The ampere
capacity which is given was deduced from experiments made in the com-
pany's laboratory, and is based on a rise of temperature of 50° F. in the wire.
In 1893 Mr. Field writes, concerning gauges in use by electrical engineers:
The B. and S. gauge seems to be in general use for the smaller sizes, up
to 100,000 c. m., and in some cases a little larger. From between one and
two hundred thousand circular mils upwards, the Edison gauge or its
equivalent is practically in use, and there is a general tendency to designate
all sizes above this in circular mils, specifying a wire as 200,000, 400,000, 500,-
000, or 1,000,000 c. m.
In the electrical business there is a large use of copper wire and rod and
other materials of these large sizes, and in ordering them, speaking of them,
specifying, and in every other use, the general method is to simply specify
the circular milage. I think it is going to be the only system in the future
for the designation of wires, and the attaining of it means practically the
adoption of the Edison gauge or the method and basis of this gauge as the
correct one for wire sizes.
THE U. S. STAN»AR» GAUGE FOR SHEET AND
PL. ATE IRON AN» STEEL., 1893.
There is in this country no uniform or standard gauge, and the same
numbers in different gauges represent different thicknesses of sheets or
plates. This has given rise to niHch misunderstanding and friction between
employers and workmen and mistakes and fraud between dealers and con-
sumers.
An Act of Congress in 1893 established the Standard Gauge for sheet iron
and^teel which is given on the next page. It is based on the fact that a
cubic foot of iron weighs 480 pounds.
A sheet of iron 1 foot square and 1 inch thick weighs 40 pounds, or 640
ounces, and 1 ounce in weight should be 1/640 inch thick. The scale has
been arranged so that each descriptive number represents a certain number
of ounces in weight and an equal number of 640ths of an inch in thickness.
The law enacts that on and after July 1, 1893, the new gauge shall be used
in determining duties and taxes levied on sheet and plate iron and steel; and
that in its application a variation of 2^4 per cent either way may be allowed.
GAUGE FOE SHEET AND PLATE IKON AND STEEL. 31
U. S. STANDARD GAUGE FOR SHEET AND PliATE
IRON AND STEEL., 1893.
£fliM
£.2 a
S «
SH-§ «5
— "o 03
Si "ft 2
-fes
Number oi
Gauge.
'i fl-Sfl
5 73 r2 «3
•lf.N
eusia
^SQ 03
%$ *
28 |
fls-1
g-g-M
gl 1
<3 ^
-111
||I{
sill.
iili
ft*!
}l|
III
S3*
£i£
^£.s
'~S !»'-
0000000
1-2
0.5
12.7
320
20.
9.072
97.65
215.28
000000
15-32
0.46875
11.90625
300
18.75
8.505
91.55
201.82
00000
7-16
0.4375
11.1125
280
17.50
7.938
85.44
188.37
0000
13-32
0.40625
10.31875
260
16.25
7.371
79.33
174.91
000
3-8
0.375
9.525
240
15.
6.804
73.24
161.46
00.
11-32
0.31375
8.73125
220
13.75
6.237
67.13
148.00
0
5-16
0.3125
7.9375
200
12.50
5.67
61.03
134.55
1
9-32
0.28125
7.14375
180
11.25
5.103
54.93
121.09
2
17-64
0.265625
6.746875
170
10.625
4.819
51.88
114.37
3
1-4
0.25
6.35
160
10.
4.536
48.82
107.64
4
15-64
0.234375
5.953125
150
9.375
4.252
45.77
100.91
5
7-32
0.21875
5.55625
140
8.75
3.969
42.72
94.18
6
13-64
0.203125
5.159375
130
8.125
3.685
39.67
87.45
7
3-16
0.1875
4.7625
120
7.5
3.402
36.62
80.72
8
11-64
0.171875
4.365625
110
6.875
3.118
33.57
74.00
9
5-32
0.15625
3.9S875
100
6.25
2.835
30.52
67.27
10
9-64
0.140625
3.571875
90
5.625
2.552
27.46
60.55
11
1-8
0.125
3.175
80
5.
2.268
24.41
53.82
1<2
7-64
0.109375
2.778125
70
4.375
1.984
21.36
47.09
13
3-32
0.09375
2.38125
60
3.75
1.701
18.31
40.36
14
5-64
0.078125
1.984375
50
3.125
1.417
15.26
33.64
15
9-128
0.0703125
1.7859375
45
2.8125
1.276
13.73
30.27
16
1-16
0.0625
1.5875
40
2.5
1.134
12.21
26.91
17
9-160
0.05625
1 .42875
36
2.25
1.021
10.99
24.22
18
1-20
0.05
1.27
32
2.
0.9072
9.765
21.53
19
7-160
0.04375
1.11125
28
1.75
0.7938
8.544
18.84
20
3-80
0.0375
0.9525
24
1.50
0.6804
7.324
16.15
21
11-320
0.034375
0.873125
22
1.375
0.6237
6.713
14.80
22
1-32
0.03125
0.793750
20
1.25
0.567
6.103
13 46
23
9-320
0.028125
0.714375
18
1.125
0.5103
5.493
12.11
24
1-40
0.025
0.635
16
1.
0.4536
4.882
10.76
25
7-320
0.021875
0.555625
14
0.875
0.3969
4.272
9.42
26
3-160
0.01875
0.47625
12
0.75
0.3402
3.662
8.07
27
11-640
0.0171875
0.4365625
11
0.6875
0.3119
3.357
7.40
28
1-64
0.015625
0.396875
10
0.625
0.2835
3.052
6.73
29
9-640
0.0140625
0.3571875
9
0.5625
0.2551
2.746
6.05
30
1-80
0.0125
0.3175
8
0.5
0.2268
2.441
5.38
81
7-640
0.0109375
0.2778125
7
0.4375
0.1984
2.136
4.71
32
13-1280
0.01015625
0.25796875
gi^
0.40625
0.1843
1.9R3
4.37
33
3-320
0.009375
0.238125
6
0.375
0.1701
1.831
4.04
34
11-1280
0.00859375
0.21828125
5^
0.34375
0.1559
1.678
3 70
35
5-640
0.0078125
0.1984375
5
0.3125
0.1417
1.526
3.36
36
9-1280
0.00703125
0.17859375
41^
0.28125
0.1276
1.373
3.03
37
17-2560
0.006640625
0.168671875
4/4
0.265625
0.1205
1.297
2.87
38
1-160
0.00625
0.15875
4
0.25
0.1134
1.221
2.69
MATHEMATICS.
Tlie Decimal Gauge.— The legalization of the standard sheet-metaj
gauge of 1893 and its adoption by some manufacturers of sheet iron have
only added to the existing confusion of gauges. A joint committee of the
American Society of Mechanical Engineers and the American Railway
Master Mechanics' Association in 1895 agreed to recommend the use of the
decimal gauge, that is, a gauge whose number for each thickness 3s the
number of thousandths of an inch in that thickness, and also to recommend
*'the abandonment and disuse of the various other gauges now in use, as
tending to confusion and error.1" A notched gauge of oval form, shown in
the cut below, has come into use as a standard form of the decimal gauge.
In 1904 The Westinghouse Electric & Mfg. Co. abandoned the use of gaug
numbers in referring to wire, sheet metal, etc.
Weight of Sheet Iron and Steel. Thickness by Decimal
Oauge
uge
00
c
1
Weight per
Square Foot
03
E
to
I
Weight per
Square Foot
o
1»
in Pounds.
.
o
s
in Pounds.
fi
be
2
!.
a
1
JL
|
DB-p
«* '
I
£|
§
5 <
So>
3
O
£*!
§
gfe
0 ^
1
|a
2
|o
|;>
"3
gg
H
2
M
^
ft
ft
c ^
1
& o
&
0 ft
® i—3 O
02
ft o
i/ (-1 0
Q
«3
£
02
H
<
•5
1
02
0.002
1/500
0.05
0.08
0.082
0.060
1/16 -
1.52
2.40
2.448
0.004
1/250
0.10
0.16
0.163
0.065
13/200
1.65
2.60
2.652
0.006
3/500
0.15
0.24
0.245
0.070
7/100
1.78
2.80
2.856
0.008
1/125
0.20
0.32
0.326
0.075
8/40
1.90
3.00
3.060
0.010
1/100
0.25
0.40
0.408
0.080
2/25
2.03
3.20
3.264
0.012
3/250
0.30
0.48
0.490
0.085
17/200
2.16
8.40
3.468
0.014
7/500
C.36
0.56
0.571
0.090
9/100
2.28
3.60
3.672
0.016
1/64 -f
0 41
0.64
0.653
0.095
19/200
2.41
3.80
3.876
0.018
9/500
0.46
0.72
0.734
0.100
1/10
2.54
4.00
4.080
0.020
1/50
0.51
0.80
0.816
0.110
11/100
2.79
4.40
4.488
0.022
11/500
0.56
0.88
0.898
0.125
1/8
3.18
5.00
5.100
0.025
1/40
0.64
1.00
1.020
0.135
27/200
3.43
5.40
5.508
0.028
7/250
0.71
1.12
1.142
0.150
3/20
3.81
6.00
6.120
0.032
1/32 +
0.81
1.28
1.306
0.165
33/200
4.19
6.60
6.732
0.036
9/250
0.91
1.44
1.469
0.180
9/50
4.57
7.20
7.344
0.040
1/25
1.02
1.60
1.632
0.200
1/5
5.08
8.00
8.160
0.045
9/200
1.14
1.80
1.836
0.220
11/50
5.59
8.80
8.976
0.050
1/20
1.27
2 00
2.040
0.240
8/25
6.10
9 60
9.792
0.055
11/200
1.40
2.20
2.244
0.250
1/4
6.35
10.00
10.200
ALGEBRA. 33
ALGEBRA.
Addition.— Add a and ft. Ans. a-\-b. Add a, 6, and -c. Ans. a-\-b — c.
Ad'l 2a and — 3«. Ans. — a. Add 2abt — Sab, — c, — 3c. Ans. - ab — 4c.
Subtraction.— Subtract a from 6. Ans. b — a. Subtract — a from — 6.
Aus. — b -f a.
Subtract b -f c from a. Ans. a — b — c. Subtract 3a26— 9c from 4a26 -f- c.
Ans. «26 4- lOc. RULE: Change the signs of the subtrahend and proceed as
in addition.
Multiplication.— Multiply a by 6. Ans. ab. Multiply ab bya-f b.
Ans. a26 + a62.
Multiply a -f 6 by a -\-b. Ans. (a-f 6)(a + 6) = a2-f 2a6 + 62.
Multiply — a by — b. Ans. a6. Multiply — a by 6. Ans. — ab. Like
signs give plus, unlike signs minus.
Powers of numbers.— The product of two or more powers of any
number is the number \\ith an exponent equal to the sum of the powers:
a2 x a3 = o5; a* IP x ab = a363; - 7ab x 2ac = - 14 a26c.
To multiply a polynomial by a monomial, multiply each term of the poly-
nomial by the monomial and add the partial products: (6a — 36) x 3c = 18ac
- 96c.
To multiply two polynomials, multiply each term of one factor by each
term of the other and add the partial products: (5a — 66) x (3a — 46) =
15a2 - 38a6 + 2462.
The square of the sum of two numbers — sum of their squares -f twice
their product. \
The square of the difference of two numbers — the sum of their squares
— twice their product.
The product of the sum and difference of two numbers = the difference
of their squares:
(a-f6)2 = a2+2a6-f 62; (a - 6)2 =a2 - 2a6-f 62;
(a + 6) x (a- 6) = a2-62.
The square of half the sums of two quantities is equal to their product pi us
the square of half their difference: (a "^ J = ab -f- (a ~ J
The square of the sum of two quantities is equal to four times their prod-
ucts, plus the square of their difference: (a -f 6;2 = 4a6 + (a — 6)2
The sum of the squares of two quantities equals twice their product, plus
the square of their difference: a2 -j- 62 = 2ab -{- (a — 6)2.
The square of a trinomial = the square of each term -f twice the product
of each term by each of the terms that follow it: (a +6 + c)2 = a2 -f-6" -f-
c2 -4- 2ab -f 2ac +26f; (a - 6 - c)2 = «2 + 62 + c2 - 2ab - Sac -f 2bc.
The square of (any number -f ^) = square of the number -4- the number
-f- 14; =*the number X (the number -f 1) -f- J4;
(a-f-U)« = a*-l-a-r.J4, -a(a+l) + %. (4^)2=42 -4- 4-4^^=
Tiie product of any number -f y> by any other number + *4 = product of
the numbers + half their sum -f J4- (a + ^) X 6 + ^) = a6 -f ^(a-f- 6)-f- J4.
4>£ X 6^ = 4 X G -f- 1^(4 + 6) + H = 24 + 5 + H = 29^.
Square, cube, 4tli poiver, etc., of a binomial a 4 6.
(a + 6)2 = a2 -f- 2«6 -f 62 ; (a + 6)3 = a* + 3a26 -f 3a62 + 63 ;
4a63 + 64.
In each case the number of terms is one greater than the exponent of
the power to which the binomial is raised.
2. In the first term the exponent of a is the same as the exponent of the
power to which the binomial is raised, and it decreases by 1 in each succeed-
ing term.
3. 6 appears in the second term with the exponent 1, and its exponent
increases by 1 in each succeeding term.
4. The coefficient of the first term is 1.
5. The coefficient of the second term is the exponent of the power to
which the binomial is raised.
6. The coefficient of each succeeding term is found from the next pre-
ceding term }yy multiplying its coefficient by the exponent of a, and divid-
ing the product by a number greater by 1 than the exponent of 6. (See
Binomial Theorem, below.)
34 ALGEBRA."
Parentheses* — When a parenthesis is preceded by a plus sign it may be
removed wuhout changing the value of the expression: a -f b -f (a -f ft) —
2a -f- 2b. When a parenthesis is preceded by a minus sign it may be removed
if we change the signs of all ihe terms within the parenthesis: 1 — (a — b
— c) — \ — • a -{- ft + c. When a parenthesis is within a parenthesis remove
the inner one first: a — |ft — •( c — (d — e) i — a — I ft — \c — d -f e !• |
= a — [6 — c -f- "d — e] = a — b -\- c — d -f- e.
A multiplication sign, X, has the effect of a parenthesis, in that the oper-
ation indicated by it must be performed before the operations of addition
or subtraction, a -f- b X a + b — a -f- ab -f- ft; while (a -f- b) X (a + b) =
a2 -f 2ab -f ft2, and (a -f b) X a + b = a2 -f- aft + ft.
Division.— The quotient is positive when the dividend and divisor
have like signs, and negative when they have unlike signs: abc -*- b = ac;
abc -. b = — ac.
To divide a monomial by a monomial, write the dividend over the divisor
with a line between them. If the expressions have common factors, remove
the common factors:
a2 bx ax a4 a3
a?bx-r-aby = — - — = — ; — = = CK
aby y a3 a5 «--
To divide a polynomial by a monomial, divide each term of the polynomial
by the monomial: (Sab — 12ac) -*• 4a = 2b — 3c.
To divide a polynomial by a polynomial, arrange both dividend and divi-
sor in the order of the ascending or descending powers of some common
letter, and keep this arrangement throughout the operation.
Divide the first term of the dividend by the first term of the divisor, and
write the result as the first term of the quotient.
Multiply all the terms of the divisor by the first term of the quotient and
subtract the product from the dividend. If there be a remainder, consider
it as a new dividend and proceed as before: (a2 — ft2) -*- (a + b).
a2 - ft2 | a + b.
a* -\-fib | a"- b.
-ab- ft2.
- ab- ft2.
The difference of two equal odd powers of any two numbers is divisible
by their difference and also by their sum:
(a3 - ft3) -t- (a - b) = a2 -f ab + ft2 ; (a3 - ft3) -*- (a -f- ft) = a2 - ab + ft2.
The difference of two equal even powers of two numbers is divisible by
their difference and also by their ^um: (a2 — ft2) -*- (a — ft) = a + b.
The sum of two equal even powers of two numbers is not divisible by
either the difference or the sum of the numbers; but when the exponent
of each of the two equal powers is composed of an odd and an even factor,
the sum of the given power is divisible by the sum of the powers expressed
by the even factor. Thus x* -f- y* is not divisible by x -f y or by x — y^ but is
divisible by x* + ?/2.
Simple equations. — An equation is a statement of equality between
two expressions; as, a -f- ft = c -f- d.
A simple equation, or equation of the first degree, is one which contains
only the first power of the unknown quantity. If equal changes be made
(by addition, subtraction, multiplication, or division) in both sides of an
equation, the results will be equal.
Any term may be changed from one side of an equation to another, pro-
vided its sign be changed: a -\- b = c -}- d; a = c -\- d — ft. To solve an
equation having one unknown quantity, transpose all the terms involving
the unknown quantity to one side of the equation, and all the other terms
to the other side; combine like terms, and divide both sides by the coefficient
of the unknown quantity.
Solve 8x - 29 = 26 - 3x. 8x -f 3x = 29 + 26; llx = 55; x = 5, ans.
Simple algebraic problems containing one unknown quantity are solved
by making x = the unknown quantity, and stating the conditions of the
problem in the form of an algebraic equation, and then solving the equa-
tion. What two numbers are those whose sum is 48 and difference 14 ? Let
x = the smaller number, x + 14 the greater, x + x -f- 14 = 48. 2x = 34, x
= 17; a; + 14 = 31, ans.
Find a number whose treble exceeds 50 as much as its double falls short
of 40. Let x = the number. 3x - 50 = 40 - 2x; 5x = 90; x - 18, ans. Prov-
ing, 54 - 50 = 40 - 36.
ALGEBRA, 35
Equations containing tfwo unknown quantities.— It one
equation contains two unknown quantities, x and ?/, an indefinite number of
pairs of values of x and y may be found that will satisfy the equation, but if
a second equation be given only one pair of values can be found that will
satisfy both equations. Simultaneous equations, or those that may be satis-
fied by the same values of the unknown quantities, are solved by combining
the equations so as to obtain a single equation containing only one unknown
quantity. This process is called elimination.
Elimination by addition or subtraction. — Multiply the equation by
such numbers as will make the coefficients of one of the unknown quanti-
ties equal in the resulting equation. Add or subtract the resulting equa-
tions according as they have unlike or like signs.
Solve J2* + 32/ = 7. Multiply by 2: 4x + Vy = U
7® •} 4X _ ty - 3. Subtract: 4x - 5y = 3 \\y = 11; y = 1.
Substituting value of ?/ in first equation, 2x -f- 3 = 7; x = 2.
Elimination by substitiLtion. — From one of the equations obtain the
value of one of the unknown quantities in terms of the other. Substitu-
tute for this unknown quantity its value in the other equation and reduce
the resulting equations.
j2o; + 3«/ = 8. (1). From (1) we find x = —-.
TQl3x+7y = 7. (2).
Substitute this value in (2): s( ~— ) + 7y = 7; = 24 - 9y -f 14y = 14,
whence y = - 2. Substitute this value in (1): 2x - 6 = 8; x = 7.
Elimination by comparison. — From each equation obtain the value of
one of the unknown quantities in terms of the other. Form an equation
from these equal values, and reduce this equation.
-9y=il. (1). From (1) we find x = 11
Solve-!
I 3x - 4y = 7. (2). From (2) we find x- l
(. <*
Equating these values of x, ~\} ' ' * - - ?/ ; IQy = - 19; y = - 1.
Substitute this value of ?/ in (1):~2# -J- 9 = 11; x = 1.
If three simultaneous equations are given containing three unknown
quantities, one of the unknown quantities must be eliminated between two
pairs of the equations; then a second between the two resulting equations.
Quadratic equations.— A quadratic equation contains the square
of the unknown quantity, but no higher power. A pure quadratic contains
the square only; an affected quadratic both the square and the first power.
To solve a pure quadratic, collect the unknown quantities on one side,
and the known quantities on the other; divide by the coefficient of the un-
known quantity and extract the square root of each side of the resulting
equation.
Solve 3#2 - 15_= 0. 3tf2 = 15; a;2 = 5; x = |/5
A root like ^5, which is indicated, but which can be found only approxi-
mately, is called a surd.
Solve 3o;2 + 15 = 0. 3x* = - 15; x* = - 5; x = V- 5.
The square root of — 5 cannot be found even approximately, for the square
of any number positive or negative is positive; therefore a root which is in-
dicated, but cannot be found even approximately, is called imaginary.
To solve an affected quadratic.—]. Convert the equation into the form
a2^2 ± 2abx = c, multiplying or dividing the equation if necessary, so as
to make the coefficient of x'2 a square number.
2. Complete the square of the first member of the equation, so as to con-
vert it to the form of a%2 ± 2abx + fc2, which is the square of the binomial
ax ± b, as follows: add to each side of the equation the square of the quo-
tient obtained by dividing the second term by twice the square root of the
first term.
3. Extract the square root of each side of the resulting equation.
Solve 3x2 - 4x = 32. To make the coefficient of x"* a square number,
multiply by 3: 9a*2 - 12# = 96; 12x H- (2 x 3x) = 2; 22 = 4.
Complete the square: 9#2 - 12x -j- 4 = 100» Extract the root: 3x — 2 = ±
36 ALGEBRA.
10, whence x — 4 or — 2 2/3. The square root of 100 is either -f 10 or - 10,
since the square of - 10 as well as -f 102 = 100.
Problems involving quadratic equations have Apparently two solutions, as
a quadratic has two roots. Sometimes botli will be true solutions, but gen-
erally one only will be a solution and the other be inconsistent with the
conditions of the problem.
The sum of the squares of two consecutive positive numbers is 481. Find
the numbers.
Let x = one number, a; -f 1 the other, x* -f (x + I)2 = 481. 2x"* -f 2x -f 1
= 481.
re2 -f- x = 240. Completing the square, #2 -f x + 0.25 = 240.25. Extracting
the root we obtain x -f- 0.5 = ± !5.5; x = 15 or — 16.
The positive root gives for the numbers 15 and 16. The negative root —
16 is inconsistent with the conditions of the problem.
Quadratic equations containing two unknown quantities require different
meihods for their solution, according to the form of the equations. For
these methods reference must be made to works on algebra.
n -
Theory of exponents.— \a when n is a positive integer is one of n
n -
equal factors of a. \ am means a is to be raised to the with power and the
u th root extracted.
(y ~a; means that the nth root of a is to be taken and the result
raised to the with power.
« . -- / «, -- \7«
y am = Vy<* / = an. When the exponent is a fraction, the numera-
tor indicates a power, and the denominator a root. «l = T°* = a3; «i =
VVr.3 = a1'5.
To extract the root of a quantity raised to an indicated power, divide
the exponent by the index of the required root; as,
n, — ™. 3,- 6
\am =z a « ' r a6 = a3 = a2.
Subtracting 1 from the exponent of a is equivalent to dividing by a :
a2-i =a» = a; a1-1^ a° = - =1; a0-1 = a -1 = - ; a -1 -» = a -a = —
A number with a negative exponent denotes the reciprocal of the number
with the corresponding positive exponent.
A factor under the radical sign whose root can be taken may, by having
the root taken, be removed from under the radical sign:
|/o2/7 = |/o2 x |/b = a tyb.
A factor outside the radical sign may be raised to the corresponding
power and placed under it:
Binomial Theorem.— To obtain any power, as the nth, of an ex-
pression of the form x -{- a
(a + * = i- f W- i + '""-r"-^ +
etc.
The following laws hold for any term in the expansion of (a -f x)n.
The exponent of x is less by one than the number of terms.
The exponent of a is n minus the exponent of x.
The last factor of the numerator is greater by one than the exponent of a,
The last factor of the denominator is the same as the exponent of x.
In the rth term the exponent of x will be r - 1.
The exponent of a will be n — (r — 1), or n — r + 1.
The last factor of the numerator will be n — r + 2.
The last factor of the denominator will be = r — 1.
Hence the rth term =L- 2> • - -- •' + ^ „„ - , + i xr-i
GEOMETRICAL PROBLEMS.
37
GEOMETRICAL PROBLEMS.
f E
1. To bisect a straight line,
or an arc of a circle (Fig. l}.—
From the ends A, B, as centres, de-
scribe arcs intersecting at C and Z>,
and draw a line through C and D
which will bisect the line at E or the
arc at F.
2. To draw a perpendicular
to a straight line, or a radial
line to a circular arc.— Same as
in Problem 1. C D is perpendicular to
the line A B, and also radial to the arc.
3. To draw a perpendicular
to a straight line from a given
point in that line (Fig. 2).— With
any radius, from the given point A in
the line B C, cut the line at B and C.
With a longer radius describe arcs
from B and (7, cutting each other at
Z), arid draw the perpendicular D A.
4. From the end A. of a given
line A D to erect a perpendic-
ular A E (Fig. 3).— From any centre
j<', above A D, describe a circle passing
through the given point A, and cut-
ting the given line at D. Draw D F
and produce it to cut the circle at E,
and draw the perpendicular A E.
Second Method (Fig. 4).— From the
given point A set off a distance A E
equal to three parts, by any scale ;
and on the centres A and E, with radii
of four and five parts respectively,
describe arcs intersecting at C. Draw
the perpendicular A C.
NOTE.— This method is most useful
on very large scales, where straight
edges are inapplicable. Any multiples
of the numbers 3, 4, 5 may be taken
with the same effect as 6, 8, 10, or 9,
12, 15.
5. To draw a perpendlcula
o a, straight line from an
lar
to a straight line' from any
point -without it (Fig. 5.)— From
the point A, with a sufficient radius
cut the given line at F and G, and
from these points describe arcs cut-
ting at E. Draw the perpendicular
AE.
A B
FIG. 6.
6. To draw a straight line
parallel to a given line, at a
given distance apart (Fig. 6).—
From the centres A, B, in the given
line, with the given distance as radius,
describe arcs C, D, and draw the par-
allel lines C D touching the arcs.
38
GEOMETRICAL PROBLEMS.
G
7. 'jfo divide a straight line
into a number of equal parts
(Fig. 7).— To divide the line A B into,
say, five parts, draw the line A C at
an angle from ^4; set off five equal
parts; draw B 5 and draw parallels to
it from the other points of division in
A C. These parallels divide A B as
required.
NOTE.— By a similar process a line
may be divided into a number of un-
equal parts; setting off divisions on
A O, proportional by a scale to the re-
quired divisions, and drawing parallel
cutting A B. The triangles All, A22,
A83, etc., are 'similar triangles.
FIG. 8.
8. Upon a straight line to
draw an angle equal to a
given angle (Fig. 8).— Let A be the
given angle and F G the line. From
the point A with any radius describe
the arc D E. From F with the same
radius describe I H. Set off the arc
/ H equal to D K, and draw F H. The
angle F is equal to A, as required.
9. To draw angles of 60°
and 30° (Fig. 9). — From f\ with
any radius FL describe an arc IH ;
and from 7, with the same radius, cut
the arc at H and draw F H to form
the required angle I F H. Draw the
perpendicular H K to the base line to
form the angle of 30- F H K.
1O. To draw an angle of 45°
(Fig. 10).— Set off the distance FT,
draw the perpendicular I H equal to
IF, and .loin HFto form the angle at
F. The angle at H is also 45°.
11. To bisect an angle (Fig.
11).— Let A C B be the angle; with G
as a centre draw an arc cutting the
sides at A, B. From A and B as
centres, describe arcs cutting each
other at D. Draw C D, dividing the
angle into two equal "parts.
FIG. 1
12. Through two given
points to describe an arc of
a circle with a given radius
(Fig. 12). — From the points A and B
as centres, with the given radius, de<
scribe arcs cutting at C , and from
Cwith the same radius describe an
arc A B.
GEOMETRICAL PROBLEMS.
39
FIG. 13.
FIG. 14.
13. To find I lie centre of a
circle or of an arc of a circle
(Fig. 13).— Select three points, A, B,
(7, in the circumference, well apart;
with the same radius describe arcs
from these three points, cutting each
other, and draw the two lines, D E,
F G, through their intersections. The
point O, where they cut, is the centre
of the circle or arc.
To describe a circle passing
through three given points.
— Let A, B, G be the given points, and
proceed as in last problem to find the
centre O, from which the circle may
be described.
14. To 'describe an arc of
a circle passing through
three given points when
the centre is not available
(Fig. 14).— From the extreme points
A, B, as centres, describe arcs A H<
B G. Through the third point O
draw A E, B F, cutting the arcs.
Divide A F and B E into any num-
ber of equal parts, and set off a
series of equal parts of the same
length on the upper portions of the
arcs beyond the points E F. Draw
straight lines, B L, B M, etc., to
the divisions in A F, and A I, A K,
etc., to the divisions in E G. The
successive intersections N, O, etc.,
of these lines are points in the
circle required between the given
points A and C. which may be
drawn in ; similarly the remaining
part of the curve B C may be
described. (See also Problem 54.)
15. To draw a tangent to
a circle from a given point
in the circumference (Fig. In).
— Through the given point A, draw the
radial line A (7, and a perpendicular
to it, F #, which is the tangent re-
quired.
16. To draw tangents to a
circle from a point without
it (Fig. 16).— From A. with the radius
A C, describe an arc B C Z>, and from
C. with a radius equal to the diameter
of the circle, cut the arc at B D. Join
B <7, C D, cutting the circle at E F,
and draw A E, A F, the tangents.
NOTE.— When a tangent is already
drawn, the exact point of contact may
be found by drawing a perpendicular
to it from the centre.
17. Between two inclined lines to draw a series of cir-
cles touching these lines and touching each other (Fig. 1?).
—Bisect the inclination of the given lines A B, CD, by the line NO. From
a point P in this line draw the perpendicular P B to the line A B, and
FIG. 15.
40
GEOMETRICAL PROBLEMS.
A
on P describe the circle B D, touching
the lines and cutting the centre line
at E. From E d raw E F perpendicular
to the centre line, cutting A B at F,
and from F describe an arc E G, cut-
ting A B at G. Draw G H parallel to
B P, giving H, the centre of the next
circle, to be described with the radius
C JJ E, and so on for the next circle IN.
Inversely, the largest circle may be
described first, and the smaller ones
in succession. This problem is of fre-
quent use in scroll-work.
18. Between two inclined
lines to draw a circular seg-
ment tangent to tlie lines and
passing through a point !«'
on tlie line /•' C which bisects
the angle of the lines (Fig. 18).
— Through .Fclraw D A at right angles
to F C ; bisect the angles A and D, as
in Problem 11, by lines cutting at C,
and from C with radius (7-Fdiaw the
arc H F G required.
19. To draw a circular arc
that will he tangent to two
given lines A Jl and C 1) in-
clined to one another, one
tangential point E being
given (Fig. 19).— Draw the centre
line G F. From l£draw E Fat right
to angles A B ; then F is the centre
of the circle required.
20. To describe a circular
arc joining two circles, and
touching one of them at a
given point (Fig. 20).— To join the
circles .4 B, F G, by an arc touching
one of them at F, draw the radius E f\
and produce it both ways. Set off F H
equal to the radius A C of the other
circle; join C H and bisect it with the
perpendicular LI, cutting E F at L
On the centre /, with radius IF, de-
scribe the arc F A as required.
21. To draw a circle with a
given radius It that will be
tangent to two given circles
A. and J* (Fig. 21) —From centre
of circled with radius equal R plus
radius of A, and from centre of B with
radius equal to R + radius of B, draw
two arcs cutting each other in (7, which
will be the centre of the circle re-
quired.
22. To construct an equi-
lateral triangle, the sides
heing given (Fig. aa).— On the ends
of one side, A, B, with A B as radius,
describe arcs cutting at C, and draw
AC, CB.
GEOMETRICAL PROBLEMS.
B-
C-
FIG. 23.
23. To construct a triangle
of unequal sides (Fig. 28).— On
either end of the base A Z>, with the
side B as radius, describe an arc;
and with the side C as radius, on the
other end of the base as a centre, cut
the arc at E. Join A E, D E.
24. To construct ft square
on a given straight line A JK
(Fig. 24).— With A B as radius and A
and B as centres, draw arcs A D and B
C, intersecting at E. Bisect EB at F.
With E as centre and E F as radius,
cut the arcs A D and B C in D and C.
Join A C, C Z>, and D J5 to form the
square.
25. To construct a rect-
angle witli given base ./<; /'
and height -E Jf (Fig. 25).— On the
base E Fdraw the perpendiculars EH,
F G equal to the height, and join Q H.
26. To describe a circle
about a triangle (Fig. 26).—
Bisect two sides A B, A C of the tri-
angle at E F, and from these points
draw perpendiculars cutting at K. On
the centre K, with the radius K A,
draw the circle A B C.
27. To inscribe a circle in
a triangle (Fig. 27).— Bisect two of
the angles A, <7, of the triangle by lines
cutting at D ; from D draw a per-
pendicular D Eto any side, and with
D E as radius describe a circle.
When the triangle is equilateral,
draw a perpendicular from one of the
angles to the opposite side, and from
the side set off one third of the per-
pendicular.
28. To describe a circle
about a square, and to in-
scribe a square in a circle (Fig.
28).— To describe the circle, draw the
diagonals A B, C D of the square, cut-
ting at E. On the centre E. with the
radius A E, describe the circle.
To inscribe the square.—
Draw the two diameters, A 5, CD, at
right angles, and join the points A, B,
C /), to form the square.
NOTE.— In the same way a circle may
be described about a rectangle. •
GEOMBTEICAL PROBLEMS.
29. To inscribe a circle in a
square (Fig. 29).— To inscribe the
Circle, draw the diagonals A B, CD
Of the square, cutting at E\ draw the
perpendicular E F to one side, and
with the radius E F describe the
circle.
30. To describe a square
about a circle (Fig. 30).— Draw two
diameters A B, CD at right angles.
With the radius of the circle and A, B,
C and D as centres, draw the four
half circles which cross one another
in the corners of the square.
9
31. To inscribe a pentagon
in a circle (Fig. 31).— Draw diam-
eters AC, B D at right angles, cutting
at o. Bisect A o at E, and from E,
with radius E B, cut A C at F ; from
B, with radius B F, cut the circumfer-
ence at Gr, H, and with the same radius
step round the circle to /and K; join
the points so found to form the penta
gon.
32. To construct a penta-
gon on a given line A B (Fig.
82).— Frotti B erect a perpendicular
B C half the length of A B\ join A C
and prolong it to D, making CD = B C.
Then B D is the radius of the circle
circumscribing the pentagon. From
A and B as centres, with B Das radius,
draw arcs cutting each other in O,
which is the centre of the circle.
33. To construct a hexagon
upon a given straight line
(Fig. 33).— From A and B, the ends of
the given line, with radius A B, de-
scribe arcs cutting at g ; from g, with
the radius g A, describe a circle ; with
the same radius set off the arcs A G,
G F, and B D, D E. Join the points so
found to form the hexagon. The side
of a hexagon = radius of its circum-
scribed circle,
34. To inscribe a hexagon
in a circle (Fig. 34).— Draw a diam-
eter A CB. From A audl? as centres,
with the radius of the circle A (7, cut
the circumference at D, E, F, G, and
drawyl D, D E, etc., to form the hexa-
gon. The radius of the circle is equal
to the side of the hexagon ; therefore
the points D, E, etc., may also be
found by stepping the radius six
times round the circle. The angle
between the diameter and the sides of
a hexagon and also the exterior angle
between a side and an adjacent side
Erolonged is 60 degrees; therefore a
exagon may conveniently be drawn
by the use of a 60-degree triangle.
GEOMETKICAL PROBLEMS.
43
m l
35. To describe a hexagon
about a circle (Fig. 35).— Draw a
diameter AD B, and with the radius
A D, on the centre A, cut the circum-
ference at C ; join A C, and bisect it
with the radius D E ; through E draw
FG, parallel to A O, cutting the diam-
eter at F, and with the radius D F de-
scribe the circumscribing circle F H.
Within this circle describe a hexagon
by the preceding problem.. A more
convenient method is by use of a 60-
degree triangle. Four of the sides
make angles of 60 degrees with the
diameter, and the other two are par-
allel to the diameter.
36. To describe an octagon
on a given straight line {Fig.
36).— Produce the given line A B both
ways, and draw perpendiculars A E,
B F', bisect the external angles A and
B by the lines A H, B C, which make
equal to A B. Draw C D and H G par-
• allel to A E, and equal to A B ; from
the centres G, D, with the radius A B,
cut the perpendiculars at E, F, and
draw E F to complete the octagon.
37. To convert a square
into an octagon (Fig. 37).— Draw
the diagonals of the square cutting at
e ; from the corners A, B, C, D, with
A e as radius, describe arcs cutting
the sides at gn, /fc, /im, and ol, and
join the points so found to form the
octagon. Adjacent sides of an octa-
gon make an angle of 135 degrees.
38. To inscribe an octagon
in a circle (Fig. 38).— Draw two
diameters, A C, B D at right angles;
bisect the arcs A Bt B (7, etc., at ef\
etc., and join A e, e B, etc., to form
the octagon.
39. To describe an octagon
about a circle (Fig. 39).— Desci it»r
a square about the given circle A B ,
draw perpendiculars h k, etc. . to the
diagonals, touchiDg the circle to form
the octagon.
4O. To describe a polygon of any number of sides upon
** given straight line (Fig. 40).— Produce the given line A B, and on A,
44
GEOMETRICAL PROBLEMS.
with the radius A B, describe a semi-
circle; divide the semi-circumference
into as many equal parts as there are
to be sides in the polygon— say, in this
example, five sides. Draw lines from
A through the divisional points D, 6,
and c, omitting one point a ; and on
the centres J5, D, with the radius A B,
cut A b at E and A c at F. Draw D E,
E F, F B to complete the polygon.
41. To Inscribe a circle
within a polygon (Figs. 41, 42).—
When the polygon has an even number
of sides (Fig. 41), bisect two opposite
sides at A and B; draw A B, and bisect
it at C by a diagonal D E, and with
the radius C A describe the circle.
When the number of sides is odd
(Fig. 42), bisect two of the sides at A
and B: and draw lines A E, B D to the
opposite angles, intersecting at (7;
from C, with the radius C A, describe
the circle.
42. To describe a circle
without a polygon (Figs. 41, 42).
— Find the centre (J as before, and with
the radius C D describe the circle.
43. To inscribe a polygon
of any number of sides with*
in a circle (Fig. 43).— Draw the
diameter A B and through the centre
E draw the perpendicular EC, cutting
the circle at F. Divide E F into four
equal parts, and set off three parts
equal to those from F to C. Divide
the diameter A B into as many equal
parts as the polygon is to have sides ;
and from C draw CD, through the
second point of division, cutting the
circle at D. Then A D is equal to one
side of the polygon, and by stepping
round the circumference with the
length A D the polygon may be com-
pleted.
TABLE OF POLYGONAL ANGLES.
Number
of Sides.
Angle
at Centre.
1 Number
of Sides.
Angle
at Centre.
Number
of Sides.
Angle
at Centre.
No.
Degrees.
No.
Degrees.
No.
Degrees.
3
120
9
40
15
24
4
90
10
36
16
22£
5
72
11
32T"T
17
21T37
6
60
12
80
18
20
7
8
S»
13
14
If
19
20
19
18
GEOMETRICAL PROBLEMS.
45
C
In this table the angle at the centre is found by dividing 360 degrees, the
number of degrees in a circle, by the number of sides in the polygon; and
by setting off round the centre of the circle a succession of angles by means
of the protractor, equal to the angle in the table due to a given number of
sides, the radii so drawn will divide the circumference into the same number
of parts.
44. To describe an ellipse
when the length and breadth
are given (Fig. 44).— A B, transverse
axis; C D, conjugate axis; F G, foci.
The sum of the distances from C to
.Fand G, also the sum of the distances
from F and G to any other point in
the curve, is equal to the transverse
axis. From the centre C, with A E as
radius, cut the axis AB at .Fand G,
the foci ; fix a couple of pins into the
axis at F and G, and loop on a thread
or cord upon them equal in length to
the axis A B, so as when stretched to
reach to the extremity C of the con-
jugate axis, as shown in dot-lining.
Place a pencil inside the cord as at H,
and guiding the pencil in this way,
keeping the cord equally in tension,
carry the pencil round the pins .F, G,
and so describe the ellipse.
NOTE.— This method is employed in
setting off elliptical garden - plots,
walks, etc.
2d Method (Fig. 45). — Along the
straight edge of a slip of stiff paper
mark off a distance a c equal to A C,
half the trans verse axis; and from the
same point a distance a b equal to
C D, half the conjugate axis. Place
the slip so as to bring the point 6 on
the line A B of the transverse axis,
and the point c on the line D E ; and
set off on the drawing the position of
the point a. Shifting the slip so that
the point b travels on the transverse
axis, and the point c on the conjugate
axis, any number of points in the
curve may be found, through which
the curve'may be traced.
3d Method (Fig. 46).— The action of
the preceding method may be em-
bodied so as to afford the means of
describing a large curve continuously
by means of a bar m fc, with steel
points m, 7, fc, riveted into brass slides
adjusted to the length of the semi-
axis and fixed with set-screws. A
rectangular cross E G, with guiding-
slots is placed, coinciding with the
two axes of the ellipse A C and B H.
By sliding the points k, I in the slots,
and carrying round the point m, the
curve may be continuously described.
A pen or pencil may be fixed at m.
4th Method (Fig. 47).— Bisect the
transverse axis at C, and through C
draw the perpendicular D E, making
C D and C E each equal to half the
conjugate axis. From D or E, with
the radius A C, cut the transverse
axis at F, F', for the foci. Divide
A C into a number of parts at the
FIG. 45.
46
GEOMETRICAL PROBLEMS.
FIG. 48.
P« 2' •& etvc* ^th fche radhls ^ 7 on F and *" as centres, describe
aics, and with the radius B I on the same centres cut these arcs as shown.
Repeat the operation for the other
divisions of the transverse axis. The
series of intersections thus made are
points in the curve, through which the
curve may be traced.
5th Method (Fig. 48).— On the two
axes A B, D E &s diameters, on centre
C, describe circles; from a number of
points a, 6, etc., in the circumference
AFB, draw radii cutting the inner
circle at a', b', etc. From a, b, etc.,
draw perpendiculars to AB; and from
a', b', etc., draw parallels to A B, cut-
ting the respective perpendiculars at
n, o, etc. The intersections are points
in the curve, through which the curve
may be traced.
6th Method (Fig. 49). — When the
transverse and conjugate diameters
are given, A B, C D, draw the tangent
EF parallel to A B. Produce CD,
and on the centre G with the radius
of half A B, describe a semicircle
HDK; from the centre G draw any
number of straight lines to the points
E, r, etc., in the line E F, cutting the
circumference at I, m, n, etc. ; from
the centre O of the ellipse draw
straight lines to the points E, r, etc. ;
and from the points I, m, n, etc., draw
parallels to G C, cutting the lines O E,
Or, etc., at Z,, M, N, etc. These are
points in the circumference of the
ellipse, and the curve may be traced
through them. Points in the other
half of the ellipse are formed by ex-
tending the intersecting lines as indi-
cated in the figure.
45. To describe an ellipse
approximately by means of
circular arcs.— First.— With arcs
of two radii (Fig. 50j.— Find the differ-
ence of the semi-axes, and set it off
from the centre O to a and c on O A
and OC; draw ac, and set off half
a c to d ; draw d i parallel to a c; set
off O e equal to O d; join e i, and draw
the parallels e m, d m. From m, with
radius m C, describe an arc through
C ; and from i describe an arc through
Z); from d and e describe arcs through
A and B. The four arcs form the
ellipse approximately.
NOTE.— This method does not apply
satisfactorily when the conjugate axis
is less than two thirds of the trans-
verse axis.
2d Method (by Carl G. Earth,
Fig. 51). -In Fig. 51 a & is the major
and c d the minor axis of the ellipse
to be approximated. Lay off b e equal
to the semi-minor axis c 0, and use a e
as radius for the arc at each extremity
of the minor axis. Bisect e o at / and
lay off e g equal to e /, and use g b as
radius for the arc at each extremity
of the major axis.
FIG. 51.
GEOMETRICAL PROBLEMS.
47
The method is not considered applicable for cases in which the minor
axis is less than two thirds of the major.
3d Method : With arcs of three radii
^~- T-^^ (Fig. 52).— On the transverse axis A B
V— ^- -^.-^-^Cl 7^.—.. _f draw the rectangle B G on the height
l\ / B^~ ^ OC; to the diagonal A C draw the
perpendicular G H D\ set off OK
equal to O C, and describe a semi-
circle on A K, and produce O Cto I/;
set off 0 M equal to C L, and from D
describe an arc with radius D M ; from
A, with radius O -L, cut A B at JV; from
H, with radius HJV, cut arc a 6 at a.
Thus the five centres D, a, 6, H, H'
are found, from which the arcs are
described to form the ellipse.
This process works well for neaily
all proportions of ellipses. It is used
in striking out vaults and stone bridges.
4th Method (by F. R,. Honey, Figs. 53 and 54).— Three radii are employed.
With the shortest radius describe the two arcs which pass through the ver-
tices of the major axis, with the longest the two arcs which pass through
the vertices of the minor axis, and with the third radius the four arcs which
connect the former.
A. simple method of determining the radii of curvature is illustrated in
Fig. 53. Draw the straight
lines a f and a c, forming any
angle at a. With a as a Centre,
and with radii a b and a c, re-
spectively, equal to the semi-
minor and semi-major axes,
draw the arcs b e and c d. Join
ed, and through b and c re-
spectively draw b g and c /
parallel to e d, intersecting a c
at g, and af at/; af is the
radius of curvature at the ver-
tex of the minor axis; and a g
vertex of the major axis.
the radius of curvature at the
Lay off d h (Fig. 53) equal to one eighth of b d. Join e h, and draw c k and
6 I parallel to e h. Take a k for the longest radius (= R), a I for the shortest
radius (= rl and the arithmetical mean, or one half the sum of the semi-axes,
for the third radius (= p), and employ these radii for the eight-centred oval
as follows:
Let a b and c d (Fig. 54)
be the major and minor
axes. Lay off a e equal
to r, and af equal to p:
also lay off c g equal to R,
and c h equal to p. With
g as a centre and g h as a
radius, draw the arc h 7c;
with the centre e and
radius e f draw the arc / fc,
intersecting hk at k. Draw
the line g k and produce it,
making g I equal to R.
Draw ke and produce it,
making k m equal to jp.
With the centre g and
radius g c (— R) draw the
arc c I ; with the centre k
and radius k I (= p) draw
the arc I m, and with the
centre e and radius e m
(=r) draw the arc m a-
The remainder of the
work is symmetrical with
respect to the axes.
48
GEOMETRICAL PROBLEMS.
E
A
G
2
rxj
F
\
J
O
\
~\rc
J
o
\
Y
/
o
\
D B
b
FIG
. 55.
' 46. The Parabola. —A parabola
(D A C, Fig. 55) is a curve such that
every point in the curve is equally
distant from the directrix KL&ud the
focus F. The focus lies in the axis
A B drawn from the vertex or head of
the curve A, so as to divide the figure
into two equal parts. The vertex A
is equidistant from the directrix and
the focus, or A e = A F. Any line
parallel to the axis is a diameter. A
straight line, as EG or DC, drawn
across the figure at right angles to the
axis is a double ordinate, and either
half of it is an ordinate. The ordinate
to the axis E F G, drawn through the
focus, is called the parameter of the
axis. A segment of the axis, reckoned
from the vertex, is an abscissa of the
axis, and it is an abscissa of the ordi-
nate drawn, from the base of the ab-
scissa. Thus, A B is an abscissa of
the ordinate B C.
Abscissae of a parabola are as the squares of their ordinates.
To describe a parabola when an abscissa and its ordi-
nate are given (Fig. 55).— Bisect the given ordinate B Cat a, draw A a,
and then a b perpendicular to it, meeting the axis at b. Set off A e, A F,
each equal to B b; and draw KeL perpendicular to the axis. Then K L is
the directrix and F is the focus. Through F and any number of points, o, o,
etc., in the axis, draw double ordinates, n o n, etc , and from the centre Fr
with the radii Fe, o e, etc., cut the respective ordinates at E} G, n, n, etc.
The curve may be traced through these points as shown.
-iL
2d Method : By means of a square
and a cord (Fig. 56). — Place a straight-
edge to the directrix EN, and apply
to it a square LEG. Fasten to the
end G one end of a thread or cord
equal in length to the edge E G, and
attach the other end to the focus F',
slide the square along the straight-
edge, holding the cord taut against the
e(ige of the square by a pencil D, by
which the curve is described.
3d Method: When the height and
the base are given (Fig. 5?).— Let A B
be the given axis, and C D & double
ordinate or base; to describe a para-
bola of which the vertex is at A.
Through A draw E F parallel to CD,
and through C and D draw C E and
D F parallel to the axis. Divide B C
and B D into any number of equal
parts, say five, at 'a, b, etc., and divide
C E and DF into the same number of
parts. Through the points a, ft, c, d in
the base C D on each side of the axis
draw perpendiculars, and through
a, 6, c, d in C E and D F draw lines to
the vertex A, cutting the perpendicu-
lars at e. /, g, h. These are points in
the parabola, and the curve C A D may
be traced as shown, passing through
then;.
FIG. 56.
A
__
V
t-
e
^x
•i^i
• '
^
3
./
\^
. :
^/
t/
g
x>
€
1
C d cbaBabcd
FIG. 57.
GEOMETRICAL PROBLEMS.
49
FIG. 58.
FIG. 59.
47. The Hyperbola (Fig. 58). — A hyperbola is a plane curve, such
that the difference of the distances from any point of it to two fixed points
is equal to a given distance. The fixed
points are called the foci.
To construct a hyperbola.
—Let F' and F be the foci, and F' F
the distance between them. Take a
ruler longer than the distance Fr F,
and fasten one of its extremities at the
focus F'. At the other extremity, H,
attach a thread of such a length that
the length of the ruler shall exceed
the length of the thread by a given
distance A B. Attach the other ex-
tremity of the thread at the focus F.
Press a pencil, P, against the ruler,
and keep the thread constantly tense,
while the ruler is turned around F' as
a centre. The point of the pencil will
describe one branch of the curve.
2d Method: By points (Fig. 59).—
From the focus F' lay off a distance
F' N equal to the transverse axis, or
distance between the two branches of
the curve, and take any other distance,
as F'H, greater than F'N.
With F' as a centre and F'H as a
radius describe the arc of a circle.
Then with Fa,s a centre and N H as a
radius describe an arc intersecting
the arc before described at p and q.
These will be points of the hyperbola, for F' q — Fq is equal to the trans-
verse axis A B.
If, with F as a centre and F' H as a radius, an arc be described, and a
second arc be described with F' as a centre and NH as a radius, two points
in the other branch of the curve will be determined. Hence, by changing
the centres, each pair of radii will determine two points in each branch.
The Equilateral Hyperbola,— The transverse axis of a hyperbola
is the distance, on a line joining the foci, between the two branches of the
curve. The conjugate axis is a line perpendicular to the transverse axis,
drawn from its centre, and of such a length that the diagonal of the rect-
angle of the transverse and conjugate axes is equal to the distance between
the foci. The diagonals of this rectangle, indefinite!}7 prolonged, are the
asymptotes of the hyperbola, lines which the curve continually approaches,
but touches only at an infinite distance. If these asymptotes are perpen-
dicular to each other, the hyperbola is called a rectangular or equilateral
hyperbola. It is a property of this hyperbola that if the asymptotes are
taken as axes of a rectangular system of coordinates (see Analytical Geom-
etry), the product of the abscissa and ordinate of any point in the curve is
equal to the product of the abscissa and ordinate of any other point ; or, if
p is the ordinate of any point and v its abscissa, and p^ and vt are the ordi-
iiate and abscissa of any other point, pv=p* v\ ; or pv = a constant.
48. The Cycloid
K J5_ / (Fig. 60).— If a circle Ad
• be rolled along a straight
line 46, any point of the
circumference as A will
describe a curve, which is
called a cycloid . The circle
is called the generating
circle, and A the generat-
ing point.
To draw a cycloid.
— Divide the circumference
of the generating circle into an even number of equal parts, as A 1, 12, etc.,
and set off these distances on the base. Through the points 1, 2, 3, etc., on
the circle draw horizontal lines, and on them set off distances la = A\,
26 = A2, 'ic = A3, etc. The points A, a, 6, c, etc., will be points in the cycloid,
through which draw the curve.
50
GEQMETKICAL PROBLEMS.
49. The Epicycloid (Fig. 61) is
generated by a point D in one circle
D C rolling upon the circumference of
another circle A C B, instead of on a
flat surface or line; the former being
the generating circle, and the latter
the fundamental circle. The generat-
ing circle is shown in four positions, in
which the generating point is succes-
sively marked D, D', D", D"'. A D'" B
is the epicycloid.
50. The Hypocycloid (Fig. 62)
is generated by a point in the gener-
ating circle rolling on the inside of the
fundamental circle.
When the generating circle — radius
of the other circle, the hypocycloid
becomes a straight line.
51. Tlie Traetrix or
Schiele's anti-friction curve
(Fig. 63).— R is the radius of the shaft,
C, 1,2, etc.. the axis. From O set off
on R a small distance, o a; with radius
R and centre a cut the axis at 1, join
a 1, and set off a like small distance
a 6; from b with radius R cut axis at
2, join 6 2, and so on, thus finding
points o, a, 6, c, d, etc., through which
the curve is to be drawn.
FIG. 63.
52. The Spiral.— The spiral is a curve described by a point which
moves along a straight line according to any given law, the line at the same
time having a uniform angular motion. The line is called the radius vector.
If the radius vector increases directly
as the measuring angle, the spires,
or parts described in each revolution,
thus gradually increasing their dis-
tance from each other, the curve is
known as the spiral of Archimedes
(Fig. 64).
This curve is commonly used for
cams. To describe it draw the radius
vector in several different directions
around the centre, with equal angles
between them; set off the distances 1, 2, 3, 4, etc., corresponding to the scale
upon which the curve is drawn, as shown in Fig. 64.
In the common spiral (Fig. 64) the pitch is uniform; that is, the spires are
equidistant. Such a spiral is made by rolling up a belt of uniform thickness.
To construct a spiral with
four centres (Fig. 65).— Given the
pitch of the spiral, construct a square
abont the centre, with the sum of the
four sides equal to the pitch. Prolong
the sides in one direction as shown;
the corners are the centres for each
arc of the external angles, forming a
quadrant of a spire.
Fig. 65.
GEOMETRICAL PROBLEMS.
51
FIG.
53. To find the diameter of a circle into which a certain
number of rings will fit on its inside (Fig. 66).— For instance,
what is the diameter of a circle into which twelve J^-inch rings will fit, as
per sketch ? Assume Uiat we have found the diameter of the required
circle, and have drawn the rings inside
of it. Join the centres of the rings
by straight lines, as shown : we then
obtain a regular polygon with 12
sides, each side being equal to the di-
ameter of a given ring. We have now
to find the diameter of a circle cir-
cumscribed about this polygon, and
add the diameter of one ring to it; the
sum will be the diameter of the circle
into which the rings will fit. Through
the centres A and D of two adjacent
rings draw the radii CA and CD;
since the polygon has twelve sides the
angle A C D = 30° and A C B = 15°.
One half of the side A D is equal to
A B. We now give the following pro-
portion : The sine of the angle A C B
is to A B as 1 is to the required ra-
dius. From this we get the following
rure : Divide A B by the sine of the angle A CB ; the quotient will be the
radius of the circumscribed circle ; add to the corresponding diameter the
diameter of one ring ; the sum will be the required diameter F G.
54. To describe an arc of a circle which is too large to
be drawn by a beam compass, by means of points in the
arc, radius being given.— Suppose the radius is 20 feet and it is
desired to obtain five points in an arc whose half chord is 4 feet. Draw a
line equal to the half chord, full size, or on a smaller scale if more con-
venient, and erect a perpendicular at one end, thus making rectangular
axes of coordinates. Erect perpendiculars at points 1, 2, 3, and 4 feet from
the first perpendicular. Find values of y in the formula of the circle.
#2 -f 2/2 = ^2 Dy substituting for x the values 0, 1, 2, 3, and 4, etc.. and fov_R*
the_squajre of _the radius, or 400. The values will be y = V R* — a2 = ^400,
^399, ^396, ^391, ^384; = 20, 19.975, 19.90, 19.774, 19.596.
Subtract the smallest,
or 19.596, leaving 0.404, 0.379, 0.304, 0.178, 0 feet.
Lay off these distances on the five perpendiculars, as ordinates from the
fcuUf chord, and the positions of five points on the arc will be found.
Through these the curve may be
drawn. (See also Problem 14.)
55. The Catenary is the curve
assumed by a perfectly flexible cord
when its ends are fastened at two
points, the weight of a unit length
being constant.
The equation of the catenary is
-
~
iV\
«|, in
which e is the
base of the Naperian system of log-
arithms.
To plot the catenary.— Let o
(Fig. 67) be the origin of coordinates.
Assigning to a any value as 3, the
equation becomes
FIG. 67.
To find the lowest point of the curve.
'0 -o1
GEOMETRICAL PROBLEMS.
Thenput* = 1; .-. y = l\e* + e 3) = | (1.396 -f 0.717) = 8.17.
= ? (1.948 -I- 0.513) = 3.69.
Fut x = 3, 4, 5, etc., etc., and find the corresponding values of y. For
each value of y we obtain two symmetrical points, as for example p 'and pl.
In this way, by making a successively equal to 2, 3, 4, 5, 6, 7, and 8, the
curves of Fig. 67 were plotted.
In each case the distance from the origin to the lowest point of the curve
is equal to a ; for putting x — o, the general equation reduces to y — a.
For values of a = 6, 7, and 8 the catenary closely approaches the parabola.
For derivation of the equation of the catenary see Bowser's Analytic
Mechanics. For comparison of the catenary with the parabola, see article
by F. R. Honey, Amer. Machinist, Feb. 1, 1894.
56. The Involute is a name given to the curve which is formed by
the end of a string which is unwound
from a cylinder and kept taut ; con-
sequently the string as it is unwound
will always lie in the direction of a
tangent to the cylinder. To describe
the involute of any given circle, Fig.
68, take any point A on its circum-
ference, draw a diameter A B, and
f rom B draw B b perpendicular to AB.
Make Bb equal in length to half the
circumference of the circle. Divide
Bb and the semi-circumference into
the same number of equal parts,
say six. From each point of division
1, 2, 3, etc., on the circumference draw
lines to the centre C of the circle.
Then draw 1 a perpendicular to C 1 ;
2a2 perpendicular to C2; and so on.
FIG 68. Make la equal to b b, ; 2a2 equal
to b 62 ; 3 a3 equal to b b2 ; and so on.
Join the points A, a^, a2, a3, etc., by a curve; this curve will be the
required involute.
57. Method of plotting angles without using a protrac-
tor.—The radius of a circle whose circumference is 360 is 57.3 (more ac-
curately 57.296). Striking a semicircle with a radius 57.3 by any scale,
spacers set to 10 by the same scale will divide the arc into 18 spaces of 10°
each, and intermediates can be measured indirectly at the rate of 1 by scale
for each 1°, or interpolated by eye according to the degree of accuracy
required. The following table shows the chords to the above-mentioned
radius, for every 10 degrees from 0° up to 1JO°. By means of one of these,
Angle. Chord.
1° 0.999
10° 9.988
20° 19.899
30° 29.658
40° 39.192
50°.. .. 48.429
Angle. Chord.
60°. 57.296
70° 65.727
80° 73.658
90° 81.029
100° 87.782
110° 93.869
a 10° point is fixed upon the paper next less than the required angle, and
the remainder is laid off at the rate of 1 by scale for each degree.
GEOMETRICAL PROPOSITIONS. 53
GEOMETRICAL PROPOSITIONS.
In a right-angled triangle the square on the hypothenuse is equal to the
sum of the squares on the other two sides.
If a triangle is equilateral, it is equiangular, and vice versa.
If a straight line from the vertex of an isosceles triangle bisects the base,
it bisects the vertical angle and is perpendicular to the base.
If one side of a triangle is produced, the exterior angle is equal to the sum
of the two interior and opposite angles.
If two triangles are mutually equiangular, they are similar and their cor-
responding sides are proportional.
If the sides of a polygon are produced in the same order, the sum of the
exterior angles equals four right angles. (Not true if the polygon has re-
entering angles )
In a quadrilateral, the sum of the interior angles equals four right angles.
In a parallelogram, the opposite sides are equal ; the opposite angles are
equal; it is bisected by its diagonal, and its diagonals bisect each other.
If three points are not in the same straight line, a circle may be passed
through them.
If two arcs are intercepted on the same circle, they are proportional to
the corresponding angles at the centre.
If two arcs are similar, they are proportional to their radii.
The areas of two circles are proportional to the squares of their radii.
If a radius is perpendicular to a chord, tt bisects the chord and it bisects
the arc subtended by the chord.
A straight line tangent to a circle meets it in only one point, and it is
perpendicular to the radius drawn to that point.
If from a point without a circle tangents are drawn to touch the circle,
there are but two; they are equal, and they make equal angles with the
chord joining the tangent points.
If two lines are parallel chords or a tangent and parallel chord, they
Intercept equal arcs of a circle.
If an angle at the circumference of a circle, between two chords, fa sub-
tended by the same arc as an angle at the centre, between two ntcJii, the
angle at the circumference is equal to half the angle at the centre.
If a triangle is inscribed in a semicircle, it is right-angled.
If two chords intersect each other in a circle, the rectangle of the seg-
ments of the one equals the rectangle of the segments of the other.
And if one chord is a diameter and the other perpendicular to it, the
rectangle of the segments of the diameter is equal to the square on half the
other chord, and the half chord is a mean proportional between the seg-
ments of the diameter.
If an angle is formed by a tangent and chord, it is measured by one half
of the arc intercepted by the chord; that is, it is equal to half the angle at
the centre subtended by the chord.
Degree of a Railway Curve. — This last proposition is useful in staking out
railway curves. A curve is designated as one of so many degrees, and the
degree is the angle at the centre subtended by a chord of 100 ft. To lay out
a curve of n degrees the transit is set at its beginning or " point of curve,1'
pointed in the direction of the tangent, and turned through Y%n degrees; a
point 100 ft. distant in the line of sight will be a point in the curve. The
transit is then swung yzn degrees further and a 100 ft. chord is measured
from the point already found to a point in the new line of sight, which is a
second point or " station " in the curve.
The radius of a 1° curve is 5729.05 ft., and the radius of a curve of any
degree is 5729.05 ft. divided by the number of degrees.
54 MENSURATION.
MENSURATION.
PLANE SURFACES.
Quadrilateral.— A four-sided figure.
Parallelogram. — A quadrilateral with opposite sides parallel.
Varieties.— Square : four sides equal, all angles right angles. Rectangle:
opposite .sides equal, all angles right angles. Rhombus: four sides equal,
opposite angles equal, angles not right angles. Rhomboid: opposite sides
equal, opposite angles equal, angles not right angles.
Trapezium. — A quadrilateral with unequal sides.
Trapezoid.— A quadrilateral with only one pair of opposite sides
parallel.
Diagonal of a square = 4/2 x side2 = 1.4142 X side.
IMag. of a rectangle = |/sum of squares of two adjacent sides.
Area of any parallelogram = base X altitude.
Area of rhombus or rhomboid = product of two adjacent sides
X sine of angle included between them.
Area of a trapezium = half the product of the diagonal by the sum
of the perpendiculars let fall on it from opposite angles.
Area of a trapezoid = product of half the sum of the two parallel
sides by the perpendicular distance between them.
To find the area of any quadrilateral figure.— Divide the
quadrilateral into two triangles; the sum of the areas of the triangles is the
area.
Or, multiply half the product of the two diagonals by the sine of the angle
at their intersection.
To find the area of a quadrilateral inscribed in a circle.
—From half the sum of the four sides subtract each side severally; multi-
ply the four remainders together; the square root of the product is the area.
Triangle.— A three-sided plane figure.
Varieties.— Right-angled, having one right angle; obtuse-angled, having
one obtuse angle ; isosceles, having two equal angles and two equal sides?
equilateral, having three equal sides and equal angles.
The sum of the three angles of every triangle = 180°.
The sum of the two acute angles of a right-angled triangle = 90°.
Hypothenuse of a right-angled triangle, the side opposite the right angle,
= |/sum of the squares of the other two sides. If a and 6 are the two sides
and c the hypothenuse, c2 = a2 + b2; a = f'c2 - 6- = \/(c -f b)(c — b).
To find the area of a triangle :
RULE 1. Multiplj7 the base by half the altitude.
RULE 2. Multiply half the product of two sides by the sine of the included
angle.
RULES. From half the sum of the three sides subtract each side severally;
multiply together the half sum and the three remainders, and extract the
square root of the product.
The area of an equilateral triangle is equal to one fourth the square of one
of its sides multiplied by the square root of 3, = , a being the side; or
4
a2 X .433013.
Hypothenuse and one side of right-angled triangle given, to find other side,
Required side = ^hyp2 — given side2.
If the two sides are equal, side = hyp -t- -1.4142; or hyp X .7071,
Area of a triangle given, to find base: Base = twice area -f- perpendicular
height
Area of a triangle given, to find height: Height = twice area -H base.
Two sides and base given, to find perpendicular height (in a triangle in
•which both of the angles at the base are acute).
RULE. — As the base is to the sum of the sides, so is the difference of the
sides to the difference of the divisions of the base made by drawing the per-
pendicular. Half this difference being added to or subtracted from half
the base will give the two divisions thereof. As each side and its opposite
PLANE SURFACES.
55
t fvision of the base constitutes a right-angled triangle, the perpendicular is
ascertained by the rule perpendicular = Vhyp2 — base2.
Polygon. — A plane figure having three or more sides. Regular or
irregular, according as the sides or angles are equal or unequal. Polygons
are named from the number of their sides and angles.
To find the area of an Irregular polygon.— Draw diagonals
dividing the polygon into triangles, and mid the sum of the areas of these
triangles.
To find the area of a regular polygon :
RULE.— Multiply the length of a side by the perpendicular distance to the
centre; multiply the product by the number of sides, and divide it by 2.
Or, multiply half the perimeter by the perpendicular let fall from the centre
on one of the sides.
The perpendicular from the centre is equal to half of one of the sides of
the polygon multiplied by the cotangent of the angle subtended by the half
Side.
The angle at the centre = 360° divided by the number of sides.
TABLE OF REGULAR POLYGONS.
Radius of Cir-
cumscribed
'd
1 0
t
§
Circle.
^ls
3
fcJO
II
</j a)
II
|
Is
B
ri
s
i
2 II
o •>
ss^
4>
||
o5
o
02
dS
^3 °r2
•° ^
II
->-> W O
<D
(D J>
c
a
OJ
0*0)
<x>
•— —
5f .5 .^5
'So
1^
d
rt
c
*
<
P*
00
?
^
<
<J
3
Triangle
.4330127
o
.5773
.2887
1.732
120°
60°
4
Square
1.
I'AU
.7071
.5
1.4142
90
90
6
Pentagon
1.7204774
1.238
.8506
.6882
1.1756
72
108
(5
7
Hexagon
Heptagon
2 5980762
3.6339124
1,155
1.11
1.
1.1524
.866
1.0383
18677
60
5126'
120
128 4-7
8
Octagon
4.8284271
1.083
1.3066
1.2071
.7653
45
135
9
Nonagon
6.1818242
1.064
1.4619
1.3737
.684
40
140
10
Decagon
7.6942088
1.051
1.618
1.5388
.618
36
144
11
Undecagon
9.3656399
1.042
1.7747
1.T028
.5634
32 43'
1473-11
12
Dodecagon
11.1961524
1.037
1.9319
1.866
.5176
30
150
To find the area of a regular polygon, when the length
of a side only is given :
RULE.— Multiply the square of the side by the multiplier opposite to the
name of the polygon in the table.
To find the area of an ir-
regular figure (Fig. 69).— Draw or-
dinates across its breadth at equal
distances apart, the first and the last
ordinate each being one half space
from the ends of the figure. Find the
average breadth by adding together
the lengths of these lines included be-
tween the boundaries of the figure,
and divide by the number of the lines
added ; multiply this mean breadth by
the length. The greater the number
of lines the nearer the approximation.
1 1 2 3 4 5 6 7 8 9 j 10
t-j Length—. »4
FIG. 69.
In a figure of very irregular outline, as an indicator-diagram from a high-
ipeed steam-engine, mean lines may be substituted for the actual lines of the
figure, being so traced as to intersect the undulations, so that the total area
of the spaces cut off may be compensated by that of the extra spaces in-
closed.
56 MENSURATION
2d Method: THE TRAPEZOIDAL RULE. — Divide the figure into any suffi-
cient number of equal parts; add half the sum of the two end ordinates to
the sum of all the other ordinates; divide by the number of spaces (that is,
one less than the number of ordinates) to obtain the mean ordinate, and
multiply this by the length to obtain the area.
3d Method: SIMPSON'S RULE.— Divide the length of the figure into an.y
even number of equal parts, at the common distance D apart, and draw or-
dinates through the points of division to touch the boundary lines. Add
together the first and last ordinates and call the sum A; add together the
even ordinates and call the sum B; add together the odd ordiuates, except
the first and last, and call the sum C, Then,
area of the figure = — — — — — — x D.
o
4th Method: DURAND'S RULE.— Add together 4/W the sum of the first and
last ordinates, 1 1/10 the sum of the second and the next to the last (or the
penultimates), and the sum of all the intermediate ordinates, Multiply the
sum thus gained by the common distance between the ordinates to obtain
the area, or divide this sum by the number of spaces to obtain the mean or-
dinate.
Prof. Duraucl describes the method of obtaining his rule in Engineering
News, Jan. 18, 1891. He claims that it is more accurate than Simpson's rule>>
and practically as simple as the trapezoidal rule. He thus describes its ap-
plication for approximate integration of differential equations. Any deft-
nite integral may be represented graphically by an area. Thus, let
Q = J*u dx
be an integral in which u is some function of #, either known or admitting of
computation or measurement. Any curve plotted with x as abscissa and u
as ordinate will then represent the variation of u with x. and the area be-
tween such curve and the axis Xwill represent the integral in question, no
matter how simple or complex may be the real nature of the function u,
Substituting in the rule as above given the word '• volume " for " area **
and the word '* section " for " ordinate," it becomes applicable to the deter-
mination of volumes from equidistant sections as well as of areas from
equidistant ordinates.
Having approximately obtained an area by the trapezoidal rule, the area
by Durand's rule may be found by adding algebraically to the sum of the
ordinates used in the trapezoidal rule (that is, half the sum of the end ordi-
nates -f- sum of the other ordinates) 1/10 of (sum of penultimates — sum of
first and last) and multiplying by the common distance between the ordi-
5th 'Method —Draw the figure on cross-section paper. Count the number
of squares that are entirely included within the boundary; then estimate
ruling o£ the cross-section paper the more accurate the result
6th Method.- Use a planimeter.
7th Method —With a chemical balance, sensitive to one milligram, draw
the figure on paper of uniform thickness and cut it out carefully; weigh the
piece cut out, and compare its weight with the weight per square inch of the
oaper as tested by weighing a piece of rectangular shape.
THE CIRCLE.
57
THE CIRCLE.
Circumference = diameter x 3.1416, nearly; more accurately, 3.14159265359.
Approximations, ^ = 3.143; ~ = 3.1415929.
7 Ho
The ratio of circum. to diam. is represented by the symbol n- (called Pi).
Multiples of TT.
ITT= 3.14159265359
277 = 6.28318530718
377 = 9.42477796077
47r = 12.56637061436
577=15.70796326795
6i7=18.84955592I54
777 = 21.99 11 4857513
877 = 25.13274122872
977 = 28.27433388231
Multiples of -.
'77 = .7853982
" x 2=1.5707963
" x 3 = 2.3561945
" x 4=3.1415927
" x 5 = 3.9269908
" x 6 = 4.7123890
" x 7 = 5.4977871
« x 8 = 6. 2831853
" x 9 = 7.0685835
Ratio of diam. to circumference = reciprocal of 77 = 0.3183099.
•procal of ^77 = 1.27324.
- = 2.22817
77
~jr = 0.261799
i
a
77
Multiples of -.
- = 2.54648
77
~-0 = 0.0087266
— = .31831
- = 2.86479
—? = 114.5915
77
77
77
— = .63662
- = 3.18310
772 = 9.86960
77
77
— = .95493
— = 3.81972
— = 0.1 01321
77
77
77^
— = 1.27324
77
-^77 = 1.570796
VTT = 1 772453
5
•j
-y/l = 0.564189
— = 1.59155
-77 = 1.047197
7T
77
3
— = 1.90986
*77= 0.523599
Log 77= 0.49714987
77
6
Log \v-= 1.895090
4
Diam. in ins. = 13.5405 Varea in sq. ft.
Area in sq. ft. = (diam. in inches)2 x .0054542.
D = diameter, R = radius, C = circumference,
A A
A = area.
C =77Z>;= 277/2; = ~; = 2*77.4; = 3.545^ ;
= Z>2 x .7854 ; = —• = 4
x .7854 ; = 7
~.
>=-; =0.31831(7; ;=2V-r; = 1.12838*^1;
R = x. ; = 0.159155C; = V - ; = 0.564189 ^A.
27r' w '
Areas of circles are to each other as the squares of their diameters.
To find the length of an arc of a circle :
RULE 1. As 360 is to the number of degrees in the arc, so is the circum-
ference of the circle to the length of the arc.
RULE 2. Multiply the diameter of the circle by the number of degrees in
the arc, and this product by 0.0087266.
58 MENSURATION.
Relations of Arc, Chord, Chord of Half the Arc,
Versed Sine, etc.
Let R = radius, D = diameter, Arc — length of arc,
Cd = chord of the arc, ch = chord of half the arc,
F = versed sine, or height of the arc,
Sch — Cd . Vcd* + 4F* x 10 Ta
Arc = __ (very nearly), = 15C^ + 33Fa + 2ch< Deai>lv'
2ch x 10F ,
ArC = GQD-27V 4 ' Uea y'
Chord of the arc = 2 Vch*-V*; = VD* - (D- 2F)~2; = Sch - 3 Arc.
= 2VJR2-(#-F)2; _ 2 V(lT_ F) x F.
Chord of half the arc, ch = \^ Cd* -f 4 Fa ; = i
ch*
Diameter = -==•;
Versed sine
1 .
(or -(D + v Z)2 - Cd2), if F is greater than radius
Half the chord of the arc is a mean proportional between the versed sine
and diameter minus versed sine: Y^Cd — |/F x (D - F)
Length of the Chord subtending an angle at the centre = twice the
sine of halt the angle. (See Table of Sines, p. 15?..)
Length of a Circular Arc.— Huyghens's Approximation.
Let C represent the length of the chord ot the arc and c the length of the
chord of half the arc; the length of the arc
3 '
Professor Williamson shows that when the arc subtends an angle of 30°, the
radius being 100,000 feet (nearly 19 miles), the error by this formula is about
two inches, or 1/600000 part of the radius. When the length of the arc is
equal to the radius, i.e., when it subtends an angle of 57°. 3, the error is less
than 1/7680 part of the radius. Therefore, if the radius is 100,000 feet, the
100000
error is less than =13 feet. The error increases rapidly with the
increase of the angle subtended.
In the measurement of an arc which is described with a short radius the
error is so small that it may be neglected. Describing an arc with a radius
of 12 inches subtending an angle of 30°, the error is 1/50000 of an inch. For
57°. 3 the error is less than 0".0015.
In order to measure an arc when it subtends a large angle, bisect it and
measure each half as before— in this case making B = length of the chord of
half the arc, and b = length of the chord of one fourth the arc ; then
T _ 166 - 2B
~F— •
Relation of the Circle to its Equal, Inscribed, and Cir-
cumscribed Squares.
Diameter of circle x .88623 » _ . , f , «,miarp
Circumference of circle x .28209 f = . equal squaie.
Circumference of circle x 1.1284 = perimeter of equal square.
THE ELLIPSE. 59
Diameter of circle x .7071 J
Circumference of circle x .22508 v = side of inscribed square.
Area of circle x .90031n- diameter j
Area of circle x 1.273-2 = area of circumscribed square.
Area of circle x .63662 = area of inscribed square.
Side of square x 1.4142 = diarn. of circumscribed circle.
x 4.4428 = circum. "
" x 1.1284 = d jam. of equal circle.
" x 3.5449 = circum. " "
Perimeter of square x 0.88623 =
Square inches x 1.2732 = circular inches.
Sectors and Segments.— To find the area of a sector of a circle.
RULE 1. Multiply the arc of the sector by half its radius.
RULE 2. As 360 is to the number of degrees in the arc, so is the area of
the circle to the area of the sector.
RULE 3. Multiply the number of degrees in the arc by the square of the
radius and by .008727.
To find the area of a segment of a circle: Find the area of the sector
which has the same arc, and also the area of the triangle formed by the
chord of the segment and the radii of the sector.
Then take the sum of these areas, if the segment is greater than a semi-
circle, but take their difference if it is less.
Another Method ; Area of segment = ^>#(arc - sin A), in which A is the
central angle, R the radius, and arc the length of arc to radius J
To find the area of a segment of a circle when its chord and height only
are given. First find radius, as follows :
1 P square of half the chord ,
radms = »L height - + he'
2. Find the angle subtended by the arc, as follows: half chord -f- radius =
sine of half the angle. Take the corresponding angle from_a table of sines,
and double it to get the angle of the arc.
3. Find area of the sector of which the segment is a part;
area of sector = area of circle x degrees of arc -f- 360.
4. Subtract area of triangle under the segment]:
Area of triangle = half chord x (radius — height of segment).
The remainder is the area of the segment.
When the chord, arc, and diameter are given, to find the area. From the
length of the arc subtract the length of the chord. Multiply the remainder
by the radius or one-half diameter; to the product add the chord multiplied
by the height, and divide the sum by 2.
Given diameter, d, and height of segment, h.
When h is from 0 to Y±d, area = h ^1.766d/i -1>; _
_
" " " " Y4d to y%d, area =-. h Vo.017d2 + 1.7d/i- Aa
(approx.). Greatest error 0.23#, when h — y^d.
To-find the chord: From the diameter subtract the height ; multiply the
remainder by four times the height and extract the square root.
When the chords of the arc and of half the arc and the rise are given: Tc
the chord of the arc add four thirds of the chord of half the arc; multiply
the sum by the rise and the product by .40426 (approximate).
Circular King:.— To find the area of a ring included between the cir-
cumferences of two concentric circles; Take the difference between the areas
of the two circles; or, subtract the square of the less radius from the square
of the greater, and multiply their difference by 3.14159.
The area of the greater circle is equal to nRV;
and the area of the smaller, wr2.
Their difference, or the area of the ring, is TrCR2 - r2).
Tlie Ellipse.— Area of an ellipse = product of its semi-axes x 3.14159
= product of its axes x .785398.
The Ellipse.— Circumference (approximate) = 3.1416 V — i — , D and d
being the two axes.
Trautwine gives the following as more accurate: When the longer axis D
is not more than five times the length of the shorter axis, d,
60 MENSUKATIOJT.
Circumference = 3.1416 •
_
/i O.O
When D is more than 5d, the divisor 8.8 is to be replaced by the following :
ForD/d = 6 7 8 9 10 1:3 14 16 18 20 30 40 50
Divisor* = 9 9.3 9.3 9.35 9.4 9.5 9.6 9.68 9.75 9.8 9.92 9.98 10
/ AI A^ A^ 2*1/48 \
An accurate formula is O = »(o + 6) (l + — + - + ~~ + ~^ . . . ) , in
which A = — -r-y. — Ingenieurs Taschenbuch, 1896.
Carl G. Barth (Machinery, Sept., 1900) gives as a very close approximation
to this formula
_, , ... 64 - 3^4*
<*="<» + »> 64^1035-
^rea o/ a segment of an ellipse the base of which is parallel to one of
the axes of the ellipse. Divide the height of the segment by the axis of
which it is part, and ftnd the area of a circular segment, in a table of circu-
lar segments, of which the height is equal to the quotient; multiply the area
thus found by the product of the two axes of the ellipse.
Cycloid.— A curve generated by the rolling of a circle on a plane.
Length of a cycloidal curve ~ 4 X diameter of the generating circle.
Length of the base = circumference of the generating circle.
Area of a cycloid = 3 X area of generating circle.
Helix (Screw).— A line generated by the progressive rotation of a
point around an axis and equidistant from its centre.
Length of a helix.— -To the square of the circumference described by the
generating-point add the square of the distance advanced in one revolution,
and take the square root of their sum multiplied by the number of revolu-
tions of the generating point. Or,
V(c2 + h"*)n = length, n being number of revolutions.
Spirals.— Lines generated by the progressive rotation of a point around
a fixed axis, with a constantly increasing distance from the axis.
A plane spiral is when the point rotates in one plane.
A conical spiral is when the point rotates around an axis at a progressing
distance from its centre, and advancing in the direction of the axis, as around
a cone.
Length of a plane spiral line. — When the distance between the coils is
uniform.
RULE.— Add together the greater and less diameters; divide their sum by
2; multiply the quotient by 3.1416, and again by the number of revolutions.
Or, take the mean of the length of the greater and less circumferences and
multiply it by the number of revolutions. Or,
length = irn -~ — -, d and d' being the inner and outer diameters.
Length of a conical spiral line.— Add together the greater and less diam-
eters; divide their sum by 2 and multiply the quotient by 3.1416. To the
square of the product of this circumference and the number of revolutions
of the spiral add the square of the height of its axis and take the square
root of the sum.
Or, length = ™ + h*.
SOLID BODIES.
Xlie Prism.— To find the surface of a right prism : Multiply the perim-
eter of the base by the altitude for the convex surface. To this add the
areas of the two ends when the entire surface is required.
Volume of a prism = area of its base X its altitude.
The pyramid.— Convex surface of a regular pyramid = perimeter of
its base X half the slant height. To this add area of the base if the whole
surface is required.
Volume of a pyramid = area of base X one third of the altitude.
SOLID BODIES. 61
To find the surface of a frustum of a regular pyramid : Multiply half the
slant height by the sum of the perimeters of the two bases for the convex
surface. To this add the areas of the two bases when the entire surface is
required.
To find the volume of a frustum of a pyramid : Add together the areas of
the two bases and a mean proportional between them, and multiply the
sum by one third of the altitude. (Mean proportional between two numbers
= square root of their product.)
Wedge.— A wedge is a solid bounded by five planes, viz.: a rectangular
base, two trapezoids, or two rectangles, meeting in an edge, and two tri-
angular ends. The altitude is the perpendicular drawn from any point in
the edge to the plane of the base.
To find the volume of auiedge: Add the length of the edge to twice the
length of the base, and multiply the sum by one sixth of the product of the
height of the wedge and the breadth of the base.
Rectangular prismoid.— A rectangular prismoid is a solid bounded
by six planes, of which the two bases are rectangles, having their corre-
sponding sides parallel, and the four upright sides of the solids are trape-
zoids.
To find the volume of a rectangular prismoid : Add together the areas of
the two bases and four times the area of a parallel section equally distant
from the bases, and multiply the sum by one sixth of the altitude.
Cylinder.— Convex surface of a cylinder = perimeter of base X altitude.
To this add the areas of the two ends when the entire surface is required.
Volume of a cylinder = area of base X altitude.
Cone.— Convex surface of a cone = circumference of base X half the slant
side. To this add the area of the base when the entire surface is required.
Volume of a cone = area of base X one third of the altitude.
To find the surface of a frustum of a cone: Multiply half the side by the
sum 6t the circumferences of the two bases for the convex surface; to this
add the areas of the two bases when the entire surface is required.
To find the volume of a frustum of a cone : Add together the areas of the
two bases and a mean proportional between them, and multiply the sum by
one third of the altitude. Or, Vol. = 0.2618a(ba + c3 + be) ; a = altitude :
6 and c, diams. of the two bases.
Sphere.— To find the surface of a sphere : Multiply the diameter by the
ciicumference of a great circle; or, multiply the square of the diameter by
3.14159.
Surface of sphere = 4 X area of its great circle.
*' *' " = convex surface of its circumscribing cylinder.
Surfaces of spheres are to each other as the squares of their diameters.
To find the volume of a sphere : Multiply the surface by one third of the
radius; or, multiply the cube of the diameter by 7r/6; that is, by 0.5236.
Value of TT/O to 10 decimal places = .5235987756.
The volume of a sphere = 2/3 the volume of its circumscribing cylinder.
Volumes of spheres are to each other as the cubes of their diameters.
Spherical triangle.— To find the area of a splierical triangle : Com-
pute the surface of the quadrantal triangle, or one eighth of the surface of
the sphere. From the sum of the three angles subtract two right angles;
divide the remainder by 90, and multiply the quotient by the area of the
quadrantal triangle.
Spherical polygon.— To find the area of a spherical polygon: Com-
pute the surface of the quadrantal triangle. From the sum of all the angles
subtract the product of two right angles by the number of sides less two;
divide the remainder by 90 and multiply the quotient by the area of the
quadrantal triangle.
The prismoid.— The prismoid is a solid having parallel end areas, and
may be composed of any combination of prisms, cylinders, wedges, pyra-
mids, or cones or frustums of the same, whose bases and apices lie in the
end areas.
Inasmuch as cylinders and cones are but special forms of prisms and
pyramids, and warped surface solids may be divided into elementary forms
of them, and since frustums may also be subdivided into the elementary
forms, it is sufficient to say that all prismoids may be decomposed into
prisms, wedges, and pyramids. If a formula can be found which is equally
applicable to all of these forms, then it will apply to any combination of
them. Such a formula is called
MENSURATION-.
The Prismoidal Formula.
Let A — area of the base of a prism, wedge, or pyramid;
%, Am = the two end and the middle areas of a prismoid, or of any of
its elementary solids;
h = altitude of the prismoid or elementary solid;
V— its volume;
For a prism, At, Am and Az are equal, = A ; V=-x6A = liA.
For a wedge with parallel ends, A^ = 0, Am = -Al ; V — ^(Al -f ZAJ = —-•
For a cone or pyramid, A% = 0, Am = -.A^ V = ~(A} + AJ - ~.
4 O O
The prismoidal formula is a rigid formula for all prismoids. The only
approximation involved in its use is in the assumption that the given solid
may be generated by a right line moving over the boundaries of the end
areas.
The area of the middle section is never the mean of the two end areas if
the prismoid contains any pyramids or cones among its elementary forms.
When the three sections are similar in form the dimensions of the middle
area are always the means of the corresponding end dimensions. This fact
often enables the dimensions, and hence the area of the middle section, to
be computed from the end areas.
Polyedrons.— A polyedron is a solid bounded by plane polygons. A
regular pblyedrou is one whose sides are all equal regular polygons.
To find the surface of a regular polyedron.— Multiply the area of one of
the faces by the number of faces ; or, multiply the square of one of the
edges by the surface of a similar solid whose edge is unity.
A TABLE OF THE REGULAR POLYEDRONS WHOSE EDGES ARE UNITY.
Names. No. of Faces. Surface. Volume.
Tetraedron .......................... 4 3.7320508 0.1178513
Hexaedron. .' ......................... 6 6.0000000 3 .0000000
Octaeclron ........................... 8 3. 4641016 0.4714045
Dodecaedron ......................... 12 20.6457288 7.6631189
Icosaedron ........................... 20 8.GCO-J540 2.1816950
To find the volume of a regular polyedron.— Multiply the
surface by one third of the perpendicular let fall from the centre on one of
the faces ; or, multiply the cube of one of the edges by the solidity of a
similar polyedron whose edge is unity.
Solid of revolution.— The volume of any solid of revolution is
equal to the product of the area of its generating surface by the length of
the path of the centre of gravity of that surface.
The convex surface of any solid of revolution is equal to the product of
the perimeter of its generating surface by the length of path of its centre
of gravity.
Cylindrical ring.— Let d = outer diameter ; d' — inner diameter ;
- (d — d') = thickness = t\ -irf2 = sectional area ; ~(d-\-d') = mean diam-
eter = M ; TT t = circumference of section ; irM — mean circumference of
ring; surface = TT t X * M; = ^ 772 (d2 - d'2); = 9.86965 1 M- = 2.46741 (d2 -d'2);
volume = 7 TT t* M TT; = 2.46741*2 M.
4
Spherical zone. — Surface of a spherical zone or segment of a sphere
= its altitude X the circumference of a great circle of the sphere. A great
circle is one whose plane passes through the centre of the sphere.
Volume of a zone of a sphere. — To the sum of the squares of the radii
of the ends add one third of the square of the height ; multiply the sum
by the height and by 1.5708.
Spherical segment.— Volume of a spherical segment with one base.—
SOLID BODIES. 63
i Multiply half the height of the segment by the area of the base, and the
cube of the height by .5236 and add the two products. Or, from three times
the diameter of the sphere subtract twice the height of the segment; multi-
ply the difference by the square of the height and by .5236. Or, to three
times the square of the radius of the base of the segment add the square of
its height, and multiply the sum by the height and by .5236.
Spheroid or ellipsoid. — When the revolution of the spheroid is about
: the transverse diameter it is prolate, and when about the conjugate it is
oblate.
Convex surface of a segment of a spheroid. — Square the diameters of the
: spheroid, arid take the square root of half their sum ; then, as the diameter
; from which the segment is cut is to this root so is the height of the
segment to the proportionate height of the segment to the mean diameter.
; Multiply the product of the other diameter and 3.1416 by the proportionate
? height.
Convex surface of a frustum or zone of a spheroid.— Proceed as by
t previous rule for the surface of a segment, and obtain the proportionate
I height of the frustum. Multiply the product of the diameter parallel to the
base of the frustum and 3.1416 by the proportionate height of the frustum.
Volume of a spheroid is equal to the product of the square of the revolving
• axis by the fixed axis and by .5236. The volume of a spheroid is two thirds
i. of that of the circumscribing cylinder.
Volume of a segment of a spheroid.—]. When the base is parallel to the
i revolving axis, multiply the difference between three times the fixed axis
and twice the height of the segment, by the square of the height and by
; .5236. Multiply the product by the square of the revolving axis, and divide
| by the square of the fixed axis.
2. When the base is perpendicular to the revolving axis, multiply the
! difference between three times the revolving axis and twice the height of
the segment by the square of the height and by .5236. Multiply the
product by the 'length of the fixed axis, and divide by the length of the
revolving axis.
Volume of the middle frustum of a spheroid.—]. When the ends are
circular, or parallel to the revolving axis : To twice the square of the
middle diameter add the square of the diameter of one end ; multiply the
sum by the length of the frustum and by .2618.
2. When the ends are elliptical, or perpendicular to the revolving axis:
To twice the product of the transverse and conjugate diameters of the
middle section add the product of the transverse and conjugate diameters
of one end ; multiply the sum by the length of the frustum and by .2618.
Spindles.— Figures generated by the revolution of a plane area, when
the curve is revolved about a chord perpendicular to its axis, or about its
double ordinate. They are designated by the name of the arc or curve
from which they are generated, as Circular, Elliptic, Parabolic, etc., etc.
Convex surface of a circular spindle, zone, or segment of it — Rule: Mul-
tiply the length by the radius of the revolving arc; multiply this arc by the
central distance, or distance between the centre of the spindle and centre
of the revolving arc ; subtract this product from the former, double the
remainder, and multiply it by 3.1416.
Volume of a circular spindle. — Multiply the central distance by half the
area of the revolving segment; subtract the product from one third of the
cube of half the length, and multiply the remainder by 12.5664.
Volume of frustum or zone of a circular spindle.— From the square of
half the length of the whole spindle take one third of the square of half the
length ofj the frustum, and multiply the remainder by the said half length
of the frustum ; multiply the central distance by the revolving area which
generates the frustum ; subtract this product from the former, and multi-
ply the remainder by 6.2832.
Volume of a segment of a circular spindle.— Subtract the length of the
segment from the half length of the spindle ; double the remainder and
ascertain the volume of a middle frustum of this length ; subtract the
result from the volume of the whole spindle and halve the remainder.
Volume of a cycloidal spindle = five eighths of the volume of the circum-
scribing cylinder. — Multiply the product of the square of twice the diameter
of the generating circle and 3.927 by its circumference, and divide this pro-
duct by 8.
Parabolic -conoid.— Volume of a parabolic conoid (generated by the
revolution of a parabola on its axis). — Multiply the area of the base by half
the height.
64 MENSURATION.
Or multiply the square of the diameter of the base by the height and by
Volume of a frustum of a parabolic conoid.— Multiply half the sum of
the areas of the two ends by the height.
Volume of a parabolic spindle (generated by the revolution of a parabola
on its base).— Multiply the square of the middle diameter by the length
and by .4189.
The volume of a parabolic spindle is to that of a cylinder of the same
height and diameter as 8 to 15.
Volume of the middle frustum of a parabolic spindle.— Add together
8 times the square of the maximum diameter, 3 times the square of the end
diameter, and 4 times the product of the diameters. Multiply the sum by
the length of the frustum and by .05236.
This rule is applicable for calculating, the content of casks of parabolic
form.
Casks.— To find the volume of a cask of any form.— Add together 39
times the square of the bung diameter, 25 times the square of the head
diameter, and 26 times the product of the diameters. Multiply the sum by
the length, and divide by 31,773 for the content in Imperial gallons, or by
26,470 for U. S. gallons.
This rule was framed by Dr. Hutton, on the supposition that the middle
third of the length of the cask was a frustum of a parabolic spindle, and
each outer third was a frustum of a cone.
To find the ullage of a cask, the quantity of liquor in it when it is not full.
1. For a lying cask : Divide the number of wet or dry inches by the bung
diameter in inches. If the quotient is less than .5, deduct from it one
fourth part of what it wants of .5. If it exceeds .5, add to it one fourth part
of the excess above .5. Multiply the remainder or the sum by the whole
content of the cask. The product is the quantity of liquor in the cask, in
gallons, when the dividend is wet inches; or the empty space, if dry inches.
2. For a standing cask : Divide the number of wet or dry inches by the
length of the cask. If the quotient exceeds .5, add to it one tenth of its
excess above .5; if less than .5, subtract from it one tenth of what it wants
of .5. Multiply the sum or the remainder by the whole content of the cask.
The product is the quantity of liquor in the cask, when the dividend is wet
inches; or the empty space, if dry inches.
Volume of cask (approxiimite) U. S. gallons = square of mean diam.
X length in inches X .0034. Mean diam. = half the sum of the bung and.
head diams.
Volume of an irregular solid.— Suppose it divided into parts,
resembling prisms or other bodies measurable by preceding rules. Find
the content of each part; the sum of the contents is the cubic contents of
the solid.
The content of a small part is found nearly by multiplying half the sum
of the areas of each end by the perpendicular distance between them.
The contents of small irregular solids may sometimes be found b)' im-
mersing them under water in a prismatic or cylindrical vessel, and observ-
ing the amount by which the level of the water descends when the solid is
withdrawn. The sectional area of the vessel being multiplied by the descent
of the level gives the cubic contents.
Or, weigh the solid in air and in water; the difference is the weight of
water it displaces. Divide the weight in pounds by 62.4 to obtain volume in
cubic feet, or multiply it by 27.7 to obtain the volume in cubic inches.
When the solid is very large and a great degree of accuracy is not
requisite, measure its length, breadth, and depth in several ( itferent
places, and take the mean of the measurement for each dimension, and
multiply the three means together.
When the surface of the solid is very extensive it is better to divide it
into triangles, to find the area of each triangle, and to multiply it by the
mean depth of the triangle for the contents of each triangular portion; the
contents of the triangular sections are to be added together,
The mean depth of a triangular section is obtained by measuring the
depth at each angle, adding together the. three measurements, and taking
one third of the sum.
PLANE TRIGONOMETRY, 65
PLANE TRIGONOMETRY.
Trigonometrical functions.
Every triangle has six parts— three angles and three sides. When any
three of these parts are given, provided one of them is a side, the other
parts may be determined. By the solution of a triangle is meant the deter-
mination of the unknown parts of a triangle when certain parts are given.
The complement of an angle or arc is what remains after subtracting the
angle or arc from 90°.
In general, if we represent any arc by A, its complement is 90° — A.
Hence the complement of an arc that exceeds 90° is negative.
Since the two acute angles of a right-angled triangle are together equal to
a right angle, each of them is the complement of the other.
The supplement of an angle or arc is what remains after subtracting the
angle or arc from 180°. If A is an arc its supplement is 180° — A. The sup-
plement of an arc that exceeds 180° is negative.
The sum of the three angles of a triangle is equal to 180°. Either angle is
the supplement of the other two. In a right-angled triangle, the right angle
being equal to 90°, each of the acute angles is the complement of the other.
In all right-angled triangles having the same acute angle, the sides have
to each other the same ratio. These ratios have received special names, as
follows:
If A is one of the acute angles, a the opposite side, b the adjacent side,
and c the hypothenuse.
The sine of the angle A is the quotient of the opposite side divided by the
a
hypothenuse. Sin. A = -•
The tangent of the angle A is the quotient of the opposite side divided by
the adjacent side. Tang. A = £•
The secant of the angle A is the quotient of the hypothenuse divided by
c
the adjacent side. Sec. A = jf
The cosine, cotangent, and cosecant of an angle are respec-
tively the sine, tangent, and secant of the complement of that angle. The
terms sine, cosine, etc., are called trigonometrical functions.
In a circle whose radius is unity, the sine of an arc, or of the angle at the
centre measured by thai arc, is the perpendicular let fall from one extrem-
ity of the arc upon the diameter passing through the other extremity.
The tangent of an arc is the line which touches the circle at one extrem-
ity of the arc, and is limited by the diameter ( produced) passing through
the other extremity.
The secant of an arc is that part of the produced diameter which is
intercepted beticeen the centre and the tangent.
The versed sine of an arc is that part of the diameter intercepted
between the extremity of the arc and the foot of the sine.
In a circle whose radius is not unity, the trigonometric functions of an arc
will be equal to the lines here defined, divided by the radius of the circle.
It 1C A (Fig. 70) is an angle in the first quadrant, and C F= radius,
FG , Oft KF
The sine of the angle = =r- r. Cos = ,-=• — r = — -
Rad. Had. Had.
IA CI ' DL
TanS- = Rad/ Secant = Rad/ Cot = Ral."
CL ._ . GA
Rad/
If radius is 1, then Rad. in the denominator is
omitted, and sine = F G, etc.
The sine of an arc = half the chord of twice the
arc.
The sine of the supplement of the arc is the same
as that of the arc itself. Sine of arc B D F = F G =
sin arc FA. Fi«. 70,
66
PLANE TRIGONOMETRY*
The tangent of the supplement is equal to the tangent of the arc, but with
a contrary sign. Tang. B D F = B M.
The secant of the supplement is equal to the secant of the arc, but with a
contrary sign. Sec. B D F = CM.
Signs of the functions in the four quadrants.— If we
divide a circle into four quadrants by a vertical and a horizontal diame-
ter, the upper right-hand quadrant is called the first, the upper left the sec-
ond, the lower left the third, and the lower right the fourth. The signs of
the functions in the four quadrants are as follows:
First quad. Second quad. Third quad. Fourth quad.
Sine and cosecant, + +
Cosine and secant, +
Tangent and cotangent, + + —
The values of the functions are as follows for the angles specified:
Ajigle..,.., ,
0
30
45
60
90
120
135
150
180
270
360
1
1
y o
Vs
1
1
Sine
0
1
(I
-1
0
2
Vg
2
2
^2
2
V3
1
1
1
1
i/3
Cosine
1
0
— —
_
-1
0
1
2
^2
2
Vo
2
Tangent
0
1
1
V*
00
-VI
1
V8
j
V3
0
00
0
Cotangent
1
1
*3
Va
~yo
— 1
~ |73
00
0
00
Secant
1
2
^2
8
00
-2
i'o
2
-1
OC
1
1/3
o
g
1/3
Cosecant
QO
2
y 'o
71
1
V2
2
oc
-1
CO
l^ersed sine
0
2- ^3
4/o 1
i
•j
3
V*+i
2+1/3
0
2
«2
2
2
^
2
TRIGONOMETRICAL. FORJNLULJE.
The following relations are deduced from the properties of similar tri-
angles (Radius = 1):
cos A : sin A :: 1 : tan A, whence tan A =
sin A : cos A :: 1 : cot A,
cos A : 1 :: 1 : sec A,
cos -4'
cos^l
cotan A = -. -•
sin A
sec A =
sin A : 1
tan A : 1
1 : cosec A, " cosec A = —
_
cos A
1
sin A*
The sum of the square of the sine of an arc and the square of its c'osine
equals unity. Sin2 A -\- cos2 A = 1.
Also, 1 -ftan2^ = sec* A: 1 + cot2 A = cosec5 A.
Functions ot the sum and difference of two angles :
Let the two angles be denoted by A and B, their sum A -f B = C, and
their difference A - B by D.
) = sin u4 cos B -\- cos A sin B; (1)
TRIGONOMETRICAL FORMULAE. 67
cos (A -f- J5) = cos A cos B — sin .4 sin P; . . • . . . (2)
sin ( A — B) = sin A cos 5 — cos A sin 5; ..... (3)
cos (A — B) = cos A cos .£ + sm -4 sin P ...... (4)
From these four formulae by addition and subtraction we obtain
sin (A + B) -f sin (A - B) = 2 sin A cos B\ ..... (5)
sin U + B) - sin U - 5) = 2cos ^ sin 5; ..... (6)
cos (A + B) 4- cos (4 - B) = 2 cos ^. cos B; ..... (7)
cos (A — B) - cos (A + 5) = 2 sin A sin 5 ...... (8)
If we put A 4- B = C, and ^ - P = A then ^ = ^«74- £>) and B = Y%(C -
Z>), and we have
sin C 4 sin D = 2 sin }£(C 4- D) cos ^(Cf - D); .... (9)
sin C - sin D = 2 cos ^«7 -f D) sin y2(C - D); . . . . (10)
cosC-f cosZ) = 2cos^(C+D)cos^(<7 - D); . . . . (11)
cos D - cos (7 = 2 sin ^((7 + D) sin ^(C - D) ..... (12)
Equation (9) may be enunciated thus: The sum of the sines of any two
angles is equal to twice the sine of half the sum of the angles multiplied by
the cosine of half their difference. These formulae enable us to transform
a sum or difference into a product.
The sum of the sines of two angles is to their difference as the tangent of
half the sum of those angles is to the tangent of half their difference.
sin A 4 sin B _ 2 sin \fljA + B) cos y%(A - B) _ tan %(A -f- B)
siu A - sin B ~ 2 cos %>(A + B) sin %>(A - B)~ tan %(A - B)' ™
The sum of the cosines of two angles is to their difference as the cotangent
of half the sum of those angles is to the tangent of half their difference.
cos A + cos B _ 2 cos y2(A + B) cos \^(A - B) _ cot ^(A + B)
eos B — cos A ~~ 2 sin %(A + B) sin y^(A - B) ~ tan fflA - W
The sine of the sum of two angles is to the sine of their difference as the
sum of the tangents of those angles is to the difference of the tangents.
sin (A + B) _ tan A + tan Bm
sin (A - B) tan A - tanJ5' '
= tan^ | t tan .1 + tang
cos A cos B
sin (A - B)
cos A cos B
cos (A 4- B)
cos ^1 cos B
cos (A — B)
cos A cos .#
= tan A - tan B;
= 1 — tan JL tan .
= 1 + tan ^1 tan 5;
tan (A-B) =
cot U + JB) =
1 — tan A tan J?'
tan A - tan B ^
1 4~ tan .4 tan B'
cot ^4 cot j? — 1 m
cot #4- cot A '
cot U - B) =
y
cot J5 — cot A '
Functions of t \vice an angle :
sin 2 A = 2 sin A cos A ;
tan 2A =
2 tan A
1 - tan2 A*
cos 2A = cos2 .4 — sin2 A\
cot 2.4 =
cot2 A — I
2 cot .4
Functions of naif an angle :
sin \4>A =
1 + cos J. '
cos \&A =
68 PLANE TRIGONOMETRY.
Solution oi Plane Right-angled Triangles.
Let A and B be the two acute angles and C the right angle, and a, 6, and
c the sides opposite these angles, respectively, then we have
1. sin A = cosB « £; 3. tan J. = cot£ = £;
2. cos A = s'mB s" -: 4. cot jt = tan B = -•„
c a
1. In any plane right-angled triangle the sine of either of the acute angles
is equal to the quotient of the opposite leg divided by the hypothenuse.
2. The cosine of either of the acute angles is equal to the quotient of the
adjacent leg divided by the hypothenuse.
3. The tangent of either of the acute angles is equal to the quotient of the
opposite leg divided by the adjacent leg.
4. The cotangent of either of the acute angles is equal to the quotient of
the adjacent leg divided by the opposite leg.
5. The square of the hypothenuse equals the sum of the squares of the
other two sides.
Solution of Oblique-angled Triangles.
The following propositions are proved in works on plane trigonometry. In
any plane triangle —
Theorem 1. The sines of the angles are proportional to the opposite sides.
Theorem 2. The sum of any two sides is to their difference as the tangent
of half the sum of the opposite angles is to the tangent of half their differ-
ence.
Theorem 3. If from any angle of a triangle a perpendicular be drawn to
the opposite side or base, the whole base will be to the sum of the other two
sides as the difference of those two sides is to the difference of the segments
of the base.
CASE I. Given two angles and a side, to find the third angle and the other
two sides. 1. The third angle = 180° — sum of the two angles. 2. The sides
may be found by the following proportion :
The sine of the angle opposite the given side is to the sine of the angle op-
posite the required side as the given s»de is to the required side.
CASE II. Given two sides and an angle opposite one of them, to find the
third side and the remaining angles.
The side opposite the given angle is to the side opposite the required angle
as the sine of the given angle is to the sine of the required angle.
The third angle is found by subtracting the sum of the other two from 180°,
and the third side is found as in Case I.
CASE III. Given two sides and the included angle, to find the third side and
the remaining angles.
The sum of the required angles is found by subtracting the given angle
from 180°. The difference of the required angles is then found by Theorem
II. Half the difference added to half the sum gives the greater angle, and
half the difference subtracted from half the sum gives the less angle. The
third side is then found by Theorem I.
Another method :
Given the sides c, b, and the included angle A, to find the remaining side a
and the remaining angles B and G.
From either of the unknown angles, as B, draw a perpendicular B e to the
opposite side.
Then
Ae = ccosA, Be = csinA, eC=b - Ae, B e-t- e C = ten C.
Or, in other words, solve B <?, A e and B e C as right-angled triangles.
CASE IV. Given the three sides, to find the angles.
Let fall a perpendicular upon the longest side from the opposite angle,
dividing the given triangle into two right-angled triangles. The two seg-
ments of the base may be found by Theorem III. There will then be given
the bypothenuse and one side of a right-angled triangle to find the angles.
For areas of triangles, see Mensuration.
r
V'
ANALYTICAL GEOMETRY. 69
ANALYTICAL GEOMETRY.
Analytical geometry is that branch of Mathematics which has for
its object the determination of the forms and magnitudes of geometrical
magnitudes by means of analysis.
Ordinates and abscissas.— In analytical geometry two intersecting
lines YY', XX' are used as coordinate axes^
XX' being the axis of abscissas or axis of Jf,
and YY' the axis of ordinates or axis of Y.
A. the intersection, is called the origin of co-
ordinates. The distance of any point P from
the axis of Y measured parallel to the axis of
X is called the abscissa of the point, as AD or'
CP, Fig. 71. Its distance from the axis of X,
measured parallel to the axis of Y, is called
the ordinate, as AC or PD. The abscissa and
ordinate taken together are called the coor-
dinates of the point P. The angle of intersec-
tion is usually taken as a right angle, in which
JTIG 7^ case the axes of X and Fare called rectangu-
lar coordinates.
The abscissa of a point is designated by the letter x and the ordinate by y.
The equations of a point are the equations which express the distances of
the point from the axis. Thus x = a,y = b are the equations of the point P.
Equations referred to rectangular coordinates.— The equa-
tion of a line expresses the relation which exists between the coordinates of
every point of the line.
Equation of a straight line, y = ax ± b, in which a is the tangent of the
angle the line makes with the axis of X, and b the distance above A in which
the line cuts the axis of Y.
Every equation of the first degree between two variables is the equation of
ft straight line, as Ay 4- Bx 4- C = 0, which can be reduced to the form y =
ax ± b.
Equation of the distance between two points:
in which x'y'^ x"y" are the coordinates of the two points.
Equation of a line passing through a given point :
y - y' = a(x — #•'),
in which x'y' are the coordinates of the given point, a, the tangent of the
angle the line makes with the axis of x, being undetermined, since any num-
ber of lines may be drawn through a given point.
Equation of a line passing through two given points :
Equation of a line parallel to a given line and through a given point;
y - y' = a(x - x'\
Equation of an angle V included between two given lines:
„ a' — a
im%v =T+tt
in which a and a' are the tangents of the angles the lines make with the
axis of abscissas.
If the lines are at right angles to each other tang V = oo, and
1 + a'a - 0.
Equation of an intersection of two lines, whose equations are
y = ax -f b, and y = a'x + &',
b - b' ab' - a'b
x = and y = •.
a - a" * a - a; '
70 ANALYTICAL GEOMETRY.
Equation of a perpendicular from a given point to a given line:
Equation of the length of the perpendicular Pi
p _ y' - ax' - b
yTT&
The circle.— Equation of a circle, the origin of coordinates being at the
centre, and radius = R :
If the origin is at the left extremity of the diameter, on the axis of X:
y* = 2Rx - it*2.
If the origin is at any point, and the coordinates of the centre are x'y' :
(x - x')* + (y- 2/')2 = &.
Equation of a tangent to a circle, the coordinates of the point of tangency
being x"y" and the origin at the centre,
Tlie ellipse. —Equation of an ellipse, referred to rectangular coordi-
nates with axis at the centre:
Aiy* 4. #2^ = ^apa,
in which A is half the transverse axis and B half the conjugate axis.
Equation of the ellipse when the origin is at the vertex of the transverse
axis:
The eccentricity of an ellipse is the distance from the centre to either
focus, divided by the semi-transverse axis, or
The parameter of an ellipse is the double ordinate passing through the
focus. It is a third proportional to the transverse axis and its conjugate, or
2B*
%A : 2B :: 2B : parameter; or parameter = — — .
Any ordinate of a circle circumscribing an ellipse is to the corresponding
ordinate of the ellipse as the semi-transverse axis to the semi-conjugate.
Any ordinate of a circle inscribed in an ellipse is to the corresponding ordi-
nate of the ellipse as the semi-conjugate axis to the semi-transverse.
Equation of the tangent to an ellipse, origin of axes at the centre :
A*yy" -f B^xx" = A*B*,
y"x" being the coordinates of the point of tangency.
Equation of the normal, passing through the point of tangency, and per-
pendicular to the tangent:
The normal bisects the angle of the two lines drawn from the point of
tangency to the foci.
The lines drawn from the foci make equal angles with the tangent.
Tlae parabola.— Equation of the parabola referred to rectangular
coordinates, the origin being at the vertex of its axis, y* = 2px, in which 2p
is the parameter or double ordinate through the focus.
ANALYTICAL GEOMETRY. 71
The parameter is a third proportional to any abscissa and its corresponding
ordinate, or
x :y :iy:2p.
Equation of the tangent:
yy" - p(x -f x"),
y''x'f being coordinates of the point of tangency.
Equation of the normal:
The sub-normal, or projection of the normal on the axis, is constant, and
equal to half the parameter.
The tangent at any point makes equal angles with the axis and with the
line drawn from the point of tangency to the focus.
The hyperbola.— Equation of the hyperbola referred to rectangular
coordinates, origin at the centre:
A*y* - B*x* = - -42B2,
in which A is the semi-transverse axis and B the semi-conjugate axis.
Equation when the origin is at the right vertex of the transverse axis:
Conjugate and equilateral hyperbolas.— If on the conjugate
axis, as a transverse, and a focal distance equal to \fA* -\- #2, we construct
the two branches of a hyperbola, the two hyperbolas thus constructed are
called conjugate hyperbolas. If the transverse and conjugate axes are
equal, the hyperbolas are called equilateral, in which case y* — #2 = — A*
when A is the transverse axis, and #a — 2/2 = — B* when B is the trans-
verse axis.
The parameter of the transverse axis is a third proportional to the trans-
verse axis and its conjugate.
2A : 2B : : 2B : parameter.
The tangent to a hyperbola bisects the angle of the two lines drawn from
the point of tangency to the foci.
The asymptotes of a tiyperbola are the diagonals of the rectangle
described on the axes, indefinitely produced in both directions.
In an equilateral hyperbola the asymptotes make equal angles with the
transverse axis, and are at right angles to each other.
The asymptotes continually approach the hyperbola, and become tangent
to it at an infinite distance from the centre.
Conic sections,— Every equation of the second degree between two
variables will represent either a circle, an ellipse, a parabola or a hyperbola.
These curves are those which are obtained by intersecting the surface of a
cone by planes, and for this reason they are called conic sections.
Logarithmic curve.— A logarithmic curve is one in which one of tho
coordinates of any point is the logarithm of the other.
The coordinate axis to v hich the lines denoting the logarithms are parallel
is called the axis of logarithms, and the other the axis of numbers. If y is
the axis of logarithms and x the axis of numbers, the equation of the curve
is y = log x.
If the base of a system of logarithms is a, we have ay = x, in which y is the
logarithm of x.
Each system of logarithms will give a different logarithmic curve. If y =
0, x = 1. Hence every logarithmic curve will intersect the axis of numbers
at a distance from the origin equal to 1.
72 DIFFERENTIAL CALCULUS.
DIFFERENTIAL CALCULUS.
The differential of a variable quantity is the difference between any two
of its consecutive values; hence it is indefinitely small. It is expressed by
writing d before the quantity, as dx, which is read differential of x.
The term -¥• is called the differential coefficient of y regarded as a func-
Q.X
tion of x.
The differential of a function is equal to its differential coefficient mul-
tiplied by the differential of the independent variable; thus, -J^dx = dy.
The limit of a variable quantity is that value to which it continually
approaches, so as at last to differ from it by less than any assignable quan-
tity.
The differential coefficient is the limit of the ratio of the increment of the
independent variable to the increment of the function.
The differential of a constant quantity is equal to 0.
The differential of a product of a constant by a variable is equal to the
constant multiplied by the differential of the variable.
If u = Av, du = Adv.
In any curve whose equation is y=f(x), the differential coefficient
— = tan a; hence, the rate of increase of the function, or the ascension of
dx
the curve at any point, is equal to the tangent of the angle which the tangent
line makes with the axis of .abscissas.
All the operations of the Differential Calculus comprise but two objects:
1. To find the rate of change in a function when it passes from one state
of value to another, consecutive with it.
2. To find the actual change in the function : The rate of change is the
differential coefficient, and the actual change the differential.
Differentials of algebraic functions.— The differential of the
sum or difference of any number of functions, dependent on the same
variable, is equal to the sum or difference of their differentials taken sepa-
rately :
If u = y -{- z — w, du — dy -\- dz — dw.
The differential of a product of two functions dependent on the same
variable is equal to the sum of the products of each by the differential of
the other :
d(uv) du , dv
d(tti>) - vdu + udv. _-=_ + _.
The differential of the product of any number of functions is equal to the
sum of the products which arise by multiplying the differential of each
function by the product of all the others:
d(uts) = tsdu -f usdt 4- uids.
The differential of a fraction equals the denominator into the differential
of the numerator minus the numerator into the differential of the denom-
inator, divided by the square of the denominator :
/u\ vdu — udv
dt = d {—J = .
If the denominator is constant, dv = 0, and dt — — 5- = — .
v v
If the numerator is constant, du = 0, and dt = —
The differential of the square root of a quantity is equal to the differen
tial of the quantity divided by twice the square root of the quantity:
If v — u^, or v = 4/w, dv = ;
2 Vu
DIFFEREHTIAL CALCULUS. 73
The differential of any power of a function is equal to the exponent multi-
plied by the function raised to a power less one, multiplied by the differen-
tial of the function, d(un} = nun - 1du.
Formula* for differentiating algebraic functions.
1. d (a) = 0.
2. d (ax) = adx.
ry A inyn\ _ ~)ixm dX.
dx
ydx - xdy
5. d (xy) = xdy + ydx.
To find the differential of the form u = (a + bxn)m:
Multiply the exponent of the parenthesis into the exponent of the varia-
ble within the parenthesis, into the coefficient of the variable, into the bi-
nomial raised to a power less 1, into the variable within the parenthesis
raised to a power less 1, into the differential of the variable.
du = d(a 4 bxn)m = mnb(a + bx1l)m ~1xn~ ldx.
To find the rate of change for a given value of the variable :
Find the differential coefficient, and substitute the value of the variable in
the second member of the equation.
EXAMPLE.— If x is the side of a cube and u its volume, u = x9 , -¥ = &e2.
Hence the rate of change in the volume is three times the square of the
edge. If the edge is denoted by 1, the rate of change is 3.
Application. The coefficient of expansion by heat of the volume of a body
is three times the linear coefficient of expansion. Thus if the side of a cube
expands .001 inch, its volume expands .003 cubic inch. 1.001s = 1.003003001.
A partial differential coefficient is the differential coefficient of
a function of two or more variables under the supposition that only one of
them has changed its value.
A partial differential is the differential of a function of two or more vari-
ables under the supposition that only one of them has changed its value.
The total differential of a function of any number of variables is equal to
the sum of the partial differentials.
If u—f(xy\ the partial differentials are -^dx, ~dy.
dx dy
Itu = x* + y*-z,du = ^dx 4- d~dy 4 ^dz\ = 2xdx + 3y*dy-dz.
ax ay dz
Integrals.— An integral is a functional expression derived from a
differential. Integration is the operation of finding the primitive function
from the differential function. It is indicated by the sign /, which is read
** the integral of." ThusfZxdx = x"* ; read, the integral of 2xdx equals x-.
To integrate an expression of the form mxm ~ 1dx or xmdx, add 1 to the
exponent of the variable, and divide by the new exponent and by the differ-
ential of the variable: f3x"*dx = x3. (Applicable in all cases except wheu
— — 1.
Forjx dx see formula 2 page 78.)
The integral of the product of a constant by the differential of a vari-
able is equal to the constant multiplied by the integral of the differential:
faxmdx = a/xmdx = a - xm + l.
J m-f 1
The integral of the algebraic sum of any number of differentials is equal to
the algebraic sum of their integrals:
du = 2ax*dx - bydy - z*dz; fda = ao;3 - y* - .
& 6 O
Since the differential of a constant is 0, a constant connected with a vari-
able by the sign + or - disappears in the differentiation; thus d(a + x™) =
dxm = mxm ~ ldx. Hence in integrating a differential expression we must
74 DIFFERENTIAL CALCULUS.
annex to the integral obtained a constant represented by C to compensate
for the term which may have been lost in differentiation. Thus if we have
dy = adx\ Jdy = afdx. Integrating,
y = ax ± C.
The constant (7, which is added to the first integral, must have such a
value as to render the functional equation true for every possible value that
may be attributed to the variable. Hence, after having found the first
integral equation and added the constant C, if we then make the variable
equal to zero, the value which the function assumes will be the true valus
of C.
An indefinite integral is the first integral obtained before the value of the
constant C is determined.
A particular integral is the integral after the value of Chas been found.
A definite integral is the integral corresponding to a given value of the
variable.
Integration "between limits e— Having found the indefinite inte-
gral and the particular integral, the next step is to find the definite integral,
and then the definite integral between given limits of the variable.
The integral of a function, taken between two limits, indicated by given
values of a?, is equal to the difference of the definite integrals correspond-
ing to those limits. The expression
/W /»
/ dy = a I dx
Jx' J
is read: Integral of the differential of ?/, taken between the limits x' and x"'
the least limit, or the limit corresponding to the subtractive integral, being
placed below.
Integrate du = Qx^dx between the limits x = 1 and x = 3, u being equal tc
81 when x = 0. fdu = fQx'2dx = 3#3 + <?; C = 81 when x = 0, then
-£.
= 3
du = 3(3)3 _j_ gl, minus 3(1)3 -f- 81 = 78.
x = 1
Integration of particular forms.
To integrate a differential of the form du - (a-f- bxn)mxn ~ *dx.
1. If there is a constant factor, place it without the sign of the integral,
and omit the power of the variable without the parenthesis and the differ
ential;
2. Augment the exponent of the parenthesis by 1, and then divide this
quantity, with the exponent so increased, by the exponent of the paren-
thesis, into the exponent of the variable within the parenthesis, into the co-
efficient of the variable. Whence
J. (m -f l)nb
Tlie differential of an arc is the hypothenuse of a right-angle triangle of
which the base is dx and the perpendicular dy.
If z is an arc, dz = Vdx* + d?/2
Quadrature of a plane figure.
T/ie differential of the area of a plane surf ace is equal to the ordinate into
the differential of the abscissa.
da = ydx.
To apply the principle enunciated in the last equation, in finding the area
of any particular plane surface :
Find the value of y in terms of x. from the equation of the bounding line;
substitute this value in the differential equation, and then integrate between
the required limits of x.
Area of the parabola,— Find the area of any portion of the com-
mon parabola whose equation is
yi = 2px't whence y = ^2px.
DIFFEKENTIAL CALCULUS. 75
Substituting this value of y in the differential equation ds = ydx gives
P
/ ds = I \/2pxdx = |/^p / x^dx = ^
xl -f C\
Tf we estimate the area from the principal vertex, x = 0. y = 0, and (7=0;
and denoting the particular integral by s', s' = r »y.
o
That is, the area of any portion of the parabola, estimated from the ver-
tex, is equal to % of the rectangle of the abscissa and ordinate of the extreme
point. The curve is therefore quadrable.
Quadrature of surfaces of revolution. —The differential of a
surface of revolution is equal to the circumference of a circle perpendicular
to the axis into the differential of the arc of the meridian curve.
ds = Ziry^d
in which y is the radius of a circle of the bounding surface in a plane per-
pendicular to the axis of revolution, and x is the abscissa, or distance of the
plane from the origin of coordinate axes.
Therefore, to find the volume of any surface of revolution:
Find the value of y and dy from the equation of the meridian curve in
terms of x and dx, then substitute these values in the differential equation,
and integrate between the proper limits of x.
By application of this rule we may find:
The curved surface of a cylinder equals the product of the circumference
of the base into the altitude*.
The convex surface of a cone equals the product of the circumference of
the base into half the slant height.
The surface of a sphere is equal to the area of four great circles, or equal
to the curved surface of the circumscribing cylinder.
€ubature of volumes of revolution.— A volume of revolution
is a volume generated by the revolution of a plane figure about a fixed line
called the axis.
If we denote the volume by F", dV — iry^ dx.
The area of a circle described by any ordinate y is iry*; hence the differ-
ential of a volume of revolution is equal to the area of a circle perpendicular
to the axis into the differential of the axis.
The differential of a volume generated by the revolution of a plane figure
about the axis of Y is irx*dy.
To find the value of Ffor any given volume of revolution :
Find the value of ?/2 in terms of x from the equation of the meridian
curve, substitute this value in the differential equation, and then integrate
between the required limits of x.
By application of this rule we may find:
The volume of a cylinder is equal to the area of the base multiplied by the
altitude.
The volume of a cone is equal to the area of the base into one third the
latitude.
The volume of a prolate spheroid and of an oblate spheroid (formed by
ihe revolution of an ellipse around its transverse and its conjugate axis re-
spectively) are each equal to two thirds of the circumscribing cylinder.
If the axes are equal, the spheroid becomes a sphere and its volume =
2 1
yrR* x D = ~irDsi -R being radius and D diameter.
o o
The volume of a paraboloid is equal to half the cylinder having the same
base and altitude.
The volume of a pyramid equals the area of the base multiplied by one
third the altitude.
Second, third, etc., differentials,— The differential coefficient
being a function of the independent variable, it may be differentiated, and
iv e thus obtain the second differential coefficient:
d(—) = d—. Dividing by dx, we have for the second differential coeffl-
\dx/ dx
76 DIFFEBEOTIAL CALCULUS.
cient -r-^, which is read: second differential of u divided by the square of
the differential of x (or dx squared).
d3u
The third differential coefficient —^ is read: third differential of u divided
by dx cubed.
The differentials of the different orders are obtained by multiplying the
differential coefficients by the corresponding powers of dx; thus —^ dx3 =
third differential of u.
Sign of the first differential coefficient.— If we have a curve
whose equation is y = /x, referred to rectangular coordinates, the curve
will recede from the axis of X when —- is positive, and approach the
axis when it is negative, when- the curve lies within the first angle of the
coordinate axes. For all angles and every relation of y and x the curve
will recede from the axis of X when the ordinate and first differential co-
efficient have the same sign, and approach it when they have different
signs. If the tangent of the curve becomes parallel to the axis of X at any
point -^ = 0. If the tangent becomes perpendicular to the axis of X at any
dx
dy
point — =co.
dx
Sign of the second differential coefficient. -The second dif-
ferential coefficient has the same sign as the ordinate when the curve is
convex toward the axis of abscissa and a contrary sign when it is concave.
Maclaurin's Theorem.— For developing into a series any function
of a single variable as u = A -f- Bx -f Ox* -\- Dx3 -f- Ex4, etc., in which A, B,
<7, etc., are independent of x:
In applying the formula, omit the expressions x = 0, although the coeffi-
cients are always found under this hypothesis.
EXAMPLES :
1 J ___ * . ^ _ ^ . X* etc
a -f- x ~~ a a2 ^ a3 a4 ^ ' an + i '
Taylor's Theorem.— For developing into a series any function of the
sum or difference of two independent variables, as u' = f(x ± y):
. du , d^u y* . d3u y3'
in which u is what u' becomes when y = 0, — is what becomes when
dx dx
y = 0. etc.
Maxima and minima.— To find the maximum or minimum value
of a function of a single variable:
1. Find the first differential coefficient of the function, place it equal to 0,
and determine the roots of the equation.
2. Find the second differential coefficient, and substitute each real root,
in succession, for the variable in the second member of the equation. Each
root which gives a negative result will correspond to a maximum value of
the function, and each which gives a positive result will correspond to a
minimum value.
EXAMPLE. — To find the value of x which will render the function y a
maximum or minimum in the equation of the circle, y* + xz = R*'t
-^ = — - ; making - - = 0 gives x = 0.
dx y y
DIFFERENTIAL CALCULUS, 77
d«M
The second differential coefficient is: -=-^ — -- —
When x = 0, ;; ^ R-, hence -^-| = — — , which being negative, y is a maxi-
mum for R positive.
In applying the rule to practical examples we first find an expression for
the function which is to be made a maximum or minimum.
2. If in such expression a constant quantity is found as a factor, it may-
be omitted in the operation; for the product will be a maximum or a mini-
mum when the variable factor is a maximum or a minimum.
3. Any value of the independent variable which renders a function a max-
imum or a minimum will render any power or root of that function •
maximum or minimum; hence we may square both members of an eo
tion to free it of radicals before differentiating.
By these rules we may find:
The maximum rectangle which can be inscribed in a triangle is one whose
altitude is half the altitude of the triangle.
The altitude of the maximum cylinder which can be inscribed in a cone is
one third the altitude of the cone.
The surface of a cylindrical vessel of a given volume, open at the top, is a
minimum when the altitude equals half the diameter.
The altitude of a cylinder inscribed in a sphere when its convex surface is
a maximum is r |/2. r = radius.
The altitude of ajcylinder inscribed in a sphere when the volume is a
maximum is 2r -*- V3.
(For maxima and minima without the calculus see Appendix, p. 1070.)
Differential of an exponential function.
If u = ax. . , ............ (1)
then du = dax = ax k dxt •••••••••(2)
in which fc is a constant dependent on a.
The relation between a and k is eft = e\ whence a = e^t ..... (3)
in which e — 2.7182818 . . . the base of the Naperian system of logarithms.
logarithms.— The logarithms in the Naperian system are denoted by
Z, Nap. log or hyperbolic log, hyp. log, or loge; and in the common system
always by log.
k — Nap. log a, log a = k log e ....... (4)
The common logarithm of e, = log 2.7182818 . . . = .4342945 . . . , is called
the modulus of the common system, and is denoted by M. Hence, if we have
the Naperian logarithm of a number we can find the1 common logarithm of
the same number by muliiplying by the modulus. Reciprocally, Nap.
log — com. log x 2 3025851.
If in equation (4) we make a = 10, we have
1 = k log e, or - = log e = M.
That is, the modulus of the common system is equal to 1, divided by the
Naperiau logarithm of the 'common base.
From equation (2) we have
du dax
— = — = kdx.
u ax
If we make a =s 10, the base of the common system, x = log ut and
That is, the differential of a common logarithm of a quantity is equal to the
differential of the quantity divided by the quantity, into the modulus.
If we make a =? e, the base of the Naperian system, x becomes the Nape-
73 DIEFEBENTIAL CALCULUS.
rian logarithm of w, and k becomes 1 (see equation (3)); hence M = 1, and
du du
d(Nap. log u) = dx — — ; = — .
a**'
That is, the differential of a Naperian logarithm of a quantity is equal to the
differential of the quantity divided by the quantity; and in the Naperian
system the modulus is 1.
Since k is the Naperian logarithm of a, du = ax I a dx. That is, the
differential of a function of the form ax is equal to the function, into the
Naperian logarithm of the base a, into the differential of the exponent.
If we have a differential in a fractional form, in which the numerator is
the differential of the denominator, the integral is the Naperian logarithm
of the denominator. Integrals of fractional differentials of other forms are
given helow:
Differential forms which have known integrals; ex-
ponential functions. (I = Nap. log.)
1. / ax I a dx = ax -f- C\
o f*dx /\
*• / — = / dxx ~ L = lx + Cl
J J
3. / (xyx~ldy -f yx ly x dx) = yx -f C\
4. C dX = l(x + |/a;2 ± a2) + C;
J yx* ± a*
5. C _d°L = l(x ± a + yxi ± 2ax) 4- C;
J MX* ± 2ax
r-^= =i(=-t
J x\/a* + x* \fVa + a;»-f
/> _ %adx fa - A/C&~~X
/ - - = Zf _ 1
J xy^- & \a + -zrr
i @.
"
+
Circular functions.— Let 2 denote an arc in the first quadrant, y tts
sine, x its cosine, v its versed sine, and t its tangent; and the following nota-
tion be employed to designate an arc by any one of its functions, viz.,
sin ~1 y denotes an arc of which y is the sine
cos"1 x u " " " " x is the cosine,
tan"1 f " •' " " " t is the tangent
DIFFERENTIAL CALCULUS.
79
<read "atv whose sine is ?/," etc.), — we have the following differential forms
which have known integrals (r = radius):
cos z dz = sin z-\-C\
sin z dz = cos z -f C;
/ — «*# _ _i
/» dv _
•C;
= ver-sin ~"1 v -f- (7;
«/ |/r2 - 2/2
/- rcte _ i
— = cos * x -f- C;
|/r2 - *2
f-
rj,
J cos2
rd_v
y-&^+& =
sin z dz = ver-sin 2; -f- C;
=: tan « -f C;
In •"•W-f'Cj
/,
:r=- = sin ~~ * — -f- O;
|/a2 - w2
/~dtC__- = cos-1-4-C;
|/a2 - w* <*
/U = ver-sin ~ J - -f (7;
|/^aw - ti2
/adit _ _ i«,
a2 + w2 a
The cycloid.— If a circle be rolled along a straight line, any point of
the circumference, as P, will describe a curve which is called a cycloid. The
circle is called the generating circle, and Pthe generating point.
The transcendental equation of the cycloid is
x — ver-sin- l ~ — \'%ry - 2/2,
ydx
and the differential equation is dx = 4/0..- _==1'
The area of the cycloid is equal to three times the area of the generating
circle.
The surface described by the arc of a cycloid when revolved about its base
is equal to 64 thirds of the generating circle.
The volume of the solid generated by revolving a cycloid about its base is
equal to five eighths of the circumscribing cylinder.
Integral calculus. — In the integral calculus we have to return from
the differential to the function from which it was derived A number of
differential expressions are given above, each of which has a known in-
tegral corresponding to it, and which being differentiated, will produce the
given differential.
In all classes of functions any differential expression may be integrated
when it is reduced to one of the known forms; and the operations of the
integral calculus consist mainly in making such transformations of given
differential expressions as shall reduce them to equivalent ones whose in-
tegrals are known.
For methods of making these transformations reference must be made to
Uie text-books on differential and integral calculus.
80
MATHEMATICAL TABLES.
RECIPROCALS OF NUMBERS.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
1
1.00000000
64
.01562500
127
.00787402
190
.00526316
253
.00395257
2
.50000000
5
.01538461
8
.00781250
1
.00523560
4
.00393701
3
.33333333
6
.01515151
9
.00775191
2
.00520833
5
.00392157
4
.25000000
7
.01492537
130
.00709231
3
.00518135
6
.00390625
5
.20000000
8
.01470588
1
.00763359
4
.00515464
ri
.00389105
6
.16666667
o
.01449275
2
.00757576
5
.00512820
8
.00387597
r-
.14285714
70
.01428571
3
.00751880
6
.00510204
9
. 00386 100
8
.12500000
1
.01408451
4
.00746269
7
.00507614
260
.00384015
9
.11111111
2
.01388889
5
.00740741
8
.00505051
1
.00383142
10
.10000000
3
.01369863
6
.00735294
9
.00502513
2
.00381079
11
.09090909
4
.01351351
7
.00729927
200
.00500000
3
.00380228
1-2
.08338333
^
.01333533
8
.00724638
1
.00497512
4
.00378188
13
.0769:2308
6
.01315789
<j
.00719424
2
.00495049
.00377358
14
.07142857
7
.01298701
140
.00714286
3
.00492611
6
.00375940
15
.06666667
8
.01282051
1
.00709220
4
.00490196
7
.00374532
16
.06250000
9
.01265823
2
.00704225
f.
.00487805
8
.00373134
17
.05882353
80
.01250000
t
.00699301
6
.00485437
9
.00371717
18
. 05555556
1
.01234568
4
.00694444
7
.00483092
270
.0037(1370
19
.05263158
£
.01219512
5
.00689655
8
.00480769
j
.00309004
20
.05000000
8
.01204819
6
.00681931
9
.00478469
<•
.00367647
1
.04761905
4
.01190476
r-
.00680272
210
.00476190
j
.00300300
2
.04545455
5
.01176471
8
.00675676
11
.00473934
L
.00364963
3
.04347826
6
.01162791
r
.00671141
12
.00471698
5
.00363636
4
.04166667
7
.01149425
150
.00606667
13
.00469484
(
.00302319
5
.04000000
8
.01136364
1
.00662252
14
.00467290
7
.00361011
6
.03846154
c
.01123595
o
.00657895
15
.00465116
h
.00359712
7
.03703704
90
.01111111
3
.00653595
16
.00462963
9
.00358423
8
.03571429
1
.01098901
4
.00649351
17
.00460829
280
.00357143
9
.03448276
5
.01086956
5
.00645101
18
.00458716
]
.00355872
30
.01333333
jj
.01075269
6
.00641026
19
.00456621
\
.00354610
1
.03225806
4
.01063830
7
.00636943
220
.00454545
;
.00353357
2
.03125000
r
.01052632
8
.00682911
1
.00452489
i.
.00352113
3
.03030303
6
.01041667
9
.00628931
c
.00450450
5
.00350877
4
.02941176
7
.01030928
160
.00625000
J
.00448430
6
.00349350
5
.02857143
8
.01020408
1
.00621118
4
.00446429
7
.00348432
6
.02777778
g
.01010101
2
.00617284
5
.00444444
8
.00347222
7
.02702703
100
.01000000
?
.00613497
6
.00442478
1
.00346021
8
.02631579
1
.00990099
4
.00609756
7
.00440529
290
.00344828
9
.02564103
o
.00980392
5
. 00606061
8
.00438596
.00343613
40
.02500000
3
.00970874
6
.00602410
c
.00436681
o
.00342406
1
.02439024
4
.00961538
7
.00598802
230
.00434783
3
.00341297
2
.02380952
5
.00952381
8
.00595238
1
.00432900
L
.00340136
3
.02325581
6
.00943396
9
.00591716
2
.00431034
5
.00338983
4
.02272727
7
.00934579
170
'.00588235
c
.00429184
(
.00337S38
5
.02222222
8
.00925926
1
.00584795
4
.00427350
7
.00330700
6
.02173913
9
.00917431
o
.00581395
^
.00425532
8
.00335570
7
.02127660
110
.00909091
3
'.00578035
6
.00423729
9
.00334448
8
.02083333
11
.00900901
4
.00574713
n
.00421941
300
.00333333
9
.02040816
12
.00892857
5
.00571429
8
.00420168
.00332226
50
.02000000
13
.00884956
6
.00568182
c
.00418410
jj
.00331120
1
.01960784
14
.00877193
7
.00564972
240
.00416667
i
.00330033
2
.01923077
15
.00869565
8
.00561798
1
.00414938
4
.00328947
3
.01886792
16
.00862069
c
.00558659
2
.00413223
5
.00327809
4
.01851852
17
.00854701
180
.00555556
3
.00411523
6
.00320797
5
.01818182
18
.00847458
1
.00552486
4
.00409836
r
.00325733
6
.01785714
19
.00840336
r
.00549451
ft
.00408163
8
.00324670
7
.01754386
120
.00833333
3
.00546448
e
.00406504
9
.003.23625
8
.01724138
1
.00826446
4
.00543478
7
.00404858
310
.00322581
9
.01694915
c
.00819672
r
.00540540
8
.00403226
11
.00321543
60
.01666667
3
.00813008
6
.00537634
9
.00401606
12
.00320513
1
.01639344
4
.00806452
7
.00534759
250
.00400000
13
.00319489
2
.01612903
i
.00800000
8
.00531914
1
.00398406
14
.00318471
3
.01587302
6
.00793651
c
.00529100
2
.00396825
15
.00317460
RECIPROCALS OF NUMBERS.
81
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
316
.00316456
381
.00262467
446
.0022-1215
511
.00195695
576
.00173611
17
.00315457
2
.00261780
7
.00223714
12
.00195312
7
.00173310
18
.00314465
3
.00261097
8
.00223214
13
.00194932
8
.00173010
19
.00313480
4
.00260417
9
.00222717
14
.00194552
9
.00172712
320
.00312500
5
.00259740
450
.00222222
15
.00194175
580
.00172414
1
.00311526
6
.00259067
1
.00221729
16
.00193798
1
.00172117
2
.00310559
7
.00258398
g
.00221239
17
.00193424
2
.00171821
3
.00309597
8
.00257732
3
.00220751
18
.00193050
3
.00171527
4
.00308642
9
.00257069
4
.00220264
19
.00192678
4
,001?J«00
5
.00307692
390
.00256410
5
.002197'80
520
.00192308
5
.00170940
6
.00306748
1
.00255754
6
.00219298
1
.00191939
6
.00170648
.00305810
2
.00255102
7
.00218818
2
.00191571
7
.00170358
8
.00304878
3
.00254453
8
.00218341
3
.00191205
8
.00170068
9
.00303951
4
.00253807
9
.00217865
4
.00190840
9
.00169779
330
.00303030
5
.00253165
460
.00217391
5
.00190476
590
.00169491
1
.00302115
6
.00252525
1
.00216920
6
.00190114
1
.00169205
2
.00301205
7
.00251889
2
.00216450
7
.00189753
2
.00168919
3
.00300300
8
.00251256
3
.00215983
8
.00189394
3
.00168634
4
.00299401
g
.00250627
4
.00215517
9
.00189036
4
.00168350
•
.00298507
400
.0025000'!
5
.00215054
530
.00188679
R
.00168007
ii
.00297619
1
.00249377
6
.00214592
1
.00188324
6
.00167785
7
.00296736
2
.00248756
7
.00214133
2
.0018797'0
7
.00167504
8
.00295858
3
.00248131)
8
.00213675
3
.00187617
8
.00167224
9
.00294985
4
.00247525
9
.00213220
4
.00187-266
9
.00166945
340
.00294118
5
.00246914
470
.00212760
5
.00186916
600
.00166667
1
.00293255
6
.002-16305
1
.00212314
6
.00186567
1
.00166389
c
.00292398
7
.00245700
2
.00211864
7
.00186220
2
.00166113
C
.00291545
8
.00245098
g
.00211416
8
.00185874
£
.00165837
4
.00290698
9
.00244490
4
.00210970
9
.00185528
4
.00165563
5
.00289855
410
.00243902
5
.00210526
540
.00185185
5
.00165289
6
.00289017
11
.00243309
6
.00210084
1
.00184^43
6
.001C5016
r<
.00288184
12
.00242718
7
.00209644
.00184502
7
.00164745
8
.00287356
13
.00242131
8
.00200205
.00184162
8
.00164474
9
.00286533
14
.00241546
9
.00208768
.00183823
9
.00164204
350
. .00285714
15
.0021096-1
480
.00208333
.00183486
610
.00163934
]
.00284900
16
.00240385
1
.00207900
.00183150
11
.0016361)6
.00784091
17
.00239808
f
.00207469
.0018-2815
12
.001 64399
f
.00283286
18
.00-J39234
3
.00207039
.0018248-2
13
.00163132
4
.00288486
19
.00238663
4
.00206612
.00182149
14
.00162866
5
.00281690
420
.00238095
e^
.00206186
55
.00181818
15
.00162602
6
.00280899
1
.00237530
6
.00205761
.00181488
16
.00162338
7
.00280112
2
.00236967
r-
.00205339
.00181159
17
.00162075
8
.00279330
3
.00286407
8
.00-204918
.00180832
18
.00161812
9
.00278551
4
.00235849
9
.00204499
.00180505
19
.00161551
360
.00277778
5
.00235294
490
.C0204082
.00180180
620
.00161-290
1
.00277008
6
.00234742
1
.00-203666
.CO 179856
1
.00161031
2
.00276243
7
.0023419!?
0
.00203252
.00179533
f
.00160772
«
.00275482
8
.00283645
c
.0020-2840
8
.00170211
3
.00160514
4
.00274725
9
.00233100
4
.00202429
9
.00178891
3
.00160256
f
.00273973
430
.00232558
5
.00202020
560
.00178571
c
.00160000
6
.00273224
1
.00232019
6
.00201613
1
.00178253
I
.00159744
r
.00272480
g
.00231481
7
.00-201207
2
.00177936
1
.00159490
8
.00271739
3
.00230947
8
.00200803
3
.00177620
8
.00159-236
9
.00271003
4
.00230415
t
.00200401
4
.00177305
9
.00158982
370
.00270270
5
.00229885
500
.00200000
5
.00176991
630
.00158730
1
.00269542
6
.00229358
1
.00199601
6
.00176678
1
.0015847-9
2
.00268817
7
.00228833
o
.00199203
7
.00176367
c
.00158228
«:
.00268096
8
.00228310
'.
.00198807
8
.00176056
\
.00157978
4
.00267380
9
.00227790
i
.00198413
9
.00175747
i
.00157729
5
.00266667
440
.00227273
r
.00198020
570
.00175439
f
.00157480
6
.00265957
1
.00226757
\
.00197628
1
.00175131
I
.00157233
7
.00265252
2
.00226244
7
.00197239
2
.00174825
ft
.00156986
8
.00264550
3
.00225734
8
.001968^0
3
.00174520
8
.00156740
9
.00263852
4
.00225225
(
.00196464
4
.00174216
9
.00156494
380
.00263158
5
! .00224719
510
.00196078
5
.00173913
640
.00156250
MATHEMATICAL TABLES.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Reci?iro-
cal.
No.
Recipro-
cal.
641
.00156006
706
.00141643
771
.001297021
836
.00119617
901
.00110988
2
.00155763
7
.00141443
2
.00129534
7
.00119474
2
.00110865
3
.001555-21
8
.00141243
3
.00129366
8
.00119332
3
.00110742
4
.00155279
9
.00141044
4
.00129199
9
.00119189
4
.00110619
5
.00155039
710
.00140845
5
.00129032
840
.00119048
5
.00110497
. 6
.00154799
11
.00140647
6
.00128866
1
.00118906
6
.00110375
7
.00154559
12
.00140449
7
.00128700
2
.00118765
7
.00110254
8
.00154321
13
.00140252
8
.00128535
3
.00118(524
8
.00110132
9
.00154083
14
.00140056
9
.00128370
4
.00118483
9
.00110011
650
.00153846
15
.00139860
780
.00128205
5
.00118343
910
.00109890
1
.00153610
16
.00139665
1
.00128041
6
.00118203
11
.00109769
2
.00153374
17
.00139470
2
.00127877
7
.00118064
12
.00109649
g
.00153140
18
.00139276
g
.00127714
8
.00117924
13
.00109529
4
.00152905
19
.00139082
4
.00127551
9
.00117786
14
.00109409
5
.00152672
720
.00138889
e
.00127388
850
.00117647
15
.00109290
6
.00152439
1
.00138696
6
.00127226
1
.00117509
16
.00109170
.00152207
2
.00138504
7
.00127065
2
.00117371
17
.00109051
8
.00151975
0
.00138313
8
.00126904
3
00117233
18
.00108932
9
.00151745
4
.00138121
c
.00126743
4
.00117096
19
.00108814
660
.00151515
5
.00137931
790
.00120582:
5
.00116959
920
.00108696
1
.00151286
6
.00137741
1
.001264221
6
.00116822
1
.00108578
.00151057
r
.00137552
2
.00126263
7
.00116686
2
.00108460
3
.00150830
8
.00137363
e
.00126103
8
.00116550
3
.00108342
i
.00150602
9
.00137174
L
.00125945
9
.00116414
4
.00108225
t
.00150376
730
.00136986
f
.00125786
860
.00116279
i
.00108108
(
.00150150
.00136799
(
.00125628
]
.00116144
6
.00107991
j
.00149925
2
.00136612
1
.00125470
2
.00116009
ij
.00107875
8
.00149701
£
.00136426
8
.00125313
3
.00115875
8
.00107759
]
.00149477
i
.00136240
9
.00125156
t
.00115741
c
.00107643
670
.00149254
5
.00136054
800
.00125000
5
.00115607
930
.00107527
.00149031
1
.00135870
.00124844
6
.00115473
.00107411
.00148809
'
.00135685
2
.00124688
7
.00115340
<
.00107296
.00148588
j
.00135501
<
.00124533
8
.00115207
]
.00107181
i
.00148368
.00135318
•
.00124378
(
.00115075
i
.00107066
.00148148
74i
.00135135
|
.00124224
870
.00114942
5
.0010695*
.00147929
.00134953
I
.00124069
;
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0
.0010683^
.00147710
.0013477
'
.00123916
J
.00114679
'
.00106724
.0014749:
.00134589
.00123762
.00114547
I
001066 1C
.00147275
i
.00134409
.00123609
t
.00114416
.00106496
68
.00147059
.00134228
8li
.00123457
j
.00114286
941
.0010638?
.00146843
.00134048
11
.00123305
1
.00114155
.0010627C
.00146628
.00133869
12
.00123153
1
.00114025
.0010615"
.00146413
.00133690
13
.00123001
.00113895
.00106044
.00146199
.0013351
14
.00122850
.00113766
i
.00105935
.00145985
75
.0013333
lo
.00122699
881
.00113636
.0010582C
.00145773
.00133156
16
.00122549
.00113507
i
.0010570*
.00145560
.0013297
r
.00122399
.00113379
i
.0010559,
.00145349
.0013280
18
.00122249
.00113250
.0010548?
.00145137
.0013262
19
.00122100
<
.00113122
.00105374
69
.00144927
.00132450
82C
.00121951
.00112994
95<
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i
.00112867
. 00105 15i
.00144509
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.00121654
r
.00112740
.0010504$
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|
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.00144092
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i
.00121359
.00112486
<.
.00104822
.00143885
76'
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j
.0012121?
891
.00112360
1
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.00143678
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i
.00121065
;
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<
.00104602
.00143472
.00131234
r
.00120919
2
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'
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|
.00120773
j
.00111982
8
.00104384
.00143061
t
.00130890
.00120627
i
.00111857
j
.00104275
70
.00142857
.00130719
i 831
.00120482
5
.00111732
960
.0010416;
.00142653
(
.00130548
.00120337
6
.00111607
.00104058
.00142450
1
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<
.00120192
\
.00111483
j
.00103950
.00142247
8
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j
.00120048
8
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j
.00103842
^
.00142045
j
.00130039
i
.00119904
9
.00111235
^
.00103734
;
.00141844
770
.00129870
5
.00119760
900
.00111111
t
,00103627
RECIPROCALS OF NUMBERS.
83
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
966
00103520
1031
000969932
1096
000912409
1161
.000861326
1226
.000815661
7
00103413
2
000968992
7
000911577
2
.000860585
.000814996
8
00103306
3
000968054
8
000910747
3
.000859845
8
.000814332
9
00103199
4
000967118
9
000909918
4
.000859106
9
.000813670
970
00103093
5
000966184
1100
.000909091
5
.000858369
1230
.000813008
1
.00102987
6
000965251
1
.000908265
6
.000857633
1
.000812348
2
00102881
7
.000964320
2
.000907441
7
.000856898
2
.000811688
3
.00102775
8
.000963391
3
.000906618
8
.000856164
3
.000811030
4
.00102669
9
000962464
4
.000905797
9
.000855432
4
.000810373
fc
.00102564
1040
.000961538
5
.000904977
1170
.000854701
5
.000809717
6
.00102459
1
.000960615
6
.000904159
1
.000853971
6
.000809061
7
.00102354
2
.000959693
n
.000903342
2
.000853242
7
.000808407
8
.00102250
3
.000958774
8
.000902527
3
.000852515
8
.000807754
9
.00102145
4
.000957854
c
.000901713
4
.000851789
9
.000807102
980
.00102041
g
.000956938
1110
.000900901
5| .000851064
1240
.000806452
I
.00101937
I
.000956023
11
000900090
6
.000850340
1
.000805802
2
.00101833
7
.000955110
12
.000899281
7
.000849618
2
.000805153
3
.00101729
8
.000954198
13
.000898473
8
.000848896
3
.000804505
4
.00101626
9
.000953289
14
.000897666
9
.000848176
4
.000803858
5
.00101523
1050
.000952381
15
.000896861
1180
.000847457
5
.000803213
6
.00101420
1
.000951475
16
.000896057
1
.000846740
6
.000802568
.00101317
.000950570
17
.000895255
2
.000846024
7
.000801925
8
.00101215
\
.000949668
18
.000894454
3
.000845308
8
.000801282
c
.00101112
i
.000948767
19
.000893655
4
.000844595
9
.000800640
990
.00101010
5
.000947867
1120
.000892857
5
.000843882
1250
.000800000
.00100908
6
.000946970
3
.000892061
6
.000843170
1
.000799360
<
.00100806
\
.000946074
<
.000891266
7
.000842460
2
.000798722
<
.00100705
8
.000945180
j
.000890472
S
.000841751
3
.000798085
c
.00100604
c
.000944287
<.
.000889680
9
.000841043
4
.000797448
t
.00100502
1060
.000943396
5
.000888889
1190
.000840336
5
.000796813
(
.00100J02
.000942507
6
.000888099
1
,000839631
6
.000796178
"(
.00100301
«
.000941620
\
.000887311
2
.000838926
"t
.000795545
8
.00100200
{
.000940734
8
.000886525
3
.000838222
8
.000794913
<
.00100100
t
.000939850
9
.000885740
4
.000837521
9
.000794281
1000
.00100000
5
.000938967
1130
.000884956
5
.000836820
1260
.000793651
.000999001
<
.000938086
.000884173
6
.000836120
1
.000793021
2
.000998004
7
.000937207
<
.000883392
7
.000835422
*
.000792393
j
.000997009
8
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<
.000882612
8
.000834724
3
.000791766
t
,000996016
<
.000935454
i
.000881834
9
.000834028
4
.000791139
5
.000995025
1070
.000934579
5
.000881057
1200
000833333
5
.000790514
(
.000994036
•
.000933707
6
.000880282
1
.000832639
6
.000789889
•
.000993049
2
.000932836
r
.000879508
2
.000831947
7
.000789266
I
.000992063
j
.000931966
8
.000878735
3
.000831255
8
.000788643
I
.000991080
c
.000931099
j
.000877963
4
.000830565
9
.000788022
1010
.000990099
I
.000930233
1140
.000877193
5
.000829875
1270
.000787402
11
.000989120
6
.000929368
.000876424
6
.000829187
1
.000786782
12
.000988142
t
.000928505
i
.000875657
7
.000828500
2
.000786163
13
.000987167
8
.000927644
.000874891
8
.000827815
3
.000785546
14
.000986193
c
.000926784
t
.000874126
9
.000827130
i
.000784929
15
.000985222
1080
.000925926
5
.000873362
1210
.000826446
5
.000784314
16
.000984252
•
.000925069
6
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11
.000825764
6
.000783699
1"
.000983284
j
.000924214
\
.000871840
12
.000825082
.000783085
18
.000982318
j
.000923361
8
.000871080
13
.000824402
8
.000782473
19
.000981354
t
.000922509
c
.000870322
14
.000823723
9
.000781861
1020
.000980392
i
.000921659
1150
.0008695G5
15
.000823045
1280
.000781250
;
.000979432
(
.000920810
.000868810
16
.000822368
1
.000780640
«
000978474
1
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<
.000868056
17
.000821693
2
.000780031
<
.000977517
8
.000919118
j
.000867303
18
.000821018
3
.000779423
t
.000976562
9
000918274
t
.000866551
19
.000820344
i
.000778816
t
.000975610
1090
.000917431
5
.000865801
1220
.000819672
5
.000778210
(
.000974659
]
.000916590
6
.000865052
1
.000819001
6
.000777605
\
.000973710
£
.000915751
1
.000864304
2
.000818331
•j
.000777001
8
.000972763
<
.000914913
8
.000863558
3
.000817661
8
.000776397
9
.000971817
i
.000914077
(
.000862813
4
.000816993
9
.000775795
1030
.000970874
5
.000913242
1160
.000862069
5
.000816326
1290
.000775194
8"4
MATHEMATICAL TABLES,
No.
Recipro-
cal.
No.
!
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
1291
.000774593
1356
.000737463
1421
.000703730
1486
.000672948
1551
.000644745
2
.00077391)4
7
000736920
2 .000703235
7
.000672495
2
.000644330
3
.000773395
8
.000736377
3
.000702741
8
.000672043
3
.000643915
4
.000772797
(
.000735835
4
.000702247
9
.000671592
4
.000643501
5
.000772:201
1360
.000735294
5
.000701754
1490
.000671141
5
.000643087
6
.000771605
1
.000734754
6
.000701262
1
.000670691
6
.000642673
7
.000771010
2
.000734214
7
.000700771
2
.000670241
.000642261
8
.000770416
f
.000733676
8
.000700280
3
.000669792
8
.000641848
9 1.000769823
4
.000733138
9
.000699790
4
.000669344
9
.000641437
1300 .000769231
r
.00073-2601
1430
.000699301
5
.000668896
1560
.000641026
1
.000768639
e
.000732064
1
.000698812
6
.000668449
1
.000640615
2
.000768049
.000731529
2
.000698324
7
.000668003
2
.000640205
3
.000767459
8
.000730994
3
.000697'837
8
.000667557
3
.000639795
4
.000766871
9
.000730460
4
.000697350
9
.000667111
4
.000639386
5
.000766283
1370
.000729927
5
.000690864
1500
.000666667
5
.000638978
6
.000765697
1
.000729395
6
.000696379
1
.000666223
6
.000638570
7
.000765111
c
.000728863
7
.000695894
2
.000665779
7
.000638162
8
.000764526
3
.000728332
8
.000695410
3
.000665336
8
.000637755
9
.000763942
4
.000727802
9
.000694927
4
.000664894
9
.000637349
1310
.000763359
s
.000727273
1440
.000694444
5
.000664452
1570
.000636943
11
.000762776
6
.000726744
1
.000693962
6
.000664011
1
.000636537
12
.000762195
7
.000726216
2
.000693481
.000663570
2 .000636132
13
.000761615
8
.000725689
3
.000693001
8
.000663130
3 !. 000635728
14
.000761035'
9
.000725163
4
.000692521
9
.000662691
4
.000635324
15
. 000760456 !
1380
.000724638
51.000692041
1510
. 000662252
5
.000634921
16
.000759878!
1
.000724113
6
.000691563
11
.000661813
6
.000634518
17
.000759301
2
.000723589
7
.000691085
12
.000661376
7
.000634115
18
.000758725;
g
.000723066
8
.000690608
13
.000660939
8
.000633714
19
.000758150;
4
.000722543
9
.000690131
14
.000660502
9
.000633312
1320
.000757576!
.000722022
1450L 000689655
15
.000660066
1580
.000632911
1
.000757002
6
.000721501
1
.000689180
16
.000659631
1
.000632511
2
.000756430
7
.000720980
a
.000688705
17
.000659196
2
.000632111
3
.000755858
8
.000720461
3
.000688231
18
.000658761
3 !. 000631712
4
.000755287
9
.000719942
4
.000687758
19
.000658328
4 .000631313
5
.000754717
1390
.000719424
5
.000687285
1520
.000657895
5
.000630915
6
.000754148
1
.000718907
6
.000686813
1
.000657462
0
.000630517
7
.000753579
2
000718391
.000686341
2
.000657030
7
.000630120
8
.000753012
3
.000717875
g
.000685871
3
.000656598
8
.000629723
9
.000752445
4
.000717360
9
.000685401
4
.000656168
9
.000629327
1330
.000751880
5
.000716846
1460
.000684932
5
.0006557381
1590
.000628931
1
.000751315
6
.000716332
1
.000684463
6
.000655308
1
.000628536
2
.000750750
7
.000715820
2
.000683994
7
.000654879
o
.000628141
3
.000750187
8
.000715308
3
.000683527
8
.000654450
3
.000627746
4
.000749625
9
.000714796
41.000683060
9
.000654022
4
.000627353
5
.000749064
1400
.000714286
5 !. 000682594
1530
.000653595
5
.000626959
6
.000748503
1
.000713776
6
.000682128
1
.000653168
6
.000626566
7
.000747943
2
.000713267
7
.000681663
2
.000652742'
7
.000626174
8
.000747384
3
.000712758
8
.000681199
3
.000652316'
8
.000625782
9
. 000746826 I
4
.000712251
9
.000680735
4
.000651890!
9
.000625391
1340
.000746269;
5
.000711744
1470
.000680272
5
. 000651466 '
1600
.000625000
1
.000745712
6
.000711238
1
.000679810
6
.000651042
2
.000624219
2
.000745156
7
.000710732
2
.000679348
7
.000650618
4
.000623441
3
.000744602!
8
.000710227
3
.000678887
8
.000650195
6
.000622665
4
.000744048!
9
.000709723
4
.000678426
9
.000649773
8
.000621890
5
.0007434941
1410
.000709220
5
.000677966
1540
.000649351
1610
.000621118
6
.000742942
11
.000708717
6
.000677507
1
.000648929
2
.000620347
7
.000742390
12
.000708215
7
.000677048
2
.000648508
4
.000619578
8
.000741840
13
.000707714
8
.000676590
3
.000648088
6
.000618812
9
.000741290
14
000707214
9
.0006-76138
4
.000647668
8
.000618047
1350
.000740741J
15
000706714
1480
000675676
5
.000647249
1620
.000617284
1
.000740192;
16
.000706215
1
.00^675219
6
.000646830
2
.000616523
2
000739645
17
.000705716
2
.0006?4"64
.000646412
4
.000615763
3
.000789098
18
.000705219
3
.000674309
8
.000645995
6
.000615006
4
.000738552
19
.000704722
4
.000673854
9
.000645578
8
.000614250
5
.000738007!
1420
.000704225
5
.0006^3*01
1550
.000645161
1630
.000613497
RECIPROCALS OF NUMBERS.
85
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
No.
Recipro-
cal.
1632
.000612745
1706
.000586166
1780
.000561798
1854
.000539374
1928
.000518672
4
.000611995
8
.000585480
2
.000561167
6
.000538793
1930
.000518135
6
.000611247
1710
.000584795
4
.000560538
8
.000538213
2
.000517599
8
.000610500
12
.000584112
6
.000559910
1860
.000537634
4
.000517063
1640
.000609756
14
.000583430
8 .000559284
2
.000537057
6
.000516528
2
.000609013
16
.000582750
1790
.000558659
4
.000536480
8
.000515996
4
.000608272
18
.000582072|
2
.000558035
6
.000535905
1940
.000515464
6
.000607533
1720
.000581395!
4
.000557413
8
.000535332
2
.000514933
8
.000606796
2
.000580720
6
.000556793
1870
.000534759
4
.000514403
1650
.000606061
4
.000580046
8
.000556174
2
.000534188
6
.000513874
2
.000305327
6
.000579374
1800
.000555556
4
.000533618
8
.000513347
4
.000604595
8
.000578704
2
.000554939
6
.000533049
1950
.000512820
6
.000603865
1730
.000578035
4
.000554324
8
.000532481
2
.000512295
8
.000603136
2
.000577367
6
.000553710
1880
.000531915
4
.000511770
1660
.000602410
4
.000576701
8
.000553097
2
.000531350
6
.000511247
o
.000601685
6
.000576037
1810
.000552486
4
.000530785
8
.000510725
4
.OOD600962
8
.000575374
12
.000551876
6
.000530222
1960
.000510204
6
.000600240
1740
.000574713
14
.000551268
8
.000529661
2
.000509684
8
.000599520
2
.000574053
16
. 000550661
1890
.000529100
4
.000509165
1670
.000598802
4
.000573394
18
.000550055
2
.000528541
6
.000508647
2
.000598086
6
.000572737
1820
.000549451
4
.000527983
8
.000508130
4
.000597371
8
.000572082
2
.000548848
6
.000527426
1970
.000507614
6
.000596658
1750
.000571429
4,
.000548246
8
.000526870
2
.000507099
8
.000595947
2
.000570776
6
.000547645
1900
.000526316
4
.000506585
1680
.000595238
4
.000570125
8
000547046
2
.000525762
6
.000506073
2
.000594530
6
.000569476
1830
.000546448
4
.000525210
8
.000505561
4
.000593824
8
.000568828
2
.000545851
6
.000524659
1980
.000505051
6
.000593120
1760
.000568182
4
.000545255
8
.000524109
2
.000504541
8
.000592417
2
.000567537
6i
.000544662
1910
.000523560
4
.000504032
1690
.000591716
4
.000566893
8
.000544069
12
000523012
6
.000503524
2
.000591017
6
.000566251
1840
.000543478
14
.000522466
8
.OOOoOSOlS
4
.000590319
8
.000565611
2
.000542888
16
.000521920
1990
.000502£13
6
.000589622
1770
.000564972
4
.000542299
18
.000521376
2
.000502008
8
.000588928
2
000564334
C
.000541711
1920
.000520833
4
.000501504
1700
.000588235
4
.000563698
8
.000541125
2
.000520291
6
.000501002
2
.000587544
6
000563063
1850
.000540540
4
.000519750
8
.000500501
4
.000586854
8
.000562430
2
.000539957 6
.000519211 2000
000500000
Use of reciprocals.— Reciprocals may be conveniently used to facili-
tate computations iu long division. Instead of dividing as usual, multiply
the dividend by the reciprocal of the divisor. The method is especially-
useful when many different dividends are required to be divided by the
same divisor. In this case find the reciprocal of the divisor, and make a
small table of its multiples up to 9 times, and use this as a multiplication-
table instead of actually performing the multiplication in each case.
EXAMPLE.— 9871 and several other numbers are to be divided by 1638. The
reciprocal of 1638 is .000610500.
Multiples of the
reciprocal :
.0006105
.0012210
.0018315
.0024420
.0030525
The table of multiples is made by continuous addition
of 6105. The tenth line is written to check the accuracy
of the addition, but it is not afterwards used.
Operation:
Dividend 9871
Take from table 1 ...
7...
.0006105
0.042735
00.48S40
005.4945
.0042735
.0048840
.0054945
10. .0061050
Quotient.. 6.0262455
Correct quotient by direct division 6.0262515
The result will generally be correct to as many figures as there are signifi-
cant figures in the reciprocal, less one, and the error of the next figure will in
general not exceed one. In the above example the reciprocal has six sig«
nificant figures, 610500, and the result is correct to five places of figures.
86
MATHEMATICAL TABLES.
SQUARES, CUBES, SQUARE ROOTS AND CUBE
ROOTS OF NUMBERS FROM .1 TO 1600.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
.1
.01
.001
.3162
.4642
3.1
0.61
29.791
1.761
1.458
.15
.0225
.0034
.3873
.5313
.2
10.24
32.768
1.789
1.474
.2
.04
-008
.4472
.5848
.3
10.89
35.937
1.817
1.489
.25
.0625
0156
.500
.6300
.4
11.56
39.304
1.844
1.504
.3
.09
027
.5477
.6694
.5
12.25
42.875
1.871
1.518
.35
.1225
0429
.5916
.7047
.6
12.96
46.656
1.897
1.533
.4
.16
064
.6325
.7368
7
13.69
50.653
1.924
1.547
.45
.2025
.0911
.6708
.7663
'.8
14.44
54.872
1.949
1.560
.5
.25
• 125
.7071
.7937
.9
15.21
59.319
1.975
1.574
.55
.3025
.1664
.7416
.8193
4.
16.
64.
2.
1.5874
.6
.36
216
.7746
.8434
.1
16.81
68.921
2.025
1.601
.65
.4225
.2746
.8062
.8662
.2
17.64
74.088
2.049
1.613
.7
.49
.343
.8367
.8879
.3
18.49
79.507
2.074
1.626
.75
.5625
.4219
.8660
.9086
.4
19.36
85.184
2.098
1.639
.8
.64
.512
.8944
.9283
.5
20.25
91.125
2.121
1.651
.85
.7225
.6141
.9219
.9473
.6
21.16
97.336
2.145
1.663
.9
.81
.729
.9487
.9655
.7
22.09
103.823
2.168
1.675
.95
.9025
.8574
.9747
.9830
.8
23.04
110.592
2.191
1.687
1.
1.
1.
1.
1.
.9
24.01
117.649
2.214
.698
1.05
1.1025
1.158
1.025
1.016
5.
25.
125.
2.2361
.7100
1.1
1.21
1.331
1.049
1.032
.1
26.01
132 651
2.258
.721
1.15
1.3225
1.521
1.072
1.048
.2
27.04
140.608
2.280
.732
1.2
1.44
1.728
1.095
1.063
.3
28.09
148.877
2.302
.744
1.25
1.5625
1.953
1.118
1.077
.4
29.16
157.464
2.324
.754
1.3
1.69
2.197
1.140
1.091
.5
30.25
166.375
2.345
.765
.35
1.8225
2.460
1.162
1.105
.6
31.36
175.616
2.366
.776
.4
1.96
2.744
1.183
1.119
7
32.49
185.193
2 . 387
.786
.45
2.1025
3.049
1.204
1.132
'.8.
33.64
195.112
2.408
.797
.5
2.25
3.375
1.2247
1.1447
.9
34.81
205.379
2.429
.807
.55
2.4025
3.724
1.245
1.157
6.
36.
216.
2.4495
.8171
.6
2.56
4.096
1.265
1.170
.1
37.21
226.981
2.470
.827
.65
2.7225
4.492
1.285
1.182
o
38.44
238.328
2.490
.837
1.7
2.89
4.913
1.304
1.193
.3
39.69
250.047
2.510
.847
1.75
3.0625
5.359
1.323
1.205
4
40.96
262.144
2.530
.857
1.8
3.24
5.832
1.342
1.216
.5
42.25
274.625
2.550
.866
1.85
3.4225
6.332
1.360
1.228
.6
43.56
287.496
2.569
.876
1.9
3.61
6.859
1.378
1.239
.7
44 89
300.763
2.588
.885
1.95
3.8025
7.415
1.396
1.249
.8
46.24
314.432
2.608
.895
2.
4.
8.
1.4142
1.2599
.9
4? 61
328.509
2.627
.904
.1
4.41
9.261
1.449
1.281
7.
49.
343.
2.6458
1.9129
.2
4.84
10.648
1.483
1.301
.1
50.41
357.911
2.665
1.922
.3
5.29
12.167
1.517
1.320
.2
51.84
373.248
2.683
1.931
.4
5.76
13.824
1.549
1.339
.3
53.29
389.017
2.702
1.940
.5
6.25
15.625
1.581
1.357
.4
54.76
405.224
2.720
1.949
.6
6.76
17.576
1.612
1.375
.5
56.25
421.875
2.739
1.957
.7
7 29
19.683
1.643
1.392
.6
57.76
438.976
2.757
1.966
.8
7^84
21.952
1.673
1.409
.7
59.29
456.533
2.775
1.975
.9
8.41
24.389
1.703
1.426
.8
60.84
474.552
2 793
1.983
3.
9.
27.
1.7321
1.4422
.9
62.41
493.039
2.81J
1.992
SQUARES, CUBES, SQUARE AKD CUBE ROOTS. 87
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
8.
64.
512.
2.8284
2.
45
2025
91125
6.7082
3.5569
.1
65.61
531.441
2.846
2 008
46
2116
97336
6.7823
3.5830
.2
67.24
551.368
2.864
2.017
47
2:209
103823
6.8557
3.6088
.3
68.89
571.787
2.881
2 0^5
48
2304
110592
6.9282
3.6342
.4
70.56
592.704
2.898
2.033
49
2401
117649
7.
3.6593
.5
72.25
614.125
2.915
2.041
50
2500
125000
7.0711
3.6840
.6
73.96
636.056
2.933
2.049
51
2601
132651
7.1414
3.7084
.7
75.69
658.503
2.950
2.057
52
2704
140608
7 2111
3.7325
.8
77.44
681.472
2.966
2.065
53
2809
148877
7.2801
3.7563
•9
79.21
704.969
2.983
2.072
54
2916
157464
7.3485
3.7798
9.
81.
729.
3.
2.0801
55
3025
166375
7.4162
3.8030
.1
82.81
753.571
3.017
2.088
56
3136
175616
7.4833
3.8259
.2
84.64
778.688
3.033
2.095
57
3249
185193
7.5498
3.8485
.3
86.49
804.35?
3.050
2.103
58
3364
195112
7.6158
3.8709
.4
88.36
830.584
3.066
2.110
59
3481
205379
7.6811
3.8930
.5
90.25
857.375
3.082
2.118
60
3600
216000
7.7460
3.9149
.6
92.16
884.736
3.098
2.125
61
3721
226981
7.8102
3.9365
.7
94.09
912.673
3.114
2 133
62
3844
238328
7.8740
3.9579
.8
96.04
941.192
3.130
2.140
63
3969
250047
7.9373
3.9791
.9
98.01
970.299
3.146
2.147
64
4096
262144
8.
4.
10
100
1000
3.1623
2.1544
65
4225
274625
8.0623
4.0207
11
121
1331
3.3166
2.2240
66
4356
287496
8.1240
4.0412
12
144
1728
3.4641
2.2894
67
4489
300763
8.1854
4.0615
13
169
2197
3.6056
2.3513
68
4624
314432
8.2462
4.0817
14
196
2744
3.7417
2.4101
69
4761
3vJ8509
8.3066
4.1016
15
225
3375
3.8730
2.4662
70
4900
343000
8.3666
4.1213
16
256
4096
4.
2.5198
71
5041
357911
8.4261
4.1408
17
289
4913
4.1231
2.5713
72
5184
373248
8.4853
4.1602
18
324
5832
4.2426
2.6207
73
5329
389017
8.5440
4.1793
19
361
6859
4.3589
2.6684
74
5476
405224
8.6023
4.1983
20
400
8000
4.4721
2./144
75
5625
421875
8.6603
4.2172
21
441
9261
4.5826
2 7589
76
5776
438976
8.7178
4.2358
22
484
10648
4.6904
2.8020
77
5929
456533
8.7750
4.2543
23
529
12167
4.7958
2.8439
78
6084
474552
8.8318
4.2727
24
576
13824
4.8990
2.8845
79
6241
493039
8.8882
4.2908
25
625
15625
5.
2.9240
80
6400
512000
8.9443
4.3089
26
676
17576
5.0990
2.9625
81
6561
531441
9.
4.3267
27
729
19683
5.1962
3.
8-.'
6724
551368
9.0554
4.3445
28
784
21952
5.2915
3 0366
83
6889
571787
9.1104
4.3621
29
841
24389
5.3852
3.0723
84
7056
592704
9.1652
4.3795
30
900
27000
5.4772
3.1072
85
7225
614125
9.2195
4.3968
31
961
29791
5.5678
3.1414
86
7396
636056
9.2736
4.4140
32
1024
32768
5.6569
3.1748
87
7569
658503
9 3276
4.4310
33
1089
35937
5.7446
3.2075
88
7744
6S1472
9.3808
4.4480
34
1156
39304
5.8310
3.2396
89
7921
704969
9.4340
4.4647
35
1225
42875
5.9161
3.2711
90
8100
729000
9.4868
4.4814
36
1296
46656
6.
3.3019
91
8281
753571
9.5394
4.4979
37
1369
50653
6.0828
3.3322
92
8464
778688
9.5917
4.5144
38
1444
54872
6.1644
3.3620
93
8649
804357
9 6437
4.5307
39
1521
59319
6.2450
3.3912
94
8836
830584
9.6954
4.5468
40
1600
64000
6.3246
3 4200
95
9025
857375
9 7468
4.5629
41
1681
689'>1 i 6. 4031
3.4482
96
9216
884736
9.7980
4.5789
42
1764
74088 6.4807
3.4760
97
9409
912673
9.8489
4.5947
43
1849
79507 6.5574
3.5034
98
9604
941192
9.8995
4.6104
44
1936
85184 6.6332
3.5303
99
9801
970-299
9.9499
4.6261
88
MATHEMATICAL TABLES.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube,
Sq.
Root.
Cube
Root.
100
10000
1000000
10.
4.6416
155
24025
3723875
12.4499
5.3717
101
10201
1030301
10.0499
4.6570
156
24336
3796416
12.4900
5.3832
10:3
10404
1061208
10.0995
4.6723
157
24649
3869893
12.5300
5.3947
103
10609
1092727
10.1489
4.6875
158
24964
3944312
12.5698
5.4061
104
10816
1124864
10.1980
4.7027
159
25281
4019679
12.6095
5.4175
105
11025
1157625
10.2470
4.7177
160
25600
4096000
12.6491
5.4288
106
11236
1191016
10.2956
4.7326
161
25921
4173281
12.6886
5.4401
107
11449
1225043
10.3441
4.7475
162
26244
4251528
12.7279
5 4514
108
11664
1259712
10.3923
4.7622
163
26569
4330747
12.7671
5.4626
109
11881
1295029
10.4403
4.7769
164
26896
4410944
12.8062
5.4737
110
12100
1331000
10.4881
4.7914
165
27225
4492125
12.8452
5.4848
111
12321
1367631
10.5357
4.8059
166
27556
4574-296
12.8841
5.4959
112
12514
1404928
10.5830
4.8203
167
27889
4657463
12.9228
5.5069
113
12769
1442897
10.6301
4.8346
168
28224
4741632
12.9615
5.5178
114
12996
1481544
10.6771
4.8488
169
28561
4826809
13.0000
5.5288
115
132-25
1520875
10.7238
4.8629
170
28900
4913000
13.0384
5.5397
116
13456
156089(5
10.7703
4.8770
171
29241
500021 1
13.0767
5.5505
117
13689
1601613
10.8167
4.8910
172
29584
5088448
13.1149
5.5613
118
13924
1643032
10.8628
4.9049
173
29929
5177717
13.1529
5.5721
119
14161
1685159
10.9087
4.9187
174
30276
5268024
13.1909
5.5828
120
14400
1728000
10.9545
4.9324
175
30625
5359375
13.2288
5.5934
121
14641
1771561
11.0000
4.9461
176
30976
5451776
13.2665
5.6041
122
14884
1815848
11.0454
4.9597
177
31329
5545233
13.3041
5.6147
123
15129
1860867
11.0905
4.9732
178
31684
5639752
13.3417
5.6252
124
15376
1906624
11.1355
4.9866
179
32041
5735339
13.3791
5.6357
125
15625
1953125
11.1803
5.0000
180
32400
583-2000
13.4164
5. 6402
126
15876
2000376
11.2250
5.0133
181
32761
5929741
13.4536
5.6567
127
16129
2018383
11.2694
5 0265
182
33124
6028568
13.4907
5.6671
128
16384
2097152
11.3137
5.0397
183
33489
6128487
13.5277
5.6774
129
16641
2146689
11.3578
5.0528
184
33856
6229504
13.5647
5.6877
130
16900
2197000
11.4018
5.0658
185
342-25
6331625
13.6015
5.6980
131
17161
2248091
11.4455
5.0788
186
34596
6434856
13.6382
5.7083
132
17424
2299968
11.4891
5.0916
187
34969
6539203
13.6748
5.7185
133
17689
2352637
11.5326
5.1045
188
35344
6644672
13.7113
5.T287
134
17956
2406104
11.5758
5.1172
189
35721
6751269
13.7477
5.7388
135
18225
2460375
11.6190
5.1299
190
36100
6859000
13.7840
5.7489
136
18496
2515456
11.6619
5.1426
191
36481
6967871
13.8203
5.7590
137
18769
2571353
11.7047
5.1551
192
36864
7077888
13.8564
5.7690
138
19044
2628072
11.7473
5.1676
193
37249
7189057
13.8924
5 7790
139
19321
2685619
11.7898
5.1801
194
37636
7301384
13.9284
5.7890
140
19600
2744000
11.8322
5.1925
195
38025
7414875
3.9642
5.7989
141
19881
2803221
11.8743
5.2048
196
38416
7529536
14.0000
5.8088
142
20164
2863286
11.9164
5.2171
197
38809
7645373
14.0357
5.8186
143
20449
29-24207
11.9583
5.2293
198
39204
7762392
14.0712
5.8285
144
20736
2985984
12.0000
5.2415
199
39601
7880599
14.1067
5.8383
145
21025
3048625
12.0416
5.2536
200
40000
8000000
14.1421
5.8480
146
21316
3112136
12.0830
5.2656
201
40401
8120601
14.1774
5.8578
147
21609
31765-23
12.1244
5.2776
202
40804
824-2408
14.2127
5.8675
148
21904
3241792
12.1655
5.2896
203
41209
8365427
14.2478
5.8771
149
22201
3307949
12.2066
5.3015
204
41616
8489664
14.2829
5.8868
150
22500
3375000
12.2474
5.3133
205
42025
8615125
14.3178
5.8964
151
2-2801
3442951
12.2882
5.3251
206
42436
8741816
14.3527
5.9059
152
23104
3511808
12.3288
5.3368
207
42849
8869743
14.3875
5.9155
153
23409
3581577
12.3603
5 . :>, 185
208
43264
8998912
14.4222
5.9250
154
23716
3652264 1? *M>~
5.3C,0!
209
43681
9129329
14.4568
5.9345
SQUARES, CUBES, SQUARE AtfD CUBE ROOTS. 89
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
210
44100
9261000
14.4914
5.9439
265
70225
18609625
16.2788
6.4232
211
44521
9393931
14.5258
5.9533
266
70756
18821096
16.3095
6.4312
212
44944
9528128
14.5602
5.9627
267
71289
19034163
16.3401
6.4393
213
45369
9663597
14.5945
5.9721
268
71824
19248832
16.3707
6.4473
214
45796
9800344
14.6287
5.9814
269
72361
19465109
16.4012
6.4553
215
46225
9938375
14.6629
5 9907
270
72900
19683000
16 4317
6.4633
216
46656
10077696
14.6969
6.0000
271
73441
19902511
16.4621
6.4713
217
47089
10218313
14.7309
6.0092
272
73984
20123648
16.4924
6.4792
218
47524
10360232
14.7648
6 0185
273
74529
20346417
16.5227
6.4872
219
47961
10503459
14.7986
6 0477
274
75076
20570824
16.5529
6.4951
220
48400
10648000
14.8324
6.0368
275
75625
20796875
16.5831
6.5030
221
48841
10793861
14.8661
6.0459
276
76176
21024576
16.6132
6.5108
222
49284
10941048
14.8997
6 0550
277
76729
21253933
16.6433
6.5187
223
49729
11089567
14.9332
6.0641
278
77284
21484952
16.6733
6.5265
224
50176
112394^4
14.9666
6.0732
279
77841
21717639
16.7033
6.5343
2-25
50625
11390625
15.0000
6.0822
280
78400
21952000
16.7332
6.5421
226
51076
11543176
15.0333
6.0912
281
78961
22188041
16.7631
6.5499
227
51529
11697083
15.0665
6.1002
282
79524
22425768
16.7929
6.5577
228
51984
11852352
15.0997
6.1091
283-
80089
22665187
16.8226
6.5654
229
52441
12008989
15.1327
6.1180
284
80656
22906304
16.8523
6.5731
230
52900
12167000
15.1658
6.1269
285
81225
23149125
16.8819
6.5808
231
53361
12326:391
15.1987
6.1358
:286
81796
23393656
16.9115
6.5885
232
53824
12487168
15.2315
6.1446
287
82369
23639903
16.9411
6.5962
233
54289
12649337
15.2643
6.1534
288
82944
23887872
16.9706
6.6039
234
54756
12812904
15.2971
6.1622
289
83521
24137569
17.0000
6.6115
235
55225
12977875
15.3297
6.1710
290
84100
24389000
17.0294
6.6191
236
55696
13144256
15.3623
6.1797
2.)1
84681
2464-J171
17.0587
6.6267
237
56169
13312053
15 3948
6.1885
292
85264
24897088
17.0880
6.6343
238
56644
13481272
15.4272
6.1972
293
85849
25153757
17.1172
6.6419
239
57121
13651919
15.4596
6.2058
294
86436
25412184
17.1464
6.6494
240
57600
13824000
15.4919
6.2145
295
87025
2567:2375
17.1756
6.6569
241
58081
13997521
15.5242
6.2231
296
87616
25934336
17.2047
6.6644
242
58564
14172488
15.5563
6.2317
297
88-^09
26198073
17.2337
6.6719
243
59049
14348907
15.5885
6.2403
r)98
88804
26463592
17.2627
6.6794
244
59536
14526784
15.6205
6.2488
299
89401
26730899
17.2916
6.6869
245
60025
14706125
15.6525
6.2573
300
90000
27000000
17.3205
6.6943
246
60516
14886936
15.6844
6.2658
301
90601
27270901
17.3494
6.7018
247
61009
15069^3
15.7162
6.2743
30.2
91204
27543608
17.3781
6.7092
248
61504
15252992
15.7480
6.2828
303
91809
27818127
17.4069
6.7166
249
62001
15438249
15.7797
6.2912
304
92416
28094464
17 4356
6.7240
250
62500
15625000
15.8114
6.2996
305
93025
28372625
17.4642
6.7313
251
63001
15813-J51
15.8430
6.3080
306
93636
28652616
17.4929
6.7387
252
63504
16003008
15.8745
6.3164
307
94249
28934443
17.5214
6.7460
253
64009
16194;77
15.9060
6.3247
308
94864
29218112
17.5499
6.7533
254
64516
16387064
15.9374
6.3330
309
95481
29503629
17.5784
6.7606
255
65025
16581375
15.9687
6.3413
310
96100
29791000
17.6068
6.7679
256
65536
16777216
16.0000
6.3496
311
96721
30080231
17.6352
6 7752
257
66049
16974593
16.0312
6.3579
312
97344
30371328
17.6635
6.7824
258
66564
17173512
16.0624
6.3661
313
97969
30664297
17.6918
6.7897
259
67081
17373979
16.0935
6.3743
314
98596
30959144
17.7200
6.7969
260
67600
17576000
16.1245
6.3825
315
99225
31255875
17.7482
6.8041
261
68121
17779581
16.1555
6.3907
316
99856
31554496
17.7764
6.8113
262
68644
17984728
16.1864
6.3988
317
100489
31855013
17.8045
6.8185
2G3
69169
18191447
16.2173
6.4070
318
101124
32157432
17.8326
6.8256
264
69696
18399744
16.2481
6.4151
319
101761
324617o9
17.8606
6.8328
90
MATHEMATICAL TABLES.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
320
102400
32768000
17.8885
6.8399
375
140625
52734375
19.3649
7.2112
321
103041
33076161
17.9165
6 8470
376
141376
58157376
19.3907
7.2177
322
103684
33386248
17.9444
6.8541
377
142129
53582633
19.4165
7.2240
323
104329
33698267
17.9722
6.8612
378
142884
54010152
19.4422
7.2304
324
104976
34012224
18.0000
6.8683
379
143641
54439939
19.4679
7.23G8
325
105625
34328125
18.0278
6.8753
380
144400
54872000
19.4936
7.2432
326
106276
34645976
18.0555
6.8824
381
145161
55306341
19.5192
7.2495
327
106929
34965783
18.0831
6.8894
382
145924
55742968
19.5448
7.2558
328
107584
35287552
18.1108
6.8964
383
146689
56181887
19.5704
7.2622
329
108241
35611289
18.1384
6.9034
384
147456
50623104
19.5959
7.2685
330
108900
35937000
18.1659
6.9104
385
148225
57066625
19.6214
7.2748
331
109561
36264691
18.1934
6.9174
386
148996
57512456
19.6469
7.2811
332
110224
36594368
18.2209
6.9244
387
149769
57960603
19.6723
7.2874
333
110889
36926037
18.2483
6.9313
388
150544
58411072
19.6977
7.2936
334
111556
37259704
18.2757
6.9382
389
151321
58863869
19.7231
7.2999
335
112225
37595375
18.3030
6.9451
390
152100
59319000
19.7484
7 3061
336
112896
37933056
18.3303
6.9521
391
152881
59776471
19.7737
7.3124
337
113569
38272753
18.3576
6.9589
392
153664
60236288
19.7990
7.3186
338
114244
38614472
18.3848
6.9658
393
154449
60698457
19.8242
7.3248
339
114921
38958219
18.4120
6.9727
394
155236
61162984
19.8494
7.3310
340
115600
39304000
18.4391
6.9795
395
156025
61629875
19.8746
7.3372
341
116281
39651821
18.4662
6.9864
396
156816
62099136
19.8997
7.3434
342
116964
40001688
18.4932
6 9932
397
157609
62570773
19.9249
7.3496
343
117649
40353607
18.5203
7.0000
398
158404
63044792
19.9499
7.3558
344
118336
40707584
18.5472
7.0068
399
159201
63521199
19.9750
7.3619
345
119025
41063625
18.5742
7.0136
400
160000
64000000
20 0000
7.3681
346
119716
41421736
18.6011
7.0203
401
160801
64481201
20 0250
7.3742
347
120409
41781923
18.6279
7.0271
402
161604
64904808
20.0499
7.3803
348
121104
42144192
18.6548
7.0338
403
162409
65450827
20 0749
7.3864
349
121801
42508549
18.6815
7.0406
404
163216
65^39264
20.0998
7.3925
350
122500
42875000
18.7083
7.0473
405
164025
66430125
20.1246
7.3986
351
123201
43243551
18.7350
7.0540
406
164836
66923416
20.1494
7.4047
352
123904
43614208
18.7617
7.0607
407
165649
67419143
20.1742
7.4108
353
124609
43986977
18.7883
7.0674
408
166464
67917312
20.1S90
7.4169
354
125316
44361864
18.8149
7.0740
409
167281
68417'929
20.2237
7.4229
355
126025
44738875
18.8414
7.0807
410
168100
68921000
20.2485
7.4290
356
126736
45118016
18.8680
7.0873
411
168921
69426531
20.2731
7.4350
357
127449
45499293
18.8944
7.0940
412
169744
69934528
20.2978
7.4410
358
128164
45882712
18 9209
7.1006
413
170569
70444997
20.3224
7.4470
359
128881
46268279
18.9473
7.1072
414
171396
70957944
20.3470
7.4530
360
129600
46056000
18.9737
7.1138
415
172225
71473375
20.3715
7.4590
361
130321
47045881
19.0000
7.1204
416
173056
71991296
20.3961
7.4650
362
131044
47437928
19.0263
7.1269
417
173889
72511713
20.4206
7.4710
363
131769
47832147
19.0526
7.1335
418
174724
73034632
20.4450
7.4770
364
132496
48228544
19.0788
7.1400
419
175561
73500059
20.4695
7.4829
365
133225
48627125
19.1050
7.1466
420
176400
74088000
20.4939
7.4889
366
133956
49027896
19.1311
7.1531
421
177241
74618461
20.5183
7.4948
367
134689
49430863
19.1572
7.1596
422
178084
75151448
20.5426
7.5007
368
135424
49836032
19.1833
7.1661
423
178929
75686967
20.5670
7.5067
369
136161
50243409
19.2094
7.1726
424
179776
76225024
20.5913
7.5126
370
136900
50653000
19.2354
7.1791
425
180625
76765625
20.6155
7.5185
371
137641
51064811
19.2614
7.1855
426
181476
77308776
20.6398
7.5244
372
138384
51478848
19.2873
7.1920
427
182329
77854483
20.6640
7.5302
373
139129
51895117
19.3132
7.1984
428
183184
78402752
20.6882
7.5361
374
139876
52313624
19.3391
7.2048
429
184041
78953589
20.7123
7.5420
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 91
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
430
184900
79507000
20.7364
7.5478
485
235225
114084125
22.0227
7.8568
431
185761
80062991
20.7605
7 . 5537
486
236196
114791256
22.0454
7.8622
432
186624
80621568
20.7846
7.5595
487
237169
115501303
22.0681
7.8676
433
187489
SI 182737
20.8087
7.5654
488
238144
116214.272
22.0907
7.8730
434
188356
81746504
20.8327
7.5712
489
239121
116930169
22.1133
7.8784
435
189225
82312875
20.8567
7.5770
490
240100
117649000
22.1359
7.8837
436
190096
82881856
20.8806
7.5828
491
241081 ,118370771
22.1585
7.8891
437
190969
83453453
20.9045
7.5886
492
242064 1119095488
22.1811
7.8944
438
191844
84027672
20.9284
7.5944
493
243049 1119823157
22.2036
7.8998
439
192721
84604519
20.9523
7.6001
494
244036
120553784
22.2261
7.9051
440
193600
85184000
20.9762
7.6059
495
245025
121287375
22.2486
7.9105
441
194481
85766121
21.0000
7.6117
496
246016
122023936
22.2711
7.9158
442
195364
86350888
21.0238
7.6174
497
247009
122763473
22.2935
7.9211
443
196249
86938307
21.0476
7.6232
498
248004
123505992
22.3159
7.9264
444
197136
87528384
21.0713
7.6289
499
249001
124251499
22 3383
7.9317
445
198025
88121125
21.0950
7.6346
500
250000
125000000
22.3607
7.9370
446
198916
88716536
21.1187
7.6403
501
251001
125751501
22.3830
7.9423
447
199809
89314623
21.1424
7.6460
502
252004
126506008
22.4054
7.9476
448
200704
8991539-3
21.1660
7.6517
503
253009
127263527
22.4277
7.9528
449
201601
90518849
21.1896
7.6574
504
254016
128024064
22.4499
7.9581
450
202500
91125000
21.2132
7.6631
505
255025
128787625
22.4722
7.9634
451
203401
91733851
21.2368
7.6688
506
256036
129554216
22.4944
7.9686
452
204804
92345408
21.2603
7.6744
507
257049
130323843
22.5167
7.9739
453
205209
92959677
21.2838
7.6800
508
258064
131096512
22.5389
7.9791
454
206116
93576664
21.3073
7.6857
509
259081
131872229
22.5610
7.9843
455
207025
94196375
21.3307
7.6914
510
260100
132651000
22.5832
7.9896
456
207936
94818816
21.3542
7.6970
511
261121
133432831
22.6053
7.9948
457
208849
95443993
21.3776
7.7026
512
262144
134217728
22.6274
8.0000
458
209764
96071912
21.4009
7.7082
513
263169
135005697
22.6495
8.0052
159
210681
96702579
21.4243
7.7138
514
264196
135796744
22.6716
8.0104
460
211600
97336000
21.4476
7.7194
515
265225
136590875
22 6936
8.0156
iQl
212521
97972181
21.4709
7.7250
516
266256
137388096
22.7156
8.0208
462
213444
98611128
21.4942
7.7306
517
267289 1138188413
22.7376
8.0260
463
214369
99252847
21.5174
7.7362
518
268324
138991832
22.7596
8.0311
464
215296
99897344
21.5407
7.7418
519
269361
139798359
22.7816
8.03G3
465
216225
100544625
21.5639
7 . 7473
520
270400
140608000
22.8035
8.0415
466
217156
101194696
21 5870
7.7529
521
271441 1141420761
22.8254
8.0466
467
218089
101847563
21.6102
7.7584
522
272484 142236648
22.8473
8.0517
468
219024
102503232
21.6333
7.7639
523
273529 143055667
22.8692
8.0569
469
219961
103161709
21.6564
7.7695
524
274576
143877824
22.8910
8.0620
470
220900
103823000
21.6795
7.7750
525
275625
144703125
22.9129
8.0671
471
221841
104487111
21.7025
7.7805
526
276676 145531576
22.9347
8.0723
472
222784
105154048
21.7256
8.7860
527
277729 146363183
22.9565
8.0774
473
223729
105823317
21.7486
7.7915
528
278784 147197952
22.9783
8.0825
474
224676
106496424
21.7715
7.7970
529
279841
148035889
23.0000
8.0876
475
225625
107171875
21.7945
7.8025
530
280900
148877000
23.0217
8.0927
476
226576
107850176 121.8174
7. 8079 1 531
281961 149721291
23.0434
8.0978
477
227529
108531333
21.8403
7. 8184 1 582
283024 150568768
23.0651
8.1028
478
228484
109215352
21 8632
7.8188 533
284089 151419437
23.0368
8.1079
479
229441
109902239
21.8861
7.8243
534
285156
152273304
23.1084
8.1130
480
230400
110592000
21 9089
7.8297
535
286225
153130375
23.1301
8.1180
481
231361
111284641
21.9317
7.8352
536
287296 153990656
23.1517
8.1231
482
232324
111980168
21.9545
7.8406
537
288369 154854153
23.1733
8.1281
483
233-»89
112678587
21.9773
7.8460
538
289444 155720872
23.1948
8.1332
484
234256
113379904
22.0000
7.8514
539
290521 156590819
23.2164
8.1382
92
MATHEMATICAL TABLES.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Root.
Cube
Root.
540
291600
157464000
23.2379
8.1433
595
354025
210644875
24.3926
8.4108
541
292681
158340421
23.2594
8.1483
596
355216
211708736
24.4131
8.4155
542
293764
159220088
23.2809
8.1533
597
356409
212776173
24.4336
8.4202
543
294849
160103007
23.3024
8.1583
598
357604
213847192
24.4540
8.4249
544
295936
160989184
23.3238
8.1633
599
358801
214921799
24.4745
8.4296
545
297025
161878625
23.3452
8.1683
6CO
360000
216000000
24.4949
8 4343
546
298116
162771336
23.3666
8.1733
601
301201
217081801
24.5153
8.4390
547
299209
163667323
23.3880
8.1783
602
362404
218167208
24.5357
8.4437
548
300304
164566592
23.4094
8.1833
603
363609
219256227
24.5561
8.4484
549
301401
165469149
23.4307
8.1882
604
364816
220348864
24.5764
8.4530
550
302500
166375000
23.4521
8.1932
605
366025
221445125
24.5967
8.4577
551
303601
167284151
23.4734
8.1982
606
367236
22254501 (»
24.6171
8.4623
552
304704
168196H08
23.4947
8.2031
607
368449
223648543
24.6374
8.4670
553
305809
169112377
23.5160
8.2081
608
369664
224755712
24.6577
8.4716
554
306916
170031464
23.5372
8.2130
609
370881
225866529
24.6779
8.4763
555
308025
170953875
23.5584
8.2180
610
372100
226981000
24 6982
8.4809
556
309136
171879616
23.5797
8.2229
611
373321
228099131
24.7184
8.4856
557
310249
172808693
23.6008
8.2278
612
374544
229220928
24 7386
8.4902
558
311364
173741112
.23.6220
8.2327
613
375769
230346397
24.7588
8.4948
559
312481
174676879
23.6432
8.2377
614
376996
231475514
24.7790
8.4994
560
313600
175616000
23.6643
8.2426
615
378225
232608375
24.7992
8.5040
561
314721
176558481
23.6854
8.2475
616
379456
233744896
24.8193
8.5086
562
315844
177504328
23.7065
8 2524
617
380689
234885113
24.8395
8.5132
563
316969
178453547
23.7276
8.2573
618
381924
236029032
24.8596
8.5178
564
318096
179406144
23.7487
8.2621
619
383161
237176659
24.8797
8.5224
565
319225
180362125
23.7697
8.2670
620
384400
238328000
24.8998
8.5270
566
320356
181321496
23.7908
8.2719
621
385641
239483061
24.9199
8.5316
567
321489
182284263
23.8118
8.2768
622
3*6884
240641848
24 . 9399
8.5362
568
322624
183250432
23.8326
8.2816
623
388129
241804367
24.9600
8.5408
569
323761
184220009
23.8537
8.2865
624
389376
242970624
24.9800
8.5453
570
324900
185193000
23.8747
8.2913
625
390625
244140625
25.0000
8.5499
571
326041
186169411
23.8956
8.2962
626
391876
245314376
25.0200
8.5544
572
327184
187149248
23.9165
8.3010
627
393129
246491883
25.0400
8.5590
573
328329
188132517
23.9374
8.3059
628
394384
247673152
25.0599
8.5635
574
329476
189119224
23.9583
8.3107
629
395641
248858189
25.0799
8.5681
575
330625
190109375
23.9792
8.3155
630
396900
250047000
25.0998
8.5726
576
331776
191102976
24.0000
8.3203
631
398161
251239591
25.1197
8.5772
577
332929
19-2100033
24.0208
8.3251
632
399424
252435968
25.1396
8.5817
578
334084
193100552
24.0416
8.3300
633
400689
253636137
25.1595
8.5862
579
335241
194104539
24.0624
8.3348
634
401956
254840104
25.1794
8.5907
580
336400
195112000
24.0832
8.3396
635
403225
256047875
25.1992
8.5952
581
337561
196122941
24.1039
8.3443
636
404496
257259456
25.2190
8 5997
582
338724
197137368
24.1247
8.3491
637
405769
258474853
25.2389
8.6043
583
339889
198155287
24.1454
8.3539
638
407044
259694072
25.2587
8.6088
584
341056
199176704
24.1661
8.3587
639
408321
260917119
25.2784
8.6132
5S5
342225
200201625
24.1868
8.3634
640
409600
262144000
25.2982
8.6177
586
343396
201230056
24.2074
8.3682
641
410881
263374721
25.3180
8.6222
587
344569
202262003
24.2281
8.3730
642
412164
264609288
25.3377
8.6267
588
345744
203297472
24.2487
8.3777
643
413449
265847707
25.3574
8.6312
589
346921
204336469
24.2693
8.3825
644
414736
267089984
25.3772
8.6357
590
348100
205379000
24.2899
8.3872
645
416025
268836125
25.3969
8.6401
591
349281
206425071
24 3105
8.3919
646
417316
269586136
25.4165
8 6446
592
350464
207474688
24.3311
8.3967
647
418609
270840023
25.4362
8.6490
593
351649
208527857
24.3516
8.4014
648
419904
272097792
25.4558
8.G535
594
352836
209584584
24.3721
8.4061
649
421201
273359449
25.4755
8.6579
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 93
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
650
422500
274625000
25.4951
8.6624
705
497025
350402625
26.5518
8.9001
651
423801
275894451
25.5147
8.66(58
706
498436
351895816
26.5707
8.9043
652
425104
277167808
25.5343
8.6713
707
499849
353393243
26.5895
8.9085
653
426409
278445077
25.5539
8.6757
708
501264
354894912
26.6083
8.9127
654
427716
279726264
25.5734
8.6801
709
502681
356400829
26.6271
8.9169
655
429025
281011375
25.5930
8.6845
710
504100
357911000
26.6458
8.9211
656
430336
282300416
25.6125
8.6890
711
505521
359425431
26.6646
8.9253
65?
431649
283593393
25.6320
8.6934
712
506944
360944128
J6.6833
8.9295
658
432964
284890312
25.6515
8.6978
713
508369
362467097
26.7021
8.9337
659
434281
286191179
25.6710
8.7022
714
509796
363994344
26.7208
8.9378
660
435600
287496000
25.6905
8.7066
715
511225
365525875
26.7395
8.9420
661
436921
288804781
25.7099
8.7110
716
512656
367061696
26.7582
8.9462
662
438244
290117528
25 7294
8.7154
717
514089
368601813
26.7769
8.9503
663
439569
291434247
25.7488
8.7198
718
515524
370146232
26.7955
8.9545
664
440896
292754944
25.7682
8.7241
719
516961
371694959
26.8142
8.9587
665
442225
294079625
25.7876
8.7285
720
518400
373248000
26.8328
8.9628
666
443556
295408296
25.8070
8.7329
721
519841
374805361
26.8514
8.9670
667
444889
296740963
25.8263
8.7373
722
521284
376367048
26.8701
8.9711
668
446224
298077632
25.8457
8.7416
723
522729
377933067
26.8887
8.9752
669
447561
299418309
25.8650
8.7460
724
524176
379503424
26.9072
8.9794
670
448900
300763000
25.8844
8.7503
725
525625
381078125
26.9258
8.9835
671
450241
302111711
25.9037
8.7547
726
527076
382657176
26.9444
8.9876
672
451584
303464448
25.9230
8.7590
727
528529
384240583
26.9629
8.9918
673
452929
304821217
25.942".
8.7G34
728
529984
385828352
26.9815
8.9959
674
454276
306182024
25.9615
8.7677
729
531441
387420489
27.0000
9.0000
675
455625
307546875
25.9808
8.7721
730
532900
389017000
27 0185
9.0041
676
456976
308915776
26.0000
8.7764
731
534361
390617891
27.0370
9.0082
677
458329
310288733
26.0192
8.7807
732
535824
392223168
27.0555
9.0123
678
459684
311665752
26.0384
8.7850
733
537289
393832837
27.0740
9.0164
679
461041
313046839
26.0576
8.7893
734
538756
395446904
27.0924
9.0205
680
462400
314432000
26.0768
8.7937
735
540225
397065375
27.1109
9.0246
681
463761
315821241
26.0960
8.7980
736
541696
398688256
27.1293
9.0287
682
465124
317214568
26.1151
8.8023
737
543169
400315553
27.1477
9.0328
683
466489
318611987
26.1343
8.8066
738
544644
401947272
27.1662
9.0369
684
467856
320013504
26.1534
8.8109
739
546121
403583419
27.1846
9.0410
685
469225
321419125
26.1725
8.8152
740
547600
405224000
27.2029
9.0450
686
470596
322828856
26.1910
8.8194
741
549801
406869021
27.2213
9.0491
687
471969
324242703
26.2107
8.8237
742
550564
408518488
27.2397
9.0532
688
473344
325660672
26.2298
8.8280
743
552049
410172407
27.2580
9.0572
689
474721
327082769
26.2488
8.8323
744
553536
411830784
27.2764
9.0613
690
476100
328509000
26.2679
8.8366
745
555025
413493625
27.2947
9.0654
691
477481
329939371
26.2869
8.8408
746
556516
415160936
27.3130
9.0694
692
478864
331373888
26.3059
8.8451
747
558009
416832723
27.3313
9.0735
693
480249
332812557
26.3249
8.8493
748
559504
418508992
27.3496
9.0775
694
481636
334255384
26.3439
8.8536
749
561001
420189749
27.3679
9.0816
695
483025
335702375
26.3629
8.8578
750
562500
421875000
27.3861
9.0856
696
484416
337153536
26.3818
8.8621
751
564001
423564751
27.4044
9.0896
697
485809
338608873
26.4008
8.8663
752
565504
425259008
27.4226
9.0937
698
487204
340068392
26.4197
8.8706
753
567009
426957777
27.4408
9.0977
699
488601
341532099
26.4386
8.8748
754
568516
428661064
27.4591
9.1017
700
490000
343000000
26.4575
8.8790
755
570025
430368875
27.4773
9.1057
701
491401
344472101
26.4764
8.8833
756
571536
432081216
27.4955
9.1098
702
492804
345948408
26.4953
8.8875
757
573049
433798093
27.5136
9.1138
703
494209
347428927
26.5141
8.8917
758
574564
435519512
27.5318
9.1178
704
495616
348913664
26.5330
8.8959
759
576081
437245479
27.55001 9.1&18
MATHEMATICAL TABLES.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
760
577600
438976000
27.5681
9.1258
815
664225
541343375
28.5482
9.3408
761
579121
440711081
27.5862
9.1298
81 6 j 665856
543338496
28.5657
9.3447
762
580644
442450728
27.6043
9.1338
817 667489
545338513
28.5832
9.3485
763
582169
444194947
27.6225
9.1378
818 669124
547343432
28.6007
9.3523
764
583696
445943744
27.6405
9.1418
819 670761
549353259
28.6182
9.3561
765
585225
447697125
27.6586
9.1458
820 672400
551368000
28.6356
9.3599
766
586756
449455096
27.6767
9.1498
821! 674041
553387661
28.6531
9.3637
767
588289
451217663
27.6948
9.1537
822
67'5684
555412248
28 . 6705
9.3675
768
589824
452984832
27.7128
9.1577
823
677329
557441767
28.6880
9.3713
769
591361
454756609
27.7308
9.1617
824
678976
559476224
28.7054
9.3751
770
592900
456533000
27.7489
9.1657
825
680625
561515625
28.7228
9.3789
771
594441
458314011
27.7669
9.1696
826
682276
563559976
28.7402
9.3827
772
595984
460099648
27.7849
9.1736
827
683929
565609283
28.7576
9.3865
773
597529
461889917
27.8029
9.1775
828
685584
567663552
28.7750
9.3902
774
599076
463684824
27.8209
9.1815
829
687241
569722789
28.7924
9.3940
775
600625
465484375
27.8388
9.1855
830
688900
571787000
28.8097
9.3978
776
602176
467288576
27.8568
9.1894
831
690561
573856191
28.8271
9.4016
777
603729
469097433
27.8747
9.1933
832
692224
575930368
28.8444
9.4053
778
779
605284
606841
470910952
472729139
27.8927
27.9106
9.1973
9.2012
883
834
693889
695556
578009537
580093704
28.8617
28.8791
9.4091
9.4129
780
608400
474552000
27.9285
9.2052
835
697'225
582182875
28.8964
9.4166
781
609961
476379541
27.9464 9.2091
836
698896
584277056
28.9137
9.4204
782
611524
478211768
27.9643 9.2130
837
700569
586376253
28.9310
9.4241
783
613089
480048687
27.9821! 9.2170
838
702244
588480472
28.9482
9.4279
784
614656
481890304
28.0000
9.2209
839
703921
590589719
28.9655
9.4316
785
616225
483736625
28.0179
9.2248
840
705600
592704000
28.9828
9.4354
786
617796
485587656
28.03571 9.2287
841
707281
594823321
29.0000
9.4391
787
619369
487443403
28.0535 9.2326
842
708964
596947688
29.0172
9.4429
788
620944
489303872
28.0713! 9.2365
843
710649
599077107
29.0345
9.4466
789
622521
491169069
28.0891 9.2404
844
712336
601211584
29.0517
9.4503
790
624100
493039000
28.10691 9.2443
845
714025
603351125
29.0689
9.4541
791
625681
494913671
28.1247. 9.2482
846
715716
605495736
29.0861
9.4578
792
627264
496793088
28.14251 9.2521
847
717409
607645423
29.1033
9.4615
793
628849
498677257
28.1603 9.2560
848
719104
609800192
29.1204
9.4652
794
630436
500566184
28.1780
9.2599
849
720801
611960049
29.1376
9.4690
795
632025
502459875
28.1957
9.2638
850
722500
614125000
29.1548
9.4727
796
633616
504358336
28.2135
9.2677
851
724201
616295051
29.1719
9.4764
797
635209
50626157'3
28.2312! 9.2716
852
725904
618470208
29.1890
9.4801
798
636804
508169592
28.2489
9.2754
853
727609
620650477
29.2062
9.4838
799
638401
510082399
28.2666
9.2793
854
729316
622835864
29.2233
9.4875
800
640000
512000000
28.2843
9.2832
855
731025
625026375
29.2404
9.4912
801
641601
513922401
28.3019
9.2870
856
732736
627222016
29.2575
9.4949
802
643204
515849608
28.3196
9.2909
857
734449
629422793
29.2746
9.4986
803
644809
517781627
28.3373
9.2948
858
736164
631628712
29.2916
9.5023
804
646416
519718464
28.3549
9.2986
859
737881
633839779
29.3087
9.5060
805
648025
521660125
28.3725
9.3025
860
739600
636056000
29.3258
9.5097
806
649636
523606616
28.3901
9.3063
861
741321
C38277381
29.3428
9.5134
807
651249
525557943
28.4077
9.3102
862
743044
640503928
29.3598
9.5171
808
652864
5275141 12 '28. 4253
9.3140
863
744769
642735647
29.3769
9.5207
809
654481
529475129
28.4429
9.3179
864
746496
644972544
29.3939
9.5244
810
656100
531441000
28.4605
9.3217
865
748225
647214625
29.4109
9.5281
811
657721
53341173128.4781 9.3255
866
749956
649461896
29.4279
9.5317
812
659344
53538732828.4956 9.3294
867
751689
651714363
29.4449
9.5354
813
660969
53736779728.5132 9.3332
868
753424
653972032
29.4618
9.5391
814
662596
53935314428.5307 9.3370
869
755161
656234909
29.4788
9.5427
SQUARES, CUBES, SQUARE AND CUBE ROOTS. 95
No.
Square.
Cube.
Sq.
Root,
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
870
756900.
658503000
29.4958
9.5464
925
855625
791453125
30.4138
9.7435
871
758641
060776311
29.5127
9.5501
926
857476
794022776,30.4302
9.7470
872
760384
663054848
29.5296
9.5537
927
859329
796597983 '30. 4467
9.7505
873
762129
665338617
29.5466
9.5574
928
861184
799178752 30.4631
9 7540
874
763876
667627624
29.5635
9.5610
929
863041
801765089
30.4795
9.7575
875
765625
669921875
29.5804
9.5647
930
864900
804357000
30.4959
9.7610
876
767376
672221376
29.5973
9.5683
931
866761
806954491
30.5123
9.7645
877
769129
674526133
29.6142
9.5719
932
868624
809557568
30.5287
9.7680
878
770884
676836152
29.6311
9.5756
933
870489
812166237
30.5450
9.7715
879
772641
679151439
29.6479
9.5792
934
872356
814780504
30.5614
9.7750
880
774400
681472000
29.6648
9.5828
935
874225
817400375
30.5778
9.7785
881
776161
683797841
29.6816
9.5865
936
876096
820025856
30.5941
9.7819
882
777924
686128968
29.6985
9.5901
937
877969
822656953
30.6105
9.7854
883
779689
688465387
29.7153
9.5937
938
879844
825293672
30.6268
9.7880
884
781456
690807104
29.7321
9.5973
939
881721
827936019
30.6431
9.7924
885
783225
693154125
29.7489
9.6010
940
883600
830584000
30.6594
9.7959
886
784996
695506456
29.7658
9.6046
941 885481
833237621
30.6757
9.799S
887
786769
697864103129.7825
9.6082
942 887364
835896888
30.6920
9.8028
888
788544
70022707229.7993
9.6118
943 889249
838561807
30.7083
9.8063
889
790321
702595369
29.8161
9.6154
944
891136
841232384
30.7246
9.8097
890
792100
704969000
29.8329
9.6190
945
893025
843908625
30.7409
9.8132
891
793881
707347971
29.8496
9.6226
946i 894916
846590536
30.7571
9.8167
892
795664
709732288
29.8664
9.6262
947 1 896809
849278123
30.7734
9.8201
893
797449
712121957
29.8831
9.6298
948 898704
851971392
30.7896
9.8236
894
799236
714516984
29.8998
9.6334
949, 900601
854670349
30.8058
9.8270
895
801025
716917375
29.9166
9.6370
950 902500
857375000
30.8221
9.8305
896 802816
719323136
29.9333
9.6406
951 904401
860085351
30.8383
9.8339
897
804609
721734273
29.9500
9.6442
952 906304
862801408
30.8545
9.8374
898
806404
724150792
29.9666
9.6477
953 908209
865523177
30.8707
9.8408
899
808201
726572699
29.9833
9 6513
954 910116
868250664
30.8869
9.8443
900
810000
729000000
30 0000
9.6549
955' 912025
870983875
30.9031
9.8477
901
811801
731432701 30.0167
9.6585
956 913936
873722816
30.9192
9.8511
902 I 813604
733870808
30.0333
9.6620
957 i 915849
876467493
30.9354
9.8546
9031 815409
736314327
30.0500
9.6656
958
917764
879217912
30.9516
9.8580
904
817216
738763264
30.0666
9.6692
959
919681
881974079
30.9677
9.8614
905
819025
741217625
30.0832
9.6727
960
921600
884736000
30.9839
9.8648
906
820836
743677416
30.0998
9.6763
961
923521
887503681
31.0000
9.8683
907
822649
746142643
30.1164
9.6799
962
925444
890277128
31.0161
9.8717
908
824464
748613312
30.1330
9.6834
963
927369
893056347
31.0322
9.8751
909
826281
751089429
30.1496
9.6870
964
929296
895841344
31.0483
9.8785
910
828100
753571000
30.1662
9.6905
965
931225
898632125
31.0644
9.8819
911
829921
756058031
30.1828
9.6941
966
933156
901428696
31.0805
9.8854
912
831744
758550528
30.1993
9.6976
967
935089
904231063
31.0966
9.8888
913
833569
761048497
30.2159
9.7012
968
937024
907039232
31.1127
9.8922
914
835396
763551944
30.2324
9.7047
969
938961
909853209
31.1288
9.8956
915
837225
766060875
30.2490
9.7082
970
940900
912673000
31.1448
9.8990
916
839056
768575296
30.2655
9.7118
971
942841
915498611
31.1609
9.9024
917
840889
771095213
30.2820
9.7153
972
944784
918330048
31.1769
9.9058
918
842724
773620632
30.2985
9.7188
973
946729
921167317
31.1929
9.9092
919
844561
776151559
30.3150
9.7224
974
948676
924010424
31.2090
9.9126
920
846400
778688000
30.3315
9.7259
975
950625
926859375
31.2250
9.9160
921
848241
781229961
30.3480
9.7294
976
952576
929714176
31.2410
9.9194
922
850084
783777448
30.3645
9.7329
977
954529
932574833
31.2570
9 9227
923
851929 786330467
30.3809
9.7364
978
956484
935441352
31.2730
9.9261
924
853776 ! 788889024
30.3974
9.7400
979
958441
938313739
31.2890
9.9295
96
MATHEMATICAL TABLES.
No.
980
981
982
983
984
Square.
Cube.
Sq.
Root.
Cube.
Root.
No.
Square.
Cube.
Sq.
Root.
Cub6
Root,
960400
962361
964324
966289
968256
941192000
944076141
946966168
949862087
952763904
31.3050
31.3209
31.3369
31.3528
31.3688
9.9329
9.9363
9.9396
9.9430
9.9464
1035
1036
1037
1038
1039
1071225
1073296
1075369
1077444
1079521
1108717875
1111934656
1115157653
1118386872
1121622319
32.1714
32.1870
32.2025
32.2180
32.2335
10.1153
10.1186
10.1218
10.1251
10.1283
985
986
987
988
989
970225
972196
974169
976144
978121
955671625
958585256
961504803
964430272
967361669
31.3847
31.4006
31.4166
31.4325
31.4484
9.9497
9.9531
9.9565
9.9598
9.9632
1040
1041
1042
1043
1044
1081600
1083681
1085764
1087849
1089936
1124864000
1128111921
1131366088
1134626507
1137893184
32.2490
32.2645
32.2800
32.2955
32.3110
10.1316
10.1348
10.1381
10.1413
10.1446
990
991
992
993
994
980100
982081
984064
986049
988036
970299000
973242271
976191488
979146657
982107784
31.4643
31.4802
31.4960
31.5119
31.5278
9.9666
9.9699
9.9733
9.9766
9.9800
1045
1046
1047
1048
1049
1092025
1094116
1096209
1098304
1100401
1141166125
1144445336
1147730823
1151022592
1154320649
32.3265
32.3419
32.3574
32.3728
32.3883
10.1478
10.1510
10.1543
10.1575
10.1607
995
996
997
998
999
990025
992016
994009
996004
998001
985074875
988047936
991026973
994011992
997002999
31.5436
31.5595
31.5753
31.5911
31.6070
9.9833
9.9866
9.9900
9 9933
9.9967
1050
1051
1052
1053
1054
1102500
1104601
1106704
1108809
1110916
1157625000
1160935651
1164252608
1167575877
1170905464
32.4037
32.4191
32.4345
32.4500
32.4654
10.1640
10.1672
10.1704
10.1736
10.1769.
1000
3001
1002
1003
1004
1000000
1002001
1004004
1006009
1008016
1000000000
1003003001
1006012008
1009027027
1012048064
31.6228
31.6386
31.6544
31.6702
31.6860
10.0000
10.0033
10.0067
10.0100
10.0133
1055
1056
1057
1058
1059
1113025
1115136
1117249
1119364
1121481
1174241375
1177583616
1180932193
1184287112
1187648379
32.4808
32.4962
32.5115
32.5269
32.5423
10.1801
10.1833
10.1865
10.1897
10.1929
1005
1006
1007
1008
1009
1010025
1012036
1014049
1016064
1018081
1015075125
1018108216
1021147343
1024192512
1027243729
31.7017
31.7175
31.7333
31.7490
31.7648
10.0166
10.0200
10.0233
10.0266
10.0299
1060
1061
1062
1063
1064
1123600
1125721
1127844
1129969
1132096
1191016000
1194389981
1197770328
1201157047
1204550144
32.5576
32.5730
32.5883
32.6036
32.6190
10 1961
10.1993
10.2025
10.2057
10.2089
1010
1011
1012
1013
1014
1020100
1022121
1024144
1026169
1028196
1030301000
1033364331
1036433728
1039509197
1042590744
31.7805
31.7962
31.8119
31.8277
31.8434
10.0332
10.0365
10.0398
10.0431
10.0465
1065
1066
1067
1068
1069
1134225
1136356
1138489
1140624
1142761
1207949625
1211355496
1214767763
1218186432
1221611509
32.6343
32.6497
32.6650
32.6803
32.6956
10.2121
10.2153
10.2185
10.2217
10.2249
1015
1016
1017
1018
1019
1030225
1032256
1034289
1036324
1038361
1045678375
1048772096
1051871913
1054977832
1058089859
31.8591
31.8748
31.8904
31.9061
31.9218
10.0498
10.0531
10.0563
10.0596
10.0629
1070
1071
1072
1073
1074
1144900
1147041
1149184
1151329
1153476
1225043000
1228480911
1231925248
1235376017
1238833224
32.7109
32.7261
32.7414
32.7567
32.7719
10.2281
10.2313
10.2345
10.2376
10.2408
1020
1021
1022
1023
1024
1040400
1042441
1044484
1046529
1048576
1061208000
1064332261
1067462648
1070599167
1073741824
31.9374
31.9531
31.9687
31.9844
32.0000
10.0662
10.0695
10.0728
10.0761
10.0794
1075
1076
1077
1078
1079
1155625
1157776
1159929
1162084
1164241
1242296875
1245766976
1249243533
1252726552
1256216039
32.7872
32.8024
32.8177
32.8329
32.8481
10.2440
10.2472
10.2503
10.2535
10.2567
1025
1026
1027
1028
1029
1050625
1052676
1054729
1056784
1058841
1076890625
1080045576
1083206683
1086373952
1089547389
32.0156
32.0312
32.0468
32.0624
32.0780
10.0826
10.0859
10.0892
10.0925
10.0957
1080
1081
1082
1083
1084
1166400
1168561
1170724
1172889
1176056
1259712000
1263214441
1266723368
1270238787
1273760704
32.8634
32.8786
32.8938
32.9090
32.9242
10.2599
10.2630
10.2662
10.2693
10.2725
1030
1031
1032
1033
1034
1060900
1062961
1065024
1067089
1069156
1092727000
1095912791
1099104768
1102302937
1105507304
32.0936
32.1092
32.1248
32.1403
32.1559
10.0990
10.1023
10.1055
10.1088
10.1121
1085
1086
1087
1088
1089
1177225
1179396
1181569
1183744
1185921
1277289125
1280824056
1284365503
1287913472
1291467969
32.9393
32.9545
32.9697
32.9848
33.0000
10.2757
10.2788
10.2820
10.2851
10.2883
SQUARES, CUBES, SQUARE AKD CUBE ROOTS. 9?
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
1090
1188100
1295029000
33.0151
10.2914
1145
1311025
1501123625
33.8378
10.4617
1091
1190281
1298596571
33.0303
10.2946
1146
1313316
1505060136
33.8526
10.4647
1092
1192464
1302170688
33.0454
10.2977
1147
1315609
1509003523
33.8674
10.4678
1093
1194649
1°;05751357
33.0606
10.3009
1148
1317904
1512953792
33.8821
10.4708
1094
1196836
1309338584
33.0757
10.3040
1149
1320201
1516910949
33.8969
10.4739
1095
1199025
1312932375
33.0908
10.3071
1150
1322500
1520875000
33.9116
10.4769
1096
1201216
1316532736
33.1059
10.3103
1151
1324801
1524845951
33.9264
10.4799
1097
1203409
1320139673
33.1210
10.3134
1152
1327104
1528823808
33.9411
10.4830
1098
1205604
1323753192
33.1361
10.3165
1153
1329409
1532808577
33.9559
10.4860
1099
1207801
1327373299
33.1512
10.3197
1154
1331716
1536800264
33.9706
10.4890
1100
1210000
1331000000
33.1662
10.3228
1155
1334025
1540798875
33.9853
10.4921
1101
1212201
1334633301
33.1813
10.3259
1156
1336336
1544804416
34.0000
10.4951
1103
1214404
1338273208
33.1964
10.3290
1157
1338649
1548816893
34.0147
10.4981
1103
1216609
1341919727
33.2114
10.3322
1158
1340964
1552836312
34.0294
10.5011
1104
1218816
1345572864
33.2264
10.3353
1159
1343281
1556862879
34.0441
10.5042
1105
1221025
1349232625
33.2415
10.3384
1160
1345600
1560896000
34.0588
10.5072
1106
1223236
1352899016
33.2566
10.3415
1161
1347921
1564936281
34.0735
10.5102
1107
1225449
1356572043
33.2716
10.3447
1162
1350244
1568983528
34.0881
10.5132
1108
1227G64
1360251712
33.2866
10.3478
1163
1352569
1573037747
34.1028
10.5162
1109
1229881
1363938029
33.3017
10.3509
1164
1354896
1577098944
34.1174
10.5192
1110
1232100
136?631000'33.3167
10.3540
1165
1357225
1581167125
34.1321
10 5223
1111
1234321
1371330631 33.3317
10.3571
1166
1359556
1585242296
34.1467
10.5253
1112
1236544
137503692833.3467
10.3602
1167
1361889
1589324463
34.1614
10.5283
1113
1238769
137874989733.3617
10.3633
1168
1364224
1593413632
34.1760
10.5313
111*
1240996
1382469544
33.3766
10.3664
1169
1366561
1597509809
34.1906
10.5343
1115
1243225
1386195875
33.3916
10 3695
1170
1368900
1601613000
34.2053
10.5373
1116
1245456
138992889633.4066
10.3726
1171
1371241
1605723211
34.2199
10.5403
1117
1247689
139366861338.4215
10.3757
1172
1373584
1609840448
34.2345
10.5433
1118
1249924
139741503233.4365
10.3788
1173
1375929
1613964717
34.2491
10.5463
1119
1252161
1401 168159|33. 4515
10.3819
1174
1378276
1618096024
34.2637
10.5493
1120
1254400
140492800033.4664
10.3850
1175
1380625
1622234375
34.2783
10.5523
11<J1
1256641
1408694561 33.4813
10.3881
1176
1382976
1626379776
34.2929
10.5553
1122
1258884
141246784833.4963
10.3912
1177
1385329
1630532233
34.3074
10.5583
1123
1261129
141624786733.5112
10.3943
1178
1387684
1634691752
34.3220
10.5612
1124
1263376
142003462433.5261
10.3973
1179
1390041
1638858339
34.3366
10.5642
1125
1265625
1423828125 33 5410
10.4004
1180
1392400
1643032000
34.3511
10.5672
1126
1267876
142762837633.5559
10.4035
1181
1394761
1647212741
34.3657
10.5702
1127
1270129
143143538333.5708
10.4066
1182
1397124
1651400568
34.3802
10.5732
1128
1272384
143524915233.5857
10.4097
1183
1399489
1655595487
34.3948
10 5762
1129
1274641
1439069689 33.6006
10.4127
1184
1401856
1659797504
34.4093 10.5791
|
1130
1276900
144289700033.6155
10.4158
1185
1404225
1664006625
34.4238
10.5821
1131
1279161
1446731091
33.6303
10.4189
1186
1406596
1668222856
34.4384
10.5851
1132
1281424
1450571968
33.6452
10.4219
1187
1408969
1672446203
34.4529
10.5881
1133
1283689
1454419637
33.6601
10.4250
1188
1411344
1676676672
34.4674
10.5910
1134
1285956
1458274104
33.0749
10.4281
1189
1413721
1680914269
34.4819
10.5940
1135
1288225
1462135375
33.6898
10.4311
1190
1416100
1685159000
34.4964
10.5970
1136
1290496
1466003456
33.7046
10.4342
1191
1418481
1689410871
34.5109
10.6000
1137
1292769
1469S78353
33.7174
10.4373
1192
1420864
1693669888
34.5254
10.6029
1138
1295044
1473760072
33.7342
10.4404
1193
1423249
1697936057
34.5398
10.6059
1139
1297321
1477648619
33.7491
10.4434
1194
1425636
1702209384
34.5543
10.6088
1140
1299600
1481544000
33.7639
10.4464
1195
1428025
1706489875
34.5688
10.6118
1141
1301881
1485446221
33.7787
10.4495
1196
1430416
1710777536
34.5832
10.6148
1142
1304164
1489355288
33.7935
10.4525
1197
1432809
1715072373
34.5977
10 6177
1143
1306449
1493271207
33.8083
10.4556
1198
1435204
1719374392
34.6121
10.6207
1144
1308736
1497198984
33.8231
10.4586
1199
1437601
1723683599
34.6266
10.6230
98
MATHEMATICAL TABLES.
No.
1200
1201
1202
1203
1304
Square.
Cube.
Sq.
Boot,
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
1440000
1442401
1444804
1447209
1449616
172800000034.6410
1732323601 34.6554
173665440834.6699
174099242734.6843
174533766434.6987
10.6266
10.6295
10.6325
10.6354
10.6384
1255
1256
1257
1258
1259
1575025
1577536
1580049
1582564
1585081
1976656375 35.4260
1981385216 35.4401
1986121593 35.4542
199086551235.4683
199561697935.4824
10.7865
10.7894
10.7922
10.7951
10.7980
1205
1206
1207
1208
1209
1452025
1454436
1456849
1459264
1461681
1749690125
1754049816
1758416743
1762790912
1767172329
34.7131
34.7275
34.7419
34.7563
34.7707
10.6413
10.6443
10.6472
10.6501
10.6530
1260
1261
1262
1263
1264
1587600
il 590 121
1592644
1595169
1597696
2000376000 35.4965
2005142581 35.5106
200991672835.5246
201469844735.5387
2019487744,35.5528
10.8008
10.8037
10.8065
10.8094
10.8122
1210
1211
1212
1213
1214
1464100
1466521
1468944
1471369
1473796
1771561000
1775956931
1780360128
1784770597
1789188344
34.7851
34.7994
34.8138
34.8281
34.8425
10.6560
10.8590
10.6619
10.6648
10.6678
1265
1266
1267
1268
1269
1600225
1602756
1605289
1607824
1610361
2024284625
2029089096
2033901163
2038720832
2043548109
35.5668
35.5809
35.5949
35.6090
35.6230
10.8151
10.8179
10 8208
10.8236
10.8265
1215
1216
1217
1218
1219
1476225
1478656
1481089
1483524
1485961
1793613375
1798045696
1802485313
1806932232
1811386459
34.8569
34.8712
34.8855
34.8999
34.9142
10.6707
10.6736
10.6765
10.6795
10.6824
1270
1271
1272
1273
1274
1612900
1615441
1617984
1620529
1623076
2048383000
2053225511
2058075648
2062933417
2067798824
35.6371
35.6511
35.6651
35.6791
35.6931
10.8293
10.8322
10.8350
10 8378
10.8407
1220
1221
1222
1223
1224
1488400
1490841
1493284
1495729
1498176
1815848000
1820316861
1824793048
1829276567
1833767424
34.9285
34.9428
34.9571
34.9714
34.9857
10.6853
10.6882
10.6911
10.6940
10.6970
1275
1276
1277
1278
1279
1625625
1628176
1630729
1633284
1635841
2072671875
2077552576
2082440933
2087336952
2092240639
35.7071
35.7211
35.7351
35.7491
35.7631
10.8435
10.8463
10.8492
10.8520
10.8548
1225
1226
12:27
1228
1229
1500625
1503076
15055-*)
1507984
1510441
1838265625
1842771176
1847284083
1851804352
1856331989
35.0000
35.0143
35.0286
35.0428
35.0571
10.6999
10.7028
10.7057
10.7086
10.7115
1280
1281
1282
1283
1284
1638400
1640961
1643524
1646089
1648656
2097152000
2102071041
2106997768
2111932187
2116874304
35.7771
35.7911
35.8050
35.8190
35.8329
10.8577
10.8605
10.8633
10.8661
10.8690
1230
1231
1232
1233
1234
1512900
1515361
1517824
1520289
1522756
1860867000
1865409391
1869959168
1874516337
1879080904
35.0714
35.0856
35.0999
35.1141
35.1283
10.7144
10.7173
10.7202
10.7231
10.7260
1285
1286
1287
1288
1289
1651225
1653796
1656369
1658944
1661521
2121824125
2126781656
2131746903
2136719872
2141700569
35.8469
35.8608
35.8748
35.8887
35.9026
10.8718
10.8746
10.8774
10.8802
10.8831
1235
1236
1237
1238
1239
1525225
1527696
1530169
1532644
1535121
1883652875
1888232256
1892819053
1897413272
1902014919
35.1426
35.1568
35.1710
35.1852
35.1994
10.7289
10.7318
10.7347
10.7376
10.7405
1290
1291
1292
1293
1294
1664100
1666681
1669264
1671849
1674436
2146689000
2151685171
2156689088
2161700757
2166720184
35.9166
35.9305
35.9444
35.9583
35.9722
10.8859
10.8887
10.8915
10.8948
10.8971
1240
1241
1242
1243
1244
1537600
1540081
1542564
1545049
1547536
1906624000
1911240521
1915864488
1920495907
1925134784
35.2136
35.2278
35.2420
35.2562
35.2704
10.7434
10.7463
10.7491
10.7520
10.7549
1295
1296
1297
1298
1299
1677025
1679616
1682209
1684804
1687401
2171747375
2176782336
2181825073
2186875592
2191933899
35.9861
36.0000
36.0139
36.0278
36.0416
10.8999
10.9027
10.9055
10.9083
10.9111
1245
1246
1247
1248
1249
1550025
1552516
1555009
1557504
1560001
1929781125
1934434936
1939096223
1943764992
19^8441249
35.2846
35.2987
35.3129
35.3270
35.3412
10.7578
10.7607
10.7635
10.7664
10.7693
1300
1301
1302
1303
1304
1690000
1692601
1695204
1697809
1700416
2197000000
2202073901
2207155608
2212245127
2217342464
36.0555
36.0694
36.0832
36.0971
36.1109
10.9139
10.9167
10.9195
10.9223
10.9251
1250
1261
1252
1253
1254
1562500
1565001
1567504
1570009
1572516
19531 25000
1957816251
1962515008
1967221277
1971935064
35.3553
35.3695
35.3836
35.3977
35.4119
10.7722
10.7750
10.7779
10 7808
10.7837
1305
1306
1307
1308
1309
1703025
1705636
1708249
17108G4J
1713481!
2222447625
2227560616
2232681443
2237810112
2242946629
36.1248
36.1386
36.1525
36.1663
36.1801
10.9279
10.9307
10.9335
10.9363
10.939
SQUARES, CUBES, SQUARE AKD CUBE ROOTS,
1)9
STo.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
310
311
312
313
314
17161002248091000
1718721 2253243231
1721344 2258403328
1723969 2263571297
1726596 2268747144
36.1939
36. 2077
36.2215
36.2353
36.2491
10.9418
10.9446
10.9474
10.9502
10.9530
1365
1366
1367
1368
1369
1863225
1865956
1868689
1871424
1874161
2543302125
2548895896
2554497863
2560108032
2565726409
36.9459
36.9594
36.9730
36.9865
37.0000
11.0929
11.0956
11.0983
11.1010
11.1037
315
31(5
317
318
319
1729225 2273930875
1731856 2279122496
17344892284322013
1737124 2289529432
1739761 2294744759
36.2629
36.2767
36.2905
36.3043
36.3180
10.9557
10.9585
10.9613
10.9640
10.9668
1370
1371
1372
1373
1374
1876900
1879641
1882384
1885129
1887876
2571353000
2576987811
2582630848
2588282117
2593941624
37.0135
37.0270
37.0405
37.0540
37.0675
11.1064
11.1091
11.1118
11.1145
11.1172
3-20
321
322
823
324
1742400
1745041
1747684
1750329
1752976
2299968000
2305199161
2310438248
2315685267
2320940224
36.3318
36.3456
36.3593
36.3731
36.3868
10.9696
10.9724
10.9752
10.9779
10.9807
1375
1376
1377
1378
1379
1890625
1893376
1896129
1898884
1901641
2599609375
2605285376
2610969633
2616662152
2622362939
37.0810
37 0945
37.1080
37.1214
37.1349
11.1199
11.1226
11.1253
11.1280
11.1307
325
326
38?
32S
329
1755625
1758276
1760929
1763584
1766241
2326203125
2331473976
2336752783
2342039552
2347334289
36.4005
36.4143
36.4280
36.4417
36.4555
10.9834
10.9862
10.9890
10.9917
10.9945
1380
1381
1382
1383
1384
1904400
1907161
1909924
1912689
1915456
2628072000
2633789341
2639514968
2645248887
2650991104
37.1484
37.1618
37.1753
37.1887
37.2021
11.1334
1 1 . 1361
11.1387
11.1414
11.1441
330
331
332
333
33 1
1768900
1771561
1774224
1776889
1779556
2352637000
2357947691
2363266368
2368593037
2373927704
36.4692
36.4829
36.4966
36.5103
36.5240
10.9972
11.0000
11.0028
11.0055
11.0083
1385
1386
1387
13S8
1389
1918225
1920996
1923769
1926544
1929321
2656741625
2662500456
2668267603
2674043072
2679826869
37.2156
37.2290
37.2424
37.2559
37.2693
11.1468
11.1495
11.1522
11.1548
11.1575
335
836
337
388
339
1782225
1784896
1787569
1790244
1792921
2379270375
2384621056
2389979753
231)5346472
2400721219
36.5377
36.5513
36.5650
36.5787
36.5923
11.0110
11.0138
11.0165
11 0193
11.0220
1390
1391
1392
1393
1394
1932100
1934881
1937664
1940449
1943236
2685619000
2691419471
2697228288
2703045457
2708870984
37.2827
37.2961
37.3095
37.3229
37.3363
11.1602
11.1629
11.1655
11.1682
11.1709
340
341
312
343
344
1795600
1798281
1800964
1803649
1806336
2406104000
2411494821
2416893688
2422300607
2427715584
36.6060
36.6197
36.6333
36.6469
36.6606
11.0247
11.0275
11.0302
11.0330
11.0357
1395
1396
1397
1398
1399
1946025
1948816
1951609
1954404
1957201
2714704875
2720547136
2726397773
2732256792
2738124199
37.3497
37.3631
37.3765
37.3898
37.4032
11.1736
11.1762
11.1789
11.1816
11.1842
345
340
347
34H
349
1809025
1811716
1814409
1817104
1819801
2433138625
2438569736
2444008923
2449456192
2454911549
36.6742
36.6879
36.7015
36.7151
36.7287
11.0384
11.0412
11.0439
11.0466
11.0494
1400
1401
1402
1403
1404
1960000
1962801
1965604
1968409
1971216
2744000000
2749884201
2755776808
2761677827
2767587264
37.4166
37.4299
37.4433
37.4566
37.4700
11.1869
11.1896
11.192?
11.1949
11.1975
350
351
352
353
354
1822500
1825201
1827904
1830609
1833316
2460375000
2465846551
2471326208
2476813977
2482309864
36.7423
36.7560
36.7696
36.7831
36.7967
11.0521
11.0548
11.0575
11.0603
11.0630
1405
1406
1407
1408
1409
1974025
1976836
1979649
1982464
1985281
2773505125
2779431416
2785366143
2791309312
2797260929
37.4833
37.4967
37.5100
37.5233
37.5366
11.2002
11.2028
11.2055
11.2082
11.2108
355
356
357
35S
359
1836025
1838736
1841449
1844164
1846881
2487813875
2493326016
2498846293
2504374712
2509911279
36.8103
36.8239
36.8375
36.8511
36.8646
11.0657
11.0684
11.0712
11.0739
11.0766
1410
1411
1412
1413
1414
1988100
1990921
1993744
1996569
1999396
2803221000
2809189531
2815166528
2821151997
2827145944
37.5500
37.5633
37.5766
87.5899
37.6032
11.2135
11.2161
11.2188
11.2214
11.2240
360
361
362
:!t)3
364
1849600
1852321
1855044
1857769
1860496
2515456000
2521008881
2526569928
2532139147
2537716544
36.8782
36.8917
36.9053
36.9188
36.9324
11.0793
11.0820
11.0847
11.0875
11.0902
1415
1416
1417
1418
1419
2002225
2005056
2007889
2010724
2013561
2833148375
2839159296
2845178713
2851206632
2857243059
37.6165
37.6298
37.6431
37.6563
37.6696
11.2267
11 2293
11.2320
11.2346
11.2373
100
MATHEMATICAL TABLES.
No.
1420
1421
1422
1423
1424
Square,
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
2016400
2019241
2022084
2024929
2027776
286328800037.6829
2869341461 37.6962
287540344837.7094
288147396737.7227
2887553024 37.7359
11.2399
11.2425
11.2452
11.2478
11.2505
1475
1476
1477
1478
1479
2175625
2178576
2181529
2184484
2187441
3209046875
3215578176
3222118333
3228667352
3235225239
38.4057
38.4187
38.4318
38.4448
38.4578
11.3832
11.3858
11.3883
11.3909
11.3935
1425
1426
1427
1428
1429
2030625
2033476
2036329
2039184
2042041
289364062537.7492
289973677637.7624
290584148337.7757
291195475237.7889
291807658937.8021
11.2531
11.2557
11.2583
11.2610
11.2636
1480
1481
1482
1483
1484
2190400
2193361
2196324
2199289
2202256
3241792000
3248367641
3254952168
3261545587
3268147904
38.4708
38.4838
38.4968
38.5097
38.5227
11.3960
11.3986
11.4012
11.4037
11.4063
1430
1431
1432
1433
1434
2044900
2047761
2050624
2053489
2056356
292420700037.8153
2930345991 37.8286
2936493568 37.8418
294264973737.8550
2948814504 ' 37. 8682
11.2662
11.2689
11.2715
11.2741
11.2767
1485
1.486
1487
1488
1489
2205225
2208196
2211169
2214144
2217121
3274759125
3281379256
3288008303
3294646272
3301293169
38.5357
38.5487
38.5616
38.5746
38.5876
11.4089
11.4114
11.4140
11.4165
11.4191
1435
1436
1437
1438
1439
2059225
2062096
2064969
2067844
2070721
295498787537.8814
2961169856 37.8946
296736045337.9078
297355967237.9210
2979767519 37.9342
11.2793
11.2820
11.2846
11.2872
11.2898
1490
1491
1492
1493
1494
2220100
2223081
22.20064
2229049
2232036
3307949000
3314613771
3321287488
3327970157
3334661784
38.6005
38.6135
38.6264
38.6394
38.6523
11.4216
11.4242
11.4268
11.4203
11.4319
1440
1441
1442
1443
1444
2073600
2076481
2079364
2082249
2085136
298598400037.9473
299220912137.9605
299844288837.9737
300468530737.9868
301093638438.0000
11.2924
11.2950
11.2977
11.3003
11.3029
1495
1496
1497
1498
1499
2235025
2238016
2241009
2244004
2247001
3341362375
3348071936
3354790473
3361517992
3368254499
38.6652
38.6782
38.6911
38.7040
38.7169
11.4344
11.4370
1 1 . 4395
11.4421
11.4446
1445
1446
1447
1448
1449
2088025
2090916
2093809
2096704
2099601
3017196125
3023464536
3029741623
3036027392
3042321849
38.0132
38.0263
38.0395
38.0526
38.0657
11.3055
11.3081
11.3107
11.3133
11.3159
1500 2250000
1501 2253001
1502 ; 2256004
1503 2259009
1504 2262016
3375000000
3381754501
3388518008
3395290527
3402072064
38.7298
38.7427
38.7556
38.7685
38.7814
11.4471
11.4497
11.4522
11.4548
11.4573
1450
1451
1452
1453
1454
2102500
2105401
2108304
2111209
2114116
3048625000
3054936851
3061257408
3067586677
3073924664
38.0789
38.0920
38.1051
38.1182
38.1314
11.3185
11.3211
11.3237
11.3263
11.3289
1505
1506
1507
1508
1509
2265025
2268036
2271049
2274064
2277081
3408862625
3415662216
3422470843
3429288512
3436115229
38.7943
38.8072
38.8201
38.8330
38.8458
11.4598
11.4624
11.4649
11.4675
11.4700
1455
1456
1457
1458
,1459
2117025
2119936
2122849
2125764
2128681
3080271375
3086626816
3092990993
3099363912
3105745579
38.1445
38.1576
38.1707
38.1838
38.1969
11.3315
11.3341
11.3367
11.3393
11.3419
1510
1511
1512
1513
1514
2280100
2283121
2286144
2289169
2292196
3442951000
3449795831
3456649728
3463512697
3470384744
38.8587
38.8716
38 8844
38.8973
38.9102
11.4725
11.4751
11.4776
11.4801
11.4820
1460
1461
1462
1463
1464
2131600
2134521
2137444
2140369
2143296
3112136000
3118535181
3124943128
3131359847
3137785344
38.2099
38.2230
38.2361
38.2492
38.2623
11.3445
11.3471
1 1 . 3496
11.3522
11.3548
1515
1516
1517
1518
1519
2295225
2298256
2301289
2304324
2307361
3477265875
3484156096
3491055413
3407963832
3504881359
38.9230
38.9358
38.9487
38.9615
38.97'44
11.485-3
11.4877
11.4902
11.4927
11.4953
1465
1466
1467
1468
1469
2146225
2149156
2152089
2155024
2157961
3144219625
3150662696
3157114563
3163575232
3170044709
38.2753
38.2884
38.3014
38.3145
38.3275
11.3574
11.3600
11.3626
11.3652
11.3677
1520
1521
1522
1523
1524
2310400
2313441
2316484
2319529
2322576
3511808000
3518743761
3525688648
3532642667
3539605824
38.9872
39.0000
39.0128
39.0256
39.0384
11.4978
11.5003
11.5028
11.5054
11.5079
1470
1471
1472
1473
1474
2160900
2163841
2166784
2169729
2172676
3176523000
3183010111
3189506048
3196010817
3202524424
38.3406
38.3536
38.3667
38 . 3797
88.3SWT
11.3703
11.3729
11.3755
11.3780
11.3806
1525
1526
1527
1528
1529
2325625
2328676
2331729
2334784
2337841
3546578125
3553559576
3560550183
3567549952
3574558£89
39.0512
39.0640
39.0768
39.0896
39.1024
11.5104
11.5129
11.5154
11.5179
11.5204
SQUARES, CUBES, SQUARE AND CUBE R<JOTS. 101
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
No.
Square.
Cube.
Sq.
Root.
Cube
Root.
1530
1531
1532
1533
1534
2340900
2343961
2347024
2350089
2353156
3581577000
3588604291
3595640768
3602080437
3609741304
39.1152
39.1280
39.1408
39.1535
39.1663
11.5230
11.5255
11.5280
11.5305
11.5330
1565
1566
1567
1568
1569
2449225 3833037125
2452356,3840389496
24554893847751263
2458624 3855123432
2461761 3862503009
39.5601
39.5727
39.5854
39.5980
39.6106
11.6102
11.6126
11.6151
11.6176
11.6200
1535
1536
1537
1538
1539
2356225
2359296
2362369
2365444
2368521
3616805375
3623878656
3630961153
3638052872
3645153819
39.1791
39.1918
39.2046
39.2173
39.2301
11.5355
11.5380
11.5405
11.5430
11.5455
1570
1571
1572
1573
1574
2464900 3869893000
2468041 3877292411
24711 84 3»84701 248
24743293892119517
24774763899547224
39.6232
39.6358
39.6485
39.6611
39.6737
11.6225
11.6250
11.6274
11.6299
11.6324
1540
1541
1542
1543
1544
2371600
2374681
2377764
2380849
2383936
3652264000
3659383421
3666512088
3673650007
2680797184
39.2428
39.2556
39.2683
39.2810
39.2938
11.5480
11.5505
11.5530
11.5555
11.5580
1575
1576
1577
1578
1579
2480625 3906984375
2483770 3914430976
2486929 3921887033
2490084 :^9^9352552
249324 lj 3936827539
39.6863
39.6989
39.7115
39.7240
39.7366
11.6348
11.6373
11.6398
11.6422
11.0447
1545
1546
1547
1548
1519
2387025
2390116
2393209
2396304
2399401
3687953625
3695119336
3702294323
3709478592
3716672149
39.3065
39.3192
39.3319
39.3446
39.3573
11.5605
11.5630
11.5655
11.5680
11.5705
1580
1581
1582
1583
1584
2496400 3944312000
2499561 3651805941
2502724 3959309368
2505889 3960822287
25090563974344704
39.7492
39.7618
39.7744
39.7869
39.7995
11.6471
11.6496
11.6520
11.6545
11,6570
1550
1551
1552
1553
1554
2402500
2405601
2408704
2411809
2414916
3723875000
3731087151
3738308608
3745539377
3752779464
39.3700
39.3827
39.3954
39.4081
39.4208
11.5729
11.5754
11.5779
11.5804
11.5829
1585
1586
1587
1588
1589
2512225 3981876625
2515396 3989418056
2518569 3996969003
2521744 4004529472
2524921 4012099469
39.8121 11.6594
39.824611.6619
39.837211.6643
39.849711.6608
39.862311.6692
1555
1556
1557
1558
1559
2418025
2421136
2424249
2427364
2430481
3760028875
3767287616
3774555693
3781833112
3789119879
39.4335 11.5854
39.4462 11.5879
39.4588 11.5903
39.4715 11.5928
39.4842 11.5953
1590
1591
1592
1593
1594
2528100 4019679000
2531281 4027268071
2534464 4034866688
2537649 4042474857
2540836 4050092584
39.874811.6717
39.887311.6741
39.8999 11.6765
39.9124 11.6790
39.924911.6814
1560
1561
1562
1563
1564
2433600
2436721
2439844
2442969
2446096
3796416000
3803721481
3811036328
3818360547
3825694144
39 496811.5978
39.5095111.6003
39.5221 11.6027
39. 5348' 11. 6052
39.547411.6077
1595
1590
1597
1598
1599
2544025 4057719875
2547216 4065356736
2550409 4073003173
2553604 4080659192
2556801 4088324799
39.937511.7839
39.950011.6863
39. 9625 jll. 6888
39.9750 11.6912
39.9875 11.6936
1600
2560000
4096000000
40.000011.6961
SQUARES AND CUBES OF
No.
Square.
Cube.
No.
Square.
Cube.
No.
Square.
Cube.
.1
.01
.001
.01
.0001
.000 001
.001
.00 00 01
.000 000 001
.2
.04
.008
.02
.0001
.000 008
.002
.00 00 04
.000 000 008
3
.09
.027
.03
.0009
.000 027
.003
.00 00 09
.000 000 027
4
.16
.064
.04
.0016
.000 064
.004
.00 00 16
.000 000 064
.5
.25
.125
.05
.0025
.000 125
.005
•00 00 25
.000 000 125
.6
.36
.216
.06
.0036
.000 216
.006
.00 00 36
.000 000 216
.7
.49
.343
.07
.0049
.000 343
007
.00 00 49
.OOO.OOQ 343
.8
.64
.512
.08
.0064
.000 512
.008
; .00 00 64
.000' 000 512
.9
.81
.729
.09
.0081
.000 729
009
>• .00 0'.) 81
.000 COu 729
1.0
1.00
1.000
.10
.0100
.001 000
.010
.^X) 01 00
.000 '001 000
1.2
1.44
1.728
.12
.0144
.001,728
.012
,00 M *4
.ooa qo1. 728
Note that the square has twice as many xlecirf al places «; an'i
times as many decimal places, as the root.
102
MATHEMATICAL TABLES.
FIFTH ROOTS AND FIFTH
(Abridged from TRAUTWINE.)
II
Power.
II
Power.
II
Power.
ji
Power.
t, .
II
Power.
.10
.000010
3.7
693.440
9.8
90392
21.8
4923597
40
102400000
.15
.000075
3.8
792.352
9.9
95099
22.0
5153632
41
115856201
.20
.000320
3.9
902.242
10.0
100000
22.2
5392186
42
130691232
.25
.000977
4.0
1024.00
10 2
110408
22.4
5639493
43
147008443
.30
.002430
4.1
1158.56
10.4
121665
22.6
5895793
44
164916224
.35
.005252
4.2
1306.91
10.6
133823
22.8
6161327
45
184528125
.40
.010240
4.3
1470.08
10.8
146933
23 0
6436343
46
205962976
.45
.018453
4.4
1649.16
11.0
161051
23^2
6721093
47
229345007
.50
.031250
4.5
1845.28
11.2
176234
23.4
7015834
48
254803968
.55
.050328
4.6
2059.63
11.4
192541
23.6
7320825
49
282475249
.60
.077760
4.7
2293.45
11.6
210084
23.8
7636332
50
312500000
.65
.116029
4.8
2548.04
11.8
228776
24.0
7962624
51
345025251
.70
168070
4.9
2824.75
12.0
248832
24.2
8299976
52
380204032
.75
,237305
5.0
3125.00
12.2
270271
24.4
8648666
53
418195498
.80
.327680
5.1
3450.25
12.4
293163
24.6
9008978
54
459165024
.85
.443705
5.2
3802 04
12. G
317580
24.8
9381200
55
503284375
.90
.590490
5.3
4181.95
12.8
343597
25.0
9765625
56
550731776
.95
.773781
5.4
4591.65
13.0
371293
25.2
10162550
57
601692057
1.00
1.00000
5.5
5032.84
13.2
400746
25.4
10572278
58
656356768
1.05
1.27628
5.6
5507.32
13.4
432040
25.6
10995116
59
714924299
1.10
1.61051
5.7
6016.92
13 6
465259
25.8
11431377
60
777600000
1.15
2.01135
5.8
6563.57
13.8
500490
26.0
11881376
61
844596301
1.20
2.48832
5.9
7149.24
14.0
537824
26.2
12345437
62
916132832
1.25
3.05176
6.0
7776.00
34.2
577353
26.4
1282388G
63
992436543
1.30
3.71293
6.1
8445.96
14.4
619174
26.6
13317055
64
1073741824
1.35
4.48403
6.2
9161.33
'A 6
663383
26.8
13825281
65
1160290625
1.40
5.37824
6.3
9924.37
14.8
710082
27.0
14348907
66
1252332576
1.45
6.40973
6 4
10737
15.0
759375
27.2
14888280
67
1350125107
1.50
7.59375
6.5
11603
15 2
811368
27.4
15443752
68
1453933568
1.55
8.94661
6.6
12523
15.4
866171
27.6
16015681
69
1564031349
1.60
10.4858
6.7
13501
15. G
923896
27.8
16604430
70
168070000C
1.65
12.2298
6.8
14539
15.8
984658
28.0
17210368
71
1804229351
1.70
14.1986
6.9
15G40
16.0
1048576
28.2
17633868
72
1934917632
1.75
16.4131
7.0
16807
16.2
1115771
28.4
18475309
73
2073071593
1.80
18.8957
7.1
18042
16.4
118G367
28.6
19135075
74
2219006G24
1.85
21.6700
7.2
19349
16.6
1260493
28.8
19813557
75
2373046875
1.90
24.7610
7.3
20731
16 8
1338278
29.0
20511149
76
2535525376
1.95
28.1951
7.4
22190
17.0
1419857
29.2
21228253
77
2706784157
2.00
32.0000
7.5
23730
17.2
1505366
29.4
21965275
78
2887174368
2.05
36.2051
7.6
25355
17.4
1594947
29.6
22722628
79
3077056399
2.10
40.8410
7.7
27'068
17.6
1688742
29 8
£3500728
80
3276800000
2.15
45.9401
7.8
28872
17.8
17'86899
30.0
24300000
81
3486784401
2 20
51.5363
7.9
30771
18.0
1889568
30.5
26393634
82
3707398432
2.25
57.6650
8.0
32768
18.2
199G903
31.0
28G29151
83
3939040643
2.30
64.3634
8.1
34868
18.4
2109061
31.5
31013642
84
4182119424
2.35
71.6703
8.2
37074
18.6
2226203
32.0
33554432
85
4437053125
2.40
79.6262
8.3
39390
18.8
2348493
32.5
36259082
86
4704270176
2.45
88.2735
8.4
41821
19.0
2476099
33.0
39135393
87
4984209207
2.50
97.6562
8.5
44371
19.2
2609193
33.5
42191410
88
5277319168
2.55
107.820
8.6
47043
19.4
2747949
34.0
45435424
89
5584059449
2.60
118.814
8.7
49842
19.6
2892547
31.5
4S875980
90
5904900000
2.70
143.489
8.8
52773
19.8
3043168
35.0
52521875
91
6240321451
2.80
172.104
8.9
55841
20.0
3200000
35.5
56382167
92
6590815232
2.90
205.111
9.0
59049
20.2
3363232
36.0
G0466176
93
6956883693
3 00
243.000
9.1
62403
20.4
3533059
36 5
64783487
94
7339040224
3,10
286.292
9.2,
05998-
20.6
3709677
37.0
69343957
95
7737809375
3 f*0
335.544
a. 3
'58509
20.8
3893289
37.5
74157715
96
815372G976
3^30
391.354
9.4
V3390
21.0
4084101
38.0
79235168
97
8587340257
ft. 40
454 . §54
,9,5,
77378
.21.2
4282322
38.5
84587005
98
90392079G8
3..M) 525 £19
96-1 81237- ,
21.4
4488166
39.0
90224199
99
950990U499
Sieol OC4.'662
9";7j 8,5873--'
21.6
4701850
39.5
96158012
CIRCUMFERENCES AND AREAS OF CIRCLES, 103
CIRCUMFERENCES AND AREAS OF CIRCLES.
Piam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
1
3.1416
0.7854
65
204.20
3318.31
129
405.27
13069.81
2
6.2832
3.1416
66
207.34
3421 . 19
130
408.41
13273.23
3
9.4248
7.0686
67
210.49
3525.65
131
411.55
13478.22
4
12.5664
12.5664
68
213.63
3631.68
132
414.69
13684 78
5
15.7080
19.635
69
216.77
3739.28
133
417.83
13892.91
6
18.850
28 274
70
219.91
3848.45
134
420.97
14102.61
7
21.991
38.485
71
223.05
3959.19
135
424.12
14313.88
8
25.133
50.266
72
226.19
4071.50
136
427.26
14526.72
9
28.274
63.617
73
229.34
4185.39
137
430.40
14741.14
ilO
31.416
78.540
74
232.48
4300 84
138
433.54
14957.12
11
34.558
95.033
75
235.62
4417.86
139
436.68
15174.68
12
37.699
113.10
76
238.76
4536.46
140
439.82
15393.80
13
40.841
132.73
77
241.90
4656.63
141
442.96
15614.50
14
43.982
153.94
78
245.04
4778.36
142
446.11
15836.77
15
47.124
176.71
79
248.19
4901.67
143
449.25
16060.61
16
50.265
201.06
80
251.33
5026.55
144
452.39
16286.02
17
53.407
226.98
81
254.47
5153.00
145
455.53
16513.00
18
56.549
254.47
82
257.61
5281.02
146
458.67
16741.55
10
59.690
283.53
83
260.75
5410.61
147
461.81
16971.67
20
62.832
314.16
84
263.89
5541.77
148
464.96
17203.36
21
65.973
346.36
85
267.04
5674 50
149
468.10
17436.62
22
69.115
380.13
86
270.18
5808.80
150
471.24
17671.46
23
72.257
415.48
8?'
273.32
5944.68
151
474.38
17907 86
24
75.398
452.39
88
276.46
6082.12
152
477.52
18145.84
25
78.540
490.87
89
279.60
6221.14
153
480.66
18385.39
26
81.681
530.93
90
282.74
6361.73.
154
483.81
18626.50
27
84.823
572.56
91
285.88
6503.88'
155
486.95
18869.19
28
87.965
615.75
92
289.03
6647.61
156
490.09
19113.45
29
91.106
660.52
93
292.17
6792.91
157
493.23
19359.28
30
94.248
706.86
94
295.31
6939.78
158
496.37
19606.68
31
97.389
754 . 77
95
298.45
7088.22
159
499.51
19855.65
32
100.53
804.25
96
301.59
7238.23
160
502.65
20106.19
33
103.67
855.30
97
304.73
7389.81
161
505.80
20358.31
34
106.81
907.92
98
307.88
7542.96
162
508.94
20611.99
35
109.96
962.11
99
311.02
7697.69
163
512.08
20867.24
36
113.10
1017.88
100
314.16
7853.98
164
515.22
21124.07
37
116.24
1075.21
101
317.30
8011.85
165
518.36
21382.46
38
119.38
1134.11
102
320.44
8171.28
166
521.50
21642.43
39
122.52
1194.59
103
323.58
8332.29
167
524.65
21903 97
40
125.66
1256.64
104
326.73
8494.87
168
527.79
22167 08
41
128.81
1320 25
105
329 87
8659.01
169
530.93
22431.76
42
131.95
1385.44
106
333.01
8824.73
170
534.07
22698.01
43
135.09
1452.20
107
336.15
8992.02
171
537.21
22965.83
44
138.23
'1520.53
108
339.29
9160.88
172
540.35
23235.22
45
141.37
1590.43
109
342.43
9331.32
173
543.50
23506.18
46
144.51
1661.90
110
345.58
9503.32
174
546.64
23778.71
47
147.65
1734.94
111
348.72
9676.89
175
549.78
24052.82
48
150.80
1809.56
112
351.86
9852.03
176
552.92
24328.49
49
153 94
1885.74
113
355.00
10028.75
177
556.06
24605.74
50
157.08
1963.50
114
358.1.4
10207.03
178
559.20
24884.56
51
160.22
2042.82
115
361.28
10386 89
179
562.35
25164.94
53
163.36
2123.72
116
364.42
10568.32
180
565.49
25446.90
53
166.50
2206.18
117
367.57
10751.32
181
568.63
25730.43
54
169.65
2290 22
118
370.71
10935.88
182
571.77
26015.53
55
172.79
2375.83
119
373.85
11122.02
183
574.91
26302.20
56
175.93
2463 01
120
376.99
11309.73
184
578.05
26590.44
57
179.07
2551.76
121
380.13
11499.01
185
581.19
26880.25
58
182.21
2642.08
122
383.27
11689.87
186
584.34
27171.63
59
185.35
2733.97
123
386.42
11882.29
187
587.48
27464.59
60
188.50
2827.43
124
389.56
12076.28
188
590.62
27759.11
61
191.64
2922.47
125
392.70
12271.85
189
593.76
28055.21
6-4
194.78
3019.07
126
395.84
12468.98
190
596.90
28352 87
63
197.92
3117.25
127
398.98
12(567.69
191
600.04
28652.11
64
201.06
3216.99
128
402.12
12867.96
192
603.19
28952.92
104
MATHEMATICAL TABLES.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
193
606.33
29255.30
260
816.81
53092.92
327
1027.30
83981.84
194
609.47
29559.25
261
819.96
53502.11
328
1030.44
84496.28
195
612.61
29864.77
262
823.10
53912.87
329
1033.58
85012.28
196
615.75
30171.86
263
826.24
54325.21
330
1036.73
85529.86
197
618.89
30480.52
264
829.38
54739.11
331
1039.87
86049.01
198
622.04
30790.75
265
832.52
55154.59
332
1043.01
86569.73
199
625.18
31102.55
266
835.66
55571.63
333
1046.15
87092.02
200
628.32
31415.93
267
838.81
55990.25
334
1049.29
87615.88
201
631.46
31730.87
268
841 . 95
56410.44
335
1052.43
88141.31
202
634.60
32047.39
269
845.09
56832.20
336
1055.58
88668.31
203
637.74
32365.47
270
848.23
57255.53
337
1058.72
89196.88
204
640.88
32685.13
271
851.37
57680.43
338
1061.86
89^27.03
205
644.03
33006.36
272
854.51
58106.90
339
1065.00
90258.74
206
647.17
33329.16
273
£57.65
58534.94
340
1068.14
90792.03
207
650.31
33653.53
274
860.80
58964.55
341
1071.28
91326.88
208
653.45
33979.47
275
863.94
59S95.74
342
1074.42
91863.31
209
656.59
34306.98
276
867.08
59828.49
343
1077.57
92401 . 31
210
659.73
34G36.06
277
870.22
60262.82
344
1080.71
92940.88
211
662.88
34966.71
278
873.36
60698.71
345
1083.85
93482.02
212
066.02
35298.94
279
876.50
61136.18
346
1086.99
94024.73
213
669.16
35632.73
280
879.65
61575.22
347
1090.13
94569.01
214
672.30
35968.09
281
882.79
62015.82
348
1093.27
95114.86
215
675.44
36305.03
282
885.93
62458.00
349
1096.42
95662.28
216
678.58
36643.54
283
889.07
62901.75
350
1099.56
96211.28
217
681.73
36983.61
284
892.21
63347.07
351
1102.70
96761.84
218
684.87
37325.26
285
895.35
63793.97
352
1105.84
97313.97
219
688.01
37668.48
286
898.50
64242.43
353
1108.98
97867.68
220
691.15
38013.27
287
901.64
64692.46
354
1112.12
98422.96
221
694.29
38359.63
288
904.78
65144.07
355
1115.27
98979.80
222
697.43
88707.56
289
907.92
65597.24
356
1118.41
99538.22
223
700.58
39057.07
290
911.06
66051.99
357
1121.55
100098.21
224
703.72
39408.14
291
914.20
66508.30
358
1124.69
100659.77
225
706.86
39760.78
292
917.35
66966.19
359
1127.83
101222.90
226
710.00
40115.00
293
920.49
67425.65
360
1130.97
101787.60
227
713.14
40470.78
294
923.63
67886.68
361
1134.11
102353.87
228
716.28
40828.14
295
926.77
68349.28
362
1137.26
102921.72
229
719.42
41187.07
296
929.91
68813.45
363
1140.40
103491.13
230
722.57
41547.56
297
933.05
69279.19
364
1143.54
104062.12
231
725.71
41909.63
298
936.19
69746.50
365
1146.68
104634.67
232
728.85
42273.27
299
939.34
70215.38
306
1149.82
105208.80
233
731.99
42638.48
300
942.48
70685.83
367
1152.96
105784.49
234
735.13
43005.26
301
945.62
71157.86
368
1156.11
106361.76
235
738.27
43373.61
3J33
948.76
71631.45
369
1159.25
106940.60
236
741.42
43743.54
303
951.90
72106.62
370
1162.39
107521.01
237
744.56
44115.03
304
955.04
72583.36
371
1165.53
108102.99
238
747.70
44488.09
305
958.19
73061.66
372
1168.67
108686.54
239
750.84
44862.73
306
961.33
73541.54
373
1171.81
109271.66
240
753.98
45238.93
307
964.47
74022.99
374
1174.96
109858.35
241
757.12
45616.71
308
967.61
74506.01
375
1178.10
110446.62
242
760.27
45996.06
309
970.75
74990.60
376
1181.24
111036.45
243
763.41
46376.98
310
973.89
75476.76
377
1184.38
111627.86
244
766.55
46759.47
311
977.04
75964.50
378
1187.52
112220.83
245
769.69
47143.52
312
980.18
76453.80
379
1190.66
112815.38
246
772.83
47529.16
313
983.32
76944.67
380
1193.81
113411.49
247
775.97
47916.36
314
986.46
77437.12
381
1196.95
114009.18
248
779.11
48305.13
315
989.60
77931.13
382
1200.09
114608.44
249
782.26
'48695.47
316
992.74
784-26.72
383
1203.23
115209.27
250
785.40
49087.39
317
995.88
78923.88
384
1206.37
115811.67
251
788.54
49480.87
318
999.03
79422.60
385
1209.51
116415.64
252
791.68
49875.92
319
1002.17
79922.90
386
1212.65
117021.18
253
794.82
50272.55
320
1005.31
80424.7?
387
1215.80
117628.30
254
797.96
50670.75
321
1008.45
80928.21
388
1218.94
118236.98
255
801.11
51070.52
322
1011.59
81433 22
389
1222.08
118847.24
256
804.25
51471.85
323
1014.73
81939.80
390
1225.22
119459.06
257
807.39
51874.76
324
1017.88
82447.96
391
1228.36
120072.46
258
810.53
52279.24
325
1021.02
82957.68
392
1231.50
120687.42
259
813.67
52685.29
326
1024.16
83468.98
393
1234.65
121303.96
CIRCUMFERENCES AND AREAS OF CIRCLES.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
394
1237.79
121922.07
461
1448.27
166913.60
528
1658.76
218956.44
395
1240.93
122541.75
462
1451.42
167638.53
529
1661.90
219786.61
396
1244.07
123163.00
463
1454.56
168365.02
530
1665.04
220618.34
397
1247.21
123785.82
464
1457.70
169093.08
531
1668.19
221451.65
398
1250.35
124410.21
465
1460.84
169822.72
532
1671.33
222286.53
399
1253.50
125036.17
466
1463.98
170553.92
533
1674.47
223122.98
400
1256.64
125663.71
467
1467.12
171286.70
534
1677.61
223961.00
401
1259.78
126292.81
468
1470.27
172021.05
535
1680.75
224800.59
402
1262.92
126923.48
469
1473.41
172756.97
536
1683.89
225641.75
403
1266.06
127555.73
470
1476.55
173494.45
537
1687.04
226484.48
404
1269.20
128189.55
471
1479.69
174233.51
538
1690.18
227328.79
405
1272.35
128824.93
472
1482.83
174974.14
539
1693.32
228174.66
406
1275.49
129461.89
473
1485.97
175716.35
540
1696.46
229022.10
407
1278.63
130100.42
474
1489.11
176460.12
541
1699.60
229871.12
408
1281.77
130740.52
475
1492.26
177205.46
542
1702.74
230721.71
409
1284.91
131382.19
476
1495.40
177952.37
543
1705.88
231573.86
410
1288.05
132025.43
477
1498.54
178700.86
544
1709.03
232427.59
411
1291.19
132670.24
478
1501.68
179450.91
545
1712.17
233282.89
412
1294.34
133316.63
479
1504.82
180202.54
546
1715.31
234139.76
413
1297.48
133964.58
480
1507.96
180955.74
547
1718.45
234998720
414
1300.62
134614.10
481
1511.11
181710.50
548
1721.59
235858.21
415
1303.76
135265.20
482
1514.25
182466.84
549
1724.73
236719.79
416
1306.90
135917.86
483
1517.39
183224.75
550
1727.88
237582.94
417
1310.04
136572.10
484
1520.53
183984.23
551
1731.02
238447.67
418
1313.19
137227.91
485
1523.67
184745.28
552
1734.16
239313.96
419
1316.33
137885.29
486
1526.81
185507 90
553
1737.30
240181.83
420
1319.47
138544.24
487
1529.96
186272.10
554
1740.44
241051.26
421
1322.61
139204.76
488
1533.10
187037.86
555
1743.58
241922.27
422
1325.75
139866.85
489
1536.241 187805.19
556
1746.73
242794.85
423
1328.89
140530.51
490
1539.38
188574.10
557
1749.87
243668.99
424
1332.04
141195.74
491
1542.52
189344.57
558
1753.01
244544.71
425
1335.18
141862 54
492
1545.66
190116.62
559
1756.15
245422.00
426
1338.32
142530.92
493
1548.81
190890.24
560
1759.29
246300.86
427
1341.46
143200.86
494
1551.95
191665.43
561
1762.43
247181.30
428
1344.60
143872.38
495
1555 09
192442.18
562
1765.58
248063.30
429
1347.74
144545.46
496
1558.23
193220.51
563
1768.72
248946.87
430
1350.88
145220.12
497
1561.37
194000.41
564
1771.86
249832.01
431
1354.03
145896.35
498
1564.51
194781.89
565
1775.00
250718 73
432
1357.17
146574.15
499
1567.65
195564.93
566
1778.14
251607.01
433
1360.31
147253.52
500
1570.80
196349.54
567
1781.28
252496.87
434
1363.45
147934.46
501
1573.94
197135.72
568
1784.42
253388.30
435
1366.59
148616.97
502
1577.08
197923.48
569
1787.57
254281.29
436
1369.73
149301.05
503
1580.22
198712.80
570
1790.71
355175.86
437
1372.88
149986.70
504
1583.36
199503.70
571
1793.85
256072.00
438
1376.02
150673.93
505
1586 50
200296.17
572
1796.99
256969.71
439
1379.16
151362.72
506
1589.65
201090.20
573
1800.13
257868.99
440
1382.30
152053.08
507
1592.79
201885.81
574
1803.27
258769.85
441
1385.44
152745.02
508
1595.93
202682.99
575
1806.42
259672.27
442
1388.58
153438.53
509
1599.07
203481.74
576
1809.56
260576.26
443
1391.73
154133.60
510
1602.21
204282.06
577
1812.70
261481.83
444
1394.87
154830.25
511
1605.35
205083.95
578
1815 84
262388.90
445
1398.01
155528.47
512
1608.50
205887.42
579
1818.98
263297.67
446
1401.15
156228.26
513
1611.64
206692.45
580
1822.12
264207.94
447
1404.29
156929.62
514
1614.78
207499.05
581
1825.27
265119.79
448
1407.43
157632.55
515
1617.92
208307.23
582
1828.41
266033.21
449
1410.58
158337,06
516
1621.06
209116.97
583
1831.55
266948.20
450
1413.72
159043.13
517
1624.20
209928.29
584
1834.69
267864.76
451
1416.86
159750.77
518
1627.34
210741.18
585
1837.83
268782.89
452
1420.00
160459.99
519
1630.49
211555.63
586
1840.97
269702.59
453
1423.14
161170.77
520
1633.63
212371.66
587
1844.11
270623.86
454
1426.28
161883.13
521
1636.77
213189.26
588
1847.26
271546.70
455
1429.42
162597.05
522
1639.91
214008.43
589
1850.40
272471.12
456
1432.57
163312.55
523
1643.05
214829.17
590
1853.54
273397.10
457
1435.71
164029.62
524
1646.19
215651.49
591
1856.68
274324.60
458
1438.85
164748.26
525
1649.34
216475.37
592
1859.82
275253.78
459
1441.99
165468.47
526
1652.48
217300.82
593
1862.96
276184.48
460
1445.13
166190.25
527
1655.62
_218127.85
594
1866.11
277116.75
106
MATHEMATICAL TABLES.
Diarn.
Circum.
Area.
Diam-
Circum.
Area.
Diana- JCircum.
Area.
595
1869.25
278050.58
663
2082.88
345236.69
731 ! 2296.50
419686.15
596
1872.39
278985.99
664
2086.02
346278.91
732 2299.65
420835.19
597
1875.53
279922.97
665
2089.16
347322.70
733
2302.79
421985.79
598
1878.67
280861.52
666
2092.30
348368.07
734
2305.93
423137.97
599
1881.81
281801 65
667
2095.44
349415.00
735
2309.07
424291.72
600
1884.96
282743.34
668
2098.58
350463.51
736
2312.211 425447.04
601
1888.10
283686.60
669
2101.73
351513.59
737
2315.35
426603.94
602
1891.24
284631.44
670
2104.87
352565.24
738
2318.50
427762.40
603
1894.38
285577.84
671
2108.01
353618.45
739
2321.64
428922.43
604
1897.52
286525.82
672
2111.15
354673 24
740
2324.78
430084.03
605
1900.6(5
287475.36
673
2114.29
355729.60
741
2327.92
431247.21
606
1903.81
288426.48
674
2117.43
356787.54
742
8981.06
432411.95
60?
1906.95
289379.17
675
2120.58
357847.04
743
2334.20
433578.27
608
1910.09
290333.43
676
2123.72
358908.11
744
2337.34
434746.16
609
1913.23
291289.26
677
2126.86
359970.75
745
2340.49
435915.62
610
1916.37
292246.66
678
2130.00
361034.97
746
2343.63
437086.64
611
1919 51
293205.63
679
2133.14
362100.75
747
2346.77
438259.24
612
1922.65
294166.17
680
2136.28
363168.11
748
2349.91
439433.41
613
1925.80
295128.28
681
2139.42
364237.04
749
2353.05
440609 16
614
1928.94
296091.97
682
2142.57
365307.54
750
2356.19
441786.47
615
1932.08
297057.22
683
2145.71
366379.60
751
2359.34
442965.35
616
1935.22
298024.05
684
2148.85
367453.24
752
2362.48
444145.80
617
1938.36
298992.44
685
2151 99
368528.45
753
2365.62
445327.83
618
1941.50
299962.41
686
2155.13
369605.23
754
2368.76
446511.42
619
1944.65
300933.95
687
2158.27
370683.59
755
2371.90
447696.59
620
1947.79
301907.05
688
2161.42
371763.51
756
2375.04
448883.32
6-21
1950.93
302881.73
689
2164.56
372845.00
757
2378.19
450071.63
622
1954.07
303857.98
690
2167.70
373928.07
758
2381.33
451261.51
623
1957.21
304835.80
691
2170.84
375012.70
759
2384.47
452452.96
624
1960.35
305815.20
692
2173.98
376098.91
760
2387.61
453645.98
625
1963.50
306796.16
693
2177.12
377186.68
761
2390.75
454840.57
626
1966.64
307778.69
694
2180.27
378276.03
762
2393.89
456036.73
627
1969.78
308762.79
695
2183.41
379366.95
763
S397.04
457234.46
628
1972.92
309748.47
696
2186.55
380459.44
764
SJ400.18
458433.77
629
1976.06
310735.71
697
2189.69
381553.50
765
2403.32
459634.64
630
1979.20
311724.53
698
2192.83
382649.13
766
2406.46
460837.08
631
1982.35
312714.92
699
2195.97
383746.33
767
2409.60
462041.10
632
1985.49
313706.88
700
2199.11
384845.10
768
2412.74
463246.69
633
1988.63
314700.40
701
2202.26
385945.44
769
2415.88
464453.84
634
1991.77
315695.50
7'02
2205.40
387047.36
770
2419.03
465662.57
635
1994.91
316692.17
703
2208.54
388150.84
771
2422.17
466872.87
636
1998.05
317690.42
704
2211.68
389255.90
772
2425.31
468084.74
637
2001.19
318690.23
705
2214.82
390362.52
773
2428.45
469298.18
638
2004.34
319691.61
706
2217.96
391470.72
774
2431.59
470513.19
639
2007.48
320694.56
707
2221.11
392580.49
775
2434.73
471729.77
640
2010.62
321699.09
708
2224,25
393691.82
776
2437.88
472947.92
641
2013.76
322705.18
709
2227.39
394804.73
777
2441.02
474167.65
642
2016.90
323712.85
710
2230.53
395919.21
778
2444.16
475388.94
643
2020.04
324722.09
711
2233.67
397035.26
779
2447.30
476611.81
644
2023.19
325732.89
712
2236.81
398152.89
780
2450.44
477836.24
645
2026.33
326745.27
713
2239.96
399272.08
781
2453.58
479062.25
646
2029.47
327759.22
714
2243.10
400392.84
782
2456.73
480289.83
647
2032.61
328774.74
715
2246.24
401515.18
788
2459.8?
481518.97
648
2035.75
329791.83
716
2249.38
402639.08
784
2463.01
482749.69
649
2038.89
330810.49
717
2252.52
403764.56
785
2466.15
483981.98
650
2042. 04
331830.72
718
2255.66
404891.60
786
2469.29
485215.84
651
2045.18
332852.53
719
2258.81
406020.22
787
2472.43
486451.28
652
2048.32
333875.90
720
2261.95
407150.41
788
2475.58
487688.28
653
2051.46
334900.85
721
2265.09
408282.17
789
2478.72
488926.85
654
2054.60
335927.36
722
2268.23
409415.50
790
2481.86
490166.99
655
2057.74
336955.45
723
2271.37
410550.40
791
2485.00
491408.71
656
2060.88
337985.10
724
2274.51
411686.87
792
2488.14
492651.99
657
2064.03
339016.33
725
2277.65
412824.91
793
2491.28
493896.85
658
2067.17
340049.13
726
2280.80
413964.52
794
2494.42
495143.28
659
2070.31
341083,50
727
22S3.94
415105.71
795
2497.57
496391.27
660
2073.45
342119.44
728
2287.08
416248.46
796
2500.71
497640.84
661
2076.59
343156.95
729
2290.22
417392.79
797
2503.85
498891.98
662
2079.73
344196.03
730
2293.36
418538.68
798 1 2506.99
500144.69
CIRCUMFERENCES AND AREAS OF CIRCLES. 107
Diam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum. Area.
799
2510.13
501398.97
867
2723.76
590375.16
935
2937.39: 686614.71
800
2513.27
502654.82
868
2726.90
591737.83
936
2940.53
688084.19
801
2516.42
503912.25
869
2730.04
593102.06
937
2943.67
689555.24
802
2519.56
505171.24
870
2733.19
594467.87
938
2946 81
691027.86
803
2522.70
506431.80
871
2736.33
595835.25
939
2949.96
692502.05
804
2525.84
507693.94
872
2739.47
597204.20
940
2953.10
693977.82
805
2528.98
508957.64
873
2742.61
598574.72
941
2956.24
695455.15
806
2532.12
510222.92
874
2745.75
599946.81
942
2959.38
696934.06
807
2535.27
511489.77
875
2748.89
601320.47
943
2962.52
698414.53
808
2538.41
512758.19
876
2752.04
602695.70
944
2965.66
699896.58
809
2541.55
514028.18
877 2755.18
604072.50
945
2968.81
701380.19
810
2544.69
515299.74
878 2758.32
605450.88
946
2971.95
702865.38
811
2547.83
516572.87
879
2761.46
606830.82
947
2975.09
704352.14
812
2550.97
517847.57
880
2764.60
608212.34
948
2978.23
705840.47
813
2554.11
519123 84
881
2767.74
609595.42
949
2981.37
707330.37
814
2557.26
520401.68
882
2770.88
610980.08
950
2984.51
708821.84
815
2560.40
521681.10
883
2774.03
612366.31
951
2987.65
710314.88
816
2563.54
522982.08
884
2777.17
613754.11
952
2990.80
711809.50
817
2566.68
524244.63
885
2780.31
615143.48
953
2993.94
713305.68
818
2569.82
525528.76
886
2783.45
616534.42
954
2997.08
714803.43
819
2572 96
526814.46
887
2786.59
617926.93
955
3000.22
716302.76
820
2576.11
528101.73
888
2789.73
619321.01
956
3003.36
717803.66
821
2579.25
529390.56
889
2792.88
620716.66
957
3006.50
719306.12
822
2582.39
530680.97
890
2796.02
622113.89
958
3009.65
720810.16
823
2585.53
531972.95
891
2799.16
623512.68
959
3012.79
722315.77
824
2588.67
533266.50
892
2802.30
624913.04
960
3015.93
723822.95
825
2591.81
534561.62
893
'2805.44
626314.98
961
3019.07
725331.70
826
2594.96
535858.32
894
2808.58
627718.49
962
3022.21
726842.02
•827
2598.10
537156.58
895
2811.73
629123.56
963
•3025.35
728353.91
828
2601.24
538456.41
896
2814.87
630530.21
964
3028.50
729867.37
829
2604.38
539757.82
897
2818.01
631938.43
965
3031.64
731382.40
830
2607.52
541060.79
898
2821.15
633348.22
966
3034.78
732899.01
831
2610.66
542365.34
899
2824.29
634759.58
967
3037.92
734417.18
832
2613.81
543671.46
900
2827.43
636172.51
968
8041.06
735936.93
833
2616.95
544979.15
901
2830.58
637587.01
969
3044.20
737458.24
834
2620.09
546288.40
902
2833.72
639003.09
970
3047.34
738981.13
835
2623.23
547599.23
903
2836.86
640420.73
971
3050.49
740505.59
836
2626.37
548911.63
904
2840.00
641839.95
972
3053.63
742031.62
837
2629.51
550225.61
905
2843.14
643260.73
973
3056.77
743559.22
838
2632.65
551541.15
906
2846.28-
644683.09
974
3059.91
745088.39
839
2635.80
552858.26
907
2849.42
646107.01
975
3063.05
746619.13
840
2638.94
554176.94
908
2852.57
647532.51
976
3066.19
748151.44
841
2642.08
555497.20
909
2855.71
648959.58
977
3069.34
749685.32
842
2645.22
556819.02
910
2858.85
650388.22
978
3072.48
751220.78
843
2648.36
558142.42
911
2861.99
651818.43
979
3075.62
752757.80
844
2651.50
559467.39
912
2865.13
653250.21
980
3078.76
754296.40
845
2654.65
560793.92
913
2868.27
654683.56
981
3081.90
755836.56
846
2657.79
562122.03
914
2871.42
656118.48
982
3085.04
757378.30
847
2660.93
563451.71
915
2874.56
657554.98
983
3088.19
758921.61
848
2664.07
564782.96
916
2877.70
658993.04
984
3091.33
760466.48
849
2667.21
566115.78
917
2880.84
600432.68
985
3094.47
762012.93
850
2670.35
567450.17
918
2883.98
661873.88
986
3097.61
763560.95
851
2673.50
568786.14
919
2887.12
663316.66
987
3100.75
765110.54
852
2676.64
570123.67
920
2890.27
664761.01
988
3103.89
766661.70
853
2679.78
571462.77
921
2893.41
666206.92
989
3107.04
768214.44
854
2682.92
572803.45
922
2896.55
667654.41
990
3110.18
769768.74
855
2686.06
574145.69
923
2899.69
669103.47
991
3113.32
771324.61
856
2689.20
575489.51
924
2902.83
670554.10
992
3116.46
772882.06
857
2692.34
576834.90
925
2905.97
672006.30
993
3119.60
774441.07
H58
2695.49
578181.85
926
2909.11
673460.08
994
3122.74
776001.66
859
2698.63
579530.38
927
2912.26
674915.42
995
31.25.88
777563.82
860
2701.77
580880.48
928
2915.40
676372.33
996
3129.03
779127.54
861
2704.91
582232.15
929
2918.54
677830.82
997
3132.17
780692.84
862
2708.05
583585.39
930
2921.68
679290.87
998
3135.31
782259.71
863
2711.19
584940.20
931
2924.82
680752.50
999
3138.45
783828.15
864
2714.34
586296.59
932
2927.96
682-215.69
1000
3141.59
785398 16
865
2717.48
587654.54
933
2931.11
683680.46
866
2720 62
589014.07
934
2934.25
685146.80
108
MATHEMATICAL TABLES.
CIRCUMFERENCES AND AREAS OF CIRCLES
Advancing: by Eighths.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
1/64
.04909
.00019
2 %
7.4613
4.4301
6 H
19.242
29.465
1/32
.09818
.00077
7/16
7.6576 '
4.6664
H
19.635
30.680
3/64
.14726
.00173
H
7.8540
4.9087
%
20.028
31.919
1/16
.19635
.00307
9/16
8.0503
5.1572
20.420
33.183
3/33
.29452
.00690
%
8.2467
5.4119
%
20.813
34.472
Ys
.39270
.0122?
11/16
8.4430
5.6727
M
21 206
35.785
5/32
.49087
.01917
n
8.6394
5.9396
%
21.598
37.122
3/16
.58905
.02761
13/16
8.8357
6.2126
7.
21.991
38.485
7/32
.08722
.03758
Vs
9.0321
6.4918
ix
22.384
39.871
15/16
9.2284
6.7771
/4
22.776
41.282
y±
.78540
.04909
ax
23.169
42.718
pa
.88357
.06213
3.
9.4248
7.0686
i^
23.562
44.179
5/16
.98175
.07670
1/16
9.6211
7.3662
%
23.955
45 664
11/33
1.0799
.09281
Hi
9.8175
7.6699
%
24.347
47.173
%
1.1781
.11045
3/16
10.014
7.9798
7X
24.740
48.707
13/32
1.2763
.12962
y*
10.210
8.2958
8.
25.133
50.265
7/16
1.3744
.15033
5/16
10.407
8.6179
/^
25.525
51.849
15/32
1.4726
. 17257
%
10.603
8.9462
f4
25.918
53.456
7/16
10.799
9.2806
%
26.311
55.088
^
1 5708
.19635
H
10.996
9.6211
y*
26.704
56.745
17/32
1.6690
.22166
9/16
11.192
9.9678
%
27.096
58.426
9/16
1.7671
.24850
%
11.388
10.321
M
27.489
60.132
19/32
1.8653
.27688
11/16
11.585
10.680
H
27.882
61.862
%
1.9635
.30680
H
11.781
11.045
9.
28.274
63.617
21/32
2.0617
.33824
13/16
11.977
11.416
/^j
28.667
65.397
11/16
2.1598
.37122
%
12.174
11.793
^4
29.060
67.201
23/32
2.2580
.40574
15/16
12.370
12.177
%
29.452
69.029
4.
12.566
12.566
L£
20.845
70.882
%
2.3562
.44179
1/16
12.763
12.962
%
30.238
72.760
25/32
2.4544
.47937
H
12.959
13.364
3£
30.631
74.662
13/16
2.5525
.51849
3/16
13.155
13.772
/^O
31.023
76.589
27/32
2.6507
.55914
H
13.352
14.186
10.
31.416
78.540
K
2.7489
.60132
5/16
13.548
14.607
H
31.809
80.516
29/32
2.8471
.64504
%
13.744
15.033
$
32.201
82 516
15/16
2.9452
.69029
7/16
13.941
15.466
32.594
84.541
31/32
3.0434
.73708
H
14.137
15.904
i^
32.987
86.590
9/16
14.334
16.349
%
33.379
88.664
I.
3.1416
.7854
%
14.530
16.800
%
33.772
90.703
1/16
3.3379
.8860
11/16
14.726
17.257
%
34.165
92.886
y&
3.5343
.9940
H
14.923
17.721
11
34.558
95.033
3/16
3.7306
1.1075
13/16
15.119
18.190
34.950
97.205
k
3.9270
1.2272
%
15.315
18.665
M
35.343
99.402
5/16
4.1233
1.3530
15/16
15 512
19.147
78
35.736
101.62
%
4.3197
1.4849
5.
15.708
19.635
^
36.128
103.87
7/16
4.5160
1.6230
1/16
15.904
20.129
%
36.521
106.14
H
4.7124
1.7671
H
16.101
20.629
%
36.914
108.43
9/16
4.9087
1.9175
3/16
16.297
21.135
%
37.306
110.75
%
5.1051
2.0739
M
16.493
21.648
12
37.699
113.10
11/16
5.3014
2.2365
5/16
16.690
22.166
/^
38.092
115.47
H
5.4978
2.4053
%
16.886
22.691
M
38.485
117.86
13/16
5.6941
2.5802
7/16
17.082
23.221
a|
38.877
120.28
%
5.8905
2.7612
y%
17.279
23.758
L^
39.270
122.72
15/16
6.0868
2.9483
9/16
17.475
24.301
Kg
39.663
125.19
%
17.671
24.850
%
40.055
127.68
2.
6.2832
3.1416
11/16
17.868
25.406
%
40.448
130.19
1/16
6.4795
3.3410
H
18.064
25.967
13.
40.841
132.73
M
6.6759
3.5466
13-16
18.261
26.535
ix
41.233
135.30
3/16
6.8722
3.7583
%
18.457
27.109
M
41.626
137.89
k
7.0686
3.9761
15-16
18.653
27.688
%
42.019
140.50
5/16
7.2649
4.2000
fi
18.850
28.274
^
42.412
143.14
CIRCUMFERENCES AND AREAS OF CIRCLES. 109
Diam.
Circum .
Area.
Diam.
Circumu
Area.
Diam.
Circum.
Area.
n%
42.804
145.80
21%
68.722
375.83
301/6
94.640
712.76
%
43.197
148.49
22.
69.115
380.13
M
95.033
718.69
%
43.590
151.20
/^
69.508
384.46
%
95.426
724 64
14.
43.982
153.94
ix
69.900
388.82
95.819
730.62
44.375
156.70
%
70.293
393.20
%
96.211
736.62
IX
44.768
159.48
12
70.686
397.61
M
96.604
742.64
az
45.160
162.30
%
71.079
402.04
To
96.997
748.69
i/
45.553
165.13
'M
71.471
406.49
31
97.389
754.77
%
45.946
167.99
%
71.864
410.97
/^
97.782
760.87
SX
46.338
170.87
23
72.257
415.48
J4
98.175
766.99
Yi
46.731
173.78
H
72.649
420.00
%
98.567
773.14
15
47.124
176.71
&
73.042
424.56
/^
98.960
779.31
^
47.517
179.67
3X
73.435
429.13
%
99.353
785.51
£|
47.909 '
182.65
ix:
73.827
433.74
%
99.746
791.73
ax
48.302
185.66
ft/.
74.220
438.36
%
100.138.
797.98
ix
48.695
188.69
M
74.613
443.01
32.
100.531
804.25
%
49.087
191.75
%
75.006
447.69
I/,
100.924
810.54
%
49.480
194.83
24.
75.398
452.39
%
101.316
816.86
%
49.873
197.93
/^
75.791
457.11
%
101.709
823.21
1 i
50.265
201.06
IX:
76.184
461.86
\fa
102.102
829.58
50.658
204.22
a»
76.576
466.64
%
102.494
835.97
ix
51.051
207.39
IX
76.969
471.44
%
102.887
842.39
ty»
51.444
210.60
%
77.362
476.26
%
103.280
848.83
/^
51.836
213.82
%
77.754
481.11
33.
103.673
855.30
5X
52.229
217.08
%
78.147
485.98
YB
104.065
861.79
sx
52.622
220.35
25.
78.540
490.87
104.458
868.31
%
53.014
223.65
78.933
495.79
%
104.851
874.85
17
53.407
226.98 '
24
79.325
500.74
/^
105.243
881.41
/6
53.800
230.33
%
79.718
505.71
%
105.636
888.00
54.192
233.71
Lj£
80.111
510.71
M
106.029
894.62
%
54.585
237.10
?B
80.503
515.72
Ys
106.421
901.26
HJ
54.978
240.53
3X
80.896
520.77
34
106.814
907.92
%
55.371
243.98
%
81.289
525.84
i^
107.207
914.61
%
55.763
247.45
26.
81.681
530.93
/4
107.600
921.32
%
56.156
250.95
i^
82.074
536.05
%
107.992
928.06
18
56.549
254.47
IX
82.467
541.19
ix.
108.385
934.82
/^
56.941
258.02
a2
82.860
546.35
%
108.778
941.61
/4
57.334
261.59
/^3
83.252
551.55
!%
109.170
948.42
%
57.727
265.18
5X.
83.645
556.76
78
109.563
955.25
V&
58.119
268.80
M
84.038
562.00
35.
109.956
962.11
%
58.512
272.45
72
84.430
567.27
^
110.348
969.00
ax
58.905
276.12
27.
84.823
572.56
y±
110.741
975.91
%
59.298
279.81
85.216
577.87
111.134
982.84
19.
59.690
283.53
\A
85.608
583.21
Xsjj
111.527
989.80
ii
60.083
287.27
s/.
86.001
588.57
%
111.919
996. 7'8
60.476
291.04
/"*»
86.394
593.96
M
112.312
1003.8
%
60.868
294.83
%
86.786
599.37
%
112.705
1010.8
v&
61.261
298.65
M
87.179
604.81
36.
113.097
1017.9
%
61.654
302.49
xo
87.572
610.27
^
113.490
1025.0
$4
62.046
306.35
28
87.965
615.75
H
113.883
1032.1
7X
62.439
310.24
88.357
621.26
%
114.275
1039.2
20.
62.832
314.16
IX
88.750
626.80
114.668
1046.3
H
63.225
318.10
a^.
89.143
632.36
%
115.061
1053.5
IX
63.617
322.06
^>
89.535
637.94
M
115.454
1060.7
5s
64.010
326.05
5?
89.928
643.55
%
115.846
1068.0
l^
64.403
330.06
%
90.321
649.18
37
116.239
1075.2
7&
64.795
334.10
7X
90.713
654.84
116.632
1082.5
%
65.188
338.16
29.
91.106
660.52
ix
117.024
1089.8
%
65.581
342.25
^
91.499
666.23
%
117.417
1097.1
21.
65.973
346.36
H
91.892
671.96
ix
117.810
1104.5
^
66.366
350.50
a|
92.284
677.71
%
118.202
1111.8
\A
66.759
354.66
VZ
92.677 1683.49
ax
118.596
1119.2
$»
67.152
358.84
%
93.070 689.30
%
118.988
1126.7
^
67.544
363.05
%
93.462 695.13
38.
119.381
1134.1
7&
67.937
367.28
so
93.855 700.98
^
119.773
1141.0
s %
68.330
371.54
30.
94.248 706.86
|
120.166
1149.1
MATHEMATICAL TABLES.
Diam.
Circum.
Area,
Diam.
Circum.
Area.
Diam.
Circum.
Area
38%
120.559
1156.6
46%
146.477
1707.4
54%
172.395
2365.0
120.951
1164.2
%
146.869
1716.5
55.
172.788
2375.8
%
121.344
1171.7
%
147.262
1725.7
H
173.180
2386.6
M
121.737
1179.3
47
147.655
1734.9
H
173.573
2397.5
/o
122.129
1186.9
/4
148.048
1744.2
%
173.966
2408 3
89
122.522
1194.6
/4
148.440
1753.5
174.358
2419.2
x*6
122.915
1202.3
%
148.833
1762.7
%
174.751
2430.1
%
123.308
1210.0
\&
149.226
1772.1
M
175.144
2441.1
%
123.700
1217.7
%
149.618
1781.4
Vs
175.536
2452.0
$&
124.093
1225.4
M
150.011
1790.8
56
175.929
2463.0
%
124.486
1233.2
xo
150.404
1800.1
*/8 '
176.322
2474.0
%
124.878
1241.0
48
150.796
1809.6
M
176.715
2485.0
%
125.271
1248.8
151.189
1819.0
%
177.107
2496.1
40.
125.664
1256.6
/4
151.582
1828.5
177.500
2507.2
K
126.056
1264.5
J^B
151.975
1837.9
%
177.893
2518.3
H
126.449
1272.4
L«£
152.367
1847.5
<£X
178.285
2529.4
%
126.842
1280.3
%
152.760
1857.0
%
178.678
2540.6
^
127.235
1288.2
3x£
153.153
1866.5
57
179.071
2551.8
%
127.627
1296.2
%
153.545
1876.1
Vs
179.463
2563.0
$4
128.020
1304.2
49
153.938
1885.7
IX
179.856
2574.2
%
128.413
1312.2
3^
154.331
1895.4
%
180.249
2585.4
41.
128.805
1320.3
x4
154.723
1905.0
IX
180.642
2596.7
H
129.198
1328.3
%
155.116
1914.7
%
181.034
2608.0
J4
129.591
1336.4
i^£
155.509
1924.4
34
181.427
2619.4
i
129.983
1344.5
%
155.902
1934.2
7/8
181.820
2630.7
130.376
1352.7
M
156.294
1943.9
58.
182.212
2642.1
ax
130.769
1360.8
7X
156.687
1953.7
182.605
2653.5
M
131.161
1309.0
50.
157.080
1963.5
IX-
182.998
2664.9
%
131.554
1377.2
157.472
1973.3
%
183.390
2676.4
42.
131.947
1385.4
\A
157.865
1983.2
x"l3
183.783
2687.8
!£
132.340
1393.7
%
158.258
1993.1
%
184.176
2699.3
M
132.732
1402.0
L/j
158.650
2003.0
34
184.569
2710.9
%
133.125
1410.3
%
159.043
2012.9
%
184.961
2722.4
IX
133.518
1418.6
M
159.436
2022.8
59.
185.354
2734.0
K^
133.910
1427.0
%
159.829
2032.8
Ys
185.747
2745.6
•M
134.303
1435.4
51
160.221
2042.8
x4
186.139
2757.2
%
134.696
1443.8
H
160.614
2052 .8
a2
186.532
2768.8
43
135.088
1452.2
M
161.007
2062.9
x-4
186.925
2780.5
^
135.481
1460.7
|
161.399
2073.0
%
187.317
2792.2
i
135.874
1469.1
161.792
2083.1
M
187.710
2803.9
%
136.267
1477.6
%
162.185
2093.2
%
188.103
2815.7
136.659
1486.2
94
162.577
2103.3
60.
188.496
2827.4
K/
137.052
1494.7
7X
162.970
2113.5
Ys
188.888
2839.2
%
137.445
1503.3
53.
163.363
2123.7
M
189.281
2851.0
§
137.837
1511.9
163.756
2133.9
%
189.674
2862.9
44.?
138.230
1520.5
14
164.148
2144.2
/^
190.066
2874.8
138.623
1529.2
%
164.541
2154.5
%
190.459
2886.6
IX
139.015
1537.9
jx
164.934
2164. H
M
190.852
2898.6
%
139.408
1546.6
%
165.326
2175.1
/o
191.244
2910.5
IX
139.801
1555.3
ax
165.719
2185.4
61
191.637
2922.5
KX
140 194
1564.0
%
166.112
2195.8
*6
192.030
2934.5
3X
140.586
1572.8
53.
106.504
2206.2
H
192.423
2946.5
7X
140.979
1581.6
166.897
2216.6
%
192.815
2958.5
45.
141.372
1590.4
IX
167.290
2227.0
193.208
2970.6
141.764
1599.3
%
167.683
2237.5
%
193.601
2982.7
IX
142.157
1608.2
x^>
168.075
2248.0
M
193.993
2994.8
KX
142.550
1617.0
RX
168.468
2258.5
%
194.386
3006.9
IX
142.942
1626.0
ax
168.861
2269.1
62
194.779
3019.1
KX
143.335
1634.9
xo
109.253
2279.6
x6
195.171
3031.3
3X
143.728
1643.9
54
169.646
2290.2
y.
195.564
3043.5
%
144.121
1652.9
170.039
2300.8
%
195.957
3055.7
46
144.513
1661.9
IX
170.431
2311.5
/12
196.350
3068.0
144.906
1670.9
a/j
170.824
2322.1
%
196.742
3080.3
IX
145.299
1680.0
IX
171.217
2332.8
a^
197.135
3092.6
az
145.691
1689.1
%
171.609
2343.5
yQ
197.528
3104.9
H
146.084
1698.2
M
172.002
2354.3
63
197.920
3117.2
CIRCUMFERENCES AND AREAS OF CIRCLES. Ill
Diam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
63^
198.313
3129.6
71 %
224.231
4001.1
79%
250.149
4979.5
i%
198.706
3142.0
224.624
4015.2
M
250.542
4995.2
%
199.098
3154.5
%
225.017
4029.2
%
250.935
5010.9
ix
199.491
3166.9
ax
225.409
4043.3
80.
251.327
5026.5
%
199.884
3179.4
%
225.802
4057.4
/^
251.720
5042.3
3X
200.277
3191.9
72 *
226.195
4071.5
/4
252.113
5058.0
%
200.669
3204.4
Y»
226.587
4085.7
^8
252.506
5073.8
64.
201.062
3217.0
(?
226.980
4099.8
1^2
252.898
5089.6
H
201.455
3229.6
%
227.373
4114.0
%
253.291
5105.4
3
201.847
3242.2
ix
227.765
4128.2
ax
253.684
5121.2
%
202.240
3254.8
%
228.158
4142.5
YH
254.076
5137.1
ix
202.633
3267.5
ax
228.551
4156.8
81.
254.469
5153.0
%
203.025
3280.1
7X
228.944
4171.1
^
254.862
5168.9
ax
203.418
3292.8
73.
229.336
4185.4
£!
255.254
5184.9
VB
203.811
3305.6
^
229.729
4199.7
%
255.647
5200.8
65.
204.204
3318.3
230.122
4214.1
^
256.040
5216.8
H
204.596
3331.1
%
230.514
4228.5
%
256.433
5232.8
8
204.989
3343.9
V&
230.907
4242.9
M
256.825
5248.9
%
205.382
3356.7
%
231.300
4257.4
TO
257.218
5264.9
205.774
3369.6
ax
231.692
4271.8
82
257.611
5281.0
%
206.167
3382.4
%
232.085
4286.3
258.003
5297.1
M
206.560
3395.3
74.
232.478
4300.8
£4
258.396
5313.3
%
206.952
3408.2
232.871
4315.4
%
258.789
5329.4
66
207.345
3421.2
/4
233.263
4329.9
1^
259.181
5345.6
YB
207.738
3434.2
9s
233.656
4344.5
%
259.574
5361.8
/4
208.131
3447.2
LX
234.049
4359.2
ax
259.967
5378.1
&x
208.523
3460.2
5^j
234.441
4373.8
%
260.359
5394.3
Via
208.916
3473.2
ax
234.834
4388.5
83
260.752
5410 6
%
209.309
3486.3
%
235.227
4403.1
H
261.145
5426.9
M
209.701
3499.4
75.
235.619
4417.9
xl
261.538
5443.3
%
210.094
3512.5
236.012
4432.6
%
261.930
5459.6
67.
210.487
3525 7
M
236.405
4447.4
%
262.323
5476.0
K
210.879
3538.8
%
236.798
4462.2
%
262.716
5492.4
H
211.272
3552.0
/^
237.190
4477.0
ax^
263.108
5508.8
%
211.665
3565.2
%
237.583
4491.8
xo
263.501
5525.3
212.058
3578.5
M
237.976
4506.7
84
263.894
5541.8
%
212.450
3591.7
/a
238.368
4521.5
/^
264.286
5558.3
M
212.843
3C05.0
76
238.761
4536.5
IX-
264.679
5574.8
%
213.236
3618.3
^6
239.154
4551.4
%
265.072
5591.4
48
213.628
3631.7
/4
239.546
4566.4
IX
265.465
5607.9
M
214.021
3645.0
%
239.939
4581.3
5^
265.857
5624.5
M
214.414
3658.4
Hi
240.332
4596.3
ax
266.250
5641.2
214.806
3671.8
%
240.725
4611.4
TO
266.643
5657.8
/^
215.199
3685.3
M
241.117
4626.4
85
267.035
5674.5
%
215.592
3698.7
%
241.510
4641.5
267.428
5691.2
^4
215.984
3712.2
77.
241.903
4656.6
/4
267.821
5707.9
%
216.377
3725.7
242.295
4671.8
a|
268.213
5724.7
69.
216.770
3739.3
/4
242.688
4686.9
ix
268.606
5741.5
Ml
217.163
3752.8
%
243.081
4702.1
&x
268.999
5758.3
H
217.555
3766.4
Vi>
243.473
4717.3
ax
269.392
5775.1
%
217.948
3780.0
^i
243.866
4732.5
%
269.784
5791.9
H
218.341
3793.7
ax
244.259
4747.8
86.
270.177
5808.8
%
218.733
3807.3
%
244.652
4763.1
270.570
5825.7
M
219.126
3821.0
78
245.044
4778.4
M
270.962
5842.6
%
219.519
3834.7
/^
245.437
4793.7
%
271.355
5859.6
so.
219.911
3848.5
/4
245.830
4809.0
^
271.748
5876.5
H
220.304
3862.2
%
246.222
4824.4
%
272.140
5893.5
220.697
3876.0
i^
246.615
4839.8
ax
272.533
5910.6
%
221.090
3889.8
%
247.008
4855.2
TO
272.926
5927.6
/^
221.482
3903.6
M
247.400
4870.7
87
273.319
5944.7
%
221.875
3917.5
7^
247.793
4886.2
273.711
5961.8
M
222.268
3931.4
79.
.248.186
4901.7
IX
274.104
5978.9
%
222.660
3945.3
248.579
4917.2
%
274.497
5996.0
71.
223.053
3959.2
M
248.971
4932.7
/^
274.889
6013.2
H
223.446
3973.1
%
249.364
4948.3
KX
275.282
6030.4
i
223.838
3987.1
^
249.757
4963.9
M
275.675
6047.6
112
MATHEMATICAL TABLES.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
Diam.
Circum.
Area.
87%
276.067
6064.9
92.
289.027
6647.6
96^
301.986
7257.1
88.
276.460
6082.1
X
289.419
6665.7
y
302.378
7276.0
YB
276.853
6099.4
M
289.812
6683.8
%
302.771
7294.9
1?
277.246
6116.7
%
290.205
6701.9
r£
303.164
7313.8
%
277.638
6134.1
/^
290.597
67^0.1
%
303.556
7332.8
/^3
278.031
6151.4
%
290.990
6738.2
M
303.949
7351.8
%
278.424
6168.8
M
291.383
6756 . 4
%
304.342
7370.8
M
278.816
6186.2
sn
291.775
0774. 7
97
304.734
7389.8
7A
279.209
6203.7
93
292.168
6792.9
H
305.127
7408.9
89.
279.602
6221 . 1
H
292.561
6811.2
M
305.520
7428.0
H
279.994
6238.6
H
292.954
6829.5
%
305.913
7447.1
Y4.
280.387
6256.1
8
293.316
6847.8
iz
306.305
7466.2
g
280.780
6273.7
293.739
6866.1
5^
306.698
7485.3
281.173
6291.2
%
294.132
6884.5
H
307.091
7504 5
%
281.565
6 08.8
M
294.524
6902.9
Vs
307.483
7523.7
M
281.958
6326.4
%
294.917
6921.3
98
307.876
7543.0
%
282.351
6344.1
94.
295.310
6939.8
YB
308.269
7562.2
90,
282.743
6361.7
^
295.702
6958.2
M
308.661
7581.5
x^J
283.136
6379.4
£!
296.095
6976.7
%
309.054
7600.8
^4
283.529
6397.1
%
296.488
6995.3
/^
309.447
7620.1
%
283.921
6414.9
Yi
296.881
7013.8
5X
309.840
7639.5
/^
284.314
6432.6
%
297.273
703^.4
M
310.232
7658.9
%
284.707
6450.4
M
297.666
7051 .0
%
310.625
7678.3
%
285.100
6468.2
*2
298.059
7069.6
99.^
311.018
7697.7
To
285.492
6486.0
95
298.451
7088.2
311.410
7717.1
91
285.885
6503.9
298.844
7106.9
IX
311.803
7736.6
/^
286.278
6521.8
M
299.237
7125.6
3X
312.196
7756.1
M
286.670
6539.7
%
299.629
7144.3
\£
312.588
7775.6
•2
287.063
6557 . 6
\^
300.022
7163.0
%
312.981
?795.2
L£
287.456
6575.5
%
300.415
7181.8
3/£
313.374
7814.8
%
287.848
6593.5
M
300.807
7200.6
%
313.767
7834.4
M
288.241
6611.5
%
301.200
7219.4
100.
314.159
7854.0
I/B
288.634
6629.6
96
301.593
7238.2
DECIMALS OF A FOOT EQUIVALENT TO INCHES
AND FRACTIONS OF AN INCH.
Inches.
0
Ys
H
%
K
YB
H
VB
0
0
.01042
.02083
.03125
.04167
.05208
.06250
.07292
1
.0833
.0938
.1042
.1146
.1250
.1354
.1458
.1563
2
.1667
.1771
.1875
.1979
.2083
.2188
.2292
.2396
3
.2500
.2604
.2708
.2813
.2917
.3021
3125
,3229
4
.3333
.3438
.3542
.3646
.3750
.3854
.3958
.4063
5
.4167
.4271
.4375
.4479
.4583
.4688
.4793
.4896
6
.5000
.5104
.5208
.5313
.5417
.5521
.5625
.5729
7
.5833
.5938
.6042
.6146
.6250
.6354
.6458
.6563
8
.6667
.6771
.6875
.6979
.7083
.7188
.7292
.7396
9
.7500
.7604
.7708
.7813
.7917
.8021
.8125
8229
10
.8333
.8438
.8542
.8646
.8750
.8854
.8958
.9063
11
.9167
.9271
.9375
.9479
.9583
.9688
.9792
.9896
CIRCUMFERENCES OF CIRCLES.
113
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T-.T-iT-i(?4^0<^5COCOrfT}i-riOiOOiO«3«5COJ.-J.-J>QOOOQ00500JOO
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^
— ( O
114
MATHEMATICAL TABLES.
LENGTHS OF CIRCULAR ARCS.
(Degrees being given. Radius of Circle = 1 .)
FORMULA.— Length of arc — - — <OA X radius X number of degrees.
loU
RULE.— Multiply the factor in table for any given number of degrees by
the radius.
EXAMPLE.— Given a curve of a radius of 55 feet and an angle of 78° 20'.
What is the length of same in feet ?
Factor from table for 78° 1.3613568
Factor from table for 20' .0058178
Factor 1.3671746
1.3671746 X 55 = 75.19 feet.
Degrees.
1
.0174533
61
1.0646508
121
2.1118484
1
.0002909
2
.0349066
62
1.0821041
122
2.1293017
2
.0005818
3
.0523599
63
1.0995574
123
2.1467550
3
.0008727
4
.0698132
64
1.1170107
124
2.1642083
4
.0011636
5
.0872665
65
1.1344640
125
2.1816616
5
.0014544
6
.1047198
66
1.1519173
126
2.1991149
6
.0017453
7
.1221730
67
1.1693706
127
2.2165682
7
.0020362
8
.1396263
68
1.1868239
128
2.2340214
8
.0023271
9
.1570796
69
1.2042772
129
2.2514747
9
.0026180
10
.1745329
70
1.2217305
130
2.2689280
10
.0029089
11
.1919862
71
1.2391838
131
2.2863813
11
.0031998
12
.2094395
72
1.2566371
132
2.3038346
12
.0034907
13
.2268928
73
1.2740904
133
2.3212879
13
.0037815
14
.2443461
74
1.2915436
134
2.3387412
14
.0040724
15
.2617994
75
1.3089969
135
2.3561945
15
.0043633
16
.2792527
76
1.3264502
136
2.3736478
16
.0046542
17
.2967060
77
1.3439035
137
2.3911011
17
.0049451
18
.3141593
78
1.3613568
138
2.4085544
18
.0052360
19
.3316126
79
1.3788101
139
2.4260077
19
.0055269
20
.3490659
80
1.3962634
140
2.4434610
20
.0058178
21
.3665191
81
1.4137167
141
2.4609142
21
.0061087
22
.3839724
82
1.4311700
142
2.4783675
22
.0063995
23
.4014257
83
1.4486233
143
2.4958208
23
.0066904
24
.4188790
84
1.4660766
144
2.5132741
24
.0069813
25
.4363323
85
1.4835299
145
2.5307274
25
.0072722
26
.4537856
86
1.5009832
146
2.5481807
26
.0075631
27
.4712389
87
1.5184364
147
2.5656340
27
.0078540
28
.4886922
88
1.5358897
148
2.5830873
28
.0081449
29
.5061455
89
1.5533430
149
2.6005406
29
.0084358
30
.5235988
90
1.5707963
150
2.6179939
30
.0087266
31
.5410521
91
1.5882496
151
2.6354472
31
.0090175
32
.5585054
92
1.6057029
152
2.6529005
32
.0093084
33
.5759587
93
1.6231562
153
2.6703538
33
.0095993
34
.5934119
94
1.6406095
154
2.6878070
34
.0098902
35
.6108652
95
1.6580628
155
2.7052603
35
.0101811
36
.6283185
96
1.6755161
156
2.7227136
36
.0104720
37
.6457718
97
1.6929694
157
2.7401669
37
.0107629
38
.6632251
98
1.7104227
158
2.7576202
38
.0110538
39
.6806784
99
1.7278760
159
2.7750735
39
.0113446
40
.6981317
100
1.7453293
160
2.7925268
40
0116355
41
.7155850
101
1.7627825
161
2.8099801
41
.0119264
42
.7330383
102
1.7802358
162
2.8274334
42
.0122173
43
• .7504916
103
1.7976891
163
2.8448867
43
.0125082
44
.7679449
104
1.8151424
164
2.8623400
44
.0127991
45
.7853982
105
1.8325957
165
2.8797933
45
.0130900
46
.8028515
106
1.8500490
166
2.8972466
46
.0133809
47
.8203047
107
1.8675023
167
2.9146999
47
.0136717
48
.8377580
108
1.8849556
168
2.9321531
48
.0139626
49
.8552113
109
1.9024089
169
2.9496064
49
.0142535
50
.8726646
110
1.9198622
170
2.9670597
50
.0145444
51
.8901179
111
1.9373155
171
2.9845130
51
.0148358
52
.9075712
112
1.9547688
172
3.0019663
52
.0151262
53
.9250245
113
1.9722-221
173
3.0194196
53
.0154171
54
.9424778
114
1.9896753
174
3.0368729
54
.0157080
55
.9599311
115
2.0071286
175
3.0543262
55
.0159989
56
.9773844
116
2.0245819
176
3.0717795
56
.0162897
57
.9948377
117
2 042o:;:.:>
177
3.0892328
57
.0165806
58
1.0122910
118
2.0594885
178
3.1066861
58
.0168715
59
1.0297443
119
2.0769418
179
3.1241394
59
.0171624
60
1.0471976
120
2.0943951
180
3.1415927
60
.0174533
LENGTHS OF CIRCULAR ARCS.
115
LENGTHS OF CIRCULAR ARCS.
(Diameter = 1. Given tlie Chord and Height of the Arc.)
RULE FOR USE OP THE TABLE. — Divide the height by the chord. Find in the
column of heights the number equal to this quotient. Take out the corre-
sponding number from the column of lengths. Multiply this last number
by the length of the given chord; the product will be length of the arc.
If the arc is greater than a semicircle, first find, the diameter from the
formula, Diam. — (square of half chord -*- rise) -f rise; the formula is true
whether the arc exceeds a semicircle or not. Theji find the circumference.
From the diameter subtract the given height of arc, the remainder will be
height of the smaller arc of the circle; find its length according to the rule,
arid subtract it from the circumference.
Hgts.
Lgths.
Hgts.
Lgths.
Hgts.
Lgths.
Hgts.
Lgths.
Hgts.
Lgths.
.001
1.00002
.15
1.05896
.238
1.14480
.326
1.26288
.414
1.40788
.005
1.00007
.152
1.06051
.24
1.14714
.328
1.26588
.416
1.41145
.01
1.00087
.154
1.06209
.242
1.14951
.33
1.26892
.418
1.41503
.015
1.00061
.156
1.06368
.244
1.15189
.332
1.27196
.42
1.41861
.02
1.00107
.158
1.06530
.246
1.15428
.331
1.27502
.422
1.42221
.025
1.00167
.16
1.06693
.248
1.15C70
.336
1.27810
.424
1.42583
.03
1.00240
.162
1.06858
.25
1.15912
.338
1.28118
.426
1.42945
.035
1.00327
.164
1.07025
.252
1.16156
.34
1.28428
.428
1.43309
.04
1.00426
.166
.07194
.254
1.16402
.342
1.28739
.43
1.43673
.045
1.00539
.168
.07365
.256
1.16650
.344
1.29052
.432
.44039
.05
1.00665
.17
.07537
.258
1.16899
.346
1.29366
.434
.44405
.055
1.00805
.172
.07711
.26
1.17150
.348
1.29681
.436
.44773
.06
1.00957
.174
.07888
.262
1.17403
.35
1.29997
.438
.45142
.065
1.01123
.176
.08066
.264
1.17657
.352
1.30315
.44
.45512
.07
1.01302
.178
.08246
.266
1.17912
.354
1.30634
.442
.45883
.075
1.01493
.18
1.08428
.268
1.18169
.356
1.30954
.444
.46255
.08
1.01698
.182
1.08611
.27
1.18429
.358
1.31276
.446
.46628
.085
1.01916
.184
1.08797
.272
1.18689
.36
1.31599
.448
.47002
.09
1.02146
.186
1.08984
.274
1.18951
.362
1.31923
.45
.47377
.095
1.02389
.188
1.09174
.276
1.19214
.364
1.32249
.452
.47753
.10
1.02646
.19
1.09365
.278
1.19479
.366
1.32577
.454
.48131
.102
1.02752
.192
1.09557
.28
1.19746
.368
1.32905
.456
.48509
.104
1.02860
.194
1.09752
.282
1.20014
.37
1.33234
.458
.48889
.106
1.02970
.196
1.09949
.284
1.20284
.372
1.33564
.46
.49269
.108
1.03082
.198
1.10147
.286
1.20555
.374
1.33896
.462
.49651
.11
1.03196
.20
1.10347
.288
1.20827
.376
1.34229
.464
.50033
.112
1.03312
.202
1.10548
.29
1.21102
.378
1.34563
.466
.50416
.114
1.03430
.204
1.10752
.292
1.21377
.38
1.34899
.468
.50800
.116
1.03551
.206
1.10958
.294
1.21654
.382
1.35237
.47
.51185
.118
1.03672
.208
1.11165
.296
1.21933
.384
1.35575
.472
.51571
.12
1.03797
.21
1.11374
.298
1.22213
.386
1.35914
.474
.51958
,122
1.03923
.212
1.11584
.30
1.22495
.388
1.36254
.476
.52346
.124
1.04051
.214
1.11796
.302
1.22778
.39
1.36596
.478
.52736
.126
1.04181
.216
1.12011
.304
1.23063
.392
1.36939
.48
.53126
.128
1.04313
.218
1.12225
.306
1.23349
.394
1.37283
.482
.53518
.13
1.04447
.22
1.12444
.308
1.23636
.396
1.37628
.484
.53910
.132
1.04584
.222
1.12664
.31
1.23926
.398
1.37974
.486
.54302
.134
1.04722
.224
1.12885
.312
1.24216
.40
1.38322
.488
.54696
.136
1.04862
.226
1.13108
.314
1.24507
.402
1.38671
.49
.55091
.138
1.05003
.228
1.13331
.316
1.24801
.404
1.39021
.492
.55487
-14
1.05147
.23
1.13557
.318
1.25095
.406
1.39372
.494
.55854
.142
1.05293
.232
1.13785
.32
1.25391
.408
1.39724
.496
.56282
.144
1.05441
.234
1.14015
,322
1.25689
.41
1.40077
.498
.56681
• 146
1.05591
.236
1.14247
.324
1.25988
.412
1.40432
.50
1.57080
.148
1.05743
116
MATHEMATICAL TABLES.
AREAS OF THE: SEGMENTS OF A
(Diameter = 1; Rise or Height in parts of Diameter being
given.)
RULE FOR USB OF THE TABLE. —Divide the rise or height of the segment by
the diameter. Multiply the area in the table corresponding to the quotient,
thus found by the square ot the diameter.
If the segment exceeds a semicircle its area is area of circle — area of seg
ment whose rise is (diam. of circle — rise of given segment)
Given chord and rise, to find diameter. Diam = (square of half chord •*-
rise) ~\- rise The half chqrd is a mean proportional between the two parts
into which the chord divides the diameter which is perpendicular to it.
Rise
-5-
Diam.
Area,
Rise
Diam
Area
Rise
-5-
Diam.
Area.
Rise
Diam
Area.
Rise
Diam
Area.
.001
.00004
.054
.01646
.107
.04514
.16
.08111
.213
.12235
.002
.00012
.055
.01691
.108
.04576
.161
.08185
.214
.12317
.003
.00022
.056
.01737
.109
.04638
.162
.08258
.215
. 12399
.004
.00034
.057
.01783
.11
.04701
.163
.08332
.216
.12481
.005
.00047
.058
.01830
.111
.04763
.164
.08406
.217
.12563
.006
.00062
.059
.01877
.112
.04826
.165
.08480
.218
.12646
.007
.00078
.06
.01924
.113
.04889
.166
.08554
.219
.12729
.008
.00095
.061
.01972
.114
.04953
.167
.08629
.22
.12811
.009
.00113
.062
.02020
.115
.05016
.168
.08704
.221
.12894
.01
.00133
.063
.02068
.116
.05080
.169
.08779
.222
.12977
.011
.00153
.064
.02117
.117
.05145
.17
.08854
.223
.13060
.012
.00175
.065
.02166
.118
.05209
.171
.08929
.224
.13144
.013
.00197
.066
.02215
.119
.05274
.172
.09004
.225
.13227
.014
.0022
.067
,02265
.12
.05338
.173
.09080
.226
.13311
.015
.00244
.068
.02315
.121
.05404
.174
.09155
.227
.13395
.016
.00268
.069
.02366
.122
.05469
.175
.09231
.228
.13478
.017
.00294
.07
.02417
.123
.05535
.176
.09307
.229
.13562
.018
.0032
.071
.02468
.124
.05600
.177
.09384
.23
.13646
.019
.00347
.072
.02520
.125
.05666
.178
.09460
.231
.13731
.02
.00375
.073
.02571
.126
.05733
.179
.09537
.232
.13815
.021
.00403
.074
.02624
.127
.05799
.18
.09613
.233
.13900
.02-2
.00432
.075
.02676
.128
.05866
.181
.09690
.234
.13984
.023
.00462
.076
.02729
.129
.05933
.182
.09767
.235
.1406S
.024
.00492
.077
.02782
.13
.06000
.183
.09845
.236
.14154
.025
.00523
.078
.02836
.131
.06067
.184
.09922
.237
.14239
.026
.00555
.079
.02889
.132
.06135
.185
.10000
.238
.14324
.027
.00587
.08
.02943
.133
.06203
.186
.10077
.239
.14409
.028
.00619
.081
.02998
.134
.06271
.187
.10155
.24
.14494
.029
.00653
.082
.03053
.135-
.06339
.188
.10233
.241
.14580
.03
.00687
.083
.03108
.136
.06407
.189
.10312
.242
.14666
.031
.00721
.084
.03163
.137
.06476
.19
. 10390
.243
. 14751
.032
.00756
.085
.03219
.138
.06545
.191
.10469
.244
.14837
.033
.00791
.086
.03275
.139
.06614
.192
.10547
.245
.14923
.034
.00827
.087
.03331
.14
.06683
.193
.10626
.246
-.15009
.035
.00864
.088
.03387
.141
.06753
.194
.10705
.247
.15095
,036
.00901
.089
.03444
.142
.06822
.195
.10784
.248
.15182
.037
.00938
.09
.03501
.143
.06892
.196
.10864
.249
. 15268
038
.00976
.091
.03559
.144
.06963
.197
.10943
.25
.15355
.039
.01015
.092
.03616
.145
.07033
.198
.11023
.251
.1,5441
.04
.01054
.093
.03674
.146
.07103
.199
.11102
.252
.15528
.041
.01093
.094
.03732
.147
.07174
.2
.11182
.253
.15615
.042
.01133
.095
.03791
.148
.07245
.201
.11262
.254
.15702
.043
.01173
.096
.03850
.149
.07316
.202
.11343
.255
.15789
.044
.01214
.097
.03909
.15
.07'387
.203
.11423
.256
.15876
.045
.01255
.098
.03968
.151
.07459
.204
.11504
.257
.15964
.046
.01297
.099
.04028
.152
.07531
.205
.11584
.258
.16051
.047
.01339
.1
.04087
.153
.07603
.206
.11665
.259
.16139
.048
.01382
.101
.04148
.154
.07675
.207
.11746
.26
.16226
.049
.01425
.102
.04208
.155
.07747
.208
.11827
.261
.16314
.05
.01468
.103
.04269
.156
.07819
.209
.11908
.262
.16402
.051
.01512
.104
.04330
.157
.07892
.21
.11990
.263
.16490
.052
.01556
.105
.04391
.158
.07965
.211
.12071
.264
.16578
.053
.01601
.106
.04452
.159
.08038
.212
.12153
.265
.16666
AREAS OF THE SEGMENTS OF A CIRCLE.
117
Rise
-5-
Diam
Area.
Rise
-i-
Diam.
Area.
Rise
-r-
Diara.
Area.
Rise
-f-
Diam.
Area
Rise
Diam
Area.
.266
.16755
.313
.21015
.36
.25455
.407
.30024
.454
.34676
.267
.16843
.314
.21108
.361
.25551
.408
.30122
.455
.34776
.268
.16932
.315
.21201
.362
.25647
.409
.30220
.456
.34876
.269
.17020
.316
.21294
.363
.25743
.41
.30319
.457
.34975
.27
.17109
.317
.21387
.364
.25839
.411
.30417
.458
.35075
.271
.17198
.318
.21480
.365
.25936
.412
.30516
.459
.35175
272
.17287
.319
.21573
.366
.26032
.413
.30614
.46
.35274
i273
.17376
.32
.21667
.367
.26128
.414
.30712
.461
.35374
.274
.17465
.321
.21760
.368
.26225
.415
.30811
.462
.35474
.275
.17554
,32~i
.21853
.369
.26321
.416
.30910
.463
.35573
.276
.17644
.323
.21947
.37
.26418
,417
.31008
.4C4
.35673
.277
.17733
.324
.22040
.371
.26514
.418
.31107
.465
.35773
.278
.17823
.325
,22134
.372
.26611
.419
.31205
.466
.35873
.279
.17912
.326
22228
.373
.26708
.42
.31304
.467
.35972
.28
.18002
.327
,22322
.374
.26805
.421
.31403
.468
.36072
.281
.18092
.328
.82415
.375
.26901
.422
.31502
.469
.36172
.282
.18182
.329
.22509
.376
.26998
.423
.31600
.47
.36272
.283
.18272
.33
.22603
.377
.27095
.424
.31699
.471
.36372
.284
.18362
.331
.22697
.378
.27192
.425
.31798
.472
.36471
.285
.18452
.332
.22792
.379
.27289
.426
.31897
.473
.36571
.286
.18542
.333
.28886
.38
.27386
.427
.31996
.474
.36671
.287
.18633
.334
.25J980
.381
.27483
.428
.32095
.475
.36771
.288
.18723
.335
.28074
.382
.27580
.429
.32194
.476
.36871
.289
.18814
.336
.23169
.383
.27678
.43
.32293
.477
.36971
.29
.18905
.337
.23263
.384
.27775
.431
.32392
.478
.37071
.291
.18996
.338
.23358
.385
.27872
.432
.32491
.479
.37171
.292
.19086
.339
.33453
.386
.27969
.433
.32590
.48
.37270
.293
.19177
.34
.513547
.387
.28067
.434
.32689
.481
.37370
.294
.19268
.341
.^8642
.388
.28164
.435
.32788
.482
.37470
.295
.19360
.342
.'23737
.389
.28262
.436
.32837
.483
.37570
.296
.19451
.343
,23832
.39
.28359
.437
.32987
.484
.37670
.297
.19542
.344
,,23927
.391
.28457
.438
.33086
.485
.37770
.298
.19634
.345
.£4022
.392
.28554
.439
.33185
.486
.37870
.299
.19725
.346
.24117
.393
.28652
.44
.33284
.487
.37970
.3
.19817
.347
,24212
.394
.28750
.441
.33384
.488
.38070
.301
.19908
.34S
,24307
.395
.28848
.442
.33483
.489
.38170
.302
.20000
.349
,24403
.396
.28945
.443
.33582
.49
.38270
.303
.20092
.35
,24498
.397
.29043
.444
.33682
.491
.38370
.304
.20184
.351
.24593
.398
.29141
.445
.33781
.492
.38470
.305
.20276
.352
.24689
.399
.29239
.446
.33880
.493
.38570
,306
.20368
,353
.24784
.4
.29337
.447
.33980
.494
.38670
.307
.20460
.854
.24880
.401
.29435
.448
.34079
.495
.38770
,308
.20553
855
.24976
.402
.29533
.449
.34179
.496
.38870
.309
.20845
.356
.25071
.403
.29631
.45
.34278
.497
.38970
.31
.20738
.357
.25167
.404
.29729
.451
.34378
.498
.39070
«11
.20830
.358
.25263
.405
.29827
.452
.34477
.499
.39170
^312
,99^3
.359
.25359
.406
.29926
.453
.34577
.5
.39270
Fof rrttes for finding the area of a segment see Mensuration, page 59.
MATHEMATICAL TABLES.
SPHERES.
(Some errors of 1 in the last figure only. From TRAUTWINE.)
Diam.
Sur-
face.
Vol-
ume.
Diam.
Sur-
face.
Vol-
ume.
Diam.
Sur-
face.
Vol-
ume.
1-32
.00307
.00002
3 M
33.183
17.974
9 Vs
306.36
504.21
1-16
.01227
.00013
5-16
34.472
19.031
10.
314.16
523.60
3-32
.02761
.00043
35.784
20.129
322.06
543.48
t*
.04909
.07670
.00102
.00200
7-16
y*
37.122
38.484
21.268
22.449
?!
330.06
338.16
563.86
584.74
3-16
.11045
.00345
9-16
39.872
23.674
L£
346.36
606.13
7-32
.15033
.00548
%
41.283
24.942
%
354.66
628.04
.19635
.00818
11-16
42.719
26.254
§4
363.05
650.46
9-32
.24851
.01165
M
44.179
27.611
7£
371.54
673.42
5-16
.30680
.01598
13-16
45.664
29.016
11.
380.13
696.91
11-32
.37123
.02127
Vs
47.173
30.466
388.83
720.95
.44179
.02761
15-16
48.708
31.965
M
397.61
745.51
13-32
.51848
.03511
4.
50.265
33.510
%
406.49
770.64
7-16
.60132
.04385
53.456
36.751
x^2
415.48
796.33
15-32
.69028
.05393
/4
56.745
40.195
%
424.50
822.58
L£
.78540
.06545
%
60.133
43.847
54
433.73
849.40
9-16
.99403
.09319
i^
63.617
47.713
Xo
443.01
876.79
%
1.2272
.12783
%
67.201
51.801
12.
452.39
904.78
11-16
1.4849
.17014
%:
70.883
56.116
^
471.44
962.52
1.7671
.22089
%
74.663
60.663
i^
490.87
1022.7
13-16
2.0739
.28084
5.
78.540
65.450
a/
510.71
1085.3
Vs
2.4053
.35077
82.516
70.482
13.
530.93
1150.3
15-16
2.7611
.43143
M
86.591
75.757
551.55
1218.0
1.
3.1416
.52360
%
90.763
81.308
i^
572.55
1288.3
1-16
3.5466
.62804
Y&
95.033
87.113
%
593.95
1361.2
3.9761
.74551
5^
99.401
93.189
14.
615.75
1436.8
3-16
4.4301
.87681
M
103.87
99.541
637.95
1515.1
M
4.9088
1.0227
%
108.44
106.18
Lj£
660.52
1596.3
5-16
5.4119
1.1839
6.
113.10
113.10
3^
683.49
1680.3
5.9396
1.3611
117.87
120.31
15.
706 85
1767.2
7-16
6.4919
1.5553
J4
122.72
127.83
y*
730.63
1857.0
7.0686
1.7671
%
127.68
135.66
754.77
1949.8
9-16
7.6699
1.9974
L£
132.73
143.79
%
779.32
2045.7
%
8.2957
2.2468
%
137.89
152.25
16.
804.25
2144.7
11-16
8.9461
2.5161
M
143.14
161.03
829.57
2246.8
H
9.6211
2.8062
%
148.49
170.14
L£
855.29
2352.1
13-16
10.321
3.1177
7.
153.94
179.59
ax
881.42
2460.6
VB
11.044
3.4514
K
159.49
189.39
17.
907.93
2572.4
15-16
11.793
3.8083
165.13
199.53
/4
934.83
2687.6
2.
12.566
4.1888
%
170.87
210.03
i^
962.12
2806.2
1-16
13.364
4.5939
i£
176.71
220.89
ax
989.80
2928.2
14.186
5.0243
%
182.66
232.13
18.
1017.9
3053.6
3-16
15.033
5.4809
54
188.69
243.73
/4
1046.4
3182.6
14
15.904
5.9641
%
194.83
255.72
L/j
1075.2
3315.3
5-16
16.800
6.4751
8.
201.06
268.08
%
1104.5
3451.5
17.721
7.0144
207.39
280.85
19.
1134.1 18681.4
7-16
18.666
7.5829
IX-
213.82
294.01
i/
1164.2 J3735.0
/^
19.635
8.1813
%
220.36
307.58
Jl2
1194.6
3882.5
9-16
20.629
8.8103
L£
226.98
321.56
3£
1225.4
4033.7
%
21.648
9.4708
R/.
233.71
335.95
20.
1256.7
4188.8
11-16
22.691
10.164
3/£
240.53
350.77
/4
1288.3
4347.8
23.758
10.889
/o
247.45
360.02
1Z
1320.3
4510.9
13-16
24.850
11.649
9.
254.47
381.70
3^
1352.7
4677.9
%
25.967
12.443
261.59
397.83
21.
1385.5
4849.1
15-16
27.109
13.272
/4
268.81
414.41
/4
1418.6
5024.3
3.
28.274
14.137
%
270.12
431.44
^
1452.2
5203.7
1-16
29.465
15.039
Y% 283.53
448.92
%
1486.2
5387.4
% 30.680
15.979
% 1291.04
466.87
22.
1520.5
5575.3
3-16 .31.919
16.957
% i 298. 65
485.31
M
1555.3 15767.6
SPHERES.
SPHERES— (Continued.)
119
Diam.
Sur-
face.
Vol-
ume.
Diam.
Sur-
face.
Vol-
ume
Diam.
Sur-
face.
Vol.
ume.
22 %
159C.4
5964.1
40 54
5153.1
34783
70 Yz
15615
183471
n
1626.0
6165.2
41.
5281.1
36087
.71.
15837
187402
23.
1661.9
6370.6
54
5410.7
37423
Yz
16061
191389
/4
1698.2
6580.6
42.
5541.9
38792
72.
16286
195433
54
1735.0
6795.2
^
5674.5
40194
Yz
16513
199532
M
1772.1
7014.3
43.
5808.8
41630
73.
16742
203689
24.
1809.6
7238.2
54
5944.7
43099
Yz
16972
207903
54
1847.5
7466.7
44.
6082.1
44602
74.
17204
212175
/4
1885.8
7700.1
M
6221.2
46141
K
17437
216505
%
1924.4
7938.3
45.
6361.7
47713
75.
17672
220894
25.
1963.5
8181.3
H
6503.9
49321
y*
17908
225341
54
2002.9
8429.2
46.
6647.6
50965
76.
18146
229848
^2
2042.8
8682.0
fcf
6792.9
52645
Yz
18386
234414
M
2083.0
8939.9
47.
6939.9
54362
77.
18626
239041
26.
2123.7
9202.8
^
7088.3
56115
Yz
18869
243728
M
2164.7
9470.8
48.
7238.3
57906
78.
19114
248475
2206.2
9744.0
K
7389.9
59734
Y*
19360
253284
M
2248.0
10022
49.
7543.1
61601
79.
19607
258155
27.
2290.2
10306
K
7697.7
63506
54
19856
263088
M
2332.8
10595
50.
7854.0
65450
80.
20106
268083
2375.8
10889
K
8011.8
67433
H
20358
273141
M
2419.2
11189
51.
8171.2
69456
81.
20612
278263
28.
2463.0
11494
H
8332.3
71519
54
20867
283447
ix
2507.2
11805
52.
8494.8
73622
82.
21124
288696
Jij
2551.8
12121
54
8658.9
75767
54
21382
294010
M
2596.7
12443
53.
8824.8
77952
83.
21642
299388
29.
2642.1
12770
54
8992.0
80178
54
21904
304831
54
2687.8
13103
54.
9160.8
82448
84.
22167
310340
/^
2734.0
13442
K
9331.2
84760
54
22432
315915
M
2780.5
13787
55.
9503.2
87114
85.
22698
321556
30.
2827.4
14137
54
9676.8
89511
H
22966
327264
54
2874.8
14494
56.
9852.0
91953
86.
23235
333039
54
2922.5
14856
54
10029
94438
54
23506
338882
a/
2970.6
15224
57.
10207
96967
87.
23779
344792
81.
3019.1
15599
^
10387
99541
K
24053
350771
^4
3068.0
15979
58.
10568
102161
88.
24328
356819
3117.3
16366
54
10751
104826
54
24606
362935
34
3166.9
16758
59.
10936
107536
89.
24885
369122
32.
3217.0
17157
K
11122
110294
54
25165
375378
54
3267.4
17563
60.
11310
113098
90.
25447
381704
%
3318.3
17974
Y%
11499
115949
54
25730
388102
M
3369.6
18392
61.
11690
118847
91.
26016
394570
33.
3421.2
18817
54
11882
121794
54
26302
401109
ix
3473.3
19248
62.
12076
124789
92.
26590
407721
Yz
3525.7
19685
H
12272
127832
54
2(5880
414405
M
3578.5
20129
63.
12469
130925
93.
27172
421161
34.
3631.7
20580
H
12668
134067
54
27464
427991
54
3685.3
21037
64.
12868
137259
94.
27759
434894
I/,
3739.3
21501
54
13070
140501
54
28055
441871
35. "
3848.5
22449
65.
• 13273
143794
95.
28353
448920
N
3959.2
23425
54
13478
147138
54
28652
456047
36.
4071.5
24429
66.
13685
150533
96.
28953
463248
34
4185.5
25461
H
13893
153980
54
29255
470524
37.
4300.9
26522
67.
14103
157480
97.
29559
477874
&
4417.9
27612
54
14314
161032
54
29865
485302
38.
4536.5
28731
68.
14527
164637
98.
30172
492808
54
4656.7
29880
Ya
14741
168295
54
30481
500388
39.
4778.4
31059
69.
14957
172007
99.
30791
508047
34
4901.7
32270
^
15175
175774
54
31103
515785
40.
5026.5
33510
70.
15394
179595
100.
31416
523598
120
MATHEMATICAL TABLES.
CONTENTS IN CUBIC FEET AND U. S. GALLONS OF
PIPES AND CYLINDERS OF VARIOUS DIAMETERS
AND ONE FOOT IN LENGTH.
1 gallon = 231 cubic inches. 1 cubic foot = 7.4805 gallons.
For 1 Foot in
For 1 Foot in
For 1 Foot in
a
Length.
jd
t- .
Length.
a
Length.
Diameter
Inches.
Cubic Ft.
also Area
in Sq. Ft.
U.S.
Gals.,
231
Cu. In.
Diametei
Inches
Cubic Ft.
also Area
in Sq. Ft.
U.S.
Gals.,
231
Cu. In.
Diamete]
Inches,
Cubic Ft.
also Area
in Sq. Ft.
U.S.
Gals.,
231
Cu. In.
H
.0003
.0025
fA
.2485
1.859
19
1.969
14.73
5-18
.0005
.004
.2673
1.999
1014
2.074
15.51
%
.0008
.0057
714
.28<57
2.145
20
2.182
16.32
7^16
.001
.0078
.3068
2.295
20^
2.292
17.15
H
,0014
.0102
7%
.3276
2.45
21
2. -105
17.99
9-16
.0017
.0129
8
.3491
2.611
2H/2
2.521
18.86
%
.0021
.0159
8J4
.3712
2.777
22
8.640
19.75
11-16
.00-20
.0193
gL£
.3941
2'. 9 48
221^
2.761
20.UO
H
.0031
.0230
8%
.4176
3.125
23
2.885
21.58
13-16
.0030
.0269
9
.4418
3.305
23^
3.012
22.53
%
.0042
.0312
9J4
.4667
3.491
24
3.142
23.50
15-16
.0048
.0359
9^£
.4922
3.682
25
• 3.409
25.50
1
.0055
.0408
9%
.5185
3.879
26
3.087
27.58
.0085
.0638
10
.5454
4.08
27
3.970
29.74
%
.0123
.0918
IOM
.5730
4.286
28
4.276
31.99
1%
.0167
.1249
10^
.6013
4.498
29
4.587
34.31
24
.0218
.1632
10%
.6303
4.715
30
4.909
36.72
2J4
.0276
.2066
11
.66
4.937
31
5.241
39.21
giz
.0341
.2550
11^4
.6903
5.164
32
5.585
41.78
2%
.0412
.3085
11^
.7213
5.396
33
5.940
44.43
3
.0491
.3672
11%
.7530
5.633
34
6.305
47.16
314
.0576
.4309
12
.7854
5.875
35
6.681
49.98
.0608
.4998
12*6
.8522
6.375
36
7.069
52.88
3M
.0767
.5788
13
.9218
6.895
37
7.467
55.86
4
.0873
.6528
13fc
.994
7.436
38
7.876
58.92
VA
.0985
.7369
14
1.069
7.997
39
8.296
62.06
41
.1104
.8263
14^
1 147
8.578
40
8.727
65.28
4%
.1231
.9200
15
1.227
9.180
41
9.168
68.58
5
.1364
1.020
15J4
1.310
9.801
42
9.621
71.97
5^
.1503
1.125
16
1.396
10.44
43
10.085
75.44
5^
.1650
1.234
16J4
1.485
11.11
44
10.559
78.99
5%
.1803
1.349
17
1.576
11.79
45
11.045
82.62
6
.1963
1.469
17^
1.670
12.49
46
11.541
86.33
6^
•.2131
1.594
18
1.788
13.22
47
12.048
90.13
6^
.2304
1.724
18J*
1.867
13.96
48
12.566
94.00
To find the capacity of pipes greater than the largest given in the table,
look in the table for a pipe of one half the given size, and multiply its capac-
ity by 4; or one of one third its size, and multiply its capacity by 9, etc.
To find the weight of water in any of the given sizes multiply the capacity
in cubic feet by 62*4 or the gallons by 8^, or, if a closer approximation is
required, by the weight of a cubic foot of water at the actual temperature in
the pipe.
Given the dimensions of a cylinder in inches, to find its capacity in U. S.
gallons: Square the diameter, multiply by the length and by .0034. If d ~
diameter, I = length, gallons = d* X 54 - = .0034cW.
CAPACITY OF CYLINDRICAL VESSELS.
121
CYLINDRICAL VESSELS, TANKS, CISTERNS, ETC.
Diameter in Feet and Indies, Area in Square Feet, and
U. S. Gallons Capacity for One Foot in Depth.
1 gallon = 231 cubic inches = 1 Cub°Ot = 0.13368 cubic feet.
Diam.
Area.
Gals.
Diam.
Area.
Gals.
Diam.
Area.
Gals.
Ft. In.
Sq. ft.
1 foot
depth.
Ft. In.
Sq. ft.
1 foot
depth.
Ft. In.
Sq. ft.
1 foot
depth.
1
.785
5.87
5 8
25.22
188.66
19
283.53
2120.9
1 1
.922
6.89
5 9
25.97
194.25
19 3
291.04
2177.1
2
1.069
8.00
5 10
26.73
199.92
19 6
298.65
2234.0
'• 3
1.227
9.18
5 11
27.49
205.67
19 9
306.35
2291.7
4
1.396
10.44
6
28.27
211.51
20
314.16
2350.1
5
1.576
11.79
6 3
30.68
229.50
20 3
322.06
2409.2
6
1.767
13.22
6 6
33.18
248.23
20 6
330.06
2469.1
7
1.969
14.73
6 9
35.78
267.69
20 9
338.16
2529.6
8
2.182
16.32
7
38.48
287.88
21
346.36
2591.0
9
2.405
17.99
7 3
41.28
308.81
21 3
354.66
2653.0
10
2.640
19.75
7 6
44.18
330.48
21 6
363.05
2715.8
11
2.885
21.58
7 9
47.17
352.88
21 9
371.54
2779.3
2
3.142
23.50
8
50.27
376.01
22
380.13
2843.6
2 1
3.409
25.50
8 3
53.46
399.88
22 3
388.82
2908.6
2 2
3.687
27.58
8 6
56.75
424.48
22 6
397.61
2974.3
2 3
3.976
29.74
8 9
60.13
449.82
22 9
406.49
3040.8
2 4
4.276
31.99
9
63.62
475.89
23
415.48
3108.0
2 5
4.587
3431
9- 3
6720
502.70
23 3
424.56
3175.9
2 6
4.909
36.72
9 6
70.88
53024
23 6
433.74
3244.6
2 7
5.241
39.21
9 9
74.66
558.51
23 9
443.01
33140
2 8
5.585
41.78
10
78.54
587.52
24
452.39
3384.1
2 9
5.940
44.43
10 3
82.52
617.26
24 3
461.86
3455.0
2 10
6.305
47.16
10 6
86.59
647.74
24 6
471.44
3526.6
2 11
6.681
49.98
10 9
90.76
678.95
24 9
481.11
3598.9
3
7.069
52.88
11
95.03
710.90
25
490.87
3672.0
3 1
7.467
55.86
11 3
99.40
743.58
25 3
500.74
3745.8
3 2
7.876
58.92
11 6
103.87
776.99
25 6
510.71
38203
3 3
8.296
62.06
11 9
108.43
811.14
25 9
520.77
3895.6
3 4
8.727
65.28
12
113.10
846.03
26
530.93
3971.6
3 5
9.168
68.58
12 3
117.86
881.65
26 3
541.19
4048.4
3 6
9.621
71.97
12 6
122.72
918.00
26 6
551.55
4125.9
3 7
10.085
75.44
12 9
127.68
955.09
26 9
562.00
4204.1
3 8
10.559
78.99
13
132.73
992.91
27
572.56
4283.0
3 9
11.045
82.62
13 3
137.89
1031.5
27 3
583.21
4362.7
3 10
11.541
86.33
13 6
143.14
1070.8
27 6
593.96
4443.1
3 11
12.048
90.13
13 9
148.49
1110.8
27 9
604.81
4524.3
4
12.566
94.00
14
153.94
1151.5
28
615.75
4606.2
4 1
13.095
97.96
14 3
159.48
1193.0
28 3
626.80
4688.8
4 2
13.685
102.00
14 6
165.13
1235.3
28 6
637.94
4772.1
4 3
14.186
106.12
14 9
170.87
1278.2
28 9
649.18
4856.2
4 4
14.748
110.32
15
176.71
1321.9
29
660.52
4941.0
4 5
15.321
114.61
15 3
182.65
1366.4
29 3
671.96
5026.6
4 G
15.90
118.97
15 6
188.69
1411.5
29 6
683.49
5112.9
4 7
16.50
123.42
15 9
194.83
1457.4
29 9
695.13
5199.9
4 8
17.10
127.95
16
201.06
1504.1
30
706.86
5287.7
4 9
17.72
132.56
16 3
207.39
1551.4
30 3
718.69
5376.2
4 10
18.35
137.25
16 6
21382
1599.5
30 6
730.62
5465.4
4 11
18.99
142.02
16 9
220.35
1648.4
30 9
742.64
5555.4
ft
19.63
146.88
17
226.98
1697.9
31
754.77
5646.1
5 1
20.29
151.82
17 3
233.71
1748.2
31 3
766.99
5737.5
5 2
20.97
156.83
17 6
240.53
1799.3
31 6
779.31
5829.7
5 3
21.65
161.93
17 9
247.45
1851.1
31 9
791.73
5922.6
5 4
22.34
167.12
18
254.47
1903.6
32
80425
6016.2
5 5
23.04
172.38
18 3
261.59
1956.8
32 3
816.86
6110.6
5 6
23.76
177.72
18 6
268.80
2010.8
32 6
829.58
6205.7
5 7
24.48
183.15
18 9
276.12
2065.5
32 9
842.39
6301.5
122
MATHEMATICAL TABLES.
GALLONS AND CUBIC FEET.
United States Gallons in a given Number of Cubic Feet.
1 cubic foot = 7.480519 U. S. gallons; 1 gallon = 231 cu. in. = .13368056 cu. ft.
Cubic Ft.
Gallons.
Cubic Ft.
Gallons.
Cubic Ft.
Gallons.
0.1
0.75
50
374.0
8,000
59,844.2
0.2
1.50
60
448.8
9,000
67,324.7
0.3
2.24
70
523.6
10,000
74,805.2
0.4
2.99
80
598.4
20,000
149,610.4
0.5
3.74
90
673.2
30,000
224,415.6
0.6
4.49
100
748.0
40,000
299,220.8
0.7
5.24
200
1,496.1
50,000
374,025.9
0.8
5.98
300
2,244.2
60,000
448,831.1
0.9
6.73
400
2,992.2
70,000
523,636.3
1
7.48
500
3,740.3
80,000
598,441.5
2
14.96
600
4,488.3
90,000
673,246.7
3
22.44
700
5,236.4
100,000
748,051.9
4
29.92
800
5,984.4
200,000
1,496,103.8
5
37.40
900
6,732.5
300,000
2,244,155.7
6
44.88
1,000
7,480.5
400,000
2,992,207.6
7
52.36
2,000
14,961.0
500,000 -
3,740,259.5
8
59.84
3,000
22,441.6.
600,000
4,488,311.4
9
67.32
4,000
29,922.1
700,000
5,236,363.3
10
74.80
5,000
37,402.6
800,000
5,984,415.2
20
149.6
6,000
44,883.1
900,000
6,732,467.1
30
224.4
7,000
52,363.6
1,000,000
7,480,519.0
40
299.2
Cubic Feet in a given Number of Gallons.
Gallons.
Cubic Ft.
Gallons.
Cubic Ft.
Gallons.
Cubic Ft.
1
.134
1,000
133.681
1,000,000
133,680.6
2
.267
2,000
267.361
2,000,000
267,361.1
3
.401
3,000
401.042
3,000,000
401,041.7
4
.535
4,000
534.722
4,000,000
534,722.2
5
.668
5,000
668.403
5,000,000
668,402.8
6
.802
6,000
802.083
6,000,000
802,083.3
7
.936
7,000
935.764
7,000,000
935,763.9
8
1.069
8,000
1,069.444
8,000,000
1,069,444.4
9
1.203
9,000
1,203.125
9,000,000
1,203,125.0
10
1.337
10,000
1,336.806
10,000,000
1,336,805.6
NUMBER OF SQUARE FEET IK PLATES.
123
NUMBER OF SQUARE FEET IN PLATES 3 TO 32
FEET LONG, AND 1 INCH WIDE.
For other widths, multiply by the width in inches. 1 sq. in. — .0069$ sq. ft.
Ft. and
In.
Long.
Ins.
Long.
Square
Feet.
Ft. and
Ins.
Long.
Ins.
Long.
Square
Feet.
Ft. and
Ins.
Long.
Ins.
Long.
Square
Feet.
8. 0
36
.25
7.10
94
.6528
13.8
152
.056
37
.2569
11
95
.6597
9
153
.063
2
38
.2639
8. 0
96
.6667
10
154
.069
3
39
.2708
1
97
.6736
11
155
.076
4
40
.2778
2
98
.6806
13.0
156
.083
5
41
.2847
3
99
.6875
1
157
.09
6
42
.2917
4
100
.6944
2
158
.097
7
43
.2986
5
101
.7014
3
159
.104
8
44
.3056
6
102
.7083
4
160
.114
9
45
.3125
103
.7153
5
161
.118
10
46
.3194
8
104
.7222
6
162
1.125
11
47
.3264
9
105
.7292
7
163
1.132
4. 0
48
.3333
10
106
.7361
8
164
1.139
1
49
.3403
11
107
.7431
9
165
1.146
2
50
.3472
9. 0
108
.75
10
166
1.153
a
51
.3542
1
109
.7569
11
167
1.159
4 .
52
.3611
2
110
.7639
14.0
168
1.167
5
53
.3681
3
111
.7708
1
169
1.174
6
54
.375
4
112
.7778
2
170
1.181
7
55
.3819
5
113
.7847
3
171
1.188
8
56
.3889
6
114
.7917
4
172
1.194
9
57
.3958
7
115
.7986
5
173
1.201
10
58
.4028
8
116
.8056
6
174
1.208
11
59
.4097
9
117
.8125
7
175
1.215
5. 0
60
.4167
10
118
.8194
8
176
1.222
1
61
.4236
11
119
.8264
9
177
1.229
2
62
.4306
10.0
120
.8333
10
178
1.236
3
63
.4375
1
121
.8403
11
179
1.243
4
64
.4444
2
122
.8472
15.0
180
1.25
5
65
.4514
3
123
.8542
1
181
1.257
6
66
.4583
4
124
.8611
2
182
1.264
7
67
.4653
5
125
.8681
3
183
1.271
8
68
.4722
6
126
.875
4
184
1.278
9
69
.4792
7
127
.8819
5
185
1.285
10
70
.4861
8
128
.8889
6
186
1.292
11
71
.4931
9
129
.8958
7
187
1.299
6. 0
72
.5
10
130
.9028
8
188
1.306
1
73
.5069
11
131
.9097
9
189
1.313
2
74
.5139
11.0
132
.9167
10
190
1.319
3
75
.5208
1
133
.9236
11
191
1.326
4
76
.5278
2
134
.9306
16.0
192
1.333
5
77
.5347
3
135
.9375
1
193
1.34
6
78
.5417
4
136
.9444
2
194
1.347
7
79
.5486
5
137
.9514
3
195
1.354
8
80
.5556
6
138
.9583
4
196
1 361
9
81
.5625
7
139
.9653
5
197
1.368
10
82
.5694
8
140
.9722
6
198
1.3T5
11
83
.5764
9
141
.9792
7
199
1.382
7. 0
84
.5834
10
142
.9861
8
200
1.389
1
85
.5903
11
143
.9931
9
201
1.396
2
86
.5972
12.0
144
1.000
10
202
1.403
3
87
.6042
1
145
1.007
11
203
1.41
4
88
.6111
2
146
1.014
17.0
204
1.417 .
5
89
.6181
3
147
1.021
1
205
1.424
6
90
.625
4
148
1.028
2
206
1.431
7
91
.6319
5
149
1.035
3
207
1.438
8
92
.6389
6
150
1.042
4
208
1.444
9
93
.6458
7
151
1.049
5
209
1.451
MATHEMATICAL TABLES.
SQUARE: FEET IN
Ft. and
Ins.
Long.
Ins.
Long.
Square
Feet.
Ft. and
Ins.
Long.
Ins.
Long.
Square
Feet.
Ft. and
Ins.
Long.
Ins.
Long.
Square
Feet.
17.6
210
1.458
22.5
269
1.868
27.4
328
2.278
211
1.465
6
270
1.875
5
329
2.285
8
21 2
1.472
7
271
1.882
6
330
2.292
9
213
1.479
8
272
1.889
7
331
2.299
10
214
1.486
9
273
1.896
8
332
2.306
11
215
1.493
10
274
1.903
9
3&3
2.313
18.0
216
1.5
11
275
1.91
10
334
2.319
1
217
1.507
38. 0
276
1.917
11
335
2.326
2
218
1.514
1
277
1.924
28.0
336
2.333
3
219
1.521
2
278
1.931
1
337
2.34
4
220
1.528
3
279
1.938
2
3:38
2.347
5
221
1.535
4
280
1.944
3
339
2.354
6
222
1.542
5
281
1.951
4
340
2.361
7
223
1.549
6
282
1.958
5
341
2.368
8
224
1.556
7
283
1.965
6
342
2.375
9
225
1.563
8
284
1.972
7
343
2.382
0
226
1.569
9
285
1.979
8
344
2.389
11
227
1.576
10
286
1.986
9
345
2.396
19.0
228
1.583
11
287
1.993
10
346
2.403
1
229
1.59
24.0
288
2
11
347
2.41
2
230
1.597
1
289
2.007
29. 0
348
2.417
3
231
1.604
2
290
2.014
1
349
2.424
4
232
1.611
3
291
2.021
2
350
2.431
5
233
1.618
4
292
2 028
3
351
2.438
6
234
1.6-25
5
293
2.035
4
352
2.444
7
235
1.632
6
294
2.042
5
353
2.451
8
236
1.639
7
295
2.049
6
354
2.458
9
237
1.645
8
296
2.056
7
355
2.465
10
238
1.653
9
297
2.0fi3
8
356
2.472
11
239
1.659
10
298
2.069
9
357
2.47d
20.0
240
1.667
11
299
2.076
10
358
2.486
241
1.674
25.0
300
2.083
11
359
2.493
2
242
1.681
1
301
2.09
30.0
360
2.5
3
243
1.688
2
302
2.097
1
361
2.507
4
244
1.694
3
303
2.104
2
362
2.514
5
245
1.701
4
304
2.111
3
363
2.521
6
246
1.708
5
305
2.118
4
364
2.528
7
247
1.715
6
306
2.125
5
365
2.535
8
248
1.722
7
307
2.132
6
366
2.542
9
249
1.729
8
308
2.139
7
367
2.549
10
250
1.736
9
309
2.146
8
368
2.556
11
251
1.743
10
310
2.153
9
369
2.563
21.0
252
1.75
11
311
2.16
10
370
2.569
1
253
1 .757
26.0
312
2.167
11
371
2.576
2
254
1.764
1
313
2.174
31.0
372
2.583
3
255
1.771
2
314
2.181
1
' 373
2.59
4
256
1.778
3
315
2.188
2
374
2.597
5
257
1.785
4
316
2.194
3
375
2.604
6
258
1.792
5
317
2.201
4
376
2.611
7
259
1.799
6
318
2.208
5
377
2.618
8
260
1.806
7
319
2.215
6
378
2.625
9
261
1.813
8
3*0
2.222
7
379
2.632
10
262
1.819
9
321
2.229
8
380
2.639
11
263
1.826
10
322
2.236
9
381
2.646
22.0
264
1.833
11
323
2.243
10
382
2.653
1
265
1.84
27.0
324
2.25
11
383
2.66
2
266
1.847
1
325
2.257
32. 0
384
2.667
3
267
1.854
2
326
2.264
1
385
2.674
4
268
1.861
3
327
2.271
2
386
2.681
CAPACITY OF KECTAHGULAR TAHKS.
125
CAPACITIES OF RECTANGULAR TANKS IN U. S.
GALLONS, FOR EACH FOOT IN DEPTH.
1 cubic foot = 7.4805 U. S. gallons.
Width
of
Tank.
Length of Tank.
feet.
2
ft. in.
2 6
feet.
3
ft. in.
3 6
feet.
4
ft. in.
4 6
feet.
5
ft. in.
5 6
feet.
6
ft. in.
6 6
feet.
7
ft, in.
2
2 6
3
3 6
4
4 6
5
5 6
6
6 6
7
29.92
37.40
46.75
44.88
56.10
67.32
52.36
65.45
78.54
91.64
59.84
74.80
89.77
104.73
119.69
67.32
84.16
100.99
117.82
134.65
151.48
74.81
93.51
112.21
130.91
149.61
168.31
187.01
82.29
102.86
123.43
144.00
164.57
185.14
205.71
226.28
89.7"
112.21
134.6J
15701
179.5;
201.9'
224.41
246. 8(
269.3(
* 97.25
121.56
> 145.87
) 170.18
J 194.49
* 218.80
243.11
) 267.43
) 291.74
316.05
104.73
130.91
157.09
183.27
209.45
235.63
261.82
288.00
314.18
340.36
366.54
Width
of
Tank.
Length of Tank.
ft. in.
7 6
feet.
8
ft. in.
8 6
feet.
9
ft. in.
9 6
feet.
10
ft. in.
10 6
feet.
11
ft. in.
11 6
feet.
12
ft. in.
2
2 6
3
3 6
4
4 6
5
5 6
6
6 6
7 3
8
8 6
9
9 6
10
10 6
11
11 6
12
112.21
140.26
168.31
196.36
224.41
252.47
280.52
308.57
336.62
364.67
392.72
420.78
119.69
149.61
179.53
209.45
239.37
269.30
299.22
329.14
359.06
388.98
418.91
448.83
478.75
127.17
158.96
190.75
222.54
254.34
286.13
317.92
349.71
381.50
413.30
44509
476.88
508.67
540.46
134.65
168.31
202.97
235.63
269.30
302.96
336.62
370.28
403.94
437.60
471.27
504.93
538.59
572.25
605.92
14213
177.66
213.19
248.73
284.26
319.79
355.32
390.85
426.39
461.92
497.45
532.98
568.51
604.05
639.58
675.11
149.61
187.01
22441
261.82
299.22
336.62
374.03
411.43
448.83
486.23
523.64
561.04
598.44
635.84
673.25
710.65
748.05
157.09
196.36
235.63
274.90
314.18
353.45
392.72
432.00
471.27
510.54
549.81
589.08
628.36
66763
706.90
746.17
785.45
824.73
164.57
205.71
246.86
288.00
329.14
370.28
411.43
452.57
493.71
534.85
575.99
617.14
658.28
699.42
740.56
781.71
822.86
864.00
905.14
172.05
215.06
258.07
301.09
344.10
387.11
430.13
473.14
516.15
559.16
602.18
645.19
688.20
731.21
774.23
817.24
860.26
903.26
946.27
989.29
179.53
224.41
269.30
314.18
359.06
403.94
448.83
493.71
538.59
583.47
628.36
673.24
718.12
763.00
807.89
852.77
897.66
942.56
987.43
1032.3
1077.2
126
MATHEMATICAL TABLES.
NUMBER OF BARRELS (31 1-2 GALLONS) IN
CISTERNS AND TANKS.
1 Barrel = 31^ gallons =
31.5 X 231
= 4.21094 cubic fret. Reciprocal = .237477.
Depth
Diameter in Feet.
in
Feet.
5
6
7
8
9
10
11
12
13
14
1
4.663
6.714
9.139
11.93'
' 15.108
18.652
22.569
26.859
31.522
36.557
5
23.3
33.6
45.7
59.7
75.5
93.3
112.8
134.3
157.6
182.8
6
28.0
40.3
54.8
71.6
90.6
111.9
135.4
161.2
189.1
219 3
7
32.6
47.0
64.0
83.6
105.8
130.6
158.0
188.0
220.7
255.9
8
37.3
53.7
73.1
95.5
120.9
149.2
180.6
214.9
252.2
292.5
9
42.0
60.4
82.3
107.4
136.0
167.9
203.1
241.7
283.7
329.0
10
46.6
67.1
91.4
119.4
151.1
186.5
225.7
268.6
315.2
365.6
11
51.3
73.9
100.5
131.3
166.2
205.2
248 3
295.4
346.7
402.1
12
56.0
80.6
109.7
143.2
181.3
223.8
270.8
322.3
378.3
438.7
13
60.6
87.3
118.8
155.2
196.4
242.5
293.4
349.2
409.8
475 2
14
65.3
94.0
127.9
167.1
211.5
261.1
316.0
376.0
441.3
511.8
15
69.9
100.7
137.1
179.1
226.6
289.8
338.5
402.9
472.8
548.4
16
74.6
107.4
146.2
191.0
241.7
298.4
361.1
429.7
504.4
584.9
17
79.3
114.1
155.4
202.9
256.8
317.1
383.7
456.6
535.9
621 .5
18
83.9
120.9
164.5
214.9
271.9
335.7
406.2
483.5
567.4
658.0
19
88.6
127.6
173.6
226.8
287.1
354.4
428.8
510.3
598.9
694.6
20
93 3
134.3
182.8
238.7
302.2
373.0
451.4
537.2
630.4
731.1
Depth
Diameter in Feet.
in
Feet.
15
16
17
18
19
20
21
22
1
iijwc
47.748
53.903
60.431
67.332
74.606
82.253
90.273
5
209.8
238.7
269.5
302.2
336.7
373.0
411.3
451.4
6
251.8
286.5
323.4
362 6
404.0
447.6
493.5
541.6
7
293.8
334.2
377.3
423 0
471.3
522.2
575.8
631.9
8
335.7
382.0
431.2
483.4
538.7
596.8
658.0
722.2
9
377.7
429.7
485.1
543.9
606.0
671.5
740.3
812.5
10
419.7
477.5
539.0
604.3
673.3
746.1
822.5
902.7
11
481.6
525.2
592.9
664.7
740.7
820.7
904.8
993.0
12
503.6
573.0
646.8
725.2
808.0
895.3
987.0
1083.3
13
545.6
620.7
700.7
785.6
875.3
969.9
1069.3
1173.5
14
587.5
668.5
754.6
846.0
942.6
1044.5
1151.5
1263.8
15
629.5
716.2
808.5
906.5
1010.0
1119.1
1233.8
1354.1
16
671.5
764.0
862.4
966.9
1077.3
1193.7
1316.0
1444.4
17
713.4
811.7
916.4
1027.3
1144.6
1268.3
1398.3
1534.5
18
755.4
859.5
970.3
1087.8
1212.0
1342.9
1480.6
1624.9
19
797.4
907.2
1024.2
1148.2
1279.3
1417.5
1562.8
1715.2
20
839.3
955.0
1078.1
1208.6
1346.6
1492.1
1645.1
1805.5
LOGARITHMS.
12?
NUMBER OF BARRELS (31 1-2 GALLONS) IN
CISTERNS AND TANKS.— Continued.
Depth
in
Feet.
Diameter in Feet.
23
24
25
26
27
28
29
30
1
98.666
107.432
116.571
126.083
135.968
146.226
157.858
167. 86S
5
493.3
537.2
582.9
630.4
679.8
731.1
784.3
839.3
6
592.0
644.6
699.4
756.5
815.8
877.4
941.1
1007.2
7
690.7
752.0
816.0
882.6
951.8
1023.6
1098.0
1175 0
8
789.3
859.5
933.6
1008.7
1087.7
1169.8
1254 9
1342.9
9
888.0
966.9
1049.1
1134.7
1223.7
1316.0
1411.7
1510.8
10
986.7
1074.3
1165.7
1260.8
1359.7
1462.2
1568.6
1678.6
11
1085.3
1181.8
1282.3
1386.9
1495.6
1608.5
1725.4
1846.5
1'2
1184.0
1289.2
1398.8
1513.0
1631.6
1754.7
1882.3
2014.4
13
1282.7
1396.6
1515.4
1639.1
1767.6
1900.9
2039.2
2182.2
14
1381.3
1504 0
1632.0
1765.2
1903.6
2047.2
2196.0
2350.1
.15
1480.0
1611.5
1748.6
1891.2
2039.5
2193.4
2352.9
2517.9
16
1578.7
1718.9
1865.1
2017.3
2175.5
2339.6
2509.7
2685.8
17
1677.3
1826.3
1981.7
2143.4
2311.5
2485.8
2666.6
2853.7
18
1776.0
1933.8
2098.3
2269.5
2447.4
2632.0
2823.4
3021.5
19
1874.7
2041.2
2214.8
2395.6
2583.4
2778.3
2980.3
3189.4
20
1973.3
2148.6
2321.4
2521.7
2719.4
2924.5
3137.2
3357.3
LOGARITHMS.
Logarithms (abbreviation log}.— The log of a number is the exponent
of the power to which it is necessary to raise a fixed number to produce the
given number. The fixed number is called the base. Thus if the base is 10,
the log of 1000 is 3, for 103 = 1000. There are two systems of logs in general
use, the common, in which the base is 10, and the Naperian, or hyperbolic,
in which the base is 2.718281828 .... The Naperian base is commonly de-
noted by e, as in the equation ey = x, in which y is the Nap. log of x.
In any system of logs, the log of 1 is 0; the log of the base, taken in that
system, is 1. In any system the base of which is greater than 1, the logs of
all numbers greater than 1 are positive and the logs of all numbers less than
1 are negative.
The modulus of any system is equal to the reciprocal of the Naperian log
of the base of that system. The modulus of the Naperian system is 1, that
of the common system is .4342945.
The log of a number in any system equals the modulus of that system X
the Naperian log of the number.
The hyperbolic or Naperian log of any number equals the common log
X 2.3025851.
Every log consists of two parts, an entire part called the characteristic, or
index, and the decimal part, or mantissa. The mantissa only is given in the
usual tables of common logs, with the decimal point omitted. The charac-
teristic is found by a simple rule, viz., it is one less than the number of
figures to the left of the decimal point in the number whose log is to be
found. Thus the characteristic of numbers from 1 to 9.99 + is 0, from 10 to
99.99 + is 1, from 100 to 999 + is 2, from .1 to .99 -f is - 1, from .01 to .099 -**
is - 2, etc. Thus
log of 2000 is 3.30103;
" " 200 " 2.30103;
•' " 20 " 1.30103;
•* " 2 " 0.30103;
log of
.2 is - 1.30103;
.02 " - 2.30103;
.002 " - 3.30103;
.0002 " - 4.30103.
MATHEMATICAL TABLES.
The minus sign is frequently written above the characteristic thus :
log .002 = 3 .30103. The characteristic only is negative, the decimal part, or
mantissa, being always positive.
When a log consists of a negative index and a positive mantissa, it is usual
to write the negative sign over the index, or else to add 10 to the index, and
to indicate the subtraction of 10 from the resulting logarithm.
Thus log .2 = Y-39103. and this may be written 9.30103 - 10.
In tables of logarithmic sines, etc., the — 10 is generally omitted, as being
understood.
Rules for use of the table of Logarithms.— To find the
log of any whole number.— For 1 to 100 inclusive the log is given
complete in the small table on page 129.
For 100 to 999 inclusive the decimal part of the log is given opposite the
given number in the column headed 0 in the table (including the two figures
to the left, making six figures). Prefix the characteristic, or index, 2.
For 1000 to 9999 inclusive : The last four figures of the log are found
opposite the first three figures of the given number and in the vertical
column headed with the fourth figure of the given number ; prefix the two
figures under column 0, and the index, which is 3.
For numbers over 10,000 having five or more digits : Find the decimal part
pf the log for the first four digits as above, multiply the difference figure
in the last column by the remaining digit or digits, and divide by 10 if there
be only one digit more, by 100 if there be two more, and so on ; add the
quotient to the log of the first four digits and prefix the index, which is 4
if there are five digits, 5 if there are six digits, and so on. The table of pro-
portional parts may be used, as shown below.
To find the log of a decimal fraction or of a whole
number and a decimal.— First find the log of the quantity as if there
were no decimal point, then prefix the index according to rule ; the index is
one less than the number of figures to the left of the decimal point.
Required log of 3.141593.
log of 3.141 =0.497068. Diff. = 138
From proportional parts 5 = 690
— 09 = 1242
** " «* 003 = 041
log 3.141593 0.4971498
To find the number corresponding to a given log.— Find
in the table the log nearest to the decimal part of the given log and take the
first four digits of the required number from the column N and the top or
foot of the column containing the log which is the next less than the given
log. To find the 5th and 6th digits subtract the log in the table from the
given log, multiply the difference by 100, and divide by the figure in the
Diff. column opposite the log ; annex the quotient to the four digits already
found, and place the decimal point according to the rule ; the number *l
figures to the left of the decimal point is one greater than the index.
Find number corresponding to the log 0.497150
Next lowest log in table corresponds to 3141 497068
Diff. = 82
Tabular diff. = 138; 82 -*• 138 = .59 -f
The Index being 0, the number is therefore 3.14159 -f.
To multiply two numbers by the use of logarithms,--
Add together the logs of the two numbers, and find the number whose log
is the sum.
To divide two numbers.— Subtract the log of the divisor from
the log of the dividend, and find the number whose log is the difference.
To raise a number to any given power.— Multiply the log of
the number by the exponent of the power, and find the number whose log in
the product.
To find any root of a given number.— Divide the log of the
Dumber by the index of the root. The quotient is the log of the root.
To find the reciprocal of a number. -Subtract the decimal
part of the log of the number from 0, add 1 to the index and change the sign
pf, the index. The result is the log of the reciprocal.
LOGARITHMS.
129
Required the reciprocal of 3.141593.
Log of 3.141593, as found above 0.4971498
Subtract decimal part from 0 gives 0.5028502
Add 1 to the index, and changing sign of the index gives.. T.5028502
which is the log of 0.31831.
To find the fourth term of a proportion by logarithms.
—Add the logarithms of tJ*e second and third terms, and from their sum
subtract the logarithm of the first term. ..
When one logarithm is to be subtracted from another, it may be more
convenient to convert the subtraction into an addition, which may be done
by first subtracting tLo given logarithm from 10, adding the difference to the
other logarithm, and afterwards rejecting the 10.
The difference between a given logarithm and 10 is called its arithmetical
complement, or cologarithm.
To subtract one logarithm from another is the same as to add its comple-
ment and then reject 10 from the result. For a — b = 10 — b + a, — 10.
To work a proportion, then, by logarithms, add the complement of the
logarithm of the first term to the logarithms of the second and third terms.
The characteristic must afterwards be diminished by 10.
Example In logarithms with a negative Index. —Solve by
7686V"
logarithms
\101l7
, which means divide 526 by 1011 and raise the quotient
to the 2.45 power.
log 526 =
log 1011 =
2.720986
3.004751
Jog of quotient = - 1.716235
Multiply by 2.45
- 2.581175
- 2.8 64940
- 1.43 2470
- 1.30 477575 = .20173, Ans.
In multiplying - 1.7 by 5, we say: 5 x 7 - 35, 3 to carry; 5 x — 1 = — 5 less
4- 3 carried = — 2. In adding -2-f-8-f3-fl carried from previous column,
we say: 1 4- 3 + 8 = 12, minus 2 = 10, set down 0 and carry 1; 1 -f 4 — 2 = 3.
LOGARITHMS OF NUMBERS FROM 1 TO 100.
N.
Log.
N.
Log.
N.
Log.
N.
Log.
N.
Log.
1
0.000000
21
1.322219
41
1.612784
61
1.785330
81
1.908485
2
0.301030
22
1.342423
42
1.623249
62
1.792392
82
1.913814
3
0.477121
23
1.361728
43
1.633468
63
1.799341
83
1.919078
4
0.602060
24
1.380211
44
1.643453
64
1.806180
84
1.924279
5
0.698970
25
1.397940
45
1.653213
65
1.812913
85
1.929419
6
0.778151
26
1.414973
46
1.662758
66
1.819544
86
1.934498
7
0.845098
27
1.431364
47
1.672098
67
1.826075
87
1.939519
8
0.903090
28
1.447158
48
1.681241
68
1.832509
88
1.944483
9
0.954243
29
1.462398
49
1.690196
69
1.838849
89
1.949390
10
1.000000
30
1.477121
50
1.698970
70
1.845098
90
1.954243
11
1.041393
31
1.491362
51
1.707570
71
1.851258
91
1.959041
12
1.079181
32
1.505150
52
1.716003
72
1.857332
92
1.963788
13
1.113943
33
1.518514
53
1.724276
73
1.863323
93
1.968483
14
1.146128
34
1.531479
54
1.732394
74
1.869232
94
1.973128
15
1.176091
35
1.544068
55
1.740363
75
1.875061
95
1.977724
16
1.204120
36
1.556303
56
1.748188
76
1.880814
96
1.982271
17
1.230449
37
1.568202
57
1.755875
77
1.886491
97
1.986772
18
1.255273
38
1.579784
58
1.763428
78
1.892095
98
1.991226
19
1.278754
39
1.591065
59
1.770852
79
1.897627
99
1.995635
20
1.301030
40
1.602060
60
1.778151
80
1.903090
100
2.000000
LOGARITHMS OF LUMBERS.
No.
100 L. 000.]
[No. lu9 L. 040.
*:
0
1
2
8 4
6
6
7
8
9
Diff.
100
000000
0434
0868
1301 1734
2166
2598
3029
3461
3891
432
i
4321
4751
5,181
5609 6038
6466
6894
7321
7748
8174
438
8600
9026
9451
9876
0300
0724
1147
1570
1993
2415
/KM
3
012837
3259
3680
4100 4521
4940
5360
5779
6197
6616
4K4
420
4
7033
7451
7868
8284 8700
9116
9532
9947
0361
0775
. , _
5
021189
1603
2016
2428 2841
3252
3664
4075
4486
4896
412
6
5306
5715
6125
6533 6942
7350
7757
8164
8571
8978
408
7
9384
9789
0195
0600 1004
1408
1812
2216
261S
3021
4A1
8
033424
3826
4227
4628 5029
5430
5830
6230
6629
7028
400
9
7426
7825
8223
8620 9017
9414
9811
04
0207
0602
0998
397
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
434
43.4
86.8
130.2
173.6
217.0
260.4
3(
)3.8
347.2
390.6
433
43.3
86.6
129.9
173.2
216.5
259
8
at
)3.1
346.4
389.7
432
43.2
86.4
12
3.6
172.8
216.0
259
2
3(
)2.4
345.6
388.8
431
43.1
86.2
129.3
172.4
215.5
258
6
301.7
344.8
387.9
430
43.0
86.0
129.0
172.0
215.0
258.0
301.0
344.0
387.0
429
42.9
85.8
12
8.7
171.6
214.5
257
4
3(
K).3
343.2
386.1
428
42.8
85.6
128.4
171.2
214.0
256
8
2(.
)9.6
342.4
385.2
427
42.7
85.4
128.1
170.8
213.5
256.2
21
)8.9
341.6
384.3
426
42.6
85.2
127.8
170.4
213.0
255.6
298.2
340.8
383.4
425
42.5
85.0
127.5
170.0
212.5
255
0
297.5
340.0
382.5
424
42.4
84.8
127 2
169.6
212.0
254
4
296.8
339.2
381.6
423
42.3
84.6
12
6.9
169.2
211.5
253
8
2J
)6.1
338.4
380.7
422
42.2
84.4
126.6
168.8
211.0
253.2
295.4
337.6
379.8
421
42:1
84.2
126.3
168.4
210.5
252.6
294.7
336.8
378.9
420
42.0
84.0
12
6.0
168.0
210.0
252
0
%
)4.0
336.0
378.0
419
43.9
83.8
125.7
167.6
209.5
251
4
20*. 3
335.2
377.1
418
41.8
83.6
12
5.4
167.2
209.0
250
8
2<
)2.6
334.4
37'6.2
417
41.7
as. 4
125.1
166.8
208.5
250
8
291.9
333.6
375.3
416
41.6
83.2
124.8
166.4
208.0
249.6
291.2
332.8
374.4
415
41.5
83.0
124.5
166.0
207.5
249.0
290,5
332.0
373.5
414
41.4
82.8
124.2
165.6
207.0
248
4
289.8
331.2
372.6
413
41.3
82.6
12
3.9
165.2
206.5
247
8
2
39.1
330.4
371.7
412
41.2
82.4
12
3.6
164.8
206.0
247
2
2
38.4
329.6
370.8
411
41.1
82.2
123.3
164.4
205.5
246
6
287.7
328.8
309. 9
410
41.0
82.0
123.0
164.0
205.0
246.0
21
37.0
328.0
369.0
409
40.9
81.8
122.7
163.6
204.5
245
.4
286.3
327.2
368.1
408
40.8
81.6
12
2.4
163.2
204.0
244
.8
21
35.6
326.4
367.2
407
40.7
81.4
122.1
162.8
203.5
244
.2
284.9
325. €
366.3
406
40.6
81.2
12
1.8
162.4
203.0
243
6
2!
34.2
324.8
365.4
405
40.5
81.0
121.5
162.0
202.5
243.0
2
33.5
324.0
364.5
404
40.4
80.8
121.2
161.6
202.0
242
.4
282.8
323.2
363.6
403
40.3
so.e
120.9
161.2
201.5
241
.8
282.1
322.4
362.7
40$
40.2
80.4
I
1$
!0.6
160.8
201.0
241
2
21
31.4
321.6
361.8
401
40.1
80.2
120.3
160.4
200.5
240
.6
280.7
320.8
360.9
400
40.0
80-0
120.0
160.0
200.0
240
.0
280.0
320.0
360.0
39<
1
39.9
79 £
J
11
9.7
159.6
199.5
239
.4
21
79.3
319.2
359.1
39*
\
39.8
79!6
119.4
159.2
199.0
238.8
278.6
318.4
358.2
39r
r
39.7
79.^
(
11
9.1
158.8
198.5
238
.2
2
77.9
317.6
357.3
396
39.6
79. $
>
118.8
158.4
198.0
237
.6
2
77.2
316.8
356.4
39
. 39.5
79.0 118.5
158.0
197.5 237.0 276.5 316.0 355.5
LOGARITHMS OF NUMBERS.
No. 110 L. 041.]
[No. 119 L. 078.
N. 0
1
2
3
4
5
6
7
8
9
Diff.
110 041393
1787
2182
2576
2969
3362
3755
4148
4540
4932
393
1 5323
5714
6105
6495
6885
7275
7664
8053
8442
8830
390
2 9218
9606
9993
0380
0766
1153
1538
1924
2309
2694
OQC
3 053078
3463
3846
4230
4613
4996
5378
5760
6142
6524
oOD
383
4 6905
7286
7666
8046
8428
8805
9185
9563
9942
0320
379
5 060698
1075
1452
1829
2206
2582
2958
sass
3709
4083
376
6 4458
4832
5206
5580
5953
6326
6699
7071
7443
7815
373
7 8186
8557
8928
9298
9668
0038
0407
0776
1145
1514
370
8 071862
2250
2617
2985
3352
3718
4085
4451
4816
5182
366
9 5547
5912
6276
6640
7004
7368
7731
8094
8457
8819
363
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
395
394
39.5
39.4
79.0
78.8
118.5
118.2
158.0
157.6
197.5
197.0
237.0
236.4
276.5
275.8
316.0
815.2
355.5
354.6
393
39.3
78.6
11
7.9
157.2
196.5
235
.8
2
75.1
314.4
353.7
392
39.2
78.4
11
7.6
156.8
196.0
235.2
274.4
313.6
352.8
391
39.1
78.2
117.3
156.4
195.5
234
.0
273.7
312.8
351.9
390
39.0
78.0
11
7.0
156.0
195.0
234
.0
2
73.0
312.0
351.0
389
38.9
77.8
116.7
155.6
194.5
233
.4
272.3
311.2
350.1
388
38.8
77.6
11
6.4
155.2
194.0
232
.8
2
71.6
310.4
349.2
387
38.7
77.4
116.1
154.8
193.5
232.2
270.9
309.6
348.3
386
38.6
77.2
11
5.8
154.4
198.0
231
.e
2
70.2
308.8
347.4
385
38.5
77.0
115.5
154.0
192.5
231
.0
269.5
308.0
346.5
384
38.4
76.8
115.2
153.6
192.0
230.4
268.8
307.2
345.6
383
38.3
76.6
114.9
153.2
191.5
229.8
2
68.1
306.4
344.7
382
38.2
76.4
[
11
4.6
152.8
191.0
228
.2
2
67.4
305.6
343.8
381
38.1
76.2
114.3
152.4
190.5
228.6
266.7
304.8
342.9
380
38.0
76.0
)
11
4.0
152.0
190.0
228
.0
2
66.0
304.0
342.0
379
37.9
75. £
!
11
3.7
151.6
189.5
227
.4
2
65.3
303.2
341.1
378
37.8
75.6
113.4
151.2
189.0
226.8
264.6
302.4
340.2
377
37.7
75.4
1
11
3.1
150.8
188.5
226
.2
2
63.9
301.6
339.3
376
37.6
75.2
112.8
150.4
188.0
225.6
263.2
300.8
338.4
375
37.5
75.0
112.5
150.0
187.5
225.0
I
62.5
300.0
337.5
374
37.4
74.8
112.2
149.6
187.0
224.4
261.8
299.2
336! 6
373
37.3
74. (
1
11
1.9
149.2
186.5
22?
.8
2
61.1
298.4
335.7
372
37.2
74.4
111.6
148.8
186.0
22c
.2
260.4
297.6
334.8
371
37.1
74. $
J
11
1.3
148.4
185.5
22$
.6
2
59.7
296.8
333.9
370
37.0
74.0
111.0
148.0
185.0
22$
.0
259.0
296.0
333.0
369
36.9
73.*
J
11
0.7
147-.6
184.5
221
.4
2
58.3
295.2
332.1
368
36.8
73.6
110.4
147.2
184.0
220.8
257.6
294.4
331.2
367
36.7
73.'
1
11
LO.l
146.8
183.5
22C
).2
i
56.9
293.6
830.3
366
36.6
73.2
109.8
146.4
183.0
219.6
256.2
292.8
329.4
365
36.5
73.0
109.5
146.0
182.5
219.0
255.7
292.0
328.5
364
36.4
72.8
109.2
145.6
182.0
218.4
254.8
291.2
327.6
363
36.3
72. (
3
1(
)8.9
145.2
181.5
217
.8
$
S54.1
290.4
326.7
362
36.2
72.4
108.6
144.8
181.0
.2
X
53.4
289.6
325.8
361
36.1
72.$
2
1(
)8.3
144.4
180.5
2ie
.6
1
52.7
288.8
324.9
360
36.0
72.
3
1(
)8.0
144.0
180.0
2ie
.0
2
52.0
288.0
324.0
359
35.9
71.8
1(
)7.7
143.6
179.5
215.4
251.3
287.2
323.1
358
35.8
71.6
107.4
143.2
179.0
214.8
250.6
286.4
322.2
357
35.7
71.
I
1(
)7.1
142.8
178.5
214
.2
2
49.9
285.6
321.3
356
35.6
71.2
106.8
142.4
178.0
213.6
249.2
284.8
320.4
LOGARITHMS OF NUMBERS.
No. 120 L. 079.] [No. 134 L. 130.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
120
079181
9543
9904
0266
0626 II 0987
1347
1707
2067
2426
360
1
082785
3144
3503
3861
4219
4576
4934
5291
5647
6004
357
2
3
6360
9905
6716
7071
7426
7781
| 8136
8490
8845
9198
9552
355
0258
0611
0963
1315
1667
2018
2370
2721
3071
352
4
093422
3772
4122
4471
4820
5169
5518
5866
6215
6562
349
5
6910
7257
7604
7951
8298
8644
8990
9335
9681
0026
346
6
100371
0715
1059
1403
1747
2091
2434
2777
3119
3462
343
7
3804
4146
4487
4828
5169
5510
5851
6191
6531
6871
341
8
7210
7549
7888
8227
8565
8903
9241
9579
9916
0253
338
9
110590
0926
1263
1599
1934
2270
2605
2940
3275
3609
335
130
3943
4277
4611
4944
5278
5611
5943
6276
6608
6940
333
1
7271
7603
7934
8265
8595
8926
9356
9586
9915
0245
330
2
120574
0903
1231
1560
1888
2216
2544
2871
3198
3525
328
3
3852
4178
4504
4&30
5156
5481
5806
6131
6456
6781
325
4
7105
7429
7753
8076
8399
8722
9045
9368
9690
13
0012
323
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
355
a5.5
71.0
106.5
142.0
177.5
213 0
248.5
284.0
319.5
354
35.4
70.8
106.2
141.6
177.0
212.4
247.8
283.2
318.6
353
35.3
70.6
105.9
141.2
176.5
211.8
247.1
282.4
317.7
352
35.2
70.4
105.6
140.8
176.0
211.2
246.4
281.6
316.8
351
35.1
70.2
105.3
140.4
175.5
210.6
245.7
280.8
315.9
350
35.0
70.0
105.0
140.0
175.0
210.0
245.0
280.0
315,0
349
34.9
69.8
104.7
139.6
174.5
209.4
244.3
279.2
314.1
348
34.8
69.6
104.4
139.2
174.0
208.8
243.6
278.4
313.2
847
34.7
69.4
104.1
138.8
173.5
208.2
242.9
277.6
312.3
346
34.6
69.2
103.8
138.4
173.0
207.6
242.2
276.8
311.4
345
34.5
69.0
103.5
138.0
172.5
207.0
241.5
276.0
310.5
344
34.4
68.8
103.2
137.6
172.0
206.4
240.8
275.2
309.6
343
34.3
68.6
102.9
137.2
171.5
205.8
240.1
274.4
308.7
342
34.2
68.4
102.6
136.8
171.0
205.2
239.4
273.6
307.8
341
34.1
68.2
102.3
136.4
170.5
204.6
238.7
272.8
306.9
340
34.0
68.0
102.0
136.0
170.0
204.0
238.0
272.0
306.0
339
33.9
67.8
101.7
135.6
169-. 5
203.4
237.3
271.2
305 J
338
33.8
67.6
101.4
135.2
169.0
202.8
236.6
270.4
304.2
337
33.7
67.4
101.1
134.8
1G8.5
202.2
235.9
269.6
303.3
336
33.6
67.2
100.8
134.4
168.0
201.6
235.2
268.8
302.4
335
33.5
67.0
100.5
134.0
167.5
201.0
234.5
268.0
301.5
334
33.4
66.8
100.2
133.6
167.0
200.4
233.8
267.2
300.6
333
33.3
66.6
99.9
133.2
166.5
199.8
233.1
266.4
299.7
332
33.2
664
99.6
132.8
166.0
199.2
232.4
265.6
298.8
331
33.1
66,2
99.3
132.4
165.5
198.6
231.7
264.8
297.9
330
33.0
66.0
99.0
132.0
165.0
198.0
231.0
264.0
297.0
329
32.9
65.8
98.7
131.6
164.5
197.4
230.3
263.2
296.1
328
32.8
65.6
98.4
131.2
164.0
196.8
229.6
262.4
295.2
327
32.7
65.4
98.1
130.8
163.5
196.2
228.9
261.6
294.3
326
32.6
65.2
97.8
130.4
163.0
195.6
228.2
260.8
293.4
325
32.5
65.0
97.5
130.0
162.5
195.0
227.5
260.0
292.5
324
32.4
64.8
97.2
129.6
162.0
194.4
226.8
259.2
291.6
323
32.3
64.6
96.9
129.2
161.5
193.8
226.1
258.4
290.7
3S2
32.2
64.4
96.6
128.8
161.0
193.2
225.4
257.6
289.8
LOGARITHMS OE NUMBERS.
No. 135 L. 130.]
[No. 149 L. 175.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
135
130334
0655
0977
1298
1619
1939
2260
2580
2900
3219
321
6
3539
3858
4177
4496
4814
5133
5451
5769
6086
6403
318
7
g
6721
9879
7037
7354
7671
7987
8303
8618
8934
9249
9564
316
0194
0508
0822
1136
1450
1763
2076
2389
2702
314
9
143015
3327
3639
3951
4263
4574
4885
5196
5507
5818
311
140
j
6128
9219
6438
9527
6748
9835
7058
7367
7676
7985
8294
8603
8911
309
0142
0449
0756
1063
1370
1676
1982
307
2
152288
2594
2900
3205
3510
3815
4120
4424
4728
5032
305
3
5336
5640
5943
6246
6549
6852
7154
7457
7759
8061
303
4
8362
8664
8965
9266
9567
9868
0168
0469
0769
1068
301
5
161368
1667
1967
2266
25G4
2863
3161
3460
3758
4055
299
6
4353
4650
4947
5244
5541
5838
6134
6430
6726
7022
297
7
7317
7613
7908
8203
8497
8792
9086
9380
9674
9968
295
8
170262
0555
0848
1141
1434
1726
2019
2311
2603
2895
293
9
3186
3478
3769
4060
4351
4641
4932
5222
5512
5802
291
PROPORTIONAL PARTS.
Diff. '
1
2
3
4
5
6
7
8
9
321
32.1
64.2
96.3
128.4
160.5
192.6
2$
4.7
256.8
288.9
320
32.0
64.0
96.0
128.0
160.0
192.0
224.0
256.0
288.0
319
31.9
63.8
95.7
127.6
159.5
191.4
2$
53.3
255.2
287.1
318
31.8
63.6
95.4
127.2
159.0
190.8
222.6
254.4
286.2
317
31.7
63.4
95.1
126.8
158.5
190.2
&
J1.9
253.6
285.3
316
31.6
63.2
94.8
126.4
158.0
189.6
221.2
252.8
284.4
315
31.5
63.0
94.5
126.0
157.5
189.0
2$
JO. 5
252.0
283.5
314
31.4
62.8
94.2
125.6
157.0
188.4
219.8
251.2
282.6
313
31.3
62.6
93.9
125.2
156.5
187.8
21
9.1
250.4
281.7
312
31.2
62.4
93.6
124.8
156.0
187.2
218.4
249.6
280.8
311
31.1
62.2
93.3
124.4
155.5
186.6
217.7
248.8
279.9
310
31.0
62.0
93.0
124.0
155.0
186.0
21
7.0
248.0
279.0
309
30.9
61.8
92.7
123.6
154.5
185.4
2]
6.3
247.2
278.1
308
30.8
61.6
92.4
123.2
154.0
184.3
215.6
246.4
277.2
307
30.7
61.4
92.1
122.8
153.5
184.2
214.9
245.6
276.3
306
30.6
61.2
91.8
122.4
153.0
183.6
21
4.2
244.8
275.4
305
30.5
61.0
91.5
122.0
152.5
183.0
21
3.5
244.0
274,5
304
30.4
60.8
91.2
121.6
152.0
182.4
212.8
243.2
273.6
303
30.3
60.6
90.9
121.2
151.5
181.8
2]
L2.1
242.4
272.7
302
30.2
60.4
90.6
120.8
151.0
181.2
211.4
241.6
271.8
301
30.1
60.2
90.3
120.4
150.5
180.6
210.7
240.8
270.9
300
30.0
60.0
90.0
120.0
150.0
180.0
21
LO.O
240.0
270.0
299
29.9
59.8
89.7
119.6
149.5
179.4
209.3
239.2
269.1
298
29.8
59.6
89.4
119.2
149.0
178.8
2(
)8.6
238.4
268.2
297
29.7
59.4
89.1
118.8
148.5
178.2
207.9
237.6
267.3
296
29.6
59.2
88.8
118.4
148.0
177.6
2(
)7.2
236.8
266.4
295
29.5
59.0
88.5
118.0
147.5
177.0
206.5
'236.0
265:5
294
29.4
58.8
88.2
117.6
147.0
176.4
2(
)5.8
235.2
264.6
293
29.3
58.6
87.9
117.2
146.5
175.8
205.1
234.4
263.7
292
29.2
58.4
87.6
116.8
146.0
175.2
204.4
233.6
262.8
291
29.1
58.2
87.3
116.4
145.5
174.6
203.7
232.8
261.9
290
29.0
58.0
87.0
116.0
145.0
174.0
2<
)3.0
232.0
261.0
289
28.9
57.8
86.7
115.6
144.5
173.4
2(
)2.3
231.2
260.1
288
28.8
57.6
86.4
115.2
144.0
172.8
2(
)1.6
230.4
259.2
287
28.7
57.4
86.1
114.8
143.5
172.2
200.9
229.6
258.3
286
28.6
57.2
85.8
114.4
143.0
171.6
200.2
228.8
257.4
134
LOGARITHMS OF KUMBERS.
No. 150 L,. 176.] [No. 169 L. 230. 1
N.
0
1
2
3
4
5
6
7
8
9
Diff.
150
176091
6381
6670
6959 7248
7536
7825
8113
8401
8689
289
j
8977
9264
9552
OH SO
mo«
0413
0699
0986
1272
1558
287
2
181844
2129
2415
2700
2985
3270
3555
3839
4123
4407
285
3
4691
4975
5259
5542
5825
6108
6391
6674
6956
7239
283
4
7521
7803
8084
8366
8647
8928
9209
9490
9771
0051
281
5
190332
0612
0892
1171
1451
1730
2010
2289
2567
2846
279
6
3125
3403
3681
3959
4237
4514
4792
5069
5346
5623
378
7
5900
6176
6453
6729
7005
7281
7556
7832
8107
8382
276
g
8657
8932
9206
9481
9755
0029
0303
0577
0850
1124
274
9
201397
1670
1943
2216
2488
2761
3033
3305
3577
3848
272
160
4120
4391
4663
4934
5204
5475
5746
6016
6286
6556
271
1
6826
7096
7365
7634
7904
8173
8441
8710
8979
9247
269
2
9515
9783
0051
0319
0586
0853
1121
1388
1654
1921
267
3
212188
2454
2720
2986
3252
3518
3783
4049
4314
4579
266
4
4844
5109
5373
5638
5902
6166
6430
6694
6957
7221
264
5
7484
7747-
8010
8273
8536
8798
9060
9323
9585
9846
262
6
220108
0370
0631
0892
1153
1414
1675
1936
2196
2456
261
7
2716
2976
3236
3496
3755
4015
4274
4533
4792
5051
259
8
5309
5568
5826
6084
6342
6600
6858
7115
7372
7630
258
9
7887
8144
8400
8657
8913
9170
9426
9682
9938
23
0193
256
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
285
28.5
57.0
85.5
114.0
142.5
171.0
199.5
228.0
256.5
284
28.4
56.8
85.2
113.6
142.0
170.4
198.8
227.2
255.6
283
28.3
56.6
84.9
113.2
141.5
169.8
198.1
226.4
254.7
282
28.2
56.4
84.6
112.8
141.0
169.2
197.4
225.6
253.8
281
28.1
56.2
84.3
112 4
140.5
168.6
196.7
224.8
252.9
280
28.0
56.0
84.0
112.0
140.0
168.0
196.0
224.0
252.0
279
27.9
55.8
83.7
111.6
139.5
167.4
195.3
223.2
251.1
278
27.8
55.6
83.4
111.2
139.0
166.8
194.6
222.4
250.2
277
27.7
55.4
83.1
110.8
138.5
166.2
193.9
221.6
249.3
276
27.6
55.2
82.8
110.4
138.0'
165.6
193.2
220.8
248.4
275
27.5
55.0
82.5
110.0
137.5
165.0
192.5
220.0
247.5
274
27.4
54.8
82.2
109.6
137.0
164.4
191.8
219.2
246.6
273
27.3
54.6
81.9
109.2
136.5
163.8
191.1
218.4
245.7
272
27.2
54.4
81.6
108.8
136.0
163.2
190.4
217.6
244.8
271
27.1
54.2
81.3
108.4
135.5
162.6
189.7
216.8
243.9
270
27.0
54.0
81.0
108.0
135.0
162,0
189.0
216.0
243.0
269
26.9
53.8
80.7
107.6
134.5
161.4
188.3
215.2
242.1
268
26.8
53.6
80.4
107.2
134.0
160.8
187.6
214.4
241.2
267
26.7
53.4
80.1
106.8
133.5
160.2
186.9
213 6
240.3
266
26.6
53.2
79.8
106.4
133.0
159.6
186.2
212.8
239.4
265
26.5
53.0
79.5
106.0
132.5
159.0
185.5
212.0
238.5
264
26.4
52.8
79.2
105.6
132.0
158.4
184.8
211.2
237.6
263
26.3
52.6
78.9
105.2
131.5
157.8
184.1
210.4
236.7
262
26.2
52.4
78.6
104.8
131.0
157.2
183.4
209.6
235.8
261
26.1
52.2
78.3
104.4
130.5
156.6
182.7
208.8
234.9
260
26.0
52.0
78.0
104.0
130.0
156.0
182.0
208.0
234.0
259
25.9
51.8
77.7
103.6
129.5
155.4
181.3
207.2
233.1
258
25.8
51.6
77.4
103.2
129.0
154.8
180.6
206.4
232.2
257
25.7
51.4
77.1
102.8
128.5
154.2
179.9
205.6
231.3
256
25.6
51.2
76.8
102.4
128.0
153.6
179.2
204.8
230.4
255
25.5
51.0
76.5
102.0
1£7.5
153.0
178.5
204.0
229.5
LOGARITHMS OF LUMBERS.
No. 170 L. 230.] [No. 189 L. 278.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
170
230449
0704
0960
1215
1470
1724
1979
2234
2488
2742
255
1
2996
3250
3504
3757
4011
4264
4517
4770
5023
5276
253
2
5528
5781
6033
6285
6537
6789
7041
7292
7544
7795
252
8046
8297
8548
8799
9049
9299
9550
9800
0050
0300
250
4
240549
0799
1048
1297
1546
1795
2044
2293
2541
2790
249
5
3038
3286
3534
3782
4030
4277
4525
4772
5019
•5266
248
6
5513
5759
6006
6252
6499
6745
6991
7237
7482
7728
246
7973
8219
8464
8709
8954
9198
9443
9687
9932
0176
245
8
250420
0664
0908
1151
1395
1638
1881
2125
2368
2610
243
9
2853
3096
3338
3580
3822
4064
4306
4548
4790
5031
242
180
5273
5514
5755
5996
6237
6477
6718
6958
7198
7439
241
1
7679
7918
8158
8398
8637
8877
9116
9355
9594
9833
239
2
260071
0310
0548
0787
1025
1263
1501
1739
1976
2214
238
3
2451
2688
2925
3162
3399
3636
3873
4109
4346
4582
237
4
4818
5054
5290
5525
5761
5996
6232
6467
6702
6937
235
5
7172
7406
7641
7875
8110
8344
8578
8812
9046
9279
234
9513
9746
9980
£213
0446
0679
0912
1144
1377
1609
233
7
271842
2074
2306
2538
2770
3001
3233
3464
3696
3927
232
8
4158
4389
4620
4850
5081
5311
5542
5772
6002
6232
230
9
6462
6692
6921
7151
7380
7609
7838
8067
8296
8525
229
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
255
25,5
51,0
76,5
102.0
127,5
153,0
17S.5
204.0
229,5
254
25.4
50.8
76.2
101.6
127.0
152.4
177.8
203.2
228.6
253
25.3
50.6
75.9
101.2
126.5
151.8
177.1
202.4
227.7
252
25.2
50.4
75.6
100.8
126.0
151.2
176.4
201.6
226.8
251
25.1
50.2
75.3
100.4
125.5
150.6
175.7
200.8
225.9
250
25 0
50.0
75.0
100.0
125.0
150.0
175.0
200.0
225.0
249
24.9
49.8
74.7
99.6
124.5
149.4
174.3
199.2
224.1
248
24.8
49.6
74.4
99.2
124.0
148.8
173.6
198.4
223.2
247
24.7
49.4
74.1
98.8
123.5
148.2
172.9
197.6
222.3
246
24.6
49.2
73.8
98.4
123.0
147.6
172.2
196.8
221.4
245
24.5
49.0
73.5
98.0
122.5
147.0
171.5
196.0
220.5
244
24.4
48.8
73.2
97.6
122.0
146.4
170.8
195.2
219.6
243
24.3
48.6
72.9
97.2
121.5
145.8
170.1
194.4
218.7
242
24.2
48.4
72.6
96.8
121.0
145.2
169.4
193.6
217.8
241
24.1
48.2
72.3
96.4
120.5
144.6
168.7
192.8
216.9
240
24.0
48.0
72.0
96.0
120.0
144.0
168.0
192.0
216.0
239
23.9
47.8
71.7
95.6
119.5
143.4
167.3
191.2
215.1
238
23.8
47.6
71.4
95.2
119.0
142.8
166.6
190.4
214.2
237
23.7
47.4
71.1
94.8
118.5
142.2
165.9
189.6
213.3
236
23.6
47.2
70.8
94.4
118.0
141.6
165.2
188.8
212.4
235
23.5
47.0
70.5
94.0 <
117.5
141.0
164.5
188.0
211.5
234
23.4
46.8
70.2
93.6
117.0
140.4
163.8
187.2
210.6
233
23.3
46.6
69.9
93.2
116.5
139.8
163.1
186.4
209.7
232
23.2
46.4
69.6
92.8
116.0
139.2
162.4
185.6
208.8
.231
23.1
46.2
69.3
92.4
115.5
138.6
161.7
184.8
207.9
230
23.0
46.0
69.0
92.0
115.0
138.0
161.0
184.0
207.0
229
22.9
45.8
68.7
91.6
114.5
137.4
160.3
183.2
206.1
228
22.8
45.6
68.4
91.2
114.0
136.8
159.6
182.4
205.2
227
22.7
45.4
68.1
90.8
113.5
136.2
158.9
181.6
204.8
226
22.6
45.2
67.8
90.4
113.0
135.6
158 2
180.8
203.4
LOGARITHMS OF HUMBEK&
No. 190 L. 278.] [No. 214 L. 332.
N.
0
1
f
3
4
5
6
7
8
9
Diff.
190
278754
8982
9211
9439
9667
9895
0123
0351
0578
0806
228
1
281033
1261
1488
1715
1942
2169
2396
2022
2849
3075
227
2
3301
3527
3753
3979
4205
4431
4656
4882
5107
5332
226
3
5557
5782
6007
6232
6456
6681
6905
7130
7354
7578
225
4
7802-
8026
8249
8473
8096
8920
9143
9366
9589
9812
223
5
290035
0257
0480
0702
0925
1147
1369
1591
1813
2034
222
6
2256
2478
2699
2920
3141
3303
3584
3804
4025
4246
221
7
4466
4687
4907
5127
5347
5567
5787
6007
6226
6446
220
8
6665
68&4
7104
7323
7542
7761
7979
8198
&416
8635
219
9
8853
9071
9289
9507
9725
9943
flifii
0378
0595
0813
218
200
301030
1247
1464
1681
1898
2114
UJ.UJ.
2331
2547
2764
2980
217
1
3196
3412
3628
3844
4059
4275
4491
4706
4921
5136
216
2
5351
5566
5781
5996
6211
6425
6639
6854
7068
7282
215
3
7496
7710
7924
8137
8351
85G4
8778
8991
9204
9417
213
4
9630
9843
0056
0268
/VjQI
flfiOQ
flQftfi
1 1 18
iQQfj
1 *vd.9
919
5
311754
1966
2177
2389
Viol
2600
UOiAJ
2812
uyuo
3023
111O
3234
loou
3445
1O4X
3656
KOI
211
6
3867
4078
4289
4499
4710
4920
5130
5340
5551
5760
210
7
5970
6180
6390
6599
6809
7018
7227
7436
7646
7854
209
8
8063
8272
8481
8689
8898
9106
9314
9522
9730
9938
208
9
320146
0354
0562
0769
0977
1184
1391
1598
1805
2012
207
210
2219
2426
2633
2839
3046
3252
3458
3665
3871
4077
206
1
4282
4488
4694
4899
5105
5310
5516
5721
5926
6131
205
2
6336
6541
6745
6950
7155
7359
7563
7767
7972
8176
204
3
8380
8583
8787
8991
9194
9398
9601
9805
0008
0211
203
4
330414
0617
0819
1022
1225
1427
1630
1832
2034
2236
202
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
225
22.5
45.0
67.5
90.0
112.5
135.0
157.5
180.0
202.5
224
22.4
44.8
67.2
89.6
112.0
134.4
156.8
179.2
201.6
223
22.3
44.6
66.9
89.2
111.5
133.8
156.1
178.4
200.7
222
22.2
44.4
66.6
88.8
111.0
133.2
155.4
177.6
199.8
221
22.1
44.2
66.3
88.4
110.5
132.6
154.7
176.8
198.9
220
22.0
44.0
66.0
88.0
110.0
132.0
154.0
176.0
198.0
219
21.9
43.8
65.7
87.6
109.5
131.4
153.3
175.2
197.1
218
21.8
43.6
65.4
87.2
109.0
130.8
152.6
174.4
196.2
217
21.7
43.4
65.1
86.8
108.5
130.2
151.9
173.6
195.3
216
-21.6
43.2
64.8
86.4
108.0
129.6
151.2
172.8
194.4
215
21.5
43.0
64.5
86.0
107.5
129.0
150.5
172.0
193.5
214
21.4
42.8
64.2
85.6
107.0
128.4
149.8
171.2
192.6
213
21.3
42.6
63.9
85.2
106.5
127.8
149.1
170.4
191.7
212
21.2
42.4
63.6
84.8
106.0
127.2
148.4
169.6
190.8
211
21.1
42.2
63.3
84.4
105.5
126.6
147.7
168.8
189.9
210
21.0
42.0
63.0
84.0
105.0
126.0
147.0
168.0
189.0
209
20.9
41.8
62.7
83.6
104.5
125.4
146.3
167.2
188.1
208
20.8
41.6
62.4
83.2
104.0
124.8
145.6
1664
187.2
207
20.7
41.4
62.1
82.8
103.5
124.2
144.9
165.6
186.3
206
20.6
41.2
61.8
82.4
103.0
123.6
144.2
164.8
185.4
205
20.5
44.0
61.5
82.0
102.5
123.0
143.5
164.0
184.5
204
20.4
40.8
61.2
81.6
102.0
122.4
142.8
163.2
183.6
203
20.3
40.6
60.9
81.2
101.5
121.8
142.1
162.4
182.7
202
20.2
40.4
60.6
/0,8
101.0
121.2
141.4
161.6
181.8
LOGARITHMS OF NtTMBEHS.
No. 215 L. 832.] [No. 239 L. 380.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
215
332438
2640
2842
3044
3246
3447
3649
3850
4051
4253
202
6
4454
4655
4856
5057
5257
5458
5658
5859
6059
6260
201
7
6460
6660
6860
7060
7260
7459
7659
7858
8058
8257
200
g
8456
8656
8855
9054
9253
9451
9650
9849
0047
0246
100
9
340444
0642
0841
1039
1237
1435
1632
1830
2028
2225
JUJJ
198
220
2423
2620
2817
3014
3212
3409
3606
3802
3999
4196
197
1
4392
4589
4785
4981
5178
5374
5570
5766
5062
6157
196
2
6353
6549
67'44
6939
7135
7330
7525
7720
7915
8110
195
3
8305
8500
8694
8889
9083
9278
9472
9666
9860
0054
194
4
350248
0442
~0636~
0829
1023
1216
1410
1603
1796
1989
193
5
2183
2375
2568
2761
2954
3147
3339
3532
3724
3916
193
6
4108
4301
4493
4685
4876
5068
5260
5452
5643
5834
192
7
6026
6217
6408
6599
6790
6981
7172
7363
7554
7744
191
8
Q
7935
9835
8125
8316
8506
8696
8886
9076
9266
9456
9646
190
0025
0215
0404
0593
0783
0972
1161
1350
1539
1ftQ
230
361728
1917
2105
2294
2482
2671
2859
3048
3236
3424
ioy
188
1
3612
3800
3988
4176
4363
4551
4739
4926
5113
5301
188
2
5488
5675
5862
6049
6236
6423
6610
6796
6983
7169
187
3
7356
7542
7729
7915
8101
8287
8473
8659
8845
9030
186
4
9216
9401
9587
9772
9958
O1 AQ
nqoQ
AK-jO
OfiQft
AQOQ
1QK
5
371068
1253
1437
1622
1806
U1<*O
1991
UcWo
2175
UO1O
2360
UOoO
2544
UOOO
2728
100
184
6
2912
3096
3280
3464
8647
3831
4015
4198
4382
4565
184
7
4748
4932.
5115
5298
5481
5664
5846
6029
6212
6394
183
8
6577
6759
6942
7124
7306
7488
7670
7852
8034
8216
182
9
8398
8580
8761
8943
9124
9306
9487
9668
9849
38
0030
181
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
202
201
20.2
20.1
40.4
40.2
60.6
60.3
80.8
80.4
101.0
100.5
121.2
120.6
141.4
140.7
161.6
160.8
181.8
180.9
200
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
199
19.9
39.8
59.7
79.6
99.5
119.4
139.3
159.2
179.1
198
19.8
39.6
59.4
79.2
99.0
118.8
138.6
158.4
178.2
197
19.7
89.4
59.1
78.8
98.5
118.2
137.9
157.6
177.3
196
19.6
39.2
58.8
78.4
98.0
117.6
137.2
156.8
176.4
195
19.5
39.0
58.5
78.0
97.5
117.0
136.5
156.0
175.5
194
19.4
38.8
58.2
77.G
97.0
116.4
135.8
156.2
174.6
193
19.3
38.6
57.9
77.2
96.5
115.8
135.1
154.4
173.7
192
19.2
38.4
57.6
76.8
96.0
115.2
134.4
153.6
172.8
191
19.1
38.2
57.3
76.4
95.5
114.6
133.7
152.8
171.9
190
19.0
38.0
57.0
76.0
95.0
114.0
133.0
152.0
171.0
189
18.9
37.8
56.7
75.6
94.5
113.4
132.3
151.2
170.1
188
18.8
37.6
56.4
75.2
94.0
112.8
131.6
150.4
169.2
187
18.7
374
56.1
74.8
93.5
112.2
130.9
149.6
168.3
186
18.6
37.3
55.8
74.4
93.0
111.6
130.2
148.8
167.4
185
18.5
37.0
55.5
74.0
92.5
111.0
129.5
148.0
166.5
184
18.4
36.8
55.2
73.6
92.0
110.4
128.8
147.2
165.6
183
18.3
36.6
54.9
73.2
91.5
109.8
128.1
146.4
164.7
182
18.2
36.4
54.6
72.8
91.0
109.2
127.4
145.6
163.8
181
18.1
36.2
54.3
72.4
90.5
108.6
126.7
144.8
162.9
380
18.0
36.0
54.0
72.0
90.0
108.0
126.0
144.0
162.0
179
17.9
35.8
53.7
71.6
89.5
107.4
125.3
143.3
161.1
138
LOGARITHMS OF NUMBERS.
No. 240 L. 380.]
[No. 269 L. 431.
N.
0
1
|
3
4
5
6
7
8
9
Difl.
240
1
2
3
4
5
6
7
8
9
250
1
2
3
4
5
6
7
8
9
260
1
2
3
4
5
6
7
8
9
380211
2017
3815
5606
7390
9166
390935
2697
4452
6199
7940
9674
401401
3121
4834
6540
8240
9933
0392
2;97
3995
5785
756.8
9343
0573
2377
4174
5964
7746
9520
0754
2557
4353
6142
7924
9698
0934
2737
4533
6321
8101
9875
1115
2917
4712
6499
8279
1296
3097
4891
6677
8456
1476
3277
5070
6856
8634
1656
345G
5249
7034
8811
1837
3636
£428
7212
8989
181
180
179
178
178
177
176
176
175
174
173
173
172
171
171
170
169
169
168
167
167
166
165
165
164
164
163
162
162
161
0051
1817
3575
5326
7071
8808
0228
1993
3751
5501
7245
8981
0405
2169
3926
5676
7419
9154
0582
2345
4101
5850
7593
9328
0759
2521
4277
6025
7766
9501
1112
2873
4627
6374
8114
9847
1288
3048
4802
6548
8287
1464
3224
4977
6722
8461
1641
3400
5152
6896
8634
0020
1745
3464
5176
6881
8579
0192
1917
3635
5346
7051
8749
0365
2089
.3807
5517
7221
8918
0538
2261
3978
5688
7391
9087
0711
2433
4149
5858
7561
9257
0883
2605
4320
6029
7731
9426
1056
2777
4492
6199
7901
9595
1228
2949
4663
6370
8070
9764
1573
3292
5005
6710
8410
0102
1788
3467
5140
6807
8467
0271
1956
3635
5307
6973
8633
0440
2124
3803
5474
7139
8798
0609
2293
3970
5641
7306
8964
0777
2461
4137
5808
7472
91^9
0946
2629
4305
5974
7638
9295
1114
2796
4472
6141
7804
9460
1283
2964
4639
6308
7970
9625
1451
3132
4806
6474
8135
9791
411620
3300
4973
6841
8301
9956
421604
3246
4882
6511
8135
9752
43
0121
1768
3410
5045
6674
8297
9914
0286
1933
3574
5208
6836
8459
0075
0451
2097
3737
5371
6999
8621
0236
0616
2261
3901
5534
7161
8783
i 0781
2426
4065
5697
7324
8944
0945
2590
4228
5860
7486
9106
1110
2754
4392
6023
7648
9268
'1275
2918
4555
6136
7811
9429
1439
3082
4718
6349
7973
9591
0398
0559
0720
0881
1042
1203
PROPORTIONAL PARTS.
Diff. 1 ,
2 3
4
5
6
106.8
106.2
105.6
105.0
104.4
103.8
103.2
102.6
102.0
101.4
100.8
100.2
99.6
99.0
98.4
97.8
97.2
96.6
7
8
9
178 17.8
177 17.7
176 17.6
175 17.5
174 17.4
173 17.3
172 17.2
171 17.1
170 17.0
169 16.9
168 16.8
167 16.7
166 16.6
165 16.5
164 16.4
163 16.3
162 16.2
161 16.1
35.6 53.4
35.4 53.1
35.2 52.8
35.0 52.5
34.8 52.2
34.6 51.9
34.4 51.6
34.2 51.3
34.0 51.0
33.8 50.7
33.6 50.4
33.4 50.1
33.2 49.8
33.0 49.5
32.8 49.2
32.6 48.9
32.4 48.5
32.2 48.3
71.2
70.8
70.4
70.0
69.6
69.2
68.8
68.4
68.0
67.6
67.2
66.8
66.4
66.0
65.6
65.2
64.8
64.4
89.0
88.5
88.0
87.5
87.0
86.5
86.0
85.5
85.0
84.5
84.0
83.5
83.0
82.5
82.0
81.5
81.0
80.5
124.6
123.9
123.2
122.5
121.8
121.1
120.4
119.7
119.0
118.3
117.6
116.9
116.2
115.5
114.8
114.1
113.4
112.7
142.4
141.6
140.8
140.0
139.2
138.4
137.6
136.8
136.0
135.2
134.4
133.6
132.8
132.0
131.2
130.4
129.6
128.8
160.2
159.3
158.4
157.5
156.6
155.7
154.8
153.9
153.0
152.1
151.2
150.3
149.4
148.5
147.6
146.7
145.8
144.9
LOGARITHMS OF NUMBERS.
No. 270 L. 431.] [No. 299 L. 476.
N.
0
1
2
3
4
5
•
7
8
9
Diff.
270
431364
1525
1685
1848
2007
2167
2328
2488
2649
2809
161
1
2969
3130
3290
3450
3610
3770 .
3930
4090
4249
4409
160
2
4569
4729
4888
5048
5207
5367
5526
5685
5844
6004
159
3
6163
6322
6481
6640
6799
6957
7116
7275
7433
7592
159
4
7751
7909
8067
8226
8384
8542
8701
8859
9017
9175
158
5
9333
9491
9648 ' Qftnft
9964
0122
0279
0437
0594
0752
158
6
440909
1066
1224
1381
isSf
1695
1852
2009
2166
2323
157
7
2480
2637
2793
2950
3106
3263
3419
3576
3732
3889
157
8
4045
4201
4357
4513
4669
4825
4981
5137
5293
5449
156
9
5604
5760
5915
6071
6226
6382
6537
6692
6848
7003
155
280
7158
7313
7468
7623
7778
7933
8088
8242
8397
8552
155
1
,8706
8861
9015
9170
9324
9478
9633
9787
9941
0095
154
2
'450249
0403
0557
0711
0865
1018
117'2
1326
1479
1633
154
3
1786
1940
2093
2247
2400
2553
2706
2859
3012
3165
153
4
3318
3471
3624
3777
3930
4082
4235
4387
4540
4692
153
5
4845
4997
5150
5302
5454
5606
5758
5910
6062
6214
152
6
6366
6518
6670
6821
6973
7125
7276
7428
7579
7731
152
7
7882
8033
8184
8336
8487
8638
8789
8940
9091
9242
151
g
9392
9543
9694
9845
9995
0146
0296
0447
AKQ7
0748
•JK-f
9
460898
1048
1198
1348
1499
1649
1799
1948
uoy<
2098
U(4O
2248
1O1
150
290
2398
2548
2697
2847
2997
3146
3296
3445
3594
3744
150
1
3893
4042
4191
4340
4490
4639
4788
4936
5085
5234
149
2
5383
5532
5680
5829
5977
6126
6274
6423
6571
6719
149
3
6868
7016
7164
7312
7460
7608
7756
7904
8052
8200
148
4
8347
8495
8643
8790
8938
9085 9233
9380
9527
9675
148
5
9822
9969
0116
0°G3
0410
0557
0704
0851
0998
1145
147
6
471292
1438
1585
1732
1878
2025
2171
2318
2464
2610
itt
146
7
2756
2903
3049
3195
3341
3487
3633
3779
3925
4071
146
8
4216
4362
4508
4653
4799
4944
5090
5235
5381
5526
146
9
5671
5816
5962
6107
6252
6397 6542
6687
6832
6976
145
PROPORTIONAL PARTS.
Diff.
1
2
3
4
5
6
7
8
9
161
16.1
32.2
48.3
64.4
80.5
96.6
112.7
128.8
144.9
160
16.0
32.0
48.0
64.0
80.0
96.0
112.0
128.0
144.0
159
15.9
31.8
47.7
63.6
79.5
95.4
111.3
127.2
143.1
158
15.8
31.6
47.4
63.2
79.0
94.8
110.6
126.4
142.2
157
15.7
31.4
47.1
62.8
78.5
94.2
109.9
125.6
141.3
156
15.6
31.2
46.8
62.4
78.0
93.6
109.2
124.8
140.4
155
15.5
31.0
46.5
62.0
77.5
93.0
108.5
124.0
139.5
154
15.4
30.8
46.2
61.6
77.0
92.4
107.8
123.2
138.6
153
15.3
30.6
45.9
61.2
76.5
91.8
107.1
122.4
137.7
152
15.2
30.4
45.6
60.8
76.0
91.2
106.4
121.6
136.8
151
15.1
30.2
45.3
60.4
75.5
90.6
105.7
1208
135.9
150
15.0
30.0
45.0
60.0
75.0
90.0
105.0
120.0
135.0
149
14.9
29.8
44.7
59 6
74.5
89.4
104.3
119.2
134.1
148
14.8
29.6
44.4
59.2
74.0
88.8
103.6
118.4
133.2
147
14.7
29.4
44.1
58.8
73.5
88.2
102.9
117.6
132.3
146
14 6
29.2
43.8
58.4
73.0
87.6
102.2
116.8
131.4
145
14.5
29.0
43.5
58.0
72.5
87.0
101.5
116.0
130.5
144
14.4
28.8
43.2
57.6
72.0
86.4
100.8
115.2
129.6
143
14.3
28.6
42.9
57.2
71.5
85.8
100.1
114.4
128.7
142
14.2
28.4
42.6
56.8
71.0
85.2
99.4
113.6
127.8
141
14.1
28.2
42.3
56.4
70.5
84.6
98 '1
112.8
126.9
140
14.0
28.0
42.0
56.0
70.0
84.0
98.0
112.0
126.0
LOGARITHMS OP NUMBERS.
No. 300 L, 4vr.]
|No. 339 L. 531.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
300
1
2
3
4
5
6
r»
8
9
310
1
2
3
4
5
6
8
9
320
1
2
3
4
5
6
7
8
9
330
1
2
3
4
5
6
7
8
9
477121
8566
7266
8711
7411
8855
7555
8999
7700
9143
7844
9287
7989
9431
8133
9575
8278
9719
8422
9863
145
144
144
143
143
142
142
141
141
140
140
139
139
139
138
138
137
137
136
13G
136
135
135
134
134
133
133
133
132
132
181
131
131
130
130
129
129
129
128
128
480007
1443
2874
4300
5721
7138
8551
9958
0151
1586
3016
4442
5863
7280
8692
0294
1729
3159
4585
6005
7421
8833
0438
1872
3302
4727
6147
7563
8974
0582
2016
3445
4869
6289
7704
9114
0725
2159
3587
5011
6430
7845
9255
0869
2302
3730
5153
657'2
7986
9396
1012
2445
3872
5295
6714
8127
9537
1156
2588
4015
5437
6855
8269
9677
1299
2731
4157
5579
6997
8410
9818
0099
1502
2900
4294
5683
7068
8448
9824
0239
1642
3040
4433
5822
7206
8586
9962
0380
1782
3179
4572
5960
7344
8724
0520
1922
3319
4711
6099
7483
8862
0661
2062
3458
4850
6238
7621
8999
0374
1744
3109
4471
5828
7181
8530
9874
0801
2201
3597
4989
6376
7759
9137
0941
2341
3737
5128
6515
•5897
9275
1081
2481
S876
5267
6653
8035
9412
1)785~
2154
3518
487'8
6234
7586
8934
1222
2621
4015
5406
6791
6173
9550
491362
2760
4155
5544
6930
8311
9687
0099
1470
2837
4199
5557
6911
8260
9606
0236
1607
297'3
4335
5693
7046
8395
9740
0511
1880
3246
4607
5964
7316
8G64
0648
2017
3382
4743
6099
7451
8799
0922
2291
8655
5014
6370
7721
9068
501059
2427
3791
5150
6505
7856
9203
1196
2564
3927
5286
6640
7991
9337
1333
2700
4063
5421
6776
8126
9471
0009
1349
9684
4016
5344
6668
79S7
9303
0143
1482
2818
4149
5476
6800
8119
9434
0745
2053
3356
4656
5951
7243
8531
9815
0277
1616
2951
4282
5609
6932
8251
9566
0411
1750
3084
4415
5741
7064
8S82
9697
510545
1883
3218
4548
5874
7196
8514
9828
521138
2444
3746
5045
G339
7630
8917
0679
2017
3351
4681
6006
7328
8646
9959
0813
2151
3484
4813
6139
7460
8777
0947
2284
3617
4946
6271
7592
8909
1081
2418
3750
5079
6403
7724
9040
1215
2551
3883
5211
6535
7855
9171
0090
1400
2705
4006
5304
6598
7888
9174
0221
1530
2835
4136
5434
6727
8016
9302
0353
1661
2966
4266
5563
6856
8145
9430
0484
1792
3096
4396
5693
6985
8274
9559
0615
1922
3226
4526
5822
7114
8402
9687
0876
2183
3486
4785
6081
7372
8060
9943
1007
2314
3616
4915
6210
7501
8788
1289
2575
3876
5174
6469
7759
9045
0072
1351
530200
0328 5 0456
0584
0712
0840
0968
1096
1223
PROPORTIONAL PARTS.
Diff. 1
2 3
4
5
6
7
8
9
139 13.9
138 13.8
137 13.7
136 13.6
135 13.5
134 13.4
133 13.3
132 13.2
131 131
130 130
129 12.9
128 12.8
127 12 7
27.8 41.7
27.6 41.4
27.4 41.1
27.2 40.8
27.0 40.5
26.8 40.2
26.6 39.9
26.4 39.6
26.2 89.3
26.0 89.0
25.8 38.7
25.6 38.4
25.4 38.1
55.6
55.2
54.8
54.4
54.0
53.6
53.2
52.8
52.4
52.0
51.6
51.2
50.8
69.5
69.0
68.5
68.0
67.5
67.0
66.5
66.0
65.5
65.0
64.5
64.0
63.5
83.4
82.8
82.2
81.6
81.0
80.4
79.8
79.2
78.6
78.0
77.4
76.8
76.2
97.3
96.6
95.9
95.2
94.5
93.8
93.1
92.4
91.7
91.0
90.3 i
89.6
88.9
111.2
110.4
109.6
108.8
108.0
107.2
106.4
105.3
104.8
104.0
103.2
102.4
101.6
125.1
124.2
123.3
122.4
121.5
120.6
119.7
118.8
117.9
117.0
116.1
115.2
114.3
kOGAKITHMS OP NUMBERS.
No. 340 L. 531.]
[No. 379 L.5,9.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
128
127
127
126
126
126
125
125
125
124
124
124
123
123
123
122
122
121
121
121
120
120
120
119
119
119
119
118
118
118
117
117
117
116
116
116
115
115
115
114
340
1
2
3
4
5
6
7
8
9
350
1
2
3
4
5
6
7
8
9
360
1
2
3
4
5
6
7
8
9
370
1
2
3
4
5
6
7
8
9
531479
2754
4026
5294
6558
7819
9076
1607
2882
4153
5421
6685
7945
9202
1734
3009
4280
5547
6811
8071
9327
1862
3136
4407
567'4
6937
8197
9452
1990
3264
4534
5800
7063
8322
9578
2117
3391
! 4001
5927
7189
8448
9703
2245
3518
4787
6053
7315
8574
9829
2372
3645
4914
6180
7441
8699
9954
2500
3772
5041
6306
7567
8825
2627
3899
5167
6432
7693
8951
0079
1330
2576
3820
5060
6296
7529
8758
9984
0204
1454
2701
3944
5183
6419
7652
8881
540329
1579
2825
4068
5307
6543
7775
9003
0455
1704
2950
4192
5431
6666
7898
9126
0580
1829
3074
4316
5555
6789
8021
9249
0705
1953
3199
4440
5078
6913
8144
9371
0830
2078
3323
4564
5802
7036
8267
9494
0955
2203
3447
4688
5925
7159
8:389
9616
1080
2327
3571
4812
6049
7282
8512
9739
1205
2452
3096
4936
6172
7405
8635
9861
0106
1328
2547
3762
4973
6182
7387
a589
9787
550228
1450
2668
3883
5094
6303
7507
8709
9907
0351
1572
2790
4004
5215
6423
7627
8829
0473
1094
2911
4126
5336
6544
7?'48
8948
0595
1816
3033
4247
5457
6664
7868
90G8
0717
1938
3155
4368
5578
6785
7988
9188
0840
2000
3276
4489
5699
6905
8108
9308
0962
2181
3398
4610
5820
7026
8228
9428
1084
2303
3519
4731
5940
7146
8349
9548
1206
2425
3640
4852
6061
7267
8469
9007
0026
12^1
2412
3600
4784
5906
7144
8319
9491
0146
1340
2531
3718
4903
6084
7262
8436
9008
0265
1459
2050
3837
5021
6202
7379
8554
9725
0385
1578
2769
3955
5139
6320
7497
8671
9842
0504
1698
2887
4074
5257
6437
7614
8788
9959
0624
1817
3006
4192
5376
6555
7732
8905
0743
1936
3125
4311
5494
6673
7849
9023
0803
2055
3244
4429
5612
6791
7967
9140
0982
2174'
3362
4548
5730
6909
8084
9257
561101
2293
3481
4666
5848
7026
8202
9374
0076
1243
2407
3568
4726
5880
7032
8181
9326
0193
1359
2523
3684
4841
5996
7147
8295
9441
0309
1476
2639
3800
4957
6111
7262
8410
9555
0426
1592
2755
3915
5072
6226
7377
8525
9669
570543
1709
2872
4031
5188
6341
7492
8639
0660
1825
2988
4147
5303
6457
7607
8754
0776
1942
3104
42o3
5419
6572
7722
8868
0893
2058
3220
4379
5534
6687
7836
8983
1010
2174
3336
4494
5650
6802
7951
9097
1126
2291
3452
4610
5765
6917
8066
9212
PROPORTIONAL PARTS.
Diff. 1
2
3
4
5
6
7
8
9
128 12.8
127 12.7
126 12.6
125 12.5
124 12.4
123 12.3
122 12.2
121 12.1
120 12.0
119 11.9
25.6
25.4
25.2
25.0
24.8
24.6
24.4
24.2
24.0
23.8
38.4
38.1 .
37.8
37.5
37.2
36.9
36.6
36.3
86.0
35.7
51.2
50.8
50.4
50.0
49.6
49.2
48.8
48.4
48.0
47.6
64.0
63.5
63.0
62.5
62.0
61.5
61.0
60.5
60.0
59.5
76.8
76.2
75.6
75.0
74.4
73.8
73.2
72.6
72.0
71.4
89.6
88.9
88.2
87.5
86.8
86.1
85.4
84.7
84.0
83.3
102.4
101.6
100.8
100.0
99.2
98.4
97.6
96.8
96.0
95.2
115.2
114.3
113.4
112.5
111.6
110.7
109.8
108.9
108.0
107.1
LOGARITHMS OF LUMBERS.
No. 380. I, 579.]
[No. 414 L. 617.
N.
380
1
2
3
4
5
6
7
8
9
390
1
2
3
4
5
G
7
8
9
400
1
2
3
4
5
6
7
8
9
410
1
2
3
4
0
1
2
3
4
5
6
7
8
9
Diff.
579784
9898
1
"0469"
1608
2745
3879
5009
6137
7262
8384
9503
0012
1153
2291
3426
4557
5686
6812
7935
9056
0126
1207
2404
3539
4670
5799
6925
8047
9167
0241
1381
2518
3652
4783
5912
7037
8100
9279
0355
1495
2031
3765
4896
6024
7149
8272
9391
0583
1722
2858
3992
5122
6250
7374
8496
9615
0697
1836
297'2
4105
5235
6362
7486
8608
9726
0811
1950
3085
4218
5348
6475
7599
8720
9838
0953
2066
3175
4282
5386
6487
7586
8681
9774
114
113
112
111
110
109
108
107
106
105
580925
2063
3199
4331
5461
6587
7711
8832
9950
1039
2177
3312
4444
5574
6700
7823
8944
0061
1176
2288
3397
4503
5606
6707
7805
8900
9992
~1082~
2169
3253
4334
5413
6489
7562
8633
9701
0173
1287
2339
3508
4614
5717
6817
7914
9009
0284
1399
2510
3018
47.24
5827
6927
8024
9119
0210
1299
2386
3469
4550
5628
6704
7777
8847
9914
0396
1510
2621
3729
4834
5937
7037
8134
9228
0507
1621
2732
3840
4945
6047
7146
8343
9337
0619
1732
2843
3950
5055
6157
7256
8353
9446
0730
1843
2954
4001
5165
6*67
7306
8462
9556
0842
1955
3004
4171
5270
6377
7476
8572
9665
0755
1843
2928
4010
5089
6166
7241
8312
9381
591065
2177
3286
4393
5496
6597
7695
8791
9883
600973
2060
3144
4226
5305
6381
7455
8526
9594
0101
1191
2277
3361
4442
5521
6596
7669
8740
9808
C319
1408
2494
3577
4G58
5736
6811
7884
8954
0428
1517
2603
3686
4706
5844
6919
7991
9001
0537
1625
2711
3794
4874
5951
7026
8098
9167
0646
1734
2819
3902
4982
6059
7133
8205
9274
0804
1951
3036
4118
5197
6274
7348
8419
9488
0021
1086
2148
3207
4264
5319
6370
7420
0128
1192
2254
3313
4370
5424
6476
7525
0234
1298
2360
3419
4475
5529
6581
7629
0341
1405
2466
3525
4581
5634
6686
7734
0447
1511
2572
3630
4686
5740
6790
7839
0554
1617
2678
8736
4792
5845
6895
7943
010660
1723
2784
3842
4897
5950
7000
0767
1829
2890
3947
5003
6055
7105
0873
1936
2996
4053
5108
6160
7210
0979
2042
3102
4159
5213
6265
7315
PROPORTIONAL PARTS.
Diff. 1
2
3
4
5
S
7
8
9
118 11.8
117 11.7
116 11.6
115 11.5
114 11.4
113 11.3
113 11.2
111 11.1
110 11.0
109 10.9
108 10.8
107 10.7
106 10.6
105 10.5
104 10.4
23.6
23.4
23.2
23.0
22.8
22.6
22.4
22.2
22.0
21.8
21.6
21.4
21.2
21.0
20.8
35.4
35.1
34.8
34.5
84.2
33.9
33.6
33.3
33.0
32.7
32.4
32.1
31.8
.81.5
31.2
47.2
46.8
46.4
46.0
45.6
45.2
44.8
44.4
44.0
43.6
43.2
42.8
42.4
42.0
41.6
59.0
58.5
58.0
57.5
57.0
56.5
56.0
55.5
55.0
54.5
54.0
53.5
53.0
52.5
52.0
70.8
70.2
69.6
69.0
68.4
67.8
67.2
66.6
66.0
65.4
64.8
64.2
63.6
63.0
62.4
82.6
81.9
81.2
80.5
79.8
79.1
78.4
77.7
77.0
76.3
75.6
74.9
74.2
73.5
72.8
94.4
93.6
92,8
92.0
91.2
90.4
89.6
88.8
88.0
87.2
86.4
85.6
84.8
84.0
83.2
100.2
105.3
104.4
103.5
102.6
101.7
100.8
99.9
99.0
98.1
97.2
96.3
95.4
94.5
93.0
LOGARITHMS OF NUMBERS.
143
No. 415 L. 618.] INo. 459 L. 662
N.
415
6
7
8
9
420
1
2
3
4
5
6
7
8
9
430
1
2
3
4
5
6
r
8
9
440
1
2
3
4
5
6
7
8
9
450
1
2
3
4
5
6
8
9
0
1
2
3
4
5
6
7
8
9
Diff.
618048
9093
8153
9198
8257
9302
8362
9406
8466
9511
8571
9615
8676
9719
0760
1799
2835
3869
4901
5929
6956
7980
9002
8780
9824
8884
9928
~0968~
2007
3042
4076
5107
6135
7161
8185
9206
8989
0032
107'2
2110
3146
4179
5210
6238
7263
8287
9308
105
104
103
102
101
100
99
98
97
96
95
620136
1176
2214
3249
4282
5312
6340
7366
8389
9410
0240
1280
2318
3353
4385
5415
6443
7468
8491
9512
0580
1545
2559
3569
4578
5584
6588
7590
8589
9586
0344
1384
2421
3456
4488
5518
6516
7571
8593
9613
0448
1488
2525
3559
4591
5621
6648
7673
8695
9715
0552
1592
2628
3663
4695
5724
6751
7775
8797
9817
0656
1695
2732
3766
4798
5827
6853
7878
8900
9919
0864
1903
2939
3973
5004
6032
7058
8082
9104
0021
1088
2052
3064
4074
5081
6087
7089
8090
9088
0123
1139
2153
3165
4175
5182
6187
7189
8190
9188
~0183~
1177
2168
3156
4143
5127
6110
7089
8067
9043
0224
1241
2255
3266
4276
5283
6287
7290
8290
9287
0283
1276
2267
3255
4342
5226
6208
7187
8165
9140
0326
1342
2356
3367
4376
5383
6388.
7'390
8389
9387
630428
1444
2457
3468
4477
5484
6488
7490
8489
9486
0631
1647
2660
3670
4679
5685
6688
7690
8689
9686
0733
1748
2761
3771
4779
5785
6789
7790
8789
9785
0835
1849
2862
3872
4880
5886
6889
7890
8888
9885
0936
1951
2963
3973
4981
5986
6989
7990
8988
9984
0084
1077
2069
3058
4044
5029
6011
6992
7969
8945
9919
0382
1375
2366
3354
4340
5324
6306
7285
8262
9237
640481
1474
2465
3453
4439
5422
6404
7383
8360
9335
0581
1573
2563
3551
4537
5521
6502
7481
8458
9432
0680
1672
2662
3650
4636
5619
6600
7579
8555
9530
0779
1771
2761
3749
4734
5717
6698
7676
8653
9627
0879
1871
2860
3847
4832
5815
6796
777'4
8750
9724,
0978
1970
2959
3946
4931
5913
6894
7872
8848
9821
0016
0987
1956
2923
3888
4850
5810
6769
7725
8679
9631
0581
1529
2475
0113
1084
2053
3019
3984
4946
5906
6864
7820
8774
9726
0676
1623
2569
0210
1181
2150
3116
4080
5042
6002
6960
7916
8870
9821
~vm
171fi
2663
650308
1278
2246
3213
4177
5138
6098
7056
8011
8965
9916
0405
1375
2343
3309
4273
5235
6194
7152
8107
9060
0502
1472
2440
3405
4369
5331
6290
7247
8202
9155
0599
1569
2536
3502
4465
5427
6386
7343
8298
9250
0696
1666
2633
3598
4562
5523
6482
7438
8393
9346
0793
17'62
2730
3695
4658
5619
6577
7534
8488
9441
0890
1859
2826
3791
4754
5715
6673
7629
8584
9536
0011
0960
1907
0106
1055
2002
0201
1150
2096
0296
1245
2191
0391
1339
2286
0486
1434
2380
660865
1813
PROPORTIONAL PARTS.
Diff. 1
234
5
6 7
8
9
105 10.5
104 10.4
103 10.3
102 10.2
101 10.1
100 10.0
99 9.9
21.0 31.5 42.0
20.8 31.2 41.6
20.6 30.9 41.2
20.4 30.6 40.8
20.2 30.3 40.4
20.0 30.0 40.0
19.8 29.7 39.6
52.5
52.0
51.5
51.0
50.5
50.0
49.5
63.0 73.5
62.4 72 8
61.8 721
61.2 714
60.6 70 7
60.0 70 0
59.4 69.3
84.0
83.2
82.4
81.6
80.8
80.0
79.2
94.5
93.6
92.7
91.8
90.9
90.0
89.1
LOGARITHMS OF LUMBERS.
No. 4GO L. 662.]
[No. 499 L. 698.'
N,
0
1
2
8
4
5
C
7
8
9
Diff.
460
662758
2852
2947
3041
3135
3230
3324
3418 3512
3607
1
3701
3795
3889
398
3
4078
4172
4266
4£
4454
4548
2
4642
4736
4830
4924
5018
5112
5206
5299
5393
5487
94
3
5581
5675
5769
586
2
5956
6050
6143
6$
5:-i7
6331
6424
4
6518
6612
6705
6799
6892
6986
7079
7173
7266
7360
5
7453
7546
7640
773
3
7826
7920
8013
81
08
8199
8293
6
8386
8479
8572
866
5
8759
8852
8945
9038
9131
9224
9317
9410
9503
959
ft
9689
9782
9875
91
)t\7
0060
0153
93
8
670246
0339
0431
0524
0617
0710
0802
0895
0988
1080
9
1173
1265
1358
1451
1543
1636
1728
1821
1913
2005
470
2098
2190
2283
2375
2467
2560
2652
2744
2836
2929
1
3021
3113
3205
329
7
3390
3482
3574
3(
3758
3850
2
3942
4034
4126
4218
4310
4402
4494
4586
4677
4769
92
3
4861
4953
5045
5137
5228
5320
5412
5503
5595
5687
4
5778
5870
5962
605
3
6145
6236
6328
fr
U9
6511
6602
5
6694
6785
6876
6968
7059
7151
7242
7333
7424
7516
6
7607
7698
7789
788
1
7972
8063
8154
nr>
8336
8427
7
8518
8609
8700
8791
8882
8973
9064
9155
9246
9337
91
g
9428
9519
9610
970
in
9791
9882
9973
0063
0154
0245
9
680336
0426
0517
0607
0698
0789
0879
0970
10GO
1151
480
1241
1332
1422
1513
1603
1693
1784
1874
1964
2055
1
2145
2235
2326
241
6
2506
2596
2686
2
•77
2867
2957
2
3047
3137
3227
3317
3407
3497
3587
3677
37G7
3857
90
3
3947
4037
4127
4217
4307
4396
4486
4576
4666
4756
4
4845
4935
5025
511
4
5204
5294
5383
fr
173
5563
5652
5
5742
5831
5921
6010
6100
6189
6279
6
J68
6458
6547
6
6636
6726
6815
69C
4
6994
7083
7172
7,
861
7351
7440
7
7529
7618
7707
7796
7886
T975
8064
8153
8242
8331
89
8
8420
8509
8598
868
7
8776
8865
8953
9(
m
9131
9220
9
9309
9398
9486
957
5
9664
9753
9841
Q
)30
0019
0107
490
690196
0285
0373
0462
0550
0639
0728
0816
0905
0993
1
1081
1170
1258
134
1435
1524
1612
ji
'00
1789
1877
2
1965
2053
2142
2:230
2318
2406
2494
2583
2671
2759
3
2847
2935
3023
311
1
3199
3287
3375
&
63
3551
3639
88
4
3727
3815
3903
3991
4078
4166
4254
4342
4430
4517
5
4605
4693
4781
48C
8
4956
5044
5131
5219
5307
5394
6
5482
5569
5657
574
4
5832
5919
6007
6(
)94
6182
6269
7
6356
6444
6531
6618
6706
6793
6880
6968
7055
7142
8
7229
7317
7404
74[
1
7578
7665
7752
7*
89
7926
8014
9
8100
8188
8275
8362
8449
8535
8622
8709
8796
8883
87
PROPORTIONAL PARTS.
Diff. 1
2 3
4
5
6
7
8
9
98 9.8
19.6 29.4
39.2
49.0
58.8
68.6
78.4
88.2
9? 9.7
19.4 29.1
38.8
48.5
58.2
67.9
77.6
87.8
96 9.6
19.2 28.8
38.4
48.0
57.6
67.2
76.8
86.4
95 9.5
19.0 28.5
38.0
47.5
57.0
66.5
76.0
85.5
94 9.4
18.8 28.2
37.6
47.0
56.4
65.8
75.2
84.6
93 9.3
18.6 27.9
37.2
46.5
55.8
65.1
74.4
83.7
92 9.2
18.4 27.6
36.8
46.0
55.2
64.4
73.6
82.8
91 9.1
18.2 27.3
36.4
45.5
54.6
63.7
72.8
81.9
90 9.0
18.0 27.0
36.0
45.0
54.0
63.0
72.0
81.0
89 8.9
17.8 26.7
35.6
44.5
53.4
62.3
71.2
80.1
88 8.8
17.6 26.4
35.2
44.0
52.8
61.6
70.4
79.2
87 8.7 17.4 26.1
34.8
43.5
52.2
60.9
69.6
78.3
86 8.6
17.2 25.8
34.4
43.0
51.6
60.2
68.8
77.4
LOGARITHMS OP NUMBERS.
145
[ No. 500 L. 698.] [No. 544 L. 736.
N.
0
1
2
3
4
6
6
7
8
9
Diff.
500
698970
9057
9144
9231
9317
9404
9491
9578
9664
9751
1
9838
9924
0011
0098
0184
0271
0358
0444
0531
0617
2
700704
0790
0877
0963
1050
1136
1222
1309
1395
1482
3
1568
1654
1741
1827
1913
1999
2086
2172
2258
2344
•
4
2431
2517
2603
2689
2775
2861
2947
3033
3119
3205
5
3291
3377
3463
3549
3635
3721
3807
3893
3979
4065
86
6
4151
4236
4322
4408
4494
4579
4665
4751
4837
4922
7
5008
5094
5179
5265
5350
5436
5522
5607
5693
5778
8
5864
5949
6035
6120
62G6
6291
6376
6462
6547
6632
9
6718
6803
6888
6974
7059
7144
7229
7315
7400
7485
510
7570
7655
7740
7826
7911
7996
8081
8166
8251
8336
1
8421
8506
8591
8676
8761
8846
8931
9015
9100
9185
85
2
9270
9355
9440
9524
9609
9694
9779
9863
9948
0033
3
710117
0202
0287
0371
0456
0540
0625
0710
0794
0879
4
0963
1048
1132
1217
1301
1385
1470
1554
1639
1723
5
1807
1892
1976
2060
2144
2229
2313
2397
2481
2566
6
2650
2734
2818
2902
2986
3070
3154
3238
3323
3407
ft4
7
3491
3575
3659
3742
3826
3910
3994
4078
4162
4246
04
8
4330
4414
4497
4581
4665
4749
4833
4916
5000
5084
9
5167
5251
5335
5418
5502
5586
5669
5753
•5836
5920
520
6003
6087
6170
6254
6337
6421
6504
6588
6671
6754
1
6838
6921
7004
7088
7171
7254
7338
7421
7504
7587
2
7671
7754
7837
7920
8003
8086
8169
8253
8336
8419
3
8502
8585
8668
8751
8834
8917
9000
9083
9165
9248
83
4
9331
9414
9497
9580
9663
9745
9828
9911
9994
0077
5
720159
0242
0325
0407
0490
0573
0655
0738
0821
0903
6
0986
1068
1151
1233
1316
1398
1481
1563
1646
1728
7
1811
1893
1975
2058
2140
2222
2305
2387
2469
2552
8
2634
2716
2798
2881
2963
3045
3127
3209
3291
3374
9
3456
3538
3620
3702
3784
3866
3948
4030
4112
4194
82
530
4276
4358
4440
4522
4604
4685
4767
4849
4931
5013
1
5095
5176
5258
5340
5422
5503
5585
5667
5748
5830
2
5912
'5993.
6075
6156
6238
6320
6401
6483
6564
6646
3
6727
6809
6890
697'2
7053
7134
7216
7297
7379
7460
4
7541
7623
7704
7785
7'866
7948
8029
8110
8191
8273
5
8354
8435
8516
8597
8678
8759
8841
8922
9003
9084
6
9165
9246
9327
9408
9489
9570
9651
9732
9813
9893
81
7
9974
0055
0136
0217
0298
0378
0459
0540
0621
0702
8
730782
0863
0944
1024
1105
1186
1266
1347
1428
1508
9
1589
1669
1750
1830
1911
1991
2072
2152
2233
2313
540
2394
2474
2555
2635
2715
2796
2876
2956
3037
3117
1
8197
3278
3358
3438
3518
3598
3679
3759
3839
3919
2
3999
4079
4160
4240
4320
4400
4480
4560
4640
4720
on
3
4800
4880
4960
5040
5120
5200
5279
5359
5439
5519
w
4
5599
5679
5759
5838
5918
5998
6078
6157
6237
6317
PROPORTIONAL PARTS.
Diff. 1
234
5
678
9
87 8.7
17.4 26.1 34.8
43.5
52.2 60.9 69.6
78.3
86 8.6
17.2 25.8 34.4
43.0
51.6 60.2 68.8
77.4
85 8.5
17.0 25.5 34.0
42.5
51.0 59.5 68.0
76.5
84 8.4
16.8 25.2 33.6
42.0
50.4 58.8 67.2
75.6
LOGARITHMS OP CUMBERS.
No. 545 L. 736.]
[No. 584 L. 767.
N.
0
1
2
8
4
5
6
7
8
9
Diff.
545
736397
6476
6556
6635
6715 1 6795
6874
6954
7034
7113
6
7193
7272
7352
7431
7511
7590
7670
7749
7829
7908
7
7987
8067
8146
8S&
25
8305
8384
8463
8543
862
2
8701
8
8781
8860
8939
9018
9097
9177
9256
9335
9414
9493
9
9572
9651
9731
98
10
9889
9968
0047
O19A
H90
C\9RA
550
740363
0442
0521
0600
0678
0757
0836
U1/*D
0915
\J4\JO
0994
\)4&±
1073
29
1
1152
1230
1309
13*
S8
1467
1546
1624
1703
178
2
1860
2
1939
2018
2096
2175
2254
2332
2411
2489
2568
2647
3
2725
2804
2882
29t
51
3039
! 3118
3196
3275
335
3
3431
4
3510
3588
3667
3745
3823
3902
3980
4058
4136
4215
5
4293
4371
4449
4528
4606
4684
4762
4840
4919
4997
6
5075
5153
5231
53(
)9
5387
; 5465
5543
5621
569
)
5777
78
7
5855
5933
6011
601
S9
6167
6245
6323
6401
647
)
6556
8
6634
6712
6790
68(
58
6945
7023
7101
7179
7256
7334
9
7412
7489
7567
7645
7722
7800
7878
7955
8oa
J
8110
560
8188
8266
8343
8421
8498
1 8576
8653
8731
880
*
8885
1
8963
9040
9118
9195
9272
| 9350
9427
9504
9582
9659
2
9736
9814
9891
99(
58
0045
0123
0200
O977
AOR
4
fMOl
3
750508
0586
0663
0740
0817
0894
0971
\)/ii t
1048
UoO^±
1125
U4ol
1202
4
1279
1356
1433
1510
1587
1664
1741
1818
1895
1972
5
2048
2125
2202
2279
2356
2433
2509
2586
2663
2740
77
6
2816
2893
2970
3fr
17
3123
3200
3277
3ar>3
343
)
3506
7
3583
3660
3736
3813
3889
3966
4042
4119
4195
4272
8
4348
4425
4501
45'
'8
4654
4730
4807
4883
496
3
5036
9
5112
5189
5265
5341
5417
i 5494
5570
5646
5722
5799
5TO
5875
5951
6027
6103
6180
1 6256
6332
6408
6484
6560
1
6636
6712
6788
6864
6940
7016
7092
7168
7244
7320
76
2
7396
7472
7548
7ft
24
7700
i 7775
7851
7927
800
3
8079
3
8155
8230
8306
8382
8458
> 8533
8609
8685
87'61
8836
4
8912
8988
9063
91,
39
9214
i 9290
9366
9441
951
I
9592
5
9668
9743
9819
DM
)4
997'0
0045
0121
0196
097
->
fiQ/17
6
760422
0498
0573
0649
0724
0799
0875
0950
\}4ii &
1025
Uo4<
1101
7
1176
1251
1326
1402
1477
1552
1627
1702
1778
1853
8
1928
2003
2078
21,
33
2228
i 2303 2378
2453
252
1
2604
9
2679
2754
2829
2904
29?'8
3053 3128
3203
3278
3353
73
580
3428
3503
3578
3653
3727
3802
3877
3952
4027
4101
1
4176
4251
4326
44(
)0
4475
4550
4624
4699
477
i
4848
2
4923
4998
5072
5147
5221
5296
5370
5445
5520
5594
3
5669
5743
5818
58<
K
5966
6041
6115
6190
62fr
1
6338
4
6413
6487
6562
6636
6710
6785
6859
6933
7007
7082
PROPORTIONAL PARTS.
Diff. 1
2 3
4
5
6 7
8
66.4
9
74.7
83 8.3
16.6 24.9
33.2
41.5
49.8 58.1
82 8.2
16.4 24.6
32.8
41.0
49.2 57.4
65.6
73.8
81 8.1
16.2 24.3
32.4
40.5
48.6 56.7
64.8
72.9
80 8.0
16.0 24.0
32.0
40.0
48.0 56.0
64.0
72.0
79 7.9
15.8 23.7
31.6
39.5
47.4 55.3
63.2
71.1
78 78
15.6 23.4
31.2
39.0
46.8 54.6
62.4
70.2
77 7.7
15.4 23.1
30.8
38.5
46.2 53.9
61.6
69.3
76 7.6
15.2 22.8
30.4
38.0
45.6 53.2
60.8
68.4
75 7.5
15.0 22.5
30.0
37.5
45.0 52.5
60.0
67.5
74 7.4
14.8 22.2
29.6
37.0
44.4 51.8
59.2
66.6
LOGARITHMS OF NUMBERS.
147
No. 585 L. 767.1
[No. 629 L. 799.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
585
767156
7230
7304
7379
7453
7527
7601
7675
7749
7823
6
7898
7972
8046
8120
8194
8268
8342
8416
8490
8564
74
7
8638
8712
8786
88t
0
8934
9008
9082
9
156
9230
9303
g
9377
9451
9525
95£
9
9673
9746
9820
9
894
9968
0042
9
770115
0189
0263
0336
0410
0484
0557
0631
0705
0778
590
0852
0926
0999
1073
1146
1220
1293
1367
1440
1514
1
1587
1661
1734
180
8
1881
1955
2028
2
102
2175
2248
2
2322
2395
2468
2542
2615
2688
2762
2835
2908
2981
3
3055
3128
3201
327
4
3348
3421
3494
a
•567
3640
3713
4
3786
3860
3933
4006
4079
4152
4225
4298
4371
4444
73
5
4517
4590
4663
473
6
4809
4882
4955
&
108
5100
5173
6
5246
5319
5392
5465
5538
5610
5683
5756
5829
5902
7
5974
6047
6120
619
3
6265
6338
6411
6-
188
6556
6629
8
6701
6774
6846
6919
6992
7064
7137
7209
7282
7354
9
7427
7499
7572
7644
7717
7789
7862
7934
8006
8079
600
8151
8224
8296
8368
8441
8513
8585
8
.58
8730
8802
1
8874
8947
9019
909
1
9163
9236
9308
9
M)
9452
9524
2
9596
9669
9741
981
3
9885
9957
0029
O
mi
0173
0245
3
780317
0389
0461
0533
0605
0677
0749
0821
0893
0965
72
4
1037
1109
1181
1253
1324
1396
1468
1540
1612
1684
5
1755
1827
1899
197
1
2042
2114
2186
21
358
2329
2401
6
2473
2544
2616
268
8
2759
2831
2902
2
J?4
3046
3117
7
3189
3260
3332
3403
3475
3546
3618
8
>s<)
3761
3832
8
3904
3975
4046
4118
4189
4261
4332
4403
4475
4546
9
4617
4689
4760
483
1
4902
4974
5045
5116
5187
5259
610
5330
5401
5472
5543
5615
5686
5757
5
328
5899
5970
1
6041
6112
6183
625
4
6325
6396
6467
6
588
6609
6680
71
2 { 6751
6822
6893
6964
7035
7106
7177
7248
7319
7390
3 7460
7531
7602
767
a
7744
7815
7885
7
)56
8027
8098
4
8168
8239
8310
838
i
8451
8522
8593
8
>r>3
8734
8804
5
8875
8946
9016
908
7
9157
9228
9299
9
369
9440
9510
9581
9651
9722
979
0
9863
9933
0004
Ot
"»74
0144
0215
7
790285
0356
0426
0496
0567
0637
0707
0778
0848
0918
8
0988
1059
1129
119
9
1269
1340
1410
1
ISO
1550
1620
9
1691
1761
1831
1901
1971
2041
2111
2181
2252
2322
620
2392
2462
2532
2602
2672
2742
2812
2!
m
2952
3022
70
1
3092
3162
3231
330
1
3371
3441
3511
a
581
3651
3721
2
3790
3860
3930
400
0
4070
4139
4209
4
279
4349
4418
3
4488
4558
4627
4697
4767
4836
4906
4976
5045
5115
4
5185
5254
5324
539
3
5463
5532
5602
5
>'«~
5741
5811
5
5880
5949
6019
6088
6158
6227
6297
6366
6436
6505
6
6574
6644
6713
678
8
6852
6921
6990
7(
MJO
7129
7198
7
7268
7337
7406
7475
7545
7614
7683
7752
7821
7890
8
7960
8029
8008
816
7
8236
8305
8374
&
i43
8513
8582
9
8651
8720
8789
8858
8927
8996
9065
9134
9203
927.8
69
PROPORTIONAL PARTS.
DiflP. 1
2 3
4
5
6
7 8
9
75 7.5
15.0 22.5
30.0
37.5
45.0
52.5 60.0
67.5
74 7.4
14.8 22.2
29.6.
37.0
44.4
51.8 59.2
66.6
73 7.3
14.6 21.9
29.2
36.5
43.8
51.1 58.4
65.7
72 7.2
14.4 21.6
28.8
36.0
43.2
50.4 57.6
64.8
71 7.1
14.2 21.3
28.4
35.5
42.6
49.7 56.8
63.9
70 7.0
14.0 21.0
28.0
35.0
42.0
49.0 56.0
63.0
69 6.9
13.8 20.7
27.6
34.5
41.4
48.3 55.2
62.1
148
LOGARITHMS OP KUMBERS.
No, 630 L. 799.] [No. 674 L. 829.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
630
799341
9409
9478
9547
9616
9685
9754
9823
9892
9961
1
800029
0098
0167
0236
0305
0373
0442
0511
0580
0640
2
0717
0786
0854
0923
0992
1061
1129
1198
1266
1335
3
1404
1472
1541
1609
1678
1747
1815
1884
1952
2021
4
2089
2158
2226
2295
2363
2432
2500
2568
2637
2705
5
2774
2842
2910
2979
3047
3116
3184
3252
3321
3389
6
3457
3525
3594
3662
3730
3798
3867
3935
4003
4071
7
4139
4208
4276
4344
4412
4480
4548
4616
4685
4753
8
4821
4889
4957
5025
5093
5161
5229
5297
5365
5433
68
9
5501
5569
5637
5705
5773
5841
5908
5976
6044
6112
640
806180
6248
6316
63&4
6451
6519
6587
6655
6723
6790
1
6858
6926
6994
7061
7129
7197
7264
7332
7400
7467
2
7535
7603
7670
7738
7806
7873
7941
8008
8076
8143
3
8211
8279
8346
8414
8481
8549
8616
8684
8751
8818
4
8886
8953
9021
9088
9156
9223
9290
9358
9425
9492
5
9560
9627
9694
9762
9829
9896
9964
0031
0098
0165
6
810233
0300
0367
0434
0501
0569
0636
0703
0770
0837
7
0904
0971
1039
1106
1173
1240
1307
1374
1441
1508
67
8
1575
1642
1709
1776
1843
1910
1977
2044
2111
2178
9
2245
2812
2379
2445
2512
2579
2646
2713
2780
2847
650
2913
2980
3047
3114
3181
3247
3314
3381
3448
3514
1
3581
3648
3714
3781
3848
3914
3981
4048
4114
4181
2
4248
431-4
4381
4447
45*4
4581
4647
4714
4780
4847
3
4913
4980
5046
5113
5179
5246
5312
5378
5445
5511
4
5578
5644
5711
5777
5843
5910
5976
6042
6109
6175
I
6241
6308
6374
6440
6506
6573
6639
6705
6771
6838
6
6904
6970
7036
7102
7169
7235
T301
7367
7433
7499
7
75G5
7631
7698
7764
7830
7896
7962
8028
8094
8160
8
8226
8292
8358
8424
8490
8556
8622
8688
8754
8820
9
8885
8951
9017
9083
9149
9215
9281
9346
9412
9478
Co
660
9544
9610
9676
9741
9807
9873
9969
0004
0070
0136
1
820201
0267
0333
0399
0464
0530
0595
0661
0727
0792
2
0858
0924
0989
1055
1120
1186
1251
1317
1382
1448
3
1514
1579
1645
1710
1775
1841
1906
1972
2037
2103
4
2168
2233
2299
2364
2430
2495
2560
2626
2691
2756
5
2822
2887
2952
3018
3083
3148
3213
3279
3344
3409
6
3474
3539
3605
3670
37'35
3800
3865
3930
3996
4061
7
4126
4191
4256
4321
4386
4451
4516
4581
4646
4711
fiK
8
4776
4841
4906
4971
5036
5101
5166
5231
5296
5361
DO
9
5426
5491
5556
5621
5686
5751
5815
5880
5945
6010
670
6075
6140
6204
6269
6334
6399
6464
6528
6593
6658
1
6723
6787
6852
6917
6981
7046
7111
7175
7240
7305
2
7369
7434
7499
7563
7628
7692
7757
7821
7886
7951
3
8015
8080
8144
8209
8273
8338
8402
8467
8531
8595
4
8660
8724
8789
8853
8918
8982
9046
9111
9175
9239
PROPORTIONAL PARTS.
Diff
1
2
3 4
5
678
9
68
6.8
13.6
20.4 27.2
34.0
40.8 47.6 544
61.2
67
6.7
13.4
20.1 26.8
33.5
40.2 46.9 53,6
60.3
66
6.6
13.2
19.8 26.4
33.0
39.6 46.2 52.8
59.4
65
6.5
13.0
19.5 26.0
32.5
39.0 45.5 52.0
58.5
64
6.4
1£.8
19.2 25. Q
32.0
38,4 44.8 51.2
57.6
LOGARITHMS OF NUMBERS.
U9
No. 675 L. 829.? [No. 719 L. 857.
N.
0
1
2
8
4
6
6
7
8
9
Diff.
675
829304
9368
9432
9497
9561
9625
9690
9754
9818
9882
g
9947
0011
0075
0139
0204
0268
0332
0396
0460
0525
7
830589
0653
0717
0781
0845
0909
0973
1037
1102
1166
8
1230
1294
1358
1422
1486
1550
1614
1678
1742
1806
64
9
1870
1984
1998
2062
2126
2189
2253
2317
2381
2445
680
2509
2573
2637
2700
2764
2828
2892
2956
3020
3083
1
3147
3211
3275
3338
3402
3466
3530
3593
3657
3721
2
3784
3848
•3912
3975
4039
4103
4166
4230
4294
4357
3
4421
4484
4548
4611
4675
4739
4802
4866
4929
4993
4
5056
5120
5183
5247
5310
5373
5437
5500
5564
5627
5
5691
5754
5817
5881
5944
6007
6071
6134
6197
6261
6
6324
6387
6451
6514
6577
6641
6704
6767
6830
6894
7
6957
7020
7083
7146
7210
7273
7336
7399
7462
7525
8
7588
7652
7715
7778
7841
7904
7967
8030
8093
8156
9
8219
8282
8345
8408
8471
8534
8597
8660
8723
8786
63
690
8849
8912
8975
9038
9t01
9164
9227
9289
9&52
9415
1"
9478
9541
9604
9667
97'29
9792
9855
9918
9981
0043
2
840106
0169
0232
0294
0357
0420
0482
0545
0608
0671
3
0733
0796
0859
0921
0984
1046
1109
1172
1234
1297
4
1359
1422
1485
1547
1610
1672
1735
1797
1860
1922
'5
1985
2047
2110
2172
2235
2297
2360
2422
2484
2547
6
2609
2672
2734
2796
2859
2921
2983
3046
3108
3170
7
3233
3295
3357
3420
3482
3544
3606
3669
3731
3793
8
3855
3918
3980
4042
4104
4166
4229
4291
4353
4415
9
447.7
4539
4601
4664
4726
4788
4850
4912
4974
5036
700
5098
5160
5222
5284
5346
5408
5470
5532
5594
5656
62
1
5718
5780
5842
5904
5966
6028
6090
6151
6213
6275
2
6337
6399
6461
6523
6585
6646
6708
6770
6832
6894
3
6955
7017
7079
7141
7202
7264
7326
7388
7449
7511
4
7573
7634
7696
7758
7819
7881
7943
8004
8066
8128
5
8189
8251
8312
8374
8435
8497
8559
8620
8682
8743
6
8805
8866
8928
8989
9051
9112
9174
9235
9297
9358
7
9419
9481
95^
9604
9665
9726
9788
9849
9911
9972
8
850033
0095
0156
0217
0279
0340
0401
0462
0524
0585
9
0646
0707
0769
0830
.0891
0952
1014
1075
1136
1197
710
1258
1320
1381
1442
1503
1564
1625
1686
1747
1809
1
1870
1931
1992
2053
2114
2175
2236
2297
2358
2419
2
2480
2541
2602
2663
2724
2785
2846
2907
2968
3029
61
3
3090
3150
3211
3272
3333
3394
3455
3516
3577
3637
4
3698
3759
3820
3881
3941
4002
4063
4124
4185
4245
5
4306
4367
4428
4488
4549
4610
4670
4731
4792
4852
6
4913
4974
5034
5095
5156
5216
5277
5337
5398
5459
7
5519
5580
5640
5701
5761
5822
5882
5943
6003
6064
8
6124
6185
6245
6306
6366
6427
6487
6548
6608
6668
9
6729
6789
6850
6910
6970
7031
7091
7152
7212
7272
PROPORTIONAL PARTS.
Diff
. 1
234
5
678
9
65
6.5
13.0 19.5 26.0
32.5
39.0 45.5 52.0
58.5
64
6.4
12.8 19.2 25.6
32.0
38.4 44.8 51.2
57.6
63
6.3
12.6 18.9 25.2
31.5
37.8 44.1 50.4
56.7
62
6.2
12.4 18.6 24.8
31.0
37.2 43.4 49.6
55 8
61
6.1
12.2 18.3 24.4
30.5
36.6 42.7 48,8
54.9
60
6.0
12.0 18.0 24.0
30.0
36.0 42.0 48.0
54.0
150
LOGARITHMS OF K UMBERS.
No. 720 L. 857.] [No. 764 L. 883.
.
0
9
Diff.
720
857332
7393
7453
7513
7574
7634
7694
7755
7815
7875
1
7935
7995
8056
8116
8176
8236
8297
8357
8417
8477
2
8537
8597
8657
8718
8778
8838
8808
8958
9018
9078
3
9138
9198
9258
9318
9879
9439
9499
9559
9619
9679
60
4
9739
9799
9859
9918
9978
0038
0098
0158
0218
0278
5
860338
0398
0458
0518
0578
0637
0697
0757
0817
0877
6
0937
0996
1056
1116
1176
1236
1295
1355
1415
1475
7
1534
1594
1654
1714
1773
1833
1893
1952
2012
2072
8
2131
2191
2251
2310
2370
2430
2489
2549'
2608
2668
9
2728
2787
2847
2906
2966
3025
3085
31 J4
3204
3263
730
3323
3382
3442
3501
3561
3620
3680
3739
3799
3858
1
3917
3977
4036
4096
4155
4314
4274
4333
4392
4452
2
4511
4570
4630
4689
4748
4808
4867
4926
4985
5045
3 v 5104
5163
5222
5282
5341
5400
5459
5519
5578
5637
4
5696
5755
5814
5874
5933
5992
6051
6110
6169
6228
5
6287
6346
6405
6465
6524
6583
G642
6701
6760
6819
6
6878
6937
6996
7055
7114
7173
7232
7291
7350
7409
59
7
7467
7526
7585
7644
7703
7762
7821
7880
7939
7998
8
8056
8115
8174
8233
8292
8350
8409
8468
8527
8586
9
8644
8703
8762
8821
8879
8938
8997
9056
9114
9173
740
9232
9290
9349
9408
9466
9525
9584
9642
9701
9760
1
9818
9877
9935
9994
0053
0111
0170
0228
O987
O'3AK
2
870404
0462
0521
0579
0638
0696
Ul t\J
0755
0813
U«o<
0872
Uo40
0930
3
0989
1047
1106
1164
1223
1281
1339
1398
1456
1515
4
1573
1631
1690
1748
1806
1865
1923
1981
2040
2008
5
2156
2215
2273
2331
2389
2448
2506
2564
2622
2681
6
2739
2797
2855
2913
2972
3030
3088
8146
3204
3262
7
3321
3379
3437
3495
3553
3611
3669
3727
3785
3844
8
3902
3960
4018
4076
4134
4192
4250
4308
4366
4424
58
9
4482
4540
4598
4656
4714
4772
4830
4888
4945
5003
750
5061
5119
5177
5235
5293
5351
5409
5466
5524
5582
1
5640
5698
5756
5813
5871
5929
5987
6045
6102
6160
2
6218
6276
6333
6391
6449
6507
6564
6622
6680
6737
3
6795
6853
6910
6968
7026
7083
7141
7199
7256
7314
4
7371
7429
7487
7544
7602
7659
7717
7774
7832
7889
5
7947
8004
8062
8119
8177
8234
8292
8349
8407
8464
6
8522
8579
8637
8694
8752
8809
8866
8924
8981
9039
7
9096
9153
9211
9268
9325
9383
9440
9497
9555
9612
g
9669
9726
9784
9841
9898
9956
0013
0070
0127
0185
9
880242
0299
0356
0413
0471
0528
0585
0642
0699
0756
760
0814
0871
0928
0985
1042
1099
1156
1213
1271
1328
1
1385
1442
1499
1556
1613
1670
1727
1784
1841
1898
2
1955
2012
2069
2126
2183
2240
2297
2354
2411
2468
57
3
2525
2581
2638
2695
2752
2809
2866
2923
2980
3037
4
3093
3150
3207
3264
3321
3377
3434
3491
3548
3605
PROPORTIONAL PARTS.
Diff
1
2
3 4
5
678
9
59
5.9
11.8
17.7 23.6
29.5
35.4 41.3 47.2
53.1
58
5.8
11.6
17.4 23.2
29.0
S4.8 40.6 46.4
52.2
57
5.7
11.4
17.1 22.8
28.5
34.2 39.9 45.6
51.3
56
5.6
11.2
16.8 22.4
28.0
33.6 39.2 44.8
50.4
LOGARITHMS OF NUMBERS.
151
No. 765 L. 883.] [No. 809 L. 908.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
765
883661
3718
3775
3832
3888
3945
4002
4059
4115
4172
6
4229
4285
4342
4399
4455
4512
4569
4625
4682
4739
7
4795
4852
4909
4965
5022
5078
5135
5192
5248
5305
8
5361
5418
5474
5531
5587
5644
5700
5757
5813
5870
9
5926
5983
6039
6096
6152
6209
6265
6321
6378
6434
770
6491
6547
6604
6660
6716
6773
6829
6885
6942
6998
1
7054
7111
7167
7223
7280
7336
7392
7449
7505
7561
2
7617
7674
7730
7786
7842
7898
7955
8011
8067
8123
3
8179
8236
8292
8348
8404
8460
8516
8573
8629
8685
4
8741
8797
8853
8909
8965
9021
9077
9134
9190
9246
5
9302
9358
9414
9470
9526
9582
9638
9694
9750
9806
56
g
9862
9918
9974
0030
0086
0141
0197
0253
0309
0365
7
890421
0477
0533
0589
0645
0700
0756
0812
0868
0924
8
0980
1035
1091
1147
1203
1259
1314
1370
1426
1482
9
1537
1593
1649
1705
1760
1816
1872
1928
1983
2039
780
2095
2150
2206
2262
2317
2373
2429
2484
2540
2595
1
2651
2707
2762
2818
2873
2929
2985
3040
3096
3151
2
3207
3262
3318
3373
3429
3484
3540
3595
3651
3706
3
3762
3817
3873
3928
3984
4039
4094
4150
4205
4261
4
4316
4371
4427
4482
4538
4593
4648
4704
4759
4814
5
4870
4925
4980
5036
5091
5146
5201
5257
5312
5367
6
5423
5478
z:m
5588
5644
5699
5754
5809
5864
5920
7
5975
6030
6085
6140
6195
6251
6306
6361
6416
6471
8
6526
6581
6636
6692
6747
6802
6857
6912
6967
7022
9
7077
7132
7187
7242
7297
7352
7407
7462
7517
7572
790
7627
7682
7737
7792
7847
7902
7957
8012
8067
8122
55
1
8176
8231
8286
8341
8396
8451
8506
8561
8615
8670
2
8725
8780
sass
8890
8944
8999
9054
9109
9164
9218
3
4
9273
9821
9328
9875
9383
9G30
9437
9985
9492
9547
9G02
9656
9711
9766
0039
0094
0149
0203
0258
0312
5
900367
0422
0476
0531
0586
0640
0695
0749
0804
0859
6
0913
09G8
1022
1077
1131
1186
1240
1295
1349
1404
7
1458
1513
1567
1622
1676
1731
1785
1840
1894
1948
8
2003
2057
2112
2166
2221
2275
2329
2384
2438
2492
9
2547
2601
2655
2710
2764
2818
2873
2927
2981
3036
800
3090
3144
3199
3253
3307
3361
8416
3470
35^
3578
1
3633
3687
3741
3795
3849
3904
3958
4012
4066
4120
2
4174
4229
4283
4337
4391
4445
4499
4553
4607
4661
3
4716
4770
4824
4878
4932
4986
5040
5094
5148
5202
54
4
5256
5310
5364
5418
5472
5526
5580
5634
5688
5742
5
5796
5850
5904
5958
6012
6066
6119
6173
6227
6281
6
6335
6389
6443
6497
6551
6604
6658
6712
6766
6820
7
6874
6927
6981
7035
7089
7143
7196
7250
7304
7358
8
7411
7465
7519
7573
7626
7680
7734
7787
7841
7895
9
7949
8002
8056
8110
8163
8217
8270
8324
8378
8431
PROPORTIONAL PARTS.
Diff. 1
234
5
6 7
8
9
57 5.7
11.4 17.1 22.8
28.5
34.2 39.9
45.6
51.3
56 5.6
11.2 16.8 22.4
28.0
33.6 39.2
44.8
50.4
55 5.5
11.0 16.5 22.0
27.5
33.0 38.5
44.0
49.5
54 5.4
10.8 16.2 21.6
27.0
32.4 37.8
43.2
48.6
LOGARITHMS OF HUMBERS.
No. 8K) L. 908.] [No. 854 L. 931.
N.
0
1
2
3
4
6
6
7
8
9
Diff.
810
908485
8539
8592
8646
8699
8753
8807
8860
8914
8967
1
9021
9074
9128
9181
9235
9289
9342
9396
9449
9503
2
9556
9610
9663
9716
9770
9823
9877
9930
9984
0037
3
910091
0144
0197
0251
0304
0358
0411
0464
0518
0571
4
0624
0678
0731
0784
0838
0891
0944
0998
1051
1104
5
1158
1211
1264
1317
1371
1424
1477
1530
1584
1637
6
1690
1743
1797
1850
1903
1956
2009
2063
2116
2169
7
2222
2275
2328
2381
2435
2488
2541
2594
2647
2700
8
2753
2806
2859
2913
2966
3019
3072
3125
3178
3231
9
3284
3337
3390
3443
3496
3549
3602
3655
3708
3761
53
820
3814
3867
3920
3973
4026
4079
4132
4184
4237
4290
1
4343
4396
4449
4502
4555
4608
4660
4713
4766
4819
2
4872
4925
4977
5030
5083
5136
5189
5241
5294
5347
3
5400
5453
5505
5558
5611
5664
5716
5769
5822
5875
4
5927
5980
6033
6085
6138
6191
6243
6296
6349
6401
5
6454
6507
6559
6012
6664
6717
6770
6822
6875
6927
6
6980
7033
7085
7138
7190
7243
7295
7348
7400
7453
7
7506
7558
7611
7063
7716
7708
7820
7873
7925
7978
8
8030
8083
8135
8188
8240
8293
8345
8397
8450
8502
9
8555
8607
8659
8712
8764
8816
8869
8921
8973
9026
830
9078
9130
9183
9235
9287
9340
9392
9444
9496
9549
1
9601
9653
9706
9758
9810
9802
9914
9967
n/vm
0071
2
920123
0176
0228
0280
0,332
0384
0436
0489
0541
0598
3
0645
0697
0749
0801
0853
0906
0958
1010
1062
1114
4
1166
1218
1270
1322
1374
1426
1478
1530
1582
1634
52
5
1686
1738
1790
1842
1894
1946
1998
2050
2102
2154
6
2206
2258
2310
2362
2414
2466
2518
2570
2622
2674
7
2725
2777
2829
2881
2933
2985
3037
3089
3140
3192
8
3244
3296
3348
3399
3451
3503
3555
3607
3658
3710
9
3762
3814
3865
3917
3969
4021
4072
4124
4176
4228
840
4279
4331
4383
4434
4486
4538
4589
4641
4693
4744
1
4796
4848
4899
4951
5003
5054
5106
5157
5209
5261
2
5312
5364
6415
5467
5518
5570
5621
5673
5725
5776
3
5828
5879
6931
5982
6034
6085
6137
6188
6240
6291
4
6342
6394
6445
6497
6548
6600
6651
6702
6754
6805
5
6857
6908
6959
7011
7062
7114
7165
7216
7268
7319
6
7370
7422
7473
7524
7576
7627
7678
7730
7781
7832
7
7883
7935
7986
8037
8088
8140
8191
8242
8293
8345
8
8396
8447
8498
8549
8601
8652
8703
8754
8805
8857
9
8908
8959
9010
9061
9112
9163
9215
9266
9317
9368
850
9419
9470
9521
9572
9623
9674
9725
9776
9827
9879
1
9930
9981
51
0032
0083
0134
0185
0236
0287
0338
0389
2
930440
0491
0542
0592
0643
0694
0745
0796
0847
0898
3
0949
1000
1051
1102
1153
1204
1254
1305
1356
1407
4
1458
1509
1560
1610
1661
1712
1763
1814
1865
1915
PROPORTIONAL PARTS.
Diff. 1
234
5
678
9
53 5.3
10.6 15.9 21.2
26.5
31.8 37.1 42.4
47.7
52 5.2
10.4 15.6 20.8
26.0
31.2 36.4 41.6
46.8
51 5.1
10.2 15.3 20.4
25.5
30.6 35.7 40.8
45.9
50 5.0
10.0 15.0 20.0
25.0
30.0 35.0 40.0
45.0
LOGARITHMS OF NUMBERS.
153
No. 855 L. 931.] [No. 899 L. 954.
N.
0
1
2
3
4
6
6
7
8
9
Diff.
855
931966
2017
2068
2118
2169
2220
2271
2322
2372
2423
6
2474
2524
2575
2626
2677
2727
2778
2829
2879
2930
7
2981
3031
3082
3133
3183
3234
3285
3335
3386
3437
8
3487
3538
3589
3639
3690
3740
3791
3841
3892
3943
9
3993
4044
4094
4145
4195
4246
4296
4347
4397
4448
860
4498
4549
4599
4650
4700
4751
4801
4852
4902
4953
1
5003
5054
5104
5154
5205
5255
5306
5356
5406
5457
2
5507
5558
5608
5658
5709
5759
5809
5860
5910
5960
3
6011
6061
6111
6162
6212
6262
6313
6363
6413
6463
4
6514
6564
6614
6665
6715
6765
6815
6865
6916
6966
5
7016
7066
7116
7167
7217
7267
7317
7367
7418
74i8
6
7518
7568
7618
7668
7718
7769
7819
7869
7919
7969
7
8019
8069
8119
8169
8219
8269
8320
8370
8420
8470
50
8
8520
8570
8620
8670
8720
8770
8820
8870
8920
8970
9
9020
9070
9120
9170
9220
9270
9320
9369
9419
9469
870
9519
9569
9619
9669
9719
9769
9819
9869
9918
9968
1
940018
0068
0118
0168
0218
0267
0317
0367
0417
0467
2
0510
0566
0616
0666
0716
0765
0815
0865
0915
0964
3
1014
1064
1114
1163
1213
1263
1313
1362
1412
1462
4
1511
1561
1611
1GGO
1710
1760
1809
1859
1909
1958
5
2008
2058
2107
2157
2207
2256
2306
2355
2405
2455
6
2504
2554
2603
2653
2702
2752
2801
2851
2901
2950
7
3000
3049
3099
3148
3198
3247
3297
3346
3396
3445
8
3495
3544
3593
3643
3692
3742
3791
3841
3890
3939
9
3989
4038
4088
4137
4186
4236
4285
4335
4384
4433
880
4483
4532
4581
4631
4680
4729
4779
4828
4877
4927
1
4976
5025
5074
5124
5173
5222
5272
5321
5370
5419
2
5469
5518
5567
5616
5665
5715
5764
5813
5862
5912
3
5961
6010
6059
6108
6157
6207
6256
6305
6354
6403
4
6452
6501
6551
6600
6649
6698
6747
6796
6845
6894
5
6943
6992
7041
7090
7139
7189
7238
7287
7336
7385
6
7434
7483
7532
7581
7630
7679
7728
7777
7826
7875
49
7
7924
7973
8022
8070
8119
8168
8217
8266
8315
8364
8
8413
8462
8511
8560
8608
8657
8706
8755
8804
8853
9
8902
8951
8999
9048
9097
9146
9195
9244
9292
9341
890
9390
9439
9488
9536
9585
9634
9683
9731
9780
9829
1
9878
9926
9975
0024
0073
0191
0170
0219
O9fl7
nq-jft
2
950365
0414
0462
0511
0560
VIXl
0608
0657
0706
U/SJlM
6754
UolO
0803
3
0851
0900
0949
0997
1046
1095
1143
1192
1240
1289
4
1338
1386
1435
1483
1532
1580
1629
1677
1726
1775
5
1823
1872
1920
1969
2017
2066
2114
2163
2211
2260
G
2308
2356
2405
2453
2502
2550
2599
2647
2696
2744
7
2792
2841
2889
2938
2986
3034
3083
3131
3180
3228
8
3276
3325
3373
3421
3470
3518
3566
3615
3663
3711
9
3760
3808
3856
3905
3953
4001
4049
4098
4146
4194
PROPORTIONAL PARTS.
Diff.
1
2
3 4
5
6
7 8
9
51
50
49
48
5.1
5.0
4.9
4.8
10.2
10.0
9.8
9.6
15.3 20.4
15.0 20.0
14.7 19.6
14.4 19.2
25.5
25.0
24.5
24.0
30.6
30.0
29.4
28.8
35.7 40.8
35.0 40.0
34.3 39.2
33.6 38.4
45.9
45.0
44.1
43.2
LOGARITHMS OP KUMBERS.
No 900 L. 954.1 [No. 944 L. 975.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
900
954243
4291
4339
4387
4435
4484
4532
4580
4628
4677
1
4725
4773
4821
4869
4918
4966
5014
5062
5110
5158
2
5207
5255
5303
5351
5399
5447
5495
5543
5592
5640
3
5688
5736
5784
5832
5880
5928
5976
6024
6072
6120
4
6168
6216
6265
6313
6361
6409
6457
6505
6553
6601
5
6649
6697
6745
6793
6840
6888
6936
6984
7032
7080
48
6
7128
7176
7224
7272
7320
7368
7416
7464
7512
7559
7
7607
7655
7703
7751
7799
7847
7894
7942
7990
8038
8
8086
8134
8181
8229
8277
8325
8373
8421
8468
8516
9
8564
8612
8659
8707
8755
8803
8850
8898
8946
8994
910
9041
9089
9137
9185
9232
9280
9328
9375
9423
9471
1
2
9518
9995
9566
9614
9661
9709
9757
9804
9852
9900
9947
0042
0090
0138
0185
0233
AOQA
0328
AQ7«
ryoQ
3
960471
0518
0566
0613
0661
0709
UcoU
0756
0804
Uo<O
0851
U4/*O
0899
4
0946
0994
1041
1089
1136
1184
1231
1279
1326
1374
5
1421
1469
1516
1563
1611
1658
1706
1753
1801
1848
6
1895
1943
1990
2038
2085
2132
2180
2227
2275
2322
7
2369
2417
2464
2511
2559
2606
2653
2701
2748
2795
8
2843
2890
2937
2985
3032
3079
3126
3174
3221
3268
! 9
3316
3363
3410
3457
3504
3552
3599
3646
3693
3741
[920
3788
3835
3882
3929
3977
4024
4071
4118
4165
4212
1
4260
4307
4354
4401
4448
4495
4542
4590
4637
4684
2
4731
4778
4825
4872
4919
4966
5013
5061
5108
5155
3
5202
5249
5296
5343
5390
5437
5484
5531
5578
5625
4
5672
5719
5766
5813
5860
5907
5954
6001
6048
6095
47
5
6142
6189
6236
6283
6329
6376
6423
6470
6517
6564
6.
6611
6658
6705
6752
6799
6845
6892
6939
6986
7033
7
7080
7127
7173
7220
7267
7314
7361
7408
7454
7501
8
7548
7595
7642
7688
7735
7782
7829
7875
7922
7969
9
8016
8062
8109
8156
8203
8249
8296
8343
8390
8436
930
8483
8530
8576
8623
8670
8716
8763
8810
8856
8903
1
8950
8996
9043
9090
9136
9183
9229
9276
9323
93G9
2
9416
9463
9509
9556
9602
9649
9695
9742
9789
9835
3
9882
9928
9975
0021
0068
0114
0161
0207
0254
0300
4
970347
0393
0440
0486
0533
0579
0626
0672
0719
0765
5
0812
0858
0904
0951
0997
1044
1090
1137
1183
1229
6
1276
1322
1369
1415
1461
1508
1554
1601
1647
1693
7
1740
1786
1832
1879
1925
1971
2018
20G4
2110
2157
8
2203
2249
2295
2342
2388
2434
2481
2527
2573
2619
9
2666
2712
2758
2804
2851
2897
2943
2989
3035
3082
940
3128
3174
3220
3266
3313
3359
3405
3451
3497
3543
1
3590
3636
3682
3728
3774
3820
3866
3913
3959
4005
2
4051
4097
4143
4189
4235
4281
4327
4374
4420
4466
3
4512
4558
4604
4650
4696
4742
4788
4834
4880
4926
4
4972
5018
5064
5110
5156
5202
5248
5294
5340
5386
46
PROPORTIONAL PARTS.
Diff. 1
234
5
678
9
47 4.7
9.4 14.1 18.8
23.5
28.2 32.9 37.6
42.3
46 4.6
9.2 13.8 18.4
23.0
27.6 32.2 36.8
41.4
LOGARITHMS OF NUMBERS.
155
No. 945 L. 975.] [No. 989 L. 995.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
945
975432
5478
5524
5570
5616
5662
5707
5753
5799
5845
6
5891
5937
5983
6029
6075
6121
6167
6212
6258
6304
7
6350
6396
6442
6488
6533
6579
6625
6671
6717
6763
8
6808
6854
6900
6946
6992
7037
7083
7129
7175
7220
9
7266
7312
7358
7403
7449
7495
7541
7586
7632
7678
950
7724
7769
7815
7861
7906
7952
7998
8043
8089
8135
1
8181
8226
8272
8317
8363
8409
8454
8500
8546
8591
2
8637
8683
8728
8774
8819
8865
8911
8956
9002
9047
3
9093
9138
9184
9230
9275
9321
93G6
9412
9457
9503
4
9548
9594
9639
9685
9730
9776
9821
9867
9912
9958
5
980003
0049
0094
0140
0185
0231
0276
0322
0367
0412
G
0458
0503
0549
0594
0640
0685
0730
0776
0821
0867
7
0912
0957
1003
1048
1093
1139
1184
1229
1275
1320
8
1366
1411
1456
1501
1547
1592
1637
1683
1728
1773
9
1819
1864
1909
1954
2000
2045
2090
2135
2181
2226
960
2271
2316
2362
2407
2452
2497
2543
2588
2633
2678
1
2723
2769
2814
2859
2904
2949
2994
3040
3085
3130
2
3175
3220
3265
3310
3356
3401
3446
3491
3536
3581
3
3626
3671
3716
37'62
3807
3852
3897
3942
3987
4032
4
4077
4122
4167
4212
4257
4302
4347
4392
4437
4482
5
4527
4572
4617
4662
4707
4752
4797
4842
4887
4932
45
6
4977
5022
5067
5112
5157
5202
5247
5292
5337
5382
7
5426
5471
5516
5561
5606
5651
5696
5741
5786
5830
8
5875
5920
5965
6010
6055
6100
6144
6189
6234
6279
9
6324
6369
6413
6458
6503
6548
6593
6637
6682
6727
970
6772
6817
6861
6906
6951
6996
7040
7085
7130
7175
1
7219
7264
7309
7353
7398
7443
7488
7532
7577
7622
2
7666
7711
7756
7800
7845
7890
7934
7979
8024
8068
3
8113
8157
8202
8247
8291
8336
8381
8425
8470
8514
4
8559
8604
8648
8693
8737
8782
8826
8871
8916
8960
5
9005
9049
9094
9138
9183
9227
9272
9316
9361
9405
6
7
9450
9895
9494
9939
9539
9983
9583
9628
9672
9717
9761
9806
9850
0028
0072
0117
0161
0206
0250
0294
8
990339
0383
0428
0472
0516
0561
0605
0650
0694
0738
9
0783
0827
0871
0916
0960
1004
1049
1093
1137
1182
980
1226
1270
1315
1359
1403
1448
1492
1536
1580
1625
1
1669
1713
1758
1802
1846
1890
1935
1979
2023
2067
2
2111
2156
2200
2244
2288
2333
2377
2421
2465
2509
3
2554
2598
2642
2686
2730
2774
2819
2863
2907
2951
4
2995
3039
3083
3127
3173
3216
3260
3304
3348
3392
5
3436
3480
3524
3568
3613
3657
3701
3745
3789
3833
6
3877
3921
3965
4009
4053
4097
4141
4185
4229
4273
7
4317
4361
4405
4449
4493
4537
4581
4625
4669
4713
44
8
4757
4801
4845
4889
4933
4977
5021
5065
5108
5152
9
5196
5240
5284
5328
5373
5416
5460
55U4
5547
5591
PROPORTIONAL PARTS.
Diff 1
234
5
678
9
46 4.6
9.2 13.8 18.4
23.0
27.6 32.2 36.8
41.4
45 4.5
9.0 33.5 18.0
22.5
27.0 31.5 86 0
40.5
44 4.4
8.8 13. 2 17.6
22.0
26.4 30.8 35.2
39.6
43 4.3
8.6 12.9 17.2
yi.5
25.8 30.1 34.4
38.7
156
No. 990 L. 995.]
MATHEMATICAL TABLES.
[No. 999 L. 999.
N.
0
1
2
3
4
5
6
7
8
9
Diff.
990
995635
5679
5723
5767
5811
5854
5898
5942
5986
6030
1
6074
6117
6161
6205
6249'
6293
6337
6380
6424
6468
44
2
6512
6555
6599
6643
6687
6731
6774
6818
6862
6906
3
6949
6993
7037
7080
7124
7168
7212
7255
7299
7343
4
7386
7430
7474
7517
7561
7C05
7648
7692
7736
7779
5
7823
7867
7910
7954
7998
8041
8085
8129
8172
8216
6
8259
8303
8347
8390
8434
8477
8521
8564
8608
8652
7
8695
8739
8782
8826
8869
8913
8956
9000
9043
9087
8
9131
9174
9218
9261
9305
9348
9392
9435
9479
9522
9
9565
9609
9652
9696
9739
9783
9826
9870
9913
9957
43
HYPERBOLIC LOGARITHMS.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
1.01
.0099
1.45
.3716
1.89
.6366
2.33
.8458
2.77
1.0188
1.02
.0198
1,46
.3784
1.90
.6419
2.34
.8502
2.78
1.0225
1.03
.0296
1.47
.3853
1.91
.6471
2.35
.8544
2.79
.0260
1.04
.0392
1.48
.3920
1.92
.6523
2.36
.8587
2.80
.0296
1.05
.0488
1.49
.3988
1.93
.6575
2.37
.8629
2.81
.0332
1.06
.0583
1.50
.4055
1.94
.6627
2.38
.8671
2.82
.0367
1.07
.0677
1.51
.4121
1.95
.6678
2.39
.8713
2.83
.0403
1.08
.0770
1.52
.4187
1.96
.6729
2.40
.8755
2.84
.0438
1.09
.0862
1.53
.4253
1.97
.6780
2.41
.8796
2.85
.0473
1.10
.0953
1.54
.4318
1.98
.6831
2.42
.8838
2.86
.0508
1.11
.1044
1.55
.4383
1.99
.6881
2.43
.8879
2.87
.0543
1.12
.1133
1.56
.4447
2.00
.6931
2.44
.8920
2.88
.0578
1.13
.1222
1.57
.4511
2.01
.6981
2.45
.8961
2.89
.0613
1.14
.1310
1.58
.4574
2.02
.7031
2.46
.9002
2.90
.0647
1.15
.1398
1.59
.4637
2.03
.7080
2.47
.9042
o gi
.0682
1.16
.1484
1.60
.4700
2.04
.7129
2.48
.9083
2^92
.0716
1.17
.1570
1.61
.4762
2.05
.7178
2.49
.9123
2.93
.0750
1.18
.1655
1.62
.4824
2.06
.7227
2.50
.9163
2.94
.0784
1.19
.1740
1.63
.4886
2.07
.7275
2.51
.9203
2.95
.Obis
1.20
.1823
1.64
.4947
2.08
.7324
2.52
.9243
2.96
.0852
1.21
.1906
1.65
,5008
2.09
.7372
2.53
.9282
2.97
.0886
1.22
.1988
1.66
.5068
2.10
.7419
2.54
.9.322
2.98
.0919
1.23
• .2070
1.67
.5128
2.11
.7467
2.55
.9361
2.99
.0953
1.24
.2151
1.68
.5188
2.12
.7514
2.56
.9400
3.00
.0986
1.25
.2231
1.69
.5247
2.13
.7561
2.57
.9439
3.01
.1019
1.26
.2311
1.70
.5306
2.14
.7608
2.58
.9478
3.02
.1053
1.27
.2390
1.71
.5365
2.15
.7655
2.59
.9517
3.03
.1086
1.28
.2469
.72
.5423
2.13
.7701
2.60
.9555
3.04
.1119
1.29
.2546
.73
.5481
2.17
.7747
2.61
.9594
3.05
.1151
1.30
.2624
.74
.5539
2.18
.7793
2.62
.9632
3.06
.1184
1.31
.2700
.75
.5596
2.19
.7839
2.63
.9670
3.07
.1217
1.32
.2776
.76
.5653
2.20
.7885
2.64
.9708
3.08
.1249
1.33
.2852
.77
.5710
2.21
.7930
2.65
.9746
3.09
.1282
1.34
.2927
.78
.5766
2.22
.7975
2.66
.9783
3.10
.1314
1.35
.3001
.79
.5822
2.23
.8020
2.67
.9821
3.11
.1346
1.36
.3075
.80
.5878
2.24
.8065
2.68
.9858
3.12
.1378
1.37
.3148
.81
.5933
2.25
.8109
2.69
.9895
3.13
.1410
1.38
.3221
.82
.5988
2.26
.8154
2.70
.9933
3.14
.1442
1.88
.3293
.83
.6043
2.27
.8198
2.71
.9969
3.15
.1474
1.40
.3365
.84
.6098
2.28
.8242
2.72
1.0006
3 16
.1506
1.41
.3436
1.85
.6152
2.29
.8286
2.73
1.0043
3.17
.1537
1.42
.3507
1.86
.6206
2.30
.8329
2.74
1.0080
3.18
.1569
1.43
.3577
1.87
.6259
2.31
.8372
2.75
1.0116
3.19
.1600
1.44
.3646
1.88
.6313
2.32
.8416
2.76
1.0152
3.20
.1632
HYPERBOLIC LOGARITHMS.
157
No,
Log.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
3.21
1.1663
3.87
1.3533
4.53
1.5107
5.19
1.6467
5.85
1.7664
3.22
1.1694
3.88
1.3558
4.54
1.5129
5.20
1.6487
5.86
1.7681
3.23
1.1725
3.89
1.3584
4.55
1.5151
5.21
1.6506
5.87
1.7699
3.24
1.1756
3.90
1.3610
4.56
1.5173
5.22
1.6525
5.88
1.7716
3.25
1.1787
3.91
1.3635
4.57
1.5195
5.23
1.6544
5.89
1.7733
3.26
1.1817
3.92
1.3661
4.58
1.5217
5.24
1.6563
5.90
1.7750
3.27
1.1848
3.93
1.3686
4.59
1.5239
5.25
1.6582
5.91
1.7766
3.28
1.1878
3.94
1.3712
4.60
1.5261
5.26
1.6601
5.92
1.7783
3.29
1.1909
3.95
1.3737
4.61
1.5282
5.27
1.6620
5.93
1.7800
3.30
1.1939
3.96
1.3762
4.62
1.5304
5.28
1.6639
5.94
1.7817
3.31
1.1969
3.97
1.3788
4.63
1.5326
5.29
1.6658
5.95
1.7834
3.32
1.1999
3.98
1.3813
4.64
1.5347
5.30
1.6677
5.96
1.7851
3.33
1.2030
3.99
1.3838
4.65
1.5369
5.31
1.6696
5.97
1.7867
3.34
1.2060
4.00
1.3863
4.66
1.5390
5.32
1.6715
5.98
1.7884
3.35
1.2090
4.01
1.3888
4.67
1.5412
5.33
1.6734
5.99
1.7901
3.36
1.2119
4.02
1.3913
4.68
1.5433
5.34
1.6752
6.00
1.7918
3.37
1.2149
4.03
1 .3938
4.69
1.5454
5.35
1.6771
6.01
1.7934
3.38
1.2179
4.04
1.3962
4.70
.5476
5.36
1.6790
6.02
1.7951
3.39
1.2208
4.05
1.3987
4.71
.5497
5.37
1.6808
6.03
1.7967
3.40
1.2238
4.06
1.4012
4.72
.5518
5.38
1.6827
6.04
1.7984
3.41
1.2267
4.07
1.4036
4.73
.5539
5.39
1.6845
6.05
1.8001
3.42
1.2296
4.08
1.4061
4.74
.5560
5.40
1.6864
6.06
1.8017
3.43
1.2326
4.09
1.4085
4.75
.5581
5.41
1.6882
6.07
1.8034
3.44
1.2355
4.10
1.4110
4.76
.5602
5.42
1.6901
6.08
1.8050
3.45
1.2384
4.11
1.4134
4.77
.5623
5.43
1.6919
6.09
1.8066
3.46
1.2413
4.12
1.4159
4.78
1.5644
5.44
1.6938
6.10
1.8083
3 47
1.2442
4.13
1.4183
4.79
1.5665
5.45
1.6956
6.11
1.8099
3.48
1.2470
4.14
1.4207
4.80
1.5686
5.46
1.6974
6.12
1.8116
8.49
1.2499
4.15
1.4231
4.81
1.5707
5.47
1.6993
6.13
1.8132
3.50
1.2528
4.16
1.4255
4.82
1.5728
5.48
1.7011
6.14
1.8148
3.51
1.2556
4.17
1.4279
4.83
1.5748
5.49
1.7029
6.15
1.8165
3.52
1.2585
4.18
1.4303
4.84
1.5769
5.50
1.7047
6.16
1.8181
3.53
1.2613
4.19
1.4327
4.85
1.5790
5.51
1.7066
6.17
1.8197
3.54
1.2641
4.20
1.4351
4.86
1.5810
5.52
1.7084
6.18
1-8213
3.55
1.3669
4.21
1.4375
4.87
1.5831
5.53
1.7102
6.19
1.8229
3.56
1.2698
4.22
1.4398
4.88
1.5851
5.54
1.7120
6.20
1.8245
3.57
1.2726
4.23
1.4422
4.89
.5872
5.55
1.7138
6.21
1.8262
3.58
1.2754
4.24
1.4446
4.90
.5892
5.56
1.7156
6.22
1.8278
3.59
1.2782
4.25
1.4469
4.91
.5913
5.57
1.7174
6.23
1.8294
3.60
1.2809
4.26
1.4493
4.92
.5933
5.58
1.7192
6.24
1.8310
3.61
1.2837
4.27
1.4516
4.93
.5953
5.59
1.7210
6.25
1.8326
3.62
1.2865
4.28
1.4540
4.94
.5974
5.60
1.7228
6.26
1.8342
3.63
1.2892
4.29
1.4563
4.95
.5994
5.61
1.7246
6.27
1.8358
3.64
1 .2920
4.30
1.4586
4.96
.6014
5.62
1.7263
6.28
1.8374
3.65
1.2947
4.31
1.4609
4.97
.6034
5.63
1.7281
6.29
1.8390
3.66
1.2975
4.32
1.4633
4.98
.6054
5.64
1.7299
6.30
1.8405
3.67
1.3002
4.33
.4656
4.99
.6074
5.65
1.7317
6.31
1.8421
3.68
1.3029
4.34
.4679
5.00
.6094
5.66
1.7334
6.32
1.8437
3.69
1.3056
4.35
.4702
5.01
.6114
5.67
1.7352
6.33
1.8453
3.70
1.3083
4.36
.4725
5.02
.6134
5.68
1.7370
6.34
1.8469
3.71
1.3110
4.37
.4748
5.03
.6154
5.69
1.7387
6.35
1.8485
3.72
1.3137
4.38
.4770
5.04
.6174
5.70
1.7405
6.36
1.8500
3.73
1.3164
4.39
.4793
5.05
.6194
5.71
1.7422
6.37
1.8516
3.74
1.3191
4.40
.4816
5.06
.6214
5.72
1.7440
6.38
1.8532
3.75
1.3218
4.41
.4839
5.07
.6233
5.73
1.7457
6.39
1.8547
3.76
1.3244
4.42
.4861
5.08
.6253
5.74
1.7475
6.40
1.8563
3.77
1.3271
4.43
.4884
5.09
.6273
5.75
1.7492
6.41
1,8579
3.78
1.3297
4.44
.4907
5.10
.6292
5.76
1.7509
6.42
1.8594
3.79
1.3324
4.45
.4929
5.11
.6312
5.77
1.7527
6.43
1.8610
3.80
1.3350
4.46
.4951
5.12
.6332
5.78
1.7544
6.44
1.8625
8.81
1.3376
4.47
.4974
5.13
.6351
5.79
1.7561
6.45
1.8641
3.82
1.3403
4.48
.4996
5.14
.6371
5.80
1.7579
6.46
1.8656
3.83
1.3429
4.49
.5019
5.15
.6390
5.81
1.7596
6.47
1.8672
3.84
1.3455
4.50
.5041
5.16
.6409
5.82
1.7613
6.48
1.8687
8.85
1.3481
4.51
.5063
5.17
.6429
5.83
1 .7630
6.49
1.8703
3.86
1.3507
4.52
.5085
5.18
1.6448
5.84
1.7647
6.50
1.8718
158
MATHEMATICAL TABLES.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
6.51
1.8733
7.15
.9671
7.79
2.0528
8.6(5
2.1587
9.94
2.2966
6.52
1.8749
7.16
.9685
7.80
2.0541
8.68
2.1610
9.96
2.2986
6.53
1.8764
7.17
.9699
7.81
2.0554
8.70
2.1633
9.98
2.3006
6.54
1.8779
7.18
.9713
7.82
2.0567
8.72
2.1656
10.00
2.3026
6.55
1.8795
7.19
.9727
7.83
2.0580
8.74
2.1679
10.25
2.3279
6.56
1.8810
7.20
.9741
7.84
2.0592
8.76
2.1702
10.50
2.3513
6.57
1.8825
7.21
.9754
7.85
2.0605
8.78
2.1725
10.75
2.3749
6.58
1.8840
7.22
.9769
7.86
2.0618
8.80
2.1748
11.00
2.3979
6.59
.8856
7.23
.9782
7.87
2.0631
8.82
2.1770
11.25
2.4201
6.60
.8871
7.24
.9796
7.88
2.0643
8.84
2.1793
11.50
2.4430
6.61
.8886
7.25
.9810
7.89
2.0656
8.86
2.1815
11.75
2.4636
6.62
.8901
7.26
1.9824
7.90
2.0669
8.88
2.1838
12.00
2.4849
6.63
.8916
7.27
1.9838
7.91
2.0681
8.90
2.1861
12.25
2.5052
6.64
.8931
7.28
1.9851
7.92
2.0694
8.92
2.1883
12.50
2.5262
6.65
.8946
7.29
1.9865
7.93
2.0707
8.94
2.1905
12.75
2.5455
6.66
.8961
7.30
1.9879
7.94
2.0719
8.96
2.1928
13.00
2.5649
6.67
.8976
7.31
1.9892
7.95
2.0732
8.98
2.1950
13.25
2.5840
6.68
.8991
7.32
1.9906
7.96
2.0744
9.00
2.1972
13.50
2.6027
6.69
.9006
7.33
1.9920
7.97
2.0757
9.02
2.1994
13.75
2.6211
6.70
.9021
7.34
1.9933
7.98
2.0769
9.04
2.2017
14.00
2.6391
6.71
.9086
7.35
1.9947
7.99
2.0782
9.06
2.2039
14.25
2.6567
6.72
.9051
7.36
1.9961
8-00
2.0794
9.08
2.2061
14.50
2.6740
6.73
.9066
7.37
1.9974
8.01
2.0807
9 10
2.2083
14.75
2.6913
6.74
.9081
7.38
1.9988
8.02
2.0819
9.12
2.2105
15.00
2.7081
6.75
.9095
7.39
2.0001
8.03
2.0832
9.14
2.2127
15.50
2.7408
6.76
.9110
7.40
2.0015
8.04
2.0844
9.1-6
2.2148
16.00
2.7726
6.77
.9125
7.41
2.0028
8.05
2.0857
9.18
2.2170
16.50
2.8034
6.78
1.9140
7.42
2.0041
8-06
2.0869
9.20
2.2192
17.00
2.8332
6.79
1.9155
7.43
2-0055
8.07
2.0882
9.22
2.2214
17.50
2.8621
6.80
1.9169
7.44
2-0069
8.08
2.0894
9.24
2.2235
18.00
2.8904
6.81
1.9184
7.45
2.0082
8-09
2.0906
9.26
2.2257
18.50
2.9178
6.82
1.9199
7.46
2.0096
8.10
2.0919
9.28
2.2279
19.00
2.9444
6.83
1.9213
7.47
2.0108
8.11
2.0931
9.30
2.2300
19.50
2.9703
6.84
1.9228
7.48
2.0122
8.12
2.0943
9.32
2.2322
20.00
2.9957
6.85
1.9242
7.49
2.0136
8.13
2.0958
9.34
2.2343
21
3.0445
6.86
1.9257
7.50
2.0149
8.14
2.0968
9.36
2.2364
22
3.0910
6.87
1.9272
7.51
2.0162
8.15
2.0980
9.38
2.2386
23
3.1355
6.88
1.9286
7.52
2.0176
8.16
2.0992
9.40
2.2407
24
3.1781
6.89
1.9301
7.53
2.0189
8-17
2.1005
9.42
2.2428
25
3.2189
6.90
1.9315
7.54
2.0202
8.18
2.1017
9.44
2.2450
26
3.2581
6.91
1.9330
7.55
2.0215
8-19
2.1029
9.46
2.2471
27
3.2958
6.92
1.9344
7.56
2.0229
8.20
2.1041
9.48
2.2492
28
3.3322
6.93
1.9359
7.57
2.0242
8.22
2.1066
9.50
2.2513
29
3.3673
6.94
1.9373
7.58
2.0255
8.24
2.1090
9.52
2.2534
30
3.4012
6.95
1.9387
7.59
2.0268
8.26
2.1114
9.54
2.2555
31
3.4340
6.96
1.9402
7.60
2.0281
8.28
2.1138
9.56
2.2576
32
3.4657
6.97
1.9416
7.61
2.0295
8.30
2.1163
9.58
2.2597
33
3.4965
6.98
.9430
7.62
2.0308
8.32
2.1187
9.60
2.2618
34
3.5263
6.99
.9445
7.63
2.0321
8.34
2.1211
9.62
2.2638
35
3.5553
7.00
.9459
7.64
2.0334
8.36
2.1235
9.64
2.ii659
36
3.5835
7.01
.9473
7.65
2.0347
8.38
2.1258
9.66
2.2680
37
3.6109
7.02
.9488
7.66
2.0360
8.40
2.1282
9.68
2.2701
38
3.6376
7.03
.9502
7.67
2.0373
8.42
2.1306
9.70
2.2721
39
3.6636
7.04
.9516
7.68
2.0386
8.44
2.1330
9.72
2.2742
40
3.6889
7.05
.9530
7.69
2.0399
8.46
2.1353
9.74
2.2762
41
3.7136
7.06
.9544
7.70
2.0412
8.48
2.1377
9.76
2.2783
42
3.7377
7.07
.9559
7.71
2.0425
8.50
2.1401
9.78
2.2803
43
3.7612
7.08
.9573
7.72
2.0438
8.52
2.1424
9.80
2.2824
44
3.7842
7.09
.9587
7.73
2.0451
8.54
2.1448
9.82
2.2844
45
3.8067
7.10
.9601
7.74
2.0464
8.56
2.1471
9.84
2.2865
46
3.8286
7.11
.9615
7.75
2.0477
8.58
2.1494
9.86
2.2885
47
3.8501
7.12
.9629
7.76
2.0490
8.60
2.1518
9.88
2.2905
48
3.8712
7.13
.9643
7.77
2.0503
8.62
2.1541
9.90
2.2925
49
3.8918
7.14
.9657
7.78
2.0516
8.64
2.1564
9.92
2.2946
50
3.9120
NATURAL TRIGONOMETRICAL FUNCTIONS.
159
NATURAL TRIGONOMETRICAL FUNCTIONS.
0
M.
Sine.
Co-Vers.
Cosec.
Tang.
Cot»n. Secant.
rer. Sin.
CoHine.
o
0
00000
.0000
nfinite
00000
Infinite 1.0000
.00000
1.0000
90
0
15
00436
.99564
229.18
00436
229.18 ! 1.0000
.00001
.99999
45
30
00873
.99127
14.59
00873
114.59
1.0000
.00004
.99996
30
45
01309
.98691
76.397
01309
76.390
1.0001
.00009
.99991
15
1
0
01745
.98255
57.299
01745
57.290
1.0001
.00015
.99985
89
0
15
02181
.97819
45.840
02182
45.829
1.0002
.00024
.99976
45
30
02618
.97382
38.202
02618
38.188
1.0003
.00034
.99966
30
45
03054
.96946
32.746
03055
32.730
1.0005
.00047
.99953
15
2
0
03490
.96510
28.654
03492
28.636
1.0006
.00061
.99939 88
0
15
03926
.96074
25.471
03929
25.452
1.0008
.00077
.99923
45
30
04362
.95638
22.926
04366
22.904
1.0009
.00095
.99905
30
45
04798
.95202
20.843
04803
20.819
1.0011
.00115
.99885
15
3
0
05234
.94766
19.107
05241
19.081
1.0014
.00137
.99863
87
0
15
05669
.94331
17.639
05678
17.611
1.0016
.00161
.99839
45
30
06105
.93895
16.380
06116
16.350
1.0019
.00187
.99813
30
45
06540
.93460
15.290
06554
15.257
1.0021
.00214
.99786
15
4
0
06976
.93024
14.336
06993
14.301 I 1.0024
.00244
.99756
86
0
15
07411
.92589
13.494
07431
13.457 1 1.0028
.00275
.99725
45
30
07846
.92154
12.745
07870
12.706
1.0031
.00308
.99692
30
45
08231
.91719
12.076
08309
12.035
1.0034
.00343
.99656
15
5
0
08716
.91284
11.474
08749
11.430
1.0038
.00381
.99619
85
0
15
09150
.90850
10.929
09189
10.883
1.0042
.00420
.99580
45
30
09585
.90415
10.433
09629
10.385
1.0046
.00460
.99540
30
45
10019
.89981
9.9812
10069
9.9310
1.0051
.00503
.99497
15
6
0
10453
.89547
9.5668
10510
9.5144
1.0055
.00548
.99452
84
0
15
10887
.89113
9.1855
10952
9.1309 1.0060
.00594
.99406
45
30
11320
.88680
8.8337
11393
8.7769 1.0065
.00643
.99357
30
45
11754
.88246
8.5079
11836
8.4490: 1.0070
.00693
.99307
15
7
0
12187
.87813
8.2055
12278
8.1443 1.0075
.00745
.99255
83
0
15
12620
.87380
7.9240
12722
7.8606 1.0081
.00800
.99200
45
30
13053
.86947
7.6613
13165
7.5958 1.0086
.00856
.99144
30
45
13485
.86515
7.4156
13609
7.3479 1.0092
.00913
.99086
15
8
0
13917
.86083
7.1853
14054
7.1154 1.0098
.00973
.99027
82
0
15
14349
.85651
6.9690
14499
6.8969; 1.0105
.01035
.98965
45
30
14781
.85219
6.7655
14945
6.6912 1.0111
.01098
.98902
30
45
15212
.84788
6.5736
15391
6.4971
1.0118
.01164
.98836
15
9
0
15643
.84357
6.3924
15838
6.3138
1.0325
.01231
.98769
81
0
15
16074
.83926
6.2211
16286
6.1402
1.0132
.01300
.98700
45
30
.16505
.83495
6.0589
16734
5.9758
1.0139
.01371
.98629
30
45
.16935
.83065
5.9049
.17183
5.8197
1.0147
.01444
.98556
15
10
0
.17365
.82635
5.7588
.17633
5.6713
1.0154
.01519
.98481
80
0
15
.17794
.82206
5.6198
.18083
5.5301
1.0162
.01596
.98404
45
30
.18224
.81776
5.4874
.18534
5.3955
1.0170
.01675
.98325
30
45
.18652
.81348
5.3612
.18986
5.2672
1.0179
.01755
.98245
15
11
0
.19081
.80919
5.2408
.19438
5.1446
1.0187
.01837
.98163
79
0
15
.19509
.80491
5.1258
.19891
5.0273
1.0196
.01921
.98079
45
30
.19937
.80063
5.0158
.20345
4.9152
1.0205
.02008
.97992
30
45
.20364
.79636
4.9106
.20800
4.8077
1.0214
.02095
.97905
15
12
0
.20791
.79209
4.8097
.21256
4.7046
1.0223
.02185
.97815
78
0
15
.21218
.78782
4.7130
.21712
4.6057
1.0233
.02277
.97723
45
30
.21644
.78356
4.6202
.22169
4.5107
1.0243
.02370
.97630
30
45
.22070
.77930
4.5311
.22628
4.4194
1.0253
.02466
.97534
15
13
0
.22495
.77505
4.4454
•23087
4.3315
1.0263
.02563
.97437
77
0
15
.22920
.77080
4.3630
•23547
4.2468
1.0273
.02662
.97338
45
30
.23345
.76655
4.2837
.24008
4.1653
1.0284
.02763
.97237
30
45
.23769
.76231
4.2072
.24470
4.0867
1.0295
.02866
.97134
15
14
0
.24192
.75808
4.1336
.24933
4.0108
1.0306
.02970
.97030
76
0
15
.24615
.75385
4.0625
.25397
3.9375
1.0317
.03077
.96923
45
30
.25038
.74962
3 993!
.25862
3.8667
1.0329
.03185
.96815
30
45
.25460
.7454C
3*.92r
.26328
3.7983
1.034
.03295
.96705
15
15
0
.25882
.74118
3.8637
.2679P
3.732C
1.0353
.03407
.96593
75
0
Cosine
Ver. Sin
Secant.
Cotan.
Tang.
Cosec.
Co-Vers
Sine.
0
M.
From 75° to 90° read from bottom of table upwards.
1GO
MATHEMATICAL TABLES.
0
M.
Sine.
Co-Vers.
Cosec.
Tang.
Cotan.
Secant.
Ver. Sin.
Cosine.
15
0
.25882
.74118
3.8637
.26795
3.7320
1.0353
.03407
.96593
75
0
15
.26303
.73697
3.8018
.27263
3.6680
1.0365
.03521
.96479
45
30
.26724
.73276
3.7420
.27732
3.6059
1.0377
.03637
.96363
at
45
.27144
.72856
3.6840
.28203
3.5457
1.0390
.03754
.96246
15
16
0
.27564
.72436
3.6280
.286?4
3.4874
1.0403
.03874
.96126
74
0
15
.27983
.72017
3.5736
.29147
3.4308
1.0416
.03995
.96005
45
30
.28402
.71598
3.5209
.29621
3.3759
1.0429
.04118
.95882
30
45
.28820
.71180
3.4699
.30096
3.3226
1.0443
.04243
.95757
15
17
0
.29237
.70763
3.4203
.30573
3.2709
1.0457
.04370
.95630
7*
0
15
.29654
.70346
3.3722
.31051
3.2205
1.0471
.04498
.95502
45
30
.30070
.69929
3.3255
.31530
3.1716
1.0485
.04628
.95372
30
45
.30486
.69514
3.2801
.32010
3.1240
1.0500
.04760
.95240
15
18
0
.30902
.69098
3.2361
.32492
3.0777
1.0515
.04894
.95106
72
0
15
.31316
.68684
3.1932
.32975
3.0326
1.0530
.05030
.94970
45
30
.31730
.68270
3.1515
.33459
2.9887
1.0545
.05168
.94832
30
45
.32144
.67856
3.1110
.33945
2.9459
1.0560
.05307
.94693
15
19
0
.32557
.67443
3.0715
.34433
2.9042
1 .0576
.05448
.94552
71
0
15
.32969
.67031
3.0331
.34921
2.8636
1.0592
.05591
.94409
45
30
.33381
.66619
2.9957
.35412
2.8239
1.0608
.05736
.94264
30
45
.33792
.66208
2.9593
.35904
2.7852
1.0625
.05882
.94118
15
20
0
.3420:2
.65798
2.9238
.36397
2.7475
1 .0642
.06031
.93969
70
0
15
.34612
.65388
2.8892
.36892
2.7106
1.0659
.06181
.93819
45
30
.35021
.64979
2.8554
.37388
2.6746
1.0676
.06333
.93667
30
45
.35429
.64571
2.8225
.37887
2.6395
1.0694
.06486
.93514
15
21
0
.35837
.64163
2.7904
.38386
2.6051
1.0711
.06642
.93358
69
0
15
.36244
.63756
2.7591
.38888
2-5715
1.0729
.06799
.93201
45
30
.36650
.63350
2.7285
.39391
2.5386
1.0748
.06958
.93042
30
45
.37056
.62944
2.6986
.39896
2.5065
1.0766
.07119
.92881
15
22
0
.37461
.62539
2.6695
.40403
2-4751
1.0785
.07282
.92718
68
0
15
.37865
.62135
2.6410
.40911
2 4443
1.0804
.07446
.92554
45
30
.38268
.61732
2.6131
.41421
2-4142
1.0824
.07612
.92388
30
45
.38671
.61329
2.5859
.41933
2-3847
1.0844
.07780
.92220
15
23
0
.39073
.60927
2.5593
.42447
2-3559
1.0864
.07950
.92050
67
0
15
.39474
.60526
2.5333
.42963
2-3276
1.0884
.08121
.91879
45
30
.39875
60125
2.5078
.43481
2-2998
1.0904
.08294
.91706
30
45
.40275
.59725
2.4829
.44001
2 2727
1.0925
.08469
.91531
15
24
0
.40674
.59326
2.4586
.44523
2-2460
1.0946
.08645
.91355
66
0
15
.41072
.58928
2.4348
.45047
2.2199
1.0968
.08824
.91176
45
30
.41469
.58531
2.4114
.45573
2.1943
1.0989
.09004
.90996
30
45
41866
.58134
2.3886
.46101
2.1692
1.1011
.09186
.90814
15
25
0
.42262
.57738
2.3662
.46631
2.1445
1.1034
.09369
.90631
65
0
15
.42657
.57343
2.3443
.47163
2-1203
1.1056
.09554
.90446
45
30
.43051
.56949
2.3228
.47697
2-0965
1.1079
.09741
.90259
30
45
.43445
.56555
2.3018
.48234
2.0732
1.1102
.09930
.90070
15
26
0
.43837
.56163
2.2812
.48773
2-0503
1.1126
.10121
.89879
64
0
15
.44229
.55771
2.2610
.49314
2.0278
1.1150
.10313
.89687
45
30
.44620
.55380
2.2412
.49858
2.0057
1.1174
.10507
.89493
30
45
.45010
.54990
2.2217
.50404
.9840
1.1198
.107'02
.89298
15
27
0
.45399
.54601
2.2027
.50952
.9626
1.1223
.10899
.89101
63
0
15
.45787
.54213
2.1840
.51503
.9415
1.1248
.11098
.88902
45
30
.46175
.53825
2.1657
.52057
.9210
1.1274
.11299
.88701
30
45
.46561
.53439
2.1477
.52612
.9007
1.1300
.11501
.88499
15
2$
0
.46947
.53053
2.1300
.53171
.8807
1.1326
.11705
.88295
62
0
15
.47332
.52668
2.1127
.53732
.8611
1.1352
.11911
.88089
45
30
.47716
.52284
2.0957
.54295
.8418
1.1379
.12118
.87882
30
45
.48099
.51901
2.0790
.54862
.8228
1.1400
.12327
.87673
15
29
0
.48481
.51519
2.0627
.55431
.8040
1.1433
.12538
.87462
61
0
15
.48862
.51138
2.0466
.56003
.7856
1.1461
.12750
.87250
45
30
.49242
.50758
2.0308
.56577
.7675
1.1490
.12964
.87036
30
45
. 49622
.50378
2.0152
.57155
.7496
1.1518
.13180
.86820
15
30
0
.50000
.50000
2.0000
.57735
1.7320
1.1547
.13397
.86603
60
0
Cosine.
Ver. Sin.
Secant.
Cotan.
Tang.
Cosec.
Co-Vers.
Sine.
'
M.
From 60° to 75° read from bottom of table upwards.
NATURAL TRIGONOMETRICAL FUNCTIONS.
161
0
M.
Sine.
Co-Vers.
Cosec.
Tang.
Cotan.
Secant.
Ver. Sin.
Cosine.
80
0
.50000
.50000
2.0000
.57735
.7320
1.1547
.13397
.86603
60
0
15
.50377
.49623
.9850
.58318
.7147
1.1576
.13616
.86384
45
30
.50754
.49246
.9703
.58904
.6977
1.1606
.13837
.86163
30
45
.51129
.48871
.9558
.59494
.6808
1.1636
.14059
.85941
15
81
0
.51504
.48496
.9416
.60086
.6643
1.1666
.14283
.85717
59
0
15
.51877
.48123
.9276
.60681
.6479
.1697
.14509
.85491
45
30
.52250
.47750
.9139
.61280
.6319
.1728
.14736
.85264
30
45
.52621
.47379
.9004
.61882
1.6160
.1760
.14965
.85035
15
32
0
.52992
.47008
.8871
.62487
1.6003
.1792
.15195
.84805
58
0
15
.53361
.46639
.8740
.63095
1.5849
.1824
.15427
.84573
45
30
.53730
.46270
.8612
.63707
1.5697
.1857
.15661
.84339
30
45
.54097
.45903
.8485
.64322
1.5547
.1890
.15896
.84104
15
33
0
.54464
.45536
.8361
.64941
1.5399
1924
.16133
.83867
57
0
15
.54829
.45171
.8238
.65563
1.5253
.1958
.16371
.83629
45
30
.55194
.44806
.8118
.66188
1.5108
.1992
.16611
.83389
30
45
.55557
.44443
.7999
.66818
1.4966
.2027
.16853
.83147
15
34
0
.55919
.44081
.7883
.67451
1.4826
.2062
.17096
.82904
56
0
15
.56280
.43720
.7768
.68087
1.4687
.2098
.17341
.82659
45
30
;56641
.43359
.7655
.68728
1.4550
.2134
.17587
.82413
30
45
.57000
.43000
.7544
. 69372
1.4415
.2171
.17835
.82165
15
85
0
.57358
.42642
.7434
.70021
1.4281
.2208
.18085
.S1915
55
0
15
.57715
.42285
.7327
.70673
1.4150
.2245
.18336
.81664
45
30
.58070
.41930
.72x>0
.71329
1.4019
.2283
.18588
.81412
30
45
.58425
.41575
.7116
.71990
1.3891
.2322
.18843
.81157
15
36
0
.58779
.41221
.7013
.72654
1.3764
.2361
.19098
.80902
54
0
15
.59131
.40869
.6912
.73323
1.3638
.2400
.19356
.80644
45
30
.59482
.40518
.6812
.73996
1.&514
.2440
.19614
.80386
30
45
.59832
.40168
.6713
.74673
1.3392
.2480
.19875
.80125
15
37
0
.60181
.39819
.6616
.75355
1.3270
.2521
.20136
.79864
53
0
15
.60529
.39471
.6521
.76042
1.3151
.2563
.20400
.79600
45
30
.60876
.39124
.6427
.76733
1.3032
.2605
.20665
.79335
30
45
.81222
.38778
.6334
. 77428
1.2915
.2647
.20931
.79069
15
38
0
.61566
.38434
.6243
.78129
1.2799
.2690
.21199
.78801
52
0
15
.61909
.38091
.6153
.78834
1.2685
1.2734
.21468
.78532
45
30
.62251
.37749
.6064
.79543
1.2572
1.2778
.21-739
.78261
3"
45
.62592-
.37408
.5976
.80258
1.2460
1.2822
.22012
.77988
15
39
0
.62932
.37068
.5890
.80978
1.2349
1.2868
.22285
.77715
51
0
15
.63271
.36729
.5805
.81703
1.2239
1.2913
.22561
.77'439
45
30
.63608
.36392
.5721
.82434
1.2131
1.2960
.22838
.77162
30
45
.63944
.36056
.5639
.83169
1.2024
1.3007
.23116
.76884
15
40
0
.64279
.35721
.5557
.83910
1.1918
1.3054
. .23396
.76604
50
0
15
.64612
.35388
.5477
.84656
1.1812
1.3102
.23677
.76323
45
30
.64945
.35055
.5398
.85408
1.1708
1.3151
.23959
.76041
30
45
.65276
.34724
1.5320
.86165
1.1606
1.3200
.24244
.75756
15
41
0
.65606
.34394
1.5242
.86929
1.1504
1.3250
.24529
.75471
49
0
15
.65935
.34065
1.5166
.87698
1.1403
1.3301
.24816
.75184
45
30
.66262
.33738
1 5092
.88472
1.1303
1.3352
.25104
. 7489(
30
45
.66588
.33412
1.5018
.89253
1.1204
1.3404
.25394
.74606
15
42
0
.66913
.33087
1.4945
.90040
1.1106
1.3456
.25686
.74314
48
0
15
.67237
.32763
1.4873
.90834
1.1009
1.3509
.25978
.7402?
45
30
.67559
.32441
1.4802
.91633
1.0913
1.3563
.2627'2
.73728
30
45
.67830
.32120
1.4732
.92439
1.0818
1.3618
.26568
.73432
15
43
0
.68200
.31800
1.4663
.93251
1.0724
1.3673
.26865
.73135
47
0
15
.68518
.31482
1.4595
.94071
1.0630
1.3729
.27163
.72837
45
30
.68835
.31165
1.4527
.94896
1.0538
1 .3786
.27463
.72537
30
45
.69151*
.30849
1.4461
.95729
1.044G
1.3843
.27764
.72236
15
44
0
.69466
.30534
1.43*96
.96569
1.0355
1.3902
.28066
.71934
46
0
15
.69779
.30221
1.4331
.97416
1.0265
1.3961
.28370
.71630
45
30
.70091
.29909
1.4267
.98270
1.0176
1.4020
.28675
.71325
30
45
.70401
.29599
1.4204
.99131
1.0088
1.4081
.28981
.71019
15
45
0
.70711
.29289
1.4142
1.0000'
1.0000
1.4142
.29289
.70711
45
0
Cosine.
Ver. Sin.
Secant.
Cotan.
Tang.
Cosec.
Co-Vers.
Sine.
o
M.
From 45° to 60° read from bottom of table upwards,
162
MATHEMATICAL TABLES.
LOGARITHMIC SINES, ETC.
Deg.
Sine.
Cosec.
Versin.
Tangent.
Cotan.
Covers.
Secant.
Cosine.
Deg.
0
In.Neg.
Infinite.
In.Neg.
In.Ne?.
Infinite.
10.00000
10.00000
10.00000
90
1
8.24186
11.75814
0.18271
8.24192
11.75808
9.99235
10.00007
9.99993
89
2
8.54282
11.45718
6.78474
8.54308
11.45692
9.98457
10.00026
9.99974
88
3
8.71880
11.28120
7.13687
8.71940
11.28060
9.97665
10.00060
9.99940
87
4
8.84358
11.15642
7.38667
8.84464
11.15536
9.96860
10.06106
9.99894
86
5
8.94030
11.05970
7.58039
8.94195
11.05805
9.96040
10.00166
9.99834
85
6
9.01923
10.98077
7.73863
9.02162
10.97838
9.95205
10.00239
9.99761
84
7
9.08589
10.91411
7.87238
9.08914
10.91086
9.94356
10.00325
9.99675
83
8
9.14356
10.85644
7.98820
9.14780
10.85220
9.93492
10.00425
9.99575
82
9
9.19433
10.80567
8.09032
9.19971
10.80029
9.92612
10.00538
9.99462
81
10
9.23967
10.76033
8.18162
9.24632
10.75368
9.91717
10.00665
9.99335
80
11
9.28060
10.71940
8.26418
9.28865
10.71135
9.90805
10.00805
9.99195
79
12
9.31788
10.68212
8.33950
9.32747
10.67253
9.89877
10.00960
9. 99f)40
78
13
9.35209
10.64791
8.40875
9.36336
10.636G4
9.88933
10.01128
9.98872
77
14
9.38368
10.61632
8.47282
9.39677
10.60323
9.87971
10.01310
9.98690
76
15
9.41300
10.58700
8.53243
9.42805
10.57195
9.86992
10.01506
9.98494
75
16
9.44034
10.55966
8.58814
9.45750
10.54250
9.85996
10.01716
9.98284
74
17
9.46594
10.53406
8.64043
9.48534
10.51460
9.84981
10.01940
9.98060
73
18
9.48998
10.51002
8.68969
9.51178
10.48822
9.83947
10.02179
9.97821
72
19
9.51264
10.48736
8.73625
9.53697
10.46303
9.82894
10.02433
9.97567
71
20
, 9. 53405
10.46595
8.78037
9.56107
10.43893
9.81821
10.02701
9.97299
70
21
9.55433
10.44567
8.82230
9.58418
10.41582
9.807*9
10.02985
9.97015
69
22
9.57358
10.42642
8.86223
9.60641
10.39359
9.79615
10.03283
9.96717
68
23
9.59188
10.40812
8.90034
9.62785
10.37215
9.78481
10.03597
9.96403
67
24
9.60931
10.39069
8.93679
9.64858
10.35142
9.77325
10.03927
9.96073
66
25
9.62595
10.37405
8.97170
9.66867
10.33133
9.7614C
10.04272
9.95728
65
26
9.64184
10.35816
9.00521
9.68818
10.31182
9.74945
10.04634
9.95366
64
27
9.65705
10.34295
9.03740
9.70717
10.29283
9.73720
10.05012
9.94988
63
28
9.67161
10.32839
9.06838
9.72567
10.27433
9.72471
10.05407
9.94593
62
29
9.68557
10.31443
9.09823
9.74375
10.25625
9.71197
10.05818
9.94182
61
30
9.69897
10.30103
9.12702
9.76144
10.23856
9.69897
10.06247
9.93753
60
31
9.71184
10.28816
9.15483
9.77877
10.22123
9.68571
10.06693
9.93307
59
32
9.72421
10.27579
•9.18171
9.79579
10.20421
9.67217
10.07158
9.92842
58
33
9.73611
10.26389
9.20771
9.81252
10.18748
9.65836
10.07641
9.92359
57
34
9.74756
10.25244
9.23290
9.82899
10.17101
9.64425
10.08143
9.91857
56
35
9.75859
10.24141
9.25731
9.84523
10.15477
9.62984
10.08664
9.91336
55
36
9.76922
10.23078
9.28099
9.86126
10.13874
9.61512
10.09204
9.90796
54
SP-
9.77946
10.22054
9.30398
9.87711
10.12289
9.60008
10.09765
9.90235
53
SS
9.78934
10.21066
9.32631
9.89281
10.10719
9.58471
10.10347
9.89653
52
39
9.79887
10.20113
9.34802
9.90837
10.09163
9.56900
10.10950
9.89050
51
40
9.80807
10.19193
9.36913
9.92381
10.07619
9.55293
10.11575
9.88425
50
41
9.81694
10.18306
9.38968
9.93916
10.06084
9.53648
10.12222
9.87778
49
42
9.82551
10.17449
9.40969
9.95444
10.04556
9.51966
10.12893
9.87107
48
43
9.83378
10.16622
9.42918
9.96966
10.03034
9.50243
10.13587
9.86413
47
44
9.84177
10.15823
9.44818
9.98484
10.01516
9.48479
10.14307
9.85693
46
^45
9.84949
10.15052
9.46671
10.00000
10.00000
9.46671
10.15052
9.84949
45
Cosine.
Secant.
Covers.
Cotan.
Tangent.
Versin.
Cosec.
Sine.
From 45° to 90° read from bottom of table upwards.
SPECIFIC GRAVITY.
MATERIALS.
THE CHEMICAL ELEMENTS.
Common Elements (42).
1o*
'i
•a--
0^
"3-;
If
Name.
si
S'S
It
Name.
s*S
$•%
||
Name.
fl bJO
£'3
gco
4fje
o^
<$
go>
<£:
Al
Aluminum
27.1
F
Fluorine
19.
Pd
Palladium
106.
Sb
Antimony
120.4
Au
Gold
197.2
P
Phosphorus
31.
As
Arsenic
75.1
H
Hydrogen
1.01
Pt
Platinum
194.9
Ba
Barium
137.4
I
Iodine
126.8
K
Potassium
39.1
Bi
Bismuth
208.1
Ir
I rid in m
193.1
Si
Silicon
28.4
B
Boron
10.9
Fe
Iron
56.
Ag
Silver
107.9
Br
Bromine
79.9
Pb
Lead
206.9
Sodium
23.
Cd
Cadmium
111.9
Li
Lithium
7.03
S?
Strontium
87.6
Ca
Calcium
40.1
Mg
Magnesium
24.3
S
Sulphur
32.1
C
Carbon
12.
Mn
Manganese
55.
Sn
Tin
119.
Cl
Chlorine
35.4
Hg
Mercury
200.
Ti
Titanium
48.1
Cr
Chromium
52.1
Ni
Nickel
58.7
W
Tungsten
184.8
Co
Cobalt
59.
N
Nitrogen
14.
Va
Vanadium
51.4
Cu
Copper
63.6
0
Oxygen
16.
Zn
Zinc
65.4
j-tureu to \j = JD ttuu n = i.vuo. vvneii n. is ttt.i4.cii tt» i, v^ = lu.o/y, uiiu 1110
other figures are diminished proportionately. (See Jour. Am. Chem. Soc.,
TV. o i.^V. -i OflC \
The Rare Elements (27).
Beryllium, Be.
Caesium, Cs.
Cerium, Ce.
Didymium, D.
Erbium, E.
Gallium, Ga.
Germanium, Ge.
Glucinum, G.
Indium, In.
Lanthanum, La.
Molybdenum, Mo.
Niobium, Nb.
Osmium, Os.
Rhodium, R.
Rubidium, Rb.
Ruthenium, Ru.
Samarium, Sm.
Scandium, Sc.
Selenium, Se.
Tantalum, Ta.
Tellurium, Te.
Thallium, Tl.
Thorium, Th.
Uranium, U.
Ytterbium, Yr.
Yttrium, Y.
Zirconium, Zr.
SPECIFIC GRAVITY.
The specific gravity of a substance is its weight as compared with the
weight of an equal bulk of pure water.
To find the specific gravity of a substance.
W = weight of body in air; w = weight of body submerged in water.
W
Specific gravity = w _ w-
If the substance be lighter than the water, sink it by means of a heavier
substance, and deduct the weight of the heavier substance.
Specific-gravity determinations are usually referred to the standard of the
weight of water at 62° F., 62.355 Ibs. per cubic foot. Some experimenters
have used 60° F. as the standard, and others 32° and 39.1° F. There is no
general agreement.
Given sp. gr. referred to water at 39.1° F., to reduce it to the standard of
62° F. multiply it by 1.00112.
Given sp. gr. referred to water at 62° F., to find weight per cubic foot mul-
tiply by 62.355. Given weight per cubic foot, to find sp. gr. multiply by
0.016037. Given sp. gr., to find weight per cubic inch multiply by .036085.
164
MATERIALS.
Weight and Specific Gravity of Metals.
Specific Gravity.
Range accord-
ing to
several
Authorities.
Specific Grav-
ity. Approx.
Mean Value,
used in
Calculation of
Weight.
Weight
per
Cubic
Foot,
Ibs.
Weight
per
Cubic
Inch,
Ibs.
2.56 to 2.71
6.66 to 6.86
9.74 to 9.90
7.8 to 8.6
8.52 to 8.96
8.6 to 8.7
1.58
5.0
8.5 to 8.6
19.245 to 19.361
8.69 to 8.92
22.38 to 23.
6.85 to 7.48
7.4 to 7.9
11.07 to 11.44
7. to 8.
1.69 to 1.75
13.60 to 13.62
13.58
13.37 to 13.38
8.279 to 8.93
20.33 to 22.07
0.865
10.474 to 10.511
0.97
7.69* to 7.932t
7.291 to 7.409
5.3
17. to 17.6
6.86 to 7.20
2.67
6.76
9.82
rs.eo
J8.40
1 8.36
[8.20
8.853
8.65
19.258
8.853
7.218
7.70
11.38
8.
1.75
13.62
13.58
13.38
8.8
21.5
10.505
7.854
7.350
7.00
166.5
421.6
612.4
536.3
523.8
521.3
511.4
552.
539.
1200.9
552.
1396.
450.
480.
709.7
499.
109.
849.3
846.8
834.4
548.7
1347.0
655.1
489.6
458.3
436.5
.0963
.2439
.3544
.3103
.3031
.3017
.2959
.3195
.3121
.6949
.3195
.8076
.2604
.2779
.4106
.2887
.0641
.4915
.4900
.4828
.3175
.7758
.3791
.2834
.2652
.2526
Antimony
Bismuth . ...
Brass: Copper 4- Zinc 1
80 20 I
70 30 >-..
60 40
50 50 J
Rron7pjCopper,95to80>
onzelTin, 5 to 20 f
Cadmium
Calcium
Cobalt
Gold pure
Copper
Iron Cast
" Wrought
Lead
Manganese
Magnesium.. ..
Mercury
Nickel
j 32°
....-< 60°
(212°
Platinum
Potassium
Silver
Sodium
Steel
Tin
Titanium
Tungsten
Zinc .
* Hard and burned.
t Very pure and soft. The sp. gr. decreases as the carbon is increased.
In the first column of figures the lowest are usually those of cast metals,
which are more or less porous; the highest are of metals finely rolled or
drawn into wire.
Specific Gravity of Liquids at 60° F.
Acid, Muriatic 1.200
" Nitric 1.217
" Sulphuric 1.849
Alcohol, pure 794
" 95 per cent 816
" 50 " " 934
Ammonia, 27.9 per cent 891
Bromine 2.97
Carbon disulphide 1 .26
Ether, Sulphuric 72
Oil, Linseed 94
Compression of tlse following Fluids under a Pressure of
15 Ibs. per Square Inch.
Water 00004663 I Ether 00006158
Alcohol 0000216 [Mercury 00000265
Oil, Olive 92
Palm 97
Petroleum 78 to .88
Rape 92
Turpentine 87
Whale 92
Tar 1.
Vinegar 1.08
Water 1.
" sea 1.026 tol.O
SPECIFIC GRAVITY.
165
The Hydrometer,
The hydrometer is an instrument for determining the density of liquids.
It is usually made of glass, and consists of three parts: (1) the upper part,
a graduated stem or fine tube of uniform diameter; (2) a bulb, or enlarge-
ment of the tube, containing air ; and (3) a small bulb at the bottom, con-
taining shot or mercury which causes the instrument to float in a vertical
position. The graduations are figures representing either specific gravities,
or the numbers of an arbitrary scale, as in Baume's, Twaddell's, Beck's,
and other hydrometers.
There is a tendency to discard all hydrometers with arbitrary scales and
;o use only those which read in terms of the specific gravity directly.
Baume's Hydrometer and Specific Gravities Compared.
Degrees
Baume.
Liquids
Heavier
than
Water,
sp. gr.
Liquids
Lighter
than
Water,
sp. gr.
Degrees
Baume.
Liquids
Heavier
than
Water,
sp. gr.
Liquids
Lighter
than
Water,
sp. gr.
Degrees
Baum6.
Liquids
Heavier
than
Water,
sp. gr.
Liquids
Lighter
than
Water,
sp. gr.
0
1
1.000
1.007
19
20
1.143
1.152
.942
.936
38
8P
1.333
1.345
.839
.834
0
1 013
21
1 160
.930
40
1 357
.830
3
4
5
1.020
1.027
1.034
22
23
24
1.169
1.178
1.188
.924
.918
.913
41
42
44
1.369
1.382
1.407
.825
.820
.811
fi
1 041
25
1 197
.907
46
1.434
.802
7'
1.048
96
1.206
.901
48
1.462
.794
8
q
1.05G
1 063
27
98
1.216
1.226
.896
.890
50
53
1.490
1.520
.785
.777
10
11
12
13
14
15
1.070
1.078
1.086
1.094
1.101
1.109
1.000
.993
.986
.980
.973
.967
29
30
31
32
33
84
1.236
1.246
1.256
1.267
1.277
1.288
.885
.880
.874
.869
.864
.859
54
56
58
60
65
70
1.551
.583
.617
.652
.747
.854
.768
,760
.753
.745
16
1 118
960
35
1 299
.854
75
1 974
17
1.126
.954
36
1 310
.849
76
2.000
18
1.134
.948
37
1.322
.844
Specific Gravity and Weight of Wood.
Specific Gravity.
Weight
per
Cubic
Foot.
Ibs.
Specific Gravity.
Weight
per
Cubic
Foot,
Ibs.
Alder
Avge.
0.56 to 0.80 .68
42
Hornbeam. . .
Avge.
.76 .76
47
Apple
A.sh
.73 to .79 .76
.60 to .84 .72
47
45
Juniper
Larch
.56 .56
.56 .56
35
35
Bamboo.. . .
Beech .
.31 to .40 .35
.62 to .85 .73
22
46
Lignum vitse
Linden
.65 to 1.33 1.00
.604
62
37
Birch
.56 to .74 .65
41
Locust
.728
46
Box,
.91 to 1.33 1.12
70
Mahogany. ..
.56 to 1.06 .81
51
Cedar ... .
.49 to .75 .62
39
Maple
.57 to .79 .68
42
Cherry
Chestnut —
Cork
.61 to .72 .66
.46 to .66 .56
.24 .24
41
35
15
Mulberry —
Oak, Live
44 White
.56 to .90 .73
.96 to 1.26 1.11
.69 to .86 .77
46
69
48
Cypress....
Dogwood . . .
Ebony
Elm . .
.41 to .66 .53
.76 .76
1.13 to 1.33 1.23
.55 to .78 .61
33
47
76
38
44 Red....
Pine, White. .
44 Yellow.
Poplar ....
.73 to .75 .74
.35 to .55 .45
.46 to .76 .61
.38 to .58 .48
46
28
-38
30
Fir
Gum
Hackmatack
.48 to .70 .59
.84 to 1.00 .92
.59 .59
37
57
37
Spruce.
Sycamore....
Teak
.40 to .50 .45
.59 to .62 .60
.66 to .98 .82
28
37
51
Hemlock . . .
Hickory
.36 to .41 .38
69 to .94 .77
24
48
Walnut
Willow.
.50 to .67 .58
.49 to .59 .54
36
34
Holly....'!.!!
.76 .76
47
166
MATE-KLAUS.
Weight and Specific Oravlty of Stones, Brick,
Cement, etc.
Pounds per
Cubic Foot.
Specific
Gravity.
Asphaltum 87
Brick, Soft 100
" Common 112
41 Hard 125
" Pressed 135
" Fire 140 to 150
Brickwork in mortar 100
" cement 112
Cement, Rosendale, loose 60
*' Portland, " 78
Clay 120 to 150
Concrete 120 to 140
Earth, loose 72 to 80
rammed 90 to 110
Emery 250
Glass 156 to 172
" flint 180tol96
Gneiss I ,«A, ^n
Granite p — ' 160 to 170
Gravel 100 to 120
Gypsum 130 to 150
Hornblende 200 to 220
Lime, quick, in bulk 50 to 55
Limestone 170 to 200
Magnesia, Carbonate 150
Marble 160 to 180
Masonry, dry rubble 140 to 160
" dressed 140 to 180
Mortar 90 to 100
Pitch 72
Plaster of Paris 74 to 80
Quartz 165
Sand 90 to 110
Sandstone 140 to 150
Slate 170tol80
Stone, various 135 to 200
Trap 170 to 200
Tile 110 to 120
Soapstone 166 to 175
1.39
1.6
1.79
2.0
2.16
2.24 to 2.4
1.6
1.79
.96
1.25
1.92 to 2.4
1.92 to 2. 24
1.15 to 1.28
1.44 to 1.76
4.
2.5 to 2.73
2. 88 to 3. 14
2.56 to 2.72
1.6 to 1.92
2. 08 to 2. 4
3.2 to 3. 52
> .8 to .88
2. 72 to 3. 2
2.4
2. 56 to 2. 88
2. 24 to 2. 56
2.24 to 2.88
1.44 to 1.6
1.15
1.18 to 1.28
2.64
1.44 to 1.76
2.24 to 2.4
2. 72 to 2. 88
2.16 to 3. 4
2. 72 to 3.4
1.76 to 1.92
2.65 to 2.8
Specific Gravity and Weight of Oases at Atmospheric
Pressure and 32° F.
(For other temperatures and pressures see pp. 459, 479.)
Density,
Air ='l.
Air
Oxygen, O
Hydrogen, H
Nitrogen, N
Carbon monoxide, CO...
Carbon dioxide, CO2
Methane, marsh-ga s, CH4
Eihylene, C2H4
Acetylene, C2H2
Ammonia, NH3
Water vapor, H2O
1.0UOO
1.1052
0.0692
0.9701
0.9671
1.5197
0.5530.
0.9674
0.8982
0.5889
0.6218
Density,
H = 1.
14.444
15.963
1.000
14.012
13.968
21 .950
7.987
13.973
12.973
8.506
8.981
per Litre.
1.2931
1.4291
0.0895
1.2544
1.2505
1.9650
0.7150
1.2510
1.1614
0.7615
0.8041
Lbs. per Cubic Ft.
Cu. Ft,
.080753
.08921
.00559
.07831
.07807
.12567
.04464
.07809
.07251
.04754
.05020
per Lb.
12.388
11.209
178.931
12.770
12.810
8.152
22.429
12.805
13.792
21.036
19.922
PROPERTIES OF THE USEFUL METAXS. 16?
PROPERTIES OF THE USEFUL METALS.
Aluminum, Al.— Atomic weight 27.1. Specific gravity 2.6 to 2.7.
The lightest of all the useful nietals except magnesium. A soft, ductile,
malleable metal, of a white color, approaching silver, but with a bluish cast.
Very non-corrosive. Tenacity about one third that of wrought-iron. For-
merly a rare metal, but since 1890 its production and use have greatly in-
creased on account of the discovery of cheap processes for reducing it from
the ore. Melts at about 1160° F. For further description see Aluminum,
under Strength of Materials.
Antimony (Stibium), Sb.— At. wt. 120.4. Sp. gr. 6.7 to 6.8. A brittle
metal of a bluish-white color and highly crystalline or laminated structure.
Melts at 842° F. Heated in the open air it burns with a bluish-white flame.
Its chief use is for the manufacture of certain alloys, as type metal (anti-
mony 1, lead 4), britannia (antimony 1, tin 9), and various anti-friction
metals (see Alloys). Cubical expansion by heat from 92° to 212° F., 0.0070.
Specific heat .050.
Bismuth, Bi.— At. wt. 208.1. Bismuth is of a peculiar light reddish
color, highly crystalline, and so brittle that it can readily be pulverized. It
melts at 510° F., and boils at about 2300° F. Sp. gr. 9.823 at 54° F., and
10.055 just above the melting-point:. Specific heat about .0301 at ordinary
temperatures. Coefficient of cubical expansion from 32° to 212°, 0.0040. Con-
ductivity for heat about 1/56 and for electricity only about 1/80 of that of
silver. Its tensile strength is about 6400 Ibs. per square inch. Bismuth ex-
pands in cooling, and Tribe has shown that this expansion does not take
place until after solidification. Bismuth is the most diamagrietic element
known, a sphere of it being repelled by a magnet.
Cadmium, Cd.— At. wt. 112. Sp. gr. 8.6 to 8.7. A bluish-white metal,
lustrous, with a fibrous fracture. Melts below 500° F. and volatilizes at
about 680° F. It is used as an ingredient in some fusible alloys with lead,
tin, and hismuth. Cubical expansion from 32° to 212° F., 0.0094.
Copper, Cu.— At. wt. 63.2. Sp. gr. 8.81 to 8.95. Fuses at about 1930°
F. Distinguished from all other metals by its reddish color. Very ductile
and malleable, and its tenacity is next to iron. Tensile strength 20,000 to
30,000 Ibs. per square inch. Heat conductivity 73. 6# of that of silver, and su-
perior to that of other metals. Electric conductivity equal to that of gold
and silver. Expansion by heat from 32° to 212° F., 0.0051 of its volume.
Specific heat .093. (See Copper under Strength of Materials: also Alloys.)
Gold (Aurum). Au«— At. wt. 197.2. Sp. gr., when pure and pressed in a
die, 19.34. Melts at about 1915° F. The most malleable and ductile of all
metals. One ounce Troy may be beaten so as to cover 160 sq. ft. of surface.
The average thickness of gold-leaf is 1/282000 of an inch, or 100 sq. ft. per
ounce. One grain may be drawn into a wire 500 ft. in length. The ductil-
ity is destroyed by the presence of 1/2000 part of lead, bismuth, or antimony.
Gold is hardened by the addition of silver or of copper. In U. S. gold coin
there are 90 parts gold and 10 parts of alloy, which is chiefly copper with a
little silver. By jewelers the fineness of gold is expressed in carats, pure
gold being 24 carats, three fourths fine 18 carats, etc.
Iridium.— Indium is one of the rarer metals. It has a white lustre, re-
sembling that of steel; its hardness is about equal to that of the ruby; in
the cold it is quite brittle, but at a white heat it is somewhat malleable. It
is one of the Heaviest of metals, having a specific gravity of *jy.3S. It is ex-
tremely infusible and almost absolutely inoxiclizable.
For uses of iridium, methods of manufacturing it, etc., see paper by W. D.
Dudley on the "Iridium Industry," Trans. A. I. M. E. 1884.
Iron (Ferrum), Fe.— At. wt. 56. Sp. gr.: Cast, 6.85 to 7.48; Wrought,
7.4 to 7.9. Pure iron is extremely infusible, its melting point being above
3000° F , but its fusibility increases with the addition of carbon, cast iron fus*
ing about 2500° F. Conductivity for heat 11.9, and for electricity 12 to 14.8,
silver being 100. Expansion in bulk by heat: cast iron .0033, and wrought iron
.0035, from 32° to 212° F. Specific heat: cast iron .1298, wrought iron .1138,
steel .1165. Cast iron exposed to continued heat becomes permanently ex-
panded 1^ to 3 per cent of its length. Grate-bars should therefore be
allowed about 4 per cent play. (For other properties see Iron and Steel
under Strength of Materials.)
Lead (Plumbum), JPb.— At. wt. 208.9. Sp. gr. 11.07 to 11.44 by different
authorities. Melte at about 625° F., softens and becomes pasty at about
617° F. If broken by a sudden blow when just below the melting-point it ia
quite brittle and the fracture appears crystalline. Lead is very malleable
168 'MATERIALS.
and ductile, but its tenacity is such that it can be drawn into wire with great
difficulty. Tensile strength, 1600 to 2400 Ibs. per square inch. Its elasticity is
very low, and the metal flows under very slight strain. Lead dissolves to
some extent in pure water, but water containing carbonates or sulphates
forms over it a film of insoluble salt which prevents further action.
Magnesium, Mg.— At. wt. 24. Sp. gr. 1.69 to 1.75. Silver-white,
brilliant, malleable, and ductile. It is one of the lightest of metals, weighing
only about two thirds as much as aluminum. In the form of filings, wire,
or thin ribbons it is highly combustible, burning with a light of dazzling
brilliancy, useful for signal-lights and for flash-lights for photographers. It
is nearly non-corrosive, a thin film of carbonate of magnesia forming on ex-
posure to damp air, which protects it from further corrosion. It may be
alloyed with aluminum, 5 per cent Mg added to Al giving about as much in-
crease of strength and hardness as 10 per cent of copper. Cubical expansion
by heat 0.0083, from 32° to 212° F. Melts at 1200° F. Specific heat .25.
Manganese, Mn.— At. wt. 55. Sp. gr. 7 to 8. The pure metal is not
used iu tne arts, but alloys of manganese and iron, called spiegeleisen when
containing below 25 per cent of manganese, and ferro-manganese when con-
taining from 25 to 90 per cent, are used in the manuf ,cture of steel. Metallic
manganese, when alloyed with iron, oxidizes rapidly in the air, and its func*
tion in steel manufacture is to remove the oxygen from the bath of steel
whether it exists as oxide of iron or as occluded gas.
Mercury (Hydrargyrum), Hg.— At. wt. 199.8. A silver-white metal,
liquid at temperatures above— 39° F., and boils at 680° F. Unchangeable as
gold, silver, and platinum in the atmosphere at ordinary temperatures, but
oxidizes to the red oxide when near its boiling-point. Sp.gr.: when liquid
13.58 to 13.59, when frozen 14.4 to 14.5. Easily tarnished by sulphur fumes,
also by dust, from which it may be freed by straining through a cloth. No
metal except iron or platinum should be allowed to touch mercury. The
smallest portions of tni, lead, zinc, and even copper to a less extent, cause it
to tarnish and lose its perfect liquidity. Coefficient of cubical expansion
from 32° to 212° F. .0182; per deg. .000101.
Nickel, Ni.— At. wt. 58.3. Sp. gr. 8.27 to 8.93. A silvery- white metal
with a strong lustre, not tarnishing on exposure to the air. Ductile, hard,
and as tenacious as iron. It is attracted to the magnet and may be made
magnetic like iron. Nickel is very difficult of fusion, melting at about
3000* F. Chiefly used in alloys with copper, as german-silver, nickel-silver,
etc., and recently in the manufacture of steel to increase its hardness and
strength, also for nickel-plating. Cubical expansion from 32° to 212° F.,
0.0038. Specific heat .109.
Platinum, Pt.— At. wt. 195. A whitish steel-gray metal, malleable,
very ductile, and as unalterable by ordinary agencies as gold. When fused
and refined it is as soft as copper. Sp. gr. 21.15. It is fusible only by the
pxyhydrogen blowpipe or in strong electric currents. When combined with
indium it forms an alloy of great hardness, which has been used for gun-
vents and for standard weights and measures. The most important uses of
platinum in the arts are for vessels for chemical laboratories and manufac-
tories, and for the connecting wires in incandescent electric lamps. Cubical
expansion from 32° to 212° F., 0.0027, less than that of any other metal. ex-
cept the rare metals, and almost the same as glass.
Silver (Argentum), Ag.— At. wt. 107.7. Sp. gr. 10.1 to 11.1, according to
condition and purity. It is the whitest of the metals, very malleable and
ductile, and in hardness intermediate between gold and copper. Melts at
about 1750° F. Specific heat .056. Cubical expansion from 32° to 212° F.,
0.0058. As a conductor of electricity it is equal to copper. As a conductor
of heat it is superior to all other metals.
Tin (Stannum) Sn.— At. wt. 118. Sp. gr. 7.293. White, lustrous, soft:
malleable, of little strength, tenacity about 3500 Ibs. per square inch. Fuses
at 442° F. Not sensibly volatile when melted at ordinary heats. Heat con-
ductivity 14.5, electric conductivity 12.4; silver being 100 in each case.
Expansion of volume by heat .0069 from 32° to 212° F. Specific heat .055. Its
chief uses are for coating of sheet-iron (called tin plate) and for making
alloys with copper and other metals.
Zinc, Zn.— At. wt. 65. Sp. gr. 7.14. Melts at 780° F. Volatilizes and
burns in the air when melted, with bluish-white fumes of zinc oxide. It is
ductile and malleable, but to a much less extent than copper, and its tenacity,
about 5000 to 6000 Ibs. per square inch, is about one tenth that of wrought
iron. It is practically non-corrosive in the atmosphere, a thin film of car-
bonate of zinc forming upon it. Cubical expansion between 32° and 212° F.,
MEASURES AKD WEIGHTS OF VARIOUS MATERIALS. 169
0.0088. Specific heat .096. Electric conductivity 29, heat conductivity 36,
silver being 100. Its principal uses are for coating iron surfaces, called
" galvanizing," and for making brass and other alloys.
Table Showing the Order of
Malleability. Ductility. Tenacity. Infusitoility.
Gold
Silver
Aluminum
Copper
Tin
Lead
Zinc
Platinum
Iron
Platinum
Silver
Iron
Aluminum
Zinc
Tin
Lead
Iron
Copper
Aluminum
Platinum
Silver
Zinc
Gold
Tin
Lead
Platinum
Iron
Copper
Gold
Silver
Aluminum
Zinc
Lead
Tin
WEIGHT OF RODS, BARS, PLATES, TUBES, AND
SPHERES OF DIFFERENT MATERIALS.
Notation : b = breadth, t = thickness, s = side of square, d = external
Diameter, dl = internal diameter, all in inches.
Sectional areas : of square bars — s2; of flat bars = bt\ of round rods »
,7854da; of tubes = .7854(da - d,a) = 3.1410(d* - f2).
Volume of 1 foot in length :" of square bars = 12s2; of flat bars = 126£ ; of
round bars = 9.4248da; ot tubes = 9.4248(<i2 - d-ft = 37.699(<i£ — ?2), in cu. in.
Weight per foot length = volume X weight per cubic inch of the material.
Weight of a sphere = diam.3 X .5236 X weight per cubic inch.
Material.
Cast iron
Wrought Iron
Steel
Copper & Bronze I
(copper and tin) f
Lead
Aluminum
Glass
Pine Wood, dry . . .
8.855
11.38
2.G7
2.62
0.481
7.218450.
7.7 480.
7.854489.6
552.
8.393523.2
709.6
166.5
163.4
30.0
37.5
40.
40.
Sit
£W£
83
$&«!
.4s'
46.
43.63.633s2
59.1 4. 93s2
13.91.16s2
13.61.13s*
2.50.21s2
3.46*
3.8336*
3.6336*
4.936*
1.166*
1.136*
0.216*
,2604
,27791.
28331.02
.31951.15
30291.09
,41061.48
3470
09630.
09450.34
0174 1-16
15-16 2. 454d2
2.618d2
2.670d2
3. Olid2
2.854d2
3.870d2
0.164d2
.0091d«
Weight per cylindrical in., 1 in. long, = coefficient of d2 in ninth col. -v- 12.
For tubes use the coefficient of d2 in ninth column, as for rods, and
multiply it into (d2 — c?r); or multiply it by 4(dt — l2).
For hollow spheres use the coefficient of d3 in the last column and
multiply it into (d3 — rfj3).
For hexagons multiply the weight of square bars by 0.866 (short
diam. of hexagon == side of square). For octagons multiply by 0.8284.
MEASURES AND WEIGHTS OF VARIOUS
MATERIALS (APPROXIMATE).
Brickworlt.— Brickwork is estimated by the thousand, and for various
thicknesses of wall runs as follows:
8*4-in. wall, or 1 brick in tbicknessv 14 bricks per superficial feet.
12% ** ** " 1U» " «* »• 21 '* " " «
17 » «' » 2 » «»
21
28
35
An ordinary brick measures about $4X4X2 inches, which is equal to 66
cubic inches, or 26.2 bricks to a cubic foot. The average weight is % Ibs.
170
MATERIALS.
Fuel.— A bushel of bituminous coal weighs 76 pounds and contains 2688
cubic inches = 1.554 cubic feet. 29 .47 bushels = 1 gross ton.
A bushel of coke weighs 40 Ibs. (35 to 42 Ibs.).
One acre of bituminous coal contains 1600 tons of 2240 Ibs. per foot of
thickness of coal worked. 15 to 25 per cent must be deducted for waste in
mining.
41 to 45 cubic feet bituminous coal when broken down = 1 ton, 2240 Ibs.
34 to 41 " " anthracite, prepared for market = 1 ton, 2240 Ibs.
123 " •' of charcoal .= 1 ton, 2240 Ibs.
70.9 ** " "coke = 1 ton, 2240 Ibs.
1 cubic foot of anthracite coal (see also page 625) = 55 to 66 Ibs.
1 *' "bituminous4* , = 50 to 55 Ibs.
1 " '* Cumberland coal. = 53 Ibs.
1 " " Cannel coal = 50.3 Ibs.
1 " " charcoal (hardwood) = 18.5 Ibs.
1 " " " (pine) =181bs.
A bushel of charcoal.— In 1881 the American Charcoal-Iron Work-
ers' Association adopted for use in its official publications for the standard
bushel of charcoal 2748 cubic inches, or 20 pounds. A ton of charcoal is to
be taken at 2000 pounds. This figure of 20 pounds to the bushel was taken
as a fair average of different bushels used throughout the country, and it
has since been established by law in some States.
Ores, Earths, etc.
13 cubic feet of ordinary gold or silver ore, in mine = 1 ton = 2000 Ibs.
20 " " " broken quartz = 1 ton = 2000 Ibs.
18 feet of gravel in bank „ =1 ton.
27 cubic feet of gravel when dry = 1 ton.
25 " *' "sand = 1 ton.
18 ' " earth in bank = 1 ton.
27 ** " ** " when dry = 1 ton.
17 " clay =lton.
Cement.— English Portland, sp. gr. 1.25 to 1.51, per bbl 400 to 430 Ibs.
Rosendale, U. S., a struck bushel 62 to 70 Ibs.
liime.— A struck bushel 72 to 75 Ibs.
Grain. — A struck bushel of wheat = 60 Ibs.; of corn = 56 Ibs. : of oats =
30 Ibs.
Salt.— A struck bushel of salt, coarse, Syracuse, N. Y. = 56 Ibs. ; Turk's
Island = 76 to 80 Ibs.
Weight of Earth Filling.
(From Howe's " Retaining Walls.")
Average weight in
Ibs. per cubic foot.
Earth, common loam, loose 72 to 80
" shaken 82 to 92
4 * rammed moderately 90 to 100
Gravel 90 to 106
Sand 90tol06
Soft flowing mud 104 to 120
Sand, perfectly wet 118 to 129
COMMERCIAL SIZES OF IRON BARS.
Flats.
Width. Thickness.
Width. Thickness. Width. Thickness.
5*
WEIGHTS OF WROUGHT IRON BARS.
171
Rounds : H to \% inches, advancing by 16ths, and \% to 5 inches by
8ths.
Squares : 5/16 to 1J4 inches, advancing by 16ths, and 1J4 to 3 inches by
8ths.
Half rounds: 7/16, %, %, 11/16, %, 1, % 1^, % 1%, 2 inches.
Hexagons : % to 1^ inches, advancing by 8ths.
Ovals : y% X y±, % X 5/16, % x %, Vs X 7/16 inch.
Half ovals : ^ X & % X 5/32, % X 3/16, % X 7/32, 1^ X H, 1% X %,
1% X % inch.
Round-edge flats : 1^ X J4 1% X %, 1% X % inch.
Rands : }4 to \y% inches, advancing by 8ths, 7 to 16 B. W. gauge.
1J4 to 5 inches, advancing by 4ths, 7 to 16 gauge up to 3* inches, 4 to 14
gauge, 3J4 to 5 inches.
WEIGHTS OF SQUARE AND ROUND RARS OF
WROUGHT IRON IN POUNDS PER LINEAL FOOT.
Iron weighing 480 Ibs. per cubic foot. For steel add 2 per cent.
Thickness or
Diameter
in Inches.
Weight of
Square Bar
One Foot
Long.
Weight of
Round Bar
One Foot
Long.
Thickness or
Diameter
in Inches.
Weight of
Square Bar
One Foot
Long.
Weight of
Round Bar
One Foot
Long.
Thickness or
Diameter
in Inches.
Weight of
Square Bar
One Foot
Long.
Weight of
Round Bar
One Foot
Long.
0
11/16
24.08
18.91
%
96.30
75.64
1/16
.013
.010
M
25.21
19.80
7/16
98.55
77.40
M
.052
.041
13/16
26.37
20.71
H
100.8
79.19
3/16
.117
.092
27.55
21.64
9/16
103.1
81.00
M
.208
.164
15/16
28.76
22.59
%
105.5
82.83
5/16
.326
.256
3
30.00
23.56
11/16
107.8
84.69
%
.469
.368
1/16
31.26
24.55
H
110.2
86.56
7/16
.638
.501
\&
32.55
25.57
13/16
112.6
88.45
.833
.654
3/16
33.87
26.60
115.1
90.36
9/16
1.055
.828
\A
35.21
27.65
15/16
117.5
92.29
Ys
1.302
1.023
5/16
36.58
28.73
6
120.0
94.25
11/16
1.576
1.237
37.97
29.82
125.1
98.22
82
1.875
1.473
7/16
39.39
30.94
^4
130.2
102.3
13/16
2.201
1.728
40.83
32.07
3X
135.5
106.4
%
2.552
2.004
9/16
42.30
33.23
L£
140.8
110.6
15/16
. 2.930
2.301
%
43.80
34.40
To
146.3
114.9
3.333
2.618
11/16
45.33
35.60
%
151.9
119.3
1/16
3.763
2.955
46.88
36.82
VR
157.6
123.7
4.219
3.313
13/16
48.45
38.05
7
163.3
128.3
3/16
4.701
3.692
50.05
39.31
169.2
132.9
/4
5.208
4.091
15/16
51.68
40.59
x4
175.2
137.6
5/16
5.742
4.510
53.33
41.89
s2
181.3
142.4
6.302
4.950
1/16
55.01
43.21
i^
187.5
147.3
7/16
6.888
5.410
56.72
44.55
%
193.8
152.2
7.500
5.890
3/16
58.45
45.91
%
200.2
157.2
9/16
8.138
6.392
60.21
47.29
y&
206.7
162.4
9&
8.802
6.913
5/16
61.99
48.69
8
213.3
167.6
11/16
9.492
7.455
'n.
63.80
50.11
226.9
178.2
M
10.21
8.018
7/16
65.64
51.55
vh
240.8
189.2
13/16
10.95
8.601
y
67.50
53.01
3^
255.2
200.4
H
11.72
9.204
9/16
69.39
54.50
9
270.0
212.1
15/16
12.51
9.828
71.30
56.00
285.2
224.0
2
13.33
10.47
11/16
73.24
57.52
/^
300.8
236.3
1/16
14.18
11.14
M
75.21
59.07
*M
316.9
248.9
^0
15.05
11.82
18/16
77.20
60.63
10
333.3
261.8
3/16
15.95
12.53
79.22
62.22
350.2
275.1
U
16.88
13.25
15/16
81.26
63.82
V%
367.5
288.6
5/16
17.83
14.00
5
83.33
65.45
%
385.2
302.5
sk
18.80
14.77
1/16
85.43
67.10
11
403.3
316.8
•7/16
19.80
15.55
87.55
68.76
421.9
331.3
20.83
16.36
3/16
89.70
70.45
^
440.8
346.2
9/16
21.89
17.19
k
91.88
72.16
34
460.2
361.4
22.97
18.04
5/16
94.08
73.89
12
480.
377.
172
MATERIALS.
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WEIGHTS OF FLAT WROUGHT IKON. 173
ft
§
8888
X*>
If
•at
1*
174
MATERIALS.
WEIGHT OF IRON AND STEEL SHEETS.
Weights per Square Foot.
(For weights by Decimal Gauge, see page 32.)
Thickness by Birmingham Gauge.
Thickness by American (Brown and
Sharpe's) Gauge.
No. of
Gauge.
Thick-
ness in
Inches.
Iron.
Steel.
No. of
Gauge.
Thick-
ness in
Inches.
Iron.
Steel.
0000
.454
18.16
18.52
0000
.46
18.40
18.77
000
.425
17.00
17.34
000
.4096
16.38
16.71
00
.38
15.20
15.50
00
.3648
14.59
14.88
0
.34
13.60
13.87
0
.3249
13.00
13.26
1
.3
12.00
12.24
1
.2893
11.57
11.80
2
.284
11.36
11.59
2
.2576
10.30
10.51
3
.259
10.36
10.57
3
.2294
9.18
9.36
4
.238
9.52
9.71
4
.2043
8.17
8.34
5
.22
8.80
8.98
5
.1819
7.28
7.42
6
.203
8.12
8.28
6
.1620
6.48
6.61
7
.18
7.20
7.34
7
.1443
5.77
5.89
8
.165
6.60
6.73
8
.1285
5.14
5.24
9
.148
5.92
6.04
9
.1144
4.58
4.67
10
.134
5.36
5.47
10
.1019
4.08
4.16
11
.12
4.80
4.90
11
.0907
3.63
3.70
12
.109
4.36
4.45
12
.0808
3.23
3.30
13
.095
3.80
3.88
13
.0720
2.88
2.94
14
.083
3.32
3.39
14
.0641
2.56
2.62
15
.072
2.88
2.94
15
.0571
2.28
2.33
16
.065
2.60
2.65
16
.0508
2.03
2.07
17
.058
2.32
2.37
17
.0453
1.81
.85
18
.049
.96
2.00
18
.0403
1.61
.64
19
.042
.68
1.71
19
.0359
1.44
.46
20
.035
.40
1.43
20
.0320
1.28
.31
21
.032
.28
1.31
21
.0,285
1.14
.16
22
.028
.12
1.14
22
.0253
1.01
.03
23
.025
.00
1.02
23
.0226
.904
.922
24
.022
.88
.898
24
.0201
.804
.820
25
.02
.80
.816
25
.0179
.716
.730
26
.018
.72
.734
26
.0159
.636
.649
27
.016
.64
.653
27
.0142
.568
.579
28
.014
.56
.571
28
.0126
.504
.514
29
.013
.52
.530
29
.0113
.452
.461
30
.012
.48
.490
30
.0100
.400
.408
31
.01
.40
.408
31
.0089
.356
.363
32
.009
.36
.367
32
.0080
.320
.326
33
.008
.32
.326
33
.0071
.284
.290
34
.007
.28
.286
34
.0063
.252
.257
35
.005
.20
.204
35
.0056
.224
.228
Specific gravity .
I
ron. Steel.
.7 7.854
4SQ fi
fnnt . 480
"g P" " inch 2778 .2833
As there are many gauges in use differing from each other, and even the
thicknesses of a certain specified gauge, as the Birmingham, are not assumed
the same by all manufacturers, orders for sheets and wires should always
state the weight per square foot, or the thickness in thousandths of an inch.
WEIGHT OF PLATE IRON.
175
8
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gfe ^3 JL 2?S:Sffa?or?cotQtrc5^coin«oQQ
gl
«J .
Djf
g* *
*2S
•^ H ^ ^^ojotof^wwoiTOWOTWWccro^^^^^ooo^'oofic^^^Qddooo
!l
H*
1
few
ll
gl
*8
2«
H^
^
^SSS^SJSi
176
MATERIALS.
WEIGHTS OF STK12L BLOOMS.
Soft steel. 1 cub;c inch = 0.284 Ib. 1 cubic foot = 490.75 Ibs.
Sizes.
Lengths.
1"
6"
12"
18"
24"
30"
36"
42"
48"
54"
60"
66"
12" x 4"
13.63
82
164
245
327
409
491
573
654
736
818
900
11 x 6
18.75
113
225
338
450
563
675
788
900
1013
1125
1238
x 5
15.62
94
188
281
375
469
562
656
750
843
937
1031
x 4
12.50
75
150
225
300
375
450
525
600
675
750
825
10 x 7
19.88
120
239
358
477
596
715
835
955
1074
1193
1312
x 6
17.04
102
204
307
409
511
613
716
818
920
1022
1125
x 5
14.20
85
170
256
341
426
511
596
682
767
852
937
x 4
11.36
68
136
205
273
341
409
477
546
614
682
750
x 3
8.52
51
102
153
204
255
306
358
409
460
511
562
9 x 7
17.89
107
215
322
430
537
644
751
859
966
1073
1181
x 6
15.34
92
184
276
368
460
552
644
736
828
920
1012
x 5
12.78
77
153
230
307
383
460
537
614
690
767
844
x 4
10.22
61
123
.184
245
307
368
429
490
552
613
674
8 x 8
18.18
109
218
327
436
545
655
764
873
982
1091
1200
x 7
15.9
95
191
286
382
477
572
668
763
859
954
1049
x 6
13.63
82
164
245
327
409
491
573
654
736
818
900
x 5
11.36
68
136
205
273
341
409
477
546
614
682
750
x 4
9.09
55
109
164
218
273
327
382
436
491
545
600
7 x 7
13.92
83
167
251
334
418
501
585
668
752
835
919
x 6
11.93
72
143
215
286
358
430
501
573
644
716
,788
x 5
9.94
60
119
179
238
298
358
417
477
536
596
656
x 4
7.95
48
96
143
191
239
286
334
382
429
477
525
x 3
5.96
36
72
107
143
179
214
250
286
322
358
393
6^x W/2
12.
72
144
216
388
360
432
504
576
648
720
792
x 4
7.38
44
89
133
177
221
266
310
354
399
443
487
6 x 6
10.22
61
123
184
245
307
368
429
490
551
613
674
x 5
8.52
51
102
153
204
255
307
358
409
460
511
562
x 4
6.82
41
82
123
164
204
245
286
327
368
409
450
x 3
5.11
31
61
92
123
153
184
214
245
276
307
337
5^x sy2
8.59
52
103
155
206
258
309
361
412
464
515
567
x 4
6.25
37
75
112
150
188
225
262
300
337
375
412
5 x 5
7.10
43
85
128
170
213
256
298
341
383
426
469
x 4
5.68
34
68
102
136
170
205
239
273
307
341
375
4^ x 4^
5.75
35
69
104
138
173
207
242
276
311
345
380
x 4
5.11
31
61
92
123
153
184
215
246
276
307
338
4 x 4
4.54
27
55
80
••
109
136
164
191
218
246
272
300
x 3}4
3.97
24
48
72
96
119
143
167
181
215
238
262
x 3
3.40
20
41
61
82
102
122
143
163
184
204
224
3^ x*3J^
3.48
21
42
63
84
104
125
146
167
188
209
230
x 3
2.98
18
36
54
72
89
107
125
14-3
161
179
197
3 x 3
2.56
15
31
46
61
77
92
108
123
138
154
169
SIZES AKD WEIGHTS OF STRUCTURAL SHAPES. 177
SIZES AND WEIGHTS OF STRUCTURAL SHAPES.
Minimum, Maximum, and Intermediate Weights and
Dimensions of Carnegie Steel I-Beams.
Sec-
tion
Index
Depth
of
Beam.
Weight
per
Foot,
Flange
Width-
Web
Thick-
ness.
Sec-
tion
Index
Depth
of
Beam.
Weight
pei-
Foot.
Flange
Width.
Web
Thick-
ness.
ins.
Ibs.
ins.
ins.
ins.
Ibs.
ins.
ins.
Bl
24
100
7.25
0.75
B19
6
17.25
3.58
0.48
44
44
95
7.19
0.69
44
44
14.75
3.45
0.35
44
<4
90
7.13
0.03
44
44
12.25
3.33
0.23
44
44
85
7.07
0.57
B21
5
14.75
3.29
0.50
44
44
89
7.00
0.50
44
44
12.25
3.15
0.36
B3
20
75
6.40
0.65
44
44
9.75
3.00
0.21
70
6.33
0.58
B23
4
1015
2.88
0.41
4k
44
65
6.25
0.50
44
44
9.5
2.81
0.34
B80
18
70
6.26
0.72
44
44
8:5
2.73
0 26
44
44
65
6.18
0.64
44
44
7.5
2.66
0.19
44
44
60
6.10
0.56
B77
3
7.5
2.52
0.36
. it
44
55
6.00
0.46
44
44
6.5
2.42
0.26
B7
15
55
5.75
0.06
44
44
5,5
2 33
0.17
44
50
5.65
0.56
B2
20
100
^.28
0.88
44
44
45
5.55
0.46
44
44
95
*" 21
0.81
44
u
42
5.50
0.41
44
44
90
".U
0.74
B9
12
35
5.09
0.44
44
44
85
*"' 06
0.66
44
31.5
5.00
0.35
44
44
80
".00
0.60
Bll
10
40
5.10
0.75
B4
15
100
6.77
1.18
35
4.95
0.60
44
44
95
6.68
1.09
44
44
30
4.81
0.46
44
44
90
6.58
0.99
44
*4
20
4.66
0.31
44
44
85
6.48
0.89
B13
9
35
4.77
0.73
44
44
80
6.40
0.81
44
44
30
4.61
0.57
B5
15
75
6.29
0.88
44
44
25
4.45
0.41
44
70
6.19
0.78
44
44
21
4.33
0.29
44
44
65
6.10
0.69
B15
8
25.5
4.27
0.54
4k
44
60
6.00
0.59
44
44
23
4.18
0 45
B8
12
55
5.61
0.82
44
44
20.5
4.09
0.36
44
44
50
5.49
0.70
44
44
18
4.00
0 27
44
44
45
5.37
0.58
B17
7
20
3.87
0.46
*4
44
40
5.25
0.46
tt
H
17.5
3.76
3.66
0.35
0.25
Sections B2, B4, B5, and B8 are
" special ^ beams, the others are
"standard."
Sectional area = weight in Ibs. per ft. -*- 3.4, or X 0.2941.
Weight in Ibs. per foot = sectional area X 3.4.
Maximum and Minimum Weights and Dimensions of
Carnegie Steel Deck Beams.
Section
Depth
of
Weight per
Foot, Ibs.
Flange Width.
Web
Thickness.
Increase of
Web and
Flange per
*
, '
Ib. increase
Min.
Max.
Min.
Max.
Min.
Max.
of Weight.
B100
10
27.23
35.70
5.25
5.50
.38
.63
.029
B101
9
26.00
30.00
4.91
5.07
.44
57
.033
BIOS
8
20.15
24.48
5.00
5.16
31
.47
.037
B103
7
18.11
23.46
4.87
5.10
31
.54
.042
BIOS
6
15.30
18.36
4.38
4.53
.28
.43
.049
178
MATERIALS.
Minimum, Maximum, and Intermediate Weights and
Dimensions of Carnegie Standard Channels.
1— I
^"3
!»
!s «•
p
t-H
^ '
froS
_c ^
!§ j
a
sd
Is"
sgl
.SP«o
*&£
0>S'J
il
5
Web Th
ness.
Inchei
Section
dex.
o.;R a
&
4J O '-^
£. ^^
A
WebTh
ness.
Inche!
01
15
55
3.82
0.82
05
8
16.25
2.44
0.40
••
44
50
3.72
0.72
44
44
13.75
2.35
0.31
4*
44
45
3.62
0.62
44
44
11.25
2.26
0.22
44
44
40
3.52
0.52
06
7
19.75
2^51
0.63
44
44
35
3.43
0.43
44
44
17.25
2.41
0.53
44
44
33
3.40
0.40
44
44
14.75
2.30
0.42
02
12
40
3.42
0.76
44
44
12.25
2.20
0.32
4-
44
35
3.30
0.64
44
i4
9.75
2.09
0.21
44
11
30
3.17
0.51
07
6
15.50
2.28
0.56
4!
44
25
20.5
3.05
2.94
0.39
0.28
u
,4
13
10.50
2.16
2.04
0.44
0.32
03
10
35
3.18
0.82
««
44
8
1.92
0.20
44
44
30
3.04
0.68
08
5
11.50
2.04
0.48
44
44
25
2.89
0.53
44
**
9
1.89
0.33
41
44
20
2.74
0.38
*4
44
6.50
1.75
0.19
**
*•
15
2.60
0.24
09
4
7 . 25
1.73
0.33
04
9
25
2.82
0.62
44
44
6^25
1.65
0.25
44
20
2.65
0.45
44
44
5.25
1.58
0.18
44
44
15
2.49
0.29
072
3
6
1.60
0.36
!•
11
13.25
2.43
0.23
•*
44
5
1.50
0.26
05
8
21.25
2.62
0.58
M
44
4
1.41
0.17
'
"
18.75
2.53
0.49
Weight* and Dimensions of Carnegie Steel Z-Bars.
Size.
Size.
02 "3
••a
Section
Index.
$ -2
i!
2 o
H
Flanges.
43
4>
il
vft
P
Section
Index.
Thicknes
of Meti
Flanges.
1
Weight.
Pounds
Zl
%
3 K
6
15.6
Z6
H
3 5/16
5 1/16
26.0
»*
7{1Q
39/16
6 1/16
18.3
44
13/16
3 %
5 X
28.3
"
&
3 %
6 Ys
21.0
Z7
Y4
3 1/16
4
8.2
Z2
9/16
3 i^
6
22.7
44
5/16
3 y&
4 1/16
10.3
••
N
T 9/16
6 1/16
25.4
44
%
3 3/16
4 K
12.4
•*
11/16
3 %
6 Ys
28.0
Z8
7/16
3 1/16
4
13.8
Z3
13/16
3 fc
3 9/1 G
6
6 1/16
29.3
32.0
;;
$,
3 K
3 3/16
4 1/16
4 K
15.8
17.9
*l
%
3 %
6 Ys
34.6
Z9
%
3 1/16
4
18.9
Z4
5/16
3 H
5
11.6
44
11/16
3 X
4 1/16
20.9
•*
%
3 5/16
5 1/16
13.9
14
%
3 3/16
4 J4
22.9
M
7/16
3 %
5 X
16.4
Z10
l/4
2 11/16
3
6.7
Z5
K
3 M
5
17.8
"
5/16
2 %
3 1/16
8.4
"
9/16
3 5/16
5 1/16
20.2
Zll
%
2 11/18
3
9.7
"
%
3 %
5 ys
22.6
4t
7/16
2 %
3 1/16
11.4
Z6
11/16
3 J4
5
23.7
Z12
Vk
2 11/16
a
12.5
'
9/16
2 M
3 1/16
14.2
SIZES AND WEIGHTS OF STRUCTURAL SHAPES. 179
Pencoyd Steel Angles.
EVEN LEGS.
Size in
Inches.
Approximate Weight in Pounds per Foot for Various
Thicknesses in Inches.
.125
3/16
.1875
H
.25
5/16
.3125
34
7/16
.4375
&
9/16
.5625
%
.625
11/16
.6875
3A
.75
13/16
.8125
.¥75
15/16
.9375
1
1.00
8x8
26.4
29.8
33.2
36.6
39.0
42.4
45.8
49.3
52.8
6x6
14.8
17.3
19.7
22.0
24.4
26.5
28.8
31.0
33.4
35.9
5 x5
12.3
14.3
16.3
18.2
20.1
22.0
23.8
25.6
27.4
29.4
4 x4
8.2
9.8
11.3
12.8
14.5
15.8
17.2
18.6
31*2 x 3Jrfjj
7.1
8.5
9.8
11.1
12.4
13.7
3 x3
4.0
6.1
7.2
8.3
9.4
10.4
11.5
2% x 2f>£
4.5
5.5
6.6
7 7
8.6
gi^j x 2^
3.1
4.1
5.0
5.9
6.9
7.8
2^x2^4
2.7
3.6
4.5
5.4
2 x2
2.5
3.2
4.0
4.8
1% x 1%
2.1
2.8
3.5
4.1
1V6 x ll/£
1.2
1.8
2.4
2.9
3.5
1)4 x 1/4
1.0
1.5
2.0
1 x 1
0.8
1.2
1.5
UNEVEN LEGS.
Size in
Approximate Weight in Pounds per Foot for Various
Thicknesses in Inches.
Inches.
H
i/^
5/16
%
7/16
i^£
9/16
%
11/16
$4
13/16
%
15/16
1
.186
.1875
.25
.3125
.375
.4375
.50
.5625
.625
.6875
.75
.8125
.875
.9375
1.00
8 x6
23.0
25.8
28.7
31.7
33.8
36.6
39.5
42.5
45.6
17.0
19.0
21.0
23.0
24.8
26.7
28.6
30.5
32.5
6J^x4
12.9
15.0
17.0
19.0
21.2
23.4
25.6
27.8
29.8
31.9
6 x4
12.2
14.3
16.3
18.1
20.1
22.0
23.8
25.6
27.4
29.4
6 x3J4
11.6
13.6
15.5
17.1
19.0
20.8
22.6
24.5
26.5
28.6
5L£ x 314
11.0
12.8
14.6
16.2
17.9
5 x4
11.0
12.8
14.6
16.2
17.9
19.6
21.3
5 x3^
8.7
10.3
12.0
13.6
15.2
16.8
18.4
20.0
5x3"
8.2
9.7
11.2
12.8
14.2
15.7
17.2
18.7
4^x3
7.7
9.1
10.5
11.9
13.3
14.7
16.0
17.4
4 x3^
7.7
9.1
10.5
11.9
13.3
14.7
16.0
17.4
4 x3 "
7.1
8.5
9.8
11.1
12.4
13.8
3^x3
6.6
7.8
9.1
10.3
11.6
12.9
4 9
6.1
7.2
8.3
9.4
gi/ x 2
I*
5.5
6.6
Q „ 21^C
4.'J
5.5
6.6
7.7
8.7
3 x2
4.1
5.0
5.9
6.9
7.9
2^x2
2.7
3.
4.5
5.4
6.2
7.0
2.3
3.7
4.4
2 xl}4
2.1
> 9
3.6
4.3
2 xl}4
1.9
2.'6
3.3
3.9
ANGLE-COVERS.
Siz« in
Inches.
3/16
y*
5/16
%
7/16
X
9/16
%
3 x3
4.8
5.9
7.1
8.2
9.3
10.4
11.5
2^x2%
2^x2^
2*4 x 2J4
3.0
2.6
4.4
4.0
3.5
5.5
5.0
4.4
6.6
6.0
5.3
7.7
7.0
8.8
8.1
2 x2
2.4
3.2
4.0
4.8
180
MATERIALS.
SQUARE-ROOT ANGLES.
Size in
Inches.
Approximate Weight in Pounds
per Foot for Various Thicknesses
in Inches.
Size in
Inches.
Approximate Weight in
Pounds per Foot for
Various Thicknesses
in Inches.
I
5/16
.3125
.375
7/16
.4375
^
.50
9/16
.5625
%
.625
Ys
.125
3/16
.1875
1
5/16
.3125
%
.375
4 x4
3^x3^
3 x3
2%x2%
2^x2^
8*4 x2fc
4.9
4.5
4.1
3.6
7.1
6.1
5.6
5.1
4.5
9.8
8.5
7.2
6.7
6.1
5.4
11.4
9.9
8.3
7.8
7.1
13.0
11.4
9.4
8.9
8.2
14.6
16.2
2 x2
l%xl%
l^xl^
iMxi^
1 xl
0.82
1.80
1.53
1.16
3.3
2.9
2.4
2.04
1.53
4.1
3.6
3.0
2.55
4.9
4.4
Pencoyd Tees.
Section
Number.
Size
in Inches.
Weight
per Foot.
Section
Number.
Size
in Indies.
Weight
per Foot.
EVEN TEES.
UNEVEN TEES.
440T
441T
4 x4
4 x4
10.9
13.7
43T
4 x3
9.0
335T
3^3 x 3Jx>
7.0
44T
4 x3
10.2
336T
3J^x3>J
9.0
45T
4 x4^
13.5
337T
3>Jx3^
11.0
38T
31^x3
7.0
330T
3 x3
6.5
39T
3^x3
8.5
33 IT
3 x3
7.7
SOT
3 xlU
4.0
225T
2^x2^
5.0
31T
3 x2J4
5.0
226T
5.8
32T
3 x2^
6.0
227T
2L£ x ;;>ij?
6.6
33T
3 x2^J
7.0
222T
2^4 x 214
4.0
34T
3 x2U
8.0
223T
2J4 x 2*4
4.0
35T
3 x3i|
8.3
220T
2 x2
3.5
36T
3 X3U
9.5
117T
l%xl%
2.4
28T
2%x 1%
6.6
115T
l^xl^
2.0
29T
OHX x 2
7.2
112T
1*4*1*4
1.5
25T
2^x114
3.3
HOT
1 xl
1.0 '
26T
2^x2%
5.7
27T
2^x3
6.0
24T
2J4x 9/16
2.2
UNEVEN TEES.
20T
29T
2 x 9/16
2 xl 1/16
2.0
2.0
21T
2 xl
2.5
64T
65T
6x4
6x5J4
17.4
39.0
23T
17T
2 xl^
l%xl 1/16
3.0
1.9
53T
5x3^
17.0
1ST
l^xl^j
3.5
54T
5x4
15.3
15T
\Y2 x 15/16
1.4
42T
4x2
6.5
12T
1^4 x 15/16
1.2
Pencoyd Miscellaneous Shapes.
Section
Number.
Section.
Size in Inches.
Weight per Foot
in Pounds.
217M
210M
260M
Heavy rails.
Floor-bars.
3 1/16x4x3
6
i/i6x*4 to y2
50.0
7.1 to 14.3
9.8 to 14.7
SIZES AND WEIGHTS OF KOOFIHG MATERIALS. 181
SIZES AND WEIGHTS OF HOOFING MATERIALS.
Corrugated Iron. (The Cincinnati Corrugating Co.)
SCHEDULE OF WEIGHTS.
. aJ
02 to
"1
Thickness in
decimal parts
of an inch.
Flat.
Weight per
100 sq. ft.
Flat, Pain ted.
Weight per
100 sq. ft.
Corrugated
and Painted.
Weight per
100 sq. ft.
Corrugated
and
Galvanized;
Weight in oz.
per sq. ft.
Flat, Galvan-
ized.
No. 28
No. 26
No. 24
No. 22
No. 20
No. 18
No. 16
.015625
.01875
.025
.03125
.0375
.05
.0625
62^ Ib
75
100
125
150
200
250
s.
70 Ib
84
111
138
165
220
275
s.
86 Ib
99
127
154
182
286
291
s.
12^0
14J4
isU
22^3
26^
342
42^
z.
The above table is on the basis of sheets rolled according to the U. S.
Standard Sheet-metal Gauge of 1893 (see page 31). It is also on the basis of
' " K' in. corrugations.
To estimate the weight per 100 sq. ft. on the roof when lapped one corru-
gation at sides and 4 in. at ends, add approximately 12^$ to the weights per
100 sq. ft., respectively, given above.
Corrugations 2^ in. wide by ^ or % in. deep are recognized generally as
the standard size for both roofing and siding; sheets are manufactured
usually in lengths 6, 7, 8, 9, and 10 ft., and have a width of 26^ or 26 in. out-
side width— ten corrugations,— and will cover 2 ft. when lapped one corruga-
tion at sides.
Ordinary corrugated sheets should have a lap of 1^6 or 2 corrugations side-
lap for roofing in order to secure water-tight side seams; if the roof is
rather steep 1^ corrugations will answer.
Some manufacturers make a special high-edge corrugation on sides of
sheets (The Cincinnati Corrugating Co.), and thereby are enabled to secure
a water-proof side-lap with one corrugation only, thus saving from 6$ to 12%
of material to cover a given area.
The usual width of flat sheets used for making the above corrugated
material is 28J4 inches.
No. 28 gauge corrugated iron is generally used for applying to wooden
buildings; but for applying to iron framework No. 24 gauge or heavier
should be adopted.
Few manufacturers are prepared to corrugate heavier than No. 20 gauge,
but some have facilities for corrugating as heavy as No. 12 gauge.
Ten feet is the limit in length of corrugated sheets.
Galvanizing sheet iron adds about 2% oz. to its weight per square foot.
Corrugated Arches.
For corrugated curved sheets for floor and ceiling construction in fire-
proof buildings, No. 16, 18, or 20 gauge iron is commonly used, and sheets
may be curved from 4 to 10 in. rise— the higher the rise the stronger the
arch.
By a series of tests it has been demonstrated that corrugated arches give
the most satisfactory results with a base length not exceeding 6 ft., and ff
ft. or even less is preferable where great strength is required.
These corrugated arches are usually made with 2^ X % i". corrugations,
and in same width of sheet as above mentioned.
Terra-Cotta.
Porous terra-cotta roofing 3" thick weighs 16 Ibs, per square foot and 2"
thick, 12 Ibs. per square foot.
Ceiling made of the same material 2" thick weighs 11 Ibs. per square foot.
Tiles.
Flat tiles 6M" X 10J4" X %ff weigh from 1480 to 1850 Ibs. per square of
roof (100 square feet), the lap being one-half the length of the tile.
Tiles with grooves and fillets weigh from 740 to 925 Ibs. per square of roof.
Pantiles 1%" X 10^/x laid 10" to the weather weigh 850 Ibs. per square.
182
MATERIALS.
Tin Plate— Tinned Sheet Steel.
The usual sizes for roofing tin are 14" X 20" and 20" X 28". Without
allowance for lap or waste, tin roofing weighs from 50 to 62 Ibs. per square.
Tin on the roof weighs from 62 to 75 Ibs. per square.
Roofing plates or terne plates (steeJ plates coated with an alloy of tin
and lead) are made only in 1C and IX thicknesses (29 and 27 Birmingham
gauge). "Coke" and "charcoal'1 tin plates, old names used when iron
made with coke and charcoal was used for the tinned plate, are still used in
the trade, although steel plates have been substituted for iron; a coke plate
now commonly meaning one made of Bessemer steel, and a charcoal plate
one of open-hearth steel. The thickness of the tin coating on the plates
varies with different " brands.1'
For valuable information on Tin Roofing, see circulars of Merchant & Co.,
Philadelphia.
The thickness and weight of tin plates were formerly designated in the
trade, both in the United States and England, by letters, such as I.C., D.C.,
I.X., D.X., etc. A new system was introduced in the United States in 1898,
known as the " American base-box system." The base-box is a package
containing 32,000 square inches of plate. The actual boxes used in the trade
contain 60, 120, or 240 sheets, according to the size. The number of square
inches in any given box divided by 32,000 is known as the " box ratio." This
ratio multiplied by the weight or price of the base-box gives the weight or
price of the given box. Thus the ratio of a box of 120 sheets 14 X 20 in. is
33,600 -*- 32,000 = 1.05, and the price at $3.00 base is $3.00 X 1.05 = $3.15. The
following tables are furnished by the American Tin Plate Co., Chicago, 111.
Comparison of Gauges and Weights of Tin Plates.
(Based on U. S. standard Sheet-metal Gauge.)
ENGLISH BASE-BOX.
(31,360 sq. in.)
Gauge. Weight.
No. 38. 00 54. 44 Ibs.
37.00 57.84
36.00 61.24
35.00 68.05
34.00... 74.85
33.24 ... 80.00
32.50 85/00
31.77 90.00
31.04 95.00
30.65 100.00
30.06 108.00
28.74 126.00
28.00 136.00
26.46 157.00
25.46 178.00
24.68 199.00
23.91 220.00
23.14 241.00
22.37 262.00
21.60 283.00
27.86 139.00
25.38 180.00
24.24 211.00
23.12 212.00
22.00 273.00
Weig
55 Ib
60 '
65 *
70 '
75 '
80 4
85 '
90 *
95 '
100 '
110 '
130 '
140 '
160 '
180 '
200 '
220 '
240 l
260 l
280 '
140 '
180 '
220 '
240 '
280 '
AMERICAN BASE-BO
(32,000 sq. in.)
ht. (
s M
X.
3auge.
o. 38.00
k 36.72
' 35.64
1 34.92
' 34.20
' 33.48
' 32 76
* 32.04
' 31.32
' 30.80
' 30.08
' 28.64
* 27.9^
1 26.48
' 25.5-)
' 24.85
1 24.08
' 23.36
' 22.64
' 21.9a
' 27.9-2
* 25.52
' 24.08
1 23.36
1 21.92
I.C.L.
I.C.
IX.L.
IX.
I.2X.
I.3X.
I.4X.
I. 5X.
I.6X.
I.7X.
I. 8X.
D.C.
D.X.
D. 2X.
D. 3X.
D. 4X.
American Packages Tin Plate.
Inches
Wide.
Length.
Sheets
per Box
Inches
Wide.
Length.
Sheets
per Box
9 to 16%
17 * 25%
26 ' 30
9 ' 10%
11 1 11%
12 ' 12%
Square.
Square.
Square.
All lengths.
To 18 in. long, incl.
18J4 and longer.
To 17 in. long, incl.
240
120
60
240
240
120
240
13 " 13%
13 to 13%
14 " 14%
14 " 14%
15 " 25%
26 " 30
17*4 and longer.
To 16 in. long, incl.
16*4 and longer.
To 15 in. long, incl.
15J4 and longer.
All lengths.
All lengths.
120
240
120
240
120
120
60
Small sizes of light base weights will be packed in double Tboxes.
SIZES AND WEIGHTS OF ROOFING MATERIALS* 183
Slate.
Number and superficial area of slate required for one square of roof.
(1 square = 100 square feet.)
Dimensions
Number
Superficial
Dimensions
Number
Superficial
in
per
Area in
in
per
Area in
Inches.
Square.
Sq. Ft.
Inches.
Square.
Sq. Ft.
6x12
533
267
12x18
160
240
7x12
457
10x20
169
235
8x12
400
11 x20
!54
9x12
355
12x20
141
7x14
374
254
14x20
121
8x14
327
16x20
137
9x14
291
12x22
126
231
10x14
261
14x22
108
8x16
277
246
12x24
114
228
9x16
246
14x24
98
10x16
221
16 x 24
86
9x18
213
240
14 x 26
89
225
10x18
192
16x26
78
As slate is usually laid, the number of square feet of roof covered by one
slate can be obtained from the following formula :
width x (length — 3 inches)
e number of square feet of roof covered.
s and thicknesses required for one square
Weight of slate of various length
of roof :
Length
in
Inches.
Weight in Pounds per Square for the Thickness.
w
M"
V
M
%
M
%
12
14
16
18
20
22
24
26
483
460
445
434
425
418
412
407
724
688
667
650
637
626
617
610
967
920
890
869
851
836
825
815
1450
1379
1336
1303
1276
1254
1238
1222
1936
1842
1784
1740
1704
1675
1653
1631
2419
2301
2229
2174
2129
2093
2066
2039
2902
2760
2670
2607
2553
2508
2478
2445
3872
3683
3567
3480
3408
3350
3306
3263
The weights given above are based on the number of slate required for one
square of roof, taking the weight of a cubic foot of slate at 175 pounds.
Pine Shingles.
Number and weight of pine shingles required to cover one square of
roof :
Number of
Number of
Weight in
Inches
Exposed to
Weather.
Shingles
per Square
of Roof.
Pounds of
Shingle on
One-square
Remarks.
of Roofs.
4
900
216
The number of shingles per square is
4}x>
800
192
for common gable-roofs. For hip«
ly^
720
655
-173
157
roofs add five per cent, to these figures.
The weights per square are based on
6
600
144
the number per square.
184
MATERIALS.
Skylight Glass.
The weights of various sizes and thicknesses of fluted or rough plate-glass
required for one square of roof.
Dimensions in
Inches.
Thickness in
Inches.
Area
in Square Feet.
Weight in Lbs. per
Square of Roof.
12x48
15x60
20x100
94x156
3.997
6.246
13.880
101.768
250
350
500
700
In the above table no allowance is made for lap.
If ordinary window-glass is used, single thick glass (about 1-16") will weigli
about 82 Ibs. per square, and double thick glass (about %") will weigh about
164 Ibs. per square, no allowance being made for lap. A box of ordinary
window-glass contains as nearly 50 square feet as the size of the panes will
admit of. Panes of any size are made to order by the manufacturers, but a
great variety of sizes are usually kept in stock, ranging from 6x8 inches to
36 x 60 inches.
APPROXIMATE WEIGHTS OF VARIOUS ROOF-
COVERINGS.
For preliminary estimates the weights of various roof coverings maybe
taken as tabulated below (a square of roof = 10 ft. square = 100 sq. ft.);
Name.
Weight in Lbs. per
Square of Roof.
Cast-iron plates (%" thick) 1500
Copper 80-125
Felt and asphalt 100
Felt and gravel 800-1000
Iron, corrugated 100-375
Iron, galvanized, flat 100- 350
Lath and plaster 900-1000
Sheathing, pine, 1" thick yellow, northern .. 300
" southeru.. 400
Spruce, 1" thick 200
Sheathing, chestnut or maple, V thick 400
" ash, hickory, or oak, 1" thick.... 500
Sheet iron (1-16" thick) 300
" and laths 500
Shingles, pine 200
Slates W thick) 900
, Skylights (glass 3--16" to J£" thick) . . .. 250- 700
Sheet lead 500- 800
Thatch ; 650
Tin 70-125
Tiles, flat 1500-2000
(grooves and fillets) 700-1000
pan 1000
" with mortar 2000-3000
Zinc ..... 100-200
Approximate Loads per Square Foot for Roofs of Span.*
under 75 Feet, Including Weight of Truss.
(Carnegie Steel Co.)
Roof covered with corrugated sheets, unboarded 8 Ibs.
Roof covered with corrugated sheets, on boards. 11
Roof covered with slate, on laths 13
Same, on boards, 1*4 in. thick 16
Roof covered with shingles, on laths : 10
Add to above if plastered below rafters 10
Snow, light, weighs per cubic foot . ... 5 to 12
For spans over 75 feet add 4 Ibs. to the above loads per square foot.
It is customary to add 30 Ibs. per square foot to the above for gnow and
when separate calculations are not made,
WEIGHT OF CAST-IRON PIPES OR COLUMKS. 185
WEIGHT OF CAST-IRON PIPES OR COLUMNS.
In L.bs. per Lineal Foot.
Cast iron = 450 Ibs. per cubic foot.
Bo*\i.
Thick,
of
Metal.
Weight
per Foot.
Bore.
Thick,
of
Metal.
Weight
per Foot.
Bore.
Thick,
of
Metal.
Weight
per Foot.
Ins.
Ins.
Lbs.
Ins.
Ins.
Lbs.
Ins.
Ins.
Lbs.
3
%
12.4
10
%
79.2
22
94
167.5
/^|
17.2
10}r<J
i^
54.0
%
196.5
%
22.2 '
%
68 2
23
94
174.9
3^2
%
14.3
M
82.8-
%
205.1
v&
19.6
11
x^
56.5
l
235.6
%
25.3
%
71.3
24
94
182.2
4
%
16.1
%
86.5
213.7
^
22.1
\\}/f>
•L<2
58.9
1 8
245.4
%
28.4
7&
74.4
25
94
189.6
4^3
%
17.9
g
90.2
%
222.3
1<£
24.5
12
61.3
l
255.3
%
31.5
E^
77.5
26
94
197.0
5
%
19.8
^4
93.9
%
230.9
L£
27.0
JO1Z
/^
63.8
l
265.1
•2
34.4
%
80.5
27
204.3
5}^>
^
21.6
%
97.6
v4
239.4
£l2
29.4
13
/^
66 3
1
274.9
76
37.6
%
83.6
28
94
211.7
6
%
23.5
94
101.2
%
248.1
1 "
31.8
14
/^
71.2
l
284.7
6^
40.7
%
89.7
29
94
219.1
gi^
7&
25.3
•£
108.6
256.6
LJJJ
34.4
15
%
95.9
i 8
294.5
Y8
43.7
§4
116.0
30
265.2
7
%
27.1
%
136.4
i 8
304.3
1^3
36.8
16
%
102.0
343 7
%
46.8
§4
123.3
31
%
273.8
71^
%
29.0
%
145.0
i
314.2
LJ£
89.3
17
%
108.2
\\/.
354.8
%
49.9
94
130.7
32
%
282.4
8
%
30.8
%
153.6
l
324.0
Hi
41.7
18
%
114.3
i/"6
365.8
%
52.9
94
138.1
33
%
291.0
8J^
^
44.2
%
162.1
l
333.8
%
56.0
19
%
120.4
i/^
376.9
94
68.1
94
145.4
34
%
299.6
9
M
46.6
%
170.7
i
343.7
%
59.1
20
%
126.6
ji^j
388.0
94
71.8
94
152.8
35
%
308.1
9^
^
49.1
%
179.3
l
353.4
%
62.1
21
%
132.7
\\£
399.0
M
75.5
94
160.1
36
%
316 6
10
/^
51.5
%
187.9
1
363.1
%
65.2
22
%
138.8
^
410.0
The weight of the two flanges may be reckoned = weight of one foot-
186
MATERIALS.
WEIGHTS OF CAST-IRON PIPE TO LAY 12 FEET
LENGTH.
Weights are Gross Weights, including Hull.
(Calculated by F. H. Lewis.)
Thickness.
Inside Diameter.
Inches.
Equiv.
Decimals.
4//
6"
8"
10"
12"
14"
16"
18"
20"
1640
1810
1980
2152
2324
2498
2672
3024
saso
3739
,&,
7-16
15-32
17-32
9-16
19-32
11--16
&
%
15-16
1
1J|
.375
.40625
.4375
.4687
.5
.53125
.5625
.59375
.625
.6875
.75
.8125
.875
.9375
1.
1.125
1.25
1.375
209
228
247
266
286
306
327
304
331
358
386
414
442
470
498
400
435
470
505
541
577
613
649
686
581
624
668
712
756
801
845
935
1026
692
744
795
846
899
951
1003
1110
1216
1324
1432
804
863
922
983
1043
1103
1163
1285
1408
1531
1656
1783
1909
1050
1118
1186
1254
1322
1460
1598
1738
1879
2021
2163
1177
1253
1329
1405
1481
1635
1789
1945
2101
2259
2418
2738
3062
3389
Thickness.
Inside Diameter.
Inches.
Equiv.
Decimals.
22"
24"
27"
30"
33"
36"
42"
48"
60"
9742
10740
11738
12744
13750
14763
15776
17821
19880
21956
11-16
H
13-16
JM
I
1^4
f
.625
.6875
'.8125
.875
.9375
'125
.25
.375
.5
.625
.75
.875
2.
2.25
2.5
2.75
1799
1985
2171
2359
2547
2737
2927
3310
3698
2160
2362
2565
2769
2975
3180
3598
4016
4439
2422
2648
2875
3103
3332
3562
4027
4492
4964
5439
2934
3186
3437
3690
3942
4456
4970
5491
6012
6539
3221
3496
3771
4048
4325
4886
5447
6015
6584
7159
7737
3507
3806
4105
4406
4708
5316
5924
6540
7158
7782
8405
4426
4773
5122
5472
6176
6880
7591
8303
9022
9742
10468
11197
5442
5839
6236
7034
7833
8640
9447
10260
11076
11898
12725
14385
CAST-IRON PIPE FITTINGS.
187
CAST-IRON PIPE FITTINGS.
Approximate Weight.
(Addyston Pipe and Steel Co., Cincinnati, Ohio.)
Size in
Inches.
Weight
in Lbs.
Size in
Inches.
Weight
in Lbs
Size in
Inches.
Weight
in Lbs.
Size in
Inches.
Weight
in Lbs.
CROSSES.
TEES.
SLEEVES.
REDUCERS.
2
3
3x2
4
4x3
4x2
6
6x4
6x3
8
8x6
8x4
8x3
10
10x8
10x6
10x4
10x3
12
12x10
12x8
12x6
- 12 x 4
12x3
14 x 10
14x8
14x6
16
16xl4
16xl2
16xlQ
16x8
16x6
16x4
18
20
20x12
20x10
20x8
20x6
20x4
24
24x20
24x6
30x20
30x12
30x8
40
110
90
120
114
90
200
160
160
325
280
265
225
575
415
450
390
350
740
650
620
540
525
495
750
635
570
1100
1070
1000
1010
825
700
650
1560
1790
1370
1225
1000
1000
1000
2400
2020
1340
2C35
2250
1995
8x4
8x3
10
10x8
10x6
10x4
10x3
12
12 x 10
12x8
12x6
12x4
14x12
14x10
14x8
14x6
14x4
14x3
16
16x14
16x12
16x10
16x8
16x6
16x4
18
20
20 x 16
20x12
20x10
20x8
20x6
20x4
20x10
24
24x12
24x8
24x6
30
30x24
30 x 20
30x12
30x10
30x6
36
36x30
36x12
250
220
390
330
370
350
310
600
555
515
550
525
650
650
575
545
525
490
790
850
850
850
755
680
655
1235
1475
1115
1025
1090
900
875
845
1465
2000
1425
1375
1450
3025
2640
2200
2035
2050
1825
5140
4200
4050
2
3
4
6
8
10
12
14
16
18
20
24
30
36
10
25
45
65
80
140
190
208
350
375
500
710
965
1200
8x3
10x8
10x6
10x4 *
12x10
12x8
12x6
12x4
14 x 12
14x 10
14x8
14x6
16 x 12
16x10
20x16
20x14
20x12
20x8
24x20
30x24
30x18
36x30
116
212
170
160
320
250
250
250
475
440
390
285
475
435
690
575
540
400
990
1305
1385
1730
90° ELBOWS.
3
4
6
8
10
12
14
16
18
20
24
30
14
34
55
120
150
260
370
450
660
850
900
1400
3000
ANGLE REDUC-
ERS FOR GAS.
6x4
6x3
95
70
S PIPES.
^ or 45° BENDS.
I
105
190
3
4
6
8
10
12
16
18
20
24
30
30
70
95
150
200
290
510
580
780
1425
2000
PLUGS.
2
3
4
6
8
10
12
14
16
18
20
24
30
3
10
10
15
30
46
66
90
100
130
150
185
370
1/16 or 2214°
BENDS.
6
8
10
12
16
24
30
150
155
205
260
450
1280
2000
CAPS.
TEES.
45° BRANCH
PIPES.
3
4
6
8
10
12
20
25
60
75
100
120
2
3
3x2
4
4x3
4x2
6
6x4
6x3
6x2
8
8x6
2H
80
76
100
90
87
150
145
145
75
300
270
3
4
6
6x6x4
8
8x6
24
24 x 24 x 20
30
36
90
125
205
145
330
330
2765
2145
4170
10300
REDUCERS.
3x2
4x3
4x2
6x4
6x3
8x6
8x4
25
42
40
95
70
126
116
DRIP BOXES.
4
6
8
10
20
295
330
375
875
1420
188
MATERIALS.
WEIGHTS OF CAST-IRON WATER- AND GAS-PIPEC
(Addyston Pipe and Steel Co., Cincinnati, Ohio.)
at
Standard Water-pipe.
*i
Standard Gas -pipe.
v°
N U
m$
Per Foot.
Thick-
ness.
Pei-
Length.
li
MM
Per Foot.
Thick-
ness.
Pei-
Length.
2
3
15
5/16
63
180
2
3
6
12K
5/16
48
150
3
17
^
204
•4
22
L£
264
4
17
%
204
6
33
^
396
6
30
7/16
360
8
42
/^
504
8
40
7'/l 6
480
8
45
^
540
10
60
9/16
720
10
50
7/16
600
12
75
9/16
900
12
70
y
840
14
117
H
1400
14
84
9/16
1000
16
125
n
1500
16
100
9/16
1200
18
167
%
2000
18
134
11/16
1600
20
200
15/16
2400
20
150
11/16
1800
24
250
1
3000
24
184
%
2200
30
350
ji^
4-,>00
30
250
%
3000
36
475
1%
5700
36
350
/&
4200
42
600
1%
7200
42
417
15/16
5000
48
775
1L£
9300
48
542
\\£
6500
60
1330
2
15960
60
900
1%
10800
72
1835
2M
22020
72
1250
m
15000
THICKNESS OF CAST-IRON WATER-PIPES.
P. H. Baermann, in a paper read before the Engineers' Club of Phila-
delphia in 1882, gave twenty different formulas for determining the thick-
ness of cast-iron pipes under pressure. The formulas are of three classes:
1. Depending upon the diameter only.
2. Those depending upon the diameter and head, and which add a con-
stant.
3. Those depending upon the diameter and head, contain an additive >i
subtractive term depending upon the diameter, and add a constant.
The more modern formulas are of the third class, and are as follows:
t= .OOOOS/id -f .01 d + .36 Shedd, No. 1.
t = .00006/id -f .0133d -f .296 Warren Foundry, No. 2.
t = .000058/id -f .0152d -f- .312 Francis, No. 3.
t= .000048/i<2 + .013^4- .32 ...Dupuit, No. 4.
t- .00004/td 4- .1 |/d-f.l5 Box, No. 5.
t = .000135/id 4- .4 — .OOlld Whitman, No. 6.
t = .00006(/i 4- 230)d -f .333 - .0033d Fanning, No. 7.
t = .00015/id 4- .25 - '.0052d Meggs, No. 8.
In which t = thickness in inches, h = head in feet, d = diameter in inches.
Rankine, "Civil Engineering," p. 721, says: "Cast-iron pipes should be
made of a soft and tough quality of iron. Great attention should be paid
to moulding them correctly, so that the thickness may be exactly uniform all
round. Each pipe should be tested for Jr-bubMes and flav s by ringing it
with a hammer, and for strength by exposing "t to *ou ie tlL intended
greatest working pressure. " The rule for competing the Jiickness of a pipe
to resist a given working pressure is t = -4-, where r is the radius in inches,
p the pressure in pounds per square inch, and / the tenacity of the iron x>er
square inch. When/ = 18000, and a factor of safety of 5 is used, the above
expressed in terms of d and h becomes
.5rf.4887t dh nnnnp
*" "3600" = 16628 = •00006d/l
"There are limitations, however, arising from difficulties in casting, and
by the strain produced by shocks, which cause the thickness to be made
greater than that given by the above formula."
THICKHESS OF CAST-IROK PIPE.
189
Thickness of Metal and Weight per Length for Different
Sizes of Cast-iron Pipes under Various Heads of Water.
(Warren Foundry and Machine Co.)
50
Ft. Head.
100
Ft. Head.
150
Ft. Head.
200
Ft. Head.
250
Ft. Head.
300
Ft. Head.
Size.
Thickness
of Metal.
Weight
i per Length.
Thickness
of Metal.
Weight
per Length.
Thickness
of Metal.
Weight
per Length.
Thickness
of Metal.
Weight
per Length.
Thickness
of Metal.
Weight
per Length.
Thickness
of Metal.
Weight
per Length.
3
.344
144
.353
149
.862
153
.371
157
.380
161
.390
166
4
.361
197
.373
204
.385
211
.397
218
.409
226
.421
235
5
.378
254
.393
265
.408
275
.423
286
.438
298
.453
309
6
.393
315
.411
330
.429
345
.447
361
.465
377
.483
393
8
.422
445
.450
475
.474
502
.498
529
.522
557
.546
584
10
.459
600
.489
641
.519
682
.549
723
.579
766
.609
808
12
.491
768
.527
826
.563
885
.599
944
.635
1004
.671
1064
14
.524
952
.566
1031
.608
1111
.650
1191
.692
1272
.734
1352
16
.557
1152
.604
1253
.652
1360
.700
1463
.748
1568
.796
1673
18
.589
1370
.643
1500
.697
1630
.751
1761
.805
1894
.859
2026
20
.622
1603
.682
1763
.742
1924
.802
2086
.862
2248
.922
2412
24
.687
2120
.759
2349
.831
2580
.903 2811
.975
3045
1.047
3279
30
.785
3020
.875
3376
.965
3735
1.055 4095
1.145
4458
1.235
4822
36
.882
4070
.990
4581
1.098
5096
1.206 5613
1.314
6133
1.422
6656
42
.980
5265
1.106
5958
1.232
6657
1.358 7360
1.484
8070
1.610
8804
48
1.078
6616
1.222
7521
1.366
8431
1.510 9340
1.654
10269
1.798
11195
All pipe cast vertically in dry sand; the 3 to 12 inch in lengths of 12 feet,
all larger sizes in lengths of 12 feet 4 inches.
Safe Pressures and Equivalent Heads of Water for Cast-
iron Pipe of Different Sizes and Thicknesses,
(Calculated by F. H. Lewis, from Fanning's Formula.)
Size of Pipe.
Thick-
ness.
£k
*s
10"
16"
18"
20"
112
140
168
116
141
166
190
MATERIALS.
Safe Pressures, etc., for Cast-iron Pipe.— (Continued.)
Thick-
ness.
Size of Pipe.
22"
24"
27"
80"
33"
36"
42"
48"
Pressure I
in Pounds, j » 1
Head in * i
Feet. 1 1
Pressure
in Pounds.
Head in
Feet.
§!
£H C
Head in
Feet.
Pressure
in Pounds.
Head in
Feet.
Pressure
in Pounds.
Head in
Feet.
Pressure
In Pounds.
ii
|h
Pressure
in Pounds.
Head in
Feet.
Pressure
in Pounds.
Head in
Feet.
Pressure
in Pounds.
Is
^
11-16
3-4
13-16
7-8
15-16
1
1 1-8
1 1-4
1 3-8
1 1-2
1 5-8
1 3-4
1 7-8
2
2 1-8
2 1-4
21-2
23-4
40
60
80
101
121
142
182
224
92
138
184
233
279
327
419
516
30
49
68
86
105
124
161
199
237
69
113
157
198
242
286
371
458
546
19
36
52
69
85
102
135
169
202
236
64
83
120
159
196
S55
311
389
465
544
24
39
54
69
84
114
144
174
204
234
55
90
124
159
194
263
332
401
470
538
42
55
69
96
124
1^1
97
127
159
221
286
348
410
472
537
32
44
57
82
1(1?
132
157
182
207
74
101
131
189
247
304
362
419
477
38
59
81
103
124
145
167
188
210
88
136
187
237
286
334
385
433
484
24
43
62
81
99
118
136
155
174
193
212
55
99
143
187
228
272
313
357
401
445
488
Si
49
64
79
94
109
124
139
154
134
214
78
113
147
182
217
251
286
320
355
424
482
178
206
233
NOTE.— The absolute safe static pressure which may be
2T S
put upon pipe is given by the formula P = ~=r X -z-, in
which formula P is the pressure per square inch.; T, the
thickness of the shell; S, the ultimate strength per square
inch of the metal in tension; and D, the inside diameter of
the pipe. In the tables S is taken as 18000 pounds per
square inch, with a working strain of one fifth this amount
or 3600 pounds per square inch. The formula for the
7200 T
absolute safe static pressure then is: P = .
It is, however, usual to allow for "water-ram" by in-
creasing tho thickness enough to provide for 100 pounds
additional static pressure, ana, to insure sufficient metal for
good casting and for wear and tear, a further increase
equal to .333 (l — JQQ)-
The expression for the thickness then becomes:
(P-flOO)D 883(l~^
7200 M V 100/'
and for safe working pressure
The additional section provided as above represents an
increased value under static pressure for the different sizes
of pipe as follows (see table in margin). So that to test
the pipes up to one fifth of the ultimate strength of the
material, the pressures in the marginal table should be
added to the pressure-values given in the table above.
Size
of
Pipe.
RIVETED HYDRAULIC PIPE.
191
RIVETED HYDRAULIC PIPE.
(Pel ton Water Wheel Co.)
Weight per foot with safe head for various sizes of double-riveted pipe.
-S
gj'
« 1
_|_j-
a
3|
•d
+= a
±
o-g
il
43 §0
OJ
t- °^j
*o"o
11
+3 CO
$_ , -S
*" OT§
i- a
qu-2 .
t- a
031— 1
i, of
°.^&
"3-gJ
.£ ^3
^1 o
u aT
^w 6
• tj
111
•S ®1?
S'l5
s ^
"O • 05
"3-3 C
IS-S^
.Sf-S^
S3
U • 5
.£ '~ Q
T3 Pi"-*
.s&s^
ft
H
§T'
w
gHl.
s
*S H^O
HHl"
l^cc
^,p.
3
18
.05
810
2)4
18
12
.109
295
2514
4
18
.05
607
3
18
11
.125
337
29
4
5
16
18
.062
.05
760
485
3%
3%
18
18
10
8
.14
.171
378
460
5*
5
16
.062
605
4^3
20
16
.062
151
16
5
14
.078
757
5%
20
14
.078
189
19%
6
18
.05
405
4J4
20
12
.109
265
6
16
.062
505
5J4
20
11
.125
304
3)i^
6
14
.078
630
6^
20
10
.14
340
35
7
18
.05
346
4%
20
8
.171
415
4514
7
16
.062
433
6
22
16
.062
138
17%
7
14
.078
540
7J><2
22
14
.078
172
22
8
16
.062
378
7
22
12
.109
240
30^3
8
14
.078
472
8%
22
11
.125
276
34(1
8
12
.109
660
12
22
10
.14
309
39
9
16
.062
336
7V*>
22
8
.171
376
50
9
14
.078
420
9J4
24
14
.078
158
23%
9
12
.109
587
12%
24
12
.109
220
32
10
16
.062
307
24
11
.125
253
37^
10
14
.078
378
10)4
24
10
.14
283
42
10
12
.109
530
14J4
24
8
.171
346
50
10
11
.125
607
16J4
24
6
.20
405
59
10
10
.14
680
18J4
26
14
.078
145
25V*»
11
16
.062
275
9
26
12
.109
203
351^
11
14
.078
344
11
26
11
.125
233
39^
11
12
.109
480
15/4
26
10
.14
261
44^
11
11
.125
553
17V&
26
8
.171
319
54
11
10
.14
617
19V6
26
6
.20
373
64
12
16
.062
252
10 "
28
14
.078
135
27^
12
14
.078
316
28
12
.109
188
38
12
12
.109
442
17 4
28
11
.125
216
12
11
.125
506
19^
28
10
.14
242
47V^
12
10
.14
567
21%
28
8
.171
295
58
13
16
.062
233
10i|
28
6
.20
346
69
13
14
.078
291
30
12
.109
176
39^
13
12
.109
407
18
30
11
.125
202
45
13
11
.125
467
20L£
30
10
.14
226
50^
13
10
.14
522
23
30
8
.171
276
61%
14
16
.062
216
H/4
30
6
.20
323
73
14
14
.078
271
14
30
H
.25
404
90
14
12
.109
378
36
11
.125
168
54
14
11
.125
433
22*4
36
10
.14
189
60^
14
15
10
16
.14
.062
485
202
25
36
36
i
.187
.25
252
337
81
109
15
14
.078
252
14%
36
.312
420
135
15
12
.109
352
20^4
40
10
.14
170
67^
15
11
.125
405
23 J4
40
.187
226
90
15
10
.14
453
26
40
M
.25
303
120
16
16
.062
190
13
40
j>
.312
378
150
16
14
.078
237
16
40
%
.375
455
180
16
12
.109
332
42
10
.14
162
71
16
11
.125
379
24/^1
42
A
.187
216
94^
16
10
.14
425
28^j
42
M
.25
289
126
18
16
.062
168
14%
42
TB5
.312
360
158
18 1
14
.078
210
18H
42
%
.375
435
190
192
MATERIALS.
STANDARD PIPE FLANGES.
Adopted August, 1894, at a conference of committees of the American
Society of Mechanical Engineers, and the Master Steam and Hot Water Fit-
ters' Association, with representatives of leading manufacturers and users
of pipe.— Trans. A. S. M. E., xxi. 29. (The standard dimensions given have
not yet, 1901, been adopted by some manufacturers on account of their un-
willingness to make a change in their patterns.)
The list is divided into two groups; for medium and high pressures, the
first ranging up to 75 Ibs. per square inch, and the second up to 200 Ibs.
a
K
6
7
8
9.
10
12
14
15
16
18
20
22
24
26
28
30
36
42
j\ 6090
NOTES.— Sizes up to 24 inches are designed for 200 Ibs. or less.
Sizes from 24 to 48 inches are divided into two scales, one for 200 Ibs., the
other for less.
The sizes of bolts given are for high pressure. For medium pressures the
diameters are % in. less for pipes 2 to 20 in. diameter inclusive, and % in.
less for larger sizes, except 48-in. pipe, for which the size of bolt is 1% in.
When two lines of figures occur under one heading, the single columns are
for both medium and high pressures. Beginning with 24 inches, the left-hand
columns tire for medium and the right-hand lines are for high pressures.
The sudden increase in diameters at 16 inches is due to the possible inser-
tion of wrought-iron pipe, making with a nearly constant width of gasket a
greater diameter desirable.
When wrought-iron pipe is used, if thinner flanges than those given are
sufficient, it is proposed that bosses be used to bring the nuts up to the
standard lengths. This avoids the use of a reinforcement around the pipe.
Figures in the 3d, 4th, 5th, and last columns refer only to pipe for high
pressure.
In drilling valve flanges a vertical line parallel to the spindles should be
midway between two holes on the upper side of the flanges.
CAST-IRON" PIPE AKD PIPE FLANGES.
193
FLANGE DIMENSIONS, ETC., FOR EXTRA HEAVY
PIPE FITTINGS (UP TO 250 LBS. PRESSURE).
Adopted by a Conference of Manufacturers, June 28, 1901.
Size of
Pipe.
Diam. of
Flange.
Thickness
of Flange.
Diameter of
Bolt Circle.
Number of
Bolts.
Size of
Bolts.
Inches.
Inches.
Inches.
Inches.
Inches.
2
6^
%
5
4
%
%
7V£
1
5^
4
%
3
3^
SJ4
9
It*
8
8
1
4
4^
10
ttM
PU
If
8
8
i
5
11
1%
9J4
8
8
6
12^
1 7-16
10%
13
M
7
14
1^4
31%
12
y&
^8
15
1%
13
12
%
9
16
1M
14
12
7^
10
12
g*
3*
Wi
im
16
16
1
14
15
22U
2^
2 3-16
20
21
20
20
ft
16
25
214
22^
20
18
27
2%
1V&
24
20
29^
2Va
26^
24
^
22
81JJ
2%
28%
28
• /^
24
84
234
31%
28
»
DIMENSIONS OF PIPE FLANGES AND CAST-IRON
PIPES.
(J. E. Codman, Engineers1 Club of Philadelphia, 1889.)
4
5
6
8
10
12
14
16
18
20
22
24
32
34
40
42
44
46
48
.So
5
3 O
Is
8
8
10
12
14
16
16
18
20
22
24
24
26
28
30
32
32
34
34
2 1-16
40 2^
Thickness
of Pipe.
Frac. Dec.
13-32
7-16
7-16
15-32
19-32
21-32
11-16
Has
27-32
31-32
1
1 1-16
1
l'5-32
1 3-16
1 5-16
111-32
1T-16
.373
.396
.420
.443
.466
.511
.557
.603
.649
.695
.741
.787
.833
.879
.925
.971
1.017
1.063
1.109
1.155
1.201
1.247
1.293
1.339
1.385
1.431
Cfe.-g o3
JUS
6.96
11.16
15.84
21.00
26.64
39.36
54.00
70.56
89.04
109.44
131.76
156.00
182.16
210.24
240.24
272.16
306.00
341.76
379.44
419.04
460.56
504.00
549.36
596.64
645.84
696.96
4.41
5.93
7.66
9.63
11.82
16.91
23.00
30.13
38.34
47.70
58.23
70.00
83.05
97.42
113.18
130.35
149.00
169.17
190.90
214.26
239.27
266.00
294 49
324.78
356.94
391.00
D = Diameter of pipe. All dimensions in inches.
FORMUUE.— Thickness of flange = 0.033D -f- 0.56 ; thickness of pipe
0 0'23D -4- 0.327* «r*»irrVif f\f i"kii-»ck r-xjii. -F/-W/-W*- n f>A TY1 I O 7~» . ,, — ^:_Ui —«xii — _._
'
194
MATERIALS.
Df Perf "°.2J2S9?2:*»S«eSJ52}2P<P«
Thread!
No. of
Threads
aerlnch.
. Tfioco^i-ieooDOiccot^i-toiocxtco^TEcoTttoo — oo — T~co — T~ei ^
per
Lin. Ft. S "~~^~'~^;S;^£Sw33$SSo^oco £
of Pipe. ___^ r-,^»-.t-i ^
Weight .Tt«CJOT*iNl~TtOOi-i^^O«OTt<Oimr~GOOeoojer««<-->^r-,<-->r-> -«
of Pipe
per »-ii-tS'totcoiot>osoW^GC2oc6coo»no:T
Li^Ft i-^i^fr^co^Tr^ioo
^ __ .^ JyQ
oyp'jpl i°-c '"ssss-ssssnssigsg ^
i\°untf?. %^e
^ IPJ.llliillliSSSISIilgligigSlS ^
-1 ^ ^ i-^ i-^ I-' o*' iy| eo
I
g
_ ^ ^
CC ' ' "T^^H'^CJUJ'C
o^
02 " ^* T-I <ri y-t & a ai *& >+*
Length j ^OQOI>OOTt(^OQOO:)V^irao;)Tt,j>j>^Heot,tOO
!Outside' fa os t- 10 -^wojcjoj « i-^i-^d B&
Surface.j
?rl?t ^Sg'g2Slgi?^^^^^^^^^^^^"^^^^SSS ^
Inside fa -^ o' i> to •*? oo ci oi i-i i-i TH ^ d ^
Surface. ^
ence.
Internal .f«3!S!iba
Circum- S °°. '-J *°. °>. w
f erence. l~l ^-< '-> — c
Thick- . GO oo — as c
A otual _^?^cocs'fjc^:^GOr:Hcb£o:3"55oTfoc$6cco^oS»oioio»cioioio ^sp
^.^1/UlO.i gg^J^^^QOQJlQ^^^CjJ^Q^^l^X^QS^^^^^^JQ^^J^^g^ ^\
Inside H ^
Diam. T-II-H i-< ri ^ 1-1 r-i 1-1 1-1 1-1 1-1 ?? g< g
°D£me - ' ^"^^^^^•^^•sdSsasftftii* g-
Nominal j
Inside flw
Diam. '
WROUGHT-IROH PIPE.
195
For discussion of the Briggs Standard of Wrought-iron Pipe Dimensions,
see Report of the Committee of the A. S. M. E. in " Standard Pipe and Pipe
Threads," 1886. Trans., Vol. VIII, p. 29. The diameter of the bottom of
the thread is derived from the formula J> — (0.05D + 1.9) x — , in which
D = outside diameter of the tubes, and n the number of threads to the
inch. The diameter of the top of the thread is derived from the formula
0.8— X 2 -f d, or 1.6 }- d, in which d is the diameter at the bottom of the
thread at the end of the .pipe.
The sizes for the diameters at the bottom and top of the thread at the end
of the pipe are as follows:
Diam.
Diam.
Diam.
Diam.
Diam.
Diam.
Diam.
Diam.
Diam.
of Pipe,
Nom-
at Bot-
tom of
at Top
of
of Pipe,
Nom-
at Bot-
tom of
at Top
of
of Pipe,
Nom-
at Bot-
tom of
at Top
of
inai.
Thread.
Thread.
inal.
Thread.
Thread.
inal.
Thread.
Thread.
in.
in.
in.
In.
in.
in.
in.
in.
in.
.334
.393
**4
2.620
2.820
8
8.334
8.534
M
.438
.522
3
3.241
3.441
9
9.327
9.527
%
.568
.658
3^
3.738
3.938
10
10.445
10.645
Ut
.701
.815
4
4.234
4.434
11
11.439
11.639
%
.911
1.025
4^
4.731
4.931
12
12.433
12.633
I
1.144
1.283
5
5.290
5.490
13
13.675
13.875
w±
1.488
1.627
6
6.346
6 546
14
14.669
14.869
i*i
1.727
1.866
7
7.340
7.540
15
15.663
15.863
8
2.223
2.339
«
Having the taper, length of full-threaded portion, and the sizes at bottom
and top of thread at the end of the pipe, as given in the table, taps and dies
can be made to secure these points correctly, the length of the imperfect
threaded portions on the pipe, aud the length the tap is run into the fittings
beyond the point at which the size is as given, or, in other words, beyond
the end of the pipe, having no effect upon the standard. The angle of the
thread is 60°, and it is slightly rounded off at top and bottom, so that, instead
of its depth being 0.866 its pitch, as is the case with a full V-thread, it is
4/5 the pitch, or equal to 0.8 -*- n, n being the number of threads per inch.
Taper of conical tube ends, 1 in 32 to axis of tube = 2£ inch to the foot
total taper.
L96
MATERIALS.
WROUGHT-IRON WELDED TUBES, EXTRA STRONG.
Standard Dimensions.
Nominal
Diameter.
Actual Out-
side
Diameter.
Thickness,
Extra
Strong.
Thickness,
Double
Extra
Strong.
Actual Inside
Diameter,
Extra
Strong.
Actual Inside
Diameter,
Double Extra
Strong.
Inches.
Inches.
Inches.
Inches.
Inches.
Inches.
V6
0.405
0.100
0.205
\*
0.54
0.123
0 294
«Z
0.675
0.127
0.421
H
0.84
0.149
0.298
0.542
0.244
•fi
1.05
0.157
0.314
0.736
0.422
1
1.315
0.182
0.364
0.951
0.587
1/4
1.66
0.194
0.388
1.272
0.884
Ii2
1.9
0.203
0.406
1.494
1.088
2
2.375
0.221
0.442
1.933
1.491
2^
2.875
0.280
0.560
2.315
1.755
3
3.5
0.304
0.608
2.892
2.284
3^
4.0
0.321
0.642
3.358
2.716
4
4.5
0.341
0.682
3.818
3.136
STANDARD SIZES, ETC., OF LAP-WELDED CHAR-
COAL-IRON BOILER-TUBES.
(National Tube Works.)
I
A
"
, .
I°J
-o'Si
£oy
*
^^•M
»-,^D
5
s
I
O §
•al
Internal
External
E^.jj
S^g
0^1
E£
Area.
Area.
1^
I1'
|H
pS
I3
11
fl*
fll
fill
ftS
§1
®hj
in.
in.
in.
in.
in.
sq. in.
sq.ft.
sq. in.
sq.ft.
ft.
ft.
ft.
Ibs.
1
.810
.095
2.545
3.142
.515
.0036
.785
.0055
4.479
3.820
4.149
.90
1 1-4
1.060
.095
3.330
3.927
.882
.0061
1.227
.0085
3.604
3.056
3.330
1.15
1 1-2
1.310
.095
4.115
4.712
1.348
.0094
1.767
.0123
2.916
2.547
2.732
1.40
13-4
1.560
.095
4.901
5.498
1.911
.0133
2.405
.0167
2.448
2.183
2.316
1.65
2
1.810
.095
5.686
6.283
2.573
.0179
3.142
.0218
2.110
1.910
2.010
1.91
2 1-4
2.060
.095
6.472
7.069
3.333
.0231
3.976
0276
1.854
1.698
1.776
2.16
2 1-2
2.282
.109
7.169
7.854
4.090
.0284
4.909
.0341
1.674
1.528
1.601
2.75
23-4
2.532
.109
7.955
8.639
6.035
.0350
5.940
.0412
1.508
1.389
1.449
3.04
3
2.782
.109
8.740
9.425
6.079
.0422
7.069
.0491
1.373
1.273
1.322
3.33
3 1-4
3.010
.120
9.456
10.210
7.116
.0494
8.296
.0576
1.269
1.175
1.222
3.96
31-2
3.260
.120
10.242
10,996
8.347
.0580
9.621
.0668
1.172
1.091
1.132
4.28
33-4
8.510
120
11.027
11.781
9.676
.0672
11.045
•07G7
1.088
1.019
1.054
4.60
4
3.732
.134
11.724
J 2.566
10.939
.0760
12.566
0873
1.024
.955
.990
5.47
41-2
4.232
.134
13.295
14.137
14.066
.0977
15.904
.1104
.903
.849
.876
6.17
5
4.704
.148
14.778
15.708
17.379
.1207
19.635
.1364
.812
.764
.788
7.58
6
5.670
.165
17.813
18.850
25.250
.1750
28.274
.1963
.674
.637
.656
10.16
7
6.670
.165
20.954
21.991
34,942
.2427
38.485
.2673
.573
.546
.560
11.90
8
7.670
.165
24.096
25.133
46.204
.3209
50.266
.3491
.498
.477
.488
13.65
9
8.640
.180
27.143
28.274
58.630
.4072
63.617
.4418
.442
.424
.433
16.76
10
9.594
.203
30.141
31.416
72.292
.5020
78.540
-5454
.398
.382
.390
21.90
11
10.560
.220
33.175
34.558
87.583
.6082
95.033
.6600
.362
.347
.355
25.00
12
11.542
.229
36.260
37.699
104.629
.7266
113.098
.7854
.331
.318
.325
28.50
13
12.524
.233
39.345
40.841
123.190
.8555
132.733
.9217
.305
.294
.300
32.06
14
13.504
.248
42.424
43.982
143.224
.9946
153.938
1.0690
.283
.273
.278
36.00
15
14.482
.259
45.497
47.124
164.721
1.1439
176.715
1.2272
.264
.255
260
40.60
16
15.458
.271
48.563
50.266
187.671
1.3033
201.062
1.3963
.247
.239
.243
45.20
17
16.432
.284
51.623
53.407
212.066
1.4727
226.981
1.5763
.232
.225
.229
49.90
18
17.416
.292
54.714
56.549
238.225
1.6543
254.470
1.7671
.219
.212
.216
54.82
19
18.400
.300
57.805
59.690
265.905
1.8466
283.529
1.9690
.208
.201
.205
59.48
20
19.360
.320
60.821
62.832
294.375
2.0443
314.159
2.1817
.197
.191
.194
66.77
21
20.320
.340
63.837
65.974
324.294
2.2520
346.361
2.4053
.188
.182
.185
73.40
surface in
bes) is to
In estimating the effective steam-heating or boiler surface of tubes, the su
contact with air or gases of combustion (whether internal or external to the tu
be taken.
For heating liquids by steam, superheating steam, or transferring heat from one
liquid or gas to another, the mean surface of the tubes is to be taken.
RIVETED TROK PIPE.
197
To find the square feet of surface, S, in a tube of a given length, L, in feet,
and diameter, d, in inches, multiply the length in feet by the diameter in
inches and by .2618. Or, 8 - -L-- - — = .2618dL. For the diameters in the
table below, multiply the length in feet by the figures given opposite the
diameter.
Inches,
Diameter.
Square Feet
per Foot
Length.
Inches,
Diameter.
Square Feet
per Foot
Length.
Inches,
Diameter.
Square Feet
per Foot
Length.
1 4
2 4
.0654
.1309
.1963
.2618
.3272
.3927
.4581
.5236
34
4 4
.5890
.6545
.7199
.7854
.8508
.9163
.9817
1.0472
5
6
7
8
9
10
11
12
1.3090
1.5708
1.8326
2.0944
2.3562
2.6180
2.8798
3.1416
RIVETED IRON PIPE.
(Abendroth & Root Mfg. Co.)
Sheets punched and rolled, ready for riveting, are packed in convenient
form for shipment. The following table shows the iron and rivets required
for punched and formed sheets.
Number Square Feet of Iron
required to make 100 Lineal
Feet Punched and Formed
I11H1
^^^3c|
Number Square Feet of Iron
required to make 100 Lineal
Feet Punched and Formed
Sheets when put together.
Sheets when put together.
"el r S^"^ 3^
•fijU^ &
If jr |
Diam-
eter in
Inches.
Width of
Lap in
Inches.
Square
Feet.
Diam-.
eter in
Inches.
Width of
Lap in
Inches.
Square
Feet.
oTS oS«2fe oSCQ
3
1
90
1,600
14
JJX
397
2,800
4
1
116
1,700
15
l^i
423
2,900
5
150
1.800
16
ji^j
452
3,000
6
•ji/
178
1,900
18
l/^
506
3,200
7
]1Z
206
2,000
20
l/'ij
562
3,500
8
1^1
234
2,200
22
l/^
617
3,700
9
JL£
258
2,300
24
1^
670
3,900
10
l^J
289
2,400
26
^/^
725
4,100
11
1^1
314
2,500
28
1/^j
779
4,400
12
ji/
343
2,600
30
1^3
836
4,600
13
%
369
2,700
36
%
998
5,200
WEIGHT OF ONE SQUARE FOOT OF SHEET-IRON
FOR RIVETED PIPE.
Thickness by the Rirmiugliam Wire-Gauge.
No. of
Gauge.
Thick-
ness in
Decimals
of an
Inch.
Weight
in Ibs.,
Black.
Weight
in Ibs.,
Galvan-
ized.
No. of
Gauge.
Thick-
ness in
Decimals
of an
Inch.
Weight
in Ibs.,
Black.
Weight
in Ibs.,
Galvan-
ized.
26
24
22
20
.018
.022
.028
.035
.80
1.00
1.25
1.56
.91
1.16
1.40
1.67
18
16
14
12
.049
.065
.083
.109
1.82
2.50 J
3.12
4.37
2.16
2 67
3.34
4.73
198
MATERIALS.
SPIRAL RIVETED PIPE.
(Abendroth & Root Mfg. Co.)
Thickness.
Diam-
eter,
Inches.
Approximate Weight
in Ibs. per Foot in
Length.
Approximate Burst-
ing Pressure in Ibs.
per Square Inch.
B. W. G.
No.
Inches.
26
24
22
20
18
16
14
12
.018
.022
.028
.035
.049
.065
.083
.109
3 to 6 1
3 to 12
3 to 14
3 to 24
3to2i
6 to 24
8 to 24
9 to 24
bs.=
= ^ofd
= .4
= .5
= .6
= .8
= 1.1
= 1.4
iam. in
ns.
27001bs.-f-diam.inins.
3600 " H- *'
4800 " -T- "
6400 " -*- "
8000 " -*- "
The above are black pipes. Galvanized weighs 10 to 30 % heavier.
Double Galvanized Spiral Riveted Flanged Pressure Pipe, tested to 150 Ibs.
hydraulic pressure.
Inside diameters, inches....
Thickness, B. W. G
Nominal wt. per foot, Ibs.. .
2020
71 8
O 1C
181818
91011
1816
811
13114151618202224
16 16 14
14 15' 20 22 24 29 34 4050
1212
DIMENSIONS OF SPIRAL PIPE FITTINGS.
Diameter
Inside
Diameter.
Outside
Diameter
Flanges.
Number
Bolt-holes.
Diameter
Bolt-holes.j
Circles on
which Bolt-
holes are
Sizes of
Bolts.
Drilled.
ins.
ins.
ins.
ins.
ins.
3
6
* 4
%
4%
7/16 x 1%
4
7
8
i^
5 15/16
7/16 x 1%
5
8
8
^
6 15/16
7/16x1%
6
8%
8
%
7%
l^> x 1%
7
10
8
%
9
^6 x 1%
8
11
8
5^
10
1^x2
9
13
8
%
tt§4
Ux2
10
14
8
%
1214
>|x2
11
15
12
%
13%
^2*2
12
16
12
%
i42
1^x2
13
17
12
%
15^4
1^x2
14
15
&
12
12
i
16*4
17 7/16
j|*2|
16
21 3/16
12
%
19^
L£ x 2J-J2
18
23^
16
11/16
2ii|
^ x 2^
20
25^
16
11/16
23V£
^ x 2V&
22
28^
16
26
%X2V^
24
30
16
A
27%
%*^
SEAMLESS BRASS TUBE. IRON-PIPE SIZES.
(For actual dimensions see tables of Wrought-iron Pipe.)
Nominal
Size.
Weight
p°r Foot.
Nom.
Size.
Weight
per Foot.
Nom.
Size.
Weight
per Foot.
Nom.
Size.
Weight
per Foot.
ins.
Ibs.
.25
.43
.62
.90
ins.
f
i
Ibs.
1.25
1.70
2.50
3.
ins.
2
P
3^
Ibs.
4.0
5.75
8.30
10.90
ins.
4
9*
6
Ibs.
12.70
13.90
15.75
18.31
BRASS TUBING; COILED PIPES.
199
SEAMLESS DRAWN BRASS TUBING.
(Randolph & Clowes, Waterbury, Conn.)
Outside diameter 3/16 to 7% inches. Thickness of walls 8 to
Gauge, length 12 feet. The following are the standard sizes:
Outside
Diam-
eter.
Length
Feet.
Stubbs'
or Old
Gauge.
Outside
Diam-
eter.
Length
Feet.
Stubbs'
or Old
Gauge.
Outside
Diam-
eter.
Length
Feet.
Stubbs1
or Old
Gauge.
H
12
20
1%
12
14
2%
12
11
5-16
12
19
12
14
2M
12
11
%
12
19
1%
12
13
3
12
11
l/;
12
18
1%
12
13
3*4
12
11
%
12
18
1 13-16
12
13
31^1
12
11
%
12
17
m
12
12
4
10 to 12
11
13-16
12
17
1 15-16
12
12
5
10 to 12
11
%
12
17
2
12
12
5/4
10 to 12
11
15-16
12
17
%
12
12
51^3
10 to 12
11
1
12
16
2^4
12
12
5M
10 to 12
11
12
16
12
12
6
10 to 12
11
1J4
12
15
2J^
12
11
BENT AND COILED PIPES.
(National Pipe Bending Co., New Haven, Conn.)
COILS AND BENDS OF IRON AND STEEL PIPE.
Size of pipe Inches
86
1-4
$£
1
1M
1^
2
2U
3
Least outside diameter of
coil Inches
2
01^
fti<£
4V£
fi
8
12
16
24
32
Size of pipe Inches
3U
4
41-6
5
Q
7
8
9
10
12
Least outside diameter of
coil Inches
40
18
50
58
66
30
92
105
130
156
Lengths continuous welded up to 3-in. pipe or coupled as desired.
COILS AND BENDS OF DRAWN BRASS AND COPPER TUBING.
Size of tube, outside diameter Inches
Least outside diameter of coil Inches
1*
«
2*
£
^
1
4
J«
JN
Size of tube, outside diameter Inches
m
1**
W
^
2M
23/tf
^
2^
Least outside diameter of coil Inches
8
9
10
12
14
16
18
20
Lengths continuous brazed, soldered, or coupled as desired.
90° BENDS. EXTRA-HEAVY WROUGHT-IRON PIPE.
Diameter of pipe Inches
Radius Inches
Centre to end Inchei
is 26
24
The radii given are for the centre of the pipe. *' Centre to end " means
the perpendicular distance from the centre of one end of the bent pipe to a
plane passing across the other end. Standard iron pipes of sizes 4 to 8 in.
are bent to radii 8 in. larger than the radii in the above table; sizes 9 to 12 in.
to radii 12 in. larger.
Welded Solid I>rawn>«steel Tubes, imported by P. S. Justice &
Co., Philadelphia, are made in sizes from ^ to 4^ in. external diameter,
varying by V£ths, and with thickness of walls from 1/16 to 11/16 in. The
maximum length is 15 feet.
200
MATERIALS.
WEIGHT OF BRASS, COPPER, AND ZINC TUBING.
Per Foot.
Thickness by Brown & Sharpens Gauge.
Brass, No. 17.
Brass, No. 20.
Copper,
Lightning-rod Tube,
No. 23.
Inch.
*\
&
#>
/&
2 4
$
Lbs.
.107
.157
.185
.234
.266
.318
.333
.377
.462
.542
.675
.740
.915
.980
1.90
1.506
2.188
Inch.
HI
3-16
5-16
$6
°!
i
m
8?
Lbs.
.032
.039
.063
.106
.126
.158
.189
.208
.220
.252
.284
.378
.500
.580
Inch.
&
A»
g
Lbs.
.162
.176
.186
.211
.229
Zinc, No. 20.
r
ijj
.161
.185
.234
.272
311
.380
.452
LEAD PIPE IN LENGTHS OF 10 FEET.
In.
3-8 Thick.
5-16 Thick.
M Thick.
3-16
Thick.
Ib.
oz.
Ib.
oz.
Ib.
oz.
Ib.
oz.
2^
17
0
14
0
11
0
8
0
3
20
0
16
0
12
0
9
0
3^3
23
0
18
0
15
0
9
S
4
25
0
21
0
16
0
12
8
4^
18
0
14
0
5
31
0
20
0
LEAD WASTE-PIPE.
in., 2 Ibs. per foot.
"3 and 4 Ibs. per foot.
" 3^6 and 5 Ibs. per foot.
in., 4 Ibs. per foot.
" 5, 6, and 8 Ibs.
6 and 8 Ibs.
5 in. 8, 10, and 12 Ibs.
LEAD AND TIN TUBING.
^ inch. J4 inch.
SHEET LEAD.
Weight per square foot, 2^, 3, 3*4 4,
Other weights rolled to order.
4 5, 6, 8, 9, 10 Ibs. and upwards.
BLOCK-TIN PIPE.
in., 4}4, 6}4, and 8 oz. per foot.
" 6, 7^j, and 10 oz. "
*' 8 and 10 oz.
" 10 and 12 oz. "
1 in., 15, and 18 oz. per foot.
154 " 114 and lUlbs. "
lj| " 2 and 2V£ Ibs.
2 4i 2^ and 3 Ibs. "
LEAD PIPE.
201
LEAD AND TIN-LINED LEAD PIPE.
(Tatham & Bros., New York.)
.s .
a
1
1
Weight per
Foot and Rod.
I
1-
I
Weight per
Foot and Rod.
S5
^§
1
S
H
0
I
Mil.
E
D
7 Ibs. per rod
10 oz. per foot
6
1 uin.
E
D
\y% Ibs. per foot
2 " "
10
11
**
C
12 " "
8
41
C
<>L£ " *4
14
"
B
1 Ib.
12
M
B
31^ « **
17
**
A
1*4 " "
16
"
A
4 || ||
21
"
AA
1*4 " "
19
'*
AA
24
44
AAA
1% " 4'
27
4'
AAA
6 " '*
30
7-16 in.
13 oz. "
1*4 in.
E
2 " *'
10
"
1 Ib. "
4
D
gi^ 4 *
12
]/2 'n«
E
9 Ibs. per rod
7
•
C
3 * '
14
D
% Ib. per foot
9
4
B
3% '
16
44
C
1 44 4t
11
A
4^4 ' *
19
"
B
1*4 " "
13
•
AA
5§4 ' '
25
44
1*4 4t **
1
AAA
6M ' '
M
A
\%L 4< 4<
16
IHJn.
E
3
12
44
AA
2 "
19
D
3*4 *
14
23
C
17
•*
AAA
3 "
25
41
B
5 | |
19
P& in.
E
12 " per rod
8
«*
A
23
44
D
1 ' per foot
9
44
AA
8 * '
27
"
C
1*4 44 4t
13
44
AAA
9 *
44
B
2 " "
16
1% in.
C
4
13
4
A
2*^3 " 4'
20
"
B
5 | |
17
'
AA
2% " "
22
44
A
21
4
AAA
3*4 " "
25
44
AA
8Va ' 4t
27
% in.
E
1 " per foot
8
2 in.
C
4M * *l
15
1
D
1*4 "
10
41
B
6 4
18
1
C
jax »« *t
12
"
A
7 '
22
"
B
0]X '« **
16
44
AA
9 || ;;
27
44
A
3 «' "
20
*•
AAA
44
AA
3^3 " 4'
23
AAA
4% "
30
WEIGHT OF LEAD PIPE WHICH SHOULD BE USED
FOR A OIVEN HEAD OF WATER.
(Tatham & Bros., New York.)
Head or
Number
Pressure
Calibre and Weight per Foot.
of Feet
Fall.
per
sq. inch.
Letter.
%inch.
*^inch.
% inch.
«inch.
1 inch.
lJ4in.
30 ft.
15 Ibs.
D
10 oz.
»Ib,
1 Ib.
1*4 Ibs
2 Ibs.
2*4 Ibs.
50ft.
25 Ibs.
C
12 oz.
1 Ib.
1*4 Ibs.
1% Ibs.
2*4 Ibs.
3 Ibs.
75ft.
38 Ibs.
B
1 Ib.
1*4 Ibs.
2 Ibs.
2*4 Ibs.
3*4 Ibs.
3% Ibs.
100 ft.
50 Ibs.
A
1*4 Ibs.
1M Ibs.
2*4 Ibs.
3 Ibs.
4 Ibs.
4% Ibs.
150 ft.
75 Ibs.
AA
1*4 Ibs.
2 Ibs.i 2% Ibs.
3*4 Ibs.
4% Ibs.
6 Ibs.
200ft.
100 Ibs.
AAA
1% Ibs.
3 Ibs. ! 3*| Ibs.
i
4% Ibs.
6 Ibs.
6% Ibs.
To find the thickness of lead pipe required when the
head of water is given. (Chadwick Lead Works).
RULE.— Multiply the head in feet by size of pipe wanted, expressed deci-
mally, and divide by 750; the quotient will give thickness required, in one-
hundredths of an inch.
EXAMPLE.— Required thickness of half -inch pipe for a head of 25 feet.
25 X 0.50 -?- 750 = 0.16 inch.
202
MATERIALS.
«
O O O g? OO *H O? O5 C? O 00 O O Tj< T-« O rH »O 00
OJ001>COCOOTj»Tj<COCOOOOJC<lOirH^THTH OJ
0>
^3 o5 ^ i- TH o* co co o r
^O* 8, £$S8S8™8ii3$3SSSg
*" I
^ tfj t^ O <> CO
«
i -
°a
•SS f-
| a«^^,
fiii§5§2§S§i§iilii|li >:, *J
__ .~OOOOOOOOOOOOOOOOOOoS *r ri
02 « M
|j
Sc
a
35 "
*i I
6C02 P« ^OQO»^COr-iOOJOOI>01£50T»«TfCQCo"(?iNNOJT
« _Q M^r-.^r-.rHrHTH
^
fc^
5,«<
£^
.fc^ CQ
«- $
O
?*9Pr^^95Otr?5Q^
^W
•s&
oi
BOLT COPPER — SHEET AND BAB BRASS.
203
WEIGHT OF ROUND BOLT COPPER,
Per Foot.
Inches.
Pounds.
Inches.
Pounds.
Inches.
Pounds.
1
.425
.756
1.18
1.70
2.31
1
3.02
3.83
4.72
5.72
6.81
2
7.99
9.27
10.64
12.10
WEIGHT OF SHEET AND BAR BRASS.
Thickness,
Side or
Diam.
Sheets
per
sq. ft.
Square
Bars 1
ft. long.
Round
Bars 1
ft. long.
Thickness,
Side or
Diam.
Sheets
per
sq. ft.
Square
Bars 1
ft. long.
Round
Bars 1
ft. long.
Inches.
Inches.
1-16
2.72
.014
.011
1 1-16
46.32
4.10
3.22
K
5.45
.056
.045
Ug
49.05
4.59
3.61
3-16
8.17
.128
.100
1 3-16
51.77
5.12
4.02
1A
10.90
.227
.178
154
54.50
5.67
4.45
5-16
13.62
.355
.278
1 5-16
57.22
6.26
4.91
%
16.35
.510
.401
1%
59.95
6.86
5.39
7-16
19.07
.695
.545
1 7-16
62.67
7.50
5.89
»
21.80
.907
.712
1*6
65.40
8.16
6.41
9-16
24.52
1.15
.902
1 9-16
68.12
8.86
6.95
%
27.25
1.42
1.11
m
70.85
9.59
7.53
11-16
29 97
1.72
1.35
1 11-16
73.57
10.34
8.12
H
13-16
3-2.70
35.43
2.04
2.40
1.60
1.88
1 fs-16
76.30
79.0-2
11.12
11.93
8.73
9.36
7/8
38.15
2.78
2.18
1%
81.75
12.76
10.01
15-16
40.87
3.19
2.50
1 15-16
84.47
13.63
10.70
1
43.60
3.63
2.85
2
87.20
14.52
11.40
COMPOSITION OF VARIOUS GRADES OF ROLLED
BRASS, ETC.
Trade Name.
Copper
Zinc.
Tin.
Lead.
Nickel.
Common high brass
61.5
38 5
Yellow metal ...
60
40
Cartridge brass
66%
33^
Low brass
80
20*
Clock brass
60
40
1L£
Drill rod
60
40
\y> to 2
Spring brass
33V<*
1V£
18 per cent German silver. .
61J^
20^
18
The above table was furnished by the superintendent of a mill in Connec-
ticut in 1894. He says: While each mill has its own proportions for various
mixtures, depending upon the purposes for which the product is intended,
the figures given are about the average standard. Thus, between cartridge
brass with 33J£ per cent zinc and common high brass with 38U per cent
zinc, there are any number of different mixtures known generally as " high
brass," or specifically as "spinning brass," "drawing brass," etc., wherein
the amount of zinc is dependent upon the amount of scrap used in the mix-
ture, the degree of working to which the metal is to be subjected, etc.
204
MATERIALS.
AMERICAN STANDARD SIZES OF DROP-SHOT.
Diameter.
No. of Shot
to the oz.
Diameter.
No. of Shot
to the oz.
Diam-
eter.
No. of Shot
to the oz. I
Fine Dust.
Dust... .
No. 12. . .
" 11. .
" 10.. .
" 10. . .
" 9. . .
" 9.. .
3-1 00"
4-100
5-100
6-100
Trap Shot
7-100"
Trap Shot
8-100"
10784
4565
2326
1346
1056
848
688
568
No. 8
" 8
7
7
6
5
4
3
Trap Shot
9-100"
Trap Shot
10-100"
11-100
12-100
13-100
14-100
472
399
338
291
218
168
132
106
No. 2...
1.. .
B...
BB.
BBB
T...
TT..
F..
FF..
15-100"
16-100
17-100
18-100
19-100
20-100
21-100
22-100
23-100
86
71
59
50
42
36
31
27
24
COMPRESSED BUCK-SHOT.
Diameter.
No. of Balls
to the Ib.
Diameter.
No. of Balls
to the Ib.
No 3 .
25-100"
284
No. 00.... ...
34-100"
115
«* 2
27-100
232
" 000
3-100
98
44 1
30 100
173
Balls
38-100
85
" 0
32 100
140
44-100
50
SCREW-THREADS, SELLERS OR U. S. STANDARD.
In 1864 a committee of the Franklin Institute recommended the adoption
of the system of screw-threads and bolts which was devised by Mr. William
Sellers, of Philadelphia. This same system was subsequently adopted as
the standard by both the Army and Navy Departments of the United States,
and by the Master Mechanics1 and Master Car Builders' Associations, so
that it may now be regarded, and in fact is called, the United States Stand-
ard.
The rule given by Mr. Sellers for proportioning the thread is as follows :
Divide the pitch, or, what is the same thiug, the side of the thread, into
eight equal parts; take off one part from the top and fill in one part in the
bottom of the thread; then the flat top and bottom will equal one eighth of
the pitch, the wearing surface will be three quarters of the pitch, and the
diameter of screw at bottom of the thread will be expressed by the for
mula
1 299
diameter of bolt -
er inch'
For a sharp V thread with angle of 60° the formula is
1.733
diameter of bolt -- -=—. -. -- = - - — r •
no. of threads per inch
The angle of the thread in the Sellers system is 60°. In the Whitworth or
English system it is 55°, and the point and root of the thread are rounded.
Screw-Threads, United States Standard.
5
B
3
ft
a
Q
5-16
11-16
20
18
16
14
13
12
11
11
13-16
&6
1 1-16
2 13-16
3
3 5-16
4 4
TT. S. OR SELLERS SYSTEM OF SCREW-THREADS. 205
Screw-Threads, Whltwortli (English) Standard.
•
A
g i
^
j
J
-•
f£4
LI
,d
§
3
u
§
w
§
^
§
S
5
S
O
flH
o
S
S
K
P
S
*4
20
&/8
11
8
194
5
3
3U
£l6
18
11-16
11
*6
7
1?6
4*6
3*4
3*4
*M6
16
14
13-16
10
10
n
7
6
2
4 S
3%
3^
I/
12
9
^
6
2*6
4
4
3
9-16
12
15-16
9
%
o
2%
3*6
U. S. OR SI^I.I.KKS S VSTK1TI OF SCREW-THREADS.
BOLTS AND THREADS.
HEX. NUTS AND HEADS.
i
Q
1
3*
CM 0)
S
*o
%&
«.s»
Root of
,d in Sq.
s.
5*1
S:i
*A
5 g3
w
00 ?
sf
cc
ll
1
S
* §
£5
~
EH
P
,g
•8
5
*%£
C60«
2«5
^
"eg o>J«
c?£ §
k&£
-<
ll
s
-w S3
{->"->
ofe
£
02
f
•81
ew
I1
|l
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
Ins.
*4
20
.185
.0062
.049
.027
y
7-16
37-64
54
3-16
7-10
5^16
18
.2^0
.0074
.077
.045
19-32
17-32
11-16
5-16
*4
10-12
96
16
.294
.0078
.110
.068
11-16
%
51-64
%
5-16
63-64
7-16
14
.344
.0089
.150
.093
25-32
^3-3"-
9-10
7-16
%
1 7-64
*6
13
.400
.0096
.196
.126
Vs
13-16
1
V>
7-16
1 15-64
9-16
12
.454
.0104
.249
.162
31-32
29-32
1*6
9-16
*6
1 23-64
%
11
.507
.0113
.307
.202
1 1-16
1
1 7-32
%
9-16
]!/>
M
10
.620
.0125
.442
.302
\y*
13-16
1 7-16
%
11-16
1 49-64
%
9
.731
.0138
.601
.420
1 7-16
1%
1 21-32
%
13-16
21-32
1
8
.837
.0156
.785
.550
!&/
1 9—16
•JT^
1
15-16
219-64
1^
7
.940
.0178
.994
.694
1 13-16
1%
2 3-32
1*6
1 1-16
29-16
IM
7
1.065
.0178
1 .227
.893
2
1 15-16
25-16
1/4
1 3-16
253-64
i^
6
1.160
.0208
1.485
1.057
23-16
2*6
2 17-32
18
15-16
33-32
ji^j
6
1.284
.0208
1.767
1.295
2%
25-16
2M
1 7-16
3 23-64
1%
5*6
1.389
.0227
2.074
1.515
29-16
2*6
2 31-32
J§
19-16
3%
m
5
5
1.491
1.G16
.0250
.0250
2.405
2.761
1.746
2.051
2%
3 15-16
211-16
2%
33-16
313-32
1 Jo
1 11-16
1 13-16
3 57-64
45-32
2
4*6
1.712
.0277
3.142
2.302
3*6
3 1-16
3%
2
1 15-16
427-64
2)4
4*6
1.962
.0277
3.976
3.023
37-16
41-16
2*4
23-16
461-64
2J^j
4
2.176
.0312
4.909
3.719
gl
3 13-16
4*6
2U
2 7-16
5 31-64
2M
4
2.426
.0312
5.940
4.620
43-16
4 29-32 2%
211-16
6
3
3*6
2.629
.0357
7.069
5.428
m
49-16
5% |3
215-16
6 17-32
3)4
3^
2.879
.0357
8.296
6.510
5
415-16
5 13-16 3U
33-16
7 1-16
354
3)4
3.100
.0384
9.621
7.548
5%
55-16
67-64
3*6
37-16
739 64
3M
3
3.317
.0413
11.045
8.641
5 11-16
6 21-32 3%
3 11-16
gi,^
4
3
3.567
.0413
12.566
9.993
6*1
61-16
7 3-32 14
3 15-16
8 41-64
4)4
2%
3.798
.0435
14.186
11.329
67-16
7 9-li? 4*4
43-16
93-16
4*6
2%
4.028
.0454
15.904
12.743
(3 7^
6 13-16
731-32,4*6
47-16
Q3/
4M
2%
4.256
.0476
17.721
14.226
7**4
73-16
8 13-324%
411-16
10*4
5
2^
4.480
.0500
19.635
15.763
<%
79-16
8 27-32 5
4 15-16
10 49-64
5)4
2*6
4.730
.0500
21.648
17.572
8
7 15-16
9 9-32 !5*4
53-16
11 23-64
5)^2
2%
4.953
.0526
23.758
19.267
8%
85-16
9 23-32 5*6
5 7-16
11%
5%i
2%
5.203
.0526
25.967
21.262
854
811-16
105-32 !5%
5 11-16
12%
6
5.423
.0555
28.274
23.098
9*6
9 1-16
10 19-32 6
515-16
12 15-16
LIMIT GAUGES FOR IRON FOR SCREW THREADS.
In adopting the Sellers, or Franklin Institute, or United States Standard,
as it is variously called, a difficulty arose from the fact that it is the habit
of iron manufacturers to make iron over- size, and as there are no over-size
206
MATERIALS.
screws in the Sellers system, if iron is too large it is necessary to cut it away
with the dies. So great is this difficulty, that the practice of making taps
and dies over-size has become very general. If the Sellers system is adopted
it is essential that iron should be obtained of the correct size, or very nearly
so. Of course no high degree of precision is possible in rolling iron, and
when exact sizes were demanded, the question arose how much allowable
variationjthere should be from the true size. It was proposed to make limit-
gauges for inspecting iron with two openings, one larger and the other
smaller than the standard size, and then specify that the iron should enter
the large end and not enter the small one. The following table of dimen-
sions for the limit-gauges was - commended by the Master Car-Builders'
Association and adopted by letter ballot in 1883.
Size of
Size of
Size of
Size of
Size of
Large
Small
Differ-
Size of
Large
Small
Differ-
Iron.
End of
End of
ence.
Iron.
End of
End of
ence.
Gauge.
Gauge.
Gauge.
Gauge.
Hin.
0.2550
0.2450
0.010
96 in.
0.6330
0.6170
0.016
5-16
0.3180
0.3070
0.011
0.7585
0.7415
0.017
%
0.3810
0.3690
0.012
so
0.8840
0.8660
0.018
7l?6
0.4440
0.4310
0.013
\
1.0095
0.9905
0.019
^
0.5070
0.4930
0.014
i*i
1.1350
1.1150
0.020
9-16
0.5700
0.5550
0.015
m
1.2605
1.2395
0.021
Caliper gauges with the above dimensions, and standard reference gauges
for testing them, are made by The Pratt & Whitney Co.
THE MAXIMUM VARIATION IN SIZE OF ROUGH
IRON FOR U. S. STANDARD BOLTS.
Am. Mach., May 12, 1892.
By the adoption of the Sellers or U. S. Standard thread taps and dies keep
their size much longer in use when flatted in accordance with this system
than when made sharp " V," though it has been found advisable in practice
in most cases to make the taps of somewhat larger outside diameter than
the nominal size, thus carrying the threads further towards the V -shape
and giving corresponding clearance to *he tops of the threads when in the
nuts or tapped holes.
Makers of taps and dies often have calls for taps and dies, U. S. Standard,
" for rough iron."
An examination of rough iron will show that much of it is rolled out of
round to an amount exceeding the limit of variation in size allowed.
In view of this it may be desirable to know what the extreme variation in
iron may be, consistent with the maintenance of U. S. Standard threads, i.e.,
threads which are standard when measured upon the angles, the only placo
where it seems advisable to have them fit closely. Mr. Chas. A. Bauer, the
general manager of the Warder, Bushnell & Glessner Co., at Springfield,
Ohio, in 1884 adopted a plan which may be stated as follows : All bolts,
whether cut from rough or finished stock, are standard size at the bottom
and at the sides or angles cf the threads, the variation for fit of the nut and
allowance for wear of taps being made in the machine taps. Nuts are
punched with holes of such size as to give 85 per cent of a full thread, expe«
rience showing that the metal of wrought nuts will then crowd into the
threads of the taps sufficiently to give practically a full thread, while if
punched smaller some of the metal will be cut out by the tap at the bottom
of the threads, which is of course undesirable. Machine taps are made
enough larger than the nominal to bring the tops of the threads up sharp,
plus the amount allowed for fit and wear of taps. This allows the iron to
be enough above the nominal diameter to bring the threads up full (sharp)
at top, while if i ia small the only effect is to give a flat at top of threads ;
neither condition affecting the actual size of the thread at the point at which
it is intended co bear. Limit gauges are furnished to the mills, by which the
iron is rolled, the maximum size being shown in the third column of the
table. The minimum diameter is not given, the tendency in rolling being
nearly always to exceed the nominal diameter.
In making the taps the threaded portion is turned to the size given in the
eighth column of the table, which gives 6 to 7 thousandths of an inch allow-
ance for fit and wear of tap. Just above the threaded portion of the tap a
SIZES OF SCKEW-THEEADS FOE BOLTS AND TAPS. 207
place is turned to the size given in the ninth column, these sizes being the
same as those of the regular U. S. Standard bolt, at the bottom of the
thread, plus the amount allowed for fit and wear of tap ; or, in other words,
d' = U. S. Standard d + (Df — D). Gauges like the one in the cut, Fig.
72, are furnished for this sizing. In finishing the threads of the tap a tool
FIG. 72.
is used which has a removable cutter finished accurately to gauge by grind-
ing, this tool being correct U. S. Standard as to angle, and flat at the point.
It is fed in and the threads chased until the flat point just touches the por-
tion of the tap which has been turned to size d'. Care having been taken
with the form of the tool, with its grinding on the top face (a fixture being
provided for this to insure its being ground properly), and also with the set-
ting of the tool properly in the lathe, the result is that the threads of the tap
are correctly sized without further attention.
It is evident that one of the points of advantage of the Sellers-system is
sacrificed, i.e., instead of the taps being flatted at the top of the} threads
they are sharp, and are consequently not so durable as they otherwise would
be ; but practically this disadvantage is not found to be serious, and is far
overbalanced by the greater ease of getting iron within the prescribed
limits ; while any rough bolt when reduced in size at the top of the threads,
by filing or otherwise, will fit a hole tapped with the U. S. Standard hand
taps, thus affording proof that the two kinds of bolts or screws made for the
two different kinds of work are practically interchangeable. By this system
\" iron can be .005" smaller or .0108" larger than the nominal diameter, or,
in other words, it may have a total variation of .0158", while 1±" iron can be
.0105" smaller or .0309" larger than nominal— a total variation of .0414"—
and within these limits it is found practicable to procure the iron.
STANDARD SIZES OF SCREW-THREADS FOR BOLTS
AND TAPS.
(CHAS. A. BAUER.)
1
2
3
4
5
6
7
8
9
10
A
n
D
d
h
/
D' -D
D'
d'
H
Inches.
Inches
Inches.
Inches.
Inches.
Inches.
Inches.
Inches
H
20
.2G08
.1855
.0379
.0062
.006
.2668
.1915
.2024
5-16
18
.3245
.2403
.0421
.0070
.006
.3305
.2463
.2589
%
16
.3885
.2938
.0474
.0078
.006
.3945
.2998
.3139
7-16
14
.4530
.3447
.0541
.0089
.006
.4590
.3507
.3670
M
13
.5166
.4000
.0582
.0096
.006
.5223
.4060
.4236
9-16
12
.5805
.4543
.0631
.0104
.007
.5875
.4613
.4802
%
11
.6447
.5069
.0689
.0114
.007
.6517
.5139
.5346
34
10
.7717
.620!
.0758
.0125
.007
.7787
.6271
.6499
%
9
.8991
.7307
.0842
.0139
.007
.9061
.7377
.7630
I
8
1.0271
.8376
.0947
.0156
.007
1.0341
.8446
.8731
V/B
7
1.1559
.9394
.1083
.0179
.007
1.1629
.9464
.9789
V/4,
7
1.2809
1.0644
.1083
.0179
.007
1.2879
1.0714
1.1039
A = nominal diameter of bolt.
D = actual diameter of bolt.
d = diameter of bolt at bottom of
thread.
n = number of threads per inch.
/ = flat of bottom of thread.
h — depth of thread.
Df and d' — diameters of tap.
H = hole in nut before tapping.
208
MATERIALS.
STANDARD SET-SCREWS AND CAP-SCREWS.
American, Hartford, and Worcester Machine-Screw Companies.
(Compiled by W. S. Dix.)
(A)
(B)
(C)
(D)
(E)
(F)
(G)
Diameter of Screw. . . .
K
3-16
/4
5-16
%
7-16
7&
Threads per Inch
Size of Tap Drill*
40
No. 43
24
No. 30
No. 5
18
17-64
16
21-64
14
12
27-64
(H)
(D
(J)
(K)
(L)
(M)
(N)
Diameter of Screw.. . .
9-16
Ys
H
%
1
1^6
1J4
Threads per Inch
12
11
10
9
8
7
7
Size of Tap Drill*....
31-64
17-32
21-32
49-64
%
63-64
*M
Set Screws.
Hex. Head Cap-screws.
Sq. Head Cap-screws.
Short
Diam.
of Head
(C) <
(D) 5-16
$ &
JM.
(I) K
(ft %
(L) 1
(M) 1L
(N) 1M
Long
Diam.
of Head
.44
.53
.62
.71
.80
.89
1.06
1.24
1.42
1.60
1.77
Lengths
(under
Head).
Short
Diam.
of
Head.
7-16
Long
Diam,
of
Head.
.51
.58
.65
.72
.87
.94
1.01
1.15
1.30
1.45
1.59
1.73
Lengths
(under
Head).
Short
Diam.
of
Head.
to 3
7-16
9-16
11-16
Loug
Diam.
of
Head.
.53
.62
.71
1.06
1.24
1.60
1.77
1.95
2.13
Lengths
(under
Head).
Round and Filister Head
Cap-screws.
Diam. of
Head.
3-16
Lengths
(under
Head).
Flat Head Cap-screws.
Button-head Cap-
screws.
Diam. of
Head.
Lengths
(including
Head).
Diam. of
Head.
7-32 (.225)
5-16
7-16
9-16
13-16
15-16
1
Lengths
(under
Head).
* For cast iron. For numbers of twist-drills see p. 29.
Threads are U. S. Standard. Cap-screws are threaded % length up to and
including I" diam. x 4" long, and &j length above. Lengths increase by J4"
each regular size between the limits given. Lengths of heads, except flat
and button, equal diam. of screws.
The angle of the cone of the flat-head screw is 76°, the sides making angles
of 52° with the top.
STANDARD MACHINE SCREWS. 209
STANDARD MACHINE SCREWS.
No.
Threads per
Inch.
Diam. of
Body.
Diam.
of Flat
Head.
Diam. of
Round
Head.
Diam. of
Filister
Head.
Lengths.
From
To
2
56
.0842
.1631
.1544
.1332
3-16
2*
3
48
.0973
.1894
.1786
.1545
3-16
K
4
32, 36, 40
,1105
.2158
.2028
.1747
3-16
%
5
32, 36, 40
.1236
.2421
.2270
.1985
3-16
%
6
30, 32
.1368
.2684
.2512
.2175
3-16
1
7
30,32
.1500
.2947
.2754
.2392
/4
l/*6
8
30, 32
.1631
.3210
.2936
.2610
/4
1/4
9
24, 30, 32
.1763
.3474
.3238
.2805
/4
I&2
10
24, 30, 32
.1894
.3737
.3480
.3035
/4
•ji^j
12
20,24
.2158
.4263
.3922
.3445
%
1%
14
20, 24
.2421
.4790
.4364
.3885
%
2
16
16, 18, 20
.2684
.5316
.4866
.4300
%
2^4
18
16, 18
,2947
.5842
.5248
.4710
i^j
2^J
20
16, 18
.3210
.6308
.5690
.5200
8
2§4
22
16,18
.3474
.6894
.6106
.5557
3
24
14, 16
.3737
.7420
.6522
.6005
/'is
3
26
14, 16
.4000
.7420
.6938
.6425
%
3
28
14, 16
.4263
.7946
.7354
.6920
%
3
30
14, 16
.4520
.8473
.7770
.7240
1
3
Lengths vary by 16ths from 3-16 to J^, by 8ths from ^ to 1J4 by 4ths from
1^ to 3.
SIZES AND WEIGHTS OF SQUARE AND
HEXAGONAL NUTS.
United States Standard Sizes. Chamfered and trimmed.
Punched to suit U. S. Standard Taps.
s
s
y±
5-16
7?16
9-?6
2
2^4
I
I
2 15-16
13-64
1*9-64
11-32
25-64
29-64
33-64
39-64
47-64
53-64
59-64
1-16
5-32
9-32
1 13-32
1 23-32
1 15-16
2 3-16
2 7-16
2%
S3'
11-16J
13-161
9-16
11-16
13-16
7-16
2' '1-16 11-16
2 5-161 1%
2 9-16 2 1-16
2 13-16 2 5-16
2 15-16
3 3-16
4 7-16
4 15-16
4 1-16
4 15-16
5 5-16
Square.
Hexagon.
8
fee
8
gj
.sj§
jb
. C 03
8jg
«.s
~f
i*
7270
4700
.0138
.0281
7615
5200
.0131
.0192
2350
.0426
3000
.0333
1630
.0613
2000
.050
1120
.0893
1430
.070
890
.1124
1100
.091
640
.156
740
.135
380
.263
450
.222
280
.357
309
.324
170
.588
216
.463
130
.769
148
.676
96
1.04
111
.901
70
1.43
85
1.18
58
1.72
68
1.47
44
2.27
56
1.79
34
2.94
40
2.50
30
3.33
37
2.70
23
4.35
29
3.45
19
5.26
21
4.76
12
8.33
15
6.67
9
11.11
11
9.09
IK
13.64
8^
11.76
210
MATERIALS.
tt
4
-
R
H
C
o
o
»vj I OD ••••.• . J>. r-< lO O ^J1 Oi CO O* T-t C
^•x .Q • • • • • •COTj<1«i5'lOlO»OCDI>-OOO
» rg
*
^ cc
»>^ o
5 10 10 10 K
^O"— COiOt^O5->— iCOiOC'-OS'-'COM
-1— itnOiCOt>-'— iCOOrfQCS^l-^^w
C'COCOCOCO'^1^9''^1^T^3'lOiOlOCOCDCOi-t^-i."-aDQOOSOSOSOOO
2^-iT*iOOOOOOOOOOOOOOOO
SOOOrH OiCOT
QOOOOO
^aocooiio^-'J>cooco<?>co>*ocoGOT-iooT
I ;i;oco;oi.~GcaoosooT-.i-,(?*cocoTfcoi--a
SQOOOOCOCOCSWOOiOOlOpiqOOOO
I _o t~ os rt" od o» co* o io" oi oo i> I-H CD o c» co" -<* ti TJ os ao co »o co <M! o oo co' 10' -i<
^cocOrf-^io»oeococDJ.--i-oOGOOSO5OT-('^cocOTf'Ocot.-aoc:osO'-iO?
O CO CO OS OJ lO 00 i-; 10 0* OS t- 10 CO i-; O O O O O O
"\ |SoO?if5J>OCOCOOST4rJ<t
TH I SG^C* OJ WCOCOCOCO^TJiT
>* TH O 10 O 10 O 10 O 10 O 10 O 10 O
' ?«?Tr^r?^90?oos^o»Ot-jcogi
> CO OS 10 r-. t>G
50 M^0^
' i- i- 10 O 10
»OT-K?JCOr>*lOt^GOOSC
^OiCO^C^OSCDCOOi.-^i-iGOlOC»
TRACK BOLTS.
With United States Standard Hexagon Nuts,
Rails used.
Bolts.
Nuts.
No. in Keg,
200 Ibs.
Kegs per Mile.
\
%x4^
H
230
6.3
%x4
1?
240
6.
45to851bs.. J
%x3%
8
254
260
5.7
5.5
1
% x 3^
/4
266
5.4
I
%x3
M
283
5.1
r
%x3^
1-16
375
4.
30to401bs.. J
%x3
1-16
1-16
410
435
3.7
3.3
1
^x2H
1 1-16
465
3.1
[
1^x3
%
715
2.
20to301bs..J
^xl^
n
760
800
2.
2.
I
1^x2
?
820
2.
RIVETS — TUIIKBUCKLES.
CONK-HEAD BOILER RIVETS, WEIGHT PER 1OO.
(Hoopes & Townsend.)
Diam., in.,
Scant.
1/2
9/16
5/8
11/16
X
13/16
%
1
i«*
W
Length.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
%inch
8.75
18.7
16.20
H "
9.35
14.4
17.22
i ;'
10.00
15.2
18.25
21.70
26.55
10.70
16.0
19.28
23.10
28.00
/4 "
11.40
16.8
20.31
24.50
29.45
37.0
46
60
% "
12.10
17.6
21.34
25.90
30.90
38.6
48
63
95
L£ "
12.80
18.4
22.37
27.30
32.35
40.2
50
65
98
133
5X "
13.50
19.2
23.40
28.70
33.80
41.9
52
67
101
137
M "
14.20
20.0
24.43
30.10
35.25
43.5
54
69
104
141
y& "
14.90
20.8
25.46
31.50
36.70
45.2
56
71
107
145
2 "
15.60
21.6
26.49
32.90
38.15
47.0
58
74
110
149
•jji^ **
16.30
22.4
27.52
34.30
39.60
48.7
60
77
114
153
2J4 "
17.00
23.2
28.55
35.70
41.05
50.3
62
80
118
157
2% "
17.70
24.0
29.58
37.10
42.50
51.9
64
83
121
161
2Vji> "
18.40
24.8
30.61
38.50
43.95
53.5
66
86
124
165
2% "
19.10
25.6
31.64
39.90
45.40
55.1
68
89
127
169
m "
19.80
26.4
32.67
41.30
46.85
56.8
70
92
130
173
2% '
20.50
27.2
33.70
42.70
48.30
58.4
72
95
133
177
3 «
21.20
28.0
34.73
44.10
49.75
60.0
74
98
137
181
3^4 '
22.60
29.7
36.79
46.90
52.65
63.3
78
103
144
189
3Vi* '
24.00
31 5
38.85
49.70
55.55
66.5
82
108
151
197
33£ '
25.40
33.3
40.91
52.50
58.45
69.8
86
113
158
205
4 *
26.80
35.2
42.97
55.30
61.35
73.0
90
118
165
213
4*4 '
28.20
36.9
45.03
58.10
64.25
76.3
94
124
172
221
4^5 '
29.60
38.6
47.09
60.90
67.15
79.5
98
130
179
229
4^4 '
31.00
40.3
49.15
63.70
70.05
82.8
102
136
186
237
5
32.40
42.0
51.21
66.50
72.95
86.0
106
142
193
245
5/4 *
33.80
43.7
53.27
69.20
75.85
89.3
no
148
200
254
5^ '
35.20
45.4
55.33
72.00
78.75
92.5
114
154
206
263
5M '
36.60
47.1
57.39
74.80
81.65
95.7
118
160
212
272
6
38.00
48.8
59.45
77.60
84.55
99.0
122
166
218
281
6J4 '
40.80
52.0
63.57
83.30
90.35
105.5
130
177
231
297
7 '
43.60
55.2
67.69
88.90
96.15
112.0
138
188
245
314
Heads
5.50
8.40
11.50
13.20
18.00
23.0
29.0
38.0
56.0
77.5
* These two sizes are calculated for exact diameter.
Rivets with button heads weigh approximately the same as cone-head
rivets.
T URN BUCK LES.
(Cleveland City Forge and Iron Co.)
Standard sizes made with right and left threads. D = outside diameter
of screw. A = length in clear between heads = 6 ins. for all sizes. B =
length of tapped heads = l^D nearly. C = 6 ins. + 3D nearly.
212
MATERIALS.
SIZES OF WASHERS.
Diameter in
inches.
Size of Hole, in
inches.
Thickness,
Birmingham
Wire-gauge.
Bolt in
inches.
No. in 100 Ibs.
a.
5-16
No. 16
M
29,300
a?
H
" 16
5—16
18,000
1
7-16
** 14
%
7,600
9-16
" 11
14
3,300
jijj?
%
44 11
9-16
2,180
1^3
11-16
** 11
%
2,350 .
1%
13-16
•* 11
%
1,680
2
31-32
*• 10
%
1,140
2^
1^
" 8
1
580
252
1J4
•* 8
l/^
470
3
1%
tt 7
jix
360
3
ig
*» 6
ift
860
TRACK SPIKES*
Rails used.
Spikes.
Number in Keg,
200 Ibs.
Kegs per Mile,
Ties 24 in.
between Centres.
45 to 85
5^x9-16
880
30
40 " 52
5 x9-16
400
27
35 ** 40
5 xU
490
22
24 " 35
550
20
24 " 30
4J4 x 7-16
725
15
18 " 24
4 x7-16
820
13
16 " 20
8J4x%
1250
9
14 " 16
3 x %
1350
8
8 " 12
2^x%
1550
7
8 " 10
2^x5-16
2200
5
STREET RAILWAY SPIKES.
Spikes.
Number in Keg, 200 Ibs.
Kegs per Mile, Ties 24 in.
between Centres.
5^x9-16
5 x^
4J^x7-16
400
575
800
30
19
13
BOAT SPIKES.
Number in Keg of 200 Ibs.
Length.
H
5-16
H
H
4 inch.
2375
5 "
2050
1230
940
6 '»
7 "
1825
1175
990
800
650
450
375
8 "
880
600
335
9 ••
525
300
10 "
475
275
SPIKES; CUT KAILS.
213
WROUGHT SPIKES.
Number of Nails in Keg of 15O Founds.
Size.
Min.
5-16 in.
fcin.
7-16 in.
Kin.
3 inches .
2250
3U "
1890
1208
f" ..
1650
1135
4U •*
1464
1064
5^ »• "
1380
930
742
6 "
1292
868
570
7 " .. .
8 M
1161
662
635
482
455
445
384
306
256
9 «•
573
424
300
240
10 *
391
270
222
11 "
249
203
IS *
236
180
WIRE SPIKES.
Size.
Approx. Size
of Wire Nails.
Ap. No.
in 1 Ib.
Size.
Approx. Size
of Wire Nails.
Ap. No.
in 1 Ib.
lOd Spike....
3 in. No. 7
50
60d Spike . . .
6 in. No. 1
10
16d "
3^ " " 6
35
6^ in.44 .. .
6^£ *' ** 1
9
20d •*
4 •• "5
26
7 " " . .
7 •• •• 0
7
30d ••
4^ " «• 4
20
8 " " .. .
8 " " 00
5
40d "
5 " "3
15
9 ** u
9 " •• 00
4 Hi
50d »*
% " ** 2
12
LENGTH AND NUJttRER OF CUT NAILS TO THE
POUND.
Size.
!
Common.
1
'§>
i
PR
Finishing.
|
s
Barrel.
1
03
1
«
Tobacco.
Cut Spikes.
M
%in
800
7/|
500
2d
1
800
1100
1000
376
3d...
WA
480
720
760
224
4d
u&
288
523
368
180
398
5d
m
200
410
130
6d
2
168
9^
84
268
224
126
96
7d
124
74
61
188
98
82
8d ....
2V6
88
62
48
146
J28
75
68
9d
9g/
70
*)S
8fi
130
110
65
lOd
3
58
46
30
102
91
55
28
)2d.
3V4
44
d°
0^
76
71
40
16d....i..
l&
34
^S
°0
62
54
27
99
20d
f~
23
88
16
54
40
14i£
SOd
VA
18
°0
33
12i/
40d
5
14
27
9vl
50d
51^
10
8
60d
6/6
8
6
214
MATERIALS.
•S9ZJS
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: o» :
• <c o •
I'd'd'd '•etS'd'd'd'CJ'd'
• oj co eo ••<3<ir3?ooooo5O<?
•saqoui '
-
SS§3 :§i :$2SS
PITB qioouis
PUB '£uisfcQ
Suiqsmj.i paqa-e
UOIUUIOQ
sil^N noraraoo
"^^ ,_ ,_ ^ ^ TH-1_4 ciwwwwcocoTf ^o »o
APPROXIMATE NUMBER OF WIRE NAILS PER POUND. 215
bT>»!»Ts
« co ^o ;.;;;;;;;;;; .M •£ g
•^rio
i
loVooo-* j I
<Ot>OOOiT-iOOlOOO
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§5S^^^io§?:SS2gg||||||| : : j
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»
o«ot>^oS^^i^o^^"w^^^
x^f • •oc^^f«ooott-cOTHTt<'— ••rfi?o(7't^JO»r:oc^'— •
«0\ • rHr-ii-ir-iOi<MOCOTt<iOt-O»!->iOOt>ir:O05CO
^o ... -S^i^S
«••«•• ~" T^ 1^1 TH 5^ CO
^
^ j i j i : : j : : i i : i : Jill
I°-
gw
2ib MATERIALS.
SIZE, WEIGHT, LENGTH, AND STRENGTH OF IRON
WIRE.
(Trenton Iron Co.)
Tensile Strength (Ap.
No. by
Wire
Gauge.
Diam.
in Deci-
mals of
One
Area of
Section in
Decimals of
One Inch.
Feet to
the
Pound.
Weight of
One Mile
in pounds.
proximate) of Charcoal
Iron Wire in Pounds.
Inch.
Bright.
Annealed.
00000
.450
.15904
1.863
2833.248
12598
9449
0000
.400
.12566
2.358
2238.878
9955
7466
000
.360
.10179
2.911
1813.574
8124
6091
00
.330
.08553
3.465
1523.861
6880
5160
0
.305
.07306
4.057
1301.678
5926
4445
1
.285
.06379
4.645
1136.678
5226
3920
2
.265
.05515
5.374
982 555
- 4570
3425
3
.245
.04714
6.286
839.942
3948
2960
4
.225
.03976
7.454
708.365
3374
2530
5
.205
.03301
8.976
588.139
2839
2130
6
.190
.02835
10.453
505.084
2476
1860
7
.175
.02405
12.322
428.472
2136
1600
8
.160
.02011
14.736
358.3008
1813
1360
9
.145
.01651
17.950
294.1488
1507
1130
10
.130
.01327
22.333
236.4384
1233
925
11
.1175
.01084
27.340
193.1424
1010
758
12
.105
.00866
34.219
154.2816
810
607
13
.0925
.00672
44.092
119.7504
631
473
14
.080
.00503
58.916
89.6016
474
356
15
.070
.00385
76.984
68.5872
372
280
16
.061
.00292
101.488
52.0080
292
220
17
.0525
.00216
137.174
38.4912
222
165
18
.045
.00159
186.335
28.3378
169
127
19
.040
.0012566
235.084
22.3872
137
103
20
.035
.0009621
308.079
17.1389
107
80
21
.031
.0007547
392.772
13.4429
22
.028
.0006157
481.234
10.9718
' £"§22 « 2~
23
.025
.000*909
603.863
8.7437
C?2iO <U~ °~ ~
24
.0225
.0003976
745.710
7.0805
41 •2*-4>a ^
25
.020
.0003142
943.396
5.5968
•£5"° °i32S** **
26
.018
.0002545
1164.689
4.5334
^J'S | ! §d
27
.017
.0002270
1305.670
4.0439
28
.016
.0002011
1476.869
3.5819
§T3 ?J D-^ ol O * 2 £
29
.015
.0001767
1676.989
3.1485
43 S^'> °-2'§'*tw fl
30
.014
.0001539
1925.321
2.7424
s S^li ^.s"*!^ **
31
.013
.0001327
2232.653
2.3649
w-g SH °.2S J^le o> ^
32
.012
.0001131
2620.607
2.0148
2-2 ujS ^'j^^to O
33
.011
.0000950
3119.092
1.6928
§id'~fi.h§^:~~ M
34
35
.010
.0095
.00007854
.00007088
3773.584
4182.508
1.3992
1.2624
1
36
.009
.00006362
4657.728
1.1336
O-^-rt — ^^ t» £>o °
37
.0085
.00005675
5222.035
1.0111
*§ w'ejf! '"•SW jf3 j|
88
.008
.00005027
5896.147
.89549
d>.Q E_S<o'«!5;S*^ •*"
39
.0075
.00004418
6724.291
.78672
40
.007
00003848
7698.253
.68587
TESTS OF 'TELEGRAPH WIRE.
217
GALVANIZED IRON WIRE FOR TELEGRAPH AND
TELEPHONE LINES.
(Trenton Iron Co.)
WEIGHT PER MILE-OHM.— This term is to be understood as distinguishing
the resistance of material only, and means the weight of such material re-
quired per mile to give the resistance of one ohm. To ascertain the mileage
resistance of any wire, divide the " weight per mile-ohm " by the weight of
the wire per mile. Thus in a grade of Extra Best Best, of which the weight
per mile-ohm is 5000, the mileage resistance of No. 6 (weight per mile 525
Ibs.) would be about 9J^ ohms; and No. 14 steel wire, 6500 ibs. weight per
mile-ohm (95 Ibs. weight per mile), would show about 69 ohms.
Sizes of \Virc used in Telegraph and Telephone Lines.
No. 4. Has not been much used until recently; is now used on important
lines where the multiplex systems are applied.
No. 5. Little used in the United States.
No. 6. Used for important circuits between cities.
No. 8. Medium size for circuits of 400 miles or less.
No. 9. For similar locations to No. 8, but on somewhat shorter circuits ;
until lately was the size most largely used in this country.
Nos. 10, 11. For shorter circuits, railway telegraphs, private lines, police
and fire-alarm lines, etc.
No. 12. For telephone lines, police and fire-alarm lines, etc.
Nos. 13, 14. For telephone lines and short private lines: steel wire is used
most generally in these sizes.
The coating of telegraph wire with zinc as a protection against oxidation
is now generally admitted to be the most efficacious method.
The grades of line wire are generally known to the trade as " Extra Best
Best " (E. B. B.), " Best Best " (B. B.). and "Steel."
" Extra Best Best " is made of the very best iron, as nearly pure as any
commercial iron, soft, tough, uniform, and of very high conductivity, its
weight per mile-ohm being about 5000 Ibs.
The " Best Best11 is of iron, showing in mechanical tests almost as good
results as the E. B. B., but not quite as soft, and being somewhat lower in
conductivity; weight per mile-ohm about 5700 Ibs.
The Trenton " Steel " wire is well suited for telephone or short telegraph
lines, and the weight per mile-ohm is about 6500 Ibs.
The following are (approximately) the weights per mile of various sizes of
galvanized telegraph wire, drawn by Trenton Iron Co.'s gauge:
No. 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.
Lbs. 720, 610, 525, 450, 375, 310, 250, 200, 160, 125, 95.
TESTS OF TELEGRAPH WIRE.
The following data are taken from a table given by Mr. Prescott relating
to tests of E. B. B. galvanized wire furnished the Western Union Telegraph
Co.:
Size
of
Wire.
Diam.
Parts of
One
Inch.
Weight.
Length.
Feet
per
pound.
Resistance.
Temp. 75.8° Fahr.
Ratio of
Breaking
Weight to
Weight
per mile.
Grains,
per foot.
Pounds
per mile.
Feet
per ohm.
Ohms
per mile.
4
.238
1043.2
886.6
6.00
958
5.51
5
.220
891.3
673.0
7.85
727
7.26
6
.203
758.9
572.2
9.20
618
8.54
3.05
7
.180
596.7
449.9
11.70
578
10.86
3.40
8
.165
501.4
378.1
14.00
409
12.92
3.07
9
.148
403.4
304.2
17.4
328
16.10
3.38
10
.134
330.7
249.4
21.2
269
19.60
3.37
11
.120
265.2
200.0
26.4
216
24.42
2.97
12
.109
218.8
165.0
32.0
179
29.60
3.43
14
.083
126.9
95.7
55.2
104
51.00
3.05
JOINTS IN TELEGRAPH WIRES.— The fewer the joints in a line the better.
All joints should be carefully made and well soldered over, for a bad joint
may cause as much resistance to the electric current as several miles of
wire.
218
MATERIALS.
»ooi-i«e<
- i T-i
»-i eo IH T- >H U
O O5 -* -^
>H o> m
Ill
15"
11
H^SSc5<N
DIMENSIONS, WEIGHT, RESISTANCE OF OOPPEB WIRE. #19
Op.
&
A
o
5
s s
»oo«
320
MATERIALS.
^t-^»
liil
3^^0*5 IS <NO£Jo5^g
Hr-lSnSlNOJCO-^lOOOOOC^
SOOOOOOOOOOrti-
§3S§SoS83M3Sll2llSl8£l§l
?SooIo^5Ǥt2t2?2ooaco2H
jJTH^oiinNoJt-lto^sceooii-tiHrHO
*§iSg?2||i|ssis|IsgigS|
rf
«OHJI>. to 10 eo •**•«*< o>
§oooo§co5)5>SS
HARD-DRAWK COPPER WIRE; INSULATED WIRE. 221
HARD-DRAWN COPPER TELEGRAPH WIRE.
(J. A. Roebling's Sons Co.)
Furnished in half-mile coils, either bare or insulated.
Size, B. & S.
Gauge.
Resistance in
Ohms
per Mile.
Breaking .
Strength.
Weight
per Mile.
Approximate
Size of E. B.B.
Iron Wire
equal to
Copper.
9
4.30
625
209
2 t?
10
5.40
525
166
3 I
11
6.90
420
131
4 I
12
8.70
330
104
6 |
13
10.90
270
83
6^3
14
13.70
213
66
8 0
15
17.40
170
52
9 £
16
22.10
130
41
10 <g
CD
In handling this wire the greatest care should be observed to avoid kinks,
bends, scratches, or cuts. Joints should be made only with Mclntire Con-
nectors.
On account of its conductivity being about five times that of Ex. B. B.
Iron Wire, and its breaking strength over three times its weight per mile,
copper maybe used of which the section is smaller and the weight less than
an equivale&t iron wire, allowing a greater number of wires to be strung on
the poles.
Besides this advantage, the reduction of section materially decreases the
electrostatic capacity, while its non-magnetic character lessens the self-in-
duction of the line, both of which features tend to increase the possible
speed of signalling in telegraphing, and to give greater clearness of enunci-
ation over telephone lines, especially those of great length.
INSULATED COPPER WIRE, WEATHERPROOF
INSULATION.
Double Braid.
Triple Braid.
Approximate
Num-
Weights,
bers,
Outside
Weights,
Outside
Weights,
Pounds.
B. &S.
Diame-
Pounds.
Diame-
Pounds.
Gauge.
ters in
ters in
32ds
Inch.
1000
Feet.
Mile.
Inch.
1000
Feet.
Mile.
Reel.
Coil.
0000
20
716
3781
24
775
4092
2000
250
000
18
575
3036
22
630
3326
2000
250
00
17
465
2455
18
490
2587
500
250
0
15
375
1980
17
400
2112
500
250
1
15
285
1505
16
306
1616
500
250
2
14
245
1294
15
268
1415
500
250
I
13
190
1003
14
210
1109
500
250
11
152
803
12
164
866
250
125
5
10
120
G34
11
145
766
260
130
6
9
98
518
10
112
691
275
140
8
8
66
349
9
78
412
200
100
10
7
45
238
8
55
290
200
100
12
6
30
158
7
35
185
....
25
14
5
20
106
6
26
137
25
16
4
14
74
5
20
106
....
25
18
3
10
53
4
16
....
25
MATERIALS,
Power Cables. Lead Incased, Jute or Paper Insulated*
(John A. Roebling's Sons Co.)
Nos,.
B.&S.G.
Circular
Mils.
Outside
Diam.
Inches.
Weights,
1000 feet.
Pounds.
Nos.,
B.&S.G.
Circular
Mils.
Outside
Diam.
Inches.
Weights,
1000 feet.
Pounds.
1000000
900000
800000
750000
700000
650000
600000
550000
500000
450000
400000
350000
1 13/16
1 23/32
21/32
19/32
9/16
17/32
1/ie
V
5/16
6685
6228
5773
5543
5315
5088
4857
4630
4278
3923
3619
3416
300000
250000
211600
168100
133225
105625
83521
66564
52441
41616
26244
1M
1 3/16
1 3/32
1 1/16
15/16
29/32
%
25/32
%
11/16
3060
2732
2533
2300
2021
1772
1633
1482
1360
1251
1046
0000 " '
000
00
0
1
2
3
4
6
Stranded Weather-proof Feed Wire.
Circular
Mils.
1000000
900000
800000
750000
700000
650000
600000
Outside
Diam.
Inches.
Weights.
Pounds.
Approximate
length on reels.
Feet.
Circular
Mils.
Outside
Diam.
Inches.
Weights.
Pounds.
Approximate 1
length on reels.
Feet.
1000
feet.
Mile.
1000
feet.
Mile.
1 13/32
1 11/32
1 5/16
1 9/32
H
1 7/32
3550
3215
2880
2713
2545
2378
2210
18744
16975
15206
14325
13438
12556
11668
800
800
850
850
900
900
1000
550000
500000
450000
400000
350000
300000
250000
3/16
X
3/32
1/16
15/16
29/32
2043
1875
1703
1530
1358
1185
1012
10787
9900
8992
8078
7170
6257
5343
1200
1320
1400
1450
1500
1600
1600
The table is calculated for concentric strands. Rope-laid strands are
larger.
Approximate Rules for the Resistance of Copper Wire.
—The resistance of any copper wire at 20° C. or 66° F., according to Mat:
thiessen's standard, is E = — ^p— » in which E is the resistance in inter-
national ohms, I the length of the wire in feet, and d its diameter in mils.
(1 mil = 1/1000 inch.)
A No. 10 Wire, A.W.G., .1019 in. diameter (practically 0.1 in.), 1000 ft. in
length, has a resistance of 1 ohm at 68° F. and weighs 31.4 Ibs.
If a wire of a given length and size by the American or Brown & Sharpc
gauge has a certain resistance, a wire of the same length and three numbers
higher has twice the resistance, six numbers higher four times the resist-
ance, etc.
Wire gauge, A.W.G. No 000 1 4 7 10 13 16 19 22
Relative resistance 16 8 4 2 11/2 1/4 1/8 1/16
section or weight.. 1/16 1/8 1/4 1/212 4 8 16
Approximate rules for resistance at any temperature :
vf :
R0 = resistance at 0°, Rf = resistance at the temperature t° C., I -
in feet, d - diameter iii cmils. (See Copper Wire Table, p. 1034.)
length
STEEL WIRE CABLES.
223
GALVANIZED STEEL-WIRE STRAND.
For Smokestack Guys, Signal Strand, etc.
(J. A. Roebling's Sons Co.)
This strand is composed of 7 wires, twisted together into a single strand.
L
4>.J
— br.~
LI
S^"
•dg5^
h
•eg'd
£
^•3?
-S^bJC
a>
-2*2 "Ss
qj
^S
I
.1
"So
ss
HI
a>
|
5?o
|ll
(0
I
||
III
p
^
1
O
1
, 3
^
W
in.
Ibs.
Ibs.
in.
Ibs.
Ibs.
in.
Ibs.
Ibs.
\$
51
8,320
9/32
18
2,600
5/32
4J^
700
15/32
48
7,500
17/64
15
2,250
9/64
3Vi*
525
7/16
37
30
6,000
4,700
7/32
\\V2
1,750
1,300
3/32
2^4
2
375
320
5^16
21
3,300
3/16
*y*
1,000
For special purposes these strands can be made of 50 to 100 per cent
greater tensile strength. When used to run over sheaves or pulleys the use
of soft-iron stock is advisable.
FLEXIBLE STEEL-WIRE CABLES FOR VESSELS.
(Trenton Iron Co., 1886.)
With numerous disadvantages, the system of working ships' anchors with
chain cables is still in vogue. A heavy chain cable contributes to the hold-
ing-power of the anchor, and the facility of increasing that resistance by
•paying out the cable is prized as an advantage. The requisite holding-
power is 'obtained, however, by the combined action of a comparatively
light anchor and a corresponding^7 great mass of chain of little service in
proportion to its weight or to the weight of the anchor. If the weight and
size of the anchor were increased so as to give the greatest holding-power
required, and it were attached by means of a light wire cable, the combined
weight of the cable and anchor would be much less than the total weight of
the chain and anchor, and the facility of handling would be much greater.
English shipbuilders have taken the initiative in this direction, and many of
the largest and most serviceable vessels afloat are fitted with steel- wire
cables. They have given complete satisfaction.
The Trenton Iron Co/s cables are made of crucible cast-steel wire, and
guaranteed to fulfil Lloyd's requirements. They are composed of 72 wires
subdivided into six strands of twelve wires each. In order to obtain great
flexibility, hempen centres are introduced in the strands as well as in the
completed cable.
FLEXIBLE STEEL-WIRE HAWSERS.
These hawsers are extensively used, They are made with six strands of
twelve wires each, hemp centres being inserted in the individual strands as
well as in the completed rope. The material employed is crucible cast steel,
galvanized, and guaranteed to fulfil Lloyd's requirements. They are only
one third the weight of hempen hawsers; and are sufficiently pliable to work
round any bitts to which hempen rope of equivalent strength can be applied.
13-inch tarred Russian hemp hawser weighs about 39 Ibs. per fathom.
10-inch white manila hawser weighs about 20 Ibs. per fathom.
1^-inch stud chain weighs about (58 Ibs. per fathom.
4-inch galvanized steel hawser weighs about 12 /6s. per fathom.
Each of the above named has about the same tensile strength.
224
MATERIALS.
SPECIFICATIONS FOR GALVANIZED IRON WIRE.
Issued by the British. Postal Telegraph Authorities.
Weight per Mile.
Diameter.
Tests for Strength and
Ductility.
sk*
&* * *
•s
*§
o
-2
•g
V)
oS^lau
Sg
T3
t£^
^9
a
fl
.2
rti 5 ®
C 8
-ed Standar
Allowed.
d Standard
Allowed.
Breakir
Weigh
d
ing Weight
ss than —
d ~
:ing Weight
ss than—
0*
ft
Resistance
of the S
Size at 6
t, being Sta
t x Resista
'o*
g
s
i
1
|
1
5
|
8
3
3
|§
&
S
a
i
I
S
1
M
i
M
a
I
g^
i
1
1
M
|
|
o
"3
o
I
N
1
O
Ibs.
Ibs.
Ibs.
mils.
mils.
mils.
Ibs.
Ibs.
Ibs.
ohms.
800
767
833
242
237
247
2480
15
2550
14
2620
13
6.75
5400
600
571
629
209
204
214
1860
17
1910
16
1960
15
9.00
5400
450
424
477
181
176
186
1390
19
1425
18
1460
17
12.00
5400
400
377
424
171
166
176
1240
21
1270
20
1300
19
13.50
5400
200
190
213
121
118
125
620
30
638
28
655
26
27.00
5400
STRENGTH OF PIANO-WIRE.
The average strength of English piano- wire is given as follows by Web
ster, Horsfals & Lean:
Numbers
Equivalents
Ultimate
Numbers
Equivalents
Ultimate.
in Music-
in Fractions
Tensile
in Music-
in Fractions
Tensile
wire
Gauge.
of Inches in
Diameters.
Strength in
Pounds.
wire
Gauge.
of inches in
Diameters.
Strength in
Pounds.
12
.029
225
18
.041
395
13
.031
250
19
.043
425
14
.033
285
20
.045
500
15
.035
305
21
.047
540
16
.037
340
22
.052
650
17
.039
360
'
These strengths range from 300,000 to 340,000 Ibs. per sq. in. The compo-
sition of this wire is as follows: Carbon, 0.570; silicon, 0.090; sulphur, C Oil;
phosphorus, 0.018; manganese, 0.425.
" PLOUGH "-STEEI, 1¥IRE.
The term "plough," given in England to steel wire of high quality, was
derived from the fact that such wire is used for the construction of ropes
used for ploughing purposes. It is to be hoped that the term will not be
Tised in this country, as it tends to confusion of terms. Plough-steel is
known here in some steel- works as the quality of plate steel used for the
mould-boards of ploughs, for which a very ordinary grade is good enough.
Experiments by Dr. Percy on the English plough-steel (so-called) gave the
following results: Specific gravity, 7.814; carbon, 0.828 per cent; manga-
nese, 0.587 per cent; silicon, 0.143 per cent; sulphur, 0.009 percent; phos-
phorus, nil; copper, 0.030 per cent. No traces of chromium, titanium, or
tungsten were found. The breaking strains of the wire were as follows:
Diameter, inch 093 .132 .159 .191
Pounds per sq. inch 344,960 257,600 224,000 201,600
The elongation was only from 0.75 to 1.1 per cent.
SPECIFICATIONS FOR HARD-DRAWH COPPER WIRE. 225
WIRES OF DIFFERENT METALS AND ALLOYS.
(J. Bucknall Smith's Treatise oil Wire.)
Brass "Wire is commonly composed of an alloy of 1 3/4 to 2 parts of
copper to 1 part of zinc. The tensile strength ranges from 20 to 40 tons per
square inch, increasing with the percentage of zinc in the alloy.
German or Nickel Silver, an alloy of copper, zinc, and nickel, ia
practically brass whitened by the addition of nickel. It has been drawn into
-wire as fine as .002" diam.
Platinum wire may be drawn into the finest sizes. On account of its
high price its use is practically confined to special scientific instruments and
electrical appliances in which resistances to high temperature, oxygen, and
acids are essential. It expands less than other metals when heated, which
property permits its being- sealed in glass without fear of cracking. It is
therefore used in incandescent electric lamps.
Phosphor-bronze Wire contains from 2 to 6 per cent of tin and
from 1/20 to 1/8 per cent of phosphorus. The presence of phosphorus is
detrimental to electric conductivity.
" Delta-metal " wire is made from an alloy of copper, iron, and zinc.
Its strength ranges from 45 to 62 tons per square inch. It is used for some
Mnds of wire rope, also for wire gauze. It is not subject to deposits of ver-
digris. It has great toughness, even when its tensile strength is over 80
tons per square inch.
Aluminum Wire. — Specific gravity .268. Tensile strength only
about 10 tons per square inch. It has been drawn as fine as 11,400 yards to
the ounce, or .042 grains per yard,
Aluminum Bronze, 90 copper, 10 aluminum, has high strength and
ductility; is inoxidizable, sonorous. Its electric conductivity is 12.6 percent.
Silicon Bronze, patented in 1882 by L. Weiler of Paris, is made as
follows : Fluosilicate or potash, pounded glass, chloride of sodium and cal-
cium, carbonate of soda and lime, are heated in a plumbago crucible, and
after the reaction takes place the contents are thrown into the molten
bronze to be treated. Silicon-bronze wire has a conductivity of from 40 to
98 per cent of that of copper wire and four times more than that of iron,
while its tensile strength is nearly that of steel, or 28 to 55 tons per square
inch of section. The conductivity decreases as the tensile strength in-
creases. Wire whose conductivity equals 95 per cent of that of pure copper
gives a tensile strength of 28 tons per square inch, but when its conductivity
is 34 per cent of pure copper, its strength is 50 tons per square inch. It is
being largely used for telegraph wires. It has great resistance to oxidation.
Ordinary Drawn and Annealed Copper Wire has a strength
of from 15 to 20 tons per square inch,
SPECIFICATIONS FOR HARD-DRAWN COPPER
WIRE.
The British Post Office authorities require that hard-drawn copper wire
supplied to them shall be of the lengths, sizes, weights, strengths, and con-
ductivities as set forth in the annexed table.
Weight per Statute
Mile.
Approximate Equiva-
lent Diameter.
!
*l
ill
43 «-
wl
a»
1^
gs
gCO
I.S
G CQ
:imum Re
ice per Mi
ire (when
60° Fahr.
5 8 g
J> ij.H
^E£
ill
11
3.3
cr1 fl
a
a
I
1
1
I
a
1
|
|
I|
a
i
1
m
a
OQ
&
S
§
%
d
a
§1
3 ti& 08
rt
p*
Ibs.
Ibs.
Ibs.
mils.
mils.
mils.
Ibs.
ohms.
Ibs.
100
97^
10^^>
79
78
80
330
30
9.10
50
150
1461^
153M
97
95^
98
490
25
6.05
50
200
195
205
112
110^
113J4
650
20
4.53
50
400
390
410
158
155X8
160^
1300
10
2.27
50
226
, MATERIALS.
WIRE ROPES.
List adopted by manufacturers in 1892. See pamphlets of John A.
Roebling's Sons Co., Trenton Iron Co., and other makers,
Pliable Hoisting Rope,
With 6 strands of 19 wires each.
IRON.
Trade Number.
q
Circumference in
inched
Weight per foot in
pounds. Rope
with Hemp Cen-
tre.
Breaking Strain,
tons of 2000 Ibs.
Proper Working
Load in tons of
2000 Ibs.
Circumference of
new Manila
Rope of equal
Strength.
Min. Size of Drum
[ or Sheave in- feet.j
1
SM
6%
8.00
74
15
14
13
2
2
6
6.30
65
13
13
12
3
1%
5^
5.25
54
11
12
10
4
1%
5
4.10
44
9
11
8J4
5
Jl^
4M
8.65
39
8
10
5^
1%
4%
3.00
33
6*4
7
6
1/4
4
2.50
27
5^
8*2
6^
7
i/ij
3^
2.00
20
4
7/^
6
8
l
1.58
16
8
6^
5M
9
2M
1.20
11.50
2^3
5V<2
XIX
10
'M
2!4
0.88
8.64
m
494
4
10M
%
2
0.60
5.13
m
lOJ'i
9-16
1^
0.48
4.27
%
v%
25^
10%
H
]i,^
0.39
3.48
H
3
2M
10a
7-16
3%
0.29
3.00
n
2%
2
10%
%
1J4
0.23
2.50
*
2^
1&
CAST STEEL.
1
2J4
6M
8.00
155
31
8U
2
2
6
6.30
125
25
8
3
5V£
5.25
106
21
714
4
^1
5^
4.10
86
17
15
5
/^3
4%
3.65
77
15
14
5%
5^
%
4%
3.00
63
12
13
5^
6
/4
4
2.50
52
10
12
5
7
1£
3^
2.00
42
8
11
4^
8
3^/
1.58
33
6
9^
4
9
%
2%
1.20
25
5
w*
3^
10
%
2*4
0.88
18
3^
7
3
10)4
%
2
0.60
12
gi^j
5^
2H
1014
9-16
1%
0.48
9
1M
5
1%
10%
^
1^
0.39
7
ip
4^j
\\£
10a
7-16
^%
0.29
5^
3%
j^4
10%
%
1M
0.23
4H
%
«
1
Cable-Traction Ropes.
According to English practice, cable-traction ropes, of about 3^ in. in
circumference, are commonly constructed with six strands of seven or fif-
teen wires, the lays in the strands varying from, say. 3 in. to 3^ in., and the
lays in the ropes from, say, 7^ in. to 9 in. In the United States, however,
strands of nineteen wires are generally preferred, as being more flexible;
but, on the other hand, the smaller external wires wear out more rapidly.
The Market-street Street Railway Company, San Francisco, has used ropes
1J4 in. in diameter, composed of six strands of nineteen steel wires, weighing
2^ Ibs. per foot, the longest continuous length being 24,125 ft. The Chicago
City Railroad Company has employed cables of identical construction, the
longest length being 27,700 ft. On the New York and Brooklyn Bridge cable-
railway steel ropes of 11,500 ft.* long, containing 114 wires, have been used.
WIRE ROPES.
227
Transmission and Standing Rope.
With 6 strands of 7 wires each.
IRON.
.2® •
•£ Q.S
a
O
11
i
i
° ^O
0*0 S
^8
11
s 1
§lld
^.s
O 1)
fc
®
u
-M
<t>
«M
a
jfl
bJC^
1!
l*£
II
cc,a
1
s
1
fill
M
w*3
|ll
Jill
^
i°
11
Lj
4%
3.37
36
9
10
13
12
13
ft
4%
4
8.77
2.28
30
25
pi
9
12
14
/^2
31^
1.82
20
5
71^2
9^
15
31^
1.50
16
4
6J^
8^
16
%
2%
1.12
12.3
3
5%
7^
17
18
11^16
^
0.92
0.70
8.8
7.6
1^
Si
6 4
19
%
2
0.57
5.8
JL^
4
5^4
20
9-16
Ja^
0.41
4.1
1
21
Ji
J1Z
0.31
2.83
2%
4
22
7-16
1%
0.23
2.13
Hi
31^
3^4
23
8^
1 V<<
0.21
1.65
O1/J
03/f
24
5-16
1
0.16
1.38
2
2V^
25
9-32
0.125
1.03
1%
2V4
CAST STEEL.
11
1^
m
3.37
62
13
13
8^
12
1%
4%
2.77
52
10
12
8
13
1^4
4
2.28
44
9
11
14
31^
1.82
36
7L£
10
6/4
15
1
31^
1.50
30
6
9
5%
16
%
2-M
1.12
22
4/^
8
5
17
18
!«
2^
0.92
0.70
17
14
3 2
7
6
19
%
2 8
0.57
11
2*4
3V£
20
9-16
1%
0.41
8
1%
4^4
3
21
i^
JL/
0.31
6
ji^
4
22
7-16
1%
0.23
4^
1/4
31^
2^j
23
1^4
0.21
4
1
3/>4
2/V
24
5-16
j
0.16
3
•^
2M
1^<
25
9-32
%
0.12
2
*!
2^
3i
Plough-Steel Rope.
Wire ropes of very high tensile strength, which are ordinarily called
"Plough-steel Ropes," are made of a high grade of crucible steel, which,
when put in the form of wire, will bear a strain of from 100 to 150 tons per
square inch.
Where it is necessary to use very long or very heavy ropes, a reduction of
the dead weight of ropes becomes a matter of serious consideration.
It is advisable to reduce all bends to a minimum, and to use somewhat
larger drums or sheaves than are suitable for an ordinary crucible rope hav
ing a strength of 60 to 80 tons per square inch. Before using Plough-stee
Ropes it is best to have advice on the subject of adaptability.
228
MATERIALS.
Plough-Steel Rope.
With 6 strands of 19 wires each.
Trade
Number.
Diameter in
inches.
Weight pel-
foot in
pounds.
Breaking
Strain in
tons of
2000 Ibs.
Proper Work-
ing Load.
Min. Size of
Drum or
Sheave in
feet.
1
®&
8.00
240
46
9
2
2 \
6.30
189
37
8
3
l«^v
5.25
157
31
7J4
4
%
4.10
123
25
6
5
^
3.65
110
22
51^8
5^
%
3.00
90
18
5J4
8
J4
2.50
75
15
5
7
iHj
2.00
60
12
4^
8
1
1.58
47
9
4J4
9
%
1.20
37
7
3-M
10
%
0.88
27
5
SH
10M
7»
0.60
18
m
3
10^
9-16
0.44
13
2U
2^
10%
M
0.39
10
2^
2
With 7 Wires to the Strand.
15
1
1.50
45
9
%
16
7^
1.12
33
6^
5
17
18
11-16
0.92
0.70
25
21
5
4
4
3^
19
%
0.57
16
3%
3
20
9-16
0.41
12
2M
21
K
0.31
9
1%
2^2
22
7-16
0.23
5
IV
2
23
%
0.21
4
1
1^
Galvanized Iron Wire Rope.
For Ships' Rigging and Guys for Derricks.
CHARCOAL ROPE.
Circum-
ference
in inches.
Weight
per Fath-
om in
pounds.
Cir. of
new
Manila
Rope of
equal
Strength.
Break-
ing
Strain
in tons
of 2000
pounds
43
40
35
33
30
26
23
20
16
14
12
10
Circum-
ference
in inches
Weight
per
Fathom
Cir. of
new
Manila
Rope of
pounds. j£&$QL
Break-
ing
Strain
in tons
of 2000
pounds
WIRE ROPES.
229
Galvanized Cast-steel Yacht Rigging.
Circum-
ference
in inches.
Weight
per Fath-
om in
pounds.
Cir. of
new
Manilla
Rope of
equal
Strength.
Break-
ing
Strain
in tons
of 2000
pounds
Circum-
ference
in inches
Weight
per
Fathom
in
pounds.
Cir. of
new
Manilla
Rope of
equal
Strength.
Break-
ing
Strain
in tons
of 2000
pounds
fa
%&
O1/
2*4
«M
T
4$
13
11
y^
8H
8
7
66
43
32
27
22
18
2
VA
i
2 2
1%
%
3 4
14
10
8
Steel Hawsers.
For Mooring, Sea, and Lake Towing.
Size of
Size of
Circumfer-
Breaking
Manilla Haw-
Circumfer-
Breaking
Manilla Haw-
ence.
Strength.
ser of equal
Strength.
ence.
Strength.
ser of equal
Strength.
Inches.
Tons.
Inches.
Inches.
Tons.
Inches.
2^
15
6^
3^
29
• 9
2%
18
7
4
35
10
3
22
8^
Steel Flat Ropes.
(J. A. Roebling's Sons Co.)
Steel-wire Flat Ropes are composed of a number of strands, alternately
twisted to the right and left, laid alongside of each other, and sewed together
with soft iron wires, These ropes are use'd at times in place of round ropes
in the shafts of mines. They wind upon themselves on a narrow winding-
drum, which takes up less room than one necessary for a round rope. The
Soft-iron sewing-wires wear out sooner than the steel strands, and then it
becomes necessary to sew the rope with new iron wires.
Width and
Thickness
in inches.
Weight per
foot in
pounds.
Strength in
pounds.
Width and
Thickness
in inches.
Weight per
foot in
pounds.
Strength in
pounds.
%x2
1.19
35,700
1^x3
2.38
71,400
%x2}4
1.86
55,800
^x3VS
2.97
89,000
%x3
2.00
60,000
^x4
3.30
99,000
%x3J^
2.50
75,000
^x4^
4.00
120,000
%x4
2.86
85,800
}^x 5
4.27
128,000
%x4J4
3.12
93,600
^x5^
4.82
144,600
%x5
3.40
100,000
1^x6
5.10
153,000
%x5^
3.90
110,000
1^x7
5.90
177,000
For safe working load allow from one fifth to one seventh of the breaking
stress.
" Lang I*ay « Rope.
In wire rope, as ordinarily made, the component strands are laid up into
rope in a direction opposite to that in which the wires are laid into strands;
that is, if the wires in the strands are laid from right to left, the strands are
laid into rope from left to right. In the " Lang Lay," sometimes known as
01 Universal Lay," the wires are laid into strands and the strands into rope
in the same direction ; that is, if the wire is laid in the strands from right to
left, the strands are also laid into rope from right to left. Its use has been
found desirable under certain conditions and for certain purposes, mostly
for haulage plants, inclined planes, and street railway cables, although it
has also been used for vertical hoists in mines, etc. Its advantages are that
230
MATERIALS.
GALVANIZED STEEL CABLES*
For Suspension Bridges. (Roebling's.)
220
200
180
13
11.3
10
2
m
t
II
3 v
il
155
110
100
8.64
6.5
5.8
il
95
75
65
5.6
4 35
3.7
COMPARATIVE STRENGTHS OF FLEXIBLE GAL-
VANIZED STEEL-WIRE HAWSERS,
With Chain Cable, Tarred Russian Hemp, and White
Manila Ropes.
Patent Flexible
Steel-wire Hawsers
and Cables.
Chain Cable.
Tarred Rus-
sian Hemp
Rope.
White
Manilla
Ropes.
5K»
11
7
9
12
15
IS
22
20
33
39
64
74
88
102
116
130
150
9-16
10-16
11-16
12-16
13-16
15-16
1 17-32
166
1' 15-16 204
2 1-16
2
3-16 256
5-16 280
14
21
30 101
35
4815'
54
68
112
1434
23!
1
02
"o
2
PH
£
I
107 1-10
12014
134^
51
35^62
42 -"
22%
NOTE.— This is an old table, and its authority is uncertain. The figures in
the fourth column are probably much too small for durability.
WIRE ROPES. 231
it is somewhat more flexible than rope of the same diameter and composed
of the same number of wi^es laid up in the ordinary manner; and (especi-
ally) that owing to the fact that the wires are laid more axially in the rope,
longer surfaces of the wire are exposed to wear, and the endurance of the
rope is thereby increased. (Trenton Iron Co.)
Notes on the Use of Wire Rope.
(J. A. Koebling's Sons Co.)
Several kinds of wire rope are manufactured. The most pliable variety
contains nineteen wires in the strand, and is generally used for hoisting and
running rope. The ropes with twelve wires and seven wires in the strand
are stiffer, and are better adapted for standing rope, guys, and rigging. Or-
ders should state the use of the rope, and advice will be given. Ropes are
made up to three inches in diameter, upon application.
For safe working load, allow one fifth to one seventh of the ultimate
strength, according to speed, so as to get good wear from the rope. When
substituting wire rope for hemp rope, it is good economy to allow for the
former the same weight per foot which experience has approved for the
latter.
Wire rope is as pliable as new hemp rope of the same strength; the for-
mer will therefore run over the same-sized sheaves and pulleys as the latter.
But the greater the diameter of the sheaves, pulleys, or drums, the longer
wire rope will last. The minimum size of drum is given in the table.
Experience has demonstrated that the wear increases with the speed. It
is, therefore, better to increase the load than the speed.
Wire rope is manufactured either wilh a wire or a hemp centre. The lat-
ter is more pliable than the former, and will wear better where there is
short bending. Orders should specify what kind of centre is wanted.
Wire rope must not be coiled or uncoiled like hemp rope.
When mounted on a reel, the latter should be mounted on a spindle or flat
turn-table to pay off the rope. When forwarded in a small coil, without reel,
roll it over the ground like a wheel, and run off the rope in that way. All
untwisting or kinking must be avoided.
To preserve wire rope, apply raw linseed-oil with a piece of sheepskin,
wool inside; or mix the oil with equal parts of Spanish brown or lamp-black.
To preserve wire rope under water or under ground, take mineral or vege-
table tar, and add one bushel of fresh-slacked lime to one barrel 9f tar,
which will neutralize the acid. Boil it well, and saturate the rope with the
hot tar. To give the mixture body, add some sawdust.
The grooves of cast-iron pulleys and sheaves should be filled with well-
seasoned blocks of hard wood, set on end, to be renewed when worn out.
This end-wood will save wear and increase adhesion. The smaller pulleys
or rollers which support the ropes on inclined planes should be constructed
on the same plan. When large sheaves run with very great velocity, the
grooves should be lined with leather, set on end, or with India rubber. This
is done in the case of sheaves used in the transmission of power between
distant points by means of rope, which frequently runs at the rate of 4000
feet per minute.
Steel ropes are taking the place of iron ropes, where it is a special object
to combine lightness with strength.
But in substituting a steel rope for an iron running rope, the object in view
should be to gain an increased wear from the rope rather than to reduce the
size.
Locked \Virc Rope.
Fig. 74 shows what is known as the Patent Locked Wire Rope, made by
the Trenton Iron Co. It is claimed to wear two to three times as long as an
FIG. 74.
ordinary wire rope of equal diameter and of like material. Sizes made are
Irom y% to ly^ inches diameter.
232
MATERIALS.
CRANE .CHAINS.
(Bradlee & Co., Philadelphia.)
11 D. B. G." Special Crane.
Crane.
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be
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to
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25-32
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1932
3864
1288
1680
3300
1120
5-16
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2898
5796
1932
2520
5040
1680
%
31-32
17-10
1H
4186
8372
2790
3640
7280
2427
7-16
1 5-32
2
1%
5796
11592
3864
5040
10080
3360
Lj£
1 11-32
31^
1 11-16
7728
15456
5182
6720
13440
4480
9-16
1 15-32
3 -,'-10
1%
9660
19320
6440
8400
16800
5600
5£
1 23-32
21-16
11914
23828
7942
10360
20720
6907
11-16
1 27-32
5 8
2^4
14490
28980
9660
12600
25200
8400
H
1 31-32
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17388
34776
11592
15120
30240
10080
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40572
13524
17640
35280
11760
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8
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22484
44968
14989
20440
40880
13627
15-16
215-32
9
31-16
25872
51744
17248
23520
47040-
15680
1
2 19-32
10 7-10
3J4
29568
59136
19712
26880
53760
17920
1 1-16
2 23-32
11 2-10
35-16
33264
66538
22176
30240
60480
20160
u|
2 27-32
3-M
37576
75152
25050
34160
68320
22773
1 3-16
35-32
13 7-10
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41888
83776
27925
38080
76160
25387
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16
46200
92400
30800
42000
84000
28000
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3 31-32
21 7-10
5
66528
133056
41352
60480
120960
40320
The distance from centre of one link to centre of next is equal to the in-
side length of link, but in practice 1/32 inch is allowed for weld. This is ap-
proximate, and where exactness is required, chain should be made so.
FOR CHAIN SHEAVES. — The diameter, if possible, should be not less than
twenty times the diameter of chain used.
EXAMPLE. —For 1-inch chain use 20-inch sheaves.
WEIGHTS OF LOOS, LUMBER, ETC.
Weight of Green Logs to Scale 1,000 Feet, Board Measure.
Yellow pine (Southern). . 8,000 to 10,000 Ibs,
Norway pine (Michigan). 7,000 to 8,000 "
Whit* ninp nVTiVhi>fln J off of Stump 6,000 to 7,000 "
White pine (Michigan) ^ out Qf water _ 7,000 to 8,000 "
White pine (Pennsylvania), bark off 5,000 to 6,000 "
Hemlock (Pennsylvania), bark off 6,000 to 7,000 a
Four acres of water are required to store 1,000,000 feet of logs.
Weight of 1,OOO Feet of Lumber, Board Measure.
Yellow or Norway pine Dry, 3,000 Ibs. Green, 5.000 Ibs.
White pine 2,500 " 4,000 "
Weight of 1 Cord of Seasoned Wood, 128 CuMc Feet per
Cord.
Hickory or sugar maple 4,500 Jbs
White oak «.- 3,850 "
Beech, red oak or black oak 3,250 "
Poplar, chestnut or elm 2,350 "
Pine (white or Norway) 2,000 "
Hemlock bark, dry 2,200 "
SIZES OF FIKE-BRICK.
233
_
\
^
\
,
thick x 4^ to 4 inches
3
iam.
SIZES OF FIRE-BRICK,
9-inch straight 9 x 4^ x 2^ inches.
Soap 9 x 2J^ x 2J*j
Checker 9x3 x3 "
2-inch 9x4^x2 **
Split... 9x4
Jamb 9 x 4
No. Ikey 9x2;
wide.
113 bricks to circle 12 feet inside diam.
No.2key ... 9x2^ thick x 4^ to 3
inches wide.
63 bricks to circle 6 ft. inside diam.
No. 3 key 9x2^ thick x 4^ to
inches wide.
38 bricks to circle 3 ft. inside diam.
No. 4 key / 9x2^ thick x 4^ to 2*4
inches wide.
25 bricks to circle 1^ ft. inside diam.
No. 1 wedge (or bullhead). 9x4^ wide x 2*4 to 2 in.
thick, tapering lengthwise.
98 bricks to circle 5 ft. inside diam.
No. 2 wedge 9 x 4*4 x 2^ to 1^ in. thick.
60 bricks to circle 2J4 ft. inside diam.
No. larch.., 9x4^x2^ to 2 in. thick,
tapering breadthwise.
72 bricks to circle 4 ft. inside diam.
No.2arch 9x4^x ;_
42 bricks to circle 2 ft. inside
No. 1 skew 9 to 7 x
Bevel on one end.
No. 2 skew 9x2^x4^
Equal bevel on both edges.
No. 3skew 9x2^x4^ to
Taper on one edge.
24 inch circle 8*4 to 5J4 x 4V£ x 2>£.
Edges curved, 9 bricks line a 24-inch circle.
36-inch circle 8% to 6^ x 4J4 x 2^.
13 bricks line a 36-inch circle.
48-inch circle 8% to 7J4 x 4^ x 2J4
17 bricks line a 48-inch circle. •
inch straight 13^ x 2^ x 6.
inch key No. 1 13^ x 2^ x 6 to 5 inch.
90 bricks turn a 12-ft. circle.
13i^-inch key No. 2 13^ x 2^ x 6 to 4% inch.
52 bricks turn a 6-ft. circle.
Bridge wall, No. 1 13x6^x6.
Bridge wall, No. 2 13x6^x3.
Mill tile 18,20,or24x6x3.
Stock-hole tiles 18, 20, or 24 x 9 x 4.
18-inch block 18x9x6.
Flat back 9x6x2^.
Flat back arch 9 x 6 x 314 to 2^.
22-inch radius, 56 bricks to circle.
Locomotive tile 32 x 10 x 3.
34 x 10 x 3.
34x 8x3.
36 x 8x3.
40x10x3.
Tiles, slabs, and blocks, various sizes 12 to 30 inches
long, 8 to 30 inches wide, 2 to 6 inches thick.
, ,
Cupola brick, 4 and 6 inches high, 4 and 6 inches radial width, to line shells
23 to 66 in diameter.
A 9-inch straight brick weighs 7 Ibs. and contains 100 cubic inches. (=120
Ibs. per cubic foot. Specific gravity 1.93.)
One cubic foot of wall requires 17 9-inch bricks, one cubic yard requires
460. Where keys, wedges, and other " shapes " are used, add 10 per cent in
estimating the number required.
234
MATERIALS.
One ton of fire-clay should be sufficient to lay 3000 ordinary bricks. To
secure the best results, fire-bricks should be laid in the same clay from which
they are manufactured. It should be used as a thin paste, and not as mor-
tar. The thinner the joint the better the furnace wall. In ordering bricks
the service for which they are required should be stated.
NUMBER OF FIRE-BRICK REQUIRED FOR
VARIOUS CIRCLES.
g ®
log
ft £
KEY BRICKS.
ARCH BRICKS.
WEDGE BRICKS.
•«^
d
&
w
|
OJ
6
fc
6
ft
. I
<?*
6
ft
d
fc
OS
a
o
E-t
si
6
&
0*
£
O5
1
ft. in.
1 6
2 0
2 6
3 0
3 6
4 0
4 6
5 0
5 6
6 0
6 6
7 0
7 6
8 0
8 6
9 0
9 6
10 0
10 6
11 0
11 6
12 0
12 6
25
17
9
25
30
34
38
42
46
51
55
59
63
67
71
76
80
84
88
92
97
101
105
109
113
117
'42
31
21
10
13
25
38
32
25
19
13
6
10
21
32
42
53
63
58
52
47
42
37
31
26
21
16
11
5
9
19
29
38
47
57
66
76
85
94
104
113
113
'is'
36
54
73
42
49
57
64
72
60
48
36
24
'26'
40
59
6fl
68
76
83
91
98
106
113
121
128
136
144
151
159
166
174
181
189
196
304
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
8
15
23
30
38
45
53
60
68
75
83
90
98
105
113
121
80
87
95
102
110
117
125
132
140
147
155
162
170
177
185
193
12
79
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
"*8
15
23
30
38
46
53
61
68
76
83
91
98
106
....
....
For larger circles than 12 feet use 113 No. 1 Key, and as many 9-inch brick
as may be needed in addition.
ANALYSES OF MET. SAVAGE FIRE-CLAY.
(1)
1871
Mass.
Institute of
Technology. -,
50.457
35.904
0.133
0.018
trace
12.744
100.760
(2)
1877.
Report on
(8)
1878.
56.80
*sey
Silica
Survey of
Pennsylvania.
44.395
80.08
,. 33.558
1.15
Titanic acid
, i 530
1 12
Peroxide iron
1 080
Lime
Magnesia
0.108
0.80
Potash (alkalies).
0.247
10.50
Water and inorg.
matter. 14.575
(4)
100.450
100.493
56.15
33.295
*6".59"
0.17
0.115
'9! ',68
100.000
MAGNESIA BRICKS. 230
MAGNESIA BRICKS.
** Foreign Abstracts " of the Institution of Civil Engineers, 1893, gives a
paper by C. Bischof on the production of magnesia bricks. The material
most in favor at present is the magnesite of Styria, which, although less
pure considered as a source of magnesia than the Greek, has the property
of fritting at a high temperature without melting. The composition of the
two substances, in the natural and burnt states, is as follows:
Magnesite. Styrian. Greek.
Carbonate of magnesia 90.0 to 96.0# 94.46#
" lime 0.5 to 2.0 4.49
" " iron 3.0 to 6.0 FeO 0.08
Silica 1.0 0.52
Manganous oxide 0.5 Water 0.54
Burnt Magnesite.
Magnesia 77.6 82.46-95.36
Lime 7.3 0.83—10.92
Alumina and ferric oxide 13.0 0.56— 3.54
Silica 1.2 0.73—7.98
At a red heat magnesium carbonate is decomposed into carbonic acid and
caustic magnesia, which resembles lime in becoming hydrated and recar-
bonated when exposed to the air, and possesses a certain plasticity, so that
it can be moulded when subjected to a heavy pressure. By long-continued
or stronger heating the material becomes dead-burnt, giving a form of mag-
nesia of high density, sp. gr. 3.8, as compared with 3.0 in the plastic form,
which is unalterable in the air but devoid of plasticity. A mixture of two
volumes of dead-burnt with one of plastic magnesia can be moulded into
bricks which contract but little in firing. Other binding materials that have
been used are: clay up to 10 or 15 per cent; gas -tar, perfectly freed from
water, soda, silica, vinegar as a solution of magnesium acetate which is
readily decomposed by heat, and carbolates of alkalies or lime. Among
magnesium compounds a weak solution of magnesium chloride may also be
used. For setting the bricks lightly burnt, caustic magnesia, with a small
proportion of silica to render it less refractory, is recommended. The
strength of the bricks may be increased by adding iron, either as oxide or
silicate. If a porous product is required, sawdust or starch may be added
to the mixture. When dead-burnt magnesia is used alone, soda is said to be
the best binding material.
See also papers by A. E. Hunt, Trans. A. I. M. E., xvi, 720, and by T. Egles-
ton, Trans. A. I. M. E., xiv, 458.
Asbestos.— J. T. Donald, Eng. and M. Jour., June 27, 1891.
ANALYSIS.
Canadian.
Italian. Broughton. Templeton.
Silica 40.30# 40.57£ 40.52£
Magnesia 43.37 41.50 42.05
Ferrous oxide 87 2.81 1.97
Alumina 2.27 .90 2.10
Water 13.72 13.55 13.46
100.53 99.33 100.10
Chemical analysis throws light upon an important point in connection
with asbestos, i.e., the cause of the harshness of the fibre of some varieties.
Asbestos is principally a hydrous silicate of magnesia, i.e., silicate of mag-
nesia combined with water. When harsh fibre is analyzed it is found to
contain less water than the soft fibre. In fibre of very fine quality from
Black Lake analysis showed 14.38$ of water, while a harsh-fibred sample
gave only 11.70#. If soft fibre be heated to a temperature that will drive off
a portion of the combined water, there results a substance so brittle that it
may be crumbled between thumb and finger. There is evidently some con-
nection between the consistency of the fibre and the amount of water in its
composition.
236 STRENGTH OF MATERIALS.
STRENGTH OP MATERIALS.
Stress and Strain.— There is much confusion among writers on
strength of materials as to the definition of these terms. An external force
applied to a body, so as to pull it apart, is resisted by an internal force, or
resistance, and the action of these forces causes a displacement of the mole-
cules, or deformation. By some writers the external force is called a stress,
and the internal force a strain; others call the external force a strain, and
the internal force a stress: this confusion of terms is not of importance, as
the words stress and strain are quite commonly used synonymously, but the
use of the word strain to mean molecular displacement, deformation, or dis-
tortion, as is the custom of some, is a corruption of the language. See En-
gineering News, June 23, 1892. Definitions by leading authorities are given
below.
Stress.— A stress is a force which acts in the interior of a body, and re-
sists the external forces which tend to change its shape. A deformation is
the amount of change of shape of a body caused by the stress. The word
strain is often used as synonymous with stress and sometimes it is also used
to designate the deformation. (Merriman.)
The force by which the molecules of a body resist a strain at any point is
called the stress at that point.
The summation of the displacements of the molecules of a body for a
given point is called the distortion or strain at the point considered. (Burr).
Stresses are the forces which are applied to bodies to bring into action
their elastic and cohesive properties. These forces cause alterations of the
forms of the bodies upon which they act. Strain is a name given to the
kind of alteration produced by the stresses. The distinction between stress
and strain is not always observed, one being used for the other. (Wood.)
Stresses are of different kinds, viz. : tensile, compressive, transverse, tor-
sional, and shearing stresses.
A tensile stress, or pull, is a force tending to elongate a piece. A com-
pressive stress, or push, is a force tending to shorten it. A transverse stress
tends to bend it. A torsional stress tends to twist it. A shearing stress
tends to force one part of it to slide over the adjacent part.
Tensile, compressive, and shearing stresses are called simple stresses.
Transverse stress is compounded of tensile and compressive stresses, and
torsional of tensile and shearing stresses.
To these five varieties of stresses might be added tearing stress, which is
either tensile or shearing, but in which the resistance of different portions
of the material are brought into play in detail, or one after the other, in-
stead of simultaneously, as in the simple stresses.
Effects of Stresses.— The following general laws for cases of simple
tension or compression have been established by experiment. (Merriman):
1. When a small stress is applied to a body, a small deformation is pro-
duced, and on the removal of the stress the body springs back to its original
form. For small stresses, then, materials may be regarded as perfectly
elastic.
2. Under small stresses the deformations are approximately proportional
to the forces or stresses which produce them, and also approximately pro-
portional to the length of the bar or body.
3. When the stress is great enough a deformation is produced which is
partly permanent, that is, the body does not spring back entirely to its
original form on removal of the stress. This permanent part is termed a
set. In such cases the deformations are not proportional to the stress.
4. When the stress is greater still the deformation rapidly increases and
the body finally ruptures.
5. A sudden stress, or shock, is more injurious than a steady stress or than
a stress gradually applied.
Elastic Limit.— The elastic limit is defined as that point at which the
deformations cease to be proportional to the stresses, or, the point at which
the rate of stretch (or other deformation) begins to increase. It is also
defined as the point at which the first permanent set becomes visible. The
last definition is not considered as good as the first, as it is found that with
some materials a set occurs with any load, no matter how small, and that
with others a set which might be called permanent vanishes with lapse of
time, and as it is impossible to get the point of first set without removing
STRESS AKD STRAIN. 237
the whole load after each increase of load, which is frequently inconvenient.
The elastic limit, defined, however, as the point at which the extensions be-
gin to increase at a higher ratio than the applied stresses, usually corresponds
very nearly with the point of first measurable permanent set.
Apparent Elastic lamit.— Prof. J. B. Johnson (Materials of Con-
struction, p. 19) defines the " apparent elastic limit " as "the point on the
stress diagram [a plotted diagram in which the ordinates represent loads
and the abscissas the corresponding elongations] at which the rate of de-
formation is 50$ greater than it is at the origin," [the minimum rate]. An
equivalent definition, proposed by the author, is that point at which the
modulus of extension (length X increment of load per unit of section H- in-
crement of elongation) is two thirds of the maximum. For steel, with a
modulus of elasticity of 30,000,000, this is equivalent to that point at which
the increase of elongation in an 8-inch specimen for 1000 Ibs. per sq. in.
increase of load is 0.0004 in.
Yield-point.— The term yield-point has recently been introduced into
the literature of the strength of materials. It is defined as that point at
which the rate of stretch suddenly increases rapidly. The difference be-
tween the elastic limit, strictly defined as the point at which the rate of
stretch begins to increase, and the yield-point, at which the rate increases
suddenly, may in some cases be considerable. This difference, however, will
not be discovered in short test-pieces unless the readings of elongations are
made by an exceedingly fine instrument, as a micrometer reading to
of an inch. In using a coarser instrument, such as calipers reading to 1/100
of an inch, the elastic limit and the yield-point will appear to be simultane-
ous. Unfortunately for precision of language, the term yield-point was not
introduced until long after the term elastic limit had been almost univer-
sally adopted to signify the same physical fact which is now defined by the
term yield-point, that is, not the point at which the first change in rate,
observable tnly by a microscope, occurs, but that later point (more or less
indefinite as to its precise position) at which the increase is great enough to
be seen by the naked eye. A most convenient method of determining the
point at which a sudden increase of rate of stretch occurs in short speci-
mens, when a testing-machine in which the pulling is done by screws is
used, is to note the weight on the beam at the instant that the beam " drops.'1
During the earlier portion of the test, as the extension is steadily increased
by the uniform but slow rotation of the screws, the poise is moved steadily
along the beam to keep it in equipoise; suddenly a point is reached at which
the beam drops, and will not rise until the elongation has been considerably
increased by the further rotation of the screws, the advancing of the poise
meanwhile being suspended. This point corresponds practically to the point
at which the rate of elongation suddenly increases, and to the point at
which an appreciable permanent set is first found. It is also the point which
has hitherto been called in practice and in text-books the elastic limit, and
it will probably continue to be so called, although the use of the newer term
"yield-point" for it, and the restriction of the term elastic limit to mean
the earlier point at which the rate of stretch begins to increase, as determin-
able only by micrometric measurements, is more precise and scientific.
In tables of strength of materials hereafter given, the term elastic limit is
used in its customary meaning, tue point at which the rate of stress has be-
gun to increase, as observable by ordinary instruments or by the drop of
the beam. With this definition it is practically synonymous with yield-
point.
Coefficient (or Modulus) of Elasticity.— This is a term express-
ing the relation between the amount of extension or compression of a mate-
rial and the load producing that extension or compression.
It is defined as the load per unit of section divided by the extension per
uuit of length.
Let P be the applied load, fc the sectional area of the piece, I the length of
the part extended, A the amount of the extension, and E the coefficient of
elasticity. Then P -f- fc = the load on a unit of section ; A -*- 1 = the elonga-
tion of a unit of length.
The coefficient of elasticity is sometimes defined as the figure expressing
the load which would be necessary to elongate a piece of one square inch
section to double its original length, provided the piece would not break, and
the ratio of extension to the force producing it remained constant. This
definition follows from the formula above given, thus: If fcssoiie square
inch, I and t- each = one inch, then E •=• P.
Within the elastic limit, when the deformations are proportional to the
238 STRENGTH OF MATERIALS.
stresses, the coefficient of elasticity is constant, but beyond the el&stic limit
it decreases rapidly.
In cast iron there is generally no apparent limit of elasticity, the deforma-
tions increasing at a faster rate than the stresses, and a permanent set being
produced by small loads. The coefficient of elasticity therefore is not con-
stant during any portion of a test, but grows smaller as the load increases.
The same is true in the case of timber. In wrought iron and steel, however,
there is a well-defined elastic limit, and the coefficient of elasticity within
that limit is nearly constant.
Resilience, or Work of Resistance of a Material.— Within
the elastic limit, the resistance increasing uniformly from zero stress to the
stress at the elastic limit, the work done by a load applied gradually is equal
to one half the product of the final stress by the extension or other deforma-
tion. Beyond the elastic limit, the extensions increasing more rapidly than
the loads, and the strain diagram approximating a parabolic form, the work
is approximately equal to two thirds the product of the maximum stress by
the extension.
The amount of work required to break a bar, measured usually in inch-
pounds, is called its resilience; the work required to strain it to the elastic
limit is called its elastic resilience. (See page 270.)
Under a load applied suddenly the momentary elastic distortion is equal
to twice that caused by the same load applied gradually.
When a solid material is exposed to percussive stress, as when a weight
falls upon a beam transversely, the work of resistance is measured by the
product of the weight into the total fall.
Elevation of Ultimate Resistance and Elastic Limit.— It
was first observed by Prof. R. H. Thurstqn, and Commander L. A. Beards«
lee, U. S. N., independently, in 1873, that if wrought iron be subjected to a
stress beyond its elastic limit, but not beyond its ultimate resistance, and
then allowed to "rest" for a definite interval of time, a considerable in-
crease of elastic limit and ultimate resistance may be experienced. In other
words, the application of stress and subsequent '* rest " increases the resist-
ance of wrought iron.
This " rest " may be an entire release from stress or a simple holding the
test-piece at a given intensity of stress.
Commander Beardslee prepared twelve specimens and subjected them to
an intensity of stress equal to the ultimate resistance of the material, with-
out breaking the specimens. These were then allowed to rest, entirely free
from stress, from 24 to 30 hours, after which period they were again stressed
until broken. The gain in ultimate resistance by the rest was found to vary
from 4.4 to 17 per cent.
This elevation of elastic and ultimate resistance appears to be peculiar to
iron and steel: it has not been found in other metals.
Relation of tlie Elastic Limit to Endurance under Re-
peated Stresses (condensed from Engineering, August 7, 1891).—
When engineers first began to test materials, it was soon recognized that
if a specimen was loaded beyond a certain point it did not recover its origi-
nal dimensions on removing the load, but took a permanent set; this point
was called the elastic limit. Since below this point a bar appeared to recover
completely its original form and dimensions on removing the load, it ap»
peared obvious that it had not been injured by the load, and hence the work-
ing load might be deduced from the elastic limit by using a small factor of
safety.
Experience showed, however, that in many cases a bar would not carry
safely a stress anywhere near the elastic limit of the material as determined
by these experiments, and the whole theory of any connection between the
elastic limit of a bar and its working load became almost discredited, and
engineers employed the ultimate strength only in deducing the safe working
load to which their structures might be subjected. Still, as experience accu-
mulated it was observed that a higher factor of safety was required for a live
load than for a dead one.
In 1871 Wohler published the results of a number of experiments on bars
of iron and steel subjected to live loads. In these experiments the stresses
were put on and removed from the specimens without impact, but it was,
nevertheless, found that the breaking stress of the materials was in every
case much below the statical breaking load. Thus, a bar of Krupp's axle
steel having a tenacity of 49 tons per square inch broke with a stress of 28.6
tons per square inch, when the load was completely removed and replaced
without impact 170,000 times. These experiments were made on a large
STRESS AXD STKAIS7 239
number Of different brands of iron and steel, and the results were concor-
dant in showing that a bar would break with an alternating stress of only,
say, one third the statical breaking strength of the material, if the repetitions
of stress were sufficiently numerous. At the same time, however, it ap-
peared from the general trend of the experiments that a bar would stand an
indefinite number of alternations of stress, provided the stress was kept
below the limit.
Prof. Bauschinger defines the elastic limit as the point at which stress
ceases to be sensibly proportional to strain, the latter being measured with
a mirror apparatus reading to r^th of a millimetre, or about </vinnA in.
OUUU lUUUUU
This limit is always below the yield-point, and may on occasion be zero. On
loading a bar above the yield-point, this point rises with the stress, and the
rise continues for weeks, months, and possibly for years if the bar is left at
resl under its load. On the other hand, when a bar is loaded beyond its true
elastic limit, but below its 3;ield-point, this limit rises, but reaches a maxi-
mum as the yield-point, is approached, and then falls rapidly^ reaching even
to zero. On leaving the bar at rest under a stress exceeding that of its
primitive breaking-down point the elastic limit begins to rise again, and
may, if left a sufficient time, rise to a point much exceeding its previous
value.
This property of the elastic limit of changing with the history of a bar has
done more to discredit it than anything else, nevertheless it now seems as if
it, owing to this very property, were once more to take its former place in
the estimation of engineers, and this time with fixity of tenure. It had long
been known that the limit of elasticity might be raised, as we have said, to
almost any point within the breaking load of a bar. Thus, in some experi-
ments by Professor Styffe, the elastic limit of a puddled-steel bar was raised
16,000 Ibs. by subjecting the bar to a load exceeding its primitive elastic
limit.
A bar has two limits of elasticity, one for tension and one for compression.
Bauschinger loaded a number of bars in tension until stress ceased to be
sensibly proportional to strain. The load was then removed and the bar
tested in compression until the elastic limit in this direction had been ex-
ceeded. This process raises the elastic limit in compression, as would be
found on testing the bar in compression a second time. In place of this,
however, it was now again tested in tension, when it was found that the
artificial raising of the limit in compression had lowered that in tension be-
low its previous value. By repeating the process of alternately testing in
tension and compression, the two limits took up points at equal distances
from the line of no load, both in tension and compression. These limits
Bauschinger calls natural elastic limits of the bar, which for wrought iron
correspond to a stress of about 8^ tons per square inch, but this is practically
the limiting load to which a bar of the same material can be strained alter-
nately in tension and compression, without breaking when the loading is
repeated sufficiently often, as determined by Wohler's method.
As received from the rolls the elastic limit of the bar in tension is above
the natural elastic limit of the bar as defined by Bauschinger, having been
artificially raised by the deformations to which it has been subjected in the
process of manufacture. Hence, when subjected to alternating stresses,
the limit in tension is immediately lowered, while that in compression is
raised until they both correspond to equal loads. Hence, in Wohler's ex-
periments, in which the bars broke at loads nominally below the elastic
limits of the material, there is every reason for concluding that the loads
' were really greater than true elastic limits of the material. This is con-
firmed by tests on the connecting-rods of engines, which of course work
under alternating stresses of equal intensity. Careful experiments on old
rods show that the elastic limit in compression is the same as that in ten-
sion, and that both are far below the tension elastic limit of the material as
received from the rolls.
The common opinion that straining a metal beyond its elastic limit injures
it appears to be untrue. It is not the mere straining of a metal beyond one
elastic limit that injures it, but the straining, many times repeated, beyond
its two elastic limits. Sir Benjamin Baker has shown that in bending a shell
plate for a boiler the metal is of necessity strained bej^ond its elastic limit,
so that stresses of as much as 7 tons to 15 tons per square inch may obtain
in it as it comes from the rolls, and unless the plate is annealed, these
stresses will still exist after it has been built into the boiler. In such a case,
however, when exposed to the additional stress due to the pressure inside
240 STRENGTH OF MATERIALS.
the boiler, the overstrained portions of the plate will relieve themselves by
stretching and taking a permanent set, so that probably after a year's work-
ing very little difference could be detected in the stresses in a plate built in-
to the boiler as it came from the bending rolls, and in one which had been
annealed, before riveting into place, and the first, in spite of its having been
strained beyond its elastic limits, and not subsequently annealed, would be
as strong as the other.
Resistance of Metals to Repeated Shocks,
More than twelve years were spent by Wohler at the instance of the Prus-
sian Government in experimenting upon the resistance of iron and steel to
repeated stresses. The results of his experiments are expressed in what is
known as Wohler's law, which is given in the following words in Dubois'S
translation of Weyrauch:
" Rupture may be caused not only by a steady load which exceeds the
carrying strength, but also by repeated applications of stresses, none of
which are equal to the carrying strength. The differences of these stresses
are measures of the disturbance of continuity, in so far as by their increase
the minimum stress which is still necessary for rupture diminishes."
A practical illustration of the meaning of the first portion of this law may
be given thus: If 50,000 pounds once applied will just break a bar of iron or
steel, a stress very much less than 50,000 pounds will break it if repeated
sufficiently often.
This is fully confirmed by the experiments of Fairbairn and Spangenberg,
as well as those of Wohler; and, as is remarked by Weyrauch, it may be
considered as a long-known result of common experience. It partially ac-
counts for what Mr. Holley has called the tl intrinsically ridiculous factor of
safety of six."
Another "long-known result of experience " is the fact that rupture may
be caused by a succession of shocks or impacts, none of which alone would
be sufficient to cause it. Iron axles, the piston-rods of steam hammers, and
other pieces of metal subject to continuously repeated shocks, invariably
break after a certain length of service. They have a "life " which is lim-
ited.
Several years ago Fairbairn wrote: *• We know that in some cases wrought
iron subjected to continuous vibration assumes a crystalline structure, and
that the cohesive powers are much deteriorated, but we are ignorant of the
causes of this change." We are still ignorant, not only of the causes of this
change, but of the conditions under which it takes place. Who knows
whether wrought iron subjected to very slight continuous vibration will en-
dure forever? or whether to insure final rupture each of the- continuous small
shocks must amount at least to a certain percentage of single heavy shock
(both measured in foot-pounds), which would cause rupture with one applica-
tion ? Wohler found in testing iron by repeated stresses (not impacts) that
in one case 400,000 applications or a stress of 500 centners to the square inch
caused rupture, while a similar bar remained sound after 48,000,000 applica-
tions of a stress of 300 centners to the square inch (1 centner = 110.2 Ibs.).
Who knows whether or not a similar law holds true in regard to repeated
shocks ? Suppose that a bar of iron would break under a single impact of
1000 foot-pounds, how many times would it be likely to bear the repetition
of 100 foot-pounds, or would it be safe to allow it to remain for fifty years
subjected to a continual succession of blows of even 10 foot-pounds each ?
Mr. William Metcalf published in the Metallurgical Rev ieiv, Dec. 1877, the
results of some tests of the life of steel of different percentages of carbon
under impact. Some small steel pitmans were made, the specifications for .
which required that the unloaded machine should run 4J4 hours at the rate
of 1200 revolutions per minute before breaking.
The steel was all of uniform quality, except as to carbon. Here are the
results; The
.30 C. ran 1 h. 21 m. Heated and bent before breaking.
.490. ". Ih. 28m., " " " " «*
.43 C. " 4 h. 57 m. Broke without heating.
.65 C. " 3 h. 50 m. Broke at weld where imperfect.
.80 C. " 5h. 40m.
.84 C. " 18 h.
.87 C. Broke in weld near the end.
.96 C. Ran 4.55 m., and the machine broke down.
Some other experiments by Mr. Metcalf confirmed his conclusion, viz.
STRESS AKB STRAIH. 241
that high-carbon steel was better adapted to resist repeated shocks and vi-
brations than low-carbon steel.
These results, however, would scarcely be sufficient to induce any en-
gineer to use .84 carbon steel in a car-axle or a bridge-rod. Further experi-
ments are needed to confirm or overthrow them.
(See description of proposed apparatus for such an investigation in the
author's paper in Trans. A. I. M. EM vol. viii., p. 76, from which the above
extract is taken.)
Stresses Produced by Suddenly Applied Forces and
Shocks.
(Mansfield Merriman, R. R. & Eng. Jour., Dec. 1889.)
Let P be the weight which is dropped from a height h upon the end of a
bar, and let y be the maximum elongation which is produced. The work
performed by the falling weight, then, is
TF=P(fc + y),
and this must equal the internal work of the resisting molecular stresses.
The stress in the bar, which is at first 0, increases up to a certain limit Qt
which is greater than P; and if the elastic limit be not exceeded the elonga-
tion increases uniformly with the stress, so that the internal work is equaJ
to the mean stress 1/2Q multiplied by the total elongation y, or
W=l/2Qy.
Whence, neglecting the work that may be dissipated in heat,
l/2Qy=Ph + Py.
If e be the elongation due to the static load P, within the elastic limit
y— p e\ whence
........ (1)
which gives the momentary maximum stress. Substituting this value of Q,
there results
which is the value of the momentary maximum elongation.
A shock results when the force P, before its action on the bar, is moving
with velocity, as is the case when a weight P falls from a height h. The
above formulas show that this height h may be small if e is a small quan-
tity, and yet very great stresses and deformations be produced. For in-
stance, let h = 4e, then Q = 4P and y = 4e ; also let h = 12e, then Q = 6P
and y = 6 e. Or take a wrought-iron bar 1 in. square and 5 ft. long: under a
steady load of 5000 Ibs. this will be compressed about 0.012 in., supposing
that no lateral flexure occurs; but if a weight of 5000 Ibs. drops upon its end
from the small height of 0.048 in. there will be produced the stress of 20,000
Ibs.
A suddenly applied force is one which acts with the uniform intensity P
upon the end of the bar, but which has no velocity before acting upon it.
This corresponds to the case of h — 0 in the above formulas, and gives Q =s
2P and y = 2e for the maximum stress and maximum deformation. Profoi I
ably the action of a rapidly-moving train upon a bridge produces stressed
of this character.
Increasing the Tensile Strength of Iron Bars by Twist-
ing them.— Ernest L. Ransome of San Francisco has obtained an English
Patent, No. 16221 of 1888, for an " improvement in strengthening and testing
wrought metal and steel rods or bars, consisting in twisting the same in a
cold state. . . . Any defect in the lamination of the metal which would
otherwise be concealed is revealed by twisting, and imperfections are shown
at once. The treatment may be applied to bolts, suspension-rods or bars
subjected to tensile strength of any description."
Results of tests of this process were reported by Lieutenant F. P. Gilmore,
U. S. N., in a paper read before the Technical Society of the Pacific Coast,
published in the Transactions of the Society for the month of December,
1888. The experiments include inajs wuu unrty-nine bars, twenty-nine of
which were variously twisted, from three-eighths of one turn to six turns per
foot. The test-pieces were cut from one and the same bar, and accurately
242
STRENGTH OF MATERIALS.
measured and numbered. From each lot two pieces without twist were
tested for tensile strength and ductility. One group of each set was twister,
until the pieces broke, as a guide for the amount of twist to be given those
to be tested for tensile strain.
The following is the result of one set of Lieut. Gilmore's tests, on iron
bars 8 in. long, .719 in. diameter.
No. of
Bars.
Conditions.
Twists
in
Turns.
Twists
per ft.
Tensile
Strength.
Tensile
per sq. in.
Gain per
cent.
2
Not twisted.
0
0
22,000
54,180
2
Twisted cold.
^
y±
23,900
59,020
9
2
" "
1
iJ2
25,800
63,500
17
2
2
3
26,300
64,750
19
1
5
3M
26,400
65,000
20
Tests that corroborated these results were made by the University of
California in 1889 and by the Low Moor Iron Works, England, in 1890.
TENSILE STRENGTH.
The following data are usually obtained in testing by tension in a testing--
machine a sample of a material of construction :
The load and the amount of extension at the elastic limit.
The maximum load applied before rupture.
The elongation of the piece, measured between gauge-marks placed a
stated distance apart before the test; and the reduction of area at the
point of fracture.
The load at the elastic limit and the maximum load are recorded in pounds
per square inch of the original area. The elongation is recorded as a per-
centage of the stated length between the gauge-marks, and the reduction
area as a percentage of the original area. The coefficient of elasticity is cal-
culated from the ratio the extension within the elastic limit per inch of
length bears to the load per square inch producing that extension.
On account of the difficulty of making accurate measurements of the frac-
tured area of a test-piece, and of the fact that elongation is more valuable
than reduction of area as a measure of ductility and of resilience or work
of resistance before rupture, modern experimenters are abandoning the
custom of reporting reduction of area. The "strength per square inch of
fractured section " formerly frequently used in reporting tests is now almost
entirely abandoned. The data now calculated from the results of a tensile
test for commercial purposes are: 1. Tensile strength in pounds per square
inch of original area. 2. Elongation per cent of a stated length between
gauge-marks, usually 8 inches. 3. Elastic limit in pounds per square inch
of original area.
The short or grooved test specimen gives with most metals, especially
with wrought iron and steel, an appaient tensile strength much higher
than the real strength. This form of test-piece is now almost entirely aban-
doned.
The following results of the tests of six specimens from the same 1*4" steel
bar illustrate the apparent elevation of elastic limit and the changes in
other properties due to change in length of stems which were turned down
in each specimen to .798" diameter. (Jas. E. Howard, Eng. Congress 1893
Section G.)
Description of Stem.
Elastic Limit,
Lbs. per Sq. In.
Tensile Strength,
Lbs. per Sq. In.
Contraction of
Area, per cent.
1.00" long...
64,900
94,400
49.0
.50 "..... ....
65 320
97,800
43 4
68,000
102,420
39.6
Semicircular groove,
A" radius. ... ...
75 000
116,380
31.6
Semicircular groove,
%" radius
80,000, about
134,960
23.0
V-shaped groove
90,000, about
117,000
Indeterminate.
TENSILE STRENGTH.
243
Tests plate made by the author in 1879 of straight and grooved test-pieces
Of boiler-plate steel cut from the same gave the following results :
5 straight pieces, 56,605 to 59,012 Ibs. T. S. Aver. 57,566 Ibs.
4 grooved " 64,341 to 67,400 " " ** 65,452 "
Excess of the short or grooved specimen, 21 per cent, or 12,114 Ibs.
Measurement of Elongation.— In order to be able to compare
records of elongation, it is necessary not only to have a uniform length of
section between gauge-marks (say 8 inches), but to adopt a uniform method
of measuring the elongation to compensate for the difference between the
apparent elongation when the piece breaks near one of the gauge-marks,
and when it breaks midway between them. The following method is rec-
ommended (Trans. A. S. M. E., vol. xi., p. 622):
Mark on the specimen divisions of 1/2 inch each. After fracture measure
from the point of fracture the length of 8 of the marked spaces on each
fractured portion (or 7 -}- on one side and 8 -f- on the other if the fracture is
not at one of the marks). The sum of these measurements, less 8 inches, is
the elongation of 8 inches of the original length. If the fracture is so
near one end of the specimen that 7 + spaces are not left on the shorter
portion, then take the measurement of as many spaces (with the fractional
part next to the fracture) as are left, and for the spaces lacking add the
measurement of as many corresponding spaces of the longer portion as are
necessary to make the 7 + spaces.
Shapes of Specimens for Tensile Tests.— The shapes shown
in Fig. 75 were recommended by the author in 1882 when he was connected
No. 1. Square or flat bar, as
rolled.
No. 2. Round bar, as rolled.
No. 3. Standard shape for
flats or squares. Fillets %
inch radius.
No. 4. Standard shape for
rounds. Fillets J^ in. radius.
No. 5. Government, shape for
marine boiler-plates of iron.
Not recommended for other
tests, as results are generally
in error.
r* 16 Vso"
FIG. 75.
with the Pittsburgh Testing Laboratory. They are now in most general
use, the earlier forms, with 5 inches or less in length between shoulders,
being almost entirely abandoned.
Precautions Required in making Tensile Tests,— The
testing-machine itself should be tested, to determine whether its weighing
apparatus is accurate, and whether it is so made and adjusted that in the
test of a properly made specimen the line of strain of the testing-machine
is absolutely in line with the axis of the specimen.
The specimen should be so shaped that it will not give an incorrect record
of strength.
It should be of uniform minimum section for not less than five inches of
its length.
Regard must be had to the i/ira* occupied in making tests of certain mate-
rials. Wrought iron and soft steel can be made to show a higher than their
actual apparent strength by keeping them under strain for a great length
of time.
Tn testing soft alloys, copper, tin, zinc, and the like, which flow under con-
stant strain their highest apparent strength is obtained by testing them
rapidly. In recording tests or such materials the length of time occupied in
the test should be stated.
244 STRENGTH OF MATERIALS.
For very accurate measurements of elongation, corresponding to incre-
ments of load during the tests, the electric contact micrometer, described
in Trans. A. S. M. E., vol. vi., p. 479, will be found convenient. When read-
ings of elongation are then taken during the test, a strain diagram may be
plotted from the reading, which is useful in comparing the qualities of dif-
ferent specimens. Such strain diagrams are made automatically by the new
Olsen testing-machine, described in Jour. Frank. Inst. 1891.
The coefficient of elasticity should be deduced from measurement ob~
served between fixed increments of load per unit section, say between 2000
and 12,000 pounds per square inch or between 1000 and 11,000 pounds instead
of between 0 and 10,000 pounds.
COMPRESSIVE: STRENGTH.
What is meant by the term "compressive strength " has not yet been
settled by the authorities, and there exists more confusion in regard to this
term than in regard to any other used by writers on strength of materials.
The reason of this may be easily explained. The effect of a compressive
stress upon a material varies with the nature of the material, and with the
shape and size of the specimen tested. While the effect of a tensile stress is
to produce rupture or separation of particles in the direction of the line of
strain, the effect of a compressive stress on apiece of material may be either
to cause it to fly into splinters, to separate into two or more wedge-shaped
pieces and fly apart, to bulge, buckle, or bend, or to flatten out and utterly re-
sist rupture or separation of particles. A piece of speculum metal under
compressive stress will exhibit no change of appearance until rupture takes
place, and then it will fly to pieces as suddenly as if blown apart by gun-
powder. A piece of cast iron or of stone will generally split into wedge-
shaped fragments. A piece of wrought iron will buckle or bend. A piece of
wood or zinc may bulge, but its action will depend upon fts shape and si:;e.
A piece of lead will flatten out and resist compression till the last degree;
that is, the more it is compressed the greater becomes its resistance.
Air and other gaseous bodies are compressible to any extent as long as
they retain the gaseous condition. Water not confined in a vessel is com-
§ressed by its own weight to the thickness of a mere film, while when con-
ned in a vessel it is almost incompressible.
It is probable, although it has not been determined experimentally, that
solid bodies when confined are at least as incompressible as water. When
they are not confined, the effect of a compressive stress is not only to
shorten them, but also to increase their lateral dimensions or bulge them.
Lateral strains are therefore induced by compressive stresses.
The weight per square inch of original section required to produce any
given amount or percentage of shortening of any material is not a constant
quantity, but varies with both the length and the sectional area, with the
shape of this sectional area, and with the relation of the area to the length.
The " compressive strength'1 of a material, if this term be supposed to mean
the weight in pounds per square inch necessary to cause rupture, may vary
with every size and shape of specimen experimented upon. Still more diffi-
cult would it be to state what is the 4t compressive strength " of a material
which does not rupture at all, but flattens out. Suppose we are testing a
cylinder of a soft metal like lead, two inches in length and one inch in diam-
eter, a certain weight will shorten it one per cent, another weight ten per
cent, another fifty per cent, but no weight that we can place upon it will
rupture it, for it will flatten out to a thin sheet. What, then, is its compres-
sive strength ? Again, a similar cylinder of soft wrought iron would prob-
ably compress a few per cent, bulging evenly all around ; it would then com-
mence to bend, but at first the bend would be imperceptible to the eye and
too small to be measured. Soon this bend would be great enough to be
noticed, and finally the piece might be bent nearly double, or otherwise dis-
torted. What is the "compressive strength1' of this piece of iron ? Is it
the weight per square inch which compresses the piece one per cent or five
per cent, that which causes the first bending (impossible to be discovered),
or that which causes a perceptible bend ?
As showing the confusion concerning the definitions of compressive
strength, the following statements from different authorities on the strength
of wrought iron are of interest.
Wood's Resistance of Materials states, " comparatively few experiments
have been made to determine how much wrought iron will sustain at the
point of crushing. Hodgkinson gives 65,000, Rondulet 70,800, Weisbach 72,000
COMPKESSIVE STKEKGTH. 245
Rankine 30,000 to 40,000. It is generally assumed that wrought iron will resist
about two thirds as much crushing as to tension, but the experiments fail
to give a" very definite ratio."
Mr. Whipple, in his treatise on bridge-building, states that a bar of good
wrought iron will sustain a tensile strain of about 60,000 pounds per square
inch, and a compressive strain, in pieces of a length not exceeding twice the
least diameter, of about 90,000 pounds.
The following values, said to be deduced from the experiments of Major
Wade, Hodgkinson, and Capt. Meigs, are given by Haswell :
American wrought iron 127,720 Ibs.
" (mean) 85,500 "
TTnHi«h « " J 65>200 "
knglisn -j 40j00o ».
Stoney states that the strength of short pillars of any given material, all
having the same diameter, does not vary much, provided the length of the
piece is not less than one and does not exceed four or five diameters, and
that the weight which will just crush a short prism whose base equals one
square Inch, and whose height is not less than 1 to 1J^ and does not exceed
4 or 5 diameters, is called the crushing strength of the material. It would
be well if experimenters would all agree upon some such definition of the
term " crushing strength,1' and insist that all experiments which are made
for the purpose of testing the relative values of different materials in com-
pression be made on specimens of exactly the same shape and size. An
arbitrary size and shape should be assumed and agreed upon for this pur-
pose. The size mentioned by Stoney is definite as regards area of section,
viz., one square inch, but is indefinite as regards length, viz., from one to
five diameters. In some metals a specimen five diameters long would bend,
and give a much lower apparent strength than a specimen having a length of
one diameter. The words " will just crush " are also indefinite for ductile
materials, in which the resistance increases without limit If the piece tested
does not bend. In such cases the weight which causes a certain percentage
of compression, as five, ten, or fifty per cent, should be assumed as the
crushing strength.
For future experiments On crushing strength three things are desirable :
First, an arbitrary standard shape and size of test specimen for comparison
of all materials. Secondly, a standard limit of compression for ductile
materials, which shall be considered equivalent to fracture in brittle mate-
rials. Thirdly, an accurate knowledge of the relation of the crushing
strength of a specimen of standard shape and size to the crushing strength
of specimens of all other shapes and sizes. The latter can only be
secured by a very extensive and accurate series of experiments upon all
kinds of materials, and on specimens of a great number of different shapes
and sizes.
The author proposes, as a standard shape and size, for a compressive test
specimen for all metals, a cylinder one inch in length, and one half square
inch in sectional area, or 0.798 inch diameter; and for the limit of compres-
sion equivalent to fracture, ten per cent of the original length. The term
"compressive strength," or "compressive strength of standard specimen,"
would then mean the weight per square inch required to fracture by com-
pressive stress a cylinder one inch long and 0.798 inch diameter, or to
reduce its length to 0.9 inch if fracture does not take place before that reduc-
tion in length is reached. If such a standard, or any standard size whatever,
had been used by the earlier authorities on the strength of materials, we
never would have had such discrepancies in their statements in regard to
the compressive strength of wrought iron as those given above.
The reasons why this particular size is recommended are : that the sectional
area, one-half square inch, is as large as can be taken in the ordinary test-
ing-machines of 100,000 pounds capacity, to include all the ordinary metals
of construction, cast and wrought iron, and the softer steels; and that the
length, one inch, is convenient for calculation of percentage of compression.
If the length were made two inches, many materials would bend in testing,
and give incorrect results. Even in cast iron Hodgkinson found as the mean
of several experiments on various grades, tested in specimens % inch in
height, a compressive strength per square inch of 94,730 pounds, while the
mean of the same number of specimens of the same irons tested in pieces 1J£
inches in height was only 88,800 pounds. The best size and shape of standard
specimen should, however, be settled upon only after consultation and
agreement among several authorities.
246
STllEKGTH OF MATERIALS.
The Committee on Standard Tests 01 the American Society of Mechanical
Engineers say (vol. xi., p. 624) :
" Although compression tests have heretofore been made on diminutive
sample pieces, it is highly desirable that tests be also made on long pieces
from 10 to 20 diameters in length, corresponding more nearly with actual
practice, in order that elastic strain and change of shape may be determined
by using proper measuring apparatus.
The elastic limit, modulus or coefficient of elasticity, maximum and ulti-
mate resistances, should be determined, as well as the increase of section at
various points, viz., at bearing surfaces and at crippling point.
The use of long compression-test pieces is recommended, because the in-
vestigation of short cubes or cylinders has led to no direct application of
the constants obtained by their use in computation of actual structures,
which have always been and are now designed according to empirical for-
mulae obtained from a few tests of long columns."
COLUMNS, PILLARS, OR STRUTS.
Hodgkinson's Formula for Columns.
P = crushing weight in pounds; d = exterior diameter in inches; dl = in-
terior diameter in inches; L = length in feet.
Kind of Column.
Both ends rounded, the
length of the column
exceeding 15 times
its diameter.
P = 33,380
-
' = 95,850
p-
Both ends flat, the
length of the column
exceeding 30 times
its diameter.
(£3.56
>= 98,920-^
P = 99,
^-
Solid cylindrical col- )
umns of cast iron )
Hollow cylindrical col- )
umns of cast iron )
Solid cylindrical col- )
umns of wrought iron. >
Solid square pillar of \
Dantzic oak (dry) — )
Solid square pillar of )
red deal (dry) . . f
The above formulae apply only in cases in which the length is so great that
the column breaks by bending and not by simple crushing. If the column
be shorter than that given in the table, and more than four or five times its
diameter, the strength is found by the following formula :
PCK
P = 299,600-
P = 24,540^
in which P= the value given by the preceding formulae, K= the transverse
section of the column in square inches, C = the ultimate compressive resis-
tance of the material, and W = the crushing strength of the column.
Hodgkinson's experiments were made upon comparatively short columns,
the greatest length of cast-iron columns being 60^ inches, of wrought iron
90% inches.
The following are some of his conclusions:
1 In all long pillars of the same dimensions, when the force is applied m
the direction of the axis, the strength of one which has flat ends is about
three times as great as one with roun Led ends.
2 The strength of a pillar with ^ne nd rounded and the other flat is an
arithmetical mean between the two given in the preceding case of the same
dimensions.
3. The strength of a pillar having both ends firmly fixed is the same as
one of half the length with both ends rounded.
4. The strength of a pillar is not increased more than one seventh by en-
larging it at the middle.
MOMENT OF INEKTIA AND RADIUS OF GYRATION. 247
Gordon's formulae deduced from Hodgkinson's experiments are more
generally used than Hodgkinson's own. They are:
Columns with both ends fixed or flat, P = — — - ;
fs
Columns with one end flat, the other end round, P = —
' f sf
Columns with both ends round, or hinged, P = — - — -«;
~
8 = area of cross-section in inches;
P— ultimate resistance of column, in pounds;
/ = crushing strength of the material in Ibs. per square inch;
. , _ Moment of inertia
r — least radius of gyration, in inches, ?-2 = —
area of section '
I — length of column in inches;
a — a coefficient depending upon the material;
/and a are usually taken as constants; they are really empirical variables,
dependent upon the dimensions and character of the column as well as upon
the material. (Burr.)
For solid wrought-iron columns, values commonly taken are: / = 36,000 to
40,000; a = 1/36,000 to 1/40,000.
For solid cast-iron columns, / = 80,000, a = 1/6400.
80 non
For hollow cast-iron columns, fixed ends, p — - - -- , I — length and
ficients derived from Hodgkinson's experiments, for cast-iron columns is to
he deprecated. See Strength of Cast-iron Columns, pp. 250, 251.
Sir Benjamin Baker gives,
For mild steel, / = 67,000 Ibs., a = 1/22,400.
For strong steel, /= 114,000 Ibs., a = VH400
Prof. Burr considers these only loose approximations for the ultimate
resistances. See his formulae on p. 259.
For dry timber Rankine gives/ = 7200 Ibs., a = 1/3000.
MOMENT OF INERTIA AND RADIUS OF GYRATION.
The moment of inertia of a section is the sum of the products of
each elementary area of the section into the square of its distance from an
assumed axis of rotation, as the neutral axis.
The radius of gyration of the section equals the square root of the
quotient of the moment of inertia divided by the area of the section. If
E = radius of gyration, 1= moment of inertia and A — area,
The moments of inertia of various sections are as follows;
d = diameter, or outside diameter; d} = inside diameter; 6 = breadth;
h = depth; 6,, &«, inside breadth and diameter;
Solid rectangle I = l/126/i3; Hollow rectangle I = l/12(67i» - Mi3);
Solid square 7= 1/126*; Hollow square 7= 1/12(6* - 6,*);
Solid cylinder I- l/647rd4; Hollow cylinder I- l/647r(d4 - c^4).
Moments of Inertia and Radius of Gyration for Various
Sections, and their Use in the Formulas for Strength of
Girders and Columns,— The strength of sections to resist strains,
either as girders or as columns, depends not only on the area but also on the
form of the section, and the property of the section which forms the basis
of the constants used in the formulas for strength of girders and columns
to express the effect of the form, is its moment of inertia about its neutral
axis. The modulus of resistance of any section to transverse bending is its
248 STRENGTH OF MATERIALS.
moment of inertia divided by the distance from the neutral axis to the
fibres farthest removed from that axis; or
Moment of inertia „ I
= Distance of extreme fibre from axis* " y'
Moment of resistance = section modulus X unit stress on extreme fibre.
IHoment of Inertia of Compound Shapes. (Pencoyd Iron
Works.)— The moment of inertia of any section about any axis is equal to the
I about a parallel axis passing through its centre of gravity -f (the area of
the section X the square of the distance between the axes).
By this rule, the moments of inertia or radii of gyration of any single sec-
tions being known, corresponding values may be obtained for any combina-
tion of these sections.
Radius of Gyration of Compound Shapes,— In the case of a
pair of any shape without a web the value of R can always be found with-
out considering the moment of inertia.
The radius of gyration for any section around an axis parallel to another
axis passing through its centre of gravity is found as follows:
Let r = radius of gyration around axis through centre of gravity; R =t
radius of gyration around another axis parallel to above; d = distance be-
tween axes: R = Vd'* -f- r*.
When r is small, R may be taken as equal to d without material error.
Graphical Method for Finding Radius of Gyration.— Ben j.
F. La Hue, Eng. Neius, Feb. 2, 1893, gives a short graphical method for
finding the radius of gyration of hollow, cylindrical, and rectangular col-
umns, as follows:
For cylindrical columns:
Lay off to a scale of 4 (or 40) a right-angled triangle, in which the base
equals the outer diameter, and the altitude equals the inner diameter of the
column, or vice versa. The hypothenuse, measured to a scale of unity (or
10), will be the radius of gyration sought.
This depends upon the formula
'Mom, oflnertia _ ^D* + d2
Area 4
in which A = area and D = diameter of outer circle, a — area and d = dia-
meter of inner circle, and G = radius of gyration. ^D'2 -f d2 is the expres-
sion for the hypothenuse of a right-angled triangle, in which D and d are the
base and altitude.
The sectional area of a hollow round column is .7854(D2 — d2). By con-
structing a right-angled triangle in which D equals the hypothenuse and d
equals the altitude, the base will equal 4/D2 — d2. Calling the value of this
expression for the base J5, the area will equal .78541?2.
Value of G for square columns:
Lay off as before, but using a scale of 10, a right-angled triangle of whicfc
the base equals D or the side of the outer square, and the altitude equals d,
the side of the inner square. With a scale of 3 measure the hypotheuuse,
which will be, approximately, the radius of gyration.
This process for square columns gives an excess of slightly more than 4#.
By deducting 4% from the result, a close approximation will be obtained.
A very close result is also obtained by measuring the hypothenuse with
the same scale by which the base and altitude were laid off, and multiplying
by the decimal 0.29; more exactly, the decimal is 0.28867.
The formula is
This may also be applied to any rectangular column by using the lesser
diameters of an unsupported column, and the greater diameters if the col-
umn is supported in the direction of its least dimensions.
ELEMENTS OF USUAI, SECTIONS.
Moments refer to horizontal axis through centre of gravity. This table is
intended for convenient application where extreme accuracy is not impor-
tant. Some of the terms are only approximate; those marked * are correct.
Values for radius of gyration in flanged beams apply to standard minimum
sections only; A = area of section; b ^ bjeadth; h = depth; D = diameter.
ELEMENTS OF USUAL SECTIONS.
249
Shape of Section.
Moment
of Inertia.
Section
Modulus.
Square of
Least
Radius of
Gyration.
Least
Radius of
Gyration.
.._....
Solid Rect-
angle.
bh* *
12
~6~
(Least side)2*
Least side *
12
3.46
*
Hollow Rect-
angle.
6W-Mi» *
bV-bfa**
/ta _f Ttja *
MtM
JJgli
Vrb+ «
12
6/1
12
4.89
T
0
Solid Circle.
AD* *
16
AD*
8
D* *
16
"4
(*- D— 1
Hollow Circle.
A, area of
large section ;
a, area of
small section.
AD*-ad*
AD* -ad*
D2+ef2*
16
D + rf
16
SD
5.64
s
Solid Triangle.
bh*
36
bh*
24
The least of
of the two:
18 °F 24
The least of
the two:
h b
4.24 °r 4.9
Even Angle.
Ah*
10.2
Ah
7.2
b*
25
6
5
JE
Uneven Angle.
Ah*
Ah
6.5
0*"
hb
9.5
13(/i2 + 62)
2.6(71 -f 6)
H8
Even Cross.
Ah*
19
Ah
9.5
M
22.5
&
4.74
i
Even Tee.
Ah*
11.1
Ah
8
62
22.5
6
4.74
^
I Beam.
Ah*
6.66
Ah
3.2
b*
21
6
4.58
lirt^x]
Channel.
Ah*
7.34
Ah
3.67
12T5
6
3.54
111
Deck Beam.
Ah*
6.9
Ah
4
62
36.5
b
6
Distance of base from centre of gravity, solid triangle, ^; even angle, -^--
6 6.6
uneven angle, $-=; ®ven tee, ^-5? deck beam, -— ; all other shapes given in
o.o o.o 4.6
the table, ~ or — .
250 STRENGTH OF MATERIALS.
The Strength of Cast-iron Columns.
Hodgkinson's experiments (first published in Phil. Trans. Royal Socy.,
1840, and condensed in Tredgold on Cast Iron, 4th ed., 1846), and Gordon's
formula, based upon them, are still used (1898) in designing cast-iron col-
umns. That they are entirely inadequate as a basis of a practical formula
suitable to the present methods of casting columns will be evident from
what follows.
Hodgkinson's experiments were made on nine " long " pillars, about 7^
ft. long, whose external diameters ranged from 1.74 to 2.23 in., and average
thickness from 0.29 to 0.35 in., the thickness of each column also varying,
and on 18 "short " pillars, 0.733 ft. to 2.251 ft. long, with external diameters
from 1.08 to 1.26 in., all of them less than J4 in. thick. The iron used was
Low Moor, Yorkshire, No. 3, said to be a good iron, not very hard, earlier
experiments on which had given a tensile strength of 14,535 and a crushing
strength of 109,801 Ibs. per sq. in. The results of the experiments on the
" long " pillars were reduced to the equivalent breaking weight of a solid
pillar 1 in. diameter and of the same length, 714 ft., which ranged from 2969
to 3587 Ibs. per sq. in., a range of over 12 per cent, although the pillars were
made from the same iron and of nearly uniform dimensions. From the 13
experiments on " short " pillars a formula was derived, and from it were
obtained the " calculated " breaking weights, the actual breaking weights
ranging from about 8 per cent above to about 8 per cent below the calcu-
lated weights, a total range of about 16 per cent. Modern cast-iron columns,
such as are used in the construction of buildings, are very different in size,
S:oportions, and quality of iron from the slender " long" pillars used in
odgkinson's experiments. There is usually no check, by actual tests or by
disinterested inspection, upon the quality of the material. The tensile, com-
pressive, and transverse strength of cast iron varies through a great range
(the tensile strength ranging from less than 10,000 to over 40,000 Ibs. per sq.
in.), with variations in the chemical composition of the iron, according to
laws which are as yet very imperfectly understood, and with variations in
the method of melting and of casting. There is also a wide variation in the
strength of iron of the same melt when cast into bars of different thick-
nesses. It is therefore impossible to predict even approximately, from the
data given by Hodgkinson of the strength of columns of Low Moor iron in
pillars 7% ft. long, 2 in. diam., and % in. thick, what will be the strength of
a column made of American cast iron, of a quality not stated, in a column
16 ft. long, 12 or 15 in. diam., and from % in. to 1^ in. thick.
Another difficulty in obtaining a practical formula for the strength of cast-
iron columns is due to the uncertainty of the quality of the casting, and the
danger of hidden defects, such as internal stresses due to unequal cooling,
cinder or dirt, blow-holes, u cold-shuts,1' and cracks on the inner surface,
which cannot be discovered by external inspection. Variation in thick-
ness, due to rising of the core during casting, is also a common defect.
In addition to^the above theoretical or a priori objections to the use of
Gordon's formula, based on Hodgkinson's experiments, for cast-iron
columns, we have the data of recent experiments on full-sized columns,
made by the Building Department of New York City (Eng'g News, Jan. 13
and 20, 1898). Ten columns in all were tested, six 15-inch, 190J inches long,
two 8-inch, 160 inches long, and two 6-inch, 120 inches long. The tests were
made on the large hydraulic machine of the Phoenix Bridge Co., of 2,000,000
pounds capacity, which was calibrated for frictiorml error by the repeated
testing within the elastic limit of a large Phoenix column, and the compari-
son of these tests with others made on the government machine at the
Watertown Arsenal. The average frictional error was calculated to be
15.4 per cent, but Engineering Neivs, revising the data, makes it 17.1 per
cent, with a variation of 3 per cent either way from the average with differ-
ent loads. The results of the tests of the volumes are given on the opposite
page.
Column No. 6 was not broken at the highest load of the testing machine.
Columns Nos. 3 and 4 were taken from the Ireland Building, which col-
lapsed on August 8, 1895; the other four 15-inch columns were made from
drawings prepared by the Building Department, as nearly as possible
duplicates of Nos. 3 and 4. Nos. 1 and 2 were made by a foundry in New
York with no knowledge of their ultimate use. Nos. 5 and 6 were made by
a foundry in Brooklyn with the knowledge that they were to be tested.
Nos. 7 to 10 were made from drawings furnished by the Department.
THE STRENGTH OF CAST-IROK COLUMNS.
251
TESTS OF CAST-IRON COLUMNS.
Thickness.
Breaking Load.
Niimhpi*
Diam.
Inches.
Max.
Min.
Average.
Pounds.
Pounds
per sq. in.
1
15
1
1
1
1,356,000
80,830
2
15
1 5/16
1
*6
1,330,000
27,700
3
15
1*4
1
*6
1,198,000
24.900
4
15J^
1 7/32
1
*6
1,246,000
25,200
5
15
1 11/16
1
11/64
1,632,000
32,100
6
15
1*4
1*6
3/16
2,082,000 +
40,400 -f
7
7% to 8M
1*4
%
651,000
31,900
8
8
1 3/32
1
3/61
612,800
26,800
9
61/16
1 5/32
1*6
9/64
400,000
22,700
10
6 3/32
1*6
1 1/16
7/64
455,200
26,300
lying Gordon's formula, as used by the Building Department,
•^ — ^, to these columns gives for the breaking strength per square
inch of the 15-inch columns 57,143 pounds, for the 8-inch columns 40,000
pounds, and for the 6-inch columns 40,000. The strength of columns Nos. 3
and 4 as calculated is 128 per cent more than their actual strength; their
actual strength is less than 44 per cent of their calculated strength; and the
factor of safety, supposed to be 5 in the Building Law, is only 2.2 for central
loading, no account being taken of the likelihood of eccentric loading.
Prof. Lanza, in Jhis Applied Mechanics, p. 372, quotes the records of 14
tests of cast-iron mill columns, made on the Watertown testing-machine in
1887-88, the breaking strength per square inch ranging from 25,100 to 63,310
pounds, and showing no relation between the breaking strength per square
inch and the dimensions of the columns. Only 3 of the 14 columns had a
strength exceeding 33,500 pounds per square inch. The average strength of
the other 11 was 29,600 pounds per square inch. Prof. Lanza says that it is
evident that in the case of such columns we cannot rely upon a crushing
strength of greater than 25,000 or 30,000 pounds per square inch of area of
section.
He recommends a factor of safety of 5 or 6 with these figures for crush-
ing strength, or 5000 pounds per square inch of area of section as the highest
allowable safe load, and in addition makes the conditions that the length of
the column shall not be greatly in excess of 20 times the diameter, that the
thickness of the metal shall be such as to insure a good strong casting, and
that the sectional area should be increased if necessary to insure that the
extreme fibre stress due to probable eccentric loading shall not be greater
than 5000 pounds per square inch.
Prof. W. H. Burr (Eng'g News, June 30, 1898) gives a formula derived
from plotting, the results of the Watertown and Phoenixville tests, above
described, which represents the average strength of the columns in pounds
per square inch. It isp = 30,500 - IQOl/d. It is to be noted that this is an
average value, and that the actual strength of many of the columns was
much lower. Prof. Burr says: " If cast-iron columns are designed with
anything like a reasonable and real margin of safety, the amount of metal
required dissipates any supposed economy over columns of mild steel."
Transverse Strength of Cast-iron Water-pipe. (Technology
Quarterly, Sept. 1897.)— Tests of 31 cast-iron pipes by transverse stress
gave a maximum outside fibre stress, calculated from maximum load,
assuming each half of pipe as a beam fixed at the ends, ranging from 12,800
Ibs. to 26,300 Ibs. per sq. in.
Bars 2 in. wide cut from the pipes gave moduli of rupture ranging from
28,400 to 51,400 Ibs. per sq. in. Four of the tests, bars and pipes:
Moduli of rupture of bar 28,400 34,400 40,000 51 ,400
Fibre stress of pipe ... 18,300 12,800 14,500 26,300
These figures show a great variation in the strength of both bars and
pipes, and also that the strength of the bar does not bear any definite rela-
tion to the strength of the pipe.
252
STRENGTH OP MATERIALS.
Safe Load, in Tons of 200O I/bs., for Round Cast-iron
Columns, with Turned Capitals and Bases,
Loads being not eccentric, and length of column not exceeding 20 times
the diameter. Based on ultimate crushing strength of 25,000 Ibs. per sq. in.
and a factor of safety of 5. (For eccentric loads see page 254.)
Thick-
ness,
/nches.
Diameter, inches.
6
7
8
9
10
54.5
62.7
70.7
78.4
85.9
93.1
11
12
13
14
15
16
18
1
IVii
IK
2
26.4
30.9
35.2
39.2
31.3
36.8
42.1
47.1
42.7
48.9
55.0
60.8
48.6
55.8
62.8
69.6
76.1
69.6
78.5
87.2
95.7
103.9
76.5
86.4
96.1
105.5
114.7
123.7
94.2
104.9
115.3
125.5
135.5
102.1
113.8
125.2
136. 3
147.8
168.4
110.0
122.6
135.0
147.1
159.0
182.1
204.2
131.4
144.8
157.9
170.8
195.8
219.9
164.'
179. (
194. <
223.!
251.;
....
For lengths greater than 20 diameters the allowable loads should be
decreased. How much they should be decreased is uncertain, since suf-
ficient data of experiments on full-sized very long columns, from which
a formula for the strength of such columns might be derived, are as yet
lacking. There is, however, rarely, if ever, any need of proportioning cast*
iron columns with a length exceeding 20 diameters.
Safe Loads in Tons of 2000 Pounds for Cast-iron Columns^
(By the Building Laws of New York City, Boston, and Chicago, 1897.)
New York. Boston. Chicago.
8a
5a
5a
Square columns
Round columns. .,
1 -f j:
Sa
! + i
5a
1 +
I*
400<2a
1 +
800da
a = sectional area in square inches; I = unsupported length of column m
inches; d = side of square column or thickness of round column in inches.
The safe load of a 15-inch round column !$• inches diameter, 16 feet long,
according to the laws of these cities would be, in New York, 361 tons; in
Boston, 264 tons; in Chicago, 250 tons.
The allowable stress per square inch of area of such a column would be,
in New York, 11,350 pounds; in Boston, 8300 pounds; in Chicago, 7850 pounds.
A safe stress of 5000 pounds per square inch would give for the safe load on
the column 159 tons.
Strengtn of Brackets on Cast-iron Columns,— The columns
tested by the New York Building Department referred to above had
brackets cast upon them, each bracket consisting of a rectangular shelf
supported by one or two triangular ribs. These were tested after the
columns had been broken in the principal tests. In 17 out of 22 cases the
brackets broke by tearing a hole in the body of the column, instead of by
shearing or transverse breaking of the bracket itself. The results were
surprisingly low and very irregular. Reducing them to strength per square
inch of the total vertical section through the shelf and rib or ribs, they
ranged from 2450 to 5600 Ibs., averaging 4200 Ibs., for a load concentrated
at the end of the shelf, and 4100 to 10,900 Ibs., averaging 8000 Ibs., for a dis-
tributed load. (Eng'g News, Jan. 20, 1898.)
SAFE LOAD OF CAST-IROK COLUMKS.
253
Safe Loads, in Tons, for Round Cast Columns.
In accordance with the Building Laws of Chicago.*)
Diame
ter in
Inches
Thick-
ness in
Inches.
Unsupported Length in Feet.
6
8
10
12
14
16
18
20
22
24
26
28
30
/> (
%
50
43
37
32
27
KT,
61
H
57
5(
42
36
31
Formula: u
; ~ ' Za '
aJ
%
62
56
49
43
38
33
1 -f-— - —
7i
YB
71
64
57
49
43
38
w = safe load in tons of
•i
f»
8(
97
(59
79
89
71
81
56
64
72
50
57
63
44
50
56
39
44
50
2000 pounds;
a = cross-section of col-
umn;
\
7A
101
94
86
78
70
63
57
I = unsupported length
9i
1
113
126
105
117
97
107
88
97
79
88
71
79
fr
7]
in inches;
d = diameter in inches.
r
%
116
109
101
93
85
78
71
64
i
1
130
122
114
105
96
88
80
72
1
l^
145
136
126
ir
107
97
8S
80
i
158
149
139
128
117
107
88
f
1
147
139
131
122
113
104
96
88
8
11 j
l^£
163
155
146
136
126
116
100
,97
8
1
1/4
179
170
160
149
138
127
119
jo;
9
l
1%
195
185
174
162
150
138
12r
10
r
1^
181
174
165
155
145
135
125
115
10
98
19 j
1M
199
191
181
170
159
148
13*
11
108
A« 1
1%
217
207
197
1ST
173
161
149
jl
12
117
1
1%
234
224
212
200
187
173
161
13
12b
f
1/^j
200
192
184
174
164
154
144
134
125
116
107
13
l^£
219
211
202
191
180
169
158
U7
127
117
1%
239
230
220
208
196
184
172
160
14
138
128
1
l^fj
258
248
237
225
212
199
186
173
16
149
138
r
1J4
232
223
213
202
191
180
168
157
147
137
128
1%
253
243
232
220
207
195
183
17
160
149
139
l^j
27£
263
251
238
224
211
198
185
173
161
150
I
1%
293
282
269
255
241! 22?
212
198
185
173
161
r
1%
266
255
243
231
219
206
194
182
171
160
150
,J
1^3
287
276
263
250
236
223
210
197
185
173
162
1
1%
309
296
283
268
254
239
225
211
198
186
174
I
1M
329
316
301
286
271
255
240
225
211
198
185
I
1/^
301
288
275
262
248
235
222
209
197
185
16-\
j^
323
310
296
282
267
253
239
225
212
199
(
1%
345
331
316
300
285
270
254
239
225
212
l%
366
351
337
322
307
293
279
264
251
18-]
1%
391
375
360
344
328
313
298
282
268
1
1%
415
399
383
366
349
333
317
300
285
r
1%
435
420
404
389
373
357
341
326
on J
1%
463
447
431
414
397
380
363
347
^ V ^
2 '
490
473
456
43S
420
402
384
367
I
2^j
517
499
481
462
443
425
406
387
f
1%
480
464
448
432
416
400
384
1
l/'O
511
494
478
461
443
426
409
1
0
541
524
506
488
470
452
434
1
%}&
581
562
543
524
504
485
465
f
2^
626
608
589
570
550
531
oj
2*4
668
639
620
600
579
559
** 1
2%
691
671
650
629
608
587
i
*"
724
703
681
659
637
614
From tables published by The Expanded Metal Co., Chicago, 1897.)
254 STRENGTH OF MATERIALS.
ECCENTRIC LOADING OF COLUMNS.
In a given rectangular cross-section, such as a masonry joint under press-
ure, the stress will be distributed uniformly over the section only when the
resultant passes through the centre of the section ; any deviation from such
a central position will bring a maximum unit pressure to one edge and a
minimum to the other; when the distance of the resultant from one edge is
one third of the entire width of the joint, the pressure at the nearer edge is
twice the mean pressure, while that at the farther edge is zero, and that
when the resultant approaches still nearer to the edge the pressure at the
farther edge becomes less than zero; in fact, becomes a tension, if the
material (mortar, etc., there is capable of resisting tension. Or, if, as usual
in masonry joints, the material is practically incapable of resisting tension,
the pressure at the nearer edge, when the resultant approaches it nearer
than one third of the width, increases very rapidly and dangerously, becom-
ing theoretically infinite when the resultant reaches the edge.
With a given position of the resultant relatively to one edge of the joint or
section, a similar redistribution of the pressures throughout the section may
be brought about by simply adding to .or diminishing the width of the
section.
Let P = the total pressure on any section of a bar of uniform thickness.
w = the width of that section — area of the section, when thickness = 1.
p = P/w — the mean unit pressure on the section.
M — the maximum unit pressure on the section.
m = the minimum unit pressure on the section.
d = the eccentricity of the resultant = its distance from the centre of
the section.
ThenM = p (l+~ ) and m = p (l - ^).
When d = - w then M = %p and m = 0.
When d is greater than l/6w, the resultant in that case being less than
one third of the width from one edge, p becomes negative. (J. C. Traut-
wine, Jr., Engineering News, Nov. 23, 1893.)
Eccentric Loading of Cast-iron Columns. — Prof. Lanza
writes the author as follows: The table on page 252 applies when the resultant
of the loads upon the column acts along its central axis, i.e., passes through
the centre of gravity of every section. In buildings and other construc-
tions, however, cases frequently occur when the resultant load does not
pass through the centre of gravity of the section ; and then the pressure is
not evenly distributed over the section, but is greatest on the side where
the resultant acts. (Examples occur when the loads on the floors are not
uniformly distributed.) In these cases the outside fibre stresses of the
column should be computed as follows, viz.:
Let P = total pressure on the section;
d = eccentricity of resultant = its distance from the centre of gravity
of the section;
A = area of the section, and Jt its moment of inertia about an axis in its
plane, passing through its centre of gravity, and perpendicular
to d (see page 26?) ;
Cj = distance of most compressed and ca = that of least compressed
fibre from above stated axis;
*j = maximum and sa = minimum pressure per unit of area. Then
*-+«2& and H-Z
Having assumed a certain trial section for the column to be designed, sl
should be computed, and, if it exceed the proper safe value, a different
section should be used for which Sj does not exceed this value.
The proper safe value, in the case of cast-iron columns whose ratio of
length to diameter does not greatly exceed 20, is 5000 pounds per square inch
when the eccentricity used in the computation of sl is liable to occur fre-
quently in the ordinary uses of the structure; but when it is one which can
only occur in rare cases the value 8000 pounds per square inch may be used.
A long cap on a column is more conducive to the production of eccen-
tricity of loading than a short one, hence a long cap is a source of weakness
in a column.
ULTIMATE STRENGTH OF WROUGHT-IROK COLUMNS. 255
ULTIMATE STRENGTH OF WROUGHT-IRON
COL.UMNS.
(Pottsville Iron and Steel Co.)
Computed by Gordon's formula, p =
14-0
p = ultimate strength in Ibs. per square inch;
I = length of column in inches;
r — least radius of gyration in inches;
/= 40,000;
C = 1/40,000 for square end-bearings; 1/30,000 for one pin and one square
bearing; 1/20,000 for two pin-bearings.
For safe working load on these columns use a factor of 4 when used in
buildings, or when subjected to dead load only; but when used in bridges
the factor should be 5.
WROUGHT-IRON COLUMNS.
Ultimate Strength in Ibs.
per square inch.
Safe Strength in Ibs. per
square inch— Factor of 5.
I
I
r
r
Square
Ends.
Pin and
Square
End.
Pin
Ends.
Square
Ends.
Pin and
Square
End.
Pin
Ends.
10
39944
39866
39800
10
7989
7973
7960
15
39776
39702
39554
15
7955
7940
7911
20
39604
39472
39214
20
7921
7894
7843
25
39384
39182
38788
25
7877
7836
7758
30
39118
38834
38278
30
7821
7767
7656
35
38810
38430
37690
35
7762
7686
7538
40
38460
37974
37036
40
7692
7595
7407
45
38072
37470
36322
45
7614
7494
7264
50
37646
36928
35525
50
7529
7386
7105
55
37186
36336
34744
55
7437
7267
6949
60
36697
35714
33898
60
7339
7143
6780
65
36182
34478
33024
65
7236
6896
6605
TO
35634
34384
32128
70
7127
6877
6426
75
35076
33682
31218
75
7015
6736
6244
80
34482
32966
30288
80
6896
6593
6058
85
33883
32236
29384
85
6777
6447
5877
90
33264
31496
28470
90
6653
6299
5694
95
32636
30750
27562
95
6527
6150
5512
100
32000
30000
26666
100
6400
6000
5333
105
31357
29250
25786
105
6271
5850
5-157
Maximum Permissible Stresses in columns used in buildings.
(Building Ordinances of City of Chicago, 1893.)
For riveted or other forms of wrought-iron columns:
# _ 12000a I = length of column in inches;
„ , Z2 r = least radius of gyration in inches;
of column in f
square inches.
a = are;
For riveted or other steel columns, if more than 60r in length:
= 17,000 - — .
S = 13,500a.
a = area of post in square inches ;
~*«ijleast side of rectangular post in inches;
I =Tengthvof post in inches;
I 600 for" *w hite*x> r J£fl_r waw pine ; •
c = •< 800 for oak ; ?~ \
( 900 for long-leaf yellow pine.
256
STRENGTH OF MATERIALS.
BUILT COLUMNS.
From experiments by T. D. Lovett, discussed by Burr, the values of / and
a in several cases are determined, giving empirical forms of Gordon's for-
mula as follows: p = pounds crushing strength per square inch of section,
I = length of column in inches, r = radius of gyration in inches.
Keystone
Keystone
Columns.
39,500
1-f
~1 Z2
18,300 r2
(D
36,000
i(2)
Flat Ends.
Square
Columns.
39,000
(4)
Phoenix
Columns.
42,000
1 Za
Am. Dr. Co.
American Bridge
Co. Columns.
(6)
35,000 r2
50,000 r2
Flat Ends, Swelled*
36,000
1 Z2
(91
46,000 ;
36,000
- * * (
r 15,000 r«
Pin Ends.
39,000
(5)
42,000
:(7)
i . -1 _ 1.1- _
^ 17,000 r2 ^ 22,700 r2
Pin Ends, Swelled*
Round Ends.
42,000
1
12,500 r»
36,000
1 J_
™21,500ra
(10)
36,000
1-f-
1 Z2
(11)
11,500 r2
With great variations of stress a factor of safety of as high as 6 or 8 may
be used, or it may be as low as 3 or 4, if the condition of stress is uniform or
essentially so.
Burr gives the following general principles which govern the resistance of
built columns :
The material should be disposed as far as possible from the neutral axis
of the cross-section, thereby increasing ?•;
There should be no initial' internal stress;
The individual portions of the column should be mutually supporting;
The individual portions of the column should be so firmly secured to each
ofher that no relative motion can take place, in order that the column may
fail as a whole, thus maintaining the original value of r.
Stoney says: **When the length of a rectangular wrought- iron tubular
column does not exceed 30 times its least breadth, it fails by the bulging or
buckling of a short portion of the plates, not by the flexure of th6 pillar as a
whole."
In Trans. A. S. C. E., Oct. 1880, are given the following formulae for the
ultimate resistance of wrought-iron columns designed by C. Shaler Smith :
BUILT COLUMNS.
257
Flat Ends.
- (!»
1 + 5820 d«
Phoenix
Column.
42,500
1 Z2
1 j *_ j_
^4500 d8
American Bridge
Co. Column.
(15)
36,500
Common
Column.
36,500
(«1>
--
3750 d*
2700 d»
One Pin End.
38,500
14— i- -^
^3000 da
(13)
40,000 -
14- i- -
^2250 da
(16)
36,500
(19)
36,500
(22)
2250
Two Fin Ends.
ootn ^75 *"T
1500
36,600
36,500
1750 d«
36,500
14-— -
^1200 d»
(23)
The "common " column consists of two channels, opposite, with flanges
outward, with a plate on one side and a lattice on the other.
The formula for " square " columns may be used without much error for
the common-chord section composed of two channel-bars and plates, with
the axis of the pin passing through the centre of gravity of the cross-
section. (Burr).
Compression members composed of two channels connected by zigzag
bracing may be treated by formulae 4 and 5, using / = 36,000 instead of
89,000.
Experiments on full-sized Phoenix columns in 1873 showed a close agree-
ment of the results with formulae 6-8. Experiments on full-sized Phoenix
columns on the Watertown testing-machine in 1881 showed considerable dis-
crepancies when the value of I -*- r became comparatively small. The fol-
lowing modified form of Gordon's formula gave tolerable results through
the whole range of experiments :
Phoenix columns, flat end, p ••
40,000 ( 14-T-J
14-50,000 ra
(24)
Plotting results of three series of experiments on Phcenix columns, a
more simple formula than Gordon's is reached as follows :
Phcenix columns, flat ends, p = 39,640 — 46-, when I -*- r is from 30 to 140;
p = 64,700 - 4600 \/- when I -*- r is less than 30.
Dimensions of Phoenix Columns*
(Phoenix Iron Co.)
The dimensions are subject to slight variations, which are unavoidable In
rolling iron shapes.
The weights of columns given are those of the 4, 6, or 8 segments of which
they are composed. The rivet heads add from 2g to 5# to the weights given.
Rivets are spaced 3, 4, or 6 in. apart from centre to centre, and somewhat
more closely at the ends than towards the centre of the column.
G columns have 8 segments, E columns 6 segments, C, £2, Bl, and A have
4 segments. Least radius of gyration •= D X .3636.
The safe loads given are computed as being one-fourth of the breaking
load, and as producing a maximum stress, in an axial direction, on a square-
end column of not more than 14,000 Ibs, per sq. in, for lengths of 90 radii
and under,
258
STRENGTH OF MATERIALS.
Dimensions of Phoenix Steel Columns.
(Least radius of gyration equals D x .3G?6.)
One Segment.
Diameters in Inches.
One Column.
S3
£
jS
.
gj .
£
S'a
^•?
*M
1-173
0
9
tt *
202
^TJ
ijtj
"~ i->
03 03
Q) Q)
.S 3
1
3
> c?
<*-, S CO
&2
"S o JS
S *«
^3 ^H
q
p
O J3$
o-2|
•SP
5 £»*§
-v <t~> *•>
f
II
0
or^
03 O o
Si2
1
»o5
J'S.S
sjjj
t^
£
<
P
02
3/16
9.7
4
6 1/16
3.8
12.9
1.45
18.2
^4
12.2
A
4/^
6 3/16
4.8
16.3
1.50
23.9
5/16
14.8
3%
4J4
6 5/16
5.8
19.7
1.55
30.0
%
17.3
4%
6 7/16
6.8
23.1
1.59
35.9
5/16
16.3
19.9
f/B
si/16
6.4
7.8
21.8
26.5
1.95
2.00
36.4
45.1
%
23.5
5%
8 5/16
9.2
31.3
2.04
54.4
7/16
27.0
B.I
5%
8 7/16
10.6
36.0
2.09
63.9
/^
30.6
4/»
5%
gl^f.
12.0
40.8
2.13
73.3
9/16
34.2
6
8 9/16
13.4
45.6
2.18
83.2
%
37.7
%
8 11/16
14.8
50.3
2.23
93.1
24
18.9
6 9/16
91^
7.4
25.2
2.39
48.3
5/16
22.9
6 11/16
9%
9.0
30.6
2.43
59.5
%
27.0
6 13/16
9 7/16
10.6
36.0
2.48
70 7
7/16
31.1
35.2
B.2
6 1/16
6 15/16
7 1/16
12.2
13.8
41.5
46.9
2.52
2.57
82.3
93.9
9/16
39.3
7 3/16
^M
15.4
52.4
2.61
105.8
%
43.3
7 5/16
9 13/16
17.0
57.8
2.66
111.9
M
25^
7 13/16
11 11/16
10.0
34.0
2.84
70.0
5/16
31
7 15/16
HM
12.1
41.3
2.88
85.1
%
36
8 1/16
11 13/16
14.1
48.0
2.93
98.8
a 6
41
8 3/16
11%
16.0
54.6
2.97
112.5
46
8 5/16
11 15/16
18.0
61 3
3.01
126.3
9/16
51
8 7/16
12
19.9
68.0
3.06
140.0
%
56
C
8 9/16
12 1/16
21.9
74.6
3.11
153.7
11/16
62
7%
8 11/16
12 3/16
24.3
82.6
3.16
170.2
M
68
8 13/16
12 5/16
26.6
90.6
3.20
186.7
13/16
73
8 15/16
12 7/16
28.6
97.3
3.24
200.3
%
78
9 1/16
12^£
30.6
104.0
3.29
214.2
1
89
9 5/16
12%
34.8
118.6
3.34
244.3
1%
99
9 9/16
12 13/10
38.8
132.0
3.48
271.7
1M
109
9 13/16
13
42.7
145.3
3.57
299.2
J4
28
11 9/16
151/
' 16.5
56.0
4.20
115.3
5/16
32^
11 11/16
15%
19.1
65.0
4.25
133.8
%
37
11 13/16
15%
21.7
74.0
4.29
152.4
7/16
42
11 15/16
15%
24.7
84.0
4.34
173.0
47
12 1/16
15 15/16
27.6
94.0
4.38
193 6
9/16
52
12 3/16
16 1/16
30.6
104.0
4.43
214.1
%
57
E
12 5/16
16 3/16
33.5
114.0
4.48
234.7
11/16
62
11 1/16
12 7/16
16 5/16
36.4
124.0
4.52
255.3
%
68
12 9/16
16 7/16
40.0
136.0
4.56
280.0
13/16
73
12 11/16
16 9/16
43.0
146.0
4.61
300 6
%
78
12 13/16
16 11/16
45.9
156.0
4.66
321.2
1
88
13 1/16
16 13/16
51.7
176.0
4.73
36',>.4
1%
98
13 5/16
17 1/16
57.6
196.0
4.84
403.6
JJ4
108
13 9/16
17 5/16
63.5
216.0
4.93
444.7
5/16
31
15H
P*
24.2
82.6
5.54
170.2
%
36
G
15%
28.1
96.0
5.59
197.7
7/16
41
14%
1514
32.0
109.3
5.64
225.1
^
46
i!5%
1/16
36.0
122.6
5.68
252.6
FORMULAE FOR IROK AtfD STEEL STRUTS.
259
One Segment.
Diameters in Inches.
One Column.
II
a
$ -
V*
K
« a
C!A
Thickness i
Inches.
Weight in L
per Yard,
d Inside.
D Outside
. 2
£ bo
£§
5>h
Area of Cro
Section, S(
Inches.
Weight per
in Pounds.
' Least Radii
of Gyratio
in Inches.
Safe Load i
Tons for 11
Lengths.
9/16
51
15%
]9££
39.9
136.0
5.73
280.0
?8
56
15%
19%
43.8
149.3
5.77
307.4
]1/16
61
16
20
47.7
162.6
5.82
334.9
M
66
20%
51.7
176.0
5.88
362.4
13/16
71
G
16^4
55.6
189.3
5.91
389.8
7£
76
16%
20%
59.6
202.6
5.95
417.3
1
86
16%
20%
67.4
229.3
6.04
472.1
1%
96
16%
20%
75.3
256.0
6.13
527.3
ig
106
17%
21
83.1
282.6
6.27
582.0
15i
116
17%
21*4
90.9
309.3
6.32
636.9
Working Formula; for Wr ought-iron and Steel Struts
of various Forms.— Burr gives the following practical formulae, which
he believes to possess advantages over Gordon's:
Pi = Working
Strength =
1/5 Ultimate,
Ibs. per sq.
in. of Section.
p = Ultimate
Strength,
Ibs. per sq. in.
of Section.
Kind of Strut.
Flat and flxed end iron angles and tees 44000 - 140 — (1) 8800-28 ~ (2)
Hinged-end iron angles and tees 46000-175 —
r
9200-35 —
r
I
Flat-end iron channels and I beams.... 40000- 110— (5) 8000-22— (6)
Flat-end mild-steel angles 52000-180— (7) 10400-36— (8)
I
Flat-end high-steel angles 76000- 290 — (9)
Pin-end solid wroughMron columns.. . .32000- 80 —
" 1(11)
15200-58- (10)
6400-16-1
32000-277 - [ 6400-55— |
d) dJ
Equations (1) to (4) are to be used only between — = 40 and — = 200
(5) and (6) " "" «• " " " = 20
(7) to (10) »' " " " « « « = 40
(11) and (12)" « •• " «« « « = ^o
=200
=200
=200
or - = 6 and -- = 65
d a
rro,s' Properly made, of steel ranging in specimens from 65,000 to
73,000 Ibs. per square inch should give a resistance 25 to 33 per cent in ex-
cess of that of wrought-iron columns with the same value of I H- r, provided
that ratio does not exceed 140.
The^uon^pport.ed Yidth of a Plate in a compression member should not
exceed 30 tunes its thickness.
In built columns the transverse distance between centre lines of rivets
securing plates to angles or channels, etc., should not exceed 35 times the
elate thickness. If this width is exceeded, longitudinal buckling of the
^60
STRENGTH OF MATERIALS.
plate takes place, and the column ceases to fail as a whole, but yields in
detail.
The same tests show that the thickness of the leg of an angle to which
latticing is riveted should not be less than 1/9 of the length of that leg or
side if the column is purely and wholly a compression member. The above
limit may be passed somewhat in stiff ties and compression members de-
signed to carry transverse loads.
The panel points of latticing should not be separated by a greater distance
than 60 times the thickness of the angle-leg to which the latticing is riveted,
if the column is wholly a compression member.
The rivet pitch should never exceed 16 times the thickness of the thinnest
metal pierced by the rivet, and if the plates are very thick it should never
nearly equal that value.
Merrimaii's Rational Formula for Columns (Eng. News,
July 19, 1894).
(2)
B = unit-load on the column = total load P-*-area of cross-section A\
C = maximum compressive unit-stress on the concave side of the column:
I — length of the column; r = least radius of gyration of the cross-section
E = coefficient of elasticity of the material ; n = 1 for both ends round
n = 4/9 for one end round and one fixed; n -* y\ for both ends fixed. Thift
formula is for use with strains within the eristic limit only: it does not
hold good when the strain C exceeds the elasUc limit.
Prof. Merriman takes the mean value otEfot timber = 1,500,000, for cast
iron = 15,000,000, for wrought-iron = 25,000,000, nud for steel = 30,000,000,
and 7T2 = 10 as a close enough approximation. With these values he com-
putes the following tables from formula (1):
I.— Wrought-iron Columns wiftb fttonnd Ends.
Unit-
load.
Maximum Compressive Unit-stress C.
p
1 = 20
- = 40
1 = 60
1 = 80
•1 = 100
i~l»
-1=140
1=160
A°T '
r
r
r
r
r
9*
r
r
5,000
6,000
5,040
6,055
5,170
6,240
5,390
6,560
5,730
7,090
6,250
7,890
6,980
9,0v>0
8-2PO
11,330
10,250
15,56(1
7,000
7,080
7,330
7,780
8,530
9,720
11,610
15,510
24,720
8,000
8,100
8,430
9,040
10,060
11,660
14,640
21,460
9000
9 130
9550
10340
11 690
14,060
18,380
10,000
10,160
10,680
11,680
13,440
16,670
23,090
11 000
11 200
11 750
13070
15 310
19 640
12000
12 240
13000
14 500
17320
23080
13,000
13,280
14,180
15,990
19,480
'
STRENGTH OF WROUGHT IROK AKD STEEL COLUMNS. 261
II.— Wrought-iron Column* with Fixed Ends*
Unit-
load.
Maximum Compressive Unit-stress C.
~orB.
A
i = 20
1 = 40
1 = 60
1 = 80
1 = 100
l-«o
~ = 140
1=160
6,000
7,000
8,000
9,000
10,000
11,000
12,000
13,000
14,000
6,010
7,020
8,025
9,030
10,040
11,050
12,060
13,070
14,080
6,060
7,080
8,100
9,130
10,160
11,200
12,240
13,280
14,320
6,130
7,180
8,240
9,300
10,370
11,450
12,540
13,640
14,740
6,240
7,330
8,430
9,550
10,710
11,830
13,000
14,210
15,380
6,380
7,530
8,700
9,890
11,110
12,360
13,640
14,940
16,280
6,570
7,780
9,040
10,340
11,680
13,070
14.510
15,990
17,530
6,800
8,- 110
9,490
10,930
12,440
14,020
15,690
17,440
19,290
7,090
8,530
10,060
11,690
13,440
15,310
17,320
19,480
21,820
III.— Steel Columns with Round Ends.
Unit-
load.
Maximum Compressive Unit-stress O.
5°rjB<
i = 20
7 = «o
1 = 60
r
1 = 80
r
1 = 100
r
1 =120
r
1 = 140
7 = 160
6,000
7,000
8,000
9,000
10,000
11,000
12,000
13,000
14,000
6,050
7,070
8,090
9,110
10,130
11,160
12.200
13,330
14,250
6,200
7,270
8,380
9,450
10,560
11,690
12,820
13,970
15,130
6,470
7,650
8,770
10,090
11,360
12,670
14,020
15,400
16,830
6,880
8,230
9,650
11,140
12,710
14,370
16,130
18,000
19,960
7,500
9,130
10,870
12,850
15,000
17,370
20,000
22,940
26,250
8,430
10,540
12,990
15,850
19,230
23,300
28,300
9,870
12,900
16,760
20,930
28,850
12,300
17,400
24,590
IV.— Steel Columns with Fixed Ends.
Unit-
load.
Maximum Compressive Unit-stress 01
^or£.
1 = 20
1 = 40
1 = 60
7,150
8,200
9,250
10,310
11,380
12,450
13,530
14,610
15,710
7 = 80
1 = 100
r
1=1*0
1=140
1=160
7,000
8,000
9,000
10,000
11,000
12,000
13,000
14,000
15,000
7,020
8,020
9,030
10,030
11,040
12,050
13,060
14,070
15,080
7,070
8,090
9,110
10,130
11,160
12,200
13,230
14,250
15,310
7,270
8,380
9,450
10,560
11,690
12,820
13,970
15,130
16,310
7,430
8,570
9,730
10,910
12,110
13,330
14,580
15,850
17,140
7,650
8,770
10,090
11,360
12,670
14,020
15,400
16,830
18,290
7,900
9,200
10,550
11,810
13,410
14,930
16,500
18,150
19,870
8,230
9,650
11,140
12,710
14,370
16,130
17,990
19,960
22,060
The design of the cross-section of a column to carry a given load with
maximum unit-stress C may be made by assuming dimensions, and then
STRENGTH OF MATERIALS.
computing C by formula (1). If the agreement between the specified and
computed values is not sufficiently close, new dimensions must be chosen,
and the computation be repeated. By the use of the above tables the work
will be shortened.
The formula (1) may be put in another form which in some cases will ab-
breviate the numerical work. For B substitute its value P-^t4, and for
Ar* write /, the least moment of inertia of the cross-section; then
Jn which I and r2 are to be determined.
For example, let it be required to find the size of a square oak column
with fixed ends when loaded with 24 000 Ibs. and 16 ft. long, so that the
maximum compressive stress C shall be 1000 Ibs. per square inch. Here
7 = 24,000, C = 1000, n = M, *2 = 10, E = 1,500,000, I = 16 X 12, and (3) be-
comes
I - 24r« = 14.75.
Now let x be the side of the square; then
so that the equation reduces to x* — 24#2 = 177, from which x* is found to be
29.92 sq. in., and the side x = 5.47 in. Thus the unit-load B is about 802
Ibs. per square inch.
WORKING STRAINS ALLOWED IN BRIDGE
MEMBERS.
Theodore Cooper gives the following in his Bridge Specifications :
Compression members shall be so proportioned that the maximum load
shall in no case cause a greater strain than that determined by the follow-
ing formula :
8000
P = - — for square-end compression members ;
P me — — - — for compression members with one pin and one square end;
1 ~*~ 30,000r«
8000
P= — for compression members^with pin-bearings;
1~*~20,000r»
(These values may be increased in bridges over 150 ft. span. See Cooper's
Specifications.)
P = the allowed compression per square inch of cross-section;
I = the length of compression member, in inches;
r = the least radius of gyration <
. f gyration of the section in inches.
No compression member, however, shall have a length exceeding 45 times
its least width.
Tension Members.— All parts of the structure shall be so proportioned
that the maximum loads shall in no case cause a greater tension than the
following (except in spans exceeding 150 feet) :
Pounds per
sq. in.
On lateral bracing 15,000
On solid rolled beams, used as cross floor-beams and stringers. 9,000
On bottom chords and main diagonals (forged eye-bars) 10,000
On bottom chords and main diagonals (plates or shapes), net
section 8,000
On counter rods anri long verticals (forged eye-bars) 8,000
On counter and long verticals (plates or shapes), net section.. 6,500
On bottom flange of riveted cross-girders, net section 8,000
On bottom flange of riveted longitudinal plate girders over
20ft. long, net section 8,000
WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 263
On bottom flange of riveted longitudinal plate girders under
20 ft. long, net section ..'.'.. 7,000
On floor-beam hangers, and other similar members liable to
sudden loading (bar iron with forged ends) 6,000
On floor-beam hangers, and other similar members liable to
sudden loading (plates or shapes), net section 5,000
Members subject to alternate strains of tension and compression shall be
proportioned to resist each kind of strain. Both of the strains shall, how-
ever, be considered as increased by an amount equal to 8/10 of the least of
the two strains, for determining the sectional area by the above allowed
strains.
The Phoenix Bridge Co. (Standard Specifications, 1895) gives the follow-
ing :
The greatest working stresses in pounds per square inch shall be as fol-
lows :
Tension.
Steel. Iron.
P = 0 OOP f 1 I Min' Stress1 Forbars» P= 75oori i MiD- stress 1
L Max. stressj forged ends. |_ Max. stress J
P - 8 500 fl -I Min' Stress1 PIatesor p_700ori , Mia, stress"]
uu L T Max. stressj shapes net. J ~ r»™|/ T Max. stressj
8,500 pounds. Floor-beam hangers, forged ends 7,000 pounds.
7,500 Floor-beam hangers, plates or shapes, net
section 6,000 "
10,000 " Lower flanges of rolled beams. 8,000 "
50,000 ** Outside fibres of pins 15,000 "
30,000 " Pins for wind-bracing 22,500 "
20,000 " Lateral bracing 15,000 "
Shearing.
9,000 pounds. Pins and rivets 7,500 pounds.
Hand-driven rivets 20# less unit stresses. For
bracing increase unit stresses 50%.
6,000 pounds. Webs of plate girders 5,000 pounds.
Bearing.
16,000 pounds. Projection semi-intrados pins and rivets.. . . 12,000 pounds.
Hand-driven rivets 20# less unit stresses. For
bracing increase unit stresses 50#.
Compression.
Lengths less than forty times the least radius of gyration, P previously
found. See Tension.
Lengths more than forty times the least radius of gyration, P reduced by
following formulae:
For both ends fixed, b =
For one end hinged,
For both ends hinged,
18,000 r«
P = permissible stress previously found (see Tension) ; b = allowable
working stress per square inch; I = length of member in inches; r = least
radius of gyration of section in inches. No compression member, how-
ever, shall have a length exceeding 45 times its least width.
io,ooo(i
264 STRENGTH OF MATEEIAL8.
Pounds per
sq. in.
In counter web members 10,500
In long verticals 10,000
In all main-web and lower-chord eye-bars 13,200
In plate hangers (net section) 9,000
In tension members of lateral and transverse bracing 19,000
In steel-angle lateral ties (net section) 15,000
For spans over 200 feet in length the greatest allowed working stresses
per square inch, in lower-chord and end main-web eye-bars, shall be taken at
min. total stress \
max. total stress J
whenever this quantity exceeds 13,200.
The greatest allowable stress in the main-web eye-bars nearest the centre
of such spans shall be taken at 13,200 pounds per square inch ; and those
for the intermediate eye-bars shall be found by direct interpolation between
the preceding values.
The greatest allowable working stresses in steel plate and lattice girders
and rolled beams shall be taken as follows :
Pounds per
sq. in.
Upper flange of plate girders (gross section) 10,000
Lower flange of plate girders (net section) 10,000
In counters and long verticals of lattice girders (net section) . . 9,000
In lower chords and main diagonals of lattice girders (net
section) " 10,000
In bottom flanges of rolled beams 10,000
In top flanges of rolled beams 10,000
RESISTANCE OF HOLLOW CYLINDERS TO
COLLAPSE.
Fairbairn's empirical formula (Phil. Trans. 1858) is
«.i»
p = 9,675,600 '-rv-, . . , (1)
Id
where p = pressure in Ibs. per square inch, t = thickness of cylinder, d =
diameter, and I = length, all in inches ; or,
p = 806,300 ~^, if L is in feet (2)
He recommends the simpler formula
p = 9,675,600^ (3)
as sufficiently accurate for practical purposes, for tubes of considerable
diameter and length.
The diameters of Fairbairn's experimental tubes were 4", 6", 8", 10", and
12", and their lengths; between the cast-iron ends, ranged between 19 inches
and 60 inches.
His formula (3) has been generally accepted as the basis of rules for
ascertaining the strength of boiler-flues. In some cases, however, limits are
fixed to its application by a supplementary formula.
Lloyd's Register contains the following formula for the strength of circular
boiler-flues, viz.,
89,600^
LA ()
The English Board of Trade prescribes the following formula for circular
flues, when the longitudinal joints are welded, or made with riveted butt-
straps, viz.,
»- M.000<«
For lap-joints and for inferior workmanship the numerical factor may be
reduced as low as 60,000.
RESISTANCE OF HOLLOW CYLINDERS TO COLLAPSE. 265
The rules of Lloyd's Register, as well as those of the Board of Trade, pre-
scribe further, that in no case the value of P must exceed the amount given
by the following equation, viz.,
In formulae (4), (5), (6) P is the highest working pressure in pounds per
square inch, t and d are the thickness and diameter in inches, L is the
length of the flue in feet measured between the strengthening rings, in case
it is fitted with such. Formula (4) is the same as formula (3), with a factor
of safety of 9. In formula (5) the length L is increased by 1 ; the influence
which this addition has on the value of P is, of course, greater for short
tubes than for long ones.
Nystrom has deduced from Fairbairn's experiments the following formula
for the collapsing strength of flues :
............
where p, £, and d have the same meaning as in formula (1), L is the length in
feet, and Tis the tensile strength of the metal in pounds per square inch.
If we assign to T the value 50,000, and express the length of the flue in
inches, equation (7) assumes the following form, viz.,
p = 692,800 -¥—. .......... (8)
d yl
Nystrom considers a factor of safety of 4 sufficient in applying his formula.
(See "A New Treatise on Steam Engineering," by J. W. Nystrom, p. 106.)
Formula (1), (4), and (8) have the common defect thai they make the
collapsing pressure decrease indefinitely with increase of length, and vice
versa. M. Love has deduced from Fairbairn's experiments an equation of
a different form, which, reduced to English measures, is as follows, viz.,
p= 5,358,150 ^ + 41,906^+ 1323 j, ...... (9)
where the notation is the same as in formula (1) .
D. K. Clark, in his " Manual of Rules," etc., p. 696, gives the dimensions of
six flues, selected from the reports of the Manchester Steam-Users Associa-
tion, 1862-69, which collapsed while in actual use in boilers. These flues
varied from 24 to 60 inches in diameter, and from 8-16 to % inch in thickness.
They consisted of rings of plates riveted together, with one or two longitud-
inal seams, but all of them unfortified by intermediate flanges or strength-
ening rings. At the collapsing pressures the flues experienced compressions
ranging from 1.53 to 2.17 tons, or a mean compression of 1.82 tons per square
inch of section. From these data Clark deduced the following formula
"for the average resisting force of common boiler-flues," viz.,
where p is the collapsing pressure in pounds per square inch, and d and t
are the diameter and thickness expressed in inches.
C. R. Roelker, in Tan Nostrand's Magazine, March, 1881, discussing f'e
above and other formulae, shows that experimental data are as yet insuffi-
cient to determine the value of any of the formulae. He says that Nystrom 's
formula, (8), gives a closer agreement of the calculated with the actual col-
lapsing pressures in experiments on flues of every description than any of
the other formulae.
Collapsing Pressure of Plain Iron Tubes or Flues.
(Clark, S. E., vol. i. p. 643.)
The resistance to collapse of plain-riveted flues is directly as the square of
the thickness of the plate, and inversely as the square of the diameter. The
support of the two ends of the flue does not practically extend over a length
of tube greater than twice or three times the diameter. The collapsing
pressure of long tubes is therefore practically independent of the length.
266 STRENGTH OF MATERIALS.
Instances of collapsed flues of Cornish and Lancashire boilers collated by
Clark, showed that the resistance to collapse of flues of %-iuch plates, 18 to
43 feet long, and 30 to 50 inches diameter, varied as the 1 75 power of the
diameter. Thus,
for diameters of ....................... 30 35 40 45 50 inches,
the collapsing pressures were ......... 76 58 45 37 30 Ibs. per sq. in;
for 7-16-inch plates the collapsing
pressures were ........... ............ • . . . 60 49 42
For collapsing pressures of plain iron flue-tubes of Cornish and Lanca
shirs steam-boilers, Clark gives:
_ 200,000*2
P = collapsing pressure, in pounds per square inch;
t = thickness of the plates of the furnace tube, in inches.
d = internal diameter of the furnace tube, in inches.
For short lengths the longitudinal tensile resistance may be effective in
augmenting the resistance to collapse. Flues efficiently fortified by flange=
joints or hoops at intervals of 3 feet may be enabled to resist from 50 Ibs.
to 60 Ibs. or 70 Ibs, pressure per square inch more than plain tubes, accord.
ing to the thickness of the plates.
Strength of Small Tubes.— The collapsing resistance of solid-
drawn tubes of small diameter, and from .134 inch to .109 inch in thickness,
Has been tested experimentally by Messrs. J. Russell & Sons. The results
lor wrought-iron tubes varied from 14.33 to 20.07 tons per square-inch sec-
tion of the metal, averaging 18.20 tons, as against 17.57 to 24.28 tons, averag-
ing 22.40 tons, for the bursting pressure.
(For strength of Segmental Crowns of Furnaces and Cylinders see Clark,
S. E., vol. i, pp. 649-651 and pp. 627, 628.)
Formula for Corrugated Furnaces (Bng'g* July 24, 1891. p.
102).— As the result of a series of experiments on the resistance to collapse
of Fox's corrugated furnaces, the Board of Trade and Lloyd's Registry
altered their formulae for these furnaces in 1891 as follows:
Board of Trade formula is altered from
T = thickness in inches;
D = mean diameter of furnace;
WP = working pressure in pounds per square inch.
Lloyd's formula is altered from
1000 X (T - '!} = wp to 1S84XCT.-2) = WR
T = thickness in sixteenths of an inch;
D = greatest diameter of furnace;
WP = working pressure in pounds per square inch.
TRANSVERSE STRENGTH.
In transverse tests the strength of bars of rectangular section is found to
rary directly as the breadth of the specimen tested, as the square of its
depth, and inversely as its length. The deflection under any load varies as
the cube of the length, and inversely as the breadth and as the cube of the
depth. Represented algebraically, if S = the strength and D the deflection,
1 the length, 6 the breadth, and d the depth,
7,,?3 19
8 varies as -r- and D varies as ^.
For the purpose of reducing the strength of pieces of various sizes to
a common standard, the term modulus of rupture (represented by K) is
used. Its value is obtained by experiment on a bar of rectangular section
TRANSVERSE STRENGTH. 267
supported at the ends and loaded in the middle and substituting numerical
values in the following formula :
to which P= the breaking load in pounds, I = the length in inches, b the
breadth, and d the depth.
The modulus of rupture is sometimes defined as the strain at the instant
of rupture upon a unit of the section which is most remote from the neutral
axis on the side which first ruptures. This definition, however, is based
upon a theory which is yet in dispute among authorities, and it is better to
define it as a numerical value, or experimental constant, found by the ap-
plication of the formula above given.
From the above formula, making I 12 inches, and b and d each 1 inch, it
follows that the modulus of rupture is 18 times the load required to break a
bar one inch square, supported at two points one foot apart, the load being
applied in the middle.
.. span in feet X load at middle in Ibs.
Coefficient of transverse strength = ^^ in inches x (dep[h in ^^^
=— th of the modulus of rupture.
lo
Fundamental Formulae for Flexure of Beams (Merriman).
Resisting shear = vertical shear;
Resisting moment =? bending moment;
Sum of tensile stresses = sum of compressive stresses;
Resisting shear = algebraic sum of all the vertical components of the in-
ternal stresses at any section of the beam.
Tf A be the area of the section and Ss the shearing unit stress, then resist-
ing shear = ASs; and if the vertical shear = V, then V — ASs.
The vertical shear is the algebraic sum of all the external vertical forces
on one side of the section considered. It is equal to the reaction of one sup-
port, considered as a force acting upward, minus the sum of all the vertical
downward forces acting between the support and the section.
The resisting moment — algebraic sum of all the moments of the inter-
nal horizontal stresses at any section with reference to a point in that sec-
or
tion, = — , in which 8 = the horizontal unit stress, tensile or compressive
c
as the case may be, upon the fibre most remote from the neutral axis, c =
the shortest distance from that fibre to said axis, and / = the moment of
inertia of the cross-section with reference to that axis.
The bending moment M is the algebraic sum of the moment of the ex-
ternal forces on one side of the section with reference to a point in that sec-
tion — moment of the reaction of one support minus sum of moments of
loads between the support and the section considered.
•£he bending moment is a compound quantity = product of a force by the
(Distance of its point of application from the section considered, the distance
being measured on a line drawn from the section perpendicular to the
direction of the action of the force.
Concerning the above formula, Prof. Merriman, Eng. News, July 21, 1894,
says: The formula just quoted is true when the unit-stress <S on the part of
the beam farthest from the neutral axis is within the elastic limit of the
material. It is not true when this limit is exceeded, because then the neutral
axis does not pass through the centre of gravity of the cross-section, and
because also the different longitudinal stresses are not proportional to their
distances from that axis, these two requirements being involved in the de-
duction of the formula. But in all cases of design the permissible unit-
stresses should not exceed the elastic limit, and hence the formula applies
rationally, without regarding the ultimate strength of the material or any
of the circumstances regarding rupture. Indeed so great reliance is placed
upon this formula that the practice of testing beams by rupture has been
almost entirely abandoned, and the allowable unit-stresses are mainly de-
rived from tensile and compressive tests.
268
STRENGTH OF MATERIALS.
+ ft, 18
'1*1 MBS
g
1,5
SjB
II II
~t
~l8S
i
!!
fe
-h
ftj
J
I
I i
•
•
:
:
^
£>
<D
: »'
•
ii
3 §
^
*»-«-»s tJ
•
> 1
1
a
s a
"3 a
*§ S
3
ii
5 5
1
§ |
g
n. el
APPROXIMATE SAFE LOADS IK LBS. OK STEEL BEAMS.
Formulae for Transverse Strength of Beams*— Referring to
table on preceding page,
P = load at middle;
W= total load, distributed uniformly;
I = length, 6 = breadth, d = depth, in inches;
E =s modulus of elasticity;
R = modulus of rupture, or stress per square inch of extreme fibre;
/ =r moment of inertia;
c = distance between neutral axis and extreme fibre.
For breaking load of circular section, replace 5d2 by 0.59d9.
For good wrought iron the value of R is about 80,000, for steel about 120,000,
the percentage of carbon apparently having no influence. (Thurston, Iron
and Steel, p. 491),
For cast iron the value of R varies greatly according to quality. Thurston
found 45,740 and 67,980 in No. 2 and No. 4 cast iron, respectively.
For beams fixed at both ends and loaded in the middle, Barlow, by experi-
ment, found the maximum moment of stress = 1/6PI instead of 1&PI, the
result given by theory. Prof. Wood (Resist. Matls. p. 155) says of this case:
The phenomena are of too complex a character to admit of a thorough and
exact analysis, and it is probably safer to accept the results of Mr. Barlow
in practice than to depend upon theoretical results.
APPROXIMATE: GREATEST SAFE LOADS IN LBS. ON
STEEL BEAMS. (Pencoyd Iron Works.)
Based on fibre strains of 16,000 Ibs. for steel. (For iron the loads should be
one-eighth less, corresponding to a fibre strain of 14,000 Ibs. per square inch.)
L = length in feet between supports; a = interior area in square
A = sectional area of beam in square inches;
inches; d = interior depth in inches.
D = depth of beam in inches. w = working load in net tons.
Shape of
' Section.
Greatest Safe Load in Pounds.
Deflection in Inches.
Load in
Middle.
Load
Distributed.
Load in
Middle.
Load
Distributed.
Solid Rect-
angle.
890.4D
1 780.4 D
wL*
S2AD*
tc£3
L
L
52AD*
HollowRect-
angle.
890UD-orf)
1780C4D-ad)
wL*
wL*
L
L
32UZ)«-ad2)
52UZ)2-ada)
Solid Cylin-
der.
M7AD
13334Z)
wLs
24AD*
wl?
3SAD*
L
L
Hollow
Cylinder.
667UD-ad)
1333(AD-ad)
wL*
wL*
L
L
24(AD*-ad*)
38(AD*-ad?)
Even-legged
Angle or
Tee.
S85AD
1710AD
wL*
wL*
L
L
32^Z>»
52AD*
Channel or
Zbar.
1525AD
3Q5QAD
wL?
wL*
85AD*
L
L
53^D2
Deck Beam.
1380 AD
2760 AD
wL*
504D*
wL*
L
L
SOAD*
I Beam.
I
1695^1)
mQAD
mL*
wL*
L
L
5&AD*
934Z>'
II
III
IV
V
270
STRENGTH OF MATERIALS.
The above formulae for the strength and stiffness of rolled beams of va-
rious sections are intended for convenient application in cases where
strict accuracy is not required.
The rules for rectangular and circular sections are correct, while those for
the flanged sections are approximate, and limited in their application to the
standard shapes as given in the Pencoyd tables. When the section of any
beam is increased above the standard minimum dimensions, the flanges re-
maining unaltered, and the web alone being thickened, the tendency will be
for the load as found by the rules to be in excess of the actual; but within
the limits that it is possible to vary any section in the rolling, the rules
will apply without any serious inaccuracy.
The calculated safe loads will be approximately one half of loads that
would injure the elasticity of the materials.
The rules for deflection apply to any load below the elastic limit, or less
than double the greatest safe load by the rules.
If the beams are long without lateral support, reduce the loads for the
ratios of width to span as follows :
Length of Beam.
20 times flange width.
30 " " "
40 " '• **
50 ** «* •*
60 " »• ••
70 " " "
These rules apply to beams supported at each end. For beams supported
otherwise, alter the coefficients of the table as described below, referring to
the respective columns indicated by number.
Proportion of Calculated Load
forming Greatest Safe Load.
Whole calculated load.
9-10 " "
8-10 " "
7-10 ••
6-10 " ••
5-10 " "
Changes of Coefficients for Special Forms of Beams.
Kind of Beam.
Coefficient for Safe
Load.
Coefficient for Deflec-
tion.
Fixed at one end, loaded
at the other.
One fourth of the coeffi-
cient, col. II.
One sixteenth of the co-
efficient of col. IV.
Fixed at one end, load
evenly distributed.
One fourth of the coeffi-
cient of col. III.
Five forty-eighths of the
coefficient of col. V.
Both ends rigidly fixed,
or a continuous beam,
with a load in middle.
Twice the coefficient of
col. II.
Four times the coeffi-
cient of col. IV.
Both ends rigidly fixed,
or a continuous beam,
with load evenly dis-
tributed.
One and one-half times
the coefficient of col.
III.
Five times the coefficient
of col. V.
ELASTIC RESILIENCE.
In a rectangular beam tested by transverse stress, supported at the ends
and loaded in the middle,
2 Rbd*
p-3-~T~;
1 PJ3
~lEbd* '
in which, if P is the load in pounds at the elastic limit, R = the modulus of
transverse strength, or the strain on the extreme fibre, at the elastic limit,
E= modulus of elasticity, A = deflection, I, 6, and d= length, breadth, and
depth in inches. Substituting for P in (2) its value in (1), we have
1 Rl*
6 JEtT
BEAMS OF UNIFORM STRENGTH THROUGHOUT LENGTH. 271
The elastic resilience = half the product of the load and deflection
and the elastic resilience per cubic inch
_1 PA
"~ 2 Ibd '
Substituting the values of P and A, this reduces to elastic resilience per
cubic inch = jg^» which is independent of the dimensions; and therefore
fhe elastic resilience per cubic inch for transverse strain may be used as a
modulus expressing one valuable quality of a material.
Similarly for tension:
Let P = tensile stress in pounds per square inch at the elastic limit;
e = elongation per unit of length at the elastic limit;
E = modulus of elasticity = P -*- e\ whence e — P-*- E.
Then elastic resilience per cubic inch = y%Pe — .
2 E
BEAMS OF UNIFORM STRENGTH THROUGHOUT
THEIR LENGTH.
The section is supposed in all cases to be rectangular throughout. The
beams shown in plan are of uniform depth throughout. Those shown in
elevation are of uniform breadth throughout.
B — iireadth of beam. D = depth of beam.
Fixed at one end, loaded at the other;
curve parabola, vertex at loaded end; BDZ
proportional to distance from loaded end.
The beam may be reversed, so that the up-
per edge is parabolic, or both edges may be
parabolic.
Fixed at one end, loaded at the other;
triangle, apex at loaded end; BD* propor-
tional to the distance from the loaded end.
Fixed at one end; load distributed; tri-
angle, apex at unsupported end; BD'* pro-
portional to square of distance from unsup-
ported end.
Fixed at one end; load distributed ; curves
two parabolas, vertices touching each other
at unsupported end; BD* proportional to
distance from unsupported end.
Supported at both ends; load at any one
point; two parabolas, vertices at the points
of support, bases at point loaded ; BD* pro-
portional to distance from nearest point oi
support. The upper edge or both edges
may also be parabolic.
Supported at both ends; load at any one
point; two triangles, apices at points of sup-
port, bases at point loaded; BD* propor-
tional to distance from the nearest point of
support.
Supported at both ends; load distributed;
curves two parabolas, vertices at the middle
of the beam; bases centre line of beam; BD*
proportional to product of distances from
points of support.
Supported at both ends; load distributed;
curve semi-ellipse; BD* proportional to the
product of the distances from the points of
support.
272 STKENGTH OF MATERIALS.
PROPERTIES OF ROLLED STRUCTURAL STEEL.
Explanation of Tables of the Properties of I Reams,
Channels, Angles, Deck -Beams, Bulb Angles, Z Bars,
Tees, Trough and Corrugated Plates.
(Tne Carnegie Steel Co., Limited.)
The tables for I beams and channels are calculated for all standard
weights to which each pattern is rolled. The tables for deck-beams and
angles are calculated for the minimum and maximum weights of the
various shapes, while the properties of Z bars are given for thicknesses
differing by 1/16 inch.
For tees, each shape can be rolled to one weight only.
Column 12 in the tables for I beams and channels, and column 9 for
deck-beams, give coefficients by the help of which the safe, uniformly
distributed load may be readily determined. To do this, divide the coeffi-
cient given by the span or distance between supports in feet. If the weight
of the deck-beams is intermediate between the minimum and maximum
weights given, add to the coefficient for the minimum weight the value given
for one pound increase of weight multiplied by the number of pounds
the section is heavier than the minimum.
If a section is to be selected (as will usually be the case), intended to carry
a certain load for a length of span already determined on, ascertain the
coefficient which this load and span will require, and refer to the table for a
section having a coefficient of this value. The coefficient is obtained by mul-
tiplying the load, in pounds uniformly distributed, by the span length in feet.
In case the load is not uniformly 'distributed, but is concentrated at the
middle of the span, multiply the load by 2, and then consider it as uniformly
distributed. The deflection will be 8/10 of the deflection for the latter load.
For other cases of loading obtain the bending moment in ft.-lbs.; this
multiplied by 8 will give the coefficient required.
If the loads are quiescent, the coefficients for a fibre stress of 16,000 Ibs.
per square inch for steel may be used ; but if moving loads are to be pro-
vided for, a coefficient of 12,500 Ibs. should be taken. Inasmuch as the effects
of impact may be very considerable (the stresses produced in an unyielding
inelastic material by a load suddenly applied being double those produced
by the same load in a quiescent state), it will sometimes be advisable to use
still smaller fibre stresses than those given in the tables. In such cases the
coefficients may be determined by proportion. Thus, for a fibre stress of
8,000 Ibs. per square inch the coefficient will equal the coefficient for 16,000
Ibs. fibre stress, from the table, divided by 2.
The section moduli, column 11, are used to determine the fibre stress per
square inch in a beam, or other shape, subjected to bending or transverse
stresses, by simply dividing the bending moment expressed in inch-pounds
by the section modulus.
In the case of T shapes with the neutral axis parallel to the flange, there
will be two section moduli, and the smaller is given. The fibre stress cal-
culated from it will, therefore, give the larger of the two stresses in the
extreme fibres, since these stresses are equal to the bending moment divided
by the section modulus of the section.
For Z bars the coefficients (C) may be applied for cases where the bars are
subjected to transverse loading, as in the case of roof-purlins.
For angles, there will be two section moduli for each position of the neutral
axis, since the distance between the neutral axis and the extreme fibres has
a different value on one side of the axis from what it has on the other. The
section modulus given in the table is the smaller of these two values.
Column 12 in the table of the properties of standard channels, giving the
distance of the center of gravity of channel from the outside of web, is used
to obtain the radius of gyration for columns or struts consisting of two
channels latticed, for the case of the neutral axis passing through the centre
of the cross-section parallel to the webs of the channels. This radius of
gyration is equal to the distance between the centre of gravity of the chan-
nel and the centre of the section, i.e., neglecting the moments of inertia of
the channels around their own axes, thereby introducing a slight error on
the side of safety.
(For much other important information concerning rolled structural
shapes, see the "Pocket Companion " of The Carnegie Steel Co., Limited,
Pittsburg, Pa., price $2.)
PROPERTIES OF ROLLED STRUCTURAL SHAPES. 273
Properties of Carnegie Standard I Beams- Steel.
1
2
3
4
5
6
7
8
9
10
11
12
£»i
rfog
§"««
»- i o
§.sS
g|§
fo.2
J3
£P^
13s
ss^*^
131
& c°
action Index.
epth of Beam.
reight per Foot,
a
.2
1
o
hickness of We
7idth of Flange
foment of In<
Neutral Axis
pendicular to
at Centre.
oment of Im
Neutral Axis
cident with C
Line of Web.
adius of Gyre
Neutral Axis
pendicular to
at Centre.
5 v
ffcll
ection Modulus,
tral Axis Perpe
ular to Web al
tre.
oefficient of Str
for Fibre Stre
1 6,000 Ibs. per s
02
3
&
<J
^
f-
5
s
«
5_
«
0
in
Ibs.
sq. in.
in
in.
I
//
r
r/
8
~C
Bl
24
100
29.41
0.75
7.25
2380.3
48.56
9.00
.28
198.4
2115800
95
27.94
0.69
7.19
2309.6
47.10
9.09
.30
192.5
2052900
»k
"
90
26.47
0.63
7.13
2239.1
45.70
9.20
.31
186.6
1990300
a
4k
85
25.000.577.07
2168.6
44.35
9.31
.33
180.7
1927600
"
11
80
23.320.50
7.00
2087.9
42.86
9.46
.36
174.0
1855900
B3
•20
75
22.06
0.65
6.40
1268.9
30.25
7.58
.17
126.9
1353500
M
70
20.590.57
6.32
1219.9
29.04
7.70
.19
122.0
1301200
44
"
65
19.080.506.25
1169.6
27.86
7.83
.21
117.0
1247600
B80
18
70
20.59
0.72
6.26
921.3
24.62
6.69
.09
102.4
1091900
65
19.12,0.646.18
881.5
23.47
6.79
.11
97.9
1044800
44
41
60
17.65
0.55
6.09
841.8
22.38
6.91
.13
93.5
997700
44
11
55
15.93,0.46 6.00
795.6
21.19
7.07
.15
88.4
943000
B7
15
55
16.18
0.66
5.75
511.0
17.06
5.23
.95
68 1
726800
•'
50
14.71;0.56'5.65
483.4
16.04
5.73
.04
64.5
687500
M
u
45
13.240.46!5.55
455.8
15.09
5.87
.07
60.8
648200
M
'*
42
12.48
0.41
5.50
441.7
14.62
5.95
.08
58.9
628300
B9
12
35
10.290.44!5.09
228.3
10.07
4.71
0.99
38.0
405800
•'
4i
31.5
9.26
0.35
5.00
215.8
9.50
4.83
1.01
36.0
383700
Bll
10
40
11.78 0.7615.10
158.7
9.50
3.67
0.90
31.7
338500
41
35
10.290.60,4.95
146.4
8.52
3 77
0.91
29.3
312400
44
"
30
8.82
0.45
4.80
134.2
7.65
3.90
0.93
26.8
286300
"
"
25
7.370.31
4.66
122.1
6.89
4.07
0.97
24.4
260500
B13
9
35
10.29
0.73
4.77
111.8
7.31
3.29
0.84
24.8
265000
41
30
8.820.57
4.61
101.9
6.42
3.40
0.85
22.6
241500
4'
25
7.35
0.41
4.45
91.9
5.65
3.54
0.88
20.4
217900
K
21
6.310.29'4.33
84.9
5.16
3.67
0.90
18.9
201300
B15
8
25.5
7.500.544.27
68.4
4.75
3.02
0.80
17.1
182500
44
"
23
6.76
0.45
4.18
64.5
4.39
3.09
0.81
16 1
172000
44
41
20.5
6.030.364.09
60.6
4.07
3 17
0.82
15.1
161600
14
"
18
5.33
0.27
4.00
56.9
3.78
3.27
0.84
14.2
151700
B17
7
20
5.880.463.87
42.2
3.24
2.68
0.74
12.1
128600
44
tk
17.5
5.150.353.76
39.2
2.94
2.76
0.76
11.2
119400
44
44
15
4.43
0.25
3.66
36.2
2.67
2.86
0.78
10.4
110400
B19
6
17M
5.070.483.58
26.2
2.36
2.27
0.68
8.7
93100
44
14
14% 4.34
0.35
3.45
24.0
2.09
2.35
0.69
8.0
85300
"
44
12J4 3.610.233.33
21.8
1.85
2.46
0.72
7.3
77500
B21
5
14%
4.34
0.50
3.29
15.2
1.70
1.87
0.63
6.1
64600
44
44
12J4
3.600.363.15
13.6
1.45
1.94
0.63
5.4
581 CO
44
44
m
2.870.21 3.00
12.1
1.23
2.05
0.65
4.8
51600
B23
4
10.5
3.09
0.41
2.88
7.1
1.01
1.52
0.57
3.6
38100
44
44
9.5
2.790.34
2.80
6.7
0.93
1.55
0.58
3.4
36000
44
"
8.5
2.50
0.26
2.73
6.4
0.85
1.59
0.58
3.2
33900
"
4t
7.5
2.21
0.192.66
6.0
0.77
1.64
0.59
3.0
31800
B77
3
7.5
2.21
0.36
2.52
2.9
0.60
1.15
0.52
1.9
20700
'•
6.5
1.91
0.26 2.42
2.7
0.53
1.19
0.52
1.8
19100
vj
"
5.5 1.630.17
2.33
2.5
0.46
1.23
0.53
1.7
17600
L = safe loads in Ibs., uniformly distributed; I = span in feet;
M = moment of forces in ft.-lbs. ; C = coefficient given above.
12 '
/ = fibre stress.
274
STRENGTH OF MATERIALS.
Properties of Special I Beams- Steel.
1
2
3
4
5
6
7
8
9
10
11
12
.££'•8
« .5 S
gfe«
= cS
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S^ 5«
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iaats
ll?5
ilfl
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02
£
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H
?
S
s
PH
P5
03^ '
o
n.
Ibs.
sq. in.
in.
in.
I
/'
r
r'
5
C
B2
20
100
29.41
0.88
7.28
1655.8
52.65
7.50
.34
165 6
1766100
k>
95
27.94
0.81
7.21
1606.8
50.78
7.58
.35
160.7
1713900
"
'I
90
26.47
0,74
7.14
1557.8
48.98
7.67
.36
155.8
1661600
«'
"
85
25.00
0.66
7.06
1508.7
47.25
7.77
.37
150.9
1609300
"
"
80
23.73
0.60
7.00
1466.5
45.81
7.86
.39
146.7
1564300
B4
15
100
29.41
1.18
5.77
900.5
50.98
5.53
.31
120.1
1280700
95
27.94
1.08
6.67
872.9
48.37
5.59
.32
116.4
1241500
*«
«
90
26.47
0.99
6.58
845.4
45.91
5.65
.32
112.7
1202300
M
«
85
25.00
0.89
6.48
817.8
43.57
5.72
.32
109.0
1163000
"
»
80
23.81
0.81
6.40
795.5
41.76
5.78
.32
106.1
1131300
B5
15
75
22.06
0.88
6.29
691.2
30.68
5.60
.18
9-2.2
983000
"
70
20.59
0.78
6.19
663.6
29.00
5.68
.19
88.5
943800
'*
14
65
19.12
0.69
6.10
636.0
27.42
5 77
.20
84.8
904600
*«
M
60
17.67
0.59
6.00
609.0
25.96
5.87
.21
81.2
866100
B8
12
55
16.18
0.82
5.61
3-^1.0
17.46
4.45
.04
53.5
570600
50
14.71
0.70
5.49
303.3
16.12
4.54
.05
50.6
539200
"
M
45
13.24
0.58
5.37
285.7
14.89
4.65
.06
47.6
507900
"
"
40
11.84
0.46
5.25
268.9
13.81
4.77
.08
44.8
478100
Properties of Carnegie Trough Plates— Steel.
Section
Index.
Size,
in
Inches.
Weight
per
Foot.
Area
of Sec-
tion.
Thick-
ness in
Inches.
Moment of
Inertia,
Neutral
Axis
Parallel to
Length.
Section
Modulus,
Axis as
before.
Radius
of Gyra-
tion,
Axis as
before.
MIO
Mil
M12
M!3
M14
9^x3%
9^| x 3%
9^ x 3%
Ibs.
16.32
18.02
19.72
21.42
23.15
sq. in.
4.8
5.3
5.8
6.3
6.8
H
9/16
%
11/16
H
I
3.68
4.13
4.57
5.02
5.46
S
1.38
1.57
1.77
1.96
2.15
0.91
0.91
0.90
0.90
0.90
Properties of Carnegie Corrugated Plates -Steel.
Moment of
Section
Index.
Size,
m
Inches.
Weight
per
Foot.
Area
of Sec-
tion.
Thick-
ness in
Inches.
Inertia,
Neutral
Axis
Parallel to
Length.
Section
Modulus,
Axis as
before.
Radius
of Gyra-
tion,
Axis as
before.
Ibs.
sq. in.
/
8
r
M30
gs/ x ji/
8.06
2.4
y*
0.64
0.80
0.52
M31
8M x \\4>
10.10
3.0
5/16
0.95
1.13
0.57
M32
33? x lV«j>
12.04
3.5
%
1.26
1.42
0.62
M33
12 3/16x2%
17.75
5.2
%
4.79
3.33
0.96
M34
M35
12 3/16 x 2%
12 3/16x294
20.71
23.67
6.1
7.0
7/16
g
5.81
6.82
3.90
4.46
0.98
0.99
PROPERTIES OF ROLLED STRUCTURAL STEEL. 275
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PROPERTIES OF ROLLED STRUCTURAL STEEL. 27?
Properties of Standard Channels— Steel.
2
3
4
5
6
7
8
9
10
11
12
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|||
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111
lie
c K r.
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5
Ibs.
sq. in.
in.
in.
i
I'
r
r,
s
C
X
55.
J6.18
0.823.82
430.2
12.19
5.16
.868
57.4
611900
.823
50.
14.71
0.723.72
402.7
11.22
5.23
.873
53.7
572700
.803
45.
13.24
0.623.62
375.1
10.29
5.32
.882
50.0
533500
.788
40.
11.76
0.523.52
347.5
9.39
5.43
.893
46.3
494200
.783
35.
10.29
0.43
3.43
320.0
8.48
5.58
.908
42.7
455000
.789
33.
9.90
0.403.40
312.6
8.23
5.62
.912
41.7
444500
794
40.
11.76
0.763.42
197.0
6.63
4.09
.751
32.8
350200
.722
35.
10.29
0.643.30
179.3
5.90
4.17
.757
29.9
318800
.694
30.
8.82
0.51 3.17
161.7
5.21
4.28
.768
26.9
287400
.677
25.
7.35
0.393.05
144.0
4.53
4.43
.785
24.0
256100
.678
20.5
6 03
0.282.94
128.1
3.91
4.61
,805
21.4
227800
.704
35.
10.29
0.823.18
115.5
4.66
3.35
.672
23.1
246400
.695
30.
8.82
0.683.04
103.2
3.99
3.42
.672
20.6
220300
.651
25.
7.35
0.532.89
91.0
3.40
3.52
.680
18.2
194100
.620
20.
5.88
0.382.74
78.7
2.85
3.66
.696
15.7
168000
.609
15.
4.46
0.24:2.60
66.9
2.30
3.87
.718
13.4
142700
.639
25.
7.35
0.61|2.81
70.7
2.98
3.10
.637
15.7
167600
.615
20.
5.88
0.45 2.65
60.8
2.45
3.21
.646
13.5
144100
.585
15.
4.41
0.292.49
50.9
1.95
3.40
665
11.3
120500
.590
13V4
3.89
0.232.43
47.3
1.77
3.49
.674
10.5
112200
.607
2114
6.25
0.58 2.62
47.8
2.25
2.77
.600
11.9
127400
.587
5.51
0.49 2.53
43.8
2.01
2.82
.603
11.0
116900
.567
16V4
4.78
0.402.44
39.9
1.78
2.89
.610
10.0
106400
.556
13%
4.04
0.31]2.35
36.0
1.55
2.98
.619
9.0
96000
.557
11J4
3.35
0.222.26
32.3
1.33
3.11
.630
8.1
86100
.576
19%
5.81
0.632.51
33.2
1.85
2.39
.565
9.5
101100
.583
17/4
5.07
0.532.41
30.2
1.62
2.44
.564
8.6
92000
.555
14%
4.34
0.422.30
27.2
1.40
2.50
.568
7.8
82800
.535
12J4
3.60
0.322.20
24.2
1.19
2.59
.575
6.9
73700
.528
9%
2.85
0.21
2.09
21.1
0.98
2.72
.586
6.0
66800
.546
15.5
4.56
0.562.28
19.5
1.28
2.07
.529
6.5
69500
.546
13.
3.82
0.442.16
17.3
1.07
2.13
.529
5.8
61600
,517
10.5
3.09
0.322.04
15.1
0.88
2.21
.534
5.0
53800
.503
8.
2.38
0.201.92
13.0
0.70
2.34
.542
43
46200
.517
11.5
3.38
0.482.04
10.4
0.82
1.75
.493
4.2
44400
.508
9.
2.65
0.33
1.89
8.9
0.64
1.83
.493
3.5
37900
.481
6.5
1.95
0.19
1.75
7.4
0.48
1.95
.498
3.0
31600
489
714
2.13
0.32
1.72
4.6
0.44,
1.46
.455
2.3
24400
.463
6^4
.84
0.25
1.65
4.2
0.38
1.51
.454
2.1
22300
.458
.55
0.18
1.58
3.8
0.32
1.56
.453
1.9
20200
.464
6.4
.76
0.36
1.60
2.1
0.31
1.08
.421
1.4
14700
.459
5.
.47
0.26
1.50
1.8
0.25
1.12
.415
1.2
13100
.443
4.
.19
0.17
1.41
1.6
0.20
1.17
.409
1.1
11600
.443
L = safe load in Ibs., uniformly distributed; I = span in feet;
M — moment of forces in ft.-lbs.; C — coefficient given above.
f=^-; C=Ll = 8M =
12 *'
/ = fibre stress.
278 PROPERTIES OF ROLLED STRUCTURAL STEEL.
Carnegie Peck-beams,
1
2
3
4'
5
G
7
8
9
10 1 11
ft
1
,
1
OJ
i
5
Eftjjo
A
rfl
3*3
II
'•Z"* o
a* 3-,-u
II
Ka
(Li
l^o
Depth of Beai
Weight per F
Area of Secti
Thickness of
Width of Fla
Moment of In
Neutral Axi
pendicular
Web.
Section Modu
Neutral Axi
pendicular
Web.
Radius of Gyr
Neutral Axi
pendicular
Web.
Coefficient of
Strengthfor
Stress of 16,0
per sq. in.
Moment of In
Neutral Axi
incident wi1
Centre Line
Web.
Radius of Gyr
Neutral Axi
incident wit
Centre Line
Wet.
in.
Ihs.
sq.in.
in
in.
I
s
r
C
F
?•'
10
35.70
10.5
.63
5.50
139.9
25.7
3.64
274100
7.41
0.84
10
27.23
8.0
.38
5.25
118.4
21.2
3.83
226100
6.12
0.87
9
30.00
8.8
.57
5.07
93.2
19.6
3.25
208500
5.18
0.75
9
26.00
7.6
.44
4.94
85.2
17.7
3.35
189100
4.61
0.76
8
24.48
7.2
.47
5.16
62.8
14.1
2.97
150100
4.45
0.79
8
20.15
5.9
.31
5.00
55.6
12.2
3.08
129800
3.90
0.82
7
23.46
6.9
.54
5.10
45.5
11.7
2.57
124600
4.30
0.79
7
18.11
5.3
.31
4.87
38.8
9.7
2 70
103000
3.55
0.82
6
18.36
5.4
.43
4.53
26.8
8.2
2.25
87700
2.73
0.72
6
15. 3C
4.5
.28
4.38
24.0
7.3
2.33
77400
2.38
0.73
Add to coefficient C for every Ib. increase in weight of beam, for 10-in.
beams, 4900 Ibs.; 9-in., 4500 Ibs.; 8-in., 4000 Ibs.; 7-in., 3400 Ibs., 6-in., 3000 Ibs.
Carnegie Bulb Angles,
10
26.50
7.80
48
3 5
104.2
19.9
3.66
211700
9
21.80
6.41
44
3,5
69.3
14.5
3.33
154200
8
19.23
5 6fi
41
3.5
48.8
11.7
2.95
124800
7
18.25
5.37
44
3 0
34.9
9,6
2.56
102300
6
17 ?0
5 06
50
3 0
23.9
7.6
2.16
80500
6
13 75
4.04
.38
3 0
20.1
6.6
2.21
70400
6
12.30
3.62
31
3 0
18.6
5.7
2.28
60400
5
10.00
2.94
.31
2.5
10.2
4.1
1.86
43300
Carnegie T Shapes.
1
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17020
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0.94
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7540
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0.60
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5230
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15.6
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1.56
10.7
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1.54
2.8
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0.79
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4 X5
12.0
3.54
1.51
8.5
2.43
1.56
2.1
1.06
0.78
19410
14.6
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1.37
8.0
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0.81
20400
4 X4Vj|j
11.4
3.36
1.31
6.3
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0.80
15840
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13.7
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1.18
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1.20
2.8
1.40
0.84
16190
4 X4
10.9
3.21
1.15
4.7
1.64
1.23
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0.84
13100
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0.78
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0.88
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0.88
7070
4 X2J<£
8.6
2.52
0.63
1.2
0.62
0.69
2.1
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0.92
4980
STRENGTH OP MATERIALS.
279
Carnegie T Shapes— (Continued).
1
2
3
4
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9
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2.16
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0.70
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4380
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5.8
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0.56
0.81
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0.71
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0.94
3350
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7.9
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0.48
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0.96
3180
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6.6
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2700
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12.8
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0.72
15870
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9.9
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1.19
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1.42
0.81
0.70
12380
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11.7
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1.06
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1.89
1.08
0.74
12000
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9.2
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9530
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11.73
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1.18
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11.8
3.48
1.32
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1.21
0.81
0.59
15480
3 X4
10.6
3.12
1.32
4.8
1.78
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1.09
0.72
0.60
14270
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9.3
2.7J
1.29
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1.57
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0.93
0.62
0.59
12540
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10.9
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11910
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1.1
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0.68
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0.93
0.62
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9680
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1.20
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8780
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0.92
2.1
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1.08
0.72
0.64
8110
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7.8
2.28
0.88
1.8
0.86
0.90
0.90
0.60
0.63
6900
3 X3
6.6
1.95
0.86
1.6
0.74
0.90
0.75
0.50
0.62
5900
3 X2)4
7.2
2.10
0.7
1.1
0.60
0.72
0.89
0.60
0.66
4800
3 X2)4
6.1
1.80
0.6
0.94
0.52
0.73
0.75
0.50
0.65
4100
2%X2
7.4
2.16
0.53
1.1
0.75
0.71
0.62
0.45
0.54
6000
2%Xl^
6.6
1.95
0.64
0.56
0.50
0.53
0.61
0.44
0.56
4000
2^X3
7.2
2.10
0.9
1.8
0.87
•0.92
0.54
0.43
0.51
6960
2)4X3
6.1
1.80
0.9
1.6
0.76
0.94
0.44
0.35
0.51
6110
2)4X2%
6.7
1.98
0.8
1.4
0.73
0.84
0.66
0.53
0.58
5860
2)4X2^
5.8
1.71
0.83
1.2
0.60
0.83
0.44
0.35
0.51
4830
2)4X2)^
6.4
1.89
0.76
1.0
0.59
0.74
0.52
0.42
0.53
4700
5.5
1.620.74
0 87
0.50
0.74
0.44
0.35
0.52
4000
2)|xi^
2.9
0.84
0.29
0.094
0.09
0.31
0.29
0.23
0.58
700
2)4x2)/s
4.9
1.44
0.69
0.66
0.42
0.68
0.33
0.30
0.48
3360
2)4X2^
4.1
1.20
0.66
0.51
0.32
0.67
0.25
0.22
0.47
2600
2 X2
4.3
1.26
0.63
0.45
0.33
0.60
0.23
0.23
0.43
2610
2 X2
3.7
1,08
0.59
0.36
0.25
0.60
0.18
0.18
0.42
2000
2 XlV*
3.1
0.90
0.42
0.16
0.15
0.42
0.18
0.18
0.45
1200
l%Xl^i
3.1
0.90
0.54
0.23
0.19
0.51
0.12
0.14
0.37
1550
1 % X 1 )^
3.6
1.05
0.91
0.12
0.15
0.33
0.19
0.22
0.41
1150
l%Xl)^
1.9
0.57
0.33
0.07
0.08
0.35
0.09
0.11
0.40
620
i)4xi)^
2.6
0.75
0.42
0.15
0.14
0.49
0.08
0.10
0.34
1150
l^jXl)/
1.8
0.54
0.44
0.11
0.11
0.45
0.06
0.07
0.31
860
i)4xiM
3.0
0.87
0.40
0.10
0.12
0.35
0.10
0.13
0.34
940
i)4xi)^
2.2
0.66
0.38
0.09
0.10
0.36
0 08
0.10
0.34
785
1.7
0.51
0.35
0.07
0.08
0.36
0.06
0.07
0.33
COO
1)^X1)^
1.3
0.39
0.35
0.04
0.05
0.33
0.03
0.04
0.29
420
i)4x ^
1.3
0.39
0.20
0.01
0.03
0.19
0.05
0.07
0.37
210
i)4xi)^
2.04
0.60
0.40
0.08
0.10
0.36
0.05
0.07
0.27
760
1)4x1)^
1.53
0.45
0.38
0.06
0.07
0 37
0.03
0.05
0.26
580
i xi)4
1.12
0.33
0.50
0.08
0.08
0.48
0.01
0.02
0.19
605
1 XI
1.23
0.36
0.32
0.03
0.05
0.29
0.02
0.04
0.21
370
1 XI
0.87
0.26
0.29
0.02
0.03
0.29
0.01
0.02
0.21
270
STRENGTH OF MATERIALS.
Properties of Standard and Special Angles of Minim um
and Maximum Thicknesses and Weights.
ANGLES WITH EQUAL LEGS.
1
2
3
4
5
6
7
8
9
w
A rj *O
£0?
iq
3 BJg
tip g\ *~j
ff*I
ll
^ 2
tf-Sn*
^s§
K'SI
? £.§!
CpQ
2 bifU
g
g
P£
1 8^
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0.20^
&
o
o
M-23 >
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^ >
93 R JO
02
t_
o
O«M
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*S"a2 S *
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1
w*
5
3
a-baJ
3^2 «
M^ P
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is "3 ® °
CO
a
c
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o
c > c
a<^to~
§2^E
si^E
s^'S;
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IB rh S
g C C O
Zj •— — O
T3 f- t- O
Ss o "^J
5
s
5
s
s
o, ,
&*"
3
3
in.
in.
sq. in.
in.
J
S
r
r'
6 x6
33.1
9.74
1.82
31.92
7.64
1.81
1.17
6 x6
7/16
17.2
5.06
1.66
17.68
4.07
1.87
1.19
*5 x5
27.2
7.99
1.57
17.75
5.17
1.49
0.98
*5 x5
%
12.3
3.61
1.39
8.74
2.42
1.56
0.99
4 x4
13/16
19.9
5.84
1.29
8.14
3.01
1.18
0.80
4 x4
5/16
8.2
2.40
1.12
3.71
1.29
1.24
0.82
13/16
17.1
5.03
1.17
5.25
2.25
1.02
0.69
3>£ x 3^1
8.5
2.48
l.Oi
2.87
1.15
1.07
0.70
3 x3
%
11.4
3.36
0.98
2.62
1.30
0.88
0.59
3 x3
\A
4.9
1.44
0.84
1.24
0.58
0.93
0.60
1Z
8.5
2.50
0.87
1.67
0.89
0.82
0.54
*2?| x 2^|
y±
4.5
1.31
0.78
0.93
0.48
0.85
0.55
2Ux2^
14
7.7
2.25
0.81
1.23
0.73
0.74
0.49
2V£ x ^V£
\A
4.1
1.19
0.72
0.70
0.40
0.77
0.50
*2}>4. x 2^4
\£
6.8
2.00
0.74
0.87
0.58
0.66
0.48
*2J4 x 2>4
%
3.7
1.06
0.66
0.51
0.32
0.69
0.46
2 x2
7/16
5.3
1.56
0.66
0.54
0.40
0.59
0.39
2 x2
3/16
2.5
0.72
0.57
0.28
0.19
0.62
0.40
7/16
4.6
1.30
0.59
0.35
0.30
0.51
0.35
1^x1%
3/16
2.1
0.62
0.51
0.18
0.14
0.54
0.36
l^xl^
%
3.4
0.99
0.51
0.19
0.19
0.44
0.31
jiz x ji/
3/16
1.8
0.53
0.44
0.11
0.104
0.46
0.32
114x114
5/16
2.4
1.0
0.69
0.30
0.42
0.35
0.09
0.044
0.109
0.049
0.36
0.38
0.25
0.26
*l^xl^
5/16
2.1
0.81
0.39
0.063
0.087
0.32
0.24
*1'*6 x 1V6
ix
0.9
0.27
0.32
0.032
0.039
0.34
0.23
l' x 1
/4
1.5
0.44
0.34
0.037
0.056
0.29
0.20
1 xl
^
0.8
0.24
0.30
0.022
0.031
0.81
0.21
*%x %
3/16
1.0
0.29
0.29
0.019
0.033
0.26
0.18
*% x %
0.7
0.21
0.26
0.014
0.023
0.26
0.19
% X %
3/16
0.8
0.25
0.26
0.012
0.024
0.22
0 16
M X %
0.6
0.17
0.23
0.009
0 017
0.23
0.17
*%X %
*
0.5
0.14
0.20
0.005
0.011
0.18
0.13
Angles marked * are special.
PROPERTIES OF ROLLED STRUCTURAL STEEL. 2795
Properties of Standard and Special Angles of Minimum
and Maximum Thickness and Weights.
ANGLES WITH UNEQUAL LEGS.
1
2
3
4
5
6
7
8
9
10
11
Moments of
Inertia.
Section
Modulus.
Radii of Gyration.
^
.
I
8
r
§
_o
•i
.
£
• t->
•
•
.1
t
i
a
3
1
h
<u
8
CO
£&
£2
rvS
<3 $)
CLt fcn
II
3
Dimens
d
2
Weight p
Area of \
2 S
eutral Axis
allel to Shoi
Flange.
eutral Axis '.
allel to Lonj
Flange.
eutral Axis '
allel to Shoi
Flange.
eutral Axis '.
allel to Lonj
Flange.
eutral Axis !
allel to Shoi
Flange.
east Radius.
Axis diagon
*
*
*
fc
~
55
£
inches.
inch.
Ibs.
sq.in.
1
32 3
9.50
7.53
45.37
2.96
10.58
0.89
2.19
.88
*7 X3H
7/16
15.0
4.40
3.95
22.56
1.47
5.01
0.95
2.26
.89
6 X4
27.2
7.99
9.75
27.73
3.39
7.15
1.11
1.86
.88
6 X4
H
12.3
3.61
4.90
13.47"
1.60
3.32
1.17
1.93
.88
6 X3^£
%
25.7
7.55
6.55
26.38
2.R9
6.98
0.93
1.87
.78
6 X3U
%
11.7
3.42
3.34
12.86
1.23
3.25
0.99
1.94
.77
*5 X4
JA
24.2
7.11
9.23
16.42
3.31
4.99
1.14
1.52
.88
*5 X4
%
11.0
3.23
4.67
8.14
1.57
2.34
1.20
1.59
.86
5 X3^
%
22.7
6.67
6.21
15.67
2.52
4.88
0.96
1.53
.77
5 X3>£
%
10.4
3.05
3.18
7.78
1.21
2.29
1.02
1.60
.76
5 X3
13/16
19.9
5.84
3.71
13.98
1.74
4.45
0.80
1.55
.66
5 X3
5/16
8.2
2.40
1.75
6.26
0.75
1.89
0.85
1.61
.66
*4^X3
13/16
18.5
5.43
3.60
10.33
1.71
3.62
0.81
1.38
.67
*4J^X3
%
9.1
2.67
1.98
5.50
0.88
1.83
0.86
1.44
.66
*4 X 3 J/a
13/16
18.5
5.43
5.49
7.77
2.30
2.92
1.01
1.19
.74
*4 X3^j
%
9.1
2.67
2.99
4.18
1.18
1.50
1.06
1.25
.73
4 X3
13/16
17.1
5.03
3.47
7.34
1.68
2.87
0.83
1.21
.66
4 X3
5/16
7.1
2.09,
1.65
3.38
0.74
1.23
0.89
1.27
.65
3^X3
13/16
15.7
4.62
3.33
4.98
1.65
2.20
0.85
1.04
.65
3^X3
5/16
6.6
1.93
1.58
2.33
0.72
0.96
0.90
1.10
.63
3V^X2^
11/16
12.4
3.65
1.7'2
4.13
0.99
1.85
0.67
1.06
.58
3J^X2i/6
y4
4.9
1.44
0.78
1.80
0.41
0.75
0.74
1.12
.55
*3J4X2
9/16
-9.0
2.64
0.75
2.64
0.53
1.30
0.53
1.00
.45
*3J4X2
M
4.3
1.25
0.40
1.36
0.26
0.63
0.57
1.04
.44
3 X2^
9/16
9 5
2,78
1.42
2.28
0.82
1.15
0.72
0.91
.54
3 X2J^
M
4.'5
1.31
0.74
1.17
0.40
0.56
0.75
0.95
.53
*3 X2
iz
2.25
0.67
1.92
0.47
1.00
0.55
0.92
.47
*3 X2
/4
4^0
1.19
0.39
1.09
0.25
0.54
0.56
0.95
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2^X2
H>
6.8
2.00
0.64
1.14
0.46
0.70
0.56
0.75
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2/^X2
3/16
2.8
0.81
0.29
0.51
0.20
0.29
0.60
0.79
.43
*2J4XlJ^
fc
5.5
1.63
0.26
0.82
0.26
0.59
0.40
0.71
.39
*~Mxi/£
3/16
2.3
0.67
0.12
0.34
0.11
0.23
0.43
0.72
.40
*2 Xl%
&
2.7
0.78
0.12
0.87
0.12
0.23
0.39
0.63
.30
*2 Xl% 3/16
2.1
0.60
0 09
0.24
0.09
0.18
0.40
0.63
.29
*1%X1 M
1.8
0.53
0.04
0.09
0.05
0.09
0.27
0.41
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IT»XI 78
i
1.0
0.28
0.02
0.05
0.03
0.06
0.29
0.44
.22
Angles marked * are special.
280
STRENGTH OF MATERIALS.
Properties of Carnegie Z Bars.
(For dimensions see table on page 178.)
1
2
3
4
5
6
7
8
9
10
11
12
g£*
•§ -a
S<w®
R-
1^.
StwOJ
|ti
!«*•£
1^.
12^
II
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£JSJ
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£°£
£ °^
£°£
£°g
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v .£8
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io°
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is
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^
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1
1
1
Section.
I-&3
§f§
f Inertij
through
ident wit
•2-gS
111
SS-3
Modulus
through
ident wit
Isi
31
'?•§!
£11
«w^2
!!
°,1
So cc r^
o!^ «J3
^3 <I5J
£ c o
a. i? — 4J
0»2 ^,!H
1 Section
I
3
Area of
a
g'Ho
o<0
III
F
d 2
o 2 d
Sfio
§<io
02
.!»!
|5l
-•2.S
S H 0
^<JO
W
=11
|«3
*!?!
Is II
o
.£^|
tiglJ
oS a-3
Ibs.
sq. in.
j
I
S
£
r
?•
r
c
C'
Zl
15.6
4.59
25.32
9.11
8.44
2.75
2.35
1.41
0.83
90,000
67,500
"
18.3
5.39
29.80
10.95
9.83
3.27
2.35
1.43
0.84
104,800
78,600
"
21.0
6.19
34.36
12.87
11.22
3.81
2.36
1.44
0.84
119,700
89,800
Z2
22.7
6.68
34.64
12.59
11.55
3.91
2.28
1.37
0.81
123,200
92,400
"
25.4
7.46
38.86
14.42
12.82
4.43
2.28
1.39
0.82
136,700
102,600
"
28.0
8.25
43.18
16.34
14.10
4.98
2.29
1.41
0.84
150,400
112,800
Z3
?9.3
8.63
42.12
15.44
14.04
4.94
2.21
1.34
0.81
149,800
112,300
41
32.0
9.40
46.13
17.27
15.22
5.47
2.22
1 .36
0.82
162,300
121,800
"
34.6
10.17
50.22
19.18
16.40
6.02
2.22
1.37
0.83
174,900
131,200
Z4
11.6
3.40
13.36
6.18
5.34
2.00
1.98
1.35
0.75
57,000
42,700
*•
13.9
4.10
16.18
7.65
6.39
2.45
1.99
1.37
0.76
68,200
51,100
"
16.4
4.81
19.07
9.20
7.44
2.92
1.99
1.38
0.77
79,400
59,500
Zo
17.8
5.25
19.19
9.05
7.68
3.02
1.91
1.31
0.74
81,900
61,400
"
20.2
5.94
21.83
10.51
8.62
3.47
1.91
1.33
0.75
91,900
69.000
"
22.6
6.64
24.53
12.06
9.57
3.94
1.92
1.35
0.76
102,100
76,600
Z6
23.7
6.96
23.68
11.37
9.47
3.91
1.84
1.28
0.73
101,000
75,800
**
26.0
7.64
26.16
12.83
10.34
4.37
1.85
1.30
0.75
110,300
82,700
44
28.3
8.33
28.70
14.36
11.20
4.84
1.86
1.31
0.76
119,500
89,600
Z7
8.2
2.41
6.28
4.23
3.14
1.44
1.62
1.33
0.67
33,500
25,100
M
10.3
3.03
7.94
5.46
3.91
1.84
1.6-2
1.34
0.68
41,700
31.300
44
12.4
3.66
9.63
6.77
4.67
2.26
1.62
1.36
0.69
49,800
37,400
Z8
3.8
4.05
9.66
6.73
4.83
2.37
1.55
1.29
0.66
51,500
38,600
M
5.8
4.66
11.18
7.96
5.50
2.77
1.55
1.31
0.67
58,700
44,000
44
7.9
5.27
12.74
9.26
6.18
3.19
1.55
1.33
0.69
65,900
49,400
Z9
8.9
5.55
12.11
8.73
6.05
3.18
-1.48
1.25
0.66
64,500
48,400
"
20.9
6.14
13.52
9.95
6.65
3.58
1.48
1.27
0.67
70,900
53,200
14
22.9
6.75
14.97
11.24
7.26
4.00
1.49
1.29
0.69
77,400
58,100
Z10
6.7
1 97
2.87
2.81
1.92
1.10
1.21
1.19
0.55
20500
15,400
"
8.4
2.48
3.64
3.64
2.38
1.40
1.21
I. '21
0.56
25,400
19,000
Zll
9.7
2.86
3.85
3.92
2.57
1.57
1.16
1.17
0.55
27,400
20,600
1.4
3.36
4.57
4.75
2.98
1.88
1.17
1.19
0.56
31,800
23,800
Z12
2.5
3.69
4.59
4.85
3.06
1.99
1.12
1.15
0.55
3'2,600
24,500
4.2
4.18
5.26
5.70
3.43
2.31
1.12
1.17
0.56
36,600
27,400
Dimensions of lightest weight bars of each size: Zl, Z2, and Z3, depth of
web 6 in., width of flange 3^ in., thickness of metal respectively %, 9/16,
and % in.; Z4, Z5, Z6, 5 x 314 X 5/16, H, and 11/16 in.; Z7, Z8, Z9, 4 X 3 1/16
X V*, 7/16, and % in.; Z10, Zll, Z12, 3x2 11/16 X Y^ %, and
dimension is increased 1/16 in. in the next heavier weight.
,
m.
TORSIOXAL STRENGTH. 281
FLOORING MATERIAL,.
For fire-proof flooring^ the space between the floor-beams may be spanned
With brick arches, or with hollow brick made especially for the purpose, the-
latter being much lighter than ordinary brick.
Arches 4 inches deep of solid brick weigh about 70 Ibs. per square foot,
including the concrete levelling material, and substantial floors are thus
made up to 6 feet span of arch, or much greater span if the skew backs at
the springing of the arch are made deeper, the rise of the arch being prefer-
ably not less than 1/10 of the span. Hollow brick for floors are usually in
depth about ^ of the span, and are used up to, and even exceeding, spans
of 10 feet. The weight of the latter material will vary from 20 Ibs. per
square foot for 3-foot spans up to 60 Ibs. per square foot for spans of 10 feet.
Full particulars of this construction are given by the manufacturers. For
supporting brick floors the beams should be securely tied with rods to resist
the lateral pressure.
In the following cases the loads, in addition to the weight of the floor
itself, may be assumed as:
For street bridges for general public traffic 80 Ibs. per sq. ft.
For floors of dwellings 40 Ibs. " "
For churches, theatres, and ball-rooms 80 Ibs. " "
For hay-lofts 80 Ibs. " ••
For storage of grain 100 Ibs. " "
For warehouses and general merchandise 250 Ibs. " •'
Forfactories 200 to 400 Ibs. " "
For snow thirty inches deep 16 Ibs.
For maximum pressure of wind 50 Ibs. " "
For brick walls % 112 Ibs. per cu. ft.
For masonry walls *. 116-144 Ibs. *' "
Roofs, allowing thirty pounds per square foot for wind and snow:
For corrugated iron laid directly on the purlins. . . 3? Ibs. per sq. ft.
For corrugated iron laid on boards 40 Ibs. " "
For slate nailed to laths 43 Ibs. " "
For slate nailed on boards 46 Ibs. " "
If plastered below the rafters, the weight will be about ten pounds per
square foot additional.
TIE-ROBS FOR BEAMS SUPPORTING BRICK
ARCHES.
The horizontal thrust of brick arches is as follows:
_ — = pressure in pounds, per lineal foot of arch:
JK
W — load in pounds, per square foot;
8 = span of arch in feet;
R = rise in inches.
Place the tie-rods as low through the webs of the beams as possible and
spaced so that the pressure of arches as obtained above will not produce a
greater stress than 15,000 Ibs. per square inch of the least section of the bolt,
TORSION Alt STRENGTH.
Let a horizontal shaft of diameter = d be fixed at one end, and at the
other or free end, at a distance = I from the fixed end, let there be fixed a
horizontal lever arm with a weight = P acting at a distance = a from the
axis of the shaft so as to twist it; then Pa = moment of the applied force.
Resisting moment = twisting moment = — , in which S = unit shearing
resistance, J = polar moment of inertia of the section with respect to the
axis, and c = distance of the most remote fibre from the axis, in a cross-
section. For a circle with diameter d,
2S2 STRENGTH OF MATERIALS.
For hollow shafts of external diameter d and internal diameter di,
Pa - .1963d4 ~ddl* Si d =
For a square whose side = d,
j — —\ c — d y% ; — = p.
For a rectangle whose sides are b and d,
The above formulae are based on the supposition that the shearing resist-
ance at any point of the cross-section is proportional to its distance from the
axis; but this is true only within the elastic limit. In materials capable of
flow, while the particles near the axis are strained within the elastic limit
those at some distance within the circumference may be strained nearly to
the ultimate resistance, so that the total resistance is something greater
than that calculated by the formulae. (See Thurston, " Matls. of Eng.," Part
HP p. 527.) Saint Venant finds for square shafts Pa = 0.208d9S (Cotterill,
44 Applied Mechanics,1' pp. 348, 355). For working strength, however, the
formulae may oe used, with S taken at the safe working unit resistance.
For a rectangle, sides b (longer) and d (shorter) and area A,
Pa - 8A*
~
The ultimate torsional shearing resistance S is about the same as the di-
rect shearing resistance, and may be taken at 20,000 to 25,000 Ibs. per square
inch for cast iron, 45,000 Ibs. for wrought iron, and 50,000 to 150,000 Ibs. for
steel, according to its carbon and temper. Large factors of safety should
be taken, especially when the direction of stress is reversed, as in reversing
engines, and when the torsional stress is combined with other stresses, as is
usual in shafting. (See "Shafting.1")
Elastic Resistance to Torsion.— Let I = length of bar being
twisted, d = diameter, P = force applied at the extremity of a lever arm
of length = a, Pa = twisting moment, G = torsional modulus of elasticity,
0 — angle through which the free end of the shaft is twisted, measured in
arc of radius = 1.
For a cylindrical shaft
*OGd*m 32PaZ. 32PM. 32
Pa=-' *=' G=Z~> -=10.186.
If a = angle of torsion in degrees,
_ an- m _ 1800 _ 180 X 32Pa7 _ 583. 6Pa*
~~ 180 ' IT rrWG d*G '
The value of G is given by different authorities as from % to 2/5 of E, the
modulus of elasticity for tension.
COMBINED STRESSES.
(From Merriman's "Strength of Materials.")
Combined Tension and Flexure.— Let A = the area of a bar
subjected to both tension and flexure, P= tensile stress applied at the ends,
jp -s- A = unit tensile stress, S = unit stress at the fibre on the tensile side most
remote from the neutral axis, due to flexure alone, then maximum tensile
unit stress = (P-*-A)-\- S. A beam to resist combined tension and flexure
should be designed so that (P-*-A)-\-S shall not exceed the proper allow-
able working unit stress.
Combined Compression and Flexure.— If P-*-^l = unit stress
due to compression alone, and S — unit compressive stress at fibre most
remote from neutral axis, due to flexure alone, then maximum compressive
unit stress = (P-*-A) + S.
Combined Tension (or Compression) and Shear.— If ap»
STRENGTH OF FLAT PLATES. 283
plied tension (or compression) unit stress = p, applied shearing unit stress
= v, then from the combined action of the two forces
Max. S = ± Vv* -{- Ml>2» Maximum shearing unit stress ;
Max. t = y»p + Vv* -|- J4p2, Maximum tensile (or compressive) unit stress.
Combined Flexure and Torsion.— If S = greatest unit stress
due to flexure alone, and Ss = greatest torsional shearing unit stress due to
torsion alone, then for the combined stresses
Max. tension or compression unit stress t =
Max. shear s = ±
Formula for diameter of a round shaft subjected to transverse load while
transmitting a given horse-power (see also Shafts of Engines):
da _ WM 16 / Jf» 402, 500,000 JJ2
where Jf = maximum bending moment of the transverse forces in pound-
inches, H — horse-power transmitted, n = No. of revs, per minute, and t =:
the safe allowable tensile or compressive working strength of the iraterial.
Combined Compression and Torsion.— For a vertical round
shaft carrying a load and also transmitting a given horse-power, the result-
ant maximum compressive unit stress
in which P is the load. From this the diameter d may be found when t and
the other data are given.
Stress due to Temperature.— Let I = length of a bar, A = its sec-
tional area, c = coefficient of linear expansion for one degree, t = rise or
fall in temperature in degrees, E = modulus of elasticity, A the change of
length due to the rise or fall t : if the bar is free to expand or contract, A .—
ctl
If the bar is held so as to prevent its expansion or contraction the stress
produced by the change of temperature = S — ActE. The following are
average values of the coefficients of linear expansion for a change in temper-
ature of one degree Fahrenheit:
For brick and stone. . ..a = 0.0000050,
For cast iron ........... a = 0.0000062,
For wrought iron ....... a = 0 . 0000067,
For steel ................ a = 0.0000065.
The stress due to temperature should be added to or subtracted from the
stress caused by other external forces according as it acts to increase or to
relieve the existing stress.
What stress will be caused in a steel bar 1 inch square in area by a change
of temperature of 100° F. ? /S = ActE = 1 X .0000065 X 100 X 30,000,000 =
19,500 Ibs. Suppose the bar is under tension of 19,500 Ibs. between rigid abut-
ments before the change in temperature takes place, a cooling of 100° F.
will double the tension, and a heating of 100° will reduce the tension to zero.
STRENGTH OF FLAT PLATES.
For a circular plate supported at the edge, uniformly loaded, according to
Grashof,
For a circular plate fixed at the edge, uniformly loaded,
/-S-p; « = 4/^rS[; P = ^;
J -3 £2^' y 3 / ' 2r9
in which /denotes the working stress; r, the radius in inches; t, the thick
ness in inches; and p, the pressure in pounds per square inch.
284 STRENGTH OF MATERIALS.
For mathematical discussion, see Lanza, "Applied Mechanics," p. 900, etc.
Lanza gives the following table, using a factor of safety of 8, with tensile
strength of cast iron 20,000, of wrought iron 40,000, and of steel 80,000 :
Supported. Fixed.
Cast iron ............ t = .0182570r \^ t = .0163300r Vp
Wrought iron ........ t = .0117850r |/p t = .0105410r \/p
Steel ................. t = .0091287r i/p t= .0081649r \Tp
For a circular plate supported at the edge, and loaded with a concen-
trated load P applied at a circumference the radius of which is r0:
for — = 10 20 30 40 50;
ro
c = 4.07 5.00 5.53 5.92 6.22;
The above formulae are deduced from theoretical considerations, and give
thicknesses much greater than are generally used in steam-engine cylinder-
heads. (See empirical formulae under Dimensions of Parts of Engines.) The
theoretical formulae seem to be based on incorrect or incomplete hypoth-
eses, but they err in the direction of safety.
The Strength of TJnstayed Flat Surfaces.— Robert Wilson
(Eng'g, Sept. 24, 1877) draws attention to the apparent discrepancy between
the results of theoretical investigations and of actual experiments on the
strength of unstayed flat surfaces of boiler-plate, such as the un stayed flat
crowns of domes and of vertical boilers.
Eankine's " Civil Engineering1' gives the following rules for the strength
of a circular plate supported all round the edge, prefaced by the remark
that " the formula is founded on a theory which is only approximately true,
but which nevertheless may be considered to involve no error of practical
importance:"
W6 _ Pfes
M~ 67T ~W
Here
M = greatest bending moment ;
W— total load uniformly distributed = — ~;
6 = diameter of plate in inches ;
P = bursting pressure in pounds per square inch.
Calling t the thickness in inches, for a plate supported round the edges,
M =i 42,0006*2; ... ^-
For a plate fixed round the edges,
|^=TOOOt»; whence P,?
where r = radius of the plate.
Dr. Grashof gives a formula from which we have the following rule:
<2 X 72,000
r*
This formula of Grashof's has been adopted by Professor Unwin in his
"Blements of Machine Design." These formulae by Rankine and Grashof
may be regarded as being practically the same.
On trying to make the rules given by these authorities agree with the
results of his experience of the strength of unstayed flat ends of cylindrical
boilers and domes that had given way after long use, Mr. Wilson was led to
believe that the above rules give the breaking strength much lower than it
STRENGTH OF FLAT PLATES. 285
actually is. He describes a number of experiments made by Mr. Nichols of
Kirkstall, which gave results varying widely from each other, as the method
of supporting the edges of the plate was varied, and also varying widely
from the calculated bursting pressures, the actual results being in all cases
very much the higher. Some conclusions drawn from these results are :
1. Although the bursting pressure has been found to be so high, boiler-
makers must be warned against attaching any importance to this, since the
plates deflected almost as soon as any pressure was put upon them and
sprang back again on the pressure being taken off. This springing of the
plate in the course of time inevitably results in grooving or channelling,
which, especially when aided by the action of the corrosive acids in the
water or steam, will in time reduce the thickness of the plate, and bring
about the destruction of an unstayed surface at a very low pressure.
2. Since flat plates commence to deflect at very low pressures, they should
never be used without stays; but it is better to dish the plates when they are
not stayed by flues, tubes, etc.
3. Against the commonly accepted opinion that the limit of elasticity
should never be reached in testing a boiler or other structure, these experi-
ments show that an exception should be made in the case of an unstayed
flat end-plate of a boiler, which will be safer when it has assumed a perma-
nent set that will prevent its becoming grooved by the continual variation
of pressure in working. The hydraulic pressure in this case simply does
what should have been done before the plate was fixed, that is, dishes it.
4. These experiments appear to show that the mode of attaching by flange
or by an inside or outside angle-iron exerts an important influence on the
manner in which the plate is strained by the pressure.
When the plate is secured to an angle-iron, the stretching under pressure is,
to a certain extent, concentrated at the line of rivet-holes, and the plate par-
takes rather of a beam supported than fixed round the edge. Instead of the
strength increasing as the square of the thickness, when the plate is attached
by an angle-iron, it is probable that the strength does not increase even
directly as the thickness, since the plate gives way simply by stretching at
the rivet-holes, and the thicker the plate, the less uniformly is the strain
borne by the different layers of which the plate may be considered to be
made up. When the plate is flanged, the flange becomes compressed by the
pressure against the body of the plate, and near the rim, as shown by the
contrary flexure, the inside of the plate is stretched more than the outside,
and it may be by a kind of shearing action that the plate gives way along
the line where the crushing and stretching meet.
5. These tests appear to show that the rules deduced from the theoretical
investigations of Lame, Rankine, and Grashof are not confirmed by experi-
ment, and are therefore not trustworthy.
The rules of Lam6, etc., apply only within the elastic limit. (Eng'g, Dec.
13, 1895.)
Unbraced Wrouglit-iroii Heads of Boilers, etc. (The Loco-
motive, Feb. 1890).— Few experiments have been made on the strength of
flat heads, and our knowledge of them comes largely from theory. Experi-
ments have been made on small plates 1-16 of an inch thick, yet the data so
obtained cannot be considered satisfactory when we consider the far thicker
heads that are used in practice, although the results agreed well with Ran-
kine1s formula. Mr. Nichols has made experiments on larger heads, and
from them he has deduced the following rule: " To find the proper thick-
ness for a flat unstayed head, multiply the area of the head by the pressure
per square inch that it is to bear safely, and multiply this by the desired
factor of safety (say 8) ; theu divide the product by ten times the tensile
strength of the material used for the head." His rule for finding the burst-
ing pressure when the dimensions of the head are given is: " Multiply the
thickness of the end-plate in inches by ten times the tensile strength of the
material used, and divide the product by the area of the head in inches."
In Mr. Nichols's experiments the average tensile strength of the iron used
for the heads was 44,800 pounds. The results he obtained are given below,
with the calculated pressure, by his rule, for comparison.
1. An unstayed flat boiler-head is 34^ inches in diameter and 9-16 inch
thick. What is its bursting pressure? The area of a circle 34^ inches in
diameter is 935 square inches; then 9-16 X 44,800 X 10 = 252,000, and 252,000 -*-
935 = 270 pounds, the calculated bursting pressure. The head actually burst
at 280 pounds.
2. Head 34^ inches in diameter and % inch thick. The area = 935
square inches; then, % X 44,800 X 10 = 168.000, and 168,000 -f- 935 = 180 pounds,
calculated bursting pressure. This head actually burst at 200 pounds.
286 STRENGTH OF MATERIALS.
3. Head 26*4 inches in diameter, aud % inch thick. The area 541 square
inches. Then, % X 44,800 X 10 = 168,000, and 168,000 -T- 541 = 311 pounds.
This head burst at 370 pounds.
4. Head 28*^ inches in diameter and % inch thick. The area = 638
square inches; then, % X 44,800 X 10 = 168,000, and 168,000 H- 638 = 263
pounds. The actual bursting pressure was 300 pounds.
In the third experiment, the amount the plate bulged under different
pressures was as follows :
At pounds per sq. in.... 10 20 40 80 120 140 170 200
Plate bulged 1/32 1/16 fc K % Y% % H
The pressure was now reduced to zero, " and the end sprang back 3-16
inch, leaving it with a permanent set of 9-16 inch. The pressure of 200 Ibs.
was again applied on 36 separate occasions during an interval of five days,
the bulging and permanent set being noted on each occasion, but without
any appreciable difference from that noted above.
The experiments described were confined to plates not widely different in
their dimensions, so that Mr. Nichols's rule cannot be relied upon for heads
that depart much from the proportions given in the examples.
Thickness of Flat Cast-iron Plates to resist Bursting
'jpressures. — Capt. John Ericsson (Church's Life of Ericsson) gave the
following rules: The proper thickness of a square cast-iron plate will be ob-
tained by the following: Multiply the side in feet (or decimals of a foot) by
14 of the pressure in pounds and divide by 850 times the side in inches; the
quotient is the square of the thickness in inches.
For a circular plate, multiply 11-14 of the diameter in feet by *4 of the
pressure on the plate in pounds. Divide by 850 times 11-14 of the diameter
in inches. [Extract the square root.]
Prof. Wm. Harkness, Eng'g News, Sept. 5, 1895, shows that these rules can
be put in a more convenient form, thus:
For square plates T = 0.00495S 4/p,
and
For circular plates T - 0.00439D \fp,
where T = thickness of plate, S = side of the square, D =» diameter of the
circle, and p = pressure in Ibs. per sq. in. Professor Harkness, however^
doubts the value of the rules, and says that no satisfactory theoretical solu-
tion has yet been obtained.
Strength of Stayed Surfaces.— A flat plate of thickness t is sup*
ported uniformly by stays whose distance from centre to centre is a, uniform
load p Ibs. per square inch. Each stay supports paa Ibs. The greatest
stress on the plate is
2 aa
/=gp-p.(Unwin).
SPHERICAL SHELLS AND DOMED BOILER-HEADS.
To find the Thickness of a Spherical Shell to resist a
given Pressure.— Let d — diameter in inches, and p the internal press-
ure per square inch. The total pressure which tends to produce rupture
around the great circle will be %7rd2p. Let S = safe tensile stress per
square inch, and t the thickness of metal in inches; then the resistance to the
pressure will be itdtS. Since the resistance must be equal to the pressure.
= irdtS. Whence t = |J-.
The same rule is used for finding the thickness of a hemispherical head
to a cylinder, as of a cylindrical boiler.
Thickness of a Domed Head of a boiler,— If S = safe tensile
stress per square inch, d = diameter of the shell in inches, and t = thickness
Of the shell, t = pd-*-2S; but the thickness of a hemispherical head of the
same diameter ist = pd-t-4S. Hence if we make the radius of curvature
of a domed head equal to the diameter of the boiler, we shall have t =
TZ = ^ or the thickness of such a domed head will be equal to the thick-
4o 2iS
ness of the shell.
THICK CYLINDERS UNDER TENSION.
287
Stresses in Steel Plating due to Water-pressure, as in
plating: of vessels and bulkheads (Engineering, May 22, 1891, page 629).
Mr. J. A. Yates has made calculations of the stresses to which steel plates
are subjected by external water-pressure, and arrives at the following con-
clusions :
Assume 2a inches to be the distance between the frames or other rigid
supports, and let d represent the depth in feet, below the surface of the
water, of the plate under consideration, t = thickness of plate in inches,
D the deflection from a straight line under pressure in inches, and P = stress
per square inch of section.
For outer bottom and ballast- tank plating, a = 420 -, D should not be
greater than .05 -|, and — not greater than 2 to 3 tons ; while for bulkheads,
etc., a = 2352-, D should not be greater than .1—, and — not greater than
7 tons. To illustrate the application of these formulae the following cases
have been taken :
For Outer Bottom, etc.
For Bulkheads, etc.
Thick-
ness of
Plating.
Depth
below
Water.
Spacing of
Frames should
not exceed
Thick-
ness of
Plating
Depth of
Water.
Maximum Spac-
ing of Rigid
Stiff eners.
in.
ft.
in.
in.
ft.
ft. in.
20
About 21
L£
20
9 10
jz
10
" 42
%
20
7 4
$8
18
44 18
%
10
14 8
%
9
" 36
M
20
4 10
^A
10
44 20
\A
10
9 8
R
5
" 40
jj
10
4 10
(/Ji4-»\*
* = r } V/T^/ " *
It would appear that the course which should be followed in stiffening
bulkheads is to fit substantially rigid stiffening frames at comparatively
wide intervals, and only work such light angles between as are necessary
for making a fair job of the bulkhead.
THICK HOLLOW CYLINDERS UNDER TENSION.
Burr, " Elasticity and Resistance of Materials," p. 36, gives
t = thickness; r = interior radius ;
h = maximum allowable hoop tension at the
interior of the cylinder;
p = intensity of interior pressure.
Merriman gives
s = unit stress at inner edge of the annulus;
r = interior radius ; t = thickness ;
I = length.
The total stress over the area 2tl = 2sl ^-r-^ ........... (1)
The total interior pressure which tends to rupture the cylinder is 2rl XP-
If p be the unit pressure, then p = , from which one of the quantities
8, p, r, or t can be found when the other three are given.
288 STRENGTH OF MATERIALS.
In eq. (1), if t be neglected in comparison with r, it reduces to 2slt, which
is the same as the formula for thin cylinders. If t = r, it becomes sit, or
only half the resistance of the thin cylinder.
The formula given by Burr and by Merriman are quite different, as will
be seen by the following example : Let maximum unit stress at the inner
edge of the annulus = 8000 Ibs. per square inch, radius of cylinder = 4 inches,
interior pressure = 4000 Ibs. per square inch. Required the thickness.
By Burr, t = 4 { (^ + ^gg)* - 1 \ = 4 ( V§ - 1) = 2.928 inches.
4 X 4000
By Merriman, t = 8000 _ 4000 = 4 inches.
Limit to Useful Thickness of Hollow Cylinders (Eiufy,,
Jan. 4, 1884).— Prof essor Barlow lays down the law of the resisting powers
of thick cylinders as follows :
'* In a homogeneous cylinder, if the metal is incompressible, the tension
on every concentric layer, caused by an internal pressure, varies inversely
as the square of its distance from the centre."
Suppose a twelve-inch gun to have walls 15 inches thick.
Pressure on exterior _ _6^ = j . 12 35
Pressure on interior ~~ 21 2 ~~
So that if the stress on the interior is 12^ tons per square inch, the stress
on the exterior is only 1 ton.
Let s = the stress on the inner layer, and s, that at a distance x from the
axis ; r — internal radius, R = external radius.
The whole stress on a section 1 inch long, extending from the interior to
the exterior surface, is S= sr X — ~ — •
K
In a 12-inch gun, let s = 40 tons, r = 6 in., R - 21 in.
8 = 40 X 6 X ^p6 = 172 tons.
Suppose now we go on adding metal to the gun outside: then R will be-
come so large compared with r, that R — r will approach the value .R, so
that the fraction — ^- becomes nearly unity.
JK
Hence for an infinitely thick cylinder the useful strength could never
exceed Sr (in this case 240 tons).
Barlow^ formula agrees with the one given by Merriman.
Another statement of the gun problem is as follows : Using the formula
-r+?
40 X 15
s = 40 tons, t = 15 in., r = 6 in., p - — •— — = 28$ tons per sq. in., 28$ x
radius = 172 tons, the pressure to be resisted by a section 1 inch long of the
thickness of the gun on one side. Suppose thickness were doubled, making
40 X 30
t = 30 in.: p = — — — = 33J^ tons, or an increase of only 16 per cent.
For short cast-iron cylinders, such as are used in hydraulic presses, it is
doubtful if the above formulae hold true, since the strength of the cylindri-
cal portion is reinforced by the end. In that case the bursting strength
would be higher than that calculated by the formula. A rule used in
practice for such presses is to make the thickness = 1/10 of the inner cir-
cumference, for pressures of 3000 to 4000 Ibs. per square inch. The latter
pressure would bring a stress upon the inner layer of 10,350 Ibs. per square
inch, as calculated by the formula; which would necessitate the use of the
best charcoal -iron to make the pi-ess reasonably safe.
HOLDING-POWER OF JSTAILS, SPIKES, AND SCREWS. 289
THIN CYLINDERS UNDER TENSION.
Let p = safe working pressure in Ibs. per sq. in. ;
d = diameter in inches;
T— tensile strength of the material, Ibs. per sq. in.;
t = thickness in inches ;
/ = factor of safety;
c — ratio of strength of riveted joint to strength of solid plate.
*,=«« ,-«?, <=H£
If T = 50000, / = 5, and c = 0.7; then
_ 14000*. _ dp
d ~ 14000'
The above represents the strength resisting rupture along a longitudinal
seam. For resistance to rupture in a circumferential seam, due to pressure
pnd* Ttirdc
on the ends of the cylinder, we have = — - — ;
4Ttc
whence p = — — .
Or the strength to resist rupture around a circumference is twice as great
as that to resist rupture longitudinally; hence boilers are commonly single-
riveted in the circumferential seams and double-riveted in the longitudinal
seams.
HOLLOW COPPER BALLS.
Hollow copper balls are used as floats in boilers or tanks, to control feed
and discharge valves, and regulate the water-level.
They are spun up in halves from sheet copper, and a rib is formed on one
half. Into this rib the other half fits, and the two are then soldered or
brazed together. In order to facilitate the brazing, a hole is left on one side
of the ball, to allow air to pass freely in or out; and this hole is made use of
afterwards to secure the float to its stem. The original thickness of the
metal may be anything up to about 1-16 of an inch, if the spinning is done
on a hand lathe, though thicker metal may be used when special machinery
is provided for forming it. In the process of spinning, the metal is thinned
down in places by stretching; but the thinnest place is neither at the equator
of the ball (i.e., along the rib) nor at the poles. The thinnest points lie along
two circles, passing around the ball parallel to the rib, one on each side of it,
from a third to a half of the way to the poles. Along these lines the thick-
ness may be 10, 15, or 20 per cent less than elsewhere, the reduction depend
ing somewhat on the skill of the workman.
The Locomotive for October, 1891, gives two empirical rules for determin-
ing the thickness of a copper ball which is to work under an external
pressure, as follows;
diameter in inches X pressure in pounds per sq. in.
1. Thickness = 16,0oo
2. Thickness = diameter X
1240
These rules give the same result for a pressure of 166 Ibs. only. Example:
Required the thickness of a 5-inch copper ball to sustain
Pressures of 50 100 150 166 200 250 Ibs. per sq. in.
Answer by first rule... .0156 .0312 .0469 .0519 .0625 .0781 inch.
Answer by second rule .0285 .0403 .0494 .0518 .0570 .0637
HOLDING-POWER OF NAILS, SPIKES, AND
SCREWS.
(A. W. Wright, Western Society of Engineers, 1881.)
Spikes.— Spikes driven into dry cedar (cut 18 months):
Size of spikes 5 X J4 in. sq. 6 X M 6 X ^ 5 X %
Length driven in 4% in. 5 in. 5 in. 4*4 in.
Pounds resistance to drawing. Av'ge, Ibs. 857 821 1691 1202
From 6 to 9 tests each j «£ '.'. '& % 33 '8?
290 STRENGTH OF MATERIALS.
A. M. Wellington found the force required to draw spikes 0/16 X 9/16 in.,
driven 4*4 inches into seasoned oak, to be 4281 Ibs.; same spikes, etc., in un-
seasoned oak, 6523 Ibs.
" Professor W. R. Johnson found that a plain spike % inch square
driven 3% inches into seasoned Jersey yellow pine or unseasoned chestnut
required about 2000 Ibs. force to extract it; from seasoned white oak about
4000 and from well-seasoned locust 6000 Ibs."
Experiments in Germany, by Funk, give from 2465 to 3940 Ibs. (mean of
many experiments about 3000 Ibs.) as the force necessary to extract a plain
nch square iron spike 6 inches long, wedge-pointed for one inch and
when driven 5 inches the force
driven 4J4 inches into white or yellow pine.
required was about 1/10 part greater. Similar spiKes y/io muiies square, <
inches long, driven 6 inches deep, required from 3700 to 6745 Ibs. to extract
them from pine; the mean of the results being 4873 Ibs. In all cases about
twice as much force was required to extract them from oak. The spikes
were all driven across the grain of the wood. When driven with the grain,
spikes or nails do not hold with more than half as much force.
Boards of oak or pine nailed together by from 4 to 16 tenpenny common cut
nails and then pulled apart in a direction lengthwise of the boards, and
across the nails, tending to break the latter in two by a shearing action,
averaged about 300 to 400 Ibs. per nail to separate them, as the result of
many trials.
Resistance of Drift-bolts in Timber.— Tests made by Rust and
Coolidge, in 1878.
Pounds,
1st Test. 1 in. square iron drove 30 in. in white pine, 15/16-in. hole 26,400
2d " 1 in. round " " 34" " " " 13/16-in. * ....16,800
3d «' 1 in. square " " 18 " " " 15/16-in.
4th
5th
6th
7th
8th
1 in. round " " 22 " " " " 13/16-in.
1 in. round " " 34" "Norw'y pine,13/16-in.
1 in. square ** u 30 " " " " 15/16-in.
1 in. square " " 18 " " " " 15/16-in.
1 in. round " " 22 " " " " 13/16-in.
.14,600
...13,200
...18,720
. . . 19,200
...15,600
. . . 14,400
NOTE.— In test No. 6 drift-bolts were not driven properly, holes not being
in line, and a piece of timber split out in driving.
Force required to draw Screws out of Norway Pine.
i^j" diam. drive screw 4 in. in wood. Power required, average 2424 Ibs,
4 threads per in. 5 in. in wood.
D'ble thr'd, 3 per in., 4 in. in "
La£-screw,7perin.,r'
2743
2730
1465
2026
2191
i^ifichR.R. spike...
Force required to draw Wood Screws out of Dry Wood*
—Tests made by Mr. Bevan. The screws were about two inches in length,
.22 diameter at the exterior of the threads, .15 diameter at the bottom, the
depth of the worm or thread being .035 and the number of threads in one
inch equal 12. They were passed through pieces of wood half an inch in
thickness and drawn out by the weights stated: Beech, 460 Ibs.; ash, 790
Ibs.: oak, 760 Ibs.; mahogany, 770 Ibs.; elm, 665 Ibs.; sycamore, 830 Ibs.
Tests of Lag-screws in Various Woods were made by A. J.
Cox, University of Iowa, 1891:
Q. _ Size T___ fv, Max.
Kind of Wood. a5r£w Hole in T£ Resist,
bcrew. bOre&m l l&' ibs.
Seasoned white oak. %in. y% in. 4^ in. 8037 3
" " " 9/16" 7/16" 3 " 6480 1
« «« " U" %" 4J4" 8780 2
Yellow-pine stick %" ^"4 3800
White cedar, unseasoned p§-** J§ ** 4 3405 2
In figuring area for lag-screws, the surface of a cylinder whose diameter is
equal to that of the screw was taken. The length of the screw part in each
case was 4 inches.— Engineering News, 1891.
Cut versus Wire Nails.— Experiments were made at the Watertown
Arsenal in 1893 on the comparative direct tensile adhesion, in pine and
spruce, of cut and wire nails. The results are stated by Prof. W. H. Burr
as follows:
HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 291
There were 58 series of tests, ten pairs of nails (a cut and a wire nail in each)
being used, making a total of 1160 nails drawn. The tests were made in
spruce wood in most instances, but some extra ones were made in white
pine, with " box nails.1' The nails were of all sizes, varying from \y& inches to
6 inches in length. In every case the cut nails showed the superior holding
strength by a large percentage. In spruce, in nine different sizes of nails,
both standard and light weight, the ratio of tenacity of cut to wire nail
was about 3 to 2, or, as he terms it, "a superiority of 47.45# of the former."
With the " finishing ". nails the ratio was roughly 3.5 to 2; superiority 72%.
With box nails (1*4 to 4 inches long) the ratio was roughly 3 to 2; superiority
51$. The mean superiority in spruce wood was 61j£. In white pine, cut nails,
driven with taper along the grain, showed a superiority of 100$, and with
taper across the grain of 135$. Also when the nails were driven in the end
of the stick, i.e., along the grain, the superiority of cut nails was 100$, or the
ratio of cut to wire was 2 to 1. The total of the results showed the ratio of
tenacity to be about 3.2 to 2 for the harder wood, and about 2 to 1 for the
softer, and for the whole taken together the ratio was 8.5 to 2. We are
led to conclude that under these circumstances the cut nail is superior to
the wire nail in direct tensile holding-power by 72.74$.
Nail-holding Power of Various Woods.
(Watertown Experiments.)
Holding-power per square inch of
Kind of Wood. Size of Nail. Surface in Wood, Ibs.
Wire Nail. Cut Nail. Mean?
8d 450
9 4| 455
White pine -j gj || 167 477 ^ 405
S63
60 " 340
f 8 " 1 f 695
Yellowpine \ Jg « I 318 I 755
I 60" J C 604
( 8" ) ( 1340 )
White oak 1 20" V 940 •{ 1292 V 1216
( 60" ) I 1018 j
Chestnut | g;; ?64 J 6g3
Laurel j 20" \ 651 { 1221 } 120°
Nail-holding Power of Various Woods.
(F. W. Clay's Experiments. Eng'g Netvs, Jan. 11, 1894.)
Wnnrt , Tenacity of 6d nails «
vvooa' Plain. Barbed. Blued. Mean.
White pine 106 94 135 111
Yellow pine 190 130 270 196
Basswood 78 132 219 143
White oak .226 300 555 360
Hemlock 141 ( 201 319 220
Tests made at the University of Illinois gave the resistance of a 1-in. round
rod in a 15/16-inch hole perpendicular to the grain, as 6000 Ibs. per lin. ft. in
pine and 15,600 Ibs. in oak. Experiments made at the East River Bridge
gave resistances of 12,000 and 15,000 Ibs. per lin. ft. for a 1-in. round rod in
holes 15/16-in. and 14/16-in. diameter, respectively, in Georgia pine.
Holding-power of Bolts in White Pine.
(Eng'g News, September 26, 1891.)
Round. Square.
Lbs. Lbs.
Average of all plain 1-in. bolts 8224 8200
Average of all plain bolts, % to 1^ in 7805 8110
Average of all bolts 8383 8598
Round drift-bolts should be driven in holes 13/16 of their diameter, and
square drift-bolts in holes whose diameter is 14/16 of th© side of the square,
292
STRENGTH OF MATERIALS.
STRENGTH OF WROUGHT IRON BOLTS.
(Computed by A. F. Nagle.)
g
5 O3
Stress u
pon Bolt
upon I
Jasis of
«M 03
o 53
<M
o«g.g
0) .
jsj]
||
Hi
o o3 j:
pq cu -^
|1
. o
. o
. o
H
m
II
&H
5«2
g^j!
o cc
O X
ii1
o 6*
I*
p;!^
5 H
<< CO
Ibs.
W
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
y>
13
.38
.12
350
460
580
810
1160
5800
9-16
12
.44
.15
450
600
750
1050
1500
7500
%
11
.49
.19
560
750
930
1310
1870
9000
M
10
.60
.28
850
1130
1410
1980
£830
14000
7^
9
.71
.39
1180
1570
1970
2760
3940
19000
1
8
.81
.52
1550
2070
2600
3630
5180
25000
\\fa
7
.91
.65
1950
2600
3250
4560
6510
30000
1/4
7
1.04
.84
2520
3360
4200
5900
8410
39000
1%
6
1.12
1.00
3000
4000
5000
7000
10000
46000
tyb
6
1.25
1.23
3680
4910
6140
8600
12280
56000
1%
51^
.35
1.44
4300
5740
7180
10000
14360
65000
1%
5
.45
1.65
4950
6600
8250
11560
16510
74000
1%
5
.57
1.95
5840
7800
9800
13640
19500
85000
2
4//£
.66
2.18
6540
8720
10900
15260
21800
95000
2^4
4H>
.92
2.88
8650
11530
14400
20180
28800
125000
2^
4
2.12
3.55
10640
14200
17730
24830
35500
150000
2%
4
2.37
4.43
13290
17720
22150
31000
44300
186000
3
3/^
2.57
5.20
15580
20770
26000
36360
52000
213000
31^3
3M
8.04
7.25
21760
29000
36260
50760
72500
290000
4
3
3.50
9.62
28860
38500
48100
67350
96200
385000
When it is known what load is to be put upon a bolt, and the judgment ol
the engineer has determined what stress is safe to put upon the iron, lool<
down in the proper column of said stress until the required load is found.
The area at the bottom of the thread will give the equivalent area of a flat
bar to that of the bolt.
Effect of Initial Strain in Bolts.— Suppose that bolts are used
to connect two parts of a machine and that they are screwed up tightly be-
fore the effective load comes on the connected parts. Let Pj = the initial
tension on a bolt due to screwing up, and P2 = the load afterwards added.
The greatest load may vary but little from Pl or P2, according as the
former or the latter is greater, or it may approach the value Pl -j- P2, de-
pending upon the relative rigidity of the bolts and of the parts connected.
Where rigid flanges are bolted together, metal to metal, it is probable that
the extension of the bolts with any additional tension relieves the initial
tension, and that the total tension is Pl or Pa, but in cases where elastic
packing, as india rubber, is interposed, the extension of the bolts may very
little affect the initial tension, and the total strain may be nearly Pj -f- P2.
Since the latter assumption is more unfavorable to the resistance of the
bolt, this contingency should usually be provided for. (See Unwin, ''Ele-
ments of Machine Design " for demonstration.)
STAND-PIPES AND THEIR DESIGN.
(Freeman C. Coffin, New England Waterworks Assoc., Enci. Neivs, March
16, 1893.) See also papers by A. H. Howlaud, Eng. Club of Phil. 1887; B. F.
Stephens, Amer. Waterworks Assoc., Eng. Neivs, Oct. 6 and 13, 1888; W.
Kiersted, Rensselaer Soc. of Civil Eng., Eng'g Record, April 25 and May 2,
1891, and W. D. Pence, Eng. News, April and May, 1894.
The question of diameter is almost entirely independent of that of height
The efficient capacity must be measured by the length from the high-water
line to a point below which it is undesirable to draw the water on account of
loss of pressure for fire-supply, whether that point is the actual bottom of
the stand-pipe or above it. This allowable fluctuation ought not to exceed
50 ft., in most cases. This makes the diameter dependent upon two condi-
STAND-PIPES AND THEIR DESIGN. 293
tions, the first of which is the amount of the consumption during the ordi-
nary interval between the stopping and starting of the pumps. This should
never draw the water below a point that will give a good fire stream and
leave a margin for still further draught for fires. The second condition is
the maximum number of fire streams and their size which it is considered
necessary to provide for, and the maximum length of time which they are
liable to have to run before the pumps can be relied upon to reinforce
them.
Another reason for making the diameter large is to provide for stability
against wind-pressure when empty.
The following table gives the height of stand-pipes beyond which they are
not safe against wind-pressures of 40 and 50 Ibs. per square foot. The area
of surface taken is the height multiplied by one half the diameter.
Heights of Stand-pipe that will Resist Wind-pressure
by its Weight alone, when l£mpty.
Diameter, Wind, 40 Ibs. Wind, 50 Ibs.
feet. per sq. ft. per sq. ft.
20 .. 45 35
25 70 55
30 150 80
35 160
To have the above degree of stability the stand-pipes must be designed
with the outside angle-iron at the bottom connection.
Any form of anchorage that depends upon connections with the sid3
plates near the bottom is unsafe. By suitable guys the wind-pressure is re-
sisted by tension in the guys, and the stand-pipe is relieved from wind
strains that tend to overthrow it. The guys should be attached to a band
of angle or other shaped iron that completely encircles the tank, and rests
upon some sort of bracket or projection, and not be riveted to the tank.
They should be anchored at a distance from the base equal to the height of
the point at which they are attached, if possible.
The best plan is to build the stand-pipe of such diameter that it will resist
the wind by its own stability.
Thickness of the Side Plates.
The pressure on the sides is outward, and due alone to the weight of the
water, or pressure per square inch, and increases in direct ratio to the
height, and also to the diameter. The strain upon a section 1 inch in height
at any point is the total strain at that point divided by two — for each side is
supposed to bear the strain equally. The total pressure at any point is
equal to the diameter in inches, multiplied by the pressure per square inch,
due to the height at that point. It may be expressed as follows:
H — height in feet, and/ = factor of safety;
d = diameter in inches;
p = pressure in Ibs. per square inch;
.434 = p for 1 ft. in height;
s = tensile strength of material per square inch;
T — thickness of plate.
Then the total strain on each side per vertical inch
T_ AUHdf _ pdf
2s 2s '
Mr, Coffin takes/ = 5, not counting reduction of strength of joint, equiv-
alent to an actual factor of safety of 3 if the strength of the riveted joint is
taken as 60 per cent of that of the plate.
The amount of the wind strain per square inch of metal at any joint can
be found by the following formula, in which
H = height of stand-pipe in feet above joint;
T = thickness of plate in inches;
p = wind -pressure per square foot:
W = wind-pressure per foot in height above joint;
W = Dp where D is the diameter in feet;
m — average leverage or movement about neutral axis
or central points in the circumference; or,
m = sine of 45°, or .707 times the radius in feet.
294 STRENGTH OF MATERIALS,
Then the strain per square inch of plate
circ. in ft. X mT
Mr. Coffin gives a number of diagrams useful in the design of stand-pipes,
together with a number of instances of failures, with discussion of their
probable causes.
Mr. Kiersted's paper contains the following : Among the most prominent
strains a stand-pipe has to bear are: that due to the static pressure of the
water, that due to the overturning effect of the wind on an empty stand-
pipe, and that due to the collapsing effect, on the upper rings, of violent
wind storms.
For the thickness of metal to withstand safely the static pressure of
water, let
/ = thickness of the plate iron in inches;
H = height of stand-pipe in feet;
D = diameter of stand-pipe in feet.
Then* assuming a tensile strength of 48,000 Ibs. per square inch, a factor
of safety of 4, and efficiency of double-riveted lap-joint equalling 0.6 of the
strength of the solid plate,
*=.OOOSMrxl>; H
which will give safe heights for thicknesses up to % to % of an inch. The
same formula may also 'apply for greater heights and thicknesses within
practical limits, if the joint efficiency be increased by triple riveting.
The conditions for the severest overturning wind strains exist when the
stand-pipe is empty.
Formula for wind-pressure of 50 pounds per square foot, when
d = diameter of stand-pipe in inches;
x = any unknown heigjkof stand-pipe;
t = 15.85 Vdt.
The following table is calculated by these formulae. The stand-pipe is
intended to be self-sustaining; that is, without guys or stiff eners.
Heights of Stand-pipes for Various Diameters and
Thicknesses of Plates.
Thickness of
Diameters in Feet.
Plate in Frac-
tions of an Inch.
5
6
7
8
9
10
12
14
15
16
18
20
25
3-16
50
55
60
65
55
50
35
7_32
55
65
60
50
40
40
4-16
60
65
70
75
75
70
55
50
45
40
35
35
25
5 16
70
75
80
85
90
85
70
60
55
50
45
40
35
6-16
75
80
00
95
100
100
85
75
70
65
55
50
40
7-16
80
90
95
100
ro
115
100
85
80
75
65
60
45
8--16
85
95
100
110
115
120
115
100
90
m
75
70
55
9 16
115
125
130
130
110
100
95
85
80
60
10-16
130
135
145
120
115
105
95
85
65
11-16
145
155
135
125
120
105
95
75
12 16 ....
150
165
145
135
130
115
105
80
13-16
160
150
140
125
110
90
14 16
160
150
135
120
95
15 16
160
145
130
105
16-16
155
140
110
Heights to nearest 5 feet. Rings are to build 5 feet vertically.
Failures of Stand-pipes have been numerous in recent years. A
list showing 23 important failures inside of nine 3Tears is given in a paper by
Prof. W. D. Pence, Eng'g. News, April 5, 12, 19 and 26, May 3, 10 and 24, and
June 7, 1894. His discussion of the probable causes of the failures is most
valuable.
WfcOUGHT-IROK AHD STEEL WATER-PIPES. 295
Kenneth Allen, Engineers Club of Philadelphia, 1886, gives the following
rules for thickness of plates for stand pipes.
Assume: Wrought iron plate T. S. 48,000 pounds in direction of fibre, and
T. S. 45,000 pounds across the fibre. Strength of single riveted joint .4 that
of the plate, and of double riveted joint, .7 that of the plate ; wind pressure
= 50 pounds per square foot ; safety factor = 3.
Let h = total height in feet ; r = outer radius in feet ; r' = inner radius
in feet ; p — pressure per square inch ; t == thickness in inches ; d = outer
diameter in feet.
Then for pipe filled and longitudinal seams double riveted
_
"
X 12
48,000 X .7 X ^
hd m
4301'
and for pipe empty and lateral seams, single riveted, we have by equating
moments :
50 X 2r (|)2 = 144 X 6000 (r« - r'*) '^~, whence r* - r'« = J^.
Table showing required Thickness of Bottom Plate.
Height iu
Diameter.
Feet.
5 feet,
10 feet.
15 feet.
20 feet.
25 feet.
30 feet.
/,
//
it
„
//
n
50
t 7-64*
^ *
11-64*
15-64
19-64
23-64
60
til -64*
9-64*
7-32
9-32
23-64
27-64
70
t 7-32
11-64*
H
21-64
13-32
31-64
80
t!9-64
3-16
9-32
'%
15-32
9-16
90
t %
7-32
5-16
27-64
17-32
%
100
t29-64
t 15-64
23-64
15-32
37-64
45-64
125
t23-64
7-16
37-64
47-64
Vs
150
t33-64
17-32
45-64
%
1 3-64
175
tll-16
39-64
13-16
1 &8
1 7-32
200
t29-32
45-64
15-16
1 11-64
125-64
* The minimum thickness should = 3-16".
N.B. — Dimensions marked t determined by wind-pressure.
"Water Tower at Yonkers, N. Y.— This tower, with a pipe 122 feet
high and 20 feet diameter, is described in Engineering News, May 18, 1892.
The thickness of the lower rings is 11-16 of an inch, based on a tensile
strength of 60,000 Ibs. per square inch of metal, allowing 65$ for the strength
of riveted joints, using a factor of safety of 3J^ and adding a constant of
^ inch. The plates diminish in thickness by 1-16 inch to the last four
plates at the top, which are J4 inch thick.
The contract for steel requires an elastic limit of at least 33,000 Ibs. per
square inch ; an ultimate tensile strength of from 56,000 to 66,000 Ibs. per
square inch ; an elongation in 8 inches of at least 20$, and a reduction of
area of at least 45$. The inspection of the work was made by the Pittsburgh
Testing Laboratory. According to their report the actual conditions de-
veloped were as follows : Elastic limit from 34,020 to 39,420 ; the tensile
strength from 58,330 to 65,390 ; the elongation in 8 inches from 22U to 32$ ;
reduction in area from 52.72 to 71.32$ ; 17 plates out of 141 were rejected in
the inspection.
WROUGHT-IRON AND STEEL WATER-PIPES.
Riveted Steel Water-pipes (Engineering Neivs, Oct. 11, 1890, and
Aug. 1, 1891.)— The use of riveted wrought-irori pipe has been common in
the Pacific States for many years, the largest being a 44-inch conduit in
connection with the works of the Spring Valley Water Co., which supplies
San Francisco. The use of wrought iron and steel pipe has been neces-
sary in the West, owing to the extremely high pressures to be withstood
and the difficulties of transportation. As an example : In connection with
296 STRENGTH OF MATERIALS.
the *ater supply of Virginia City and Gold Hill, Nev., there was laid in
187? an 11^-inch riveted wrought-iron pipe, a part of which is under a head
of .720 feet.
In the East, the most important example of the use of riveted steel water
pipe is that of the East Jersey Water Co., which supplies the city of Newark.
The contract provided for a maximum high service supply of 25,000,000 gal-
lons daily. In this case 21 m lies of 48-inch pipe was laid, some of it under 340
feet head. The plates from which the pipe is made are about 13 feet long
by 7 feet wide, open-hearth steel. Four plates are used to make one section
of pipe about 27 feet long. The pipe is riveted longitudinally with a double
row, and at the end joints with a single row of rivets of varying diameter,
corresponding to the thickness of the steel plates. Before being rolled into
the trench, two of the 27-feet lengths are riveted together, thus diminishing
still further the number of joints to be made in the trench and the extra
excavation to give room for jointing. All changes in the grade of the pipe-
line are made by 10° curves and all changes in line by 2^>, 5, 7J^ and 10°
curves. To lay on curved lines a standard bevel was used, and the different
curves are secured by varying the number of beveled joints used on a
certain length of pipe.
The thickness of the plates varies with the pressure, but only three thick-
nesses are used, J4, 5-16, and % inches, the pipe made of these thicknesses
having a weight of 160, 185, and 225 Ibs. per foot, respectively. At the works
all the pipe was tested to pressure \y% times that to which it is to be sub-
jected when in place.
Man iiesm aim Tubes for High Pressures,— At the Mannes-
inaun Works at Komotau, Hungary, more than 600 tons or 25 miles of 3-inch
and 4-inch tubes averaging ^4 inch in thickness have been successfully
tested to a pressure of 2000 Ibs. per square inch. These tubes were intended
for a high-pressure water-main in a Chilian nitrate district.
This great tensile strength is probably due to the fact that, in addition to
being much more worked than most metal, the fibres of the metal run
spirally, as has been proved by microscopic examination. While cast-iron
tubes will hardly stand more than 200 Ibs. per square inch, and welded tubes
are not safe above 1000 Ibs. per square inch, the Mannesmann tube easily
withstands 2000 Ibs. per square inch. The length up to which they can
be readily made is shown by the fact that a coil of 3-inch tube 70 feet long
was made recently.
For description of the process of making Mannesmann tubes see Trans.
&. I. M. E , vol. xix., 384.
STRENGTH OF VARIOUS MATERIALS. EXTRACTS
FROM K1RKAL1WS TESTS.
The recent publication, in a book by W. G. Kirkaldy, of the results of many
thousand tests made during a quarter of a century by his father, David Kir-
kaldy, has made an important contribution to our knowledge concerning
the range of variation in strength of numerous materials. A condensed
abstract of these results was published in'the American Machinist, May 11
and 18, 1893, from which the following still further condensed extracts are
taken:
The figures for tensile and compressive strength, or, as Kirkaldj' calls
them, pulling and thrusting stress, are given in pounds per square inch of
original section, and for bending strength in pounds of actual stress or
pounds per BD* (breadth X square of depth) for length of 36 inches between
supports. The contraction of area is given as a percentage of the original
area, and the extension as a percentage in a length of 10 inches, except when
otherwise stated. The abbreviations T. S., E. L., Contr., and Ext. are used
for the sake of brevity, to represent tensile strength, elastic limit, and per-
centages of contraction of area, and elongation, respectively.
Cast Iron.— 44 tests: T. S. 15,468 to 28,740 pounds: 17 of these were un-
sound, the strength ranging from 15,468 to 24,357 pounds. Average of all,
23,805 pounds.
Thrusting stress, specimens 2 inches long, 1.34 to 1.5 in. diameter: 43 tests,
all sound, 94,352 to 131,912; one, unsound, 93,759; average of all, 113,825.
Bending stress, bars about 1 in. wide by 2 in. deep, cast on edge. Ulti-
mate stress 2876 to 3854; stress per BD* - 725 to 892; average, 820. Average
modulus of rupture, E, = 3/<J stress per BD* X length, = 44,280. Ultimate
deflection, .29 to .40 in.; average, .34 Inch.
Other tests of cast iron, 460 tests, 10 lots from various sources, gave re-
EXTRACTS FROM KIRKALDY5S TESTS. 297
suits with total range as follows: Pulling stress, 12,688 to 33,616 pounds;
thrusting stress, 66,363 to 175,950 pounds; bending stress, per J5Z>2, 505 to
1128 pounds; modulus of rupture, R, 27,270 to 61,91 2. Ultimate deflection,
.21 to .45 inch.
The specimen which was the highest in thrusting stress was also the high-
est in bending, and showed the greatest deflection, but its tensile strength
was only 26,502.
The specimen with the highest tensile strength had a thrusting stress of
143,939, and a bending strength, per #D2, of 979 pounds with 0.41 deflection.
The specimen lowest in T. S. was also lowest in thrusting and bending, but
gave .38 deflection. The specimen which gave .21 deflection had T. S., 19,188:
thrusting, 101.281; and bending, 561.
Iron Castings.— 69 tests; tensile strength, 10,416 to 31,652; thrusting
stress, ultimate per square inch, 53,502 to 132,031.
Channel Irons.— Tests of 18 pieces cut from channel irons. T. S.
40,693 to 53,141 pounds per square inch; contr. of area from 3.9 to 32.5 %.
Ext. in 10 in. from 2.1 to 22.5 %. The fractures ranged all the way from 100 %
fibrous to 100 # crystalline. The highest T. S., 53,141, with 8.1 % contr. and
5.3 % ext., was 100 % crystalline; the lowest T. S., 40,693, with 3.9 contr. and
2.1 £ext., was 75 $ crystalline. All the fibrous irons showed from 12.2 to
22.5 % ext., 17.3 to 32.5 contr., and T. S. from 43,426 to 49,615. The fibrous
irons are therefore of medium tensile strength and high ductility. The
crystalline irons are of variable T. S., highest to lowest, and low ductility.
Ijowmoor Iron Bars. — Three rolled bars 2^ inches diameter; ten-
sile tests: elastic, 23,200 to 24,200; ultimate, 50,875 to 51,905; contraction, 44.4
to 42.5; extension, 29.2 to 24.3. Three hammered bars, 4% inches diameter,
elastic 25,100 to 24,200; ultimate, 46,810 to 49,223; contraction, 20.7 to 46.5;
extension, 10. 8 to 31. 6. Fractures of all, 100 percent fibrous. In the ham-
mered bars the lowest T. S. was accompanied by lowest ductility.
Iron Bars, Various.— Of a lot of 80 bars of various sizes, some rolled
and some hammered (the above Lowmoor bars included) the lowest T. S.
(except one) 40,808 pounds per square inch, was shown by the Swedish
"hoop L " bar 314 inches diameter, rolled. Its elastic limit was 19,150
pounds; contraction 68.7 % and extension 37.7$ in 10 inches. It was also
the most ductile of all the bars tested, and was 100 % fibrous. The highest
T. S., 60,780 pounds, with elastic limit, 29,400; contr., 36.6; and ext., 24.3 %,
was shown by a " Farnley " 2-inch bar, rolled. It was also 100 % fibrous.
The lowest ductility 2.6$ contr., and 4.1 % ext., was shown by a 3%-inch
hammered bar, without brand. It also had the lowest T. S., 40,278 pounds,
but rather high elastic limit, 25,700 pounds. Its fracture was 95 % crystal-
line. Thus of the two bars showing the lowest T. S., one was the most duc-
tile and the other the least ductile in the whole series of 80 bars.
Generally, high ductility is accompanied by low tensile strength, as in the
Swedish bars, but the Farnley bars showed a combination of high ductility
and high tensile strength.
Locomotive Forgings, Iron.— 17 tests: average, E. L., 30,420; T. S.,
50,521; contr., 36.5: ext. in 10 inches, 2M.8.
Broken Anchor Forgings. Iron.— 4 tests: average, E.L., 23, 825;
T. S., 40,083; contr., 3.0; ext. in 10 inches, 3.8.
Kirkaldy places these two irons in contrast to show the difference between
good and bad work. The broken anchor material, he says, is of a most
treacherous character, and a disgrace to any manufacturer.
Iron Plate Girder. —Tensile tests of pieces cut from a riveted iron
girder after twenty years1 service in a railway bridge. Top plate, average
of 3 tests, E. L., 26,600; T. S., 40,806; contr. 161; ext. in 10 inches, 7.8.
Bottom plate, average of 3 tests, E. L., 31,200; T. S., 44,288; contr., 13.3; ext.
in 10 inches, 6.3. Web-plate, average of 3 tests, E. L., 28,000; T. S., 45,902;
contr., 15 9; ext. in 10 inches, 8.9. Fractures all fibrous. The results of 30
tests from different parts of the girder prove that the iron has undergone
no change during twenty years of use.
Steel Plates.— Six plates 100 inches long, 2 inches wide, thickness vari-
ous, .36 to .97 inch T. S., 55,485 to 60,805; E. L., 29,600 to 33,200; contr., 52.9
to 59.5; ext., 17.05 to 18.57.
Steel Bridge Links.— 40 links from Hammersmith Bridge, 1886.
298
STRENGTH OF MATERIALS.
.2
Fracture.
8
u,
.
.
C
a
>
1
cc
"
d
H
M
2
H
N
0
M
DQ
O
67,294
60,753
38,294
36,030
34.5*
30.1
14.11*
15 51
Lowest T. S
Highest T. S. and E. L
75,936
44,166
31.2
12.42
15
85
Lowest EL
64,044
32,441
34.7
13.43
30
70
Greatest Contraction
63,745
38,118
52.8
15.46
100
0
Greatest Extension
65,980
36,792
40.8
17.78
35
65
Least Contr. and Ext
63,980
39,017
6.0
6.62
0
100
The ratio of elastic to ultimate strength ranged from 50.6 to 65.2 per cent;
average, 56.9 per cent.
Extension in lengths of JOO inches. At 10,000 Ibs. per sq. in., .018 to .024;
mean, .020 inch; at 20.000 Ibs. per sq. in. .049 to .063; mean, .055 inch; at
30,000 Ibs. per sq. in., .083 to .100; mean, .090; set at 30,000 pounds per sq. in.,
0 to .002; mean, 0.
The mean extension between 10,000 to 30,000 Ibs. per sq. in. increased regu-
larly at the rate of .007 inch for each 2000 Ibs. per sq. in. increment of strain.
This corresponds to a modulus of elasticity of 28,571,429. The least increase
of extension for an increase of load of 20,000 Ibs. per sq. in., .065 inch, cor-
responds to a modulus of elasticity of 30,769,231, and the greatest, .076 inch,
to a modulus of 26,315,789.
Steel ~
rails 72 p<
Elastic stress. Ultimate stress. Deflection at 50,000 Ultimate
Pounds. Pounds. Pounds. Deflection.
Hardest.... 34,200 60,960 3.24 ins. 8 ins.
Softest.... 32,000 56,740 3.76 " 8 "
Mean 32,763 59,209 3.53 " 8 "
All uncracked at 8 inches deflection.
Pulling tests of pieces cut from same rails. Mean results.
Elastic Ultimate Contraction of
Stress. Pounds. area of frac- Extension
per sq. in. per sq. in. ture. in 10 ins.
Top of rails 44,200 83,110 19.9* 13.5*
Botton of rails 40,900 77,820 30.9* 22.8*
i. UlUvIUlUB VJL (VU,*J1«;, I u«7.
teel Rails.— Bending tests, 5 feet between supports, 11 tests of flange
s 72 pounds per yard, 4.63 inches high.
Steel Tires.— Tensile tests of specimens cut from steel tires.
KRUPP STEEL.— 262 Tests.
Highest..
Mean ....
Lowest . .
E. L.
68,250
52,869
41,700
T. S.
119,079
104,112
90,523
Contr.
31.9
29.5
45.5
VICKERS, SONS & Co.— 70 Tests.
Highest. .
Mean
Lowest..,
E. L.
58,600
51,066
43,700
T. S.
120,789
101,264
87,697
Contr.
11.8
17.6
24.7
Ext. in
5 inches.
18.1
19.7
23.7
Ext. in
5 inches.
8.4
12.4
16.0
Note the correspondence between Krupp's and Vickers' steels as to ten-
sile strength and elastic limit, and their great difference in contraction and
elongation. The fractures of the Krupp steel averaged -22 per cent silky,
78 per cent granular; of the Vicker steel, 7 per cent silky, 93 per cent granu-
lar.
EXTRACTS FROM KIRKALDY^S TESTS. 299
Steel Axles.— Tensile tests of specimens cut from steel axles.
PATENT SHAFT AND AXLE TREE Co.— 157 Tests.
Ext. in
E. L. T. S. Contr. 5 inches.
Highest 49,800 99,009 21.1 16.0
Mean 36,267 72,099 33.0 23.6
Lowest 31,800 61,382 34.8 25.3
VICKERS, SONS & Co.— 125 Tests.
Ext. in
E. L. T. S. Contr. 5 inches.
Highest 42,600 83,701 18.9 13.2
Mean 37,618 70,572 41.6 27.5
Lowest 30,250 56,388 49.0 37.2
The average fracture of Patent Shaft and Axle Tree Co. steel was 33 per
cent silky, 67 per cent granular.
The average fracture of Vickers' steel was 88 per cent silky, 12 per cent
granular.
Tensile tests of specimens cut from locomotive crank axles.
VICKERS'.— 82 Tests, 1879.
Ext. in
E. L. T. S. Contr. 5 inches.
Highest 26,700 68,057 28.3 18.4
Mean 24,146 57,922 32.9 24.0
Lowest 21,700 50,195 52.7 36.2
VICKERS'.— 78 Tests, 1884.
Ext. in
E. L. T. S. Contr. 5 inches.
Highest 27,600 64,873 27.0 20.8
Mean 23,573 56,207 32.7 25.9
Lowest 17,600 47,695 35.0 27.2
FRIED. KRUPP.— 43 Tests, 1889.
Ext. in
E. L. T. S. Contr. 5 inches.
Highest 31,650 66,868 48.6 35.6
Mean 29,491 61 ,774 47.7 32.3
Lowest 21,950 55,172 55.3 35.6
Steel Propeller Shafts.— Tensile tests of pieces cut from two shafts,
mean of four tests each. Hollow shaft, Whitworth, T. S., 61,290; E. L.,
80,575; contr., 52.8; ext. in 10 inches, 28.6. Solid Shaft, Vickers', T. SM
46,870; E. L. 20,425; contr., 44.4; ext. in 10 inches, 30.7.
Thrusting tests, Whitworth, ultimate, 56,201; elastic, 29,300; set at 30,000
Ibs., 0.18 per cent; set at 40,000 Ibs., 2.04 per cent; set at 50,000 Ibs., 3.82 per
cent.
Thrusting tests, Vickers', ultimate, 44,602; elastic, 22,250; set at 30,000 Ibs.,
2.29 per cent; set at 40,000 Ibs., 4.69 per cent.
Shearing strength of the Whitworth shaft, mean of four tests, was 40,654
Ibs. per square inch, or 66.3 per cent of the pulling stress. Specific gravity
of the Whitworth steel, 7.867: of the Vickers', 7.856.
Spring Steel.— Untempered, 6 tests, average, E. L., 67,916: T. S.,
115,608; contr., 37.8; ext. in 10 inches, 16.6. Spring steel untempered, 15
tests, average, E. L., -38, 785; T. S., 69,496; contr., 19.1 ; ext. in 10 inches, 29.8.
These two lots were shipped for the same purpose, viz., railway carriage
leaf springs.
Steel Castings.— 44 tests, E. L., 31,816 to 35,567; T. S., 54,928 to 63,840;
contr., 1.67 to 15.8; ext., 1.45 to 15.1. Note the great variation in ductility.
The steel of the highest strength was also the most ductile.
Riveted Joints, Pulling Tests of Riveted Steel Plates,
Triple Riveted Lap Joints, Machine Riveted.
Holes Drilled.
Plates, width and thickm ss, inches :
13.50 X .25 13.00 X .51 11.75 X .78 12.25 X 1.01 14.00 X .77
Plates, gross sectional area square inches :
3.375 6.63 9.165 12.372 10.780
Stress, total, pounds :
199,830 332,640 483,180 528,000 455,210
300 STRENGTH OF MATERIALS.
Stress per square inch of gross area, joint :
59,058 50,172 46,173 42,696 42,32V
Stress per square inch of plates, solid :
70,705 65,300 64,050 62,280 68,045
Ratio of strength of joint to solid plate :
83.46 76.83 72.09 68.55 62.06
Ratio net area of plate to gross :
73.4 65c5 62.7 64.7 72.9
Where fractured :
plate at plate at plate at plate at rivets
holes. holes. holes. holes. sheared.
Rivets, diameter, area and number :
.45, .159, 24 .64, .321, 21 .95, .708, 12 1.08, .916, 12 .95, .708, 13
Rivets, total area :
3.816 6.741 8.496 10.992 8.496
Strength of Welds.— Tensile tests to determine ratio of strength of
weld to solid bar.
IRON TIE BARS.— 28 Tests.
Strength of solid bars varied from 43,201 to 57,065 Ibs.
Strenth of welded bars varied from 17,816 to 44,586 Ibs.
Ratio of weld to solid varied from 37.0 to 79. \%
IRON PLATES.— 7 Tests.
Strength of solid plate from 44,851 to 47,481 Ibs.
Strength of welded plate from 26,442 to 38,931 Ibs.
Ratio of weld to solid 57 .7 to 83 . 9#
CHAIN LINKS.— 216 Tests.
Strength of solid bar from 49,122 to 57,875 Ibs.
Strength of welded bar from . . . 39,575 to 48,824 Ibs.
Ratio of weld to solid 72.1 to 95. 4#
IRON BARS.— Hand and Electric Machine Welded.
32 tests, solid iron, average , 52,444
17 k electric welded, average 46,836 ratio 89. 1#
19 " hand " 46,899 " 89.3*
STEEL BARS AND PLATES.— 14 Tests.
Strength of solid . . 0 54,226 to 64,580
Strength of weld 28,553 to 46,019
Ratio weld to solid 52.6to82.1#
The ratio of weld to solid in all the tests ranging from 37.0 to 95.4 is proof
of the great variation of workmanship in welding.
Cast Copper.— 4 tests, average, E. L., 5900; T. S., 24,781; contr., 24.5;
ext., 21.8.
Copper Plates.— As rolled, 22 tests, .26 to .75 in. thick; E. L.,9766 to
18,650; T. S., 30,993 to 34,281 ; contr., 31.1 to 57.6; ext., 39.9 to 52.2. The va-
riation in elastic limit is due to difference in the heat at which the plates
were finished. Annealing reduces the T. S. only about 1000 pounds, but the
E. L. from 3000 to 7000 pounds.
Another series, .38 to .52 thick; 148 tests, T. S., 29,099 to 31,924; contr., 28.7
to 56.7; ext. in 10 inches, 28.1 to 41.8. Note the uniformity in tensile
strength.
Drawn Copper.— 74 tests (0.88 to 1.08 inch diameter); T. S., 31,634 to
40,557; contr., 37.5 to 64.1; ext. in 10 inches, 5.8 to 48.2.
Bronze from a Propeller Blade.— Means of two tests each from
centre and edge. Central portion (sp. gr. 8.320). E. L., 7550; T. S., 26,312;
contr., 25.4; ext. in 10 inches, 32.8. Edge portion (sp. gr. 8550). E. L., 8950;
T. S., 35,960; contr., 37.8; ext. in 10 inches, 47.9.
Cast German Silver.— 10 tests: E. L., 13,400 to 29,100; T. S., 23,714 to
46,540; contr., 3.2 to 21.5; ext. in 10 inches, 0.6 to 10.2.
Thin Sheet Metal.— Tensile Strength.
German silver, 2 lots 75,816 to 87,129
Bronze, 4 lots 73,380 to 92,086
Brass, 2 lots 44,398 to 58, 188
Copper, 9 lots , 30,470 to 48,450
Iron, 13 lots, lengthway 44,331 to 59,484
Iron, 13 lots, crossway 39,838 to 57,350
Steel,61ots 49,253 to 78,251
Steel, 6 lots, crossway « 55,948 to 80,799
EXTRACTS PROM KIRKALD1 S TESTS.
301
"Wire.— Tensile Strength.
German silver, 5 lots 81,735 to 92,224
Bronze, 1 lot 78,049
Brass, as drawn, 4 lots 81,114 to 98,578
Copper, as drawn, 31ots.. 37,607 to 46,494
Copper annealed, 3 lots 34,936 to 45,210
Copper (another lot), 4 lots 35,052 to 62,190
Copper (extension 36.4 to 0.6$).
Iron, 8 lots... 59,246 to 97,908
Iron (extension 15.1 to 0.7$).
Steel, Slots 103,272 to 318,823
The Steel of 318,823 T. S. was .047 inch diam., and had an extension of only
0.3 per cent; that of 103,272 T. S, was .107 inch diam. and had an extension
of 2.2 per cent. One lot of .044 inch diam. had 267,114 T. S., and 5.2 per cent
extension.
Wire Ropes.
Selected Tests Showing Range of Variation.
Description.
Circumference,
inches.
Sa-
il
£h
Strands.
Diameter of
Wires, inches.
Hemp Core.
Ultimate
Strength,
Ibs.
%*J
°.i
0 g
fc£
O2
o o>
££
Galvanized
Ungalvanized. . . .
Ungalvanized. . . .
Galvanized . .
7.70
7.00
6.38
7.10
6.18
6.19
4.92
5.36
4.8:2
3.65
3.50
3.8~
4.11
3.31
3.02
2.68
2.87
2.46
1.75
2.04
1.76
53.00
53.10
42.50
37.57
40.46
40.33
20.86
18.94
21.50
12.21
12.65
14.12
11.35
7.27
8.62
6.26
5.43
3.85
2.80
2.72
1.85
6
7
7
6
7
7
6
6
6
6
7
6
6
6
6
6
6
6
6
6
6
19
19
19
30
19
19
30
12
19
7
7
12
12
7
6
12
12
7
12
12
.1563
.1495
.1347
.1004
.1302
.1316
.0728
.1104
.1693
.0755
.122
.135
.080
.068
.105
.0963
.0560
.0472
.0619
.0378
.0305
Main
Main and Strands
Wire Core
Main and Strands
Wire Core
Wire Core
Main and Strands
Main and Strands
Main
Main
Wire Core
Main
Main and Strands
Main and Strands
Main
Main and Strands
Main and Strands
Main and Strands
Main
Main and Strands
Main
339,780
314,860
295,920
272,750
268,470
221,820
190,890
136,550
129,710
110,180
101,440
98,670
75,110
55,095
49,555
41,205
38,555
28,075
24,552
20,415
14,634
Ungalvanized....
Ungalvanized. . . .
Galvanized..
Galvanized
Galvanized .
Ungalvanized. . . .
Ungalvanized
Ungalvanized. . . .
Galvanized
Galvanized ..
Ungalvanized. . . .
Ungalvanized. . . .
Galvanized
Galvanized .
Ungalvanized. . . .
Galvanized
Galvanized
Hemp Ropes, Untarred.— 15 tests of ropes from 1.53 to 6.90 inches
circumference, weighing 0.42 to 7.77 pounds per fathom, showed an ultim-
ate strength of from 1670 to 33,808 pounds, the strength per fathom weight
varying from -2872 to 5534 pounds.
Hemp Ropes, Tarred. —15 tests of ropes from 1.44 to 7.12 inches
circumference, weighing from 0.38 to 10.39 pounds per fathom, showed an
ultimate strength of from 1046 to 31,549 pounds, the strength per fathom
weight varying from 1767 to 5149 pounds.
Cotton Ropes.— 5 ropes, 2.48 to 6.51 inches circumference, 1.08 to 8.17
pounds per fathom. Strength 3089 to 23,258 pounds, or 2474 to 3346 pounds
per fathom weight.
Manila Ropes.— 35 tests: 1.19 to 8.90 inches circumference, 0.20 to
11.40 pounds per fathom. Strength 1280 to 65,550 pounds, or 3003 to 7394
pounds per fathom weight.
302
STRENGTH OF MATERIALS.
Belting.
No. of Tensile strength
lots. per square inch.
11 Leather, single, ordinary tanned 3248 to 4824
4 Leather, single, Helvetia ........ 5631 to 5944
7 Leather, double, ordinary tanned 2160 to 3572
8 Leather, double Helvetia 4078 to 5412
6 Cotton, solid woven 5648 to 8869
14 Cotton, folded, stitched 4570 to 7750
1 Flax, solid, woven 9946
1 Flax, folded, stitched ." 6389
6 Hair, solid, woven , 3852 to 5159
2 Rubber, solid, woven 4271 to 4343
Canvas.— 35 lots: Strength, lengthwise, 113 to 408 pounds per inch;
Crossways, 191 to 468 pounds per inch.
The grades are numbered 1 to 6, but the weights are not given. The
strengths vary considerably, even in the same number.
Marbles.— Crushing strength of various marbles. 38 tests, 8 kinds.
Specimens were 6-inch cubes, or columns 4 to 6 inches diameter, and 6 and
12 inches high. Range 7542 to 13,720 pounds per square inch.
Granite.— Crushing strength, 17 tests; square columns 4X4 and 6X4,
1 to 24 inches high, 3 kinds. Crushing strength ranges 10,026 to 13,271
pounds per square inch. (Very uniform.)
Stones.— (Probably sandstone, local names only given.) 11 kinds, 43
tests, 6x6, columns 12, 18 and 24 inches high. Crushing strength ranges
from 2105 to 12,122. The strength of the column 24 inches long is generally
from 10 to 20 per cent less than that of the 6-inch cube.
Stones.— (Probably sandstone) tested for London & Northwestern Rail-
way. 16 lots, 3 to 6 tests in a lot. Mean results of each lot ranged from
3785 to 11,956 pounds. The variation is chiefly due to the stones being from
different lots. The different specimens in each lot gave results which gen-
erally agreed within 30 per cent.
Bricks.— Crushing strength, 8 lots; 6 tests in each lot; mean results
ranged from 1835 to 9209 pounds per square inch. The maximum variation
in the specimens of one lot was over 100 per cent of the lowest. In the most
uniform lot the variation was less than 20 per cent.
"Wood.— Transverse and Thrusting Tests.
4
*
Sizes abt. in
square
Span,
inches
Ultimate
Stress
S =
LW
Thrust-
ing
Stress
EH
4BD*
per sq,
in.
Pitch pine
10
11^ to 12>£
144
45,856
to
1096
to
3586
to
Dantzic fir
1?
12 to 13
144
80,520
37,948
to
1403
657
to
5438
2478
to
English oak
3
4J^ X 12
120
54,152
32,856
to
790
1505
to
3423
2473
to
American white
oak
5
4^ X 12
120
39,084
23,624
to
1779
1190
.to
4437
2656
to
26,952
1372
3890
Demerara greenheart, 9 tests (thrusting) 8169 to 10,785
Oregon pine, 2 tests 5888 and 7284
Honduras mahogany, 1 test 6769
Tobasco mahogany, 1 test 5978
Norway spruce, 2 tests 5259 and 5494
American yellow pine, 2 tests 3875 and 3993
English ash, 1 test 3025
Portland Cement.-(Austrian.) Cross-sections of specimens 2 x 2V£
inches for pulling tests only ; cubes, 3x3 inches for thrusting tests; weight,
MISCELLANEOUS TESTS OF MATERIALS.
305
98.8 pounds per imperial bushel; residue, 0.7 per cent with sieve 2500 meshes
per square inch; 38.8 per cent by volume of water required for mixing; time
of setting, 7 days; 10 tests to each lot. The mean results in Ibs. per sq. in.
for
were as follows:
Cement
alone,
Age. Pulling.
10 days 376
20 days 420
30 days 451
1 Cement,
4 Sand,
Thrusting.
228
275
Cement 1 Cement, 1 Cement,
alone, 2 Sand, 3 Sand,
Thrusting. Thrusting. Thrusting.
2910 893 407
3342 1023 494
3724 1172 594
Portland Cement.— Various samples pulling tests, 2x2^> inches
cross-section, all aged 10 days, 180 tests; ranges 87 to 643 pounds per square
inch.
TENSILE STRENGTH: OF WIRE.
(From J. Bucknall Smith's Treatise on Wire.)
Tons per sq. Pounds per
in. sectional sq. in. sec-
area, tional area.
Black or annealed iron wire 25 56,000
Bright hard drawn 35 78,400
Bessemer, steel wire 40 89,600
Mild Siemens-Martin steel wire 60 134,000
High carbon ditto (or " improved ") 80 179,200
Crucible cast-steel "improved" wire 100 224,000
•* Improved " cast-steel " plough " 120 268,800
Special qualities of tempered and improved cast-
steel wire may attain 150 to 170 336,000 to 380,800
MISCEI^LANEOUS TESTS OF MATERIALS.
Reports of Work of tlie Watertown Testing-machine in
1883.
TESTS OF RIVETED JOINTS, IRON AND STEEL PLATES.
Thickness Plate.
Diameter, Rivets,
inches.
Diameter,
Punched Holes,
inches.
Width Plate
Tested, inches.
of
1
S
I
Pitch Rivets,
inches.
Tensile Strength
Joint in Net Sec-
tion of Plate per
square inch,
pounds.
Tensile Strength
Plate per square
inch, pounds.
Efficiency of Joint,
Per Cent.
%
11-16
M
10K
6
1%
39,300
47,180
47.0 J
%
11-16
%
1014
6
1%
41,000
47,180
49.0 J
L£
%
13-16
10
5
2
35,650
44,615
45.6 $
Irfjj
3/
13-16
10
5
2
35,150
44,615
44.9 J
%
11-16
M
10
5
2
46,360
47,180
59.9 §
%
11-16
%
10
5
2
46,875
47,180
60.5 §
1^
K
13-16
10
5
2
46,400
44,615
59.4 §
^
H
13-16
10
5
2
46,140
44,615
59.2 §
%
i
1 1-16
10^
4
2%
44,260
44,635
57.2 §
6,£
i
1 1-16
10*6
4
2%
42,350
44,635
54.9 §
%
1/^6
1 3-16
11.9
4
2 9
42,310
46,590
52.1 §
M
1^
1 3-16
11.9
4
2^9
41,920
46,590
51.7 §
%
M
13-16
10^2
6
1%
61,270
53.330
59.5 *
%
M
13-16
iog
6
1%
60,830
53,330
59.1 $
i^
15-16
10
5
2
47,530
57,215
40.2 $
V%
15-16
10
5
2
49,840
57,215
42.3 t
%
11-16
3£
10
5
2
62,770
53,330
71.7 §
%
11-16
%
10
5
2
61,210
53,330
69.8 §
L?2
15-16
10
5
2
68,920
57,215
57.1 «j
Lj£
15-16
10
5
2
66,710
57,215
55.0 §
%
1
1-16
9^6
4
2%
62,180
52,445
63.4 §
%
1
1-16
9^
4
2%
62,590
52,445
63.8 §
M
l/^
3-16
10
4
2^3
54,650
51,545
54.0 §
M
1^
8-16
10
4
2^i
54,200
51,545
53.4 §
*Iron.
t Steel.
J Lap-joint.
§ Butt-joint.
304
STRENGTH OF MATERIALS.
The efficiency of the joints is found by dividing the maximum tensile
stress on the gross sectional area of plate by the tensile strength of the
material.
COMPRESSION TESTS OF 3 X 3 INCH WROUGHT-IRON BARS.
Length, inches.
Tested with Two Pin Ends, Pins
1*^ inch in Diameter.
Tested with One
Flat and One Pin
End, Ultimate
Compressive
Strength, pounds
per square inch.
Ultimate Com-
pressive Strength
pounds per square
inch.
Tested with Two
Flat Ends, Ulti-
mate Compressive
Strength, pounds
per square inch.
30
j 28,260
"131,990
j 26,310
1 26,640
j 24,030
1 25,380
20,660
' 20,200
16,520
' 17,840
j 13,010
( 15 700
60
90
j 26,780
1 25,580
j 23,010
1 22,450
j 25,120
1 25,190
j 22,450
\ 21,870
120
150
180
Tested with two
ends. Length o
120 inches.
{Diameter
of Pins.
% inch. ..
Ult. Comp. Str.,
per sq. in., Ibs.
16250
}^ inches
VA
2if «
17,740
21,400
22,210
TENSILE TEST OF SIX STEEL EYE-BARS.
COMPARED WITH SMALL TEST INGOTS.
The steel was made by the Cambria Iron Company, and the eye-bar heads
made by Keystone Bridge Company by upsetting and hammering. All the
bars were made from one ingot. Two test pieces, %-inch round, rolled from
a test-ingot, gave elastic limit 48,040 and 42,210 pounds; tensile strength,
73,150 and 69,470 pounds, and elongation in 8 inches, 22.4 and 25.6 per cent,
respectively. The ingot from which the eye-bars were made was 14 inches
square, rolled to billet, 7X6 inches. The eye-bars were rolled to 6^ x 1 inch.
Cnemical tests gave carbon .27 to .30: manganese, .64 to .73; phosphorus,
074 to .098.
Gauged
Length,
inches.
160
160
160
200
200
200
200
Elastic
limit, Ibs.
per sq. in.
37,480
36,650
37,600
35,810
33,230
37,640
Tensile
strength per
sq. in., Ibs.
67,800
64,000
71,560
68,720
65,850
64,410
68,290
Elongation
per cent, in
Gauged Length.
15.8
6.96
8.6
12.3
12.0
16.4
13.9
The average tensile strength of the %-inch test pieces was 71,310 Ibs., that
of the eye-bars 67,230 Ibs., a decrease of 5.7$. The average elastic limit of
the test pieces was 45,150 Ibs., that of the eye-bars 36,402 Ibs., a decrease of
19.4$. The elastic limit of the test pieces was 63.3$ of the ultimate strength,
that of the eye-bars 54.2$ of the ultimate strength.
MISCELLANEOUS TESTS OF MATERIALS.
305
COMPRESSION OF WROUGHT-IRON COLUMNS, LATTICED BOX
AND SOLID WEB.
ALL TESTED WITH PIN ENDS.
Columns made of
-M
1
i
a
3
Sectional Area,
square inch.
Total Weight
of Column,
pounds.
Ultimate
Strength, per
square inch,
pounds.
6-inch channel solid web ... . ...
10 0
9 831
432
30,220
15 0
9 977
592
21,050
g « U It *«
20 0
9762
755
16,220
8 " " " *' ..
20 0
16 281
1,290
22,540
g ,4 it U (|
26 8
16 141
1,645
17,570
8-inch channels, with 5-16-in. continuous
plates
26 8
19417
1 940
25,290
6-16-inch continuous plates and angles.
Width of plates, 12 in., 1 in. and 7.35 in.
7-16-inch continuous plates and angles.
Plates 12 in wide
26.8
26 8
16.168 -
20954
1,765
2 242
28,020
25,770
8-inch channels latticed
13 3
7.628
679
33,910
8 " " "
20.0
7.621
924
34,120
8 " " " .. .
26 8
7.673
1,255
29,870
8-lnch channels, latticed, swelled sides..
8 •* " " " " ..
8 " " " " " ..
10 " " '*
13.4
20 0
26.8
16 8
7.624
7.517
7.702
11 944
684
921
1,280
1,470
33,530
33,390
30,770
33,740
10 " " '*
25.0
12.175
1,926
32,440
10-inch channels, latticed, swelled sides.
* 10-inch channels, latticed one side; con-
tinuous plate one side
1 10-inch channels, latticed one side; con-
tinuous plate one side
16.7
25.0
25.0
25.0
12.366
11.932
17.622
17.721
1,549
1,962
1,848
1,827
31,130
32,740
26,190
17,270
* Pins in centre of gravity of channel bars and continuous plate, 1.63
inches from centre line of channel bars,
•f Pins placed in centre of gravity of channel bars.
EFFECT OF COLD-DRAWING ON STEEL,
Three pieces cut from the same bar of hot -rolled steel:
1. Original bar, 2.03 in. diam., gauged length 30 in., tensile strength 65,400
Ibs. per square in.; elongation 23.9$.
2. Diameter reduced in compression dies (one pass) .094 in.; T, S. 70,420; el.
2.7# in 20 in.
3. " " " " " l< " .222 in. ; T. S. 81,890; el.
0.075# in 20 iir.
Compression test of cold-drawn bar (same as No. 3), length 4 in., diam.
1.808 in.: Compressive strength per sq. in , 75,000 Ibs.; amount of compres-
sion .057 in.; set .04 in. Diameter increased by compression to 1.821 in. in
the middle; to 1.813 in. at the ends.
Tests of Cold-rolled and Cold-drawn Steel, made by the
Cambria Iron Co, in 1897, gave the following results (averages of 12 tests of
each)
Before cold-rolling, E. L. 35,390
After " " , " 72,530
After cold-drawing, " 76,350
T. S. 59,980
79,830
El. in 8 in. 28. 3 #
" " 9.6"
" " 8.9"
Red. 58.5*
" 349"
" 34.2"
The original bars were 2 in. and % in. diameter. The test pieces cut from
the bars were % in. diam., 18 in. long. The reduction in diameter from the
hot-rolled to the cold-rolled or cold-drawn bar was I/16 in» m each case.
306
STRENGTH OF MATERIALS.
TESTS OF AMERICAN WOODS. (See also page 309.)
In all cases a large number of tests were made of each wood. Minimum
and maximum results only are given. All of the test specimens had a sec-
tional area of 1.575 X 1.575 inches. The transverse test specimens were 39.3?
inches between supports, and the compressive test specimens were 12.6Q
inches long. Modulus of rupture calculated from formula R = - •— ; P =
load in pounds at the middle, I = length in inches, b = breadth, d = depth:
Name of Wood.
Transverse Tests
Modulus of
Rupture.
Compression
Parallel to
Grain, pounds
per square inch.
Min.
Max.
Min.
Max.
7,410
5,790
6,480
9.940
7,500
11,940
9,120
7,620
9,400
7,480
8,080
8,830
5,970
8,790
8,040
7,340
6,810
8,850
10,280
8,470
9,070
8,970
8,550
6,650
7,840
8,590
6,510
5,810
7,040
7,140
5.600
4,680
10,600
5.300
7,420
9,800
10,700
Cucumber tree (Magnolia acuminata). .
Yellow poplar white wood (Lirioden-
7,440
6,560
6,720
9,680
8,610
12,200
8,310
7,470
10,190
9,830
10,290
5,950
5,180
10,220
8,250
6,720
4,700
8,400
14,870
11,560
7 010
12,050
11,756
11,530
20.130
13,450
21,730
16,800
11,130
14.560
14,300
18,500
15,800
10,150
13,952
15,070
11,360
11,740
16,320
20,710
19,430
18,360
18,370
18,420
12,870
18,840
17,610
13,430
9,530
15,100
10,030
11,530
10,980
21,060
11,650
14,680
17,920
16,770
4,560
4,150
3,810
7,460
6,010
8,330
5,830
5,630
6,250
6,240
6,650
4,520
4,050
6,980
4,960
4,960
5,480
6,940
7,650
7,460
5,810
4,960
4,540
3,680
5,770
5,770
3,790
2,660
4,400
5,060
3,750
2,580
4,010
4,150
4,500
4,880
6,810
White wood, Basswood (Tilia Ameri-
Sugar-maple, Rock-maple (Acer sac-
charinum
Re<1 maple (Acerrubrum)
Wild cherry (Prunus serotina)
Sweet gum (Liquidambar styraciflua) . .
Dogwood (Cornusflorida)
Sour gum, Pepperidge (Ni/ssa sylvatica).
Persimmon (Diospyros Virginiana). . . .
\Vhittj ash (Fraxunis Americana) . . .
Sassafras (Sassafras officinale)
Slippery elm ( Ulmus fitlva)
White elm (Ul)tius Americana)
Sycamore; Buttonwood (Platanus occi-
Butternut; white walnut (Juglans ci-
nerea) .
Black walnut (Juglans nigra)
Shellbark hickory (Carya alba)
Red oak ( Ouercus rubra) ..........
9,760
7,900
5,950
13,850
11,710
8,390
6,310
5,640
9,530
5,610
3,780
9,220
9,900
7,590
8,220
10,080
Chestnut (Castanea vulgar is)
Beech (Faous ferruginca) ,
Canoe-birch, paper-birch (Betidapapy-
Cottonwood (Populus moniliferd)
White cedar (Thuja occidentalis)
Red cedar (Juniperus Virginiana)
Cypress (Saxodium Distichuni)
Spruce pine (Pinus qldbra)
Long-leaved pine, Southern prae (Pinus
Hemlock (Tsuqa Canadensis)
Red fir, yellow fir (Pseudotsuga Doug-
Tamarack (Larix Americana")
SHEARING STRENGTH OF IRON AND STEEL.
H. V. Loss in American Engineer and Railroad Journal, March and April,
3893, describes an extensive series of experiments on the shearing of iron
and steel bars in shearing machines. Some of his results are :
CHAIKS.
307
Depth of penetration at point of maximum resistance for soft steel bars
is independent- of the width, but varies with the thickness. If d = depth of
penetration and t = thickness, d = .Bt for a flat knife, d = .25 t for a 4° bevel
knife and d = .16 4/^f or an 8° bevel knife. The ultimate pressure per inch
of width in flat steel bars is approximately 50,000 Ibs. X t. The energy con-
sumed in foot pounds per inch width of steel bars is, approximately: 1
thick, 1300 ft.-lbs.; W, 2500; 1%", 3700; 1%", 4500; the energy increasing
at a slower rate than the square of the thickness. Iron angles require more
energy than steel angles of the same size ; steel breaks while iron has to be
cut off. For hot-rolled steel the resistance per square inch for rectan-
gular sections varies from 4400 Ibs. to 20,500 Ibs., depending partly upon its
hardness and partly upon the size of its cross-area, which latter element
indirectly but greatly indicates the temperature, as the smaller dimensions
require a considerably longer time to reduce them down to size, which time
again means loss of heat.
It is not probable that the resistance in practice can be brought very
much below the lowest figures here given— viz., 4400 Ibs. per square inch-
as a decrease of 1000 Ibs. will henceforth mean a considerable increase in
cross-section and temperature.
HOLDING-POWER OF BOILER-TUBES EXPANDED
INTO TUBE-SHEETS.
Experiments by Chief Engineer W. H. Shock, U. S. N., on brass tubes, 2^
inches diameter, expanded into plates %-inch thick, gave results ranging
from 5850 to 46,060 Ibs. Out of 48 tests 5 gave figures under 10,000 Ibs., 12
between 10,000 and 20,000 Ibs., 18 between 20,000 and 30,000 Ibs., 10 between
30,000 and 40,000 Ibs., and 3 over 40,000 Ibs.
Experiments by Yarrow & Co., on steel tubes, 2 to 2*4 inches diameter,
gave results similarly varying, ranging from 7900 to 41,715 Ibs., the majority
ranging from 20,000 to 30,000 Ibs. In 15 experiments on 4 and 5 inch tubes
the strain ranged from 20,720 to 68,040 Ibs. Beading the tube does not neces-
sarily give increased resistance, as some of the lower figures were obtained
with beaded tubes. (See paper on Rules Governing the Construction of
Steam Boilers, Trans. Engineering Congress, Section G-, Chicago, 1893.)
CHAINS.
Weight per Foot, Proof Test and Breaking Weignt.
(Pennsylvania Railroad Specifications, 1809.)
Nominal
Diameter
of Wire.
Inches.
Description.
Maximum
L.ength of
100 Links.
Inches.
Weight
>er Foot.
Lbs.
Proof
Test.
Lbs.
breaking
Weight.
Lbs.
5/32
Twisted chain .
103 1
0 20
3/16
96.2
0.35
3/16
VA
'erfection twisted chain.
Straight link chain
151.25
102 0
0.266
0 70
1 500
3 000
5/16
%
U U It
114.7
114 7
1.10
1.50
3,000
3,500
5,500
7,000
%
113.6
1.50
4,000
7,500
7/16
7/16
Straight-link chain
Crane chain .
137.5
126 3
1.90
1.90
5,000
5,500
9,500
10,000
Straight-link chain
Crane chain
153.0
138.9
2.50
2.50
7,000
7,500
12,500
13,000
P
Straight-link chain
Crane chain .
178.5
176 7
4.00
4.00
11,000
11,000
20,000
20,000
o/
Straight-link chain
204.0
5.50
16,000
29,000
Q/
Crane chain . . .
202 0
5.50
16,000
29,000
I/
252 5
7.40
22,000
40,000
1
d
277.7
9 50
30000
55,000
1L£
tt
303 0
12 00
40000
66,000
u
353 5
15 00
50,000
82,000
\v
it
416 6
21 00
70000
116,000
2
Elongation of all sizes, 10 per cent. All chain must stand the proof test
without deformation. A piece 2 ft. long out of each 200 ft. is tested to
destruction.
308
STRENGTH OF MATERIALS.
it IS * *& *& ^ 1& 1& IT'S 1&.
3£§ 15^ 18 20& 22£§ 265^ 28,& 31 34 37^.
British Admiralty Proving Tests of Chain Cables.— Stud-
links. Minimum size in inches and 16ths. Proving test in tons of 2240 Ibs.
Min. Size: , H if II
Test, tons: 8^ 10& 11£§ 1
Min. Size: I8 I9 I10 I11 I12 I13 I14 I15 2 2* 2* 23.
Test, tons: 40£g 43£§ 47£g 515% 552% 595% 635% 67^ 72 76^ 81,% 91&.
Wrought-iron Chain Cables.— The strength of a chain link is
less than twice that of a straight bar of a sectional area equal to that of one
side of the link. A weld exists at one end and a bend at the other, each re-
quiring at least one heat, which produces a decrease in the strength. The
report of the committee of the U. S. Testing Board, on tests of wrought-iron
and chain cables contains the following conclusions. That beyond doubt,
when made of American bar iron, with cast-iron studs, the studded link is
inferior in strength to the un studded one.
" That when proper care is exercised in the selection of material, a varia-
tion of 5 to 17 per cent of the strongest may be expected in the resistance
of cables. Without this care, the variation may rise to 25 per cent.
" That with proper material and construction the ultimate resistance of
the chain may be expected to vary from 155 to 170 per cent of that of the
bar used in making the links, and show an average of about 163 per cejit.
"• That the proof test of a chain cable should be about 50 per cent of the
ultimate resistance of the weakest link.'1
The decrease of the resistance of the studded below the unstudded cable
is probably due to the fact that in the former the sides of the link do not
remain parallel to each other up to failure, as they do in the latter, The re-
sult is an increase of stress in the studded link over the unstudded in the
proportion of unity, to the secant of half the inclination of the sides of the
former to each other.
From a great number of tests of bars and unfinished cables, the commit-
tee considered that the average ultimate resistance, and proof tests of chain
cables made of the bars, whose diameters are given, should be such as are
shown in the accompanying table.
ULTIMATE RESISTANCE AND PROOF TESTS OF CHAIN CABLES.
Diam.
of
Bar.
Average resist.
= 163$ of Bar.
Proof Test.
Diam.
of
Bar.
Average resist.
= 163# of Bar.
Proof Test.
Inches .
Pounds.
Pounds.
Inches.
Pounds.
Pounds.
1 1/16
71,172
33,840
1 9/16
162,283
77,159
1 1/16
79,544
37,820
\%
174,475
82,956
Jl^C
88,445
42,053
1 11/16
187,075
88,947
1 3/16
97,731
107,440
46,468
51,084
1 '13/16
200,074
213,475
95,128
101,499
1 5/16
117,577
55,903
1%
227,271
108,058
128,129
60,920
1 15/16
241,463
114,806
1 7/16
139,103
66,138
2 '
256,040
121,737
IK
150,485
71,550
STRENGTH OF GLASS.
(Fairbairn's "Useful Information for Engineers,'1 Second Series.)
Best Common Extra White
Flint Glass. Green Glass. Crown Glass,
Mean specific gravity 3.078 2.528 2.450
Mean tensile strength, Ibs. per sq. in., bars.. 2,413 2,896 2,546
do. thin plates. 4,200 4,800 6,000
Mean crush'g strength, Ibs. p. sq. in., cylMrs. 27,582 39,876 31,003
do. cubes. 13,130 20,206 21,867
The bars in tensile tests were about ^ inch diameter. The crushing tests
were made on cylinders about % inch diameter and from 1 to 2 inches high,
and on cubes approximately 1 inch on a side. The mean transverse strength
of glass, as calculated by Fairbairn from a mean tensile strength of 2560
Ibs. and a mean compressive strength of 30,150 Ibs. per sq. in., is, for a bar
supported at the ends and loaded in the middle,
STKEKGTH OF TIMBER.
309
In which w = breaking weight in Ibs., b = breadth, d = depth, and I = length,
in inches. Actual tests will probably show wide variations in both direc-
tions from the mean calculated strength.
STRENGTH OF COPPER AT HIGH TEMPERATURES.
The British Admiralty conducted some experiments at Portsmouth Dock-
yard in 1877, on the effect of increase of temperature on the tensile strength
of copper and various bronzes. The copper experimented upon was in rods
.72-in. diameter.
The following table shows some of the results:
Temperature
Fahr.
Tensile Strength
in Ibs. per sq. in.
Temperature
Fahr.
Tensile Strength
in Ibs. per sq. in.
Atmospheric.
100°
200°
23,115
23,366
22,110
300°
400°
500°
21,607
21,105
19,597
Up to a temperature of 400° F. the loss of strength was only about 10 per
cent, and at 500° F. the loss was 16 per cent. The temperature of steam at
200 Ibs. pressure is 382° F., so that according to these experiments the loss
of strength at this point would not be a serious matter. Above a tempera-
ture of 500° the strength is seriously affected.
STRENGTH OF TIMBER.
Strength of Long-leaf Pine (Yellow Pine, Pinus Palustris) from
Alabama (Bulletin No. 8, Forestry Div., Dept. of Agriculture, 1893. Tests
by Prof, J. B. Johnson.)
The following is a condensed table of the range of results of mechanical
tests of over 2000 specimens, from 26 trees from four different sites in
Alabama ; reduced to 15 per cent moisture :
Butt Logs.
Middle Logs.
Top Logs.
Av'g of
all Butt
Logs.
SDecific gravity
0.449 to 1.039
4,762 to 16,200
4,930 to 13,110
1,119 to 3,117
0.23 to 4.69
4,781 to 9,850
675 to 2,094
8,600 to 31,890
464 to 1,299
0.575 to 0.859
7,640 to 17,128
5,540 to 11,790
1,136 to 2,982
1.34 to 4.21
5,030 to 9,300
656 to 1,445
6,330 to 29,500
539 to 1,230
0.484 to 0.907
4,268 to 15,554
2,553 to 11,950
842 to 2,697
^-09 to 4. 65
4,587 to 9,100
584 to 1,766
4,170 to 23,280
484 to 1156
0.767
12,614
9,460
1,926
2.98
7,452
1,598
17,359
866
icgidvuy •••"gffL
Trans versestrength,- yyj
do do. atelast. limit.
Mod. of elast., thous. Ibs.
Relative elast. resilience,
inch-pounds per cub. in.
Crushing endwise, str.per
sq. in. -Ibs
Crushing across grain,
strength per sq. in., Ibs.
Tensile strength per sq. in.
Shearing strength (with
grain), mean per sq. in .
Some of the deductions from the tests were as follows :
1. With the exception of tensile strength a reduction of moisture is ac-
companied by an increase in strength, stiffness, and toughness.
2. Variation in strength goes generally hand-in-hand with specific gravity.
3. In the first 20 or 30 feet in height the values remain constant ; then
occurs a decrease of strength which amounts at 70 feet to 20 to 40 per cent
of that of the butt-log.
4. In shearing parallel with the grain and crushing across and parallel
with the grain, practically no difference was found.
5. Large beams appear 10 to 20 per cent weaker than small pieces.
6. Compression tests endwise seem to furnish the best average statement
of the value of wood, and if one test only can be made, this is the safest, as
was also recognized by Bauschinger.
7. Bled timber is in no respect inferior to unbled timber.
310
STRENGTH OP MATERIALS.
The figures for crushing across the grain represent the load required to
cause a compression of 15 per cent. The relative elastic resilience, in inch-
pounds per cubic inch of the material, is obtained by measuring the area
of the plotted-strain diagram of the transverse test from the origin to the
point in the curve at which the rate of deflection is 50 per cent greater than
the rate in the earlier part of the test where the diagram is a straight line.
This point is arbitrarily chosen since there is no definite *' elastic limit " in
timber as there is in iron. The ** strength at the elastic limit'1 is the
strength taken at this same point. Timber is not perfectly elastic for any
load if left on any great length of time.
The long-leaf pine is found in all the Southern coast states from North
Carolina to Texas. Prof. Johnson says it is probably the strongest timber
in large sizes to be had in the United States. In small selected specimens,
other species, as oak and hickory, may exceed it in strength and tough-
ness. The other Southern yellow pines, viz., the Cuban, short-leaf and
the loblolly pines are inferior to the long-leaf about in the ratios of their
specific gravities ; the long-leaf being the heaviest of all the pines. It
averages (kiln-dried) 48 pounds per cubic foot, the Cuban 47, the short-leaf
40, and the loblolly 34 pounds.
Strength of Spruce Timber.— The modulus of rupture of spruce
is given as follows by different authors : Hatfield, 9900 Ibs. per square inch ;
Rankine, 11,100 ; Laslett, 9045 ; Trautwine, 8100 ; Rodman, 6168. Traut-
wine advises for use to deduct one-third in the case of knotty and poor
timber.
Prof. Lanza, in 25 tests of large spruce beams, found a modulus of
rupture from 2995 to 5666 Ibs.; the average being 4613 Ibs. These were
average beams, ordered from dealers of good repute. Two beams of
selected stock, seasoned four years, gave 7562 and 8748 Ibs. The modulus
of elasticity ranged from 897,000 to 1,588,000, averaging 1,294,000.
Time tests show much smaller values for both modulus of rupture and
modulus of elasticity. A beam tested to 5800 Ibs. in a screw machine was
left over night, and the resistance was found next morning to have dropped
to about 3000, and it broke at 3500.
Prof. Lanza remarks that while it was necessary to use larger factors of
safety, when the moduli of rupture were determined from tests with smaller
pieces, it will be sufficient for most timber constructions, except in factories,
to use a factor of four. For breaking strains of beams, he states that it is
better engineering to determine as the safe load of a timber beam the load
that will not deflect it more than a certain fraction of its span, say about
1/300 to 1/400 of its length.
Properties of Timber.
(N. J. Steel & Iron Co.'s Book.)
Description.
Weight
per
cubic
foot, in
Ibs.
Tensile
Strength
per sq. inch,
in Ibs.
Crushing
Strength per
sq. inch,
in Ibs.
Relative
Strength
for Cross
Breaking.
White
Pine =100.
Shearing
Strength
with the
Grain, •
Ibs. per
sq. inch
Ash
43 to 55.8
43 to 53.4
50 to 56.8
11,000 to 17,207
11,500 to 18,000
10,300 to 11,400
4,400 to 9,363
5,800 to 9,363
5,600 to 6,000
130 to 180
100 to 144
55 to 63
130
96 to 123
96
88 to 95
150 to 210
132 to 227
122 to 220
130 to 177
155 to 189
100
98 to 170
86 to 110
458 to 700
Beech.
Cedar
Cherry
Chestnut
33
34 to 36.7
10,500
13,400 to 13,489
8,700
12.800 to 18,000
20,500 to 24,800
10,500 to 10,584
10,253 to 19,500
5,350 to 5,600
6,831 to 10,331
5,700
8,925
9,113 to 11,700
8,150
4,684 to 9,509
6,850
5,000 to 6,650
5, 400 to 9,500
5,050 to 7,850
7,500
Elm
Hemlock
44
49
45 to 54.5
70
30
28. 8 to 33
Maple
367 to 647
752 to 966
225 to 423
286 to 415
253 to 374
Oak, White
Oak, Live
Pine, White....
Pine, Yellow...
Spruce
10,000 to 12,000
12,600 to 19,200
10,000 to 19,500
9,286 to 16,000
Walnut, Black.
42
STRENGTH OF TIMBER.
311
The above table should be taken with caution. The range of variation in
the species is apt to be much greater than the figures indicate. See Johnson's
tests on long-leaf pine, and Lanza's on spruce, above. The weight of yellow
pine in the table is much less than that given by Johnson. (W. K.)
Compressive Strengths of American "Woods, when slowly
and carefully seasoned.— Approximate averages, deduced from many exper-
iments made with the U. S. Government testing-machine at Watertown,
Mass., by Mr. S. P. Sharpless, for the Census of 1880. Seasoned ivoods resist
crushing much better than green ones; in many cases, twice as well. Differ-
ent specimens of the same wood vary greatly. The strengths may readily
vary as much as one-third part more or less from the average.
End-
wise,*
Ibs. per
sq. in.
Side-
wise,t
Ibs. per
sq. in.
End-
wise,*
Ibs. per
sq. in.
Side-
wise^
Ibs. per
sq. in.
.01
.1
.01
.1
Ash, red and white
Aspen
6800
4400
7000
8000
4400
5400
6000
6000
4400
5000
8000
5300
5200
6000
6800
7700
5300
8000
10000
5000
9800
7000
9000
5300
1300
800
1100
1300
600
700
1300
700
500
700
1700
900
1300
500
1300
1300
600
2000
1600
500
1900
1600
1700
1400
3000
1400
1900
2600
1400
1600
2600
1000
900
1300
2600
1600
2600
1200
2600
2600
1100
4000
13000
900
4400
2600
5300
2600
Maple :
sugar and black.,
white and red.. ..
Oak :
white, post (or
iron), swamp
white, red, and
black
8000
6800
7000
6000
7500
6500
5400
6300
5000
8500
5000
5000
5700
4500
6000
8000
5400
4400
1900
1300
1600
1700
1600
1300
5600
600
1000
1300
600
1300
700
600
1300
1300
700
700
4300
2900
4000
4200
4500
3000
1200
1400
2000
2600
1100
2100
1300
1200
2600
2600
1600
1400
Beech
Birch ..
Butternut . .
Buttonwood
(sycamore)
Cedar, red
scrub and basket,
chestnut and Jive
pin....
Cedar, white (arbor-
vitae)
Catalpa (Ind.bean)
Cherry, wild
Pine :
white
Chestnut
red or Norway.. . .
pitch and Jersey
scrub
Coffee-tree, Ky....
Cypress, bald
Elm, Am. or white
" red .
Georgia .
Poplar
Hemlock
Hickory
Sassafras
Spruce, black..
" white
Sycamore (button-
wood)
Lignum-vitce
Linden, American.
Locust:
black and yellow.
Walnut :
black
Mahogany
white (butternut).
Willow
Maple:
broad-leafed, Ore.
* Specimens 1.57 ins. square X 12.6 ins. long.
t Specimens 1.57 ins. square X 6.3 ins. long. Pressure applied at mid-length
by a punch covering one-fourth of the length. The first column gives the
loads producing an indentation of .01 inch, the second those producing an
indentation of .1 inch. (See also page 306).
Expansion of Timber Due to the Absorption of Water,
(De Volson Wood, A. S. M. E., vol. x.)
Pieces 36 X 5 in., of pine, oak, and chestnut, were dried thoroughly, and
then immersed in water for 37 days.
The mean per cent of elongation and lateral expansion were:
Pine. Oak. Chestnut.
Elongation, per cent 0.065 0.085 0.165
Lateral expansion, percent — 2.6 3.5 3.65
Expansion of "Wood by Heat.— Traut wine gives for the expansion
of ^hite pine for 1 degree Fahr. 1 part in 440,530, or for 180 degrees 1 part in
2447. or about one-third of the expansion of iron.
312
STRENGTH OF MATERIALS.
Shearing Strength of American Woods, adapted for
Pins or Treenails.
J. C. Trautwine (Jour. Franklin Inst.). (Shearing across tne grain.)
per sq. in.
Ash -. .. 6280
Beech 5223
Birch 5595
Cedar (white) 1 372
" 1519
Cedar (Central American) 3410
Cherry 2945
Chestnut 1536
Dogwood 6510
Ebony 7750
Gum 5890
Hemlock 2750
Locust 7176
per sq. in.
Hickory 6045
" 7285
Maple 6355
Oak 4425
Oak (live) 8480
Pine (white) 2480
Pine (Northern yellow 4340
Pine (Southern yellow) 5735
Pine (very resinous yellow). . . . , 5053
Poplar 4418
Spruce 3255
Walnut (black) 4728
Walnut (common) 2830
THE STRENGTH OF BRICK, STONE, ETC.
A great advance has recently been made in the manufacture of brick, in
the direction of increasing their strength. Chas. P. Chase, in Engineering
Neivs, says: " Taking the tests as given in standard engineering books eight
or ten years ago, \ye find in Trautwine the strength of brick given as 500 to
4200 Ibs. per sq. in. Now, taking recent tests in experiments made at
Watertown Arsenal, the strength ran from 5000 to 22,000 Ibs. per sq. in. In
the tests on Illinois paving-brick, by Prof, I. O. Baker, we find an average
strength in hard paving brick of over 5000 Ibs. per square inch. The average
crushing strength of ten varieties of paving-brick much used in the West, I
find to be 7150 Ibs. to the square inch."
A recent test of brick made by the dry-clay process at Watertown Arsenal,
according to Paving, showed an average compressive strength of 3972 Ibs.
per sq. in. In one instance it reached 4973 Ibs. per sq. in. A test was made
at the same place on a "fancy pressed brick." The first crack developed
at a pressure of 305,000 Ibs., and the brick crushed at 364,300 Ibs., or 11,130
Ibs. per sq. in. This indicates almost as great compressive strength as
granite paving-blocks, which is from 12,000 to 20,000 Ibs. per sq. in.
The following notes on bricks are from Trautwine's Engivleer's Pocket'
book :
Strength of Brick.— 40 to 300 tons per sq. ft., 622 to 4668 Ibs. per sq. in,
A soft brick will crush under 450 to 600 Ibs. per sq. in., or 30 to 40 tons per
square foot, but a first-rate machine-pressed brick will stand 200 to 400 tons
per sq. ft. (3112 to 6224 Ibs. per sq. in.).
Weight of Bricks. — Per cubic foot, best pressed brick, 150 Ibs.; good
pressed brick, 131 Ibs.; common hard brick, 125 Ibs.; good common brick,
118 Ibs. ; soft inferior brick, 100 Ibs.
Absorption of Water.— A brick will in a few minutes absorb ^ to
% Ib. of water, the last being 1/7 of the weight of a hand-moulded one, or ^
of its bulk.
Tests of Bricks, full size, on flat side. (Tests made at Water-
town Arsenal in 1883.)— The bricks were tested between flat steel buttresses.
Compressed surfaces (the largest surface) ground approximately flat. The
bricks were all about 2 to 2.1 inches thick, 7.5 to 8.1 inches long, and 3.5 to
3.76 inches wide. Crushing strength per square inch: One lot ranged from
11,056 to 16,734 Ibs. ; a second, 12,995 to 22,351 ; a third, 10,390 to 12,709. Other
tests gave results from 5960 to 10.250 Ibs. per sq. in.
Crushing Strength of Masonry Materials. (From Howe's
41 Retaining. Walls.")
tons per sq. ft. tons per sq. ft.
Brick, best pressed. . 40 to 300 Limestones and marbles. 250 to 1000
Chalk 20to 30 Sandstone 150 to 550
Granite 300tol200 Soapstone 400 to 800
Strength of Granite.— The crushing strength of granite is commonly
rated at 12,000 to 15,000 Ibs. per sq. in. when tested in two-inch cubes, and
only the hardest and toughest of the commonly used varieties reach a
strength above 20,000 Ibs. Samples of granite from a quarry on the Con-
STRENGTH OF LIME AND CEMENT MORTAR. 313
necticut River, tested at the Watertown Arsenal, have shown a strength of
35,965 Jbs. per sq. in. (Engineering News, Jan. 12, 1893).
Strength of Ayoiidale, Pa., Limestone— (Engineering News,
Feb. 9, 1893).— Crushing strength of 2-in. cubes: light stone 12,112, gray stone
18,040, Ibs. per sq. in. ,
Transverse test of lintels, tool-dressed, 42 in. between knife-edge bear-
ings, load with knife-edge brought upon the middle between bearings:
Gray stone, section 6 in. wide X 10 in. high, broke under a load of 20,950 Ibs.
Modulus of rupture 2,200 4
Light stone, section 8J4 in. wide X 10 in. high, broke under 14,720 *'
Modulus of rupture 1,170 "
Absorption.— Gray stone 051 of \%
Light stone , .052 of \%
Transverse Strength of Flagging.
(N. J. Steel & Iron Co.'s Book.)
EXPERIMENTS MADE BY R. G. HATFIELD AND OTHERS.
b r= width of the stone in inches; d = its thickness in inches; I = distance
between bearings in inches.
The breaking loads in tons of 2000 Ibs., for a weight placed at the centre
of the space, will be as follows:
bd?
I
X
bd*
I
X
Dorchester freestone .264
Aubigny freestone 216
Caen freestone 144
Glass 1.000
Slate 1.2 to 2.7
Bluestone flagging 744
Quincy granite 624
Little Falls freestone 576
Belleville, N. J., freestone 480
Granite (another quarry) 432
Connecticut freestone 312
Thus a block of Quincy granite 80 inches wide and 6 inches thick, resting
on beams 36 inches in the clear, would be broken by a load resting midway
80 V" S6
between the beams = • :: X .624 = 49.92 tons,
oo
STRENGTH OF LIM13 AND CEMENT MORTAR.
(Engineering, October 2, 1891.)
Tests made at the University of Illinois on the effects of adding cement to
lime mortar. In all the tests a good quality of ordinary fat lime was used,
slaked for two days in an earthenware jar, adding two parts by weight of
water to one of lime, the loss by evaporation being made up oy fresh addi-
tions of water. The cements used were a German Portland, Black Diamond
(Louisville), and Rcsendale. As regards fineness of grinding, 85 per cent of
the Portland passed through a No. 100 sieve, as did 72 per cent of the Rosen-
dale. A fairly sharp sand, thoroughly washed and dried, passing through »
No. 18 sieve and caught on a No. 30, was used. The mortar in all cases con-
sisted of two volumes of sand to one of lime paste. The following results
were obtained on adding various percentages of cement to the mortar:
Tensile Strength, pounds per square Inch.
Age -j
4
Days.
7
Days.
14
Days.
21
Days.
28
Days.
50
Days.
84
DaySo
Lime mortar
4
8
10
13
18
21
26
20 per cent Rosendale.
5
9^
12
17
17
18
20 " " Portland..
5
gi^
14
20
25
24
26
30 " " Rosendale
7
11
13
18fc
21
22)4
23
30 " Portland..
8
16
18
22
25
28
27
40 '* Rosendale
10
12
16^
21^
22^
24
36
4e " Portland..
27
39
38
43
47
59
57
60 " Rosendale
9
13
20
16
22
22^
23
60 " Portland..
45
58
55
68
67
102
78
80 " Rosendale
12'
18J*
22^ .
27
29
31^
33
80 " Portland..
87
91
103
124
94
210
145
100 " Rosendale
18
33
26
31
34
46
48
100 " Portland..
90
120
146
152
181
205
202
314 STRENGTH OF MATERIALS.
RIODULI OF ELASTICITY OF VARIOUS MATERIALS*
The modulus of elasticity determined from a tensile test of a bar of any
material is the quotient obtained by dividing the tensile stress in pounds per
square inch at any point of the test by the elongation per inch of length
produced by that stress ; or if P = pounds of stress applied, K = the sec-
tional area, I = length of the portion of the bar in which the measure-
ment is made, and A = the elongation in that length, the modulus of
n \ pi
elasticity E = •== -*- r = -=? . The modulus is generally measured within the
JL L A.A
elastic limit only, in materials that have a well-defined elastic limit, such as
iron and steel, and when not otherwise stated the modulus is understood to
be the modulus within the elastic limit. Within this limit, for such materials
the modulus is practically constant for any given bar, the elongation being
directly proportional to the stress. In other materials, such as cast iron,
which have no well-defined elastic limit, the elongations from the beginning
of a test increase in a greater ratio than the stresses, and the modulus is
therefore at its maximum near the beginning of the test, and continually
decreases. The moduli of elasticity of various materials have already been
given above in treating of these materials, but the following table gives
some additional values selected from different sources :
Brass, cast 9,170,000
" wire 14,230,000
Copper 15,000,000 to 18,000,000
Lead 1,000,000
Tin, cast 4,600,000
Iron, cast 12.000,000 to 27,000,000 (?)
Iron, wrought. 88,000,000 to 29,000,000 (?)
Steel 28,000,000 to 32,000,000 (see below)
Marble 25,000,000
Slate 14,500,000
Glass 8,000,000
Ash 1,600,000
Beech 1,300,000
Birch 1,250,000 to 1,500,000
Fir.... 869,000 to 2,191,000
Oak 974,000 to 2,283,000
Teak.. 2,414,000
Walnut 306,000
Pine, long-leaf (butt-logs)... 1,119,000 to 3,117,000 Avge. 1,926,000
The maximum figures given by many writers for iron and steel, viz.,
40,009,000 and 42,000,000, are undoubtedly erroneous. The modulus of elas-
ticity of steel (within the elastic limit) is remarkably constant, notwithstand-
ing great variations in chemical analysis, temper, etc. It rarely is found
below 29,000,000 or above 31,000,000. It is generally taken at 30,000,000 in
engineering calculations. Prof. J. B. Johnson, in his report on Long-leaf
Pine, 1893, says : ** The modulus of elasticity is the most constant and reliable
property of all engineering materials. The wide range of value of the
modulus of elasticity of the various metals found in public records must be
explained by erroneous methods of testing."
In a. tensile test of cast iron by the author (Van Nostrand's Science Series,
No. 41, page 45), in which the ultimate strength was 28,285 Ibs. per sq. in.,
the measurements of elongation were made to .0001 inch, and the modulus
of elasticity was found to decrease from the beginning of the test, as
follows : At 1000 Ibs. per sq. in., 25,000,000 ; at 2000 Ibs., 16,666,000 ; at 4000
Ibs., 15,384,000 ; at 6000 Ibs., 13,636,000 ; at 8000 Ibs., 12,500,000 ; at 12,000 Ibs.,
11,250,000 : at 15,000 Ibs., 10,000,000; at 20,000 Ibs., 8,000,000 ; at 33,000 lbs.s
6.140,000.
FACTORS OF SAFETY.
A factor of safety is the ratio in which the load that is just sufficient to
overcome instantly the strength of a piece of material is greater than the
greatest safe ordinary working load. (Rankine.)
Rankine gives the following " examples of the values of those factors
which occur in machines ":
T^ A T A Live Load, Live Load,
Dead Load. Greatest.' Mean.
Iron and steel 3 6 from 6 to 40
Timber 4 to 5 8 to 10
Masonry .•< 4 »••«•
tfACTOKS OF SAFETY. 315
The great factor of safety, 40, is for shafts in millwork which transmit
very variable efforts.
Unwin gives the following " factors of safety which have been adopted in
certain cases for different materials." They " include an allowance for
ordinary contingencies."
n Yi , Live Load. s
[ In Temporary In Permanent In Structures
•Ll0au< Structures. Structures, sub j. to Shocks.
Wrought iron and steel. 3 4 4 to 5 10
Cast iron 34 5 10
Timber 4 10.
Brickwork .... 6 ....
Masonry 20 .... 20 to 30
Unwin says says that " these numbers fairly represent practice based on
experience in many actual cases, but they are not very trustworthy."
Prof. Wood in his "Resistance of Materials" says: "In regard to the
margin that should be left for safety, much depends upon the character of
the loading. If the load is simply a dead weight, the margin may be com-
paratively small; but if the structure is to be subjected to percussive forces
or shocks, the margin should be comparatively large on account of the
indeterminate effect produced by the force. In machines which are sub-
jected to a constant jar while in use, it is very difficult to determine the
proper margin which is consistent with economy and safety. Indeed, in
such cases, economy as well as safety generally consists in making them
excessively strong, as a single breakage may cost much more than the extra
material necessary to fully insure safety."
For discussion of the resistance of materials to repeated stresses and
shocks, see pages 238 to 240.
Instead of using factors of safety it is becoming customary in designing
to fix a certain number of pounds per square inch as the maximum stress
which will be allowed on a piece. Thus, in designing a boiler, instead of
naming a factor of safety of 6 for the plates and 10 for the stay-bolts, the
ultimate tensile strength of the steel being from 50,000 to 60,000 Ibs. per sq. in.,
an allowable working stress of 10,000 Ibs. per sq. in. on the plates and 6000
Ibs. per sq. in. on the stay-bolts may be specified instead. So also in
Merriman's formula for columns (see page 260) the dimensions of a column
are calculated after assuming a maximum allowable compressive stress per
square inch on the concave side of the column.
The factors for masonry under dead load as given by Rankine and by Tin win,
viz. , 4 and 20, show a remarkable difference, which may possibly be explained
as follows : If the actual crushing strength of a pier of masonry is known
from direct experiment, then a factor of safety of 4 is sufficient for a pier of
the same size and quality under a steady load; but if the crushing strength
is merely assumed from figures given by the authorities (such as the crush-
ing strength of pressed brick, quoted above from Howe's Retaining Walls, 40
to 300 tons per square foot, average 170 tons), then a factor of safety of 20
may be none too great. In this case the factor of safety is really a " factor
of ignorance."
The selection of the proper factor of safety or the proper maximum unit
stress for any given case is a matter to be largely determined by the judg-
ment of the engineer and by experience. No definite rules can be given.
The customary or advisable factors in many particular cases will be found
where these cases are considered throughout this book. In general the
following circumstances are to be taken into account in the selection of
a factor :
1. When the ultimate strength of the material is known within narrow
limits, as in the case of structural steel when tests of samples have been
made, when the load is entirely a steady one of a known amount, and there
is no reason to fear the deterioration of the metal by corrosion, the lowest
factor that should be adopted is 3.
2. When the circumstances of 1 are modified by a portion of the load being
variable, as in floors of warehouses, the factor should be not less than 4.
3. When the whole load, or nearly the whole, is apt to be alternately x>ut
on and taken off, as in suspension rods of floors of bridges, the factor should
be 5 or 6.
4. When the stresses are reversed in direction from tension to compres-
sion, as in some bridge diagonals and parts of machines, the factor should
be not less than 6.
316 STRENGTH OF MATERIALS.
5. When the piece is subjected to repeated shocks, the factor should be
not less than 10.
6. When the piece is subject to deterioration from corrosion the section
should be sufficiently increased to allow for a definite amount of corrosion
before the piece be so far weakened by it as to require removal.
7. When the strength of the material, or the amount of the load, or both
are uncertain, the factor should be increased by an allowance sufficient tc
cover the amount of the uncertainty.
8. When the strains are of a complex character and of uncertain amount,
such as those in the crank-shaft of a reversing engine, a very high factor is
necessary, possibly even as high as 40, the figure given by Rankine for shafts
in mill work.
THE MECHANICAL PROPERTIES OF CORK.
Cork possesses qualities which distinguish it from all other solid or liquid
bodies, namely, its power of altering its volume in a very marked degree in
consequence of change of pressure. It consists, practically, of an aggrega-
tion of minute air-vessels, having thin, water-tight, and very strong walls,
and hence, if compressed, the resistance to compression rises in a manner
more like the resistance of gases than the resistance of an elastic solid such
as a spring. In a spring the pressure increases in proportion to the dis*
tance to which the spring is compressed, but with gases the pressure in-
creases in a much more rapid manner; that is, inversely as the volume
which the gas is made to occupy. But from the permeability of cork to
air, it is evident that, if subjected to pressure in one direction only, it will
gradually part with its occluded air by effusion, that is, by its passage
through the porous walls of the cells in which it is contained. The gaseous
part of cork constitutes 53$ of its bulk. Its elasticity has not only a very
considerable range, but it is very persistent. Thus in the better kind of corks
used in bottling the corks expand the instant they escape from the bottles.
This expansion may amount to an increase of volume of 75$, even after the
corks have been kept in a state of compression in the bottles for ten years.
If the cork be steeped in hot water, the volume continues to increase till
it attains nearly three times that which it occupied in the neck of the bottle.
When cork is subjected to pressure a certain amount of permanent defor-
mation or "permanent set" takes place very quickly. This property is
common to all solid elastic substances when strained beyond their elastic
limits, but with cork the limits are comparatively low. Besides the perma-
nent set, there is a certain amount of sluggish elasticity— that is, cork on,
being released from pressure springs back a certain amount at once, but
the complete recovery takes an appreciable time.
Cork which had been compressed and released in water many thousand
times had not changed its molecular structure in the least, and had contin-
ued perfectly serviceable. Cork which has been kept under a pressure of
three atmospheres for many weeks appears to have shrunk to from 80$ to
85$ of its original volume.— Few Nostrand's Eng'g Mag, 1886, xxxv. 307.
TESTS OF VULCANIZED INDIA-RUBBER.
Lieutenant L. Vladomiroff , a Russian naval officer, has recently carried
out a series of tests at the St. Petersburg Technical Institute with a view to
establishing rules for estimating the quality of vulcanized india-rubber.
The following, in brief, are the conclusions arrived at, recourse being had
to physical properties, since chemical analysis did not give any reliable re-
sult: 1. India-rubber should not give the least sign of superficial cracking
when bent to an angle of 180 degrees after five hours of exposure in a closed
air-bath to a temperature of 125° C. The test-pieces should be 2.4 inches
thick. 2. Rubber that does not contain more than half its weight of metal-
lic oxides should stretch to five times its length without breaking. 3. Rub-
ber free from all foreign matter, except the sulphur used in vulcanizing it,
should stretch to at least seven times its length without rupture. 4. The
extension measured immediately after rupture should not exceed 12$ of the
original length, with given dimensions. 5. Suppleness may be determined
by measuring the percentage of ash formed in incineration. This may form
the basis for deciding between different grades of rubber for certain pur-
Eoses. 6. Vulcanized rubber should not harden under cold. These rules
ave been adopted for the Russian navy.— Iron Age, June 15, 1893.
XYI.OL.ITH, OR WOODSTONE
is a material invented in 1883, but only lately introduced to the trade by
Otto Serrig & Co., of Pottschappel, near Dresden. It is made of magnesia
ALUMINUM — ITS PROPERTIES AND USES. 31?
cement, or calcined magnesite, mixed with sawdust and saturated with a
solution of chloride of calcium. This pasty mass is spread out into sheets
and submitted to a pressure of about 1000 Ibs. to the square inch, and then
simply dried in the air. Specific gravity 1.553. The fractured surface shows
a uniform close grain of a yellow color. It has a tensional resistance when
dry of 100 Ibs. per square inch, and when wet about 66 Ibs. When immersed
in water for 12 hours ifc takes up 2.1$ of its weight, and 3.8# when immersed
216 hours.
When treated for several days with hydrochloric acid it loses 2.3$ in
weight, and shows no loss of weight under boiling in water, brine, soda-lye,
and solution of sulphates of iron, of copper, and of ammonium. In hardness
the material stands between feldspar and quartz, and as a non-conductor of
heat it ranks between asbestos and cork.
It stands fire well, and at a red heat it is rendered brittle and crumbles at
the edges, but retains its general form and cohesion. This xylolith is sup-
plied in sheets from J4 in. to 1^ in. thick, and up to one metre square. It
is extensively used in Germany for floors in railway stations, hospitals, etc.,
and for decks of vessels. It can be sawed, bored, and shaped with ordinary
woodworking tools. Putty in the joints and a good coat of paint make it
entirely water-proof. It is sold in Germany for flooring at about 7 cents per
square foot, and the cost of laying adds about 4. cents more.—Eng'lg JVetus,
July 28, 1892, and July 27, 1893.
ALumiNumr— ITS PROPERTIES AN» USES.
(By Alfred £. Hunt, Pres't of the Pittsburgh Reduction Co.)
The specific gravity of pure aluminum in a cast state is 2.58 ; in rolled
bars of large section it is 2 6 ; in very thin sheets subjected to high com-
pression under chilled rolls, it is as much as 2.7. Taking the weight of a
given bulk of cast aluminum as 1, wrought iron is 2.90 times heavier ; struc-
tural steel, 2.95 times ; copper, 3.60 ; ordinary high brass, 3.45. Most wood
suitable for use in structures has about one third the weight of aluminum,
which weighs 0.092 Ib. to the cubic inch.
Pure aluminum is practically not acted upon by boiling water or steam.
Carbonic oxide or hydrogen sulphide does not act upon it at any tempera-
ture under 600° F. It is not acted upon by most organic secretions.
Hydrochloric acid is the best solvent for aluminum, and strong solutions
of caustic alkalies readily dissolve it. Ammonia has a slight solvent action,
and concentrated sulphuric acid dissolves aluminum upon heating, with
evolution of sulphurous acid gas. Dilute sulphuric acid acts but slowly on
the metal, though the presence of any chlorides in the solution allow rapid
decomposition. Nitric acid, either concentrated or dilute, has very little
action upon the metal, and sulphur has no action unless the metal is at a red
heat. Sea-water has very little effect on aluminum. Strips of the metal
placed on the sides of a wooden ship corroded less than 1/1000 inch after six
months' exposure to sea- water, corroding less than copper sheets similarly
placed.
In malleability pure aluminum is only exceeded by gold and silver. In
ductility it stands seventh in the series, being exceeded by gold, silver,
platinum, iron, very soft steel, and copper. Sheets of aluminum have been
rolled down to a thickness of 0.0005 inch, and beaten into leaf nearly as
thin as gold leaf. The metal is most malleable at a temperature of between
400° and 600° F., and at this temperature it can be drawn down between
rolls with nearly as much draught upon it as with heated steel. It has also
been drawn down into the very finest wire. By the Mannesmann process
aluminum tubes have been made in Germany.
Aluminum stands very high in the series as an electro-positive metal, anc}
contact with other metals should be avoided, as it would establish a galvanic
couple.
The electrical conductivity of aluminum is only surpassed by pure copper,
silver, and gold. With silver taken at 100 the electrical conductivity of
aluminum is 54.20 ; that of gold on the same scale is 78; zinc is 29.90; iron is
only 16, and platinum 10.60. Pure aluminum has no polarity, and the
metal in the market is absolutely non-magnetic.
Sound castings can be made of aluminum in either dry or " green " sand
moulds, or in metal "chills." It must not be heated much beyond its
melting-point, and must be poured with care, owing to the ready absorption
of occluded gases and air. The shrinkage in cooling is 17/64 inch per foot,
or a little more than ordinary brass. It should be melted in plumbago
crucibles, and the metal becomes molten at a temperature of 1120° F. ac-
cording to Professor Roberts- Austen, or at 1300° F. according to Richards.
338 STRENGTH OF MATERIALS.
The coefficient of linear expansion, as tested on %-inch round aluminum
rods, is 0.00002295 per degree centigrade between the freezing and boiling
point of water. The mean specific heat of aluminum is higher than that of
any other metal, excepting only magnesium and the alkali metals. From
zero to the melting-point it is 0.2185; water being taken as 1, and the latent
heat of fusion at 28.5 heat units. The coefficient of thermal conductivity of
unannealed aluminum is 37.96; of annealed aluminum, 38.37. As a conductor
of heat aluminum ranks fourth, being exceeded only by silver, copper, and
gold.
Aluminum, under tension, and section for section, is about as strong as
cast iron. The tensile strength of aluminum is increased by cold rolling or
cold forging, and there are alloys which add considerably to the tensile
strength without increasing the specific gravity to over 3 or 3.25.
The strength of commercial aluminum is given in the following table as
the result of many tests :
Elastic Limit Ultimate Strength Percentage
per sq. in. in per sq. in. in of Reduct'n
Form. Tension, Tension, of Area in
Ibs. Ibs. Tension.
Castings 6,500 15,000 15
Sheet 12,000 24,000 35
Wire 16,000-30,000 30,000-65,000 60
Bars.. 14,000 28,000 40
The elastic limit per square inch under compression in cylinders, with
length twice the diameter, is 3500. The ultimate strength per square inch
under compression in cylinders of same form is 12,000. The modulus of
elasticity of cast aluminum is about 11,000,000. It is rather an open metal in
its texture, and for cylinders to stand pressiire an increase in thickness must
be given to allow for this porosity. Its maximum shearing stress in castings
is about 12,000, and in f orgings about 16,000, or about that of pure copper.
Pure aluminum is too soft and lacking in tensile strength and rigidity for
many purposes. Valuable alloys are now being made which seem to give
great promise for the future. They are alloys containing from 2?* to 1% or 8$
of copper, manganese, iron, and nickel. As nickel is one of the principal
constituents, these alloys have the trade name of " Nickel-aluminum.1'
Plates and bars of this nickel alloy have a tensile strength of from 40,000 to
50,000 pounds per square inch, an elastic limit of 55$ to 60$ of the ultimate ten-
sile strength, an elongation of 20$ in 2 inches, and a reduction of area of 25$.
This metal is especially capable of withstanding the punishment and
distortion to which structural material is ordinarily subjected. Nickel-
aluminum alloys have as much resilience and spring as the very hardest of
hard-drawn brass.
Their specific gravity is about 2.80 to 2.85, where pure aluminum has a
specific gravity of 2.72.
In castings, more of the hardening elements are necessary in order to give
the maximum stiffness and rigidity, together with the strength and ductility
of the metal; the favorite alloy material being zinc, iron, manganese, and
copper. Tin added to the alloy reduces the shrinkage, and alloys of alumi-
num and tin can be made which have less shrinkage than cast iron.
The tensile strength of hardened aluminum-alloy castings is from 20,000
to 25,000 pounds per square inch.
Alloys of aluminum and copper form two series, both valuable. The
first is aluminum-bronze, containing from 5$ to 11^$ of aluminum; and the
second is copper-hardened aluminum, containing from 2$ to 15$ of copper.
Aluminum-bronze is a very dense, fine-grained, and strong alloy, having good
ductility as compared with tensile strength. The 10$ bronze in forged bars
will give 100,000 Ibs. tensile strength per square inch, with 60,000 Ibs. elastic
limit per square inch, and 10$ elongation in 8 inches. The 5$ to 7^1$ bronze
has a specific gravity of 8 to 8.30, as compared with 7.50 for the 10# to 11*4$
bronze, a tensile strength of 70,000 to 80,000 Ibs., an elastic limit of 40,000
Ibs. per square inch, and an elongation of 30$ in 8 inches.
Aluminum is used by steel manufacturers to prevent the retention of the
occluded gases in the steel, and thereby produce a solid ingot. The propor-
tions of the dose range from ^ Ib. to several pounds of aluminum per ton of
steel. Aluminum is also used in giving extra fluidity to steel used in castings,
making them sharper and sounder. Added to cast iron, aluminum causes
the iron to be softer, free from shrinkage, and lessens the tendency to "chill."
With the exception of lead and mercury, aluminum unites with all metals,
ALLOYS.
319
though It unites with antimony with great difficulty. A small percentage
of silver whitens and hardens the metal, and gives it added strength; and
this alloy is especially applicable to the manufacture of fine instruments
and apparatus. The following alloys have been found recently to be useful
in the arts: Nickel-aluminum, composed of 20 parts nickel to 80 of aluminum;
rosine, made of 40 parts nickel, 10 parts silver, 30 parts aluminum, and 20
parts tin, for jewellers1 work; mettaline, made of 35 parts cobalt, 25 parts
aluminum, 10 parts iron, and 30 parts copper. The aluminum-bourbounz
metal, shown at the Paris Exposition of 1889, has a specific gravity of 2.9 to
2.96, and can be cast in very solid shapes, as it has very little shrinkage.
From analysis the following composition is deduced: Aluminum, 85.74$; tin,
12.94#; silicon, 1.32$; iron, none.
The metal can be readily electrically welded, but soldering is still not sat-
isfactory. The high heat conductivity of the aluminum withdraws the heat
of the molten solder so rapidly that it "freezes" before it can flow suffi-
ciently. A German solder said to give good results is made of 80# tin to 20#
zinc, using a flux composed of 80 parts stearic acid, 10 parts chloride of
zinc, and 10 parts of chloride of tin. Pure tin, fusing at 250° C., has also
been used as a solder. The use of chloride of silver as a flux has been
patented, and used with ordinary soft solder has given some success. A
pure nickel soldering-bit should be used, as it does not discolor aluminum
as copper bits do.
ALLOYS.
ALLOYS OF COPPER AND TIN.
(Extract from Report of U. S. Test Board.*)
1
I
1
la
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
2'2
23
24
25
26
Mean Com-
position by
Analysis.
Tensile Strength,
Ibs. per sq. in.
Elastic Limit,
Ibs. per sq. in.
Elongation,
per cent in 5
inches.
Transverse Test,
Modulus of
Rupture.
Deflection, 1" sq.
Bar 22 in. long,
inches.
Crushing
Strength,
Ibs. per sq. in.
Torsion
Tests.
Maximum
Tor. Mom-
ent, ft.-lbs.
Angle of
Torsion,
degrees.
Orp-
per.
Tin.
100.
100.
97.89
96.06
94.11
92.11
90.27
88.41
87.15
82.70
80.95
77.56
76.63
72.89
69.84
68.58
67.87
65.34
56.70
44.52
34.22
23.35
15.08
11.49
8.57
3.72
0.
27,800
12,760
24,580
32,000
14,000
11,000
10,000
16,000
6.47
0.47
13.33
14.29
29,848
21,251
33,232
38,659
43,731
49,400
60,403
34,531
67,930
56,715
29,926
32.210
9,512
12,076
9,152
9,477
4,776
2,126
4,776
5,384
12,408
9,063
10,706
6,305
6,925
3,740
bent.
2.31
bent,
tt
4.00
0.63
0.49
0.16
0.19
0.05
0.06
0.04
0.05
0.02
0.02
0.03
0.04
0.27
0.86
5.85
bent.
42,000
39,000
34,000
42,048
143
65
150
157
153
40
317
247
1.90
3.76
5.43
7.80
9.58
11.59
12.73
17.34
18.84
22.25
23.24
26.85
29.88
31.26
32.10
34.47
43.17
55.28
65.80
76.29
84.62
88.47
91.39
96.31
100.
28,540
26,860
19,000
15,750
5.53
3.66
42,000
38,000
160
175
126
114
29,430
"32,986
20,000
3.33
"6! 04*'
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
53,000
" 78^666
182
"i9o"
100
""16"
22,010
22,010
114,000
122
3.4
5,585
5,585
147,000
18
1.5
2,201
1,455
3,010
3,371
6,775
2,201
1,455
3,010
3,371
6,775
84,700
16
1
35,800
19,600
23
17
1
2
6,500
10,100
9,800
9,800
6,400
23
23
23
23
12 J
25
62
132
220
557
6,380
6,450
4,780
3,505
3,500
3,500
2,750
4.10
6.87
12.32
35.51
* The tests of the alloys of copper and tin and of copper and zinc, the re-
sults of which are published in the Report of the U. S. Board appointed to
test Iron, Steel, and other Metals, Vols. T and II, 1879 and 1881, were made
by the author under direction of pfof. R. H. Thurston, chairman of the
Committee on Alloys. See preface to the report of the Committee, in Vol. J.
320 ALLOYS.
Nos. la and 2 were full of biow-holes.
Tests Nos. 1 and la show the variation in cast copper due to varying coiv
ditions of casting. In the crushing tests Nos. 12 to 20, inclusive, crushed and
broke under the strain, but all the others bulged and flattened out. In these
cases the crushing strength is taken to be that which caused a decrease of
10$ in the length. The test-pieces were 2 in. long and % in. diameter. The
torsional tests were made in Thurston's torsion-machine, on pieces % in.
diameter and 1 in. long between heads.
Specific Gravity of tlie Copper-tin Alloys.— The specific
gravity of copper, as found in these tests, is 8.874 (tested in turnings from
the ingot, and reduced to 39.1° F.). The alloy of maximum sp. gr. 8.956
contained 62.42 copper, 37.48 tin, and all the alloys containing less than 37$
tin varied irregularly in sp. gr. between 8.65 and 8.98, the density depending
not on the composition, but on the porosity of the casting. It is probable
that the actual sp. gr. of all these alloys containing less than 37$ tin is about
8.95, and any smaller figure indicates porosity in the specimen.
From 37$ to 100$ tin, the sp. gr. decreases regularly from the maximum of
8.956 to that of pure tin, 7.293.
Note on the Strength of the Copper-tin Alloys.
The bars containing from 2$ to 24$ tin, inclusive, have considerable
strength, and all the rest are practically worthless for purposes in which
strength is required. The dividing line between the strong and brittle alloys
is precisely that at which the color changes from golden yellow to silver-
white, viz., at a composition containing between 24$ and 30$ of tin. .
It appears that the tensile and compressive strengths of these alloys are
in no way related to each other, that the torsional strength is closely pro-
portional to the tensile strength, and that the transverse strength may de-
pend in some degree upon the compressive strength, but it is much more
nearly related to the tensile strength. The modulus of rupture, as obtained
by the transverse tests, is, in general, a figure between those of tensile and
compressive strengths per square inch, but there are a few exceptions in
which it is larger than either.
The strengths of the alloys at the copper end of the series increase rapidlj
with the addition of tin till about 4$ of tin is reached. The transverse
strength continues regularly to increase to the maximum, till the alloy con-
taining about 17^$ of tin is reached, while the tensile and torsional
strengths also increase, but irregularly, to the same point. This irregularity
is probably due to porosity of the metal, and might possibly be removed by
any means which would make the castings more compact. The maximum
is reached at the alloy containing 82.70 copper, 17.34 tin, the transverse
strength, however, being very much greater at this point than the tensile
or torsional strength. From the point of maximum strength the figure*
drop rapidly to the alloys containing about 27.5$ of tin, and then more slowly
to 37.5$, at which point the minimum (or nearly the minimum) strength, by
all three methods of test, is reached. The alloys of minimum strength are
found from 37.5$ tin to 52.5$ tin. The absolute minimum is probably about
45$ of tin.
From 52.5$ of tin to about 77.5$ tin there is a rather slow and irregular in-
crease in strength. From 77.5$ tin to the end of the series, or all tin, the
strengths slowly and somewhat irregularly decrease.
The results of these tests do not seem to corroborate the theory given by
some writers, that peculiar properties are possessed by the alloys which
are compounded of simple multiples of their atomic weights or chemical
equivalents, and that these properties are lost as the compositions vary
more or less from this definite constitution. It does appear that a certain
percentage composition gives a maximum strength and another certain
percentage a minimum, but neither of these compositions is represented by
simple multiples of the atomic weights.
There appears to be a regular law of decrease from the maximum to the
minimum strength which does not seem to have any relation to the atomic
proportions, but only to the percentage compositions.
Hardness* — The pieces containing less than 24$ of tin were turned in
the lathe without difficulty, a gradually increasing hardness being noticed,
the last named giving a very short chip, and requiring frequent sharpening
of the tool.
With the most brittle alloys it was found impossible to turn the test-pieces
in the lathe to a smooth surface. No. 13 to No. 17 (26.85 to 34.47 tin) could
not be cut with a tool at all. Chips would fly off in advance of tfce tool and
ALLOYS OF COPPER AND ZINC.
321
beneath it, leaving a rough surface; or the tool would sometimes, apparentl
crush off portions of the metal, grinding it to powder. Beyond 40& tin t
hardness decreased so that the bars could be easily turned.
ALLOTS OF COPPER ANJ> ZINC. (U. S. Test Board).
the
No.
1
2
3
4
5
6
7
8
9
10
11
:3
'A
15
16
17
18
19
20
21
22
23
24
25
Mean Com-
position by
Analysis.
Tensile
Strength,
Ibs. per
sq, in.
Elastic
Limit
tot
Break-
TinS,
Load,
Ibs. per
sq. in.
1 Elongation %
in 5 inches.
Trans-
verse
Test
Modu-
lus of
Rup-
ture.
cl.
.2*- .a
PeJ
|s-|
Crush-
ing
Str'gth
per sq.
in., Ibs.
Torsional
Tests.
if*]
^6*
* 0-M
|S~
o§
®'55
Cop-
per.
Zinc.
!«
97.83
82.93
81.91
77.39
76.65
73.20
71.20
69.74
66.2?
63.44
60.94
58.49
55.15
54.86
49.66
48.99
47.56
43.36
41.30
32.94
29.20
20.81
12.12
4.35
Cast
1.88
16.98
17.99
22.45
23.08
26.47
28.54
30.06
33.50
36.36
38.65
41.10
44.44
44.78
50.14
50.82
52.28
56.22
58.12
66.23
70.17
77.63
86.6?
94.59
Zinc.
27,240
32,600
32,670
35,630
30,520
31,580
30,510
28,120
37,800
48,300
41,065
50,450
44,280
46,400
30,990
26,050
24,150
9,170
3,727
1,774
6,414
9,000
12,413
18,065
5,400
-
130
155
166
169
165
168
164
143
176
202
194
227
209
223
172
176
155
88
18
29
40
65
82
81
37
357
329
345
311
267
293
269
202
257
230
202
93
109
72
38
16
13
2
2
2
1
3
22
142
26. i
30.6
20.0
24.6
23.7
29.5
28.7
25.1
32.8
40.1
54.4
44.0
53.9
54.5
100.
100.
100.
100.
100.
100.
100.
100.
100.
75.
26.7
31.4
35.5
35.8
38.5
29.2
20.7
37.7
31.7
20.7
10.1
15.3
8.0
5.0
0.8
0.8
*6!2
0.4
0.5
0.7
23,197
21,193
25,374
22,325
25,894
24,468
26,930
28,459
43,216
38,968
63,304
42,463
47,955
33,467
40,189
48,471
17,691
7,761
8,296
16,579
22,972
35,026
26,162
7,539
Bent
M
lit
(t
M
U
it
ct
(1
1.26
0.61
1.17
0.10
0.04
0.04
0.04
0.13
0.31
0.46
0.12
42,000
75,000
78,000
117,400
121,000
52,152
22,000
Variation in Strength of Gun-bronze, and Means of
Improving tlie Strength*— The figures obtained for alloys of from
7.8# to 12.7$ tin, viz., from 20,860 to 29,430 pounds, are much less than are
usually given as the strength of gun-metal. Bronze guns are usually cast
under the pressure of a head of metal, which tends to increase the strength
and density. The strength of the upper part of a gun casting, or sinking
head, is not greater than that of the small bars which have been tested in
these experiments. The following is an extract from the report of Major
Wade concerning the strength and density of gun- bronze (1850):— Extreme
variation of six samples from different parts of the same gun (a 32-pounder
howitzer): Specific gravity, 8.487 to 8.835; tenacity, 26,428 to 52,192. Extreme
variation of all the samples tested: Specific gravity, 8.308 to 8.850; tenacity,
23,108 to 54,531. Extreme variation of all the samples from the gun heads:
Specific gravity, 8.308 to 8.756; tenacity, 23,529 to 35,484.
Major Wade says: The general results on the quality of bronze as it is
found in guns are mostly of a negative character. They expose defects in
density and strength, develop the heterogeneous texture of the metal in dif-
ferent parts of the same gun, and show the irregularity and uncertainty of
quality which attend the casting of all guns, although made from similar
materials, treated in like manner.
Navy ordnance bronze containing 9 parts copper and 1 part tin, tested at
Washington, D. C., in 1875-6, showed a variation in tensile strength from
29,800 to 51,400 Ibs. per square inch, in elongation frcm 3# to 58$, and in spe-
cific gravity from 8.39 to 8.88.
That a great improvement may be made in the density and tenacity of
gun-bronze by compression has been shown by the experiments of Mr. S. B.
Dean in Boston, Mass., in 1869, and by those of General Uchatius in Austria
in 1873. The former increased the density of the metal next the bore of the
gun from 8.321 to 8.875, and the tenacity from 27,238 to 41,471 pounds per
322
ALLOYS.
square inch. The* latter, by a similar process, obtained the following figures
for tenacity:
Pounds per sq. in.
Bronze with 10# tin 72,053
Bronze with 8$ tin 73,958
Bronze with 6# tin 77,656
ALLOYS OF COPPER, TIN, AND ZINC.
(Report of U. S. Test Board, Vol. II, 1881.)
No.
in
Report.
Analysis,
Original Mixture.
Transverse
Strength.
Tensile
Strength per
square inch.
Elongation
per cent in
5 inches.
Cu.
Sn.
Zn.
Modulus
of
Rupture
Deflec-
tion,
ins.
A.
23,660
32,000
28,840
35,680
34,500
36,000
33,600
37,560
32,830
32,350
35,500
36,000
33,140
33,700
35,320
35,440
23,140
32,700
30,000
38,000
38,000
33,140
33,440
17,000
34,720
34,000
29,500
41,350
37,140
25,720
6,820
3,765
44,400
57,400
41,160
21,780
18,020
66,500
Broke
725
68,900
27,400
25,400
23,000
B.
A.
P.
9.68
19.5
5.28
2 25
2.79
.92
.68
3.59
1.67
.44
1.00
.59
3.19
1.33
1.25
.54
"3"! 78"
.49
.99
.40
72
5
70
71
89
88
77
67
68
69
86
87
63
85
64
65
66
83
84
59
82
60
61
62
81
74
75
80
55
56
57
58
79
78
52
53
54
12
3
4
73
50
51
49
90
88.14
85
85
85
82.5
82.5
80
80
80
77.5
77.5
75
75
75
75
75
72.5
72.5
70
70
70
70
70
67.5
67.5
67.5
65
65
65
65
65
62.5
60
60
60
60
58.22
58.75
57.5
55
55
55
50
5
1.86
5
10
12.5
12.5
15
5
10
15
10
12.5
5
7.5
10
15
20
7.5
10
5
7.5
10
15
20
2.5
5
7.5
2.5
5
10
15
20
2.5
2.5
5
10
15
2.30
8.75
21.25
0.5
5
10
5
5
10
10
5
2.5
5
2.5
15
10
5
12.5
10
20
17.5
15
10
5
20
17.5
25
22.5
20
15
10
30
27.5
25
32.5
30
25
20
15
35
37.5
35
30
25
39.48
32.5
21.25
44.5
40
35
45
41,334
31,986
44,457
62,470
62,405
60,960
69,045
42,618
67,117
54,476
63,849
01,705
55,355
62,607
58,345
51,109
40,235
51,839
53,230
57,349
48,836
36,520
37,924
15,126
50,34:
55,976
46,875
56,949
51,369
27,075
13,591
11,932
69,255
69,508
46,076
24,699
18,248
95,623
35,752
2,752
72,308
38,174
28,258
20,814
2.63
3.67
2.85
2.56
2.83
1.61
1.09
3.88
2.45
.44
1.19
.71
2.91
1.39
.73
.31
.21
2.86
.74
1.37
.36
.18
.20
.08
2.91
.49
.32
2.36
.56
.14
.07
.05
2.34
1.46
.28
.13
.09
1.99
.18
.02
3.05
.22
.14
.11
30,740
33,000
28,560
36,000
32,800
34,000
33,800
32,300
31,950
30,760
36,000
32,500
34,960
39,300
34,000
28,000
27,660
34,800
30,000
32,940
32,400
26,300
27.800
12,900
45.850
34,460
1,000
38.300
36,000
22,500
7,231
2,665
45,000
52,900
38,330
21,240
12,400
67,600
3ef ore t
1,300
68,900
30,500
18,500
31,300
2.34
17.6
6.80
2.51
1.29
.86
11.6
1.57
.55
1.00
.72
2.50
1.56
1.13
.59
.43
3.73
.48
2.06
.84
.31
.25
.03
7.27
1.06
.36
3.26
1.21
.15
"3!69*"
.43
.26
3.02
.61
.19
2.15
4.87
.39
.15
2.19
3.02
.40
3.13
est ; ver
3.15
y brittle
9.43
.46
.29
.66
2.88
.43
.10
.45
The transverse tests were made in bars 1 in. square, 22 In. between sup-
ports. The tensile tests were made on bars 0.798 in. diam. turned from the
two halves of the transverse-test bar, one half being marked A and the
other B.
ALLOYS OF COPPER, TI^, AOT> ZINC. 323
Ancient Bronzes.— The usual composition of ancient bronze was the
game as that of modern gun-me^al — 90 copper, 10 tin; but the proportion of
tin varies from 5$ to 15$, and in some cases lead has been found. Some an-
cient Egyptian tools contained 88 copper, 12 tin.
Strength of the Copper-zinc Alloys.— The alloys containing less
than 16% of zinc by original mixture were generally defective. The bars
were full of blow-holes, and the metal showed signs of oxidation. To insure
good castings it appears that copper-zinc alloys should contain more than
15$ of zinc.
From No. 2 to No. 8 inclusive, 16.98 to 30.06$ zinc the bars show a remark-
able similarity in all their properties. They have all nearly the same
strength and ductility, the latter decreasing slightly as zinc increases, and
are nearly alike in color and appearance. Between Nos. 8 and 10, 30.06 and
36.36$ zinc, the strength by all methods of test rapidly increases. Between
No. 10 and No. 15, 36.36 and 50.14$ zinc, th?re is "another group, distinguished
by high strength and diminished ductility. The alloy of maximum tensile,
transverse and torsional strength contains about 41$ of zinc.
The alloys containing less than 55$ of zinc are oM yellow metals. Beyond
55$ the color changes to white, and the alloy becomes weak and brittle. Be-
tween 70$ and pure zinc the color is bluish gray, the brittleness decreases
and the strength increases, but not to such a degree as to make them useful
for constructive purposes.
Difference between Composition by Mixture and by
Analysis.— There is in every case a smaller percentage of zinc in the
average analysis than in the original mixture, and a larger percentage of
copper. The loss of zinc is variable, but in general averages from 1 to 2%.
Liquation or Separation of the Metals.— In several of the
bars a considerable amount of liquation took place, analysis showing a
difference in composition of the two ends of the bar. In such cases the
change in composition was gradual from one end of the bar to the other,
the upper end in general containing the higher percentage of copper. A
notable instance was bar No. 13, in the above table, turnings from the upper
end containing 40.36$ of zinc, and from the lower end 48.52$.
Specific Gravity. — The specific gravity follows a definite law. varying
with the composition, and decreasing with the addition of zinc. From the
plotted curve of specific gravities the following mean values are taken:
Percentzinc , 0 10 20 30 40 50 60 70 80 90 100.
Specific gravity 8.80 8.72 8.60 8.40 8.36 8.20 8.00 7.72 7.40 7.20 7.14.
Graphic Representation of the Law of Variation of
Strength of Copper-Tin-Zinc Alloys.— In an equilateral triangle
the sum of the perpendicular distances from any point within it to the three
sides is equal to the altitude. Such a triangle can therefore be used to
show graphically the percentage composition of any compound of three
parts, such as a triple alloy. Let one side represent 0 copper, a second
0 tin, and the third 0 zinc, the vertex opposite each of these sides repre-
senting 100 of each element respectively. On points in a triangle of wood
representing different alloys tested, wires were erected of lengths propor-
tional to the tensile strengths, and the triangle then built up with plaster to
the height of the wires. The surface thus formed has a characteristic
topography representing the variations of strength with variations of
composition. The cut shows the surface thus made. The vertical section
to the left represents the law of tensile strength of the copper-tin alloys,
the one to the right that of tin-zinc alloys, and the one at the rear that of
the copper-zinc alloys. The high point represents the strongest possible
alloys of the three metals. Its composition is copper 55, zinc 43, tin 2, and its
strength about 70,000 Ibs. The high ridge from this point to the point of
maximum height of the section on the left is the line of the strongest alloys,
represented by the formula zinc + (3 X tin) = 55.
All alloys lying to the rear of the ridge, containing more copper and less
tin or zinc are alloys of greater ductility than those on the line of maximum
strength, and are the valuable commercial alloys; those in fronton the decliv-
ity toward the central valley are brittle, and those in the valley are both brit-
tle and weak. Passing from the valley toward the section at the right the
alloys lose their brittleness and become soft, the maximum softness being
at tin = 100, but they remain weak, as is shown by the low elevation of the
surface. This model was planned and constructed by Prof. Thurston in
1877. (See Trans. A. S. C. E. 1881 Report of the U. S. Board appointed tQ
324
ALLOYS.
test Iron, Steel, etc., yol. II., Washington, 1881, and Thurston's Material*
of Engineering ', vol. iii.)
The best alloy obtained in Thurston's research for the TJ. S. Testing Board
has the composition, Copper 55, Tin 0.5, Zinc 44.5. The tensile strength in a
FIG. 77.
In which z Is the percentage of zinc and t that of tin. Alloys proportioned
according to this formula should have a strength of about 40,000 Ibs.
per sq. in. -f- 5002?. The formula fails with alloys containing less than 1 per
The following would be the percentage composition of a number of alloys
made according to this formula, and their corresponding tensile strength in
castings :
Tensile
Tensile
Tin.
Zinc.
Copper.
Strength,
Ibs. per
Tin.
Zinc.
Copper.
Strength,
Ibs. per
sq. in.
sq. in.
r i
52
47
66,000
S
31
61
55,500
*
49
49
64,500
9
28
63
54,000
3
46
51
63,000
10
25
65
52,500
4
43
53
61,500
12
19
69
49,500
5
40
55
60,000
14
13
73
46,500
6
87
57
58,500
16
7
77
43,500
7
81
59
57,000
18
1
81
40,500
These alloys, while possessing maximum tensile strength, would in general
be too hard* for easy working by machine tools. Another series made on
the formula z 4- 4 t = 50 would have greater ductility, together with con-
siderable strength, as follows, the strength being calculated as before,
tensile strength in Ibs. per sq. in. = 40,000 + 500z.
ALLOTS OP COPPER, TItf, AND ZINC.
325
Tensile
Tin, Zinc. Copper.
46
42
38
34
80
26
63
66
69
62
65
68
sq. in.
63,000
61,000
69,000
57,000
65,000
53,000
Tin. Zinc. Copper.
7
8
9
10
11
12
18
14
10
0
2
71
74
77
80
83
Tensile
Strength,
Ibs. per
sq. in.
51,000
49,000
47,000
45,000
43,000
41,000
Composition of Alloys in E very-day Use in Brass
Foundries. (American Machinist.)
Cop-
per.
Zinc.
Tin.
Lead.
Admiralty metal .
Ibs.
87
Ibs.
5
Ibs.
8
Ibs.
For parts of engines on board
Bell metal
16
4
naval vessels.
Bells for ships and factories
Brass (yellow) .....
16
8
V*
For plumbers, ship and house
64
8
4
4
brass work.
For bearing bushesf or shafting.
G un metal . . »
32
1
3
For pumps and other hydraulic
Steam metal . . .
20
I
1U
1
purposes.
Castings subjected to steam
Hard gun metal...
16
60
40*
2^
pressure.
For heavy bearings.
Metal from which bolts and nuts
Phosphor bronze.,
ti it
Brazing metal .
9:2
90
16
8
8 phc
10 "
)S. tin
n
are f orged,valve spindles, etc.
For valves, pumps and general
work.
For cog and worm wheels,
bushes, axle bearings, slide
valves, etc.
Flanges for copper pipes
" solder
50
50
Solder for the above flanges.
Ourley's Bronze.— 16 parts copper, 1 tin, 1 zinc, y% lead, used by
W. & L. E. Gurley of Troy for the framework of their engineer's transits.
Tensile strength 41,114 Ibs. per sq. in., elongation 27# in 1 inch, sp. gr. 8.696.
(W. J. Keep, Trans. A. I. M. E. 1890.)
Useful Alloys of Copper, Tin, and Zinc,
(Selected from numerous sources.)
Copper. Tin. Zinc.
U. S. Navy Dept. Journal boxes V \ 6
and guide-gibs J^f 82.8
Tobin bronze 58.22
Naval brass 62
Composition, U. S. Navy. 88
Brass bearings ( J. Rose) j g* 7
Gun metal 92*.5
" " 91
" " 87.75
•* " , 85
4 1S
Tough brass for engines 1 76 5
Bronze for rod-boxes (Laf ond)
" pieces subject to shock . .
Red brass parts
" ** percent
Bronze for pump casings (Laf ond)...
" eccentric straps. *'
** ** shrill whistles
1
H
parts.
13.8
34
per cent.
2.30
39.48
" "
1
37
Cl «t
10
2
It i« .
8
1
parts.
11.0
1.3
per cent.
5
2.5
" "
7
2
it tt
9.75
2.5
<t ««
6
10
ti 14
2
15
(t «<
2
2
parts.
11.8
16
11.7
2
per cent,
slightly malleable,
15
1.50
0.50 lead.
1
1
1 "
4.4
4.3
4.3 "
10
2
14
2
18
17
2.0 antimony.
2.0 ••
326
ALLOYS.
Copper. Tin.
Art bronze, dull red fracture 97
Gold bronze 89.5
Bearing metal ... 89
*» «• fi(j
2.8 lead.
lead,
lead.
3^ lead.
«• •* 80
*• •• 79
«• •• 74
English brass of A.D. 1504 64
Tobin Bronze. —This alloy is practically a sterro or delta metal with
the addition of a small amount of lead, which tends to render copper softer
and more ductile. (F. L. Garrison, J. F. I., 1891.)
The following analyses of Tobiu bronze were made by Dr. Chas. B. Dudley:
Pig Metal, Test Bar (Rolled),
per cent. per cent.
Copper 59.00 61.20
Zinc 38.40 37.14
Tin 2.16 0.90
Iron O.lt 0.18
Lead 0.31 0.35
Drc Dudley writes, "We tested the test bars and found 78,500 tensile
strength with 15# elongation in two inches, and 40^$ in eight inches. This
high tensile strength can only be obtained when the metal is manipulated.
Such high results could hardly be expected with cast metal."
The original Tobin bronze in 1875, as described by Thurston, Trans.
A. S. C. E 1881, had, composition of copper 58.22, tin 2.30, zinc 39.48. As
cast it had a tenacity of 66,000 Ibs. per sq. in., and as rolled 79,000 Ibs. ; cold
rolled it gave 104,000 Ibs.
A circular of Ansonia Brass & Copper Co. gives the following :— The tensile
strength of six Tobin bronze one-inch round rolled rods, turned down to a
diameter of % of an inch, tested by Fairbanks, averaged 79,600 Ibs. per sq.
in., and the elastic limit obtained on three specimens averaged 54,257 Ibs. per
sq. in.
At a cherry-red heat Tobin bronze can be forged and stamped as readily
as steel. Bolts and nuts can be forged from it, either by hand or by ma-
chinery, with a marked cfygree of economy. Its great tensile strength, and
resistance to the corrosive action of sea-water, render it a most suitable
metal for condenser plates, steam-launch shafting, ship sheathing and
fastenings, nails, hull plates for steam yachts, torpedo and life boats, and
ship deck fittings.
The Navy Department has specified its use for certain purposes in the
machinery of the new cruisers. Its specific gravity is 8.071. The weight of
a cubic inch is .291 Ib.
Special Alloys. (Engineer, March 24, 1893.)
JAPANESE ALLOYS for art work :
Copper.
Silver.
Gold.
Lead.
Zinc.
Iron.
Shaku-do
Shibu-ichi
94.50
67.31
1.55
32.07
3.73
traces.
0.11
.52
trace.
trace.
GILBERT'S ALLOY for cera-perduta process, for casting in plaster-of-paris.
Copper 91.4 Tin 5.7 Lead 2.9 Very fusible.
ALLOYS.
(F. L. Garrison, Jour. Frank. lust., June and July, 1891.)
Helta Metal.— This alloy, which was formerly known as sterro-metal,
is composed of about 60 copper, from 34 to 44 zinc, 2 to 4 iron, and 1 to 2 tin.
The peculiarity of all these alloys is the content of iron, which appears to
have the property of increasing their strength to an unusual degree. In
making delta metal the iron is previously alloyed with zinc in known and
definite proportions. When ordinary wrought-iron is introduced into
molten zinc, the latter readily dissolves or absorbs the former, and will take
, PHOSPHO&-BROH2E AND OTHER SPECIAL BUOK2ES. 327
it up to the extent of about 5# or more. By adding the zinc-iron alloy thus
obtained to the requisite amount of copper, it is possible to introduce any
definite quantity of iron up to 5% into the copper alloy. Garrison gives the
following as the range of composition of copper-zinc-iron, and copper-zinc-
tin-iron alloys :
Per cent. Per cent.
Iron 0.1 to5 Iron 0.1 to 5
Copper 50to65 Tin 0.1 to 10
Zinc 49.9 to 30 Zinc 1 .8 to 45
Copper 98 to 40
The advantages claimed for delta metal are great strength and toughness.
It produces sound castings of close grain. It can be rolled and forged hot,
and can stand a certain amount of drawing and hammering when cold. It
takes a high polish, and when exposed to the atmosphere tarnishes less than
brass.
When cast in sand delta metal has a tensile strength of about 45,000 pounds
per square inch, and about 10# elongation ; when rolled, tensile strength of
60,000 to 75,000 pounds per square inch, elongation from 9# to Yi% on bars 1.128
inch in diameter and 1 inch area.
Wallace gives the ultimate tensile strength 33,600 to 51,520 pounds per
square inch, with from 10$ to 20% elongation.
Delta metal can be forged, stamped and rolled hot. It must be forged at
a dark cherry-red heat, and care taken to avoid striking when at a black
heat.
According to Lloyd's Proving House tests, made at Cardiff, December 20,
1887, a half -inch delta metal-rolled bar gave a tensile strength of 88,400
pounds per square inch, with an elongation of 30$ in three inches.
PHOSPHOR-BRONZE AND OTHER SPECIAL
BRONZES.
Phosphor-bronze.— In the year 18G8, Montefiore & Kunzel of Liege,
Belgium, found by adding small proportions of phosphorus or "phosphoret
of tin or copper" to copper that the oxides of that metal, nearly always
present as an impurity, more or less, were deoxidized and the copper much
improved in strength and ductility, the grain of the fracture became finer,
the color brighter, and a greater fluidity was attained.
Three samples of phosphor-bronze tested by Kirkaldy gave :
Elastic limit, Ibs. per sq. in 23,800 24,700 16,100
Tensile strength, Ibs. per sq. in. ... 52,625 46,100 44,448
Elongation, per cent 8.40 1.50 33.40
The strength of phosphor-bronze varies like that of ordinary bronze
according to the percentages of copper, tin, zinc, lead, etc., in the alloy.
Deoxidized Bronze,— This alloy resembles phosphor bronze some-
what in composition and also delta metal, in containing zinc and iron. The
following analysis gives its average composition:
Copper. 82.67
Tin 12.40
Zinc 3.23
Lead 2.14
Iron 0.10
Silver 0.07
Phosphorus 0.005
100.615
Comparison of Copper, Silicon-bronze, and Phosphor*
bronze Wires. (Engineer ing, Nov. 23, 1883.)
Description of Wire.
Tensile Strength.
Relative Conductivity.
39,827 Ibs. per sq. in.
41,696 " " " "
108,080 " " " "
100 per cent.
96 " "
34 " "
26 " "
Silicon bronze (telegraph)
" (telephone)
Phosphor bronze (telephone). .
Penn. R. R. Co.'s Specifications for Phosphor-Bronze
(1902).— Tbe metal desired is homogeneous,allo7 of copper, 79.70; tin 10 00-
lead, 9.50; phosphorus, 0.80. Lots will not be accepted if samples do not
show tin, between 9 and \\%\ lead, between 8 and 1 \%\ phosphorus, between
0.7 and \%\ nor if the metal contains a sum total of other substances than
copper, tin, lead, and phosphorus in greater quantity than 0,50 per cent. (See
328
ALLOYS.
Silicon Bronze. (Aluminum World, May, 1897.)
The most useful of the silicon bronzes are the 3$ (97$ copper, 3$ silicon)
and the 5% (95$ copper, 5# silicon), although the hardness and strength of
the alloy can be increased or decreased at will by increasing or decreasing
silicon. A 3$ silicon bronze has a tensile strength, in a casting, of about
55,000 Ibs. per sq. in., and from 50$ to 60$ elongation. The 5$ bronze has a
tensile strength of about 75,000 Ibs. and about 8$ elongation. More than 5$
or 5^$ of silicon in copper makes a brittle alloy. In using silicon, either as
a flux or for making silicon bronze, the rich alloy of silicon and copper
which is now on the market should be used. It should be free from iron
and other metals if the best results are to be obtained. Ferro-silicon is not
suitable for use in copper or bronze mixtures.
ALUMINUM ALLOYS.
Aluminum Bronze* (Cowles Electric Smelting and Al. Co.'s circular.)
The standard A No. 2 grade of aluminum bronze, containing \Q% of alumi-
num and 90# of copper, has many remarkable characteristics which dis-
tinguish it from all other metals.
The tenacity of castings of A No. 2 grade metal varies between 75,000 and
90,000 Ibs. to the square inch, with from 4# to 14$ elongation.
Increasing the proportion of aluminum in bronze beyond 11$ produces a
brittle alloy; therefore nothing higher than the A No. 1, which contains 11#,
is made.
The B, C, D, and E grades, containing 7^#, 5£, 2^>$, and 1J4$ of aluminum,
respectively, decrease in tenacity in the order named, that of the former
being about 65,000 pounds, while the latter is 25,000 pounds. While there is
also a proportionate decrease in transverse and torsional strengths, elastic
limit, and resistance to compression as the percentage of aluminum is low-
ered and that of copper raisedv the ductility on the other hand increases in
the same proportion. The specific gravity of the A No. 1 grade is 7.56.
Bell Bros., Newcastle, gave the specific gravity of the aluminum bronzes
as follows:
3$, 8.691 ; 4& 8.621 ; 5$, 8.369; 10$, 7.689.
Tests of Aluminum Bronzes.
(By John H. J. Dagger, in a paper read before the British Association, 1889.)
11
Per cent
of
Aluminum.
Tensile Strength.
Elonga-
tion,
per cent.
Specific
Gravity.
Tons per
square inch.
Pounds per
square inch.
40 to 45
33 ki 40
25 ** 30
15 " 18
13 " 15
11 " 13
89,600 to 100,800
73,920 " 89,600
56,000 " 67,200
33,600 " 40,320
29,120 " 33,600
24,640 " 29,120
8
14
40
40
50
55
7.23
7.69
8.00
8.37
8.69
10
5-5V
Q
V
£ ...
1:
I ......
!
Both physical and chemical tests made of samples cut from various sec -
tions of 2J^g, 5$, 7^$, or 10$ aluminized copper castings tend to prove that
the aluminum unites itself with each particle of copper with uniform pro-
portion in each case, so that we have a product that is free from liquation
and highly homogeneous. (R. 0. Cole, Iron Afje, Jan. 16, 1890.)
Casting:,— The melting point of aluminum bronze varies slightly with
the amounc of aluminum contained, the higher grades melting at a some-
what lower temperature than the lower grades. The A No. 1 grades melt
at about 1700° F.» a little higher than ordinary bronze or brass.
Aluminum bronze shrinks more than ordinary brass. As the metal solidi-
fies rapidly it is necessary to pour it quickly and to make the feeders amply
large, so that there will be no " freezing" in them before the casting is
properly fed. Baked-sand moulds are preferable to green sand, except for
small castings, and when fine skin colors are desired in the castings. (See
paper by Thos. D. West, Trans. A. S. M. E. 1886, vol. viii.)
All grades of aluminum bronze can be rolled, swedged, spun, or drawn
cold except A 1 and A 2. They can all be worked at a bright red heat.
In rolling, swedging, or spinning cold, it should be annealed very often, and
at a brighter red heat than is used for annealing brass.
Brazing.— Aluminum bronze will braze as well as any other metal,
using one quarter brass solder (zinc 500, copper 500 (and three quarters
borax, or, better, three quarters cryolite.
ALUMINUM ALLOYS.
329
Soldering. — To solder aluminum bronze with ordinary soft (pewter)
solder: Cleanse well the parts to be joined free from grease and dirt. Then
place the parts to be soldered in a strong solution of sulphate of copper and
place in the bath a rod of soft iron touching the parts to be joined. After
a while a coppery-like surface will be seen on the metal. Remove from
bath, rinse quite clean, and brighten the surfaces. These surfaces can then
be tinned by using a fluid consisting of zinc dissolved in hydrochloric acid, in
the ordinary way, with common soft solder.
Mierzinski recommends ordinary hard solder, and says that Hulot uses
an alloy of the usual half-and-half lead-tin solder, with 12.5& 25# or 50# of
zinc amalgam.
Aluminum-Brass (E. H. Cowles, Trans. A. I. M. E., vol. xviii.)—
Cowles aluminum- brass is made by fusing together equal weights of A 1
aluminum-bronze, copper, and zinc. The copper and bronze are first thor-
oughly melted and mixed, and the zinc is finally added. The material is left
in the furnace until small test-bars are taken from it and broken. When
these bars show a tensile strength of 80,000 pounds or over, with 2 or 3 per
cent ductility, the metal is ready to be poured. Tests of this brass, on small
bars, have at times shown as high as 100,000 pounds tensile strength.
The screw of the United States gunboat Petrel is cast from this brass»
mixed with a trifle less zinc in order to increase its ductility.
Tests of Aluminum-Brass.
(Cowles E. S. & Al. Co.)
Specimen (Castings.)
Diameter
of Piece,
Inch.
Area,
sq. in.
Tensile
Strength,
Ibs. per
sq. in.
Elastic
Limit,
Ibs. per
sq. in.
Elonga-
tion,
per ct.
Remarks.
15£ A grade Bronze. )
11% Zinc V
465
1698
41 225
17,668
411^
$*B
U P <D
68% Copper
I- Is
1 part A Bronze....
1 part Zinc -
.465
.1698
78,327
2^£
12 §3
1 part Copper
1 part A Bronze ....
1 part Zinc . . . •
.460
1661
72246
2U
;llj
III*
1 part Copper — .. j
e*
The first brass on the above list is an extremely tough metal with low
elastic limit, made purposely so as to " upset " easily. The other, which is
called Aluminum-brass No. 2, is very hard.
We have not in this country or in England any official standard by which
to judge of the physical characteristics of cast metals. There are two con-
ditions that are absolutely necessary to be known before we can make a
fair comparison of different materials: namely, whether the casting was
made in dry or green sand or in a chill, and whether it was attached to a
larger casting or cast by itself. It has also been found that chill-castings
give higher results than sand-castings, and that bars cast by themselves
purposely for testing almost invariably rim higher than test-bars attached
to castings. It is also a fact that bars cut out from castings are generally
weaker than bars cast alone, (E. H. Cowles.)
Caution as to Reported Strength of Alloys.— The same
variation in strength which has been found in tests of gun-metal (copper
and tin) noted above, must be expected in tests of aluminum bronze and in
fact of all alloys. They are exceedingly subject to variation in density and
in grain, caused by differences in method of molding and casting, tempera-
ture of pouring, size and shape of casting, depth of "sinking head," etc.
Aluminum Hardened by Addition of Copper.
Rolled Sheets .04 inch thick. (The Engineer, Jan. 2, 1891.)
Al.
Per cent.
100
98
96
94
93
Cu.
Per cent.
Sp. Gr.
Calculated.
2.90
3.02
8.14
Sp. Gr.
Determined.
2.67
2.71
2.77
2.82
2.85
Tensile Strength
in pounds per
square inch.
26,535
43,563
44,130
54,773
60,374
330
ALLOTS.
Tests of Aluminum Alloys*
(Engineer Harris, U. S. N., Trans. A. I. M. E., vol. xviii.)
Composition.
Tensile
Strength,
persq. in.
Ibs.
60,700
66,000
67,600
72,830
82,200
70,400
59,100
53,000
69,930
46,530
Elastic
Limit,
Ibs. per
sq. in.
18,000
27,000
24,000
33,000
60,000
55,000
19,000
19,000
33,000
17,000
Elonga-
tion,
per ct.
23.2
3.8
13.
2.40
2.33
0.4
15.1
6.2
1.33
7.8
Reduc«
tion of
Area,
per ct.
30.7
7.8
21.62
5.78
9.88
4.33
23,59
15.5
3.30
19.19
Cop-
per.
Alumi-
num.
6.50£
9.33
6.50
9.00
3.33
3.33
6.50
6.50
9.33
6.50
Silicon.
Zinc.
Iron.
0.25*
0.50
0.25
91.50#
88.50
91.50
90.00
63.00
63.00
91.50
93.00
88.50
92.00
I.75£
1.66
1.75
1.00
0.33
0.33
1.75
0.50
1.66
0.50
33 '.33%
33.33
0.25
0.50
For comparison with the above 6 tests of " Navy Yard Bronze," Cu 88.
Sn 10, Zn 2, are given in which the T. S. ranges from 18,000 to 24,590. E. L.
from 10,000 to 13,000, El. 2.5 to 5.8*. Red. 4.7 to 10.89.
Alloys of Aluminum, Silicon and Iron*
M. and E. Bernard have succeeded in obtaining through electrolysis, by
treating directly and without previous purification, the aluminum earths
(red and white bauxites) the following :
Alloys such as f erro-aluminum, ferro-silicon-aluminum and silicon-alumi-
num, where the proportion of silicon may exceed 10$ which are employed
in the metallurgy of iron for refining steel and cast-iron.
Also silicon-aluminum, where the proportion of silicon does not exceed
10$, which may be employed in mechanical constructions in a rolled or
hammered condition, in place of steel, on account of their great resistance,
especially where the lightness of the piece in construction constitutes one
of the main conditions of success.
The following analyses are given:
1. Alloys applied to the metallurgy of iron, the refining of steel and cast
iron: No. 1. Al, 70£; Fe, 25£; Si, 5g. No. 2. Al, 70; Fe, 20; Si, 10. No. 3. Al,
70; Fe, 15; Si, 15. No. 4. Al, 70; Fe, 10; Si, 20. No. 5. Al, 70; Fe, 10; Si, 10;
Mn, 10. No. 6. Al. 70; Fe, trace; Si, 20; Mn, 10.
2. Mechanical alloys: No. 1. Al, 92; Si, 6.75; Fe, 1.25. No. 2. Al, 90; Si,
9.25; Fe, 0.75. No. 3. Al, 90; Si, 10; Fe, trace. The best results were with
alloys where the proportion of iron was very low, and the proportion of
silicon in the neighborhood of 10$. Above that proportion the alloy be-
comes crystalline and can no longer be employed. The density of the alloys
of silicon is approximately the same as that of aluminum. — La JMetallurgie,
1892.
Tungsten and Aluminum.— Mr. Leinhardt Mannesmann says that
the addition of a little tungsten to pure aluminum or its alloys communi-
cates a remarkable resistance to the action of cold and hot water, salt
water and other reagents. When the proportion of tungsten is sufficient
the alloys offer great resistance to tensile strains.
Aluminum*, Copper, and Tin.— Prof. R. C. Carpenter, Trans.
A. S. M. E., vol. xix., finds the following alloys of maximum strength in a
series in which two of the three metals are in equal proportions:
Al, 85; Cu, 7.5; Sn, 7.5; tensile strength, 30,000 Ibs. per sq. in.; elongation
in 6 in, 4£; sp. gr., 3.02. Al, 6.25; Cu, 87.5; Sn, 6.25; T. S., 63,000; El., 3.8;
Sp. gr.. 735. Al, 5; Cu, 5: Sn, 90; T. S., 11,000; El., 10.1; sp. gr., 6.82.
Aluminum and Zinc.— Prof. Carpenter finds that the strongest
alloy of these metais consists of two parts of aluminum and one part of zinc.
Its tensile strength is 24,000 t- 26,000 Ibs. per sq. in.; has but little ductility,
is readily cut with machine-tools, and is a good substitute for hard cast
Aluminum and Tin.— M. Bourbouze has compounded an alloy of
aluminum and tin, by fusing together 100 parts of the former with 10 parts
of the latter. This alloy is paler than aluminum, and has a specific gravity
of 2,85, The alloy is not as easily attacked by several reagents as aluini-
ALLOYS OF MANGANESE AKD COPP.ER. 331
Hum is, and it can also be worked more readily. Another advantage is that
it can be soldered as easily as bronze, without further preliminary prepara-
tions.
Aluminum-Antimony Alloys.— Dr. C. R. Alder Wright describes
some aluminum-antimony alloys in a communication read before the-Society
of Chemical Industry. The results of his researches do not disclose the
existence of a commercially useful alloy of these two metals, and have
greater scientific than practical interest. A remarkable point is that the
alloy with the chemical composition Al Sb has a higher melting point than
either aluminum or antimony alone, and that when aluminum is added to
pure antimony the melting-point goes up from that of antimony (450° C.)
to a certain temperature rather above that of silver (1000° C.).
AI^OYS OF MANGANESE AND COPPER.
Various Manganese Alloys.— E. H. Cowles, in Trans. A. I. M. E.,
vol. xviii, p. 495, states that as the result of numerous experiments on
mixtures of the several metals, copper, zinc, tin, lead, aluminum, iron, and
manganese, and the metalloid silicon, and experiments upon the same in
ascertaining tensile strength, ductility, color, etc., the most important
determinations appear to be about as follows :
1. That pure metallic manganese exerts a bleaching effect upon copper
more radical in its action even than nickel. In other words, it was found
that 18>£$ of manganese present in copper produces as white a color in the
resulting alloy as 25$ of nickel would do, this being the amount of each
required to remove the last trace of red.
2. That upwards of 20$ or 25$ of manganese may be added to copper with-
out reducing its ductility, although doubling its tensile strength and chang-
ing its color.
3. That manganese, copper, and zinc when melted together and poured
into moulds behave very much like the most " yeasty " German silver,
producing an ingot which is a mass of blow-holes, and which swells up
above the mould before cooling.
4. That the alloy of manganese and copper by itself is very easily
oxidized.
5. That the addition of 1.25$ of aluminum to a manganese-copper alloy
converts it from one of the most refractory of metals in the casting process
into a metal of superior casting qualities, and the non-corrodibility of which
is in many instances greater than that of either German or nickel silver.
A " silver-bronze " alloy especially designed for rods, sheets, and wire
lias the following composition : Manganese, 18; aluminum, 1.20; silicon, 0.5 ;
iiinc, 13; and copper, 67.5$. It has a tensile strength of about 57,000 pounds
on small bars, and 20$ elongation. It has been rolled into thin plate and
drawn into wire .008 inch in diameter. A test of the electrical conductivity
of this wire (of size No. 32) shows its resistance to be 41.44 times that of pure
copper. This is far lower conductivity than that of German silver.
Manganese Bronze. (F. L. Garrison, Jour. F. I., 1891.)— This alloy
h&s been used extensively for casting propeller-blades. Tests of some made
by B. H. Cramp & Co., of Philadelphia, gave an average elastic limit of
30,000 pounds per square inch, tensile strength of about 60,000 pounds per
square inch, with an elongation of 8$ to 10$ in sand castings. When rolled,
the elastic limit is about 80,000 pounds per square inch, tensile strength
1)5,000 to 106,000 pounds per square inch, with an elongation of 12$ to 15$.
Compression tests made at United States Navy Department from the
metal in the pouring-gate of propeller-hub of U. S. S. Maine gave in two tests
a crushing stress of 126,450 and 135,750 Ibs. per sq. in. The specimens were
1 inch high by 0.7 X 0.7 inch in cross-section = 0.49 square inch. Both spec*-
mens gave way by shearing, on a plane making an angle of nearly 45° with;
the direction of stress.
A test on a specimen IxlXl inch was made from a piece vf the same
pouring-gate. Under stress of 150,000 pounds it was flattened to 0.72 inch
high by about 1J4 X 1^4 inches, but without rupture or any sign of distress.
One of the great objections to the use of manganese bronze, or in fact
any alloy except iron or steel, for the propellers of iron ships is on account
of the galvanic action set up between the propeller and the stern-posts.
This difficulty has in great measure been overcome by putting strips of
rolled zinc around the propeller apertures in the stern-frames.
The following analysis of Parsons' manganese bronze No. 2 was made
from a chip from the propeller of Mr, W, K, Vanderbilt's yacht Alva,
333 ALLOYS.
Copper 88.644
Zinc 1.570
Tin 8.700
Iron. 0.720
Lead 0.295
Phosphorus trace
99.929
It will be observed there is no manganese present and the amount of zinc
is very small.
E. H. Cowles, Trans. A. I. M. E., vol. xviii, says : Manganese bronze, so
called, is in reality a manganese brass, for zinc instead of tin is the chief
element added to the copper. Mr. P. M. Parsons, the proprietor of this
brand of metal, has claimed for it a tensile strength of f rom 24 to 28 tons on
small bars when cast in sand. Mr. W. C. Wallace states that brass-founders
of high repute in England will not admit that manganese bronze has more
than from 12 to 17 tons tensile strength. Mr. Horace See found tensile
strength of 45,000 pounds, and from 6$ to 12}^$ elongation.
GERMAN-SILVER AND OTHER NICKEL AL.L.OYS.
German Silver, — The composition of Gferman silver is a very uncertain
thing and depends largely on the honesty of the manufacturer and the
price the purchaser is willing to pay. It is composed of copper, zinc, and
nickel in varying proportions. The best varieties contain from 18$ to 25$ of
nickel and from 20$ to 30$ of zinc, the remainder being copper. The more
expensive nickel silver contains from 25$ to 33$ of nickel and from 75$ to 66$
of copper. The nickel is used as a whitening element; it also strengthens
the alloy and renders it harder and more non-corrodible than the brass
made without it, of copper and zinc. Of all troublesome alloys to handle in
the foundry or rolling-mill, German silver is the worst. It is 'unmanageable
and refractory at every step in its transition from the crude elements into
rods, sheets, or wire. (E. H. Cowles, Trans. A. I. M. E., vol. xviii. p. 494.)
Copper. Nickel. Tin. 2toc.
German silver 51.6 25.8 22.6
" 50.2 14.8 3.1 31.9
" " 51.1 13.8 3.2 31.9
" " 52to55 18to25 20to30
Nickel " 75to66 25to33
A refined copper-nickel alloy containing 50$ copper and 49$ nickel, with
very small amounts of iron, silicon and carbon, is produced direct from
Bessemer matte in the Sudbury (Canada) Nickel Works. German silver
manufacturers purchase a ready-made alloy, which melts at a low heat and
requires simple addition of zinc, instead of buying the nickel and copper
separately. This alloy, t; 50-50" as it is called, is almost indistinguishable
from pure nickel. Its cost is less than nickel, its melting-point much lower,
it can be cast solid in any form desired, and furnishes a casting which works
easily in the lathe or planer, yielding a silvery white surface unchanged by
air or moisture. For bullet casings now used in various British and conti-
nental rifles, a special alloy of 80$ copper and 20$ nickel is made.
Copper. Nickel. Zinc.
Chinese packfong 40.4 31, * 6.5 parts.
** tutenag 8 3 6.5
German silver 2 1 1
" (cheaper) 8 2 3.5
(closely resembles sil). 8 3 3.5
AL.L.OYS OF BISMUTH.
By adding a small amount of bismuth to lead that metal may be hard-
ened and toughened. An alloy consisting of three parts of lead and two of
bismuth has ten times the hardness and twenty times the tenacity of lead.
The alloys of bismuth with both tin and lead are extremely fusible, and
take fine impressions of casts and moulds. An alloy of one part bismuth,
two parts tin, and one part lead is used by pewter-workers as a soft solder,
and by soap-makers for moulds. An alloy of five parts bismuth, two parts
tin, and three parts lead melts at 199° F., and is somewhat used for ster-
eotyping, and for metallic writing-pencils. Thorpe gives the following
proportions for the better-known fusible metals:
BEAKING-METAL ALLOYS.
333
Name of Alloy.
Bismuth.
Lead.
Tin.
Cad-
mium
Mer-
cury.
Melting-
point.
Newton's
50
31.25
18.75
202° F.
Hose's . • •
50
28.10
24.10
203°
D' Arcet's
50
25.00
25.00
201°
D'Arcet's with mercury.
Wood's
50
50
25.00
25.00
25.00
12.50
12.50
250.0
113°
149°
Lipowitz's . . —
Guthrie's "Entectic"...
50
50
26.90
20.55
12.78
21.10
10.40
14.03
149°
" Very low."
The action of heat upon some of these alloys is remarkable. Thus, Lipo-
witz's alloy, which solidifies at 149° Fah., contracts very rapidly at first, as
it cools from this point. As the cooling goes on the contraction becomes
slower and slower, until the temperature falls to 101.3° Fah. From this
point the alloy expands as it cools, until the temperature falls to about 77°
Fah., after which it again contracts, so that at 32° F. a bar of the alloy has
the same length as at 115° F.
Alloys of bismuth have been used for making fusible plugs for boilers, but
it is found that they are altered by the continued action of heat, so that one
cannot rely upon them to melt at the proper temperature. Pure Banca tin
is used by the U. S. Government for fusible plugs.
FUSIBLE: ALLOYS. (From various sources.)
Sir Isaac Newton's, bismuth 5, lead 3, tin 2, melts at 212° F.
Rose's, bismuth 2, lead 1, tin 1, melts at 200 "
Wood's, cadmium 1, bismuth 4, lead 2, tin 1, melts at 165 '*
Guthrie's, cadmium 13.29, bismuth 47.38, lead 19.36, tin 19.97, melts at. 160 "
Lead 3, tin 5, bismuth 8, melts at 208 "
Lead 1, tin 3, bismuth 5, melts at 212
Lead 1, tin 4, bismuth 5, melts at 240
Tin 1, bismuth 1, melts at ., 286
Lead 2, tin 3, melts at 334
Tin 2, bismuth 1, melts at 336
Lead 1, tin 2, melts at 360
Tin 8, bismuth 1, melts at 392
Lead 2, tin 1, melts at 475
Lead 1, tin 1, melts at ,.. 466 "
Lead 1, tin 3, melts at 334 "
Tin 3, bismuth 1, melts at 392 **
Lead 1, bismuth 1, melts at 257 "
Lead 1, Tin 1, bismuth 4, melts at ;.. 201 "
Lead 5, tin 3, bismuth 8, melts at 202 *'
Tin 3, bismuths, melts at , 202 "
BEARING-WETAL ALLOYS.
(C, B. Dudley, Jour. F. I., Feb. and March, 1892.)
Alloys are used as bearings in place of wrought iron, cast iron, or steel,
partly because wear and friction are believed to be more rapid when two
metals of the same kind work together, partly because the soft metals are
more easily worked and got into proper shape, and partly because it is de-
sirable to use a soft metal which will take the wear rather than a hard
metal, which will wear the journal more rapidly.
A good bearing-metal must have five characteristics: (1) It must be strong
enough to carry the load without distortion. Pressures on car-journals are
frequently as high as 350 to 400 Ibs. per square inch.
(2) A good bearing-metal should not heat readily. The old copper-tin
bearing, made of seven parts copper to one part tin, is more apt to heat
than some other alloys. In general, research seems to show that the harder
tne bearing-metal, the more likely it is to heat.
(3) Good bearing-metal should work well in the foundry. Oxidation while
melting causes spongy castings. It can be prevented by a liberal use of
. powdered charcoal while melting. The addition of \% to 2% of zinc or a
small amount of phosphorus greatly aids in the production of sound cast-
ings. This is a principal element of value in phosphor-bronze.
334
ALLOYS.
(4) Good bearing petals should show small friction. It is true that friction
is almost wholly a question of the lubricant used; but the metal of the bear-
ing has certainly some influence.
(5) Other things being equal, the best bearing-metal is that which wears
slowest.
The principal constituents of bearing-metal alloys are copper, tin, lead,
zinc, antimony, iron, and aluminum. The following table gives the constitu-
ents of most of the prominent bearing-metals as analyzed at the Pennsyl-
vania Railroad laboratory at Altoona.
Analyses of Bearing-metal Alloys.
Metal.
Cop-
per.
Tin.
Lead.
Zinc.
Anti-
mony.
Iron.
Camelia metal
Anti-friction metal.
70.20
l.GO
4.25
98.13
14.75
*87 92
10.20
12 08
0.55
trace
Car-brass lining
trace
84.87
15.10
Salgee anti-friction
Graphite bearing-metal
4.01
9.91
14.38
1.15
67.73
85.57
"ie.73
" YYri
Antimonial lead
80.69
18.83
*
Carbon bronze
Cornish bronze
75.47
77.83
92.39
9.72
9.60
2.37
14.57
12.40
5.10
trace
(2)
trace(3)
0 07
^Magnolia metal
trace
83 55
trace
16 45
traced
American anti-friction metal . . .
78 44
0.98
19.60
065
Tobin bronze
59.00
2.16
0.31
38.40
0 11
Graney bronze
75.80
9.20
15:06
76.41
10.60
12.52
Manganese bronze
\jaxmetal •.
A.nti-f riction metal
90.52
81.24
9.58
10.98
'Y.27
88.32
(5)
... .(6)
Harrington bronze
Car-box metal ..... ........
55.73
0.97
'84.33
42.67
trace
"14*38'
0.68
0 61
94 40
6 03
Phosph or-bronze
79.17
76.80
10.22
8.00
9.61
15.00
(7)
(8)
Other constituents:
(1) No graphite. (5) No manganese.
(2) Possible trace of carbon. (6) Phosphorus or arsenic, 0.37.
(3) Trace of phosphorus. (7) Phosphorus, 0.94.
(4) Possible trace of bismuth. (8) Phosphorus, 0.20.
* Dr. H. Co Torrey says this analysis is erroneous and that Magnolia
metal always contains tin.
As an example of the influence of minute changes in an alloy, the Har-
rington bronze, which consists of a minute proportion of iron in a copper-
zinc alloy, showed after rolling a tensile strength of 75,000 Ibs. and 20$ elon-
gation in 2 inches.
In experimenting on this subject on the Pennsylvania Railroad, a certain
number of the bearings were made of a standard bearing-metal, and the
same number were made of the metal to be tested. These bearings were
placed on opposite ends of the same axle, one side of the car having tiie
standard bearings, the other the experimental. Before going into service
the bearings were carefully weighed, and after a sufficient time they were
again weighed.
The standard bearing-metal used is the " S bearing-metal " of the Bhos-
phor-bronze Smelting Co. It contains about 79.70$ copper, 9.50* lead, 16#
tin, and 0.80# phosphorus. A large number of experiments have shown that
the loss of weight of a bearing of this metal is 1 Ib. to each 18,000 to 25,000
miles travelled. Besides the measurement of wear, observations were made
on the frequency of " hot boxes " with the different metals.
The results of the tests for wear, so far as given, are condensed into the ,
following table ;
UEARIHG-METAL ALLOYS. 335
Composition. Rate
Metal. ^ , of
Copper. Tin. Lead. Phos. Arsenic. Wear.
Standard 79.70 10.00 9.50 0.80 100
Copper-tin 87.50 12.50 148
Copper-tin, second experiment, same metal 153
Copper-tin, third experiment, same metal .. 147
Arsenic-bronze 89.20 10.00 .... .... 0.80 142
Arsenic-bronze 79.20 10.00 7.00 .... 0.80 115
Arsenic-bronze 79.70 10.00 9.50 0.80 101
"K"bronze 77.00 10.50 12.50 .... .... 92
"K" bronze, second experiment, same metal..... 92.7
Alloy"B" 77.00 8.00 15.00 .... .... 86.5
The old copper- tin alloy of 7 to 1 has repeatedly proved its inferiority to the
phosphor-bronze metal. Many more of the copper-tin bearings heated
than of the phosphor-bronze. The showing of these tests was so satisfac-
tory that phosphor-bronze was adopted as the standard bearing-metal of
the Pennsylvania R.R., and was used for a long time.
The experiments, however, were continued. It was found that arsenic
practically takes the place of phosphorus in a copper-tin alloy, and three
tests were made with arsenic- bronzes as noted above. As the proportion
to lead is increased to correspond with the standard, the durability increases
as well. In view of these results the " K " bronze was tried, in which neither
phosphorus nor arsenic were used, and in which the lead was increased
above the proportion in the standard phosphor-bronze. The result was that
the metal wore 7.30$ slower than the phosphor-bronze. No trouble from
heating was experienced with the " K " bronze more than with the standard.
Dr. Dudley continues:
At about this time we began to find evidences that wear of bearing-metal
alloys varied in accordance with the following law: " That alloy which has
the greatest power of distortion without rupture (resilience), will best resist
wear." It was now attempted to design an alloy in accordance with this
law, taking first the proportions of copper and tin, 9^ parts copper to 1 of
tin was settled on by experiment as the standard, although some evidence
since that time tends to show that 12 or possibly 15 parts copper to 1 of tin
might have been better. The influence of lead on this copper-tin alloy seems
to be much the same as a still further diminution of tin. However, the
tendency of the metal to yield under pressure increases as the amount of
tin is diminished, and the amount of the lead increased, so a limit is set to
the use of lead. A certain amount of tin is also necessary to keep the lead
alloyed with the copper.
Bearings were cast of the metal noted in the table as alloy " B," and it
wore 13.5$ slower than the standard phosphor-bronze. This metal is now
the standard bearing- metal, of the Pennsylvania Railroad, being slightly
changed in composition to allow the use of phosphor-bronze scrap. The
formula adopted is: Copper, 105 Ibs. ; phosphor-bronze, 60 Ibs. ; tin, 9% Ibs. ;
lead, 25*4 Ibs. By using ordinary care in the foundry, keeping the metal
well covered with charcoal during the melting, no trouble is found in casting
good bearings with this metal. The copper and the phosphor-bronze can be
put in the pot before putting it in the melting-hole. The tin and lead should
be added after the pot is taken from the fire.
It is not known whether the use of a little zinc, or possibly some other
combination, might not give still better results. For the present, however,
this alloy is considered to fulfil the various conditions required for good
bearing-metal better than any other alloy. The phosphor-bronze had an
ultimate tensile strength of 30,000 Ibs., with 6# elongation, whereas the alloy
" B " had 24,000 Ibs. tensile strength and \\% elongation.
White Metal for Engine Bearings. (Report of a British Naval
Committee, Eng'g, July 18, 1902.)— For lining bearings, crankpin bushes, and
other parts exclusive of cross-head bushes: Tin 12, copper 1, antimony 1.
Melt 6 tin 1 copper, and 6 tin 1 antimony separately and mix the two together.
For cross-head bushes a harder alloy, viz., 85$ tin, 5$ copper, 10% antimony,
has given good results.
(For other bearing-metals, see Alloys containing antimony, on next page.)
336
ALLOYS.
ALLOYS CONTAINING ANTIMONY.
VARIOUS ANALYSES OF BABBITT METAL AND OTHER ALLOYS CONTAINING
ANTIMONY.
Tin.
Copper
Antimony.
Zinc.
Lead.
Bismuth.
Babbitt metal 1 50
for light duty j=89.3
Harder Babbitt | 96
for bearings* j" = 88. 9
Britannia 85.7
" 81 9
1
1.8
4
3.7
1.0
5 parts
8.9perct.
8 parts
7.4perct.
10.1
16.2
16.
25.5
62.
13.
7.1
10.
2.9
1.9
I.
" .... 81.0
" 70.5
" 22
"Babbitt" ... 45.5
Plate pewter . 89.3
White metal. . 85
2
4
10
1.5
I-8
6.
40 0
1.8
comotives.
Bearings on Ger. lo
* It is mixed as follows: Twelve parts of copper are first melted and then
36 parts of tin are added; 24 parts of antimony are put in, and then 36 parts
of tin, the temperature being lowered as soon as the copper is melted in
order not to oxidize the tin and antimony, the surface of the bath being
protected from contact with the air. The alloy thus made is subsequently
remelted in the proportion of 50 parts of alloy to 100 tin. (Joshua Rose.)
Wliite-metal Alloys.— The following alloys are used as lining metals
by the Eastern Kailroad of France (1890):
Number.
3.
4..
Lead.
.. 65
.. 0
.. 70
.0 80
Antimony.
25
11.12
20
8
Tin.
0
83.33
10
12
Copper.
5.55
0
0
No. 1 is used for lining cross-head slides, rod-brasses and axle-bearings:
No. 2 for lining axle-bearings and connecting-rod brasses of heavy engines;
No. 3 for lining eccentric straps and for bronze slide-valves; and No. 4 for
metallic rod-packing.
Some of the best-known white-metal alloys are the following (Circular
of Hoveler & Dieckhaus, London, 1893):
Tin. Antimony. Lead.
1. Parsons'
2. Richards'
3. Babbitt's
4. Fentons'
5. French Navy.
6. German Navy
86
70
55
16
8?1
1
15
18
0
0
Copper.
2
Zinc.
27
0
0
79
87«
ould reduce the plasticity of the compound and make it brittle^
Hardest alloy of tin and lead: 6 tin, 4 lead. Hardest of all tin alloys (?): 74
"There are engineers who object to white metal containing lead or zinc.
This is, however, a prejudice quite unfounded, inasmuch as lead and zinc
often have properties of great use in white alloys."
It is a further fact that an "easy liquid" alloy must not contain more
than 18$ of antimony, which is an invaluable ingredient of white metal for
improving its hardness; but in no case must it exceed that margin, as this
would re '
Harde
tin, 18 antimony, 8 copper.
Alloy for thin open-work, ornamental castings: Lead 2, antimony 1.
White metal for patterns: Lead 10, bismuth 6, antimony 2, common brass 8,
tin 10.
Type-metal is made of various proportions of lead and antimony, from
17ft to 20$ antimony according to the hardness desired.
Babbitt Metals. (C. R. Tompkins, Mechanical Neius, Jan. 1891.)
The practice of lining journal-boxes with a metal that is sufficiently fusi-
ble to be melted in a common ladle is not always so much for the purpose
of securing anti-friction properties as for the convenience and cheapness of
forming a perfect bearing in line with the shaft without the necessity of
ALLOYS CONTAINING ANTIMONY. 337
feoring them. Boxes that are bored, no matter how accurate, require great
care in fitting and attaching them to the frame or other parts of a machine.
It is not good practice, however, to use the shaft for the purpose of cast-
ing the bearings, especially if the shaft be steel, for the reason that the hot
metal is apt to spring it; the better plan is to use a mandrel of the same
size or a trifle larger for this purpose. For slow-running journals, where
the load is moderate, aim ,st any metal that may be conveniently melted
and will run free will answer the purpose. For wearing properties, with a
moderate speed, there is probably nothing superior to pure zinc, but when
not combined with some other metal it shrinks so much in cooling that it
cannot be held firmly in the recess, and soon works loose; and it lacks those
anti-friction properties which are necessary in order to stand high speed.
For line-shafting, and all work where the speed is not over 300 or 400 r. p.
m., an alloy of 8 parts zinc and 2 parts block-tin will not only wear longer
than any composition of this class, but will successfully resist the force of
a heavy load. The tin counteracts the shrinkage, so that the metal, if not
overheated, will firmly adhere to the box until it is worn out. But this
mixture does not possess sufficient anti-friction properties to warrant its use
in fast-running journals.
Among all the soft metals in use there are none that possess greater anti-
friction properties than pure lead; but lead alone is impracticable, for it is so
soft that it cannot be retained in the recess. But when by any process lead
can be sufficiently hardened to be retained in the boxes without materially
injuring its anti-friction properties, there is no metal that will wear longer
in light fast-running journals. With most of the best and most popular
anti-friction metals in use and sold under the name of the Babbitt metal,
the basis is lead.
Lead and antimony have the property of combining with each other in
all proportions without impairing the an ti- friction properties of either. The
antimony hardens the lead, and when mixed in the proportion of 80 parts
lead by weight with 20 parts antimony, no other known composition of
metals possesses greater anti-friction or wearing properties, or will stand a
higher speed without heat or abrasion. It runs free in its melted state, has
no shrinkage, and is better adapted to light high-speeded machinery than
any other known metal. Care, however, should be manifested in using it,
and it should never be heated beyond a temperature that will scorch a dry
pine stick.
Many different compositions are sold under the name of Babbitt metal.
Some are good, but more are worthless; while but very little genuine Babbitt
metal is sold that is made strictly according to the original formula. Most
of the metals sold under that name are the refuse of type-foundries and
other smelting-works, melted and cast into fancy ingots with special brands,
and sold under the name of Babbitt metal.
It is difficult at the present time to determine the exact formulas used by
the original Babbitt, the inventor of the recessed box, as a number of differ,
ent formulas are given for that composition. Tin, copper, and antimony
were the ingredients, and from the best sources of information the original
proportions were as follows :
Another writer gives:
50partstin = 89. 3# 83. 3#
2parts copper = 3.6# 8.3#
4 parts antimony .... = 7.1# 8.3#
The copper was first melted, and the antimony added first and then about
ten or fifteen pounds of tin, the whole kept at a dull-red heat and constantly
stirred until the metals were thoroughly incorporated, after which the
balance of the tin was added, and after being thoroughly stirred again it
was then cast into ingots. When the copper is thoroughly melted, and
before the antimony is added, a handful of powdered charcoal should be
thrown into the crucible to form a flux, in order to exclude the air and pre-
vent the antimony from vaporizing; otherwise much of it will escape in the
form of a vapor and consequently be wasted. This metal, when carefully
prepared, is probably one of the best metals in use for lining boxes that are
subjected to a heavy weight and wear; but for light fast-running journals
the copper renders it more susceptible to friction, and it is more liable to
heat than the metal composed of lead and antimony in the proportions just
given.
338
STRENGTH OF MATERIALS.
SOLDERS.
Common solders, equal parts tin and lead ; fine solder, 2 tin to I lead; cheap
solder, 2 lead, 1 tin.
Fusing-point of tin- lead alloys:
Tin
to lead 25
" " 10.
" " 5.
" " 3.
" *' 2
" " 1.
...558°
...541
...511
...482
...441
...370
F.
Tin 1^ to lead 1 .
. .334°
..340
. 356
..365
..378
..381
F.
Common pewter contains 4 lead to 1 tin.
Gold solder: 14 parts gold, 6 silver, 4 copper. Gold solder for 14-carat
gold: 25 parts gold, 25 silver, 12^ brass, 1 zinc.
Silver solder: Yellow brass 70 parts, zinc 7, tin ll^j. Another: Silver 145
parts, brass (3 copper, 1 zinc) 73, zinc 4.
German-silver solder: Copper 38, zinc 54, nickel 8.
Novel's solders for aluminum:
Tin 100 parts, lead 5; melts at 536° to 572° F.
" 100 " zinc 5; " 536 to 612
"1000 " copper 10 to 15; " 662 to 842
"1000 " nickel 10 to 15; " 662 to 842
Novel's solder for aluminum bronze: Tin 900 parts, copper 100, bismuth 2
to 3. It is claimed that this solder is also suitable for joining aluminum to
copper, brass, zinc, iron, or nickel.
HOPES AND CABLES.
STRENGTH OF ROPES.
(A S. Newell & Co., Birkenhead. Klein's Translation, of Weisbach, vol. iii,
part 1, sec. 2.)
Hemp.
Iron.
Steel.
Girth.
Weight
per
Fathom.
Girth.
Weight
per
Fathom.
Girth.
Weight
per
Fathom.
Tensile
Strength.
Inches.
Pounds.
Inches.
Pounds.
Inches.
Pounds.
Gross tons.
2M
2
1
1
2
l^jj
1
1
3
3%
4
1%
2
4
1%
2V*»
ji£
ji£
5
41^
5
1<%
3
6
2
3^
JBX
2
7
5t<j
7
%i£
4
1M
31^
8
2^4
9
6
9
2%
5
J7^
3
10
2^
5V£
11
gLj'
10
2%
6
2
3^1a
12
2M
6V^
gix
4
13
7
12
2%-
7
2M
41^
14
3
71^
15
7^
14
3^
8
2%
5
16
3*4
gt^
17
8
16
3%
9
2L£
5V£
18
3/^
10
2%
6
20
gi^
18
3%
11
8%
6V^
22
3«^
12
24
91,^
S2
3%
13
3/4
8
26
10
26
4
14
28
11
30
4/4
15
3%
9
30
4%
16
82
4LZ
18
3L£
10
86
12
84
4^
20
3^4
12
40
STRENGTH OF ROPES.
Flat Ropes.
339
Hemp.
Iron.
Steel.
Girth.
Weight
per
Fathom .
Girth.
Weight,
per
Fathom .
Girth.
Weight
per
Fathom.
Tensile
Strength.
Inches.
Pounds.
Inches.
Pounds.
Inches.
Pounds.
Gross tons.
4 x ^
20
J2M x ^
11
20
5 x ^
24
21^j X l^j
13
23
5^ x §•§
26
294 x%
15
27
5^4 x 1^2
28
3 x ^
16
2 x^
10
28
6 x i|
30
3J4 x %
18
2J4 x V6
11
32
7 x %
36
31^3 x %
20
2/4 x ^
12
36
gi^ x 2J^
40
3MX 11/16
22
2^ x ^
13
40
8^ x 2^4
45
4 x 11/16
25
2% x %
15
45
9 x &/2
50
4}^ x %
28
8 x ^
16
50
9^ x 2%
55
41^ x^
32
^/4 x %
18
56
*0 x 2^2
60
4%x^[
34
3^x%
20
60
Working Load, Diameter, and Weight of Ropes and
Chains. (Klein's Weisbach, vol. iii, part 1, sec. 2, p. 561.)
Hemp ropes: d = diam. of rope. Wire rope: d = diam. of wire, n =
number of wires, G = weight per running foot, k = permissible load in
pounds per square inch of section, P = permissible load on rope or chain.
Oval chains : d = diam of iron used ; inside dimensions of oval 1.5d and
2.6d. Each link is a piece of chain 2.6d long. G0 = weight of a single link =
2.10d3 Ibs. ; G = weight per running foot = 9.73d2 Ibs.
fc (Ibs.) =
d (ins.) =
P(lbs.) =
Hempen Rope.
Wire Rope.
Dry and Untarred.
Wet or Tarred.
1420
1120d2 = 28550
1.28d2 = 0.00035P
1160
0.033 tfp
1.54d2 = 0.0005P
17000
0.0087 \ —
13350nd» =r 4590(7
fc (Ibs.) =
d (ins.) =
P(lbs.) =
G (Ibs.) =
Open-link Chain.
Stud-link Chain.
8500
0.0087 VP
13350d« = 13606?
9.73d2 - 0.000737P
11400
0.0076 I/P
17800d2 = 1660(7
10.65d2 = 0.0006P
Stud Chains 4/3 times as strong as open-link variety. [This is contrary to
the statements of Capt. Beardslee, U. S. N., in the report of the U, S. Test
Board. He holds that the open link is stronger than the studded link. See
p. 308 ante].
340
STRENGTH OF MATERIALS.
STRENGTH AND WEIGHT OF WIRE ROPE, HEMPEN ROPE, AND
CHAIN CABLES. (Klein's Weisbach.)
Breaking Load
in tons of
2240 Ibs.
Kind of Cable.
Girth of Wire Rope
and of Hemp Rope
Diameter of Iron
of Chain, inches.
Weight of One
Foot In length.
Pounds.
1 Ton
( Wire Rope
K Hemp Rope
( Chain
( Wire Ropo
•< Hemp Rope
( Chain
( Wire Rope
K Hemp Rope
( Chain
j Wire Rope
•< Hemp Rope
| Chain
j Wire Rope
•< Hemp Rope
( Chain
Wire Rope
K Hemp Rope
( Chain
j Wire Rope
•< Hemp Rope
( Chain
Wire Rope
Hemp Rope
Chain
Wire Rope
Hemp Rope
Chain
j Wire Rope
•< Hemp Rope
( Chain
1.0
2.0
^
5.0
&
7.0
11/16
3.0
8.0
13/16
3.5
9.0
29/32
4.0
10.0
31/32
4.5
11.0
1.1/16
5.0
12.5
1.3/16
5.5
14.0
1.5/16
6.0
15.0
1.7/16
0.125
0.177
0.500
0.438
0.978
2.667
0.753
2.036
4.502
1.136
2.365
6.169
1.546
3.225
7.674
2.043
4.166
8.836
2.725
5.000
10.335
3.723
5.940
13.01
4.50
6.94
16.00
5.67
7.92
19.16
8 Tons
12 Tons
16 Tons......,, ...
20 Tons
24 Tons
30 Tons
36 Tons
44 Tons...
54 Tons
Length sufficient to provide the maximum working stress :
Hempen rope, dry and untarred 2855 feet.
14 wetortarred 1975 "
Wire rope 4590 *'
Open-link chain 1360 '•
Stud chain 1660 *
Sometimes, when the depths are very great, ropes are given approximately
the form of a body of uniform strength, by making them of separate pieces,
whose diameters diminish towards the lower end. It is evident that by this
means the tensions in the fibres caused by the rope's own weight can be
considerably diminished.
Rope for Moisting or Transmission. Manila Rope
(C. W. Hunt Company, New York.) — Rope used for hoisting or for trans-
mission of power is subjected to a very severe test. Ordinary rope chafes
and grinds to powder in the centre, while the exterior may look as though
it was little worn.
In bending a rope over a sheave, the strands and the yarns of these strands
slide a small distance upon each other, causing friction, and wear the rope
internally.
The " Stevedore " rope used by the C. W. Hunt Co. is made by lubricating
the fibres with plumbago, mixed with sufficient tallow to hold it in position.
This lubricates the yarns of the rope, and prevents internal chafing and
wear. After running a short time the exterior of the rope gets compressed
and coated with the lubricant.
In manufacturing rope, the fibres are first spun into a yarn, this yarn
being twisted in a direction called "right hand." From 20 to 80 of these
yarns, depending on the size of the rope, are then put together and twisted
m the opposite direction, or "left hand," into a strand. Three of these
STRENGTH OF RO£ES. 341
strands, for a 3-strand, or four for a 4-strand rope, are then twisted
together, the twist being again in the "right hand " direction. When the
strand is twisted, it untwists each of the threads, and when the three
strands are twisted together into rope, it untwists the strands, but again
twists up the threads. It is this opposite twist that keeps the rope in its
E roper form. When a weight is hung on the end of a rope, the tendency is
;>r the rope to untwist, and become longer. In untwisting the rope, it
would twist the threads up, and the weight will revolve until the strain of
the untwisting strands just equals the strain of the threads being twisted
tighter. In making a rope it is impossible to make these strains exactly
balance each other. It is this fact that makes it necessary to take out the
"turns" in a new rope, that is, untwist it when it is put at work. The
proper twist that should be put in the threads has been ascertained approx-
imately by experience.
The amount of work that the rope will do varies greatly. It depends nofc
only on the quality of the fibre and the method of laying up the rope, but
also on the kind of weather when the rope is used, the blocks or sheaves
over which it is run, and the strain in proportion to the strain put upon the
rope. The principal wear comes in practice from defective or badly set
sheaves, from excess of load and exposure to storms.
The loads put upon the rope should not exceed those given in the tables,
for the most economical wear. The indications of excessive load will be the
twist coming out of the rope, or one of the strands slipping out of its proper
position. A certain amount of twist comes out in using it the first day or
two, but after that the rope should remain substantially the same. If it
does not, the load is too great for the durability of the rope. If the rope
wears on the outside, and is good on the inside, it shows that it has been
chafed in running over the pulleys or sheaves. If the blocks are very small,
it will increase the sliding of the strands and threads, and result in a more
rapid internal wear. Rope made for hoisting and for rope transmission is
usually made with four strands, as experience has shown this to be the most
serviceable.
The strength and weight of " stevedore " rope is estimated as follows:
Breaking strength in pounds = 720 (circumference in inches)2;
Weight in pounds per foot = .032 (circumference in inches)2.
The Technical Words relating to Cordage most frequently
heard are:
YARN. — Fibres twisted together.
THREAD.— Two or more small yarns twisted together.
STRING.— The same as a thread but a little larger yarns.
STRAND.— Two or more large yarns twisted together.
CORD.— Several threads twisted together.
ROPE.— Several strands twisted together.
HAWSER.— A rope of three strands.
SHROUD-LAID. — A rope of four strands.
CABLE. — Three hawsers twisted together.
YARNS are laid up left-handed into strands.
STRANDS are laid up right-handed into rope.
HAWSERS are laid up left-handed into a cable.
A rope is :
LAID by twisting strands together in making the rope.
SPLICED by joining to another rope by interweaving the strands.
WHIPPED. — By winding a string around the end to prevent untwisting.
SERVED.— When covered by winding a yarn continuously and tightly
around it.
PARCELED.— By wrapping with canvas.
SEIZED. — When two parts are bound together by a yarn, thread or string.
PAYED.— When painted, tarred or greased to resist wet.
HAUL. — To pull on a rope.
TAUT. — Drawn tight or strained.
Splicing of Ropes, — The splice in a transmission rope is not only the
weakest part of the rope but is the first part to fail when the rope is worn
out. If the rope is larger at the splice, the projecting part will wear on the
pulleys and the rope fail from the cutting off of the strands. The following
directions are given for splicing a 4-strand rope.
The engravings show each successive operation in splicing a 1% inch
manila rope. Each engraving was made from a full-size specimen.
342
STRENGTH OF MATERIALS."
Fra. 81.
OF EOPKS.
SPLICING OF ROPES.
343
Tie a piece of twine, 9 and 10, around the rope to be spliced, about 6 feet
from each end. Then unlay the strands of each end back to the twine.
Butt the ropes together and twist each corresponding pair of strands
loosely, to keep them from being tangled, as shown in Fig. 78.
The twine 10 is now cut, and the strand 8 unlaid and strand "carefully laid
in its place for a distance of four and a half feet from the junction.
The strand 0 is next unlaid about one and a half feet and strand 5 laid in
its place.
The ends of the cores are now cut off so they just meet.
Unlay strand 1 four and a half feet, laying strand 2 in its place.
Unlay strand 3 one and a half feet, laying in strand 4.
Cut all the strands off to a length of about twenty inches, for convenience
in manipulation.
The rope now assumes the form shown in Fig. 79 with the meeting points
of the strands three feet apart.
Each pair of strands is successively subjected to the following operation:
From the point of meeting of the strands 8 and 7, unlay each one three
turns ; split both the strand 8 and the strand 7 in halves as far back as they
are now unlaid and " whip " the end of each half strand with a small
piece of twine.
The half of the strand 7 is now laid in three turns and the half of 8 also
laid in three turns. The half strands now meet and are tied in a simple
knot, 11, Fig. 80, making the rope at this point its original size.
The rope is now opened with a marliii spike and the half strand of 7
worked around the half strand of 8 by passing the end of the half strand 7
through the rope, as shown in the engraving, drawn taut and again worked
around this half strand until it reaches the half strand 13 that was not laid
in. This half strand 13 is now split, and the half strand 7 drawn through
the opening thus made, and then tucked under the two adjacent strands, as
shown in Fig. 81. The other half of the strand 8 is now wound around the
other half strand 7 in the same manner. After each pair of strands has
been treated in this manner, the ends are cut off at 12, leaving them about
four inches long. After a few days' wear they will draw into the body of the
rope or wear off. so that the locality of the splice can scarcely be detected.
Coal Hoisting. (C. W. Hunt Co.).— The amount of coal that can be
hoisted with a rope varies greatly. Under the ordinary conditions of use
a rope hoists from 5000 to 8000 tons. Where the circumstances are more
favorable, the amounts run up frequently to 12,000 or 15,000 tons, occasion-
ally to 20,000 and in one case 32,400 tons to a single fall.
When a hoisting rope is first put in use, it is likely from the strain put upon
it to twist up when the block is loosened from the tub. This occurs in the
first day or two only. The rope should then be taken down and the
" turns " taken out of the rope. When put up again the rope should give
no further trouble until worn out.
It is necessary that the rope should be much larger than is needed to bear
the strain from the load.
Practical experience for many years has substantially settled the most
economical size of rope to be used which is given in the table below.
Hoisting ropes are not spliced, as it is difficult to make a splice that will
not pull out while running over the sheaves, and the increased wear to be
obtained in this way is very small.
Coal is usually hoisted with what is commonly called a " double whip; "
that is, with a running block that is attached to the tub which reduces the
strain on the rope to approximately one half the weight of the load hoisted.
The following table gives the usual sizes of hoisting rope and the proper
working strain:
Stevedore Hoisting-rope.
C. W. Hunt Co.
Circumference of
the rope in ins.
Proper Working
Strain on the Rope
in Ibs.
Nominal size of
Coal tubs. Double
whip.
Approximate
Weight of a Coil,
in Ibs.
3
f«
¥
350
500
650
800
1000
1/6 to 1/5 tons.
1/5 ;; g ;;
360
480
650
830
960
Hoisting rope is ordered by circumference, transmission rope by diameter.
344
STRENGTH OF MATERIALS.
Weight and Strength of Manila Rope*
Spencer Miller (Enq^g Neivs, Dec. 6, 1890) gives a table of breaking strength
which varies from 900 for y%" to 700 for 2" diameter rope, as below:
Circumference
Coefficient
2 2Jrf
845 82i
3
780
4J4 ft
745 73
,_ 5 5^ 6
735 725 712
700
The following table gives the breaking strength of manila rope as cal-
culated by Mr. Hunt's formula, and also by Mr. Miller^s, using in the latter
the coefficient 900 for sizes "below 1^ in. circumference and 700 for sizes above
6 in. The differences between the figures for any given size are probably
not greater than the difference in actual strength of samples from different
makers. Both sets of figures are considerably lower than those given in
tables published by some makers of rope, but they are believed to be more
reliable. The figures for weight per 100 ft. are from manufacturers' tables.
B
i
•4-1 4J (D
e s 5.
Ultimate
£
^,
et-i 4-> D
Q jj p
Ultimate
s* .
<D 02
+3 0)
®J3
go
.» d .
Is*
S3 O y
<£ o
«fcfl[5 «
A ^^
fc£o ~
Strength of
Rope in Ibs.
Jig
<uS
g^>
S a .
t-t-S «j
S o,S
3 §•§
-^rf
'So "
Strength of
Rope in Ibs.
§.2
•j a ~
l* 0).5
?So.S
°3.3
eel •s'S'go
5
b
&
Hunt.
Miller.
s
0
EC
Hunt.
Miller.
3/16
9/16
2
230
280
1 5/16
4
52
11,500
12,000
^4
H
3
400
500
1%
4U
58
13,000
13,500
5/1 G
1
4
630
790
li^j
4|2
65
14,600
14,900
%
m
5
900
1,140
1 9/16
4%
72^
16,200
16,500
7/16
m
6
1,240
1,550
m
5
80
18,000
18,100
1^
m
Tfc
1,620
2,020
1%
5^
97
21,800
21.500
9/16
1%
11
2,050
2,480
2
6
113
25,900
25,200
%
2
13^
2,880
3,380
2^j
6^
133
30,400
29,600
%
2J4
16^
3,610
4,150
2J4
r.
153
35,300
34,300
13/13
2V6
20
4,500
5,030
**fy%.
7H
184
40,500
39,400
%
2%
23%
5,440
5,970
2%
8
211
46,100
44,800
3
28^
6,480
7,020
2^
8^
237
5'2.000
50,600
1 1/16
314
33^
7,600
8,160
3
9
262
58,300
56,700
3}4
38
8,820
9,370
3/^
»H
293
65,000
63,200
VA
3^
45
10,120
10,090
3^
10
325
72,000
70,000
For rope-driving Mr. Hunt recommends that the working strain should
not exceed 1/20 of the ultimate breaking strain. For further data on ropes
see " Rope-d living."
Knots.— A great number of knots have been devised of which a few
only are illustrated, but those selected are the most frequently used. In
the cuts. Fig. 82, they are shown open, or before being drawn taut, in order
to show the position of the parts. The names usually given to them are:
P. Flemish loop.
Q. Chain knot with toggle.
R. Half-hitch.
S. Timber-hitch.
T. Clove-hitch.
U. Rolling-hitch.
V. Timber-hitch and half -hitch.
W. Blackwall-hitch.
X. Fisherman's bend.
A. Bight of a rope.
B. Simple or Overhand knot.
C. Figure 8 knot.
Double knot.
Boat knot.
Bowline, first step.
Bowline, second step.
Bowline completed.
Square or reef knot.
Sheet bend or weaver's knot.
Sheet bend with a toggle.
Carrick bend.
M. Stevedore knot completed.
N. Stevedore knot commenced.
O. Slip knot.
D.
K.
F.
G.
H.
I.
J.
K.
L.
Y. Round turn and half-hitch.
Z. Wall knot commenced.
A A. " " completed.
B B. Wall knot crown commenced.
C C. ** ** " completed.
KNOTS.
345
The principle of a knot is that no two parts, which would move in the
same direction if the rope were to slip, should lay along side of and touch-
ing each other.
The bowline is one of the most useful knots, it will not slip, and after
being strained is easily untied. Commence by making a bight in the rope,
then put the end through the bight and under the standing part as shown in
(?, then pass the end again through the bight, and haul tight.
The square or reef knot must not be mistaken for the " granny " knot
that slips under a strain. Knots H, K and M are easily untied after being
under strain. The knot M is useful when the rope passes through an eye
and is held by the knot, as it will not slip and is easily untied after being
strained.
ABC 0 E
FIG. 82.— KNOTS,
The timber hitch S looks as though it would give way, but it will not; the
greater the strain the tighter it will hold. The wall knot looks complicated,
but is easily made by proceeding as follows: Form a bight with strand 1
and pass the strand 2 around the end of it, and the strand 3 round the end
of 2 and then through the bight of 1 as shown in the cut Z. Haul the ends
taut when the appearance is as shown in AA. The end of the strand 1 is
now laid over the centre of the knot, strand 2 laid over 1 and 3 over 2, when
the end of 3 is passed through the bight of 1 as shown in BB. Haul all the
strands taut as shown in CG.
346
STRENGTH OF MATERIALS.
To Splice a "Wire Rope.— The tools required will be a small marline
spike, nipping cutters, and either clamps or a small hemp-rope sling with
which to wrap around and untwist the rope. If a bench-vise is accessible
it will be found convenient.
In splicing rope, a certain length is used up in making the splice. An
allowance of not less than 16 feet for ^ inch rope, and proportionately
longer for larger sizes, must be added to the length of an endless rope in
ordering.
Having measured, carefully, the length the rope should be after splic-
ing, and marked the points M and M', Fig. 83, unlay the strands from each
end 2£and E' to M and M' and cut off the centre at M and M', and then:
(1). Interlock the six unlaid strands of each end alternately and draw
them together so that the points M and M' meet, as in Fig. 84.
(2). Unlay a strand from one end, and following the unlay closely, lay into
the seam or groove it opens, the strand opposite it belonging to the other
end of the rope, until within a length equal to three or four times the length
-. of one lay or the rope, and cut the other strand to about the same length
from the point of meeting as at A, Fig. 85.
(3). Unlay the adjacent strand in the opposite direction, and following the
unlay closely, lay in its place the corresponding opposite strand, cutting the
ends as described before at J5, Fig. 85.
There are now four strands laid in place terminating at A and J9, with the
eight remaining at M Mf, as in Fig. 85.
It will be well after laying each pair of strands to tie them temporarily at
the points A and B.
Pursue the same course with the remaining four pairs of opposite strands,
FIG. 83.
Fia. 86. FIG. 87.
SPLICING WIRE ROPE.
stopping each pair about eight or ten turns of the rope short of the preced-
ing pair, and cutting the ends as before.
We now have all the strands laid in their proper places with their respect-
ive ends passing each other, as in Fig. 86.
All methods of rope-splicing are identical to this point: their variety con-
sists in the method of tucking the ends. The one given below is the one
most generally practiced.
Clamp the rope either in a vise at a point to the left of A, Fig. 86, and by a
hand-clamp applied near A, open up the rope by untwisting sufficiently to
cut the core at A, and seizing it with the nippers, let an assistant draw it
out slowly, you following it closely, crowding the strand in its place until it
is all laid in. Cut the core where the strand ends, and push the end back
into its place. Remove the clamps and let the rope close together around it.
Draw out the core in the opposite direction and lay the other strand in the
centre of the rope, in the same manner. Repeat the operation at the five
remaining points, and hammer the rope lightly at the points where the ends
pass each other at A, A, B, B, etc., with small wooden mallets, and the
splice is complete, as shown in Fig. 87.
If a clamp and vise are not obtainable, two rope slmgs and short wooden
levers may be used to untwist and open up the rope.
A rope spliced as above will be nearly as strong as the original rope and
smooth everywhere. After running a few days, the splice, if well made,
cannot be found except by close examination.
The above instructions have been adopted by the leading rope manufac-
turers of America.
HELICAL STEEL SPRIXGS. 347
SPRINGS.
•definitions.— A spiral spring is one which is wound around a fixed
point or centre, and continually receding from it like a watch spring. A
helical spring is one which is wound around an arbor, and at the same time
advancing like the thread of a screw. An elliptical or laminated spring is
made of flat bars, plates, or "leaves,11 of regularly varying lengths, super-
posed one upon the other.
Laminated Steel Springs.— Clark (Rules, Tables and Data) givea
the following from his work on Railway Machinery, 1855:
A = elasticity, or deflection, in sixteenths of an inch per ton of load,
s — working strength, or load, in tons (2240 Ibs.),
L = span, when loaded, in inches,
b = breadth of plates, in inches, taken as uniform,
t — thickness of plates, in sixteenths of an inch,
n = number of plates.
NOTE.— The span and the elasticity are those due to the spring when
weighted.
2 When extra thick back and short plates are used, they must be replaced
by an equivalent number of plates of the ruling thickness, prior to the em-
ployment of the first two formulae. This is found by multiplying the num-
ber of extra thick plates by the cube of their thickness, and dividing by the
cube of the ruling thickness. Conversely, the number of plates of the ruling
thickness given by the third formula, required to be deducted and replaced
by a given number of extra thick plates, are found by the same calculation.
3. It is assumed that the plates are similarly and regularly formed, and
that they are of uniform breadth, and but slightly taper at the ends.
Reuleaux's Constructor gives for semi-elliptic springs:
Snbh* GPl*
P=~6T and '-ISW?''
S = max. direct fibre-strain in plate; b = width of plates;
n = number of plates in spring; h = thickness of plates;
I = one half length of spring; / = deflection of end of spring;
P = load on one end of spring; E = modulus of direct elasticity.
The above formula for deflection can be relied upon where all the plates
of the spring are regularly shortened; but in semi-el Jiptic springs, as used,
there are generally several plates extending the full length of the spring,
and the proportion of these long plates to the whole number is usually about
one fourth. In such cases/ = ^y (&• R- Henderson, Trans. A. S. M. E.,
vol. xvi.)
In order to compare the f ormulee of Reuleaux and Clark we may make
the following substitutions in the latter: s in tons = P in Ibs. -*- 1120; AS =
16/; L = 2Z; t ^ 16/t; then
which corresponds with Reuleaux's formula for deflection if in the latter we
take E = 33,162,800.
P 256n67i» 12,687n67i»
Also , = —*.——, whence P--^ - ,
which corresponds with Reuleaux's formula for working load when Sin the
latter is taken at 76,120.
The value of E is usually taken at 30,000,000 and S at 80,000, in which case
Reuleaux's formulae become
13,333nb/i2
•r
Helical Steel Springs.— Clark quotes the following from the report
on Safety Valves (Trans, Inst. Engrs. and Shipbuilders in Scotland, 1874-5):
348 SPRINGS.
E = compression or extension of one coil in inches,
d = diameter from centre to centre of steel bar constituting the spring
in inches,
w = weight applied, in pounds,
D = diameter, or side of the square, of the steel bar, in sixteenths of ai
inch,
C = a constant, which may be taken as 22 for round steel and 30 foi
square steel.
NOTE.— The deflection Efor one coil is to be multiplied by the number of
free coils, to obtain the total deflection for a given spring.
The relation between the safe load, size of steel, and diameter of coil, may
be taken for practical purposes as follows:
q '
~, for round steel;
or square steel
q '
= ,//
Rankine's Machinery and Millwork, p. 390, gives the following:
W cd* .196/^3 12.566n/r*
T -eE^5 W* = —T-* V*= - ~cd~ 5
Wt
—^ = greatest safe sudden load.
In which d is the diameter of wire in inches; c a co-efficient of transverse
elasticity of wire, say 10,500,000 to 12,000,000 for charcoal iron wire and steel;
r radius to centre of wire in coil; n effective number of coils; /greatest safe
shearing stress, say 30,000; W any load not exceeding greatest safe load;
v corresponding extension or compression; Wj greatest safe load; and vl
greatest safe steady extension or compression.
If the wire is square, of the dimensions d x d, the load for a given deflec-
tion is greater than for a round wire of the diameter d in the ratio of 2.81 tc
1.96 or of 1.43 to 1, or of 10 to 7, nearly.
Wilson Hartnell (Proc. Inst. M. E., 1882, p. 426), says: The size of a spiral
spring may be calculated from the formula on page 304 of " Rankine's Use
ful Rules and Tables"; but the experience with Salterns springs has showr
that the safe limit of stress is more than twice as great as there given
namely 60,000 to 70,000 Ibs. per square inch of section with % inch wire, auc
about 50,000 with % inch wire. Hence the work that can be done by
springs of wire is four or five times as great as Rankine allows.
For % inch wire and under,
Weight in ibs. to deflect spring , in. = g
The work in foot-pounds that can be stored up in a spiral spring woulc
lift it above 50 ft.
In a few rough experiments made with Salter's springs the coefficient oi
rigidity was noticed to be 12,600,000 to 13,700,000 with % inch wire; 11,000,0(X
for 11/32 inch; and 10,600,000 to 10,900,000 for % inch wire.
Helical Springs.— J. Begtrup, in the American Machinist of Aug
18, 1892, gives formulas for the deflection and carrying capacity of helica
springs of round and square steel, as follow:
V-**>F^ 1
" round steel.
*r=. 471^1
HELICAL SVKIKGS.
349
fF s= carrying capacity in pounds,
8 = greatest tensile stress per square inch of material,
d = diameter of steel,
D = outside diameter of coil,
F = deflection of one coil,
E = torsional modulus of elasticity,
P = load in pounds.
From these formulas the following table has been calculated by Mr. Beg-
trup. A spring being made of an elastic material, and of such shape as to
allow a great amount of deflection, will not be affected by sudden shocks or
blows to the same extent as a rigid body, and a factor of safety very much
less than for rigid constructions may be used.
HOW TO USE THE TABLE.
When designing a spring for continuous work, as a car spring, use a
greater factor of safety than in the table; for intermittent working, as in
a steam-engine governor or safety valve, use figures given in table; for
square steel multiply line W by 1.2 and line F by .59.
Example 1.— How much will a spring of %" round steel and 3" outside
diameter carry with safety ? In the line headed D we find 3, and right un-
derneath 473, which is the weight it will carry with safety. How many coils
must this spring have so as to deflect 3" with a load of 400 pounds ? Assum-
ing a modulus of elasticity of 12 millions we find in the centre line headed
F the figure .0610; this is deflection of one coil for a load of 100 pounds;
therefore .061 X 4 = .244" is deflection of one coil for 400 pounds load, and 3
.244 = 12}^ is the number of coils wanted. This spring will therefore be
ind stretch to 7%".
" steel is wound close;
cceeding the limit of safety ? We
find maximum safe load for this spring to be 702 pounds, and deflection of
one coil for 100 pounds load .0405 inches; therefore 7.02 x .0405 = .284" is the
greatest admissible opening between coils. We may thus, without know-
ing the load, ascertain whether a spring is overloaded or not.
Carrying Capacity and Deflection of Helical Springs of
Round Steel.
d — diameter of steel. D = outside diameter of coil. W = safe working
load in pounds— tensile stress not exceeding 60,000 pounds per square inch.
F = deflection by a load of 100 pounds of one coil, and a modulus of elasti-
city of 10, 12 and 14 millions respectively. The ultimat e carrying capacity
will be about twice the safe load.
tb «o
°'l
'tt
la
A
D
W
H
D
W
-\
.25
35
.0276
.0236
.0197
.50
15
.3588
.3075
.2562
.75
9
1.433
1.228
1.023
1.00
7
3.562
3.053
2.544
1.25
5
7.250
6.214
5.178
1.50
4.5
12.88
11.04
9.200
1.75
3.8
20.85
17.87
14.89
2.00
3.3
31.57
27.06
22.55
,
.50
107
.0206
.0176
.0147
.75
65
.0937
.0804
.0670
1.00
46
.2556
.2191
.182
1.25
36
.5412
.4639
.3866
1.50
29
.9856
.8448
.7010
1.75
25
1.624
1.392
1.160
2.00
22
2.492
2.136
1.780
2.25
19
3.625
3.107
2.589
2.50
17
5.056
4.334
3.612
"ill
tJ
v
X
11
•8
D
W
H
75
241
.0137
.0118
.0098
1.00
167
.0408
.0350
.0292
1.25
128
.0907
.0778
.0648
1.50
104
.1703
.1460
.1217
1.75
88
.2866
.2457
.2048
2.00
75
.4466
.3828
.3190
2.25
66
.6571
.5632
.4693
2.50
59
.9249
.7928
.6607
2.75
53
1.256
1.077
.8975
3.00
49
1.660
1.423
1.186
D
W
*\
1.25
368
.0190
.0171
.0142
1.50
294
.0389
.0333
.0278
1.75
245
.0672
.0576
.0480
2.00
210
.1067
.0914
.0762
2.25
184
.1593
.1365
.1137
2.50
164
.2270
.1944
.1610
2.75
147
.3109
.2665
.2221
3.00
134
.4139
.3548
.2957
3.25
123
.5375
.4607
.3839
3.50
113
6835
5859
4883
350
SPKIKGS.
Carrying Capacity and Deflection of 'Helical Springs of
Round Steel.— (Continued).
cb
s
It
*8
D
W
*\
1.50
605
.0136
.0117
.0097
1.75
500
.0242
.0207
.0173
2.00
426
.0392
.0336
.0280
2.25
371
.0593
.0508
.0424
2.50
329
.0854
.0732
.0610
2.75
295
.1187
.1012
.0853
3.00
267
.1583
.1357
.1131
3.25
245
.2066
.1771
.1476
3.50
226
.2640
.2263
.1886
3.75
209
.3312
.2839
.2366
4.00
195
.4089
.3505
.2921
!?
ii
•8
D
W
H
2.00
765
.0169
.0145
.0120
2.25
663
.0259
.0222
.0185
2.50
589
.0377
.0323
.0269
2.75
523
.0528
.0452
.0376
3.00
473
.0711
.0610
.0508
3.25
433
.0935
.0801
.0668
3.50
398
.1200
.1029
.0858
3.75
368
.1513
.1297
.1081
4.00
343
.1874
.1606
.1338
4.25
321
.2290
. 1963
.1635
4.50
301
.2761
.2367
.1972
<b
g
II
•8
D
W
3
2.00
1263
.0081
.0069
.0058
2.25
1089
.0126
.0108
.0090
2.50
957
.0186
.0160
.0133
2.75
853
.0262
.0225
.0187
3.00
770
.0357
.0306
.0255
3.25
702
.0472
.0405
.0337
3.50
644
.0617
.0529
.0441
3.75
596
.0772
.0661
.0551
4.00
544
.0960
.0823
.0686
4.50
486
.1423
.1220
.1017
5.00
432
.2016
.1728
.1440
SR
ii
•8
D
W
$
2.00
1963
.0042
.0036
.0030
2.25
1683
.0067
.0057
.0048
2.50
1472
.0099
.0085
.0071
2.75
1309
.0141
.0121
.0101
3.00
1178
.0194
.0167
.0139
3.25
1071
.0259
.0222
.0185
3.50
982
.0336
.0288
.0240
3.75
906
.0427
.0366
.0305
4.00
841
.0534
.0457
.0381
4.50
735
.0796
.0683
.0569
5.00
654
.1134
.0972
.0810
b
1
II
•8
D
W
H
2.50
2163
.0056
.0048
.0040
2.75
1916
.0081
.0070
.0058
3.00
1720
.0112
.0096
.0080
3.25
1560
.0151
.0129
.0108
3.50
1427
.0197
.0169
.0141
3.75
1315
.0252
.0216
.0180
4.00
1220
.0316
.0271
.0225
4.25
1137
.0390
.0334
.0278
4.50
1065
.0474
.0406
.0339
5.00
945
.0679
.0582
.0485
5.50
849
.0935
.0801
.0668
fe
II
t3
D
W
•\
2.50
3068
.0034
.0029
.0024
2.75
2707
.0049
.0042
.0035
3.00
2422
.0068
.0058
.0049
3.25
2191
.0092
.0079
.0066
3.50
2001
.0121
.0104
.0086
3.75
1841
.0155
.0133
.0111
4.00
1704
.0196
.0168
.0140
4.25
1587
.0243
.0208
.0173
4.50
1484
.0297
.0254
.0212
5.00
1315
.0427
.0366
.0305
5.50
1180
.0591
.0506
.0422
III
«>
D
W
1
3.00
3311
.0043
.0037
.0030
3.25
2988
.0058
.0050
.0042
3.50
2723
.0077
.0066
.0055
3.75
2500
.0100
.0086
.0071
4.00
2311
.0127
.0108
.0090
4.25
2151
.0157
.0135
.0112
4.50
2009
.0193
.0165
.0138
4.75
1885
.0233
.0200
.0167
5.00
1776
.0279
.0239
.0199
5.50
1591
.0388
.0333
.0277
6.00
1441
.0522
.0447
.0373
It
II
•8
D
W
1
3.00
4418
.0028
.0024
.0020
3.25
3976
.0038
0033
.0027
3.50
3615
.0051
.0044
.0036
3.75
3313
.0066
.0057
.0047
4.00
3058
.0084
.0072
.0060
4.25
2810
.0105
.0090
.0075
4.50
2651
.0129
.0111
.0093
4.75
2485
.0157
.0135
.0113
5.00
2339
.0189
.0162
.0135
5.50
2093
.0264
.0226
.0188
6.00
1893
.0356
.0305
.0254
Is
II
•8
D
W
ii
3.50
6013
.0021
.0018
.0015
3.75
5490
.0027
.0024
.0020
4.00
5051
.0035
.0030
.0025
4.25
4676
.0045
.0038
.0032
4.50
4354
.0055
.0047
.0039
4.75
4073
.0067
.0058
.0048
5.00
3826
.0081
.0070
.0058
5 25
3607
.0097
.0083
.0059
5.50
3413
.0115
.0098
.0082
6.00
3080
.0156
.0134
.0112
6.50
2806
.0207
.0177
.0148
2
rt
ts
D
W
-I
3.50
9425
.0012
.0010
.0008
3.75
8568
.0016
.0014
.0011
4.00
7854
.0021
.0018
.0015
4.25
7250
.0026
.0023
.0019
4.50
6732
.0033
.0028
.0023
4.75
6283
.0041
.0035
.0029
5.00
5890
.0049
.0043
.0035
5.25
5544
.0059
.0051
.0043
5.50
5236
.0071
.0061
.0051
6.00
4712
.0097
.0083
.0069
6.50
4284
.0129
.0111
.001)2
The formulae for deflection or compression given by Clark, Hartneli, and
Begtrup, although very different in form, show a substantial agreement
when reduced to the same form. Let d = diameter of wire in inches, Dl 2=
mean diameter of coil, n the number of coils, w the applied weight ia
pounds, and C a coefficient, then
HELICAL SPRINGS. 35i
Compression or extension of one coil = -fr-nfl
Cd4
Weight in pounds to cause comp. or ext. of 1 in. = 3.
The coefficient C reduced from Hartnell's formula is 8 X 180,000 = 1,440,000;
according to Clark, 16* X 22 = 1,441,792, and according to Begtrup (using
12,000,000 for the torsional modulus of elasticity) = 12,000,000-4- 8 = 1,500,000.
12 566j//r2
Rankine's formula for greatest safe extension, vl = '' . ' — may take
the form vl = '^o^f1' if we use 30'000 and 32,000,000 as the values for/
and c respectively.
The several formulae for safe load given above may be thus compared.
letting d = diameter of wire, and Dl — mean diameter of coil, Raukine,
w = i; Clark, TT= * ; Begtrup, W= ; Hartnell.
vl vl
Substituting for/ the value 30,000 given by Rankine, and for
S, 60,000 as given by Begtrup, we have W= 11,760 4r Rankine ; 12,238 ~
JJl U\
Clark; 23,562 ~ Begtrup; 24,000 ~ Hartnell.
L>i U\
Taking from the Pennsylvania Railroad specifications the capacity when
closed of the following springs, in which d — diameter of wire, D diameter
outside of coil. Dl = D — d, c capacity, H height when free, and h height
when closed, all in inches.
No. T. d = y± D = iyz Dl = 1M c = 400 H= 9 h = 6
8. Y2 3 214 1,900 8 5
K. M 5% 5 2,100 7 4}>4
D. 1 54 8,100 10^ 8
/. 1J4 8 6M 10,000 9 5%
C. iy8 tf/8 3M 16,000 4% 3%
d3
and substituting the values of c in the formula c — W = x— we find ar, the
coefficient of ~ to be respectively 32,000; 38,000; 3-2,400; 24,888; 34,560;
42,140, average 34,000.
Taking 12,000 as the coefficient of — according to Rankine and Clark for
safe load, and 24,000 as the coefficient1 according to Begtrup and Hartnell,
we have for the safe load on these springs, as we take one or the other co-
efficient,
T. S. K. D. I. C.
Rankine and Clark ........ _____ 150 600 1,012 3,000 3,750 5,400 Ibs.
Hartnell. .. ...... 300 1.200 2,0'.'4 6,000 7,500 10,800 4'
Capacity when closed, as above 400 1,000 2,100 8,100 10,000 16,000 "
J. W. Cloud (Trans. A. S. M. E., v. 173) gives the following:
Sird* WPRn
P--- and f=-r>
P = load on spring;
£ = maximum shearing fibre-strain in bar;
d = diameter of steel of which spring is made;
B — radius of centre of coil;
I = length of bar before coiling;
G = modulus of shearing elasticity;
/ = deflection of spring under load.
Mr. Cloud takes 8 = 80,000 and G = 12,600,000.
The stress in a helical spring is almost wholly one of torsion. For method
ef deriving the formulae for springs from torsioual formula see Mr. Cloud's
paper, above quoted.
352
SPRINGS.
ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS.
Pennsylvania Railroad Specifications, 189t>.
&
,.H
^ a
*
Tests.
Class.
.ogr
> a>
Plates.
,a <B
PI °
No. Size, in.
tl
.0
5 s
"3"*
Ins. high. Ibs.
(«) (b)
Ins. Ibs.
•^•3
£71, Triple
40
11%
5 3x11/32
334 0% 4800
3 5500
2
£72, Quadruple
£73, Triple
40
36
11%
6 3x11/32
3% 9% 6650
4 9% COOO
3 8000
2
£74, Singlet...
40
—
8 -
5* - free
3 2350
£75, " f...
40
—
7 3x%
IIBB* — 3000
0 4970
—
£76, " f...
42
—
1J4* — 4375
0 6350
£77, Triple
36
ii%
8 3 x' 11/3:2
2^ gi£ 11,800
—
£78, Double
32
7^
6 3x%
3 9 8000
— —
—
£79, kl ....
36
9V6
5 4x11/32
3^ 8r7s 5400
3 6000
_
£7 10, Quadruple
40
4 10 8000
3 10,000
2
£711, "
40
151^
5 3 x %
3% 9% 10,600
3 12,200
2
£712, " ....
34
l5^T)
5 3x%
3M 9% 13,100
3 15,780
2
£713, Double...
30
9V£
3% 9 5600
2 10,600
—
£714, " ...
40
91^
6 4x11/32
3% 9 6840
2 8600
__
E 15, Quadruple
£716, " .;..
36
30
IS!
6 3x11/32
6
3T£ 9% 11,820
41^ 10)4 8000
2^ 14,370
2% 15,500
2
£717, Double...
36
91^
5 4x%
2% 8 8070
2 9540
—
£718, Singlet..
42
—
9 3^x%
1* — 5-250
0 7300
—
£719, Double...
22
lOVjji
g 4J^1 1/32
13/16 6T7B 13,800
— —
—
£7 20,
22
10^2
7
13/16 7)4 15,600
— —
—
£721,
24
10V£
1 714 15,750
0 28,800
—
£7 22,
24
10V£
8 2"
1 8^ 18.000
0 32,930
—
£723,
36
10 ~
2«4 8 8750
114 10,750
£724,
36
10
5 X^
2J4 8 7500
1^4 9500
—
(a) Between bands ; (If) over all ; a.p.t., auxiliary plates touching.
* Between bottom of eye and top of leaf, t semi- elliptical.
Tracings are furnished for each class of spring.
PHOSPHOR-BRONZE SPRINGS.
Wilfred Lewis (Engineers' Club, Philadelphia, 1887) made some tests with
phosphor-bronze wire, .12 in. diameter, coiled in the form of a spiral spring,
1J4 m- diameter from centre to centre, making 52 coils.
Such a spring of steel, according to the practice of the P. R. R., might be
used for 40 Ibs. A load of 30 Ibs. gradually applied gave a permanent set.
With a load of 21 Ibs. in 30 hours the spring lengthened from 20% inches to
2114 inches, and in 200 nours to 21J4 inches. It was concluded that 21 Ibs. was
too great for durability. For a given load the extension of the bronze spring
was just double the extension of a similar steel spring, that is, for the same
extension the steel spring is twice as strong.
SPRINGS TO RESIST TGRSIONAL FORCE.
(Reuleaux's Constructor.)
Flat spiral or helical spring. . . P = - ~ ; J
b R
Round helical spring P = -£- — ; j
& r/3
Round bar, in torsion P=— — ; j
lo R
Flat bar, in torsion
8^
: ZR'
7T G
~~a~
P = force applied at end of radius or lever-arm R ; & = angular motion at
end of radius B; S = permissible maximum stress, = 4/5 of permissible
stress in flexure; £7 = modulus of elasticity in tension; G — torsional modu<
lus, = 2/5 £7; I = developed length of spiral, or length of bar; d = diametei
of wire; b = breadth of flat bar; h = thickness.
HELICAL SPRINGS — SIZES AND CAPACITIES. 353
HEL.ICAL, SPRINGS-SIZES AND CAPACITIES.
(Selected from Specifications of Penna. R. R. Co., 1899.)
cc
^
*
Test. Height and Loads.
I
w
t-l
ad
c
tic
~
£
o
&
CQ
'o
5
.5
to
CM
s
O
'o
^
o
£
fl
^q
03
_fl
•§ ^
£~
^
ft
||
I
o
If
O
oT
^
"o
C/J
1
I
'o^T
|3
Q
bs. oz.
H 26
9/64
57J4
59
0 4
1
5%
3
3*4
110
130
H 18
11/64
75
0 8
1
8
5
6
170
270
H55
3/16
45*6
46 ,C
0 f-%
1
4*^
3_pB
4
103
245
H73
3/16
426
427%
3 5*4
l^g
39 "
22*^
35
45
185
H29
7/32
20)4
22/j
o 314
Iff
Hi
H*
1%
110
200
HI
1/4
4514
47
0 10
5j|
3%
4%
250
500
H5
1/4
25*4
2<KV
0 6
2*4
2J4
1*^
1*^
164
240
H 58
5/16
25314
25(5 V<
5 7
2/4
23
13
18
248
495
H74
5/16
180
182%
3 1414
HB
19%
13
14*6
587
700
H68,*
3/8
99*4
10314
3 1*4
^%
9
5
7
350
700
H79
3/8
88
90^
2 12
2%
8%
6
6%
676
946
H802
13/32
192%
195%
7 l*i
2T95
18
lit!
15)4
380
975
H 43
H 64
7/16
7/16
96
75%
!78^
4 1
3 3
sg
8J8
'.%
^
5%
450
1350
660
,440
H53a
H272
15/52
1/2
169^
90%
172ft
95^
8 4
5 0
3*1
101/2
^
56%
330
810
,410
,500
H61
1/2
1514
21%
0 13%
4*4
1%
0%
1
532
,050
H 19
17/32
8114
85*4
5 2
3^2
8
5i%
6 IB
1200
,900
H863
17/32
153%
159
9 10
4
1 3%
714
8jg
1156
1,360
H 63
9/16
98 *
103
6 15
3%
9)4
514
7
1050
,800
H 35.)
9/16
84%
5 10**;
8
5%
6ri
1000
2,200
H592
5/8
74 y
77%
6 7
2%
^*4
7*4
2100
3,500
H80,
5/8
192V£
197%
16 11
18
H I '8
15K)
900
2,315
H722
21/32
60*6
63*^
5 11%
2%
7T^
6
6%
3260
4,240
H 15a
H41
11/16
11/16
\rA
59%
123J4
5 14
12 10
;%
5%
10%
m
8%
1400
1500
3,500
2,720
H40
3/4
17714
186%
22 2V£
614
16
7%
8%
1900
2,300
H70
3 4
62
66
7 12 *
3%
7
5%
6*4
2750
5,050
H 172
13/16
100
106%
14 12
9%
6
7%
1700
3,700
H662
13/16
105*4
110%
15 7
45|
10%
8%
8%
3670
5,040
H37
27/32
77
81%
12 214
STB
7y2
3300
6,250
H872
H 122
27/32
7/8
8515
1371
91J4
20 9
14 7
5 8
12*|
si
3540
2000
4,165
5200
H332
H2
H 16
1/8
15/16
15/16
82
46
85
881
529/
my
13 15
8 15*d
16 10
5
6
8 3
f/3
5
4 S
6
2250
3250
3600
5000
7.000
5,100
H 10
85
92
18 14
514
8*4
6
7
* 4500
7.000
H 42i
36
42?/
8 0
5%
3%
2%
3%
1795
7.180
M4
i
98%
105
24 12
5
10%
8**>
9%
6000
9,570
88,
ig
153%
1641/
38 9
8
13%
7*^
4624
5,440
H3
*6
35%
41*^
9 15
4%
4%
3%
3%
6000
12,000
H 14j
\A
51
58</|
14 4
6%
5*^
31i
4rl
5000
8,950
H 6,
£,
99*1
109^
31 1
8
9V6
5V6
7
4550
7,750
H47
T3g
73 V*
79*/
23 0
5/1
8*4
O'TR
740
12,500
H9
*4
97*1
108
33 12
8
9
5%
*18
4000
9,100
/4
62%
(589/
21 8)4
5%
75
6
%
10,70
14,875
H8 l
T5S
96
106!/
36 12
8
9V^
6
*4
635
10,600
H62
i
70
'•I
26 12
5r|
8
6*ij
*4
790
15,800
H 12t
87
97<K
36 7
8
8/4
5%
M
500
12.200
H39t
%
75%
83J/
31 11
C%
8%
C%
Hi
815
16,300
HSfc,
HI
95
37 3
8
5%
6%
732
13,250
* The subscript 1 means the outside coil of a concentric group or cluster;
2 and 3 are inner coils.
354 KIVETED JOINTS.
RIVETED JOINTS.
Fairbairn' s Jtoxperiments. (From Report of Committee on
Riveted Joints, Proc. Inst. M. E., April, 1881.)
The earliest published experiments on riveted joints are contained in the
memoir by Sir W. Fairbairn in the Transactions of the Ro3'al Society.
Making certain empirical allowances, he adopted the following ratios as ex-
pressing the relative strength of riveted joints :
Solid plate 100
Double-riveted joint 70
Single-riveted joint 56
These well-known ratios are quoted in most treatises on riveting, and are
' still sometimes referred to as having a considerable authority. It is singular,
however, that Sir W. Fairbairn does not appear to have been aware that the
proportion of metal punched out in the line of fracture ought to be different
in properly designed double and single liveted joints. These celebrated
ratios would therefore appear to rest on a very unsatisfactory analysis of
the experiments on which they were based.
L.OSS of Strength in Punched Plates.— A report by Mr. W.
Parker and Mr. John, made in 1878 to Lloyd's Committee, on the effect of
punching and drilling, showed that thin steel plates lost comparatively little
from punching, but that in thick plates the loss was very considerable.
Tho following table gives the results for plates punched and not annealed
or reamed :
Thickness of Material of Loss of Tenacity,
Plates. Plates. per cent.
YA Steel 8 .
% 18
V* " 26
% " 33
% Iron 18 to 23
The effect of increasing the size of the hole in the die-block is shown in
the following table :
Total Taper of Hole Material of Loss of Tenacity due to
in Plate, inches, Plates. Punching, per cent.
1-16 Steel 17.8
H " 12.3
Y± (Hole ragged) 24.5
The plates were from 0.675 to 0.712 inch thick. When %-in. punched holes
were reamed out to 1% in. diameter, the loss of tenacity disappeared, and
the plates carried as high a stress as drilled plates. A'nnealing also restores
to punched plates their original tenacity.
Strength of Perforated Plates.
(P. D. Bennett, Eng^g, Feb. 12, 1886, p. 155.)
Tests were made to determine the relative effect produced upon tensile
strength of a flat bar of iron or steel : 1. By a %-inch hole drilled to the re-
quired size ; 2. by a hole punched ^ inch smaller and then drilled to the
size of the first hole ; and, 3, by a hole punched in the bar to the size of the
drilled bar. The relative results in strength per square inch of original area
were as follows :
1. 2. 3. 4.
Iron. Iron. Steel. Steel.
Un perforated bar 1.000 1.000 1.000 1.000
Perforated by drilling 1.029 1.012 1.068 1.103
" " punching and drilling. 1.030 1.008 1.059 1.110
" punching only 0.795 0.894 0.935 0.927
In tests 2 and 4 the holes were filled with rivets driven by hydraulic pres-
sure. The increase of strength per square inch caused by drilling is a phe-
nomenon of similar nature to that of the increased strength of a grooved bar '
over that of a straight bar of sectional area equal to the smallest section of
the grooved bar. Mr. Bennett's tests on an iron bar 0.84 in. diameter, 10 in.
EFFICIENCY OF RIVETING BY DIFFERENT METHODS. 355
long, and a similar bar turned to 0.84 in. diameter at one point only, showed
that the relative strength of the latter to the former was 1.328 to 1.000.
Riveted Joints.— Drilling versus Punching of Holes.
The Report of the Research Committee of the Institution of Mechanical
Engineers, on Riveted Joints (1881), and records of investigations by Prof.
A. B. W. Kennedy (1881, 1882, and 1885), summarize the existing information
regarding the comparative effects of punching and drilling upon iron and
steel plates. From an examination of the voluminous tables given in Pro-
fessor Uiiwin's Report, the results of the greatest number of the experi-
ments made on iron and steel plates lead to the general conclusion that,
while thin plates, even of steel, do not suffer very much from punching, yet
in those of i^-inch thickness and upwards the loss of tenacity due to punch-
ing ranges from 10$ to 23% in iron plates, and from \\% to 33% in the case cf
mild steel. In drilled plates there is no appreciable Joss of strength. It is
possible to remove the bad effects of punching by subsequent reaming or
annealing; but the speed at which work is turned out in these days is not
favorable to multiplied operations, and such additional treatment is seldom
practised. The introduction of a practicable method of drilling the plating
of ships and other structures, after it has been bent and shaped, is a matter
of great importance. If even a portion of the deterioration of tenacity can
be prevented, a much stronger structure results from the same material and
the same scantling. This has been fully recognized in the modern English
practice (188?) of the construction of steam-boilers with steel plates; punch-
ing in srnch cases being almost entirely abolished, and all rivet-holes being
drilled after the plates have been bent to the desired form.
Comparative Efficiency of Riveting done by Different
Methods,
The Reports of Professors Unwin and Kennedy to the Institution of Me-
chanical Engineers (Proc. 1881, 188v>, and 1885) tend to establish the four fol-
lowing points:
1. That the shearing resistance of rivets is not highest in joints riveted by
means of the greatest pressure;
2. That the ultimate strength of joints is not affected to an appreciable
extent by the mode of riveting; and, therefore,
3. That very great pressure upon the rivets in riveting is not the indispen-
achine-
rvete wor conssts n te act tat n an-rvete joints visible slip
commences at a comparatively small load, thus giving such joints a low
value as regards tightness, and possibly also rendering them liable to failure
under sudden strains after slip has once commenced.
Total Breaking Load.
Load at which Visible Slip began.
Hand-riveting.
Hydraulic Rivet-
ing.
Hand-riveting.
Hydraulic Rivet-
ing.
Tons.
86.01
'82.1Q
1*9.2
m.3
Tons.
85.75
77.00
82.70
78.58
145.5
140.2
183.1
183.7
Tons.
21.7
25i6
31 ."7
25!6
Tons.
47.5
35.0
53.7
54.0
49.7
46.7
56.0
In these figures hand-riveting appears to be rather better than hydraulic
riveting, as far as regards ultimate strength of joint; but is very much in-
ferior to hydraulic work, in view of the small proportion of load borne by
it before visible slip commenced,
356
RIVETED JOINTS.
Some of tli e Conclusions of the Committee of Research,
on Riveted Joints,
(Froc. Inst. M. E., Apl. 1885.)
The conclusions all refer to joints made in soft steel plate with steel
rivets, the holes all drilled, and the plates in their natural state (unannealed).
In every case the rivet or shearing area has been assumed to be that of the
holes, not the nominal (or real) area of the rivets themselves. Also, the
strength of the metal in the joint has been compared with that of strips
cut from the same plates, and not merely with nominally similar material.
The metal between the livet-holes has a considerably greater tensile re-
sistance per square inch than the unperf orated metal. This excess tenacity
amounted to more than 20$, both in %-iuch and %-inch plates, when the
pitch of the rivet was about 1.9 diameters. In other cases %-inch plate gave
an excess of 15$ at fracture with a pitch of 2 diameters, of 10$ with a pitch
of 3.6 diameters, and of 6.6$, with a pitch of 3.9 diameters; and %-inch plate
gave 7.8$ excess with a pitch of 2.8 diameters.
la single-riveted joints it may be taken that about 22 tons per square inch
is the shearing resistance of rivet steel, when the pressure on the rivets does
not exceed about 40 tons per square inch. In double-riveted joints, with
rivets of about % inch diameter, most of the experiments gave about 24 tons
per square inch as the shearing resistance, but the joints in one series went
at 22 tons.
The ratio of shearing resistance to tenacity is not constant, but diminishes
very markedly and not very irregularly as the tenacity increases.
The size of the rivet heads and ends plays a most important par%t in the
strength of the joints— at any rate in the case of single-riveted joints. An
increase of about one third in the weight of the rivets (all this increase, of
course, going to the heads and ends) was found to add about 8^$ to the
resistance of the joint, the plates remaining unbroken at the full shearing
resistance of 22 tons per square inch, instead of tearing at a shearing stress
of only a little over 20 tons. The additional strength is probably due to the
prevention of the distortion of the plates by the great tensile stress in the
rivets.
The intensity of bearing pressure on the rivet exercises, with joints propor-
tioned in the ordinary way, a very important influence on their strength.
So long as it does not exceed 40 tons per square inch (measured on the pro-
jected area of the rivets), it does not seem to affect their strength ; but pres-
sures of 50 to 55 tons per square inch seem to cause the rivets to shear in
most cases at stresses varying from 16 to 18 tons per square inch. For or-
dinary joints, which are to be made equally strong in plate and in rivets,
the bearing pressure should therefore probably not exceed 42 or 43 tons per
square inch. For double-riveted butt-joints perhaps, as will be noted later
a higher pressure may be allowed, as the shearing stress may probably not
be more than 10 or 18 tons per square inch when the plate tears.
A margin (or net distance from outside of holes to edge of plate) equal to the
diameter of the drilled hole has been found sufficient in all cases hitherto tried.
To attain the maximum strength of a joint, the breadth of lap must be
such as to prevent it from breaking zigzag. It has been found that the net
metal measured zigzag should be from 30$ to 35$ in excess of that measured
straight across, in order to insure a straight fracture. This corresponds to
a diagonal pitch of 2/3 p + d/3, if p be the straight pitch and d the diam-
eter of the rivet-hole.
Visible slip or " give " occurs always in a riveted joint at a point very
much below its breaking load, and by no means proportional to that load.
A collation of the results obtained in measuring the slip indicates that it de-
pends upon the number and size of the rivets in the joint, rather than upon
anything else ; and that it is tolerably constant for a given size of rivet in a
given type of joint. The loads per rivet at which a joint will commence to
slip visibly are approximately as follows ;
Diameter of Rivet.
Type of Joint.
Riveting.
Slipping Load per
Rivet.
94 inch
linen
1 "
1 "
Single-riveted
Double-riveted
Double- riveted
Single-riveted
Double-riveted
Double-riveted
Hand
Hand
Machine
Hand
Hand
Machine
2.5 tons
3.0 to 3.5 tons
7 tons
3.2 tons
4.3 tons
8 to 10 tons
DOUBLE-RIVETED LAP-JOINTS.
357
To find the probable load at which a joint of any breadth will commence
to slip, multiply the number of rivets in the given breadth by the proper
figure taken from the last column of the table above. It will be understood
that the above figures are not given as exact; but they represent very well
the results of the experiments.
The experiments point to simple rules for the proportioning of joints of
maximum strength. Assuming that a bearing pressure of 43 tons per square
inch may be allowed on the rivet, and that the excess tenacity of the plate
is 10# of its original strength, the following table gives the values of the ratios
of diameter d of hole to thickness t of plate (d •*- t), and of pitch p to diam-
eter of hole (p -5- d) in joints of maximum strength in %-iuch plate.
For Single-riveted Plates.
Original Tenacity of
Plate.
Shearing Resistance of
Rivets.
Ratio.
d-*-t
Ratio.
p -*-d
Eatio.
Plate Area
Tons per
sq. in.
Lbs. per
sq. in.
Tons per
sq. in.
Lbs. per
sq. in.
Rivet. Area
30
28
30
28
67,200
62,720
67,200
62,720
22
22
24
24
49,200
49,200
53,760
53,760
2.48
2.48
2.28
2.28
2.30
2.40
2.27
2.36
0.667
0.785
0.713
0.690
This table shows that the diameter of the hole (not the diameter of the
rivet) should be 2^ times the thickness of the plate, and the pitch of the
rivets 2% times the diameter of the hole. Also, it makes the mean plate area
71 % of the rivet area.
If a smaller rivet be used than that here specified, the joint will not be of
uniform, and therefore not of maximum, strength; but with any other size
of rivet the best result will be got by use of the pitch obtained from the
simple formula
where, as before, d is the diameter of the hole.
The value of the constant a in this equation is as follows:
For 30-ton plate and 22-ton rivets, a — 0.524
" 28 " 22 " " 0.558
" 30 " 24 " " 0.670
" 28 24 " " 0.606
d*
Or, in the mean, the pitch p = 0.56 -r- -f d.
It should be noticed that with too small rivets this gives pitches often con-
siderably smaller in proportion than 2% times the diameter.
For double-riveted lap-joints a similar calculation to that given
above, but with a somewhat smaller allowance for excess tenacity, on
account of the large distance between the rivet-holes, shows that for joints
of maximum strength the ratio of diameter to thickness should remain pre-
cisely as in single-riveted joints; while the ratio of pitch to diameter of hole
should be 3.64 for 30-ton plates and 22 or 24 ton rivets, and 3.82 for 28-ton
plates with the same r ivets.
Here, still more than in the former case, it is likely that the prescribed
size of rivet may often be inconveniently large. In this case tne diameter
of rivet should be taken as large as possible; and the strongest joint for a
given thickness of plate and diameter of hole can then be obtained by using
the pitch given by the equation
where the values of the constant a for different strengths of plates and
rivets may be taken as follows:
358 RIVETED JOINTS.
Table of Proportions of Double-riveted Lap-joints,
d2
in which p = a — -f- d.
Original tenacity Shearing: Resist- Value of Con-
Thickness of of Plate, " ance of Rivets. stant.
Plate. Tons per sq. in. Tons per sq. in. a
%inch 30 24 .15
% " 28 24 .22
% " 30 22 .05
28 22 .13
30 24 .17
28 24 .25
30 22 .07
28 23 .14
Practically, having1 assumed the rivet diameter as large as possible, we
can fix the pitch as follows, for any thickness of plate from % to % inch:
For 30-ton plate and 24-ton rivets? p _ j^g ^ _j_ ^.
28 '' 22 '•* C £
" 30 " " " 22 " " p = 1.06 y -f d;
44 28 " " " 24 " " p = 1.24y-fd.
In double-riveted butt-joints it is impossible to develop the full
shearing resistance of the joint without getting excessive bearing pressure,
because the shearing area is doubled without increasing the area on whicL
the pressure acts. Considering only the plate resistance and the bearing
pressure, and taking this latter as 45 tons per square inch, the best pitch
would be about 4 times the diameter of the hole. We may probably say
with some certainty that a pressure of from 45 to 50 tons per square inch on
the rivets will cause shearing to take place at from 16 to 18 tons per square
inch. Working out the equations as before, but allowing excess strength of
only 5$ on account of the large pitch, we find that the proportions of double-
riveted butt-joints of maximum strength, under given conditions, are those
ot the following table:
Double-riveted Butt-joints.
Ratio Ratio
1 P
t d
1.80 3.85
1.80 4.06
1.70 4.03
1.70 4.27
2.00 4.20
2.00 442
Practically, therefore, it may bfi said that we get a double-riveted butt-joint
of maximum strength by making the diameter of hole about 1.8 times the
thickness of the plate, and making the pitch 4.1 times the diameter of the
hole.
The proportions just given belong to joints of maximum strength. But in
a boiler the one part of the joint, the plate, is much more affected by time
than the other part, the rivets. It is therefore not unreasonable to estimate
the percentage by which the plates might be weakened by corrosion, etc.,
before the boiler would be unfit for use at its proper steam -pressure, and to
add correspondingly to the plate area. Probably the best thing to do in this
case is to proportion the joint, not for the actual thickness of plate, but for
a nominal thickness less than the actual by the assumed percentage. In
this case the joint will be approximately one of uniform strength by the
time it has reached its final workable condition; up to which time the joint
as a whole will not really have been weakened, the corrosion only gradually
bringing the strength of the plates down to that of rivets.
Original Ten-
Shearing Re-
Bearing
acity
sistance
Pres-
of Plate,
of Rivets,
sure,
Tons per
Tons per
Tons per
sq. in.
<?q. in.
sq. in.
30
16
45
28
16
45
30
18
48
28
18
48
30
16
50
28
16
50
KIVETED JOINTS.
359
Efficiencies of Joints*
The average results of experiments by the committee gave: For double-
riveted lap-joints in %-inch plates, efficiencies ranging from 67.1$ to 81.2$.
For double-riveted bvtt-joints (in double shear) 61.4$ to 71.3$. These low re-
sults were probably due to the use of very soft steel in the rivets. For single-
riveted lap-joints of various dimensions the efficiencies varied from 54. 8$ to
60.8$.
The experiments showed that the shearing resistance of steel did not in-
crease nearly so fast as its tensile resistance. With very soft steel, for
instance, of only 26 tons tenacity, the shearing resistance was about 80$ of
the tensile resistance, whereas with very hard steel of 52 tons tenacity the
shearing resistance was only somewhere about 65$ of the tensile resistance.
Proportions of Pitch and Overlap of Plates to Diameter
of Rivet-Mole and Thickness of Plate.
(Prof. A. B. W. Kennedy, Proc. Inst. M. E.t April, 1885.)
t — thickness of plate;
d = diameter of rivet (actual) in parallel hole;
p = pitch of rivets, centre to centre;
s = space between lines of rivets;
I = overlap of plate.
The pitch is^as wide as is allowable without imparing the tightness of the
joint under steam.
For single-riveted lap-joints in the circular seams of boilers which have
double- riveted longitudinal lap joints,
d = i x 2.25;
p = dx 2. 25 =2 x 5 (nearly);
I — t x 6.
For double-riveted, lap-joints:
d = 2.25#;
p = 8<;
s = 45f;
I = 10.5*.
Single -rive ted Joints.
Double-riveted Joints.
3-16
H
5-16
7-16
9-16
11-16
13-16
15-16
1«
19-16
1%
2 3-16
2 lVl6
3-16
5-J6
A
9^6
7-16
9-16
11-16
13-16
13-16
With these proportions and good workmanship there need be no fear of
leakage of steam through the riveted joint.
The net diagonal area, or area of plate, along a zigzag line of fracture
should not be less than 30$ in excess of the net area straight across the
joint, and 35$ is better.
Mr. Theodore Cooper (R. R. Gazette, Aug. 22, 1890) referring to Prof. Ken-
nedy's statement quoted above, gives as a sufficiently approximate rule for
the proper pitch between the rows in staggered riveting, one half of the
pitch of the rivets in a row plus one quarter the diameter of a rivet-hole.
Apparent Excess in Strength of Perforated over Unper-
forated Plates. (Proc. Inst. M. E., October, 1888.)
The metal between the rivet-holes has a considerably greater tensile re-
sistance per square inch than the unperforated metal. This excess tenacity
amounted to more than 20$, both in %-inch and ^-inch plates, when che
pitch of the rivets was about 1.9 diameters. In other cases %-inch plate
gave an excess of 15# at fracture with a pitch of 2 diameters, of 10# with a
pitch of 3.6 diameters, and of 6.6$ with a pitch of 3.9 diameters; and %-inch
plate gave 7,8# excess with a pitch of 2.8 diameters.
360
RIVETED JOINTS.
(1) The "excess strength due to perforation " is increased by anything
which tends to make the stress in the plate uniform, and to diminish the
effect of the narrow strip of metal at the edge of the specimen.
(2) It is diminished by increase in the ratio of p/d, of pitch to diameter of
hole, so that in this respect it becomes less as the efficiency of the joint
increases.
(3) It is diminished by any increase in hardness of the plate.
(4) For a given ratio p/d, of pitch to diameter of hole, it is also apparently
diminished as the thickness of the plate is increased. The ratio of pitch to
thickness of plate does not seem to affect this matter directly, at least
within the limits of the experiments.
Test of Double-riveted Lap and Butt Joints.
(Proc. Inst. M. E., October, 1888.)
Steel plates of 25 to 26 tons per square inch T. S., steel rivets of 24.6 tons
shearing-strength per square inch.
Comparative
Kind of Joint.
Lap..
Butt.
Lap..
Butt*.
Lap..
Butt".
Thickness of
Plate.
Diameter of
Rivet-holes.
0.8"
Ratio of Pitch
to Diameter.
3.62
3.93
2.82
3.41
4.00
3.94
2.42
3.00
3.92
Efficiency of
Joint.
75.2
76.5
68.0
73.6
72.4
76.1
63.0
70.2
76.1
Some Rules which have been Proposed for the Diameter
of the Rivet in Single Shear. (Iron, June 18, 1880.)
Browne .................... d = 2t (with double covers \]^t) (1)
Fairbairn .................. d — 2t for plates less than % in. (2)
" .................. d = l]4t for plates greater than % in. (3)
Lemaitre ................... d =1.5* + 0.16 <4)
Antoine .................... d = 1.1 V* (5)
Pohlig .................... d = 2t for boiler riveting (6)
" ................. d — 3£ for extra strong riveting (7)
Redtenbacher .............. d = 1.5* to 2* (8)
Unwin ...................... d = %t +_5/16 to %* + % (9)
" .................... d = 1.2V* (10)
The following table contains some data ot the sizes of rivets used in
practice, and the corresponding sizes given by some of these rules.
Diameter of Rivets for Different Thicknesses of Plates.
Thick-
ness of
plate.
Inches.
5/16
I6
9/16
13/16
15/16
Diameter of Rivets, in inches.
.a "2
13/16
13/16
15/16
1 3/16 1
F
V
1 1/16
21/32
27/32
15/16
1 1/32
1 7/32
mai
(4).
23/32
13/16
15/16
1 3
5/16
11/16
13/16
15/16
1
1
1 1/16
11/16
13/16
H
15/16
1
1 1/16
1 3/32
1 3/16
ils
RIVETED JOIKTS.
361
Strength of Double - riveted Seams, Calculated. — W. B.
Ruggles, Jr., in Power for June, 189U, gives tables of relative strength of
rivets and parts of sheet between rivets in double-riveted seams, compared
with strength of shell, based on the assumption that the shearing strength
of rivets and the tensile strength of steel are equal. The following figures
Pitch
of
Rivets,
inches.
Size of
Rivet-
holes,
inches.
9/16
1?/16
9/16
1?/16
11/16
13/16
11/16
Percentage of
Strength of
Plate.
Rivets. Plate.
.739
.795
.785
.819
.749
.748
.761
.780
.727
.755
.754
.762
.777
.714
.765
!800
.810
.735
.762
.780
.793
.722
.738
.760
.776
.788
.711
13/16
15/16
1
1 1/16
Percentage of
Strength of
Plate.
Rivets. Plate.
.758
.758
.765
.707
.721
.740
.736
.761
.701
.714
.727
.745
.742
.728
.740
.759
.773
.700
.718
.731
.750
.758
.690
.708
.722
.733
.750
H. De B. Parsons (Am. Engr. &B. R. Jour., 1893) holds that it is an error to
assume that the shearing strength of the rivet is equal to the tensile strength.
Also, referring to the apparent excess in strength of perforated over unper-
forated plates, he claims that on account of the difficulty in properly match-
ing the holes, and of the stress caused by forcing, as is too often the case
in practice, this additional strength cannot be trusted much more than
that of friction.
Adopting the sizes of iron rivets as generally used in American practice
for steel plates from 14 to 1 inch thick: the tensile strength of the plates as
60,000 Ibs. ; the shearing strength of the rivets as 40,000 for single-shear and
35,500 for double - shear, Mr. Parsons calculates the following table of
pitches, so that the strength of the rivets against shearing will be approxi-
mately equal to that of the plate to tear between rivet-holes. The diameter
of the rivets has in all cases been taken at 1/16 in. larger than the nominal
size, as the rivet is assumed to fill the hole under the power riveter.
Riveted Joints.
LAP OR BUTT WITH SINGLE WELT— STEEL PLATES AND IRON RIVETS.
Thickness
Diameter
Pitch.
Efficiency.
of
Plates.
of
Rivets.
Single.
Double.
Single.
Double.
in.
in.
in.
in.
/4
HJ
1 3/16
]%
56.7*
70. 0£
%
M
1 11/16
2 11/16
52.7
68.6
£2
/8
1%
2%
49.0
66.9
%
1 11/16
2 7/16
43.6
60.4
%
1 8
1%
2%
42.0
59.5
r
1
1 1/8
2 3/16
2 7/16
m
38.6
38.1
55.4
54.9
362
RIVETED JOINTS.
Calculated Efficiencies— Steel Plates and Steel Rivets,—
The differences between the calculated efficiencies given in the two tables
above are notable. Those given by Mr. Ruggles are probably too high, since
he assumes the shearing strength of the rivets equal to the tensile strength
of the plates. Those given by Mr. Parsons are probably lower than will be
obtained in practice, since the figure he adopts for shearing strength is
rather low, and he makes no allowance for excess of strength of the perfo-
rated over the unperforated plate. The following table has been calculated
by the author on the assumptions that the excess strength of the perforated
late is 10#, and that the shearing strength of the rivets per square inch is
our fifths of the tensile strength of the plate. If t = thickness of plate,
d - diameter of rivet-hole, p - pitch, and T = tensile strength per square
inch, then for single-riveted plates
(p - d)t X 1.10T = -jd2 X g^, whence p = -571-j- + &
For double-riveted plates, p — 1-142-r -f d.
The coefficients .571 and 1.142 agree closely with the averages of those
given in the report of the committee of the institution of Mechanical En-
gineers, quoted on pages 357 and 358, ante.
p
f
Pitch.
Efficiency.
Pitch.
Efficiency.
1
Diam.
of
.
.
ti
„-, bL
1
Diam.
of
.
si
ti
c
Rivet-
,2.2
3 G
4J
if
J2
Rivet-
,2 a
^.S
•^.S
3-5
1
hole.
P 3J
P"S
cf®
.0
hole.
&jc*r3
3 "•£
Q "S
3 "£
s
"3
*$
S3
«!
H
»|
fig
y
^2
in.
in.
in.
in.
*
%
in.
in.
in.
in.
Jt
J
3/16
7/16
1.020
1.603
57.1
72.7
Y?
§4
1.392
2.035
46.1
63.1
M
1.261
2.023
60.5
75.3
%
1.749
2.624
50.0
66.6
M
^ij
1.071
1.642
53.3
69.6
»*
i
2.142; 3.284
to •>
70.0
"
9/16
1.285
2.008
56.2
72.0
«'
2.570! 4.016
56.2
72.0
5/16
9/16
1.137
1.712
50.5
67.1
9/16
ax
1 321 1.892
43.2
60.3
«
%
1.339
2.053
53.3
69.5
/&
1.652 2.429
47.0
64.0
"
11/16
1.551
2.415
55.7
71.5
M
1
2.015
3.030
50.4
67.0
%
%
1.218
1.810
48.7
65.5
•'
l/^
2.410
3.694
53.3
69.5
•"
M
1.607
2.463
53.3
69.5
**
jix
2.836
4.422
55.9
71.5
**
%
2.041
3.206
57.1
72.7
s^
34
1.264
1.778
40.7
57.8
7/16
%
1.136
1.647
45.0
62.0
*»
%
1.575
2.274
44.4
61.5
3/
1.484
2.218
49.5
66.2
"
j
1.914
2.827
47.7
64.6
"
%
1.869
2.864
53.2
69.4
t*
1^4
2.281
3.438
50.7
67.3
1
2.305
3.610
56.6
72.3
"
2
2.678
4.105
53.3
69.5
Riveting Pressure Required for Bridge and Boiler
Work.
(Wilfred Lewis, Engineers' Club of Philadelphia, Nov., 1893.)
A number of %j-inch rivets were subjected to pressures between 10,000 and
60,000 Ibs. At 10,000 Ibs. the rivet swelled and filled the hole without forming
a head. At 20,000 Ibs. the head was formed and the plates were slightly
pinched. At 30.000 Ibs. the rivet was well set. At 40,000 Ibs. the metal in the
plate surrounding the rivet began to stretch, and the stretching became
more and more apparent as the pressure was increased to 50,000 and 60,000
Ibs. From these experiments the conclusion might be drawn that the pres-
sure required for cold riveting was about 300,000 Ibs. per square inch of rivet
section. In hot riveting, until recently there was never any call for a pres-
sure exceeding 60,000 Ibs., but now pressures as high as 150,000 Ibs. are not
uncommon, and even 300,000 Ibs. have been contemplated as desirable.
SHEARING RESISTAKCE OF RIVET IRO^I AND STEEL. 363
Apparent Shearing Resistance of Rivet Iron and Steel.
(Proc. List. M. E., 1879, Engineering, Feb. 20, 18SO.)
The true shearing resistance of the rivets cannot be ascertained from
experiments on riveted joints (1) because the uniform distribution of the
load to all the rivets cannot be insured; ('.) because of the friction of the
plates, which has the effect of increasing the apparent resistance to shear-
ing in an element uncertain in amount. Probably in the case of single*
riveted joints the shearing resistance is not much affected by the friction.
Ultimate Shearing Stress
Tons per sq. in. Lbs. per sq. in.
Iron, single shear (12 bars). . 24.15 54=090 \ m „•.!,-,
41 double shear (8 bars). . 22.10 49.504 f uarke-
" .. 22.62 50.669 Barnaby. >,
" " .. 22.30 49.952 Rankine. '
" 34-in. rivets 23.05 to 25.57 51.632 to 57.277 )
^-in. rivets 24.32 to 27.94 54.477 to 62.362 VRiley.
' mean value
" %-in. rivets
Steel
Landore steel, ?4-in. rivets. .
25.0 56.000 )
19.01 42.58-2 Greig and Eyth.
17 to 26 38.080 to 58.240 Parker.
31.67 to 33.69 70.941 to 75.466 )
in rivets. . 30.45 to 33.73 68.208 to 80.035 VRiley.
mean value. .
33.3
22.18
Brown's steel
Fairbairn's experiments show that a rivet ii
74.592 )
49.683 Greig and Eyth.
weaker in a drilled than
in a punched hole. By rounding the edge of the rivet-hole the apparent
shearing resistance is increased 12$. Mr. Maynard found the rivets 4%
weaker in drilled holes than in punched holes. But these results were
obtained with riveted joints, and not by direct experiments on shearing.
There is a good deal of difficulty in determining the true diameter of a
punched hole, and it is doubtful whether in these experiments the diameter
was very accurately ascertained. Messrs. Greig and Eyth's experiments
also indicate a greater resistance of the rivets in punched holes than in
drilled holes.
If, as appears above, the apparent shearing resistance is less for donble
than for single shear, it is probably due to unequal distribution of the stress
on the two rivet sections.
The shearing resistance of a bar, when sheared in circumstances which
prevent friction, is usually less than the tenacity of the bar. The following
results show the decrease :
1
Tenacity of
Bar.
Shearing
Resistance.
Ratio.
26 4
16.5
0 62
Lavulley iron.
25.4
20 2
0 79
Greig and Eyth, iron...
" " steel..
22.2
28.8
19.0
22.1
0.85
0.77
In Wohler's researches (in 1870) the shearing strength of iron was found
to be four-fifths of the tenacity. Later researches of Bauschinger confirm
this result generally, but they show that for iron the ratio of the shearing
resistance and tenacity depends on the direction of the stress relatively to
the direction of rolling. The above ratio is valid only if the shear is in a
plane perpendicular to the direction of rolling, and if the tension is applied
parallel to the direction of rolling. The shearing resistance in a plane
parallel to the direction of rolling is different from that in a plane perpen-
dicular to that direction, and again differs according as the plane of shear is
perpendicular or parallel to the breadth of the bar. In the former case the
resistance is 18 to 20% greater than in a plane perpendicular to the fibres, or
is equal to the tenacity. In the latter case it is only half as great as in a
plane perpendicular to the fibres.
AKD STEEL.
IRON AND STEEL.
CLASSIFICATION OF IRON AND STEEL.
§*i .§ ^
».s .a ? c
fS
i
O *-
»5
1
i
^E^^
1
S
§
Is*01
t
i
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CAST IKOtf. 365
CAST IRON.
Grading of Pig Iron,— Pig iron is commonly graded according to its
fracture, the number of grades .varying in different districts. In Eastern
Pennsylvania the principal grades recognized are known as No. 1 and 2
foundry, gray forge or No. 3, mottled or No. 4, and white or No. 5. Inter-
mediate grades are sometimes made, as No. 2 X, between No. 1 and No. 2,
and special names are given to irons more highly silicized than No. 1, as
No. 1 X, silver-gray, and soft. Charcoal foundry pig iron is graded by num-
bers 1 to 5, but the quality is very different from the corresponding num-
bers in anthracite and coke pig. Southern coke pig iron is graded into ten
or more grades. Grading by fracture is a fairly satisfactory method of
grading irons made from uniform ore mixtures and fuel, but is unreliable as
a means of determining quality of irons produced in different sections or
from different ores. Grading by chemical analysis, in the latter case, is the
only satisfactory method. The following analyses of the five standard
grades of northern foundry and mill pig irons are given by J. M. Hartman
(Bull. 1. db S. A., Feb., 1892):
No. 1. No. 2. No. 3. No. 4. No. 4 B. No. 5.
Iron 92.37 92.31 94.66 94.48 94.08 94.68
Graphitic carbon . . 3.52 2.99 2.50 2.02 2.02
Combined carbon.. .13 .37 1.52 1.98 1.43 3.83
Silicon 2.44 2.52 .72 .56 .92 .41
Phosphorus 1.25 1.08 .26 .19 .04 .04
Sulphur 02 .02 trace .08 .04 .02
Manganese 28 .72 .34 .67 2.02 .98
CHARACTERISTICS OP THESE IRONS.
No. 1. Gray. — A large, dark, open-grain iron, softest of all the numbers
and used exclusively in the foundry. Tensile strength low. Elastic limit
low. Fracture rough. Turns soft and tough.
No. 2. Gray.— A mixed large and small dark grain, harder than No. 1 iron,
and used exclusively in the foundry. Tensile strength and elastic limit
higher than No. 1. Fracture less rough than No. 1. Turns harder, less
tough, and more brittle than No. 1.
No. 3. Gray.-— Small, gray, close grain, harder than No. 2 iron, used either
in the rolling-mill or foundry. Tensile strength and elastic limit higher than
No. 2. Turns hard, less tough, and more brittle than No. 2.
No. 4. Mottled.— White background, dotted closely with small black spots
of graphitic carbon; little or no grain. Used exclusively in the rolling-mill.
Tensile strength and elastic limit lower than No. 3. Turns with difficulty;
less tough and more brittle than No. 3. The manganese in the B pig iron
replaces part of the combined carbon, making the iron harder and closing
the grain, notwithstanding the lower combined carbon.
No. 5. White.— Smooth, white fracture, no grain, used exclusively in the
rolling mill. Tensile strength and elastic limit much lower than No. 4. Too
hard to turn and more brittle than No. 4.
Southern pig irons are graded as follows, beginning with the highest in
silicon: Nos. 1 and 2 silvery, Nos. 1 and 2 soft, all containing over 3# of
silicon; Nos. 1, 2, and 3 foundry, respectively about 2.75$, 2.5# and 2% silicon;
No. 1 mill, or "foundry forge;" No. 2 mill, or gray forge; mottled; white
Good charcoal chilling iron for car wheels contains, as a rule, 0.56 to 0.95
silicon, 0.08 to 0.90 manganese, 0.05 to 0.75 phosphorus. The following is an
analysis of a remarkably strong car wheel: Si, 0.734; Mn, 0.438; P. 0.428,
S, 0.08; Graphitic C, 3.083; Combined C, 1.247; Copper, 0.029. The chill was
very hard— J4 in. deep at root of flange, y% in. deep on tread. A good
ordnance iron analyzed: Si, 0.30; Graphitic C, 2.20; Combined C, 1.70; F,
0.44; Mn, 3.55 (?). Its specific gravity was 7.22 and tenacity 31,734 Ibs.
per sq. in.
Influence of Silicon, Phosphorus, Sulphur, and Man-
ganese upon Cast Iron. — W. J. Keep, of Detroit, in several papers
(Trans. A. I. M. E., 1889 to 1893), discusses the influence of various chemical
elements on the quality of cast iron. From these the following notes have
been condensed:
SILICON.— Pig iron contains all the carbon that it could absorb during its
reduction in the blast-furnace. Carbon exists in cast iron in two distinct
forms. In chemical union, as " combined " carbon, it cannot be discerned,
except as it may increase the whiteness of the fracture, in so-called white
366 IRON AND STEEL.
iron. Carbon mechanically mixed with the iron as graphite is visible, vary-
ing in color from gray to black, while the fracture of the iron ranges from a
light to a very dark gray.
Silicon will expel carbon, if the iron, when melted, contains ail the carbon
that it can hold and a portion of silicon be added.
Prof. Turner concludes from his tests that the amount of silicon producing
the maximum strength is about 1.80$. But this is only true when a white
base is used. If an iron is used as a base which will produce a sound casting
to begin with, each addition of silicon will decrease strength. Silicon itself
is a weakening agent. Variations in the percentage of silicon added to a pig
iron will not insure a given strength or physical g-tructure, but these results
will depend upon the physical properties of the original iron.
After enough silicon has been added to cause solid castings, any further
addition and consequent increase of graphite weakens the casting.
As strength decreases from increase of graphite and decrease of combined
carbon, deflection increases ; or, in other words, bending is increased by
graphite. When no moie graphite can form and silicon still increases, de-
flection diminishes, showing that high silicon not only weakens iron, but
makes it stiff. This stiffness is not the same strength-stiffness which is
caused by compact iron and combined carbon. It is a brittle-stiffness.
Silicon of itself, however small the quantity present, hardens cast-iron;
but the decrease of hardness from the change of the combined carbon to
graphite, caused by the silicon, is so much more rapid than the hardening
produced by the increase of silicon, that the total effect is to decrease hard-
ness, until the silicon reaches from 3 to 5$.
As practical foundry-work does not call for more than 3$ of silicon, the
ordinary use of silicon does reduce the hardness of castings; but this is pro-
duced through its influence on the carbon, and not its direct influence on the
iron.
When the change from combined to graphite carbon has ceased to dimin-
ish hardness, say at from 2% to 5$ of silicon, the hardening by the silicon it.
self becomes more and more apparent as the silicon increases.
The term " chilling " irons is generally applied to such as, cooled slowly,
would be gray, but cooled suddenly become white either to a depth suffi-
cient for practical utilization (e.g., in car-wheels) or so far as to be detrimen-
tal. Many irons chill more or less in contact with the cold surface of the
mould in which they are cast, especially if they are thin. Sometimes this is
a valuable quality, but for general foundry purposes it is desirable to have
all parts of a casting an even gray.
Silicon exerts a powerful influence upon this property of irons, partially
or entirely removing their capacity of chilling.
When silicon is mixed with irons previously low in silicon the fluidity is
increased.
It is not the percentage of silicon, but the state of the carbon and the
action of silicon through other elements, which causes the iron to be fluid.
Silicon irons have always had the reputation of imparting fluidity to other
irons. This comes, no doubt, from the fact that up to C6% or 4% they increase
the quantity of graphite in the resulting casting.
A white iron which will invariably give porous and brittle castings can be
made solid and strong by the addition of silicon; a further addition of sib
con will turn the iron gray; and as the grayness increases the iron will grow
weaker. Excessive silicon will again lighten the grain and cause a hard and
brittle as well as a very weak iron. The only softening and shrinkage-les-
sening influence of silicon is exerted during the time when graphite is being
produced, and silicon of itself is not a softener or a lessener of shrinkage;
but through its influence on carbon, and only during a certain stage, does it
produce these effects.
PHOSPHORUS.— While phosphorus of itself, in whatever quantity present,
weakens cast-iron, yet in quantities less than 1.5$ its influence is n t suffi-
ciently great to overbalance other beneficial effects, which are exerted
before the percentage reaches 1$. Probably no element of itself weakens
cast iron as much as phosphorus, especially when present in large quantities.
Shrinkage is decreased when phosphorus is increased. All high-phosphorus
pig irons have low shrinkage. Phosphorus does not ordinarily harden cast
iron, probably for the reason that it does not increase combined carbon.
The fluidity of the metal is slightly increased by phosphorus, but not to
any such great extent as has been ascribed to it.
The property of remaining long in the fluid state must not be confounded
With fluidity, for it is not the measure of its ability to make sharp castings,
INFLUENCE OF SILICON, ETC., UPON CAST IRON. 367
or to run into the very thin parts of a mould. Generally speaking, the state
ment is justified that, to some extent, phosphorus prolongs the fluidity of
the iron while it is filling the mould.
The old Scotch irons contained about 1# of phosphorus. The foundry -irons
which are most sought for for small and thin castings in the Eastern States
contain, as a general thing, over \% of phosphorus.
Certain irons which contain from 4% to 7# silicon have been so much used
on account of their ability to soften other irons that they have come to be
known as " softeners " and as les?eners of shrinkage. These irons are valu-
able as carriers of silicon ; but the irons which are sold most as softeners
and shrinkage-lesseners are those containing from \% to 2% of phosphorus.
We must therefore ascribe the reputation of some of them largely to the
phosphorus and not wholly to the silicon which they contain.
From y±% to I# of phosphorus will do all that can be done in a beneficial
way, and all above that amount weakens the iron, without corresponding
benefit. It is not necessary to search for phosphorus-irons. Most irons
contain more than is needed, and the care should be to keep it within limits.
SULPHUR.— Only a small percentage of sulphur can be made to remain
in carbonized iron, and it is difficult to introduce sulphur into gray cast iron
or into any carbonized iron, although gray cast iron often takes from the
fuel as much more sulphur as the iron originally contained. Percentages
of sulphur that could be retained by gray cast iron cannot materially injure
the iron except through an increase of shrinkage. The higher the carbon,
or the higher the silicon, the smaller will be the influence exerted by
sulphur.
The influence of sulphur on all cast iron is to drive out carbon and
silicon and to increase chill, to increase shrinkage, and, as a general thing, to
decrease strength ; but if in practice sulphur will not enter such iron, we
shall not have any cause to fear this tendency. In every-day work, however,
it is found at times that iron which was gray when put into the cupola comea
out white, with increased shrinkage and chill, and often with decreased
strength. This is caused by decreased silicon, and can be remedied by an
increase of silicon.
Mr. Keep's opinion concerning the influence of sulphur, quoted above, is
disagreed with by J. B. Nau (Iron Aye, March 29, 1894). He says :
"Sulphur, in whatever shape it may be present, has a deleterious influence
on the iron. It has the tendency to reader the iron white by the influence
it exercises on the combination between carbon and iron. Pig iron contain-
ing a certain percentage of it becomes porous and full of holes, and castings
made from sulphurous iron are of inferior quality. This happens especially
when the element is present in notable quantities. With foundry-iron con-
taining as high as Q.\% of sulphur, castings of greater strength may be ob-
tained than when no sulphur is present.
That the sulphur contents of pig iron may be increased by the sulphur
contained in the coke used, is shown by some experiments in the cupola,
reported by Mr. Nau. Seven consecutive heats were made.
The sulphur content of the coke was 1$, and 11.7$ of fuel was added to the
charge.
Before melting, the silicon ranged from 0.320 to 0.830 in the seven heats ;
after melting, it was from 0.110 to 0.534, the loss in melting being from .100
to .375. The sulphur before melting was from .076 to .090, and after melting
from .132 to .174, a gain from .044 to .098.
From the results the following conclusions were drawn :
1. In all the charges, without exception, sulphur increased in the pig iron
after its passage through the cupola. In some cases this increase more
than doubled the original amount of sulphur found in the pig iron.
2. The increase of the sulphur contents in the iron follows the elimination
of a greater amount of silicon from that same iron. A larger amount of
limestone added to these charges would have produced a more basic cinder,
and undoubtedly less sulphur would have been incorporated in the iron.
3. This coke contained \% of sulphur, and if all its sulphur had passed into
the iron there would have been an average increase of 0.12 of sulphur for
the seven charges, while the real increase in the pig iron amounted to only
0.081. This shows that two thirds of the sulphur of the coke was taken up
by the iron in its passage through the cupola.
MANGANESE.— Manganese is a nearly white metal, having about the same
appearance when fractured as white cast iron. As produced commercially,
it is combined with iron, and with small percentages of silicon, phosphorus,
and sulphur.
If the manganese is under 40& with the remainder mostly iron, and silicon
368 IROtf AND STEEL.
not over 0.50$, the alloy is called spiegeleisen, and the fracture will show flat
reflecting surfaces, from which it takes its name.
With manganese above 50$, the iron alloy is called ferro-manganese.
As manganese increases beyond 50$, the mass cracks in cooling, and when
it approaches 98$ the mass crumbles or falls in small pieces.
Manganese combines with iron in almost any proportion, but if an iron
containing manganese is remelted, more or less of the manganese will escape
by volatilization, and by oxidation with other elements present in the iron.
If sulphur be present, some of the manganese will be likety to unite with it
and escape, thus reducing the amount of both elements in the casting.
Cast iron, when free from manganese, cannot hold more than 4.50$ of car-
bon, and 3.50$ is as much as is generally present; but as manganese increases,
carbon also increases, until we of ten 'find it in spiegel as high as 5$, and in
ferro-manganese as high as 6$. This effect on capacity to hold carbon is
peculiar to manganese.
Manganese renders cast iron less plastic and more brittle.
Manganese increases the shrinkage of cast iron. An increase of 1$ raised
the shrinkage 26$. Judging from some test records, manganese does not
influence chill at ail; but other tests show that with a given percentage ol
silicon the carbon may be a little more inclined to remain in the combined
form, and therefore the chill may be a little deeper. Hence, to cause the
chill to be the same, it would seem that the percentage of silicon should be
a little higher with manganese than without it.
An increase of 1$ of manganese increased the hardness 40$. If a hard
chill is required, manganese gives it by adding hardness to the whole casting
J. B. Nau (Iron Age, March 29, 1894), discussing the influence of manga-
nese on cast iron, says:
Manganese favors the combination between carbon and iron. Its influ
ence, when present in sufficiently large quantities, is even great enough no'
only to keep the carbon which would be naturally found in pig iron com-
bined, but it increases the capacity of iron to retain larger amounts of car"
bon and to retain it all in the combined state.
Manganese iron is often used for foundry purposes when some chill and
hardness of surface is required in the casting. For the rolls of steel-rail
mills we always put into the mixture a large amount of manganiferous iron,
and the rolls so obtained alwaj'S presented the desired hardness of surface
and in general a mottled structure on the outside. The inside, which al-
ways cooled much slower, was gray iron. One of the standard mixtures that
invariably gave good results was the following:
50$ of foundry iron with 1.3$ silicon and 1.5$ manganese;
35$ of foundry iron with 1$ silicon and 1.5$ manganese;
15$ steel (rail ends) with about 0.35$ to 0.40$ carbon.
The roll resulting from this mixture contained about 1$ of silicon and \%
of manganese.
Another mixture, which differed but little from the preceding, was as
follows:
45$ foundry iron with about 1.3$ silicon and 1.5$ manganese;
30$ foundry iron with about 1$ silicon and 1.5$ manganese;
10$ white or mottled iron with about 0.5$ to 0.6$ Si. and 1.2$ Mn.
15$ Bessemer steel-rail ends with about 0.35$ to 0.40$ C. and 0.6$ to 1$ Mn.
The pig iron used in the preceding mixtures contained also invariably
from 1.5$ to 1.8$ of phosphorus, so that the rolls obtained therefrom carried
about 1.3$ to 1.4$ of that element. The last mixture used produced rolls
containing on the average 0.8$ to 1$ of silicon and 1$ of manganese. When-
ever we tried to make those rolls from a mixture containing but 0.2$ to 0.3$
manganese our rolls were invariably of inferior quality, grayer, and con-
sequently softer. Manganese iron cannot be used indiscriminately for
foundry purposes. When greater softness is required in the castings man-
ganese has to be avoided, but when hardness to a certain extent has to be
obtained manganese iron can be used with advantage.
Manganese decreases the magnetism of the iron. This characteristic in-
creases with the percentage of manganese that enters into the composition
of the iron. The iron loses all its magnetism when manganese reaches 25$
of its composition. For tins reason manganese iron has to be avoided in
castings of dynamo fields and other pieces belonging to electric machinery,
where magnetic conductibility is one of the first considerations.
Shrinkage of Cast Iron.— Mr. Keep gives a series of curves show-
ing that shrinkage depends on silicon and on the cross-section of the
casting, decreasing as the silicon and the section increase. The following
figures are obtained by inspection of the curves:
ZESTS OF CAST IRON.
3G9
--(j
Size of Square Bars.
.
Size of Square Bars.
J5
§£
Jo
i in.
1 in.
2 in.
3 in.
4 in.
tin.
1 in.
2 in.
3 in.
4 in.
02 «
rr> ®
PH
Shrinkage, In. per Foot.
PH
Shrinkage, In. per Foot.
1.00
.178
.158
.129
.112
.102
2.50
.142
.121
.091
.072
.060
1 .50
.166
.145
.116
.099
.088
3.00
.130
.109
.078
.058
.046
2.00
.154
.133
.104
.086
.074
3.50
.118
.097
.065
.045
.032
Mr. Keep says- " The measure of shrinkage is practically equivalent to a
chemical analysis of silicon. It tells whether more or less silicon is needed
to bring the quality of the casting to an accepted standard of excellence."
Strength In Relation to Silicon and Cross-section.—
In castings one half-inch square in section the strength increases as silicon
increases from 1.00 to 3.50; in castings 1 in. square in section the strength
is practically independent of silicon, while in larger castings the strength
decreases as silicon increases.
The following table shows values taken from Mr. Keep's curves of the
approximate transverse strength of £-in. X 12-in. cast bars of different sizes.
MO
ft V
^
:3S3
m&
Size of Square Cast Bars.
Silicon.
Per Cent.
Size of Square Cast Bars.
i'in.
1 in.
2 in.
3 in.
4 in.
iin.
lin.
2 in.
Sin.
4 in.
Strength of a Hn. X 12-in.
Section, Ibs.
Strength of a i -in. X 12-in.
Section, Ibs.
1.00
1.50
2.00
290
324
358
260
272
278
232
228
220
222
212
202
220
208
196
2.50
3.00
3.50
392
426
446
278
276
264
212
202
192
190
180
168
184
172
160
Irregular Distribution of Silicon in Pig Iron.— J. W.
Thomas (Iron Age, Nov. 12, 1891) finds in analyzing samples taken from every
other bed of a cast of pig iron that the silicon varies considerably, the iron
coming first from the furnace having generally the highest percentage. In
one series of tests the silicon decreased from 2.040 to 1.713 from the first bed
to the eleventh. In another case the third bed had 1.260 Si., the seventh 1.718,
and the eleventh 1.101. He also finds that the silicon varies in each pig, be-
ing higher at the point than at the butt. Some of his figures are: point of
pig: 2.328 Si., butt of same 2 157; point of pig 1.834, butt of same 1.787.
Some Tests of Cast Iron. (G. Lanza, Trans. A. S. M. E., x., 187.)—
The chemical analyses were as follows:
Gun Iron, Common Iron,
per cent. per cent.
Total carbon .................... 3.51 .....
Graphite _____ ................... 2.80 .....
Sulphur ............ ............. 0.133 0.173
Phosphorus .................... 0.155 0.413
Silicon ........ . ................. 1.140 1.89
The test specimens were 26 inches long and square in section; those tested
with the skin on being very nearly one inch square, and those tested with
the skin removed being cast nearly one and one quarter inches square, and
afterwards planed down to one inch square.
Tensile Elastic
Strength. Limit.
Unplaned common. 20,200 to 23,000 T. S. Av. = 22,066 6,500
Planed common.... 20,300 to 20,800 ** " =20,520 5,833
Unplaned gun ..... 27,000 to 28,775 " " =28,175 11,000
Planed gun ...... ^ . . 29,500 to 31,000 " " = 30,500 8,500
13,194,233
11,943,953
16,130,300
15,932,880
370 IRON AND STEEL.
The elastic limit is not clearly defined in cast iron, the elongations increas-
ing faster than the increase of the loads from the beginning of the test.
The modulus of elasticity is therefore variable, decreasing as the loads in-
crease. For example, see the results of test of a cast-iron bar on p. 314.
The Streiigftlt of Cast ITron depends on many other things besides
its chemical composition. Among them are the size and shape of the
casting, the temperature at which the metal is poured, and the rapidity of
cooling. Internal stresses are apt to be induced by rapid cooling, and slow
cooling tends to cause segregation of the chemical constituents and opening
of the grain of the metal, making it weak. The relation of these variable
conditions to the strength of cast iron is a complex one and as yet but im-
perfectly understood. (See "Cast-iron Columns," p. 250.)
The author recommends that in making experiments on the strength of
cast iron, bars of several different sizes, such as 14, 1, 1^, and 2 in. square (or
round), should be taken, and the results compared. Tests of bars of one
size only do not furnish a satisfactory criterion of the quality of the iron of
which they are made. See Trans. A. I. M. E., xxvi., 1017.
CHEMISTRY OF FOUNDRY IRONS.
(C. A. Meissner, Columbia College Q'ly, 1890; Iron Age, 1890.)
Silicon is a very important element in foundry irons. Its tendency when
not above 2%% is to cause the carbon to separate out as graphite, giving the
casting the desired benefits of graphitic iron. Between 2\£$ and Sy&t silicon
is best adapted for iron carrying a fair proportion of low silicon scrap and
close iron, for ordinarily no mixture should run below 1J4£ silicon to get
good castings.
From 3^ to 5$ silicon, as occurs in silvery iron, will carry heavy amounts
of scrap. Castings are liable to be brittle, however, if not handled carefully
as regards proportion of scrap used.
From \y%% to 2f0 silicon is best adapted for machine work ; will give strong
clean castings if not much scrap is used with it.
Below \% silicon seems suited for drills and castings that have to stand
great variations in temperature.
Silicon has the effect of making castings fluid, strong, and open-grained ;
also sound, by its tendency to separate the graphite from the total carbon,
and consequent slight expansion of the iron on cooling, causing it to fill out
thoroughly. Phosphorus, when high, has a tendency to make iron fluid,
retain its heat longer, thereby helping to fill out all small spaces in casting.
It makes iron brittle, however, when above %$ in castings. It is excellent
when high to use in a mixture of low-phosphorus irons, up to 1V£$ giving
good results, but, as said before, the casting should be below %%. "it has a
strong tendency when above \% in pig to make the iron less graphitic, pre-
venting the separation of graphite.
Sulphur in open iron seldom bothers the founder, as it is seldom present
to any extent. The conditions causing open iron in the furnace cause low
sulphur. A little manganese is an excellent antidote against sulphur in the
furnace. Irons above \% manganese seldom have any sulphur of any con-
sequence.
Graphite is the all-important factor in foundry irons ; unless this is present
in sufficient amount in the casting, the latter will be liable to be poor.
Graphite causes iron to slightly expand on cooling, makes it soft, tough and
fluid. (The statement as to expansion on coolinsr is denied by W. J. Keep.)
Relation of the Appearance of Fracture to tlie Chemical
Composition.— S. H. Chauvenet says when run [from the blast-fur-
nace] the lower bed is almost always close grain, but shows practically the
same analysis as the large grain in the rest of the cast. If the iron runs
rapidly, the lower bed may have as large grain as any in the cast. If the
iron runs rapidly, for, say six beds and some obstruction in the tap-hole
causes the seventh bed to fill up slowly and sluggishly, this bed may be
close-grain, although the eighth bed, if the obstruction is removed will be
open-grain. Neither the graphitic carbon nor the silicon seems to have any
influence on the fracture in these cases, since by analysis the graphite and
silicon is the same in each. The question naturally arises whether it would
not be better to be guided by the analysis than by the fracture. The f rac-
ture is a guide, but it is not an infallible guide. Should not the open- and
the close-grain iron of the same cast be numbered under the same grade
when they have the same analysis ?
Mr, Meissner had many analyses made for the comparison of fracture
CHEMISTRY OF FOUNDRY IRONS.
371
A.
B.
C.
D.
E.
F.
Silicon
Sulphur
4.315
0 008
4.818
0 008
4.270
0 007
3.328
0 033
3.869
0 006
3.861
0 006
Graphitic car..
Comb carbon
3.010
2.757
2.680
2.243
3.070
0 108
3.100
0 096
A. Very close-grain iron, dark color, by fracture, gray forge.
jB. Open-grain, dark color, by fracture. No. 1.
C. Very close-grain, by fracture, gray forge.
D. Medium -grain, by fracture, No. 2, but much brighter and more open
than A, C, or F.
E. Very large, open-grain, dark color, by fracture, No. 1.
F. Very close-grain, by fracture, gray forge.
By comparing analyses A and B, or E and F, it appears that the close-
grain iron is in each case the highest in graphitic carbon. Comparing A
and E, the graphite is about the same, but the close-grain is highest in
silicon.
Analyses of Foundry Irons. (C. A. Meissner.)
SCOTCH IRONS.
Name.
Grade.
Silicon.
Phos-
phorus.
Manga-
nese.
Sul-
phur.
Graph-
ite.
Com.
Carbon.
Summerlee
2.70
0.545
1.80
0.01
3 09
0 25
2.47
0 760
2 51
0 015
Eglinton . .
3.44
2.70
2.15
1.000
0.810
0.618
1.70
2.90
2.80
0.015
0.02
0.025
2.00
3.76
0.80
0.21
Coltness
Ca rn b roe .
2.59
1 70
0.840
1.100
1.70
1 83
0.010
0 008
3.75
3 50
3.75
0 40
Glengarnock ....
Glengarnock said
to carry % scrap
2
3.03
4.00
1.200
0.900
2.85
3.41
0.010
1.78
0.90
AMERICAN SCOTCH IRONS.
No.
Sample
Silicon.
Phos-
phorus.
Manganese
Sulphur.
No.
Grade.
1
6.00
0 430
1.00
1
1.67
1.920
1.90
casting.
3
2 40
1 000
1 70
2
4
1 28
0 690
1 40
2
5a
3.50
0 613
2 51
1
56
2.90
0.733
1 40
casting.
6a
3.44
1.000
1 70
0 015
1
66
3.35
1.300
1.50
0 012
1
7
3.68
0.503
2.96
1
DESCRIPTION OP SAMPLES. — No. 1. Well known Ohio Scotch iron, almost
silvery, but carries two-thirds scrap ; made from part black-band ore. Very
successful brand. The high silicon gives it its scrap-carrying capacity.
No. 2. Brier Hill Scotch castings, made at scale works ; castings demand-
ing more fluidity than strength.
372
IRON" AND STEEL.
No. 3. Formerly a famous Ohio Scotch brand, not now in the market
Made mainly from black-band ore.
No. 4. A good Ohio Scotch, very soft and fluid; made from black-band
ore-mixture.
Nos. 5a and 56. Brier Hill Scotch iron and casting; made for stove pur-
poses; 350 Ibs. of iron used to 150 Ibs. scrap gave very soft fluid iron; worked
well.
No. 6a. Shows comparison between Summerlee (Scotch) (6a) and Brier Hill
Scotch (66). Drillings came from a Cleveland foundry, which found both
irons closely alike in physical and working quality.
No. 7. One of the best southern brands, very hard to compete with, owing
to its general qualities and great regularity of grade and general working.
MACHINE IRONS.
Sample
No
Silicon.
Phos-
phorus.
Manga-
nese.
Sulphur.
Graphite.
Comb.
Carbon.
Grade
No.
8
2 80
0 492
0 61
0 015
1
9
1 30
0.262
0.70
0.030
3
10a
2 66
0 770
1 20
0 020
2 51
2
106
3 63
0.411
1.25
0.014
3.05
1
11
2.10
0.415
0.60
0 050
2
12
13
1.37
3 10
0.294
0.124
1.51
trace
0.080
0 021
2.31
0.78
2
2
14
2 12
0.610
0.80
15
1 70
0 632
1 60
I6a
1 45
0 470
1 25
0 009
2
166
1 40
0 316
1 37
0.008
17
3 26
0 426
0 25
1
18
0 80
0 164
0.90
0 015
1
DESCRIPTION OP SAMPLES.— No. 8. A famous Southern brand noted for fine
machine castings.
No. 9. Also a Southern brand, a very good machine iron.
Nos. 10a and 106. Formerly one of the best known Ohio brands. Does not
shrink; is very fluid and strong. Foundries having used this have reported
very favorably on it.
No. 11. Iron from Brier Hill Co., made to imitate No. 3 ; was stronger
than No. 3; did not pull castings; was fluid and soft.
No. 12. Copy of a very strong English machine iron.
No. 13. A Pennsylvania iron, very tough and soft. This is partially Besse-
mer iron, which accounts for strength, while high silicon makes it soft.
No. 14. Castings made from Brier Hill Co/s machine brand for scale works,
very satisfactory, strong, soft and fluid.
No. 15. Castings made from Brier Hill Co.'s one half machine brand, one
half Scotch brand, for scale works, castings desired to be of fair strength,
but very fluid and soft.
No. 16a. Brier Hill machine brand made to compete with No. 3.
No. 166. Castings (clothes-hooks) from same, said to have worked badly,
castings being white and irregular. Analysis proved that some other iron
too high in manganese had been used, and probably not weii mixed.
No. 17. A Pennsylvania iron, no shrinkage, excellent macnine iron, soft
and strong.
No. 18. A very good quality Northern charcoal iron.
" Standard Grades" of the Brier Hill Iron and Coal
Company,
Brier Hill Scotch Iron.— Standard Analysis, Grade Nos. 1 and 2.
Silicon 2.00 to 3.00
Phosphorus 0.50to0.75
Manganese 2.00 to 2.50
Used successfully for scales, mowing-machines, agricultural implements,
novelty hardware, sounding-boards, stoves, and heavy work requiring no
special strength.
CHEMISTRY OF FOUNDRY IRO^TS.
373
Brier Hill Silvery Iron.— Standard Analysis, Grade No. 1.
Silicon 3. 50 to 5. 50
Phosphorus 1.00 to 1.50
Manganese 2.00 to 2.25
Used successfully for hollow-ware, car-wheels, etc., stoves, bumpers, and
similar work, with heavy amounts of scrap in all cases. Should be mainly
used where fluidity and no great strength is required, especially for heavy
work. When used with scrap or close pig low in phosphorus, castings of
considerable strength and great fluidity can be made
Fairly Heavy Machine Iron. — Standard Analysis, Grade No. 1.
Silicon 1 .75 to 2.50
Phosphorus... 0.50 to 0.60
Manganese 1.20 to 1.40
The best iron for machinery, wagon-boxes, agricultural implements,
pump-works, hardware specialties, lathes, stoves, etc., where no large
amounts of scrap are to be carried, and where strength, combined with
great fluidity and softness, are desired. Should not have much scrap with
Regular Machine Iron. — Standard Analysis, Grade Nos. 1 and 2.
Silicon 1.50 to 2. 00
Phosphorus 0.30 to 0.50
Manganese 0.80 to 1 .00
Used for hardware, lawn-mowers, mower and reaper works, oil-well
machinery, drills, fine machinery, stoves, etc. Excellent for all small fine
castings requiring fair fluidity, softness, and mainly strength. Cannot be
well used alone for large castings, but gives good results on same when used
with above-mentioned heavy machine grade; also when used with the
Scotch in right proportion. Will carry but little scrap, and should be used
alone for good strong castings.
For Axles and Materials Requiring Great Strength, Grade No. 2.
Silicon 1 .50
Phosphorus 0.200 and less.
Manganese 0 . 80
This gave excellent results.
A good neutral iron for guns, etc., will run about as follows :
Silicon , 1.00
Phosphorus 0.25
Sulphur 0.20
Manganese none.
It should be open No. 1 iron.
This gives a very tough, elastic metal. More sulphur would make tough
but decrease elasticity.
For fine castings demanding elegance of design but no strength, phos-
phorus to 3.00$ is good. Can also stand 1.50$ to 2. 00$ manganese. For work
of a hard, abrasive character manganese can run 2.00$ in casting.
Analyses of Castings.
Sample
No.
Silicon.
Phos-
phorus.
Manganese
Sulphur.
Graphite.
Comb.
Carbon.
31
32
33
34a
346
34c
35a
356
35o
35e
36
37a
376
2.50
0.85
1.53
1.84
2.20
2.50
2.80
3.10
3.30
2.88
4.50
3.43
2.68
1.90
1.400
0.351
0.327
0.577
0.742
1.208
0.418
1.280
0.879
0.408
0.660
1.439
0.900
0.980
2.20
0.92
1.08
1.04
1.10
1.16
0.54
1.14
0.80
1.10
0.78
0.90
1.30
1.20
0.030
0.040
3.10
0.58
0.025
374 IEOK AKD STEEL.
No. 81. Sewing-machine casting, said to be very fluid and good casting.
This is an odd analysis. I should say it would have been too hard and brit-
tle, yet no complaint was made.
No. 32. Very good machine casting, strong, soft, no shrinkage.
No. 33. Drillings from an annealer-box that stood the heat very well.
No. 34a. Drillings from door-hinge, very strong and soft.
No. 346. Drillings from clothes-hooks, tough and soft, stood severe ham-
mering.
No. 34c. Drillings from window-blind hinge, broke off suddenly at light
strain. Too high phosphorus.
No. 35«. Casting for heavy ladle support, very strong.
Nos 356 and 35c. Broke after short usage. Phosphorus too high. Car-
bumpers.
No. 35d. Elbow for steam heater, very tough and strong.
No. 36. Cog wheels, very good, shows absolutely no shrinkage.
No. 37. Heater top network, requiring fluidity but no strength.
No. 37a. Gray part of above.
No. 376. White, honeycombed part of above. Probably bad mixing and
got chilled suddenly.
STRENGTH OF CAST IRON.
Rankine gives the following figures:
Various qualities, T. S 13,400 to 29,000, average 16,500
Compressive strength 82,000 to 145,000, " 112,000
Modulus of elasticity 14,000,000 to 22,900,000, " 17,000,000
Specific Gravity and Strength. (Major Wade, 1856.)
Third-class guns: Sp. Gr. 7.087, T. S. 20,148. Another lot: least Sp. Gr. 7.163,
T. S. 22,402.
Second-class guns: Sp. Gr. 7.154, T. S. 24,767. Another lot : mean Sp. Gr.
7.302, T. S. 27,232.
First class guns: Sp. Gr. 7.204, T. S. 28,805. Another loft greatest Sp. Gr.
7.402, T. S. 31,027.
Strength of Charcoal Pig Iron. -Pig iron made from Salisbury
ores, in furnaces at Wassaic and Millerton, N. Y., has shown over 40,000 Ibs.
T. S. per square inch, one sample giving 42,281 Ibs. Muirkirk, Md., iron
tested at the Washington Navy Yard showed: average for No. 2 iron, 21,601
Ibs. ; No. 3, 23,959 Ibs. ; No. 4, 41,329 Ibs. ; average density of No. 4, 7.336 (J. C.
I. W., v. p. 44.)
Nos. 3 and 4 charcoal pig iron from Chapinville, Conn., showed a tensile
strength per square inch of from 34,761 Ibs. to 41,882 Ibs. Charcoal pig iron
from , Shelby, Ala. (tests made in August, 1891), showed a strength of
34,800 Ibs. for No. 3; No. 4, 39,675 Ibs.; No. 5, 46,450 Ibs.; and a mixture of
equal parts of Nos. 2, 3, 4, and 5, 41.470 Ibs. (Bull. I. & S. A.)
Variation of Density and Tenacity of Gun-irons.— An in-
crease of density invariably follows the rapid cooling of cast iron, and as a
general rule the tenacity is increased by the same means. The tenacity
generally increases quite uniformly with the density, until the latter ascends
to some given point; after which an increased density is accompanied by a
diminished tenacity.
The turning-point of density at which the best qualities of gun-iron attain
their maximum tenacity appears to be about 7.30. At this point of density,
or near it, whether in proof-bars or gun-heads, the tenacity is greatest.
As the density of iron is increased its liquidity when melted is diminished.
This causes it to congeal quickly, and to form cavities in the interior of the
casting. (Pamphlet of Builders1 Iron Foundry, 1893.)
Specifications for Cast Iron for the World's Fair Build-
ings, 1892. — Except where chilled iron is specified, all castings shall be
of tough gray iron, free from injurious cold-shuts or blow-holes, true to
pattern, and of a workmanlike finish. Sample pieces 1 in. square, cast from
the same heat of metal PI sand moulds, shall be capable of sustaining on a
ciear span of 4 feet 6 inches a central load of 500 Ibs. when tested in the
rough bar.
Specifications for Tests of Oast Iron in 12" B. 1^. Mortars,
(Pamphlet of Builders Iron Foundry, 1893.) — Charcoal Gun Iron. — The tensile
strength of the metal must average at each end at least 30,000 Ibs. per
square inch ; no specimen to be over 37,000 Ibs. per square inch ; but one
specimen from each end may be as low as 28,000 Ibs. per square inch. The
MALLEABLE CAST IRON". 375
long extension specimens will not be considered in making up these aver-
ages, but must show a good elongation and an ultimate strength, for each
specimen, of not less than 24,000 Ibs. The density of the metal must be such
as to indicate that the metal has been sufficiently refined, but not carried s0
high as t-> impair the other qualities.
Specifications for Grading Pig Iron for Car Wheels by
Chill Tests made at the Furnace. (Penna. K. II. Specifications,
1883.)— The chill cup is to be filled, even full, at about the middle of every
cast from the furnace. The test-piece so made will be 7J^ inches long, 3^
inches wide, and 1% inches thick, and is to be broken across the centre when
entirely cold. The depth of chill will be shown on the bottom of the test-
piece, and is to be measured by the clean white portion to the point where
gray specks begin to show in the white. The grades are to be by eighths of
an inch, viz., *&, J4, %, ^, %, %, %, etc., until the iron is mottled ; the lowest
grade being y% of an inch in depth of chill. The pigs of each cast are to be
marked with the depth of chill shown by its test-piece, and each grade is to
be kept by itself at the furnace and in forwarding.
Mixture of Cast Iron with Steel.— Car wheels are sometimes
made from a mixture of charcoal iron, anthracite iron, and Bessemer
steel. The following shows the tensile strength of a number of tests of
wheel mixtures, the average tensile strength of the charcoal iron used being
22, 000 Ibs.:
Ibs. per sq. in.
Charcoal iron with 2^ steel 22,46?
" *' 3%$ steel 26,733
" " Q14% steel and 6J4# anthracite 24,400
14 " "<%* steel and ty>% anthracite 28,150
" *' " 2%$ steel, 2^ wro't iron, and 6%% anth... 25,550
*• " ** 5 % steel, b% wro't iron, and 10# anth. ... 26,500
(Jour. C. 1. W., iii. p. 184.)
Cast Iron Partially Bessemerized.— Car wheels made of par-
tialby Bessemerized iron (blown in a Bessemer converter for 3^j minutes),
chilled in a chill test mould over an inch deep, just as a test of cold blast
charcoal iron for car wheels would chill. Car wheels made of this blown
iron have run 250,000 miles. (Jew. (7. I. W., vl. p. 77.)
Bad Cast Iron.— On October 15, 1891, the cast-iron fly-wheel of a large
pair of Corliss engines belonging to the Amoskeag Mfg. Co., of Manchester,
N. H., exploded from centrifugal force. The fly-wheel was 30 feet diam-
eter and 110 inches face, with one set of 12 arms, and weighed 116.000 Ibs.
After the accident, the rim castings, as well as the ends of the arms, were
found to be full of flaws, caused chiefly by the drawing and shrinking of the
metal. Specimens of the metal were tested for tensile strength, and varied
from 15,000 Ibs. per square inch in sound pieces to 1000 Ibs. in spongy ones.
None of these flaws shewed on the surface, and a rigid examination of the
parts before they were erected failed to give any cause to suspect their true
nature. Experiments were carried on for some time after the accident in
the Amoskeag Company's foundry in attempting to duplicate the flaws, but
with no success in approaching the badness of these castings.
MALLEABLE CAST IRON.
Malleableized cast iron, or malleable iron castings, are castings made
of ordinary cast iron which have been subjected to a process of decarboni-
zation, wrhich results in the production of a crude wrought iron. Handles,
latches, and other similar articles, cheap harness mountings, plowshares,
iron handles for tools, wheels, and pinions, and many small parts of ma-
chinery, are made of malleable cast iron. For such pieces charcoal cast iron
of the best quality (or other iron of similar chemical composition), should
be selected. Coke irons low in silicon and sulphur have been used in place
of charcoal irons. The castings are* made in the usual way, and are then
imbedded in oxide of iron, in the form, usually, of hematite ore, or in per-
oxide of manganese, and exposed to a full red-heat for a sufficient length of
time, to insure the nearly complete removal of the carbon. This decarboniza-
tion is conducted in cast-iron boxes, in which the articles, if small, are
packed in alternate layers with the decarbonizing material. The largest
pieces require the longest time. The fire is quickly raised to the maximum
temperature, but at the close of the process the furnace is cooled very
slowly. The operation requires from three to five days with ordinary small
castings, and may take two weeks for large pieces.
376
AKD STEEL.
Rules for Use of Malleable Castings, by Committee of Master
Car-builders1 Ass'n, 1890.
1. Never run abruptly from a heavy to a light section.
2. As the strength of malleable cast iron lies in the skin, expose as much
surface as possible. A star-shaped section is the strongest possible from
which a casting can be made. For brackets use a number of thin ribs instead
of one thick one.
3. Avoid all round sections; practice has demonstrated this to be the
weakest form. Avoid sharp angles.
4. Shrinkage generally in castings will be 3/16 in. per foot.
Strength of Malleable Cast Iron.— Experiments on the strength
of malleable cast iron, made in 1891 by a committee of the Master Car-
builders' Association. The strength of this metal varies with the thickness,
as the following results on specimens from 14 in. to \y% in. in thickness show:
Dimensions.
Tensile Strength.
Elongation.
Elastic Limit.
in. in.
Ib. per sq. in.
percent in 4 in.
Ib. per sq. in.
1.52 by .25
1.52 " .39
34,700
33,700
2
2
21,100
15,200
1.53 " .5
32,800
2
17,000
1.53 " .64
32,100
2
19,400
2. " .78
25,100
JL£
15,400
1.54 " .88
33,600
tyn
19,300
1.06 " 1.02
30,600
1
17,600
1.28 " 1.3
27,400
1
1.52 '* 1.54
28,200
IH
The low ductility of the metal is worthy of notice. The committee gives
the following table of the comparative tensile resistance and ductility of
malleable cast iron, as compared with other materials:
Ultimate
Strength,
Ib. per sq. in
Comparative
Strength ;
Cast Iron
= 1.
Elongation
Per Cent
in 4 in.
Comparative
Ductility;
Malleable
Cast Iron
= 1.
Cast iron
20,000
1
0 35
0 17
Malleable cast iron.
Wrought iron
Steel castings
32,000
50,000
60,000
1.6
2.5
1 3
2.00
20.00
10.00
1
10
5
Another series of tests, reported to the Association in 1892, gave the
following:
Thick-
ness.
Width.
Area.
Elastic
Limit.
Ultimate
Strength.
Elongation
in 8 in.
in.
.271
in.
2.81
sq. in.
.7615
Ib. per sq.
23.520
Ib. per sq. in.
32,620
percent.
1.5
.293
2.78
.8145
22,650
28,160
.6
.39
2.82
1.698
, 20,595
32,060
.5
.41
2.79
1.144
20,230
28,850
.11
.529
2.76
1.46
19.520
27,875
.1
.661
2.81
1.857
18,840
25,700
.7
.ft
2.76
2. SOS
18.390
25,120
.1
1.025
2.82
2.890
18,220
28,720
.5
1.117
2.81
3.138
17,050
25,510
.3
1.021
2.82
2.879
18,410
26,950
.3
WROUGHT IRON".
377
WROUGHT IRON.
Influence of Chemical Composition, on the Properties
of Wrought Iron. (Beaidslee on Wrought Iron and Chain Cables.
Abridgement by W. Kent. Wiley & Sons, 1879.)— A series of 2000 tests of
specimens from 14 brands of wrought iron, most of them of high repute,
was made in 1877 by Capt. L. A. Beardslee, U.S.N., of the United States
Testing Board. Forty-two chemical analyses were made of these irons,
with a view to determine what influence the chemical composition had
upon the strength, ductility, and welding power. From the report of these
tests by A. L, Holley the following figures are taken :
Average
Chemical Composition.
Brand.
Tensile
Strength.
S.
P.
Si.
C.
Mn.
Slag.
L
66,598
trace
(0.065
( 0.084
0.080
0.105
0.212
0.512
0.005
0.029
0.192
0.452
P
54,363
JO. 009
(0.001
0.250
0.095
0.182
0.028
0.033
0.066
0.033
0.009
0.848
1.214
B
52,764
0.008
0.231
0.156
0.015
o.oir
K1 i~KA
JO. 003
0.140
0.182
0.027
trace
0.678
10.005
0.291
0.321
0.051
0.053
1.724
0
51,134
JO. 004
(0.005
0.067
0.078
. 0.065
0.073
0.045
0.042
0.007
0.005
1.168
0.974
C
50,765
0.007
0.169
0.154
0.042
0.021
Tensile
Strength.
Reduction
of Area.
Elongation.
Welding Power.
1
18
19
most imperfect.
6
6
3
badly.
12
16
15
best.
16
18
19
18
4
rather badly,
very good. v
19
12
16
•
Where two analyses are given they are the extremes of two or more ana-
lyses of the brand. Where one is given it is the only analysis. Brand L
should be classed as a puddled steel.
ORDER OF QUALITIES GRADED FROM No. 1 TO No. 19.
Brand.
L
P
B
O
C
The reduction of area varied from 54.2 to 25.9 per cent, and the elonga-
tion from 29.9 to 8.3 per cent.
Brand O, the purest iron of the series, ranked No. 18 in tensile strength,
but was one of the most ductile; brand B, fquite impure, was below the
average both in strength and ductility, but was the best in welding power;
P, also quite impure, was one of the best in every respect except welding,
while L, the highest in strength, was not the most pure, it had the least
ductility, and its welding power was most imperfect. The evidence of the
influence of chemical composition upon quality, therefore, is quite contra-
dictory and confusing. The irons differing remarkably in their mechanical
properties, it was found that a much more marked influence upon their
qualities was caused by different treatment in rolling than by differences in
composition.
In regard to slag Mr. Holley says : " It appears that the smallest and
most worked iron often has the most slag. It is hence reasonable to con-
clude that an iron may be dirty and yet thoroughly condensed."
In his summary of " What is learned from chemical analysis,'1 he says :
** So far, it may appear that little of use to the makers or users of wrought
Iron has been learned. . . . The character of steel can be surely pred-
icated on the analyses of the materials; that of wrought iron is altered by
subtle and unobserved causes."
Influence of Reduction in Rolling from Pile to Bar on
the Strength of Wrought Iron.— The tensile strength of the irons
used in Bearaslee's tests ranged from 46,000 to 62,700 Ibs. per sq. in., brand
L, which was really a steel, not being considered. Some specimens of L
gave figures as high as 70,000 Ibs. The amount of reduction of sectional
378 IKON AND STEEL.
area in rolling the bars has a notable influence on the strength and elastic
limit; the greater the reduction from pile to bar the higher the strength.
The following are a few figures from tests of one of the brands:
Size of bar, in. diam. 4 3 2 1 U y*
Area of pile, sq. in.: 80 80 72 25 9 3
Bar per cent of pile: 15.7 8.83 4.36 3.14 2.17 16
Tensile strength, lb.: 46,322 47,761 48.280 51,128 52,275 59,585
Elastic limit, lb.: 23,430 26,400 31,892 36,467 39,126
Specifications for Wrowglit Iron (F. H. Lewis, Engineers' Club
of Philadelphia, 1891). — 1. All wrought iron must be tough, ductile, fibrous,
and of uniform quality for each class, straight, smooth, free from cinder-
pockets, flaws, buckles, blisters, and injurious cracks along the edges, and
must have a workmanlike finish. No specific process or provision of
manufacture will be demanded, provided the material fulfils the require-
ments of these specifications.
2. The tensile strength, limit of elasticity, and ductility shall be deter-
mined from a standard test-piece not less than 14 inch thick, cut from the
full-sized bar, and planed or turned parallel. The area of cross-section shall
not be less than % square inch. The elongation shall be measured after
breaking on an original length of 8 inches.
3. The tests shall show not less than the following results:
For bar iron in tension T. S. = 50,000; E. L. = 26,000; E. L. in 8 in., 18#
For shape iron in tension ... " = 48,000; " = 20,000; 15$
For plates under 36 in. wide " =48.000- " =26,000; " 12J
For plates over 36 in. wide.. '« =46,000; " =25,000; " IQJt
4. When full-sized tension members are tested to prove the strength of
their connections, a reduction in their ultimate strength of (500 X width of
bar) pounds per square inch will be allowed.
5. All iron shall bend, cold, 180 degrees around a curve whose diameter
is twice the thickness of piece for bar iron, and three times the thickness
for plates and shapes.
6. Iron which is to be worked hot in the manufacture must be capable
of bending sharply to a right angle at a working heat without sign of
fracture.
7. Specimens of tensile iron upon being nicked on one side and bent shall
show a fracture nearly all fibrous.
8. All rivet iron must be tough and soft, and be capable of bending cold
until the sides are in close contact without sign of fracture on the convex
side of the curve.
Pcnna. R. It. Co. 's Specifications for Merchant-bar Iron
(1902-).— One bar will be selected for test from each 100 bars in a pile.
All the iron of one size in the shipment will be rejected if the average ten-
sile strength of the specimens representing it falls below 47,000 Ibs. or ex-
ceeds 53,000 Ibs. per sq. in., or if any single specimens show less than 45,000
Ibs. per sq. in.
In the case of flat bars which have to be reduced in width for test an allow-
ance of 1,000 Ibs. per sq. in. will be made, making the rejection limit 46,000 Ibs.
per sq. in. All the iron of one size in. the shipment will be rejected if the
average elongation in 8 ins. falls below the following limits : Rounds, y% in.
and over, 20^ ; less than 14 in., 16#. Flats pulled as rolled. 20#; flats reduced,
W.
Niclcing and Bending Tests — "When necessary to make nicking and bend-
ing tests 'the iron will be held firmly in a vise, nicked lightly on one side and
then broken by a succession of light blows on the nicked side. It must
when thus broken show a generally fibrous structure, not more than 25#
crystalline, and must be free from admixture of steel.
Stay-bolt Iron. (Penna. R. R. Co.'s specifications, 1900.) — Sample bars must
show a tensile strength of not less than 48,000 Ibs. per sq. in. and an elonga-
tion of not less than i.'5# in 8 ins. One piece from each lot will be threaded in
dies with a sharp V thread, 12 to 1 in. and firmly screwed through two
holders having a clear space between them of 5 ins. Om holder will be
rigidly secured toths bed of a suitable machine and the other vibrated at
right angles to the axis over a space of % in. or % in. each side of the centre
line. Acceptable iron should stand 2,200 double vibrations, before breakage.
FORMULAE FOR UKIT STRAINS FOR IROK AHD STEEL. 379
Specifications for Wrought Iron for the World's Fair
Buildings. (Eng'g News, March 26, 1892.)— All iron to be used in the
tensile members of open trusses, laterals, pins and bolts, except plate iron
over 8 inches wide, and shaped iron, must show by the standard test-pieces
a tensile strength in Ibs. per square inch of :
52 000 — 7,000 X area of original bar in sq. in.
circumference of original bar in inches
with an elastic limit not less than half the strength given by this formula,
and an elongation of 20$ in 8 in.
Plate iron 24 inches wide and under, and more than 8 inches wide, must
show by the standard test-pieces a tensile strength of 48,000 Ibs. per sq. in.
with an elastic limit not less than 26,000 Ibs. per square inch, and an elon-
gation of not less than 12$. All plates over 24 inches in width must have a
tensile strength not less than 46,000 Ibs. with an elastic limit not less than
20,000 Ibs. per square inch. Plates from 24 inches to 36 inches in width must
have an elongation of not less than 10$; those from 36 inches to 48 inches in
width, 8$; over 48 inches in width. 5%.
All shaped iron, flanges of beams and channels, and other iron not herein-
before specified, must show by the standard test-pieces a tensile strength in
Ibs. per square inch of :
no 010 — 7,000 X area of original bar
' ~~ circumference of original bar*
with an elastic limit of not less than half the strength given by this formula,
and an elongation of 15$ for bars % inch and less in thickness, and of 12$ for
bars of greater thickness. For webs of beams and channels, specifications
for plates will apply.
All rivet iron must be tough and soft, and pieces of the full diameter of
the rivet must be capable of bending cold, until the sides are in close contact,
without sign of fracture on the convex side of the curve.
Stay-bolt Iron.— Mr. Vauclain, of the Baldwin Locomotive Works,
at a meeting of the American Railway Master Mechanics' Association, in
1892, says: Many advocate the softest iron in the market as the best for
stay-bolts. He believed in an iron as hard as was consistent with heading
the bolt nicely. The higher the tensile strength of the iron, the more vibra-
tions it will stand, for it is not so easily strained beyond the yield-point.
The Baldwin specifications for stay-bolt iron call for a tensile strength of
50,000 to 52,000 Ibs. per square inch, the upper figure being preferred, and
the lower being insisted upon as the minimum.
FORMULAE FOR UNIT STRAINS FOR IRON AND
STEEI, IN STRUCTURES.
(F. H. Lewis, Engineers' Club of Philadelphia, 1891.)
The following formulae for unit strains per square inch of net sectional
area shall be used in determining the allowable working stress in each mem-
ber of the structure. (For definitions of soft and medium steel see Specifi-
cations for Steel.)
Tension Members.
Wrought Iron.
Soft Steel.
Medium Steel.
Floor-beam hangers or
suspenders, forged
bars
Will not be used
6000
5000
8000
7000 (l 1 miM
Will not be used
5500
8000
8$ greater than
iron
Will not be used
16,000
7000
7000
7000
Will not be used
9000(1 + — )
v max./
9000(1 i min>)
Counter-ties ... .
Suspenders, hangers
and counters, riveted
members, net sec-
tion
Solid rolled beams
Riveted truss members
and tension flanges
of girders, net sec-
tion
Forged eyebars • .
V ' max./
Will not be used
15,000
Lateral or cross sec-
tion rods
"v\.* ' max./
/For eyebars\
V only, 17,000 )
380
IROK AND STEEL.
Shearing.
Wrought Iron.
Soft Steel.
Medium Steel.
On pin sand shop rivets
On field rivets
6000
4800
6600
5200
7200
\Vill not be used
In webs of girders
Will not be used
5000
6000
Bearing.
Wrought Iron.
Soft Steel.
Medium Steel.
On projected semi-
intrados of main-pin
holes ....
12000
13 200
14 500
On projected semi-in-
trados of rivet-holes*
On lateral pins
Of bed-plates on ma-
sonry
12,000
15,000
250 Ibs. per sq. in.
13,200
16,500
14,500
18,000
* Excepting that in pin-connected members taking alternate stresses, the
bearing stress must not exceed 9000 Ibs. for iron or steel.
Bending.
On extreme fibres of pins when centres of bearings are considered as
points of application of strains:
Wrought Iron, 15,000. Soft Steel, 16,000. Medium Steel, 17,000.
Compression Members.
Wrought Iron.
Soft Steel.
Medium
Steel.
Chord sections :
Flat ends
700o(l+^)- 3).?
One flat and one pin end..
Chords with pin ends and
all end-posts • .
V ' max./ r
rooo(! + i™-)-35-
V max./ r
TOOO (i+™^-)-40-
10#
20£
'00°0 + ^)-357.
greater
than
greater
than
Intermediate posts
7500 - 40 -
iron
iron
Lateral struts, and com-
pression in collision
struts, stiff suspenders
and stiff chords
10,500 - 50 -
r
J
In which formulae I — length of compression member in inches, and r -
least radius of gyration of member in inches. No compression member
shall have a length exceeding 45 times its least width, and no post should be
used in which I -=-r exceeds 125.
Members Subject to Alternate Tension and Compression.
Wrought Ir<3n.
Soft Steel.
Medium
Steel.
For compression only. . .
For the greatest stress . .
Use the formulae above
~ooo(i max< lesser )
8% greater
than iron
20$ greater
than iron
|00(V 2 max. greater/
Use the formula giving the greatest area of section.
The compression flanges of beams and plate girders shall have the same
cross-section as the tension flanges.
FORMULA FOE UNIT STRAINS FOR IRON AND STEEL. 381
W. H. Burr, discussing the formulae proposed by Mr. Lewis, says: " Taking
the results of experiments as a whole, I am constrained to believe that they
indicate at least 15% increase of resistance for soft-steel columns over those
of wrought iron, with from 20% to 25% for medium steel, rather than 10% and
2Q% respectively.
"The high capacity of soft steel for enduring torture fits it eminently for
alternate and combined stresses, and for that reason I would give it 15%
increase over iron, with about 22% for medium steel.
"Shearing tests on steel seem to show that 15% and 22% increases, for the
two grades respectively, are amply justified.
" I should not hesitate to assign 15% and 22% increases over values for iron
for bearing and bending of soft and medium steel as being within the safe
limits of experience. Provision should also be made for increasing pin-
shearing, bending and bearing stresses for increasing ratios of fixed to mov-
ing loads "
Maximum Permissible Stresses in Structural Materials
used in Buildings. (Building Ordinances of the City of Chicago, 1893.)
Cast iron, crushing stress: For plates, 15,000 Ibs. per square inch; for lintels,
brackets, or corbels, compression 13,500 Ibs. per square inch, and tension
3000 Ibs per square inch. For girders, beams, corbels, brackets, and trusses,
16,000 Ibs. per square inch for steel and 12,000 Ibs. for iron.
For plate girders :
maximum bending moment in ft.-lbs.
Flange area = - — g^—
D — distance between centre of gravity of flanges in feet.
n _ \ 13,500 for steel.
0 - 1 10,000 for iron.
maximum shear ( 10,000 for steel,
Web area = — - — — .. C = \ ^m f or iron.
For rivets in single shear per square inch of rivet area :
Steel. Iron.
If shop-driven. 9000 Ibs. 7500 Ibs.
If field-driven 7500 " 6000 "
For timber girders :
b = breadth of beam in inches.
d = depth of beam in inches.
_ cbd* I = length of beam in feet.
6 — jT ' (160 for long-leaf yellow pine,
c = •< 120 for oak,
( 100 for white or Norway pine.
Proportioning of Materials in the Memphis Bridge (Geo.
S. Morison, Trans. A. S. C. E., 1893).-— The entire superstructure of the Mem-
phis bridge is of steel and it was all worked as steel, the rivet-holes being
drilled in all principal members and punched and reamed in the lighter
members.
The tension members were proportioned on the basis of allowing the dead
load to produce a strain of 20,000 Ibs. per square inch, and the live load a
strain of 10,000 Ibs. per square inch. In the case of the central span, where
the dead load was twice the live load, this corresponded to 15,000 Ibs. total
strain per square inch, this being the greatest tensile strain.
The compression members were proportioned on a somewhat arbitrary
basis. No distinction was made between live and dead loads. A maximum
strain of 14,000 Ibs. per square inch was allowed on the chords and other
large compression members where the length did not exceed 16 times the
least transverse dimension, this strain being reduced 750 Ibs. for each addi-
tional unit of length. In long compression members the maximum length
was limited to 30 times the least transverse dimension, and the strains
limited to 6,000 Ibs. per square inch, this amount being increased by 200 lb;s.
for each unit by which the length is decreased.
Wherever reversals of strains occur the member was proportioned to re-
sist the sum of compression and tension on whichever basis (tension or
compression) there would be the greatest strain per square inch ; and, in
addition, the net section was proportioned to resist the maximum tension,
and the gross section to resist the maximum compression.
The floor beams and girders were calculated on the strain being limited to
10,000 Ibs. per square inch in extreme fibres. Rivet-holes in cover-plates and
flanges were deducted.
383
IROK AKD STEEL.
The rivets of steel in drilled or reamed holes were proportioned on the
basis of a bearing strain of 15,000 Ibs. per square inch and a shearing strain
of 7500 Ibs. per square inch, and special pains were taken to get the. double
shear in as many rivets as possible. This was the requirement for shop
rivets. In the case of field rivets, the number was increased one-half.
The pins were proportioned on the basis of a bearing strain of 18,000 Ibs.
per square inch and a bending strain of 20,000 Ibs. per square inch in ex-
treme fibre, the diameters of the pins being never made more than one inch
less than the width of the largest eye-bar attaching to them.
The weight on the rollers of the expansion joint on Pier II is 40,000 Ibs,
per linear foot of roller, or 3,333 Ibs. per linear inch, the rollers being 15 ins.
111 diamete*
As the sections of the superstructure were unusually heavy, and the strains
from dead load greatly in excess of those from moving load, it was thought
best to use a slightly higher steel than is now generally used for lighter
structures, and to work this steel without punching, all holes being drilled.
A somewhat softer steel was used in the floor-system and other lighter
parts.
The principal requirements which were to be obtained as the results of
tests on samples cut from finished material were as follows:
Max.
Ultimate
Strength,
Ibs. per
sq. inch.
Min.
Ultimate
Strength,
Ibs. per
sq. inch.
Min. Elastic
Limit, Ibs,
per sq. in.
Min. per-
centage of
Elongation
in 8 inches.
Min. Per-
centage of
Reduction
at Fracture
High-grade steel.
Eye-bar steel
Medium steel —
78,500
75,000
72,500
69,000
66,000
64,000
40,000
38,000
37,000
18
20
22
38
40
44
Soft steel
63,000
55,000
30,000
28
50
TENACITY OF METAL.S AT VARIOUS
TEMPERATURES.
The British Admiralty made a series of experiments to ascertain what loss
of strength and ductility takes place in gun-metal compositions when raised
to high temperatures. It was found that all the varieties of gun-metal
suffer a gradual but not serious loss of strength and ductility up to a certain
temperature, at which, within a few degrees, a great change takes place,
the strength falls to about one half the original, and the ductility is wholly
gone. At temperatures above this point, up to 500, there is little, if any,
further loss of strength; the temperature at which this great change and
loss of strength takes place, although uniform in the specimens cast from
the same pot, varies about 100° in the same composition cast at different
temperatures, or with some varying conditions in the foundry process.
The temperature at which the change took place in No. 1 series was ascer-
tained to be about 370°, and in that of No. 2, at a little over 250°. Whatever
may be the cause of this important difference in the same composition, the
fact stated may be taken as certain. Rolled Muntz metal and copper are
satisfactory up to 500°, and may be" used as securing-bolts with safety.
Wrought iron, Yorkshire and remanufactured, increase in strength up to
500°, but lose slightly in ductility up to 300°, where an increase begins and
continues up to 500°, where it is still less than at the ordinary temperature
of the atmosphere. The strength of Landore steel is not affected by temper-
ature up to 500°, but its ductility is reduced more than one half. (Iron, Oct.
6, 1877.)
Tensile Strength of Iron and Steel at High Tempera-
tures.—James E. Howard's tests (Iron Age, April 10, 1890) show that the
tensile strength of steel diminishes as the temperature increases from 0°
until a minimum is reached between 200° and 300° F., the total decrease
being about 4000 Ibs. per square inch in the softer steels, and from 6000 to
8000 Ibs. in steels of over 80,000 Ibs. tensile strength. From this minimum point
the strength increases up to a temperature of 400° to 650° F., the maximum
being reached earlier in the harder steels, the increase amounting to from
10,000 to 20,000 Ibs, per square inch above the minimum strength at from 200°
TENACITY OF METALS AT VARIOUS TEMPERATURES. 383
575°
63,080
66,083
38
925°
65,343
21
64,350
33
68,600
21
to 300°. From this maximum, the strength of all the steel decreases steadily
at a rate approximating 10,000 Ibs. decrease per 100° increase of tempera-
ture. A strength of 20,000 Ibs. per square inch is still shown by .10 C. steel
at about 1000° F., and by .60 to 7.00 C. steel at about 1600° F.
The strength of wrought iron increases with temperature from 0° up to a
maximum at from 400 to 600° F., the increase being from 8000 to 10,000 Ibs.
per square inch, and then decreas.es steadily till a strength of only 6000 Ibs.
per square inch is shown at 1500° F.
Cast iron appears to maintain its strength, with a tendency to increase,
until 900° is reached, beyond which temperature the strength gradually
diminishes. Under the highest temperatures, 1500° to 1600° F., numerous
cracks on the cylindrical surface of the specimen were developed prior to
rupture. It is remarkable that cast iron, so much inferior in strength to the
steels at atmospheric temperature, under the highest temperatures has
nearly the same strength the high-temper steels ther have.
Strength of Iron and Steel Boiler-plate at High Tem-
peratures. (Chas. Huston, Jour. F. /., 1877.)
AVERAGE OF THREE TESTS OP EACH.
Temperature F. 68°
Charcoal iron plate, tensile strength, Ibs 55.366
44 " contr. of area % 26
Soft open-hearth steel, tensile strength, Ibs 54,600
44 contr. % 47
" Crucible steel, tensile strength, Ibs 64,000
" contr. % 36
Strength of Wrought Iron and Steel at High Temper-
atures. (Jour. F. /., cxii., 1881, p. 241.) Kollmann's experiments at Ober-
hausen included tests of the tensile strength of iron and steel at tempera-
tures ranging between 70° and 2000° F. Three kinds of metal were tested,
viz., fibrous iron having an ultimate tensile strength of 52,464 Ibs., an elastic
strength of 38,280 Ibs., and an elongation of 1?.5#; fine-grained iron having
for the same elements values of 56,892 Ibs., 39,113 Ibs., and 20$; and Bes-
semer steel having values of 84,826 Ibs., 55,029 Ibs., and 14.5$. The mean
ultimate tensile strength of each material expressed in per cent of that at
ordinary atmospheric temperature is given in the following table, the fifth
column of which exhibits, for purposes of comparison, the results of experi-
ments carried on by a committee of the Franklin Institute in the years
1832-36.
Fine-grained
Iron,
per cent.
100.0
100.0
100.0
100.0
100.0
98.5
95.5
90.0
77.5
51.5
36.0
30.5
28.0
23.0
19.0
15.5
12.5
10.5
8.5
7.0
5.0
The Effect of Cold on the Strength of Iron and Steel.—
The following conclusions were arrived at by Mr. Styffe in 1805 :
(1) That the absolute strength of iron and steel is not diminished by
cold, but that even at the lowest temperature which ever occurs in Sweden
it is at least as great as at the ordinary temperature (about CO0 F,).
Fibrous
Temperature
Degrees F.
Wrought
Iron, p. c.
0
100.0
100
100.0
200
100.0
300
97.0
400
95.5
500
92.5
600
88.5
700
81.5
800
67.5
900
44.5
1000
26.0
1100
20.0
1200
18.0
1300
16.5
1400
13.5
1500
10.0
1600
7.0
1700
5.5
1800
4.5
1900
3.5
2000
3.5
Bessemer
Franklin
Steel,
Institute,
per cent.
per cent.
100.0
96.0
100.0
102.0
100.0
105.0
100.0
106.0
100.0
106.0
98.5
104.0
92.0
99.5
68.0
92.5
44.0
75.5
36.5
53.5
31.0
36.0
26.5
....
22.0
18.0
ff
15.0
m f
12.0
tt
m
10.0
8.5
7.5
6.5
5.0
..
.
364 IROK AND STEEL.
(2) That neither in steel nor in iron is the extensibility less in severe cold
than at the ordinary temperature.
(3) That the limit of elasticity in both steel and iron lies higher in severe
cold.
(4) That the modulus of elasticity in both steel and iron is increased on
reduction of temperature, and diminished on elevation of temperature ; but
that these variations never exceed 0.05 % for a change of temperature of 1.8°
F., and therefore such variations, at least for ordinary purposes, are of no
special importance.
Mr. C. P. Sandberg made in 1867 a number of tests of iron rails at various
temperatures by means of a falling weight, since he was of opinion that,
although Mr. Styffe's conclusions were perfectly correct as regards tensile
strength, they might not apply to the resistance of iron to impact at low
temperatures. Mr. Sandberg convinced himself that " the breaking strain "
of iron, such as was usually employed for rails, *' as tested by sudden blows
or shocks, is considerably influenced by cold ; such iron exhibiting at 10° F.
only from one third to one fourth of the strength which it possesses at
84° F." Mr. J. J. Webster (Inst. C. E., 1880) gives reasons for doubting
the accuracy of Mr. Sandberg's deductions, since the tests at the lower
temperature were nearly all made with 21 -ft. lengths of rail, while those at
the higher temperatures were made with short lengths, the supports in
every case being the same distance apart.
W. H. Barlow (Proc. Inst. C. E.) made experiments on bars of wrought
iron, cast iron, malleable cast iron, Bessemer steel, and tool steel. The bars
were tested with tensile and transverse strains, and also by impact ; one
half of them at a temperature of 50° F., and the other half at 5° F. The
lower temperature was obtained by placing the bars in a freezing mixture,
care being taken to keep the bars covered with it during the whole time of
the experiments.
The results of the experiments were summarized as follows :
1. When bars of wrought iron or steel were submitted to a tensile strain
and broken, their strength was not affected by severe cold (5° F.), but their
ductility was increased about \% in iron and 3$ in steel.
2. When bars of cast iron were submitted to a transverse strain at a low
temperature, their strength was diminished about 3% and their flexibility
about 16#.
3. When bars of wrought iron, malleable cast iron, steel, and ordinary
cast iron were subjected to impact at a temperature of 5° F., the force re-
quired to break them, and the extent of their flexibility, were reduced as
follows, viz.:
Eeduction of Force Reduction of Flexi-
of Impact, per cent. bility, per cent.
Wrought iron, about 3 18
Steel (best cast tool), about 3^
Malleable cast iron, about 4^| 15
Cast iron, about 21 not taken
The experience of railways in Russia, Canada, and other countries where
the winter is severe is that the breakages of rails and tires are far more
numerous in the cold weather than in the summer. On this account a
softer class of steel is employed in Russia for rails than is usual in more
temperate climates.
The evidence extant in relation to this matter leaves no doubt that the
capability of wrought iron or steel to resist impact is reduced by cold. On
the other hand, its static strength is not impaired by low temperatures.
Effect of Low Temperatures on Strength of Railroad
Axles. (Thos. Andrews, Proc. Inst. C. E., 1891.)— Axles 6 ft. 6 in. long
between centres of journals, total length 7 ft. 1% in., diameter at middle 4%
in., at wheel-sets 5^ in., journals 33$ X 7 in. were tested by impact at temper-
atures of 0° and 100° F. Between the blows each axle was half turned over,
and was also replaced for 15 minutes in the water-bath.
The mean force of concussion resulting from each impact was ascertained
as follows :
Let h = height of free fall in feet, w = weight of test ball, hw = W =
" energy," or work in foot-tons, x = extent of deflections between bearings,
then F (mean force) = — = -— -.
x x
DURABILITY OF IKO^ CORROSION, ETC.
385
The results of these experiments show that whereas at a temperature of
0* F. a total average mean force of 179 tons was sufficient to cause the
breaking of the axles, at a temperature of 100° F. a total average mean
force of 428 tons was requisite to produce fracture. In other words, the re-
sistance to concussion of the axles at a temperature of 0° F. was only about
42% of what it was at a temperature of 100° F.
The average total deflection at a temperature of 0° F. was 6.48 in., as
against 15.06 in. with the axles at 100° F. under the conditions stated; this
represents an ultimate reduction of flexibility, under the test of impact, of
about 57# for the coid axles at 0° F., compared with the warm axles at
100° F.
EXPANSION OF IRON AND STEEI, BY HEAT.
James E. Howard, engineer in charge of the U. S. testing-machine at Wa-
tertown, Mass., gives the following results of tests made on bars 35 inches
long (Iron Age, April 10, 1890):
Metal.
Marks.
Chemical composition.
Coefficient of
Expansion.
C.
Mn.
Si.
Feby
difference.
Per degree
F. per unit
of length.
Wrought iron
.0000067302
.0000067561
.0000066259
.0000065149
.0000066597
.0000066202
.0000063891
.0000064716
.0000062167
.0000062335
.0000061700
.0000059261
.0000091286
Steel
la
2a
3a
4a
5a
6a
7a
8a
9a
lOa
.09
.20
.31
.37
.51
.57
.71
.81
.89
.97
.11
.45
.57
.70
.58
.93
.58
.56
.57
.80
99.80
99.35
99.12
98.93
98.89
98.43
98.63
98.46
98.35
97.95
.02
.07
.08
.17
.19
.28
DURABILITY OF IRON, CORROSION, ETC.
Durability of Cast Iron.— Frederick Graff, in an article on the
Philadelphia water-supply, says that the first cast-iron pipe used there was
laid in 1820. These pipes were made of charcoal iron, and were in constant
use for 53 years. They were uncoated, and the inside was well filled with
tubercles. In salt water good cast iron, even uncoated, will last for a cen-
tury at least; but it often becomes sofc enough to be cut by a knife, as is
shown in iron cannon taken up from the bottom of harbors after long sub-
mersion. Close-grained, hard white metal lasts the longest in sea water.—
Eiig'g News, April 23, 1887, and March 26. 189-2.
Tests of Iron after Forty Years' Service.— A square link 12
inches broad, 1 inch thick and about 12 feet long was taken from the Kieff
bridge, then 40 years old, and tested in comparison with a similar link which
had been preserved in the stock-house since the bridge was built. The fol-
lowing is the record of a mean of four longitudinal test-pieces, 1 X 1^ X 8
inches, taken from each link (Stahl und Eisen, 1890):
Old Link taken New Link from
from Bridge. Store-house.
21.8
11.1
Tensile strength per square inch, tons ,
Elastic limit
Coi
longation, percent 14.05
Dntraction, per cent 17.35
22.2
11.9
13.42
18.75
Durability of Iron in Bridges. (G. Lindenthal, Eng'g, May 2,
1884, p. 139.)— The Old Monongahela suspension bridge in Pittsburgh, built
in 1845, was taken down in 1882. The wires of the cables were frequently
strained to half of their ultimate strength, yet on testing them after 37 years'
386 IRON AND STEEL.
use they showed a tensile strength of from 72,700 to 100,000 Ibs. per square
inch. The elastic limit was from 67,100 to 78,600 Ibs. per square inch. Re-
duction at point of fracture, 35% to 75$. Their diameter was 0.13 inch.
A new ordinary telegraph wire of same gauge tested for comparison
showed: T. S., of 100,000 Ibs.; E. L., 81,550 Ibs.; reduction, 57$. Iron rods
used as stays or suspenders showed: T. S., 43,770 to 49,720 Ibs. per square
inch; E. L., 26,380 to 29,200. Mr. Lindenthal draws these conclusions from
his tests:
" The above tests indicate that iron highly strained for a long number of
years, but still within the elastic limit, and exposed to slight vibration, will
not deteriorate in quality.
" That if subjected to only one kind of strain it will not change its texture,
even if strained beyond its elastic limit, for many years. It will stretch and
behave much as in a testing-machine during a long test.
14 That Iron will change its texture only when exposed to alternate severe
straining, as in bending in different directions. If the bending is slight but
very rapid, as in violent vibrations, the effect is the same."
Corrosion of Iron Bolts,— On bridges over the Thames in London,
bolts exposed to the action of the atmosphere and rain-water were eaten
away in 25 years from a diameter of % in. to y% in., and from % in. diameter
to 5/16 inch.
Wire ropes exposed to drip in colliery shafts are very liable to corrosion.
Corrosion of Iron and Steel.— Experiments made at the Riverside
Iron Works, Wheeling, W. Va., on the comparative liability to rust of iron
and soft Bessemer steel: A piece of iron plate and a similar piece of steel,
both clean and bright, were placed in a mixture of yellow loam and sand,
with which had been thoroughly incorporated some carbonate of soda, nitrate
of soda, ammonium chloride, and chloride of magnesium. The earth as
prepared was kept moist. At the end of 33 days the pieces of metal were
taken out, cleaned, and weighed, when the iron was found to have lost 0.84$
of its weight and the steel 0.72$. The pieces were replaced and after 28 days
weighed again, when the iron was found to have lost 2.06$ of its original
weight and the steel 1.79$. (Eng'g, June 26, 1891.)
Corrosive Agents in the Atmosphere,— The experiments of F,
Grace Gal vert (Chemical News, March 3, 1871) show that carbonic acid, in
the presence of moisture, is the agent which determines the oxidation of
iron in the atmosphere. He subjected ^perfectly cleaned blades of iron and
steel to the action of different gases for a period of four months, with
results as follows:
Dry oxygen, dry carbonic acid, a mixture of both gases, dry and damp
oxygen and ammonia: no oxidation. Damp oxygen: in three experiments
one blade only was slightly oxidized.
Damp carbonic acid: slight appearance of a white precipitate upon the
iron, found to be carbonate of iron. Damp carbonic acid and oxygen:
oxidation very rapid. Iron immersed in water containing carbonic acid
oxidized rapidly.
Iron immersed in distilled water deprived of its gases by boiling rusted
the iron in spots that were found to contain impurities.
Galvanic Action is a most active agent of corrosion. It takes place
when two metals, one electro-negative to the other, are placed in contact
and exposed to dampness.
Sulphurous acid (the product of the combustion of the sulphur in coal) is
an exceedingly active corrosive agent, especially when the exposed iron is
coated with soot. This accounts for the rapid corrosion of iron in railway
bridges exposed to the smoke from locomotives. (See account of experi-
ments by the author on action of sulphurous acid in Jour Frank Inst., June,
1875, p. 437.) An analysis of sooty iron rust from a railway bridge showed
the presence of sulphurous, sulphuric, and carbonic acids, chlorine, and
ammonia, Bloxam states that ammonia is formed from the nitrogen of the
air during the process of rusting.
Corrosion in Steam-boilers.— Internal corrosion may be due
either to the use of water containing free acid, or water containing sulphate
or chloride of magnesium, which decompose when heated, liberating the
acid, or to water containing air or carbonic acid in solution. External
corrosion rarely takes place when a boiler is kept hot, but when cold it is
apt to corrode rapidly in those portions where it adjoins the brickwork or
where it may be covered by dust or ashes, or wherever dampness may
lodge. (See Impurities of Water, p. 551, and Incrustation and Corrosion,
p. 716.)
PRESERVATIVE COATINGS. 387
PRESERVATIVE COATINGS.
(The following notes have been furnished to the author by Prof.
A. H. Sabin.)
Cement,— Iron-work is sometimes protected by bedding in concrete,
in which case it is first cleaned and then washed with neat cement before
being imbedded.
Asphaltum.— This is applied hot either by dipping (as water-pipe) or
by pouring it on (as bridge floors). The asphalt should be slightly elastic
when cold, with a high melting-point, not softening much at 100° F., applied
at 300° to 400°; surface must be dry and should be hot; coating should be of
considerable thickness.
Paint,— Composed of a vehicle or binder, usually linseed oil or some
inferior substitute, or varnish (enamel paints); and a pigment which is a
more or less inert solid in the form of powder, either mixed or ground
together. The principal pigments are white lead (carbonate) and white
zinc (oxide), red lead (peroxide), oxides of iron, hydra ted and dehydrated,
graphite, lamp-black, chrome yellow, ultramarine and Prussian blue, and
various tinting colors. White lead has the greatest body or opacity of white
pigments; three coats of it equal five of white zinc; zinc is more brilliant
and permanent, but it is liable to peel, and it is customary to mix the two.
These are thei standard white paints for all uses and the basis of all light-
colored paints. Anhydrous iron oxides are brown and purplish brown,
hydrated iron oxides are yellowish red to reddish yellow, with more or less
brown; most iron oxides are mixtures of both sorts. They also contain
frequently manganese and clay. They are cheap, and are serviceable
paints for woDd, and are often used on iron, but for the latter use are
falling into disrepute. Graphite used for painting iron contains from 10
to 90$ foreign matter, usually silicates and iron oxides. It is very opaque,
hence has great covering power, and may be applied in a very thin coat
which should be avoided. It retards the drying of oil, hence the necessity
of using dryery; these are lead and manganese compounds dissolved in oil
and turpentine or benzine, and act as carries of oxygen; they are necessary
in most paints, but should be used as little as possible. There are many
grades of lamp-black; as a rule the cheaper sorts contain oily matter and
are especially hard to dry; all lamp-black is slow to dry in oil. It is the
principal black on wood, and is used some on iron, usually in combination
with varnish or varnish-like compounds. It is very permanent on wood.
A gallon of oil takes only a pound of lamp-black to make a paint, while
the same amount of oil requires about 40 Ibs. of red lead. On this account
red-lead paint, which weighs about 30 Ibs. per gallon, is the most expensive
of all comon paints. It does not dry slowly like other oil paints, but com-
bines with the oil to make a sort of cement; on this account it is used on
the joints of steam-pipes, etc. To prevent the mixture of red lead and oil
setting into a cake, and also to cheapen it, it is often adulterated with
whiting or sometimes with white zinc, the proportion of adulterant being
sometimes double the lead. Red lead has long had a high reputation as a
paint for iron and steel and is still used very extensively; but of late years
some of the new paints and varnish-like preparations have displaced it to
some oxtent even on the most important work.
Varnishes.— These are made by melting fossil resin, to which is then
added from half its weight to three times its weight of refined Unseed oil,
and the compound is thinned with turpentine; they usually contain a little
dryer. They are chiefly used on wood, being more durable and more ;
brilliant than oil, and are often used over paint to preserve it. Asphaltum
is sometimes substituted in part or in whole for the fossil resin, and in this
way are made varnishes which have been applied to iron and steel with
good results. Asphaltum and animal and vege able tar and pitch have also
been simply dissolved in solvents, as benzine or carbon disulphide, and used
for the same purpose.
All these preservative coatings are supposed to form impervious films,
keeping out air and moisture; but in fact all are somewhat porous. On this
account it is necessary to have a film of appreciable thickness, best formed
by successive coats, so that the pores of one will be closed by the next. The
pigment is used to give an agreeable color, to help fill the pores of the oil
film, to make the paint harder so that it will resist abrasion, and to make a
thicker film. In varnishes these results are sought to be attained by the
resin which is dissolved in the oil. There is no sort of agreement among
388 IRON" AND STEEL.
practical men as to which is the best coating for any particular case; this is
probably because so much depends on the preparation of the surface and
the care with which the coating is applied, and also because the conditions
of exposure vary so greatly.
Methods of Application.— Too much care cannot be given to the
preparation of the surface. If it is wood, it should be dry, and the surface
of knots should be coated with some preparation which will keep the tarry
matter in the wood from the coating. All old paint or varnish should be
removed by burning and scraping. Metallic surfaces should be cleaned by
wire brushes and scrapers, and if the permanence of the work is of much
importance the scale and oxide should be completely removed by acid
pickling or by the sand-blast or some equally efficient means. Pickling is
usually done with a 10$ solution of sulphuric acid; as the solution becomes
exhausted it may be made more active by heating. All traces of acid must
be removed by washing and the metal must be rapidly dried and painted
before it becomes in the slightest degree oxidized. The sand-blast, which
has been applied to large work recently and for many years to small work
with good results, leaves the surface perfectly clean and dry; the paint
must be applied immediately. Plenty of time should always be allowed,
usually about a week, for each coat of paint to dry before the next coat is
applied; less than two coats should never be used. Two will last three
times as long as one coat. Benzine should not be an ingredient in coatings
for iron-work, because its rapid evaporation lowers the temperature of the
iron and may cause formation of dew on the surface adjacent to the paint
which is immediately to be painted.
Cast iron water-pipes are usually coated by dipping in a hot mixture of
coal-tar and coal-tar pitch; riveted steel pipes by dipping in hot asphalt or
by a japan enamel which is baked on at about 400° F. Ships' bottoms are
usually coated with some sort of paint to prevent rusting, over which is
spread, hot, a poisonous, slowly soluble compound, usually a copper soap,
to prevent adhesion of marine growths.
Galvanized-iron and tin surfaces should be thoroughly cleaned with
benzine and scrubbed before painting. When new they are covered with
grease and chemicals used in coating the plates, and these must be removed
or the paint will be destroyed.
Quantity of" Paint for a Given Surface.— One gallon of paint
will cover 250 to 350 sq. ft. as a first coat, depending on the character of the
surface, and from 350 to 450 sq. ft. as a second coat.
Qualities of Paints.— The Railroad and Engineering Journal, vols.
liv and Iv, 1890 and 1891, has a series of articles on paint as applied to wooden
structures, its chemical nature, application, adulteration, etc., by Dr. C. B.
Dudley, chemist, and F. N. Pease, assistant chemist, of the Penna. R. R.
They give the results of a long series of experiments on paint as applied to
railway purposes.
Rustless Coatings for Iron and Steel,— Tinning, enamelling,
lacquering, galvanizing, electro-chemical painting, and other preservative
methods are discussed in two important papers by M. P. Wood, in Trans.
A. S. M. E., vols. xv and xvi.
A Method of Producing an Inoxidizable Surface on
iron and steel by means of electricity has been developed by M. A. de JMeri-
tens (Engineering). The article to be protected is placed in a bath of ordi-
nary or distilled water, at a temperature of from 158° to 176° F., and an
electric current is sent through. The water is decomposed into its elements,
oxygen and hydrogen, and the oxygen is deposited on the metal, while the
hydrogen appears at the other pole, which may either be the tank in which
the operation is conducted or a plate of carbon or metal. The current has
only sufficient electromotive force to overcome the resistance of the circuit
and to decompose the water; for if it be stronger than this, the ox}'gen com-
bines with the iron to produce a pulverulent oxide, which has no adherence.
If the conditions are as they should be, it is only a few minutes after the
oxygen appears at the metal before the darkening of the surface shows
that the gas has united with the iron to form the magnetic oxide Fe3O4,
which will resist the action of the air and protect the metal beneath it.
After the action has continued an hour or two the coating is sufficiently
solid to resist the scratch-brush, and it will then take a brilliant polish.
If a piece of thickly rusted iron be placed in the bath, its sesquioxide
(FeaO3) is rapidly transformed into the magnetic oxide. This outer layer
CHEMICAL COMPOSITION AKD PHYSICAL CHARACTER. 389
has no adhesion, but beneath it there will be found a coating vhich is
actually a part of the metal itself.
In the early experiments M. de Meritens employed pieces of steel only,
but in wrought and cast iron he was not successful, for the coating came off
with the slightest friction. He then placed the iron at the negative pole of
the apparatus, after it had been already applied to the positive pole. Here
the oxide was reduced, and hydrogen was accumulated in the pores of the
metal. The specimens were then returned to the anode, when it was found
that the oxide appeared quite readily and was very solid. But the result
was not quite perfect, and it was not until the bath was filled with distilled
water, in place of that from the public supply, that a perfectly satisfactory
result was attained.
Manganese Plating of Iron as a Protection from Rust.
— According to the Italian Progreso, articles of iron can be protected against
rust by sinking them near the negative pole of an electric bath composed of
10 litres of water, 50 grammes of chloride of manganese, and 200 grammes
of nitrate of ammonium. Under the influence of the current the bath
deposits on the articles a protecting film of metallic manganese.
A Non-oxidizing Process of Annealing is described by H. P.
Jones, in Eng'g News, Jan. 2, 1892. The new process uses a non-oxidizing
gas, and is the Invention of Mr. Horace K. Jones, of Hartford, Conn. Its
principal feature consists in keeping the annealing retort in communication
with the gas-holder or gas-main during the entire process of heating and
cooling, the gas thus being allowed to expand back into the main, and being,
therefore, kept at a practically constant pressure.
The retorts are made from wrought-iron tubes. The gas is taken directly
from the mains supplying the city with illuminating gas. If metal which
has been blued or slightly oxidized is subjected to the annealing process it
comes out bright, the oxide being reduced by the action of the gas.
Comparative tests were made of specimens of steel wire annealed in
illuminating gas, in nitrogen, and in an open fire and cooled in ashes, and of
specimens of the unannealed metal. The wires were .188 in. in diameter
and were turned down to .150 in.
The average results were as follows:
Unannealed, two lots, 5 pieces each, tensile strength av. 97,120 and 80,790
IDS. per sq. in., elongation 7.12$ and 8.80$. Annealed in open fire, 8 tests, av.
t. s. 63,090, el. 26.76$. Annealed in nitrogen, av. of 3 lots, 13 pieces, t. s.
59,820, el. 29.33$. Annealed in illuminating gas, av. of 3 lots, 13 pieces, t. s.
60,180, el. 28.29#. The elongations are referred to an original length of
1.15 ins.
STEEL.
RELATION BETWEEN THE CHEMICAL COMPOSI-
TION AND PHYSICAL CHARACTER OF STEEL.
W. R. Webster (see Trans. A. I. M. E., vols. xxi and xxii, 1893-4) gives re-
sults of several hundred analyses and tensile tests of basic Bessemer steel
plates, and from a study of them draws conclusions as to the relation of
chemical composition to strength, the chief of which are condensed as
follows :
The indications are that a pure iron, without carbon, phosphorus, man-
ganese, silicon, or sulphur, if it could be obtained, would have a tensile
strength of 34,750 Ibs. per square inch, if tested in a %-inch plate. With
this as a base, a table is constructed by adding the following hardening
effects, as shown by increase of tensile strength, for the several elements
named.
Carbon, a constant effect of 800 Ibs. for each 0.01$.
Sulphur, " 500 " " 0.01$.
Phosphorus, the effect is higher in high-carbon than in low-carbon steels.
With carbon hundreths $ 9 10 11 12 13 14 15 16 17
Each . 01$ P has an effect of Ibs. 900 1000 1100 1200 1300 1400 1500 1500 1500
Manganese, the effect decreases as the per cent of manganese increases.
( .00 .15 .20 .25 .30 .35 .40 .45 .50 .55
Mn being per cent •{ to to to to to to to to to to
( .15 .20 .25 .30 .35 .40 .45 .50 .55 .65
Str'gth increases for .01$ 240 240 220 -JOO 180 160 140 120 100 100 Ibs.
Total incr. from 0 Mn . .. 3600 4800 51)00 GOOO 7800 8GOO 9 iOO 9900 10,400 11,400
390
STEEL.
Silicon is so low in this steel that its hardening effect has not been con-
sidered.
With the above additions for carbon and phosphorus the following table
has been constructed (abridged from the original by Mr. Webster). To the
figures given the additions for sulphur and manganese should be made as
above.
Estimated Ultimate Strengths of Basic Bessemer Steel
Plates.
For Carbon, .06 to .24; Phosphorus, .00 to .10; Manganese and Sulphur, .00 in
all cases.
Carbon.
.06
.08
.10
.12
.14 i .16 .18
.20 [ .22 j .24
I
Phos. .005
39,950
41,550
43,250
44,950
46,650
48,3(X)i 49,900
51,500
53,100
54,700
44 .01
40,350
41,950
43,750
45,550
47,350
49,050 50,650
52,250
53,850
55,450
44 .02
41,150
42,750
44,750
46,750
48,750
50,550 52,150
53,750
55,350
56.950
44 .03
41,950
43,550
45,750
47,950
50, 150 152,050 '53, 650
55,250
56,850
58.450
44 .04
42,750
44,350
46,750
49,150
51,550
53.550 55,150
56,750
58,350
59,950
" .05
43,550
45,150
47,750
50.350
52,950
55.050 56,650
58,250
59,850
61.450
44 .06
44,350
45,950
48,750
51,550
54,350
56,550 58,150
59,750
61,350
62.950
44 .0?
45,150
46,750
49,750
52,750
55,750
58,050 59,650
61,250
62,850
64.450
44 .08
45,950
47,550
50,750
53.950
57,150
59,550 61,150
62,750
64,350
65,950
44 .09
46,750
48,350
51,750
55,15C
58,550
61,05062,650
64,250
65,850
67,450
4' .10
47,550
49,150
52,750
56,350
59,950
62,55064,150
65.750
67.350
68.950
.001 Phos ~
801bs.
80 Ibs.
100 Ib
120 Ib
140 Ib
150 Ib 1501bll501bI1501bl 150 Ib
In all rolled steel the quality depends on the size of the bloom or ingot
from which it is rolled, the work put on it, and the temperature at which it
is finished, as well as the chemical composition.
The above table is based on tests of plates % inch thick and under 70
inches wide; for other plates Mr. Webster gives the following corrections
for thickness and width. They are made necessary only by the effect of
thickness and width on the finishing temperature in ordinary practice.
Steel is frequently spoiled by being finished at too high a temperature.
Corrections for Size of Plates,
Plates. Up to 70 ins. wide. Over 70 ins. wide.
Inches thick. Lbs. Lbs.
% and over. —2000 —1000
11/16 44 —1750 — 750
— 1500 — 500
7/6
5/4
— 1250
— 1000
— 500
0
+ 3000
— 250
- 0
± 500
+ 1000
+ 5000
Comparing the actual result of tests of 408 plates with the calculated
results, Mr. Webster found the variation to range as in the table below.
Summary of the Differences Between Calculated and
Actual Results in 408 Tests of Plate Steel.
In the first three columns the effects of sulphur were not considered; in
the last three columns the effect of sulphur was estimated at 500 Ibs. for
each .01$ of S.
J-.TJ
_
03
r-H
00
03** C3
!_.
•o
0)
£
*J
^
S'S %£
> s
rt
^
>'^H
c3
^
O g^S
e
W
1
6
£
o
i|f
Per cent within 1000 Ibs .
" il " 2000 " .
23.4
40.9
32.1
48.9
28.4
45.6
24.6
48.5
27.0
54.9
26.0
52.2
28.4
55.1
3000 " .
62.5
71.3
67.6
67.8
73.0
70.8
74.7
4000 44 .
75 5
81.0
78.7
82.5
85.2
84.1
89.9
" " 44 5000 " .
89.5
91.1
90.4
93.0
92.8
92.9
94.9
STRENGTH OF BESSEMER AND OPEN-HEARTH STEELS.
The last figure in the table would indicate that if specifications were drawn
calling for steel plates not to vary more than 5000 Ibs. T. S. from a specified
figure (equal to a total range of 10,000 Ibs.), there would be a probability of
the rejection of 5# of the blooms rolled, even if the whole lot was made from
steel of identical chemical analysis. In 1000 heats only 2# of the heats failed
to meet the requirements of the orders on which they were graded; the loss
of plates was much less than 1#, as one plate was rolled from each heat and
tested before rolling the remainder of the heat.
R. A. Hadfield (Jour. Iron and Steel Inst., No. 1, 1894) gives the strength of
very pure Swedish iron, rernelted and tested as cast, 20.1 tons (45,024 Ibs.)
per sq. in.; remelted and forged, 21 tons (47,040 Ibs.). The analysis of the
cast bar was: C, 0 08: Si. 0.04; S, 0.02; P, 0.02; Mn. 0.01; Fe, 99.82.
Effect of Oxygen upon Strength of Steel.— A. Lantz, of the
Peine works, Germany, in a letter to Mr. Webster, says that oxygen plays
an important role — such that, given a like content of carbon, phosphorus,
and manganese, a blow with greater oxygen content gives a greater hard-
ness and less ductility than a blow with less oxygen content. The method
used for determining oxygen is that of Prof. Ledebur, given in Stahl und
Eisen, May, 1892, p. 193. The variation in oxygen may make a difference in
strength of nearly ]4 Ion per sq. in. (Jour. Iron and Steel Inst., No. 1, 1894.)
RANGE OF VARIATION IN STRENGTH OF BESSEMER
AND OPEN-HEARTH STEELS.
The Carnegie Steel Co. in 1888 published a list of 1057 tests of Bessemer
and open-hearth steel, from which the following figures are selected :
Kind of Steel.
No. of Tests.
Elastic Limit.
I Ultimate
Strength.
Elongation
per cent
in 8 inches.
High't.1
Lowest
High't.
Lowest
High't.
Lowest
(«) Bess, structural. . .
(b) »
(c) Bess, angles
(d) O. H. fire-box
100
170
72
05
46,570
47,690
41,890
39,230
39,970
32,630
71,300
73,540
63,450
62,790
69.940
61,450
65,200
56,130
50,350
63,970
33.00
30.25
34.30
36.00
30.00
23.75
23.15
26.25
25.62
22.75
(e) O. H. bridge
20
REQUIREMENTS OF SPECIFICATIONS.
(a) Elastic limit, 35.000; tensile strength, 62,000 to 70,000; elong. 22# in 8 in.
(6) Elastic limit, 40,000; tensile strength, 67,000 to 75,000.
(c) Elastic limit, 30,000; tensile strength, 56,000 to 64,000; elong. 20# in 8 in.
(d) Tensile strength 50,000 to 62,000; elong. 26# in 4 in.
(e) Tensile strength. 64,000 to 70,000; elong. 20# in 8 in.
Strength of Open -hearth Structural Steel. (Pencoyd Iron
Works.)— As a general rule, the percentage of carbon in steel determines its
hardness and strength. The higher the carbon the harder the steel, the
higher the tenacity, and the lower the ductility will be. The following list
exhibits the average physical properties of good open-hearth basic steel :
Per cent
Carbon.
SUSS .
eg fl as
a 2 os^
5£5Sr
P
.fe .
O.13 ftfl
111*
H
fl .
"•"*&
p
£00
02
32
31
31
30
30
29
29
28
28
•bi
^«f
w <u
f
-L3 C*
fl °
il
Is
P-i
,a
<gtjo£ .
as s P. a
llli
&
-fls
silt
H
d
M*
3 d
2S
02
•fei
1^
,08
.09
.10
.11
.12
.13
.14
.15
.16
54000
54800
55700
56500
57400
58200
59100
60000
60800
32500
33000
33500
34000
34500
35000
35500
36000
36500
60
58
57
56
55
54
53
52
51
.17
.18
.19
.20
.21
.22
.23
.24
.25
61600
62500
63300
64200
65000
65800
66600
67400
68-200
37000
37500
38000
38500
39000
39500
40000
40500
41000
27
27
26
26
25
25
24
24
23
50
49
48
47
46
45
44
43
42
The coefficient of elasticity is practically uniform for all grades, and is
the same as for iron, viz., 29,000,000 Ibs. These figures form the average of
a numerous series of tests from rolled bars, and can only serve as an ap-
392
STEEL.
proximation in single instances, when the variation from the average may
be considerable. Steel below .10 carbon should be capable of doubling flat
without fracture, after being chilled from a red heat in cold water. Steel
of .15 carbon will occasionally submit to the same treatment, but will
usually bend around a curve whose radius is equal to the thickness of
the specimen ; about 90$ of specimens stand the latter bending test without
fracture. As the steel becomes harder its ability to endure this bending
test becomes more exceptional, and when the carbon ratio becomes .20,
little over 25% of specimens wi •! stand the last-described bending test. Steel
having about .40$ carbon will usually harden sufficiently to cut soft iron
and maintain an edge.
Mehrtens gives the following tables in Stahl und Eisen (Iron Age, April 20,
1893) showing the range of variation in strength, etc., of basic Bessemer and
of basic open-hearth structural steel. The figures in the columns headed
Per Cent show the per cent of the total number of charges which came
within the range given.
BASIC BESSEMER STEEL, 680 CHARGES.
Elastic Limit,
pounds per
sq. in.
35,500 to 38,400. .
38,400 to 39,800 . .
39, 800 to 41, 200..
41,200 to 42,700. .
42, 700 to 46,400..
BASIC
84,400 to 37,000..
37,000 to 39,800..
39, 800 to 42, 700..
42,700 to 4 1,100..
44,100 to 48,400..
Hi yet steel, 19
.. 15.0
.. 81.6
.. 27.5
.. 16.0
.. 9.9
OPEN-HI
.. 12.3
.. 85. 9
.. 30,2
... 11.4
... 8.5
charges
o »•> A >)S O
Tensile Strength, p
pounds per c&nt
sq. in.
55,600 to 56,900.... 18.67
56,900 to 58,300.... 38.67
58,300 to 59,700... 23.53
59, 700 to 6 1,200.... 15.60
61, 200 to 62,300.... 3.53
ARTH STRUCTURAL STEEL,
55,800 to 56,900 8.0
56,900 to 59,700 51.8
59,700 to 61,200 19.6
61,200 to 62,600 11.2
62,600 to 65, 100. ... 9.4
showed a total range fix
Elongation,
per cent.
21 to 25
Per
Cent.
, 2.65
25 to 27
27 to 29
25.88.
50.44
29 to 30
30 to 32.5....
489 CHARGES.
20 to 25
14.41
6.62
21 7
r< ~
26 to 28.
21.3
23 to 30
30 to 37 1
25.3
. .. . 24.3
>m 51,800 to
56,900 Ibs.
Low Strength Due to Insufficient Work. (A. E. Hunt,
Trans. A. I. M. E., 1886.)— Soft steel ingots, made in the ordinary way for
boiler plates, have only from 10,000 to 20,000 Ibs. tensile strength per sq. in.,
In the basic Bessemer steel over 90$ was below 0.08 phosphorus, and afr
were below 0.10; manganese was below 0.6 in over 90$, and below 0.9 in all ,
sulphur was below 0.05 in 84$, the maximum being 0.071 ; carbon was below
0.10, and silicon below 0.01 in all. In the basic open-hearth steel phosphorus
was below 0.06 in 96$, the maximum being 0.08; manganese below 0.50 in 97$;
sulphur below 0.07 in 88$, the maximum being 0.12. The carbon ranged
from 0.09 to 0.14.
Low Tensile Strength of Very Pure Steel.— Swedish nail-rod
open-hearth steel, tested by the author in 1881, showed a tensile strength of
only 42,591 Ibs. per sq. in. A piece of American nail-rod steel showed 45,021
Ibs. per sq. in. Both steels contained about .10 carbon and .015 phosphorus,
and were very low in sulphur, manganese, and silicon. The pieces tested
were bars about 2 x %\r\. section.
steel ingots, made in the ordinary way for
,000 to 20,000 Ibs. tensile strength per sq. in.,
an elongation of only about 10$ in 8 in., and a reduction of area of less than
20$. Such ingots, properly heated and rolled down from. 10 in. to % in.
thickness, w^i give from 55,000 to 65,000 Ibs. tensile strength, an elongation
in 8 in. of from 23$ to 33$, and a reduction of area of from 53$ to 70$. Any
work stopping short of the above reduction in thickness ordinarily yields
intermediate results in its tensile tests.
Effect of Finishing Temperature in Rolling.— The strength
and ductility of steel depend to a high degree upon fineness of grain, and
this may be obtained by having the temperature of the steel rather low, say
at a dull red heat, 1300° to 1400° F., during the finishing stage of rolling. In
the manufacture of steel rails a great improvement in quality has been
obtained by finishing at a low temperature. An indication of the finishing
temperature is the amount of shrinkage by cooling after leaving the rolls.
' The Philadelphia and Heading Railway Company's specification for rails
(1902) says, " The temperature of the ingot or blooin shall be such that with
rapid rolling and without holding before or in the finishing passes or subse-
quently, and withoutarrificial cooling after leaving the last pass, the distance
between hot saws shall not exceed 30 ft. 6 in. for a 30-ft. rail."
. fining the Grain by Annealing.— Steel which is coarse-grained
STRENGTH 037 BESSEMER AND OPEN-HEARTH STEELS. 393
on account of leaving the rolls at too high a temperature may be made fine-
grained and have its ductility greatly increased without lowering its tensile
strength by reheating to a cherry red and cooling at once in air. (See paper
on "Steel Rails,1' by Robert Job, Trans. A. I. M. E., 1902.)
Effect of Cold Rolling.— Cold rolling of iron and steel increases the
elastic limit and the ultimate strength, and decreases the ductility. Major
Wade's experiments on bars rolled and polished cold by Lauth's process
showed an average increase of load required to give a slight permanent set
as follows : Transverse, 162$; torsion, 130$; compression, 161$ on short
columns 1J^ in. long, and 64$ on columns 8 in. long; tension, 95$. The hard-
ness, as measured by the weight required to produce equal indentations,
was increased 50$; and it was found that the hardness was as great in the
centre of the bars as elsewhere. Sir W. Fairbairn's experiments showed an
increase in ultimate tensile strength of 50$, and a reduction in the elongation
in 10 in. from 2 in. or 20$, to 0.79 in. or 7.9#.
Hardening of Soft Steel.— A. E. Hunt (Trans. A. I. M. E., 1883, vol.
xii), says that soft steel, no matter how low in carbon, will harden to a cer-
tain extent upon being heated red-hot and plunged into water, and that it
hardens more when plunged into brine and less when quenched in oil.
An illustration was a heat of open-hearth steel of 0.15$ carbon and 0.29$ of
manganese, which gave the following results upon test-pieces from the same
34 in. thick plate.
Maximjum
Load.
Ibs. per sq. in.
Unhardened 55,000
Hardened in water 74,000
Hardened in brine 84,000
Hardened in oil 67,700
While the ductility of such hardened steel does not decrease to the extent
that the increased tenacity would indicate, and is much superior to that of
normal steel of the high tenacity, still the greatly increased tenacity after
hardening indicates that there must be a considerable molecular change in
the steel thus hardened, and that if such a hardening should be created
locally in a steel plate, there must be very dangerous internal strains caused
thereby.
Comparison of Tests of Full-size Eye-bars and Sample
Test-pieces of Same Steel Used in the Memphis Bridge.
(Geo. S. Morison, Trans. A. S. C. E., 1893.)
Elongation Reduction
in 8 in.
Per cent.
27
25
22
of Area.
Per cent.
62
50
43
49
Full-Sized Eyebars,
Sections 10" wide X 1 to 2 3/16" thick.
Reduc-
Elongation.
Elastic
Max.
Reduc-
Elon-
Elastic
Max.
tion of
Limit,
Load,
tion,
gation,
Limit,
Load,
Area,
in 8 ins.
p.c.
Inches.
p.c.
Ibs. per
sq. in.
p.c.
p.c.
Ibs. per
sq. in.
39.6
20.2
16.8
35,100
67,490
47.5
27.5
41,580
73,050
39.7
26.6
8.2
37,680
70,160
52.6
24.4
42,650
75,620
44.4
36.8
11.8
39,700
65,500
47.9
28.8
40,280
70,280
38.5
38.5
17.3
33,140
65,060
47.5
27.5
41,580
73,050
40.0
32.5
13.5
32,860
65,600
44.5
20.0
43,750
75,000
39.4
36.8
15.3
31,110
61,060
42 7
28.8
42,210
69,730
34.6
32.9
13.7
33,990
63,220
52 .'2
28.1
40,230
69,720
32.6
13.0
13.5
29,330
63,100
48.3
28.8
38,090
71,300
7.3
20.8
6.9
28,080
55,160
43.2
24.2
38,3 ?0
70,220
38.1
28.9
14.1
29,670
62,140
59.6
26.3
40,200
71,080
31.8
24.0
11.8
32,700
65,400
40.3
25.0
39,360
69,360
48.6
39.4
19.3
30,500
58,870
40.3
25.0
40,910
70,360
10.3
11.8
12.3
33,360
73,550
51.5
25.5
40,410
69,900
44.6
32.0
15.7
32,520
60,710
43.6
27.0
40,400
70,490
46.0
35:8
14.9
28,000
58,720
44.4
29.5
40,000
66,800
41.8
23.5
13.1
32,290
62,270
42.8
21.3
40,530
72,240
41.2
47.1
15.1
29,970
58,680
45.7
27.0
40,610
70,480
Sample Bars from Same Melts,
about 1 in. area.
The average strength of the full-sized eye-bars was about 8000 Ibs. per sq.
in., or about 12$, less than that Qf the sample test-pieces.
394 STEEL.
TREATMENT OF STRUCTURAL STEEL.
(James Christie, Trans. A. S. C. E., 1893.)
Effect of Punching and Shearing,— There is no doubt that steefc
of higher tensile strength than is now accepted for structural purposes
should not be punched or sheared, or that the softer material may contain
elements prejudicial to its use however treated, but especialty if punched.
But extensive evidence is on record indicating that steel of good quality, in
bars of moderate thickness and below or not much exceeding 80.000 Ibs.
tensile strength, is not any more, and frequently not as much, injured as
wrought iron by the process of punching or shearing.
The physical effects of punching and shearing as denoted by tensile test
are for iron or steel:
Reduction of ductility; elevation of tensile strength at elastic limit; reduc-
tion of ultimate tensile strength.
In very thin material the superficial disturbance described is less than in
thick; in fact, a degree of thinness is reached where this disturbance prac-
tically ceases. On the contrarj', as thickness is increased the injury
becomes more evident.
The effects described do not invariably ensue; for unknown reasons there
are sometimes marked deviations from what seems to be a general result.
By thoroughly annealing sheared or punched steels the ductility is to a
large extent restored and the exaggerated elastic limit reduced, the change
being modified by the temperature of reheating and the method of cooling.
It is probable that the best results combined with least expenditure can
be obtained by punching all holes where vital strains are not transferred by
the rivets; and by reaming for important joints where strains on riveted
joints are vital, or wherever perforation may reduce sections to a minimum.
The reaming should be sufficient to thoroughly remove the material dis-
turbed by punching; to accomplish this it is best to enlarge punched holes
at least £& in. diameter with the reamer.
Riveting.— It is the current practice to perforate holes 1/16 in. larger
than the rivet diameter. For work to be reamed it is also a usual require-
ment to punch the holes from ^ to 3/10 in. less than the finished diameter,
the holes being reamed to the proper size after the various parts are
assembled.
It is also excellent practice to remove the sharp corner at both ends of
the reamed holes, so that a fillet will be formed at the junction of the body
and head of the finished rivets.
The rivets of either iron or mild steel should be heated to a bright red or
yellow heat and subjected to a pressure of not less than 50 tons per square
inch of sectional area.
For rivets of ordinary length this pressure has been found sufficient to
completely fill the hole. If, however, tie holes and the rivets are excep-
tionally long, a greater pressure and a slower movement of the closing tool
than is used for shorter rivets has been found advantageous in compelling
the more sluggish flow of the metal throughout the longer hole.
"Welding.— No welding should be allowed on any steel that enters into
structures.
Upsetting.— Enlarged ends on tension bars for screw-threads, eye oars,
etc., are formed by upsetting the material. With proper treatment and a
sufficient increment of enlarged sectional area over the body of the bar the
result is entirely satisfactory. The upsetting process should be performed
so that the properly heated inetal is compelled to flow without folding or
lapping.
Annealing.— The object of annealing structural steel is for the purpose
of securing homogeneity of structure that is supposed to be impaired by un-
equal heating, or by the manipulation necessarily attendant on certain pro-
cesses. The objects to be annealed should be heated throughout to a
uniform temperature and uniformly cooled.
The physical effects of annealing, as indicated by tensile tests, depend on
the grade of steel, or the amount of hardening elements associated with it;
also on the temperature to which the steel is raised, and the method or rate
of cooling the heated material.
The physical effects of annealing medium-grade steel, as indicated by ten-
sile test, are reported very differently by different observers, some claiming
directly opposite results from others. It is evident, when all the attendant
conditions are considered, that the obtained results must vary both in kind
and. degree.
TREATMENT OF STRUCTURAL STEEL. 395
The temperatures employed will vary from 1000° to 1500° F.; possibly even
a wider range is used. In some cases the heated steel is withdrawn at full
temperature from the furnace and allowed to cool in the atmosphere ; in
others the mass is removed from the furnace, but covered under a muffle,
to lessen the free radiation; or, again, the charge is retained in the furnace,
and the whole mass cooled with the furnace, and more slowly than by either
of the other methods.
The best general results from annealing will probably be obtained by in-
troducing the material into a uniformly-heated oven in which the tempera-
ture is not so high as to cause a possibility of cracking by sudden and
unequal changing of temperature, then gradually raising the temperature
of the material until it is uniformly about 1200° F., then withdrawing the
material after the temperature is somewhat reduced and cooling under
shelter of a muffle, sufficiently to prevent too free and unequal cooling on
the one hand or excessively slow cooling on the other.
G. G. Mehrtens, Trans. A. S. C. E. 1893, says : " Annealing is of advantage
to all steel above 64,000 Ibs. strength per square inch, but it is questionable
whether it is necessary in softer steels. The distortions due to heating
cause trouble in subsequent straightening, especially of thin plates.
k' In a general way all unannealed mild steel for a strength of 56,000 to
64,000 Ibs. may be worked in the same way as wrought iron. Rough treat-
ment or working at a blue heat must, however, be prohibited. Shearing is
to be avoided, except to prepare rough plates, which should afterwards be
smoothed by machine tools or flies before using. Drifting is also to be
avoided, because the edges of the holes are thereby strained beyond the
yield point. Reaming drilled holes is not necessary, particularly when
sharp drills are used and neat work is done. A slight countersinking of the
edges of drilled holes is all that is necessary. Working the material while
heated should be avoided as far as possible, and the engineer should bear
this in mind when designing structures. Upsetting, cranking, and bending
ought to be avoided, but when necessary the material should be annealed
after completion.
"The riveting of a mild-steel rivet should be finished as quickly as pos-
sible, before it cools to the dangerous heat. For this reason machine work
is the best. There is a special advantage in machine work from the fact
that the pressure can be retained upon the rivet until it has cooled suffi-
ciently to prevent elongation and the consequent loosening of the rivet."
Flinching and Drilling of Steel Plates. (Froc. lust. M. E.,
Aug. 1887, p. 3v.'6.)— In Prof. Un win's report the results of the greater num
ber of the experiments made on iron and steel plates lead to the general
conclusion that, while thin plates, even of steel, do not suffer very much
from punching, yet in those of ^ in. thickness and upwards the loss of te-
nacity due to punching ranges from 10$ to 23$ in iron plates and from 11$ to
33$ in the case of mild steel. Mr. Parker found the loss of tenacity in steel
plates to be as high as fully one third of the original strength of the plate.
In drilled plates, on the contrary, there is no appreciable loss of strength.
It is even possible to remove the bad effects of punching by subsequent
reaming or annealing.
Working Steel at a Blue Heat.— Not only are wrought iron and
steel much more brittle at a blue heat (i.e., the heat that would produce an
oxide coating ranging from light straw to blue on bright steel, 430° to 600°
F.), but while they are probably not seriously affected by simple exposure
to blueness, even if prolonged, yet if they be worked in this range of tem-
perature they remain extremely brittle after cooling, and may indeed be
more brittle than when at blueness ; this last point, however, is not certain.
(Howe, "Metallurgy of Steel,1' p. 534.)
Tests by Prof. Krohn, for the German State Railways, show that working
at blue heat has a decided influence on all materials tested, the injury done
being greater on wrought iron and harder steel than on the softer steel.
The fact that wrought iron is injured by working at a blue heat was reported
by Stromeyer. (Engineering JNeivs, Jan. 9, 1892.)
A practice among boiler-makers for guarding against failures due to work-
ing at a blue heat consists in the cessation of work as soon as a plate which
had been red-hot becomes so cool that the mark produced by rubbing a
hammer-handle or other piece of wood will not glow. A plate which is not
hot enough to produce this effect, yet too hot to be touched by the hand, is
most probably blue hot, and should under no circumstances be hammered
or bent. (0. E. Stromeyer, Proc. Inst. C. E. 1886.)
Welding of Steel.— A. E. Hunt (A. I. M. E., 1892) says : I have never
seen so-called " welded " pieces of steel pulled apart in a testing-machine or
396
STEEL.
otherwise broken at the joint which have not shown a smooth cleavage-
plane, as it were, such as in iron would be condemned as an imperfect
weld. My experience in this matter leads me to agree with the position
taken by Mr. William Metcalf in his paper upon Steel in the Trans. A. S.
C. EM vol. xvi., p. 301. Mr. Metcalf says, "I do not believe steel can be
welded."
Oil-tempering and Annealing of Steel Forgiiigs.— H. F. J.
Porter says (1897) that all steel forgiugs above 0.\% carbon should be an-
nealed, to relieve them of forging and annealing strains, and that the
process of annealing reduces the elastic limit to 47$ of the ultimate strength.
Oil- tempering should only be practised on thin sections, and large forgings
should be hollow for the purpose. This process raises the elastic limit
above 50% of the ultimate tensile strength, and in some alloys of steel,
notably nickel steel, will bring it up to 60$ of the ultimate.
Hydraulic Forging of Steel. (See pages 618 and 619.)
INFLUENCE OF ANNEALING UPON MAGNETIC
CAPACITY.
Prof. D. E. Hughes (Eng^g, Feb. 8, 1881, p. 130) has invented a " Magnetic
Balance," for testing the condition of iron and steel, which consists chiefly of
a delicate magnetic needle suspended over a graduated circular index, and
a magnet coil for magnetizing the bar to be tested. He finds that the fol-
lowing laws hold with every variety of iron and steel :
1. The magnetic capacity is directly proportional to the softness, or mo-
lecular freedom.
2. The resistance to a feeble external magnetizing force is directly as the
hardness, or molecular rigidity.
The magnetic balance shows that annealing not only produces softness in
iron, and consequent molecular freedom, but it entirely frees it from all
strains previously introduced by drawing or hammering. Thus a bar of
iron drawn or hammered has a peculiar structure, say a fibrous one, which
gives a greater mechanical strength in one direction than another. This
bar, if thoroughly annealed at high temperatures, becomes homogeneous in
all directions, and has no longer even traces of its previous strains, provided
that there has been no actual separation into a distinct series of fibres.
Effect of Annealing upon tlie Magnetic Capacity of
Different Wires; Tests foy tiie Magnetic Balance.
Description.
Magnetic Capacity.
Bright as sent.
Annealed.
Best Swedish charcoal iron,
Swedish Siemens-Martin ire
first variety,
second "
third "
n
deg. on scale.
230
236
275
165
212
150
115
50
deg. on scale.
525
510
503
430
340
291
172
84
" hard
Crucible fine cast steel
Crucible Fine Steel. Tempered.
Magnetic
Capacity.
Bright-yellow heat, cooled completely in cold water. . . .
28
32
33
43
51
58
66
72
84
Yellow-red heat, cooled completely in cold water
Bright yellow, let down in cold water to straw color.
" " " " " blue
cooled completely in oil
" let down in water to wnite
Reheat, cooled completely in water
** "oil
Annealed, " " "oil
i
STANDARD SPECIFICATIONS FOR STEEL. 397
STANDARD SPECIFICATIONS FOR STEEL.
The following specifications are abridged from those adopted Aug. 10,
1901, by the American Section of the International Association for Testing
Materials.*
Kinds of Steel Used for Different Purposes. — O, open-
hearth; B, Bessemer; C, crucible.'
(1) Castings, O, B, C. (2) Axles, O. (3) Forgings, O, B, C. (4) Tires,
O, C. (5) Kails, O. B. (6) Splice-bars, O. B. (7) Structural Steel for
buildings, O, B. (8) Structural steel for ships, O. (9) Boiler-plate and
rivets, O.
CHEMICAL REQUIREMENTS FOR THE ABOVE NINE CLASSES.
(The minus sign after the figures means "or less.")
(1) ordinary, P, 0.08- ; C, 0.40- ; tested castings, P, 0.05— ; S, 0.05 -.
(2) P, 0.06- ; S, 0.06- . Nickel steel, Ni, 3.00 to 4.00; P, 0.04 -; S,
0.04 — . (3) soft or low carbon, P, 0.10- ; S, 0.10 -; Class B (see below),
P, 0.06 -; S, 0.06- . Classes C and D, P, 0.04 - ; S, 0.04- . (4) P, 0.05- ;
S, 0.05 -; Mn,0.80-; Si, 0.20 + . (5) P, 0.10-; Si, 0.20 -; C, a, 0.35
to 0.45; b, 0.38 to 0.48; c, 0.40 to 0.50; d, 0.43 to 0.53; e, 0.45 to 0.55; Mn,
a, 6, 0.70 to 1.00; c, 0.75 to 1.05; d,e, 0.80 to 1.10. [a, 50 to 59+ Ibs. per
yard; 6, 60 to 69+ Ibs.; c, 70 to 79 + Ibs.; d, 80 to 89 + Ibs.; e, 90 to 100
bs.] (6) P, 0.10- ; C, 0 15- ; Mn, 0.30 to 0.60. (7) P, 0.10- . (8) acid,
P, 0.08- ; S, 0.06 -; basic, P, 0.06- ; S,0.06-. (9) a, P, 0.06- ; b,c,
e, P,O.C4-; d,P, 0.03- ; a, 6,8,0.05-; Mn, 0.30 to 0.60; c, d, e, S, 0.04- ;
Mn, 0.30 to 0.50. [a, flange or boiler steel, acid; b, do. basic; c, fire-box,
acid; d, do. basic; e, extra soft.]
"Where the physical properties desired are clearly and properly specified,
the chemistry of the steel, other than prescribing the limits of the injurious
impurities, P and S, may in the present state of the art of making steel be
safely left to the manufacturer."
PHYSICAL REQUIREMENTS.
(1) Castings subjected to physical tests.
Quality. Hard. Medium. Soft.
Tensile strength, Ibs. per sq. in 85,000 70,000 60,000
Yield-point, Ibs. per sq. in 38,250 31,500 27,000
Elongation, per cent in 2 ins 15 18 22
Contr. of area, per cent 20 25 30
The above are the minimum requirements. Test-piece £ in. diam. .tend-
ing test: Specimen 1 X 1£ ins. to bend cold around a diam. of 1 in. through
120° for soft and 90° for medium castings.
(2} Axles. — For car, engine-truck, and tender-truck axles no tensile
test is required. For driving-axles, minimum requirements: T. S. 80,000;
Y. P. 40,000 for carbon steel (a), 50,000 for nickel steel, 3 to 4 per cent
Ni, oil-tempered or annealed (6). Elongation in 2 ins., 18 per cent for a, 25
per cent for 6. Contraction of area, 45 per cent for 6. Test-piece £ in.
diam.
Drop -test. --Not required for driving-axles. For other axles one axle
from each melt to be tested on a standard R.R. drop-testing apparatus, with
supports 3 ft. apart, tup 1640 Ibs., anvil 17,500 Ibs., supported on springs.
The axle shall stand the number of blows named below without rupture and
without exceeding at the first blow the deflection stated. It is to be turned
over after the first, third, and fifth blows.
Diam. of axle at centre, ins.. . 4i 4| 4/s 4f 4$ 5| 5|
No. of blows 5 5 5 5 5 5 7
Height of drop, ft 24 26 28}- 31 34 43 43
Deflection, ins 8i 8i 8i 8 8 7 5£
(3) Steel Forgings. — Classification: A, soft or low carbon; B, carbon
steel, not annealed; C, do., annealed; D, do., oil-tempered; E, nickel-steel,
annealed; F, do., oil-tempered. Sub-classes: a, solid or hollow forgings,
diam. or thickness not over 10 ins.; b, solid forgings, diam. not over 20. ins.,
or thickness of section not over 15 ins.; c, solid, over 20 ins. diam.; d, solid
*The complete specifications may be found in book form in "American
Standard Specifications for Steel," by Albert Ladd Colby (Chemical Pub-
lishing Co., Easton, Pa., 1902).
398
STEEL.
or hollow, diam. or thickness not over 3 ins.* e, do., not over 6 ins. Mini-
mum requirements of test-piece % in. diameter, 2 ins. between gauge-marks:
Kind.
Ten-
sile
St'gth.
Elastic
Limit.
El. in
2 ins.,
PerCt.
Contr. ,
PerCt.
Kind.
T. S.
E.L.:
El. in
2 ins.,
PerCt
Contr.,
PerCt.
Aa
Ba
58,000
75,000
29.000Y.P.
37.500Y.P.
28
18
35
30
Da
Ea
80,000
80,000
45,000
50.000
23
25
40
45
Ca
80,000
40,000
22
35
E6
80,000
45,000
25
45
Cb
75,000
37,500
23
35
EC
80,000
45,000
24
40
Cc
70,000
35,000
24
30
Fd
95,000
65,000
21
50
Dd
90,000
55,000
20
45
Fe
90,000
60.000
22
50
Ve
85,000
50,000
22
45
Fa
85,000
55,000
24
45
The number and location of test specimens to be taken from a melt, blow,
or forging depend upon its character and importance, and must therefore
be regulated by individual cases. The yiefcl -point (in steels A and B) shall
be determined by observation of the drop of the beam or halt in the gauge of
the testing-machine. The elastic limit shall be determined by means of an
extensometer, and will be taken at that point where the proportionality
changes.
Bending Test. — A specimen 1 X H ins. shall bend cold 180°;without fracture
on outside of bent portion, as follows. The test may be made by bending or
by blows.
Around a diam. of ins \ \\ 1£ 1 1 1
For kind A B Cc Cab D E F
(4) Tires. — Physical requirements of test-piece % in. diam.; Tires for
passenger engines: T. S., 100,000; El. in 2 ins., 12 per cent. Tires for freight
engines and car wheels: T. S., 110,000; EL, 10 per cent. Tires for switching
engines: T. S., 120,000; EL, 8 per cent.
Drop-test. — If a drop-test is called for, a selected tire shall be placed verti-
cally under the drop on a foundation at least 10 tons in weight and subjected
to successive blows from a tup weighing 2240 Ibs. falling from increasing
heights until the required deflection is obtained , without breaking or crack-
ing. The minimum deflection must equal Da-r (40!Ta + 2D), D being inter-
nal diameter and T thickness of tire at centre of tread.
(5) Kails. — One drop-test shall be made on a piece of rail not more than
6 ft. long, selected from every fifth blow of steel. The rail shall be placed
head upwards on solid supports 3 ft. apart, which are part of, or firmly
secured to, an anvil-block weighing at least 20,000 Ibs., and subjected to. the
following impact tests.
Weight of rails, Ibs. per yd. 45 to 55 55 to 65 65 to 75 75 to 85 85 to 100
Height of drop, ft 15 16 17 18 19
If any rail break when subjected to the drop -test, two additional tests
will be made of other rails from the same blow of steel, and if either of these
latter tests fail, all the rails of the blow which they represent will be rejected,
but if both tests meet the requirements, all the rails of the blow will be ac-
cepted.
(6) Splice-bars. — Tensile strength of a specimen cut from the head of
the bar, 54,000 to 64,000 Ibs.; yield-point, 32,000 Ibs. Elongation in 8 ins.,
not less than 25 per cent. A test specimen cut from the head of the bar
shall bend 180° flat on itself without fracture on the outside of the bent
portion. If preferred, the bending test may be made on an unpunched splice-
bar, which shall be first flattened and then bent. One tensile test and one
bending test to be made from each blow or melt of steel.
(7) Structural Steel for Buildings.
Class.
Rivet -steel.
Medium Steel.
Tensile strength, Ibs per sq in
50,000-60,000
60 000-70 000
Yield-point, not less than ....
frT.S.
i T. S.
Elongation in 8 ins., not less than
26 per cent.
22 per cent.
STANDARD SPECIFICATIOKS FOR STEEL.
309
Modifications in elongation requirements: For each increase of £ in. in
thickness above £ in., a deduction of 1 per cent in the specified elongation.
For each decrease of fs in. in thickness below 15 in., a deduction of 2£ per
cent.
For pins the required elongation shall be 5 per cent less than that speci-
fied, as determined on a test specimen the centre of which shall be 1 in.
from the surface.
Bending Tests. — Rivet-steel shall bend cold 180° flat on itself, and me-
dium steel 180° around a diameter equal to the thickness of the specimen,
without fracture on the outside of the bent portion.
One tensile and one bending-test specimen shall be taken from the finished
material of each melt or blow.
(8) Structural Material for Bridges and
Class.
Rivet-steel.
Soft Steel.
Medium Steel.
Tens, str., Ibs. per sq. in..
Y P not less than
50,000-60,000
% T. S.
52,000-62,000
i T S
60,000-70,000
i T S
El. in 8 ins. not less than.
26 per cent.
25 per cent.
22 per cent.
Modifications in elongation: Same as in structural steel for buildings.
Eyebars. — Full-sized tests: T. S. not less than 55,000 Ibs.; EL, 12£ per
cent, in 15 ft. of the body.
Bending Tests. — Rivet and soft steel, 180° flat on itself, and medium steel
180° around a diameter equal to the thickness of the specimen, without
fracture on the outside of the bent portion.
(9) Boiler-plate and Rivet-steel.
Class.
Flange- or
Boiler-steel.
Fire-box Steel.
Extra-soft
Steel.
T S , Ibs per sq. in
55,000-65,000
52,000-62,000
45,000-55,000
Y. P., not less than
El. in 8 ins. not less than
* T. S.
25 per cent.
* T. S.
26 per cent.
1 T. S.
28 per cent.
Modifications in elongation requirements for thin and thick material same
as in structural steel for buildings.
Bending Tests. — A specimen cut from the rolled material, both before and
after quenching, shall bend cold 180° flat on itself without fracture on the
outside of the bent portion. For the quenched test the specimen shall be
heated to a light cherry-red as seen in the dark and quenched in water of a
temperature between 80° and 90° F. Number of test-pieces: One tensile,
one cold-bending, and one quenched-bending specimen will be furnished
from each plate as it is rolled, and two specimens for each kind of test from
each melt of rivet-rounds.
Homogeneity Test /or Fire-box Steel. — This test is made on one of the
broken tensile-test specimens, as follows:
A portion of the test-piece is nicked with a chisel, or grooved on a ma-
chine, transversely about a sixteenth of an inch deep, in three places about
2 in. apart. The first groove should be made on one side, 2 in. from the
square end of the piece; the second, 2 in. from it on the opposite side; and
the third, 2 in. from the last, and on the opposite side from it. The test-
piece is then put in a vise, with the first groove about i in. above the jaws,
care being taken to hold it firmly. The projecting end of the test-piece is
then broken off by means of a hammer, a number of light blows being used,
and the bending being away from the groove. The piece is broken at the
other two grooves in the same way. The object of this treatment is to open
and render visible to the eye any seams due to failure to weld up, or to
foreign interposed matter, or cavities due to gas bubbles in the ingot. After
rupture, one side of each fracture is examined, a pocket lens being used if
necessary, and the length of the seams and cavities is determined. The
sample shall not show any single .seam or cavity more than £ in. long in
either of the three fractures.
400 STEEL.
VARIOUS SPECIFICATIONS FOR STEEIi.
Structural Steel.— There has been a change during the ten years from
1880 to 1890, in the opinions of engineers, as to the requirements in specifica-
tions for structural steel, in the direction of a, preference for metal of low
tensile strength and great ductility. The following specifications of differ-
ent dates are given by A. E. Hunt and G. H. Clapp, Trans. A. I. M. E. 1390
xix, 926:
TENSION MEMBERS. 1879. 1881. 1882. 1885. 1887. 1888.
Elastic limit... .. 50,000 40®45,000 40.000 40.000 40,000 38,000
Tensile strength 80,000 70@80,000 70,000 70,000 67@75,000 63@70,00(
Elongation in 8 in 12* 18* 18* 18* 20* 22*
Reduction of area 20* 30* 45* 42* 42* 45*
F. H. Lewis (Iron Age, Nov. 3, 1892) says: Regard ing steel to be used under
the same conditions as wrought iron, that is, to be punched without ream-
ing, there seems to be a decided opinion (and a growing one) among engi-
neers, that it is not safe to use steel in this way, when the ultimate tensile
strength is above 65,000 Ibs. The reason for this is, not so much because
there is any marked change in the material of this grade, but because all
steel, especially Bessemer steel, has a tendency to segregations of carbon
and phosphorus, producing places in the metal which are harder than they
normally should be. As long as the percentages of carbon and phosphorus
are kept low, the effect of these segregations is inconsiderable; but when
these percentages are increased, the existence of these hard spots in the
metal becomes more marked, and it is therefore less adapted to the treat-
ment to which wrought iron is subjected.
There is a wide consensus of opinion that at an ultimate of 64,000 to 65,000
Ibs. the percentages of carbon and phosphorus (which are the two harden-
ing elements) reach a point where the steel has a tendency to become tender,
and to crack when subjected to rough treatment.
A grade of steel, therefore, running in ultimate strength from 54,000 to
62,000 Ibs., or in some cases to 64,000 Ibs., is now generally considered a
proper material for this class of work.
A. E. Hunt, Trans. A. I. M. E. 1892, says: Why should the tests for steel
be so much more rigid than for iron destined fo;' the same purpose ? Some
of the reasons are as follows: Experience shows that the acceptable quali-
ties of one melt of steel offer no absolute guarantee that the next melt to it,
even though made of the same stock, will be equally satisfactory.
Again, good wrought iron, in plates and angles, has a narrow range (from
25,000 to 27,000 Ibs.) in elastic limit per square inch, and a tensile strength of
from 46,000 to 52,000 Ibs. per square inch; whereas for steel the range in
elastic limit is from 27,000 to 80,000 Ibs., and in tensile strength from 48,000 to
120,000 Ibs. per square inch, with corresponding variations in ductility.
Moreover, steel is much more susceptible than wrought iron to widely vary-
ing effects of treatment, by hardening, cold rolling, or overheating.
It is now almost universally recognized that soft steel, if properly made
and of good quality, is for many purposes a safe and satisfactory substitute
for wrought iron, being capable of standing the same shop-treatment as
wrought iron. But the conviction is equally general, that poor steel, or an
unsuitable grade of steel, is a very dangerous substitute for wrought iron
even under the same unit strains.
For this reason it is advisable to make more rigid requirements in select-
ing material which may range between the brittleness of glass and a duc-
tility greater than that of wrought iron.
Boiler. Ship. and. Tan*t jPlates.— Different specifications are the
following (1889) :
United States Navy.— Shell : Tensile strength, 58,000 to 67,000 Ibs. per sq.
in. : elongation, 22* in 8-in. transverse section, 25* in 8-in. longitudinalsection.
Flange : Tensile strength, 50,000 to 58,000 Ibs. ; elongation, 26* in 8 inches.
Chemical requirements : P. not over .035* ; S. not over .040*.
Cold-bending test : Specimen to stand being bent flat on itself.
Quenching test : Steel heated to cherry-red, plunged in water 82° F., and
to be bent around curve 1^ times thickness of the plate.
British Admiralty.— Tensile strength, 58,240 to 67,200 Ibs.; elongation in
8 in., 20* ; same cold-bending and quenching tests as U. S. Navy.
American Boiler-makers'1 Association.— Tensile strength, 55,000 to 65,000
Ibs. ; elongation in 8 in., 20* for plates % in. thick and under ; 22* for plates
% in. to % in, ; %>% for plates % in, and over.
VARIOUS SPECIFICATIONS FOR STEEL. 401
Cold-bending test : For plates fy> iu. thick and under, specimen must bend
back on itself without fracture; for plates over y% in. thick, specimen must
withstand bending 180° around a mandril 1^ times the thickness of the
plate.
Chemical requirements: P not over .040$; S not over .030$.
American Shipmasters' Association.— Tensile strength, 62,000 to 72,000
Ibs.; elongation, 16$ on pieces 9 iu. long.
Strips cut from plates, heated to a low red and cooled in water the tem-
perature of which is 82° F., to undergo without crack or fracture being
doubled over a curve the diameter of which does not exceed three times the
thickness of the piece tested.
Steel Plate Used in tlie Construction of Cars. (Penna. R. R.,
1899.*)— The material desired has the following composition: 0,0.12; Mn,0.35;
Si, 0.05; P, not above 0.04; S, not above 0.03. It will be rejected if P ex-
ceeds 0.05, or if it shows a tensile strength below 52.000 or above 62,000 Ibs.
per sq. in., or if the percentage of elongation in 8 ins. is less than the
quotient of 1,500,000 H- the tensile strength.
Steel Billets for Main and Parallel Rods. (Penna. R. R., 1893.)
—One billet from each lot of 25 billets or smaller shipment of steel for main
or parallel rods for locomotives will have a piece drawn from it under the
hammer and a test-section will be turned down on this piece to % in. in
diameter and 2 in. long. Such test-piece should show a tensile strength of
85,000 Ibs. and an elongation of 15$.
No lot will be acceptable if the test shows less than 80,000 Ibs. tensile
strength or 12$ elongation in 2 in.
Bar Spring Steel. (Penna. R R., 1901.)— Bars which vary more than
0.01 in. in thickness, or more than 0.02 in. in width, from the stee ordered, or
which break where they are not nicked, or which, when properly nicked
and held, fail to break square across where they are nicked, will be returned.
The metal desired has the following composition: Carbon, 1.00$; manganese^
0.25$; phosphorus, not over 0.03$; silicon, not over 0.15$; sulphur, not over
0.03$; copper, not over 0.03$.
Shipments will not be accepted which show on analysis less than 0.90$ or
over 1.10$ of carbon, or over 0.50$ of manganese, 0.05$ of phosphorus, 0.25$
of silicon, 0.05$ of sulphur, and 0.05$ of copper.
Steel for Crank-pins. (Penna. R. R., 1897.)— The metal desired has
the following composition : C, 0.45; Mn, not above 0.60; Si, not above 0.05;
P, not above 0.03; S, not above 0.04. The tensile strength should be 85,000
Ibs. per sq. in., and the elongation 18$ in 8 in. Borings for analysis will be
taken from one axle out of i lot of 51. They will be drilled parallel with the
axis with a %-in. drill, starting from a punch-march located on the end, 40
per cent of the distance from the centre to the circumference. Two pieces
from this pin will also be tested physically. The lot will be rejected if the
P is above 0.05$, or if either test-piece shows less than 80,000 Ibs. or above
95,000 Ibs. T. S., less than 12$ elongation, or if the T. S. of the two test-
pieces differs more than 5,000 Ibs. or the elongation more than 5$.
Dr. Chas. B. Dudley, chemist of the P. R. R. (Trans. A. I. M. E. 1892), re-
ferring to tests of crank-pins, says: In testing a recent shipment, the piece
from one side of the pin showed 88,000 Ibs. strength and 22$ elongation, and
the piece from the opposite side showed 106,000 Ibs. strength and 14$ elonga-
tion. Each piece was above the specified strength and ductility, but the
lack of ..uniformity between the two sides of the pin was so marked that it
was finally determined not to put the lot of 50 pins in use. To guard against
trouble of this sort in future, the specifications are to be amended to require
that the difference in ultimate strength of the two specimens shall not be
more than 3000 Ibs.
Steel Rivets. (H. C. Torrance, Amer. Boiler Mfrs. Assn., 1890.)— The
Government requirements for the rivets used in boilers of the cruisers built
in 1890 are: For longitudinal seams, 58,000 to 67,000 Ibs. tensile strength;
elongation, not less than 26$ in 8 in., and all others a tensile strength of
50,000 to 58,000 Ibs., with an elongation of not less than 30$. They shall be
capable of being flattened out cold under the hammer to a thickness of one
half the diameter, and of being flattened out hot to a thickness of one third
* The Penna. R. R. specifications of the several dates given are still in
force, July, 1902.
402 STEEL.
the diameter without showing cracks or flaws. The steel must not contain
more than .035 of \% of phosphorus, nor more than .04 of \% of sulphrr.
A lot of 20 successive tests of rivet steel of the low tensile strength quality
and 12 tests of the higher tensile strength gave the following results :
Low Steel. Higher.
Tensile strength, Ibs. per sq. in. . . 51,230 to 54,100 59,100 to 61,850
Elastic limit, Ibs. per sq. in 31,050 to 33,190 32,080 to 33,070
Elongation in 8 in., per cent 30.5 to 35.25 28.5 to 31,75
Carbon, per cent .11 to »14 .16 to .18
Phosphorus 027 to .029 .03
Sulphur 033 to .035 .033 to .035
The safest steel rivets are those of the lowest tensile strength, since they
are the least liable to become hardened and fracture by hammering, or to
break from repeated concussive and vibratory strains to which they are
subjected in practice. For calculations of the strength of riveted joints the
tensile strength may be taken as the average of the figures abovo given, or
52,665 Ibs., and the shearing strength at 45,000 Ibs. per sq. in.
MISCELLANEOUS NOTES ON STEEL. .
May Carbon foe Burned Out of Steel ?— Experiments made at
the Laboratory of the Penna. Railroad Co. (Specifications for Springs, 1888)
with the steel of spiral springs, show that the place from which the borings
are taken for analysis has a very important influence on the amount of car-
bon found. If the sample is a piece of the round bar, and the borings are
taken from the end of this piece, the carbon is always higher than if the
borings are taken from the side of the piece. It is common to find a differ-
ence of 0.10$ between the centre and side of the bar, and in some cases the
difference is as high as 0.23$. Furthermore, experiments made with samples
taken from the drawn out end of the bar show, usually, less carbon than
samples taken from the round part of the bar, even though the borings may
be taken out of the side in both cases.
Apparently during the process of reducing the metal from the ingots to the
round bar, with successive heatings, the carbon in the outside of the bar is
burned out.
46 BLecalescence " of Steel.— If we heat a bar of copper by a flame
of constant strength, and note carefully the interval of time occupied in
passing from each degree to the next higher degree, we find that these in-
tervals increase regularly, i e., that the bar heats more and more slowly, as
its temperature approaches that of the flame. If we substitute a bar of
steel for one of copper, we find that these intervals increase regularly up to
a certain point, when the rise of temperature is suddenly and in most cases
greatly retarded or even completely arrested. After this the regular rise of
temperature is resumed, though other like retardations may recur as the
temperature rises farther. So if we cool a bar of steel slowly the fall of
temperature is greatly retarded when it reaches a certain point in dull red-
ness. If the steel contains much carbon, and if certain favoring conditions
be maintained, the temperature, after descending regularly, suddenly rises
spontaneously very abruptly,, remains stationary a while, and then rede-
scends. This spontaneous reheating is known as " recalescence."
These retardations indicate that some change which absorbs or evolves
heat occurs within the metal. A retardation while the temperature is rising
points to a change which absorbs heat; a retardation during cooling points
to some change which evolves heat. (Henry M. Howe, on " Heat Treatment
of Steel,'1 Trans. A. I. M. E., vol. xxii.)
Effect of Nicking a Steel Bar.— The statement is sometimes made
that, owing to the homogeneity of steel, a bar with a surface crack or nick
in one of its edges is liable to fail by the gradual spreading of the nick, and
thus break under a very much smaller load than a sound bar. With iron it
is contended this does not occur, as this metal has a fibrous structure. Sir
Benjamin Baker has, however, shown that this theory, at least so far as
statical stress is concerned, is opposed to the facts, as he purposely made
nicks in specimens of the mild steel used at the Forth Bridge, but found
that the tensile strength of the whole was thus reduced by only about one
ton per square inch of section. In an experiment by the Union Bridge Com-
pany a full- sized steel counter-bar, with a screw- turned buckle connection,
was tested under a heavy statical stress, and at the same time a weight
weighing 1040 Ibs. was allowed to drop on it from various heights. The bar
was ficst broken by ordinary statical strain, and showed a breaking stress of
MISCELLANEOUS NOTES ON STEEL. 403
66,800 Ibs. per square inch. The longer of the broken parts was then placed
in the machine and put under the following loads, whilst a weight, as already
mentioned, was dropped on it from various heights at a distance of five
feet from the sleeve-nut of the turn-buckle, as shown below:
Stress in pounds per sq. in 50,000 55,000 60,000 63,000 65,000
ft. in. ft. in. ft. in. ft. in. ft. in.
Heightoffall 21 20 30 40 50
The weight was then shifted so as to fall directly on the sleeve-nut, and
the test proceeded as follows :
Stress on specimen in Ibs. per square inch 65,350 65,350 68,800
Height of fall, feet 366
It will be seen that under this trial the bar carried more than when origi-
nally tested statically, showing that the nicking of the bar by screwing
had not appreciably weakened its power of resisting shocks.— Eng'g News.
Electric Conductivity of Steel. — Louis Campredon reports in Le
Genie Civil [prior to 1895} the results of experiments on the electric resist-
ance of steel wires 4of different composition, ranging from 0.09 to 0.14 C;
0.21 to 0.54 Mn; Si, S, and P low. The figures show that the purer and
softer the steel the better is its electric conductivity, and, furthermore, that
manganese is the element which most influences the conductivity. The
results may be expressed by the formula # = 5. 2 + 6.2$ ±0.3; in which R =
relative resistance, copper being taken as 1, and S = the sum of the percent-
ages of C, P, S, Si, and Mn. The conclusions are confirmed by J. A. Capp,
in 1903, Trans. A. I. M. E., vol. xxxiv, who made forty-five experiments on
steel of a wide range of composition. His results may be expressed by the
formula 22 = 5.5 + 4/S± 1. High manganese increases the resistance at an
increasing rate. Mr. Capp proposes the following specification for steel to
make a satisfactory third rail, having a resistance eight times that of
copper: C, 0.15; Mn, 0.30; P, 0.06; S, 0.06; Si, 0.05; none of these figures
to be exceeded.
Specific Qravity of Soft Steel. (W. Kent, Trans. A. I. M. E., xiv.
680.) — Five specimens of boiler-plate of C. 0.14, P. 0.03 gave an average sp.
gr. of 7.932, maximum variation 0.008. The pieces were first planed to re-
move all possible scale indentations, then filed smooth, then cleaned in
dilute sulphuric acid, and then boiled in distilled water, to remove all traces
of air from the surface.
The figures of specific gravity thus obtained by careful experiment on
bright, smooth pieces of steel are, however, too high for use in determining
the weights of rolled plates for commercial purposes. The actual average
thickness of these plates is always a little less than is shown by the calipers,
on account of the oxide of iron on the surface, and because the surface is
not perfectly smooth and regular. A number of experiments on commercial
plates, and comparison of other authorities, led to the figure 7.854 as the
average specific gravity of open-hearth boiler-plate steel. This figure is
easily remembered as being the same figure with change of position of the
decimal point (.7854) which expresses the relation of the area of a circle to
that of its circumscribed square. Taking the weight of a cubic foot of water
at 62° F. as 62.36 Ibs. (average of several authorities), this figure gives 489.775
Ibs. as the weight of a cubic foot of steel, or the even figure, 490 Ibs., may be
taken as a convenient figure, and accurate within the limits of the error of
observation.
A common method of approximating the weight of iron plates is to con-
sider them to weigh 40 Ibs. per square foot one inch thick. Taking this
weight and adding 2% gives almost exactly the weight of steel boiler-plate
given above (40 X 12 X 1.02 = 489.6 Ibs. per cubic foot).
Occasional Failures of Bessemer Steel.— G. H. Clapp and A.
E. Hunt, in their paper on " Tiie Inspection of Materials of Construction in
404 STEEL.
the United States" (Trans. A. I. M. E., vol. xix), say: Numerous instances
could be cited to show the unreliability of Bessemer steel for structural pur-
poses. One of the most marked, however, was the following: A 12-in. I-beam
weighing 30 Ibs. to the foot, 20 feet long, on being unloaded from a car
broke in two about 6 feet from one end.
The analyses arid tensile tests made do not show any cause for the failure.
The cold and quench bending tests of both the original %-in. round test-
pieces, and of pieces cut from the finished material, gave satisfactory re-
sults; the cold-bending tests closing down on themselves without sign of
fracture.
Numerous other cases of angles and plates that were so hard in piaces as
to break off short in punching, or, what was worse, to break the punches,
have come under our observation, and although makers of Bessemer steel
claim that this is just as likely to occur in open-hearth as in Bessemei steel,
we have as yet never seen an instance of failure of this kind in open-hearth
steel having a composition such as C 0.25$, Mn 0.70$, P 0.80&
J. W. Wailes, in a paper read before the Chemical Section of the British
Association for the Advancement of Science, in speaking of mysterious
failures of steel, states that investigation shows that " these failures occur
in steel of one class, viz., soft steel made by the Bessemer process.11
Segregation in Steel Ingots. (A. Pourcel, Trans. A. I. M. E. 1893.J
— H. M. Howe, in his " Metallurgy of Steel,'1 gives a resume of observations
with the results of numerous analyses, bearing upon the phenomena or seg;
regation.
In 188! Mr. Stubbs, of Manchester, showed the heterogeneous results of
analyses made upon different parts of an ingot of large section.
A test-piece taken 24 inches from the head of the ingot 7.5 feet in length
gave by analysis very different results from those of a test-piece taken 30
inches from the bottom.
C. Mn. Si. S. P.
Top 0.92 0.535 0.043 0.181 0.261
Bottom 0.37 0.498 0.006 0.025 0.096
Windsor Richards says he had often observed in test-pieces taken from
different points of one plate variations of 0.05$ of carbon. Segregation is
specially pronounced in an ingot in its central portion, and around the
space of the piping.
It Is most observable in large ingots, but In blocks of smaller weight and
limited dimensions, subjected to the influence of solidification as rapid as
casting within thick walls will permit, it may still be observed distinctly.
An ingot of Martin steel, weighing about 1000 Ibs., and having a height of
1.10 feet and a section of 10.24 inches square, gave the following:
1. Upper section: C. S. P. Mn.
Border 0.330 0.040 0.033 0.420
Centre 0.530 0.077 0.057 0.430
2. Lower section? C. S. P. Mn.
Border 0.280 0.029 0.016 0.390
Centre 0.290 0.030 0.038 0.390
3. Middle section: C. S. P. Mn.
Border 0.320 0.025 0.025 0.400
Centre 0.320 0.048 0.048 0.40^
Segregation is less marked in ingots of extra-soft metal cast in cast-iron
moulds of considerable thickness. It is, however, still important, and ex-
Elains the difference often shown by the results of tests on pieces taken
rom different portions of a plate. Two samples, taken from the sound part
of a flat ingot, one on the outside and the other in the centre, 7.9 inches from
the upper edge, gave:
C. S. P. Mn.
Centre 0.14 0.053 0.072 0.576
Exterior ... 0.11 0.036 0.027 0.610
Manganese is the element most uniformly disseminated in hard or soft
steel.
For cannon of large calibre, if we reject, in addition to the part cast in
sand and called the masselotte (sinking-head), one third of the upper parl
of the ingot, we can obtain a tube practically homogeneous in composition,
because the central part is naturally removed by the boring of the tube.
With extra-soft steels, destined for ship- or boiler-plates, the solution for
practically perfect homogeneity lies in the obtaining of a metal more closely
deserving its name of ?xtra-soft
STEEL CASTINGS. 405
The injurious consequences of segregation must be suppressed by reduc-
ing, as far as possible, the elements subject to liquation.
Earliest Uses of Steel for Structural Purposes. (G. G.
Mehrtens, Trans. A. S. C. E. 1893).— Tbe Pennsylvania Railroad Company
first introduced Bessemer steel in America in locomotive boilers in the year
1863, but the steel was too hard and brittle for such use. The first plates
made for steel boilers had a tenacity of 85,000 to 92,OCO Ibs. and an elongation
of but 1% to 10$. The results were not favorable, and the steel works were
soon forced to offer a material of less tenacity and more ductility. The re-
quirements were therefore reduced to a tenacity of 78,000 Ibs. or less, and
the elongation was increased to 15% or more. The use of Bessemer steel in
bridge-building was tried first on the Dutch State railways in 1863-64, then
in England and Austria. The first use of cast steel for bridges was in
America, for the St. Louis Arch Bridge and for the wire of the East River
Bridge. Before 1880 the Glasgow and Plattsmouth bridges over the Missouri
River were also built of ingot metal. Steel eyebars were applied for the first
time in the Glasgow Bridge. Since 1880 the introduction of mild steel in
all kinds of engineering structures has steadily increased.
Messrs. Joseph Adamson & Co., of Hyde, England, in a letter to the author
say: "The first steel for boiler purposes was used for a locomotive firebox
sent to Africa in 1858. The first steel steamships were built in Liverpool for
4 blockade-running ' during the American Civil War about 1862, and at least
5000 tons of Bessemer steel plates were rolled at Penistone by Benson,
Adamson & Garnett for this purpose. The first Bessemer steel boilers were
made in this neighborhood in 1858. Drilling the rivet- holes was adopted in
1859. Some of these boilers built in 1862 worked 29 years night and day. We
have lost trace of these boilers now, but we know that after working this
length of time they were found good enough to be worth resetting and were
set to work again for a time. Between 1870 and 1880 about 2000 steel land
boilers were working in this country. The pressures ranged up to 150 Ibs."
STEEL CASTINGS.
(E. S. Cramp, Engineering Congress, Dept. of Marine Eng'g, Chicago, 1893.)
In 1891 American steel-founders had successfully produced a considerable
variety of heavy and difficult castings, of which the following are the most
noteworthy specimens:
Bed-plates up to 24,000 Ibs.; stern-posts up to 54,000 Ibs.; stems up to
21,000 Ibs. ; hydraulic cylinders up to 11,000 Ibs. ; shaft-struts up to 32,000 Ibs. ;
hawse-pipes up to 7500 Ibs.; stern-pipes up to 8000 Ibs.
The percentage of success in these classes of castings since 1890 has ranged
from 65$ iq the more difficult forms to 90$ in the simpler ones; the tensile
strength has been from 62,000 to 78,000 Ibs., elongation from 15$ to 25$. The
best performance recorded is that of a guide, cast in January, 1893, which
developed 84,000 Ibs. tensile strength and 15.6$ elongation.
The first steel castings of which anything is generally known were
crossing-frogs made for the Philadelphia & Reading R. R. in July, 1867, by
the William Butcher Steel Works, now the Midvale Steel Co. The moulds
were made of a mixture of ground fire-brick, black-lead crucible-pots
ground fine, and fire-clay, and washed with a black-lead wash. The steel
was melted in crucibles, and was about as hard as tool steel. The surface
of these castings was very smooth, but the interior was very much honey-
combed. This was before the days when the use of silicon was known for
solidifying steel. The sponginess, which was almost universal, was a great
obstacle to their general adoption.
The next step was to leave the ground pots out of the moulding mixture
and to wash the mould with finely ground fire-brick. This was a great im-
provement, especially in very heavy castings; but this mixture still clung so
strongly to the casting that only comparatively simple shapes could be made
with certainty. A mould made of such a mixture became almost as hard as
fire-brick, and was such an obstacle to the proper shrinkage of castings,
that, when at all complicated in shape, they had so great a tendency to
crack as to make their successful manufacture almost impossible. By this
time the use of silicon had been discovered, and the only obstacle in the way
of making good castings was a suitable moulding mixture. This was ulti-
mately found in mixtures having the various kinds of silica sand as the
principal constituent.
One of the most fertile sources of defects in castings is a bad design.
Very intricate shapes can be cast successfully if they are so designed as to
406
STEEL.
cool uniformly. Mr. Cramp says while he is not yet prepared to state that
anything that can be cast successfully in iron can be cast in steel, indica-
tions seem to point that way in all cases where it is possible to put on suit-
able sinking-heads for feeding the casting.
H. L. Gantt (Trans. A. S. M. E., xii. 710) says: Steel castings not only
shrink much more than iron ones, but with less regularity. The amount of
shrinkage varies with the composition and the heat of the metal; the hotter
the metal the greater the shrinkage ; and, as we get smoother castings from
hot metal, it is better to make allowance for large shrinkage and pour the
metal as hot as possible. Allow 3/16 or y± in. per ft. in length
for shrinkage, and y± in. for finish on machined surfaces, except such as are
cast 4%up." Cope surfaces which are to be machined should, in large or
hard castings, have an allowance of from %to^ in. for finish, as a large
mass of metal slowly rising in a mould is apt to become crusty on the sur-
face, and such a crust is sure to be full of imperfections. On small, soft
castings ^ in. on drag side and % in. on cope side will be sufficient. No core
Should have less th^n y± in. finish on a side and very large ones should have
as much as ^> in. on a side. Blow-holes can be entirely prevented in cast-
ings by the addition of manganese and silicon in sufficient quantities; but
both of these cause brittleness, and it is the object of the conscientious steel-
maker to put no more manganese and silicon in his steel than is just suffi-
cient to make it solid. 1 The best results are arrived at when all portions of
the castings are of a uniform thickness, or very nearly so.
The following table will " illustrate the effect of annealing on tensile
strength and elongation of steel castings :
Carbon.
Unannealed.
Annealed.
Tensile Strength.
Elongation.
Tensile Strength.
Elongation.
£a*
.37
.53
68,738
85,540
90,121
22.40%
8.20
2.35
67,210
82,228
106,415
31.40*
21.80
9.80
The proper annealing of large castings takes nearly a week.
The proper steel for roll pinions, hammer dies, etc., seems to be that con-
taining about .60$ of carbon. Such castings, properly annealed, have worn
well and seldom broken. Miscellaneous gearing should contain carbon .40$
to 60$, gears larger in diameter being softest. General machinery castings
should, as a rule, contain less than .40$ of carbon, those exposed to great
shocks containing as low at .20$ of carbon. Such castings will give a tensile
strength of from 60,000 to 80,000 Ibs. per sq. in. and at least 15$ extension in
a 2 in. long specimen. Machinery and hull castings for war-vessels for the
United States Navy, as well as carriages for naval guns, contain from .20$ to
.30$ of carbon.
The following is a partial list of castings in which steel seems to be
rapidly taking the place of iron: Hydraulic cylinders, crossheads and pistons
for large engines, roughing rolls, rolling-mill spindles, coupling-boxes, roll
pinions, gearing, hammer-heads and dies, riveter stakes, castings for ships,
car-couplers, etc.
For description of methods of manufacture of steel castings by the Besse-
mer, open-hearth, and crucible processes, see paper by P. G. Salom, Trans.
A. I. M. E. xiv, 118.
Specifications for steel castings issued by the U. S. Navy Department, 1889
(abridged) : Steel for castings must be made by either the open-hearth or
the crucible process, and must not show more than .06$ of phosphorus. All
castings must be annealed, unless otherwise directed. The tensile strength
of steel castings shall be at least 60,000 Ibs., with an elongation of at least
15$ in 8 in. for all castings for moving parts of the machinery, and at least
10$ in 8 in. for other castings. Bars 1 in. sq. shall be capable of bending
cold, without fracture, through an angle of 90°, over a radius not greater
than \y% in. AJ1 castings must be sound, free from injurious roughness,
sponginess, pitting, shrinkage, or other cracks, cavities, etc.
Pennsylvania Railroad specifications, 1888: Steel castings should have a
tensile strength of 70,000 Ibs. per sq. in. and an elongation of 15$ in section
originally 2 in. long. Steel castings will not be accepted if tensile strength
MANGANESE, NICKEL, AND OTHER "ALLOY" STEELS. 40?
falls below 60,000 Ibs., nor if the elongation is less than 12#, nor if cast-
ings have blow-holes and shrinkage cracks. Castings weighing 80 Ibs. or
more must have cast with them a strip to be used as a test-piece. The di-
mensions of this strip must be % in. sq. by 12 in. long.
MANGANESE, NICKEL, AN» OTHER "ALLOY"
STEELS.
Manganese Steel, (H. M. Howe, Trans. A. S. M. E., vol. xii.)— Man-
ganese sieel is an alloy of iron and manganese, incidentally, and probably
unavoidably, containing a considerable proportion of carbon.
The effect of small proportions of manganese on the hardness, strength,
and ductility of iron is probably slight. The point at which manganese
begins to have a predominant effect is not known : it may be somewhere
about 2.5^. As the proportion of manganese rises above 2.5% the strength
and ductility diminish, while the hardness increases. This effect reaches a
maximum with somewhere about §% of manganese. When the proportion
of this element rises beyond 6$ the strength and ductility both increase-
while the hardness diminishes slightly, the maximum of both strength and
ductility being readied with about 14% of manganese. With this proportion
the metal is still so hard that it is very difficult to cut it with steel tools. As
the proportion of manganese rises above 15# the ductility falls off abruptly,
the strength remaining nearly constant till the manganese passes 18#, when
it in turn diminishes suddenly.
Steel containing from 4f0 to 6.5$ of manganese, even if it have but 0.37# of
carbon, is reported to be so extremely brittle that it can be powdered under
a hand-hammer when cold ; yet it is ductile when hot.
Manganese steel is very free from blow-holes ; it welds with great diffi-
culty; its toughness is increased by quenching from a yellow heat ; its elec-
tric resistance is enormous, and very constant M'ith changing temperature ;
it is low in thermal conductivity. Its remarkable combination of great hard-
Aiess, which cannot be materially lessened by annealing, and great tensile
strength, with astonishing toughness and ductility, at once creates and
limits its usefulness. The fact that manganese steel cannot be softened,
that it ever remains so hard that it can be machined only with great diffi-
culty, sets up a barrier to its usefulness.
The following comparative results of abrasion tests of manganese and
eel were reported by T. T. Morrell :
ABRASION BY PRESSURE AGAINST A REVOLVING HARDENED-STEEL SHAFT.
Loss of weight of manganese steel ....................... 1.0
blue -tempered hard tool steel ......... 0.4
annealed hard tool steel ............. 7.5
hardened Otis boiler-plate steel ....... 7.0
annealed '* " ....... 14.0
ABRASION BY AN BMERY-WHEEL.
Loss of weight of hard manganese-steel wheels .......... 1 .00
softer " .......... 1.19
hardest carbon-steel wheels .......... 1 .23
soft " ........... 2.85
The hardness of manganese steel seems to be of an anomalous kind. The
alloy is hard, but under some conditions not rigid. It is very hard in its
resistance to abrasion ; it is not always hard in its resistance to impact.
Manganese steel forges readily at a yellow heat, though at a bright white
heat it crumbles under the hammer. But it offers greater resistance to
deformation, i.e., it is harder when hot, than carbon steel.
The most important single use for manganese-steel is for the pins which
hold the buckets of elevator dredges. Here abrasion chiefly is to be
resisted.
Another important use is for the links of common chain-elevators.
As a material for stamp-shoes, for horse-shoes, for the knuckles of an
automatic car-coupler, manganese steel has not met expectations.
Manganese steel has been regularly adopted for the blades of the Cyclone
pulverizer. Some manganese-steel wheels are reported to have run over
300.000 miles each without turning, on a New England railroad.
Nickel Steel.— The remarkable tensile strength and ductility of nickel
steel, as shown by the test-bars and the behavior of nickel-steel armor-
plate under shot tests, are witness of the valuable qualities conferred upon
steel by the addition of a few per cent of nickel. ,
408
STEEL.
The following tests were made on nickel steels by Mr. Maunsel White of
the Bethlehem Iron Company (Eng. & M. Jour., Sept. 16, 1893.) :
Specimen
from—
Is
ft
Is
1
Tensile
Str'gth,
Ibs. per
sq. in.
Elastic
Limit,
Ibs. per
sq. in.
Elonga-
tion,
Reduc-
tion of
Area,
f
i 625
4
276,800
2 75
|
Special
, 1
Forged
i .ep
246,595
4.25
6.0 j"
treatment.
05
bars. *
1 "
u
105,300
19.25
55 0
Annealed.
to
1.564
4
142,800
74,000
13.0
28.2
05
44
"
143,200
74,000
12.32
27.6
lj "
.
44
"
117,600
64,000
17.0
46.0
'c
round
rolled bar.t
' •"
«
119,200
91,600
91,200
65,000
51,000
51,000
16.66
22.25
21.62
42.1
53.2
53.4
»
i
"
85,200
53,000
21.82
49.5
4
44
86,000
48,000
21.25
47.4
—; :
'."98
8
115,464
51,820
36.25
66.23
05
1^4-in. sq.
*
14
112,600
60,000
37.87
62.82
to
bar, rolled, $
'
44
102,010
39,180
41.37
69.59
Annealed.
'oS
4
44
102,510
40,200
44.00
68.34
44
^ i
!.500
2
114,590
56,020
47.25
68.4
.-H
1-in. round
"
4<
115,610
59.080
45.25
62.3
bar, rolled. §
i
44
105,240
45,170
49.65
72.8
Annealed.
& I
I "
41
106,780
45,170
55.50
63.6
**
* Forged from 6-in. ingot to % in. diam., with conical heads for holding.
t Showing the effect of varying carbon.
j Rolled down from 14-in. ingot to lJ4-in. square billet, and turned to size.
§ Rolled down from 14-in. ingot to 1-in. round, and turned to size.
Nickel steel has shown itself to be possessed of some exceedingly valuable
properties; these are, resistance to cracking, high elastic limit, and homo-
geneity. Resistance to cracking, a property to which the name of non fissK
bility has been given, is shown more remarkably as the percentage of nickel
increases. Bars of 27$ nickel illustrate this property. A lJ4-in. square bar
was nicked J4 in. deep and bent double on itself without further fracture
than the splintering off, as it were, of the nicked portion. Sudden failure or
rupture of this steel would be impossible ; it seems to possess the toughness
of rawhide with the strength of steel. With this percentage of nickel the
steel is practically non-corrodible and non-magnetic. The resistance to
cracking shown by the lower percentages of nickel is best illustrated in the
many trials of nickel-steel armor.
The elastic limit rises in a very marked degree with the addition of about
3$ of nickel, the other physical properties of the steel remaining unchanged
or perhaps slightly increased.
In such places (shafts, axles, etc.) where failure is the result of the fatigue
Of the metal this higher elastic limit of nickel steel will tend to prolong in-
definitely the life of the piece, and at the same time, through its superior
toughness, offer greater resistance to the sudden strains of shock.
Howe states that the hardness of nickel steel depends on the proportion
of nickel and carbon jointly, nickel up to a certain percentage increasing
the hardness, beyond this lessening it. Thus while steel with 2$ of nickel
and 0.90$ of carbon cannot be machined, with less than 5$ nickel it can be
worked cold readily, provided the proportion of carbon be low. As the
proportion of nickel rises higher, cold-working becomes less easy. It forges
easily whether it contain much or little nickel.
The presence of manganese in nickel steel is most important, as it appears
that without the aid of manganese in proper proportions, the conditions of
treatment would not be successful.
Tests of Nickel Steel.— Two heats of open hearth steel were made by
the Cleveland Rolling Mill Co., one ordinary steel made with 9000 Ibs. each
scrap and pig, and 165 Ibs. ferro-manganese, the other the same with the
addition of 3$, or 540 Ibs. of nickel. Tests of six plates rolled from each
heat., 0.24 to 0.3 in. thick, gave results as follows :
Ordinary steel, T. S. 52,500 to 56,500 ; E.'L. 32,800 to 37,900 ; elong. 26 to 32$.
Nickel steel, " 63,370 to 67,100 ; " 47,100 to 48,200 ; " 23)4 to 26$.
MANGANESE, NICKEL, AND OTHER "ALLOY" STEELS. 409
The nickel steel averages 31 # higher in elastic limit, 20# higher in ultimate
tensile strength, with but slight reduction in ductility. (Eng. & M. Jour..
Feb. 25, 1893.)
Aluminum Steel.— R. A. Haclfield (Trans. A. I. M. E. 1890) says:
Aluminum appears to be of service as an addition to baths of molten iron or
steel unduly saturated with oxides, and this in properly regulated steel
manufacture should not often occur. Speaking generally, its role appears
to be similar to that of silicon, though acting more powerfully. The state-
ment that aluminum lowers the melting-point of iron seems to have no
foundation in fact. If any increase of heat or fluidity takes place by the
addition of small amounts of aluminum, it may be due to evolution of heat,
owing to oxidation of the aluminum, as the calorific value of this metal is
very high— in fact, higher than silicon. According to Berthollet, the con-
version of aluminum to A12O3 equals 7900 cal.; silicon to SiO2 is stated as 1 800.
The action of aluminum may be classed along with that of silicon, sulphur,
phosphorus, arsenic, and copper, as giving no increase of hardness to iron,
in contradistinction to carbon, manganese, chromium, tungsten, and nickel.
Therefore, whilst for some special purposes aluminum may be employed in
the manufacture of iron, at any rate with our present knowledge of its
properties, this use cannot be large, especially when taking into considera-
tion the fact of its comparatively high price. Its special advantage seems to
be that it combines In itself the advantages of both silicon and manganese ;
but so long as alloys containing these metals are so cheap and aluminum
dear, its extensive use seems hardly probable.
J. E. Stead, in discussion of Mr. Hadfield's paper, said : Every one of our
trials has indicated that aluminum can kill the most fiery steel, providing,
of course, that it is added in sufficient quantity to combine with all the oxy-
gen which the steel contains. The metal will then be absolutely dead, and
will pour like dead-melted silicon steel. If the aluminum is added as metal-
lic aluminum, and not as a compound, and if the addition is made just be-
fore the steel is cast, 1/10$ is ample to obtain perfect solidity in the steel.
Chrome Steel. (F. L. Garrison, Jour. F. I., Sept. 1891.)— Chromium
increases the hardness of iron, perhaps also the tensile strength and elastic
limit, but it lessens its weldibility.
Ferro chrome, according to Berthier, is made by strongly heating the
mixed oxides of iron and chromium in brasqued crucibles, adding powdered
charcoal if the oxide of chromium is in excess, and fluxes to scorify the
earthy matter and prevent oxidation. Chromium does not appear to give
steel the power of becoming harder when quenched or chilled. Howe slates
that chrome steels forge more readily than tungsten steels, and when not
containing over 0.5 of chromium nearly as well as ordinary carbon steels of
like percentage of carbon. On the whole the status of chrome steel is not
satisfactory. There are other steel alloys coming into use, which are so
much better, that it would seem to be only a question of time when it will
drop entirely out of the race. Howe states that many experienced chemists
have found no chromium, or but the merest traces, in chrome steel sold in
the markets.
J. W. Langley (Trans. A. S. C. E. 1892) says : Chromium, like manganese,
is a true hardener of iron even in the absence of carbon. The addition of \%
or 2fc of chromium to a carbon steel will make a metal which gets exces-
sively hard. Hitherto its principal employment has been in the production
of chilled shot and shell. Powerful molecular stresses result during cooling,
and the shells frequently break spontaneously months after they are made.
Tungsten Steel-Mushet Steel. (J. B. Nau, Iron Age, Feb. 11, 1892.)
—By incorporating simultaneously carbon and tungsten in iron, it is possi-
ble to obtain a much harder steel than with carbon alone, without danger of
an extraordinary brittleness in the cold metal or an increased difficulty in
the working of the heated metal.
When a special grade of hardness is required, it is frequently the custom
to use a high tungsten steel, known in England as special steel. A specimen
from Sheffield, used for chisels, contained 9.3$ of tungsten, 0.7$ of silver,
and 0.6$ of carbon. This steel, though used with advantage in its untem-
pered state to turn chilled rolls, was not brittle ; nevertheless it was hard
enough to scratch glass.
A sample of Mushet's special steel contained 8.3$ of tungsten and 1.73$ of
manganese. The hardness of tungsten steel cannot be increased by the or-
dinary process of hardening.
The only operation that it can be submitted to when cold is grinding. It
has to be given its final shape through hammering at a red heat, and even
410 STEEL.
then, when the percentage of tungsten is high, it has to be treated very
carefully; and in order to avoid breaking it, not only is it necessary to reheat
it several times while it is being hammered, but when the tool lias acquired
the desired shape hammering must still be continued gently and with nu-
merous blows until it becomes nearly cold. Then only can it be cooled en-
tirely.
Tungsten is not only employed to produce steel of an extraordinary hard-
ness, but more especially to obtain a steel which, with a moderate hardness,
allies great toughness, resistance, and ductility. Steel from Assailly, used
for this purpose, contained carbon, 0.52$; silicon, 0.04#; tungsten, 0-3#;
phosphorus, 0.04#; sulphur, 0.005#.
Mechanical tests made by Styffe gave the following results :
Breaking load per square inch of original area, pounds.. 172,424
Reduction of area, per cent 0. 54
Average elongation after fracture, per cent 13
According to analyses made by the Due de Luynes of ten specimens of the
celebrated Oriental damasked steel, eight contained tungsten, two of them
in notable quantities (0.518$ to 1$), while in all of the samples analyzed
nickel was discovered ranging from traces to nearly 4%.
Stein & Schwartz of Philadelphia, in a circular say : It is stated that
tungsten steel is suitable for the manufacture of steel magnets, since it re-
tains its magnetism longer than ordinary steel. Mr. Kniesche has made
tungsten up to 98# fine a specialty. Dr. Heppe, of Leipsig, has written a
number of articles iu German publications on the subject. The following
instructions are given concerning the use of tungsten: In order to produce
cast iron possessing great hardness an addition of one half to one and one
half of tungsten is all that is needed. For bar iron it must be carried up to
\% to 2$, but should not exceed 2^$. For puddled steel the range is larger,
but an addition beyond 3^$ only increases the hardness, so that it is brought
up to \ytfo only for special tools, coinage dies, drills, etc. For tires 2^$ to 5$
have proved best, and for axles % to $#. Cast steel to which tungsten has
been added needs a higher temperature for tempering than ordinary steel,
and should be hardened only between yellow, red, and white. Chisels made
of tungsten steel should be drawn between cherry-red and blue, and stand
well on iron and steel. Tempering is best done in a mixture of 5 parts of
yellow rosin, 3 parts of tar, and 2 parts of tallow, and then the article is
once more heated and then tempered as usual in water of about 15° C.
Fluid-compressed fSteel by tlie " Wliitworth Process."
(Proc. Inst. M. EM May, 1887, p. 167.)— In this system a gradually increasing
pressure up to 6 or 8 tons per square inch is applied to the fluid ingot, and
within half an hour or less after the application of the pressure the column
of flwid steel is shortened 1^ inch per foot or one-eighth of its length; .the
pressure is then kept on for several hours, the result being that the metal
is compressed into a perfectly solid and homogeneous material, free from
blow-holes.
In large gun-ring ingots during cooling the carbon is driven to the centre,
the centre containing 0.8 carbon and the outer ring 0.3. The centre is bored
out until a test shows that the inside of the ring contains the same percent-
age of carbon as the outside
Fluid-compressed steel is made by the Bethlehem Iron Co. for gun and
other heavy forgings.
CRUCIBLE STEEL.
Selection of Grades by tlie Eye, and Effect of Heat Treat*
iiieiit. (J. W. Langley, Amer. Chemist, November, 1876.)— In 1874, Miller,
Metcalf & Parkin, of Pittsburgh, selected eight samples of steel which were
believed to form a set of graded specimens, the order being based on the
quantity of carbon which they were supposed to contain. They were num-
bered from one to eight. On analysis, the quantity of carbon was found to
follow the order of the numbers, while the other elements present— silicon,
phosphorus, and sulphur— did not do so. The metfaod of selection is
described as follows :
The steel is melted in black-lead crucibles capable of holding about eighty
pounds; when thoroughly fluid it is poured into cast-iron moulds, and when
cold the top of the ingot is broken off, exposing a freshly-fractured surface.
The appearance presented is that of confused groups of crystals, all appear-
ing to have started from the outside and to have met in the centre; this
general form is common to all ingots of whatever composition, but to the
trained eye, and only to one long and critically exercised, a minute but in-
CRUCIBLE STEEL.
411
describable difference is perceived between varying samples of steel, and
this difference is now known to be owing almost wholly to variations in the
amount of combined carbon, as the following table will show. Twelve sam-
ples selected by the eye alone, and analyses of drillings taken direct from
the ingot before it had been heated or hammered, gave results as below:
Ingot
Nos.
Iron by
Diff.
Carbon.
Diff. of
Carbon.
Silicon.
Phos.
Sulph.
1
99.614
.302
.019
.047
.018
2
99.455
.490
.188
.034
.005
.016
3
99.363
.529
.039
.043
.047
.018
4
99.270
.649
.120
.039
.030
.012
5
99.119
.801
.152
.029
.035
.016
6
99.086
.841
.040
.039
.024
.010
7
99.044
.867
.026
.057
.014
.018
8
99.040
.871
.004
.053
.024
.012
9
98.900
.955
.084
.059
.070
.016
10
98.861
1.005
.050
.088
.034
.012
11
98.752
1.058
.053
.120
.064
.006
12
98.834
1.079
.021
.039
.044
.004
Here the carbon is seen to increase in quantity in the order of the num-
bers, while the other elements, with the exception of total iron, bear no rela-
tion to the numbers on the samples. The mean difference of carbon is .071.
In mild steels the discrimination is less perfect.
The appearance of the fracture by which the above twelve selections
were made can only be seen in the cold ingot before any operation, except
the original one of casting, has been performed upon it. As soon as it is
hammered, the structure changes in a remarkable manner, so that all trace
of the primitive condition appears to be lost.
Another method of rendering visible to the eye the molecular and chemi-
cal changes which go on in steel is by the process of hardening or temper-
ing. When the metal is heated and plunged into water it acquires an
increase of hardness, but a loss of ductility. If the heat to which the steel
has been raised just before plunging is too high, the metal acquires intense
hardness, but it is so brittle as to be worthless; the fracture is of a bright,
granular, or sandy character. In this state it is said to be burned, and it
cannot again be restored to its former strength and ductility by annealing;
it is ruined for all practical purposes, but in just this state it again shows
differences of structure corresponding with its content in carbon. The
nature of these changes can be illustrated by plunging a bar highly heated
at one end and cold at the other into water, and then breaking it off in
pieces of equal length, when the %actures will be found to show appear-
ances characteristic of the temperature to which the sample was raised.
The specific gravity of steel is influenced not only by its chemical analy-
sis, but by the heat to which it is subjected, as is shown by the following
table (densities referred to 60° F.):
Specific gravities of twelve samples of steel from the ingot; also of six
hammered bars, each bar being overheated at one end and cold at the
other, in this state plunged into water, and then broken into pieces of
equal length.
1
2
3
4
5
6
7
8
9
10
11
12
Ingot
Bar:
*Burned 1 .
o
3".
4.
5.
Cold 6.
7.855
7.836
7.841
7.818
7.814
7.823
7.826
7.831
7.844
7.829
7.791
7.811
7.830
7.849
7.806
7.824
7.838
7.834
7.789
7.784
7.780
7.808
7.812
7.829
7.819
7.818
7.752
7.755
7.758
7.773
7.790
7.825
7.813
7.807
7.744
7.749
7.755
7.789
7.812
7.826
7.803
7.805
7.690
7.741
7.769
7.798
7.811
7.825
•"•••'
'.'.'.'..
* Order of samples from bar.
412
STEEL.
Effect of Heat on the Grain of Steel. (W. Me teal f,— Jeans on
Steel, p. 642.) — A simple experiment will show the alteration produced in a
high-carbon steel by different methods of hardening. If a bar of such steel
be nicked at about 9 or 10 places, and about half an inch apart, a suitable
specimen is obtained for the experiment. Place one end of the bar in a
good fire, so that the first nicked piece is heated to whiteness, while the rest
of the bar, being out of the fire, is heated up less and less as we approach
the other end. As soon as the first piece is at a good white heat, which of
course burns a high carbon steel, and the temperature of the rest of the bar
gradually passes down to a very dull red, the metal should be taken out of
the fire and suddenly plunged in cold water, in which it should be left till
quite cold. It should then be taken out and carefully dried. An examina-
tion with a file will show that the first piece has the greatest hardness,
while the last piece is the softest, the intermediate pieces gradually passing
from one condition to the other. On now breaking off the pieces at each
nick it will be seen that very considerable and characteristic changes have
been produced in the appearance of the metal. The first burnt piece is very
open or crystalline in fracture; the succeeding pieces become closer and
closer in the grain until one piece is found to possess that perfectly
even grain and velvet-like appearance which is so much prized by experi-
enced steel users. The first pieces also, which have been too much hard-
ened, will probably be cracked; those at the other end will not be hardened
through. Hence if it be desired to make the steel hard and strong, the
temperature used must be high enough to harden the metal through, but
not sufficient to open the grain.
Changes in intimate Strength and Elasticity due to
Hammering. Annealing, and Tempering, (J. W. Langley,
Trans. A. S. C. E. 1892.)— The following table gives the result of tests made
on some round steel bars, all from the same ingot, which were tested by
tensile stresses, and also by bending till fracture took place:
2 *
O ti
Carbon .
d
fsi
|l
O 4J
g"*8'
«
Treatment.
&
4,1
S
oj
^3 C o3
|l-§
|§'
^ y
1
11
1
||
.§
f> P 2
Ila
I-&
11
£
<J-°
H
&
o
H
1
Cold-hammered bar
153
1.25
.47
.575
92,420
141,500
2.00
2.42
2
Bar dra WIT black —
75
1.25
.47
.577
114,700
138,400
6.00
12.45
3
Bar annealed
175
1.31
.70
.580
68,110
98,410
10.00
11.69
4
Bar hardened and
drawn black
30
1.09
.36
.578
152,800
248,700
8.33
17.9
The total carbon given in the table was found by the color test, which is
affected, not only by the total carbon, but by the condition of the carbon.
The analysis of the steel was:
Silicon 242 Manganese 24
Phosphorus ..".... .02 Carbon (true total carbon, by
Sulphur 009 combustion) 1.31
Heating Tool Steel. (Crescent Steel Co., Pirtsburg, Pa.)— There are
three distinct stages or times of heating: First, for forging; second, for
hardening; third, for tempering.
The first requisite for a good heat for forging is a clean fire and plenty of
fuel, so that jets of hot air will not strike the corners of the piece; next, the
fire should be regular, and give a good uniform heat to the whole part to be
forged. It should be keen enough to heat the piece as rapidly as may be,
and allow it to be thoroughly heated through, without being so fierce as to
overheat the corners.
Steel should not be left in the fire any longer than is necessary to heat it
clear through, as " soaking " in fire is very injurious; and, on the other hand,
it is necessary that it should be hot through, to prevent surface cracks.
By observing these precautions a piece of steel may always be heated
safely, up to even a bright yellow heat, when there is much forging to be
done on i£
CRUCIBLE STEEL. 413
The best and most economical of welding fluxes is clean, crude borax,
which should be first thoroughly melted and then ground to fine powder.
After the steel is properly heated, it should be forged to shape as quickly
as possible; and just as the red heat is leaving the parts intended for cutting
edges, these parts should be refined by rapid, light blows, continued until
the red disappears.
For the second stage of heating, for hardening, great care should be used:
first, to protect the cutting edges and working parts from heating more
rapidly than the body of the piece: next, that the whole part to be hardened
be heated uniformly through, without any part becoming visibly hotter
than the other. A uniform heat, as low as will give the required hardness,
is the best for hardening.
For every variation of heat, which is great enough to be seen, there will
result a variation in grain, which may be seen by breaking the piece: and.
for every such variation in temperature, there is a very good chance for a
crack to be seen. Many a costly tool is ruined by inattention to this point.
The effect of too high heat is to open the grain; to make the steel coarse.
The effect of an irregular heat is to cause irregular grain, irregular strains,
and cracks.
As soon as the piece is properly heated for hardening, it should be
promptly and thoroughly quenched in plenty of the cooling medium, water,
brine, or oil, as the case may be.
An abundance of the cooling bath, to do the work quickly and uniformly
all over, is very necessary to good and safe work.
To harden a large piece safely a running stream should be used.
Much uneven hardening is caused by the use of too small baths.
For the third stage of heating, to temper, the first important requisite is
again uniformity. The next is time; the more slowly a piece is brought
down to its temper, the better and safer is the operation.
When expensive tools are to be made it is a wise precaution to try small
pieces of the steel at different temperatures, so as to find out how low a heat
will give the necessary hardness. The lowest heat is the best for any steel.
Heating to Forge.— The trouble in the forge fire is usually uneven
heat, and not too high heat. Suppose the piece to be forged has been put
into a very hot fire, and forced as quickly as possible to a high yellow heat,
so that it is almost up to the scintillating point. If this be done, in a few
minutes the outside will be quite soft and in a nice condition for forging,
while the middle parts will not be more than red-hot. Now let the piece be
placed under the hammer and forged, and the soft outside will yield so
much more readily than the hard inside, that the outer particles will be torn
asunder, while the inside will remain sound.
Suppose the case to be reversed and the inside to be much hotter than the
outside; that is, that the inside shall be in a state of semi-fusion, while the
outside is hard and firm. Now let the piece be forged, and the outside will
be all sound and the whole piece will appear perfectly good until it is
cropped, and then it is found to be hollow inside,
In either case, if the piece had been heated soft all through, or if it had been
only red-hot all through, it would have forged perfectly sound.
In some cases a high heat is more desirable to save heavy labor but in
every case where a fine steel is to be used for cutting purposes it must be
borne in mind that very heavy forging refines the bars as they slowly cool,
and if the smith heats such refined bars until they are soft, he raises the
grain, makes them coarse, and he cannot get them fine again unless he has
a very heavy steam-hammer at command and knows how to use it well.
Annealing. (Crescent Steel Co.)— Annealing or softening is accom-
plished by heating steel to a red heat and then cooling it very slowly,
to prevent it from getting hard again.
The higher the degree of heat, the more will steel be softened, until the
limit of softness is reached, when the steel is melted.
It does not follow that the higher a piece of steel is heated the softer it
will be when cooled, no matter how slowly it may be cooled; this is proved
by the fact that an ingot is always harder than a rolled or hammered bar
made from it.
Therefore there is nothing gained by heating a piece of steel hotter than
a good, bright, cherry-red; on the contrary, a higher heat has several dis-
advantages: First. If carried too far, it may leave the steel actually harder
than a good red heat would leave it. Second. If a scale is raised on the
steel, this scale will be harsh, granular oxide of iron, and will spoil the tools
used to cut it. Third. A high scaling heat continued for a little time
414 STEEL.
Changes the structure of the steel, makes it brittle, liable to crack in hard.
ening, and impossible to refine.
To anneal any piece of steel, heat it red-hot ; heat it uniformly and heat it
through, taking care not to let the ends and corners get too hot.
As soon as it is hot, take it out of the fire, the sooner the better, and cool
it as slowly as possible. A good rule for heating is to heat it at so low a red
that when the piece is cold it will still show the blue gloss of the oxide that
was put there by the hammer or the rolls.
Steel annealed in this way will cut yerj'- soft ; it will harden very hard,
without cracking; and when tempered it will be very strong, nicely refined,
and will hold a keen, strong edge.
Tempering.— Tempering steel is the act of giving it, after it has been
shaped, the hardness necessary for the work it has to do. This is done by
first hardening the piece, generally a good deal harder than is necessary,
and then toughening it by slow heating and gradual softening until it is just
right for work.
A piece of steel properly tempered should always be finer in grain than
the bar from which it is made. If it is necessary, in order to make the piece
as hard as is required, to heat it so hot that after being hardened the grain
will be as coarse as or coarser than the grain in the original bar, then the
steel itself is of too low carbon for the desired work.
If a great degree of hardness is not desired, as in the case of taps, and
most tools of complicated form, and it is found that at a moderate heat the
tools are too hard and are liable to crack, the smith should first use a lower
heat in order to save the tools already made, and then notify the steelmaker
that his steel is too high, so as to prevent a recurrence of the trouble.
For descriptions of various methods of tempering steel, see " Tempering
of Metals," by Joshua Rose, in App. Cyc. Mech., vol. ii. p. 863 ; also,
44 Wrinkles and Recipes, " from the Scientific American. In both of these
works Mr. Rose gives a " color scale,11 lithographed in colors, by which the
following is a list of the tools in their order on the color scale, together with
the approximate color and the temperature at which the color appears on
brightened steel when heated in the air :
Scrapers for brass ; very pale yel- Hand-plane irons.
low, 430° F. Twist-drills.
Steel-engraving tools. . Flat drills for brass.
Slight turning tools.j Wood-boring cutters.
Hammer faces. Drifts.
Planer tools for steeL Coopers' tools.
Ivory-cutting tools. Edging cutters ; light purple^ 530° F»
Planer tools for iron. Augers.
Paper-cutters. Dental and surgical instruments.
Wood-engraving tools. Cold chisels for steel.
Bone cutting tools. Axes ; dark purple, 550° F.
Milling-cutters ; straiv yellow, 460° F. Gimlets.
Wire-drawing dies. Cold chisels for cast iron.
Boring-cutters. Saws for bone and ivory.
Leather-cutting dies. Needles.
Screw-cutting dies. Firmer-chisels.
Inserted saw-teeth. Hack-saws.
Taps. Framing-chisels.
Rock-drills. Cold chisels for wrought iron.
Chasers. Moulding and planing cutters to bt.
Punches and dies. filed.
Penknives. Circular saws for metal.
Reamers. Screw-drivers.
Half-round bits. Springs.
Planing and moulding cutters. Saws for wood.
Stone-cutting tools ; brown yellow* Dark blue, 570° F.
500° F. Pale blue, 610°.
Gouges. Blue tinged with green, 630*.
FORCE, STATICAL MOMENT,, EQUILIBRIUM, ETC. 415
MECHANICS.
FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC.
MECHANICS is the science that treats of the action of force upon bodies.
A Force is anything that tends to change the state of a body with respect
to rest or motion. If a body is at rest, anything that tends to put it in mo-
tion is a force; if a body is in motion, anything that tends to change either
its direction or its rate of motion is a force.
A force should always mean the pull, pressure, rub, attraction (or repul-
sion) of one body upon another, and always implies the existence of a simul-
taneous equal and opposite force exerted by that other body on the first body,
i.e., the reaction. In no case should we call anything a force unless we can
conceive of it as capable of measurement by a spring-balance, and are able
to say from what other body it comes. (I. P. Church.)
Forces may be divided into two classes, extraneous and molecular: extra-
neous forces act on bodies from without; molecular forces are exerted be-
tween the neighboring particles of bodies.
Extraneous forces are of two kinds, pressures and moving forces: pres-
sures simply tend to produce motion; moving forces actually produce
motion. Thus, if gravity act on a fixed body, it creates pressure; if on a free
body, it produces motion.
Molecular forces are of two kinds, attractive and repellent: attractive
forces tend to bind the particles of a body together; repellent forces tend
to thrust them asunder. Both kinds of molecular forces are continually
exerted between the molecules of bodies, and on the predominance of one
or the other depends the physical state of a body, as solid, liquid, or gaseous
The Unit of Force used in engineering, by English writers, is the
pound avoirdupois. (For some scientific purposes, as in electro-dynamics,
forces are sometimes expressed in ** absolute units." The absolute unit of
force is that force which acting on a unit of mass during a unit of time pro-
duces a unit of velocity; in English measures, that force which acting on
the mass whose weight is one pound in London will in one second produce a
Velocity of one foot per second = 1 -f- 32.187 of the weight of the standard
pound avoirdupois at London. In the French C. G. S. or centimetre-gramme
second system it is the force which acting on the mass whose weight is one
gramme at Paris will produce in one second a velocity of one centimetre per
second. This unit is called a *' dyne " = 1/981 gramme at Paris.)
Inertia is that property of a body by virtue of which it tends to continue
in the state of rest or motion in which it may be placed, until acted on by
some force.
Newton's Laws of Motion.— 1st Law. If a body be at rest, it will
remain at rest; or if in motion, it will move uniformly in a straight line till
acted on by some force.
2d Law. If a body be acted on by several forces, it will obey each as
though the others did not exist, and this whether the body be at rest or in
motion.
3d Law. If a force act to change the state of a body with respect to rest
or motion, the body will offer a resistance equal arid directly opposed to the
force. Or, to every action there is opposed an equal and opposite reaction.
Graphic .Representation of a Force.— Forces may be repre-
sented geometrically by straight lines, proportional to the forces. A force
is given when we know its intensity, its point of application, and the direc-
tion in which it acts. When a force is represented by a line, the length of the
line represents its intensity; one extremity represents the point of applica-
tion; and an arrow-head at the other extremity shows the direction of the
force.
Composition of Forces is the operation of finding a single force
whose effect is the same as that of two or more given forces. The required
force is called the resultant of the given forces.
Resolution of Forces is the operation of finding two or more forces
whose combined effect is equivalent to that of a given force. The required
forces are called components of the given force.
The resultant of two forces applied at a point, and acting in the same di-
rection, is equal to the sum of the forces. If two forces act in opposite
directions, their resultant is equal to their difference, and it acts in the
direction of the greater.
116
MECHANICS.
If any number of forces be applied at a point, some in one direction and
others in a contrary direction, their resultant is equal to the sum of those
that act in one direction, diminished by the sum of those that act in the op-
posite direction; or, the resultant is equal to the algebraic sum of the com-
ponents.
Parallelogram of Forces,— If two forces acting on a point be rep-
resented in direction and intensity by adjacent sides of a parallelogram,
their resultant will be represented by that diagonal of the parallelogram
which passes through the point. Thus OR, Fig.
88, is the resultant of OQ and OP.
Polygon of Forces.— If several forces are
applied at a point and act in a single plane, their
resultant is found as follows:
Through the point draw a line representing the
first force ; through the extremity of this draw
a line representing the second force; and so on,
_ throughout the system; finally, draw a line from
1 IG- °8' the starting-point to the extremity of the last line
drawn, and this will be the resultant required.
Suppose the body A, Fig. 89, to be urged in the directions A\% A2, ^43, A4,
and A5 by forces which are to each other as the lengths of those lines.
Suppose these forces to act successively and the body to first move from A
to 1; the second force A2 then acts and finding the body at 1 would take it
to 2'* the third force would then carry it to 3', the fourth to 4', and the fifth
to 5'. The line A5' represents in magnitude and direction the resultant of
all the forces considered. If there had
been an additional force, Ax, in the group,
the body would be returned by that force
to its original position, supposing the
forces to act successively, but if they had
acted simultaneously the body would never
have moved at all; the tendencies to mo-
tion balancing each other.
It follows, therefore, that if the several
forces which tend to move a body can be
represented in magnitude and direction
by the sides of a closed polygon taken in
order, the body will remain at rest; but if
the forces are represented by the sides of
an open polygon, the body will move and the direction will be represented
by the straight line which closes the polygon.
Twisted Polygon.— The rule of the polygon of forces holds true even
when the forces are not in one plane. In this case the lines Al, 1-3', 2'-3',
etc form a twisted polygon, that is, one whose sides are not in one plane.
Parallelopipedon of Forces.— If three forces acting on a point be
represented by three edges of a parallelopipedon which meet in a common
point, their resultant will be represented by the diagonal of the parallelo-
pipedon that passes through their common point.
Thus OR, Fig. 90, is the resultant of OQ, OS, and OP. OM is the result-
ant of OP and OQ, and OR is the resultant of OM and OS.
Moment of a Force.— The mo-
ment of a force (sometimes called stat-
ical moment), with respect to a point,
is the product of the force by the per-
pendicular distance from the point to
the direction of the force. The fixed
point is called the centre of mo-
RO. 90.
FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 417
ments ; the perpendicular distance is the lever-arm of the force; and the
moment itself measures the tendency of the force to produce rotation about
the centre of moments.
If the force is expressed in pounds and the distance in feet, the moment
is expressed in foot-pounds. It is necessary to observe the distinction be-
tween foot-pounds of statical moment and foot-pounds of work or energv.
(See Work.)
In the bent lever, Fig. 91 (f rom Trautwine), if the weights n and m repre-
sent forces, their moments about the point / are respectively n X af and
m X fc. If instead of the weight m a pulling force to balance the weight
n is applied in the direction bs, or by or bd, s, y, and d being the amounts of
these forces, their respective moments are s X ft, y X fb, d X fh.
If the forces acting on the lever are in equilibrium it remains at rest, and
the moments on each side of /are equal, that is, n X af = m X /c, or s X ft,
or y X fb, or d X hf.
The moment of the resultant of any number of forces acting together in
the same plane is equal to the algebraic sum of the moments of the forces
taken separately.
Statical Moment. Stability.— The statical moment of a body is
the product of its weight by the distance of its line of gravity from some
assumed line of rotation. The line of gravity is a vertical line drawn from
its centre of gravity through the body. The stability of a body is that re-
sistance which its weight alone enables it to oppose against forces tending
to overturn it or to slide it along its foundation.
To be safe against turning on an edge the moment of the forces tending to
overturn it, taken with reference to that edge, must be less than the stati-
cal moment. When a body rests on an inclined plane, the line of gravity
being vertical, falls toward the lower edge of the body, and the condition of
its not being overturned by its own weight is that the line of gravity must
fall within this edge. In the case of an inclined tower resting on a plane
the same condition holds— the line of gravity must fall within the base. The
condition of stability against sliding along a horizontal plane is that the hor-
izontal component of the force exerted tending to cause it to slide shall be
less than the product of the weight of the body into the coefficient of fric-
tion between the base of the body and its supporting plane. This coefficient
of friction is the tangent of the angle of repose, or the maximum angle at
which the supporting plane might be raised from the horizontal before the
body would begin to slide. (See Friction.)
Tlie Stability of a Dam against overturning about its lower edge
is calculated by comparing its statical moment referred to that edge with
the resultant pressure of the water against its upper side. The horizontal
pressure on a square foot at the bottom of the dam is equal to the weight of
a column of water of one square foot in section, and of a height equal to the
distance of the bottom below water-level ; or, if H is the height, the pressure
at the bottom per square foot = 62.4 x H Ibs. At the water-level the pres-
sure is zero, and it increases uniformly to the bottom, so that the sum of the
pressures on a vertical strip one foot in breadth may be represented by the
area of a triangle whose base is 62.4 XH and whose altitude is H, or 62 4H2-*~2.
The centre of gravity of a triangle being J^ of its altitude, the resultant of
all the horizontal pressures may be taken as equivalent to the sum of the
pressures acting at }£H, and the moment of the sum of the pressures is
therefore 62.4 X H3 -v- 6.
Parallel Forces,— If two forces are parallel and act in the same direc-
tion, their resultant is parallel to both, and lies between them, and the inten-
sity of the resultant is equal to the sum of the intensities of the two forces.
Thus in Fig. 91 the resultant of the forces n and m acts vertically down-
ward at /, and is equal ton-\-m.
If two parallel forces act at the extremities of a straight line and in the
same direction, the resultant divides the line joining the points of application
of the components, inversely as the components. Thus in Fig. 91, msn ::
af : fc; and in Fig. 92, P : Q : : SN : SM. N
The resultant of two parallel forces s^~
acting in opposite directions is parallel / [
to both, lies without both, on the side sp' \^ > Q
and in the direction of the greater, /
and its intensity is equal to the differ- M <£ ! ^ p
ence of the intensities of the two L
forces. FIG. 92.
418 MECHANICS.
Thus the resultant of the two forces Q and P, Fig. 93, is equal to Q - P=
R. Of any two parallel forces and their
N resultant each is proportional to the dis-
/
j^ —
£> tance between the other two; thus in both
Figs. 92 and 93, P : Q : R : : SN : SM : M N.
Couples.— If P and Q be equal and act
/in opposite directions, R = 0; that is, they
have no resultant. Two such forces con-
'• t ft stitute what is called a couple.
C The tendency of a couple is to produce
FIG. 93. rotation; the measure of this tendency,
called the moment of the couple, is the
product of one of the forces by the distance between the two.
Since a couple has no single resultant, no single force can balance a
couple. To prevent the rotation of a body acted on by a couple the applica-
tion of two other forces is required, forming a second couple. Thus in Fig,
94, P and Q forming a couple, may be balanced
by a second couple formed by R and S. The
point of application of either R or S may be a
fixed pivot or axis.
Moment of the couple PQ = P(c + 6 -f a) =
moment of RS = Rb, Also, P -}- R = Q -f- S.
The forces R and S need not be parallel to P
and Q, but if not, then their components parallel
to PQ are to be taken instead of the forces
themsolves.
Equilibrium of Forces.— A system of
forces applied at points of a solid body will be
in equilibrium when they have no tendency to
produce motion, either of translation or of rota-
rs
FIG. 94.
tion.
The conditions of equilibrium are : 1. The algebraic sum of the compo-
nents of the forces in the direction of any three rectangular axes must be
separately equal to 0.
X. The algebraic sum of the moments of the forces, with respect to any
three rectangular axes, must be separately equal to 0.
If the forces lie in a plane : 1. The algebraic sum of the components of the
forces, in the direction of any two rectangular axes, must be separately
equal to 0.
2. The algebraic sum of the moments of the forces, with respect to any
point in the plane, must be equal to 0.
If a body is restrained by a fixed axis, as in case of a pulley, or wheel and
axle, the forces will be in a equilibrium when the algebraic sum of the mo-
ments of the forces with respect to the axis is equal to 0.
CENTRE OF GRAVITY.
The centre of gravity of a body, or of a system of bodies rigidly connected
together, is that point about which, if suspended, all the parts will be in
equilibrium, that is, there will be no tendency to rotation. It is the point
through which passes the resultant of the .efforts of gravitation on each of
the elementary ^particles of a body. In bodies of equal heaviness through-
out, the centre of gravity is the centre of magnitude.
(The centre of magnitude of a figure is a point such that if the figure be
divided into equal parts the distance of the centre of magnitude of the
whole figure from any given plane is the mean of the distances of the centres
of magnitude of the several equal parts from that plane.)
If a body be suspended at its centre of gravity, it will be in equilibrium in
all positions. If it be suspended at a point out of its centre of gravity, it
will swing into a position such that its centre of gravity is vertically beneath
its point of suspension.
To find the centre of gravity of any plane figure mechanically, suspend
the figure by any point near its edge, and mark on it the direction of a
plumb-line hung from that point ; then suspend it from some other point,
and again mark the direction of the plumb-line in like manner. Then the
centre of gravity of the surface will be at the point of intersection of the
two marks of the plumb-line.
The Centre of Gravity of Regular Figures, whether plane or
solid, is the same as their geometrical centre ; for instance, a straight line,
MOMENT OF INERTIA. 419
parallelogram, regular polygon, circle, circular ring, prism, cylinder,
sphere, spheroid, middle frustums of spheroid, etc.
Of a triangle : On a line drawn from any angle to the middle of the op-
posite side, at a distance of one third of the line from the side; or at the
intersection of such lines drawn from any two angles.
Of a trapezium or trapezoid : Draw a diagonal, dividing it into two tri-
angles. Draw a line joining their centres of gravity. Draw the other
diagonal, making two other triangles, and a line joining their centres. The
intersection of the two lines is the centre of gravity required.
Of a sector of a circle : On the radius which bisects the arc, 2cr -*- 3/ from
the centre, c being the chord, r the radius, and I the arc.
Of a semicircle : On the middle radius, ,4244r from the centre.
Of a quadrant: On the middle radius, .6002r from the centre.
Of a segment of a circle ; c3 -*- 12a from the centre, c = chord, a = area.
Of a parabolic surface : In the axis, 3/5 of its length from the vertex.
Of a semi-parabola (surface) : 3/5 length of the axis from the vertex, and
% of the semi-base from the axis.
Of a cone or pyramid : In the axis, % of its length from the base.
Of a paraboloid ; In the axis, % of its length from the vertex.
Of a cylinder, or regular prism ; In the middle point of the axis.
Of a frustum of a cone or pyramid ; Let a = length of a line drawn from
the vertex of the cone when complete to the centre of gravity of the base, and
a' that portion of it between the vertex and the top of the frustum; then
distance of centre of gravity of the frustum from centre of gravity of its
_ a 3a/8
~ 4 ~ 4(a2-f aa'-f-a'2)*
For two bodies, fixed one at each end of a straight bar, the common
centre of gravity is in the bar, at that point which divides the distance
• between their respective centres of gravity in the inverse ratio of the
weights. In this solution the weight of the bar is neglected. But it may
be taken as a third body, and allowed for as in the following directions :
For more than two bodies connected in one system: Find the common
centre of gravity of two of them ; and find the common centre of these two
jointly with a third body, and so on to the last body of the group.
Another method, by the principle of moments : To find the centre of
gravity of a system of bodies, or a body consisting of several parts, whose
several centres are known. If the bodies are in a plane, refer their several
centres to two rectangular co-ordinate axes. Multiply each weight by its
distance from one of the axes, add the products, and divide the sum by the
sum of the weights: the result is the distance of the centre of gravity from
that axis. Do the same with regard to the other axis. If the bodies are
not in a plane, refer them to three planes at right angles to each other, and
determine the mean distance of the sum of the weights from each of the
three planes.
MOMENT OF INERTIA.
The moment of inertia of the weight of a body with respect to an axis is
the algebraic sum of the products obtained by multiplying the weight of
each elementary particle by the square of its distance from the axis. If the
moment of inertia with respect to any axis = 7, the weight of any element
of the body = w, and its distance from the axis = r, we have I = 2(t0r2) .
The moment of inertia varies, in the same body, according to the position
of the axis. It is the least possible when the axis passes through the centre
of gravity. To find the moment of inertia ^of a body, ^referred to a given
axis, div' "
of each }
axis. The sum of the pr
moment of inertia thus obtained will be more nearly exact, the smaller and
more numerous the parts into which the body is divided.
MOMENTS OP INERTIA OF REGULAR SOLIDS.— Rod, or bar, of uniform thick-
ness, with respect to an axis perpendicular to the length of the rod,
r=jr (! + <*>) a)
W= weight of rod, 2Z = length, d — distance of centre of gravity from axis.
Thin circular plate, axis in its)
own plane, f
r ss radius of plate.
420
MECHANICS.
Circular plate,axis perpendicular ) r r*r(r* t ^\ ,*
to the plate, f J = ^Yjfr / ........ ^
Circular ring, axis perpendicular f T /r2 -f- ?'/a , .."N /«
to its own plane, ^ V — g " /» ••••(«»
r and r' are the exterior and interior radii of the ring.
Cylinder, axis perpendicular to ) ( r9 I9 , \
the axis of the cylinder, v \ 7 + -jf * <* V • • • • • <5>
r — radius of base, 21 = length of the cylinder.
By making d = 0 in any of the above formulae we find the moment ot
inertia for a parallel axis through the centre of gravity.
The moment of inertia. 2?vr2, numerically equals the weight of a body
which, if concentrated at the distance unity from the axis of rotation, would
require the same work to produce a given increase of angular velocity that the
actual body requires. It bears the same relation to angular acceleration
which weight does to linear acceleration (Rankine). The term moment of
inertia is also used in regard to areas, as the cross-sections of beams under
strain. In this case I— 2ar2, in which a is any elementary area, and r its
entre. (See under Strength of Materials, p. 247.) Some
distance from the cen
writers call 2nir2 = 2tt?r2 -
g the moment of inertia.
CENTRE AND RADIUS OF GYRATION.
The centre of gyration, with reference to an axis, is a point at which, if
tfie entire weight of a body be concentrated, its moment of inertia will re-
main unchanged; or, in a revolving body, the point in which the whole
weight of the body may be conceived to be concentrated, as if a pound of
platinum were substituted for a pound of revolving feathers, the angular
velocity and the accumulated work remaining the same. The distance of
this point from the axis is the radius of gyration. If W =f the weight of a
body, I = 2w;r2 = its moment of inertia, and k = its radius of gyration,
1 = Wk* - 2w;?-2; Jc = i-.
The moment of inertia = the weight X the square of the radius of gyration.
To find the radius of gyration divide the body into a considerable number
of equal small parts — the more numerous the more nearly exact is the re-
sult,— then take the mean of all the squares of the distances of the parts
from the axis of revolution, and find the square root of the mean square.
Or, if the moment of inertia is known, divide it by the weight and extract
the square root. For radius of gyration of an area, as a cross-section of a
beam, divide the moment of inertia of the area by the area and extract the
square root.
The radius of gyration is the least possible when the axis passes through
the centre of gravity. This minimum radius is called the principal radius
of gyration. If we denote it by k and any other radius of gyration by fc',
we have for the five cases given under the head of moment of inertia above
the following values :
(3) Circular plate, axis )
perpen. to plane,
(4) Circular ring, axis)
perpen. to plane, f
(5) Cylind
+<*•.
) Cylinder, axis per- > ,. _ M I* . , , __ /r2 , Z2 , ..
pen. to length, 1 j/ 4"+3"' yT"*"jf*
CENTRES OF OSCILLATION AND OF PERCUSSION. 421
Principal Radii of Gyration and Squares of Radii of
Gyration*
(For radii of gyration of sections of columns, see page 249.)
Surface or Solid.
Rad. of Gyration;
Square of R.
of Gyration.
Parallelogram: ) axis at its base
.5773k
.2886/1
.5773Z
.2886Z
577 V^M1^5
U^l
l/12/ia
YB^
1/12/a
(52 -f ca) -^ 3
4i2 + 62
12
(7ia + 7i'2)--12
/i2-*- 6
fc« 7i + 36
height h J " mid-height
Straight rod: jaxisatend
recf^:^emf " mid-length..
Rectangular prism:
axes 2«, 26, 2c, referred to axis 2a...
Parallelepiped: length Z, base 6, axis }
at one end, at mid-breadth )
.289 |/4i2 -f- 6*
.289 V/i2 -f /i/2
,408k
•™^WI
w
Hollow square tube:
out. side h, inn'r /i', axis mid-length . .
very thin, side = /t, " **
Thin rectangular tube: sides fc, 7i, )
axis mid-length J
12 7i-f6
^r2 = W -^- 16
(7i2-|-/i/2)H-16
/» r2
12^4
^'2
(R2 -f r2) -H 2
/2 ^2 4. ra
12+ 4
I* E2
12+"2
r2
,.2
y&i
2/5r2
2/5ra
Hra
ft2 f c2
Thin circ. plate: rad.r,diam.7i,ax. diam.
Flat circ. ring: diams. /*, h', axis diam.
Solid circular cylinder: length I, \
axis diameter at mid-length )
M Vw+ v*
.289 VI* -f 3r2
7071r
Circular plate: solid wheel of uni- J
form thickness, or cylinder of any >
length, referred to axis of cyl )
Hollow circ. cylinder, or flat ring:l
I, length; R, r, outer and inner!
radii. Axis, 1, longitudinal axis; f
2 diam at mid-length J
.7071 \'R*±r*
.289 fia + 3(Sa + ra)
.289 4/Z2 + 6^a
r
.7071r
.6325r
.6325r
.5773r
.4472 f&a -f ca
t /R& - ?-5
Same: very thin, axis its diameter. . . .
** radius r; axis, longitud'l axis..
Circumf . of circle, axis its centre
" " " " " diam
Sphere* radius r axis its diam
Spheroid : equatorial radius r, re- 1
volving polar axis a \
Paraboloid : r = rad. of base, rev. |
Ellipsoid: semi-axes a, 6, c; revolv- f
5
2 J?6 - r5
Spherical shell: radii R, r, revolving {
on its diam J
.G325/I/ ^3 _ ?.3
8165r
5477r
5 #3 - r3
%r*
0.3r2
Same: very thin, radius r
Solid cone: r = rad. of base, rev. on |
axis . )
CENTRES OF OSCULATION AND OF PERCUSSION.
Centre of Oscillation.— If a body oscillate about a fixed horizontal
axis, not passing through its centre of gravity, there is a point in the line
drawn from the centre of gravity perpendicular to the axis whose motion
is the same as it would be if the whole mass were collected at that point
and allowed to vibrate as a pendulum about the fixed axis. This point is
called the centre of oscillation.
The Radius of Oscillation, or distance of the centre of oscillation
from the point of suspension = the square of the radius of gyration H- dis-
tance of the centre of gravity from the point of suspension or axis. The
centres of oscillation and suspension are convertible.
If a straight line, or uniform thin bar or cylinder, be suspended at one end,
oscillating about it as an axis, the centre of oscillation is at % the length of
422 MECHANICS.
the rod from the axis. If the point of suspension is at ^ the length from
the end, the centre of oscillation is also at % the length from the axis, that
is, it is at the other end. In both cases the oscillation will be performed in
the same time. If the point of suspension is at the centre of gravity, the
length of the equivalent simple pendulum is infinite, and therefore the time
of vibration is infinite.
For a sphere suspended by a cord, r = radius, h = distance of axis of
motion from the centre of the sphere, h' — distance of centre of oscillation
2 ra
from centre of the sphere, I = radius of oscillation = h + h' = h -j- - — •
5 ft
If the sphere vibrate about an axis tangent to its surface, h = r, and I = r
•f 2/5r. If h -= lOr, I - lOr-J- |r-
Lengths of the radius of oscillation of a few regular plane figures or thin
plates, suspended by the vertex or uppermost point.
1st. When the vibrations are flatwise, or perpendicular to the plane of the
figure:
In an isosceles triangle the radius of oscillation is equal to % of the height
of the triangle.
In a circle, % of the diameter.
In a parabola, 5/7 of the height.
2d. When the vibrations are edgewise, or in the plane of the figure!
In a circle the radius of oscillation is % of the diameter.
In a rectangle suspended by one angle, % of the diagonal.
In a parabola, suspended by the vertex, 5/7 of the height, plus £6 of the
parameter.
In a parabola, suspended by the middle of the base, 4/7 of the height plus
14 the parameter.
Centre of Percussion.— The centre of percussion of a body oscillat-
ing about a fixed axis is the point at which, if a blow is struck by the body,
the percussive action is the same as if the whole mass of the body were con«
centrated at the point. This point is identical with the centre of oscillation.
THE PENJDIJL.UM.
A body of any form suspended from a fixed axis about which it oscillates
by the force of gravity is called a compound pendulum. The ideal body
concentrated at the centre of oscillation, suspended from the centre of sus-
pension by a string without weight, is called a simple pendulum. This equi-
valent simple pendulum has the same weight as the given body, and also
the same moment of inertia, referred to an axis passing through the point
of suspension, and it oscillates in the same time.
The ordinary pendulum of a given length vibrates in equal times when the
angle of the vibrations does not exceed 4 or 5 degrees, that is, 2° or 2.V£° each
side of the vertical. This property of a pendulum is called its isochronism.
The time of vibration of a pendulum varies directly as the square root of
the length, and inversely as the square root of the acceleration due to grav-
ity at the given latitude and elevation above the earth's surface.
If T = the time of vibration, I = length of the simple pendulum, g = accel-
eration = 32.16, T = if A/ -; since v is constant, Tec — -. At a given loca-
\ ^ \/g
tion g is constant and T<x VI. If I be constant, then for any location
TQC — . If !Tbe constant, gT* = ir2/; I oc g; g - ^. From this equation
the force ot gravity at any place may be determined if the length of the
simple pendulum, vibrating seconds, at that place is known. At New York
this length is 39.1017 inches = 3.2585 ft., whence g = 32.16 ft. At London the
length is 39.1393 inches. At the equator 39.0152 or 39.0168 inches, according
to different authorities.
Time of vibration of a pendulum of a given length at New York
t-A/^ '^L
~ y 39.1017 ~~ 6.253*
t being in seconds and I in inches. Length of a pendulum having a given
time of vibration, I = t* X 39.1017 inches.
VELOCITY, ACCELERATION, FALLING BODIES. 423
The time of vibration of a pendulum may be varied by the addition of a
weight at a point above the centre of suspension, which counteracts the
lower weight, and lengthens the period of vibration. By varying the height
of the upper weight the time is varied.
To find the weight of the upper bob of a compound pendulum, vibrating
seconds, when the weight of the lower bob, and the distances of the weights
from the point of suspension are given:
(39.1 x
W = the weight of the lower bob, w = the weight of the upper bob; D =
the distance of the lower bob and d = the distance of the upper bob from
the point of suspension, in inches.
Thus, by means of a second bob, short pendulums may be constructed to
vibrate as slowly as longer pendulums.
By increasing w or d until the lower weight is entirely counterbalanced,
the time of vibration may be made infinite.
Conical Pendulum.— A weight suspended by a cord and revolving
at a uniform speed in the circumference of a circular horizontal plane
whose radius is r, the distance of the plane below the point of suspension be-
ing fc, is held in equilibrium by three forces— the tension in the cord, the cen-
trifugal force, which tends to increase the radius r, and the force of gravity
acting downward. If v = the velocity in feet per second, the centre of
gravity of the weight, as it describes the circumference, g =s 32.16, and r
and h are taken in feet, the time in seconds of performing one revolution is
..»=.. ft,
If t = 1 second, h = .8146 foot = 9.775 inches.
The principle of the conical pendulum is used in the Ordinary fly-ball
governor for steam-engines. (See Governors.)
CENTRIFUGAL FORCE,
A body revolving in a curved path of radius = R in feet exerts a force,
called centrifugal force, F, upon the arm or cord which restrains it from
moving in a straight line, or "flying off at a tangent." If W = weight of
the body in pounds, N — number of revolutions per minute, v = linear
velocity of the centre of gravity of the body, in feet per second, g = 32.16,
then
If n = number of revolutions per second, F = 1.2276TT7??t2.
(For centrifugal force in fly-wheels, see Fly-wheels.)
VELOCITY, ACCELERATION, FALLING BODIES*
Velocity is the rate of motion, or the distance passed over by a body in
a given time.
If s = space in feet passed over in t seconds, and v «= velocity in feet per
second, if the velocity is uniform,
s s
v = -; s = vti t =t -.
t v
If the velocity varies uniformly, the mean velocity v9 =s -1 ~£ "a, in which
v, is the velocity at the beginning and v, the velocity at the end of the time t.
Acceleration is the change in velocity which takes place in a unit of
time. Unit of acceleration = a = 1 foot per second in one second. For
uniformly varying velocity, the acceleration is a constant quantity, and
9 = Vj + at\ Vj « va - at\ t - V* ~ v*. . . . (2)
424 MECHANICS.
If the body start from rest, vl = 0; then
vo = ^; va = 2v0; « = y; va = ai; r8-a* = 0; f«^«
Combining (1) and (2), we have
.-&££-. -*«+£ ; .-**-*£
If Vl = 0, s = ^-t.
Retarded Motion*— If the body start with a velocity Vi and come to
rest, i?2 = 0; then s = ~-t.
In any case, if the change in velocity is v,
v. va a±n
S=3<! S = <Ta' S=2('-
For a body starting from or ending at rest, we have the equations
v = at; s = ~£; s = — ; i;2 = 2as,
Falling Bodies.— In the case of falling bodies the acceleration due
to gravity is 32.16 feet per second in one second, = g. Then if v = velocity
acquired at the end of t seconds, or final velocity, and h = height or space
in feet passed over in the same time,
t; = gt « 32.16* = ^2gh = 8.02 tfh = 7;
£ -32T6
w = space fallen through in the Tth second = g(T— }£).
From the above formula for falling bodies we obtain the following :
During the first second the body starting from a state of rest (resistance
of the air neglected) falls g -*- 2 = 16.08 feet ; the acquired velocity is g =
32.16 ft. per sec. ; the distance fallen in two seconds is h = ~- = 16.08 X 4 =
64.32 ft. ; and the acquired velocity is v = gt = 64.32 ft. The acceleration, or
increase of velocity in each second, is constant, and is 32.16 ft. per sec. Solv-
ing the equations for different times, we find for
Seconds,* ............. ...... . ................. 1 2845 6
Acceleration, g ........................ 32.16 X 1 1 1 1 1 1
Velocity acquired at end of time, v.... 32.16 X 1 2 8 4 5 6
Height of fall in each second, w... ... —^ X 1 3 5 7 9 11
Total height of fall, h .................. ^~ XI 4 9 16 25 36
Value of g.— The value of g increases with the latitude, and decreases
with the elevation. At the latitude of Philadelphia, 40°, its value is 32.16. At
the sea-level, Everett gives g = 32.173 — .082 cos 2 lat. —.000003 height in
feet. At Paris, lat. 48° 50' N., g = 980.87 cm. = 32.181 ft.
Values of 4/2#, calculated by an equation given by C. S. Pierce, are given
in a table in Smith's Hydraulics, from which we take the following :
Latitude...^.. 0° 10° 20° 30° 40° 50° 60°
Value of V20.. 8.0112 8.0118 8.0137 8.0165 8.0199 8.0235 8.0269
The value of V2g decreases about .0004 for every 1000 feet increase in ele-
vation above the sea-level.
"For all ordinary calculations for the United States, g is generally taken at
32.16, and |/2gr at 8.02. In England g = 32.2, ^2g = 8.025. Practical limit-
ing values of g for the United States, according to Pierce, are :
Latitude 49° at sea-level .......................... .. p = 32.186
" 25° 10,000 feet aboVe the sea ........... . ...... G = 32.08'
VELOCITY, ACCELERATION, FALLING BODIES. - 425
Fig. 95 represents graphically the velocity, space, etc., of a body falling tor
six seconds. The vertical line at the left is -
the time in seconds, the horizontal lines
represent the acquired velocities at the
end of each second — 32.16£. The area of
the small triangle at the top represents
the height fallen throug in the first
second = ^g = 16.08 feet, and each of the
other triangles is an equa space. The
number of triangles between each pair of
horizontal lines represents *he height of
fall in each second, and the number of
triangles between any horizontal line and
the top is the total height fallen during 16
the time. The figures under 7i, w, and v
adjoining the cut are to be multiplied by
16.08 to obtain the actual velocities and 25
heights for the given times.
Angular and Linear Velocity
of a Turning Body.— Let r = radius of a
turning body in feet, n = number of revo-
lutions per minute, v = linear velocity of
a point on the circumference in feet per
per minute.
h
u
v
t
1
1
2
1"
\
4
3
4
3"
\
\
9
5
G
3"
\
\
\
16
7
8
4"
\
\
\
\
25
9
10
5"
\
\
\!
\\
3G
11
12
6"
\
\
\
\N\
FIG. 95.
second, and 60v = velocity in feet
Angular velocity is a term used to denote the angle through which any
radius of a body turns in a second, or the rate at which any point in it
having a radius equal to unity is moving, expressed in feet per second. The
nnit of angular velocity is the angle which at a distance = radius from the
180
centre is subtended by an arc equal to the radius. This unit angle = —
degrees = 57.3°. 2ir X 57.3? = 360°, or the circumference. If A = angular
v 2nn
velocity, v = Ar, A = - = -^-.
T OU
180
The unit angle — is called a radian.
Height. Corresponding to a Given Acquired Velocity*
>>
>>
>»
£
•
£
-j
£
1
>
-a
§
8
£
§
9
K
1
o
£
1
W
1
1
1
1
1
1
I
1
I
f
feet
p. sec.
feet.
feet
p. sec.
feet.
feet
p. sec.
feet.
feet
p. sec.
feet.
feet
D.sec.
feet.
feet
p. sec.
feet.
.25
.0010
13
2.62
3
17.9
55
47.0
76
89.8
97
146
.50
.0039
14
3.04
35
19.0
56
48.8
77
92.2
98
149
.75
.0087
15
3.49
36
20.1
57
50.5
78
94.6
99
152
1.00
.016
16
3.98
37
21.3
5o
52.3
79
97.0
100
155
1.25
.024
17
4.49
38
22.4
59
54.1
80
99.5
105
171
1.50
.035
18
5.03
39
23.6
60
56.-
81
102.0
110
188
1.75
.048
19
5.61
40
24.9
61
57.9
82
104.5
115
205
2
.062
20
6.22
41
26.1
62
59.8
83
107.1
120
224
2.5
.097
21
6.85
42
27.4
63
61.7
84
109.7
130
263
3
.140
22
7.52
43
28.7
64
63.7
85
112.3
140
304
3.5
.190
23
8.21
44
30.1
65
65.7
86
115.0
150
350
4
.248
24
8.94
45
31.4
66
67.7
87
117.7
175
476
4.5
.314
25
9.71
46
32.9
67
69.8
88
120.4
200
622
5
.388
26
10.5
47
34.3
68
71.9
89
123.2
300
1399
6
.559
27
11.3
48
35.8
69
74.0
90
125.9
400
2488
7
.761
28
12.2
49
37.3
70
76.2
91
128.7
500
3887
8
.994
29
13.1
50
38.9
71
78.4
92
131.6
600
5597
9
1.26
30
14.0
51
40.4
72
80.6
93
134.5
700
7618
10
1.55
31
14.9
52
42.0
73
82.9
94
137.4
800
9952
11
1.88
32
15.9
53
43.7
74
85.1
95
140.3
900
12693
12
2.24
33
16.9
54
45.3
•75
87.5
96
143.3
1000
15547
426
MECHANICS.
Falling Bodies : Velocity Acquired by a Body Falling a
Given Height.
1
w
Velocity.
J
§
'£
ffi
Velocity.
i
§
Velocity.
45
1
Velocity.
|
.£?
°S
«
Velocity.
t
&
Velocity.
feet.
feet
p. sec.
feet.
feet
p.sec.
eet.
feet
p.sec.
feet.
feet
p.sec.
feet.
feet
p.sec.
feet.
feet
p.sec.
.005
.57
.39
5.01
1.20
8.79
5.
17.9
23.
38.5
72
68.1
.010
.80
.40
5.07
1.22
8.87
.2
18.3
.5
38.9
73
68.5
.015
.98
.41
6.14
1.24
8.94
A
18.7
24.
39.3
74
69.0
.020
1.13
.42
5.20
1.26
9.01
.6
19.0
.5
39.7
75
69.5
.025
1.27
.43
5.26
1.28
9.08
.8
19.3
25
40.1
76
69.9
.030
1.39
.44
5.32
1.30
9.15
6.
19.7
26
40.9
77
70.4
.035
1.50
.45
5.38
1.32
9.21
.2
20.0
27
41.7
78
70.9
.040
1.60
.46
5.44
1.34
9.29
.4
20.3
28
42.5
79
71.3
.045
1.70
.47
5.50
1.36
9.36
.6
20.6
29
43.2
80
71 .8
.050
1.79
.48
5.56
1.38
9.43
.8
20.9
30
43.9
81
72.2
.055
1.88
.49
5.61
1.40
9.49
7.
21.2
81
44.7
82
72.6
.060
1.97
.50
5.67
1.42
9.57
.2
21.5
82
45.4
83
73.1
.065
2.04
.51
5.73
1.44
9.62
.4
21.8
33
46.1
84
73.5
.070
2.12
.52
6.78
1.46
9.70
.6
22.1
34
46.8
85
74.0
,075
2.20
.53
5.84
1.48
9.77
.8
22.4
85
47.4
86
74.4
.080
2.27
.54
5.90
1.50
9.82
8.
22.7
86
48.1
87
74.8
.085
2.34
.55
5.95
1.52
9.90
.2
23.0
87
48.8
88
75.3
.090
2.41
.56
6.00
1.54
9.96
.4
23.3
88
49.4
89
75.7
.095
2.47
.57
6.06
1.56
10.0
.6
23.5
39
50.1
90
76.1
.100
2.54
.58
6.11
1.58
10.1
.8
23.8
40
50.7
91
76.5
.105
2.60
.59
6.16
1.60
10.2
9.
24.1
41
61.4
92
76.9
.110
2.66
.60
6.21
1.65
10.3
.2
24.3
42
62.0
93
77.4
.115
2.72
.62
6.82
1.70
10.5
.4
24.6
43
62.6
94
77.8
.1.20
2.78
.64
6.42
1.75
10.6
.6
24.8
44
63.2
95
78.2
.125
2.84
.66
6.52
1.80
10.8
.8
25.1
45
53.8
96
78.6
.130
2.89
.68
6.61
1.90
11.1
10.
25.4
46
54.4
97
79.0
.14
3.00
.70
6.71
2.
11.4
.5
26.0
47
65.0
98
79.4'
.15
3.11
.72
6.81
2.1
11.7
11.
26.6
48
55.6
99
79.8
.16
3.21
.74
6.90
2.2
11.9
.5
27.2
49
56.1
100
80.2
.17
3.31
.76
6.99
2.3
12.2
12.
27.8
50
56.7
125
89.7
.18
3.40
.78
7.09
2.4
12.4
i .5
28.4
61
57.8
150
98.3
.19
3.50
.80
7.18
2.5
12.6
13.
28.9
52
57.8
175
106
.20
3.59
.82
7.26
2.6
12.0
.5
29.5
53
58.4
200
114
.21
3.68
.84
7.35
2.7
13.2
14.
30.0
54
59.0
225
120
.22
8.76
.86
7.44
2.8
13.4
.5
3 .5
55
69.5
250
126
.23
3.85
.88
7.53
2.9
13.7
15.
31.1
56
60.0
275
133
.24
8:93
.90
7.61
3.
13.9
.5
31.6
57
60.6
300
139
.25
4.01
.92
7.69
3.1
14.1
16.
32.1
58
61.1
350
150
.26
4.09
.94
7.78
3.2
14.3
.5
32.6
59
61.6
400
160
.27
4.17
.96
7.86
3.3
14.5
17.
33.1
60
62.1
450
170
.28
4.25
.98
7.94
3.4
14.8
.5
33.6
61
62.7
500
179
.29
4.32
1.00
8.02
3.5
15.0
18.
34.0
32
6L.2
550
188
.30
4.39
1.02
8.10
3.6
15.2
.5
34.5
63
63.7
600
197
.31
4.47
1.04
8.18
3-7
15.4
19.
35.0
64
64.2
700
212
.32
4.54
1.06
8.26
8.8
15.6
.5
35.4
65
64.7
800
227
.33
4.61
1.08
8.34
3.9
15.8
20.
35.9
66
65.2
900
241
.34
4.68
1.10
8.41
4*
16.0
.5
36.3
67
65.7
1000
254
.85
4.74
1.12
8.49
.2
16.4
21.
36.8
68
66.1
2000
359
.36
4.81
1.14
8.57
.4
16.8
.5
37.2
69
66.6
3000
439
.37
4.88
1.16
8.64
,6
17.2
22.
87.6
70
67.1
4000
507
.38
4.94
1.18
8.72
.8
17.6
.5
38.1
71
67.6
5000
567
Parallelogram of Velocities.— The principle of the composition
and resolution of forces may also be applied to velocities or to distances
moved in given intervals of time. Referring to Fig. 88, page 416, if a body
at O has a force applied to it which acting alone vyould give it a velocity
represented by OQ per second, and at the same time it is acted on by
VELOCITY, ACCELERATION, FALLING BODIES. 427
another force which acting alone would give ft a velocity OP per second^
the result of the two forces acting together for one second will carry it to
R, OR being the diagonal of the parallelogram of OQ and OP, and the
resultant velocity. If the two component velocities are uniform, the result-
ant will be uniform and the line OR will be a straight line; but if either
velocity is a varying one, the line will be a curve. Fig. 96 shows tha
resultant velocities, also the path traversed
by a body acted on by two forces, one of A i o o g
which would carry it at a uniform velocity
over the intervals 1, 2, 3, B, and the other of
which would carry it by an accelerated mo-
tion over the intervals «, 6, c, D in the same
times. At the end of the respective inter-
vals the body will be found at C,, <72, C3, C,
and the mean velocity during each interval
is represented by the distances between
these points. Such a curved path is trav-
ersed by a shot, the impelling force from
the gun giving it a uniform velocity in the
direction the gun is aimed, and gravity giv-
ing it an accelerated velocity downward. FIG. 96.
The path of a projectile is a parabola. The
distance it will travel is greatest when its initial direction is at an angle 45°
above the horizontal.
Mass— Force of Acceleration.— The mass of a body, or the quantity
of matter it contains, is a constant quantity, while the weight varies according
to the variation in the force of gravity at different places. If g = the acceler-
ation due to gravity, and w = weight, then the mass m = — , w = mg. Weight
here means the resultant of the force of gravity on the particles of a body,
auch as may be measured by a spring-balance, or by the extension or
deflection of a rod of metal loaded with the given weight.
Force has been defined as that which causes, or tends to cause, or to
destroy, motion. It may also be defined (Kennedy's Mechanics of Ma-
chinery) as the cause of acceleration; and the unit of force as the force
required to produce unit acceleration in a unit of free mass.
Force equals the product of the mass by the acceleration, or f = ma.
Also, if v = the velocity acquired in the time t, ft = mv\ f = mv -*- t\ the
acceleration being uniform.
The force required to produce an acceleration of g (that is, 32.16 ft. per
sec.) in one second is / = mg = ~ g = w, or the weight of the body. Also,
/ ss ma ss m-2-^ — -» in which v8 is the velocity at the end, and Vj. the
velocity at the beginning of the time f, and/= mg = — V* ~ Vl — —a\
— -s -; or, the force required to give any acceleration to a body is to the
weight of the body as that acceleration is to the acceleration produced by
gravity. (The weight w is the weight where g is measured.)
EXAMPLE.— Tension in a cord lifting a weight. A weight of 100 Ibs. is
. lifted vertically by a cord a distance of 80 feet in 4 seconds, the velocity
uniformly increasing from 0 to the end of the time. What tension must be
maintained in the cord? Mean velocity = v9 = 20 ft. per sec.; final velocity
es va = 2v0= 40; acceleration a = -^ = — - = 10. Force / = ma = ~ = g^X
10 = 31.1 Ibs. This is the force required to produce the acceleration only;
to it must be added the force required to lift the weight without accelera-
tion, or 100 Ibs., making a total of 131.1 Ibs.
The Resistance to Acceleration is the same as the force required to pro-
w (v2— ft)
duce the acceleration = — — ^ — .
Formulae for Accelerated Motion.— For cases of uniformly
accelerated motion other than those of falling bodies, we have the formula
already given, / *- -^a, = ~ v?~Vl, jf the body starts from rest, Vj «* 0, Vi
428 MECHANICS.
s= v, and /=s — ~, fgt ms wv. We also have s = --. Transforming and sul>
Btituting for g its value 32.16, we obtain
*
32367
For any change In velocity/ =t w(^~
(See also Work of Acceleration, under Work.)
Motion on Inclined Planes.— The velocity acquired by a body
descending an inclined plane by the force of gravity (friction neglected) is
equal to that acquired by a body falling freely from the height of the plane.
The times of descent do^vn different inclined planes of the same height
vary as the length of the planes.
The rules for uniformly accelerated motion apply to inclined planes. If a
is the angle of the plane with the horizontal, sin a = the ratio of the height
to the length = y, and the constant accelerating force is g sin a. The final
velocity at the end of t seconds is v = gt sin a. The distance passed over in
t seconds is I = % Qt* sin a. The time of descent is
g sin a 4>01
MOMENTUM, VIS-VIVA.
Momentum, or quantity of motion in a body, is the product of the mass
by the velocity afc any instant = mv = — v.
Since the moving force = product of mass by acceleration, / = ma; and if
the velocity acquired in t seconds = v, or a = T, / = —r » ft = w*v» that is,
the product of a constant force into the time in which it acts equals numer
ically the momentum.
Since ft = mv, if t = 1 second mv = /, whence momentum might be de-
fined as numerically equivalent to the number of pounds of force that will
stop a moving body in 1 second, or the number of pounds of force which
acting during 1 second will give it the given velocity.
Vis-viva, or living force, is a term used by early writers on Mechanics
to denote the energy stored in a moving body. Some defined it as the pro-
duct of the mass into the square of the velocity, mv2, — — vz others as one
half of this quantity or ^wv2, or the same as what is now known as energy.
The term is now practically obsolete, its place being taken by the word
energy.
WORK, ENERGY, POWER.
Worfc is the overcoming of resistance through a certain distance. It is
measured by the product of the resistance into the space through which it
is overcome. It is also measured by the product of the moving force into
the distance through which the force acts in overcoming the resistance.
Thus in lifting a body from the earth against the attraction of gravity, the
resistance is the weight of the body, and the product of this weight into the
height the body is lifted is the work done.
The Unit of Work, in British measures, is the foot-pound, or the
amount of work done in overcoming a pressure or weight equal to one
pound through one foot of space.
WOKK, ENERGY, POWER. 429
The work performed by a piston in driving a fluid before ft, or by a fluid
In driving a piston before it, may be expressed in either of the following
ways:
Resistance X distance traversed
ss Intensity of pressure X area X distance traversed ;
js- intensity of pressure X volume traversed.
The work performed in lifting a body is the product of the weight of the
body into the height through which its centre of gravity is lifted.
If a machine lifts the centres of gravity of several bodies at once to heights
either the same or different, the whole quantity of work performed in so
doing is the sum oi the several products of the weights and heights ; but
that quantity can also be computed by multiplying the sum of all the
weights into the height through which their common centre of gravity is
lifted. (Rankine.)
T?ower is the rate at which work is done, and is expressed by the quo-
tient of the work divided by the time in which it is done, or by units of work
£jor second, per minute, etc., as foot-pounds per second. The most common
limit of power is the horse-power, established by James Watt as the power of
a strong London draught-horse to do work during a short interval, and used
by him to measure the power of his steam-engines. This unit is 33,000 foot-
pounds per minute = 550 foot-pounds per second s= 1,980,000 foot-pounds per
hour.
Expressions for Force, Work, Power, etc*
The fundamental conceptions in Dynamics are:
Mass, Force, Time, Space, represented by the letters M, F, T, 8.
Mass = weight -s- g. If the weight of a body is determined by a spring
balance standardized at London it will vary with the latitude, and the value
of g to be taken in order to find the mass is that of the latitude where the
weighing is done. If the weight is determined by a balance or by a plat-
form scale, as is customary in engineering and in commerce, the London
value of g, =- 32.2, is to be taken.
Velocity = space divided by time, V - S -f- T, if V be uniform.
"Work = force multiplied by space = FS = y^MY* = FVT. (Funiform.)
Power = rate of v/ork = work divided by time = FS •*- T = P = prod-
uct of force into velocity = FV.
Power exerted for a certain time produces work; PT ='FS - FVT.
Effort is a force which acts on a body in the direction of its motion.
Resistance is that which is opposed to a moving force. It is equal and
opposite force.
Horse-power Hours, an expression for work measured as the
product of a power into the time during which it acts = PT. Sometimes it
is the summation of a variable power for a given time, or the average power
multiplied by the time.
Energy, or stored work, is the capacity for performing work. It is
measured by the same unit as work, that is, in foot-pounds. It may be
either potential, as in the case of a body cf water stored in a reservoir,
capable of doing work by means of c, water-wheel, or actual, sometimes
called kinetic, which is the energy of a moving body. Potential energy is
measured by the product of the weight of the stored body into the distance
through which it is capable of acting, or by the product of the pressure it
exerts into the distance through which that pressure is capable of acting.
Potential energy may also exist as stored heat, or as stored chemical energy,
as in fuel, gunpowder, etc., or as electrical energy, the measure of these
energies being the amount of work that they are capable of performing.
Actual energy of a moving body is tho work which it is capable of performing
against a retarding resistance before being brought to rest, and is equal to
the work which must be done upon ifc to bring it from a state of rest to its
actual velocity.
The. measure ot actual energy is tho product of the weight of the body
into the height from which it must fall to acquire its actual velocity. If v =
the velocity in feet per second, according to the principle of falling bodies,
h, the height due to the velocity sr --, and if w = the weight, the energy =
%mv9 = wv* -*- 2<7 = wh. Since energy is the capacity for performing
work, the units of work and energy are equivalent, or FS s= ^mva = wh.
Energy exerted = work done,
430 MECHANICS.
The actual energy of a rotating body whose angular velocity is A and
moment of inertia Stor8 = I is -— , that is, the product of the moment of
inertia into the height due to the velocity, A, of a point whose distance from
the axis of rotation is unity; or it is equal to — — , in which w is the weight of
the body and v is the velocity of the centre of gyration.
Work, of Acceleration. -The work done in giving acceleration to a
body is equal to the product of the force producing the acceleration, or of
the resistance to acceleration, into the distance moved in a given time. This
force, as already stated equals the product of the mass into the acceleration,
or/=s ma = — -^-j- — -1. If the distance traversed in the time t = s, then
W V* — Vi
work = fs = ?-j — ls.
EXAMPLE.— What work is required to move a body weighing 100 Ibs. hpri.
zontally a distance of 80 ft. in 4 seconds, the velocity uniformly increasing,
friction neglected T
Mean velocity v0 = 20 ft. per second; final velocity = v% — 2v0 = 40; initial
velocity vl = 0; acceleration, a = Vy ~ Vj = — = 10; force = —a = — - - X
JO = 31.1 Ibs. ; distance 80 ft. ; work = fs = 31.1 X 80 = 2488 footpounds.'
The energy stored in the body moving at the final velocity of 40 ft. pe*
second is
= 2488 foot-pounds,
which equals the work of acceleration,
~~ ~g ts ~~~g~t 2 ~2 ~gv* "
If a body of the weight W falls from a height H, the work of acceleration
Is simply TFH, or the same as the work required to raise the body to the
same height.
Work of Accelerated Rotation.— Let A = angular velocity of a
solid body rotating about an axis, that is, the velocity of a particle whose
radius is unity. Then the velocity of a particle whose radius is r is v = Ar.
If the angular velocity is accelerated from Aj to A^ the increase of the
velocity of the particle is v% — vl^= r(Ai — -42), and the work of accelerating
it is
w v.2* - v^ ivr* AJ—A
7X
in which w is the weight of the particle.
The work of acceleration of the w
hole body is
Tne term 2wr2 is the moment of inertia of the body.
" Force of the Blow » of a Steam Hammer or Other Fall"
Ing Weight.— The question is often asked: •* With what force does a
falling hammer strike?" The question cannot be answered directly, and
pounds, which is the product of the weight into the height through which
it fails, or the product of its weight -s- 64.32 into the square of the velocity,
in feet per second, which it acquires after falling through the given height.
If F = weight of the body, M its mass, g the acceleration due to gravity,
S the height of fall, and v the velocity at the end of the fall, the energy in
the body just before striking, is FS = ^M;2 = Wv* -H 2g = Wv* -*- 64.32,
which is the general equation of energy of a moving body. Just as the
energy of the body is a product of a force into a distance, so the work it
does vrhep it strikes is not the manifestation of a force, which can be ex-
pressed simply in pounds, but it is the overcoming of a resistance through
a certain distance, which is expressed as the product of the average resist.-
WORK, EKERGY, POWER. 431
ance into the distance through which it is exerted. If a hammer weighing
100 Ibs. falls 10 ft., its energy is 1000 foot-pounds. Before being brought to
rest it must do 1000 foot-pounds of work against one or more resistances.
These are of various kinds, such as that due to motion imparted to the body
struck, penetration against friction, or against resistance to shearing or
other deformation, and crushing and heating of both the falling body and the
body struck. The distance through which these resisting forces act is gen-
erally indeterminate, and therefore the average of the resisting forces,
which themselves generally vary with the distance, is also indeterminate.
Impact of Bodies.— If two inelastic bodies collide, they will move on
together as one mass, with a common velocity. The momentum of the com-
bined mass is equal to the sum of the momenta of the two bodies before im-
pact. If Wj and ma are the masses of the two bodies and vt and va their re-
spective velocities before impact, and v their common velocity after impact,
(mi 4~ wia)v = wijVj -f- m jV2 »
_
mt -f ma '
If the bodies move in opposite directions v = ll 1~ la^ or^ tne veiocjty
of two inelastic bodies after impact is equal to the algebraic sum of their
momenta before impact, divided by the sum of their masses.
If two inelastic bodies of equal momenta impinge directly upon one an-
other from opposite directions they will be brought to rest.
Impact of Inelastic Bodies Causes a &oss of Energy, and
this loss is equal to the sum of the energies due to the velocities lost and
gained by the bodies, respectively.
J^WiV -f ^w2Vaa - J^OH -f wi2)v2 = ^w1(t71 - v)* + ^ma(va — v)2.
In which vl — v is the velocity lost by m1 and v — v2 the velocity gained by raa.
Example— ~Let m-, = 10, ma = 8, v, = 12, v., = 15.
10 v 12 — 8 y 1*i
If the bodies collide they will come to rest, for v = * , ° = 0.
1U -f o
The energy loss is
1^10 X 144 + ^8 X 225 - 3^ 18 X 0 = £610(12 - 0)* -f ^8(15 - 0)« = 1620 ft. Ibs.
What becomes of the energy lost ? Ans. It is used doing internal work
on the bodies themselves, changing their shape and heating them.
For imperfectly elastic bodies, let e = the elasticity, that is, the ratio
which the force of restitution, or the internal force tending to restore the
shape of a body after it has been compressed, bears to the force of compres-
sion; and let mx and rr*a be the masses, vx and vz their velocities before im-
pact, and va'va' their velocities after impact: then
-f ma?;2
_ _
ml -f- »*a mt -f- ma '
v / = mivi +.Wa^a • rnle(v1 - v^
8 mi ~\~ ma mi ~\~ mi
If the bodies are perfectly elastic, their relative velocities before and after
impact are the same. That is : vt' — ua' = v% — vlf
In the impact of bodies, the sum of their momenta after impact is the
same as the sum of their momenta before impact.
wixiV -f w2v2' = miVi + wav2.
For demonstration of these and other laws of impact, see Smith's Me-
chanics; also, Weisbach's Mechanics.
Energy of Recoil of Guns.— (Eny'g, Jan. 25, 1884, p. 73.)
Let W = the weight of the gun and carriage;
V = the maximum velocity of recoil;
iv = the weight of the projectile;
v = the muzzle velocity of the projectile.
Then, since the momentum of the gun and carriage is equal to the momen-
tum of the projectile, we have WV = ivv, or V — ivv -*- W.
* The statement by Prof. W. D. Marks, in Nystrom's Mechanics, 20th edi-
tion, p. 454, that this formula is in error is itself erroneous.
4:32 MECHANICS.
Taking the case of a 10-inch gun firing a 400-lb. projectile with a muzzle
velocity of 1400 feet per second, the weight of the gun and carriage being 23
tons = 49,280 Ibs., we find the velocity of recoil =
1400 X 400
" 49 280 = Per second'
Now the energy of a body in motion is WV* -*- 2g.
Therefore the energy of recoil = 49'^ * \^- = 92,593 foot-pounds.
'
The energy of the projectile is = 12,173,913 foot-pounds,
4 X 04.6
Conservation of Energy.— No form of energy can ever be pro
duced except by tiie expenditure of some other form, nor annihilated ex-
cept by being reproduced in another form. Consequently the sum total of
energy in the universe, like the sum total of matter, must always remain
the same. (S. Newcomb.) Energy can never be destroyed or lost; it can
be transformed, can be transferred from one body to another, but no
matter what transformations are undergone, when the total effects of the
exertion of a given amount of energy are summed up the result will be
exactly equal to the amount originally expended from the source. This law
is called the Conservation of Energy. (Cotterill and Slade.)
A heavy body sustained at an elevated position has potential energy.
When it falls, just before it reaches the earth's surface it has actual or
kinetic energy, due to its velocity. When it strikes it may penetrate the
earth a certain distance or may be crushed. In either case friction results
by which the energy is converted into heat, which is gradually radiated
into the earth or into the atmosphere, or both. Mechanical energy and heat
are mutually convertible. Electric energy is also convertible into heat or
mechanical energy, and either kind of energy may be converted into the
other.
Sources of Energy.— The principal sources of energy on the earth's
surface are the muscular energy of men and animals, the energy of the
wind, of flowing water, and of fuel. These sources derive their energy
from the rays of the sun. Under the influence of the sun's rays vegetation
grows and wood is formed. The wood may be used as fuel under a steam
boiler, its carbon being burned to carbonic acid. Three tenths of its heat
energy escapes in the chimney and by radiation, and seven tenths appears
as potential energy in the steam. In the steam-engh)e, of this seven tenths
six parts are dissipated in heating the condensing water and are wasted;
the remaining one tenth of the original heat energy of the wood is con-
verted into mechanical work in the steam-engine, which may be used to
drive machinery. This work is finally, by friction of various kinds, or pos-
sibly after transformation into electric currents, transformed into heat,
which is radiated into the atmosphere, increasing its temperature. Thus
all the potential heat energy of the wood is, after various transformations,
converted into heat, which, mingling with the store of heat in the atmos-
phere, apparently is lost. But the carbonic acid generated by the combus-
tion of the wood is, again, under the influence of the sun's rays, absorbed
by vegetation, and more wood may thus be formed having potential energy
equal to the original.
Perpetual Motion.— The law of the conservation of energy, than
which no law of mechanics is more firmly established, is an absolute barrier
to all schemes for obtaining by mechanical means what is called " perpetual
motion," or a machine which will do an amount of work greater than the
equivalent of the energy, whether of heat, of chemical combination, of elec-
tricity, or mechanical energy, that is put into it. Such a result would be
the creation of an additional store of energy in the universe, which is not
possible by any human agency.
The Efficiency of a Machine is a fraction expressing the ratio of
the useful work to the whole work performed, which is equal to the energy
expended. The limit to the efficiency of a machine is unity, denoting the
efficiency of a perfect machine in which no work is lost. The difference
between the energy expended and the useful work done, or the loss, is
usually expended either in overcoming friction or in doing work on bodies
surrounding the machine from which no useful work is received. Thus in
an engine propelling a vessel part of the energy exerted in the cylinder
ANIMAL POWER.
433
Joes the useful work of giving motion to the vessel, and the remainder is
spent in overcoming the friction of the machinery and in making currents
and eddies in the surrounding water.
ANIMAL POWER.
Work of a Man against Known Resistances* (Rankine.)
Kind of Exertion.
R,
Ibs.
F,
ft. per
sec.
T"
3600
(hours
day).
#F,
ft.-lbs.
per sec.
RVT<
ft.-lbs.
per day.
1. Raising his own weight up
stair or ladder .
143
0.5
8
72.5
2 088 000
2. Hauling up weights with rope,
and lowering the rope un-
loaded • ...
40
0.75
6
30
648 000
3. Lifting weights by hand
44
0.55
6
24.2
522,'?20
4. Carrying weights up -stairs
and returning unloaded —
143
0.13
6
18.5
399,600
5. Shovelling up earth to a
height of 5 ft 3 in
6
1.3
10
7.8
280,800
6. Wheeling earth in barrow up
slope of 1 in 12, % horiz.
veloc. 0.9 ft. per sec. and re-
turning unloaded
7. Pushing or pulling horizon-
132
0.075
10
9.9
356,400
tally (capstan or oar)
26 5
2 0
8
53
1,526 400
I 12.5
5.0
?
62.5
8. Turning a crank or winch —
4 18.0
( 20.0
2.5
14.4
8
2min.
45
288
i,296,ob(f
13 2
2.5
10
33
1 188 000
15
?
8?
?
'480',000
time, in hours "per day; RV, effective power, in 'foot-pounds per second:
R FT, daily work.
Performance of a Man in Transporting: Loads
Horizontally* (Runkiue.)
T
3600
LV,
Ibs
LVT,
Kind of Exertion.
£
ft.-sec.
(hours
per
con-
veyed
Ibs. con-
veyed
1ff\f\t-
day).
1 foot.
11. Walking unloaded,transport-
ing his own weight
12. Wheeling load L in 2-whld.
14C
5
10
700
25,200,000
barrow, return unloaded..
224
J2^
10
373
13,428,000
13. Ditto in 1-wh. barrow, ditto..
132
1^1
10
220
7,920,000
14. Travelling with burden
15. Carrying burden, returning
unloaded «
90
140
1%
7
6
225
233
5,670,000
5,032,800
{252
0
0
16. Carrying burden, for 30 sec-
onds only
126
11.7
90 •«
1474.2
•
°
EXPLANATION.— L, load; F, effective velocity, computed as before; Tf'9
time of working, in seconds per day; T"-s-3600, same time in hours per day;
£F, transport per second, in Ibs. conveyed one foot; LVT, daily transport.
434
MECHANICS.
In the first line only of each of the two tables above is the weight of* the
man taken into account in computing the work done.
Clark says that the average net daily work of an ordinary laborer at a
pump, a winch, or a crane may be
taken at 3300 foot-pounds per minute.
or one- tenth of a horse-power, for 8
hours a day; but for shorter periods
from four to five times this rate may
be exerted.
Mr. Glynn says that a man may
exert a force of 25 Ibs. at the handle
of a crane for short periods; but that
for continuous work a force of 15 Ibs.
is all that should be assumed, moving
through 220 feet per minute.
Mail-wheel .—Fig. 97 is a sketch
of a very efficient man-power hoist-
ing-machine which the author saw in
Berne, Switzerland, in 1889. The face
of the wheel was wide enough for
__^_ three men to walk abreast, so that
FIG. 97. nine men could work in it at one time.
Work of a Horse against a Known Resistance. (Rankine.)
Kind of Exertion.
R.
V.
T.
3600
EV.
RVT.
3. Cantering and trotting, draw-
ing a light railway carriage
(thoroughbred) ...
( min. 22^
-j mean 30^§
( max 50
\$i
4
Wy2
6,444,000
2. Horse drawing cart or boat,
walking (draught-horse). . . .
3. Horse drawing a gin or mill,
walking
120
100
3.6
3 0
8
g
432
300
12,441,600
8 640 000
4 Ditto trotting .
66
6 5
4U
429
6 950 000
EXPLANATION.— R, resistance, in Ibs.; F, velocity, in feet per second; T"
•*- 3600, hours work per day; JRF, work per second; RVT, work per day.
The average power of a draught-horse, as given in line 2 of the above table,
being 432 foot-pounds per second, is 432/550 = 0.785 of the conventional value
assigned by Watt to the ordinary unit of the rate of work of prime movers.
It is the mean of several results of experiments, and may be considered the
average of ordinary performance under favorable circumstances.
Performance of a Horse in Transporting Loads
Horizontally, (Rankine.)
Kind of Exertion.
L.
V.
T.
LV.
LVT.
5. Walking with cart, always
loaded
1500
3 6
10
5400
194,400 000
6 Trotting ditto
750
7 2
414
5400
87 480 000
7. Walking'with cart, going load-
ed, returning empty; F,
1500
2.0
10
3000
108,000,000
8. Carrying burden, walking....
9. Ditto trotting
270
180
3.6
7.2
10
7
972
1296
34,992,000
32 659,200
EXPLANATION.— £, load in Ibs.; F, velocity in feet per second; T-j-3600,
working hours per day; LV, transport per second; L FT, transport per day.
This table has reference to conveyance on common roads only, and those
evidently iu bad order as respects the resistance to traction upon them.
Horse Gin.— In this machine a horse works less advantageously
than in drawing a carriage along a straight track. In order that the best
ELEMENTS OF MACHINES. 435
possible results may be realized with a horse-gin, the diameter of the cir.
cular track in which the horse walks should not be less than about forty
feet.
Oxen, Mules, Asses.— Authorities differ considerably as to the power
of these animals. The following may be taken as an approximative com-
parison between them and draught-horses (Rankine):
Ox.— Load, the same as that of average draught-horse; best velocity and
work, two thirds of horse.
Mule. — Load, one half of that of average draught-horse; best velocity,
the same with horse; work one half.
Ass.— Load, one quarter that of average draught-horse; best velocity the
same; work one quarter.
Reduction of Draught of Horses by Increase of Grade
of Roads* (Engineering Record, Prize Essays on Roads, 1892.)— Experi-
ments on English roads by Gayffier & Parnell:
Calling load that can be drawn on a level 100:
On a rise of 1 in 100. 1 in 50. 1 in 40. 1 in 30. 1 in 26. 1 in 20. 1 in 10.
A horse can draw only 90. 81. 72. 64. 54. 40. 25.
The Resistance of Carriages on Roads is (according to Gen.
Moriu) given approximately by the following empirical formula:
# = ^[a-f 6(w- 3.28)].
In this formula R = total resistance; r = radius of wheel in inches; W =
gross load ; u = velocity in feet per second ; while a and b are constants,
whose values are: For good broken-stone road, a = .4 to .55, b = .024 to .026;
for paved roads, a = .27, 6 = .0684.
Rankine states that on gravel the resistance is about double, and on
sand five times, the resistance on good broken-stone roads.
ELEMENTS OF MACHINES.
The object of a machine is usually to transform the work or mechanical
energy exerted at the point where the machine receives its motion into
work at the point where the final resistance
is overcome. The specific end may be to ^ C B
change the character or direction of mo-
tion, as from circular to rectilinear, or vice
versa, to change the velocity, or to overcome
a great resistance by the application of a
moderate force. In all cases the total energy
exerted equals the total work done, the latter
including the overcoming of all the frictional FlO. 98.
resistances of the machine as well as the use-
ful work performed. No increase of power
can be obtained from any machine, since this
is impossible according to the law of conser-
vation of energy. In a f rictionless machine the
product of the force exerted at the driving-
point into the velocity of the driving-point,
or the distance it moves in a given interval
of time, equals the product of the resistance
into the distance through which the resist-
ance is overcome in the same time. FIG. 99.
The most simple machines, or elementary
machines, are reducible to three classes, viz.,
the Lever, the Cord, and the Inclined Plane.
The first class includes every machine con-
sisting of a solid body capable of revolving
on an axis, as the Wheel and Axle.
The second class includes every machine in
which force is transmitted by means of flexi-
ble threads, ropes, etc., as the Pulley. ^ ..
The third class includes every machine in JTIG JQQ>
which a hard surface inclined to the direc-
tion of motion is introduced, as the Wedge and the Screw.
A Lever is an inflexible rod capable of motion about a fixed poict,
called a fulcrum. The rod may be straight or bent at any angle, or curved.
It is generally regarded, at first, as without weight, but its weight may be
<jw
Ow
436 MECHANICS.
considered as another force applied in a vertical direction at its centre of
gravity.
The arms of a lever are the portions of it intercepted between the force,
P, and fulcrum, (7, and between the weight, W, and fulcrum.
Levers are divided into three kinds or orders, according to the relative
positions of the applied force, weight, and fulcrum.
In a lever of the first order, the fulcrum lies between the points at which
the force and weight act. (Fig. 98.)
In a lever of the second order, the weight acts at a point between the
fulcrum and the point of action of the force. (Fig. 99.)
In a lever of the third order, the point of action of the force is between
that of the weight and the fulcrum. (Fig. 100.)
In all cases of levers the relation between the force exerted or the pull,
P, and the weight lifted, or resistance overcome, W, is expressed by the
equation P X AC = W X BC, in which AC is the lever-arm of P, and BC
is the lever-arm of W, or moment of the force = the moment of the resist-
ance. (See Moment.)
In cases in which the direction of the force (or of the resistance) is not at
right angles to the arm of the lever on which it acts, the " lever-arm" is the
length of a perpendicular from the fulcrum to the line of direction of the
force (or of the resistance). W : P : : A C : BC, or, the ratio of the resistance to
the applied force is the inverse ratio of their lever-arms. Also, if Vw is the
velocity of Wy and Vp is the velocity of P, W : P : : Vp : Vw, and Px Vp
= Wx Vw.
If SP is the distance through which the applied force acts, and Sw is the
distance the weight is lifted or through which the resistance is overcome,
W : P i : Sp : Sw; W X Sw = PX SP, or the weight into the distance it is lifted
equals the force into the distance through which it is exerted.
These equations are general for all classes of machines as well as for
levers, it being understood that friction, which in actual machines increases
the resistance, is not at present considered.
Tlie Bent I^ever.— In the bent lever (see Fig. 91, page 416) the lever-
arm of the weight m is cf instead of bf. The lever is in equilibrium when
n X af = wi X c/, but it is to be observed that the action of a bent lever may
be very different from that of a straight lever. In the latter, so long as the
force and the resistance act in lines parallel to each other, the ratio of the
lever-arms remains constant, although the lever itself changes its inclina-
tion with the horizontal. In the bent lever, hoTever, this ratio changes:
thus, in the cut, if the arm bf is depressed to a horizontal direction, the dis-
tance cf lengthens while the horizontal projection of af shortens, the latter
becoming zero when the direction of af becomes vertical. As the arm af
approaches the vertical, the wreight m which may be lifted with a given
force s is very great, but the distance through which it may be lifted is
very small. In all cases the ratio of the weight m to the weight n is the in-
verse ratio of the horizontal projection of their respective lever-arms.
The JWLoving Strut (Fig. 101) is similar to the bent lever, except that
one of the arms is missing, and that the force and the resistance to be
overcome act at the same end of the
single arm. The resistance in the
case shown in the cut is not the
weight W, but its resistance to
being moved, P, which may be sim-
ply that due to its friction on the
horizontal plane, or some other op-
posing force. When the angle be-
tween the strut and the horizontal
plane changes, the ratio of the
resistance to the applied force
changes. When the angle becomes
very small, a moderate force will
FIG. 101. overcome a very great resistance,
which tends to become infinite as
the angle approaches zero. If a = the angle, P X cos a = R X sin a. If
a = 5 degrees, cos a = .99619, sin a = .08716, R = 11.44 P.
The stone-crusher (Fig. 102) shows a practical example of the use of two
moving struts.
The Toggle-joint is an elbow or knee-joint consisting of two bars so
connected that they may be brought into a straight line and made to pro-
duce great endwise pressure when a force is applied to bring them into this
ELEMENTS OF MACHINES.
437
Eosition. It is a case of two moving struts placed end to end, the moving
3rce being applied at their point of junction, in a direction at right angles
to the direction of the resistance, the other end of one of the struts resting
against a fixed abutment, and that of the other against the body to be
moved. If a = the angle each strut makes with the straight line joining the
points about which their outer ends rotate, the ratio of the resistance
to the applied force is R : P :: cos a : 2 sin a ; 2R sin a = Pcos a. The
FIG. 102.
FIG. 103.
ratio varies when the angle varies, becoming infinite when the angle
becomes zero.
The toggle-joint is used where great resistances are to be overcome
through very small distances, as in stone-crushers (Fig. 103).
The Inclined Plane9 as a mechanical element, is supposed perfectly
hard and smooth, unless friction be considered. It assists in sustaining a
heavy body by its reaction. This reaction, however, being normal to the
plane, cannot entirely counteract the weight of the body, which acts verti-
cally downward. Some other force must therefore
be made to act upon the body, in order that it may
be sustained.
If the sustaining force act parallel to the plane
(Fig. 104), the force is to the weight as the height of
the plane is to its length, measured on the incline.
If the force act parallel to the base of the plane,
the power is to the weight as the height is to the
base.
If the force act at any other angle, let i = the
angle of the plane with the horizon, and e = the
angle of the direction of the applied force with the
angle of the plane. P : W :: sin i : cos e\ P X cos e —
W
FIG. 104.
— sin i.
Problems of the inclined plane may be solved by the parallelogram of
forces thus :
Let the weight Wbe kept at rest on the incline by the force P, acting in
the line bP\ parallel to the plane. Draw the vertical line ba to represent
the weight ; also bb' perpendicular to the plane, and complete the parallelo-
gram b'c. Then the vertical weight ba is the resultant of bb', the measure of
support given by the plane to the weight, and be, the force of gravity tend-
ing to draw the weight down the plane. The force required to maintain
the weight in equilibrium is represented by this force be. Thus the force
and the weight are in the ratio of be to ba. Since the triangle of forces abc
is similar to the triangle of the incline ABC, the latter may be substituted
for the former in determining the relative magnitude of the forces, and
P : W : : be : ab : : BC : AB.
The "Wedge is a pair of inclined planes united by their bases. In the
application of pressure to the head or butt end of the wedge, to cause it to
penetrate a resisting body, the applied force is to the resistance as the
thickness of the wedge is to its length. . Let t be the thickness, I the length,
W the resistance, and Pthe applied force or pressure on the head of the
W = ~.
wedge. Then, friction neglected, P : W : : t : l\ P = ~ ;
The Screw is an inclined plane wrapped around a cylinder in such a
way that the height of the plane is parallel to the axis of the cylinder. If
the screw is formed upon the internal surface of a hollow cylinder, it is
usually called a nut. When force is applied to raise a weight or overcome
a resistance by means of a screw and nut, either the screw or the nut may
438
MECHANICS.
be fixed, the other being movable. The force is generally applied at the end
of a wrench or lever-arm, or at the circumference of a wheel. If r = radius
of the wheel or lever-arm, and p = pitch of the screw, or distance between
threads, that is, the height of the inclined plane
for one revolution of the screw, P = the applied
force, and W= the resistance overcome, then, neg-
lecting resistance due to friction, 2irr X P — Wp ;
W = 6.283Pr -f- p. The ratio of P to W is thus
independent of the diameter of the screw. In
actual screws, much of the power transmitted is
lost through friction.
Tlie Cam is a revolv-
ing inclined plane. It may
be either an inclined plane
wrapped around a cylin-
der in such a way that the
height of the plane is ra-
dial to the cylinder, such
FIG. 105.
the ordinary lifting-
cam, used in stamp-mills
FIG. 106.
(Fig. 105), or it may be an inclined plane curved edgew'se, and rotating in a
plane parallel to its base (Fig. 106). The relation of the weight to the applied
force is calculated in the same manner as in the case of the screw.
JW
A.,
Pulleys or Blocks.— P = force applied, or pull ; W= weight lifted
or resistance. In the simple pulley A (Fig. 107) the point Pon the pulling
rope descends the same amount that the weight is lifted, therefore P = W.
In B and Othe point P moves twice as far as the weight is lifted, there-
fore W = 2P. In B and C there is one movable block, and two plies of the
rope engage with it. In D there are three sheaves in the movable block,
each with two plies engaged, or six in all. Six plies of the rope are there-
fore shortened by the same amount that the weight is lifted, and the point
P moves six times as far as the weight, consequently W = 6P. In general,
the ratio of Wto Pis equal to the number or plies of the rope that are
shortened, and also is equal to the number of plies that engage the lower
block. If the lower block has 2 sheaves and the upper 3, the end of the rope
is fastened to a hook in the top of the lower block, and then there are 5
plies shortened instead of 6, and W = 5P. If V — velocity of W, and v —
velocity of P, then in all cases VW ^= vP, whatever the number of sheaves
or their arrangement. If the hauling rope, at the pulling end, passes first
around a sheave in the upper or stationary block, it makes no difference in
what direction the rope is led from this block to the point at which the puJl
on the rope is applied ; but if it first passes around the movable block, it is
necessary that the pull be exerted in a direction parallel to the line of action
of the resistance, or a line joining the centres of the two blocks, in order to
obtain the maximum effect. If the rope pulls on the lower block at an
angle, the block will be pulled out of the line drawn between the weight
and the upper block, and the effective pull will be less than the actual pull
ELEMEKTS OF MACHINES.
439
FIG. 108.
fln the rope in the ratio of the cosine of the angle the pulling rope makes
with the vertical, or line of action of the resistance, to unity.
Differential Pulley. (Fig. 108.)— Two pulleys, B and C, of different
radii, rotate as one piece about a fixed axis, A. An end-
less chain, BDECLKH, passes over both pulleys. The
rims of the pulleys are shaped so as to hold the chain and
prevent it from slipping. One of the bights or loops in
which the chain hangs, DE, passes under and supports the
running block F. The other loop or bight, HKL, hangs
freely, and is called the hauling part. It is evident that
the velocity of the hauling part is equal to that of the
pitch-circle of the pulley B.
In order that the velocity-ratio may be exactly uniform,
the radius of the sheave F should be an exact mean be-
tween the radii of B and C.
Consider that the point B of the cord BD moves through
an arc whose length = AB, during the same time the
point C or the cord CE will move downward a distance =
AC. The length of the bight or loop BDEC will be
shortened by AB — AC, which will cause the pulley F to
be raised half of this amount. If P = the pulling force on
the cord HK. and W the weight lifted at F, then P X
AB = W X V^(AB - AC).
To calculatethe length of chain required for a differential
pulley, take the following sum: Half the circumference of
A -f- half the circumference of # -f half the circumference
of F -f- twice the greatest distance of F from A + the
least length of loop HKL. The last quantity is fixed
according to convenience.
The Differential Windlass (Fig. 109) is identical in principle
with the differential pulley, the difference in con-
struction being that in the differential windlass the
running block hangs in the bight of a rope whose two
parts are wound round, and have their ends respec-
tively made fast to two barrels of different radii,
which rotate as one piece about the axis A. The dif-
ferential windlass is little used in practice, because
of the great length of rope which it requires.
The Differential Screw (Fig. 110) is a com-
pound screw of different pitches, in which the
threads wind the same way. NI and _ZV2 are the two
nuts; 81$!, the longer-pitched thread; S9S^ tfae
shorter-pitched thread: in the figure both these
threads are left-handed. At each turn of the screw
the nut JtVa advances relatively to N* through a dis-
tance equal to the difference of the pitch. The use
of the differential screw is to combine the slowness
of advance due to a fine pitch with the strength of thread which can be
obtained by means of a coarse pitch only.
A Wheel and Axle, or Windlass, resembles two pulleys on one axis,
having different diameters. If a weight be lifted by means of a rope wound
over the axle, the force being applied at the
rim of the wheel, the action is like that of a
lever of which the shorter arm is equal to
the radius of the axle plus half the thick-
ness of the rope, and the longer arm is
ec*ual to the radius of the wheel. A wheel
and axle is therefore sometimes classed
as a perpetual lever. If P = the applied force, D = diameter of the wheel,
W = the weight lifted, and d the diameter of the axle -f- the diameter of
the rope, PD = Wd.
Toothed-wheel Gearing is a combination of two or more wheels
and axles (Fig. 111;. If a series of wheels and pinions gear into each other,
as in the cut, friction neglected, the weight lifted, or resistance over-
come, is to the force applied inversely as the distances through which
they act in a given time. If jR, Rlt R? be the radii of the successive wheels,
measured to the pitch-line of the teeth, and r, rt, ra the radii of the cor-
responding pinions, Pthe applied force, and W the weight lifted, PX
FIG.
FIG. 110.
440 MECHANICS.
R X RI X RI = W X r X rx X ra, or the applied force is to the weight
as the product of the radii of the pinions is to the product of the radii of
the wheels; or, as the product of the numbers expressing the teeth in
each pinion is to the product of the numbers expressing the teeth in each
wheel.
Endless Screw, or Worm-gear. (Fig. 112.)— This gear is com-
monly used to convert motion at high speed into motion at very slow
FIG. 111. ''FiG.
speed. When the handle P describes a complete circumference, the -pitch-
line of the cog-wheel moves through a distance equal to the pitch of the
screw, and the weight TFis lifted a distance equal to the pitch of the screw
multiplied by the ratio of the diameter of the axle to the diameter of the
pitch-circle of the wheel. The ratio of the applied force to the weight
lifted is inversely as their velocities, friction not being considered; but the
friction in the worm-gear is usually very great, amounting sometimes to
three or four times the useful work done.
If v = the distance through which the force Pacts in a given time, say 1
second, and V = distance the weight W is lifted in the same time, r =
radius of the crank or wheel through which Pacts, t = pitch of the screw,
and also of the teeth on the cog-wheel, d = diameter of the axle,
and D = diameter of the pitch-line of the cog-wheel, v = — ^- — - —
XF;F=vXfd-*- 6.283rd. Pv = WV+ friction,
STRESSES IN FRAMED STRUCTURES.
Framed structures in general consist of one or more triangles, for the
reason that the triangle is the one polygonal form whose shape cannot be
changed without distorting one of its sides. Problems in stresses of simple
framed structures may generally be solved either by the application of the
triangle, paralellogram, or polygon of forces, by the principle of the lever,
or by the method of moments. We shall give a few examples, referring the
student to the works of Burr, Dubois, Johnson, and others for more elabo-
rate treatment of the subject.
1. A Simple Crane. (Figs. 113 and 114.)—^! is a fixed mast, B a brace or
boom, T a tie, and P the load. Required the strains in B and T. The weight
P, considered as acting at the end of the boom, is held in equilibrium by
three forces: first, gravity acting downwards; second, the tension in T: and
third, the thrust of B. Let the length of the line p represent the magnitude
of the downward force exerted by the load, and draw a parallelogram with
sides bt parallel, respectively, to B and T, such that p is the diagonal of the
parallelogram. Then b and t are the components drawn to the same scale
as p, p being the resultant. Then if the length p represents the load, t is
the tension in the tie, and b is the compression in the brace.
Or, more simply, 7', B, and that portion of the mast included between them
or A' may represent a triangle of forces, and the forces are proportional to
the length of the sides of the triangle; that is, if the height of the triangle A'
a= the load, then B = the compression in the brace, and T = the tension in the
T
tie; or if P = the load in pounds, the tension in T = P X ~j/t and the corn*
A
STRESSES IK FRAMED STRUCTURES.
441
pression in B = P X — . Also, if a = the angle the inclined member makes
with the mast, the other member being horizontal, and the triangle being
right-angled, then the length of the inclined member = height of the tri-
angle X secant a, and the strain in the inclined member = P secant a. Also,
the strain in the horizontal member = P tan a.
The solution by the triangle or parallelogram of forces, and the equations
Tension in T = P X T/A', and Compression in B = P X B/A', hold true even
if the triangle is not right-angled, as in Fig. 115; but the trigonometrical rela-
FIG. 113.
FIG. 114.
FIG. 115.
tlons above given do not hold, except in the case of a right-angled triangle.
It is evident that as A' decreases, the strain in both Tand B increases, tend-
ing to become infinite as A' approaches zero. If the tie 2'is not attached to
the mast, but is extended to the ground, as shown in the dotted line, the
tension in it remains the same.
2. A Guyed Crane or Derrick. (Fig. 116.)— The strain in B is, as
before, PxB/A', A' being that portion of the vertical included between B and
T, wherever Tmay be attached to A. If, however, the tie Tis attached to B
beneath its extremity, there may be in addition a bending strain in B due to
a tendency to turn about the point of attachment of T as a fulcrum.
The strain in T may be calculated by the principle of moments. The mo-
ment of P is PC, that is, its weight X its perpendicular distance from the
point of rotation of B on the mast. The moment of the strain on T is the
product of the strain into the perpendicular distance from the line of its
direction to the same point of rotation of B, or Td. The strain in T there-
fore = PC -*- d. As d decreases the strain on T increases, tending to infin-
ity as d approaches zero.
The strain on the guy-rope is also calculated by the method of moments.
The moment of the load about the bottom of the mast O is, as before, PC.
If the guy is horizontal the strain in it is F and its moment is Ff, and F =
PC -f- /. If it is inclined, the moment is the strain G X the perpendicular
distance of the line of its direction from O, or Gg, and G = PC -*- g.
The guy-rope having the least strain is the horizontal one^1, and the strain
442
MECHANICS.
in G — the strain in J? X the se-
cant of the angle between F and
6r. As G is made more nearly
vertical g decreases, and th«
strain increases, becoming infi-
nite when g = 0.
3. Shea r-p oleswitlt
Guys. (Fig. 117.)— First assume'
that the two masts act as one
placed at BD, and the two guys
as one at AB. Calculate the
strain in BD and AB as in Fig.
115. Multiply half the strain in
BD (or AB) by the secant of half
Fra. 117. the angle the two masts (or
guys) make with each other to find the strai» in each mast (or guy).
Two Diagonal Braces and a Tie-rod. (Fig. 118.)— Suppose the braces
are used to sustain a single load P. Compressive stress on AD = y$P X AD -f-
AB ; on CA = J&P X CA -*- AB. This is true only if CB and BD are of equal
length, in which case ^ of P is supported by each abutment C and D. If
they are unequal in length (Fig. 119), then,
by the principle of the lever, find the re-
actions of the abutments Rt and jRa. If P
is the load applied at the point B on the
lever CD, the fulcrum being D, then Rt X
CD = P X BD and R? X CD - P X BC;
• CD\ R? = P X BC -f- CD.
The strain on AC = Rl X AC-*-AB, and
on AD = RI X AD -*- AB.
The strain on the tie = #x X CB H- AB
FIG. 119.
When CB=BD, Rl=R<2. The strain
on CB and BD is the same, whether
the braces are of equal length or
not, and is equal to %P X %CD-irAB.
If the braces support a uniform load,
as a pair of rafters, the strains caused
by such a load are equivalent to that
caused by one half of the load applied
at the centre. The horizontal thrust
of the braces against each other at the
apex equals the tensile strain in the tie.
King-post Truss or Bridge. (Fig. 120.)— If the load is distributed
over the whole length of the truss, the effect is the same as if half the load
were placed at the centre, the other half being carried by the abutments. Let
P = one half the load on the truss, then
tension in the vertical tie AB = P. Com-
pression in each of the inclined braces =
%P X AD -4- AB. Tension in the tie CD
= %P X BD -s- AB. Horizontal thrust of
inclined brace AD at D = the tension in
the tie. If W = the total load on one truss
uniformly distributed, I = its length and
d = its depth, then the tension on the hor-
wi
izontal tie = ~.
L
FIG. 120.
Inverted King-post Truss. (Fig. 121.V-- If P = a load applied a|
B, or one half of a uniformly distributed load, then compression on AB — P
(the floor-beam CD not being considered
to have any resistance to a slight bending).
Tension on ^Cor AD = ^P X AD -*- AB.
> Compression on CD = Y%P X BD -*- AB.
Queen-post Truss. (Fig. 122.)— It
uniformly loaded, and the queen-posts di-
vide the length into three equal bays, the
A" load may be considered to be divided into
w__ 121 three equal parts, two parts of which, Pt
and P«, are concentrated at the pane J Joints
STRESSES' IK FRAMED STRUCTURES.
443
and the remainder is equally divided between the abutments and supported
by them directly. The two parts Pj, and P2 only are considered to affect
the members of the truss. Strain in
the vertical ties BE and CF each
equals PJ or P8. Strain on AB and
CD each = Pt X CD -i- CF. Strain
on the tie AE or EFor ED = P, X
FD -4- CF. Thrust on BC = tension
on EF.
For stability to resist heavy un-
equal loads the queen-post truss
should have diagonal braces from
B to F and from C to E. *•
Inverted Queens-post
Truss. (Fig. 123.) — Compression
on EB and FC each = Pl or P2.
Compression on ^4j5 or BC or (7Z) =
P, X AB -s- £P.. Tension on AE or
FD = P1X AE^r- EB. Tension on
EF — compression on BC. For sta-
bility to resist unequal loads, ties
should be run from CtoE and from
I IG. 146. p to p
Burr Truss of Five Panels. (Fig. 124.)— Four fifths of the load may
be taken as concentrated at the points E, K, L and F, the other fifth being
supported directly by the two abutments. For the strains in BA and CD
the truss may be considered as a queen-post truss, with the loads Pj , P9
concentrated at E&nd the loads P3 , Pi concentrated at F. Then, compres-
sive strain on AB = (Pl -f Pa) X AB -*-BE. The strain on CD is the same if
the loads and panel lengths are equal. The tensile strain on BE or CF =
P\ 4- P«. That portion of the truss between E and l^may be considered as
a smaller queen-post truss, supporting the loads P2 P3 at K and L. The
strain on EG or HF = Pa X EG -*- GK. The diagonals GL and KH receive no
strain unless the truss is unequally loaded. The verticals GK and HL each
receive a tensile strain equal to P2 or P3.
For the strain in the horizontal members: BG and CH receive a thrust
equal to the horizontal component of the thrust in AB or CD, = (P! -f-P3)
X tan angle ABE, or (P, +P«) X AE-*- BE. GH receives this thrust and
also, in addition, a thrust equal to the horizontal component of the thrust in
EG or HF, or, in all, (Pt H- Pa -f P3) X AE-*- BE.
The tension in AE or FD equals the thrust in BG or HCy and the tension
in EK, KL, and LF equals the thrust in GH.
Pratt or Wliipple Truss* (Fig. 125.)— In this truss the diagonals are
ties, and the verticals are struts or columns.
Calculation by the method of distribution of strains: Consider first the
load Pj. The truss having six bays or panels, 5/6 of the load is transmitted
to the abutment H, and 1/6 to the abutment O, on the principle of the lever.
As the five sixths must be transmitted through JA and AH, write on these
members the figure 5. The one sixth is transmitted successively through
JC, CK, KD, DL, etc., passing alternately through a tie and a strut. Write
on these members, up to the strut GO inclusive, the figure 1. Then consider
the load P2 , of which 4/6 goes to AH and 2/6 to GO. Write on KB, BJ, JA,
and AH the figure 4, and on KDt DL, LE, etc., the figure 2. The load Pt
444
MECHANICS.
Tension on d^onals] tf **
transmit 3/6 in each direction; write 3 on each of the members through
which this stress passes, and so on for all the loads, when the figures on tl v
several members will appear as on the cut. Adding them up, we have the
following totals :
** ** <» <* *>? »* f ™ ft ™ **
<f »*• ** ™ <$
Each of the figures in the first line is to be multiplied by 1/6PX secant of
angle HAJ, or 1/6P X AJ-t- AH, to obtain the tension, and each figure in the
lower line is to be multiplied by 1/6P to obtain the compression. The diag-
onals HB and FO receive no strain.
A B
Compression on vertical { *
**
6 6 & 6 6
P3 P4
FIG. 125.
It is common to build this truss with a diagonal strut at HB instead of the
post HA and the diagonal AJ; in which case 5/6 of the load Pis carried
through JB and the strut BH, which latter then receives a strain = 15/6P X
secant of HBJ.
The strains in the upper and lower horizontal members or chords increase
from the ends to the centre, as shown in the case of the Burr truss. AB
receives a thrust equal to the horizontal component of the tension in AJ, or
15/6PX tan AJB. BC receives the same thrust -{- the horizontal component
of the tension in BK, and so on. The tension in the lower chord of each panel
is the same as the thrust in the upper chord of the same panel. (For calcu-
lation of the chord strains by the method of moments, see below.)
The maximum thrust or tension is at the centre of the chords and is equal
to -— -, in which W is the total load supported by the truss, L is the length,
and D the depth. This is the formula for maximum stress in the chords
of a truss of any form whatever.
The above calculation is based on the assumption that all the loads Pj. P8,
etc., are equal. If they are unequal the value of each has to be taken into
account !n distributing the strains. Thus the tension in AJ, with unequal
loads, instead of being 15 X 1/6 P secant 0 would be sec 0 x (5/6 Pj -f 4/6 P2 +
3/6 P3 -f 2/6 P4 4- 1/6 P5.) Each panel load, Px etc., includes its fraction of
the weight of the truss.
General Formula for Strains in Diagonals and Verticals.
—Let n = total number of panels, x = number of any vertical considered
from the nearest end, counting the end as 1, r = rolling load for each panel,
P - total load for each panel,
Strain on verticals = [("-*)+(n-*)*-(*-l)+(*-OTP ,r(*-l)+(g-l)«
2n 2n
For a uniformly distributed load, leave out the last term,
[r(a?-l)+(a;-l)»]-*-2».
Strain on principal diagonals = strain on verticals X secant 0, that is
secant of the angle the diagonal makes with the vertical.
Strain on the counterbraces : The strain on the counterbrace in the first
panel is 0, if the load is uniform. On the 2d, 3d, 4th, etc., it is P secant &
1 1-1-2 II 21 3
, etc., P being the total load in one panel.
STRESSES
FRAMED STRUCTURES.
445
Strain in the Chords— Method of Moments.— Let the truss be
uniformly loaded, the total load acting on it = W. Weight supported at
each end, or reaction of the abutment = W/2. Length of the truss = L.
Weight on a unit of length = W/L. Horizontal distance from the nearest
abutment to the point (say M in Fig. 125) in the chord where the strain is to
be determined = x. Horizontal strain at that point (tension on the lower
chord, compression in the upper) = H. Depth of the truss = D. By the
method of moments we take the difference of the moments, about the point
M. of the reaction of the abutment and of the load between If and the abut-
ments, and equate that difference with the moment of the resistance, or of
the strain in the horizontal chord, considered with reference to a point in
the opposite chord, about which the truss would turn if the first chord were
severed at M.
The moment of the reaction of the abutment is Wx/2. The moment of
the load from the abutment to M is W/Lx X the distance of its centre of
gravity from .M, which is x/2, or moment = Wx? -5- %L. Moment of the stress
in the chord = HD = — - ^-t whence H = — (x - ^\ Itx=OorL
WL
H = 0. If x = L/2, H = — — , which is the horizontal strain at the middle
oD
of the chords, as before given.
The Howe Truss. (Fig. 126.)— In the Howe truss the diagonals are
struts, and the verticals are ties. The calculation of strains may be made
FIG. 12Q.
In the same method a?5 described above fo; the Pratt truss.
The Warren Girder. (Fig. 127.)— In the Warren girder, or triangular
truss, there are no vertical struts, and the diagonals may transmit either
(7)
FIG. 127.
tension or compression. The strains in the diagonals may be calculated by
the method of distribution of strains as in the case of the rectangular truss.
On the principle of the lever, the load Pj being 1/10 of the length of the
span from the line of the nearest support a, transmits 9/10 of its weight to a
and 1/10 to g. Write 9 on the right hand of the strut la. to represent the
compression, and 1 on the right hand of 16, 2c, 3d, etc., to represent com-
pression, and on the left hand of 62, c3, etc., to represent tension. The load P,
transmits 7/10 of its weight to a and 3/10 to g. Write 7 on each member from
2 to a and 3 on each member from 2 to gr, placing the figures representing
compression on the right hand of the member, and those representing
tension on the left. Proceed in the same manner with all the loads, then
446
MECHANICS.
sum up the figures on each side of each diagonal, and write the difference
of each sum beneath, and on the side of the greater sum, to show whether
the difference represents tension or compression. The results are as follows:
Compression, la, 25; 2ft, 15; 3c, 5; 3d, 5; 4e, 15; 5g, 25. Tension, 16, 15; 2c,
5; 4d, 5; 5e, 15. Each of these figures is to be multiplied by 1/10 of one of
the loads as PI , and by the secant of the angle the diagonals make with a
vertical line.
The strains in the horizontal chords may be determined by the method of
moments as in the case of rectangular trusses.
Roof-truss.— Solution by Method of Moments. — The calculation of
strains in structures by the method of statical moments consists in taking a
cross-section of the structure at a point where there are not more than
three members (struts, braces, or chords).
To find the strain in either one of these members take the moment about
the intersection of the other two as an axis of rotation. The sum of the
moments of these members must be 0 if the structure is in equilibrium.
But the moments of the two members that pass through the point of refer-
ence or axis are both 0, hence one equation containing one unknown quan-
tity can be found for each cross-section.
H ,
FIG. 128.
In the truss shown in Fig. 128 take a cross-section at fs, and determine the
strain in the three members cut by it, viz., CE, ED, and DF. Let X = force
exerted in direction CE, Y = force exerted in direction DE, Z = force ex-
erted in direction FD.
For X take its moment about the intersection of Y and Z at D = Xx. For
Y take its moment about the intersection of JSf and Z at A — Yy. For Z take
its moment about the intersection of X and Y at E = Zz. Let z — 15, x —
18.6, y - 38.4, AD - 50, CD = 20 ft. Let P,, P2, Pa, P4 be equal loads, as
shown, and 3^ P the reaction of the abutment A.
The sum of all the moments taken about D or A or E will be 0 when the
structure is at rest. Then — Xx -j- 3.5P X 50 — P3 X 12.5 - Pa X 25 - P, X
37.5 = 0.
The -K signs are for moments in the direction of the hands of a watch or
" 61ockwise " and — signs for the revei se direction or anti-clockwise. Since
P = Pt = Pa = P8, - 18.63T+ 175P - 75P = 0; - 1S.GX = - 100P; X =
1 OOP -s- 18.6 = 5.376P.
_ Yy + P3 X 37.5 -f P« X 25 f P, X 12.5 = 0; 38.4F = 75P; Y = 75P-*- 38.4
= 1.953P.
-Zz + 3.5P X 37.5 - P, X 25 - P2 X 12.5 - P3 X 0 = 0; 15Z = 93.75P; Z =
6.25P.
In the same manner the forces exerted in the other members have been
found as follows: EG = 6.73P: GJ= 8.07P; JA = 9.42P; JH = 1.35P; GF =
1.59P; AH- 8.75F; UF = 7.50P.
The Fink Roof-truss. (Fig. 129.)— An analysis by Prof. P. H. Phil-
brick (Fan, N. Mag.. Aug. 1880) gives the following results:
STRESSES TO FRAMED STRUCTURES.
447
0
FIG. 129.
W ' = total load on roof;
N = No. of panels on both rafters;
W/N = P = load at each joint 6, d, /, etc.?"
V = reaction at A = % FT = Y^NP = 4P;
*i, 'a» ^s = tension on De, eg, gA, respectively;
'i, ca, c3, c4 = compression on Cb, 6d, d/, and/^4.
Strains in
1, orDe = *
'
7/2 PS -
' Af = ct = 7/2PL -*- Z);
* fd = c3 = 7/2PL/D -PD/L;
• lb = C2=7/2PL/D-2PD/L;
7, or 6C = cx =7/2 PL/D - 3 PD/Li
8, *'4 be or fg = PS + L;
10, " cd or dp = UP5 -j- 1>;
11, " ec =PS-j-D:
12, u ca
Example.— Given a Fink roof-truss of span C4 ft., depth 16 ft., with four
panels on each side, as in the cut; total load 32 tons, or 4 tons each at the
points /, d, 6, C, etc. (and 2 tons each at A and B, which transmit no strain
to the truss members). Here W — 32 tons, P = 4 tons, S = 32 ft., D — 16
ft., L = j/S2 4- £>2 = 2.236 X D. L -*- D = 2.236, D -*- L = .4472, S -f- D = 2,
S -t- L = .8944. The strains on the numbered members then are as follows:
1, 2X4X2 =16 tons; 7, 31.3 - 12 X .447 = 25.94 tons.
2, 3X4X2 =24 «4 8, 4 X .8944 = 358 "
3, 7/2 X 4 X 2 = 28 9, 8 X .8944 = 7.16 •«
4, 7/2 X 4 X 2.286 = 31.3 *' 10; 2X2=4 ••
5, 31.3- 4 X .447 =29.52** M, 4 X 2 = 8
6, 31.3- 8 X. 447 =27.72'* l£ 0 X S = W **
The Economical Angle.— A structure of tri-
angular form, Fig. lx;9a, is supported at a and b. It
sustains any load i, the elements cc being in compres-
sion and t in tension. Required the angle Q so that
the total weight of the structure shall be a minimum.
F. R. Honey (Sci. Am. Supp., Jan. 17, Ib95) gives a solu-
/rt \
in which (7 and T represent the crushing and the ten-
sile strength respectively of the material employed.
FIG. 129a.
ft is applicable to any material. For C = T, 9 = i.^
For C = OAT (yellow pine), 0 = 49%°. For C = 0.87' (soft steel), 0 - 53^4°,
For C = 6T feast iron), 0 = 6914°.
448 HEAT.
HEAT.
THERMOMETERS.
The Fahrenheit thermometer is generally used in English-speaking coun-
tries, and the Centigrade, or Celsius thermometer, in countries that use the
metric system. In many scientific treatises in English, however, the Centi-
grade temperatures are also used, either with or without their Fahrenheit
equivalents. The R6aumur thermometer is used to some extent on the
Continent of Europe.
In the Fahrenheit thermometer the freezing-point of water Is taken at 32°,
and the boiling-point of water at mean atmospheric pressure at the sea-
level, 14.7 Ibs. per sq. in., is taken at 212°, the distance between these two
points being divided into 180°. In the Centigrade and Reaumur thermometer^
the freezing-point is taken at 0°. The boiling-point is 100° in the Centigrade
scale, and 80° in the Reaumur.
1 Fahrenheit degree = 5/9 deg. Centigrade s= 4/9 deg. Reaumur.
1 Centigrade degree = 9/5 deg. Fahrenheit =r 4/5 deg. R6aumur.
1 Reaumur degree = 9/4 deg. Fahrenheit = 5/4 deg. Centigrade.
Temperature Fahrenheit = 9/5 X temp. C. -j- 32° = 9/4 R. -f 32°.
Temperature Centigrade = 5/9 (temp. F. — 32°) = 5/4 R.
Temperature R6aumur = 4/5 temp. C. = 4/9 (F. — 32°).
mercurial Thermometer. (Rankine, S. E., p. 234.)— The rate of
expansion of mercury with rise of temperature iucreasesas the temperature
becomes higher ; from which it follows, that if a thermometer showing the
dilatation of mercury simply were made to agree with an air thermometer
at 32° and 212°, the mercurial thermometer would show lower temperatures
than the air thermometer between those standard points, and higher tem-
peratures be37ond them.
For example, according to Regnault, when th* air thermometer marked
350° C. (= 662° F.), the mercurial thermometer would mark 862.16° C. (=
683.89° F.), the error of the latter being in excess 12.16° C. (= 21.89° F.).
Actual mercurial thermometers indicate intervals of temperature propor-
tional to the difference between the expansion of mercury and that of glass.
The inequalities in the rate of expansion of the glass (which are very
different for different kinds of glass) correct, to a greater or less extent, the
errors arising from the inequalities in the rate of expansion of the mercury.
For practical purposes connected with heat engines, the mercurial ther-
mometer made of common glass may be considered as sensibly coinciding
with the air-thermometer at all temperatures not exceeding 500° F.
PYROMETRY.
Principles Used in Various Pyrometers.— Contraction of clay
by heat, as in the Wedgwood pyrometer used by potters. Not accurate, as
the contraction varies with the quality of the clay.
Expansion of air, as in the air-thermometers, Wiborgh's pyrometer, Ueh*
ling and Steinbart's pyrometer, etc.
Specific heat of solids, as in the copper-ball, platinum-ball, and fire-clay
pyrometers.
Relative expansion of two metals or other substances, as copper and iron,
as in Brown's and Bulkley's pyrometers, etc.
Melting-points of metals, or other substances, as in approximate deter-
minations of temperature by melting pieces of zinc, lead, etc.
Measurement of strength of a thermo-electric current produced by heat-
ing the junction of two metals, as in Le Chatelier's pyrometer.
Changes in electric resistance of platinum, as in the Siemens pyrometer*
Mixture of hot and coKt air, as m Hobson's hot-blast pyrometer.
Time required to heat a weighed quantity of water enclosed in a vessel,
as in the water pyrometer.
Thermometer for Temperatures up to 950° F.— Mercury
with compressed nitrogen in the tube above the mercury. Made by Queen
& Co., Philadelphia.
TEMPERATURES, CENTIGRADE AND
FAHRENHEIT.
449
c.
F.
^
F.
C.
F.
C.
F.
C.
F.
C.
F.
C.
F.
^40
-40.
26
78.8
92
197.6
158
316.4
224
435.2
290
554
950
1742
-39
-38.2
27
80.6
93
199.4
159
318.2
225
37.
300
572
960
1760
-38
-36.4
28
82.4
94
201.2
160
320.
226
438.8
310
590
970
1778
-37
—34 6
29
84.2
95
203.
161
321.8
227
440.6
320
008
980
1796
-36
—32.8
30
86.
96
204.8
162
323.6
228
44-2.4
330
(326
990
1814
-35
-31.
31
87.8
97
206. 0
163
325.4
229
444.2
340
644
1000
1832
-34
—29.2
32
89.6
98
208.4
164
327.2
230
446.
3,-jO
662
1010
1850
-33
-27.4
33
91.4
99
210.2
165
329.
231
447.8
360
680
1020
1868
-32
-25.6
34
93.2
100
212.
166
330.8
232
449.6
370
698
1030
1886
-31
-23.8
35
95.
101
213.8
167
332.6
233
451.4
380
716
1040
1904
-30
-22.
36
96.8
102
215. tJ
168
334.4
234
453.2
390
734
1050
1922
-29
-20.2
37
98.6
103
217.4
169
336.2
235
455.
400
752
1060
1940
-28
-18.4
38
100.4
104
219.2
170
338.
236
56.8
410
770
1070
1958
-27
-16.6
39
102.2
105
221.
171
339.8
237
58.6
420
788
1080
1976
-26
-14.8
40
104.
106
^22.8
172
341.6
238
60.4
430
806
1090
1994
-25
-13.
41
105.8
107
224.6
173
343.4
239
62.2
440
824
1100
2012
—34
-11.2
42
107.6
108
226.4
174
345.2
240
464.
450
842
1110
2030
-23
- 9.4
43
109.4
109
228.2
175
347.
241
465.8
460
860
1120
2048
-22
— 7.6
44
111.2
110
230.
176
348.8
242
67.6
470
878
1130
2066
-21
— 5.8
45
113.
111
231.8
177
350.6
243
69.4
480
896
1140
2084
-20
- 4.
46
114.8
112
233. G
178
352.4
244
71.2
490
914
1150
2102
-19
- 2.2
47
116.6
113
235.4
179
354.2
245
473.
500
93-2
1160
2120
-18
- 0.4
48
118.4
114
237.2
180
356.
246
474.8
510
950
1170
2138
-IT
4- 1.4
49
120.2
115
239.
181
357.8
247
476.6
520
968
1180
2156
-16
3.2
50
122.
116
240.8
182
359.6
248
478.4
530
986
1190
2174
-15
5.
51
123.8
117
242.6
183
361.4
249
480.2
540
1004
1200
2192
.-14
6.8
52
125.6
118
244.4
184
363.2
250
482.
550
1022
1210
2210
-13
8.6
53
127.4
119
246.2
185
365.
251
483.8
560
1040
1220
2228
-12
10.4
54
129.2
120
248.
186
366.8
252
485.6
570
1058
1230
2246
-11
12.2
55
131.
121
249.8
187
368.6
253
487.4
580
1076
1240
2264
-10
14.
56
132.8
122
251.8
188
370.4
254
489.2
590
1094
1250
2282
- 9
15.8
57
134.6
123
253.4
189
372.2
255
491.
600
1112
1260
2300
- 8
17.6
58
136.4
124
255.2
190
374.
256
492.8
610
1130
1270
2318
- 7
19.4
59
138.2
125
257.
191
375.8
257
494.6
620
1148
1280
2336
- 6
21.2
60
140.
126
258.8
192
377.6
258
496.4
630
1166
1290
2354
- 5
23.
61
141.8
127
260. (5
193
379.4
259
498.2
640
1184
1300
2372
- 4
24.8
62
143.6
128
262.4
194
381.2
260
500.
650
1202
1310
2390
- 3
26.6
63
145.4
129
264.2
195
383.
261
501.8
660
1220
1320
2408
- 2
28.4
64
147.2
130
266.
196
384.8
262
503.6
670
1238
1330
2426
— 1
30.2
65
149.
131
267.8
197
386.6
263
505.4
680
1256
1340
2444
0
32.
66
150.8
13-3
269.6
198
388.4
264
507.2
690
1274
1350
2462
-f 1
33.8
6?
152.6
133
271.4
199
390.2
265
509.
700
1292
1360
2480
2
35.6
68
154.4
134
273.2
200
392.
266
510.8
710
1310
1370
2498
3
37.4
69
156.2
135
275.
201
393.8
267
512.6
720
1328
1380
2516
4
39.2
70
158.
136
276.8
202
395.6
268
514.4
730
1346
1390
2534
5
41.
71
159.8
137
278.6
203
097.4
269
516. "2
740
1364
1400
2552
6
42.8
72
161.6
138
280.4
204
399.2
270
518.
750
1382
1410
2570
7
44.6
73
163.4
139
282.2
205
401.
271
519.8
76C
1400
1420
2538
8
46.4
74
165.2
140
284.
206
402.8
272
521.6
77C
1418
1430
2606
9
48.2
75
167.
141
285.8
207
404.6
273
523.4
780
1436
1440
2624
10
50.
76
168.8
142
287.6
208
406.4
274
525.2
790
1454
1450
2642
11
51.8
77
170.6
143
289.4
209
408.2
275
527.
800
1472
1460
2660
12
53.6
78
172.4
144
291.2
210
410.
276
528.8
810
1490
1470
2678
13
55.4
79
174.2
145
293.
211
411.8
277
530.6
820
1508
1480
2696
14
57.2
80
176.
146
294.8
212
413.6
278
532.4
830
1526
1490
2714
15
59.
81
177.8
147
296.6
213
415.4
279
534.2
840
1544
1500
2732
16
60.8
82
179.6
148
298.4
214
417.2
280
536.
850
1562
1510
2750
17
62.6
83
181.4
149
300.2
215
419.
281
537.8
8GO
1580
1520
2768
18
64.4
84
183.2
150
302.
216
420.8
282
539.6
870
1598
1530
2786
19
66.2
85
185.
151
303.8
217
422.6
283
541.4
880
1616
1540
2804
20
68.
86
186.8
152
305.6
218
424.4
284
543.2
890
1634
1550
2822
21
69.8
87
188.6
153
307.4
219
426.2
285
545.
900
1652
1600
2912
22
71.6
88
190.4
154
309.2
220
428.
286
546.8
910
1670
1650
3002
23
73.4
89
192.2
155
811.
221
429.8
287
548.6
920
1688
1700
3092
24
75.2
90
194.
156
312.8
222
431.6
288
550.4
930
1706
1750
3182
25
77.
91
195.8
157
314. G
223
433.4
289
552.2
940
1724
1800
3272
TEMPERATURES, FAHRENHEIT AND
CENTIGRADE.
F.
c.
F.
C.
F.
C.
F
C.
F.
C.
F.
C.
F.
C.
-40
-40.
26
— 3.3
92
33.3
158
70.
224
106.7
290
143.3
360
182.2
—39
-39.4
27
— 2.8
93
33.9
159
70.6
225
107.2
291
143.9
370
187.8
—38
-38.9
28
— 2 2
94
34.4
160
71.1
226
107.8
292
144.4
380
193.3
—37
—38.3
29
— 1.7
35
35.
161
71.7
227
108.3
293
145.
390
198.9
-36
-37.8
30
— 1.1
96
35.6
162
72.2
228
108.9
29^
145.6
400
204.4
-35
—37.2
31
— 0.6
97
36.1
163
72.8
229
109.4
295
146.1
410
210.
-34
—36.7
32
0.
98
86.7
164
73.3
230
110.
296
146.7
420
215.6
-33
-36.1
33
-f 0.6
99
87.2
165
73.9
231
110.6
29"
147.2
430
221.1
-32
—35.6
34
1.1
100
87.8
166
74.4
232
111.1
298
147.8
440
226.7
-31
-35.
35
1.7
101
38.3
167
75.
233
111.7
299
148.3
450
2322
—30
—34.4
36
2.2
102
38.9
168
75.6
234
112.2
300
148.9
460
237.8
-29
-33.9
37
2.8
103
89.4
169
76.1
235
112.8
801
149.4
470
243.3
—28
-33.3
38
3.3
104
40.
0
76.7
236
113.3
302
150.
480
248.9
—27
—32.8
39
3.9
105
40.6
]
77.2
237
113.9
303
150.6
490
254.4
-26
—32.2
40
4.4
108
41.1
\
778
238
114.4
304
151.1
500
260.
-25
-31.7
41
5.
107
41.7
<
78.3
239
115.
305
151.7
510
265.6
—24
—31.1
42
5.6
108
42,2
t
78.9
240 115.6
306
152.2
520
271.1
-23
-30.6
43
6.1
109
42.8
5
79.4
241
116.1
307
152.8
530
276.7
-22
—30.
44
6.7
110
43.3
76
80.
242
116.7
308
153.3
540
282.2
-21
—29.4
45
7.2
111
43.9
\
80.6
243
117.2
309
153.9
550
287.8
-20
-28.9
46
7.8
112
44.4
8
81.1
244
117.8
310
154.4
560
293.3
-19
—28.3
47
8.3
113
45.
1 9
81.7
245
118.8
311
155.
570
298.9
-18
—27.8
48
8.9
114
45.6
180
82.2
246
118.9
812
155.6
580
304.4
-17
—27.2
49
9.4
115
46.1
181
82.8
247
119.4
813
156.1
590
310.
-16
—26.7
50
10.
116
46.7
182
83.3
248
120.
814
156.7
600
315 6
—15
-26.1
51
10.6
117
47.2
183
83.9
249
120.8
315
157.2
610
321.1
—14
—25.6
52
11.1
118
47.8
184
84.4
250
181.1
316
157.8
620
326.7
-13
—25.
53
11.7
119
48.3
185
85.
251
121.7
817
158.8
630
332.2
-12
—24.4
54
12.2
120
48.9
186
85.6
252
122.2
818
158.9
640
337.8
-11
-23.9
55
12.8
121
49.4
187
86.1
S53
122.8
319
159.4
650
343.3
—10
—23.3
56
13.3
122
50.
188
86.7
254
123.3
320
160.
660
348.9
- 9
—22.8
57
13.9
123
50.6
189
87.2
255
183.9
821
160.6
670
354.4
— 8
-22.2
58
14.4
124
51.1
190
87.8
256
124.4
32'.
161.1
680
360.
- 7
—21.7
59
15.
125
51.7
191
88.3
257
125.
323
161.7
690
365.6
— 6
—21.1
60
15.6
126
52.2
192
88.9
258
125.6
324
162.2
700
371.1
— 5
—20.6
61
16.1
127
52.8
193
89.4
259
126.1
825
162.8
710
376.7
- 4
-20.
62
16.7
128
53.3
194
90.
260
126.7
326
163.3
720
382.2
— 3
—19.4
63
17.2
129
53.9
195
90.6
261
127.2
327
168.9
730
387.8
— 2
—18.9
64
17.8
130
54.4
196
91.1
262
127.8
828
164.4
740
393.3
— 1
—183
65
18.3
131
55.
197
91.7
263
128.8
329
165.
750
398.9
0
—17.8
66
18.9
132
55.6
198
92.2
264
128.9
330
165.6
760
404.4
+ 1
—17.2
67
19.4
133
56.1
199
92.8
265
129.4
331
166.1
770
410.
2
-16.7
68
20.
134
56.7
200
93.3
266
130.
332
166.7
780
415.6
3
-16.1
69
20.6
135
57.2
201
93.9
267
130.6
333
167.2
790
421.1
4
—15.6
70
21.1
136
57.8
202
94.4
268
131.1
334
167.8
800
426.7
5
-15.
71
21.7
m
58.3
203
95.
269
131.7
335
168.3
810
432.2
6
-14.4
72
22.2
138
58.9
204
95.6
270
132.2
336
168.9
820
437.8
7
—13.9
73
22.8
139
59.4
205
96.1
271
182.8
337
169.4
830
443.3
8
—13.3
74
23.3
140
60.
206
96.7
272
133.3
338
170.
840
448.9
9
—12.8
75
23.9
141
60.6
207
97.2
273
133.9
339
170.6
850
454.4
10
—12.2
76
24.4
142
61.1
208
97.8
274
134.4
340
171.1
860
460.
11
-11.7
77
25.
143
61.7
209
98.3
275
185.
841
171.7
870
465.6
12
—11.1
78
25.6
144
62.2
210
98.9
276
135.6
342
172.2
880
471.1
13
—10.6
79
26.1
145
62.8
211
99.4
277
136.1
343
172.8
890
476.7
14
-10.
80
26.7
146
63.3
212
100.
278
136.7
344
173.3
900
482.2
15
— 9.4
81
27.2
147
63.9
213
100.6
279
137.2
845
173.9
910
487.8
16
-8.9
82
27.8
148
64.4
214
101.1
280
137.8
846
174.4
920
493.3
17
— 8.3
83
28.3
149
65.
215
101.7
281
138.3
347
175.
930
498.9
18
-7.8
84
28.9
150
65.6
216
102.2
282
138.9
348
175.6
940
504.4
19
— 7.2
85
29.4
151
66.1
217
102.8
283
139.4
349
176.1
950
510.
20
— 6.7
86
80.
152
66.7
218
103.3
284
140.
350
176.7
960
515.6
21
— 6.1
87
80.6
153
67.2
219
103.9
285
140.6
351
177.2
970
521.1
22
- 5.6
88
31.1
154
67.8
220
104.4
286
141.1
352
177.8
980
526.7
23
— 5.
89
81.7
155
68.3
221
105.
287
141.7
353
178.3
990
532.2
24
— 4.4
90
32.2
156
68.9
222
105.6
288
142.2
354
178.9
000
537.8
25
— 3.9
91
32.8
157
69.4
223
106.1
289
142.8
355
179.4
010
543.3
PYROMETRY, 451
Platinum or Copper Ball Pyrometer.— A weighed piece of
platinum, copper, or iron is allowed to remain in the furnace or heated
chamber till it has attained the temperature of its surroundings. It is then
suddenly taken out and dropped into a vessel containing water of a known
weight and temperature. The water is stirred rapidly and its maximum
temperature taken. Let W= weight of the water, w the weight of the ball,
t = the original and T the final heat of the water, and <S the specific heat of
the metal; then the temperature of fire may be found from the formula
The mean specific heat of platinum between 32° and 446° F. is .03333 or
1/30 that of water, and it increases with the temperature about .000305 for
each 100° F. For a fuller description, by J. C. Hoadley, see Trans. A. S. M. E.,,
vi. 702. Compare also Henry M, Howe, Trans. A. I. M. E., xviii. 7*8.
For accuracy corrections are required for variations in the specific heat of
the water and of the metal at different temperatures, for loss of heat by
radiation from the metal during the transfer from the furnace to the water,
and from the apparatus during the heating of the water; also for the heat-
absorbing capacity of the vessel containing the water.
Fire-clay or firo-brick may be used instead of the metal ball.
I^e Chatelier's Tnermo-electric Pyrometer*— For a very full
description see paper by Joseph Struthers, School of Mines Quarterly, vol.
xii, 1891 ; also, paper read by Prof. Roberts- Austen before the Iron and Steel
Institute, May 7, 1891.
The principle upon which this pyrometer is constructed is the measure-
ment of a current of electricity produced by heating a couple composed of
two wires, one platinum and the other platinum with 10$ rhodium— the cur-
rent produced being measured by a galvanometer.
The composition of the gas which surrounds the couple has no influence
on the indications.
When temperatures above 2500° F. are to be studied, the wires must have
an isolating support and must be of good length, so that all parts of a fur-
nace can be reached.
For a Siemens furnace, about llt£ feet is the general length. The wires
are supported in an iron tube, % inch interior diameter and held in place by
a cylinder of refractory clay having two holes bored through, in which the
wires are placed. The shortness of time (five seconds) allows the tempera-
ture to be taken without deteriorating the tube.
Tests made by this pyrometer in measuring furnace temperatures under
a great variety of conditions show that the readings of the scale uncorrected
are always within 45° F. of the correct temperature, and in the majority of
industrial measurements this is sufficiently accurate. Le Chatelier's py-
rometer Is sold by Queen & Co., of Philadelphia.
Graduation of lie Chatelier's Pyrometer.— W. C. Roberts-
Austen in his Researches on the Properties of Alloys, Proc. Inst. M. E. 1892,
says : The electromotive force produced by heating the thermo-j unction
to any given temperature is measured by the movement of the spot of light
on the scale graduated in millimetres. A formula for converting the divi-
sions of the scale into thermometric degrees is given by M. Le Chatelier; but
it is better to calibrate the scale by heating the thermo-junction to temper-
atures which have been very carefully determined by the aid of the air-
thermometer, and then to plot the curve from the data so obtained. Many
fusion and boiling-points have been established by concurrent evidence of
various kinds, and are now very generally accepted. The following table
contains certain of these :
Deg. F. Deg. C.
212 100 Water boils.
618 326 Lead melts.
676 358 Mercury boils.
779 415 Zinc melts.
838 448 Sulphur boils.
1157 625 Aluminum melts.
1229 665 Selenium boils.
Deg. F. Deg. C.
1733 945 Silver melts.
1859 1015 Potassium sul-
phate melts.
1913 1045 Gold melts.
1929 1054 Copper melts.
2732 1500 Palladium melts.
3227 1775 Platinum melts.
The Temperatures Developed In Industrial Furnaces.—
M. Le Chatelier states that by means of his pyrometer he has discovered
that the temperatures which occur in melting steel and iu Other industrial
operations have beea hitherto overestimated.
452 HEAT.
M. Le Chatelier finds the melting heat of white cast iron 1135* (2075° F.),
and that of gray cast iron 1220° (22-28° F.). Mild steel melts at 1475° (2687*
F.). semi-mild at 1455° (2651° !?.), and hard steel at 1410° (2570° F.). The
furnace for hard porcelain at the end of the baking has a heat of 1370"
(2498° F.). The heat of a normal incandescent lamp is 1800° (3272° F.), but
it may be pushed to beyond CICO0 (3812° F.).
Prof. Roberts-Austen (Recent Advances in Pyrometry, Trans. A. I. M. E..
Chicago Meeting, 1893) gives an excellent description of modern forms oi
pyrometers. The following are some o2 his temperature determinations.
GOLD-MELTING, ROYAL MINT.
Degrees. Degrees.
Centigrade. Fahr.
Temperature of standard alloy, pouring into moulds. . . . 1180 2156
Temperature of standard alloy, pouring into moulds (on
a previous occasion, by thermo-couple) 1147 2097
Annealing blanks for coinage, temperature of chamber.. 890 1634
SiLVES-MELTING, ROYAL MlNT.
Temperature of standard alloy, pouring into mould 980 1796
TEN-TON OPEN-HEARTH FURNACE, WOOLWICH ARSENAL.
Temperature of steel, 0.3# carbon, pouring into ladle 1645 2993
Steel, 0.3# carbon, pouring into large mould 1580 2876
Reheating furnace, interior 930 1706
Cupola furnace, No. 2 cast iron, pouring into ladle 1600 2912
The following determinations have been effected by M. Le Chatelier:
BESSEMER PROCESS.
Six-ton Converter.
Degrees. Degree*
Centigrade Fahr.
A. Bath of slag 1580 2876
B. Metal in ladle 1640 2984
C. Metal in ingot mould , 1580 2876
P. Ingot in reheating furnace 1200 2192
E. Ingot under the hammer 1080 1976
OPEN-HEARTH FURNACE (Siemens).
Semi-Mild Steel.
A. Fuel gas near gas generator 720 1328
B. Fuel gas entering into bottom of regenerator chamber 400 752
C. Fuel gas issuing from regenerator chamber 1200 2192
Air issuing from regenerator chamber 1000 1832
Chimney gases. Furnace in perfect condition « 300 590
End of the melting of pig charge 1420 2588
Completion of conversion 1500 2733
Molten steel. In the ladle-— Commencement of casting. . 1580 2876
Endofcasting , 1490 2714
In the moulds 1520 2768
For very mild (soft) steel the temperatures are higher by 50° C.
SIEMENS CRUCIBLE OR POT FURNACE.
1600° C., 2912° F.
ROTARY PUDDLING FURNACE.
Degrees C. Degrees F
Furnace 1340-1230 2444-2246
Puddled ball— End of operation 1330 2426
BLAST-FURNACE (Gray -Bessemer Pig).
Opening in face of tuyere 1930 3506
Molten metal— Commencement of fusion 1400 2552
End, or prior to tapping 1570 2858
HOFFMAN RED-BRICK KILN.
Burning temperatures „„,„ lift) MM
PYROMETRY. 453
Hobson's Hot-blast Pyrometer consists of a brass chamber
having three hollow arms and a handle. The hot blast enters one of the
arms and induces a current of atmospheric air to flow into the second arm.
The two currents mix in the chamber and flow out through the third arm,
im which the temperature of the mixture is taken by a mercury thermom-
eter. The openings in the arms are adjusted so that the proportion of hot
blast to the atmospheric air remains the same.
Tlie Wiborgh Air-pyrometer. (E. Trotz, Trans. A. I. M.E.
1892.) — The inventor using the expansion-coefficient of air, as determined
by Gay-Lussac, Dulon, Rudberg, and Regnault, bases his construction on
the following theory : If an air-volume, F, enclosed in a porcelain globe
and connected through a capillary pipe with the outside air, be heated to
the temperature T (which is to be determined) and thereupon the connection
be discontinued, and there be then forced into the globe containing V
another volume of air V of known temperature t, which was previously
under atmospheric pressure H, the additional pressure hy due to the addi-
tion of the air-volume V to the air-volume V, can be measured by a ma-
nometer. But this pressure is of course a function of the temperature T.
Before the introduction of V, we have the two separate air- volumes, Fat
the temperature Tand V at the temperature t, both under the atmospheric
pressure H. After the forcing in of V into the globe, we have, on the
contrary, only the volume F of the temperature T, but under the pressure
H-{~h.
The Wiborgh Air-pyrometer is adapted for use at blast-furnaces, smelting-
works, hardening and tempering furnaces, etc., where determinations of
temperature from 0° to 2400° F. are required.
_ pyran
(" normal-kegel "). When the series is placed in a furnace whose temper-
ature is gradually raised, one after another will bend over as its range of
plasticity is reached ; and the temperature at which it has bent, or " wept,"
so far that its apex touches the hearth of the furnace or other level surface
on which it is standing, is selected as a point on Seger's scale. These points
may be accurately determined by some absolute method, or they may
merely serve to give comparative results. Unfortunately, these pyramids
afford no indications when the temperature is stationary or falling.
Mesure and Novel's Pyrometric Telescope. (Ibid.)— Masure"
and Nouel's pyrometric telescope gives us an immediate determination of
the temperature of incandescent bodies, and is therefore much better
adapted to cases where a great number of observations are to be made, and
at short intervals, than Seger's. Such cases arise in the careful heating of
steel. The little telescope, carried in the pocket or hung from the neck, can
be used by foreman or heater at any moment.
It is based on the fact that a plate of quartz, cut at right angles to the
axis, rotates the plane of polarization of polarized light to a degree nearly
inversely proportional to the square of the length of the waves ; and,
further, on the fact that while a body at dull redness merely emits red
light, as the temperature rises, the orange, yellow, green, and blue waves
successively appear.
If, now, such a plate of quartz is placed between two Nicol prisms at
right angles, "a ray of monochromatic light which passes the first, or
polarizer, and is watched through the second, or analyzer, is not extin-
guished as it was before interposing the quartz. Part of the light passes
the analyzer, and, to again extinguish it, we must turn one of the Nicols a
certain angle," depending on the length of the waves of light, and hence on
the temperature of the incandescent object which emits this light. Hence
the angle through which we must turn the analyzer to extinguish the light
is a measure of the temperature of the object observed.
For illustrated descriptions of different kinds of pyrometers see circular
issued by Queen & Co., Philadelphia.
The Uehling and Steinbart Pyrometer. (For illustrated descrip-
tion see Engineering, Aug. 24, 1894.)— The action of the pyrometer is based
on a principle which involves the law of the flow of gas through minute
apertures in the following manner : If a closed tube or chamber be supplied
with a minute inlet and a minute outlet aperture and air be caused by a
constant suction to flow in through one and out through the other of these
apertures, the tension in the chamber between the apertures will vary with
454
HEAT.
the difference of temperature between the inflowing and outflowing air. If
the inflowing air be made to vary with the temperature to be measured,
and the outflowing air be kept at a certain constant temperature, then the
tension in the space or chamber between the two apertures will be an exact
measure of the temperature of the inflowing air, and hence of the tem-
perature to be measured.
In operation it is necessary that the air be sucked into it through the first
minute aperture at the temperature to be measured, through the second
aperture at a lower but constant temperature, and that the suction be of a
constant tension. The first aperture is therefore located in the end of a
platinum tube in the bulb of a porcelain tube over which the hot blast
sweeps, or inserted into the pipe or chamber containing the gas whose tern
perature is to be ascertained.
The second aperture is located in a coupling, surrounded by boiling water,
and the suction is obtained by an aspirator and regulated by a column of
water of constant height.
The tension in the chamber between the apertures is indicated by a
manometer.
Tlie Air-thermometer. (Prof. B. C. Carpenter, Eng'g News, Jan. 5,
1893.)— Air is a perfect therrnometric substance, and if a given mass of air
be considered, the product of its pressure and volume divided by its
absolute temperature is in every case constant. If the volume of air
remain constant, the temperature will vary with the pressure; if the
pressure remain constant the temperature will vary with the volume. As
the former condition is more easily attained air-thermometers are usually
constructed of constant volume, in which case the absolute temperature
will vary with the pressure.
If we denote pressure by p and p', the corresponding absolute temper*
atures by Tand I", we should have
p:p'-.:T:T' and T'
-p'—.
P
The absolute temperature Tis to be considered in every case 460 higher
than the thermometer-reading expressed in Fahrenheit degrees. From the
form of the above equation, if the pressure p corresponding to a known
absolute temperature T be known, T' can be found. The quotient T/p is a
constant which may be used in all determinations with the instrument. The
pressure on the instrument can be expressed in inches of mercury, and ia
evidently the atmospheric pressure b as shown by a barometer, plus or
minus an additional amount h shewn by a manometer attached to the air
thermometer. That is, in general, p = b ± h.
The temperature of 32° F. is fixed as the point of melting ice, in which
case T = 460 + 32 = 492° F. This temperature can be produced by sur-
rounding the bulb in melting ice and leaving several minutes, so that the
temperature of the confined air shall acquire that of the surrounding ice.
When the air is at that temperature, note the reading of the attached
manometer h, and that of a barometer; the sum will be the value of p cor-
responding to the absolute temperature of 49~° F. The constant of the
instrument, K = 492 •*- p, once obtained, can be used in all future determina-
tions.
Higb Temperatures judged by Color. —The temperature of a
body can be approximately judged by the experienced eye unaided, and
M. Pouillet has constructed a table, which has been generally accepted,
giving the colors and their corresponding temperature as below:
Deg. C.
Incipient red heat.. 525
Dull red heat 700
Incipient cherry-red
heat
Cherry-red heat .
Clear cherry • red
heat
800
900
1000
Deg. F.
977'
1292
1472
1652
1832
Deg. C. Deg. F.
Deep orange heat. . . 1 100 2021
Clear orange heat .. 1200 2192
White heat 1300 2372
Bright white heat.. 1400 2552
) 1500 2732
Dazzling white heat > to to
i 1600 2912
The results obtained, however, are unsatisfactory, as much depends on
the susceptibility of the retina of the observer to light as well as tne degree
of illumination under which the observation is made.
QUANTITATIVE MEASUREMENT OF HEAT. 455
A bright bar of iron, slowly heated m contact with air, assumes the fol-
lowing tints at annexed temperatures (Claudel):
Cent. Fahr.
Yellowat 225 437
Orange at 243 473
Redat 265 509
Violet at 277 531
Cent. Fahr.
Indigo at 288 550
Blue at 293 559
Green at 332 630
"Oxide-gray'1 400 752
BOILING POINTS AT ATMOSPHERIC PRESSURE.
14.7 Ibs. per square inch.
Ether, sulphuric 100° F. Average sea- water 213.2° F.
Carbon bisulphide 118 Saturated brine 226
Ammonia 140 Nitric acid 248
Chloroform HO Oil of turpentine 315
Bromine 145 Phosphorus 554
Wood spirit., 150 Sulphur 570
Alcohol 173 Sulphuric acid 590
Benzine 176 Linseed oil 597
Water 212 Mercury 676
The boiling points of liquids increase as the pressure increases. The boil-
ing point of water at any given pressure is the same as the temperature of
saturated steam of the same pressure. (See Steam.)
MELTING-POINTS OF VARIOUS SUBSTANCES.
The following figures are given by Clark (on the authority of Pouillet,
Claudel, and Wilson), except those marked *, which are given by Prof. Rob-
erts-Austen in his description of the Le Chatelier pyrometer. These latter
are probably the most reliable figures.
Sulphurous acid - 148° F. Alloy, 1 tin, 1 lead. . 370 to 466° F.
Carbonic acid — 108 Tin 442 to 446
Mercury - 39 Cadmium 442
Bromine -f- 9.5 Bismuth 504 to 507
Turpentine 14 Lead 608 to 618*
Hyponitric acid 16 Zinc 680 to 779*
Ice 32 Antimony 810 to 1150
Nitre-glycerine 45 Aluminum 1157*
Tallow 92 Magnesium 1200
Phosphorus 112 Calcium Full red heat.
Acetic acid. 113 Bronze 1692
Stearine 109 to 120 . Silver 1733* to 1873
Spermaceti .„.. 120 Potassium sulphate 185<J*
Margaricacid 131 to 140 Gold, 1913* to 2282
Potassium 136 to 144 Copper 1929* to 1996
Wax 142 to 154 Cast iron, white. . . 1922 to 2075*
Stearic acid 158 " gray 2012 to 2786 2228*
Sodium 194to208 Steel 2372 to 2532
Alloy, 3 lead, 2 tin, 5 bismuth 199 " hard 2570*; mild, 2687*
Iodine 225 Wrought iron 2732 to 2912
Sulphur 239 Palladium 2732*
Alloy, \y% tin, 1 lead 334 Platinum 3227*
For melting-point of fusible alloys, see Alloys.
Cobalt, nickel, and manganese, fusible in highest heat of a forge. Tung-
sten and chromium, not fusible in forge, but soften and agglomerate. Plati-
num and iridium, fusible only before the oxy hydrogen blowpipe.
QUANTITATIVE MEASUREMENT OF HEAT.
Unit of Heat,— The British unit of heat, or British thermal unit
(B. T. U.), is that quantity of heat which is required to raise the temperature
of 1 Ib. of pure water 1° Fahr., at or near 39°. 1 F., the temperature of maxi-
mum density of water.
The French thermal unit, or calorie, is that quantity of heat which is re-
quired to raise the temperature of 1 kilogramme of pure water 1° Cent., at or
about 4° C., which is equivalent to 39°. 1 F.
1 French calorie = 3.968 British thermal units; 1 B. T. U. = .252 calorie.
The " pound calorie " is sometimes used by English writers; it is the quan-
156
HEAT.
tity of heat required to raise the temperature of 1 Ib. of water 1° C. 1 Ib.
calorie = 9/5 B.T.U. = 0.4536 calorie. The heat of combustion of carbon, to
CO2, is said to be 8080 calories. This figure is used either for French calories or
for pound calories, as it is the number of pounds of water that can be raised
1° C. by the complete combustion of 1 Ib. of carbon, or the number of
kilogrammes of water that can be raised 1° C. by the combustion of 1 kilo,
of carbon; assumiug in each case that all the heat generated is transferred
to the water.
The Mechanical Equivalent of Heat is the number of foot-
pounds of mechanical energy equivalent to one British thermal unit, heat
and mechanical energy being mutually convertible. Joule's experiments,
1843-50, gave the figure 772, which is known as Joule's equivalent. More re-
cent experiments by Prof. Rowland (Proc. Am. Acad. Arts and Sciences,
1880; see also Wood's Thermodynamics} give higher figures, arid the most
probable average is now considered to be 778.
1 heat-unit is equivalent to 778 ft.-lbs. of energy. 1 ft. Ib. = 1/778 =.0012852
heat-units. 1 horse-power = 33,000 ft.-lbs. per minute = 2545 heat-uuits per
hour = 42,416 4- per minute = .70694 per second. 1 Ib. carbon burned to CO2
= 14,544 heat-units. 1 Ib. C. per H.P. per hour = 2545 -*-;i4544 = 17^ efficiency
(.174986).
Heat of Combustion of Various Substances in Oxygen.
Heat-units.
Authority.
Cent.
Fahr.
Hydrogen to liquid water at 0° C ....
** to steam at 100° C
( 34,462
4 33,808
( 34,342
28,732
I 8,080
4 7,900
8.137
7,859
7,861
7,901
2,473
( 2,403
4 2,431
2,385
5,607
( 13,120
•<13,108
( 13,063
ill, 858
11,942
11,957
10,102
9,915
62,032
60,854
61,816
51,717
14,544
14,220
14,647
14,146
14,150
14,222
4,451
4,325
4,376
4,293
10,093
23,616
23,594
33,513
21,344
21,496
21,523
18,184
17,847
Favre and Silbermann.
Andrews.
Thomsen.
Favre and Silbermann.
Andrews.
Berthelot.
Favre and Silbermaun.
Andrews.
Thomsen.
Favre and Silbermann.
Thomsen.
Andrews.
Favre and Silbermann.
Andrews.
Thomsen.
Favre and Silbermann.
Carbon (wood charcoal) to carbonic
acid, COa; ordinary temperatures.
Carbon diamond to COo .
" ' black diamond to CO3
'* graphite to CO2
Carbon to carbonic oxide CO
Carbonic oxide to CO2, per unit of CO
CO to CO3 per unit of C = 2^ X 2403
Marsh-gas, Methane, CH4 to water
and COo . . .
Olefiant gas, Ethylene, C2H4 to
water and COo .. . .
Benzole gas, C6H8 to water and COa
In burning 1 pound of hydrogen with 8 pounds of oxygen to form 9 pounds
of water, the units of heat evolved are 62,033 (Favre and S.); but if the
resulting product is not cooled to the initial temperature of the gases,
heat evolved by the combustion of 1 Ib. of hydrogen and 8 Ibs. of oxygen at
32° F. to form steam at 212° F.
By the decomposition of a chemical compound as much heat is absorbed
or rendered latent as was evolved when the compound was formed. If 1 Ib.
of carbon is burned to CO2, generating 14,544 B.T.U., and the CO2 thus formed
is immediately reduced to CO in the presence of glowing carbon, by the
reaction COa 4- C = 2CO, the result is the same as if the 2 Ibs. C had been
burned directly to 2CO, generating 2 X 4451 = 8902 heat-units; consequently
14,544 - 8902 = 5642 heat-units have disappeared or become latent, and the
SPECIFIC HEAT. 457
"unburning " of COS to CO is thus a cooling operation. (For heats of com-
bustion of various fuels, see Fuel.)
SPECIFIC HEAT.
Thermal Capacity.— The thermal capacity of a body is the quantity
of heat required to raise its temperature one degree. The ratio of the heat
required to raise the temperature of a certain weight of a given substance
oiie degree to that required to raise the temperature of the same weight of
water one degree from the temperature of maximum density 39.1 is com-
monly called the specific heat of the substance. Some writers object to the
term as being an inaccurate use of the words "specific " and "heat." A
more correct name would be " coefficient of thermal capacity "
Determination of Specific Heat.— Method by Mixture.— The
body whose specific heat is to be determined is raised to a known tempera-
ture, and is then immersed in a mass of liquid of which the weight, specific
heat, and temperature are known. When both the body and the liquid
have attained the same temperature, this is carefully ascertained.
Now the quantity of heat lost by the body is the same as the quantity of
heat absorbed by the liquid.
Let c, w, and t be the specific heat, weight, and temperature of the hot
body, and c', to', and t' of the liquid. Let T be the temperature the mix-
ture assumes.
Then, by the definition of specific heat, cXwX(t-T} = heat-units lost
by the hot body, and c' X W X (T - t') = heat-units gained by the cold
liquid. If there is no heat lost by radiation or conduction, these must be
equal, and
cw(t-T)=c'w'(T-t>) or c=
Specific Heats of Various Substances.
The specific heats of substances, as given by different authorities, show
considerable lack of agreement, especially in the case of gases.
The following tables give the mean specific heats of the substances named
according to Regnault. (From Rontgen's Thermodynamics, p. 134.) These
specific heats are average values, taken at temperatures which usually come
under observation in technical application. The actual specific heats of all
substances, in the solid or liquid state, increase slowly as the body expands
or as the temperature rises. It is probable that the specific heat of a body
when liquid is greater than when solid. For many bodies this has been
verified by experiment.
SOLIDS.
Antimony 0.0508
Copper 0.0951
Gold 0.03-24
Wrought iron 0.1138
Glass 0.1937
Cast iron 0 . 1298
Lead 0.0314
Platinum 0.0324
Silver 0.0570
Tin 0.0562
Steel (soft) 0.1165
Steel (hard).... 01175
Zinc 0.0956
Brass 0.0939
Ice 0.5040
Sulphur 0.2026
Charcoal 0.2410
Alumina 0. 1970
Phosphorus 0.1887
Water 1.0000
Lead (melted)..., 0.0402
Sulphur 4k 0.2340
Bismuth " 0.0308
Tin " 0.0637
Sulphuric acid 0.3350
LIQUIDS.
Mercury 0.0333
Alcohol (absolute) 0.7000
Fusel oil 0.5640
Benzine 0.4500
Ether 0.5034
458
HEAT.
GASES.
Constant Pressure, Constant Volume.
Air 0.23751 0.16847
Oxygen 0.21751 *).15507
Hydrogen 3.40900 2.41226
Nitrogen 0.24380 0.17273
Superheated steam 0.4805 0.346
Carbonic acid 0.217 0.1535
Olefiant Gas (CHa) 0.404 0.173
Carbonic oxide 0.2479 0.1758
Ammonia 0.508 0.299
Ether 0.4797 0.3411
Alcohol 0.4534 0.3200
Acetic acid 0.4125
Chloroform 0.1567
In addition to the above, the [following are given by other authorities.
(Selected from various sources.)
METALS.
Platinum, 32° to 446° F 0333
(increased .000305 for each 100° F.)
Cadmium 0567
Brass 0939
Copper, 32° to 212° F 094
32° to 572° F 1013
Zinc 32°to212°F 0927
32° to 572° F 1015
Wrought iron (Petit & Dulong).
32° to 21 2° 1098
" 32° to 392° 115
32° to 572° 1218
** 32° to 662°... 1255
Wrought iron (J. C. Hoadley,
A. S. M. E., vi. 713),
Wrought iron, 32° to 200°
32° to 600°
" 32° to 2000°
.1129
.1327
Nickel 1086
Aluminum, 0° F. to melting-
point (A. E. Hunt) 0.2185
OTHER SOLIDS.
Coal 20to241
Coke 203
Graphite 202
Quicklime 217 Sulphate of lime 197
Magnesian limestone 217 Magnesia 222
Soda 231
Quartz 188
River sand 195
Brickwork and masonry, about. .20
Marble 210
Chalk 215
uicklime 217
agnesian limestone 217
Silica 191
Corundum 198
Stones generally 2 to 22
WOODS.
Pine (turpentine) 467 Oak
Fir
.650
570
Pear 500
Alcohol, density .793 622
Sulphuric acid, density 1.87 . .335
1.30 661
Hydrochloric acid 600
LIQUIDS.
Olive oil 310
Benzine 393
Turpentine, density .872 472
Bromine 1.111
GASES.
At Constant At Constant
Pressure. Volume.
Sulphurous acid .1553 .1246
Light carburetted hydrogen, marsh gas (CH4). .5929 .4683
Blast-furnace gases 2277
Specific Heat of Salt Solution. (Schuller.)
Per cent salt in solution 5 10 15 20 25
Specific heat 9306 .8909 .8606 .8490 .8073
Specific Heat of Air.-Regnault gives for the mean value
Between — 30° C. and -f 10° C 0.23771
0°C. " 100° C 0.23741
*' 0° C. " 200° C 0.23751
Hanssen uses 0.1686 for the specific heat of air at constant volume. The
value of this constant has never been found to any degree of accuracy by
direct experiment. Prof. Wood gives 0.2375 -*- 1.406 = 0.1689, The ratio of
EXPANSION BY HEAT.
459
perati
En
the specific heat of a fixed gas at constant pressure to the sp. ht. at con-
stant volume is given as follows by different writers (Eng'g, July 12, 1889):
Renault, 1.3953; Moll and Beck, 1.4085; Szathmari, 1.4027; J. Macfarlane
Gray, 1.4. The first three are obtained from the velocity of sound in air. The
fourth is derived from theory. Prof. Wood says: The value of the ratio for
air, as found in the days of La Place, was 1.41, and we have 0.237? -*- 1.41
= 0.1686, the value used by Clausius, Hanssen, and many others. But this
ratio is not definitely known. Rankine in his later w.ri tings used 1.408, and
Tait in a recent work gives 1.404, while some experiments gives less than
1.4 and others more than 1.41. Prof. Wood uses 1.406.
Specific Heat of Gases.— Experiments by Mallard and Le Chatelier
indicate a continuous increase in the specific heat at constant volume of
steam, CO2, and even of the perfect gases, with rise of temperature. The
variation is inappreciable at 100° C., but increases rapidly at the high tem-
itures of the gas-engine cylinder. (Robinson's Gas and Petroleum
gines.)
Specific Heat and Latent Heat of Fusion of Iron and
Steel. (H. H. Campbell, Trans. A. I. M. E., xix. 181.)
o
Akerman. Troilius.
Specific heat pig iron, 0 to 1200° C 0.16
1200tol800°C 0.21
«* " " Otol500°C 0.18
" " 1500tol800°C 0.20
Calculating by both sets of data we have :
Akerman. Troilius.
Heating from 0 to 1800° C 318 330 calories per kilo.
Hence probable value is about 325 calories per kilo.
Specific heat, steel (probably high carbon) (Troilius) 1175
" softiron " 1081
Hence probable value solid rail steel 1125
' melted rail steel 1275
Akerman. Troilius.
Latent heat of fusion, pig iron, calories per kilo.. 46
44 gray pig 33
white pig 23
From which we may assume that the truth is about : Steel, 20 ; pig iron, 30.
EXPANSION BY HEAT.
In the centigrade scale the coefficient of expansion of air per degree is
0.003665 = 1/273; that is, the pressure being constant, the volume of a perfect
gas increases 1/273 of its volume at 0° C. for every increase in temperature
of J° C. In Fahrenheit units it increases 1/491.2 = .002036 of its volume at
32° F. for every increase of 1° F.
Expansion of Oases by Heat from 32° to 212° F. (Regnault.)
Increase in Volume,
Pressure Constant.
Volume at 32° Fahr.
= 1.0, for
Increase in Pressure,
Volume Constant.
Pressure at 32°
Fahr. = 1.0, for
100° C.
1°F.
100° 0.
1°F.
Hydrogen
0.3661
0.3670
0.3670
0.3669
0.3710
0.3903
0.002034
0.002039
0.002039
0.002038
0.002061
0.002168
0.3667
0.3665
0.3668
0.3667
0.3688
0.3845
0.002037
0.002036
0.002039
0.002037
0.002039
0.002136
Atmospheric air
Carbonic oxide
Carbonic acid
Sulphurous acid
If the volume is kept constant, the pressure varies directly as the absolute
temperature.
4GO
HEAT.
Lineal Expansion of Solids at Ordinary Temperatures.
(British Board of Trade; from CLARK.)
For
1° Fahr.
For
1° Cent.
Coef-
ficient
of
Expan-
sion
from
32° to
212° F.
Accord-
ing to
Other
Author-
ities.
Length = 1
.00001234
Length=l
00002221
002°°1
Antimony (cryst )
.00000627
.00000957
.00001052
00000306
.00000986
.00000975
.00001129
.00001722
.00001894
.00000550
.00001774
.00001755
.00001070
.00001430
.00001596
.00007700
.00000812
.00000897
.00000714
.00000789
.00000897
.00001415
.00000641
.00001166
.00001001
.00002828
.001129
.001722
.001894
.000550
.001774
.001755
.001070
.001430
.001596
.007700
.000812
.000897
.000714
.000789
.000897
.001415
.000641
.001166
.001001
.002828
.001083
.001868
Brass, cast
*' plate
Brick . . . .
Bronze (Copper, 17; Tin, 2J^; Zinc 1).
Bismuth
.001392
Cement. Portland (mixed), pure
Concrete : cement, mortar, and pebbles
Copper
.00000594
.00000795
.00000887
.00004278
.00000451
.00000499
.00000397
.00000438
.00000498
.00000786
.00000356
.00000648
.00000556
.00001571
.odms
Ebonite
Glass English flint
" hard . . .
Granite gray dry
41 red, dry
Gold, pure
Iridium pure ...
Iron, wrought
.001235
.001110
44 cast
Lead
Magnesium
.002694
•»/r 1,1 • I from . .
.00000308
.00000786
.00000256
.00000494
.00009984
.00000695
.00001129
.00000922
.00000479
.00000453
.00000200
.00000434
.00000788
.00001079
.00000577
.00000636
.00000689
.00000652
.00000417
.00001163
.00000489
.00000276
.00001407
.00001496
.00000554
.00001415
.00000460
.00000890
.00017971
.00001251
.00002033
.00001660
.00000863
.00000815
.00000380
.00000781
.00001419
.00001943
.00001038
.00001144
.00001240
.00001174
.00000750
.00002094
.00000881
.00000496
.00002532
.00002692
000554
.001415
.000460
.000890
.017971
.001251
.002033
.001660
.000863
.000815
.000360
.000781
.001419
.001943
.001038
.001144
.001240
.001174
.000750
.002094
.000881
.000496
.002532
.002692
Marbles, various •< j^
__ , . , i from
Masonry, brick -j J0
Mercury (cubic expansion)
.018018
.001279
Plaster white .... ...
Platinum
Platinum, 85 per cent I
.000884
Iridium, 15 " " )
Porcelain
Quartz, parallel to major axis, t 0° to
40° C : .
Quartz, perpendicular to major axis,
£0° to 40° C
.001*908
.001079
Silver, pure
Slate
Steel, cast
44 tempered
Stone (sandstone), dry
"• " Rauville ...
Tin
.001938
Wedgwood ware
Wood, pine
.002942
Zinc
Zinc, 8 \
Tin, 1 S "
Cubical expansion, or expansion of volume = linear expansion x 3.
LATEKT HEATS OF FUSION. 461
Absolute Temperature— Absolute Zero.— The absolute zero of a
gas is a theoretical consequence of the law of expansion by heat, assuming
that it is possible to continue the cooling of a perfect gas until its volume is
diminished to nothing.
If the volume of a perfect gas increases 1/273 of its volume at 0° C. for
every increase of temperature of 1° C., and decreases 1/273 of its volume for
every decrease of temperature of 1° C., then at - 273° C. the volume of the
imaginary gas would be reduced to nothing. This point — 273° C.. or 491.2°
F. below the melting-point of ice on the air thermometer, or 492.66° F. be-
low on a perfect gas thermometer = — 459.2° F. (or — 460.66°), is called the
absolute zero; and absolute temperatures are temperatures measured, on
either the Fahrenheit or centigrade scale, from this zero. The freezing
point, 32° F., corresponds to 491.2° F. absolute. If p0 be the pressure and
t'o the volume of a gas at the temperature of 32° F. = 491.2° on the absolute
scale = T0t andp the pressure, and v the volume of the same quantity of
gas at any other absolute temperature T, then
pv = JT _ £ + 459.2 pv __ p0v0
POVO ~~ To ~~ 491.2 ' T ~ T0 '
The value of POVO -H T0 for air is 53.37, and pv = 53.37IT, calculated as fol-
lows by Prof. Wood:
A cubic foot of dry air at 32° F. at the sea-level weighs 0.080728 Ib. The
volume of one pound is VQ = • ntm^0.. = 12.387 cubic feet. The pressure per
square foot is 2116.2 Ibs.
POVO _ 2116.2 X 12.387 __ 26214
TO " 491.13 ~~ 491.13
The figure 491.13 is the number of degrees that the absolute zero is below
the melting-point of ice, by the air thermometer. On the absolute scale,
•whose divisions would be indicated by a perfect gas thermometer, the cal-
culated value approximately is 492.66, which would makepv = 53.212'. Prof.
Thomson considers that — 273.1° C., = — 459.4° F., is the most probable value
Of the absolute zero. See Heat in Ency. Brit.
Expansion of Liquids from 32° to 212° F.— Apparent ex-
pansion in glass (Clark). Volume at 212°, volume at 32° being 1:
Water ......................... 1.0466 Nitric acid ...................... 1.11
Water saturated with salt ____ 1 .05 Olive and linseed oils ........... 1 .08
Mercury ...................... 1.0182 Turpentine and ether .......... 1.07
Alcohol ..... . ................ 1.11 Hydrochlor. and sulphuric acids 1 .06
For water at various temperatures, see Water.
For air at various temperatures, see Air.
LATENT HEATS OF FUSION AND EVAPORATION.
Latent Heat means a quantity of heat which has disappeared, having
been employed to produce some change other than elevation of temperature.
By exactly reversing that change, the quantity of heat which has dis
appeared is reproduced. Maxwell defines it as the quantity of heat which
must be communicated to a body in a given state in order to convert it into
another state without changing its temperature.
Latent Heat of Fusion.— When a body passes from the solid to the
liquid state, its temperature remains stationary, or nearly stationary, at a
certain melting point during the whole operation of melting; and in order
to make that operation go on, a quantity of heat must be transferred to the
substance melted, being a certain amount for each unit of weight of the
substance. This quantity is called the latent heat of fusion.
When a body passes from the liquid to the solid state, its temperature
remains stationary or nearly stationary during the whole operation of freez-
ing; a quantity of heat equal to the latent heat of fusion is produced in the
body and rejected into the atmosphere or other surrounding bodies.
The following are examples in British thermal units per pound, as given
in Landolt & Bornstein's Physikalische-Chemische Tabellen (Berlin, 1894).
S Latent Heat a , „. Latent Heat
ubstances. of Fusion< Substances. of Fusion>
Bismuth ............. 22.75 Silver ................. 37.93
Cast Iron, gray ...... 41.4 Beeswax ............. 76.14
Cast Iron, white ....... 59.4 Paraffine .............. 63.27
Lead ____ , .............. 9.66 Spermaceti .......... 66.56
Tin .................... 2565 Phosphorus .......... 9.06
Zinc .................. 50.63 Sulphur ............... 16.86
462 HEAT.
Prof. Wood considers 144 heat units as the most reliable value for the
latent hea^ of fusion of ice. Person gives 142 65.
Latent Keat Off Evaporation.— When a body passes from the
solid or liquid to the gaseous state, ks temperature during the operation
remains stationary at a certain boiling point, depending on the pressure ol
the vapor produced ; and in order to make the evaporation go on, a quantity
of heat must be transferred to the substance evaporated, whose amount for
each unit of weight of the substance evaporated depends on the temperature.
That heat does not raise the temperature of the substance, but disappears
in causing it to assume the gaseous state, and it is called the latent heat of
evaporation.
When a body passes from the gaseous state to the liquid or solid state, its
temperature remains stationary, during that operation, at the boiling-point
corresponding to the pressure of the vapor: a quantity of heat equal to the
(atent heat of evaporation at that temperature is produced in the body; and
in order that the operation of condensation may go on, that heat must be
transferred from the body condensed to some other body.
The following are examples of the latent heat of evaporation in British
thermal units, of one pound of certain substances, when the pressure of the
vapor is one atmosphere of 14.7 Ibs. on the square inch:
^iihstflnpp Boiling-point under Latent Heat in
stance. one arm Fam% British units.
Water 212.0 965.7 (Regnault )
Alcohol,. 172.2 364.3 (Andrews.)
Ether 95.0 162.8 "
Bisulphide of carbon 114.8 156.0
The latent heat of evaporation of water at a series of boiling-points ex-
tending from a few degrees below its freezing-point up to about 375 degrees
Fahrenheit has been determined experimentally by M. Regnault. The re-
sults of those experiments are represented approximately by the formula.
in British thermal units per pound,
I nearly = 1091.7 - 0.7(t - 32°) = 965.7- 0.7(* - 212°).
The Total Heat of Evaporation is the sum of the heat which
disappears in evaporating one pound of a given substance at a given tem-
perature (or latent heat of evaporation) and of the heat required to raise its
temperature, before evaporation, from some fixed temperature up to the
temperature of evaporation. The latter part of the total heat is called the
sensible heat.
In the case of water, the experiments of M. Regnault show that the total
heat of steam from the temperature of melting ice increases at a uniform
rate as the temperature of evaporation rises. The following is the formula
in British thermal units per pound :
h = 1091.7 -j-0.305(£ - 82°).
For the total heat, latent heat, etc., of steam at different pressures, see
table of the Properties of Saturated Steam. For tables of total heat, latent
heat, and other properties of steams of ether, alcohol, acetone, chloroform,
chloride of carbon, and bisulphide of carbon, see Rontgen's Thermodynam-
ics (Dubois's translation.) For ammonia and sulphur dioxide, see Wood's
Thermodynamics; also, tables under Refrigerating Machinery, in this book,
EVAPORATION AND DRYING.
In evaporation, the formation of vapor takes place on the surface; in boil-
ing, '.vithin the liquid: the former is a slow, the latter a quick, method of
evaporation.
If we bring an open vessel with water under the receiver of an air-pump
and exhaust the air the water in the vessel will commence to boil, and if wo
keep up the vacuum the water will actually boil near its freezing point. The
formation of steam in this case is due to the heat which the water takes out
of the surroundings.
Steam formed under pressure has the same temperature as the liquid in
which it was formed, provided the steam is kept under the same pressure.
By properly cooling the rising steam from boiling water, as in the multiple-
effect evaporating systems, we can regulate the pressure so that the water
bofls at low temperatures.
EVAPORATION. 463
Evaporation of Water in Reservoirs.— Experiments* at the
Mount Hope Reservoir, Rochester, N. Y., in 1891, gave the following results:
July. Aug. Sept. Oct.
Meau temperature of air in shade 70.5 70.3 68.7 53.3
" water in reservoir 68.2 70.2 66.1 54.4
humidity of air, per cent 67.0 74.6 75.2 74.7
Evaporation in inches during month 5.59 4.93 4.05 3.23
Rainfall in inches during month 3.44 2.95 1.44 2.16
Evaporation of "Water from Open Channels. (Flynn's
Irrigation Canals and Flow of Water.)— Experiments from 1881 to 1885 in
Tulare County, California, showed an evaporation from a pan in the river
equal to an average depth of one eighth of an inch per day throughout the
year.
When the pan was in the air the average evaporation was less than 3/16
of an inch per day. The average for the month of August was 1/3 inch per
day, and for March and April 1/12 of an inch per day. Experiments in
Colorado show that evaporation ranges from .088 to .16 of an inch per day
during the irrigating season.
In Northern Italy the evaporation was from 1/12 to 1/9 inch per day, while
in the south, under the influence of hot winds, it was from 1/6 to 1/5 irch
per day.
In the hot season in Northern India, with a decidedly hot wind blowing,
the average evaporation was ^ inch per day. The evaporation increases
with the temperature of the water.
Evaporation by the Multiple System.— A multiple effect is a
series of evaporating vessels each having a steam chamber, so connected
that the heat of the steam or vapor produced in the first vessel heats the
second, the vapor or steam produced in the second heats the third, and so
on. The vapor from the last vessel is condensed in a condenser. Three
vessels are generally used, in which case the apparatus is called a Triple
Effect. In evaporating in a triple effect the vacuum is graduated so that the
liquid is boiled at a constant and low temperature.
Resistance to Boiling.— Brine. (Rankine.)— The presence in a
liquid of a substance dissolved in it (as salt in water) resists ebullition, and
raises the temperature at which the liquid boils, under a given pressure; but
unless the dissolved substance enters into the composition of the vapor, the
relation between the temperature and pressure of saturation of the vapor
remains unchanged. A resistance to ebullition is also offered by a vessel of
a material which attracts the liquid (as when water bcils in a glass vessel),
and the boiling take place by starts. To avoid the errors which causes of
this kind produce in the measurement of boiling-points, it is advisable to
place the thermometer, not in the liquid, but in the vapor, which shows the
. ng-poii _ ._
pure water by 1.2° Fahr., for each 1/32 of salt that the water contains.
Average sea- water contains 1/32; and the brine in marine boilers is not suf-
fered to contain more than from 2/32 to 3/32.
Methods of Evaporation Employed in the Manufacture
of Salt. (F. E. Engelhardt, Chemist Onondaga Salt Springs; Report for
1889.)—!. Solar heat— solar evaporation. 2. Direct fire, applied to the heat'
ing surface of the vessels containing brine— kettle and pan methods. 3. The
steam-grainer system— steam-pans, steam-kettles, etc. 4. Use of steam and
a reduction of the atmospheric pressure over the boiling brine— vacuum
system.
When a saturated salt solution boils, it is immaterial whether it is done
under ordinary atmospheric pressure at 228° F., or under four atmospheres
with a temperature of 320° F., or in a vacuum under 1/10 atmosphere, the
result will always be a fine-grained salt.
The fuel consumption is stated to be as follows: By the kettle method, 40
to 45 bu. of salt evaporated per ton of fuel, anthracite dust burned on per-
forated grates; evaporation, 5.53 Ibs. of water per pound of coal. By the
pan method, 70 to 75 bu. per ton of fuel. By vacuum pans, single effect, 86
bu. per ton of anthracite dust (2000 Ibs.). With a double effect nearly
double that amount can be produced.
HEAT.
Solubility of Common Salt in Pure Water. (Andreas.)
Temp, of brine, F 32 50 88 104 140 176
100 parts water dissolve parts.... 35.63 35.69 30.03 36 32 37.06 38.00
100 parts brine contain salt 26.27 26.30 26.49 26.64 27.04 27.54
According to Poggial, 100 parts of water dissolve at 229.66° F., 40.35 parts
of salt, or in per cent of brine, 28.749. Gay Lussac found that at 229.72° F.,
100 parts of pure water would dissolve 40.38 parts of salt, in per cent of
brine, 28.764 parts.
The solubility of salt at 229° F. is only 2.5# greater than at 32°. Hence we
cannot, as in the case of alum, separate the salt from the water by allowing
a saturated solution at the boiling point to cool to a lower temperature.
Solubility of Sulphate of Lime in Pure Water. (Marignac.)
Temperature F. degrees. 32 64.5 89.6 100.4 105.8 127.4 186.8 212
PTparT^psumdiSS°lVe } 415 386 371 368 37° 375 417 452
Parts water to dissolve 1 1 *-OE *QO *r*(\ too too *** too tryo
part anhydrous CaS04f 525 474 528 572
In salt brine sulphate of lime is much more soluble than in pure water.
In the evaporation of salt brine the accumulation of sulphate of lime tends
to stop the operation, and it must be removed from the pans to avoid wasta
of fuel.
The average strength of brine in the New York salt districts in 1889 was
69.38 degrees of the salinometer.
Strength of Salt Brines.— The following table is condensed from
one given in U. S. Mineral Resources for 1888, on the authority of Dr.
Englehardt.
Relations between Salinometer Strength, Specific Gravity,
Solid Contents, etc., of Brines of Different Strengths.
Salinometer, degrees.
Baume, degrees.
Specific gravity.
Per cent of salt.
Weight of a gallon of
this brine in pounds.
Pounds of snlt in a gal-
lon of brine of 231
cubic inches.
Gallons of brine required
for a bushel of salt.
Pounds of water to be
evaporated to produce
a bushel of salt.
Lbs. of coal required to
produce a bushel of
salt, 1 Ib. coal evapo-
rating 6 Ibs. of water.
Bushels of salt that can
be made with a ton of
coal of 2000 pounds.
1
.26
1.002
.265
8 347
022
2 531
21 076
3 513
5(59
2
.52
1.003
.530
8.356
.044
1^264
lo'sio
1 752
1.141
4
1.04
1.007
1.060
8 389
088
629 7
5 2k>7
871 2
2 295
6
1.56
.010
1 590
8.414
.133
4186
3' 4 66
577 7
3462
8
2.08
.014
2.120
8.447
.179
3127
2 585
4309
4.641
10
2.60
.017
2650
8.472
.364
2494
2057
3429
5833
12
3.12
.021
8.180
8.506
270
2070
705
284 2
7038
14
3 64
1 025
3710
8 539
316
176 8
453
242 2
^256
16
4.16
1028
4.240
8564
364
154 2
265
2108
9488
18
20
4.68
520
.032
.035
4.770
5300
8.597
8 622
.410
457
136.5
122 5
,118
001
186.3
176 8
10.73
11 99
SO
7.80
.054
7.950
8.781
.698
80 21
648.4
108 1
18 51
40
1040
073
10 600
8939
947
5909
472 3
7871
25 41
50
13.00
1.093
13250
9.105
1.206
46 41
360 6
61 10
3273
60
70
1560
1820
.114
1.136
15.900
18 550
9.280
9.464
1.475
1 755
37.94
31 89
296.2
245 9
49.36
40 98
40.51
4880
80
2080
1 158
21 200
9 647
2 045
27 38
208 1
34 69
57 65
90
2340
1.182
23 850
9847
2 348
23 84
178 8
29 80
67 11
100
2600
1 205
26500
iO 039
2 660
21 04
155 3
25 88
EVAPORATION. 465
Concentration of Sugar Solutions.* (From *' Heating and Con-
centrating Liquids by Steam," by John G. Hudson; The Engineer, June 13,
1890.)— In the early stapes of the process, when the liquor is of low density, the
evaporative duty will be high, say two to three (British) gallons per square
foot of heating surface with 10 Ibs. steam pressure, but will gradually fall to
an almost nominal amount as the final stage is approached. As a generally
safe basis for designing, Mr. Hudson takes an evaporation of one gallon per
hour for each square foot of gross heating surface, with steam of the pres-
sure of about 10 Ibs.
As examples of the evaporative duty of a vacuum pan when performing
the earlier stages of concentration, during which all the heating surface
can be employed, he gives the following:
COIL VACUUM PAN.— 4% in. copper coils, 528 square feet of surface;
steam in coils, 15 Ibs.; temperature in pan, 141° to 148°; density of feed, 25°
Beaum6, and concentrated to 31°-Beaum6.
First Trial. — Evaporation at the rate of 2000 gallons per hour = 3.8 gallons
per square foot; transmission, 376 units per degree of difference of tem-
perature.
Second Trial.— Evaporation at the rate of 1503 gallons per hour = 2.8 gal-
lons per square foot; transmission, 265 units per degree.
As regards the total time needed to work up a charge of massecuite from
liquor of a given density, the following figures, obtained by plotting the
results from a large number of pans, form a guide to practical working.
The pans were all of the coil type, some with and some without jackets,
the gross heating surface probably averaging, and not greatly differing
from, .25 square foot per gallon capacity, and the steam pressure 10 Ibs. per
square inch. Both plantation and refining pans are included, making
various grades of sugar:
Density of Feed (degs. Beaum6).
10° 15° 20° 25° 30°
Evaporation required per gallon masse-
cuite discharged 6.123 3.6 2.26 1.5 .97
A-verage working hours required per
charge 12. 9. 6# 5. 4.
Equivalent average evaporation per hour
per square foot of gross surface, as-
suming .25 sq. ft. per gallon capacity.. 2.04 1.6 1.39 1.2 .97
Fastest working hours required per
charge 8.5 5.5 3.8 2.75 2.0
Equivalent average evaporation per
hour per square foot 2.88 2.6 2.38 2.18 1.9
The quantity of heating steam needed is practically the same in vacuum
as in open pans. The advantages proper to the vacuum system are pri-
marily the reduced temperature of boiling, and incidentally the possibility
of using heating steam of low pressure.
In a solution of sugar in water, each pound of sugar adds to the volume
of the water to the extent of .061 gallon at a low density to .0638 gallon at
high densities.
A Method of Evaporating by Exhaust Steam is described
by Albert Stearns in Trans. A. S. M. E., vol. viii. A pan 17' 6" x 11' x 1' 6",
fitted with cast-iron condensing pipes of about 250 sq. ft. of surface, evapo-
rated 120 gallons per hour from clear water, condensing only about one half
of the steam supplied by a plain slide-valve engine of 14" x 32" cylinder,
making 65 revs, per min., cutting off about two thirds stroke, with steam at
75 Ibs. boiler pressure.
It was found that keeping the pan-room warm and letting only sufficient
air in to carry the vapor up out of a ventilator adds to its efficiency, as the
average temperature of the water in the pan was only about 165° F.
Experiments were made with coils of pipe in a small pan, first with no
agitator, then with one having straight blades, and lastly with troughed
blades; the evaporative results being about the proportions of one, two, and
three respectively.
In evaporating liquors whose boiling point is 220° F., or much above that
of water, it fs found that exhaust steam can do but little more than bring
them up to saturation strength, but on weak liquors, syrups, glues, etc., it
should be very useful.
* For other sugar data see Bagasse as Fuel, under Fuel.
4G6 HEAT.
Drying In Vacuum.— An apparatus for drying grain and other sub-
stances in vacuum is described by Mr, Emil Passburg in Proc. Inst. Mecb.
Engrs., 1889. The three essential requirements for a successful and eco-
nomical process of drying are: 1. Cheap evaporation of the moisture;
2. Quick drying at a low temperature; 3. Large capacity of the apparatus
employed.
The removal of the moisture can be effected in either of two ways: either
by slow evaporation, or by quick evaporation — that is, by boiling.
Slow Evaporation.— The principal idea carried into practice in machines
acting by slow evaporation is to bring the wet substance repeatedly into
contact with the inner surfaces of the apparatus, which are heated by
stearn, while at the same time a current of hot air is also passing through
the substances for carrying off the moisture. This method requires much
heat, because the hot-air current has to move at a considerable speed in
order to shorten the drying process as much as possible; consequently a
great quantity of heated air passes through and escapes unused. As a car-
rier of moisture hot air cannot in practice be charged beyond half its full
saturation; and it is in fact considered a satisfactory result if even this
proportion be attained. A great amount of heat is here produced which is
not used ; while, with scarcely half the cost for fuel, a much quicker re-
moval of the water is obtained by heating it to the boiling point.
Quick Evaporation by Boiling.— This does not take place until the water
is brought up to the boiling point and kept there, namely, 212° F., under
atmospheric pressure. The vapor generated then escapes freely. Liquids
are easily evaporated in this way, because by their motion consequent on
boiling the heat is continuously convoyed from the heating surfaces through
the liquid, but it is different with solid substances, and many more difficul-
ties have to be overcome, because convection of the heat ceases entirely in
solids. The substance remains motionless, and consequently a much
greater quantity of heat is required than with liquids for obtaining the
same results.
Evaporation in Vacuum.— All the foregoing disadvantages are avoided if
the boiling-point of water is lowered, that is, if the evaporation is carried
out under vacuum.
This plan has been successfully applied in Mr. Passburg's vacuum drying
apparatus, which is designed to evaporate large quantities of water con-
tained in solid substances.
The drying apparatus consists of a top horizontal cylinder, surmounted
by a charging vessel at one end, and a bottom horizontal cylinder with &
discharging vessel beneath it at the same end. Both cylinders are encased
in steam-jackets heated by exhaust steam. In the top cylinder works a re-
volving cast-iron screw with hollow blades, which is also heated by exhaust
steam. The bottom cylinder contains a revolving drum of tubes, consisting
of one large central tube surrounded by 24 smaller ones, all fixed in tube-
plates at both ends; this drum is heated by live steam direct from the boiler.
The substance to be dried is fed into the charging vessel through two man-
holes, and is carried along the top cylinder by the screw creeper to the back
end, where it drops through a valve into the bottom cylinder, in which it is
lifted by blades attached to the drum and travels forwards in the reverse
direction; from the front end of the bottom cylinder it falls into a discharg-
ing vessel through another valve, having by this time become dried. The
vapor arising during the process is carried off by an air-pump, through a
dome and air-valve on the top of the upper cylinder, and also through
a throttle-valve on the top of the lower cylinder; both of these valves are
supplied with strainers.
As soon as the discharging vessel is filled with dried material the valve
connecting it with the bottom cylinder is shut, and the dried charge taken
out without impairing the vacuum in the apparatus. When the charging
vessel requires replenishing, the intermediate valve between the two cylin-
ders is shut, and the charging vessel filled with a fresh supply of wet mate-
rial; the vacuum still remains unimpaired in the bottom cylinder, and has
to be restored only in the top cylinder after the charging vessel has been
closed again.
In this vacuum the boiling-point of the water contained in the wet mate-
rial is brought down as low as 110° F. The difference between this tempera-
ture and that of the heating surfaces is amply sufficient for obtaining good
results from the employment of exhaust steam for heating all the surfaces
except the revolving drum of tubes. The water contained in the solid sub-
stance to be dried evaporates as soon as the letter is heated to about 110° F, ;
KADIATIOH OF HEAT. 467
and as long as there is any moisture to be removed the solid substance is
not heated above this temperature.
Wet grains from a brewery or distillery, containing from 75$ to 78$ of
water, have by this drying process been converted in some localities from
a worthless incumbrance into a valuable food-stuff. The water is removed
by evaporation only, no previous mechanical pressing being resorted to.
At Messrs. Guinness's brewery in Dublin two of these machines are em-
ployed. In each of these the top cylinder is 20' 4" long, and 2' 8" diam., and
the screw working inside it makes 7 revs, per min.; the bottom cylinder is
19' 2" long and 5' 4" diam., and the drum of the tubes inside it makes 5 revs.
per min. The drying surfaces of the two cylinders amount together to a
total area of about 1000 sq. ft., of which about 40% is heated by exhaust steam
direct from the boiler. There is only one air-pump, which is made large
enough for three machines; ifc is horizontal, and has only one air-cylinder,
which is double-acting, 17% in. diam. and 17% if1- stroke; aud it is driven at
about 45 revs, per min. As the result of about eight mouths' experience, the
two machines have been drying the wet grains from about 500 cwt. of malt
per day of 24 hours.
Roughly speaking, 3 cwt. of malt gave 4 cwt. of wet grains, and the latter
yield 1 cwt. of dried grains; 500 cwt. of malt will therefore yield about 670
cwt. of wet grains, or 335 cwt. per machine. The quantity of water to be
evaporated from the wet grains is from 75# to 78$ of their total weight, or
say about 512 cwt. altogether, being 25(5 cwt. per machine.
RADIATION OF HEAT.
Radiation of heat takes place between bodies at all distances apart, and
follows the laws for the radiation of light.
The heat rays proceed in straight lines, and the intensity of the rays
radiated from any one source varies inversely as the square of their distance
from the source.
This statement has been erroneously interpreted by some writers, who
have assumed from it that a boiler placed two feet above a fire would re-
ceive by radiation only one fourth as much heat as if it were only one foot
above. In the case of boiler furnaces the side walls reflect those rays that
are received at an angle— following the law of optics, that the angle of inci-
dence is equal to the angle of reflection,— with the result that the intensity
of heat two feet above the fire is practically the same as at one foot above,
instead of only one-fourth as much.
The rate at which a hotter body radiates heat, and a colder body absorbs
heat, depends upon the state of the surfaces of the bodies as well as on their
temperatures. Tlio rate of radiation and of absorption are increased by
darkness and roughness of the surfaces of the bodies, and diminished by
smoothness and polish. For this reason the covering of steam pipes and
boilers should be smooth and of a light color: uncovered pipes and steam-
cylinder covers should be polished.
The quantity of heat radiated by a body is also a measure of its heat-
absorbing power, under the same circumstances. When a polished body is
struck by a ray of heat, it absorbs part of the heat and reflects the rest.
The reflecting power of a body is therefore the complement of its absorbing
power, which latter is the same as its radiating power.
The relative radiating and reflecting power of different bodies has been
determined by experiment, as shown in the table below, but as far as quan-
tities of heat are concerned, says Prof. Trowbridge (Johnson's Cyclopaedia,
art. Heat), it is doubtful whether anything further than the said relative
determinations can, in the present state of our knowledge, be depended
upon, the actual or absolute quantities for different temperatures being still
uncertain. The authorities do not even agree on the relative radiating
powers. Thus, Leslie gives for tin plate, gold, silver, and copper the figure
12, which differs considerably from the figures in the table below, given by
Clark, stated to be on the authority of Leslie, De La Provostaye and De-
gains, and Melloni,
4:68
HEAT.
Relative Radiating and Reflecting Power of Different
Substances.
Radiating or
Absorbing
Power.
Reflecting
Power.
o&o
6fl|C
C>S *
Is!
S^PH
r
Reflecting
Power.
100
0
Zinc, polished
19
81
Water .
100
o
Steel polished
17
83
Carbonate of lead. . .
Writing-paper
100
98
0
2
Platinum, polished..
" in sheet
24
17
76
83
Ivory, jet, marble. . .
93 to 98
7 to 2
Tin
15
85
Ordinary glass
90
10
Brass cast dead
Ice
85
15
polished
11
89
72
28
Brass, bright pol-
Silver-leaf on glass . .
27
73
ished . . ....
7
93
Cast iron, bright pol-
ished
25
75
Copper, varnished . .
" hammered
14
86
93
Mercury, about
Wrought iron, pol-
ished
23
23
77
77
Gold, plated
" on polished
steel
5
3
95
97
Silver, polished
bright
3
97
Experiments of Dr. A. M. Mayer give the following: The relative radia-
tions from a cube of cast iron, having faces rough, as from the foundry,
planed, 4l drawflled,'1 and polished, and from the same surfaces oiled, are as
below (Prof. Thurston, in Trans. A. S. M. E., vol. xvi.) :
Surface.
Oiled.
Dry.
Rough
100
100
Planed
60
32
Drawfiled
49
20
Polished
45
18
It here appears that the oiling of smoothly polished castings, as of cylin-
der-heads of steam-engines, more than doubles the loss of heat by radiation,
while it does riot seriously affect rough castings.
CONDUCTION AND CONVECTION OF HEAT.
Conduction is the transfer of heat between two bodies or parts of a
body which touch each other. Internal conduction takes place between the
parts of one continuous body, and external conduction through the surface
of contact of a pair of distinct bodies.
The rate at which conduction, whether internal or external, goes on,
being proportional to the area of the section or surface through which it
takes place, may be expressed in thermal units per square foot of area por
hour.
Internal Conduction varies with the heat conductivity, which de-
pends upon the nature of the substance, and is directly proportional to the
difference between the temperatures of the two faces of a layer, and in-
versely as its thickness. The reciprocal of the conductivity is called the
internal thermal resistance of the substance. If r represents this resistance,
x the thickness of the layer in inches, T' and Tthe temperatures on the two
faces, and q the quantity in thermal units transmitted per hour per square
foot of area, q =
T' - T
(Rankine.)
PSclet gives the following values of r :
Gold, platinum, silver 0.0016
Copper 0.0018
Iron 0 . 0043
Zinc 0.0045
Lead 0.0090
Marble 0.0716
Brick... 0.1500
CONDUCTION AND CONVECTION OF HEAT. 469
Relative Heat-conducting Power of Metals.
(* Calvert & Johnson ; t Weidemann & Franz.)
Metals. *C. & J. tW. & F.
Bilver 1000 1000
Gold 981 532
Gold, with \% of silver 840
Copper, rolled 845 736
Copper, cast. — 811
Mercury 677
Mercury, with 1.25#
of tin 412
Aluminum 665 ....
Zinc:
cast vertically 628 ....
Metals. *C.&J. tW.&F.
Cadmium 577
Wrought iron 436 119
Tin .422 145
Steel 397 116
Platinum 380 84
Sodium 365
Cast iron 359 ....
Lead 287 85
Antimony :
cast horizontally.. 215 ....
cast vertically.... 192 ....
Bismuth 61 18
cast horizontally... 608
rolled 641 .
INFLUENCE OF A NON-METALLIC SUBSTANCE IN COMBINATION ON THE
CONDUCTING POWER OF A METAL.
Influence of carbon on iron :
Wrought iron .
Steel 397
Cast iron 359
Cast copper .................... 811
Copper with \% of arsenic ....... 570
with .5* of arsenic ...... 669
" with .25% of arsenic ..... 771
The Rate of External Conduction through the bounding surface
between a solid body and a fluid is approximately proportional to the
difference of temperature, when that is small ; but when that difference is
considerable the rate of conduction increases faster than the simple ratio of
that difference. (Rankine.)
If r, as before, is the coefficient of internal thermal resistance, e and e' the
coefficient of external resistance of the two surfaces, x the thickness of the
plate, and T' and T the temperatures of the two fluids in contact with the
T' — T
two surfaces, the rate of conduction is q = — • — — - . According to
e -p- e -f- rx
Peclet, e + e' = — — ^-r, in which the constants A and B have
the following values :
B for polished metallic surfaces ...... . ...................... 0028
B for rough metallic surfaces and for non-metallic surfaces. . .0037
A for polished metals, about ................................... 90
A for glassy and varnished surfaces ................... . ....... 1 .34
A for dull metallic surfaces ............ ...................... 1 .58
A for lamp-black .............................................. 1 .78
When a metal plate has a liquid at each side of it, it appears from experi-
ments by Peclet that B = .058, ^4 = 8.8.
The results of experiments on the evaporative power of boilers agree very
well with the following approximate formula for the thermal resistance of
boiler plates and tubes :
- 4. -/ -
- (r/_2y
which givjs for the rate of conduction, per square foot of surface per Lour,
This formula is proposed by Rankine as a rough approximation, near
enough to the truth for its purpose. The value of a lies between 160 and 200.
Convection, or carrying of heat, means the transfer and diffusion of
the heat in a fluid mass by means of the motion of the particles of that
mass.
The conduction, properly so called, of heat through a stagnant mass of
fluid is very slow in liquids, and almost, if not wholly, inappreciable in
gases. It is only by the continual circulation and mixture of the particles of
the fluid that uniformity of temperature can be maintained in the fluid
mass, or heat transferred between the fluid mass and a solid body.
The free circulation of each of the fluids which touch the side of a solid
plate is a necessary condition of the correctness of Rankine's formulae for
the conduction of heat through that plate; and in these formulae it is im-
470
HEAT.
plied that the circulation of each of the fluids by currents and eddies is
such as to prevent any considerable difference of temperature between the
fluid particles in contact with one side of the solid plate and those at con-
siderable distances from it.
When heat is to be transferred by convection from one fluid to another,
through an intervening layer of metal, the motions of the two fluid masses
should, if possible, be in opposite directions, in order that the hottest par-
ticles of each fluid may be in communication with the hottest particles of
the other, and that the minimum difference of temperature between the
adjacent particles of the two fluids may be the greatest possible.
Thus, in the surface condensation of steam, by passing it through metal
tubes immersed in a current of cold water or air, the cooling fluid should
be made to move in the opposite direction to the condensing steam.
Steam-pipe Coverings.
(Experiments by Prof. Ordway, Trans. A. S. M. E., vi, 168; also Circular No.
27 of Boston Mfrs. Mutual Fire Ins. Co., 1890.)
Substance 1 inch thick. Heat
applied, 310° F.
Pounds of
Water
heated
10° F., pel-
hour,
through
1 sq. ft.
British
Thermal
Units
per sq. ft.
per
minute.
Solid
Matter in
1 sq. ft.
1 inch
thick,
parts in
1000.
Air included,
parts in 1000.
8.1
1.35
56
944
9 6
.60
50
950
3 Carded cotton wool . ...»
10 4
73
20
980
4 Hair felt
10.3
185
815
9 8
.63
56
944
10.6
.77
244
75R
11.9
1.98
53
947
13 9
2 32
119
881
9 Anthracite-coal powder
35.7
5.95
506
494
10 Loose calcined magnesia ....
12 4
2.07
23
977
11. Compressed calcined magnesia. .
12. Light carbonate of magnesia —
13. Compressed carb. of magnesia. .
42.6
13.7
15.4
14 5
7.10
2.28
2.57
2.42
285
60
150
60
715
940
850
94ft
15 Crowded fossil-meal . ...
15 7
2 62
112
888
16. Ground chalk (Paris white)
20.6
30.9
3.43
5.15
253
368
747
632
49 0
8.17
81
919
19 Air alone -
48.0
8.00
0
1000
62.1
10.35
529
471
13.
2 17
22 P(lf)PT .... .... ..
14
2.33
23.' Blotting-paper wound tight
21.
°1 7
3.50
3 62
ot* r^ -1 ?;• I? j
14 6
2 43
OR <?/• i d • -'r~ilhi
18
3
97 T ' 1 if
18.7
3.12
28 Paste of fossil-meal with hair
16 7
2 78
°2
3 67
^y. iraste or ross ^ c-
21
3 50
ou. ijoobe ,V •{ i flc;i pc, ""
27
4 50
32. Paste of clay and vegetable fibre
30.9
5.15
It will be observed that several of the incombustible materials are nearly
as efficient as wool, cotton, and feathers, with which they may be compared
in the preceding table. The materials which may be considered wholly free
from the danger of being carbonized or ignited by slow contact with pipes
or boilers are printed in Roman type. Those which are more or less liable
to be carbonized are printed in italics.
The results Nos. 1 to 20 inclusive were from experiments with the
various non-conductors each used in a mass one inch thick, placed on a flat
surface of iron kept heated by steam to 310° F. The substances Nos. 21 to
CONDUCTION AND CONVECTION OF HEAT, 471
32 were tried as coverings for two-inch steam pipe; the results being re»
duced to the same terms as the others for convenience of comparison.
Experiments on still air gave results which differ little from those of Nos.
3, 4, and 6. The bulk of matter in the best non-conductors is relatively too
small to have any specific effect except to trap the air and keep it stagnant.
These substances keep the air still by virtue of the roughness of their fibres
or particles. The asbestos, No. 18, had smooth fibres. Asbestos with ex-
ceedingly fine fibre made a somewhat better showing, but asbestos is really
one of the poorest non-conductors. It may be used advantageously to hold
together other incombustible substances, but the less of it the better. A
"magnesia" covering, made of carbonate of magnesia with a small per-
centage of good asbestos fibre and containing 0.25 of solid matter, trans-
mitted 2.5 B. T. U. per square foot per minute, and one containing 0.396 of
solid matter transmitted 3.33 B. T. U.
Any suitable substance which is used to prevent the escape of steam heat
should not be less than one inch thick.
Any covering should be kept perfectly dry, for not only is water a good
carrier of heat, but it has been found that still water conducts heat about
eight times as rapidly as still air.
Tests of Commercial Coverings were made by Mr. Geo. M. Brill
and reported in Trans. A. S. M. E., xvi. 827. A length of 60 feet of 8-inch
steam-pipe was used in the tests, and the heat loss was determined by the
condensation. The steam pressure was from 109 to 117 Ibs. gauge, and the
temperature of the air from 58° to 81° F. The difference between the tem-
perature of steam and air ranged from 263° to 286°, averaging 272°.
The following are the principal results :
bb
—
F4
.
.9
q 3
s.'sg
P '-»
fll O)
cr .Pk
Kind of Covering.
o
o
f!
t-'
fill
ue to cov
. steam p
er sq. ft.
Heat lost
> Covered
||
* M
II
*%
£8
s*|fl
||§
•2 11
S^S
|f
3
pq
",-CJ 03 o
ti-**^
02
(gWf
a^
Bare pipe
846
12.27
2.706
100.
2.819
Magnesia
1.25
.120
1.74
.384
.7v>6
14.2
.400
Rock wool. . .
1 60
OHO
1 16
256
.766
9.5
.267
Mineral wool ....
1 30
.089
1.29
.285
.757
10.5
.297
Fire-felt
1 30
157
2.28
.502
.689
18.6
.523
Manville sectional
1.70
.109
1.59
.350
.737
12.9
.564
Manv. sect. & hair-felt.
2.40
.006
0.96
.212
.780
7.8
.221
Manville wool cement.
2.20
.108
1.56
.345
.738
12.7
.359
Championmineralwool
1.44
.099
1.44
.317
.747
11.7
.330
Hair-felt
.82
.132
1 91
.422
.714
15.6
.439
.75
.298
4.32
.953
.548
35.2
.993
75
k)75
3 09
879
.571
32.5
.916
Transmission of Heat, through Solid Plates, from
Water to "Water. (Clark, S.E.).— M. Peclet found, from experiments
made with plates of wrought iron, cast iron, copper, lead, zinc, and tin,
that when the fluid in contact with the surface of the plate was not circu-
lated by artificial means, the rate of conduction was the same for different
metals and for .plates of the same metal of different thicknesses. But
when the water was thoroughly circulated over the surfaces, and when
these were perfectly clean, the quantity of transmitted heat was inversely
proportional to the 'thickness, and directly as the difference in temperature
of the two faces of the plate. When the metal surface became dull, the
rate of transmission of beat through all the metals was very nearly the
It follows, says Clark, that the absorption of heat through metal plates is
more active whilst evaporation is in progress— when the circulation of the
water is more active— than while the water is being heated up to the boiling
point.
472
HEAT.
Transmission from Steam to Water.— M. Peclet's principle is
supported by the results of experiments made in 1867 by Mr. Isherwood on
the conductivity of different metals. Cylindrical pots, 10 inches in diameter,
21*4 inches deep inside, and ^ inch, y± inch, and % inch thick, turned and
bored, were formed of pure copper, brass (60 copper and 40 zinc), rolled
wrought iron, and remelted cast iron. They were immersed in a steam
bath, which was varied from 220° to 320° F. Water at 21 z° was supplied to
the pots, which were kept filled. It was ascertained that the rate of evapora-
tion was in the direct ratio of the difference of the temperatures inside and
outside of the pots; that is, that the rate of evaporation per degree of
difference of temperatures was the same for all temperatures; and that the
rate of evaporation was exactly the same for different thicknesses of the
metal. The respective rates of conductivity of the several metals were as
follows*, expressed in weight of water evaporated from and at 212° F. per
square foot of the interior surface of the pots per degree of difference of
temperature per hour, together with the equivalent quantities of heat-units:
Water at 212°. Heat-units. Ratio.
Copper 6651b. 642.5 1.00
Brass 577" 556.8 .87
Wrought iron 387" 373.6 .58
Castiron 327" 315.7 .49
Whitham, "Steam Engine Design," p. 283, also Trans. A. S. M. E. ix, 425, in
using these data in deriving a formula for surface condensers calls these
figures those of perfect conductivity, and multiplies them by a coefficient
O, which he takes at 0.323, to obtain the efficiency of condenser surface in
ordinary use, i.e., coated with saline and greasy deposits.
Transmission of Heat from Steam to \Vater through
Coils of Iron Pipe.— H. G. C. Kopp and F. J. Meystre (Stevens Indi-
cator, Jan., 1894), give an account of some experiments on transmission of
heat through coils of pipe. They collate the results of earlier experiments
as follows, for comparison:
Experimenter.
$
02
«M
O
(H
I
Steam Con-
densed per
Square foot per
degree differ-
ence of temper-
ature per hour.
Heat trans-
mitted per
square foot per
degree differ-
ence of temper-
ature per hour.
Remarks.
1
o3£ 53
Irf
o tucP
Laurens
Havrez..
Perkins.
ii
Box
Havrez..
Copper coils...
2 Copper coils.
Copper coil...
Iron coil
.292
.268
.981
1.20
1.26
.24
315
'280
974
1120
1200
215
208.2
100
Steam pressure
' = 100.
Steam pressure
= 10.
U It
.22
Iron tube ....
Cast-iron boil-
er
.235
.196
.206
.077
.105
230
207
210
82
From the above it would appear that the efficiency of iron surfaces is less
than that of copper coils, plate surfaces being far inferior.
In all experiments made up to the present time, it appears that the tem-
perature of the condensing water was allowed to rise, a mean between the
initial and final temperatures being accepted as the effective temperature.
But as water becomes warmer it circulates more rapidly, thereby causing
the water surrounding the coil to become agitated and replaced by cooler
water, which allows more heat to be transmitted.
CONDUCTION AND CONVECTION OF HEAT. 473
Again, in accepting the mean temperature as that of the condensing me-
dium, the assumption is made that the rate of condensation is in direct pro-
portion to the temperature of the condensing water.
In order to correct and avoid anjr error arising from these assumptions
and approximations, experiments were undertaken, in which all the condi-
tions were constant during each test.
The pressure was maintained uniform throughout the coil, and provision
was made for the free outflow of the condensed steam, in order to obtain
at all times the full efficiency of the condensing surface. The condensing
water was continually stirred to secure uniformity of temperature, which
was regulated by means of a steam-pipe and a cold-water pipe entering the
tank in which the coil was placed.
The following is a condensed statement of the results
HEAT TRANSMITTED PER SQUARE FOOT OF COOLING SURFACE, PER HOUR,
PER DEGREE OF DIFFERENCE OF TEMPERATURE. (British Thermal Units.)
Temperature
of Condens-
ing Water.
1-in. Iron Pipe;
Steam inside,
60 Ibs. Gauge
Pressure.
1^ in. Pipe;
Steam inside,
10 Ibs.
Pressure.
1^ in. Pipe;
Steam outside,
10 Ibs.
Pressure.
1^ in. Pipe;
Steam inside,
60 Ibs.
Pressure.
80
10(X
120
140
160
180
200
265
269
272
277
281
299
313
128
130
137
145
158
174
200
230
260
267
271
270
*239
247
276
306
349
419
The results indicate that the heat transmitted per degree of difference of
temperature in general increases as the temperature of the condensing
water is increased.
The amount transmitted is much larger with the steam on the outside of
the coil than with the steam inside the coil. This may be explained in part by
the fact that the condensing water when inside the coil flows over the sur-
face of conduction very rapidly, and is more efficient for cooling than when
contained in a tank outside of the coil.
This result is in accordance with that found by Mr. Thomas Craddock,
which indicated that the rate of cooling by transmission of heat through
metallic surfaces was almost wholly dependent on the rate of circulation of
the cooling medium over the surface to be cooled.
Transmission of Heat in Condenser Tubes* (Eng^g, Dec.
10, 1875, p. 449.).— In 1874 B. C. Nichol made experiments for determining the
rate at which heat was transmitted through a condenser tube. The results
went to show that the amount of heat transmitted through the walls of the
kibe per estimated degree of mean difference of temperature increased
considerably with this difference. For example:
Estimated mean difference of Vertical Tube. Horizontal Tube
128 151.9 J52.9 111.6 146.2 150.4
temperature between inside and
outside of tube, degrees Fahr. .
Heat-units transmitted per hour
per square foot of surface per
degree of mean diff. of temp.... 422 531 561 610 737 823
These results seem to throw doubt upon Mr. Isherwood's statement that
the rate of evaporation per degree of difference of temperature is the same
for all temperatures.
Mr. Thomas Craddock found that water was enormously more efficient
than air for the abstraction of heat through metallic surfaces in the process
of cooling. He proved that the rate of cooling by transmission of heat
through metallic surfaces depends upon the rate of circulation of the cool-
ing medium over the surface to be cooled. A tube filled with hot water,
moved by rapid rotation at the rate of 59 ft. per second, through air, lost as
much heat in one minute as it di4 in still air in 12 minutes. In water, at a
velocity of 3 ft. per second, as much heat was abstracted in half a minute as
was abstracted in one minute when it was at rast in the water. Mr. Crad-
dock concluded, further, that the circulation of the cooling fluid became of
474
HEAT.
greater importance as the difference of temperature on the two sides of the
plate became less. (Clark, R. T. D., p. 461.)
Heat Transmission through Cast-iron Plates Pickled In
Nitric Acid.— Experiments by R. C. Carpenter (Trans. A. S. M. E., xii
179) show a marked change in the conducting: power of the plates (from
steam to water), due to protonged treatment with dilute nitric acid.
The action of the nitric acid, by dissolving the free iron and not attacking
the carbon, forms a protecting surface to the iron, which is largely com-
posed of carbon. The following is a summary of results:
Increase in
Tempera-
Proportionate
Thermal Units
Transmitted for
Rela-
tive
Character of Plates, each plate 8.4 in.
by 5.4 in., exposed surface 27 sq. ft.
ture of
3.125 Ibs. of
Water
each
each Degree of
Difference of
Temperature per
Trans-
mission
of
Minute.
Square Foot per
Hour.
Heat.
Cast iron— untreated skin on, but
clean, free from rust
13.90
113 2
100 0
Cast iron— nitric acid, \% sol., 9 days. .
11.5
97.7
86^3
" \% sol., 18 days.
9.7
80.08
70.7
l£sol., 40 days.
9.6
77.8
68.7
5$ sol., 9 days..
9.93
87.0
76.8
" 5$ sol., 40 days.
10.6
77.4
68.5
Plate of pine wood, same dimensions
as the plate of cast iron
0.33
1.9
1.6
The effect of covering cast-iron surfaces with varnish has been investi-
gated by P. M. Chamberlain. He subjected the plate to the action of strong
acid for a few hours, and then applied a non conducting varnish. One sur-
face only was treated. Some of his results are as follows:
170. As finished— greasy.
152. " " washed with benzine and dried.
169. Oiled with lubricating oil.
162. After exposure to nitric acid sixteen hours, then oiled (lin-
seed oil.)
166 After exposure to hydrochloric acid twelve hours, then oiled
(linseed oil.)
113' /After exposure to sulphuric acid 1, water 2, for 48 hours,
jj7 T then oiled, varnished, and allowed to dry for 24 hours.
Transmission of Heat through Solid Plates from Air
or other Dry Gases to "Water. (From Clark on the Steam Engine.)
— The law of the transmission of heat from hot air or other gases to water,
through metallic plates, has not been exactly determined by experiment.
The general results of experiments on the evaporative action of different
portions of the heating surface of a steam-boiler point to the general law
that the quantity of heat transmitted per degree difference of temperature
is practically uniform for various differences of temperature.
The communication of heat from the gas to the plate surface is much
accelerated by mechanical impingement of the gaseous products upon the
surface.
Clark says that when the surfaces are perfectly clean, the rate of trans-
mission of heat through plates of metal from air or gas to water is greater
for copper, next for brass, and next for wrought iron. But when the sur-
faces are dimmed or coated, the rate is the same for the different metals.
With respect to the influence of the conductivity of metals and of the
thickness of the plate on the transmission of heat from burnt gases to
water, Mr. Napier made experiments with small boilers of iron and copper
placed over a gas-flame. The vessels were 5 inches in diameter and 2}g
inches deep. From three vessels, one of iron, one of copper, and one of iron
sides and copper bottom, each of them 1/30 inch in thickness, equal quanti-
ties of water were evaporated to dryness, in the times as follows :
CONDUCTION AND CONVECTION OF HEAT. 475
Water. Iron Vessel. Copper Vessel. Iron
4 ounces 19 minutes 18.5 minutes
11 " 33 " 30.75 "
5^ " 50 u 44 '•
4 " 35.7 •* 36. 83 minutes.
Two other vessels of iron sides 1/30 inch thick, one having a ^-inch copper
oottom and the other 'a J^-inch lead bottom, were tested against the iron
and copper vessel, 1/30 inch thick. Equal quantities of water were evapo-
rated in 54, 55, and 53)^ minutes respectively. Taken generally, the results
of these experiments show that there are practically but slight differences
between iron, copper, and lead in evaporative activity, and that the activity
is not affected by the thickness of the bottom.
Mr. W. B. Johnson formed a like conclusion from the results of his obser-
vations of two boilers of 160 horse-power each, made exactly alike, ex-
cept that one had iron flue-tubes and the other copper flue-tubes. No dif-
ference could be detected between the performances of these boilers.
Divergencies between the results of different experimenters are attribut-
able probably to the difference of conditions under which the heat was
transmitted, as between water or steam and water, and between gaseous
matter and water. On one point the divergence is extreme: the rate of
transmission of heat per degree of difference of temperature. Whilst from
400 to 600 units of heat are transmitted from water to water through iron
plates, per degree of difference per square foot per hour, the quantity of
heat transmitted between water and air, or other dry gas, is only about
from 2 to 5 units, according as the surrounding air is at rest or in movement.
In a locomotive boiler, where radiant heat was brought into play, 17 units
of heat were transmitted through the plates of the fire-box per degree of
difference of temperature per square foot per hour.
Transmission of Heat through Plates and Tubes from
Steam or Hot Water to Air.— The transfer of heat from steam or
water through a plate or tube into the surrounding air is a complex opera-
tion, in which the internal and external conductivity of the metal, the radi-
ating power of the surface, and the convection of heat in the surrounding
air are all concerned. Since the quantity of heat radiated from a surface
varies with the condition of the surface and with the surroundings, according
to laws not yet determined, and since the heat carried away by convection
varies with the rate of the flow of the air over the surface, it is evident that
no general law can be laid down for the total quantity of heat emitted.
The following is condensed from an article on Loss of Heat from Steam-
pipes, in The Locomotive, Sept. and Oct., 1892.
A hot steam pipe is radiating heat constantly off into space, but at the
same time it is cooling also by convection. Experimental data on which to
base calculations of the heat radiated and otherwise lost by steam-pipes are
neither numerous nor satisfactory.
In Box's Practical Treatise on Heat a number of results are given for the
amount of heat radiated by different substances when the temperature of
the air is 1° Fahr. lower than the temperature of the radiating body. A
portion of this table is given below. It is said to be based on Peclet's ex-
periments.
HEAT UNITS RADIATED PER HOUR, PER SQUARE FOOT OP SURFACE, FOR
1° FAHRENHEIT EXCESS IN TEMPERATURE.
Copper, polished 032? Sheet-iron, ordinary 5662
Tin, polished 0440 Glass 5948
Zinc and brass, polished 0491
Tinned iron, polished 0858
Sheet-iron, polished 0920
Sheet lead "... 1329
Cast iron, new .6480
Common steam-pipe, inferred.. .6400
Cast and sheet iron, rusted 6868
Wood, building stone, and brick .7358
When the temperature of the air is about 50° or 60° Fahr., and the radiat-
ing body is not more than about 30° hotter than the air, we may calculate
the radiation of a given surface by assuming the amount of heat given off
by it in a given time to be proportional to the difference in temperature be-
tivcen the radiating body and the air. This is *' Newton's law of cooling.1'
But when the difference in temperature is great, Newton's law does not hold
good; the radiation is no longer proportional to the difference in tempera-
ture, but must be calculated by a complex formula established experiment,
ally by Dulong and Petit. Box has computed a table from this formula,
which greatly facilitates its application, and which is given below :
476 HEAT.
FACTORS FOR REDUCTION TO DULONG'S LAW OF RADIATION.
Differences in Tem-
perature between
Radiating Body
and the Air.
Deg. Fahr.
36
54
72
90
108
126
144
162
180
198
. 216
234
252
270
288
306
324
342
360
378
396
414
432
Temperature of the Air on the Fahrenheit Scale.
32°
50°
59°
68°
86°
104°
122°
140°
158°
176°
194°
>,*.
1.00
1.07
1.12
1.16
1.25
1.36
1.47
1.58
1.70
1.85
1.99
2.15
1.03
1.08
1.16
1.21
1.30
1.40
1.52
1.68
1.76
1.91
2.06
2.23
1.07
1.16
1.20
1.25
1.35
1.45
1.58
1.70
1.83
1.99
2.14
2.31
1.12
1.20
1.25
1.30
1.40
1.52
1.64
1.76
1.90
2.072.23
2.40
1.16
1.25
1.31
1.36
1.46
1.58
1.71
1.84
1.98
2.152.33
2.51
1.21
1.31
1.36
1.42
1.52
1.65
1.78
1.92
2.0?
2.28
2.42
2.62
1.26
1.36
1.42
1.48
1.50
1.72
1.86
2.00
2.16
2.34!2.52
2.72
1.32
1.42
1.48
1.54
1.65
1.79
1.94
2.08
2.24
2.442.64
2.83
1.37
1.4811.54
1.60
1.73
1.86
2.02
2.1?
2.34
2.542.74
2.96
1.44
1.55
1.61
1.68
1.81
1.95
2.11
2.2?
2.46
2.66
2.87
3.10
1.50
1.62
1.69
1.75
1.89
2.04
2.21
2.38
2.56
2.783.00
3.24
1.58
1.691.76
1.83
1.97
2.13
2.32
2.48
2.68
2.91
3.13
3.38
1.64
1.77
1.84
1.90
2.06
2.28
2.43
2.52
2.80
3.03
3.28
3.46
1.71
1.85
1.92
2.00
2.15
2.33
2.52
2.71
2.92
3.183.43
3.70
1.79
1.93
2.01
2.09
2.22
2.44
2.64
2.84
3.06
3.323.58
3.87
1.89
2.03
2.12
2.20
2.3?
2.56
2.78
2.99
3.22
3.503.?7
4.07
1.98
2.1312.22
2.31
2.49
2.69
2.90
3.12
3.37
3.66
3.95
4.26
2.07
2.232.33
2.42
2.62
2.81
3.04
3.28
3.53
3.844.14
4.46
2.17
2.342.44
2.54
2.73
2.95
3.19
3.44
3.70
4.02
4.34
4.68
2.27
2.45
2.56
2.66
2.86
3.09
3.35
3.60
3.88
4.224.55
4.91
2.39
2.57
2.68
2.79
3.00
3.24
3.51
3.78
4.08
4.424.77
5.15
2.50
2.70
2.81
2.93
3.15
3.40
3.68
3.97
4.28
4.64!5.01
5.40
2.63
2.84
2.95
3.0?
3.31
3.51
3.87
4.12
4.48
4.87
5.26
5.6?
2.76
2.983.10
3.23
3.47
3.76
4.10
4.32
4.61
5.125.33
6.04
1
1
The loss of heat by convection appears to be independent of the nature of
the surface, that is, it is the same for iron, stone, wood, and other materials.
It is different for bodies of different shape, however, and it varies with the
position of the body. Thus a vertical steam-pipe will not lose so much heat
by convection as a horizontal one will; for the air heated at the lower part
of the vertical pipe will rise along the surface of the pipe, protecting it to
some extent from the chilling action of the surrounding cooler air. For a
similar reason the shape of a body has an important influence on the result,
those bodies losing most heat whose forms are such as to allow the cool air
free access to every part of their surface. The following table from Box
gives the number of heat units that horizontal cylinders or pipes lose by
convection per square foot of surface per hour, for one degree difference in
temperature between the pipe and the air.
HEAT UNITS LOST BY CONVECTION PROM HORIZONTAL PIPES, PER SQUARE
FOOT OF SURFACE PER HOUR, FOR A TEMPERATURE
DIFFERENCE OF 1° FAHR.
External
External
External
Diameter of
Heat Units
Diameter
Heat Units
Diameter
Heat Units
Pipe
in inches.
Lost.
of Pipe
in inches.
Lost.
of Pipe
in inches.
Lost.
2
0.728
7
0.509
18
0.455
3
0.626
8
0.498
24
0.447
4
0.574
9
0.489
36
0.438
5
0.544
10
0.482
48
0.434
6
0.523
12
0.472
The loss of heat by convection is nearly proportional to the difference in
temperature between the hot body and the air; but the experiments of
CONDUCTION AND CONVECTION OF HEAT. 477
Dulong and PSclet show that this is not exactly true, and we may here also
resort to a table of factors for correcting the results obtained by simple
proportion.
FACTORS FOR REDUCTION TO DULONG'S LAW OP CONVECTION.
Difference
Difference
Difference
in Temp,
between Hot
Factor.
in Temp,
between Hot
Factor.
in Temp,
between
Factor.
Body and
Body and
Hot Body
Air.
Air.
and Air.
18° F.
0.94
180° F.
1.62
342° F.
1.87
36°
.11
198°
1.65
360°
1.90
54°
.22
216°
1.68
378°
1.92
72°
.30
234°
1.72
396°
1.94
90°
.37
252°
1.74
414°
1.96
108°
.43
270°
1.77
432°
1.98
126«
.49
288°
1.80
450°
2.00
144°
.53
306°
1.83
468°
2.02
162°
.58
324°
1.85
....
EXAMPLE IN THE USE OF THE TABLES. — Required the total loss of heat by
both radiation and convection, per foot of length of a steam-pipe 2 11/32
in. external diameter, steam pressure 60 Ibs., temperature of the air in the
room 68° Fahr.
Temperature corresponding to 60 Ibs. equals 307° ; temperature difference
= 307 - 68 = 239°.
Area of one foot length of steam-pipe = 2 11/32 X 3.1416 -*- 12 = 0.614 sq.
ft.
Heat radiated per hour per square foot per degree of difference, from
table, 0.64.
Radiation loss per hour by Newton's law = 239° X .614 ft. X .64 = 93.9
heat units. Same reduced to conform with Dulong's law of radiation: factor
from table for temperature difference of 239° and temperature of air 68° =
1.93. 93.9 X 1.93 = 181.2 heat units, total loss by radiation.
Convection loss per square foot per hour from a 2 11/32-inch pipe: by in-
terpolation from table, 2" = .728. 3" = .626, 2 11/32" = .693.
Area, .614 X .693 X 239° = 101.7 heat units. Same reduced to conform with
Dulong's law of convection: 101.7 X 1.73 (from table) = 175.9 heat units per
hour. Total loss by radiation and convection = 181.2 -j- 175.9 = 357.1 heat
units per hour. Loss per degree of difference of temperature per linear
foot of pipe per hour = 357.1 -*- 239 = 1.494 heat units = 2.433 per sq. ft.
It is not claimed, says The Locomotive, that the results obtained by this
method of calculation are strictly accurate. The experimental data are not
sufficient to allow us to compute the heat-loss from steam-pipes with any
great degree of refinement; yet it is believed that the results obtained as
indicated above will be sufficiently near the truth for most purposes. An
experiment by Prof. Ordway, in a pipe 2 11/32 in. diam. under the above
conditions (Trans. A. S. M. E., v. 73), showed a condensation of steam of 181
grammes per hour, which is equivalent to a loss of heat of 358.7 heat units
per hour, or within half of one per cent of that given by the above calcula-
tion.
According to different authorities, the quantity of heat given off by steam
and hot- water radiators in ordinary practice of heating of buildings by
direct radiation varies from 1.8 to about 3 heat units per hour per square
foot per degree of difference of temperature.
The lowest figure is calculated from the following statement by Robert
Briggs in his paper on "American Practice in Warming Buildings by
Steam " (Proc. Inst. C. E., 1882, vol. Ixxi): " Each 100 sq. ft. of radiating
surface will give off 3 Fahr. heat units per minute for eacn degree F. of dif-
ference in temperature between the radiating surface and the air in which
it is exposed."
The figure 2 1/2 heat units is given by the Nason Manufacturing Company
in their catalogue, and 2 to 2 1/4 are given by many recent writers.
For the ordinary temperature difference in low-pressure steam-heating,
say 212° - 70° = 142° F., 1 Ib. steam condensed from 212° to water at the
4?8 HEAT.
same temperature gives up 965.7 heat units. A loss of 2 heat units per sq.
ft. per hour per degree of difference, under these conditions, is equivalent
to 2 X 142 -T- 965 = 0.3 Ibs. of steam condensed per hour per sq. ft. of heating
surface. (See also Heating and Ventilation.)
Transmission of Heat through Walls, etc., of Buildings
(Nason Manufacturing Co.). (See also Heating and Ventilation.) — Heat
has the remarkable property of passing through moderate thicknesses of air
and gases without appreciable loss, so that air is not warmed by radiant
heat, but by contact with surfaces that have absorbed the radiation.
POWERS OF DIFFERENT SUBSTANCES FOR TRANSMITTING HEAT.
Window-glass 1000 Bricks, rough 200 to 250
Oak or walnut.... 66 Bricks, whitewashed.... 200
White pine 80 Granite or slate 250
Pitch-pine 100 Sheet iron 1030to 1110
Lath or plaster 75 to 100
A square foot of glass will cool 1.279 cubic feet of air from the tempera-
ture inside to that outside per minute, and outside wall surface is generally
estimated at one fifth of the rate of glass in cooling effect.
Box, in his " Practical Treatise on Heat," gives a table of the conducting
powers of materials prepared from the experiments of Peclet. It gives the
quantity of heat in units transmitted per square foot per hour by a plate 1
inch in thickness, the two surfaces differing in temperature 1 degree:
Fine-grained gray marble 28.00
Coarse-grained white marble 22.4
Stone, calcareous, fine , 16.7
Stone, calcareous, ordinary 13.68
Baked clay, brickwork 4.83
Brick-dust, sifted 1.33
Hood, in his "Warming and Ventilating of Buildings," p. 249, gives the
results of M. Depretz, which, placing the conducting power of marble at 1.00,
give .483 as the value for firebrick.
THERMODYNAMICS.
Thermodynamics, the science of heat considered as a form of
energy, is useful in advanced studies of the theory of steam, gas, and air
engines, refrigerating machines, compressed air, etc. The method of treat-
ment adopted by the standard writers is severely mathematical, involving
constant application of the calculus. The student will find the subject
thorougly treated in the recent works by Rontgen (Dubois's translation),
Wood, and Peabody.
First I^aw of Thermodynamics.— Heat and mechanical energy
are mutually convertible in the ratio of about 778 foot-pounds for the British
thermal unit. (Wood.) Heat is the living force or vis viva due to certain
molecular motions of the molecules of bodies, and this living force may be
stated or measured in units of heat or in foot-pounds, a unit of heat in
British measures being equivalent to 772 [778] foot-pounds. (Trowbridge,
Trans. A. S. M. E., vii. 727.)
Second Law of Thermodynamics.— The second law has by dif-
ferent writers been stated in a variety of ways, and apparently with ideas
so diverse as not to cover a common principle. (Wood, Therm., p. 389.)
It is impossible fora self-acting machine, unaided by any external agency
to convert heat from one body to another at a higher temperature. (Clau-
sius.)
If all the heat absorbed be at one temperature, and that rejected be at
one lower temperature, then will the heat which is transmuted into work be
to the entire heat absorbed in the same ratio as the difference between the
absolute temperature of the source and refrigerator is to the absolute tem-
perature of the source. In other words, the second law is an expression for
the efficiency of the perfect elementary engine. (Wood.)
The living force, or vis viva, of a body (called heat) is always proportional
to the absolute temperature of the body. (Trowbridge.)
y-\ __ f\ rri rp
The expression • V2 = —*-* — - may be called the symbolical or al-
gebraic enunciation of the second law,— the law which limits the efficiency
of heat engines, and which does not depend on the nature of the working
medium employed. (Trowbridge.) Qi and TI = quantity and absolute
PHYSICAL PROPERTIES OF GASES. 479
temperature of the heat received, Qa and T9 = quantity and absolute tem-
perature of the heat rejected.
rii _ rri
The expression — ~ — ? represents the efficiency of a perfect heat engine
which receives all its heat at the absolute temperature T7,, and rejects heat
at the temperature T2, converting into work the difference between the
quantity received and rejected.
EXAMPLE.— What is the efficiency of a perfect heat engine which receives
heat at 388° F. (the temperature of steam of 200 Ibs. gauge pressure) and
rejects heat at 100° F. (temperature of a condenser, pressure 1 Ib. above
vacuum).
388 + 459.2-(100-f459.2) _
388 + 459.2 M*' n€
In the actual engine this efficiency can never be attained, for the difference
between the quantity of heat received into the cylinder and that rejected
into the condenser is not all converted into work, much of it being lost by
radiation, leakage, etc. In the steam engine the phenomenon of cylinder
condensation also tends to reduce the efficiency.
PHYSICAL PROPERTIES OP GASES.
(Additional matter on this subject will be found under Heat, Air, Gas, and
• Steam.)
When a mass of gas is enclosed in a vessel it exerts a pressure against the
walls. This pressure is uniform on every square inch of the surface of the
vessel; also, at any point in the fluid mass the pressure is the same in every
direction.
In small vessels containining gases the increase of pressure due to weight
may be neglected, since all gases are very light; but where liquids are con-
cerned, the increase in pressure due to their weight must always be taken
Into account.
Expansion of Gases, Marriotte's Law,— The volume of a gas
diminishes in the same ratio as the pressure upon it is increased.
This law is by experiment found to be very nearly true for all gases, and
is known as Boyle's or Mariotte's law.
If p = pressure at a volume v, and P! = pressure at a volume vlt P^VI =
v
pv'i Pi = — p; pv = a constant.
Vi
The constant, C, varies with the temperature, everything else remaining
the same.
Air compressed by a pressure of seventy-five atmospheres has a volume
about 2fc less than that computed from Boyle's law, but this is the greatest
divergence that is found below 160 atmospheres pressure.
Law of Charles.— The volume of a perfect gas at a constant pressure
is proportional to its absolute temperature. If v0 be the volume of a gas
at 32° F., and v^ the volume at any other temperature, tlt then
or «! = [! + 0.002036(<1 - 32°)]v0.
If the pressure also change fromp0 topx,
The Densities of the elementary gases are simply proportional to
their atomic weights. The density of a compound gas, referred to hydrogen
as 1, is one-half its molecular weight ; thus the relative density of COQ is
1^(12 + 32) = 22.
A vogadro's Law.— Equal volumes of all gases, under the same con-
ditions of temperature and pressure, contain the same number of molecules.
To find the weight of a gas in pounds per cubic foot at 32° F., multiply half
the molecular weight of the gas by .00559. Thus 1 cu. ft. marsh-gas, CH^ ,
= J^(12 + 4) X .00559 = ,0447 Ib,
4:80 PHYSICAL PROPERTIES OF GASES.
When a'certain volume of hydrogen combines with one half its volume of
oxygen, there is produced an amount of water vapor which will occupy the
same volume as that which was occupied by the hydrogen gas when at the
same temperature and pressure.
Saturation-point of Vapors.— A vapor that is not near the satura-
tion-point behaves like a gas under changes of temperature and pressure;
but if it is sufficiently compressed or cooled, it reaches a point where it be-
gins to condense: it then no longer obeys the same laws as a gas, but its
pressure cannot be increased by diminishing the size of the vessel containing
it, but remains constant, except when the temperature is changed. The
only gas that can prevent a liquid evaporating seems to be its own vapor.
Dalton's I^aw of Gaseous Pressures.— Every portion of amass
of gas inclosed in a vessel contributes to the pressure against the sides of
the vessel the same amount that it would have exerted by itself had no
other gas been present. ,
Mixtures of Vapors and Gases.— The pressure exerted against
the interior of a vessel by a given quantity of a perfect gas enclosed in it
is the sum of the pressures which any number of parts into which such quan-
tity might be divided would exert separately, if each were enclosed in a
vessel of the same bulk alone, at the same temperature. Although this law
is not exactly true for any actual gas, it is very nearly true for many. Thus
if 0.080728 Ib. of air at 32° F., being enclosed in a vessel of one cubic foot
capacity, exerts a pressure of one atmosphere or 14.7 pounds, on each square
inch of the interior of the vessel, then will each additional 0.080728 Ib. of air
which is enclosed, at 32°, in the same vessel, produce very nearly an addi-
tional atmosphere of pressure. The same law is applicable to mixtures of
gases of different kinds. For example, 0,12344 Ib. of carbonic-acid gas, at
32°, being enclosed in a vessel of one cubic foot in capacity, exerts a pressure
of one atmosphere; consequently, if 0.080728 Ib. of air and 0.12344 Ib. of
carbonic acid, mixed, be enclosed at the temperature of 32°, in a vessel of
one cubic foot of capacity, the mixture will exert a pressure of two atmos-
pheres. As a second example: Let 0.080728 Ib. of air, at 212°, be enclosed in
a vessel of one cubic foot; it will exert a pressure of
212 + 459.2
32 + 459.2 = J.366 atmospheres.
Let 0.03797 Ib. of steam, at 212°, be enclosed in a vessel of one cubic foot; it
will exert a pressure of one atmosphere. Consequently, if 0.080728 Ib. of air
and 0.03797 Ib. of steam be mixed and enclosed together, at 212°, in a vessel of
one cubic foot, the mixture will exert a pressure of 2.366 atmospheres. It is
a common but erroneous practice, in elementary books on physics, to de-
scribe this law as constituting a difference between mixed and homogeneous
gases; whereas it is obvious that for mixed and homogeneous gases the law
of pressure is exactly the same, viz., that the pressure of the whole of a
gaseous mass is the sum of the pressures of all its parts This is one of the/
laws of mixture of gases and vapors.
A second law is that the presence of a foreign gaseous substance in con
tact with the surface of a solid or liquid does not affect the density of the
vapor of that solid or liquid unless there is a tendency to chemical com-
bination between the two substances, in which case the density of the
vapor is slightly increased. (Rankine, S. E., p. 239.)
Flow of Gases.— By the principle of the conservation of energy, it may
be shown that the velocity with which a gas under pressure will escape into
a vacuum is inversely proportional to the square root of its density; that is,
oxygen, which is sixteen times as heavy as hydrogen, would, under exactly
the same circumstances, escape through an opening only one fourth as fast
as the latter gas.
Absorption of Gases by liquids.— Many gases are readily ab-
sorbed by water. Other liquids also possess this power in a greater or less
degree. Water will for example, absorb its own volume of carbonic-acid
gas, 430 times its volume of ammonia, 2J£ times its volume of chlorine, and
only about 1/20 of its volume of oxygen.
The weight of gas that is absorbed by a given volume of liquid is propor-
tional to the pressure. But as the volume of a mass of gas is less as the
pressure is greater, the volume which a given amount of liquid can absorb
at a certain temperature will be constant, whatever the pressure. Water,
for example, can absorb its own volume of carbonic-acid gas at atmospheric
pressure; it will also dissolve its own volume if the pressure is twice as
great, but in that case the gas will be twice as dense, and consequently twice
the weight of gas is dissolved.
OF THE ATMOSPHERE.
481
AIR.
Properties of Air. — Air is a mechanical mixture of the gases oxygen
and nitrogen; 20.7 parts O and 79.3 parts N by volume, 23 parts O and 77 parts
N by weight.
The weight of pure air at 32° F. and a barometric pressure of 29.92 inches
of mercury, or 14.6963 Ibs. per sq. in., or 2116.3 Ibs. per sq. ft., is .080728 Ib. per
cubic foot. Volume of 1 Ib. = 12.387 cu. ft. At any other temperature and
barometric pressure its weight in Ibs. per cubic foot is W — '. °' — — ,
where B = height of the barometer, T= temperature Fahr., and 1.3253 =
weight in Ibs. of 459.2 c. ft. of air at 0° F. and one inch barometric pressure.
Air expands 1/491.2 of its volume at 32° F. for every increase of 1° F., and
its volume varies inversely as the pressure.
Volume, Density, and Pressure of Air at Various
Temperatures. (D. K. Clark.)
Volume at Atmos.
Pressure at Constant
Pressure.
Density, Ibfi.
Volume.
Fahr.
per Cubic Foot at
Atmos. Pressure.
Cubic Feet
Compara-
Lbs. per
Compara-
in 1 Ib.
tive Vol.
Sq. In.
tive Pres.
0
11.583
. .881
.086331
12.96
.881
32
12.387
.943
.080728
13.86
.943
40
12.586
.958
.079439
14.08
.958
50
12.840
.977
.077884
14.36
.977
62
13.141
1.000
.076097
14.70
1,000
70
13.342
1.015
.074950
14.92
1.015
80
13.593
1.034
.073565
15.21
1.034
90
13.845
1.054
.072230
15.49
1.054
100
14.096
1.073
.070942
15.77
1.073
110
14.344
1.092
.069721
16.05
1 .092
120
14.592
1.111
.068500
16.33
1.111
130
14.846
1.130
.067361
16.61
1.130
140
15.100
1.149
.066221
16.89
1.149
150
15.351
1.168
.065155
17.19
1.168
160
15.603
1.187
.064088
17.50
1.187
170
15.854
1.206
.063089
17.76
1.206
180
16.106
1.226
.062090
18.02
1.226
200
16.606
1.264
.060210
18.58
1.264
210
16.860
1^283
.059313
18.86
1.283
212
16.910
1.287
.059135
18.92
1.287
The Air-manometer consists of a long vertical glass tube, closed at
the upper end, open at the lower end, containing air, provided with a scale,
and immersed, along with a thermometer, in a transparent liquid, such as
water or oil, contained in a strong cylinder of glass, which communicates
with the vessel in which the pressure is to be ascertained. The scale shows
the volume occupied by the air in the tube.
Let VQ be that volume, at the temperature of 32° Fahrenheit, and mean
pressure of the atmosphere, p*\ let Vi be the volume of the air at the tem-
perature t, and under the absolute pressure to be measured pt ; then
Pi
491.2°
Pressure of the Atmosphere at Different Altitudes.*
At the sea-level the pressure of the air is 14.7 pounds per square inch; at
YA of a mile above the sea-level it is 14.02 pounds; at y^ mile, 13.33; at %
mile, 12.66; at 1 mile, 12.02; at 1J£ mile, 11.42; at 1^ mile, 10.88; and at 1
482
AIR.
miles, 9.80 pounds per square inch. For a rough approximation we may
assume that the pressure decreases % pound per square inch for every 1000
feet of ascent.
It is calculated that at a height of about 3}£ miles above the sea-level the
weight of a cubic foot of air is only one half what it is at the surface of the
earth, at seven miles only one fourth, at fourteen miles only one sixteenth,
at twenty-one miles only ona sixty-fourth, and at a height of over forty-
five miles it becomes so attenuated as to have no appreciable weight.
The pressure of the atmosphere increases with the depth of shafts, equal
to about one inch rise in the barometer for each 900 feet increase in depth:
this may be taken as a rough-and-ready rule for ascertaining the depth of
shafts.
Pressure of the Atmosphere per Square Inch and per
Square Foot at Various Readings of the Barometer.
RULE.— Barometer in inches x .4908 = pressure per square inch; pressure
per square inch x 144 = pressure per square foot.
Barometer.
Pressure
per Sq. In.
Pressure
per Sq. Ft.
Barometer.
Pressure
per Sq. In.
Pressure
per Sq. Ft.
in.
Ibs.
Ibs.*
in.
Ibs.
Ibs.*
28.00
13.74
1978
29.75
14.60
2102
28.25
13.86
1995
30.00
14.70
2119
28.50
13.98
2013
30.25
14.84
2136
28.75
14.11
2031
30.50
14.96
2154
29.00
14.23
2049
30.75
15.09
2172
29.25
14.35
2066
31.00
15.21
2190
29.50
14.47
2083
* Decimals omitted.
For lower pressures see table of the Properties of Steam.
Barometric Readings corresponding with Different
Altitudes, in French and English Measures.
Alti-
tude.
Read-
ing of
Barom-
Altitude.
Reading
of
Barom-
Alti-
tude.
Reading
of
Barom-
Altitude.
Reading
of
Barom-
eter.
eter.
eter.
eter.
meters.
mm.
feet.
inches.
meters.
mm.
feet.
inches.
0
762
0.
30.
1147
660
3763.2
25.98
21
760
68.9
29.92
1269
650
4163.3
25.59
127
750
416.7
29.52
1393
640
4568.3
25.19
234
740
767.7
29.13
1519
630
4983.1
24.80
342
730
1122.1
28.74
1647
620
5403.2
24.41
453
720
1486.2
28.35
1777
610
5830.2
24.01
564
710
1850.4
27.95
1909
600
6243.
23.62
678
700
2224.5
27.55
2043
590
6702.9
23.22
793
690
2599.7
27.16
2180
580
7152.4
22.83
909
680
2962.1
26.77
2318
570
7605.1
22.44
1027
670
3369.5
26.38
2460
560
8071.
22.04
Levelling by the Barometer and by Boiling Water.
(Traut wine.)— Many circumstances combine to render the results of this
kind of levelling unreliable where great accuracy is required. It is difficult
to read off from an aneroid (the kind of barometer usually employed for
engineering purposes) to within from two to five or six feet, depending on
its size. The moisture or dryness of the air affects the results; also winds,
the vicinity of mountains, and the daily atmospheric tides, which cause
incessant and irregular fluctuations in the barometer. A barometer hang-
ing quietly in a room will often vary 1/4 of an inch within a few hours, cor-
responding to a difference of elevation of nearly 100 feet. No formula can
possibly be devised that shall embrace these sources of error.
MOISTURE IN THE ATMOSPHERE.
483
To Find the Difference in Altitude of Two Places.— Take
from the table the altitudes opposite to the two boiling temperatures, or to
the two barometer readings. Subtract the one opposite the lower reading
from that opposite the upper reading. The remainder will be the required
height, as a rough approximation. To correct this, add together the two
thermometer readings, and divide the sum by 2, for their mean. From
table of corrections for temperature, take out the number under this mean.
Multiply the approximate height just found by this number.
At 70° F. pure water will boil at 1° less of temperature for an average of
about 550 feet of elevation above sea-level, up to a height of 1/2 a mile. At
the height of 1 mile, 1° of boiling temperature will correspond to about 560
feet of elevation. In the table the mean of the temperatures at the two
stations is assumed to be 32°F., at which no correction for temperature is
necessary in using the table.
1
.g _g ® .g
r^. C |T
I-2'
111!
-"oS =3^
.2 -S £'**
&"*
•§«|
llil
lift
jd
*o?
!l!l
5§ft.S
W
3*1
PQ ""*
W
**J
« -S
pi
^ 02
184°
16.79
15,221-
196
21.71
8,481
208
27.73
2,063
185
17.16
14,649
197
22.17
7,932
208.5
28.00
1,809
186
17.54
14,075
198
22.64
7,381
209
28.29
1,539
187
17.93
13,498
199
23.11
6,843
209.5°
28.56
1,290
188
18.32
12,934
200
23.59
6,304
210
28.85
1,025
389
18.72
12,367
201
24.08
5,764
210.5
29.15
754
190
19.13
11,799
202
24.58
5,225
211
29.42
512
191
19.54
11,243
203
25.08
4,691?
211.5
29.71
255
192
19.96
10,685
204
25.59
4,169
212
30.00
S.L.= 0
193
20.39
10,127
205
26.11
3,642
212.5
30.30
-261
194
20.82
9,579
206
26.64
3,115
213
30.59
-511
195
21.26
9,031
207
27.18
2,589
CORRECTIONS FOR TEMPERATURE.
Mean temp. F. in shade. 0! 10° 20° I 30° I 40a I 50° 60° 70° 180° 190° I 100M
Multiply by MS (.954 .975|.996| 1.0161 1.036 1.058 1.079|l.lOO|l.l8l|l.l48j
Moisture in the Atmosphere.— Atmospheric air always contains
a small quantity of carbonic acid (see Ventilation, p. 528) and a varying
quantity of aqueous vapor or moisture. The relative humidity of the air at
any time is the percentage of moisture contained in it as compared with the
amount it is capable of holding at the same temperature.
The degree of saturation or relative humidity of the air is determined by
the use of the dry and wet bulb thermometer. The degree of saturation for
a number of different readings of the thermometer is given in the following
table, condensed from the Hygrometric Tables of the IT. S. Weather Bureau:
RELATIVE HUMIDITY, PER CENT.
Difference between the Dry and Wet Thermometers, Deg. F.
l^to
1
2
3
4
5
G
'
8
9
to
11
12
13
14
15
16
17
18
1'J
•20
21
22
23
24
2G
28
30
ft
Relative Humidity, Saturation being 100. (Barometer = 30 ins.)
32
89
79
09
59
49
39
80
20
11
o
40
92
83
75
68
60
52
45
37
29
23
15
7
0
50
93
87
80
74
G7
61
55
49
13
38
32
27
21
1G
11
5
0
60
70
94
95
89
90
83
HG
78
81
73
7' 7'
68
72
63
G8
58
G4
53
59
18
55
43
51
39
48
34
44
30
40
2621J17
36 33 29
13
25
9
22
5
19
1
15
12
9
G
80
96
91
87
88
79
75
72
68
G4
Gl
5?
54
5047
4441
38
35
32
29
26
23
20
18
12
7
90
96
92
S9
85
81
78
71
71
68
65
Gl
58
5552
4947
44
41
39
36
34
31
29
2G
22
17
13
100
9G
93
89
8G
88
HO
73
70
.18
G5
G2
59j56
54
51
49
4644
41
39
37
35
33
28
24
21
110
120
140
97
97
97
93
94
95
90
91
92
87
88
89
S4
85
87
81
82
84
7'8
so
82
75
77
79
73
74
77
ro
75
G9
73
65
G?
7'0
62
G5
G8
60
G2
GG
5755
6058
6162
5-2
55
GO
5048
5351
58 ' 56
4G
49
54
44 42
47 45
53 51
40
43
49
38
41
47
34
38
44
30
34
41
26
31
38
484
AIR.
Weights of Air, \a.por of Water, and Saturated Mixtures
of Air and Vapor at Different Temperatures, under
tbe Ordinary Atmospheric Pressure of 29.921
inches of Mercury.
til
o
MIXTURES OP AIR SATURATED WITH VAPOR.
£
*** <D .
.2&JD
^a
52*
&£
^0
O <jj
Elastic
Force of
Weight of Cubic Foot of the
Mixture of Air and Vapor.
Weight
of
34
*2l
§?
the Air in
Mixture
,
If \
Vapor
Tempera
Fahrenh(
°3g
fbg,
151 ,
fcjoH
Elastic Fo
Inches ol
of Air and
Vapor,
Inches of
Mercury.
Weight
of the
Air, Ibs.
' Weight
of the
Vapor,
pounds.
Total
W'ght of
Mixture,
pounds.
mixed
with lib.
of Air,
pounds.
0°
.0864
.044
29.877
.0863
.000079
.086379
.00092
12
.0842
.074
29.849
.0840
.000130
.084130
.00155
22
.0824
.118
29.803
.0821
.000202
.082302
.00245
32
.0807
.181
29.740
.0802
.000304
.080504
.00379
42
.0791
.267
29.654
.0784
.000440
.078840
.00561
52
.0776
.388
29.533
.0766
.000627
077227
.00819
62
.0761 -
.556
29.365
-T0747.
.000881
! 075581 -
.01179
72*
.0747
.785
29.136
.0727 .
.001221 «
.073921-
e- .01680
82
.0733
1.092
28.829
.0706
.001667
.072267
.02361
92
.0720
1.501
28.420
.0684
.002250
.070717
.03289
102
.0707
2.036
27.885
.0659
.002997
.068897
.04547
112
.0694
2.731
27.190
.0631
.003946
.067046
.06253
122
.0682
3.621
26.300
.0599
.005142
.065042
.08584
132
.0671
4.752
25.169
.0564
.006639
.063039
.11771
142
.0660
6.165
23.756
.0524
.008473
.060873
.16170
152
.0649
7.930
21.991
.0477
.010716
.058416
.22465
162
.0638
10.099
19.822
.0423
.013415
.055715
.31713
172
.0628
12.758
17.163
.0360
.016682
.052682
.46338
182
.0618
15.960
13.961
.0288
.020536
.049336
.71300
192
.0609
19.828
10.093
.0205
.025142
.045642
1.22643
202
.0600
24.450
5.471
.0109
.030545
.041445
2.80230
212
.0591
29.921
0.000
.0000
.036820
.036820
Infinite.
The weight in Ibs. of the vapor mixed with 100 Ibs. of pure air at any
given temperature and pressure is given by the formula
62.3 X E 29.98
29.92 - E X p '
where E = elastic force of the vapor at the given temperature, in inches of
mercury; p = absolute pressure in inches of mercury, = 29.92 for ordinary
atmospheric pressure.
Specific Heat of Air at Constant Volume and at Constant
Pressure.— Volume of 1 Ib. of air at 32° F. and pressure of 14.7 Ibs. per sq
iu. = 12.387 cu. ft. = a column 1 sq. ft. area X 12,387 ft. high. Raising temper-
ature 1° F. expands it -rJ-r-z, or to 12.4122 ft. high— a rise of .02522 foot.
Work done = 2116 Ibs. per sq, ft. X .02522 = 53.37 foot-pounds, or 53.37-^-778
= .0686 heat units.
The specific heat of air at constant pressure, according to Regnault, is
0.2375; but this includes the work of expansion, or .0686 heat units; hence
the specific heat at constant volume = 0.2375 — .0686 = 0.1689.
Ratio of specific heat at constant pressure to specific heat at constant
volume = .2375 -*- .1689 = 1.406. (See Specific Heat, p. 458.)
Flow of Air through Orifices.— The theoretical velocity in feet
per second of flow of any fluid, liquid, or gas through an orifice is v =
yZgh = 8.02 1//i, in which h = the " head" or height of the fluid in feet
required to produce the pressure, of the fluid at the level of the orifice.
(For gases the formula holds good only for small differences of pressure on
the two sides of the orifice.) The quantity of flow in cubic feet per second
FLOW OJF AIE IK PIPES. 485
is equal to the product of this velocity by the area of the orifice, in square
feet, multiplied by a "coefficient of flow," which takes into account the
contraction of the vein or flowing stream, the friction of the orifice, etc.
For air flowing through an orifice or short tube, from a reservoir of the
pressure Pi into a reservoir of the pressure p2' Weisbach gives the follow*
ing values for the coefficient of flow, obtained from his experiments.
FLOW OP AlR THROUGH AN ORIFICE.
Coefficient c in formula v — c .
Diameter ) Ratio of pressures Pi-t-p? 1.05 1.09 1.43 1.65 1.89 2.15
1 centimetre, f Coefficient ................. 555 .589 .692 .724 .754 .788
Diameter f Ratio of pressures ........ 1.05 1.09 1.36 1.67 2.01 ....
2. 14 centimetres j Coefficient ................. 558 .573 .634 .678 .723 ....
FLOW OP AIR THROUGH A SHORT TUBE.
Diam. 1 cm., ? Ratio of pressures p^p? 1.05 1.10 1.30 ............
Length3cm. {Coefficient ............... . .730 .771 .830 ............
Diam. 1.414cm., | Ratio of pressures ........ 1.41 1.69 ................
Length 4.242 cm. \ Coefficient ................. 813 .822 ................
Diam 1 cm. ) Ratio of pressures ........ 1.24 1.38 1.59 1.85 2.14 .
979 -986 '965 -971 -978 —
FLIEGNKR'S EQUATION FOR FLOW OF AIR FROM A RESERVOIR THROUGH AN
ORIFICE. (Proc. Inst. C. E., Iv, 379.)
G = (3465 - 10000Z>)F
V ^;
G — the flow in kilogramme^ per second ; ptpQ — the internal and external
pressures in atmospheres of 10,000 kg. per sq. metre; D = diameter of the
orifice in metres; F = its cross-section in sq. metres; T— absolute temper-
ature, Centigrade, of the air in the reservoir. The experiments were made
with six orifices from 3.17 to 11.36 mm. diameter, in brass plates 12 mm. thick,
drilled cylindrically for about y% mm., and conically enlarged towards the
outside at an angle of 45°.
Clark (Rules, Tables, and Data, p. 891) gives, for the velocity of flow of air
through an orifice due to small differences of pressure,
or, simplified,
V- 352 C
A/(l
In which V— velocity in feet per second ; 2g = 64.4; h = height of the column
of water in inches, measuring the difference of pressure; t = the tempera-
ture Fahr.; and p = barometric pressure in inches of mercury. 773.2 is the
volume of air at 32° under a pressure of 29.92 inches of mercury when that of
an equal weight of water is taken as 1.
For 62° F., the formula becomes V = 363C 1/s and if p = 29.92 inchesF =
66.35C \/h
The coefficient of efflux C, according to Weisbach, is:
For conoidal mouthpiece, of form of the contracted vein,
with pressures of from .23 to 1.1 atmospheres ....... ..... C = .97 to .99
Circular orifices in thin plates .................................. C = .56 to .79
Short cylindrical mouthpieces ................................ C = .81 to .84
The same rounded at the inner end ........... „ ............... C = .92 to .93
Conical converging mouthpieces .............................. C — .90 to .99
Flour of Air in Pipes.— Hawksley (Proc. Inst. C. E., xxxiii, 55)
states that his formula for flow of water in pipes v = 48 A/ —=— may also
be employed for flow of air. In this case II = height in feet of a column of
ftir required to produce the pressure causing the flow, or the loss of head
48S
AIR.
for a given flow; v = velocity in feet per second, D = diameter in feet, L =»
length in feet.
If the head is expressed in inches of water, h, the air being taken at
62° F., its weight per cubic foot at atmospheric pressure = .0761 Ib. Then
= 68-3/i- Ud = diameter in inches, D = , and the formula
12
becomes v = 114.5 A/ y , in which h = inches of water column, d = diam-
eter in inches and L — length in feet; h •
The quantity in cubic feet per second is
Lv* m
13110cT
Lv1*
IStlO/i*
The horse-power required to drive air through a pipe is the volume Q in
cubic feet per second multiplied by the pressure in pounds per square foot
and divided by 550. Pressure in pounds per square foot = P = inches of
water column X 5.196, whence horse-power =
HP..
QP Qh Q*L
550 ~~ 105.9 ~ 41.3d5*
If the head or pressure causing the flow is expressed in pounds per square
inch = p, then ft = 27.71p, and the above formulas become
Lv*
Lv*
HP.
.2618Qp = .02421^.
oliiine of Air Transmitted in Cubic Feet per Minute in
Pipes of Various Diameters.
7S54
Formula Q = 'Jd1v x 60.
Actual Diameter of Pipe in Inches.
8 oa
1
2
3
4
5
6
8
10
12
16
20
24
1 .327
1.31
2.95
5.24
8.18
11.78
20.94
32.73
47.12
83.77
130.9
188.5
2
.655
2.62
5.89
10.47
16.36
23.56
4189
65.45
94.25
167.5
261.8
377
3
.982
3.93
8.84
15.7
24.5
35.3
62.8
98.2
141.4
251.3
392.7
565.5
4
1.31
5,24
H.78
20.9
32.7
47.1
83.8
131
188
335
523
754
5
1.64
6.54
14.7
26.2
41
59
104
163
235
419
654
942
6
1.96
7.85
17.7
31.4
49.1
70.7
1°5
196
283
502
785
1131
7
2.29
9.16
20.6
36.6
57.2
82.4
146
229
330
586
916
1319
8
2.62
105
23.5
41.9
65.4
94
167
262
877
670
1047
1508
9
2.95
1178
26.5
47
73
106
188
294
4?4
754
1178
1696
10
3.27
13.1
29.4
52
82
118
209
327
471
838
1309
1885
12
3.93
15.7
35.3
63
98
141
251
393
565
1005
1571
2262
15
4.91
19.6
44.2
78
122
177
314
491
707
1256
1963
2827
18
5.89
23.5
53
94
147
212
377
589
848
1508
2356
3393
20
6.54
26.2
59
105
164
235
419
654
942
1675
2618
3770
24
7.85
31.4
71
125
196
283
502
785
1131
2010
3141
4524
25
8.18
32.7
73
131
204
294
523
818
1178
2094
3272
4712
28
9.16
36.6
82
146
229
330
586
916
1319
2346
3665
5278
30
9.8
39.3
88
157
245
353
628
982
1414
2513
3927
5655
tfLOW OF AIR IK PIPES. 487
In Hawksley's formula and its derivatives the numerical coefficients are
constant. It is scarcely possible, however, that they can be accurate except
within a limited range of conditions. In the case of water it is found that
the coefficient of friction, on which the loss of head depends, varies with the
length and diameter of the pipe, and with the velocity, as well as with the
condition of the interior surface. In the case of air and other gases we
have, in addition, the decrease in density and consequent increase in volume
and in velocity due to the progressive loss of head from one end of the pipe
to the other.
Clark states that according to the experiments of D'Aubuisson and those of
E Sardinian commission on the resistance of air through long conduits or
pipes, the diminution of pressure is very nearly directly as the length, and
as the square of the velocity and inversely as the diameter. The resistance
is not varied by the density.
If these statements are corr.ect, then the formulas h = —^ and h = ^-^'
cd c'd5
and their derivatives are correct in form, and they may be used when the
numerical coefficients c and c' are obtained by experiment.
If we take the forms of the above formulae as correct, and let C be a vari-
able coefficient, depending upon the length, diameter, and condition of sur-
face of the pipe, and possibly also upon the velocity, the temperature and
the density, to be determined by future experiments, then for h = head in
inches of water, d = diameter in inches, L = length in feet, v = velocity in
feet per second, and Q = quantity in cubic feet per second:
C2<*6
For difference or loss of pressure p in pounds per square inch,
h = 27.71p Vh =« 5.264 \fp\
(For other formulae for flow of air, see Mine Ventilation.)
Loss of Pressure in Ounces per Square Iiicli.— B. F. Sturte.
vant Company uses the following formulae :
Lv* /20000dpi , _ Lv*
Pl - 2500M ; * - Y L " 25000Pl;
In which pt = loss of pressure in ounces per square inch, y = velocity of air
in feet per second, and L = length of pipe in feet. If p is taken in pounds
per square inch, these formulae reduce to
,0000025Z,v2
. 0000025—; v = 632.5
/dpi
5 J -^\
I v*
These are deduced from the common formula (Weisbach's), p = /^ =-, in
which /= .0001608.
The following table is condensed from one given in the catalogue of B. F.
Sturtevant Company.
Loss of pressure in pipes 100 feet long, in ounces per square inch. For
any other length, the loss is proportional to the length.
488
AIR.
3.3
Diameter of Pipe in Inches.
® t-,
1
2
3
4
5
6
7
8
9
10
11
12
ga
Loss of Pressure in Ounces.
600
.400
.200
.133
.100
.080
.067
.057
.050
.044
.040
.036
.033
1200
1.600
.800
.533
.400
.320
.267
.229
.200
.178
.160
.145
.133
1800
3.600
1.800
1.200
.900
.720
.600
.514
.450
.400
.360
,327
.300
2400
6.400
3.200
2.133
1.600
1.280
1.067
.914
.800
.711
.640
.582
.533
3000
10.
5.
3.333
2.5
2.
1.667
1.429
1.250
1.111
1.000
.909
.833
3600
14.4
7.2
4.8
3.6
2.88
S.4
2.057
1.8
1.6
1.44
1.309
1.200
4300
9.8
6.553
4.9
3.92
3.267
2.8
2.45
2.178
1.96
1.782
1.633
4800
12.8
8.533
6.4
5.12
4.267
3.657
3.2
2.844
2.56
2.327
2.133
6000
20.
13.333
10.0
8.0
6.667
5.714
5.0
4.444
4.0
3.636
3.333
Diameter of Pipe in Inches.
14
16
18
20
22
24
28:
32
36
40
44
48
600
Loss of Pressure in Ounces.
.029
.026
.022
.020
.018
.017
.014
.012
.011
.010
.009
.008
1200
.114
.100
.089
.080
.073
.067
.057
.050
.044
.040
.036
.033
1800
.257
.225
.200
.180
.164
.156
.129
.112
.100
.090
.082
.075
2400
.457
.400
.356
.320
.291
.267
.239
.200
.178
.160
.145
.133
3600
1.029
.900
.800
.720
.655
.600
.514
.450
.400
.360
.327
.300
4200
1.400
1.225
1.089
.980
.891
.817
.700
.612
.544
.490
.445
.408
4800
1.829
1.600
1.422
1.280
1.164
1.067
.914
.800
.711
640
.582
.533
6000
2.857
2.500
2.222
2.000
1.818
1.667
1.429
1.250
1.111
1.000
.909
.833
Effect of Bends in Pipes. (Norwalk Iron Works Co.)
Radius of elbow, in diameter of pipe = 5 3 2 1^ 1*4 1 H M
Equivalent Igths. of straight pipe, diams 7.85 8.24 9.03 10.36 12.72 17.51 35.09 121.2
Compressed-air Transmission. (Frank Richards, Am. Mach.^
March 8, 1894 )— The volume of free air transmitted may be assumed to be
directly as the number of atmospheres to which the air is compressed.
Thus, if the air transmitted be at 75 pounds gauge-pressure, or six atmos-
pheres, the volume of free air will be six times the amount given in the
table (page 486). It is generally considered that for economical transmission
the velocity in main pipes should not exceed 20 feet per second. In the
smaller distributing pipes the velocity should be decidedly less than this.
The loss of power in the transmission of compressed air in general is not
a serious one, or at all to be compared with the losses of power in the opera-
tion of compression and in the re-expansion or final application of the air.
The formulas for loss by friction are all unsatisfactory. The statements
of observed facts in this line are in a more or less chaotic state, and self-
evidently unreliable.
A statement of the friction of air flowing through a pipe involves at least
all the following factors: Unit of time, volume of air, pressure of air, diam-
eter of pipe, length of pipe, and the difference of pressure at the ends of
the pipe or the head required to maintain the flow. Neither of these factors
can be allowed its independent and absolute value, but is subject to modifi-
cations in deference to its associates. The flow of air being assumed to be
uniform at the entrance to the pipe, the volume and flow are not uniform
after that. The air is constantly losing some of its pressure and its volume
is constantly increasing. The velocity of flow is therefore also somewhat
accelerated continually. This also modifies the use of the length of the
pipe as a constant factor.
Then, besides the fluctuating values of these factors, there is the condition
of the pipe .itself. The actual diameter of the pipe, especially in the
smaller sizes, is different from the nominal diameter. The pipe may be
straight, or it may be crooked and have numerous elbows. Mr. Richards
considers one elbow as equivalent to a length of pipe.
FLOW OF COMPEESSED AIR
PIPES.
489
Formulae for Flow of Compressed Air in Pipes.— The for-
mulse on pages 486 and 487 are for air at or near atmospheric pressure. For
compressed air the density has to be taken into account. A common
formula for the flow of air, gas, or steam in pipes is
in which Q = volume in cubic feet per minute, p = difference of pressure
in Ibs. per sq. in. causing the flow, d — diameter of pipe in in., L = length
of pipe in ft., w = density of the entering gas or steam in Ibs. per cu. ft.,
and c = a coefficient found by experiment. Mr. F. A. Halsey in calculating
a table for the Rand Drill Co.'s Catalogue takes the value of c at 58, basing
it upon the experiments made by order of the Italian government prelim-
inary to boring the Mt. Cenis tunnel. These experiments were made with
pipes of 3281 feet in length and of approximately 4, 8, and 14 in. diameter.
The volumes of compressed air passed ranged between 16.64 and 1200 cu. ft.
per minute. The value of c is quite constant throughout the range and
shows little disposition to change with the varying diameter of the pipe. It
is of course probable, says Mr. Halsey, that c would be smaller if determined
for smaller sizes of pipe, but to offset that the actual sizes of small com-
mercial pipe are considerably larger than the nominal sizes, and as these
calculations are commonly made for the nominal diameters it is probable
that in those small sizes the loss would really be less than shown by the
table. The formula is of course strictly applicable to fluids which do not
change their density, but within the change of density admissible in the
transmission of air for power purposes it is probable that the errors intro-
duced by this change are less than those due to errors of observation in the
present state of knowledge of the subject. Mr. Halsey's table is condensed
below.
Diameter of Pipe,
in inches.
Cubic feet of free air compressed to a gauge-pressure of 80 Ibs.
and passing through the pipe each minute.
50
100
200
400
800
1000
1500
2000
3000
4000
5000
Loss of pressure in Ibs. per square inch for each 1000 ft.
of straight pipe.
1*4
P
P
y
5
6
8
10
12
14
3.61
1.45
0.20
0.12
5.8
1.05
0.35
0.14
4.30
1.41
0.57
0.26
0.14
5.80
2.28
1.05
0.54
0.18
4.16
2.12
0.68
0.28
0.07
6.4
3.27
1.08
0.43
0.10
7.60
2.43
1.00
0.24
0.08
4.32
1.75
0.42
0.14
9.6
3.91
0.93
0.30
0.12
7.10
1.68
0.55
0.22
0.10
10.7
2.59
0.84
0.34
0.16
To apply the formula given above to air of different pressures it may be
given other forms, as follows:
Let Q = the volume in cubic feet per minute of the compressed air; Q} =
the volume before compression, or " free air," both being taken at mean
atmospheric temperature of 62° F.; w^ = weight per cubic foot of Ql =
0.0761 lb.; r = atmospheres, or ratio of absolute pressures, = (gauge-pres-
sure _|_ 14.7) _«_ 14.7. w — weight per cu. ft. of Q; p = difference of pressure,
in Ibs. per sq. in., causing the flow; d = diam. of pipe iu in.; L = length of
pipe in ft.; c = experimental constant. Then
490
AIR.
c«pr
The value of e according to the Mt. Cenis experiments is about 58 for pipes
water in pipes, ranging from 45.3 for 1 in. diameter to 63.2 for 24 in., are given
under " Flow of Steam,1' p. 671. For approximate calculations the value 60
may be used for all pipes of 4 in. diameter and upwards. Using c ~ GO, the
above formulae become
= 0.1161
p = 0.00002114^— = 0.00002114^^-
5 s
Loss of Pressure In Compressed Air Pipe-main, at
St. Gothard Tunnel.
(E. Stockalper.)
§
l'|«| _
p'^
y
ia
•3
Observed Pressures.
1
g
a; ? Q ^fr
<U CD M
o 5
«C O
'> °
<M
£ "tJ t-3
cj
0
a
0)
a
liljc?
||fl
lill
|!
B:
D "S
ts&
® ^
Loss of
1"V
C
i
1 1 -g § 3
flj C 5)
13 ^^
4-2 P<
?s
^'o
Pressure.
Q
g
S 8s
c £g
"SS
3s
I'Sbft
«-«
» II
<3
"0*0 t>"c3 w
3*0 e3
« 8^-
t>"^
^«H
2-° S.
2 **
"rt ^
H
^
^
s
^
^
PH
£
f>
Ibs.
per
No,
in.
cu.ft.
cu.ft.
den.
Ibs.
feet.
at.
at.
sq.m.
*
. <
7,87
1 o-» n~* \
6.534
.00650
2.609
19.32
5.60
5.24
5.292
6.4
7'5.2
M
5.91
7'. 063
.00603
2669
37.14
5.24
5.00
3.528
4.6
63.9
7.87
5 91
[ 22.002 \
5.509
5 863
.00514
00482
1.776
1 776
16.30
4.35
4 13
4.13
3.234
5.1
70.7
i
7.87
5.91
1 18. 364]
5.262
5.580
.00449
.00423
1.483
1.483
15.58
29.34
3.84
3.65
3.65
3.54
2 793
1.617
5.0
3.0
67.6
62.8
The length of the pipe 7.87 in diameter was 15,092 ft., and of the smaller
pipe 1712.6 ft. The mean temperature of the air in the large pipe was 70° F.
and in the small pipe 80g F.
MEASUREMENT OF VELOCITY OF AIR.
491
Equation of Pipes.— It is frequently desired to know what number
of pipes of a given size are equal in carrying capacity to one pipe of a larger
size. At the same velocity of flow the volume delivered by ttvo pipes of
different sizes is proportional to the squares of their diameters; thus, one
4-inch pipe will deliver the same volume as four 2-iuch pipes. With the same
head, however, the velocity is less in the smaller pipe, and the volume de-
livered varies about as the square root of the fifth power (i.e., as the 2.5
power). The -following table has been calculated on this basis. The figures
opposite the intersection of any two sizes is the number of the smaller-sized
pipes required to equal one of the larger. Thus, one 4-inch pipe is equal to
5.72-inch pipes.
oj a
5"*
1
2
3
4
5
6
7
8
9
10
12
14
16
18
20
24
2
5.7
1
3
15.6
2.8
1
4
32
5.7
2.1
1
5
55.9
9.9
3.6
L5
1
6
88.2
15.6
5.7
2.8
1.6
1
7
130
22.9
8 3
4.1
2.3
1.5
1
8
181
32
11.7
5.7
3.2
2.1
1.4
1
9
243
43.
15. C
7.6
4.3
2.8
1.9
1.3
1
10
316
55.9
20.3
9.9
5.7
3.6
2.4
1.7
1.3
1
11
401
70.9
25.7
12.5
7.2
4.6
3.1
2.2
1.7
1.3
12
499
88.2
32
15.6
8.9
5.7
3.8
2.8
2.1
1.6
1
13
009
108
39.1
19
10.9
7.1
4.7
3.4
2.5
1.9
1.2
14
733
130
47
22.9
13.1
8.3
5.7
4.1
3.0
2.3
1.5
1
15
871
154
55.9
27.2
15.6
9.9
6.7
4.8
3.6
2.8
1.7
1.2
16
181
65.7
32
18.3
11.7
7.9
5.7
4.2
3.2
2.1
1.4
1
17
211
76.4
37.2
21.3
13.5
9.2
6.6
4.9
3.8
2.4
1.6
1.2
18
243
88.2
43
24.6
15.6
10.6
7.6
5.7
4.3
2.8
1.9
1.3
1
19
278
101
49.1
28.1
17.8
12.1
8.7
6.5
5
3.2
2.1
1.5
1.1
20
316
115
55.9
32
20.3
13.8
9.9
7.4
5.7
3.6
2.4
1.7
1.3
1
22
401
146
70.9
40.6
25.7
17.5
12.5
9.3
7.2
4.6
3.1
2.2
1.7
1.3
24
499
181
88.2
50.5
32
21.8
15.6
11.6
8.9
5.7
3.8
2.8
2.1
1.6
1
26
609
221
108
61.7
39.1
26.6
19.
14.2
10.9
7.1
4.7
3.4
2.5
1.9
l.fc
28
733
266
130
74.2
47
32
22.9
17.1
13.1
8.3
5.7
4.1
3
2.3
1.5
30
871
316
154
88.2
55.9
38
27.2
20.3
15.6
9.9
6.7
4.8
3.6
2.8
1.7
36
499
243
130
88.2
60
43
32
24.6
15.6
10.6
7.6
5.7
4.3
2.8
42
733
357
205
130
88.2
63.2
47
36.2
19
15.6
11.2
8.3
6.4
4.1
48
499
286
181
123
88.2
62.7.
50.5
32
21.8
15.6
11.6
8.9
5.7
54
070 '
383
243
165
118
88.2
67.8
43
23.2
20.9
15.6
12
7.6
00
871
499
316
215
154
115
88.2
55.9
38
27.2
20.8
15.6
9.9
Measurement of tlie Telocity of Air in Pipes by an Ane-
mometer,— Tests were made by B. Donkin, Jr. (List, Civil Engrs. 1892),
to compare the velocity of air in pi'pes from 8 in. to 24 in. diam., as shown by
an anemometer 2% in. diam. with the true velocity as measured by the time
of descent of a gas-holder holding 1622 cubic feet. A table of the results
with discussion is given in Entfg News, Dec. 22, 1892. In pipes from 8 in. to 20
in. diam. with air velocities of from 140 to 690 feet per minute the anemome-
ter showed errors varying from 14.5$ fast to 10# slow. With a 24-inch pipe
and a velocity of 73 ft! per minute, the anemometer gave from 44 to 63 feet,
or from 13.6 to 39.6jg slow. The practical conclusion drawn from these ex-
periments is that anemometers for the measurement of velocities of air in
pipes of these diameters should be used with great caution. The percentage
of error is not constant, and varies considerably with the diameter of the
pipes and the speeds of air. The use of a baffle, consisting of a perforated
plate, which tended to equalize the velocity in the centre and at the sides in
some cases diminished the error.
492
AIK.
The impossibility of measuring the true quantity of air by an anemometer
held stationary in one position is shown by the following figures, given by
Wm. Daniel (Proc. Inst. M. E., 1875), of the velocities 9f air found at different
points in the cross-sections of two different airways in a mine.
DIFFERENCES OF ANEMOMETER READINGS IN AIRWAYS.
8 ft. square. 5 X 8 ft.
1712
1795
1859
1329
1622
1685
1782
1091
1477
1344
1524
1049
1262
1356
1293
1333
Average 1469.
Average 1132.
WIND.
Force of tlie "Wind.— Smeaton in 1759 published a table of the
velocity and pressure of wind, as follows:
VELOCITY AND FORCE OF WIND, IN POUNDS PER SQUARE INCH.
03 ^
S|
8, --0
Common Appella-
tion of the
CO Q
fi
33 _ «)
Common Appella-
tion of the
J2j§
® 8
|^o
Force of Wind.
:SW
9 o>
0 S*p,
Force of Wind.
3
fa w
fa
s
faw
fa
i
1.47
0.005
j Hardly percepti-
( ble.
18
20
26.4
29.34
1.55
1.968
vVery brisk.
2
3
4
2.93
4.4
5.87
0.020
0.044
0.079
i Just perceptible.
25
30
35
36.67
44.01
51.34
3.075
4.429
6.027
(
j- High wind.
5
6
7
7.33
8.8
10.25
0.123
0.177
0.241
Gentle pleasant
wind.
40
45
50
58.68
66.01
73.35
7.873
9.963
12.30
}- Very high storm.
8
11.75
0.315
55
80.7
14.9
j
9
13.2
0.400
60
88.02
17.71
10
12
14.67
17.6
0.492
0.708
Pleasant brisk
66
70
95.4
102.5
20.85
24.1
>• Great Storm.
14
15
20.5
22.00
0.964
1.107
gale.
75
80
110.
117.36
27.7
31.49
I Hurricane.
16
23.45
1.25
100
146.67
49.2
j Immense hurri-
| cane.
The pressures per square foot in the above table correspond to the
formula P = 0.005F', in which V is the velocity in miles per hour. Eng^g
Neivs, Feb. 9, 1893, says that the formula was never well established, and
has floated chiefly on Smeaton's name and for lack of a better. It was put
forward only for surfaces for use in windmill practice. The trend of
modern evidence is that it is approximately correct only for such surfaces,
and that for large solid bodies it often gives greatly too large results,
vations by others are thus compared with Smeaton's formula:
Observa
Old Smeaton formula.
,.P =
As determined by Prof . Martin P= .004F2
" Whipple and Dines P= .0029^
WIND. 493
At 60 miles per hour these formulas give for the pressure per square foot,
18, 14.4 and 10.44 Ibs., respectively, the pressure varying by all of them as
the square of the velocity. Lieut. Crosby's experiments (Eng^g, June 13,
1890), claiming to prove that P = fV instead of P = /F2, are discredited.
A. R. Wolff (The Windmill as a Prime Mover, p. 9) gives as the theoretical
pressure per sq. ft. of surface, P = — — , in which d = density of air in pounds
per cu. ft. = ' — • — 2~i — - ; p being the barometric pressure per square
foot at any level, and temperature of 32° F., t any absolute temperature,
Q = volume of air carried along per square foot in one second, v = velocity
of the wind in feet per sec., g = 32.16. Since Q = v cu. ft. per sec., P= — .
Multiplying this by a coefficient 0.93 found by experiment, and substituting
the above value of d, he obtains P = — - ^— ^ - — - >, and when p
* XJ"lb - .018743
s= 2116.5 Ibs. per sq. ft. or average atmospheric pressure at the sea-level,
36 8929
» an expression in which the pressure is shown to vary
with the temperature; and he gives a table showing the relation between
velocity and pressure for temperatures from 0° to 100° F., and velocities
from 1 to 80 miles per hour. For a temperature of 45° F. the pressures agree
with those in Smeaton's table, for 0° F. they are about 10 per cent greater,
and for 100° 10 per cent less. Prof. H. Allen Hazen, Eng^g News, July 5,
1890, says that experiments with whirling arms, by exposing plates to direct
wind, and on locomotives with velocities running up to 40 miles per hour,
have invariably shown the resistance to vary with F2. In the formula
P = .005SF2, in which P — pressure in pounds, <8 = surface in square feet,
V = velocity in miles per hour, the doubtful question is that regarding
the accuracy of the first two factors in the second member of this equation.
The first factor has been variously determined from .003 to .005 [it has been
determined as low as .0014.— Ed. Eng'g News].
The second factor has been found in some experiments with very short
whirling arms and low velocities to vary with the perimeter of the plate,
but this entirely disappears with longer arms or straight line motion, and
the only question now to be determined is the value of the coefficient. Per-
haps some of the best experiments for determining this value were tried in
France in 1886 by carrying flat boards on trains. The resulting formula in
this case was, for 44.5 miles per hour, p = .00535SF*.
Mr. Crosby's whirling experiments were made with an arm 5.5 ft. long.
It is certain that most serious effects from centrifugal action would be set
up by using such a short arm, and nothing satisfactory can be learned with
arms less than 20 or 30 ft. long at velocities above 5 miles per hour.
Prof. Kernot, of Melbourne (Engineering Record, Feb. 20, 1894), states that
experiments at the Forth Bridge showed that the average pressure on sur-
faces as large as railway carriages, houses, or bridges never exceeded two
thirds of that upon small surfaces of one or two square feet, such as have
been used at observatories, and also that an inertia effect, which is frequently
overlooked, may cause some forms of anemometer to give false results
enormously exceeding the correct indication. Experiments of Mr. O. T.
Crosby showed that the pressure varied directly as the velocity, whereas all
the early investigators, from the time of Smeaton onwards, made it vary as
the square of the velocity. Experiments made by Prof. Kernot at speeds
varying from 2 to 15 miles per hour agreed with the earlier authorities, and
tended to negative Crosby's results. The pressure upon one side of a cube,
or of a block proportioned like an ordinary carriage, was found to be .9 of
that upon a thin plate of the same area. The same result was obtained for
a square tower. A square pyramid, whose height was three times its base,
experienced .8 of the pressure upon a thin plate equal to one of its sides, but
if an angle was turned to the wind the pressure was increased by fully 20#.
A bridge consisting of two plate-girders connected by a deck at the top was
found to experience .9 of the pressure on a thin plate equal in size to one
girder, when the distance between the girders was equal to their depth, and
this was increased by one fifth when the distance between the girders was
494 AtfL
double the depth. A lattice-work in which the area of the openings was 5o%
of the whole area experienced a pressure of 80# of that upon a plate of the
same area. The pressure upon cylinders and cones was proved to be equal
to half that upon the diametral planes, and that upon an octagonal prism to
be 20# greater than upon the circumscribing cylinder. A sphere was sub-
ject to a pressure of .36 of that upon a thin circular plate of equal diameter.
A hemispherical cup gave the same result as the sphere; when its concavity
was turned to the wind the pressure was 1.15 of that on a flat plate of equal
diameter. When a plane surface parallel to the direction of the wind was
brought nearly into contact with a cylinder or sphere, the pressure on the
latter bodies was augmented by about 20#, owing to the lateral escape of the
air being checked. Thus it is possible for the security of a tower or chimney
to be impaired by the erection of a building nearly touching it on one side.
Pressures of Wind Registered in Storms.— Mr. Frizell has
examined the published records of Greenwich Observatory from 1849 to 1869,
and reports that the highest pressure of wind he finds recorded is 41 Ibs.
per sq. ft., and there are numerous instances in which it was between 30 and
40 Ibs. per sq. ft. Prof. Henry says that on Mount Washington, N. H., a ve-
locity of 150 miles per hour has been observed, and at New York City 60
miles an hour, and that the highest winds observed in 1870 were of 72 and 63
miles per hour, respectively.
Lieut. Dun woody, U. S. A., says, in substance, that the New England coast
is exposed to storms which produce a pressure of 50 Ibs. per sq. ft Engi-
neering News, Aug. 20, 1880.
WINDMILLS.
Power and Efficiency of Windmills.— Rankine, S. EM p. 215,
gives the following: Let Q = volume of air which acts on the sail, or part
of a sail, in cubic feet per second, v = velocity of the wind in feet per
second, s = sectional area of the cylinder, or annular cylinder of wind,
through which the sail, or part of the sail, sweeps in one revolution, c = a
coefficient to be found by experience; then Q — cvs. Rankine, from experi-
mental data given by Smeaton, and taking c to include an allowance for
friction, gives for a wheel with four sails, proportioned in the best manner,
c = 0.75. Let A — weather angle of the sail at any distance from the axis,
i.e., the angle the portion of the sail considered makes with its plane of
revolution. This angle gradually diminishes from the inner end of the sail
to the tip; u = the velocity of the same portion of the sail, and E = the effi-
ciency. The efficiency is the ratio of the useful work performed to whole
energy of the stream of wind acting on the surface s of the wheel, which
energy is -^Lt D being the weight of a cubic foot of air. Rankine's formula
for efficiency is
29
in which c = 0.75 and / is a coefficient of friction found from Smeaton's
data = 0.016. Rankine gives the following from Smeaton's data:
A = weather-angle .................... = 7° 13° 19*
F-4-v = ratio of speed of greatest effi-
ciency, for a given weather-
angle, to that of the wind ..... =2.63 1.86 1.41
E = efficiency ....................... =0.24 0.29 0.31
Rankine gives the following as the best values for the angle of weather at
different distances from the axis:
Distance in sixths of total radius... 1 23456
Weatherangle ................. ... 18* 19° 18° 16° 12^° 7°
but sin
istence m"his time. " Wolff says that they " ca'nnot in the nature of things
be the most desirable angles." Mathematical considerations, he says, con-
clusively show that the angle of impulse depends on the relative velocity of
each point of the sail and the wind, the angle gixnying larger as the ratio be-
comes greater. Smea tort's angles do not fulfil this condition. Wolff devel-
WINDMILLS.
495
ops a theoretical formula for the best angle of weather, and from it
calculates a table for different relative velocities of the blades (at a distance
of one seventh of the total length from the centre of the shaft) and the wind,
from which the following is condensed:
Ratio of the
Speed of Blade
at 1/7 of Radius
to Velocity of
Wind.
Distance from the axis of the wheel in sevenths of radius.
1
2
3
4
5
6
7
Best angles of weather.
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
42° 9'
40 44
39 21
37 59
36 39
35 21
34 6
32 53
31 43
39° 21'
36 39
34 6
36 43
29 31
27 30
25 40
24 0
22 30
36° 39'
32 53
29 31
26 34
24 0
21 48
19 54
18 16
16 51
34* 6'
29 31
25 40
22 30
19 54
17 46
16 0
14 32
13 17
31° 43'
26 34
22 30
19 20
16 51
14 52
13 17
11 59
10 54
29° 31'
24 0
19 54
16 51
14 32
12 44
11 19
10 10
9 13
27° 30'
21 48
17 46
14 52
12 44
11 6
9 50
8 48
7 58
The effective power of a windmill, as Smeaton ascertained by experiment,
varies as s, the sectional area of the acting stream of wind; that is, for simi-
lar wheels, as the squares of the radii.
The value 0.75, assigned to the multiplier c in the formula Q = cvs, is
founded on the fact, ascertained by Smeaton, that the effective power of a
windmill with sails of the best form, and about 15^ ft. radius, with a breeze
of 13 ft. per second, is about 1 horse-power. In the computations founded
on that fact, the mean angle of weather is made — 13°. The efficiency of
this wheel, according to the formula and table given, is 0.29, at its best
speed, when the tips of the sails move at a velocity of 2.6 times that of the
wind.
Merivale (Notes and Formulae for Mining Students), using Smeaton's co-
efficient of efficiency, 0.29, gives the following:
U = units of work in foot-lbs. per sec.;
W — weight, in pounds, of the cylinder of wind passing the sails each
second, the diameter of the cylinder being equal to the diameter
of the sails;
V = velocity of wind in feet per second;
H.P. = effective horse-power;
_ TTFa TT p _ 0.29 TTF*
U~ 64 ' ~ 64X550'
A. R. Wolff, in an article in the American Engineer, gives the following
Jsee also his treatise on Windmills):
Let c = velocity of wind in feet per second;
n = number of revolutions of the windmill per minute;
&o» &i» &2> bx be the breadth of the sail or blade at distances 10, Zx, /2,
la, and Z, respectively, from the axis of the shaft;
10 = distance from axis of shaft to beginning of sail or blade proper;
I = distance from axis of shaft to extremity of sail proper;
v0, Vi, v2, v3, vx — the velocity of the sail in feet per second at dis-
tances 10, In /2, I, respectively, from the axis of the shaft;
«0, aj, aa» «s> ax — tne anSles of impulse for maximum effect at dis-
tances 10, Zx, Z2. Z3, I respectively from the axis of the shaft;
a = the angle of impulse when the sails or blocks are plane surfaces,
so that there is but one angle to be considered;
N = number of sails or blades of windmill;
K = .93.
d = density of wind (weight of a cubic foot of air at average tempera^
ture and barometric pressure where mill is erected);
W '= weight of wind-wheel in pounds;
/ = coefficient of friction of shaft and bearings;
D = diameter of bearing of windmill in feet.
496
AIR.
The effective horse-power of a windmill with plane sails will equal
a _ «g
N c
(sin g -- cos «)
The effective horse-power of a windmill of shape of sail for maximum
effect equals
^^— p^V sin,
fW X .05236?tP
.
6. . .
. -1
sin 3 ax
-&<r 1 -
550
The mean value of quantities in brackets is to be found according to
Simpson's rule. Dividing I into 7 parts, finding the angles and breadths
corresponding to these divisions by substituting them in quantities within
brackets will be found satisfactory. Comparison of these formulae with the
only fairly reliable experiments in windmills (Coulomb's) showed a close
agreement of results.
Approximate formulae of simpler form for windmills of present construc-
tion can be based upon the above, substituting actual average values for a,
c, d, and e, but since improvement in the present angles is possible, it is
better to give the formulae in their general and accurate form.
Wolff gives the following table based on the practice of an American
manufacturer. Since its preparation, he says, over 1500 windmills have been
sold on its guaranty (1885), and in all cases the results obtained did not vary
sufficiently from those presented to cause any complaint. The actual re-
sults obtained are in close agreement with those obtained by theoretical
analysis of the impulse of wind upon windmill blades.
Capacity of the Windmill.
~
a
il
!•
Gallons of Water raised per Minute to
an Elevation of—
11
Hi
0
**
... jr
II
||
0 3*->
• .2
o3
0 P4
.1 «*
-13 53
!oo!a>£$ ,
a
M
'§
II
5^
73
>
25
feet.
50
feet.
75
feet.
100
feet.
150
feet.
200
feet.
!«f Iff!
0
>
tf
H^ <~**
wheel
gi/ £+
16
70 to 75
6.162
3016
004
8
10
16
60 to 65
19.179
9 563
6 638
4.750
0 12
8
12
16
55 to 60
33.941
17.952
11.851
8.485
5.680
0.21
8
14
16
50 to 55
45.139
22.569
15.304
11.246
7.807
4998
0.28
8
16
16
45 to 50
64600
31.654
19.542
16.150
9.771
8.075
0.41
8
18
16
40 to 45
97.682
52.165
32.513
24.421
17.485
12.211
0.61
8
20
16
35 to 40
124.950
63.750
40.800
31.248
19.284
15.938
0.78
8
25 '
16
30to35212.H81
106.964
71.604
49.725
37.349
26.741
1.34
8
These windmills are made in regular sizes, as high as sixty feet diameter of
wheel; but the experience with the larger cla?s of mills is too limited to
enable the presentation of precise data as to their performance.
If the wind can be relied upon in exceptional localities to average a higher
velocity for eight hours a day than that stated in the above table, the per-
formance or horse-power of the mill will be increased, and can be obtained
by multiplying the figures in the table by the ratio of the cube of the higher
average velocity of wind to the cube of the velocity above recorded
He also gives the following table showing the economy of the windmill.
All the items of expense, including both interest and repairs, are reduced to
the hour by dividing the costs per annum by 365 X 8 = 2920; the interest,
WINDMILLS.
497
etc., for the twenty -four hours being charged to the eight hours of actual
work. By multiplying the figures in the 5th column by 584, the first cost of
the windmill, in dollars, is obtained.
Economy of the "Windmill.
|
3T3
to
£3
Expense of Actual Useful Power
f .
gjt
Developed, in cents, per hour.
• p.
Designation
of Mill.
ons of Water i
25 ft. per hour
ivalent Actual
•se-power deve
rage Number
)urs per Day d
lich this Quan
11 be raised.
Interest on
rst Cost (First
st, including
st of Wind-
11, Pump, and
wer, 5# per
num).
Repairs and
preciation (5$
First Cost per
nnm).
Attendance.
O
If
g 1 fl
£3
=>o
^ *T< to? ">
i« s* iS iS s cS ^
b
{_,
3
Q.O O
1
<
£
£ftl
£
i
e
£**
8^3 ft. wheel
370
0.04
8
0.25
0.25
0.06
0.04
0.60
15.0
10 "
1151
0.12
8
0.30
O.30
0.06
0.04
0.70
5.8
12 "
2036
0.21
8
0.36
0.36
006
004
0.82
3.9
14 "
2708
0.28
8
0.75
0.75
0.06
0.07
1.63
5.8
16 "
3876
0.41
8
1.15
1.15
006
007
243
5.9
18 "
5861
0.61
8
1.35
1.35
0.06
0,07
2.83
4.6
20 "
7497
0.79
8
1.70
1.70
0.06
0.10
3.56
4.5
25 «'
12743
1.34
8
2.05
2.05
0.06
0.10
4.26
3.2
Lieut. I. N. Lewis (Eng'g Mag., Dec. 1894) gives a table of results of ex-
periments with wooden wheels, from which the following is taken :
Velocity of Wind, miles per hour.
uiameter
of wheel,
Feet.
8
10 j 12
16
20 25
30
Actual Useful Horse-power developed.
12
16
20
25
30
0
2 4
3
2
3
4
3
1
4 4
6
7
8
9
2
4 '
7
10
12
The wheels were tested by driving a differentially wound dynamo. The
'• useful horse-power " was measured by a voltmeter and ammeter, allow-
ing 500 watts per horse-power. Details of the experiments, including the
means used for obtaining the velocity of the wind, are not given. The re-
sults are so far in excess of the capacity claimed by responsible manufactu-
rers that they should not be given credence until established by further
experiments.
A recent article on windmills in the Iron Age contains the following: Ac-
cording to observations of the United States Signal Service, the average
velocity of the wind within the range of its record is 9 miles per hour for
the year along the North Atlantic border and Northwestern States, 10 miles
on the plains of the West, and 6 miles in the Gulf States.
The horse-powers of windmills of the best construction are proportional
to the squares of their diameters and inversely as their velocities; for ex-
ample, a 10-ft. mill in a 16-mile breeze will develop 0.15 horse-power at 65
revolutions per minute; and with the same breeze
A 20-ft. mill, 40 revolutions, 1 horse-power.
A 25-ft. mill, 35 revolutions, 1% horse-power.
A 30-ft. mill, 28 revolutions, 3^£ horse-power.
A 40-ft. mill, 22 revolutions, 7^ horse-power.
A 50-ft. mill, 18 revolutions, 12 horse-power.
The increase in power from increase in velocity of the wind is equal to the
square of its proportional velocity; as for example, the 25-ft. mill rated
498 AIR.
above for a 16-mile wind will, with a 32-mile wind, have its horsepower in.
creased to 4 X 1% — 7 horse-power, a 40-ft. mill in a 3'J-mile wind will run
up to 30 horse-power, and a 50- ft. mill to 48 horse-power, with a small de
duction for increased friction of air on the wheel and the machinery.
The modern mill of medium and large size will run and produce work in a
4-mile breeze, becoming very efficient in an 8 to 16-mile breeze, and increase
its power with safety to the running-gear up to a gale of 45 miles per hour
Prof. Thurston, in an article on modern uses of the windmill, Engineer-
ing Magazine, Feb. 1893, says : The best mills cost from about $600 for the
10-ft. wheel of ^ horse-power to $1200 for the 25-ft. wheel of 1^ horse-power
or less. In the estimates a working-day of 8 hours is assumed ; but the ma-
chine, when used for pumping, its most common application, may actually
do its work 24 hours a day for days, weeks, and even months together,
whenever the wind is " stiff " enough to turn it. It costs, for work done in
situations in which its irregularity of action is no objection, only one half or
one third as much as steam, hot-air, and gas engines of similar power. At
Faversham, it is said, a 15-horse-pow er mill raises 2,000,000 gallons a month
from a depth of 100 ft., saving 10 tons of coal a month, which would other-
wise be expended in doing the work by steam.
Electric storage and lighting from the power of a windmill has been tested
on a large scale for several years by Charles F. Brush, at Cleveland, Ohio.
In 1887 he erected on the grounds of his dwelling a windmill 56 ft. in diam-
eter, that operates with ordinary wind a dynamo at 500 revolutions per
minute, with an output of 12,000 watts— 16 electric horse-power— charging
a storage system that gives a constant lighting capacity of 100 16 to 20
candle-power lamps. The current from the dynamo is automatically regu-
lated to commence charging at 330 revolutions and 70 volts, and cutting the
circuit at 75 volts. Thus, by its 24 hours' work, the storage system of 408
cells in 12 parallel series, each cell having a capacity of 100 ampere hours, is
kept in constant readiness for all the requirements of the establishment, it
being fitted up with 350 incandescent lamps, about 100 being in use each
evening. The plant runs at a mere nominal expense for oil, repairs, and at-
tention. (For a fuller description of this plant, and of a more recent one at
MarbleheadNeck, Mass., see Lieut. Lewis's paper in Engineering Magazine*
Dec. 1894, p. 475.)
COMPRESSED AIR.
Heating of Air by Compression.— Kimball, in his treatise on Physi-
cal Properties of Gases, says: When air is compressed, all the work which is
done in the compression is converted into heat, and shows itself in the rise in
temperature of the compressed gas. In practice many devices are employed
to carry off the heat as fast as it is developed, and keep the temperature down.
But it is not possible in any way to totally remove this difficulty. But. it may
be objected, if all the work done in compression is convarted into heat, and
if this heat is got rid of as soon as possible, then the work may be virtually
thrown away, and the compressed air can have no more energy than it had
before compression. It is true that the compressed gas has no more energy
than the gas had before compression, if its temperature is no higher, but
the advantage of the compression lies in bringing its energy into more avail-
able form.
The total energy of the compressed and uncompressed gas is the same at
the same temperature, but the available energy is much greater in tfce former.
When the compressed air is used in driving a rock-drill, or any other piece
of machinery, it gives up energy equal in amount to the work it does, and
its temperature is accordingly greatly reduced.
Causes of Iioss of Energy in Use of Compressed Air.
(Zahner, on Transmission of Power by Compressed Air.)— 1. The compression
of air always develops heat, and as the compressed air always cools down to
the temperature of the surrounding atmosphere before it is used, the me-
chanical equivalent of this dissipated heat is work lost.
2. The heat of compression increases the volume of the air, and hence it
is necessary to cany the air to a higher pressure in the compressor in order
that we may finally have a given volume of air at a given pressure, and at
the temperature of the surrounding atmosphere. The work spent in effect-
ing this excess of pressure is work lost.
3 Friction of the air in the pipes, leakage, dead spaces, the resistance of-
fered by the valves, insufficiency of valve-area, inferior workmanship, and
slovenly attendance, are all more or less serious causes o£ loss o£ power.
COMPRESSED AI&.
409
T-he first cause of loss of work, namely, the heat developed by compres-
sion, is entirely unavoidable. The whole of the mechanical energy which
the compressor-piston spends upon the air is converted into heat. This heat
is dissipated by conduction and radiation, and its mechanical equivalent is
work lost. The compressed air, having again reached thermal equilibrium
with the surrounding atmosphere, expands and does work in virtue of its
intrinsic energy.
The intrinsic energy of a fluid is the energy which it is capable of exert-
ing against a piston in changing from a given state as to temperature and
volume to a total privation of heat and indefinite expansion.
Adiabatlc and Isothermal Compression.— Air may be com-
pressed either adiabatically, in which all the heat resulting from com-
pression is retained in the air compressed, or isothermally, in which the
heat is removed as rapidly as produced, by means of some form of refrig-
erator.
Volumes, Mean Pressures per Stroke, Temperatures, etc.,
in I lie Operation of Air-compression from 1 Atmosphere
and 60° Fahr. (F. Richards, Am. Mach., March 30, 1893.)
.b •
cu -
c
0
* p, * fc ,
b
o
p
<5
a
05
gS
^
l^t
g^.
c5
b
J
0)
t5H
gScj,
£fl
s-fc-d
O>
A
'£§
o
P!s
I ""1
r!l
1
o>
&
'El
1g
I?J
1^1
u *r
M|
A
£ <L C
Ck
0) CO
03
O
a
S c
!§
§P
c P
03,3
a
3
d
I
s§
I1
"o
||l
§1
P.
1
«i
> c3
SUJ
jj
H
0
5
>"§
^02
|02
H
2
3
4
5
6
7
1
2
3
4
5
6
7
1
1
1
0
0
60°
80| 6.442
.1552
.266
27.38
36.64
432
1.068
.9363
.95
.96
.975
71
85 6.782
.1474
.2566
28.16
37.94
447
1.136
.8803
.91
1.87
1.91
80.4
90' 7.122
.1404
.248
28.89
39.18
459
1.204
.8305
.876
2.72
2.8
88.9
95
7.462
.134
.24
29.57
40.4
472
1.272
.7861
.84
3.53
3.67
98
100 7.802
.1281
.2324
30.21
41.6
485
1.34
.7462
.81
4.3
4.5
106
105 8.142
.1228
.2254
30.81
42.78
496
1.68
.5952
.69
7.62
8.27
145
110
8.483
.1178
.2189
31.39
43.91
507
2.02
.495
.606
10.33
11.51
178
115 8.823
.1133
.2129
31.98
44.98
518
2.36
.4237
.543
12.62
14.4
207
120 9.163
.1091
.2073
32.54
46.04
529
2.7
.3703
.494
14.59
17.01
234
125 9.503
.1052
.2020
33.07
47.06
540
3.04
3289
.4538
16.34
19.4
252
130
9.843
.1015
.1969
33.57
48.1
550
3.381
.2957
.42
17.92
21.6
281
135 10.183
.0981
.1922
34.05
49.1
560
3.721
.2687
.393
19.32
23.66
302
140 10.523
.095
.1878
34.57
50.02
570
4.061
.2462
.37
20.57
25.59
321
145 10.864
.0921
.1837
35.09
51.
580
4.401
.2272
.35
21.69
27.39
339
15011.204
.0892
.1796
35.48
51.89
589
4.741
.2109
.331
22.76
29.11
357
16011.88
.0841
.17'22
36.29
53.65
607
5.081
.1968
.3144
23.78
30.75
375
170 12.56
.0796
.1657
87.2
55.39
624
5.422
.1844
.301
24.75
32.32
389
180 13.24
.0755
.1595
37.96
57.01
640
5.762
.1735
.288
25.67
33.83
405
190 13.93
.0718
.154
38.68
58.57
657
6.102
.1639
.276
26.55
35.27
420
200
14.61
.0685
.149
39.42
60.14
672
Column 3 gives the volume of air after compression to the given pressure
and after it is cooled to its initial temperature. After compression air loses
its heat very rapidly, and this column may be taken to represent the volume
of air after compression available for the purpose for which the air has
been compressed.
Column 4 gives the volume of air more nearly as the compressor has to
deal with it. In any compressor the air will lose some of its heat during
compression. The slower the compressor runs the cooler the air and the
smaller the volume.
Column 5 gives the mean effective resistance to be overcome by the air-
cylinder piston in The stroke of compression, supposing the air to remain
constantly at its initial temperature. Of course it will not so remain, but
this column is the ideal to be kept in view in economical air- compression,
500
AIB.
Column 6 gives the mean effective resistance to be overcome by the pis-
ton, supposing that there is no cooling of the air. The actual mean effec-
tive pressure will be somewhat less than as given in this column; but for
computing the actual power required for operating air-compressor cylinders
the figures in this column may be taken and a certain percentage added —
say 10 per cent— and the result will represent very closely the power required
by the compressor.
The mean pressures given being for compression from one atmosphere
upward, they will not be correct for computations in compound compression
or for any other initial pressure.
Loss .Due to Excess of Pressure caused by Heating In
the Compression-cylinder.— If the air during compression weie
kept at a constant temperature, the compression-curve of an indicator-dia'
gram taken from the cylinder would be an isothermal curve, and would fol-
low the law of Boyle and Marriotte, pv=a constant, or p\v^ =POVO» °r
Pi = Po — » Po and VQ being the pressure and volume at the beginning of
compression, audp^Vi the pressure and volume at the end, or at any inter-
mediate point. But as the air is heated during compression the pressure
increases faster than the volume decreases, causing the work required for
any given pressure to be increased. If none of the heat were abstracted
by radiation or by injection of water, the curve of the diagram would be an
adiabatic curve, with the equation pt = p0(^— ) Cooling the air dur-
ing compression, or compressing it in two cylinders, called compounding,
and cooling the air as it passes from one cylinder to the other, reduces the
exponent of this equation, and reduces the quantity of work necessary to
effect a given compression. F. T. Gause (Am. Mach., Oct. 20, 1892), describ-
ing the operations of thePopp air-compressors in Paris, says : The greatest
saving realized in compressing in a single cylinder was 33 per cent of that
theoretically possible. In cards taken from the 2000 H.P. compound com-
pressor at Quai De La Gare, Paris, the saving realized is 85 per cent of the
theoretical amount. Of this amount only 8 per cent is due to cooling dur-
ing compression, so that the increase of economy in the compound com-
pressor is mainly due to cooling the air between the two stages of compres-
sion. A compression-curve with exponent 1.25 is the best result that was
obtained for compression in a single cylinder and cooling with a very fine
spray. The curve with exponent 1.15 is that which must be realized in a
single cylinder to equal the present economy of the compound compressor
at Quai De La Gare.
Horse-power required to
compress and deliver one
cubie foot of Free Air per
minute to a given pressure with no
cooling of the air during the com-
pression; also the horse-power re-
quired, supposing the air to be main-
tained at constant temperature
during the compresion.
Gauge- Air not Air constant
pressure. cooled. temperature.
5 .0196 .0188
10 .0361 .0333
20 .0628 .0551
30 .0846 .0713
40 .1032 .0843
50 .1195 .0946
60 .1342 .1036
70 .1476 .1120
80 .1599 .1195
90 .1710 .1261
100 ,1815 .1318
Horse-power required tt»
compress and deliver one
cubie foot of Compressed
Air per minute at a given pressure
with no cooling of the air during
the compression; also the horse-
power required, supposing the air to
be maintained at constant tempera-
ture during the compression.
Gauge- Air not Air constant
pressure. cooled. temperature.
5 .0263 .0251
10 .0606 .0559
20 .1483 .1300
30 .2573 .2168
40 .3842 .3138
50 .5261 .4166
60 .6818 .5266
70 .8508 .6456
80 1.0302 .7700
90 1.2177 .8979
100 1.4171 1.0291
The horse-power given above is the theoretical power, no allowance being
made for friction of the compressor or other losses, which may amount to
10 per cent or more.
COMPRESSED AIR. 501
Formulae for Adiabatic Compression or Expansion of
Air (or other sensibly perfect gas).
Let air at an absolute temperature Tj, absolute pressure p^, and volume
vl be compressed to an absolute pressure p2 ancl corresponding volume va
and absolute temperature T2; or let compressed air of an initial pressure,
volume, and temperature p2, v2, and 7'2 be expanded to p1, v!t and rl\, there
being no transmission of heat from or into the air during the operation. Then
the following equations express the relations between pressure, volume,
and temperature (see works on Thermodynamics):
The exponents are derived from the ratio cp-t-cv = k of the specific heats
of air at constant pressure and constant volume. Taking k = 1.406, 1 -f- k —
0 711 ; k - 1 = 0.406 ; 1 -*• (k - 1) = 2.463; A; -5- (k - 1) = 3.463; (A; - 1) -*- fc =
0.289.
Work of Adiabatic Compression of Air.— If air is com-
pressed in a cylinder without clearance from a volume vt and pressure pl
to a smaller volume v2 and higher pressure p2, work equal to piv1 is done by
the external air on the piston while the air is drawn into the cylinder.
Work is then done by the piston on the air, first, in compressing it to the
pressure p^ and volume va, and then in expelling the volume v9 from the
cylinder against the pressure p2. If the compression is adiabatic, Piv* =s
p2vafc = constant, k = 1.41.
The work of compression of 1 pound of air is
. /£?
fc-l
The work of expulsion is pav2 = plvl
The total work is the sum of the work of compression and expulsion less
the work done on the piston during admission, and it equals
= 3.463 PlV
The mean effective pressure during the stroke is
P! and pa are absolute pressures above a vacuum in atmospheres or in
pounds per square inch or per square foot.
EXAMPLE.— Required the work done in compressing 1 cubic foot of air per
second from 1 to 6 atmospheres, including the work of expulsion from the
C3rlinder.
Pa -»-Pi = 6? 6°'29 " 1 = 0.681; 3.463 X 0.681 = 2.358 atmospheres, X 14.7 =
34.66 Ibs. per sq. in. mean effective pressure, X 144 = 4991 Ibs. per sq. ft., X 1
ft. stroke = 4991 £t.-lbs.t -*- 550 ft.-lbs. per second = 9.08 H.P.
AIR.
If R = ratio of pressures = p2 •*• Pi' ancl if Vi = 1 cubic foot, the work done
in compressing 1 cubic foot frompl to pa is in foot-pounds
o-" - 1),
pl being taken in Ibs. per sq. ft. For compression at the sea-level pj may be
taken at 14 Ibs. per sq. in. = 2016 Ibs. per sq. ft., as there is some loss of
pressure due to friction of valves and passages.
Indicator-cards from compressors in good condition and under working-
speeds usually follow the adiabatic line closely. A low curve indicates
piston leakage. Such cooling as there may be from the cylinder-jacket and
the re-expansion of the air in clearance-spaces tends to reduce the mean
effective pressure, while the " camel-backs " in the expulsion-line, due to
resistance to opening of the discharge-valve, tend to increase it.
Work of one stroke of a compressor, with adiabatic compression, in foot-
pounds,
W = S.^G.SPjFjCR0'29 - 1),
in which Pj = initial absolute pressure in Ibs. per sq. ft. and Vl = volume
traversed by piston in cubic feet.
The work done during adiabatic compression (or expansion) of 1 pound of
air from a volume vl and pressure pl to another volume i>2 and pressure pa
is equal to the mechanical equivalent of the heating (or cooling). If /j is thy
higher and £2 the lower temperature, Fahr., the work done is cvJ(tl - /2)
foot-pounds, cv being the specific heat of air at constant volume = 0.1U89and
J = 778, cvJ = 131.4.
The work during compression also equals
Ea being the value of pv -4- absolute temperature for 1 pound of air = 53.37.
The work during expansion is
in which p^i are the initial and pava the final pressures and volumes.
Compressed-air JEiigin.es, Adiabatic Expansion. — Let
the initial pressure and volume taken into the cylinder be pl Ibs. per
sq. ft. and Vi cubic feet; let expansion take place to p2 and va according to
the adiabatic law p^1-41 =pat7al>41; then at the end of the stroke let the
pressure drop to the back-pressure p3, at which the air is exhausted
Assuming no clearance, the work done by one pound of air during ad
mission, measured above vacuum, is Pivlt the work during expansion is
2.463 pivA 1 — ( — J , and the negative or back pressure work is — p3va.
The total work isp1vl-{ 2.4Q3plv1[l - (^-2Y '2> ~|- p,va, and the mean effec-
L ^Pi^ -'
tive pressure is the total work divided by va.
If the air is expanded down to the back-pressure p3 the total work is
or, in terms of the final pressure and volume,
^H^r'-
and the mean effective pressure is
The actual work is reduced by clearance. When this is considered, the
Eroduct of the initial pressurepi by the clearance volume is to be subtracted
•om the total work calculated from the initial volume vl including clearance.
(See p. 744, under "Steam-engine,'1)
COMPRESSED AIR.
5015
Effective Pressures of Air Compressed Adiabatically.
(F. A. Halsey, Am. Mach., Mar. 10, 1898.)
R
£0.29
M EP from
14 Ibs. Initial.
R
£0.2»
MEP from
14 Ibs. Initial.
1.25
1.067
3.24
4.75
1.570
27.5
1.50
1.125
6.04
5.
1.594
28.7
1.75
1.176
8.51
5.25
1.617
29.8
2.
1.223
10.8
5.5
1.639
30.8
2.25
1.265
12.8
5.75
1.660
31.8
2.5
1.304
14.7
6.
1.681
&t.8
2.75
1.341
16.4
6.25
1.701
33.8
3. '
1.375
18.1
6.5
1.720
34.7
3.25
1.407
19.6
6.75
1.739
35.6
3.5
1.438
21.1
7.
1.757
36.5
3.75
1.467
22.5
7.25
1.775P
37.4
4.
1.495
23.9
7.5
1.793
38.3
4.25
1.521
25.2
8.
1.037
39.9
4.5
1.546
26.4
R — final -5- initial absolute pressure.
MEP = mean effective pressure, Ibs. per sq. in., based on 14 Ibs. initial.
Compound Compression, with Air Cooled between tlie
Two Cylinders. (Am. Mack., March 10 aud 31, 1898.)— Work in low-pres-
sure cylinder = Wit in high-pressure cylinder PF2. Total work
W1 + W2 = WePiFiDv" -f B-"rj - -29 - 2].
r, = ratio of_pressures in 1. p. cyl., ra = ratio in h. p. cyl., R = TW When
TJ = ra = V-K, the sum IF", 4- W% is a minimum. Hence fora given total ratio
of pressures, R, the work of compression will be least when the ratios of the
pressures in each of the two cylinders are equal.
The equation may be simplified, when rt = 4/.K, to the following!
Wl -f TF2 = e^PjFjLK"'145 - 1].
Dividing by Fj gives the mean effective pressure reduced to the low-pressure
cylinder MEP= 6.92^ [/2°-"5 - 1].
In the above equation the compression in each cylinder is supposed to be
adiabatic, but the intercooler is supposed to reduce the temperature of the
air to that at which compression began.
Mean Effective Pressures of Air Compressed fin Two
Stages, assuming the lutereooler to Reduce the Tem-
perature to That at which Compression Began., (F. A.
Halsey, Am. Mack., Mar. 31, 1898.)
R
^0-145
MEP
from 14
Ibs.
Initial.
Ultimate
Saving
by Com-
pound-
ing, %
R
#0.149
MEP
from
14 Ibs.
Initial.
Ultimate
Saving
by Com-
pound-
ing, %
5.0
1.263
25.4
11.5
9.0
1.375
36.3
5.5
1.280 '
27.0
12 3
9.5
.386
37.3
6.0
1.296
28.6
12.8
10
.396
38.3
6.5
1.312
30.1
13.2
11
.416
40.2
7.0
1.326
31.5
13.7
12
.434
41.9
7.5
1.336
fcj.8
14,3
13
.451
43.5
8.0
1.352
34.0
14.8
14
.466
45.0
8.5
1.364
35.2
15
.481
46.4
R — final -r- initial absolute pressure.
MEP= mean effective pressure Ibs. per sq. in. based on 14 Ibs. absolute
initial pressure reduced to the low-pressure cylinder.
To Find the Index of the Curve of an Air-diagram.—
If P^ be pressure and volume at one point on the curve, and PV ihe pres.
sure and volume at another point, then — = (-^) . iu which x is the index
to be found. Let P-*- Pj = R, and Vi -i- F" = r ; then R = rx log R = x log r,
whence x = log R -*- log 9%
502
AIR.
Table for Adiabatic Compression or Expansion of Air.
(Proc. Inst. M.E., Jan. 1881, p. 123.)
Absolute Pressure.
Absolute Temperature.
Volume.
Ratio of
Ratio of
Ratio of
Ratio of
Ratio of
Ratio of
Greater
Less to
Greater
Less to
Greater
Less to
to Less.
Greater.
to Less.
Greater.
to Less.
Greater.
(Expan-
sion.)
(Compres-
sion.)
(Expan-
sion.)
(Compres-
sion.)
(Compres-
sion.)
(Expan-
sion.)
1.2
.833
.054
.948
1.138
.879
1.4
.714
.102
.907
1.270
.788
1.6
.625
.146
.873
1.396
.716
1.8
.556
.186
.843
1.518
.659
2.0
.500
.222
.818
1.636
,611
2.2
.454
.257
.796
1.750
.571
2.4
.417
.289
.776
1.862
.537
2.6
.385
.319
.758
1.971
.507
2.8
.357
.348
.742
2.077
.481
3.0
.333
.375
.727
2.182
.458
3.2
.312
.401
.714
2.284
.438
3.4
.294
.426
.701
2.384
.419
3.6
.278
.450
.690
2.483
.403
3.8
.263
.473
.679
2.580
.388
4.0
.250
.495
.669
2.676
.374
4.2
.238
.516
.660
2.770
.361
4.4
.227
.537
.651
2.863
.349
4.6
.217
.557
.642
2.955
.338
4.8
.208
.576
.635
3.046
.328
5.0
.200
.595
.627
3.135
.319
6.0
.167
.681
.595
3 569
.280
7.0
.143
.758
.569
3.981
.251
8.0
.125
.828
.547
4.377
.228
9.0
.111
.891
.529
4.759
.210
10.0
.100
.950
.513
5.129
.195
Mean Effective Pressures for the Compression Part only
of the Stroke when compressing and delivering: Ajr
from one Atmosphere to given Gauge-pressure in a Sin-
gle Cylinder. (F. Richards, Am. Mach., Dec. 14, 1893.)
Gauge-
pressure.
Adiabatic
Compression.
Isothermal
Compression.
Gauge-
pressure.
Adiabatic
Compression.
Isothermal
Compression.
1
.44
.43
45
13.4)5
12.62
2
.96
.95
50
15.05
13.48
3
1.41
1.4
55
15.98
14.3
4
1.86
1.84
60
16.89
15.05
5
2.26
2.22
65
17.88
15.76
10
4.26
4.14
70
18.74
16.43
15
5.99
5.77
75
19.54
17.09
20
7.58
7.2
80
20.5
17.7
25
9.05
8.49
85
31.22
18.3
30
10.39
9.66
90
22.
18.87
35
11.59
10.72
95
22.77
19.4
40
12.8
11.7
100
23.43
19.92
The mean effective pressure for compression only is always lower than
the mean effective pressure for the whole work
COMPRESSED AIR.
503
Mean and Terminal Pressures of Compressed Air used
Expansively tor Gauge-pressures from 6O to 10O Ibs.
(Frank Richards, Am. Mack., April 13, 1893.)
Initial
Pres-
60.
70.
80.
90.
100.
sure.
" -sa-
\i\
1,2
a, 2'
1.2
s-1
IJ
0 , 2
1,2
p|
1,|
II
EH ft
ft
H 0.
1
e s,
p.
EH ft
ft
fl
.25
23.6
1O.65
28.74
12.V7
33.89 13.49
39.04
14.91
44.19
1.33
.30
28.9
13.77
34.75
.6
40.61
2.44
46.46
4.27
53.32
6.11
32.13
.96
38.41
3.09
44.69
5.22
50.98
7.35
57.26
9.48
.35
33.66
2.33
40.15
4.38
46.64
6.66
53.13
8.95
59.62
11.23
%
35.85
3.85
42.63
6.36
49.41
7.88
56.2
11.39
62.98
13.89
.40
37.93
5.64
44.99
8.39
52.05
11.14
59.11
13.88
66.16
16.64
.45
41.75
10.71
49.31
12.61
56.9
15.86
64 45
19.11
72.02
22.36
.50
45.14
13.26
53.16
17.
61.18
20.81
69.19
24.56
77.21
28.33
.60
50.75
21.53
59.51
26.4
68.28
31.27
77.05
36.14
85.82
41.01
%
51.92
23.69
60.84
28.85
69.76
34.01
78.69
39.16
87.61
44.32
a^
53.67
27.94
62.83
33.03
71.99! 38.68
81.14
44.33
90.32
49.97
70
54.93
30.39
64.25
36.44
73.57 42.49
82,9
48.54
92.22
54.59
.75
56.52
35.01
66.05
41.68
75.59
48.35
85.12
55.02
94.66
61.69
.80
57.79
39.78
67.5
47.08
77.2
54.38
86.91
61.69
96.61
68.99
59.15
47.14
69.03
55.43
78.92
63.81
88.81
72.
98.7
80.28
.90
59.46
49.65
69.38
58.27
79.311 66.89
89.24
75.52
99.17
87.82
The pressures in the table are all gauge-pressures except those in italics,
which are absolute pressures (above a vacuum).
mountain or High-altitude Compressors.
(Norwalk Iron Works Co.l
Diameter Air-
cylinder.
Length of
Stroke.
Diameter of
Compressing
Cylinder.
Diameter of
Steam-
cylinder.
Revolutions
per minute.
At Sea-
level.
At 2000
feet.
At 6000
feet.
At 10,000
feet.
Capacitj7.
cubic
feet.
Horse-
power.
Capacity.
k
i 0)
sg
&a
w
£>
<3
O
Horse-
power.
£»
I-
Horse-
power,
12
16
20
22
26
12
16
20
24
30
7
13^
17J4
10
14
18
20
24
190
150
120
110
90
298
558
872
1100
1659
35
70
110
145
215
280
524
819
1090
1560
34
68
107
140
207
244
462
722
960
1373
32
64
100
132
195
214
405
634
843
1200
30
60
94
124
184
As the capacity decreases in a greater ratio than the power necessary to
compress, it follows that operations at a high altitude are more expensive
than at sea-level. At 10,000 feet this extra expense amounts to over 20 per
cent.
Compressors at High Altitudes. (Ingersoll-Sergeant Drill Co.)
Alt. above sea-level, ft...
Barometer, in. mercury.
lbs.persq.in.
0
30.0
14.7
100
0
0
1000
28.9
14.2
97
3
1.8
2000
27.8
13.7
93
7
3.5
3000
26.8
13.2
90
10
5.2
4000
25.8
12.7
87
13
6.9
5000
24.8
12.2
84
16
8.5
6000
23.9
11.7
81
19
10.1
7000
23.0
11.3
78
22
11.6
8000
22.1
10.9
76
24
13.1
9000
21.3
10.5
73
27
14.6
10000
20.5
10.1
70
30
16.1
Loss of capacity, %
Decreased power re-
quired, %
504
AIR.
Air-compressors. Rand Drill Co*
RAND-CORLISS, CLASS "BB-3" (COMPOUND
STEAM, CONDENSING; COMPOUND AIR).
CLASS " E " (STRAIGHT-
LINE, BELT-DRIVEN).
FOR STEAM-PRESSURE OF 125 LBS. AND TERMINAL
F3R TERMINAL PRESSURES
AIR-PRESSURES OF 80 AND 100 LBS.
OF 80 AND 100 LBS. PER SQ IN.
A
Cylinder Diameters, Ins.
et
a
§
fe
*
rQ O
53 .
~ 03 ®
Air-Cyl-
inder,
Inches.
§
Ll
Indi-
cated
H.P.
SS s
Steam.
Air.
-
&
•tJ 1
*»fe .-,
a
Air-
03^^*
1
o ^
§0^
a
M
pres-
lei
h.p.
l.p.
h.p.
l.p.
GO
a>
K
IS
a '
.i
Q
2
0>
M
sure
80 Ibs.
670
10
18
10i
17
30
85
102
97
8
12
140
17
1196
12
22
13
21
36
83
182
1C5
10
14
130
29
1562
14
26
15
24
36
83
238
251
12
16
120
45
1650
14
26
15
24
42
75
252
392
14
2-3
100
69
1920
16
30
I7i
28
36
75
293
527
16
24
95
94
2242
16
30
17j
28
42
75
342
633
m
24
95
112
2395
16
30
17*
28
48
70
365
2520
18
34
20"
32
30
75
384
2897
18
34
20
32
42
75
442
3128
18
34
20
32
48
70
475
3960
20
38
22^
36
48
70
604
4100
22
40
24
38
48
65
625
4530
22
42
25
40
48
05
690
5000
24
44
ft*
42
48
65
763
6000
26
48
' 29
46
48
65
915
6820
28
52
30
48
48
65
1040
In the first four sizes (Class " BB-3 ") the air-cylinders have poppet inlet
and outlet valves; in the next six the low-pressure air-cylinders have me-
chanical inlet-valves and poppet outlet- valves; and in the last six the low-
pressure air-cylinders have Corliss inlet-valves and poppet outlet-valves.
All high-pressure air-cylinders have poppet inlet and outlet valves.
* Terminal air-pressure at 80 pounds.
CLASS " B-2 " (DUPLEX STEAM, NON-
CONDENSING, COMPOUND AIR).
FOR STEAM- AND TERMINAL AIR-PRESSURES
OF 80 AND 100 LBS.
CLASS " C " (STRAIGHT-LINE.
STEAM-DRIVEN).
FOR STEAM- AND TERMINAL AIR-
PRESSURES OF 100 LBS. PER SQ. IN.
33,
a a>-2
III
fs&
Cylinder Diam-
eters, Inches.
Stroke, Ins.
Revs, per Min.
35
Capacity in Cu.
Ft. of Free Air
per Minute.
Cyl.
Diam.,
Ins.
02
C
1— I
I
OQ
p
9
.w
0)
Indicated
Horse-power.
lit
Air-cyls.
Steam.
£
h.p.
l.p.
220
300
393
565
770
882
1152
1812
2085
2356
2848
8
9
10
12
14
14
16
18
20
20
22
Ti
9
li2
13
13
15:
19*
19
21
12
14
15
18
21
21
24
28
30
30
33
12
12
16
16
16
22
22
30
30
48
48
140
140
120
120
120
100
100
85
85
60
60
35
47
62
89
121
139
182
285
328
370
446
97
165
251
071
950
1335
8
10
12
14
16
18
20
24
8
10
12
14
16
18
20
24
12
14
16
22
24
24
30
30
140
130
120
100
95
95
87
85
20
35
52
82
110
140
200
280
AH air-cylinders have poppet
inlet and outlet valves.
The first six sizes (Class " B-2") have both air-cylinders fitted with poppet-
valves (inlet and discharge). The last four have low-pressure air-cylinders
fitted with mechanical inlet-valve; high-pressure air-cylinders fitted with
poppet inlet and discharge valves.
STANDARD AItt COMPRESSORS.
(The Ingersoll-Sergeant Drill Co., New York City.)
505
Diam. of Cyl.
c
.=' a
<T5
, S3*
;- ^
i£
Class
Steam.
.Air.
ti
t-
z2
SH 3>
«!8
he 5°
Occupied.
v
£
and
S.
En a
IS
Ml
Type.
A
.
,d
1
CO
h-£
44
W
»
w
a
a
he
s
u
02
s
|5
o
Length.
Width.
O
w
10
10V4
12
160
177
50-100
10' 2"
3' 0"
25-35
18
isy
14
155
285
50-100
12 6
3 9
40-56
Straight-
Hua
14
16
14*4
16*4
18
18
120
120
382
498
50-100
50-100
15 3
15 3
4 3
4 3
50-76
66-100
Steam-
driven.
18
20
22
IBM
20*2
82M
24
24
24
94
94
94
657
809
960
50-100
50-100
50-100
19 1
19 1
19 1
5 3
5 3
5 3
86-131
113-160
126-192
24
24*4
30
80
13:25 1 50-100
22 0
6 0
160-245
B. Straight-line, belt-driven. Same as A in sizes up to 16 X 16*4 X 18 ins.
c.t
Duplex
steam,
Duplex air.
\oy2
16
20
24
30
32
16*4
20*4
24*4
32*4
30
36
42
42
48
60
90
82
75
75
65
62
576
1346
2239
3208
4932
6717
100
100
100
100
100
100
31' 0"
36 6
41 0
43 0
41 0
60 0
10' 6"
12 6
13 6
14 6
16 6
19 6
115
274
454
646
1011
1375
ca.
Compound
Corliss
steam,
Compound
air.t
10*£
14
16
18
22
24
18
26
30
34
40
44
16*4
22*4
28*4
34*4
36*4
13*4
15*4
17*4
20*4
22*4
30
36
42
48
48
48
90
85
78
75
72
70
615
1306
1668
2137
3515
3850
100
100
100
100
100
100
39 6
43 0
49 6
55 6
56 6
58 0
14 0
14 6
15 6
15 6
18 6
19 6
97
225
284
367
604
664
Small
straight-
line.
6
8
10
12
12
6
8
10
12
16*4
6
8
10
12
12
150
150
150
150
150
28
69
134
237
415
50-80
50-80
50-80
50-80
15-40
5 8
6 8
7 10
8 6
10 10
22
25
30
30
35
4-5*4
9&f-13
18^4-25
3314-44
E. Belt-driven. Same as .Fin sizes up to 14*4 diam. by 10 ins. stroke.
G.
Steam-
actuated,
duplex
or half
duplex.
10
16
20
10
12
14
16
18
20
;_:
10*4
12*4
14*4
16*4
18*4
20*4
12
14
18
18
24
24
160
155
120
120
94
94
354
570
764
996
1314
1618
100
100
100
100
100
100
14' V
16 6
20 0
20 0
25 6
25 6
7' 0"
9 0
10 0
10 0
11 6
12 0
75
121
163
212
280
344
G.
Duplex st.,
cornp. air.
16*4
24*4
30M
10*4
15*4
18*4
12
18
24
160
120
100
446
1130
1963
344
950
1710
80-100
80-100
100
16 3
23 0
30 0
7 3
10 0
12 0
71-80
180-203
353
G.
Comp. st.,
cornp. air.
10
16
20
17
26
32
1414
2*1/4
28*4
9*4
14*4
17*4
12
18
24
160
120
100
80-100
80-100
80-100
16 3
23 0
30 0
7 6
10 0
12 0
55-62
152-171
274-308
H.
Duplex st.,
duplex air.
8
10
12
8
10
12
8
10
12
150
150
150
138
268
474
60-100
70-100
80-100
8 6
10 0
11 8
4 6
4 9
5 10
20-28
43-54
83-95
H.
Duplex st.,
com p. air.
8
10
12
14
16
18
9
10
12
8
10
12
150
150
150
210
342
519
80-100
80-100
80-100
8 6
10 2
11 10
5 3
5 9
6 9
32-36
52-58
78-88
J. Belted duplex or compound. 8 f o 98 H.P. ; 56 to 1059 cu. ft. per m.
* Classes A, C, G, and H are also built in intermediate sizes for lower
pressures, t Furnished either duplex or half duplex. J Most economical
^orrn of compressor. Compound air-cylinders are two-stage. § Self-con-
tained steam-compressor.
5050
AIR.
Cubic Feet of Free Air Required to Run from One to
Forty Machines with 6O IDS. Pressure. (Ingersoll-Sergeant
Drill Co.)
For 75 Ibs. Pressure add 1/5. For 90 Ibs. add 2/5.
ROCK-DRILLS.
COAL-
CUTTERS.
No. of
A
B
C
D
E
F
G
H
Machines
2 in.
2^ in.
2%in.
3 in.
3!4in.
3^ in.
414 in.
5 in.
3^in.
4 in.
1
65
70
95
110
115
125
140
165
70
93
2
110
120
160
190
200
230
250
280
140
186
3
156
174
234
279
294
333
360
405
210
279
4
196
220
304
356
372
428
460
524
280
372
5
230
260
370
425
445
510
555
635
350
465
6
264
294
426
486
516
588
642
738
420
558
7
294
329
476
546
581
658
721
826
490
651
8
320
360
520
600
640
720
800
920
560
744
9
360
405
585
675
720
810
900
1035
630
837
10
400
450
650
750
800
900
1000
1150
700
930
12
480
540
780
900
960
1080
1200
1380
840
1116
15
675
975
1125
1200
1350
1500
1725
1050
1395
20
1300
1500
1600
1800
2000
2300
1400
1860
25
16 .'5
1875
2000
2250
2500
5775
1750
23<25
30
1950
2250
2400
2700
3000
3450
2100
2790
40
2600
3000
3200
3600
4000
4600
2800
3720
Compressed-air Table for Pumping Plants.
(Ingersoll-Sergeant Drill Co.)
For the convenience of engineers and others figuring on pumping plants
to be operated by compressed air, we subjoin a table by which the pressure
and volume of air required for any size pump can be readily ascertained.
Reasonable allowances have been made for loss due to clearances in pump
and friction in pipe.
Ratio of
Diam-
eters.
Perpendicular Height, in Feet, to which the Water is to be
Pumped.
25
50
75
100
;i25
150
175
200
250
300
400
1 tol-j
Ifcgtolj
l«tolj
2 tol]
2^ to 1 j
2^ to 1 j
A
I?
A
B
A
B
A
B
A
B
A
B
13.75
0.21
27.5
0.45
12.22
0.65
41.25
0.60
18.33
0.80
13.75
0.94
55.0
0.75
24.44
0.95
19.8
1.14
13.75
1.23
68.25
0.89
30.113
1.09
22.8
1.24
17.19
1.37
13.75
1.533
8'J.5
1.04
36.66
1.24
27.5
1.30
20.63
1.52
16.5
1.68
13.2
1.79
96.25
1.20
42.76
1.39
32.1
1.54
24.06
1.66
19.25
1.83
15.4
1.98
110.0
1.84
48.88
1.53
36.66
1.69
27.5
1.81
22.0
1.97
17.6
2.06
61.11
1.83
45.83
1.99
34.38
2.11
27.5
2.26
22.0
2.34
73.32
2.12
55.0
2.39
41.25
2.40
33.0
2.56
26.4
2.62
97.66
2.70
73.33
2.88
55.0
2.98
44.0
3.15
35.2
3.18
A = air-pressure at pump. B = cubic feet of free air per gallon of water.
To find the amount of air and pressure required to pump a given quantity
of water a given height, find the ratio of diameters between water and air
cylinders, and multiply the number of gallons of water by the figure found
in the column for the required lift. The result is the number of cubic feet
of free air. The pressure required on the pump will be found directly above
in the same column. For example: The ratio between cylinders being 2 to
1, required to pump 100 gallons, height of lift 250 feet. We find under 250
feet at ratio 2 to 1 the figures 2.11 ; 2.11 X 100 = 211 cubic feet of free air.
The pressure required is 34,38 pounds.
COMPRESSED AIR.
5056
Compressed-air Table for Hoisting-ermines.
(Ingersoll-Sergeant Drill Co.)
The following table gives an approximate idea of the volume of free air
required for operating hoisting-engines, the air being delivered at 60 Ibs.
gauge-pressure. There are so many variable conditions to the operation of
hoisting-engines in common use that accurate computations can only be
offered when fixed data are given. In the table the engine is assumed to
actually run but one-half of the time for hoisting, while the compressor, of
course, runs continuously. If the engine runs less than one-half the time,
as it usually does, the volume of air required will be proportionately less,
and vice versa. The table is computed for maximum loads, which also in
practice may vary widely. From the intermittent character of the work of
a hoisting-engine the pails are able to resume their normal temperature
between the hoists, and there is little probability of the annoyance of freez-
ing up the exhaust-passages.
VOLUME OF FREE AIR REQUIRED FOR OPERATING HOISTING-
ENGINES, THE AIR COMPRESSED TO 60 POUNDS GAUGE-
PRESSURE.
SINGLE-CYLINDER HOISTING-ENGINE.
Diam. of
Cylinder,
Inches.
Stroke,
Inches.
Revolu-
tions per
Minute.
Normal
Horse-
power.
Actual
Horse-
power.
Weight
Lifted,
Single
Rope.
Cubic Ft.
of Free Air
Required.
5
6
200
3
5.9
600
75
5
8
160
4
6.3
1,000
80
6V4
8
160
6
9.9
1,500
125
7
10
125
10
12.1
2,000
151
8#
10
125
15
16.8
3,000
170
8^3
12
110
20
18.9
5,000
238
10
12
110
25
26.2
6,000
330
DOUBLE-CYLINDER HOISTING-ENGINE.
5
6
200
6
11.8
1,000
150
5
8
160
8
12.6
1,650
160
6^4
8
160
12
19.8
2,500
250
7
10
125
20
24.2
3,500
302
8J4
10
1:25
30
33.6
6,000
340
8^
12
110
40
37.8
8,000
476
10
12
110
50
52.4
10,000
660
19L£
15
100
75
89 °
1,125
14
18
90
100
125.
1,587
Practical Results with Compressed Air.— Compressed-air
System at the Chapin Mines, Iron Mountain, Mich. — These mines are three
miles from the falls which supply the power. There are four turbines at the
falls, one of 1000 horse-power and three of 900 horse-power each. The press-
ure is 60 pounds at 60° Fahr. Each turbine runs a pair of compressors.
The pipe to the mines is 24 ins. diameter. The power is applied at the mines
to Corliss engines, running pumps, hoists, etc., and direct to rock-drills.
A test made in 1888 gave 1430.27 H.P. at the compressors, and 390.17 H.P.
as the sum of the horse-power of the engines at the mines. Therefore, only
27$ of the power generated was recovered at the mines. This includes the
loss due to leakage and the loss of energy in heat, but not the friction in the
engines or compressors. (F. A. Pocock, Trans. A. I. M. E., 1890.)
W. L. Saunders (Jour. F. I. 1892) says: "There is not a properly designed
compressed-air installation in operation to-day that loses over b% by trans-
mission alone. The question is altogether one of the size of pipe; and if the
pipe is large enough, the friction loss is a small item.
"The loss of power in common practice, where compressed air is used to
drive machinery in mines and tunnels, is about 70$. In the best practice,
with the best air-compressors, and Avithout reheating:, the loss is about 60#.
These losses may be reduced to a point as low as 20# by combining the best
systems of reheating with the best air-compressors."
506 AIR.
Gain due to Reheating.— Prof. Kennedy says compressed-air
transmission system is now being carried on, on a large commercial scale,
in such a fashion that a small motor four miles away from tne central sta-
tion can indicate in round numbers 10 horse-power, for 20 horse-power at
the station itself, allowing for the value of the coke used in heating the air.
The limit to successful reheating lies in the fact that air-engines cannot
work to advantage at temperatures over 350°.
The efficiency of the common system of reheating is shown by the re-
sults obtained with the Popp system in Paris. Air is admitted to the re-
heater at about 83°, and passes to the engine at about 315°, thus being in-
creased in volume about 42%. The air used in Paris is about 11 cubic feet of
free air per minute per horse-power. The ordinary practice in America
with cold air is from 15 to 25 cubic feet per minute per horse power. When
the Paris engines were worked without reheating the air consumption was
increased to about 15 cubic feet per horse-power per minute. The amount
of fuel consumed during reheating is trifling.
Efficiency of Compressed-air Engines.— The efficiency of an
air-engine, that is, the percentage which the power given out by the air-en-
gine bears to that required to compress the air in the compressor, depends
on the loss by friction in the pipes, valves, etc., as well as in the engine itself.
This question is treated at length in the catalogue of the Norwalk Iron Works
Co., from which the following is condensed. As the friction increases the
most economical pressure increases. In fact, for any given friction in a
pipe, the pressure at the compressor must not be carried below a certain
limit. The following table gives the lowest pressures which should be used
at the compressor with varying amounts of friction in the pipe:
Friction, Ibs 2.9 5.8 8.8 11.7 14.7 17.6 20.5 23.5 26.4 29.4
Lbs. at Compressor... 20.5 29.4 38.2 47. 52.8 61.7 70.5 76.4 82.3 88.2
Efficiency #. 70.9 64.5 60.6 57.9 55.7 54.0 52.5 51.3 50.2 49.2
An increase of pressure will decrease the bulk of air passing the pipe and
its velocity. This will decrease the loss by friction, but we subject ourselves
to a new loss, i.e. the diminishing efficiencies of increasing pressures. Yet as
each cubic foot of air is at a higher pressure and therefore carries more
power, we will not need as many cubic feet as before, for the same work.
With so many sources of gain or loss, the question of selecting the proper
pressure is not to be decided hastily.
The losses are, first, friction of the compressor. This will amount ordinarily
to 15 or 20 per cent, and cannot probably be reduced below 10 per cent.
Second, the loss occasioned by pumping the air of the engine-room, rather
than the air drawn from a cooler place. This loss varies with the season and
amounts from 3 to 10 per cent. This can all be saved. The third loss, or series
of losses, arises in the compressing cylinder, viz., insufficient supply, difficult
discharge, defective cooling arrangements, poor lubrication, etc. The fourth,
loss is found in the pipe. This loss varies with the situation, and is subject
to somewhat complex influences. The fifth loss is chargeable to fall of
temperature in the cylinder of the air-engine. Losses arising from leaks
are often serious.
Effect of Temperature of Intake upon tne Discharge of a
Compressor.— Air should be drawn from outside the engine-room, and
from as cool a place as possible. The gain amounts to one per cent for every
five degrees that the air is taken in lower than the temperature of the engine-
room. The inlet conduit should have an area at least 50$ of the area of the
air-piston, and should be made of wood, brick, or other non-conductor of
heat.
Discharge of a compressor having an intake capacity of 1000 cubic feet
per minute, and volumes of the discharge reduced to cubic feet at atmos-
pheric pressure and at temperature of 62 degrees Fahrenheit:
Temperature of Intake, F 0° 32° 62° 75° 80° 90° 100° 110°
Relative volume discharged, cubic ft... 1135 1060 1000 975 966 949 932 916
Requirements of Rock-drills Driven by Compressed
Air. (Norwalk Iron Works Co.)— The speed of the drill, the pressure of
air, and the nature of the rock affect the consumption of power of drills.
A three-inch drill using air at 30 Ibs. pressure made 300 blows per minute
and consumed the equivalent of 64 cubic feet of free air per minute. The
same drill, with air of 58 Ibs. pressure, made 450 blows per minute and
consumed 160 cubic feet of free air per minute. At Hell Gate different
COMPRESSED AIR.
507
machines doing the same woi k used from 80 to 150 cubic feet free air per
minute.
An average consumption may be taken generally from 80 to 100 cubic feet
per minute, according to the nature of the work.
The Popp Compressed-air System in Paris.— A most exten-
sive system of distribution of power by means of compressed air is that of
M. Popp, in Paris. One of the central stations is laid out for 24,000 horse-
power. Fora very complete description of the system, see Engineering,
Feb. 15, June 7, 21, and 28, 1889, and March 13 and 20, April 10, and May 1,
1891. Also Proc. Inst. M. E., July, 1889. A condensed description will be
found in Modern Mechanism, p. 12.
Utilization of Compressed Air in Small Motors.— In the
earliest stages of the Popp system in Paris it was recognized that no good
results could be obtained if the air were allowed to expand direct into the
motor; not only did the formation of ice due to the expansion of the air
rapidly accumulate and choke the exhaust, but the percentage of useful
work obtained, compared with that put into the air at the central station,
was so small as to render commercial results hopeless.
After a number of experiments M. Popp adopted a simple form of cast-
iron stove lined with fire-clay, heated either by a gas jet or by a small coke
fire. This apparatus answered the desired purpose until some better ar-
rangement was perfected, and the type was accordingly adopted through-
out the whole system. The economy resulting from the use of an improved
form was very marked, as will be seen from the following table.
EFFICIENCY OF AIR-HEATING STOVES.
Cast-iron Box
Stoves.
Wrought-
iron Coiled
Tubes.
14
20,342
45
215
17,900
1,278
2,032
14
11,054
45
364
17,200
1,228
2,058
46.3
38,428
41
347
39,200
830
2,545
Air heated per hour cu ft ....
Temp of ait* admitted to oven deg F
" " " at exit deg F.... . ....
Total heat absorbed per hour calories
Do. per sq. ft. of heating surface per hour, cals
The results given in this table were obtained from a large number of
trials. From these trials it was found that more than 70$ of the total num-
ber of calories in the fuel employed was absorbed by the air and trans-
formed into useful work. Whether gas or coal be employed as the fuel, the
amount required is so small as to be scarcely worth consideration; accord-
ing to the experiments carried out it does not exceed 0.2 Ib. per
horse-power per hour, but it is scarcely to be expected that in regular prac-
tice this quantity is not largely exceeded. The efficiency of fuel consumed
in this way is at least six times greater than when utilized in a boiler and
steam-engine.
According to Prof. Riedler, from 15#to 20$ above the power at the central
station can be obtained by means at the disposal of the power users, and it
has been shown by experiment that by heating the air to 480° F. an in-
creased efficiency of 30$ can be obtained.
A large number of motors in use among the subscribers to the Compressed
Air Company of Paris are rotary engines developing 1 horse-power and
less, and these in the early times of the industry were very extrava'gant in
their consumption. Small rotary engines, working cold air without expan-
sion, used as high as 2330 cu. ft. of air per brake horse-power per
hour, and with heated air 1624 cu. ft. Working expansively, a 1 horse-
power rotary engine used 1469 cu. ft. of cold air, or 960 cu. ft. of heated air,
and a2-horse-power rotary engine 1059 cu. ft. of cold air, or 847 cu. ft. of air,
heated to about 50° C.
The efficiency ef this type of rotary motors, with air heated to 50° C., may
now be assumed at 43*. With such an efficiency the use of small motors in
many industries becomes possible, while in cases where it is necessary to
have a constant supply of cold air economy ceases to be a matter of the first
importance.
Tests of a small Riedinger rotary engine, u^ed for driving sewing-machines
and indicating about 0.1 H.P. showed an air-consumption of 1377 cu. ft. per
508 AIR.
H P. per hour when the initial pressure of the air was 86 Ibs. per sq. in. and
its temperature 54° F., and 988 cu. ft. when the air was heated to 338° F., its
pressure being 72° Ibs. With a one-half horse-power variable-expansion'
rotary engine the air-consumption was from 800 to 900 cu. ft. per H.P. per
hour for initial pressures of 54 to 85 Ibs. per sq. in. with the air heated from
336° to 388° F., and 1148 cu. ft. with cold air, 40° F., and an initial pressure
of 72 Ibs. The volumes of air were all taken at atmospheric pressure.
Trials made with an old single-cylinder 80-horse-power Farcot steam-en .
gine, indicating 72 horse-power, gave a consumption of air per brake horse-
power as low as 465 cu. ft. per hour. The temperature of admission was
320° F., and of exhaust 95° F.
Prof. Elliott gives the following as typical results of efficiency for various
systems of compressors and air-motors :
Simple compressor and simple motor, efficiency 39. 1#
Compound compressor and simple motor, " 44.9
" compound motor, efficiency. . . 50.7
Triple compressor and triple motor, *• 55.3
The efficiency is the ratio of the indicated horse-power in the motor cylin*
ders to the indicated horse-power in the steam-cylinders of the compressor.
The pressure assumed is 6 atmospheres absolute, and the losses are equal
to those found in Paris over a distance of 4 miles.
Summary of Efficiencies of Compressed-air Transmission
at Paris, between the Central Station at St. Fargeau and
a 10-horse-power Motor Working with Pressure Re-
duced to 4>£ Atmospheres.
(The figures below correspond co mean results of two experiments cold and
two heated.)
1 indicated horse-power at central station gives 0.845 indicated horse-power
in compressors, and corresponds to the compression of 348 cubic feet of air
per hour f rom atmospheric pressure to 6 atmospheres absolute. (The weight
of this air is about 25 pounds.)
0.845 indicated horse-power in compressors delivers as much air as will do
0.52 indicated horse-power in adiabatic expansion after it has fallen in tem-
perature to the normal temperature of the mains.
The fall of pressure in mains between central station and Paris (say 5 kilo-
metres) reduces the possibility of work from. 0.52 to 0.51 indicated horse-
power.
The further fall of pressure through the reducing valve to 4^ atmospheres
(absolute) reduces the possibility of work from 0.51 to 0.50.
Incomplete expansion, wire-drawing, and other such causes reduce the
actual indicated horse-power of the motor from 0.50 to 0.39.
By heating the air before it enters the motor to about 320° F., the actual
indicated horse-power at the motor is, however, increased to 0.54. The ratio
of gain by heating the air is, therefore, 0.54 -f- 0.39 = 1.38.
In this process additional heat is supplied by the combustion of about 0.39
pounds of coke per indicated horse-power per hour, and if this be taken into
account, the real indicated efficiency of the whole process becomes 0.47
instead of 0.54.
Working with cold air the work spent in driving the motor itself reduces
the available horse-power from 0.39 to 0.26.
Working with heated air the work spent in driving the motor itself reduces
the available horse-power from 0.54 to 0.44.
A summary of the efficiencies is as follows :
Efficiency of main engines 0.845.
Efficiency of compressors 0.52-4-0.845= 0.61.
Efficiency of transmission through mains 0.51 -s- 0.52 = 0.98.
Efficiency of reducing valve 0.50-*- 0.51 = 0.98.
The combined efficiency of the mains and reducing valve between 5 and
4^ atmospheres is thus 0.98 X 0.98 = 0.96. If the reduction had been to 4,
3^, or 3 atmospheres, the corresponding efficiencies would have been 0.93,
0.89, and 0.85 respectively.
Indicated efficiency of motor 0.39 -f- 0.50 = 0.78.
Indicated efficiency of whole process with cold air 0.39. Apparent indi-
cated efficiency of whole process with heated air 0.54.
Real indicated efficiency of whole process with heated air 0.47.
Mechanical efficiency of motor, cold, 0.67.
Mechanical efficiency of motor, hot, 0.81.
COMPRESSED AIR. 509
Most of the compressed air in Paris is used for driving motors, but the
work done by these is of the most varied kind. A list of motors driven f rom
St. Fargeau station shows 225 installations, nearly all motors working at
from ^ horse-power to 50 horse-power, and the great majority of them more
than two miles away from the station. The new station at Quai de la Gare
is much larger than the one at St. Fargeau. Experiments on the Riedler
air-compressors at Paris, made in December, 1891, to determine the ratio
between the indicated work done by the air-pistons and the indicated work
in the steam-cylinders, showed a ratio of 0.8997. The compressors are driven
by four triple-expansion Corliss engines of 2000 horse-pow'er each.
Shops Operated by Compressed Air.— The Iron Age, March 2,
1893, describes the shops oftlie Wuerpei Switch and Signal Co., East St. Louis,
the machine tools of which are operated by compressed air, each of the
larger tools having its own air engine, and the smaller tools being belted
from shafting driven by an air engine. Power is supplied by a compound
compressor rated at 55 horse-power. The air engines are of the Kriebel
make, rated from 2 to 8 horse-power.
Pneumatic Postal Transmission.— A paper by A. Falkenau,
Eug'rs Club of Philadelphia, April 1894, entitled the "First United States
Pneumatic Postal System,1" gives a description of the system used in London
and Paris, and that recently introduced in Philadelphia between the main
post-office and a substation. In London the tubes are 2*4 and 3 inch lead
pipes laid in cast-iron pipes for protection. The carriers used in 2% -inch
tubes are but 1^ inches diameter, the remaining space being taken up by
packing. Carriers are despatched singly. First, vacuum alone was used;
later, vacuum and compressed air. The tubes used in the Continental cities
in Europe are wrought iron, the Paris tubes being 2^ inches diameter.
There the carriers are despatched in trains of six to ten, propelled by a
piston. In Philadelphia the size of tube adopted is 6^ inches, the tubes
being of cast iron bored to size. The lengths of the outgoing and return
tubes are 2928 feet each. The pressure at the main station is 7 Ibs., at the
substation 4 Ibs., and at the end of the return pipe atmospheric pressure.
The compressor has two air-cylinders 18 x 24 in. Each carrier holds about
200 letters, but 100 to 150 are taken as an average. Eight carriers may be
despatched in a minute, giving a delivery of 48,000 to 72,000 letters per hour.
The time required in transmission is about 57 seconds.
Pneumatic postal transmission tubes were laid in 1898 by the Batcheller
Pneumatic Tube Co. between the general post-offices in New York and
Brooklyn, crossing the East River on the bridge. The tubes are cast iron,
12-ft. lengths, bored to 8*4 in. diameter. The joints are bells, calked with
lead and yarn. There are two tubes, one operating in each direction. Both
lines are operated by air-pressure above the atmospheric pressure. One
tube is operated by an air-compressor in the New York office and the other
by one located in the Brooklyn office.
The carriers are 24 in. long, in the form of a cylinder 7 in. in diameter,
and are made of steel, with fibrous bearing-rings which fit the tube. Each
carrier will contain about 600 ordinary letters, and they are despatched at
intervals of 10 seconds in each direction, the time of transit between the two
offices being 3^ minutes, the carriers travelling at a speed of from 30 to 35
miles per hour.
The air-compressors were built by the Rand Drill Co. and the Ingersoll-
Sergeant Drill Co. The Rand Drill Co. compressor is of the duplex type
and has two steam-cylinders 10 X 20 in. and two air-cylinders 24 X 20 in.,
delivering 1570 cu. ft. of free air per minute, at 75 revolutions, the power
being about 50 H.P. Corliss valve-gear is on the steam cylinders and the
Rand mechanical valve-gear on the air-cylinders.
The Ingersoll -Sergeant Drill Co. furnished two duplex Corliss air-com-
pressors, with mechanically moved valves on air-cylinders. The steam-
cylinders are 14 x 18 in. and the air-cylinders 26*4 X 18 in. They are de-
signed for 80 to 90 revs, per min. and to compress to 20 Ibs. per sq. in.
Another double line of pneumatic tubes has been laid between the main
office and Postal Station H, Lexington Ave. and 44th St., in New York City.
This Hue is about 3J4 miles in length. There are three intermediate stations:
Third Ave. and 8th St., Madison Square, and Third Ave. and 28th St. The
carriers can be so adjusted when they are put into the tube that they will
traverse the line and be discharged automatically from the tube at the sta-
tion for which they are intended. The tubes are of the same size as those
of the Brooklyn line and are operated in a similar manner. The initial air-
compression is about 12 to 15 Ibs. On the Brooklyn line it is about 7 Ibs.
510 AIR.
There is also a tube system between the New York Post-office and the
Produce Exchange. For a very complete description of the system and its
machinery see "The Pneumatic Despatch Tube System," by B. C. Batchel-
ler. .T. B. Lippincott Co., Philadelphia, 1897.
The Mekarski Compressed-air Tramway at Berne,
Switzerland. (Eng'g News, April 20, 1898.)— The Mekarski system has
been introduced in Berne, Switzerland, on a line about two miles long, with
grades of 0.25$ to 3.7$ and 5.2$. The air is heated by passing it through
superheated water at 330° F. It thus becomes saturated with steam, which
subsequently partly condenses, its latent heat being absorbed by the ex-
panding air. The pressure in the car reservoirs is 440 Ibs. per sq. in.
The engine is constructed like an ordinary steam tramway locomotive,
and drives two coupled axles, the wheel-base being 5.2 ft. It has a pair of
outside horizontal cylinders, 5.1 x 8.6 in.; four coupled wheels, 27.5 in.
diameter. The total weight of the car including compressed air is 7.25 tons,
and with 30 passengers, including the driver and conductor, about 9.5 tons.
The authorized speed is about 7 miles per hour. Taking the resistance
due to the grooved rails and to curves under unfavorable conditions at 30
Ibs. per ton of car weight, the engine has to overcome on the steepest grade,
5#, a total resistance of about 0.63 ton, and has to develop 25 H.P. At the
maximum authorized working pressure in cylinders of 176 Ibs. persq. in. the
motors can develop a tractive force of 0.64 ton. This maximum is, there-
fore, just sufficient to take the car up the 5.2# grade, while on the natter
sections of the line the working pressure does not exceed 73 to 147 Ibs. per
sq. in. Sand has to be frequently used to increase the adhesion on the 2% to
5# grades.
Between the two car frames are suspended ten horizontal compressed-air
storage-cylinders, varying in length according to the available space, but of
uniform inside diameter of 17.7 in., composed of riveted 0.27-in. sheet iron,
and tested up to 588 Ibs. per sq. in. These cylinders have a collective
capacity of 64.25 cu. ft., which, according to Mr. Mekarski's estimate,
should have been sufficient for a double trip, f6% miles. The trial trips,
however, showed this estimate to be inadequate, and two further small
storage-cylinders had therefore to be added of 5.3 cu. ft. capacity each,
bringing the total cubic contents of the 12 storage-cylinders per car up to
75 cu. ft., divided into two groups, the working and the reserve battery, the
former of 49 cu. ft. the latter of 26 cu. ft. capacity.
From the results of six official trips, the pressure and the mean consump-
tion of air during a double journey per motor car are as follows:
Pressure of air in storage-cylinders at starting 440 Ibs. per sq. in.; at end
of up-journey 176 Ibs., reserve 260 Ibs.; at end of down-journey 103 Ibs.,
reserve 176 Ibs. Consumption of air during up-journey 92 Ibs., during down-
journey 31 Ibs.
The working experience of 1891 showed that the air consumption per
motor car for a double journey was from 103 to 154 Ibs., mean 123 Ibs., and
per car mile from 28 to 42 Ibs., mean 35 Ibs.
The principal advantages of the compressed-air system for urban and
suburban tramway traffic as worked at Berne consist in the smooth
and noiseless motion; in the absence of smoke, steam, or heat, of overhead
or underground conductors, of the more or less grinding motion of most
electric cars, and of the jerky motion to which underground cable traction
is subject. On all these grounds the system has vindicated its claims as
being preferable to any other so far known system of mechanical traction
for street tramways. Its disadvantages, on ihe other hand, consist in the
extremely delicate adjustment of the different parts of the system, in the
comparatively small supply of air carried by one motor car, which necessi-
tates the car returning to the depot for refilling after a run of only four
miles or 40 minutes, although on the Nogent and Paris lines the cars,
which are, moreover, larger, and carry outside passengers on the top,
run seven miles, and the loading pressure is 5J7 Ibs. per sq. in. as against
only 440 Ibs. at Berne
Longer distances in the same direction would involve either more power-
ful motors, a larger number of storage-cylinders, and consequently heavier
cars, or loading stations every four or seven miles; and in this respect the
system is manifestly inferior to electric traction, which easily admits of a
line of 10 to 15 miles in length being continuously fed from one central
station without the loss of time and expense caused by reloading.
The cost of working the Berne line is compared in the annexed table
.
FANS AND BLOWERS. 511
with some other tramways worked under similar conditions by horse and
mechanical traction for the year 1891.
For description of the Mekarski system as used at Nantes, France, see
paper by Prof. D. S. Jacobus, Trails. A. I. M. E., xix. 553.
American Experiments on Compressed Air for Street
Rail ways.— Experiments have been made recently in Washington, D. C.,
and in New York City on the use of compressed air for street-railway trac-
tion. The air was compressed to 2000 Ibs. per sq. in. and passed through a
reducing- valve and a heater before being admitted to the engine. For an
extended discussion of the relative merits of compressed air and electric
traction, with an account of a test of a four-stage compressor giving a
pressure of 2500 Ibs. per sq. in., see Eng'g News, Oct. 7 and Nov. 4, 1897. A
summarized statement of the probable efficiency of compressed-air traction
is given as follows: Efficiency of compression to 2000 Ibs. per sq. in. 65#.
By wire-drawing to 100 Ibs. 57.5^ of the available energy of the air will be
lost, leaving 65 X .425 = 27.625^ as the net efficiency of the air. This may
be doubled by heating, making 55 25#, and if the motor has an efficiency of
80$ the net efficiency of traction by compressed air will be 55.25 x .80 = 44.2£.
For a description of the Hardie compressed-air locomotive, designed for
street-railway work, see Eng'g News, June 24, 1897. For use of compressed
air in mine haulage, see Eng'g News, Feb. 10, 1898.
Compressed Air for Working Underground Pnmps in
Mines,— Eng'g Record, May 19, 1894, describes an installation of com-
pressors for working a number of pumps in the Nottingham No. 15 Mine,
Plymouth, Pa., which is claimed to be the largest in America. The com-
pressors develop above 2300 H.P., and the piping, horizontal and vertical, is
6000 feet in length. About 25,000 gallons of water per hour are raised.
FANS AND BLOTTERS.
Centrifugal Fans.— The ordinary centrifugal fan consists of a num-
ber of blades fixed to arms, revolving on a shaft tot high speed. The width
of the blade is parallel to the axis of the shaft. Most engineers' reference
books quote the experiments of W. Buckle, Proc. Inst. M.E., 1847, as still
standard. Mr. Buckle's conclusions are given below, together with data of
more recent experiments.
Experiments were made as to the proper size of the inlet openings and on
the proper proportions to be given to the vane. The inlet openings in the
sides of the fan-chest were contracted from 17^ in., the original diameter,
to 12 and 6 in. diam., when the following results were obtained:
First, that the power expended with the opening contracted to 12 in. diam.
was as 2*4 to 1 compared with the opening of 17*4 io. diam.; the velocity of
the fan being nearly the same, as also the quantity and density of air
delivered.
Second, that the power expended with the opening contracted to 6 in.
diam. was as 2^£ to 1 compared with the opening of 17J^ in. diam.; the
velocity of the fan being nearly the same, and also the area of the efflux
pipe, but the density of the air dec-reared one fourth.
These experiments show that the inlet openings must be made of sufficient
size, that the air may have a free and uninterrupted action in its passage to
the blades of the fan; for if we impede this action we do so at the expense
of power.
With a vane 14 in. long, the tips of which revolve at the rate of 236.8 ft.
per second, air is condensed to 9.4 ounces per square inch above the pres-
sure of the atmosphere, with a power of 9.6 H. P. ; but a vane 8 inches long,
the diameter at the tips being the same, and having, therefore, the same
velocity, condenses air to 6 ounces per square inch only, and takes 12 H. P.
Thus the density of the latter is little better than six tenths of the former,
while the power absorbed is nearly 1.25 to I. Although the velocity of the
tips of the vanes is the same in each case, the velocities of the heels of the
respective blades are very different, for, while the tips of the blades in each
case move at the same rate, the velocity of the heel of the 14-inch is in the
ratio of 1 to 1.67 to the velocity of the heel of the 8-inch blade. The
longer blades approaching nearer the centre, strikes the air with less velo-
city, and allows it to enter on the blade with greater freedom, and with
considerably less force than the shorter one. The inference is, that the
short blade must take more power at the same time that it accumulates a
less quantity of air. These experiments lead to the conclusion that the
length of the vane demands as great a consideration as the proper
diameter of tho inlet opening. If there were no other object in view, it
512
AIR.
would be useless to make the vanes of the fan of a greater width than the
inlet opening can freely supply. On the proportion of the length and width
of the vane and the diameter of the inlet opening rest the three most im-
portant points, viz., quantity and density of air, and expenditure of power.
In the 14-inch blade the tip has a velocity 2.6 times greater than the
heel; and, by the laws of centrifugal force, the air will have a density 2.6
times greater at the tip of the blade than that at the heel. The air cannot
enter on the heel with a density higher than that of the atmosphere; but in
its passage along the vane it becomes compressed in proportion to its
centrifugal force. The greater the length of the vane, the greater will be
the difference of the centrifugal force between the heel and the tip of the
blade; consequently the greater the density of the air.
Reasoning from these experiments, Mr. Buckle recommends for easy ref-
erence the following proportions for the construction of the fan:
1. Let the width of the vanes be one fourth of the diameter; 2. Let the
diameter of the inlet openings in the sides of the fan-chest be one half the
diameter of the fan; 3. Let the length of the vanes be one fourth of the
diameter of the fan.
In adopting this mode of construction, the area of the inlet openings in
the sides of the fan-chest will be the same as the circumference of the heel
of the blade, multiplied by its width; or the same area as the space
described by the heel of the blade.
Best Proportions of Fans, (Buckle.)
PRESSURE FROM 3 OUNCES TO 6 OUNCES PER SQUARE INCH; OR 5.2 INCHES
TO 10.1 INCHES OF WATER.
Diameter
Vanes.
Diameter
of Inlet
Diameter
Vanes.
Diameter
of Inlet
of Fan
Open-
of Fan
Open-
Width.
Length.
ings.
Width.
Length.
ings.
ft. ins.
ft. ins.
ft. ins.
ft. ins.
ft. ins.
ft. ins.
ft. ins.
ft. ins.
3 0
0 9
0 9
1 6
4 6
1 1*6
1 VA
2 3
3 6
O-lOfc
0 101^
1 9
5 0
1 3
1 3
2 6
4 0
1 0
1 0
2 0
6 0
1 6
1 6
3 0
PRESSURE FROM 6 OUNCES TO 9 OUNCES PER SQUARE INCH, AND UPWARDS,
OR 10.4 INCHES TO 15.6 INCHES OF WATER.
3 0
0 7
1 0
1 0
4 6
o wy2
1 4Y2
1 9
3 6
0 8^
1 V/2
1 3
5 0
1 0
1 6
2 0
4 0
0 9^
1 3^
1 6
6 0
1 2
1 10
2 4
The dimensions of the above tables are not laid down as prescribed limits,
but as approximations obtained from the best results in practice.
Experiments were also made with reference to the admission of air into
the transit or outlet pipe. By a slide the width of the opening into this pipe
was varied from 12 to 4 inches. The object of this was to proportion the
opening to the quantity of air required, and thereby to lessen the power
necessary to drive the fan. It was found that the less this opening is made,
Erovided we produce sufficient blast, the less noise will proceed from the
a,n; and by making the tops of this opening level with the tips of the vane,
the column of air has little or no reaction on the vanes.
The number of blades may be 4 or 6. The case is made of the form of
an arithmetical spiral, widening the space between the case and the revolv-
ing blades, circumferentially, from the origin to the opening for discharge.
The following rules deduced from experiments are given in Spretson's
treatise on Casting and Founding:
The fan-case should be an arithmetical spiral to the extent of the depth
of the blade at least.
The diameter of the tips of the blades should be about double the diameter
of the hole in the centre; the width to be about two thirds of the radius of
the tips of the blades. The velocity of the tips of the blades should be rather
FANS AND BLOWERS. 513
more than the velocity due to the air at the pressure required, say one
eighth more velocity.
In some cases, two fans mounted on one shaft would be more useful than
one wide one, as in such an arrangement twice the area of inlet opening is
obtained as compared with a single wide fan. Such an arrangement may
be adopted where occasionally half the full quantity of air is required, as
one of them may be put out of gear, thus saving power.
Pressure due to Velocity of the Fan-blades.— " By increas-
ing the number of revolutions of the fan the head or pressure is increased,
the law being that the total head produced is equal (in centrifugal fans) to
twice the height due to the velocity of the extremities of the blades, or
v '
H"= — approximately in practice" (W. P. Trowbridge, Trans. A. S. M. E.,
vii. 536.) This law is analogous to that of the pressure of a jet striking a
plane surface. T. Hawksley, Proc. Inst. M. E., 1882, vol. Ixix.. says: "The
Eressure of a fluid striking a plane surface perpendicularly and then escap-
ig at right angles to its original path is that due to twice the height h due
the velocity."
(For discussion of this question, showing that it is an error to take the
pressure as equal to a column of air of the height h = v2 -f- 2g, see Wolff on
Windmills, p. 17.)
Buckle says: " From the experiments it further appears that the velocity
of the tips of the fan is equal to nine tenths of the velocity a body would
acquire in falling the height of a homogeneous column of air equivalent to
the density." D. K. Clark (R. T. & D., p. 924), paraphrasing Buckle, appar
ently, says: " It further appears that the pressure generated at the circum
ference is one ninth greater than that which is due to the actual circumfer-
ential velocity of the fan." The two statements, however, are not in
harmony, for lfv = 0.9 V^gH, H = • Q 0 = 1.234 and not 1$ .
U.ol x tiff *<7 *ff
If we take the pressure as that equal to a head or column of air of twice
the height due the velocity, as is correctly stated by Trowbridge, the para-
doxical statements of Buckle and Clark— which would indicate that the
actual pressure is greater than the theoretical— are explained, and the
formula becomes H= .617— and v = 1.273 VgH = 0.9 V^H, in which H
is the head of a column producing the pressure, which is equal to twice the
theoretical head due the velocity of a falling body (or h - |- j, multiplied
by the coefficient .617. The difference between 1 and this coefficient ex-
presses the loss of pressure due to friction, to the fact that the inner por-
tions of the blade have a smaller velocity than the outer edge, and probably
to other causes. The coefficient 1.273 means that the tip of the blade must
be given a velocity 1.273 times that theoretically required to produce the
head H.
To convert the head H expressed in feet to pressure in Ibs. per sq. in.
multiply it by the weight of a cubic foot of air at the pressure and tempera-
ture of the air expelled from the fan (about .08 Ib. usually) and divide by
144. Multiply this by 16 to obtain pressure in ounces per sq. in. or by 2.035
to obtain inches of mercury, or by 27.71 to obtain pressure in inches of
water column. Taking .08 as the weight of a cubic foot of air,
p Ibs. per sq. in. = .00001066v2; v = 310 4/jT nearly;
Pi ounces per sq. in. = .0001 706v2; v = 80 Vp± "
p2 inches of mercury = .00002169u2; v = 220 1/p, '»
pz inches of water = .0002954v2; v= 60 i/ps •*
In which v = velocity of tips of blades in feet per second.
Testing the above formula by the experiment of Buckle with the vane
14 inches long, quoted above, we have p = .00001066v2 = 9.56 oz. The ex-
periment gave 9.4 oz.
Testing it by the experiment of H. I. Snell, given below, in which the
circumferential speed was about 150 ft. per second, we obtain 3.85 ounces,
while the experiment gave from 2.38 to 3.50 ounces, according to the amount
of opening for discharge. The numerical coefficients of the above formulae
are all based on Buckle's statement that the velocity of the tips of the fan
is equal to nine tenths of the velocity a body would acquire in falling the
514
Atft.
height of a homogeneous column of air equivalent to the pressure. Should
other experiments show a different law, the coefficients can be corrected
accordingly. It is probable that they will vary to some extent with differ-
ent proportions of fans and different speeds.
Taking the formula v = 80 Vpi, we have for different pressures in ounces
per square inch the following velocities of the tips of the blades in feet per
second:
p,= ounces per square inch.... 2 3 4 5 6 7 8 10 12 14
v = feet per second ............ 113 139 160 179 196 212 226 253 277 299
A rule in App. Cyc. Mech^ article " Blowers," gives the following velocities
of circumference for different densities of blast in ounces: 3, 170; 4, 180; 5,
195; 6, 205; 7, 215.
The same article gives the following tables, the first of which shows that
the density of blast is not constant for a given velocity, but depends on the
ratio of area of nozzle to area of blades:
Velocity of circumference, feet per second. 150 150 150 170 200 200 220
Area of nozzle -*- area of blades 2 1 y% J4 Vz V6 /4
Density of blast, oz. per square inch 1 2 3 4 4 6 6
QUANTITY OF AIR OF A GIVEN DENSITY DELIVERED BY A FAN.
Total area of nozzles in square feet X velocity in feet per minute corre-
sponding to density (see table) = air delivered in cubic feet per minute.
DounncE' Velocity, feet
5000
7000
8600
10,000
Velocity, feet
11,000
12,250
13,200
14,150
pesqn.
9
10
11
12
Velocity, feet
linute.
15,000
15,800
16,500
17,300
Experiments with Blowers. (Henry I. Snell, Trans. A. S. M. E.
ix. 51.)— The following tables give velocities of air discharging through an
aperture of any size under the given pressures into the atmosphere. The
volume discharged can be obtained by multiplying the area of discharge
opening by the velocity, and this product by the coefficient of contraction:
.65 for a thin plate and .93 when the orifice is a conical tube with a conver-
gence of about 3.5 degrees, as determined by the experiments of Weisbach.
The tables are calculated for a barometrical pressure of 14.69 Ibs. (=
235 oz.), and for a temperature of 50° Fahr., from the formula V= ^2gh.
Allowances have been made for the effect of the compression of the air,
but none for the heating effect due to the compression.
At a temperature of 50 degrees, a cubic foot of air weighs .078 Ibs., and
calling g = 32.1602, the above formula may be reduced to
Vl = 60 t'31.5812 X (235 + P) X P,
where V\ = velocity in feet per minute.
P = pressure above atmosphere, or the pressure shown by gauge, in oz,
per square inch.
Pressure
per sq. in.
in inches of
water.
Corre-
sponding
Pressure in
oz. per sq.
inch.
Velocity
due the
Pressure in
feet per
minute.
Pressure
per sq. in.
in inches of
water.
Corre-
sponding
Pressure in
oz. per sq.
inch.
Velocity due
the Pressure
in feet per
minute.
1/32
1/16
ft
.!•
.01817
.03634
.07268
.10902
.14536
.18170
.21804
.29072
696.78
987.66
1393.75
1707.00
1971.30
2204.16
2414.70
2788.74
1
1%
2
.36340
.43608
.50870
.58140
.7267
.8721
1.0174
1.1628
3118.38
3416.64
3690.62
3946.17
~ 4362.62
4836.06
5224.98
5587.58
FAKS AKD BLOWERS.
515
Press-
ure
Velocity
due the
Press-
ure
Velocity
due the
Press-
ure
Velocity
due the
Pressure
Velocity
due the
in oz.
Pressure
in oz.
Pressure
in oz.
Pressure
in oz.
Pressure
per sq.
inch.
in ft. per
minute.
per sq.
inch.
in ft. per
minute.
per sq.
inch.
in ft. per
minute.
persq. in.
in ft. per
minute.
.25
2,582
2.25
7,787
5.50
12,259
11.00
17,534
.50
3,658
2.50
8,213
6.00
12,817
12.00
18,350
.75
4,482
2.75
8,618
6.50
13,354
13.00
19,138
1.00
5,178
3.00
9,006
7.00
13,878
14.00
19,901
1.25
5,792
3.50
9,739
7.50
14,374
15.00
20.641
1.50
6,349
4.00
10,421
8.00
14,861
16.00
21,360
1.75
6,801
4.50
11,065
9.00
15,795
2.00
7,338
5.00
11,676
10.00
16,684
Pressure in ounces
per square inch.
Velocity in feet
per minute.
Pressure in ounces
per square inch.
Velocity in feet per
minute.
.01
.02
.03
.04
.05
516.90
722.64
895.26
1033.86
1155.90
.06
.07
.08
.09
.10
12C6.24
1367.76
1462.20
1550.70
1635.00
Experiments on a Fan with Varying Discharge-opening*
Revolutions nearly constant.
2
* d
<H '
M*4
^.i
evolutions per
minute.
rea of Dischan
in square inche
bserved Pressu
in ounces.
olume of Air d
charged per mi
cubic feet.
orse-power.
ctual Number
cu. ft. of Air d
livered per H.I
heoret. Vol. p
min. that may
discharged wi
1 H.P. at corres
Pressure.
fficiency of Bio
ers as per Expe
ment.
a
^
O
>
W
1
EH
*
1519
0
3.50
0
.80
1048
1479
6
3.50
406
1.15
353*
1048
!,337
1480
10
3.50
676
1.30
520
1048
.496
1471
20
3.50
1353
1.95
694
1048
.66
1485
28
3.50
1894
2.55
742
1048
.709
1485
36
3.40
2400
3.10
774 '
1078
.718
1465
40
3.25
2605
3.30
790
1126
.70
1468
44
3.00
2752
3.55
775
1222
.635
1500
48
3.00
3002
3.80
790
1222
.646
1426
89.5
2.38
3972
4.80
827
1544
.536
The fan wheel was 23 inches in diameter, 6% inches wide at its periphery,
and had an inlet of 12J^ inches in diameter on either side,' which was
partially obstructed by the pulleys, which were 5 9/16 inches in diameter. It
had eight blades, each of an area of 45.49 square inches.
The discharge of air was through a conical tin tube with sides tapered at
an angle of 3^ degrees. The actual area of opening was 1% greater than
given in the tables, to compensate for the vena contracta.
In the last experiment, 89.5 sq. in. represents the actual area of the mouth
of the blower less a deduction for a narrow strip of wood placed across it for
the purpose of holding the pressure-gauge. In calculating the volume of air
discharged in the last experiment the value of vena contracta is taken at .80,
516
AIK.
Experiments were undertaken for the purpose of showing the results ob-
tained by running the same fan at different speeds with the discharge-open-
ing the same throughout the series.
The discharge-pipe was a conical tube 8V£ inches inside diameter at the
end, having an area of 56.74, which is 7% larger than 53 sq. inches ; therefore
53 square inches, equal to .868 square feet, is called the area of discharge, as
that is the practical area by which the volume of air is computed.
Experiment* on a Fan with Constant Discharge-open-
ing and Varying Speed.— The first four columns are given by Mr.
Snell, the others are calculated by the author.
*
4^
«H O
^«
•
CM
fi
o>
o
a
gU*
gj
g S
fe^"£
?E<§
o
§
.2
s
0
.33
tl
HO.
ȣv
O M ®
'^ aT
Wg
t*
i
S
p
"3 1
CM
&
i*
Ji
f-
' *$
2s! *
1 J«
i'^
0 0
tS a
£
P
t
1
0 b
i
1|
1 £ p
111
iii
o
Si
'o
&
|
*o A
i
^
Is
3
^ •
S
1
600
.50
1336
.25
60.2
56.6
85.1
3,630
.182
73
800
.88
1787
.70
80.3
75.0
85.6
4,856
.429
61
1000
1.38
2245
1.35
100.4
94.
85.4
6,100
.845
63
1200
2.00
2712
2.20
120.4
113.
85.1
7,370
1.479
67
1400
2.75
3177
3.45
140.5
133.
84.8
8,633
2.283
66
1600
3.80
3670
5.10
160.6
156.
82.4
9,973
3.803
74
1800
4.80
4172
8.00
180.6
175.
82.4
11,337
5.462
68
2000
5.95
4674
11.40
200.7
195.
85.6
12,701
7.586
67
Mr. Snell has not found any practical difference between the efficiencies
of blowers with curved blades and those with straight radial ones
From these experiments, saj s Mr. Snell, it appears that we may expect to
receive back 65$ to 75$ of the power expended, and no more.
The great amount of power often used to run a fan is not due to the fan
itself, but to the method of selecting, erecting, and piping it.
(For opinions on the relative merits of fans and positive rotary blowers,
see discussion of Mr. Snell's paper, Trans. A. S. M. E., ix. 66, etc.)
Comparative Efficiency of* Fans and Positive Blowers.—
(H. M. Howe, Trans. A. I. M. E., x. 482.) — Experiments with fans and positive
(Baker) blowers working at moderately low pressures, under 20 ounces, show
that they work more efficiently at a given pressure when delivering large
Tolumes (/.e., when working nearly up to their maximum capacity) than
when delivering comparatively small volumes. Therefore, when great vari-
ations in the quantity and pressure of blast required are liable to arise, the
highest efficiency would be obtained by having a number of blowers, always
driving them up to their full capacity, and regulating the amount of blast
by altering the number of blowers at work, instead of having one or two
very large blowers and regulating the amount of blast by the speed of the
blowers.
There appears to be little difference between the efficiency of fans and of
Baker blowers when each works under favorable conditions as regards
quantity of work, and when each is in good order.
For a given speed of fan, any diminution in the size of the blast-orifice de-
creases the consumption of power and at the same time raises the pressure
of the blast ; but it increases the consumption of power per unit of orifice
for a given pressure of blast. When the orifice has been reduced to the
normal size for any given fan, further diminishing it causes but
slight elevation of the blast pressure; and, when the orifice becomes com.
paratively small, further diminishing it causes no sensible elevation of the
blast pressure, which remains practically constant, even when the orifice is
entirely closed.
Many of the failures of fans have been due to too low speed, to too small
pulleys, to improper fastening of belts, or to the belts being too nearly ver-
tical; in brief, to bad mechanical arrangement, rather than to inherent de-
fects in the principles of the machine.
FAHS AND BLOWERS.
517
If several fans are used, it is probably essential to high efficiency to pro-
vide a separate blast pipe for each (at least if the fans are of different size
or speed), while any number of positive blowers may deliver into the same
pipe without lowering their efficiency.
Capacity of Fans and Blowers.
The following tables show the guaranteed air-supply and air-removal of
leading forms of blowers and exhaust fans. The figures given are often
exceeded in practice, especially when the blowers and fans are driven at
higher speeds than stated. The ratings, particularly of the blowers, are
below those generally given in catalogues, but it was the desire to present
only conservative and assured practice. (A. R. Wolff on Ventilation.)
QUANTITY OP AIR SUPPLIED TO BUILDINGS BY BLOWERS OF VARIOUS SIZES.
Capacity
Capacitv
Diam-
eter of
Wheel
in feet.
Ordinary
Number
of Revs,
per min.
Horse-
power
to Drive
Blower.
cu. ft.
per min.
against a
Pressure
of 1 ounce
Diam-
eter of
Wheel
in feet.
Ordinary
Number
of Revs,
per min.
Horse-
power
to Drive
Blower.
cu. ft.
per min.
against a
Pressure
of 1 ounce
per sq. in
per sq. in.
4
350
6.
10,635
9
175
29
56,800
5
325
9.4
17,000
10
160
35.5
70,340
6
275
13.5
29,618
12
130
49.5
102,000
7
230
18.4
42,700
14
110
66
139,000
8
200
24
46,000
15
100
77
160,000
If the resistance exceeds the pressure of one ounce per square inch, of
above table, the capacity of the blower will be correspondingly decreased,
or power increased, and allowance for this must be made when the distrib-
uting ducts are small, of excessive length, and contain many contractions
and bends.
QUANTITY OF AIR MOVED BY AN APPROVED FORM OF EXHAUST FAN, THE
FAN DISCHARGING DIRECTLY FROM ROOM INTO THE ATMOSPHERE.
Diam-
eter of
Wheel
in feet.
Ordinary
Number
of Revs.
per min.
Horse-
power
to Drive
Fan.
Capacity
in cu. ft.
per min.
Diam-
eter of
Wheel
in feet.
Ordinary
Number
of Revs,
per min.
Horse-
power
to Drive
Fan.
Capacity
in cu. ft.
per min.
2.0
2.5
3.0
3.5
600
550
500
500
0.50
0.75
1.00
2.50
5,000
8,000
12,000
20,000
4.0
5.0
6.0
7.0
475
350
300
250
3.50
4.50
7.00
9.00
28,000
35,000
50,000
80,000
The capacity of exhaust fans here stated, and the horse-power to drive
them, are for free exhaust from room into atmosphere. The capacity de-
creases and the horse-power increases materially as the resistance, resulting
from lengths, smallness and bends of ducts, enters as a factor. The differ-
ence in pressures in the two tables is the main cause of variation in the re-
spective records. The fan referred to in the second table could not be used
with as high a resistance as one ounce per square inch, the rated resistance
of the blowers.
Caution in Regard to Use of Fan and Blower Tables.—
Many engineers report that manufacturers' tables overrate the capacity of
their fans and underestimate the horse-power required to drive them. In
some cases the complaints may be due to restricted air outlets, long and
crooked pipes, slipping of belts, too small engines, etc.
518
AIB.
CENTRIFUGAL FANS.
Flow of Air througli an Orifice.
VELOCITY, VOLUME, AND H P. REQUIRED WHEN AIR UNDER GIVEN PRESSURE
IN OUNCES PER SQ. IN. IS ALLOWED TO ESCAPE INTO THE ATMOSPHERE.
(B. F. Sturtevant Co.)
D W
3 85
11?
Pn
«
1,828
2,585
3,165
3,654
4,084
4,473
4,830
5,162
5,473
5,708
6,048
6,315
6,571
6,818
7,055
!*«£
5 *
12.69
17.95
21.98
25.37
28.36
31.06
33.54
35.85
38.01
40.06
42.00
43.86
45.63
47.34
49.00
a
.00043
.00122
.00225
.00346
.00483
.00635
.00800
.00978
.01166
.01366
.01575
.01794
.02022
.02260
.02505
AO g
111
W
.0340
.0680
.1022
.1363
.1703
.2044
.2385
.2728
.3068
.3410
.37'50
.4090
.4431
.4772
.5112
!§£
Is
7,284
7,507
7,722
7,932
8,136
8,334
8,528
8,718:
8,903
9,084
9,262
9,435
9,606
9,773
9,938
10,100
50.59
52.13
53.63
55.08
56.50
57.88
59,22
60.54
61.83
63.08
64.32
65.52
66.71
67.87
69.01
70.14
I O y>
r s
.02759
.03021
.03291
.03852
.04144
.01442
.04747
.05058
.05376
.05701
.06031
.06368
.06710
.07058
.07412
.5454
.5795
.6136
.6476
.6818
.7160
.7500
.7841
.8180
.8522
.8863
.9205
.9546
.9887
1.0227
1.056?
The headings of the 2d and 3d columns in the above table have been
abridged from the original, which read as follows: Velocity of dry air, 50°
F., escaping into the atmosphere througli any shaped orifice in any pipe or
reservoir in which the given pressure is maintained. Volume of air in cubic
feet which may be discharged in one minute through an orifice having an
effective area of discharge of one square inch. The 5th column, not in the
original, has been calculated by the author. The figures represent the
horse-power theoretically required to move 1000 cu. ft. of air of the given
pressures through an orifice, without allowance for the work of compression
or for friction or other losses of the fan. These losses may amount to from
60$ to 100$ of the given horse-power.
The change in density which results from a change in pressure has been
taken into account in the calculations of the table. The volume of air at a
given velocity discharged through an orifice depends upon its shape, and is
always less than that measured by its full area. For a given effective area
the volume is proportional to the velocity. The power required to move air
tli rough an orifice is measured by the product of the velocity and the total
resisting pressure. This power for a given orifice varies as the cube of the
velocity. For a given volume it varies as the square of the velocity. In the
movement of air by means of a fan there are unavoidable resistances
which, in proportion to their amount, increase the actual power consider-
ably above the amount here given.
For any size of centrifugal fan there exists a certain maximum area over
which a given pressure may be maintained, dependent upon and propor«
tional to the speed at which it is operated. If this area, known as its
''capacity area," or square inches of blast, be increased, the pressure is
lowered (the volume being increased), but if decreased the pressure remains
constant. The revolutions of a given fan necessary to maintain a given
pressure under these conditions are given in the table on p. 519, which is
based upon the abve table. The pressure produced by a given fan and its
effective capacity area being known, its nominal capacity and the horse-
power required, without allowance for frictional losses, may be determined
from the table above.
In practice the outlet of a fan greatly exceeds the capacity area; hence
the volume moved and the horse-power required are in excess of the
determined as above.
CENTRIFUGAL FANS,
519
Steei-plate Full Housing Fans. (Buffalo Forge Co.)
Capacities in cubic feet of air per minute. (See also table on p. 525.)
Size
Revolutions per Minute.
in.'
100
150
200
250
300
350
400
450
500
550
600
50
1650
2475
3300
4125
4950
5775
6600
7425
8250
9075
9000
60
2480
3720
4960
6200
7440
8680
9920
11160
12400
13640
14880
70
4500
6750
9000
11250
13500
15750
18000
20250
22500
80
7070
10605
14140
17675
21210
24745
28280
31815
90
10400
15600
20800
26000
31200
36400
41600
100
14280
21420
28560
35700
42840
49980
57120
110
18960
28440
37920
47400
56880
66360
120
24800
37200
49600
62000
74400
130
31200
46800
62400
78000
109200
140
38354
57531
76708
95885
150
49260
73890
98520
123150
The Sturtevant Steel Pressure-blower Applied to Cupola
Furnaces and Forges.
Cupola Furnaces.
Forges.
Number
Diameter
of
Melting
Blast-
pressure
Rev. per
min. of
Number
Rev. per
min. Blower
of
Blower.
Cupola
inside of
Capacity
of Cupola
required
in Wind-
Blower nec-
essary to
of Forges
supplied
necessary
to produce
Lining,
in.
per hour
in Ibs.
box in
ounces
produce
required
by
Blower.
pressure
for
persq. in.
pressure.
forge fire.
4/0
1
5,548
2/0
2
4,294
0
3
3,645
1
22
1,200
5
3,569
4
3,199
2
26
1,900
6
3,282
6
2,691
3
30
2,900
7
3,030
8
2,305
4
35
4,200
8
2,818
10
2,009
5
40
6,§00
10
2,690
14
1,722
6
46
8,900
12
2,670
19
1,567
7
53
12,500
14
2,316
25
1,264
8
60
16,500
14
2,023
35
1,104
9
72
24.000
16
1,854
45
950
10
84
34,000
16
1,627
60
834
The above table relates to common cupolas under ordinary conditions and
to forges of medium size. The diameter of cupola given opposite each size
blower is the greatest which is recommended; in cases where there is a sur-
plus of power one size larger blower may be used to advantage. 'I he melt-
ing capacity per hour is based upon an average of tests on some of the best
cupolas found, and is reliable in cases where the cupola is well constructed
and carefully operated. The blast-pressure required in wind-box is the
maximum under ordinary conditions when coal is used as fuel. When coke
is employed the pressure may be lower.
The cupola pressures given are those in the wind-box, while the basis
pressure for forges is 4 ounces in the tuyere pipe. The corresponding rev-
olutions of fan given are in each case sufficient to maintain these pressures
at the fan outlet when the temperature is 50°. The actual speed must be
higher than this by an amount proportional to the resistance of pipes and
the increase of temperature, and can only be determined by a knowledge of
the existing conditions.
(For other data concerning Cupolas see Foundry Practice,)
520
AIR.
Diameters of Blast-pipes Required for Steel Pressure-
blowers. (B. F. Sturtevaut Co.)
Based on the loss of pressure resulting from transmission being limited to
one-half ounce per square inch.
Pres-
sure per
sq. in.
*]
M
Length
of Pipe
in ft.
Number of Blower.
100
200
300
400
100
200
300
400
" The above table has been constructed on the following basis: Allowing a
loss of pressure of ^ oz. in the process of transmission through any length
of pipe of any size as a standard, the increased friction due to lengthening
the pipe has been compensated for by an enlargement of the pipe sufficient
to keep the loss still at ^ oz. Thus if air under a pressure of 8 oz. is to be
delivered by a No. 6 blower, through a pipe 100 ft. in length, with a loss of
^£ oz. pressure, the diameter of the pipe must be 11% in. If its length is
increased to 400 ft. its diameter should also be increased to 15J^ in., or if
the pressure be increased to 12 oz. the pipe, if 100 ft. long, must be V2% in.
in diameter, providing the loss of ^ oz. is not to be exceeded. This loss of
\^ oz. is to be added to the pressure to be maintained at the fan if the
tabulated pressure is to be secured at the other end of the pipe.1'
Kflicieiic-y of Fans.— Much useful information on the theory and
practice of fans and blowers, with results of tests of various forms, will be
found in Heating and Ventilation, June to Dec. 1897, in papers by Prof.
R. C. Carpenter and Mr. W. G. Walker. It is shown by theory that the
volume of air delivered is directly proportional to the speed of rotation,
that the pressure varies as the square of the speed, and that the horse-
power varies as the cube of the speed. For a given volume of air moved
the horse-power varies as the square of the speed, showing the great ad-
vantage of large fans at slow speeds over small fans at high speeds deliver-
ing the same volume. The theoretical values are greatly modified by varia-
tions in practical conditions. Prof. Carpenter found that with three fans
running at a speed of 6200 ft. per minute at the tips of the vanes, and an air-
pressure of 2^ in. of water column, the mechanical efficiency, or the horse-
power of the air delivered divided by the power required to drive the fan,
ranged from 32$ to 4?#, under different conditions, but with slow speeds it
was much less, in some cases being under 20$. Mr. Walker in experiments
on disk fans found efficiencies ranging all the way from 1A% to 43$. the size
of the fans and the speed being constant, but the shape and angle of the
blades varying. It is evident that there is a wide margin for improvements
in the forms of fans and blowers, and a wide field for experiment to deter"
mine the conditions that will give maximum efficiency.
CENTRIFUGAL FANS. 521"
Centrifugal Ventilators for Mines.— Of different appliances for
ventilating mines various forms of centrifugal machines having proved their
efficiency have now almost completely replaced all others. Most if not all
of the machines in use in this country are of this class, being either open-
periphery fans, or closed, with chimney and spiral casing, of a more or less
modified Guibal type. The theory of such machines has been demonstrated
by Mr. Daniel Murgue in " Theories and Practices of Centrifugal Ventilating
Machines,11 translated by A. L Stevenson, and is discussed in a paper by R.
Van A. Norris, Trans. A. I. M. E. xx. 637. From this paper the following for-
mulae are taken:
Let a = area in sq. ft. of an orifice in a thin plate, of such area that its re-
sistance to the passage of a given quantity of air equals the
resistance of the mine;
o = orifice in a thin plate of such area that its resistance to the pas-
sage of a given quantity of air equals that of the machine;
Q = quantity of air passing in cubic feet per minute;
V= velocity of air passing through a in feet per second;
F0 = velocity of air passing through o in feet per second;
h = head in feet air -column to produce velocity V\
h0 = head in feet air-column to produce velocity F0.
Q = 0.65aF; V = 1/2^/T; Q = 0.65a V%gh\
a = - " = equivalent orifice of mine;
0.65 1
or, reducing to water-gauge in inches and quantity in thousands of feet per
minute,
0.65o 1/2^f0;
3 t) = equivalent orifice of machine.
The theoretical depression which can be produced by any centrifugal ven-
tilator is double that due to its tangential speed. The formula
T* F*
= -* - w
in which Tis the tangential speed, Fthe velocity of exit of the air from the
space between the blades, and H the depression measured in feet of air-
column, is an expression for the theoretical depression which can be pro-
duced by an uncovered ventilator; this reaches a maximum when the air
leaves the blades without speed, that is, F= 0, and H = T2 -f- 2g.
Hence the theoretical depression which can be produced by any uncovered
ventilator is equal to the height due to its tangential speed, and one half-
that which can be produced by a covered ventilator with expanding
chimney.
So long as the condition of the mine remains constant:
The volume produced by any ventilator varies directly as the speed of
rotation .
The depression produced by any ventilator varies as the square of the
speed of rotation.
For the same tangential speed with decreased resistance the quantity of
air increases and the depression diminishes.
The following table shows a few results, selected from Mr. Norris's paper,
giving the range of efficiency which may be expected under different cir-
cumstances. Details of these and other fans, with diagrams of the results
are given in the paper.
522
AIR.
Experiments on Mine-ventilating Fans.
ons per
, Fan.
1'a
JL
.«
VQ
Contents
blades.
CW
^^ c
oT
bo
H
a
0)
I Horse-
Engine.
§
"So .
S|
•c
l|
^gfc
'•S-2
!*&
^l
fe >
~a
o> -^^
<D O>^<
*•§
§4
lo
°S
-So|
"o a
H®
.2 fc,
.S
sP*
o3 o3
.Sfr
*.£t
^5
«J
t
If
•§§
oj o3
> O J3
1
Is
1s
*§ a
o
Q'l
P
•§3*
O1"1
o
ffi
|8*
r
84
5517
236,684
2818
3040
4290
1.80
67.13
88.40
75.9
1 o
A J
100
6282
336,862
3369
3040
5393
2.50
132.70
155.4385.4
CO
1
111
6973
347,396
3130
3040
5002
3.20
175.17
209.64 83.6
L8
I
123
7727
394,100
3204
3040
5100
3.60
223.56
295.21 75.7
1 >
100
6282
188,888
1889
1520
3007
1.40
41.67
97.9942.5
1
130
8167
274,876
2114
1520
3366
2.00
86.63
194.9544.6
22
r ]
59
3702
59,587
1010
1520
1610
1.20
11.27
16.7667.83
C1
83
5208
82,969
1000
1520
1593
2.15
27.86
48.5457.38
40
3140
49,611
1240
3096
1580
0.87
6.80
13.8249.2
32
1
70
5495
137,760
1825
3096
2507
2.55
55.35
67.4482.07
i
50
2749
147,232
2944
1522
5356
0.50
11.60
88.6540.68
sJ
69
3793
205,761
2982
1522
5451
1.00
32.42
45.9870.50
83
I
96
5278
299,600
3121
1522
5676
2.15
101.50 120.64 84.10
200
7540
133,198
666
746
1767
3.35
70.30
102.7968.40
26.9
F •%
200
7540
180,809
904
746
2398
3.05
86.89
129.07:67.30
38.3
|
200
7540
209,150
1046
746
2774
2.80
92.50
150.0861.70
46.3
10
785
28,896
2890
3022
3680
0.10
0.45
1.30
35.
20
1570
57,120
2856
3022
3637
0.20
1.80
3.70
49.
25
1962
66,640
2665
3022
3399
0.29
2.90
6.10
48.
30
2355
73,080
2436
3022
3103
0.40
4.60
9.70
47.
52
35
2747
94,080
2688
3022
3425
0.50
7.40
15.00
48.
•
40
3140
112,000
2800
3022
3567
0.70
12.30
24.90
49.
50
3925
132,700
2654
3022
3381
0.90
18.80
38.80
48.
60
4710
173,600
2893
3022
3686
1.35
36.90
66.40
55.
70
5495
203,280
2904
3022
3718
1.80
57. 701107. 10
54.
80
6280
222,320
2779 !
3022
3540
2.25
78. 80| 152. 60
52.
g
Type of Fan.
Guibal double
Diam.
20ft.
Width.
6ft.
No. Inlets.
4
Diam.
8ft.
Inlets
10 in.
B.
0
Same, only left hand running.
Guibal
20
20
6
6
4
2
8
8
10
10
p
Guibal
25
8
1
11
6
F,
Guibal, double
17U
4
4
8
F
Capell
12
10
2
7
G
Guibal
25
8
1
12
An examination of the detailed results of each test in Mr. Norris's table
shows a mass of contradictions from which it is exceedingly difficult to draw
any satisfactory conclusions. The following, he states, appear to be more
or less warranted by some of the figures :
1. Influence of the Condition of the Airways on the Fan. — Mines with
varying equivalent orifices give air per 100 feet periphery-motion of fan,
witkin limits as follows, the quantity depending on the resistance of the
mine :
Equivalent Cu Ft. Air per Aver-
Orifice. 100 ft. Periphery- age.
speed.
Under 20 sq. ft. 1100 to 1700 1300
ontnan 1300 to 1800 1600
1500 to 2500 2100
2300 to 3500 2700
2700 to 4800 3500
4.CJL *V/ OV£. .
20 to 30
80 to 40
40 to 50
50 to 60
Equivalent Cu. Ft. Air per Aver-
Orifice. 100 ft. Periphery- age.
speed.
3300 to 5100 4000
4000 to 4700 4400
3000 to 5600 4800
60 to 70
70 to 80
80 to 90
90 to 100
100 to 114
5200 to 6200 5700
The influence of the mine on the efficiency of the fan does not seem to be
very clear. Eight fans, with equivalent orifices over 50 square feet, give
CENTRIFUGAL FAKS. 523
efficients over 70# 5 four, with smaller equivalent mine-orifices, give about
the same figures ; while, on the contrary, six fans, with equivalent orifices of
over 50 square feet, give tower efficiencies, as do ten fans, all drawing from
mines with small equivalent orifices.
It would seem that, on the whole, large airways tend to assist somewhat
in attaining large efficiency.
2. Influence of the Diameter of the Fan. — This seems to be practically ni'Z,
the only advantage of large fans being in their greater width and the lower
speed required of the engines.
3. Influence of the Width of a Fan.— This appears to be small as regards
the efficiency of the machine ; but the wider fans are, as a rule, exhausting
more air.
4. Influence of Shape of Blades.— This appears, within reasonable limits,
to be practically nil. Thus, six fa as with tips of blades curved forward,
three fans with flat blades, and one with blades curved back to a tangent
with the circumference, all give very high efficiencies- over 70#.
5. Influence of the Shape of the Spiral Casing.— This appears to be con-
siderable. The shapes of spiral casing in use fall into two classes, the first
presenting a large spiral, beginning at or near the point of cut-off, and the
second a circular casing reaching around three quarters of the circumference
of the fan, with a short spiral reaching to the evasee chimney.
Fans haying the first form of casing appear to give in almost every case
large efficiencies.
Fans that have a spiral belonging to the first class, but very much con-
tracted, give only medium efficiencies. It seems probable that the proper
shape of spiral casing would be one of such form that the air between each
pair of blades could constantly and freely discharge into the space between
the fan and casing, the whole being swept along to the evasee chimney. This
would require a spiral beginning near the point of cut-off, enlarging by
gradually increasing increments to allow for the slowing of the air caused by
its friction against the casing, and reaching the chimney with an area such
that the air could make its exit with its then existing speed— somewhat less
than the periphery-speed of the fan.
6. Influence of the Shutter. — This certainly appears to be an advantage, as
by it the exit area can be regulated to suit the varying quantity of air given
by the fan, and in this way re-entries can be prevented. It is not uncommon
to find shutterless fans into the chimneys of which bits of paper may be
dropped, which are drawn into the fan, make the circuit, and are again
thrown out. This peculiarity has not been noticed with fans provided with
shutters.
7. Influence of the Speed at ivhich a Fan is .Rtm.— It is noticeable that
most of the fans giving high efficiency were running at a rather high
periphery velocity. The best speed seems to be between 5000 and 6000 feet
per minute.
The fans appear to reach a maximum efficiency at somewhere about the
speed given, and to decrease rapidly in efficiency when this maximum point
is passed.
In discussion of Mr. Norris's paper, Mr. A. H. Storrs says: From the "cu-
bic feet per revolution " and " cubical contents of fan-blades," as given in the
table, we find that the enclosed fans empty themselves from one half to
twice per revolution, while the open fans are emptied from one and three-
Suarter to nearly three times. This for fans of both types, on mines cover-
ig the same range of equivalent orifices. One open fan, on a very large
orifice, was emptied nearly four times, wh^e a closed fan, on a still larger
orifice, only shows one and one-half times. For the open fans the "cubic
feet per 100 ft. motion " is greater, in proportion to the fan width and equiv-
alent orifice, than for the enclosed type. Notwithstanding this apparently
free discharge of the open fans, they snow very low efficiencies.
As illustrating the very large capacity of centrifugal fans to pass air, if
the conditions of the mine are made favorable, a 16-ft. diam. fan, 4 ft. 6 in.
, of same
00,000 cm
v , tiio wa,i/er-j£tiugt5 m 00111 instances uem^ auuui> yz AU.
T. D. Jones says : The efficiency reported in some cases by Mr. Norris is
larger than I have ever been able to determine by experiment. My own ex-
periments, recorded in the Pennsylvania Mine Inspectors' Reports from 1875
to 1881, did not show more than 60# to 65$.
524
AIR.
BISK FANS.
Experiments made with a Blackmail Bisk Fail, 4 ft.
diam , by Geo. A. Suter, to determine the volumes of air delivered under
various conditions, and the power required; with calculations of efficiency
and ratio of increase of power to increase of velocity, by G. H. Babcock.
(Trans. A. S. M. E., vii. 547):
1
fe
PH
I
Cu. ft. of Air
delivered
per min.,
1
h
o
w
il«
£§
be
Ratio of In-
crease of
Speed.
Ratio of In-
crease of
Delivery.
Ratio of In-
crease of
Power.
Exponent #,
HP aFX.
Exponent y,
hxVv .
Efficiency
of Fan.
350
25,797
0.65
1.682
440
32,575
2.29
1.257
1.262
3.523
5 4
.9553
534
41,929
4.42
1.186
1.287
1.843
2.4
1.062
612
47,756
7.41
1.146
1.139
1.677
3.97
.9358
For
series
1.749
1.851
11.140
4
340
20,372
0 76
.7110
453
26,660
1.99
1.332
1.308
2 618
3 55
.6063
536
31,649
3.86
1.183
1.187
1.940
3.86
.5205
627
36,543
6.47
1.167
1.155
1 676
3 59
.4802
For
series
] 761
1 794
8 513
3 63
^
340
9,983
1.12
0 28
.3939
430
534
570
13,017
17,018
18,649
For
3.17
6.07
8.46
series
0.47
0.75
0.87
1.265
1.242
1.068
1.676
1.304
1.307
1.096
1.704
2.837
3.915
1.394
7.554
3.93
2.25
3.63
3 24
1.95
1.74
1.60
1 81
.3046
.3319
.3027
330
8,399
1.31
0 26
2631
437
516
10,071
11,157
For
3.27
6.00
series
0.45
0.75
1.324
1.181
1.563
1.199
1.108
1.329
3.142
1.457
4.580
6.31
3.66
5.35
3.06
4.96
3.72
.2188
.2202
Nature of the Experiments.— "First Series: Drawing air through 30 ft. of
48-in. diam. pipe on inlet side of the fan.
Second Series: Forcing air through 30 ft. of 48-in. diam. pipe on outlet side
of the fan.
Third Series: Drawing air through 30 ft. of 48-in. pipe on inlet side of the
fan— the pipe being obstructed by a diaphragm of cheese-cloth.
Fourth Series: Forcing air through 30 ft. of 48-in. pipe on outlet side of fan
—the pipe being obstructed by a diaphragm of cheese-cloth.
Mr. Babcock says concerning these experiments : The first four experi-
ments are evidently the subject of some error, because the efficiency is such
as to prove on an average that the fan was a source of power sufficient to
overcome all losses andlielp drive the engine besides. The second series in
less questionable, but still the efficiency in the first two experiments is larger
than might be expected. In the third and fourth series the resistance of the
cheese-cloth in the pipe reduces the efficiency largely, as would be expected.
In this case the value has been calculated from the height equivalent to the
water-pressure, rather than the actual velocity of the air.
This record of experiments made with the disk fan shows that this kind of
fan is not adapted for use where there is any material resistance to the flow
of the air. In the centrifugal fan the power used is nearly proportioned to
the amount of air moved under a given head, while in this fan the power re-
quired for the same number of revolutions of the fan increases very mate-
rially with the resistance, notwithstanding the quantity of air moved is at the
same time considerably reduced. In fact, from the inspection of the third
and fourth series of tests, it would appear that the power required is very
nearly the same for a given pressure, whether more or less air be in motion.
It would seem that the main advantage, if any, of the disk fan over the cen-
trifugal fan for slight resistances consists in the fact that the delivery is the
full area of the disk, while with centrifugal fans intended to move the same
quantity of air the opening is much smaller.
DISK FANS.
525
It will be seen by columns 8 and 9 of the table that the ppwer used in.
creased much more rapidly than the cube of the velocity, as in centrifugal
fans. The different experiments do not agree with each other, but a general
average may be assumed as about the cube root of the eleventh power.
Full and Three-quarter Housing Fans. (Buffalo Forge Co.)
Capacities at different velocities and pressures. (See also table on p. 519.)
c
Size of
Outlet.
of Inlet.
Pulleys.
Velocities in cubic feet per minute; Pres-
sures in ounces at Fan Outlets.
3654 ft. per
min, % oz.
4482 ft. per
min., % oz.
5175 ft. per
min., 1 oz.
§
QQ
|
1
ft
®
1
Capac-
ity.
Revs,
per
mm.
Capac-
ity.
Revs,
per
min.
Capac-
ity.
Revs*
per
mm.
50
18^x18^
24%
9
7
8,140
"492
9,900
600
11,440
693
60
22H x 22J4
26%
10
8
11,470
462
13.950
562
16,120
650
70
26 x26
3414
11
9
16,280
361
19,800
441
22,880
509
80
29% x 29%
39J4
12
10
21,460
303
26,100
369
30,160
426
90
100
33^x33^6
37^x37^4
43
45%
14
16
11
12
27,750
34,410
266
242
33,750
41,850
325
294
39,000
48,360
376
340
110
41 x41
61U
18
13
41,540
217
50,400
265
58,240
307
120
44% x 44%
54%
20
14
49,580
195
60,300
243
69,680
280
130
48^x48^
61
22
15
58,460
187
71,100
227
82,160
263
140
52&X52H
64%
24
16
67,710
172
82,350
214
95,160
248
150
56 x56
«9V$
26
17
77,700
161
94,500
196
109,200
227
160
59% x 59%
74^4
28
18
88,800
149
108,000
181
124,800
209
170
63^ x 63^
79
30
19
100,270
140
121,950
171
140,920
197
180
112,480
136
136,800
165
158,080
191
For J4 oz. pressure, speed 2584 f c. per minute, the capacity and the revolu-
tions are each one-half of those for 1 oz. pressure.
Efficiency of Disk Fans.— Prof . A. B. W. Kennedy (Industries, Jan.
17, 1890) made a series of tests on two disk fans, 2 and 3 ft. diameter, known
as the Verity Silent Air-propeller. The principal results and conclusions
are condensed below.
In each case the efficiency of the fan, that is, the quantity of air delivered
per effective horse-power, increases very rapidly as the speed diminishes,
eo that lower speeds are much more economical than higher ones. On the
•other hand, as the quantity of air delivered per revolution is very nearly
constant, the actual useful wcrk done by the fan increases almost directly
with its speed. Comparing the large and small fans with about the same
air delivery, the former (running at a much lower speed, of course) is much
the more economical. Comparing the two fans running at the same speed,
however, the smaller fan is very much the more economical. The delivery
of air per revolution of fan is very nearly directly proportional to the area
of the fan's diameter.
The air delivered per minute by the 3-ft. fan is nearly 12.51? cubic feet
(72 being the number of revolutions made by the fan per minute). For the
£-ft. fan the quantity is 5.7JB cubic feet. For either of these or any other
similar fans of which the area is A square feet, the delivery will be about
1.8AR cubic feet. Of course any change in the pitch of the blades might
entirely change these figures.
The net H.P. taken up is not far from proportional to the square of the
number of revolutions above 100 per minute. Thus for the 3-ft. fan the net
H.P. is (J, while for the 2-ft. fan the net H.P. is
The denominators of these two fractions are very nearly proportional in-
versely to the square of the fan areas or the fourth power of the fan diam-
eters. The net H.P. required to drive a fan of diameter D feet or area A
square feet, at a speed of R revolutions per minute, will therefore be ap-
, , D*(R — 100)2 A\R — 100)2
,,ro*,mately ^^ or ~^mm-.
The 2-ft. fan was noiseless at all speeds. The 3-ft. fan was also noiseless
up to over 450 revolutions per minute.
526
AIR.
Propeller,
2 ft. diam.
Propeller,
3 ft. diam.
Speed of fan, revolutions per minute.
Net H P to drive fan and belt
750
0.42
4,183
593
1,830
9,980
1.77
5.58
676
0.32
3,830
543
1,220
11,970
1.81
5.66
577
0.227
3,410
482
1,085
15,000
1.88
5.90
576
1.02
7,400
1,046
' 7,250
1.82
12.8
459
0.575
5,800
820
10*676
1.79
12.6
373
0.324
4,470
632
13,800
1.70
12.0
Mean velocity of air in 3-f t. flue, feet
per minute ••• . •
Mean velocity of air in flue, same
diameter as fan
Cu.ft.of air per min. per effective H. P.
Motion given to air per rev. of fan, ft.
Cubic feet of air per rev. of fan
POSITIVE BOTANY BLOWERS. (P. H. & F. M Roots.)
Size number
V4
i/
1
2
3
4
5
6
<•
Cubic feet per revolution . ., . %
li^
3
5
8
13
22
37
63
Revolutions per minute,
Smith fires. ... -- "
'to
'350
to
300
225
to
275
200
to
250
175
to
225
150
to
200
125
to
175
100
to
150
75
to
125
Furnishes blast
fires
for Smith
2
to
6
to
10
to
16
to
24
to
32
to
47
to
70
to
80
to
Revolutions per minute
cupola, melting iron. .
for
4
8
14
275
to
375
20
275
to
325
30
200
to
300
43
185
to
275
67
170
to
250
100
150
to
200
135
137
'' to
175
Size of cupola,
side lining
inches,
in-.
l!
...
18
to
24
24
to
CO
80
to
36
36
to
42
42
to
50
50 72
to or
602.55's
Will melt iron per hour, tons
...
...
to
to
3
to
4%
to
8
to
~to
to
( ...
. . .
2
3
4%
7
12
16%
22%
Horse-power requ
lirprl
1
2
3^
BU
C
11U
17?i
27
40
The amount of iron melted
is based
on 30,000 cubic feet
of air per ton of
iron. The horse-power is for maximum speed and a pressure of
ordinary cupola pressure. (See also Foundry Practice.)
^ pound,
BLOWING-ENGINES.
Corliss Horizontal Cross-compound Condensing
Bio wing-'CZfigS lies, (Hnlatlelpina Engineering Works.)
Indicated
Horse-power.
Revs,
per
min.
Cu. Ft.
Free
Air per
Blast-
pres-
sure
per
i -s'
On''0^
M
CM
0'S*
^P-T
g'tl
^—•0)
g|||
15Exp.
ISExp.
325 Ibs.
100 Ibs.
min.
sq.m.,
^.Sft
.fiS
cS'Ofl
'->"$
RCC^
C^OQ^^
Steam.
Steam.
Ibs.
w
a
P
CC
<J
^
1,572
2,280
40
60
30,400
45,600
1 15
44
78
(2)84
60
505,000
605,000
1,290
2,060
40
60
30,400
45,600
j- 12
42
72
(2)84
60
475,000
550,000
1,050
1,596
40
60
30,400
45,600
f»
32
60
(2)84
60
355,000
436,000
1,340
1.980
40
60
26,800
39,600
40
72
(2)78
60
445,000
545,000
1,152
1,702
40
60
26,800
39.600
h2
38
70
(2)78
60
425,000
491,000
938
1,386
40
60
26,FOO
39.600
h
36
66
(2)78
60
415,000
450,000
780
1,175
40
60
15,680
23,500
h
34
60
(2)72
60
340,000
430,000
543
823
40
60
15,680
23,500
28
50
(2)72
60
270,000
300,000
the stroke is 48 in. instead of 60, and they are run at a higher number of
revolutions to give the same pigtou-speed aud the same I. H, P,
STEAM-JET BLOWER AND EXHAUSTER.
527
The calculations of power, capacity, etc., of blowing-engines are the same
as those for air-compressors. They are built without any provision for
cooling the air during compression. About 400 feet per minute is the usual
STEAM-JET BLOWER AND EXHAUSTER.
A blower and exhauster is made by L. Schutte & Co., Philadelphia, on
the principle of the steam-jet ejector. The following is a table of capacities:
Size
No.
Quantity of
Air per hour
in
cubic feet.
Diameter of
Pipes in inches.
Size
No.
Quantity of
Air per hour
in
cubic feet.
Diameter of
Pipes in inches.
Steam.
Air.
Steam.
Air.
000
00
0
1
2
3
4
1,000
2,000
4,000
6,000
12,000
18,000
24,000
1
m
f
2
|K
*
&A
4
5
6
7
8
9
10
30,000
36,000
42,000
48.000
54,000
60,000
V4
y/2
3
3
5
6
6
7
7
8
The admissible vacuum and counter pressure, for which the apparatus is
constructed, is up to a rarefaction of 20 inches of mercury, and a counter-
pressure up to one sixth of the steam-pressure.
The table of capacities is based on a steam- pressure of about 60 Ibs., and
a counter-pressure of about 8 Ibs. With an increase of steam-pressure or
decrease of counter-pressure the capacity will largely increase.
Another steam-jet blower is used for boiler-firing, ventilation, and similar
purposes where a low counter-pressure or rarefaction meets the require-
ments.
The volumes as given in the following table of capacities are under the
supposition of a steam-pressure of 45 Ibs. and a counter-pressure of, say,
2 inches of water :
Size
No.
Cubic
feet of
Air
delivered
per hour.
Diameter
of
Steam-
pipe in
inches.
Diameter in
inches of—
Size
No.
Cubic
feet of
Air de-
livered
per hour
Diam.
of
Stearn-
pipe in
inches.
Diameter in
inches of —
Inlet
Disch.
Tnlet.
Disch.
00
0
1
2
3
6,000
12,000
30,000
60,000
125,000
%
f|
I
4
5
8
11
14
3
4
6
8
10
4
6
8
10
250,000
500,000
1,000,000
2,000,000
1
2 2
17
24
32
42
14
20
27
36
Tlie Steam-jet as a Means for Ventilation.— Between 1810
and 1850 the steam-jet was employed to a considerable extent for ventilat-
ing English collieries, and in 1852 a committee of the House of Commons
reported that it was the most powerful and at the same time the cheapest
method for the ventilation of mines ; but experiments made shortly after-
wards proved that this opinion was erroneous, and that furnace ventilation
was less than half as expensive, and in consequence the jet was soon aban-
doned as a permanent method of ventilation.
For an account of these experiments see Colliery Engineer, Feb. 1890.
The jet, however, is sometimes advantageously used as a substitute, for
instance, in the case of a fan standing for repairs, or after an explosion,
when the furnace may not be kept going, or in the case of the fan having
been rendered useless.
528 HEATING AKk VEKTILATIOff.
HEATING AND VENTILATION.
Ventilation. (A. R. Wolff, Stevens Indicator, April, 1890.)— The pop-
ular impression that the impure air falls to the bottom of a crowded room
is erroneous. There is a constant mingling of the fresh air admitted with
the impure air due to the law of diffusion of gases, to difference of temper-
ature, etc. The process of ventilation is one of dilution of the impure pir
by the fresh, and a room is properly ventilated in the opinion of the hygien*
ists when the dilution is such that the carbonic acid in the air does not ex-
ceed from 6 to 8 parts by volume in 10,000. Pure country air contains about
4 parts CO2 in 10,000, and badly-¥entilated quarters as high as 80 parts.
An ordinary man exhales 0.6 of a cubic foot of CO8 per hour. New York
gas gives out 0.75 of a cubic foot of CO2 for each cubic foot of gas burnt.
An ordinary lamp gives out 1 cu. ft. of CO2 per hour. An ordinary candle
gives out 0.3 cu. ft. per hour. One ordinary gaslight equals in vitiating
effect about 5^ men, an ordinary lamp \% men, and an ordinary candle y%
man.
To determine the quantity of air to be supplied to the inmates of an un-
lighted room, to dilute the air to a desired standard of purity, we can estab-
lish equations as follows:
Let v = cubic feet of fresh air to be supplied per hour;
r = cubic feet of CO2 in eacli 10,000 cu. ft. of the entering air:
R = cubic feet of CO2 which each 10,000 cu. ft. of the air in the room
may contain for proper health conditions;
n = number of persons in the room;
.6 = cubic feet of CO2 exhaled by one man per hour.
V X Y
Then + ^n equals cubic feet of C02 communicated to the room dur
10,UUu
ing one hour.
This value divided by v and multiplied by 10,000 gives the proportion of
CO2 in 10,000 parts of the air in the room, and this should equal .R, the stan-
dard of purity desired. Therefore
If we place r at 4 and R at 6, v -
or the quantity of air to be supplied per person is 3000 cubic feet per hour.
If the original air in the room is of the purity of external air, and the cubic
contents of the room is equal to 100 cu. ft. per inmate, only 3000 - 100 = 2900
cu. ft. of fresh air from \yithout will have to be supplied the first hour to
keep the air within the standard purity of 6 parts of CO2 in 10,000. If the
cubic contents of the room equals 200 cu. ft. per inmate, only 3000 - 200 = 2800
cu. ft. will have to be supplied the first hour to keep the air within the
standard purity, and so on.
Again, if we only desire to maintain a standard of purity of 8 parts of
carbonic acid in 10,000, equation (1) gives as the required air-supply per hour
6000
v = _ n = 150071, or 1500 cu. ft. of fresh air per inmate per hour.
Cubic feet of air containing 4 parts of carbonic acid in 10,000 necessary per
person per hour to keep the air in room at the composition of
ft 7 ft q in 1^ 2rt j parts of carbonic acid in
7 15 KJO -j 10,000.
3000 2000 1500 1200 1000 545 375 cubic feet.
If the original air in the room is of purity of external atmosphere (4 parts
of carbonic acid in 10,000), the amount of air to be supplied the first hour,
for given cubic spaces per inmate, to have given standards of purity not
exceeded at the end of the hour is obtained from the following table :
VENTILATION,
529
Cubic Feet
of
Space
in Room
per
Individual.
Proportion of Carbonic Acid in 10,000 Parts of the Air, not to
be Exceeded at End of Hour.
6
7
8
9
10
15
20
Cubic Feet of Air, of Composition 4 Parts of Carbonic Acid in
10,000, to be Supplied the First Hour.
100
200
300
400
500
600
700
800
900
1000
1500
2000
2500
2900
2800
2700
2600
2500
2400
2300
2200
2100
2000
1500
1000
500
1900
1800
1700
1600
1500
1400
1300
1200
1100
1000
500
None
1400
1300
1200
1100
1000
900
800
700
600
500
None
1100
1000
900
800
700
600
500
400
300
200
None
900
800
700
600
500
400
300
200
100
None
445
345
245
145
45
None
275
175
75
None
It is exceptional that systematic ventilation supplies the 3000 cubic feet
per inmate per hour, which adequate health considerations demand. Large
auditoriums in which the cubic space per individual is great, and in which
the atmosphere is thoroughly fresh before the rooms are occupied, and the
occupancy is of two or three hours' duration, the systematic air-supply may
be reduced, and 2000 to 2500 cubic feet per inmate per hour is a satisfactory
allowance.
Hospitals where, on account of unhealthy excretions of various kinds, the
air-dilution must be largest, an air-supply of from 4000 to 6000 cubic feet per
inmate per hour should be provided, and this is actually secured in some
hospitals. A report dated March 15, 1883, by a commission appointed to
examine the public schools of the District of Columbia, says :
" In each class-room not less than 15 square feet of floor-space should be
allotted to each pupil. In each class-room the window-space should not be
less than one fourth the floor-space, and the distance of desk most remote
from the window should not be more than one and a half times the height of
the top of the window from the floor. The height of the class-room should
never exceed 14 feet. The provisions for ventilation should be such as to
provide for each person in a class-room not less than 30 cubic feet of fresh
air per minute (1800 per hour), which amount must be introduced and
thoroughly distributed without creating unpleasant draughts, or causing any
two parts of the room to differ in temperature more than 2° Fahr., or the
maximum temperature to exceed 70° Fahr."
When the air enters at or near the floor, it is desirable that the velocity of
inlet should not exceed 2 feet per second, which means larger sizes of
register openings and flues than are usually obtainable, and much higher
velocities of inlet than two feet per second are the rule in practice. The
velocity of current into vent-flues can safely be as high as 6 or even 10 feet
per second, without being disagreeably perceptible.
The entrance of fresh air into a room is co-incident with, or dependent on,
the removal of an equal amount of air from the room. The ordinary means
of removal is the vertical vent-duct, rising to the top of the building. Some-
times reliance for the production of the current in this vent-duct is placed
solely on the difference of temperature of the air in the room and that of
the external atmosphere: sometimes a steam coil is placed within the flue
near its bottom to heat the air within the duct; sometimes steam pipes
(risers and returns) run up the duct performing the same functions; or steam
jets within the flue, or exhaust fans, driven by steam or electric power, act
directly as exhausters; sometimes the heating of the air in the flue is ac-
complished by gas-jets.
The draft of such a duct is caused by the difference of weight of the
530
HEATING AND VENTILATION.
heated air in the duct, and a column of equal height and cross-sectional area
of weight of the external air.
Let d = density, or weight in pounds, of a cubic foot of the external air.
Let dl = density, or weight in pounds, of a cubic foot of the heated air
within the duct.
Let h = vertical height, in feet, of the vent-duct.
h(d — d,) = the pressure, in pounds per square foot, with which the air is
forced into and out of the vent-duct.
This pressure can be expressed in height of a column of the air of density
within the vent-duct, and evidently the height of such column of equal
(3)
Or, if t = absolute temperature of external air, ami 1 1 = absolute temper-
ature of the air in vent-duct in the form, then the pressure equals
... , h(d — di)
presssure would be] v — 5— -
(4)
The theoretical velocity, in feet per second, with which the air would
travels through the vent-duct under this pressure is
t
The actual velocity will be considerably less than this, on account of loss
due to friction. This friction will vary with the form and cross-sectional
area of the vent-duct and its connections, and with the degree of smooth-
ness of its interior surface. On this account, as well as to prevent leakage
of air through crevices in the wall, tin lining of vent-flues is desirable.
The loss by friction may be estimated at approximately 50#, and so we find
for the actual velocity of the air as it flows through the vent-duct :
-y-^i or, approximately, v = 4j/ h ^ * ~ • . . (6)
If F= velocity of air in vent-duct, in feet per minute, and the external air
be at 32° Fahr., since the absolute temperature on Fahrenheit scale equals
thermometric temperature plus 459.4,
491.4
(7)
from which has been computed the following table :
Quantity of Air. in Cubic Feet, Discharged per
through a Ventilating Duct, of which the Cr
minute
Cross-sec-
tional Area is One Square Foot (the External Tempera-
ture of Air being 32° Fall r.).
Height of
Vent-duct in
Excess of Temperature ot Air in Vent-duct above that of
External Air.
feet.
5°
10»
15°
20°
25°
30°
50°
100°
150°
10
77
108
133
153
171
188
242
342
419
15
94
133
362
188
210
230
297
419
514
20
108
153
188
217
242
265
342
484
593
25
121
171
210
242
271
297
383
541
663
30
133
188
230
2a5
297
325
419
593
726
35
143
203
248
286
320
351
453
640
784
40
153
?17
265
306
342
375
484
656
838
45
162
230
282
325
363
398
514
476
889
50
171
242
297
342
383
419
541
278
937
Multiplying the figures in above table by 60 gives the cubic feet of air dis-
charged per hour per square foot of cross-section of vent-duct. Knowing
MINE-VENTILATION. 531
the cross-sectional area of vent-ducts we can find the total discharge; or
for a desired air-removal, we can proportion the cross-sectional area of
vent-ducts required.
Artificial Cooling of Air for Ventilation. (Engineering
News, July 7, 1892.)— A pound of coal used to make steam for a fairly effi-
cient ref rigerating-machine can produce an sactual cooling effect equal to
that produced by the melting of 16 to 46 Ibs. of ice, the amount varying
with the conditions of working. Or, 855 heat-units per Ib. of coal converted
into work in the refrigerating plant (at the rate of 3. Ibs. coal per horse-
po.wer hour) will abstract 2275 to 6545 heat-units of heat from the refriger-
ated body. If we allow 2000 cu. ft. of fresh air per hour per person as suffi-
cient for fair ventilation, with the air at an initial temperature of 80° F., its
weight per cubic foot will be .0736 Ib.; hence the hourly supply per person
will weigh 2000 X .0736 Ib. = 147.2 Ibs. To cool this 10°, the specific heat of
air being 0.238, will require the abstraction of 147.2 X 0.238 X 10 = 350 heat-
units per person per hour.
Taking the figures given for the refrigerating effect per pound of coal as
above stated, and the required abstraction of 350 heat-units per person per
hour to have a satisfactory cooling effect, the refrigeration obtained from a
pound of coal will produce this cooling effect for 2275 -f- 350 = 6^ hours with
the least efficient working, or 6545 -f- 350 = 18.7 hours with the most efficient
working. With ice at $5 per ton, Mr. Wolff computes the cost of cooling with
ice at about $5 per hour per thousand persons, and concludes that this is too
expensive for any general use. With mechanical refrigeration, however, if
we assume 10 hours' cooling per person per pound of coal as a fair practical
service in regular work, we have an expense of only 15 cts. per thousand
persons per hour, coal being estimated at $3 per short ton. This is for fuel
alone, and the various items of oil. attendance, interest, and depreciation on
the plant, etc., must be considered in making up the actual total cost of
mechanical refrigeration.
Mine-ventilation— Friction of Air in Underground Pas-
sages.— In ventilating a mine or other underground passage the resistance
to be overcome is, according to most writers on the subject, proportional to
the extent of the frictional surface exposed; that is, to the product lo of the
length of the gangway by its perimeter, to the density of the air in circula-
tion, to the square of its average speed, vy and lastly to a coefficient fc, whose
numerical value varies according to the nature of the sides of the gangway
and the irregularities of its course.
The formula for the loss of head, neglecting the variation in density as
unimportant, is p = - , in which p = loss of pressure in pounds per square
foot, s — square feet cf rubbing-surface exposed to the air, v the velocity of
the air in feet per minute, a the area of the passage in square feet, and k the
coefficient of friction. W. Fairley, in Colliery Engineer, Oct. and Nov.
1893, gives the following formulae for all the quantities involved, using the
same notation as the above, with these additions : h = horse-power of ven-
tilation; I = length of air-channel; o = perimeter of air-channel; q '= quan-
tity of air circulating in cubic feet per minute; u = units of work, in foot-
pounds, applied to circulate the air: w = water-gauge in inches. Then,
_ ksv* _ ksv^q __ ksv3 u _ q
p ~ u ~ pv — pv~ v
_
33,000 " 33,000 " 33,000 *
3 7j= Pa^ u
- ,
sv* sv* •*- a st?a -*- a
pa
*'u\*ks_ksv*_ u
av '
532
HEATING AND VENTILATION.
pa
= Jo.
St> g
10. tt = gp = vpa = = ksv* = 5.2qw = 33,000ft
«•— fe-S
To find the quantity of air with a given horse-power and efficiency (e) of
engine:
_h X 33,000 X e
The value of fc, the coefficient of friction, as stated, varies according to
the nature of the sides of the gangway. Widely divergent values have been
given by different authorities (see Colliery Engineer, Nov. 1893), the most
generally accepted one until recently being probably that of J. J. Atkinson,
.0000000217, which is the pressure per square foot in decimals of a pound for
each square foot of rubbing-surface and a velocity of one foot per minute.
Mr. Fairley, in his " Theory and Practice of Ventilating Coal-mines," gives a
value less'than half of Atkinson's, or .00000001 ; and recent experiments by D.
Murgue show that even this value is high under most conditions. Murgue's
results are given in his paper on Experimental Investigations in the Loss of
Head of Air currents in Underground Workings, Trans. A. I. M. E., 1893.
vol. xxiii. 63. His coefficients are given in the following table, as determined
in twelve experiments:
Coefficient of Loss cf
Head by Friction.
French.
f Straight, normal section 00092
J Straight, normal section 00094
| Straight, large section 00104
t Straight, normal section .00122
f Straight, normal section 00030
| Straight, normal section .00036
4 Continuous curve, normal section 00062
Sinuous, intermediate section 00051
I Sinuous, small section 00055
( Straight, normal section 00168
•J Straight, normal section 00144
gangways. | sightly sinuous, small section 00238
Rock,
gangways.
Brick-lined
arched
gangways.
British.
.000,000,00486
.000,000,00497
.000,000,00549
.000,000,00645
.000,000,00158
.000,000,00190
.000,000,00328
.000,000,00269
.000,000,00291
.000,000,00888
.000,000,00761
.000,000,01257
The French coefficients which are given by Murgue represent the height
of water-gauge in millimetres for each square metre of rubbing-surface and
a velocity of one metre per second. To convert them to the British measure
of pounds per square foot for each square foot of rubbing-surface and a
velocity of one foot per minute they have been multiplied by the factor of
conversion, .000005283. For a velocity of 1000 feet per minute, since the loss
of head varies as v2, move the decimal point in the coefficients six places to
FAHS AND HEATED CHIMHEYS FOR VEHTILATIOK. 533
Equivalent Orifice,— The head absorbed by the working-chambers
of a mine cannot be computed a priori, because the openings, cross-pas-
sages, irregular-shaped gob-piles, and daily changes in the size and shape of
the chambers present much too complicated a network for accurate
analysis. In order to overcome this difficulty Murgue proposed in 1872 the
method of equivalent orifice. This method consists in substituting for the
mine to be considered the equivalent thin-lipped orifice, requiring the same
height of head for the discharge of an equal volume of air. The area of
this orifice is obtained when the head and the discharge are known, by
means of the following formulae, as given by Fairley:
Let Q = quantity of air in thousands of cubic feet per minute;
iv = inches of water-gauge;
A = area in square feet of equivalent orifice.
Then
motive Column or the Head of Air Due to Differences
of Temperature, etc. (Fairley.)
Let-M = motive column in feet;
T = temperature of upcast;
/ = weight of one cubic foot of the flowing air;
t = temperature of downcast;
D = depth of downcast.
Then
To find diameter of a round airway to pass the same amount of air as a
square airway the length and power remaining the same:
Let D = diameter of round airway, A = area of square airway; O= peri-
5/ A3 X 3.1416.
meter of square airway. Then D3 = 4/ 73543 ^ O '
If two fans are employed to ventilate a mine, each of which when worked
separately produces a certain quantity, which may be indicated by A and B
then the quantity of air that will pass when the two fans are worked together
will be A/A3 + Bs. (For mine-ventilating fans, see page 521.)
Relative Efficiency of Fans and Heated Cnimneys for
Ventilation.— W. P. Trowbridge, Trans. A. S. M. E. vii. 531, gives a theo-
retical solution of the relative amounts- of heat expended to remove a given
volume of impure air by a fan and by a chimney. Assuming the total effi-
ciency of a fan to be only 1/^5, which is made up of an efficiency of 1/10 for
the engine, 5/10 for the fan itself, and 8/10 for efficiency as regards friction,
the fan requires an expenditure of heat to drive it of only 1/38 of the amount
that would be required to produce the same ventilation by a chimney 100 ft.
high. For a chimney 500 ft. high the fan will be 7.6 times more efficient.
In all cases of moderate ventilation of rooms or buildings where the air
is heated before it enters the rooms, and spontaneous ventilation is pro-
duced by the passage of this heated air upwards through vertical flues,
no special heat is required for ventilation ; and if such ventilation be suffi-
cient, the process is faultless as far as cost is concerned. This is a condition
of things which may be realized in most dwelling-houses, and in many halls,
schoolrooms, and public buildings, provided inlet and outlet flues of ample
cross-section be provided, and the heated air be properly distributed.
If a more active ventilation be demanded, but such as requires the small-
est amount of power, the cost of this power may outweigh the advantages
of the fan. There are many cases in which steam-pipes in the base of a
chimney, requiring no care or attention, may be preferable to mechanical
ventilation, on the ground of cost, and trouble of attendance, repairs, etc.
* Murgue gives A = ^—==, and Norris A - _ . See page 521, ante.
534: UEATIKG AKD VENTILATION.
The following figures are given by Atkinson (Coll. Engr., 1889), showing
the minimum depth at which a furnace would be equal to a ventilating-
machine, assuming that the sources of loss are the same in each case, i.e.,
that the loss of fuel in a furnace from the cooling in the upcast is equivalent
to the power expended in overcoming the friction in the machine, and also
assuming that the ventilating-machine utilizes 60£ of the engine-power. The
coal consumption of the engine per I.H.P. is taken at 8 Ibs. per hour:
Average temperature in upcast 100° F. 150° F. 200° F.
Minimum depth for equal economy... 960 yards. 1040 yards. 1130 yards.
Heating: and Ventilating of Large Buildings, (A. R.
Wolff, Jour. Frank. lust., 1893.)— The transmission of heat from the interior
to the exterior of a room or building, through the walls, ceilings, windows,
etc., is calculated as follows :
S = amount of transmitting surface in square feet;
t = temperature F. inside, f0 = temperature outside;
K = a coefficient representing, for various materials composing buildings,
the loss by transmission per square foot of surface in British ther-
mal units per hour, for each degree of difference of temperature
on the two sides of the material;
Q = total heat transmission = SK (t - t „).
This quantity of heat is also the amount that must be conveyed to the
room in order to make good the loss by transmission, but it does not cover
the additional heat to be conveyed on account of the change of air for pur-
poses of ventilation. The coefficients K given below are those prescribed by
law by the German Government in the design of the heating plants of its
public buildings, and generally used in Germany for all buildings. They
have been converted into American units by Mr. Wolff, and he finds that
they agree well with good American practice:
VALUE OP K FOR EACH SQUARE FOOT OP BRICK WALL.
f 4" 8" 12" 16" a°" 24" 28" 32" 36" 40"
K = 0.68 0.46 0.32 0.26 0.23 0.20 0.174 0.15 0.129 0.115
1 sq. ft., wooden-beam construction, ) as flooring, K = 0.083
planked over or ceiled, f as ceiling, K — 0.104
1 sq. ft., fireproof construction,) as flooring, K= 0.124
noo red over, j" as ceiling, K = 0.145
1 sq. ft., single window K = 1.030
1 sq. ft., single skylight K— 1.118
1 sq. ft., double window K= 0.518
Isq. ft., double skylight K = 0.621
1 sq. ft., door £"=0.414
These coefficients are to be increased respectively as follows: 10# when the
exposure is a northerly one, and winds are to be counted on as important
factors; 10^ when the building is heated during the daytime only, and the
location of the building is not an exposed one; 30# when the building is
heated during the daytime only, and the location of the building is exposed;
50jC when the building is heated during the winter months intermittently,
with long intervals (say days or weeks) of non-heating.
The value of the radiating-surface is about as follows: Ordinary bronzed
cast-iron radiating-surfaces, in American radiators (of Bundy or similar
type), located in rooms, give out about 250 heat-units per hour for each
square foot of surface, with ordinary steam-pressure, say 3 to 5 Ibs. per sq.
in., and about 0.6 this amount with ordinary hot-water heating.
Non-painted radiating-surfaces, of the ordinary "indirect" type (Climax
or pin surfaces), give out about 400 heat-units per hour for each square foot
of heating-surface, with ordinary steam-pressure, say 3 to 5 Ibs. per sq. in.;
and about 0.6 this amount with ordinary hot-water heating.
A person gives out about 400 heat-units per hour; an ordinary gas-burner,
about 4800 heat-units per hour; an incandescent electric (16 candle-power)
light, about 1600 heat-units per hour.
The following example is given by Mr. Wolff to show the application of
the formula and coefficients:
Lecture-room 40 X 60 ft., 20 ft. high, 48,000 cubic feet, to be heated to
69° F.; exposures as follows: North wall, 60 x 20 ft., with four windows,
each 14 X 8 feet, outside temperature O8 F. Boom beyond west wall and
HEATlHG AND VENTILATING OF LABGE BUILDINGS. 535
room overhead heated to 69°, except a double skylight in ceiling, 14 X 24 ft»,
exposed to the outside temperature of 0°. Store-room beyond east wall at
86°. Door 6 X 12 ft. in wall. Corridor beyond south wall heated to 59°.
Two doors, 6 X 12, in wall. Cellar below, temperature 36°.
The following table shows the calculation of heat transmission:
fl
Kind of Transmitting
Surface.
Thickness
of Wall in
inches.
Calculation
of Area of
Transmitting
Surface.
IB ®
£J
|l
•*-
1
Thermal
Units.
,
69°
69
33
33
10
10
10
10
69
69
33
36"
36"
24"
36"
63 X 22 - 448
4X 8X 14
42X22- 72
6X12
45X22- 72
6X12
17X22- 72
6x 12
32 X 42 - 336
14X24
62X42
utside wall, 10
utside windov
day or night i
938
448
852
72
918
72
302
72
1,008
336
2,604
%
9
72
4
19
2
5
1
•5
10
43
4
8,442
32,256
3,408
1,368
1,836
360
302
360
10,080
14,448
10,416
'844
3,226
Four windows (single)
Inside wall (store-room)
Door
Roof •
Floor
Supplementary allowance, north o
'* north c
Exposed location and intermittent
Total thermal units
ise, 30^ ....
87,346
26.204
113,550
If we assume that the lecture-room must be heated to 69 degrees Fahr. in
the daytime when unoccupied, so as to be at this temperature when first
persons arrive, there will be required, ventilation not being considered, and
bronzed direct low-pressure steam -radiators being the heating media, about
113,550-5-250 = 455 sq. ft. of radiating-surface. (This gives a ratio of about
405 cu. ft. of contents of room for each sq. ft. of heating-surface.)
If we assume that there are 160 persons in the lecture-room, and we pro-
vide 2500 cubic feet of fresh air per person per hour, we will supply 160 X
2500 = 400,000 cubic feet of air per hour (i.e.,
= over eight changes of
contents of room per hour).
To heat thi* air from 0° Fahr. to 69° Fahr. will require 400,000 X 0.0189 X
69 = 521,640 thermal units per hour (0.0189 being the product of a weight of
a cubic foot by the specific heat of air). Accordingly there must be provided
521,640-s-400= 1304 sq. ft. of indirect surface, to heat the air required for
ventilation, in zero weather. If the room were to be warmed entirely indi-
rectly, that is, by the air supplied to room (including the heat to be conveyed
to cover loss by transmission through walls, etc.)» there would have to be
room would have to be at a temperature of about 84° Fahr., viz., 69° =
.
The above calculations do not, however, take into account that S60 per-
sons in the lecture-room give out 160 X 400 = 64,000 thermal units per hour;
and thao, say, 50 electric Tights give out 50 X 1600 = 80,000 thermal units per
hour; or, say, 50 gaslights, 50 X 4800 = 240,000 thermal units per hour. The
presence of 160 people and the gas-lighting would diminish considerably the
amount of heat required. Practically, it appears that the heat generated
by the presence of 160 people, 64,000 heat-units, and by 50 electric lights,
80,000 heat-units, a total of 144,000 heat-units, more than covers the amount
of heat transmitted through walls, etc. Moreover, that if the 50 gaslights
give out 240,000 thermal units per hour, the air supplied for ventilation must
enter considerably below 69° Fahr., or the room will be heated to an
unbearably high temperature. If 400.000 cubic feet of fresh air per hour
536
HEATING AND VENTILATION.
are supplied, and 240,000 thermal units per hour generated by the gas must
be abstracted, it means that the air must, under these conditions, enter
400 000 'x°0\89 = aboufc*32° less than 84°> or at about 52° Fahr. Further-
more, the additional vitiation due to gaslighting would necessitate a much
larger supply of fresh air than when the vitiation of the atmosphere by the
people alone is considered, one gaslight vitiating the air as much as five
men.
Various Rules for Computing Radiating-surface.— The
following rules are compiled from various sources. They are more in the
nature of " rule-of -thumb " rules than those given by Mr. Wolff, quoted
above, but they may be useful for comparison.
Divide the cubic feet of space of the room to be heated, the square feet
of wall surface, and the square feet of the glass surface by the figures
given under these headings in the following table, and add the quotients
together; the result will be the square feet of radiating-surface required.
(F. Schumann.)
SPACE, WALL AND GLASS SURFACE WHICH ONE SQUARE FOOT OP RADIATING-
SURFACE WILL HEAT.
Air Change.
1 Steam-pressure]
ctw~| in pounds.
Space in cubic 1
feet. 1
Exposure of Rooms.
All Sides.
Northwest.
Southeast.
Wall
Surface,
sq. ft.
Glass
Surface,
sq. ft.
Wall
Surface,
sq. ft.
Glass
Surface,
sq. ft.
Wall
Surface,
sq. ft.
Glass
Surface,
sq. ft.
Once
per
hour.
190
210
225
13.8
15.0
16.5
7
7.7
8.5
15.87
17.25
18.97
8.05
8.85
9.77
16.56
18.00
19.80
8.4
9.24
10.20
Twice
per
hour.
1
3
5
75
82
90
11.1
12.1
13.0
5.7
6.2
6.7
12.76
13.91
14.52
6.55
7.13
7.60
13.22
14.52
15.60
6.84
7.44
8.04
EMISSION OF HEAT-UNITS PER SQUARE FOOT PER HOUR FROM CAST-IRON PIPES
OR RADIATORS. TEMP. OF AIR IN ROOM, 70° F. (F. Schumann.)
Mean Temperature of
Heated Pipe, Radm-
tor, etc.
By Contact.
By Radi-
ation.
By Radiation
and Contact.
Air quiet.
Air
moving.
Air quiet.
Air
moving.
Hot water 140°
•« ** 150°
55.51
65.45
75.68
86.18
96.93
107.90
119.13
130.49
142.20
153.95
165.90
178.00
189.90
202.70
215.30
228.55
240.85
92.52
109.18
126.13
143.30
161.55
179.83
198.55
217.48
237.00
256.58
279.83
296.65
316.50
337.83
358.85
380.91
401.41
59.63
69.69
80.19
91.12
102.15
114.45
127.00
139.96
155.27
169.56
184.58
200.18
214.36
233.42
251.21
267.73
279.12
115.14
135.14
155.87
177.30
199.43
222.35
246.13
270.49
297.47
323.51
350.48
378.18
404.26
436.12
466.51
496.28
519.97
152.15
178.87
206.32
234.42
264.05
294.28
325.55
357.48
392.27
426.14
464.41
496.81
530.86
571.25
610.06
648.64
680.53
" •• „ 160°
•* •• , 170°
•• •• 180°
•* «« 190°
" ** 200°
44 " or steam . .210°
Steam 220°
•• 230°
«• 240°
•• 250°
•• 260°
" 270°
•» 280°
•« 290°
M 300°
INDIRECT HEATIKG-SURFACE. 537
RADIATE-SURFACE REQUIRED FOR DIFFERENT KlNDS OF BUILDINGS.
The Nason Mfg. Co. 's catalogue gives the following: One square foot of
surface will heat from 40 to 100 cu. ft. of space to 75° in - 10° latitudes
This range is intended to meet conditions of exposed or corner rooms of
buildings, and those less so, as intermediate ones of « block. As a general
Tn,le' *q* surface will heat 70 cu. ft. of air In outer or front rooms and
00 cu. ft in inner rooms. In large stores in cities, with buildings on each
Ride, 1 to 100 is ample. The following are approximate proportions:
One square foot radiating-surface will heat:
Indwellings, In hall, stores, In churches, large
schoolrooms, lofts, factories, auditoriums,
offices, etc. etc. etc
By direct radiation... 60 to 80 ft. 75 to 100 ft. 150 to 200 ft.
By indirect radiation. 40 to 50 u 50 to 70 " 100 to 140 "
Isolated buildings exposed to prevailing north or west winds should have
a generous addition made to the heating-surface on their exposed sides
The following rule is given in the catalogue of the Babcock & Wilcox Co .
and is also recommended by the Nason Mfg. Co.:
Radiating surface may be calculated by the rule: Add together the square
feet of glass in the windows, the number of cubic feet of air required to be
changed per minute, and one twentieth the surface of external wall and
roof; multiply this sum by the difference between the required temperature
of the room and that of the external air at its lowest point, and divide the
product by the difference in temperature between the steam in the pipes
and the required temperature of the room. The quotient is the required
radiating-surface in square feet.
Prof. R. C. Carpenter (Heating and Ventilation, Feb. 15, 1897), gives the
following handy formula for the amount of heat required for heating build-
ings by direct radiation:
in which W= wall-surface, G = glass- or window-surface, both in sq. ft.,
O = contents of building in cu. ft., n = number of times the air must be
changed per hour, and h = total heat units required per degree of difference
of temperature between the room and the surrounding space. To heat the
building to 70° F. when the outside temperature is 0°, 70 times the above
quantity of heat will be required. Under ordinary conditions of pressure
and temperature 1 sq. ft. of steam-heating surface will supply 380 heat units
per hour, and 1 sq. ft. of hot- water heating surface 175 heat units per hour.
The square feet of radiating-surface required under these conditions will
be R = 0.257i for steam- heating, and R = OAh for hot- water heating. Prof.
Carpenter says that for residences it is safe to assume that the air of the
principal living-rooms will change twice in an hour, that of the halls three
times and that of the other rooms once per hour, under ordinary condi-
tions.
Overhead Steam-pipes. (A. R. Wolff, Stevens Indicator, 1887.)—
When the overhead system of steam-heating is employed, in which system
direct radiating-pipes, usually 1*4 in. in diam., are placed in rows overhead,
suspended upon horizontal racks, the pipes running horizontally, and side
by side, around the whole interior of the building, from 2 to 3 ft. from the
walls, and from 2 to 4 ft. from the ceiling, the amount of 1*4 in. pipe re-
quired, according to Mr. C. J. H. Woodbury, for heating mills (for which
use this system is deservedly much in vogue), is about 1 ft. in length for
every 90 cu. ft. of space. Of course a great range of difference exists, due
to the special character of the operating machinery in the mill, both in re-
spect to the amount of air circulated by the machinery, and also the aid to
warming the room by the friction of the journals.
Indirect Heating-surface.— J. H. Kinealy, in Heating and Ven-
tilation, May 15, 1894, gives the following formula, deduced from results of
experiments by C. B. Richards, W. J. Baldwin, J. H. Mills, and others, upon
indirect heaters of various kinds, supplied with varying amounts of air per
hour per square foot of surface:
*- rr - ; r. = or. - r.) o^+
538 HEATING AXD VENTILATION.
N s cubic feet of air, reduced to 70° F., supplied to the heater per square
foot of heating-surface per hour; TQ = temperature of the steam or water
in the heater; TI — temperature of the air when it enters the heater;
T3 = temperature of the air when it leaves the heater.
As the formula is based upon an average of experiments made upon all
sorts of indirect heaters, the results obtained by the use of the equation
may in some cases be slightly too small and in others slightly too large,
although the error will in no case be great. No single formula ought to be
expected to apply equally well to all dispositions of heating-surface in in-
direct heaters, as the efficiency of such heater can be varied between such
wide limits by the construction and arrangement of the surface.
ID indirect heating, the efficiency of the radiatiug-surface will increase,
and the temperature of the air will diminish, when the quantity of the air
caused to pass through the coil increases. Thus 1 sq. ft. radiating-surface,
with steam at 212°, has been found to heat 100 cu. ft. of air per hour from
zero to 150°, or 300 cu. ft. from zero to 100° in the same time. The best re-
sults are attained by using indirect radiation to supply the necessary venti-^
lation, and direct radiation for the balance of the heat. (Steam.)
In indirect steam-heating the least flue area should be 1 to 1*4 sq. in,
to every square foot of heating-surface, provided there are no long horizon
tal reaches in the duct, with little rise. The register should have twice the*
area of the duct to allow for the fretwork. For hot water heating from 25#
to 30# more heating-surface and flue area should be given than for low-
pressure steam. (Engineering Record, May 26, 1894.)
Boiler Heating-surface Required. (A. R. Wolff, Stevens Indi-
cator, 1887.)— When the direct system is used to heat buildings in which the
street floor is a storef and the upper floors are devoted to sales and stock-
rooms and to light manufacturing, and in which the fronts are of stone or
iron, and the sides and the rear of building of brick— a safe rule to follow is to
supply 1 sq. ft. of boiler heating-surface for each 700 cu. ft., and I sq. ft. of
radiating-surface for each 100 cu. ft. of contents of building.
For heating mills, shops, and factories, 1 sq. ft. of boiler heating-surface
should be supplied for each 475 cu. ft. of contents of building; and the same
allowance should also be made for heating exposed wooden dwellings. For
heating foundries and wooden shops, 1 sq. ft. of boiler heating-surface
should be provided for each 400 cu. ft. of contents; and for structures in
which glass enters very largely in the construction— such as conservatories,
exhibition buildings, and the like— 1 sq. ft. of boiler heating-surface should
be provided for each 275 cu. ft. of contents of building.
When the indirect system is employed, the radiator-surface and the boiler
capacity to be provided will each have to be, on an average, about 25# more
than where direct radiation is used. This percentage also marks approxi-
mately the increased fuel consumption in the indirect system.
Steam (Babcock & Wilcox Co.) has the following: 1 sq. ft. of boiler-surface
will supply from 7 to 10 sq. ft. of radiating-surface, depending upon the size
of boiler and the efficiency of its surface, as well as that of the radiating-
surface. Small boilers for house use should be much larger proportionately
than large plants. Eacli horse-power of boiler will supply from 240 to 360
ft. of 1-in. steam -pipe, or 80 to 120 sq. ft. of radiating-surface. Cubic feet
of space has little to do with amount of steam or surface required, but is a
convenient factor for rough calculations. Under ordinary conditions 1
horse-power will heat, approximately, in-
Brick dwellings, in blocks, as in cities 15,000 to 20,000 cu. ft.
" stores " " 10,000 " 15.000 "
•• dwellings, exposed all round 10,000 " 15,000
44 mills, shops, factories, etc 7,000 " 10,000
Wooden dwellings, exposed 7,000 " 10,000
Foundries and wooden shops 6,000 "10,000 ••
Exhibition buildings, largely glass, etc 4,000 " 15,000 ••
Steam-consumption in Car-heating.
C., M. & ST. PAUL RAILWAY TESTS. (Engineering, June 27, 1890, p. 764.)
Water of Condensation
Outside Temperature, Inside Temperature. per Car per Hour.
40 70 70 Ibs.
30 70 85
10 70 100
REGISTERS AND COLD-AIR DUCTS.
539
internal Diameters of Steam Supply-mains, with Total
Resistance equal to 2 indies of Water-column.*
Steam, Pressure 10 Ibs. per_square inch above atm., Temperature 239° F.
Formula, d « 0.5374 A/ Q--\ where d = internal diameter in inches:
r *
O = 9.2 cubic feet of steam per minute per 100 sq. ft. of radiating-surface ;
I = length of mains in feet; h = 159.3 feet head of steam to produce flow.
I Radiating-
i surface.
Internal Diameters in inches for Lengths of Mains from 1 ft. to 600 ft.
1ft.
10ft.
20ft.
40ft.
60ft.
80ft.
100 ft.
200 ft.
300ft.
400ft.
600 ft.
sq.ft.
inch.
inch.
inch.
inch.
inch.
inch.
inch.
inch.
inch.
inch.
inch.
1
0.075
0.119
0.136
0.157
0.170
0.180
0.189
0.216
0.234
0.248
0.270
10
0.19
0.30
0.84
0.39
0.43
0.45
0.47
0.54
0.59
0.62
0.68
20
0.25
0.39
0.45
0.52
0.56
0 60
0.62
0.72
0.78
0.82
0.89
40
0.33
0.52
0.60
0.69
0.74
0.79
0.82
0.95
1.03
1.09
1.18
60
0.39
0.61
0.71
0.81
0.87
0.93
0.97
1.11
1.21
1.28
1.39
80
0.43
0.68
0.79
0.90
0.98
1.04
1.09
1.25
1.35
1.43
1.55
100
0.47
0.75
0.86
0.99
1.07
1.14
1.19
1.36
1.48
1.57
1.70
200
0 62
0.99
1.14
1.30
1.41
1.50
1.57
1.80
1.95
2.07
2.24
300
0,73
1.16
1.34
1.53
1.66
1.76
1.84
2.12
2.30
,2.43
2.64
400
0.82
1.30
1.50
1.72
1.86
1.98
2.07
2.37
2.57
2.73
2.96
500
0.90
1.43
1.64
1.88
2.04
2.16
2.26
2.60
2.81
2.98
3.23
600
0.97
1.53
1.76
2.03
2.20
2.33
2.43
2.79
3.03
3.21
3.48
800
.09
1.72
1.98
2.27
2 46
2.61
2.73
3.13
3.40
3.60
3.90
1,000
.19
1.88
2.16
2.48
2.69
2.85
2.98
3.43
3.71
3.94
4.27
1,200
.28
2.04
2.33
2.67
2.90
3.07
3.21
3.68
4.00
4.23
4.59
1,400
.36
2.15
2.47
2.84
3.08
3.26
3.41
3.92
4.25
4.50
4.88
1,600
.43
2.27
2.61
3.00
3.25
3.44
3.60
4.13
4.49
4.75
5.15
1,800
.50
2.38
2.74
3.14
3.41
3.61
3.78
4.34
4.70
4.98
5.40 '
2,000
.57
2.48
2.85
3.28
3.55
3.76
3.93
4.52
4.90
5.19
5.63
3,000
1.84
2.92
3.36
3.85
4.18
4.43
4.63
5.32
5.77
6.11
6.63
4,000
2.07
3.28
3.76
4.32
4.69
4.96
5.19
5.96
6.47
6. .85
7.44
* From Robert Briggs's paper on American Practice of Warming Buildings
by Steam (Proc. Inst. 0. E., 1882, vol. Ixxi).
For other resistances and pressures above atmosphere multiply by the
respective factors below :
Water col . . G in. 12 in. 24 in. I Press, ab. atm. 0 Ibs. 3 Ibs. 30 Ibs. 60 Ibs.
Multiply by 0.8027 0.6988 0.6084 | Multiply by 1.023 1.015 0.973 0.948
Registers and Cold-air Ducts for Indirect Steam Heating.
—The Locomotive gives the following table of openings for registers and
cold-air ducts, which has been found to give satisfactory results. The cold-
air boxes should have 1V£ sq. in. area for each square foot of radiator suface,
and never less than % the sectional area of the hot-air ducts. The hot air
ducts should have 2 sq. in. of sectional area to each square fpot of radiator
surface on the first floor, and from 1*4 to 2 inches on the second floor.
Heating Surface
in Stacks.
Cold-air Supply, First Floor.
Size
Register.
Cold-air
Supply,
2d Floor.
30 square feet
40 "
50
60
70
80
90 "
100
laches
45 square inches =B 5 by 9
60 " " as 6 by 10
75 ** *• « 8 by 10
90 " " as 9 by 10
108 " " = 9 by 12
120 " " =10 by 12
135 " " = 11 by 12
150 « " =12 by 12
inches
9 by 12
10 by 14
10 by 14
12 by 15
12 by 19
12 by 22
14 by 24
16 by 20
inches
4 by 10
4 by 14
5 by 15
6 by 15
6 by 18
8 by 15
9 by 15
12 by 12
The sizes in the table approximate to the rules given, and it will be found
that they will allow an easy flow of air and a full distribution throughout the
room to be heated.
540
HEATING AND VENTILATION.
Physical Properties of Steam and Condensed Water,
under Conditions of Ordinary Practice in Warming by
Steam. (T '
j Steam-pressure j above atm. . .
i per souare incli f total
Ibs.
Ibs.
0
14.7
3
17.7
10
24.7
30
44.7
~60r.
Temperature of steam
Temperature of nir ....
Fahr.
Fahr.
Fahr.
212°
60°
152°
222°
60
163°
239°
60°
179°
274°
60°
214°
307°
60»
247°
Difference = B — C
I Heat given out per minute per
"{ 100 sq. ft. of radiatiug-sur-
>• units
456
483
537
642
741
{ face = D X 3
\
Latent heat of steam
Fahr.
965°
958°
94fi<>
921°
898°
Volume of 1 Ib. weight of steam
cu. ft.
26.4
22.1 16.2
9.24
5.70
Weight of 1 cubic foot of steam
Ib.
0.0380
0.04520.0618
0.1082
0.1752
( Volume Q of steam per minute
•< to give out E units
tcu.ft.
12.48
11.21; 9.20
6.44
4.70
( = £ X G -*- F.
\
( Weight of 1 cubic foot of con-
)
's densed water at tempera-
V Ibs.
59.64
59.51 59.05
58.07
57.03
( ture B,
i
i
( Volume of condensed water to
1
< return to boiler per minute
leu. ft.
0.0079
0.0085 0.0096
0.0120
0.0144
/ = J X H -^ K,
f
j
i Head of steam equivalent to
•< 12 inches water-column
j =KH-H.
j- feet
1569
1317
955.5
536.7
325.5
STEAM-SUPPLY MAINS.
{Head h of steam, equivalent
]
to assumed 2 inches water-
column for producing steam
j- feet
261.5
219.5
159.3
89.45
54.25
flow $, = M H- 6,
j
j Internal diameter d of tube*
\ for flow Q when I = 1 foot,
j- inch
0.484
0.481
0.474
0.461
0.449
Do. do. when I = 100 feet,
inch
1.217
1.207
1.190
1.158
1.128
Ratios of values of d.
ratio
1.023
1.015
1.000
0.973
0.948
WATER-RETURN MAINS.
( Head h assumed at J^-inch
)
< water-column for producing
f full-bore water-flow Q,
V foot
0.0417
0.0417
0.0417
0.0417
0.0417
j Internal diameter d of tube*
! • _T,
"j for flow Q when 1 = 1 foot,
> men
0.147
0-151
0.158
0.173
0.186
Do. do. when 1 = 100 feet,
inch
0.368
0.379
0.398 0.434
0.468
Ratios of values of d ...
ratio
0.926
0.952
1.0001 1.092
1.176
* P, R, U, V are each determined from the formula d = 0.5374 A / -%- .
r
Size of Steam Pipes for Steam Heating. (See also Flow of
Steam in Pipes.)— Sizes of vertical main pipes. Direct radiation. (J. R.
Willett, Heating and Ventilation, Feb., 1894.)
Diameter of pipe, inches. 1 \Y± 1*4 2 2^ 3 3^ 4 5 6
Sq. ft. of radiator surface 40 70 110 220 360 560 810 1110 2000 3000
A horizontal branch pipe for a given extent of radiator surface should be
one size larger than a vertical pipe for the same surface.
The Nason Mfg. Co. gives the following:
Diameter of pipe, in 1J4 1^ 2 2^ 3 3^
Radiator surface sq.ft. (maximum).. 125 200 500 1000 1500 2500
When mains and surfaces are very much above the boiler the pipes need
not be as large as given above; under very favorable circumstances and
EEATIKG A GREENHOUSE BY STEAM.
541
conditions a 4-inch pipe may supply from 2000 to 2500 sq. ft. of surface a 6-
inch pipe for 5000 sq. ft., and a 10-inch pipe for 15,000 to 20,000 sq. ft., if the
distance of run from boiler is not too great. Less than 1^-inch pipe should
not be used horizontally in a main unlessTor a single radiator connection
Steam, by the Babcock & Wilcox Co., says: Where the condensed water
is returned to the boiler, or where low pressure of steam is used, the diame-
ter of mains leading from the boiler to the radiating-surface should be
equal in inches to one tenth the square root of the radiating-surface mains
included, in square feet. Thus a 1-inch pipe will supply 100 square feet of
surface, itself included. Return-pipes should be at least % inch in diame-
ter, and never less than one half the diameter of the main— longer returns
requiring larger pipe. A thorough drainage of steam-pipes will effectually
prevent all cracking and pounding noises therein.
A. R. Wolff's Practice.— Mr. Wolff gives the following figures showing his
nresent practice (1897) in proportioning mains and returns. They are based
on an estimated loss of pressure of 2$ for a length of 100 ft. of pipe, not in-
cluding allowance for bends and valves (see p. 678). For longer runs divide
the thermal units given in the table by 0.1 I/length in ft. Besides giving the
thermal units the table also indicates the amount of direct radiating surface
which the steam-pipes can supply, on the basis of an emission of 250 thermal
units per hour for each square foot of direct radiating surface.
Size of Pipes for Steam Heating.
. &
II
In.
2 '
3 "
3^
4
°s
ll
In.
1
1
2 Ibs. Pressure
5 Ibs. Pressure
9
18
30
70
132
225
330
480
690
36
72
120
280
528
900
1320
1920
2760
Q »?T
w§
15
30
50
120
220
375
550
800
1150
60
120
200
480
880
1500
2200
3200
4600
^Ir^
5
6
2 Ibs Pressure's Ibs. Pressure
11
Ir..
^ H b X
-Spl|
930
1500
2250
3200
4450
5800
9250
13500
.19000
•Sfi£
&*i
ssW
ing
rface
. Ft.
3720
6000
9000
12800
17800
23200
37000
54000
76000
1550
2500
3750
5400
7500
9750
15500
23000
32500
6200
10000
15000
21600
30000
39000
62000
92000
130000
Heating a Greenhouse Iby Steam.— Wm. J. Baldwin answers a
question in the American Machinist as below : With five pounds steam-
Eressure, how many square feet or inches of heating-surface is necessary to
eat 100 square feet of glass on the roof, ends, and sides of a greenhouse
in order to maintain a night heat of 55° to 65°, while the thermometer out-
side ranges at from 15° to 20» below zero ; also, what boiler-surface is neces-
sary ? Which is the best for the purpose to use — 2" pipe or 1J4" pipe ?
Ans.— Reliable authorities agree that 1.25 to 1.50 cubic feet of air in an
enclosed space will be cooled per minute per sq. ft. of glass as many degrees
,as the internal temperature of the house exceeds that of the air outside.
Between -f- 65* and — 20° there will be a difference of 85°, or, say, one cubic
foot of air cooled 127.5° F. for each sq ft. of glass for the most extreme
condition mentioned. Multiply this by the number of square feet of
glass and by 60, and we have the number of cubic feet of air cooled 1° per
hour within the building or house. Divide the number thus found by 48, and
it gives the units of heat required, approximately. Divide again by 953,
and it will give the number of pounds of steam that must be condensed from
a pressure and temperature of five pounds above atmosphere to water at
the same temperature in an hour to maintain the heat. Each square foot
of surface of pipe will condense from 14 to nearly y% Ib. of steam per hour,
according as the coils are exposed or well or poorly arranged, for which
an average of ^ Ib. may be taken. According to this, it will require 3 s(j. ft.
of pipe surface per Ib. of steam to be condensed. Proportion the heating-
surface of the boiler to have about one fifth the actual radiating-surface, if
you wish to keep steam over night, and proportion the grate to burn not
more than six pounds of coal per sq. ft. of grate per hour. With very slow
combustion, suoh as takes place in base-burning boilers, the grate might be
proportioned for four to five pounds of coal per hour. It is cheaper to make
coils of 1*4" pipe than of 2", and there is nothing to be gained by using 2'
pipe unless the coils are very long. The pipes in a greenhouse should b»
542 HEATING AND VENTILATION.
under or in front of the benches, with every chance for a good circulation
of air. " Header" coils are better than "return-bend" coils for this purpose.
Mr. Baldwin's rule may be given the following form : Let H = heat-units
transferred per hour, T — temperature inside the greenhouse, t = tempera-
ture outside, S = sq. ft. of glass surface; then H = 1.5S(T — t) X 60 H- 48
= 1.8755(3"- <). Mr. Wolff's coefficient K for single skylights would give
H= 1.118SCT- t).
Heating a Greenhouse by Hot Water.— W. M. Mackay, of the
Richardson & Boynton Co., in a lecture before the Master Plumbers' Asso-
ciation, N. Y., 1889, says: I find that while greenhouses were formerly
heated by 4-inch and 3-inch cast-iron pipe, on account of the large body of
water which they contained, and the supposition that they gave better satis-
faction and a more even temperature, florists of long experience who
have tried 4-inch and 3-inch cast-iron pipe, and also 2 inch wrought-iron
pipe for a number of years in heating their greenhouses by hot water,
and who have also tried steam-heat, tell me that they get better satisfaction,
greater economy, and are able to maintain a more even temperature with 2-
inch wrought-iron pipe and hot water than by any other system they have
used. They attribute this result principally to the fact that this size pipe
contains less water and on this account tne heat can be raised and lowered
quicker than by any other arrangement of pipes, and a more uniform tem-
perature maintained than by steam or any other system.
HOT-WATER HEATING.
(Nason Mfg. Co.)
There are two distinct forms or modifications of hot- water apparatus, de-
pending upon the temperature of the water.
In the first or open-tank system the water is never above 212° tempera-
ture, and rarely above 200°. This method always gives satisfaction where
the surface is sufficiently liberal, but in making it so its cost is considerably
greater than that for a steam-heating apparatus.
In the second method, sometimes called (erroneously) high-pressure hot-
water heating, or the closed-system apparatus, the tank is closed. If it is
provided with a safety-valve set at 10 Ibs. it is practically as safe as the open-
tank system.
Law of Velocity of Flow.— The motive power of the circulation
in a hot -water apparatus is the difference between the specific gravities of
the water in the ascending, and the descending pipes. This effective pressure
is very small, and is equal to about one grain for each foot in height for each
degree difference between the pipes; thus, with a height of 12" in "up" pipe,
and a difference between the temperatures of the up and down pipes of 8°,
the difference in their specific gravities is equal to 8. 16 grains on each square
inch of the section of return-pipe, and the velocity of the circulation is pro-
portioned to these differences in temperature and height.
To Calculate Velocity of Flow.— Thus, with a height of ascend-
ing pipe equal to 10' and a difference in temperatures of the flow and return
pipes of 8°, the difference in their specific gravities will equal 81.6 grains, or
-i- 7000 = .01166 Ibs., or X 2.31 (feet of water in one pound) = .0269 ft., and by
the law of falling bodies the velocity will be equal to 8 I/.0269 = 1.312 ft. per
second, or X 60 = 78.7 ft. per minute. In this calculation the effect of fric-
tion is entirely omitted. Considerable deduction must be made on this
account. Even in apparatus where length of pipe is not great, and with
pipes of larger areas and with few bends or angles, a large deduction for
friction must be made from the theoretical velocity, while in large and
complex apparatus with small head, the velocity is so much reduced by
friction that sometimes as much as from 50# to 90$ must be deducted to ob-
tain the true rate of circulation.
Main flow-pipes from the heater, from which branches may be taken, are
to be preferred to the practice of taking off nearly as many pipes from the
heater as there are radiators to supply.
It is not necessary that the main flow and return pipes should equal in
capacity that of all their branches. The hottest water will seek the highest
level, while gravity will cause an even distribution of the heated water if the
surface is properly proportioned.
It is good practice to reduce the size of the vertical mains as they ascend^
Bay at the rate of one size for each floor.
As with steam, so with hot water. ust be unconfined to allow
HOT-WATER HEATING.
543
for expansion of the pipes consequent on having their temperatures ia
creased.
An expansion tank is required to keep the apparatus filled with water,
which latter expands 1/24 of its bulk on being heated from 40° to 212°, and
the cistern must have capacity to hold certainly this increased bulk. It is
recommended that the supply cistern be placed on level with or above the
highest pipes of the apparatus, in order to receive the air which collects in
the mains and radiators, and capable of holding at least 1/20 of the water
in the entire apparatus.
Approximate Proportions of Radiatiiig-surfaces to
Cubic Capacities of Space to be Heated.
One Square Foot of Ra-
diating-surface will
heat with—-
In Dwellings,
School-rooms,
Offices, etc.
In Halls, Stores,
Lofts, Facto-
ries, etc.
In Churches,
Large Audito-
riums, etc.
High temperature di- )
rect hot- water radi- >
ation . . )
50 to 70 cu. ft.
65 to 90 cu. ft.
130 to 180 cu. ft.
Low temperature di-
rect hot-water radi-
30 to 50 " "
35 to 65 ** "
70 to 130 '4 "
High temperature in-
direct hot- water ra-
diation
Low temperature in- )
direct hot-water ra- >•
diation )
30 to 60 " "
20 to 40'* "
35 to 75 " "
25 to 50 " •«
70 to 150 " "
50 to 100 " «•
Diameter of Main and Branch Pipes and square feet of coil
surface they will supply, in a low-pressure hot-water apparatus (212°) for
direct or indirect radiation, when coils are at different altitudes for direct
radiation or in the lower story for indirect radiation:
Ij
1.1
Direct Radiation. Height of Coil above Bottom of Boiler,
ll
a'S
in feet.
5
0
10
20
30 | 40
50
60
70
80
90
100
sq. ft.
sq. ft.
sq. ft.
sq. ft. sq.ft.
sq. ft.
sq. ft.
sq. ft.
sq.ft.
sq. ft.
sq. ft.
M
49
50
52
53
55
57
59
61
63
65
68
l
87
89
92
95
98
101
103
108
112
116
121
1J4
136
140
144
149
153
158
161
169
175
182
189
1H*
196
202
209
214
222
228
235
243
252
261
271
2
349
359
370
380
393
405
413
433
449
465
483
546
561
577
595
613
633
643
678
701
727
755
g
785
807
835
856
888
912
941
974
1009
1046
1086
gvx
1069
1099
1132
1166
1202
1241
1283
1327
1374
1425
1480
4
1395
1436
1478
1520
1571
1621
1654
1733
1795
1861
1933
1767
1817
1871
1927
1988
2052
2120
2193
2272
2356
2445
5
2185
2244
2309
2376
2454
2531
2574
2713
2805
2907
3019
6
3140
3228
3341
3424
3552
3648
3763
3897
4036
4184
4344
7
4276
4396
4528
4664
4808
4964
5132
5308
5496
5700
5920
8
5580
5744
5912
6080
6284
6484
6616
6932
7180
7444
7735
9
7068
7268
7484
7708
7952
8208
8482
8774
9088
9424
9780
10
8740
8976
9236
9516
9816
10124
10296
10852
11220
11628
12076
11
10559
10860
11180
11519 11879
12262
12666
13108
13576
14078
14620
12
12560
12912
13364
13696 14208
14592
15052
15588
16144
16736
17376
13
14748
15169
15615
16090
16591
17126
17697
18307
18961
19633
20420
14
17104
17584
18109
18656
19232
19856
20528
21232
21984
22800
23680
15
19634
4)195
20789
21419 22089
22801
23561
24373
25244
26179
27168
16
22320
22978
23643
24320 25136
25936
^6464
27728
28720
29776
30928
044 HEATING AND VENTILATION.
The best forms of hot-water-heating boilers are proportioned about as
follows:
1 sq. ft. of grate-surface to about 40 sq. ft. of boiler-surface.
1 ** boiler- 5 '* " radiating-surface.
1 " " grate- • 200 ** " "
Rules for Hot-water Heating.— J. L. Saunders (Heating and
Ventilation, Dec. 15, 1894) gives the following : Allow 1 sq. ft. of radiating
surface for every 3 ft. of glass surface, and 1 sq. ft. for every 30 sq. ft. of
wall surface, also 1 sq. ft. for the following numbers of cubic feet of space
in the several cases mentioned.
Indwelling-houses: Libraries and dining-rooms, first floor. . 35 to 40 cu ft.
Reception halls, first floor 40 to 50 l
Stair halls, " " 40 to 55 •
Chambers above, " " 50 to 65 (
Libraries, sewing-rooms, nurseries, etc.,
above first floor 45 to 55 •
Bath-rooms 30 to 40 '
Public-schoolrooms . 60to 85 '
Offices 50 to 65 '
Factories and stores 65 to 90 '
Assembly halls and churches 90 to 150 '
To find the necessary amount of indirect radiation required to heat a room:
Find the required amount of direct radiation according to the foregoing
method and add 50$. This if wrought-iron pipe coil surface is used ; if cast-
iron pin indirect-stack surface is used it is advisable to add from 70% to 80$.
Sizes of hot-air flues, cold-air ducts, and registers for indirect ivork.—
Hot-air flues, first floor: Make the net internal area of the flue equal to
% sq. in. to every square foot of radiating surface in the indirect stack. Hot-
air flues, second floor: Make the net internal area of the flue equal to % sq. in.
to every square foot of radiating surface in the indirect stack.
Cold-air ducts, first floor : Make the net internal area of the duct equal
to % sc[. in. to every square foot of radiating surface in the indirect stack.
Cold air ducts, second floor : Make the net internal area of the duct equal
to Y% sq. in. to every square foot of radiating surface in the indirect stack.
Hot-air registers should have their net area equal in full to the area of the
hot-air flues. Multiply the length by the width of the register in inches ; %
of the product is the net area of register.
Arrangement of Mains for Hot-water Heating. (W. M.
Mackay, Lecture before Master Plumbers' Assoc., N. Y., 1889 )— There are
two different systems of mains in general use, either of which, if properly
placed, will give good satisfaction. One is the taking of a single large-flow
main from the heater to supply all the radiators on the several floors, with a
corresponding return main of the same size. The other is the taking of a
number of 2-inch wrought-iron mains from the heater, with the same num-
ber of return mains of the same size, branching off to the several radiators
or coils with l*4-inch or 1-inch pipe, according to the size of the radiator or
coil. A 2-inch main will supply three 1 ^4-inch or four 1-inch branches, and
these branches should be taken from the top of the horizontal main with a
nipple and elbow, except in special cases where it is found necessary to retard
the flow of water to the near radiator, for the purpose of assisting the circu-
lation in the far radiator ; in this case the branch is taken from the side of
the horizontal main. The flow and return mains are usually run side by side,
suspended from the basement ceiling, and should have a gradual ascent from
the heater to the radiators of at least 1 inch in 10 feet. It is customary, and
an advantage where 2-inch mains are used, to reduce the size of the main at
every point where a branch is taken off.
The single or large main system is best adapted for large buildings ; but
there is a limit as to size of main which it is not wise to go beyond— gener-
ally 6- inch, except in special cases.
The proper area of cold-air pipe necessary for 100 square feet of indirect
radiation in hot-water heating is 75 square inches, while the hot air pipe
should have at least 100 square inches of area. There should be a damper in
the cold-air pipe for the purpose of controlling the amount of air admitted to
the radiator, depending on the severity of the weather.
BLOWER SYSTEM OF HEATIKG AXD VENTILATING. 545
THE BLOWER SYSTEM OF HEATING AND
VENTILATING.
The system provides for the use of a fan or blower which takes its supply
of fresh air from the outside of the building to be heated, forces it over
steam coils, located either centrally or divided up into a number of indepen-
dent groups, and then into the several ducts or flues leading to the various
rooms. The movement of .the warmed air is positive, and the delivery of
the air to the various points of supply is certain and entirely independent
of atmospheric conditions. For engines, fans, and steam-coils used with the
blower system, see page 519.
Experiments with Radiators of 60 sq. ft. of Surface.
(Mech. News, Dec., 18'J3.)— After having determined the volume and tem-
perature of the warm air passing through the flues and radiators from
natural causes, a fan was applied to each flue, forcing in air, and new sets of
measurements were made. The results showed that more than two and one-
third times as much air was warmed with the fans in use, and the falling off
in the temperature of this greatly increased air-volume was only about 12.6%.
The condensation of steam in the radiators with the forced-air circulation
also was only 66%$ greater than with natural-air draught. One of the
several sets of test figures obtained is as follows :
Natural Forced-
Draught air
in Flue. Circulation.
Cubic feet of air per minute 457.5 1227
Condensation of steam per minute in ounces 11.7 19.6
Steam pressure in radiator, pounds 9 9
Temperature of air after leaving radiator 14'2° 124°
** ** before passing through radiator. 61° 61°
Amount of radiating surface in square feet 60 60
Size of flue in both cases 12 x 18 inches.
There was probably an error in the determination of the volume of air in
these tests, as appears from the following calculation. (W. K.) Assume
that 1 Ib. of steam in condensing from 9 Ibs. pressure and cooling to the tem-
perature at which the water may have been discharged from the radiator
gave up 1000 heat-units, or 62.5 h. u. per ounce; that the air weighed .076 Ib.
per cubic foot, and that its specific heat is .238. We have
Natural Forced
Draught. Draught.
Heat given up by steam, ounces x 62.5 = 731 1225 H.U.
Heat received by air, cu. ft. x .076 x diff. of tern, x .238 = 673 1399 "
Or, in the case of forced draught the air received 14# more heat than the
steam gave out, which is impossible. Taking the heat given up by the steam
as the correct measure of the work done by the radiator, the temperature
of the steam at 237°, and the average temperature of the ai? in the case of
natural draught at 102° and in the other case at 93°, we have for the tem-
perature difference in the two cases 135° and 144° respectively; dividing
these into the heat-units we find that each square foot of radiating surface
transmitted 5.4 heat-units per hour per degree of difference of temperature,
in the case of natural draught, and 8.5 heat-units in the case of forced
draught (= 8.5 X 144° = 1224 heat-units per square foot of surface).
In the Women's Homoeopathic Hospital in Philadelphia, 2000 feet of
one-inch pipe heats 250.000 cubic feet of space, ventilating as well; this
equals one square foot of pipe surface for about 350 cubic feet of space, or
IFSS than 3 square feet for 1000 cubic feet. The fan is located in a sepa-
rate building about 100 feet from the hospital, and the air, after being heated
to about 135°, is conveyed through an underground Lrick duct with a loss of
only five or six degrees in cold weather. (H. I. Snell, Trans. A. S. M. E.,ix. 106.
Heating a Building to 7O° F. Inside when the Outside
Temperature is Zero.— It is customary in some contracts for heating
to guarantee that the apparatus will heat the interior of the building to 70°
in zero weather. As it may not be practicable to obtain zero weather for
the purpose of a test, it may be difficult to prove the performance of the
guarantee. E. E. Macgovern, in Engineering Record, Feb. 3, 1894, gives a
calculation tending to show that a test may be made in weather of a higher
temperature than zero, if the heat of the interior is raised above 70°. The
higher the temperature of the rooms the lower is the efficiency of the radi-
Rting-surface, since the efficiency depends upon the difference between the
546 HEATING AKD VENTILATION.
temperature inside of the radiator and the temperature of the room. He
concludes that a heating apparatus sufficient to heat a given building to 70°
in zero weather with a given pressure of steam will be found to heat the
same building, steam-pressure constant, to 110° at 60°, 95° at 50°, 82° at 40°,
and 74° at 32°, outside temperature. The accuracy of these figures, however
has not been tested by experiment.
The following solution of the question is proposed by the author. It gives
results quite different from those of Mr. Macgoveru, but, like them, lacks ex-
perimental confirmation.
Let S — sq. ft. of surface of the steam or hot-water radiator;
W = sq. ft. of surface of exposed walls, windows, etc.;
Ts = temp, of the steam or hot water, T^ = temp, of inside of building
or room, TQ = temp, of outside of building or room;
a = heat-units transmitted per sq. ft. of surface of radiator per hour
per degree of difference of temperature;
ft = average heat-units transmitted per sq. ft. of walls per hour, per
degree of difference of temperature, including allowance for
ventilation.
It is assumed that within the range of temperatures considered Newton's
law of cooling holds good, viz., that it is proportional to the difference of
temperature between the two sides of the radiating-surface.
bW
Then aS(Ts - TJ = bW(^ - T0). Let — = <7; then
cut
If Tj = 70, and T0 = 0, C = T* ~ 7°.
Let Ts = 140°, 213.5°, 308°;
Then C = 1, 2.05, 3.4.
From these we derive the following:
Temperature of Outside Temperatures, TQ.
Steam or Hot - 20° - 10° 0° 10° 20° 30° 40°
Water, Ts. Inside Temperatures, T,.
140° 60 65 70 75 80 85 90
213.5 56.6 63.3 70 76.7 83.4 90.2 96.9
308 54.5 62.3 70 77.7 85.5 93.2 100.9
sive, since tne steam-engine wastes in tne exnaust-steam and by raaiauon
about 90$ of the heat-units supplied to it. In direct steam -heating, with a
good boiler and properly covered supply-pipes, we can utilize about 60$ of
the total heat value of the fuel. One pound of coal, with a heating value of
13,000 heat-units, would supply to the radiators about 13,000 X .60 = 7800
heat-units. In electric heating, suppose we have a first-class condensing-;
engine developing 1 H.P. for every 2 Ibs. of coal burned per hour.
This would be equivalent to 1,980,000 ft.-lbs. H- 778 = 2545 heat-units, or 1272
heat-units for 1 Ib. of coal. The friction of the engine and of the dynamo and
the loss by electric leakage, and by heat radiation from the conducting
wires, might reduce the heat- units delivered as electric current to the elec-
tric radiator, and these converted into heat to 50# of this, or only 636 heat-
units, or less than one twelfth of that delivered to the steam-radiators in
direct steam-heating. Electric heating, therefore, will prove uneconomical
unless the electric current is derived from \yater or wind power, which would
otherwise be wasted. (See Electrical Engineering.)
WEIGHT Otf WATEB.
547
WATEB.
Expansion of "Water.— The following table gives the relative vol.
ernes of water at different temperatures, compared with its volume at 4* C.
according to Kopp, as corrected by Porter.
Cent.
Fahr.
Volume .
Cent.
Fahr.
Volume.
Cent.
Fahr.
Volume.
4°
39.1°
.00000
35°
95°
1 .00586
70»
158°
1.02241
5
41
.00001
40
104
1.00767
75
167
1.0-2548
10
50
.00025
45
113
1 .00967
80
176
1.02872
|3
59
.00083
50
122
1.01186
85
185
1.03213
20
68
.00171
55
131
1.01423
90
194
1.03570
25
77
.00286
60
140
1.01678
95
203
1.03943
30
86
.00425
65
149
1.01951
100
212
1.04332
Weight of 1 cu. ft. at 39.1° F. = 62.4245 Ib. -5-1.04332 = 59.833, weight of 1 cu.
ft. at 212° F.
Weight of Water at Different Temperatures.— The weight
of water at maximum density, 39.1°, is generally taken at the figure given
by Rankine, 62.425 Ibs. per cubic foot. Some authorities give as low as
62.379. The figure 62.5 commonly given is approximate. The highest
authoritative figure is 62.425. At 62° F. the figures range from 62.291 to 62.300.
The figure 62.355 is generally accepted as the most accurate.
A't 32° F. figures given by different writers range from 62.379 to 62.418.
Clark gives the latter figure, and Hamilton Smith, Jr., (from Rosetti,) gives
62.416.
Weight of Water at Temperatures afcove 212° F.— Porter
(Richards' " Steam-engine Indicator," p. 52) says that nothing is known
about the expansion of water above 212°. Applying formulae derived from
experiments made at temperatures below 212°, however, the weight and
volume above 212° may be calculated, but in the absence of experimental
data we are not certain that the formulae hold good at higher temperatures.
Thurston, in his " Engine and Boiler Trials," gives a table from which we
take the following (neglecting the third decimal place given by him) :
!•£*
J3 ^
||^
* ti
%£t
£
Weight, Ibs.
per cubic
foot.
jii
Weight, Ibs.
per cubic
foot.
H
||
i|g
|l
212
220
230
240
250
260
270
59.71
59.64
59.37
59.10
58.81
58.52
58.21
280
290
300
310
320
330
840
57.90
57.59
57.26
56.93
56.58
56.24
55.88
350
360
370
380
390
400
410
55.52
55.16
54.79
54.41
54.03
53.64
53.26
420
430
440
450
460
470
480
52.86
52.47
52.07
51.66
61.26
50.85
50.44
490
500
510
520
530
540
550
50.03
49.61
49.20
48.78
48.36
47.94
47.52
Box on Heat
Temperature
LbSo per cubic
gives tt
F ... .
te following :
212° 250® 300° 350° 400° 450° 500° 600°
59.82 58.85 57.42 55.94 54.34 52.70 51.02 47.64
foot...
At 212° figures given by different writers (see Trans. A. S. M. E., xiii. 409)
range from 59.56 to 59.845, averaging about 59.77.
548
WATER.
Weight of "Water per Cubic Foot, from 32° to 212° F., and heat-
units per pound, reckoned above 32° F.: The following table, made by in-
terpolating the table given by Clark as calculated from Rankine's formula,
with corrections for apparent errors, was published by the author in 1884,
Trans. A. S. M. E., vi. 90. (For heat units above 212° see Steam Tables.)
J*
s ^
jr
ill
1
w
Tempera-
ture,
deg. F.
Weight, Ibs.
per cubic
foot.
Heat-units.
Tempera-
ture,
deg. F.
j» 0
Heat-units.
<rf
j§.2
Heat-units.
32
62.42
0.
78
62.25
46.03
123
61.68
91.16
168
60.81
136.44
33
62.42
i.
79
62.24
47.03
124
61.67
92.17
169
60.79
137.45
34
62.42
2.
80
62.23
48.04
125
•61.65
93.17
170
60.77
138.45
35
62.42
3.
81
62.22
49.04
126
61.63
94.17
171
60.75
139.46
36
62.42
4.
82
62.21
50.04
127
61.61
95.18
172
60.73
140.47
37
62.42
5.
83
62.20
51.04
128
61.60
96.18
173
60.70
141.48
38
62.42
6.
84
62.19
52.04
129
61.58
97.19
174
60.68
142.49
39
62.42
7.
85
62.18
53.05
130
61.56
98.19
175
60.66
143.50
40
62.42
8.
86
62.17
54.05
131
61.54
99.20
176
60.64
144.51
41
62.42
9.
87
62.16
55.05
132
61.52
100.20
177
60.62
145.52
42
62.42
10.
88
62.15
56.05
133
61.51
101.21
178
60.59
146.52
43
62.42
11.
89
62.14
57.05
134
61.49
102.21
179
60.57
147.53
44
62.42
12.
90
62.13
58.06
135
61.47
103.22
180
60.55
148.54
45
62.42
13.
91
62.12
59.06
136
61.45
104.22
181
60.53
149.55
46
62.42
14.
92
62.11
60.06
137
61.43
105.23
182
60.50
150.56
47
62.42
15.
93
62.10
61.06
138
61.41
106.23
183
60.48
151.57
48
62.41
16.
94
62.09
62.06
139
61.39
107.24
184
60.46
152.58
49
62.41
17.
95
62.08
63.07
140
61.37
108.25
185
60.44
153.59
50
62.41
18.
96
62.07
64.07
141
61.36
109.25
186
60. 41 1154.60
51
62.41
19.
97
62.06
65.07
142
61.34
110.26
187
60.391165.61
52
62.40
20.
98
62.05
66.07
143
61 32
111.26
188
60.37
156.62
53
62.40
21.01
99
62.03
67.08
144
61.30
112.27
189
60.34
157.6?
54
62.40
22.01
100
62.02
68.08
145
61.28
113.28
190
60.32
158.64
55
62.39
23.01
101
62.01
69.08
146
61.26
114.28
191
60.29
159.65
56
62.39
24.01
102
62.00
70.09
147
61.24
115.29
192
60.27
160.67
57
62.39
25.01
103
61.99
71.09
148
61.22
116.29
193
60.25
161.68
58
62.38
26.01
104
61.97
72.09
149
61.20
117.30
194
60.22
162.69
59
62.38
27.01
105
61.96
73.10
150
61.18
118.31
195
60.20
163.70
60
62.37
28.01
106
61.95
74.10
151
61.16
119.31
196
60.17
164.71
61
62.37
29.01
107
61.93
75.10
152
61.14
120.32
197
60.15
165.72
62
62.36
30.01
108
61.92
76.10
153
61.12
121.33
198
60.12
166.73
63
62.36
31.01
109
61.91
77.11
154
61.10
122.33
199
60.10
167.74
64
62. B5
32.01
110
61.89
78.11
155
61.08
123.34
200
60.07
168.75
65
62.34
33.01
111
61.88
79.11
156
61.06
124.35
201
60.05
169.77
66
62.34
34.02
112
61.86
80.12
157
61.04
125.35
202
60,02
170.78
67
62.33
35. OS
113
61.85
81.12
158
61.02
126.36
203
60.00
171.79
68
62.33
36.02
114
61.83
82.13
159
61.00
127.37
204
59.97
172.80
69
62.32
37.02
115
61.82
83.13
160
60.98
128.37
205
59.95
173.81
70
62.31
38.02
116
61.80
84.13
161
60.96
129.38
206
59.92
174.83
71
62.31
39.02
117
61.78
85.14
162
60.94
130.39
207
59.89
175.84
72
62.30
40.02
118
61.77
86.14
163
60.92
131.40
208
59.87
176.85
73
62.29
41.02
119
61.75
87.15
164
60.90
132.41
209
59.84
177.86
74
62.28
42.03
120
61.74
88.15
165
60.87
133.41
210
59.82
178.87
75
62.28
43.03
121
61.72
89.15
166
60,85
134.4*
211
59.79
179.89
76
62.27
44.03
122
61.70
90.16
167
60.83
135.43
212
59.76
180.90
77
62.26
45.03
Comparison of Heads of "Water in Feet with Pressure* in
Various Units,
One foot of water at 39°. 1 Fahr. =•
=• 62.425 Ibs. on the square foot;
= 0.4335 Ibs. on the square inch;
= 0.0295 atmosphere;
= 0.8826 inch of mercury at 32° ;
•! ^eefc °^ air at 3?° & n(i
\ atmospheric pressure:
PKESSUKE OF WATER.
549
One Ib. on the square foot, at 39°. 1 Fahr
One Ib. on the square inch " .-.;*.
One atmosphere of 29.922 inches of mercury....
One inch of mercury at 32°. 1
One foot of air at 32 deg., and one atmosphere..
One foot of average sea-water
One foot of water at 62° F
** »» " ** ** 62° F
One inch of water at 62° F ...!..! '= 0.5774 'ounce
One pound of water on the square inch at 62° F. :
One ounce of water on the square inch at 62° F. ;
= 0.01602 foot of water;
= 2.307 feet of water;
= 33.9 " " "
= 1.133 " " "
= 0.001293 " •• ••
= 1.026 foot of pure water;
= 62.355 Ibs. per sq. foot;
= 0.43302 Ib. per sq. inch-
= 0.036085 Ib. per sq. inch-
: 2.3094 feet of water.
= 1.732 inches of water.
Pressure in Pounds per Square Inch for Biflereiit Heads
of Water.
At 62° F. 1 foot head = 0.433 Ib. per square inch, .433 X 144 = 62.352 Ibs.
per cubic foot.
Head, feet.
0
1
2
3
4
5
6
7
8
9
0
0.433
0.866
1.299
1.732
2.165
2.598
3.031
3.464
3.897
10
4.330
4.763
5.196
5.629
6.062
6.495
6.928
7.361
7.794
8.227
20
8.660
9.093
9.526
9.959
10.392
10.825
11.258
11.691
12.124
12.557
30
12.990
13.423
13.856
14.289
14.722
15.155
15.588
16.021
16.454
16.887
40
17.320
17.753
18.186
18.619
19.052
19.485
19.918
20.351
20.784
21.217
50
21.650
22.083
22.516
22.949
23.382
23.815
24.248
24.681
25.114
25.547
60
25.980
26.413
26.846
27.279
27.712
28.145
28.578
29.011
29.444
29.877
70
30.310
30.743
31.176
31.609
32.042
32.475
32.908
33.341
33.774
34.207
80
34.640
35.073
35.506
35.939
36.372
36.805
37.238
37.671
38.104
38.537
90
38.970
39.403
39.836
40.269
40.702
41.185
41.568
42.001
42.436
42.867
Head in Feet of Water, Corresponding to
Pounds per Square Iiicli.
1 Ib. per square inch = 2.30947 feet head, 1 atmosphere =
Inch = 33.94 ft. head.
Pressures in
14.7 Ibs. per sq.
Pressure.
0
1
2
3
4
5
6
7
8
9
0
2.309
4.619
6.928
9.238
11.547
13.857
16.166
18.476
20.785
10
23.0947
25.40427.714
30.023 32.333
34.642
36.952
39.261
41.570
43.880
20
46.189448.49950.808
53.11855.427
57.737
60.046
62.356
64.665
66.975
30
69.2841J71.594'73.903
76.213 78.522
80.831
83.141
85.450
87.760
90.069
40
92.378894.68896.998
99.307101.62
103.93
106.24
108.55
110.85
113.16
50
115.4735117.78
120.09
122.40 124.71
127.02
129.33
131.64
133.95
136.26
60
138.56821140.88
143.19
145.50 147.81
150.12
152.42
154.73
157.04
159.35
70
161. 6629|l63. 971166. 28
168.59170.90
173.21
175.52
177.83
180.14
182.45
80
184. 7576 187. 07J189.38
191.69194 00
196.31
198.61
200.92
203.23
205.54
90
£07.8523
210.16
212.47
214.78
217.09
219.40
221.71
224.02
226.33
228.64
Pressure of Water due to its Weight.— The pressure of still
water in pounds per square inch against the sides of any pipe, channel, or
vessel of any shape whatever is due solely to the "head," or height of the
level surface of the water above the point at which the pressure is con-
sidered, and is equal to .43302 Ib. per square inch for every foot of head,
or 62.355 Ibs. per square foot for every foot of head (at 62° F.).
The pressure per square inch is equal in all directions, downwards, up-
wards, or sideways, and is independent of the shape or size of the containing
vessel.
The pressure against a vertical surface, as a retaining- wall, at any point
is in direct ratio to the head above that point, increasing from 0 at the level
surface to a maximum at the bottom. The total pressure against a vertical
Strip of a unit's breadth increases as the area of a right-angled triangle
550 WATER.
whose perpendicular represents the he'ight of the strip and whose base
represents the pressure on a unit of surface at the bottom; that is, it in-
creases as the square of the depth. The sum of all the horizontal pressures
is represented by the area of the triangle, and the resultant of this Bum is
equal to this sum exerted at a point one third of the height from the bottom.
(The centre of gravity of the area o£ a triangle is one third of its height.)
The horizontal pressure is the same it' the surface is inclined instead of
vertical.
(For an elaboration of these principles see Trautwine's Pocket-Book, or
the chapter on Hydrostatics in any work on Physics. For dams, retaining-
walls, etc., see Trautwine.)
The amount of pressure on the interior walls of a pipe has no appreciable
effect upon the amount of flow.
Buoyancy.— When a body is immersed in a liquid, whether it float or
sink, it is buoyed up by a force equaJ to the weight of the bulk of the liquid
displaced by the body. The weight of a floating body is equal to the weight
of the bulk of the liquid that it displaces. The upward pressure or buoy-
ancy of the liquid may be regarded as exerted at the centre of gravity of
the displaced water, which is called the centre of pressure or of buoyancy.
A vertical line drawn through it is called the axis of buoyancy or of flota-
tion. In a floating body at rest a line joining the centre of gravity and the
centre of buoyancy is vertical, and is called the axis of equilibrium. When
an external force causes the axis of equilibrium to lean, if a vertical line be
drawn upward from the centre of buoyancy to this axis, the point where it
cuts the axis.is called the metacentre. If the metacentre is above the centre
of gravity the distance between them is called the metacentric height, and
the body is then said to be in stable equilibrium, tending to return to its
original position when the external force is removed.
Boil iiig-point.— Water boils at 212° F. (100° C.) at mean atmospheric
pressure at the sea-level, 14.696 Ibs. per square inch. The temperature at
which water boils at any given pressure is the same as the temperature of
saturated steam at the same pressure. For boiling-point of water at other
pressure than 14.696 Ibs. per square inch, see table of the Properties of
Saturated Steam.
Tne Boiling-point of Water may be Raised.— When water
is entirely freed of air, which may be accomplished by freezing or boiling,
the cohesion of its atoms is greatly increased, so that its temperature may
be raised over 50° above the ordinary boiling-point before ebullition takes
place. It was found by Faraday that when such air-freed water did boil,
the rupture of the liquid was like an explosion. When water is surrounded
by a film of oil, its boiling temperature may be raised considerably above
its normal standard. This has been applied as a theoretical explanation in
the instance of boiler-explosions.
The freezing-point also may be lowered, if the water is perfectly quiet, to
— 10° C., or 18° Fahrenheit below the normal freezing-point. (Hamilton
Smith, Jr., on Hydraulics, p. 13.) The density of water at 14° F. is .99814, its
density at 39°. 1 being 1, and at 32°, .9 —
Freezing-point.— Water freezes at 32° F. at the ordinary atmospheric
pressure, and ice melts at the same temperature. In the melting of 1 pound
of ice into water at 32° F. about 142 heat-units are absorbed, or become
latent: and in freezing 1 Ib. of water into ice a like quantity of heat is given
out to the surrounding medium.
Sea-water freezes at 27° F. The ice is fresh. (Trautwine.)
Ice and Snow. (From Clark.)-! cubic foot of ice at 32B F. weighs
57.50 Ibs. ; 1 pound of ice at 32° F. has a volume of .0174 cu, ft. = 30.067 cu. in.
Relative volume of ice to water at 32° F., 1.0855, the expansion in passing
into the solid state being 8.55#. Specific gravity of ice = 0.922, water at
62° F. being 1.
At high pressures the melting-point of ice is lower than 32° F., being at
the rate of .0133° F. for each additional atmosphere of pressure
The specific heat of ice is .504, that of water being 1.
1 cubic foot of fresh snow, according to humidity of atmosphere: 5 Ibs. to
12 Ibs. ] cubic foot of snow moistened and compacted by rain: 15 Ibs. to
50 Ibs. (Trautwine).
Specific Heat of "Water. (From Clark's Steam-engine.)— Calcu-
lated by means of Regnault's formula, c = 1 -f- 0.00004* -J- 0.0000009*2, in
which c is the specific heat of water at any temperature t in centig* ade de-
grees, the specific heat at the freezing-point being 1.
THE IMPURITIES OF WATER.
551
Tempera-
tures.
|||?
tasS
«P
o fl o>
§i£d
g£^£
CL^ C 0>
Tempera-
tures.
ijs-st
Sflg
v a>5
W.^«8
ǤS50.
*3 ^'JS Q«
!^s
S~S s <x>
tilt
l|l
I"S
si*?
-3 -t^ [v'l S3
jSjU
o ^5
£,§ a
M^*.^
slM
Cent.
Fahr.
§fi&5
* -t-s D
|wfei
Cent.
Fahr.
§5 &•§
1"^
jnfc-&
0°
32»
0.000
1.0000
120°
248°
217.449
1.0177
1.0067
10
50
18.004 .0005
1.0002
130
266
235.791
1.0204
1.0076
20
68
36.018 .0012
1.0005
140
284
254.187
1.0232
1.0087
30
86
54. 047 i 1.0020
1.0009
150
302
272.628
1.0262
1.0097
40
104
72.090
.0030
1.0013
160
320
291.132
1.0294
1.0109
50
122
90.157
.0042
1.0017
170
338
309.690
1.0328
1.0121
60
140
108.247
.0056
1 .0023
180
356
328.320
1.0364
1.0133
70
158
126.378
.0072
1.0030
190
374
347.004
.0401
1.0146
80
176
144.508
1 .0089
1.0035
200
392
365.760
.0440
1.0160
90
194
162.686
1.0109
1.0042
210
410
384.588
.0481
1.0174
100
212
180.900
1.0130
1.0050
220
428
403.488
.0524
1.0189
110
230
199.152
1 .0153
1.0058
230
446
422.478
.0568
1.0204
Compressibility of Water.— Water is very slightly compressible.
Its compressibility is from .000040 to .000051 for one atmosphere, decreasing
be diminished in volume .0000015 to .0000013. Water is so incompressible
that even at a depth of a mile a cubic foot of water will weigh only about
half a pound more than at the surface.
THE IMPURITIES OF WATER.
(A. E. Hunt and G. H. Clapp, Trans. A. I. M. E. xvii. 338.)
Commercial analyses are made to determine concerning a given water:
(1) its applicability for making steam; (2) its hardness, or the facility with
which it will " form a lather " necessary for washing; or (3) its adaptation
to other manufacturing purposes.
At the Buffalo meeting of the Chemical Section of the A. A. A. S. it was de-
cided to report all water analyses in parts per thousand, hundred-thousand,
and million.
To convert grains per imperial (British) gallons into parts per 100,000, di-
vide by 0.7. To convert parts per 100,000 into grains per U. S. gallon, mul-
tiply by 7/12 or .583.
The most common commercial analysis of water is made to determine it*
fitness for making steam. Water containing more than 5 parts per 100,000
of free sulphuric or nitric acid is liable to cause serious corrosion, not only
of the metal of the boiler itself, but of the pipes, cylinders, pistons, and
valves with which the steam comes in contact.
The total residue in water used for making steam causes the interior lin-
ings of boilers to become coated, and often produces a dangerous hard
scale, which prevents the cooling action of the water from protecting the
metal against burning.
Lime and magnesia bicarbonates in water lose their excess of carbonic
acid on boiling, and often, especially when the water contains sulphuric
pal IS PCI 1UU,UUU Ul lUlcll SU11U ICOIVIUO win v/i vnuw<« ".7 v/w«^.-.~ ~- ^~..™~
scale, and should condemn the water for use in steam-boilers, unless a
better supply cannot be obtained.
The following is a tabulated form of the causes of trouble with water for
steam purposes, and the proposed remedies, given by Prof. L. M. Norton.
CAUSES OP INCRUSTATION.
1. Deposition of suspended matter.
2. Deposition of deposed salts from concentration.
3. Deposition of carbonates of lime and magnesia by boiling off carbonic
acid, which holds them in solution.
552
WATER.
4. Deposition of sulphates of lime, because sulphate of lime is but slightly
soluble in cold water, less soluble in hot water, insoluble above 270° F.
5. Deposition of magnesia, because magnesium salts decompose at high
temperature.
6. Deposition of lime soap, iron soap, etc., formed by saponification of
grease.
MEANS FOB PREVENTING INCRUSTATION.
1. Filtration.
2. Blowing off.
3. Use of internal collecting apparatus or devices for directing the cir-
culation.
4. Heating feed-water.
5. Chemical or other treatment of water in boiler.
6. Introduction of zinc into boiler.
7. Chemical treatment of water outside of boiler.
TABULAR VIEW.
Troublesome Substance.
Sediment, mud, clay, etc.
Readily soluble salts.
Bicarbonates of lime, magnesia, J
iron. f
Sulphate of lime.
Chloride and sulphate of magne- 1
aium.
Carbonate of soda in large j
amounts, f
Acid (in mine waters).
Dissolved carbonic acid and )
oxygen. f
Grease (from condensed water), j-
Trouble. Remedy or Palliation.
Incrustation. Filtration ; blowing off.
Blowing off.
( Heating feed. Addition of
•< caustic soda, lime, or
magnesia, etc.
«( j Addition of carb. soda,
1 barium hydrate, etc.
j Addition of carbonate of
I soda, etc.
j Addition of barium chlo-
1 ride, etc.
Alkali.
( Feed milk of lime to the
•{ boiler, to form a thin in-
ternal coating.
Corrosion.
Priming.
Corrosion.
Corrosion.
Organic matter (sewage).
1
Corrosion or *l
incrustation. | Different cases require dif-
Priming, i- ferent remedies. Consult
corrosion, or j a specialist on the subject,
incrustation. J
The mineral matters causing the most troublesome boiler-scales are bicar*
Donates and sulphates of lime and magnesia, oxides of iron and alumina,
«tnd silica. The analyses of some of the most common and troublesome
boiler-scales are given in the following table :
Analyses of Boiler-scale. (Chandler.)
Sul-
Per-
Car-
phate
of
Mag-
nesia.
Silica.
oxide
of
Water.
bonate
of
Lime.
Iron.
Lime.
N.Y.C.&H.R.Ry.,No. 1
74.07
9 19
0.65
0.08
1.14
14.78
" " " No. 2
71 37
1.76
11 " No. 3
62.86
18.95
2.60
6.92
1.28
12.62
" " " No. 4
53.05
4.79
" " No. 5
46.83
5.32
No. 6
30.80
31.17
7.75
1.08
2.44
26.93
4< •• No. 7
4.95
2.61
2.07
1.03
0.63
86.25
" " No. 8
0.88
2.84
0.65
0.36
0.15
93.19
•• •« No. 9
4.81
2.92
•• " " No. 10
30.07
8.24
THE IMPURITIES OF WATER.
553
Analyses in Parts per 100.OOO of Water giving Bad
Results in Steam-boilers. (A. E. Hunt.)
<D •
, tuc
& =
t««
g
£|
?a
cj
-6
<x>
-3
Q
ofl
5?
.
i
d
%
w
<M
I1
•£»
||
3
8f
s
*S
j
d*
1
03
_d
0
3
^ cj
-^
.S
ft
,0
d
fee
B
o
«•§
MS
fl
I
3
02
43
O
-
O
5
6
Coal-mine water
110
95
119
39
890
590
780
30
610
Salt- well
151
38
190
48
360
990
38
30
1310
Spring . ... .
75
89
95
120
310
91
75
10
80
36
Monongahela River
130
161
33
910
38
70
80
70
94
81
919
210
90
tt **
39
8?,
61
104
98
190
38
Allegheny R., near Oil- works
30
50
41
68
890
42
23
Many substances have been added with the idea of causing chemical
action which will prevent boiler-scale. As a general rule, these do more
harm than good, for a boiler is one of the worst possible places in which to
carry on chemical reaction, where it nearly always causes more or less
corrosion of the metal, and is liable to cause dangerous explosions.
In cases where water containing large amounts of total solid residue is
necessarily used, a heavy petroleum oil, free from tar or wax, which is not
acted upon by acids or alkalies, not having sufficient wax in it to cause
saponification, and which has a vaporizing-point at nearly 600° F., will give
the best results in preventing boiler-scale. Its action is to form a thin
greasy film over the boiler linings, protecting them largely from the action
of acids in the water and greasing the sediment which is formed, thus pre-
venting the formation of scale and keeping the solid residue from the
evaporation of the water in such a plastic suspended condition that it can
be easily ejected from the boiler by the process of " blowing off." If the
water is not blown off sufficiently often, this sediment forms into a " putty"
that will necessitate cleaning the boilers. Any boiler using bad water should
be blown off every twelve hours.
Hardness of Water.— The hardness of water, or its opposite quality,
indicated by the ease with which it will form a lather with soap, depends
almost altogether upon the presence of compounds of lime and magnesia.
Almost all soaps consist, chemically, of oleate, stearate, and palniitate, of
an alkaline base, usually soda and potash. The more lirne and magnesia in a
sample of water, the more soap a given volume of the water will decompose,
so as to give insoluble oleate, palmitate, and stearate of lime and magnesia,
and consequently the more soap must be added to a gallon of water in order
that the necessary quantity of soapmayremain in solution to form the lather.
The relative hardness of samples of water is generally expressed in terms
of the number of standard soap-measures consumed by a gallon of water in
yielding a permanent lather.
The standard soap-measure is the quantity required to precipitate one
grain of carbonate of lime.
It is commonly reckoned that one gallon of pure distilled water takes one
soap-measure to produce a lather. Therefore one is deducted from the
total number of soap-measures found to be necessary to use to produce a
lather in a gallon of water, in reporting the number of soap-measures, or
" degrees " of hardness of the water sample. In actually making tests for
hardness, the " miniature gallon," or seventy cubic centimetres, is used
rather than the inconvenient larger amount. The standard measure is made
by completely dissolving ten grammes of pure castile soap (containing 60 per
cent olive-oil) in a litre of weak alcohol (of about 35 per cent alcohol). This
yields a solution containing exactly sufficient soap in one cubic centimeter
of the solution to precipitate one milligramme of carbonate of lime, or, in
other words, the standard soap solution is reduced to terms of the " minia-
ture gallon ' ' of water taken.
If a water charged with a bicarbonate of lime, magnesia, or iron is boiled,
554
WATER.
it will, on the excess of the carbonic acid being expelled, deposit a consid-
erable quantity of the lime, magnesia, or iron, and consequently the water
will be softer. The hardness of the water after this deposit of lime, after
long boiling, is called the permanent hardness and the difference between it
and the total hardness is called temporary hardness.
Lime salts in water react immediately on soap-solutions, precipitating the
oleate, palmitate, or ste«*rate of lime at once. Magnesia salts, on the con-
trary, require some considerable time for reaction. They are, however,
more powerful hardeners; one equivalent of magnesia salts consuming us
much soap as one and one-half equivalents of lime.
The presence of soda and potash salts softens rather than hardens water.
Each grain of carbonate of lime per gallon of water causes an increased
expenditure for soap of about 2 ounces per 100 gallons of water. (Eng'g.
News, Jan. 31, 1885.)
Purifying Feed-water for Steam-boilers* (See also Incrus
tation and Corrosion, p. TIG.)— When the water used for steam-boilers con-!
tains a large amount of scale-forming material it is usually advisable to
purify it before allowing it to enter the boiler rather than to attempt tho
prevention of scale by the introduction of chemicals into the boiler. Car-
bonates of lime and magnesia may be removed to a considerable extent by
lime, soda-ash, caustic soda, etc.— in tanks, the precipitates being separated
by settling or filtering. For a description of several systems of water
purification see a series of articles on the subject by Albert A. Cary in Eny'g
Mag., 1897.
Mr. W. B. Coggswell, of the Solvay Process Co.'s Soda Works in Syracuse,
N. Y., thus describes the sj^stem of purification of boiler feed-water in use
at these works (Trans. A. S. M. E., xiii. 255):
For purifying, we use a weak eoda liquor, containing about 12 to 15 grams
Na2Co, per litre. Say 1^ to 2 M3 (or 397 to 530 gals.) of this liquor is run
into the precipitating tank. Hot water about 60° C. is then turned in, and
the reaction of the precipitation goes on while the tank is filling, which re-
quires about 15 minutes. When the tank is full the water is filtered through
the Hyatt (4), 5 feet diameter, and the Jewell (1), 10 feet diameter, filters in
30 minutes. Forty tanks treated per 24 hours.
Charge of water purified at once 35 M3, 9,275 gallons.
Soda in purifying reagent 15 kgs. NaaCO3.
Soda used per 1,000 gallons 3.5 Ibs.
A sample is taken from each boiler every other day and tested for deg.
Baume, soda and salt. If the deg. B. is more than 2, that boiler is blown to
reduce it below 2 deg. B.
The following are some analyses given by Mr. Coggswell :
Lake
WTater,
grams per
litre.
Mud from
Hyatt
Filter.
Scale from
Boiler-
tube.
Scale
found
in
Pump.
.261
3.70
51.24
10.9
Calcium chloride .....
.186
.091
63.37
19.76
87.
Magnesium carbonate . ....
.015
1. 11
25 21
.087
Salt NaCl
.63
14
Silica
15 17
2.29
.8
Iron and aluminum oxide .
1.10
1 2
Total
1.270
87.10
99.74
99.9
Softening Hard Water for Locomotive Use.— A water-soft-
ening plant in operation at -Fossil, in Western Wyoming, on the Union Pa-
cific Railway, is described in Eng'g News, June 9, 1892. It is the invention
FLOW OF WATER. 555
of Arthur Pennell, of Kansas City. The general plan adopted is to first dis-
solve the chemicals in a closed tank, and then connect this to the supply main
so that its contents will be forced into the main tank, the supply-pipe being
so arranged that thorough mixture of the solution with the water is ob-
tained. A waste-pipe from the bottom of the tank is* opened from time to
time to draw off the precipitate. The pipe leading to the tender is arranged
to draw the water from near the surface.
A water-tank 24 feet in diameter and 16 feet high will contain about 46,600
gallons of water. About three hours should be allowed for this amount of
water to pass through the tank to insure thorough precipitation, giving a
permissible consumption of about 15,000 gallons per hour. Should more
than this be required, auxiliary settling-tanks should be provided.
The chemicals added to precipitate the scale-forming impurities are so-
dium carbonate and quicklime, varying in proportions according to the rela-
tive proportions of sulphates and carbonates in the water to be treated.
Sufficient sodium carbonate is added to produce just enough sodium sulphate
to combine with the remaining lime and magnesia sulphate and produce
glauberite or its corresponding magnesia salt, thereby to get rid of the
sodium sulphate, which produces foaming, if allowed to accumulate.
For a description of a purifying plant established by the Southern Pacific
E. E, Co. at Port Los Angeles, Cal., see a paper by Howard Stillmann in
Trans. A. S. M. E., vol. xix, Dec. 1897.
HYDRAULICS-PLOW OF WATER.
Formulae for Discharge of Water though Orifices and
"Weirs.— For rectangular or circular orifices, with the head measured from
centre of the orifice to the surf ace of the still water in the feeding reservoir.
(1)
For weirs with no allowance for increased head due to velocity of approach:
Q = C% V2g7lX LH. ....... ... (2)
For rectangular and circular or other shaped vertical or inclined orifices;
formula based on the proposition that each successive horizontal layer of
water passing through the orifice has a velocity due to its respective head:
(3)
For rectangular vertical weirs:
Q = c%V2gJfXLh ........... (4)
Q =± quantity of water discharged in cubic feet per second; C = approxi-
mate coefficient for formulas (1) and (2) ; c = correct coefficient for (3)
and (4).
Values of the_coefficients c and C are given below.
g — 32.16; y%g = 8.02; H — head in feet measured from centre of orifice
to level of still water; Hb — head measured from bottom of orifice; Ht =
head measured from top of orifice; h = H, corrected for- velocity of ap-
proach, Fa, — H-\ --- — ; a = area in square feet; L = length in feet.
3 2g
Flow of Water from Orifices.— The theoretical velocity of water
flowing from an orifice is the same as the velocity of a falling body which
has fallen from a height equal to the head of water, = ^2gH. The actual
velocity at the smaller section of tho vena contracta is substantially the
same as the theoretical, but the velocity at the plane of the orifice is
C y^yH, in which the coefficient C has the nearly constant value of .62. The
smallest diameter of the vena contracta is therefore about .79 of that of the
orifice. If C be the approximate coefficient = .62, and c the correct coeffi-
556
HYDRAULICS.
cient, the ratio - varies with different ratios of the head to the diametei
c
TT
of the vertical orifice, or to — . Hamilton Smith, Jr., gives the following:
For|= .5
.875
1.5
2.5
10.
— = .9604 .9849 .9918 .9965 .9980 .9987 .9997 1.
c
For vertical rectangular orifices of ratio of head to width W\
For ^ = .5 .6 .8 1 1.5 2. 3. 4. 5. S.
.9953 .9974 .9988 .9993 ,9996 ,9998
For H -J- D or H-*- TFover 8, C = c, practically.
— = .9428 .9657 .9823 .9:
c
Weisbacb gives the following values of c for circular orifices in a thin wall.
H = measured head from centre of orifice.
Dft.
H ft.
.066
.33
.82
2.0
3.0
45.
340.
.033
.066
.10
.13
.711
.665
.637
.629
.622
.614
.628
.621
.614
.607
.641
.632
.600
For an orifice of D = .033 ft. and a well-rounded mouthpiece, H being the
effective head in feet,
H - .066
c = .959
1.64
.967
11.5
.975
56
.994
.994
Hamilton Smith, Jr., found that for great heads, 312 ft. to 336 ft., with con.
verging mouthpieces, c has a value of about one, and for small circular
orifices in thin plates, with full contraction, c = about .60. Some of Mr.
Smith's experimental values of c for orifices in thin plates discharging into
air are as follows. All dimensions in feet.
Circular, in steel, D = .020, j &[
Circular, in brass, D = .050, j HC ;
Circular, in brass,D = .100, j HC '_
Circular, in iron, D = .100, -j ^f :
Square, in brass, .05 X .05, -j & \
Square, in brass, .10 X .10, -j ^ [
Rectangular, in brass, j H =
£= .300, W= .050 1 c =
For the rectangular orifice, L, the length, is horizontal.
Mr. Smith, as the result of the collation of much experimental data of
others as well as his own, gives tables of the value of c for vertical orifices,
with full contraction, with a free discharge into the air, with the inner face
of the plate, in which the orifice is pierced, plane, and with sharp inner
corners, so that the escaping vein only touches these inner edges. These
tables are abridged below. The coefficient c is to be used in the formulae (3)
and (4) above. For formulas (1) and (2) use the coefficient C found from the
values of the ratios — above.
: .739
2.43
3.19
.6495
.6298
.6264
: .185
.536
1.74
2.
73
3
.57
4.63
.6525
.6265
.6113
eoro
.6060
.6051
.129
.457
.900
1.
73
2
.05
3.18
.6337
.6155
.6096
6042
.6038
.6025
1.80
1.81
2.81
4.
68
.6061
.6041
.6033
6026
.313
.877
1.79
0
81
3
.70
4.63
.6410
.6238
.6157
6127
.6113
.6097
.181
.939
1.71
2]
75
3
.74
4.59
.6292
.6139
.6084
6076
.6060
.6065
.261
.917
1.82
2.
83
3
.75
4.70
.6476
.6280
.6203
.6180
.6176
.6168
HYDKAULIC FORMULJE.
557
Values of Coefficient c for Vertical Orifices with Sharp
Edges, Full Contraction, and Free Discharge into
Air. (Hamilton Smith, Jr.)
Head from
Centre of
Orifice H.
Square Orifices. Length of the Side of the Square, in feet.
.02
.03
.04
.05
.07
.ly
.is
.15
.20
.40
.60
.80
1.0
A
.6
1.0
3.0
0.0
10.
20.
100.(?)
.660
.648
.632
.623
.616
.606
.599
.645
.636
.622
.616
.611
.605
.598
.643
.636
.628
.616
.612
608
.604
.598
.63?
.630
.622
.612
.609
.606
.603
.598
.628
.623
.618
.609
.607
.605
.602
.598
.621
.617
.613
.607
.605
.604
.602
.598
.616
.613
.610
.606
.605
.604
.602
.598
.611
.610
.608
.606
.605
.603
.602
.598
.605
.605
.605
.604
.603
.602
.598
.601
.603
.605
.604
.603
.601
598
.598
.601
.604
.603
.602
.601
.598
.596
.600
.603
.602
.602
.601
.598
.599
.603
.602
.601
.600
.598
H.
Circular Orifices. Diameters, in feet.
.02
.03
.04
.630
.623
.614
.609
.607
.603
.599
.595
.592
.05
~^637
.624
.617
.610
.605
.604
.601
.598
.595
.592
.07
.628
.618
.612
.607
.603
.602
.599
.597
.594
.592
.10
.12
.15
.20
.40
.596
.598
.599
.598
.598
.597
.596
.594
.592
.60
.593
.595
.597
.597
.597
.596
.596
.594
.592
.80
1.0
.591
.595
.596
.596
.595
.594
.593
.592
A
.6
1.0
2.
4.
6.
10.
20.
50.(?)
100.(?)
.655
.644
.632
.623
.618
.611
.601
.596
.593
.640
.631
.621
.614
.611
.606
.600
.596
.593
.618
.613
.608
.604
.602
.600
.598
.596
.594
592
.612
.609
.605
.601
.600
.599
.598
.596
.594
.592
.606
.605
.603
.600
.599
.599
.597
.596
.594
.592
.601
.600
.599
.599
.598
.597
.596
.594
.592
.590
.593
.596
.597
.596
.596
.595
.593
.592
HYDflAFLIC FORMUL,JE.-F1,OW OF WATER IN
OPEN AND CLOSED CHANNELS.
Flow of Water in Pipes.— The quantity of water discharged
through a pipe depends on the "head;" that is, the vertical distance be-
tween the level surface of still water in the chamber at the entrance end of
the pipe and the level of the centre of the discharge end of the pipe ;
also upon the length of the pipe, upon the character of its interior surface
as to smoothness, and upon the number and sharpness of the bends: but
it is independent of the position of the pipe, as horizontal, or inclined
upwards or downwards.
The head, instead of being an actual distance between levels, may be
caused by pressure, as by a pump, in which case the head is calculated as a
vertical distance corresponding to the pressure 1 Ib. per sq. in. = 2.309 ft.
head, or 1 ft. head = .433 Ib. per sq. in.
The total head operating to cause flow is divided into three parts: 1. The
velocity -head) which is the height through which a body must fall in vacuo
to acquire the velocity with which the water flows into the pipe = t;2 -+- 2g, in
which v is the velocity in ft. per sec. and 2g = 64.32; 2. the entry-head, that
required to overcome the resistance to entrance to the pipe. With sharp-
edged entrance the entry-head = about 14 the velocity-head; with smooth
rounded entrance the entry-head is inappreciable; 3. the friction-head, due
to the frictional resistance to flow within the pipe.
In ordinary cases of pipes of considerable length the sum of the entry and
velocity heads required scarcely exceeds 1 foot. In the case of long pipes
with low heads the sum of the velocity and entry heads is generally so small
that it may be neglected.
General Formula for Flow of Water in Pipes or Conduits,
Mean velocity in ft. per sec. = c I/mean li3Tdraulic radius X slope
/diameter s
Do. for pipes running full = CA/ —
In which c is a coefficient determined by experiment. (See pages 559-564.)
558
HYDRAULICS.
area of wet cross-section
The mean hydrauhc radrn* = wet peri,neter. •
In pipes running full, or exactly half full, and in semicircular open chan-
nels running full it is equal to % diameter.
The slope = the head (or pressure expressed as a head, in feet)
-v- length of pipe measured in a straight line from end to end.
In open channels the slope is the actual slope of the surface, or its fall per
unit of length, or the sine of the ajngle of the slope with the horizon.
Chezy's Formula: v = c^-Vs : = c^Vs; r = mean hydraulic radius,
s = slope = head -5- length, v = velocity in feet per second, all dimensions
in feet.
Quantity of "Water Discharged. -If Q = discharge in cubic feel
per second and a = area of channel, Q = av — ac \/rs»
a Vr is approximately proportional to the discharge. It is a maximum a«
308°, corresponding to 19/20 of the diameter, and the flow of a conduit 19/20
full is about 5 per cent greater than that of one completely filled.
Table giving Fall in Feet per Mile, the Distance on Slope
corresponding to a Fall of 1 Ft., and also the Values
of s and \'s for Use in the Formula v — c \ W,
s = H-+-L= sine of angle of slope =
tance (L), divided by that distance.
fall of water-surface (H), in any dis
Fall in
Feet
per Mi.
Slope,
1 Foot
in
Sine of
Slope,
s.
i£
Fall in
Feet
per Mi
Slope,
1 Foot
in
Sine of
Slope,
s.
f*.
0.25
21120
.0000473
.006881
17
310.6
.0032197
.056742
.80
17600
.0000568
.007538
18
293.3
.0034091
.058388
.40
13200
.0000758
.008704
19
277.9
.0035985
.059988
.50
10560
.0000947
.009731
20
264
.0037879
.061546
.60
8800
.0001136
.010660
22
240
.0041667
.064549
.702
7520
.0001330
.011532
24
220
.0045455
.067419
.805
6560
.0001524
.012347
26
203.1
.0049242
.070173
.904
5840
.0001712
.013085
28
188.6
.0053030
.072822
1.
5280
.0001894
.013762
30
176
.0056818
.075378
1.25
4224
.0002367
.015386
35.20
150
.0060667
.081650
1.5
3520
.0002841
.016854
40
132
.0075758
.087039
1.75
3017
.0003314
.018205
44
120
.0083333
.091287
2.
2640
.0003788
.019463
48
110
.0090909
.095346
2.25
2347
.0004261
.020641
52.8
100
.010
.1
2.5
2112
.0004735
.021760
60
88
.0113636
.1066
2.75
1920
.0005208
.022822
66
80
.0125
.111803
3.
1760
.0005682
.023837
70.4
75
.0133333
.115470
3.25
1625
.0006154
.024807
80
66
.0151515
123091
3.5
1508
.0006631
.025751
88
60
.0166667
,1291
3.75
1408
.0007102
.026650
96
55
.0181818
.134839
4
1320
.0007576
.027524
105.6
50
.02
.141421
5
1056
.0009470
.030773
120
44
.0227273
,150756
6
880
.0011364
.C3371
132
40
.025
.158114
7
754.3
.0013257
.036416
160
33
.0303030
J 74077
8
660
.0015152
.038925
220
24
.0416667
,204124
9
586.6
.0017044
.041286
264
20
.05
.223607
10
528
.0018939
.043519
330
16
.06:25
.25
11
443.6
.0020833
.045643
440
12
.0833333
.288675
12
440
.0022727
.047673
528
10
.1
,316228
13
406.1
.0024621
.04962
660
8
.125
.353553
14
377.1
.0026515
.051493
880
6
.1666667
.408248
15
352
.0028409
.0533
1056
5
.2
.447214
16
330
.0030303
.055048
1320
4
.25
.5
HYDRAULIC FORMULAE.
559
Values of \/r for Circular Pipes, Sewers, and Conduits ot
different Diameters.
r = mean hydraulic depth =
ning full or exactly half full.
perimeter
- = 14 diam. for circular pipes run-
Diam.,
ft. in.
v?
in Feet.
Diam.,
ft. in.
in Feet.
Diam.,
ft. in.
in Feet.
Diam.,
ft. in.
in Feet.
•K S/Q
.088
2
.707
4 6
.061
9
1.500
Jl3
.102
2 1
.722
4 7
.070
9 3
1.521
M
.125
2 2
736
4 8
.080
9 6
1.541
1
.144
2 3
.750
4 9
.089
9 9
1.561
i}4
.161
2 4
.764
4 10
.099
10
1.581
^Nj
.177
2 5
.777
4 11
.109
10 3
1.601
1%
•191
2 6
.790
5
.118
10 6
1.620
2
.204
2 7
.804
5 1
.127
10 9
1.639
g^£
.228
2 8
.817
5 2
.137
11
1.658
3
.251
2 9
.829
5 3
.146
11 3
1.677
4
.290
2 10
.842
5 4
.155
11 6
1.696
5
.323
2 11
.854
5 5
.164
11 9
1.714
6
.354
3
.866
5 6
.173
12
1.732
7
.382
3 1
.878
5 7
.181
12 3
1.750
8
.408
3 2
.890
5 8
.190
12 6
1.768
9
.433
3 3
.901
5 9
.199
12 9
1.785
10
.456
3 4
.913
5 10
.208
13
1.803
11
.479
3 5
.924
5 11
.216
13 3
1.820
1
.500
3 6
.935
6
.225
13 6
1.837
1 1
.520
3 7
.946
6 3
.250
14
1.871
1 2
.540
3 8
.957
6 6
.275
14 6
1.904
3
.559
3 9
.968
6 9
: .299
15
1.936
4
.577
3 10
.979
7
.323
15 6
1.968
5
.595
3 11
.990
7 3
.346
16
2.
6
.612
4
1.
7 6
.369
16 6
2.031
7
.629
4 1
1.010
7 9
.392
17
2.061
8
.646
4 2
1.021
8
.414
17 6
2.091
1 9
.661
4 3
1.031
8 3
.436
18
2.121
1 10
.677
4 4
1.041
8 6
.458
19
2.180
1 11
.692
4 5
1.051
8 9
.479
20
2.236
Values of the Coefficient c. (Chiefly condensed from P. J. Flynn
on Flow of Water.) — Almost all the old hydraulic formulae for finding the
mean velocity in open and closed channels have constant coefficients, and are
therefore correct for only a small range of channels. They have often been
found to give incorrect results with disastrous effects. Ganguillet and Kut-
ter thoroughly investigated the American, French, and other experiments,
and they gave as the result of their labors the formula now generally known
as Kutter's formula. There are so many varying conditions affecting the
flow of water, that all hydraulic formulae are only approximations to the
correct result.
When the surface-slope measurement is good, Kutter's formula will give
results seldom exceeding iy%% error, provided the rugosity coefficient of the
formula is known for the site. For small open channels D'Arcy's and
Bazin's formulas, and for cast-iron pipes D'Arcy's formulae, are generally
accepted as being approximately correct.
. flutter's Formula for measures in feet is
00281 \
-
1
1
X Vrs,
in which v ••
mean velocity in feet per second ; r = - =
hydraulic mean
560 HYDRAULICS.
depth in feet = area of cross-section in square feet divided by wetted perim-
eter in lineal feet ; s = fall of water-surface (h) in any distance (I) divided
by that distance, = -, = sine of slope ; n = the coefficient of rugosity, de-
pending on the nature of the lining or surface of the channel. If we let the
first term of the right-hand_side of the equation equal c, we have Chezy's
formula, v = c \/rs — c X 1/V X Vs.
Values of n in Kutter's Formula.— The accuracy of Kutter's for-
mula depends, in a great measure, on the proper selection of the coefficient
of roughness n. Experience is required in order to give the right value to
this coefficient, and to this end great assistance can be obtained, in making
this selection, by consulting and comparing the results obtained from ex-
periments on the flow of water already made in different channels.
In some cases it would be well to provide for the contingency of future
deterioration of channel, by selecting a high value of n, as, for instance,
where a dense growth of weeds is likely to occur in small channels, and also
where channels are likely not to be kept in a state of good repair.
The foliowing table, giving the value of n for different materials, is com-
piled from Kutter, Jackson, and Hering, and this value of n applies also in
each instance, to the surfaces of other materials equally rough.
VALUE OP n IN KUTTER'S FORMULA FOB DIFFERENT CHANNELS.
n = .009, well-planed timber, in perfect order and alignment ; otherwise,
perhaps .01 would be suitable.
n = .010, plaster in pure cement ; planed timber ; glazed, coated, or en-
amelled stoneware and iron pipes ; glazed surfaces of every sort in perfect
order.
n = .011, plaster in cement with one third sand, in good condition ; also for
iron, cement, and terra cotta pipes, well joined, and in best order.
n = .012, unplaned timber, when perfectly continuous on the inside ;
flumes.
n = .013, ashlar and well-laid brickwork ; ordinary metal ; earthen and
stoneware pipe in good condition, but not new ; cement and terra-cotta pipe
not well jointed nor in perfect order , plaster and planed wood in imperfect
or inferior condition ; and, generally, the materials mentioned with n = .010,
when in imperfect or inferior condition.
n — .015, second class or rough-faced brickwork ; well-dressed stonework ;
foul and slightly tuberculated iron ; cement and terra-cotta pipes, with im-
perfect joints and in bad order ; and canvas lining on wooden frames.
n = .017, brickwork, ashlar, and stoneware in an inferior condition ; tu^
berculated iron pipes ; rubble in cement or plaster in good order ; fine gravelv
well rammed, % to % inch diameter ; and, generally, the materials men-
tioned with n = .013 when in bad order and condition.
n = .020, rubble in cement in an inferior condition ; coarse rubble, rough
sel in a normal condition ; coarse rubble set dry ; ruined brickwork and
masonry ; coarse gravel well rammed, from 1 to \y% inch diameter ; canals
with beds and banks of very firm, regular gravel, carefully trimmed and
rammed in defective places ; rough rubble with bed partially covered with
silt and mud ; rectangular wooden troughs, with battens on the inside two
inches apart ; trimmed earth in perfect order.
n = .0225, canals in earth above the average in order and regimen.
n = .055, canals and rivers in earth of tolerably uniform cross-section ;
slope and direction^ in moderately good order and regimen, and free from
stones and weeds.
n = .0^75, canals and rivers in earth below the average in order and regi-
men.
?i = .030, canals and rivers in earth in rather bad order and regimen, hav-
ing stones and weeds occasionally, and obstructed by detritus.
n = .035, suitable for rivers and canals with earthen beds in bad order and
regimen, and having stones and weeds in great quantities.
n — ,05, torrents encumbered with detritus.
Kutter's formula has the advantage of being easily adapted to a change
in the surface of the pipe exposed to the flow of water, by a change in the
value of 71. For cast-iron pipes it is usual to use n = .013 to provide for the
future deterioration of the surface. _ _
Reducing Kutter 'a formula to the form v = c X Vr X Vs, and taking n, the
coefficient of roughness in the formula = .011, .012, and .013, and s = .001, we
have the following values of the coefficient c for different diameters of
conduit.
HYDRAULIC FORMULAE.
561
Values or* e in Formula v = c x Vr X VHt'or Metal Pipes and
Moderately Smooth Conduits Generally,
By KUTTER'S FORMULA (s = .001 or greater.)
Diameter.
n= .011
n = .012
71 = .013
Diameter.
n = .011
n = .012
n = .013
ft. in.
0 1
c =
47 1
c =
c =
ft.
7
c =
152 7
c —
139 2
c —
127 9
2
61.5
8
155 4
141 9
130 4
4
77 4
9
157 7
144 1
132 7
6
1
1 6
2
3
4
5
6
87.4
105.7
116.1
123.6
133.6
140.4
145.4
149.4
77.5
94.6
104.3
111.3
120.8
127.4
132.3
136.1
69.5
85.3
94.4
101.1
110.1
116.5
121.1
124.8
10
11
12
14
16
18
20
159.7
161.5
163
165.8
168
169.9
171.6
146
147.8
149.3
152
154.2
156.1
157.7
134.5
136.2
137.7
140.4
142.1
144.4
146
For circular pipes the hj7draulic mean depth r equals *4 °f the diameter.
According to Kutter's formula the value of c, the coefficient of discharge,
is the same for all slopes greater than 1 in 1000; that is, within these limits
c is constant. We further find that up to a slope of 1 in 2640 the value of c
is, for all practical purposes, constant, and even up to a slope of 1 in 5000
the difference in the value of c is very little. This is exemplified in the
following :
Value of c for Different Values of V^and s in Kutter's
Formula, with n — .013.
v = c V~r X Vs~.
Slopes.
Vr
1 in 1000
1 in 2500
1 in 3333.3
1 in 5000
1 in 10,000
.6
1
2
93.6
116.5
142.6
91.5
115.2
142.8
90.4
114.4
143.0
88.4
113.2
143.1
83.3
109.7
143.8
The reliability of the values of the coefficient of Kutter's formula for
pipes of less than 6 in. diameter is considered doubtful. (See note under
table on page 564.)
Values of c for Earthen Channels, by Kutter's Formula,
for Use in Formula v = c \/rs.
Coefficient of Roughness,
Coefficient of Roughness,
n = .0225.
n — .035.
Vr in feet.
Vr in feet.
0.4
1.0
1.8
2.5
4.0
0.4
1.0
1.8
2.5
4.0
Slope, 1 in
c
c
c
c
c
c
c
c
c
c
1000
35.7
62.5
80.3
89.2
99.9
19.7
37.6
51.6
59.3
69.2
1250
35.5
62.3
80.3
89.3
100.2
19.6
37.6
51.6
59.4
69.4
1667
35.2
62.1
80.3
89.5
100 6
19.4
37.4
51.6
59.5
6D.8
2500
34.6
61.7
80.3
89.8
101.4
19.1
37.1
51.6
59.7
70.4
3333
34.
61.2
80.3
90.1
102.2
18.8
36.9
51.6
59.9
71.0
5000
33.
60.5
80.3
90. r
103.7
18.3
36.4
51.6
60.4
72 2
7500
31.6
59.4
80.3
91.5
106.0
17.6
35.8
51.6
60.9
73.9
10000
30.5
58.5
80.3
92.3
107.9
17.1
35.3
51.6
60.5
75.4
15840
28.5
56.7
80.2
93.9
112.2
16.2
34.3
51.6
62.5
78.6
20000
27.4
55.7
80.2
94.8
115.0
15.6
33.8
51.5
63.1
80.6
562
HYDKAULICS.
Mr. Molesworth, in the 22d edition of his " Pocket-book of Engineering
Formulae," gives a modification of Kutter's formula as follows : For flow in
cast-iron pipes, v = c |/rs, in which
in which d = diameter of the pipe in feet.
(This formula was given incorrectly in Molesworth's 21st edition.)
Molesworth's Formula.— v = Vfcrs, in which the values of k are
as follows :
Values of k for Velocities.
nature or unannei.
Less than
4 ft. per sec.
More than
4 ft. per sec.
8800
8500
Earth .
7200
6800
Shingle
6400
5900
Rough, with bowlders
5300
4700
In very large channels, rivers, etc., the description of the channel affects
the result so slightly that it may be practically neglected, and k assumed =
from 8500 to 9000.
Fly mi's Formula.— Mr. Flynn obtains the following expression of
the value of Kutter's coefficient for a slope of .001 and a value of n = .013 :
c = .
183.72
.013
The following table shows the close agreement of the values of c obtained
from Kutter's, Molesworth's, and Flyun's formulae :
Diameter.
6 inches
6 inches
4 feet
4 feet
8 feet
8 feet
Slope.
lin 40
1 in 1000
1 in 400
1 in 1000
1 in 700
1 in 2600
Kutter.
71.50
69.50
117.
116.5
130.5
129.8
Molesworth.
71.48
69.79
317.
116.55
130.68
129.93
Flynn.
69.5
69.5
116.5
116.5
130.5
130.5
Mr. Flynn gives another simplified form of Kutter's formula for use with
different values of n as follows :
In the following table the value of Kia given for the several values of n :
n
K
n
K
n
K
n
K
n
K
.009
.010
245.63
225.51
.012
.013
195.33
183.72
.015
.016
165.14
157.6
.018
.019
145.03
139.73
.021
.022
130.65
126.73
.011
209.05
.014
137.77
.017
150.94
.020
134.96
.0225
124.9
If in the application of Mr. Flynn's formula given above within the limits
of n as given in the table, we substitute for n, K. and i/r their values wo
have a simplified form of Kutter's formula.
HYDRAULIC FORMULA. 563
For instance, when n = .011, and d = 3 feet, we have
t. - 209.05 v A/~
Bazin's Formulae :
For very even surfaces, fine plastered sides and bed, planed planks, etc.,
v = A/1 -*• .0000045(i0.16 -f *
X Vrs.
For even surfaces such as cut-stone, brickwork, unplaned planking, mortar,
etc. :
v = A/1 -4- .000013(4.354 + 1) x Vrs>
For slightly uneven surfaces, such as rubble masonry :
v = |/1 -*- .00006(l.219 + 1) X Vrs.
For uneven surfaces, such as earth :
v= A/ 1-*- .00035(0.2438 + -) X VTS-
A modification of Bazin's formula, known as D'Arcy's Bazin's :
1000s
.08534r -f 0.35'
For small channels of less than 20 feet bed Bazin's formula for earthen
channels in good order gives very fair results, but Kutter's formula is super-
seding it in almost all countries where its accuracy has been investigated.
The last table on p. 561 shows the value of c, in Kutter's formula, for a wide
range of channels in earth, that will cover anything likely to occur in the
ordinary practice of an engineer.
D> Arcy's Formula for clean iron pipes under pressure is
.00007726 + -°°716^
Flynn's modification of D'Arcy's formula is
in which d — diameter in feet.
D'Arcy's formula, as given by J. B. Francis, C.E., for old cast-iron pipe
lined with deposit and under pressure, is
_ f _ l44^2? ^
" \.0082(12d -f 1 /
Flynn's modification of D'Arcy's formula for old cast-iron pipe is
v-
564
HYDRAULICS.
For Pipes Less than 5 indies in Diameter , coefficients (c)
in the formula v = c 1/rs, from the formula of D'Arcy, Kutter, and Fanning.
Diam.
in
inches.
D'Arcy,
for Clean
Pipes.
Kutter,
for
n = .011
s = .001
Fanning,
for Clean
Iron
Pipes
Diam.
in
inches
D'Arcy,
for Clean
Pipes.
Kutter,
for
71 = .011
s = .001
Fanning,
for Clean
Iron
Pipes.
%
59.4
32.
1%
90.7
58.8
92.5
^
65.7
36.1
2
92.9
61.5
94.8
&£
74.5
42.6
2J4
96.1
66.
1
80.4
47.4
80.4
3
98.5
70.1
96.6
1/4
84.8
51.9
4
101.7
77.4
103.4
1Ka
88.1
55.4
88.
5
103.8
82.9
Mr. Flynn, in giving the above table, says that the facts show that the co-
efficients diminish from a diameter of 5 inches to smaller diameters, and it
is a safer plan to adopt coefficients varying with the diameter than a con-
stant coefficient. No opinion is advanced as to what coefficients should be
used with Kutter's formula for small diameters. The facts are simply
stated, giving the results of well-known authors.
Oider Formulae.— The following are a few of the many formulae for
flow of water in pipes given by earlier writers. As they have constant coef*
ficients, they are not considered as reliable as the newer formulae.
Prony, v = 97 Vrs - .08;
Eytelwein, v = 50
Hawksley, v = 48
; Neville, v = 140 Vrs - 11 \frs.
In these formulae d = diameter in feet; h = head of water in feet; I =
length of pipe in feet; s = sine of slope = y ; r = mean hydraulic depth,
= area -*- wet perimeter = — for circular pipe.
Mr. Santo Crimp (Eng'g, August 4, 1893) states that observations on flow
in brick sewers show that the actual discharge is 33$ greater than that cal-
culated by Eytelwein's formula. He thinks Kutter's formula not superior
to D'Arcy's for brick sewers, the usual coefficient of roughness in the
former, viz., .013, being too low for large sewers and far too small in the case
of small sewers.
D'Arcy's formula for brickwork is
v=
~
~rs; m = a(l-f— ); a =.0037285; B = .229663.
VELOCITY OF WATER IN OPEN CHANNELS.
Irrigation Canals.— The minimum mean velocity required to prevent
the deposit of silt or the growth of aquatic plants is in Northern India
taken at 1*4 feet per second. It is stated that in America a higher velocity
is required for this purpose, and it varies from 2 to 3^ feet per second. The
maximum allowable velocity will vary with the nature of the soil of the
bed. A sandy bed will be disturbed if the velocity exceeds 3 feet per
second. Good loam with not too much sand will bear a velocity of 4 feet
per second. The Cavour Canal in Italy, over a gravel bed, has a velocity of
about 5 per second. (Flynn 's " Irrigation Canals.1')
Mean Surface and Bottom Velocities.— According to the for-
mula of Bazin,
c - 25.4 1/fs; v = vb + 10.87 Vrsl
v =
VELOCITY OF WATER IK OPEN CHANNELS. 565
/. vb - v - 10.87 Virs, in which v = mean velocity in feet per second,
vmax — maximum surface velocity in feet per second, vb = bottom velocity
in feet per second, r — hydraulic mean depth in feet = area of cross-section
in square feet divided by wetted perimeter in feet, s = sine of slope.
The least velocity, or that of the particles in contact with the bed, is
almost as much less than the mean velocity as the greatest velocity is
greater than the mean.
Rankine states that in ordinary cases the velocities may be taken as bear-
ing to each other nearly the proportions of 3, 4, and 5. In very slow cur-
rents they are nearly as 2, 3, and 4.
Safe Bottom and Mean Velocities.— Ganguillet & Kutter give
the following table of safe bottom and mean velocity in channels, calculated
from the formula v — vb -\- 10.87 \/rs'.
Material of Channel.
Safe Bottom Veloc
ity vb, in feet
per second.
Mean Velocity v,
in feet per
second.
0.249
0.328
Soft loam
0.499
0.656
Sand
1 000
1.312
1.998
2.625
Pebbles
2.999
3 938
4 003
5.579
Conglomerate soft slate
4.988
6 564
6.006
8.204
Hard rock
10.009
13.127
Ganguillet & Kutter state that they are unable for want of observations
to judge how far these figures are trustworthy. They consider them to be
rather disproportionately small than too large, and therefore recommend
them more confidently.
Water flowing at a high velocity and carrying large quanties of silt is very
destructive to channels, even when constructed of the best masonry.
Resistance of Soils to Erosion by Water.— W. A. Burr, Eng'g
News, Feb. 8, 1894, gives a diagram showing the resistance of various soils to
erosion by flowing water.
Experiments show that a velocity greater than 1.1 feet per second will
erode sand, while pure clay will stand a velocity of 7.35 feet per second.
The greater the proportion of clay carried by any soil, the higher the per-
missible velocity. Mr. Burr states that experiments have shown that the line
describing the power of soils to resist erosion is parabolic. From his dia-
gram the following figures are selected representing different classes of
soils:
Pure sand resists erosion by flow of 1.1 feet per second.
Sandy soil, 15$ clay 1.2
Sandy loam, 40% clay 1.8
Loamy soil, 65$ clay 3.0
Clay loam, 85$ clay 4.8
Agricultural clay, 95$ clay. . . . . 6.2
Clay 7.35
Abrading and Transporting Power of Water.— Prof. J.
LeConte, in his ''Elements of Geology," states :
The erosive power of water, or its power of overcoming cohesion, varies as
the square of the velocity of the current.
The transporting power of a current varies as the sixth power of the ve-
locity. * * * If the velocity therefore be increased ten times, the transport-
ing power is increased 1,000,000 times. A current running three feet per
second, or about two miles per hour, will bear fragments of stone of the
size of a hen's egg, or about three ounces weight. A current of ten miles an
hour will bear fragments of one and a half tons, and a torrent of twenty
miles an hour will carry fragments of 100 tons.
The transporting power of water must not be confounded with its erosive
power. The resistance to be overcome in the one case is weight, in the
other, cohesion ; the latter varies as the square : the former as the sixth
power of the velocity.
In many cases of removal of slightly cohering material, the resistance is a
566 HYDBAULICS.
mixture of these two resistances, and the power of removing material will
vary at some rate between v2 and v6.
Baldwin Latham has found that in order to prevent deposits of sewage silt
in small sewers or drains, such as those from 6 inches to 9 inches diameter,
a mean velocity of not less than 3 feet per second should be produced.
Sewers from 12 to 24 inches diameter should have a velocity of not less than
2*4 feet per second, and in sewers of larger dimensions in no case should the
velocity be less than 2 feet per second.
The specific gravity of the materials has a marked effect upon the mean
velocities necessary to move them. T. E. Blackwell found that coal of a
sp. gr. of 1.26 was moved by a current of from 1.25 to 1.50 ft. per second,
while stones of a sp. gr. of 2.32 to 3.00 required a velocity of 2.5 to 2.75 ft. per
second.
Chailly gives the following formula for finding the velocity required to
move rounded stones or shingle :
in which v = velocity of water in feet per second, a = average diameter in
feet of the body to be moved, g = its specific gravity.
Geo. Y. Wisner, Eng^g News, Jan 10, 1895, doubts the general accuracy of
statements made by many authorities concerning the rate of flow of a cur-
rent and the size of particles which different velocities will move. He says:
The scouring action of any river, for any given rate of current, must be an
inverse function of the depth. The fact that some engineer has found that
a given velocity of current on some stream of unknown depth will move
sand or gravel has no bearing whatever on what may be expected of cur-
rents of the same velocity in streams of greater depths. In channels 3 to 5
ft. deep a mean velocity of 3 to 5 ft. per second may produce rapid scouring,
while in depths of 18 ft. and upwards current velocities of 6 to 8 ft. per
second often have no effect whatever on the channel bed.
Grade of Sewers.— The following empirical formula is given in Bau-
meister's " Cleaning and Sewerage of Cities," for the minimum grade for a
sewer of clear diameter equal to d inches, and either circular or oval in
section :
Minimum grade, in per cent, = .
As the lowest limit of grades which can be flushed, 0.1 to 0.2 per cent may
be assumed for sewers which are sometimes dry, while 0.3 per cent is allow-
able for the trunk sewers in large cities. The sewers should run dry as
rarely as possible.
Relation of Diameter of Pipe to Quantity Discharged.—
In many cases which arise in practice the information sought is the diame-
ter necessary to supply a given quantity of water under a given head. The
diameter is commonly taken to vary as the two-fifth power of the dis-
charge. This is almost certainly too large. Hagen's formula, with Prof.
Un win's coefficients, give d = cj-——] , where c = .239 when d and Q
are in feet and cubic feet per second.
Mr. Thrupp has proposed a formula which makes d vary as the .383 power
of the discharge, and the formula of M. Vallot, a French engineer, makes d
vary as the .375 power of the discharge. (Engineering.)
FLOW OF WATER-EXPERIMENTS AND TABLES*
The Flow of Water through New Cast-iron Pipe was
measured by S. Bent Russell, of the St. Louis, Mo., Water-works. The
pipe was 12 inches in diameter, 1031 feet long, and laid on a uniform
grade from end to end. Under an average total head of 3.36 feet the flow
was 43,200 cubic feet in seven hours; under an average head of 3.37 feet the
flow was the same; under an average total head of 3.41 feet the flow was
46,700 cubic feet in 8 hours and 35 minutes. Making allowance for loss
of head due to entrance and to curves, it was found that the value of c in
the formula v— c |/rs was from 88 to 93. (Eng'g Record, Apr»l 14, 1894.
Flow of Water in a 20-ineh Pipe 75,OOO Feet Long.— A
comparison of experimental data with calculations by different formulae is
FLOW OF WATER — EXPERIMENTS AND TABLES. 567
given by Chas. B. Brush, Trans. A. S. C. E., 1888. The pipe experimented
with was that supplying the city of Hoboken, N. J.
RESULTS OBTAINED BY THE HACKENSACK WATER COMPANY, PROM 1888-1887.
IN PUMPING THROUGH A 20-iN. CAST- IRON MAIN 75,000 FEET LONG.
Pressure in Ibs. per sq. in. at pumping-station;
95 100 105 110 115
Total effective head in feet j
55 66 77
69
100
130
119
128
130
189
Discharge in U. S. gallons in 24 hours, 1 = 1000 1
2,848 3,165 3,354 3,566 8,804 8,904 4,110 4,255
Actual velocity in main in feet per second :
2.00 2.24 2.36 2.52 2.68 2.78 2.92 3.00
Cost of coal consumed in delivering each million gals, at given velocities,
$8.40 $8.15 $8.00 $8.10 $8.30 $8.60 $9.00 $9.60
Theoretical discharge by D'Arcy's formula :
2,743 3,004 3,244 8,488 3,699 8,915 4,102 4,297
Velocities in Smooth Cast-iron Water-pipes from 1 Foot
to 9 Feet in Diameter, on Hydraulic Grades of O.5
Foot to 8 Feet^ per Mile ; witn Corresponding Values
of c in F= c yrs. (D. M. Greene, in Eng'g News, Feb. 24, 1894.)
ol
ijd
Hydraulic Grade; Feet per Mile = ft.
S *"*
5 ®
Ii^
7i-05
1.0
1.5
2.0
3.0
4.0
D.
r.
s = 0.0000947
0.0001894
0.0002841
0.0003788
0.000568S
0.0007576
,
V~ 0.4542
0.6673
0,8356
0.9803
1.2277
1.4402
1.
0.25<
c= 92.7
97.0
99.1
100.7
103.0
104.7
j
V= 0.7359
1.0793
1.3516
1.5856
1.9857
2.3294
2.
0.5 ]
c= 106.6
110.9
113.4
115.2
117.9
119.7
n r-R i
V= 0.9733
1.4298
1.7906
2.1017
2.6306
3.0860
3.
0.75]
c= 115.5
119.9
122.6
124.4
127.5
129.5
F= 1.1883
1.7456
2.1861
2.5645
3.2116
3.7676
4.
1 n
1.0 j
c= 122.1
126.8
129 c 7
131.8
134.7
136.9
V- 1.3872
2.0379
2.5521
2.9939
3.7493
4.3983
5.
1.25-j
c ^ 127.5
132.4
135.5
137.6
140.7
142.9
(
V= 1.5742
2.3126
2.8961
3.3975
4.2548
4.9913
6.
1.5 -j
c= 132.1
137.8
140.3
142.6
145.8
148.1
V.
1.75J
V= 1.7518
c= 135.9
2.5736
141.4
3.2230
146.0
3.7809
146.8
4.7350
150.2
5.5546
152.5
t
V= 1,9218
2.8234
3.5358
4.1479
5.1945
6 0936
8.
2.0 •<
c= 139.7
145 1
148.4
150.7
154.1
156.5
[
F= 2.0854
3.0638
3.8368
4.5010
5.6368
6.6125
9.
2.25-j
c = 142.9
148.4
151.7
154.2
157 6
160.1
The velocities in this table have been calculated by Mr. Greene's modifi-
cation of the Chezy formula, which modification is found to give results
which differ by from 1.29 to - 2.65 per cent (average 0.9 per cent) from very
carefully measured flows in pipes from 16 to 48 inches in diameter, on grades
from 1.68 feet to 10.296 feet per mile, and in which the velocities ranged
from 1.577 to 6.195 feet per second. The only assumption made is that the
modified formula for V gives correct results in conduits from 4 feet to 9
feet in diameter, as it is known to do in conduits less than 4 feet in diameter.
Other articles on Flow of Water in long tubes are to be found in Eng'g
News as follows : G. B. Pearsons, Sept. 23, 18,6; E. Sherman Gould, Feb. 16,
23 March 9 16 and 23, 1889; J. L. Fitzgerald, Sept. 6 and 13, 1890; Jas. Duaue,
Jan. 2, 1892; J. T. Fanning, July 14, 1892; A. N. Talbot, Aug. 11, 189&
568
HYDRAULICS.
Plow of Water In Circular Pipes, Sewers, etc.. Flowing;
Full. Based on K fitter's Formula, with n - .013.
Discharge in cubic feet per second.
Diam-
eter.
5 in.
6 "
7 "
§"
9 "
Slope, or Head Divided by Length of Pipe.
Iin40
Iin70
1 in 100
1 in 200
1 in 300
1 in 400
1 in 500
1 in 600
.456
.762
1.17
1.70
2.37
.344
.576
.889
1.29
1.79
.288
.482
.744
1.08
1.50
.204
.341
.526
.765
1.06
.166
.278
.430
.624
.868
.144
.241
.372
.54
.75
.137
.230
.355
.516
.717
.118
.197
.304
.441
.613
Slope ....
10 in.
11 "
12 '*
13 "
14 "
1 in 60
£.89
3.39
4.32
5.38
6.60
1 in 80
2.24
2.94
3.74
4.66
5.72
1 in 100
2.01
2.63
3.35
4.16
5.15
1 in 200
1.42
1.86
2.37
2.95
3.62
1 in 300
1.16
1 52
1.93
2.40
2.95
1 in 400
1.00
1.31
1.67
2.08
2.57
1 in 500
.90
1.17
1.5
1.86
2.29
1 in 600
.82
1.07
1.37
1.70
2.09
Slope ....
15 in.
16 "
18 "
20 "
22 "
1 in 100
6.18
7.38
10.21
13.65
17.71
1 in 200
437
5.22
7.22
9.65
12.52
1 in 400
11.23
13.96
17.07
20.56
24.54
1 in 300
3.57
4.26
5.89
7.88
10.22
1 in 600
9.17
11.39
13 94
16.79
20.04
1 in 400
3.09
3.69
5.10
6.82
8.85
1 in 500
2.77
3.30
4.56
6.10
7.92
1 in 600
2.52
3.01
4.17
5.57
7.23
1 in 700
2.34
2.79
3.86
5.16
6.09
1 in 1500
5 80
7.20
8.82
10.62
12.67
1 in 800
2.19
2.61
3.61
4.83
6.26
1 in 1800
5.29
6.68
8.05
9. 08
11.57
Slope ....
2ft.
2 ft. 2 in.
2 u 4 "
2 " 6 "
2 " 8 "
1 in 200
15.88
19.73
24.15
29.08
34.71
1 in 800
7.94
9.87
12.07
14.54
II. 35
1 in 1000
7.10
8.82
10.80
13.00
15.52
1 in 1250
6.35
7.89
9 66
11.63
13.88
Slope ....
2ft. 10 in.
3 "
3 " 2 in.
3 " 4 "
3 " 6 "
1 in 500
25.84
30.14
34.90
40.08
45.66
1 in 500
51.74
58.36
65.47
89.75
118.9
1 in 750
21.10
24.61
28.50
82.72
37.28
1 in 1000
18.27
21.31
24.68
28.34
32.28
1 in 1250
16.34
19.06
22.07
25.35
28.87
1 in 1500
14.92
17.40
20.15
23.14
26.36
1 in 1750
13.81
16.11
18.66
21.42
24.40
1 in 2000
12.92
15.07
17.45
20.04
22.83
1 In 2500
11.55
13.48
15.61
17.93
20.41
Slope
3ft. Sin.
3 " 10 "
4 <>
4 " 6 in.
5 "
1 in 750
42.52
47.65
53.46
73.28
97.09
1 in 1000
36.59
41.27
46.30
63.47
84.08
1 in 1250
32.72
36 91
41.41
56.76
75.21
1 in 1500
29.87
33.69
37.80
51.82
68.65
1 in 1750
27.66
31.20
34.50
47.97
63.56
1 in 2000
25.87
29.18
32.74
44.88
59.46
1 in 2500
23.14
26.10
29.28
40.14
53.18
Slope ....
5 ft. 6 in.
6 t4
6 " 6 •»
7 u
7 " 6 "
1 in 750
125.2
157.8
195.0
237.7
285.3
1 in 1000
108.4
136.7
168.8
205.9
247.1
1 in 1500
88.54
111 6
137.9
168.1
201.7
1 in 2000
76.67
96.66
119.4
145.6
174.7
1 in 2500
68.58
86.45
106.8
130.2
156.3
1 in 3000
62.60
78.92
97.49
118.8
142.6
1 in 3500
57.96
73.07
90.26
110.00
132.1
1 in 4000
54.21
68 35
84.43
102.9
123.5
Slope ....
8ft.
8 " 6 in.
9 "
9 " 6 "
10 "
1 in 1500
239.4
281.1
327.0
376.9
431.4
1 in 2000
207.3
243.5
283.1
326.4
373.6
1 in 2500
195.4
217.8
253.3
291.9
334.1
1 in 3000
169.3
198.8
231.2
266.5
305.0
1 in 3500
156.7
184.0
214.0
246.7
282.4
1 in 4000
146.6
172.2
200.2
230.8
264.2
1 in 4500
138.2
163.3
188.7
217.6
249.1
1 in 5000
131.1
154.0
179.1
200.4
2S6.3
For U. S. gallons multiply the figures in the table by 7.4805,
For a given diameter the quantity of flow varies as the square root of tho
Bine of the slope. From this principle the flow for other slopes than those
FLOW OF WATER IN CIRCULAR PIPES, ETC. 569
given in the table may be found. Thus, what is the flow for a pipe 8 feet
diameter, slope 1 in 125 ? From the table take Q = 207.3 for slope 1 in 2000.
The given slope 1 in 125 is to 1 in 2000 as 16 to 1, and the square root of this
ratio is 4 to 3. Therefore the flow required is 207.3 X 4 = 829.2 cu. ft.
Circular Pipes, Conduits, etc., Flowing Full.
Values of the factor ac |/r in the formula Q = ac |/r X V& correspond-
ing to different values of the coefficient of roughness, n. (Based on Kutter'a
formula.)
i
S
ft, in.
Value of ac Vr.
n = .010.
71 = .011.
n = .012.
n = .013.
n - .015.
n = .017.
6
6.906
6.0627
5.3800
4.8216
3.9604
3 329
9
21.25
18.742
16.708
15.029
12.421
10.50
1
46.93
41.487
37.149
33.497
27.803
23.60
1 3
86.05
76.347
68.44
61.867
51.600
43.93
1 6
141.2
125.60
112.79
102.14
85.496
-72.99
1 9
214.1
190.79
171.66
155.68
130.58
111.8
2
307.6
274.50
247.33
224.63
188.77
164
2 3
421.9
3:7.07
340.10
309.23
260.47
223.9
2 6
559.6
500.78
452.07
411.27
347.28
299.3
2 9
722.4
647.18
584.90
532.76
451.23
388.8
3
911.8
817.50
739.59
674.09
570.90
493.3
3 3
1128.9
1013.1
917.41
836.69
709.56
613.9
3 6
1374.7
1234.4
1118.6
1021.1
866.91
750.8
3 9
1652.1
1484.2
1345.9
1229.7
1045
906
4
1962.8
1764.3
1600.9
1463.9
1245.3
1080.7
4 6
2682.1
2413.3
2193
2007
1711.4
1487.3
5
3543
3191.8
2903.6
2659
2272.7
1977
5 6
4557.8
4111.9
3742.7
8429
2934.8
2557.2
6
5731.5
5176.3
4713.9
4322
3702.3
3232.5
6 6
7075.2
6394.9
5825.9
5339
4588.3
4010
7
8595.1
7774.3
7087
6510
5591.6
4893
7 6
10296
9318.3
8501.8
7814
6717
5884.2
8
12196
11044
10083
9272
7978.3
6995.3
8 6
14298
12954
11832
10889
9377.9
8226.3
9
16604
15049
13751
12663
10917
9580.7
9 6
19118
17338
15847
14597
12594
11061
10
21858
19834
18134
16709
14426
12678
10 6
24823
22534
20612
18996
16412
14434
11
28020
25444
23285
21464
18555
16333
11 6
31482
28593
26179
24139
20879
18395
12
35156
31937
29254
26981
23352
20584
12 6
39104
35529
32558
30041
26012
22938
13
43307
39358
36077
33301
28859
25451
13 6
47751
43412
39802
3?752
31860
28117
14
52491
47739
43773
40432
35073
30965
14 6
57496
52308
47969
44322
38454
33975
15
62748
57103
52382
48413
42040
37147
16
74191
67557
62008
57343
49823
44073
17
86769
79050
72594
67140
58387
51669
18
100617
91711
84247
77932
67839
60067
19
115769
105570
96991
89759
78201
69301
20
132133
120570
110905
102559 '
89423
79259
Flow of Water in Circular Pipes, Conduits, etc., Flowing
under Pressure.
Based on D'Arcy's formulae for the flow of water through cast-iron pipes.
With comparison of results obtained by Kutter's formula, with n = .013.
(Condensed from Flynn on Water Power.)
Values of a, and also the val ues of_ the factors c |/r and ac tfr for use in
the formuls9 Q = av; v = c 1/r X Vst and Q - ac |/f X Vs*
570
HYDRAULICS.
Q s discharge in cubic feet per second, a = area in square feet, v = veloc-
ity in feet per second, r * mean hydraulic depth, % diam. for pipes running
full, s = sine of slope.
(For values of 4/« see page 558.)
Size of Pipe.
Clean Cast-iron
Pipes.
Value of
Old Cast-iron Pipes
Lined with Deposit.
ac ^r by
d= diam
in
a = area
in
square
For
Velocity,
For Dis-
charge,
Kutter's
Formula
when
For
Velocity,
For
Discharge,
ft. in.
feet.
cy-r.
ac Vr-
n = .013.
cVr.
ac ^r.
~%
.00077
5.251
.00403
3.532
.00272
H
.00136
6.702
.00914
4.507
.00613
%
.00307
9.309
.02855
6.261
.01922
i
.00545
11.61
.06334
7.811
.04257
j^
.00852
13.68
.11659
9.255
.07885
ift
.01227
15.58
.19115
'
10.48,
11.65
J885K.
.19462
2
.*02182
18! 96
!41357
12.75
.27824
2^
.0341
21.94
.74786
14.76
.50321
3
.0491
24.63
1.2089
16.56
.81333
4
.Og73
29.37
2.5630
19.75
1.7246
6
.136
33.54
4.5610
22.56
3.0681
6
.196
37.28
7.3068
4.822
25.07
4.9147
7
.267
40.65
10.852
27.34
7.2995
8
.349
43.75
15.270
29.43
10.271
9
.442
46.73
20.652
15.03
31.42
13.891
10
.545
49.45
26.952
33.26
18.129
11
.660
52.16
34.428
35.09
23.158
785
54.65
42.918
33.50
36.75
28.867
2
1.000
59.34
63.435
39 91
42.668
4
1.396
63.67
88.886
42.83
59.788
6
1.767
67.75
119.72
142 *-4
45.57
80.531
8
2.182
71.71
156.46
48.34
105.25
10
2.640
75.32
198.83
50.658
133.74
2
3.142
78.80
247.57
224.63
52.961
166.41
2 2
3.687
82.15
302.90
55.258
203.74
2 4
4.276
85.39
365.14
57.436
245.60
2 6
4.909
88.39
433.92
411.37
59.455
291.87
2 8
5.585
91.51
511.10
61.55
343.8
2 10
6.305
94.40
595.17
63.49
400.3
3
7.068
97.17
686.76
674.09
€5.35
461.9
3 2
7.875
99.93
786.94
67.21
529.3
3 4
8.726
102.6
895.7
69
602
3 6
9.621
105.1
1011.2
102L1
70.70
680.2
3 8
10.559
107.6
1136.5
72.40
764.5
3 10
11.541
110.2
1271.4
74.10
855.2
4
12.566
112.6
1414.7
1463 9
75.73
951.6
4 3
14.186
116.1
1647.6
78.12
1108.2
4 6
15.904
119.6
1901.9
2007
80.43
1279.2
4 9
17.721
122.8
2176.1
82.20
1456.8
5
19.636
126.1
2476.4
2659
84.83
1665.7
5 3
21.648
129.3
2799.7
86.99
1883.2
5 6
23.758
132.4
3146.3
3429
89.07
2116.2
5 9
25.967
135.4
3516
91.08
2365
6
88.274
138.4
3912.8
4322
93.0^
2681.7
6 6
33.183
144.1
4782.1
5339
96.93
3216.4
7
38.485
149.6
5757.5
6510
I00.6i
3872.5
7 6
44.179
154 9
6841.6
7814
104.1'
4601.9
8
50.266
160
8043
9272
107.61
5409.9
8 6
56.745
165
9364.7
10889
111 I 6299.1
9
63.617
169.8
0804
12663
114.2 7267.3
9 6
70.882
174.5
2370
14597 117.4
8320.6
10
78.540
179.1
4066
16709 120.4
9460.9
FLOW OF WATER IN CIRCULAR PIPES, ETC. 571
Size of Pipe.
Clean Cast-iron
Pipes.
Value of
Old Cast-iron Pipes
Lined with Deposit.
ac Yr by
Kutter's
d— diam.
in
a = area
in
For
Velocity,
For Dis-
charge,
Formula,
when
. For
Velocity,
For
Discharge,
ft. in.
feet.
cVr.
ac Yr»
n as .013
c Yr>
acYr.
10 6
11
86.590
95.033
183.6
187.9
15893
17855
18996
21464.
123.4
126.3
10690
12010
11 6
103.869
192.2
19966
24139
129.3
13429
12
113.098
196.3
22204
26981
132
14935
12 6
122.719
200.4
24598
30041
134.8
16545
13
132.733
204.4
27134
33301
137.5
18252
13 6
143.139
208.3
29818
36732
140.1
20056
14
153.938
212.2
32664
40432
142.7
21971
14 6
165.130
216.0
35660
44322
145.2
23986
15
176.715
219.6
38807
48413
147.7
26103
15 6
188.692
223.3
42125
52753
150.1
28335
16
201.062
226.9
45621
57343
152.6
30686
16 6
213.825
230.4
49273
62132
155
33144
17
226.981
233.9
53082
67140
157.3
35704
17 6
240.529
237.3
57074
72409
159.6
38389
18
254.470
240.7
61249
77932
161.9
41199
19
283.529
247.4
70154
89759
166.4
47186
20
314.159
253.8
79736
102559
170.7
53633
Flow of Water in Circular Pipes from % inch to 12 inches
Diameter.
Based on D'Arey's formula for clean cast-iron pipes. Q = ac Yr YS-
Value of
Dia.
Slope, or Head Divided by Length of Pipe.
ac Yr>
in.
1 in
1 in
1 in
linlO.
1 in 20.
1 in 40.
1 in 60.
1 in 80.
100.
150.
200.
*—
Quan
tity in
cubic
feet p
er sec
ond.
.00403
%
.00127
.00090
.00064
.00052
.00045
.00040
.00033
.00028
.00914
L£
.00289
.00204
.00145
.00118
.00102
.00091
.00075
.00065
.02855
(U
.00903
.00638
.00451
.00369
.00319
.00286
.00233
.00202
.06334
1
.02003
.01416
.01001
.00818
.00708
.00633
.00517
.00448
.11659
1J4 .03687
.02607
.01843
.01505
.01303
.01166
.00952
.00824
.19115
\y>
.06044
.04274
.03022
.02468
.02137
.01912
.01561
.01352
.28936
1%
.09140
.06470
.04575
.03736
.03235
.02894
.02363
.02046
.41357
2
.13077
.09247
.06539
.05339
.04624
.04136
.03377
.02927
.74786
2^
.23647
.16722
.11824
.09655
.08361
.07479
.06106
.05288
1.2089
i2
.38225
.27031
.19113
.15607
.13515
.12089
.09871
.08548
2.5630
4
.81042
.57309
.40521
.33088
.28654
.25630
.20927
.18123
4.5610
5
1.4422
1.0198
.72109
.58882
.50992
.45610
.37241
.32251
7.3068
6
2.3104
1.6338
1.1552
.94331
.81690
.73068
.59660
.51666
10.852
7
3.4314
2.4265
1.7157
1.4110
1.2132
1.0852
.88607
.76734
15.270
8
4.8284
3.4143
2.4141
1.9713
1.7072
1.5270
1.2468
1.0797
20.652
9
6.5302
4.6178
3.2651
2.6662
2.3089
2.0652
1.6862
1.4603
26.952
10
8.5222
6.0265
4.2611
3.4795
3.0132
2.6952
2.2006
1.9058
34.428
11
10.886
7.6981
5.4431
4.4447
3.8491
3.4428
2.8110
2 4344
42.918
12
13.571
9.5965
6.7853
5.5407
4.7982
4.2918
3.5043
3.0347
Value of Y* =
.3162
.2236
.1581
.1291
.1118
.1
.08165
.07071
573
HYDRAULICS.
Slope, or Head Divided by Length of Pipe.
Value of
Dia.
ac Vr.
in.
lin
lin
lin
lin
lin
lin
lin
1 in 250.
300.
350.
400.
450.
500.
550.
600.
.00403
%
.00025
.00023
.00022
.00020
.00019
.00018
.00017
.00016
.00914
.00058
.00053
.00049
.00046
.00043
.00041
.00039
.00037
.02855
3X
.00181
.00165
.00153
.00143
.00134
.00128
.00122
.00117
.06334
1
.00400
.00366
.00339
.00317
.00-298
.00283
.00270
.00259
.11659
1^4
.0073?
.00673
.00623
.00583
.00549
.00521
.00497
.00476
.19115
.01209
.01104
.01022
.00956
.00901
.00855
.00815
.00780
.28936
\VA
.01830
.t)1671
.01547
.01447
.01363
.01294
.01234
.01181
.41357
2
.02615
.02388
.02211
.02068
.01948
.01849
.01763
.01688
. 74786
2^
.04730
.04318
.03997
.03739
.03523
.03344
.03189
.03053
1.2089
3
.07645
.06980
.06462
.06045
.05695
.05406
.05155
.04935
2.5630
4
.16208
.14799
.13699
.12815
.12074
.11461
.10929
.10463
4.5610
5
.28843
.26335
.24379
.22805
.21487
.20397
.19448
.19620
7.3068
6
.46208
.42189
.39055
.36534
.34422
.32676
.31156
.29830
10.852
7
.68628
.62660
.58005
.54260
.51124
.48530
.46273
.44303
15.270
8
.96567
.88158
.81617
.76350
.71936
.68286
.65111
.62340
20.652
9
1.3060
1.1924
1.1038
1.0326
.97292
.92356
.88060
.84310
26.952
10
1.7044
1.5562
1 .4405
1.3476
1.2697
1.2053
1.1492
1.1003
34.428
11
2.1772
1.9878
1.8402
1.7214
1.6219
1.5396
1.4680
1.4055
42.918
12
2.7141
2.4781
2.2940
2.1459
2.0219
1.9193
1.8300
1.7521
Value of Vs =
.06324
.05774
.05345
.05
.04711
.04472
.04264
.04082
For U. S. gals, per sec., multiply the figures in the table by ...... 7.4805
" " " " min., •» " " " . ..... 448.83
" " •* " hour, •' " •* * ...... 26929.8
" " " M 24hij., " *• a 44 ...... 646315<
For any other slope the flow is proportional to the square root of the
slope ; thus, flow in slope of 1 in 100 is double that in slope of 1 in 400.
Flow of Water In Pipes from % Inch to 12 Inches
Diameter for a Uniform Velocity of 1OO Ft. per Min.
Diameter
in
Inches.
Area
in
Square Feet.
Flow in Cubic
Feet per
Minute.
Flow in U. S.
Gallons per
Minute.
Flow in U. S.
Gallons per
Hour.
%
.00077
0.077
.57
34
£2
.00136
0.136
1.02
61
rm
.00307
0.307
2.30
138
1
.00545
0.545
4.08
245
.00852
0.852
6.38
383
.01227
1.227
9.18
551
.01670
1.670
12.^0
750
.02182
2.182
' 16.32
979
2^
.0341
3.41
25.50
1,530
8
.0491
4.91
36.72
2,203
4
.0873
8.73
65.28
3,917
5
.136
13.6
102.00
6,120
6
.196
19.6
146.88
8,813
7
.267
26.7
199.92
11,995
8
.349
34.9
261.12
15,667
9
.443
44.2
330.48
19,829
10
.545
54.5
408.00
24,480
11
.660
66.0
493.68
29,621
12
.785
78.5
587.52
35,251
Given the diameter of a pipe, to find the quantity in gallons it will deliver,
the velocity of flow being 100 ft. per minute. Square the diameter in inches
and multiply by 4.08.
LOSS OF HEAD. 573
If Qf = quantity in gallons per minute and d * diameter in inches, then
Q> - d* x '7854 x 10° x 7'4805 = 4.08d*.
Vr
For any other velocity, F', in feet per minute, Q' = 4.08cP^g = .0408d9F'.
Given diameter of pipe in inches and velocity in feet per second, to find
discharge in cubic feet and in gallons per minute.
Q, = da x '78^4X V X 6° = 0.32725d'v cubic feet per minute.
= .32725 X 7,4805 or 2.448d2v U. S. gallons per minute.
To find the capacity of a pipe or cylinder in gallons, multiply the square
of the diameter in inches by the length in inches and by .0034. Or multiply
the square of the diameter in inches by the length in feet and by .0408.
Q = gal = .0034<W (exact) .0034 X 12 s .0408.
LOSS OF HEAD.
The loss of head due to friction when water, steam, air, or gas of any kind
flows through a straight tube is represented by the formula
h =» /— r^; whence v = A
d 2g
in which I = the length and d = the diameter of the tube, both in feet; v =
velocity in feet per second, and / is a coefficient to be determined by experi-
ment. According to Weisbach, / = .00644, in which case
which is one of the older formulae for flow of water (Downing's). Prof. Un-
win says that the value of / is possibly too small for tubes of small bore,
and he would put/ = .006 to .01 for 4-inch tubes, and/ » .0084 to .012 for 2-
inch tubes. Another formula by Weisbach is
(.0144 +
Rankine gives
.01716\ I t£
From the general equation for velocity of flow of water v s
for round pipes ct/ — A/ -, we have va = c2- - and h = , in which
Y 4 \ I 41 c*d
c is the coefficient c of D'Arcy's, Bazin's, Kutter's, or other formula, as found
by experiment. Since this coefficient varies with the condition o^ the inner
surface of the tube, as well as with the velocity, it is to be expected that
values of the loss of head given by different writers will vary as much as those
of quantity of flow. Two' tables for loss of head per 100 ft. in length in pipes
of different diameters with different velocities are given below. The first
is given by Clark, based on Ellis' and Rowland's experiments; the second is
from the Pelton Water- wneel Co.'s catalogue, based on Cox's formula, see
p. 575, with the divisor 1000 instead of 1200, as it is for riveted steel pipe.
The loss of head as given in these two tables for any given diameter and
velocity differs considerably. Either table should be used with caution and
the results compared with the quantity of flow for the given diameter and
head as given in the tables of flow based on Kutter's and D'Arcy's formulae.
574
HYDRAULICS.
Relative JLo** of Head by Friction for each 100 Feet
Length of clean Cast-iron Pipe.
(Based on Ellis and Howland's experiments.)
Velocity
in Feet
per
Second.
Diameter of Pipes in Inches.
3
4 | 5 | 6 | 7
8
9 | 10 | 12
14
Loss of Head in Feet, per 100 Feet Long.
Feet
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
Feet
of
Head
2
2.5
3
3.5
4.5
5
5.5
6
.97
1.49
1.9
2.6
3.3
.55
.92
1.2
1.6
2.2
.41
.64
.82
1.2
1.7
.32
.50
.72
1.0
1.3
1.6
.27
.43
.61
.T
.9
1.2
.23
.36
.51
.71
.92
1.2
.19
.30
.44
.61
.79
1.01
1.2
.18
.27
.39
.52
.69
.87
1.1
.15
.23
.33
.45
.59
.75
.90
.12
.19
.27
.37
.49
.61
76
.92
15
18
21
24
27
30
33
36
42
48
2
2.5
3
3.5
4
4.5
5
5.5
6
.11
.17
.25
.34
.44
.56
.70
.84
.095
.147
.21
.29
.36
.46
.58
.70
.075
.117
.17
.23
.31
.39
.48
.59
.065
.109
.15
.20
.27
.34
.41
.50
.59
o055
.088
.13
.18
.23
.30
.37
.44
.53
.052
.085
.12
,16
.22
.28
.34
.39
.49
.049
.076
.108
.15
.20
.25
.30
.36
43
.047
.067
.10
.14
.17
.22
.27
.82
.4
.036
-.056
.081
.111
.14
.18
.22
.27
.32
.030
.046
.067
.092
.116
.15
.18
.22
.27
Loss of Head in Pipe by Friction.— Loss of head by friction in
each 100 feet in length of different diameters of pipe when discharging the
following quantities of water per minute (Pelton Water-wheel Co.) :
Inside Diameter of Pipe in Inches.
2
3
2.37
4.89
12.33
17.23
.65
.99
1.32
1.65
1.98
2.31
1.185
2.44
4.10
6.17
8.61
11.45
.2 fl
f
2.62
3.92
5.23
6.54
7.85
9.16
.791
1.62
2.73
4.11
5.74
7.62
Ofl
h
5.
8.83
11.80
14.70
17.70
20.6
.503
1.22
2.05
3.08
4.31
5.72
10.4
15.7
20.9
26.2
31.4
.474
.978
.64
2.46
3.45
4.57
16.3
24.5
32.7
40.9
49.1
57.
2)3
.395
.815
.37
.05
2.87
.81
(Continued on next page.)
Flow of Water in Riveted Steel Pipes.— The laps and rivets
book on " 115 Experiments on the Carrying Capacity of Large Riveted Metal
Conduits," John Wiley & Sons, 1897.
LOSS OF HEAD.
575
Inside Diameter of Pipe in Inches.
7
8
9 j
10
11
12
V
To
8.0
4.0
5.0
6.0
7.0
h
Q
h
Q
h
Q
h
Q
h
Q
h
Q
.338
.698
1.175
1.76
2.46
3.26
32.0
48.1
64.1
80.2
96.2
112.0
.296
.611
1.027
1.54
2.15
2.85
41.9
62.8
83.7
105
125
146
.264
.544
.913
1.37
1.92
2.52
53
79.5
106
132
159
185
.237
.488
.822
1.23
1.71
2.28
65.4
98.2
131
163
196
229
.216
.444
.747
1.122
1.56
2.07
79.2
119
158
198
237
277
.198
.407
.685
1.028
1.43
1.91
94.2
141
188
235
283
:^30
Inside Diameter of Pipe in Inches,
13
14
15
16
18
20
V
h
Q
h
Q
h
Q
h
Q
167
251
335
419
502
586
h
Q
h
Q
262~
393
523
654
785
916
2.0
3.0
4.0
5.0
6.0
7.0
.183
1 .375
.632
.949
1.325
1.75
110
166
221
276
332
387
.169
.349
.587
.881
1.229
I.d3
128
192
256
321
385
449
.158
.325
.548
.822
1.148
1.52
147
221
294
368
442
515
.147
.306
.513
.770
1.076
1,43
.132
.271
.456
.685
.957
1.27
212
318
424
530
636
742
.119
.245
.410
.617
.861
1.143
V
sTo
3.0
4.0
5.0
6.0
7.0
Inside Diameter of Pipe in Inches.
22
24
26
28
30
36
h
Q
h
Q
h
Q
h
Q
h
Q
h
Q
.108
.222
.373
.561
.782
1.040
316
475
633
792
950
1109
.098
.204
.342
,513
.717
.953
377
565
754
942
1131
1319
.091
.188
.315
.474
.662
.879
442
663
885
1106
1327
1548
.084
.174
.293
.440
.615
.817
513
770
1026
1283
1539
1796
.079
.163
.273
.411
.574
.762
589
883
1178
1472
1767
2061
.066
.135
.228
.342
.479
.636
848
1273
1697
2121
2545
2868
EXAMPLE.— Given 200 ft. head and 600 ft. of 11 -inch pipe, carrying 119 cubic
feet of water per minute. To find effective head : In right-hand column,
under 11-inch pipe, find 119 cubic ft.; opposite this will be found the loss by
friction in 100 ft. of length for this amount of water, which is .444. Multiply
this by the number of hundred feet of pipe, which is 6, and we have
2.66 ft., which is the loss of head. Therefore the effective head is 200 - 2.66
EXPLANATION.— The loss of head by friction in pipe depends not only upon
diameter and length, but upon the quantity of water passed through it. Th ^
head or pressure is what would be indicated by a pressure-gauge attached
to the pipe near the wheel. Readings of gauge should be taken while the
water is flowing from the nozzle.
To reduce heads in feet to pressure in pounds multiply by .433. To reduce
pounds pressure to feet multiply by 2.309.
Cox's Formula.— Weisbacb/s formula for loss of head caused by the
friction of water in pipes is as follows :
Faction-head = .
5.367d
where L = length of pipe in feet;
V = velocity of the water in feet per second;
d = diameter of pipe in inches.
William Cox (Amer. Much., Dec. 28, 1893) gives a simpler formula which
gives almost identical results :
B = friction-head in feet = - -- 12QQ ~ • . • ...(!)
Hd _ 4F24-5F-2 (Q
L "' 1300" .......... W
576
HYDRAULICS.
He gives a table by means of which the value of
obtained when F is known, and vice versa.
4F2-f 5F- 2
-.
is at once
VALUES OP
__
1200
V
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
\
.00583
.00695
.00813
.00938
.01070
.01208
.01353
.01505
.01663
.01828
2
.02000
.02178
.02363
.02555
.02753
.02958
.03170
.03388
.03613
.03845
3
.04083
.04328
.04580
.04838
.05103
.05375
.05653
.05938
.06230
.06528
4
.06833
.07145
.07463
.07788
.08120
.08458
.08803
.09155
.09513
.09878
5
.10250
.10628
.11013
.11405
. 11803
.12208
.12620
.13038
.13463
.13895
6
.14333
.14778
15230
.15688
.16153
.16625
.17103| .17588
.18080
. 18578
7
.19083
.19595
.20113
.20638
.21170
.21708
.22253
.22805
.22363
.23928
8
.24500
.25078
.25663
.26255
.26853
.27458
.28070
.28688
.29313
.29945
9
.30583
.31228
.31880
.32538
.33203
.33875
.34553
.35238
.35930
.36628
10
.37333
.38045
.38763
.39488
.40220
.40958
.41703
.42455
.43213
.43978
11
.44750
.45528
.46313
.47105
.47903
.48708
.49520
.50338
.51163
.51995
12
.52833
.53678
.54530
.55388
.56253
.57125
.58003
.58888
.59780
.60678
13
.61583
.62495
.63413
.64338
.65270
.66208
.67153
.68105
.69063
.70028
14
.71000
.71978
.72963
.73955
.74953
.75958
.76970
.77988
.79013
.80045
15
.81083
=82128
.83180
.84238
.85303
.86375
.87453
.88538
.89630
.90728
1G
.91833
.92945
.94063
.95188
.96320
.97458
.98603
.99755
1.00913
1.02078
17
.03250
1.04428
1.0561S
1.06805
1.08003
1.09208
1.10420
1.11638
1.12863
1.14095
18
.15333
1.16578
1.17830
1.19088
1.20353
1.21625
1.22903
1.24188
1.25480
1.26778
19
.28083
1 .29395
1.30713
1.32038
1.33370
1.34708
1.36053
1.37405
1.38763
1.40128
20
.41500
1.42878
1.44263
1.45655
1.47053
1.48458
1.49870
1.51288
1.52713
1.54145
21
.55583
1.57028
1.58480
1.59938
1.61403
1.62875
1.64353
1.65838
1.67330
1.68828
The use of the formula and table is illustrated as follows:
Given a pipe 5 inches diameter and 1000 feet long, with 49 feet head, what
will the discharge be?
If the velocity Fis known in feet per second, the discharge is 0.32725daF
cubic foot per minute.
By equation 2 we have
4F« + 5F-2 Hd 49X5 .
1200 -Tr- looo--0'245'
whence, by table, F = real velocity = 8 feet per second.
The discharge in cubic feet per minute, if F is velocity in feet per second
and d diameter in inches, is 0.32725d2F, whence, discharge
= 0.32725 X 25 X 8 = 65.45 cubic feet per minute.
The velocity due the head, if there were no friction, is 8.025 ^H = 56.175
feet per second, and the discharge at that velocity would be
0.32725 X 25 x 06. 175 = 460 cubic feet per minute.
Suppose it is required to deliver this amount, 460 cubic feet, at a velocity
of 2 feet per second, what diameter of pipe will be required and what will be
the loss of head by friction?
d — diameter
= J
V
F X 0.32725
_ _
2 X 0.32725
26.5 inches.
Having now the diameter, the velocity, and the discharge, the friction-head
is calculated by equation 1 and uce of the table; thus,
100(? X 0.02 = -f- = 0.75 foot,
L 4F2 + 5F-
d ~ 1200
thus leaving 49 — 0.75
- 26.5 A 26.5 ~
say 48 feet effective head applicable to power-pro-
ducing purposes.
Problems of the loss of head may be solved rapidly by means of Cox's
Pipe Computer, a mechanical device on the principle of the slide-rule, for
sale by Keuffel & Esser, New York.
tOSS OF HEAD.
577
Frictional Heads at Given Rates of Discharge in Clean
Cast-iron Pipes for Kadi 1OOO Feet of Length.
(Condensed from Ellis and Howland^s Hydraulic Tables.)
U. S. Gallons t
Discharged
per Minute.
4-inch
Pipe.
6-inch
Pipe.
8-inch
Pipe.
10-inch
Pipe.
12-inch
Pipe.
14-inch
Pipe.
ft
tt
ri-
ll
Si
?*
%$
•8
j«
O c8
1S
c o
55
|8
>*
J
.2 -
I5
c c5
Ss
P
J'ti
-M
fl*
«
£»
o>
||
S o
0>
§*
11
1!
o &
•SJ 0
£*
fl
|«
.07
.14
.28
.43
.57
.71
.85
.99
1.13
1.42
1.70
1.98
2.27
2.55
2.84
3.40
3.97
4.54
5.11
5.67
7.09
8.51
.2 0)
&*
g£
£<s
25
50
100
150
200
250
300
350
400
500
600
700
800
000
1000
1200
1400
1600
1800
2000
2500
3000
4000
.64
1.28
2.55
3.83
5.11
6.37
7.66
8.94
10.21
12.77
15.32
17.87
.59
2.01
7.36
16.05
28.09
43.47
62.20
84.26
109.68
170.53
244.76
332.36
.28
.57
1.13
1.70
2.27
2.84
3.40
3.97
4.54
5.67
6.81
7.94
9.08
10.21
11.35
13.61
15.88
18.15
20.42
22.69
.11
.32
1.08
2.28
3.92
6.00
8.52
11.48
14.89
23.01
32.89
44.54
57.95
73.12
90.05
129.20
175.38
228.62
288.90
356.22
.16
.32
.64
.96
1.28
1.60
1.91
2.23
2.55
3.19
3.83
4,47
5.09
5.74
6.38
7.66
8.94
10.21
11.47
12.77
15.96
.04
.10
.29
.60
1.01
1.52
2.13
2.85
3.68
5.64
8.03
10.83
14.05
17.68
21.74
31.10
42.13
54.84
69.22
85.27
132.70
.10
.20
.41
.61
.82
1.02
1.23
1.43
1.63
2.04
2.45
2.86
3.27
3.68
4.08
4.90
5.72
6.53
7.35
8.17
10.21
12.25
.02
.04
.11
.22
.36
.54
.75
.99
1.27
1.93
2.72
3.66
4.73
5.93
7.28
10.38
14.02
18.22
22.96
28.25
43.87
62.92
.01
.02
.05
.10
.16
.24
.32
.43
.54
.81
1.14
1.52
1.96
2.45
3.00
4.26
5.74
7.44
9.36
11.50
17.82
25.51
.10
.21
.31
.42
.52
.63
.73
.83
1.04
1.25
1.46
1.67
1.88
2.08
2.50
2.91
3.33
3.75
4.17
5.21
6.25
8.34
.01
.03
.05
.08
.12
.16
.21
.27
.40
.55
.73
.94
1.17
1.43
2.02
2.72
3.51
4.41
5.41
8.35
11.93
21.00
U. S. Gallons 1
Discharged
per Minute. 1
16-inch
Pipe.
18-inch
Pipe.
20-inch
Pipe.
24-inch
Pipe.
30-inch
Pipe.
36-inch
Pipe.
c o
£$,
]8
gj
J
£*
U
C3 O
w
18
jM
ii
Ii
E*
P CJ
5^
i&
*j
.If
||
|l
rj r>
»3 JJ
K
fa
gz
A
11
t^
52
is
3*
A
"•3 "2
•p
ft
y
4J
ii
O c3
B«
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
6000
7000
8000
9000
10000
12000
14000
16000
18000
20000
.80
1.60
2.39
3 19
3.99
4.79
5.59
6.38
7.18
7.98
.22
.76
1.63
2.82
4.34
6.19
8.37
10.87
13.70
16.85
.63
1.26
1.89
2.52
3.15
3.78
4.41
5.04
5.67
6.30
7.57
.13
.44
.93
1.60
2 45
3.48
4.70
6.09
7.67
9.43
13.49
.51
1.02
1.53
2.04
2.55
3.06
3.57
4.08
4.59
5.11
6.13
7.15
.08
.27
.56
.96
1.47
2.09
2.81
3.64
4.58
5.62
8.03
10.86
.35
.71
1.06
1.42
1.77
2.13
2.48
2.84
3.19
3.55
4.26
4.96
5.67
6.38
.04
.12
.24
.41
.62
.87
1.16
1.50
1.88
2.31
3.28
4.43
5.75
7.25
.23
.45
.68
.91
1.13
1.36
1.59
1.82
2.04
2.27
2.72
3.18
3.63
4.08
4.54
5.44
6.36
.01
.04
.09
.15
.22
.30
.40
.52
.64
.78
1.11
1.49
.16
.32
.47
.63
.79
.95
1.10
1.26
1.42
1.58
1.89
2.21
2.52
2.84
3.15
3.78
4.41
5.05
5.68
6.30
.01
.0-2
.04
.06
.09
.13
.17
.22
.27
.33
.46
.62
.80
1.00
1.23
1.74
2.35
3.04
3.83
4.71
2.43
2.98
4.25
5.75
578
HYDRAULICS.
Effect of Bends and Curves In Pipes.— Weisbach's rule for
131 + 1.847 * X — X in which r
T.
bends : Loss of head in feet
a= internal radius of pipe in feet, R = radius of curvature of axis of pipe, v
= velocity in feet per second, and a = the central angle, or angle subtended
by the bend.
Hamilton Smith, Jr., in his work on Hydraulics, says: The experimental
data at hand are entirely insufficient to permit a satisfactory analysis of
this quite complicated subject; iu fact, about the only experiments of value
are those made by Bossut and Dubuat with small pipes.
Curves.— If the pipe has easy curves, say with radius not less than 5
diameters of the pipe, the flow will not be materially diminished, provided
the tops of all curves are kept below the hydraulic grade-line and provision
be made for escape of air from the tops of all curves. (Trautwine.)
Hydraulic Grade-line.— In a straight tube of uniform diameter
throughout, running full and discharging freely into the air, the hydraulic
grade-line is a straight line drawn from the discharge end to a point imme-
diately over the entry end of the pipe and at a depth below the surface
equal to the entry and velocity heads. (Trautwine.)
In a pipe leading from a reservoir, no part of its length should be above
the hydraulic grade-line.
Flow of Water in House-service Pipes.
Mr. E. Kuichlmg, C.E., furnished the following table to the Thomson
Meter Co.:
Condition
of
Discharge.
Pressure in Main,
pounds per
square inch.
Discharge, or Quantity capable of being delivered, in
Cubic Feet per Minute, from the Pipe,
under the conditions specified in the first column.
Nominal Diameters of Iron or Lead Service-pipe in
Inches.
H
%
SA
1
m
2
3
4
6
Through 35
feet of
service-
pipe, no
back
pressure.
30
40
50
60
75
100
130
1.10
1.27
1.42
1.56
1.74
2.01
2.29
1.92
2.22
2.48
2.71
3.03
3.50
3.99
1.16
1.34
1.50
1.65
1.84
2.13
2.42
3.01
3.48
3.89
4.26
4.77
5.50
6.28
6.13
7.08
7.92
8.67
9.70
11.20
12.77
16.58
19.14
21.40
23.44
26.21
30.27
34.51
33.34
38.50
43.04
47.15
52.71
60.87
69.40
88.16
101.80
113.82
124.68
139.39
160.96
183.52
173.85
200.75
224.44
245.87
274.89
317.41
361.91
444.63
513.42
574.02
628.81
703.03
811.79
925.58
Through
100 feet of
service-
pipe, no
back
pressure.
30
40
50
60
75
100
130
0.66
0.77
0.86
0.94
1.05
1.22
1.39
1.84
2.12
2.37
2.60
2.91
3.36
3.83
3.78
4.36
4.88
5.34
5.97
6.90
7.86
10.40
12.01
13.43
14.71
16.45
18.99
21.66
21.30
1 24.59
27.50
30.12
33.68
38.89
44.34
58.19
67.19
75.13
82.30
92.01
106.24
121.14
118.13
136.41
152.51
167.06
186.78
215.68
245.91
317.23
366.30
409.54
4^8.63
501.58
579.18
660.36
Through
100 feet of
service-
pipe and
15 feet
vertical
rise.
30
40
50
60
75
100
130
0.55
0.66
0.75
0.83
0.94
1.10
1.26
0.96
1.15
1.31
1.45
1.64
1.92
2.20
1.52
1.81
2.06
2.29
2.59
3.02
3.48
3.11
3 72
4.24
4.70
5.32
6.21
7.14
8.57
10.24
11.67
12.94
14.64
17.10
19.66
17.55
20.95
23.87
26.48
29.96
35.00
40.23
47.90
57.20
65.18
72.28
81.79
95.55
109.82
97.17
116.01
132.20
'146.61
165.90
193.82
222.75
260.56
311.09
354.49
393.13
444.85
519.72
597.31
Through
100 feet of
service-
pipe, and
30 feet
vertical
rise.
30
40
60
60
75
100
130
0.44
0.55
0.65
0.73
0.84
1.00
1.15
0.77
0.97
1.14
1.28
1.47
1.74
2.02
1.22
1.53
1.79
2.02
2.32
2.75
3.19
2.50
3.15
3.69
4.15
4.77
5.65
6.55
6.80
8.68
10.16
11.45
13.15
15.58
18.07
14.11
17.79
20.82
23.47
26.95
31.93
37.02
38.63
48.68
56.98
64.22
73.76
87.38
101.33
78.54211.54
98.98^266.59
115.87 312.08
130.59351.73
149.99 403.98
177.67478.55
206.04554.96
FIRE-STREAMS.
579
In this table it is assumed that the pipe is straight and smooth inside; that
the friction of the main and meter are disregarded; that the inlet from the
main is of ordinary character, sharp, not flaring or rounded, and that the
outlet is the full diameter of pipe. The deliveries given will be increased if,
first, the pipe between the meter and the main is of larger diameter than the
outlet; second, if the main is tapped, say for 1-inch pipe, but is enlarged
from the tap to 1J4 or 1^ inch; or, third, if pipe on the outlet is larger than
that on the inlet side of the meter. The exact details of the conditions given
are rarely met in practice; consequently the quantities of the table may be
expected to be decreased, because the pipe is liable to be throttled at the
joints, additional bends may interpose, or stop-cocks may be used, or the
back-pressure may be increased.
Air-bound Pipes.— A pipe is said to be air-bound when, in conse-
quence of air being entrapped at the hign points of vertical curves in the
line, water will not flow out of the pipe, although the supply is higher than
the outlet. The remedy is to provide cocks or valves at the high points,
through which the air may be discharged. The valve may be made auto-
matic by means of a float.
Vertical Jets. (Moles worth. )—H = head of water, h = height of jet,
d = diameter of jet, K = coefficient, varying with ratio of diameter of jet
to head; then h = KH.
If H = d X 300 600 1000 1500 1800 2800 3500 4500,
K= .96 .9 .85 .8 .7 .6 .5 .25
Water Delivered through Meters. (Thomson Meter Co.).— The
best modern practice limits the velocity in water-pipes to 10 lineal feet per
second. Assume this as a basis of delivery, and we find, for the several sizes
of pipes usually metered, the following approximate results:
Nominal diameter of pipe in inches:
% % % 1 IK 2 3 4 6
Quantity delivered, in cubic feet per minute, due to said velocity:
0.46 1.28 1.85 3.28 7.36 13.1 29.5 52.4 117.9
Prices Charged for Water in Different Cities (National
Meter Co.):
Average minimum price for 1000 gallons in 163 places 9.4 cents.
" maximum " " " " " " " 28 "
Extremes, 2^ cents to 100 "
FIRE-STREAMS.
Discharge from Nozzles at Different Pressures.
(J. T. Fanning, Am. Water-works Ass'n, 1892, Eng'g News, July 14, 1892.)
Nozzle
diam.,
in.
Height
of
stream,
ft.
Pressure
at Play-
pipe,
Ibs.
Horizon-
tal Pro-
jection of
Streams,
ft.
Gallons
per
minute.
Gallons
per 24
hours.
Friction
per 100
ft. Hose,
Ibs.
Friction
per 100
ft. Hose,
Net
Head, ft.
1
70
46.5
59.5
303
292,298
10.75
24.77
1
80
59.0
67.0
230
331,200
13,00
31.10
1
90
79.0
76.6
267
384,500
17.70
40.78
1
100
130.0
88.0
311
447.900
22.50
54.14
]i^
70
44.5
61.3
249
358,520
15.50
35.71
li^
80
55.5
69.5
281
404,700
19.40
44.70
31^
90
72.0
78.5
324
466,600
25.40
58.52
]i£
100
103.0
89.0
376
54l;500
33.80
77.88
1^4
70
43.0
66.0
306
440,613
22.75
52.42
1/4
80
53.5
72.4
343
493.900
28.40
65.43
1J4
90
68.5
81.0
388
558,800
35.90
82.71
m
100
93.0
92.0
460
662,500
57.75
86.98
1%
- 70
41.5
77.0
368
530,149
32.50
74.88
1%
80
51.5
74.4
410
590,500
40.00
92.16
1%
90
65.5
82.6
468
674,000
51.40
118.43
gL
100
88.0
92.0
540
777,700
72.00
165.89
580
HYDRAULICS.
Friction Losses In Hose.— In the above table the volumes of
water discharged per jet were for stated pressures at the play-pipe.
In providing for this pressure due allowance is to be made for friction
losses in each hose, according to the streams of greatest discharge which are
to be used.
The loss of pressure or its equivalent loss of head (h) in the hose may be
found by the formula h =
In this formula, as ordinarily used, for friction per 100 ft. of %in. hose
there are the following constants : 2^ in. diameter of hose d = .20833 ft.;
length of hose I — 100 ft., and 2g = 64.4. The variables are : v = velocity in
feet per second; h = loss of head in feet per 100 ft. of hose; m = a coeffi-
cient found by experiment ; the velocity v is found from the given dis-
charges of the jets through the given diameter of hose.
Head and Pressure Losses by Friction in 100 -ft.
Lengths of Rubber-lined Smooth 2H>-in. Hose.
Discharge
per minute,
Velocity
per second,
Coefficient,
m.
Head Lost,
ft.
Pressure
Lost, Ibs.
Gallons per
24 hours.
gallons.
ft.
per sq. in.
200
13.072
.00450
22.89
9.93
288,000
250
16.388
.00446
35.55
15.43
360,000
300
18.858
.00442
46.80
20.31
432.000
347
21.677
.00439
61.53
26.70
499,680
350
22.873
.00439
68.48
29.73
504,000
400
26.144
.00436
88.83
38.55
576,000
450
29.408
.00434
111.80
48.52
648,000
500
32.675
.00432
137.50
59.67
720,000
520
33.982
.00431
148.40
64.40
748,800
These frictions are for given volumes of flow in the hose and the veloci-
ties respectively due to those volumes, and are independent of size of
nozzle. The changes in nozzle do not affect the friction in the hose if there
is no change in velocity of flow, but a larger nozzle with equal pressure at
the nozzle augments the discharge and velocity of flow, and thus materially
increases the friction loss in the hose.
Loss of Pressure (p) and Head (h) in Rubber-lined
Smooth 234-in. Hose may be found approximately by the formulas
/o2 Z<72
p = . * ,& and h = , in which p = pressure lost by friction, in
pounds per square inch; I = length of hose in feet; q = gallons of water
discharged per minute; d = diam.of the hose in inches, 2^ in.; h = friction-
head in feet. The coefficient of d5 would be decreased for rougher hose.
The loss of pressure and head for a l^j-in. stream with power to reach a
height of 80 ft. is, in each 100 ft. of 2^-in. hose, approximately 20 Ibs., or 45
ft. net, or, say, including friction in the hydrant, ^ ft. loss of head for each
foot of hose.
If we change the nozzles to 1^4 or 1% in. diameter, then for the same 80 ft.
height of stream we increase the friction losses on the hose to approxi-
mately % ft. and 1 ft. head, respectively, for each foot-length of hose.
These computations show the great difficulty of maintaining a high
stream through large nozzles unless the hose is very short, especially for a
gravity or direct-pressure system.
This single 1^-in. stream requires approximately 56 Ibs pressure, equiva-
lent to 129 ft. head, at the play-pipe, and 45 to 50 ft. head for each 100 ft.
length of smooth 2^-in. hose, so that for 100, 200, and 300 ft. of hose we
must have available heads at the hydrant or fire engine of 179, 229, and 279
ft., respectively. If we substitute lJ4-in. nozzles for same height of stream
we must have available heads at the hydrants or engine of 193, 259, and 325
ft., respectively, or we must increase the diameter of a portion at least of
the long hose and save friction-loss of head.
Rated Capacities of Steam Fire-engines, which is perhaps
one third greater than their ordinary rate of work at fires, are substantially
as follows :
3d size, 550 gals, per min., or 792,000 gals, per 24 hours.
2d " 700 " " 1,008.000 " "
1st »' 900 " " 1,296,000 " "
1 ext., 1,100 " " 1.584,000 «* "
THE SIPHON.
581
Pressures required, at Nozzle and at Pnmp,witli Quantity
and Pressure of "Water Necessary to throw Water
Various Distances through Different-sized Nozzles-
using 2!->iiich Rubber Hose and Smooth Nozzles,
(From Experiments of Ellis & Leshure, Farming's " Water Supply.'1)
Size of Nozzles.
1 Inch.
1^ Inch.
Pressure at nozzle Ibs per sq in
40
48
155
109
79
60
73
189
142
108
80
97
219
168
131
100
121
245
186
148
40
54
196
113
81
60
81
240
148
112
80
108
277
175
137
100
135
310
193
157
* Pressure at pump or hydrant with
100 ft 2J^-inch rubber hose
Horizontal distance thrown feet . .
Vertical distance thrown, feet
Size of Nozzles.
\Y± Inch.
1% Inch.
Pressure at nozzle, Ibs. per sq in
40
61
242
118
82
60
92
297
156
115
80
123
342
186
142
100
154
383
207
164
40
71
293
124
85
60
107
358
16(>
118
80
144
413
200
146
100
180
462
224
169
* Pressure at pump or hydrant with
100 feet 2^-inch rubber hose
Gallons per minute
Horizontal distance thrown, feet
iVertical distance thrown, feet
* For greater length of 2^-inch hose the increased friction can be ob-
tained by noting the differences between the above given " pressure at
nozzle1' and "pressure at pump or hydrant with 100 feet of hose." For
instance, if it requires at hydrant or pump eight pounds more pressure
than it does at nozzle to overcome the friction when pumping through 100
feet of 2^-inch hose (using 1-inch nozzle, with 40-pound pressure at said
nozzle) then it requires 16-pounds pressure to overcome the friction in
-forcing through 200 feet of same size hose.
Decrease of Flow due to Increase of Length of Hose.
<J. R. Freeman's Experiments, Trans. A. S. C. E. 1889.)— If the static pres-
sure is 80 Ibs. and the hydrant-pipes of such size that the pressure at the hy-
drant is 70 Ibs., the hose 2% in. nominal diam., and the nozzle 1}^ in. diam.,
the height of effective fire-stream obtainable and the quantity in gallons per
minute will be :
Best Rubber-
Linen Hose. lined Hose.
Height, Gals. Height, Gals,
feet. per min. feet, per min.
73 261 81 282
42 184 61 229
27 146 46 192
With 50ft. of 2^-in. hose..
u 250 ,. u 72u ., ;;
" 500 " " " " ..
With 500 ft. of smoothest and best rubber-lined, hose, if diameter be
exactly 2^ in., effective height of stream will be 39 ft. (177 gals.); if diameter
be J4 in. larger, effective height of stream will be 46 ft. (192 gals.)
THE SIPHON.
The Siphon is a bent tube of unequal branches,"open at both ends, and
is used to convey a liquid from a higher to a lower level, over an intermedi-
ate point higher than either. Its parallel branches being in a vertical plane
and plunged into two bodies of liquid whose upper surfaces are at different
levels, the fluid will stand at the same level both within and without each
branch of the tube when a vent or small opening is made at the bend. If
the air be withdrawn from the siphon through this vent, the water will rise
in the branches by the atmospheric pressure without, and when the two
columns unite and the vent is closed, the liquid will flow from the upper
reservoir as long as the end of the shorter branch of the siphon is below the
surface of the liquid in the reservoir.
If the water was free from air the height of the bend above the supply
level might be as great as 33 feet,
582 HYDRAULICS,
If A = area of cross-section of the tube in square feet, 17=: the difference
in level between the two reservoirs in feet, D the density of the liquid in
pounds per cubic foot, then ADH measures the intensity of the force which
causes the movement of the fluid, and V— \/2gH = 8.02 ^H is the theoretical
velocity, in feet per second, which is reduced by the loss of head for entry
and friction, as in other cases of flow of liquids through pipes. In the case
of the difference of level being greater than 33 feet, however, the velocity of
the water in the shorter leg is limited to that due to a height of 33 feet, or
that due to the difference between the atmospheric pressure at the entrance
and the vacuum at the bend.
Leicester Allen (Am. Mach., Nov. 2, 1893) says: The supply of liquid to a
siphon must be greater than the flow which would take place f rom the dis-
charge end of the pipe, provided the pipe were filled with the liquid, the
supply end stopped, and the discharge end opened when the discharge end
is left free, unregulated, and unsubmerged.
To illustrate this principle, let us suppose the extreme case of a siphon
haying a calibre of 1 foot, in which the difference of level, or between the
point of supply and discharge, is 4 inches. Let us further suppose this
siphon to be at the sea-level, and its highest point above the level of the
supply to be 2? feet. Also suppose the discharge end of this siphon to be un-
regulated, unsubmerged. It would be inoperative because the water in the
longer leg would not be held solid by the pressure of the atmosphere against
it, and it would therefore break up and run out faster than it could be re-
placed at the inflow end under an effective head of only 4 inches.
Long Siphons.— Prof. Joseph Torrey, in the Amer. Machinist,
describes a long siphon which was a partial failure.
The length of the pipe was 1792 feet. The pipe was 3 inches diameter, and
rose at one point 9 feet above the initial level. The final level was 20 feet
below the initial level. No automatic air valve was provided. The highest
point in the siphon was about one third the total distance from the ponu and
nearest the pond. At this point a pump was placed, whose mission was to
fill the pipe when necessary. This siphon would flow for about two hours
and then cease, owing to accumulation of air in the pipe. When in full
operation it discharged 43^ gallons per minute. The theoretical discharge
from such a sized pipe with the specified head is 55^ gallons per minute.
Siphon on the Water-supply of Mount Vernon, N. Y.
(Entfg News, May 4, 1893.)— A 12-inch siphon, 925 feet long, with a maximum
lift of 22.12 feet and a 45° change in alignment, was put in use in 1892 by the
New York City Suburban Water Co., which supplies Mount Vernon, N. Y.
At its summit the siphon crosses a supply main, which is tapped to charge
the siphon.
The air-chamber at the siphon is 12 inches by 16 feet long. A ^-inch tap
and cock at the top of the chamber provide an outlet for the collected air.
It was found that the siphon with air-chamber as desc.ibed would run
until 125 cubic feet of air had gathered, and that this took place only half as
soon with a 14-foot lift as with the full lift of 22.12 feet. The siphon will
operate about 12 hours without being recharged, but more water can be
gotten over by charging every six hours. It can be kept running 23 hours
out of 24 with only one man in attendance. With the siphon as described
above it is necessary to close the valves at each end of the siphon to
recharge it.
It has been found by weir measurements that the discharge of the siphon
before air accumulates at the summit is practically the same as through a
straight pipe.
MEASUREMENT OF FLOWING WATER.
Piezometer.— If a vertical or oblique tube be inserted into a pipe con-
taining water under pressure, the water will rise in the former, and the ver-
tical height to which it rises will be the head producing the pressure at the
point where the tube is attached. Such a tube is called a piezometer or
pressure measure. If the water in the piezometer falls below its proper
level it shows that the pressure in the main pipe has been reduced by an
obstruction between the piezometer and the reservoir. If the water rises
ubove its proper level, it indicates that the pressur* there has been in-
creased by an obstruction beyond the piezometer.
If we imagine a pipe full of water to be provided with a number of pie-
zometers, then a line joining the tops of the columns of water in them is
the hydraulic grade-line.
MEASUREMENT OF FLOWING WATER. 583
Pitot Tube Gauge.— The Pitot tub" is used for measuring the veloc-
ity of fluids in motion. It has been used with great success in measuring
the flow of natural gas. (S. W. Robinson, Report Ohio Geol. Survey, 1890.)
(See also VanNostrand'lsMag., vol. xxxv.) It is simply a tube so bent that
a short leg extends into the current of fluid flowing from a tube, with the
plane of the entering orifice opposed at right angles to the direction of the
current. The pressure caused by the impact of the current is transmitted
through the tube to a pressure-gauge of any kind, such as a column of
water or of mercury, or a Bourdon spring-gauge. From the pressure thus
indicated and the known density and temperature of the flowing gas is ob-
tained the head corresponding to the pressure, and from this the velocity,
In a modification of the Pitot tube described by Prof. Robinson, there are
two tubes inserted into the pipe conveying the gas, one of which has the
plane of the orifice at right angles to the current, to receive the static pres-
sure plus the pressure due to impact; the other has the plan** of its oriftce
parallel to the current, so as to receive the static pressure on}/. These
tubes are connected to the legs of a ?7tube partly filled with mercury, which
then registers the difference in pressure in the two tubes, from which the
velocity may be calculated. Comparative tests of Pitot tubes with gas-
meters, for measurement of the flow of natural gas, have shown an agree-
ment within 3f0.
The Ventnri JJIeter, invented by Clemens Herschel, and described in
a pamphlet issued by the Builders' Iron Foundry of Providence, R. I., is
named from Venturi, who first called attention, in 1796, to the relation be-
tween the velocities and pressures of fluids when flowing through converging
and diverging tubes.
It consists of two parts— the tube, through which the water flows, and the
recorder, which registers the quantity of water that passes through the
tube.
The tube takes the shape of two truncated cones joined in their smallest
diameters by a short throat-piece. At the up-strearn end and at the throat
there are pressure-chambers, at which points the pressures are taken.
The action of the tube is based on that property which causes the small
section of a gently expanding frustum of a cone to receive, without material
resultant loss of head, as much water at the smallest diameter as is dis-
charged at the large end, and on that further property which causes the
pressure of the water flowing through the throat to be less, by virtue of its
greater velocity, than the pressure at the up-stream end of the tube, each
pressure being at the same time a function of the velocity at that point and
of .the hydrostatic pressure which would obtain were the water motionless
within the pipe,
The recorder is connected with the tube by pressure-pipes which lead to
it from the chambers surrounding the up-stream end and the throat of the
tube. It may be placed in any convenient position within 1000 feet of the
tube. It is operated by a weight and clockwork.
The difference of pressure or head at the entrance and at the throat of the
meter is balanced in the recorder by the difference of level in two columns
of mercury in cylindrical receivers, one within the other. The inner carries
a float, the position of which is indicative of the quantity of water flowing
through the tube. By its rise and fall the float varies the time of contact
between an integrating drum and the counters by which the successive
readings are registered.
There is no limit to the sizes ot the meters nor the quantity of water that
may be measured. Meters with 24-inch, 36-inch, 48-inch, and even 20-foot
tubes can be readily made.
Measurement by Venturi Tubes. (Trans. A. S. C. E., Nov., 1887,
and Jan., 1888.)— Mr. Herschel recommends the use of a Venturi tube, in-
serted in the force-main of the pumping engine, for determining the quantity
of water discharged. Such a tube applied to a 24-inch main has a total
length of about 20 feet. At a distance of 4 feet from the end nearest the
engine the inside diameter of the tube is contracted to a throat having a
diameter of about 8 inches. A pressure-gauge is attached to each of two
chambers, the one surrounding and communicating with the entrance or
main pipe, the other with the throat. According to experiments made upon
two tubes of l his kind, one 4 in. in diameter at the throat and 12 in. at the en-
trance, and the other about 36 in. in diameter at the throat and 9 feet at its
entrance, the quantity of water which passes through the tube is very nearly
the theoretical discharge through an opening having an area equal to that
of the throat, and a velocity which is that due to the difference in ueaci shown
584
HYDRAULICS.
by the two gauges. Mr. Herschel states that the coefficient for these tw*
widely-varying sizes of tubes and for a wide range of velocity through the
pipe, was found to be within two per cent, either way, of 98/£. In other
words, the quantity of water flowing through the tube per second is ex-
pressed within two per cent by the formula W— 0.98 X A X VVgh, in which
A is the area of the throat of the tube, h the head, in feet, correspond-
ing to the difference in the pressure of the water entering the tube and that
found at the throat, and g = 32.16.
Measurement of Discharge of Pumping-engines by
Means of Nozzles. (Trans. A. S. M. E., xii. 575).— The measurement
of water by computation from its discharge through orifices, or through the
nozzles of fire-hose, furnishes a means of determining the quantity of water
delivered by a pumping-engine which can be applied without much difficulty.
John R. Freeman, Trans. A. S. C. E., Nov., 1889, describes a series of experi-
ments covering a wide range of pressures and sizes, and the results showed
that the coefficient of discharge for a smooth nozzle of ordinary good form
was within one half of one per cent, either way, of 0.977 ; the diameter of
the nozzle being accurately calipered, and the pressures being determined
by means of an accurate gauge attached to a suitable piezometer at the base
Df the play-pipe.
In order to use this method for determining the quantity of water dis-
charged by a pumping-engine, it would be necessary to provide a pressure-
box, to which the water would be conducted, and attach to the box as many
nozzles as would be required to carry off the water. According to Mr.
Freeman's estimate, four 1 ^4-inch nozzles, thus connected, with a pressure
of 80 Ibs. per square inch, would discharge the full capacity of a two-and-a-
half-million engine. He also suggests the use of a portable apparatus with
a single opening for discharge, consisting essentially of a Siamese nozzle,
so-called, the water being carried to it by three or more lines of fire-hose.
To insure reliability for these measurements, it is necessary that the shut-
off valve in the force-main, or the several shut-off valves, should be tight,
so that all the water discharged by the engine may pass through the nozzles.
Flow through Rectangular Orifices. (Approximate. See p. 556.)
CUBIC FEET OP WATER DISCHARGED PER MINUTE THROUGH AN ORIFICE ONE
INCH SQUARE, UNDER ANY HEAD OP WATER FROM 3 TO 72 INCHES.
For any other orifice multiply by its area in square inches.
Formula, Q' = .624 Vh"X a* Q' = cu. ft. per min. ; a = area in sq. in.
4JT3
-u'O
-t=TJ
.o'CS
^^
aj T3
• j-rt "
CD <X>
CD CD
CU CO
3
S Sc .
n2
CD tx .
CD
«3
CO bD •
Vl
CO bJD •
5R
CD bC •
T
CO IX •
•c w
K.S
Ill
Oft P.
Heads
in inch
oft S
<£"*
111
Oft P.
ii c
D •~1
E.S
lls
Oft P-
te.£
s*s
l.i|
OQ &
Heads
in inch<
oj'l
£!&
Oft &
1!
CD
W.S
^ eS-S
°^ a
ill
ofta
3
1.12
13
2.20
23
2.90
33
3.47
43
3.95
53
4.39
63
4.78
4
1.27
14
2.28
24
2.97
34
3.52
44
4.00
54
4.42
64
4.81
6
1.40
15
2.36
25
3.03
35
3.57
45
4 05
55
4.46
65
4.85
6
1.52
16
2.43
26
3.08
36
3.62
46
4.09
56
4.52
66
4.89
7
1.64
17
2.51
27
3.14
37
3.67
47
4.12
57
4 55
67
4.92
8
1.75
18
2.58
28
3.20
38
3.72
48
4.18
58
4.58
68
4.97
9
1.84
19
2.64
29
3.25
39
3.77
49
4.21
59
4.63
69
5.00
10
1.94
20
2.71
30
3.31
40
3.81
50
4.27
60
4.65
70
5.03
11
2.03
21
2.78
31
3.36
41
3.86
51
4.30
61
4.72
71
5.07
12
2.12
22
2.84
32
3.41
42
3.91
52
4.34
62
4.74
72
5.09
Measurement of an Open Stream by Velocity and Cross*
section. — Measure the depth of the water at from 6 to 12 points across
the stream at equal distances between. Add all the depths in feet together
and divide by the number of measurements made; this will be the average
depth of the stream, which multiplied by its width will give its area or cross-
section. Multiply this by the velocity of the stream in feet per minute, and
the result will be the discharge in cubic feet per minute of the stream.
The velocity of the stream can be found by laying off 100 feet of the bank
and throwing a float into the middle, noting the time taken in passing over
the 100 ft. Do this a number of times and take the average ; then, dividing
MEASUREMENT OF FLOWING WATER.
585
this distance by the time gives the velocity at the surface. As the top of the
stream flows faster than the bottom or sides — the average velocity being
about 83# of the surface velocity at the middle— it is convenient to measure
a distance of 120 feet for the float and reckon it as 100.
FIG. 130.
Miners' Incli Measurements. (Pelton Water Wheel Co.)
The cut, Fig. 130, shows the form of measuring-box ordinarily used, and the
following table gives the discharge in cubic feet per minute of a miner's inch
of water, as measured under the various heads and different lengths and
heights of apertures used in California.
Length
Openings 2 Inches High.
Openings 4 Inches High.
of
Opening
Head to
Head to
Head to
Head to
Head to
Head to
in
Centre,
Centre,
Centre,
Centre,
Centre,
Centre,
inches.
5 inches.
6 inches.
7 inches.
5 inches.
6 inches.
7 inches.
C
i.ft.
Cu. ft.
Cu. ft.
Cu. ft.
Cu. ft.
Cu. ft.
4
.348
1.473
1.589
1.320
.450
1.570
6
.355
1.480
1.596
.336
.470
1.595
8
.359
1.484
1.600
.344
.481
1.608
10
.361
1.485
1.602
.349
.487
1.615
12
.363
.487
1.604
.352
.491
.620
14
.364
.488
.604
.354
.494
.623
16
.365
.489
1.605
.356
.496
.626
18
.365
•489
.606
.357
.498
.628
20
.365
.490
.606
.359
.499
.630
22
.366
.490
.607
.359
.500
.631
24
.366
.490
.607
.360
.501
.632
26
.366
.490
.607
.361
.502
.633
28
1.367
.491
.607
.361
.503
.634
30
1.367
.491
.608
.362
.503
.635
40
1.367
.492
1.608
.363
.505
.637
50
1.368
.493
1.609
.364
.507
.639
60
1.368
.493
1.609
.365
.508
.640
70
1.368
.493
1.609
.365
.508
.641
80
1.368
.493
1.609
.366
.509
.641
90
1.369
.493
1.610
.366
.509
.641
100
1.369
.494
1 610
1.3(56
.509
.642
NOTE.— The apertures from which the above measurements were obtained
586
HYDRAULICS.
were through material \\i inches thick, and the lower edge 2 inches above
the bottom of the measuring-box, thus giving full contraction
'fJ&**ir*f Water Over Weirs. Weir Dam Measurement.
(Pelton Water Wheel Co.)— Place a board or plank in the stream, as shown
Fia. 131.
in the sketch, at some point where a pond will form above. The length of
the notch in the dam should be from two to four times its depth for small
quantities and longer for large quantities. The edges of the notch should
be bevelled toward the intake side, as shown. The overfall below the notch
should not be less than twice its depth. [Francis says a fall below the crest
equal to one-half the head is sufficient, but there must be a free access of
air under the sheet.!
In the pond, about 6 ft. above the dam, drive a stake, and then obstruct the
water until it rises precisely to the bottom of the notch and mark the stake
at this level. Then complete the dam so as to cause all the water to flow
through the notch, and, after time for the water to settle, mark the stake
again for this new level. If preferred the stake can be driven with its top
precisely level with the bottom of the notch and the depth of the water be
measured with a rule after the water is flowing free, but the marks are pre-
ferable in most cases. The stake can then be withdrawn; and the distance
between the marks is the theoretical depth of flow corresponding to the
quantities in the table on the following page.
Francis's Formulas for Weirs.
As given by As modified by
Francis. Smith.
Weirs with both end contractions )
suppressed f
Weirs with one end contraction I
suppressed f
3.29(7+^-
= 3.33(Z - .
-0-fo)
1
Weirs with full contraction Q =
The greatest variation of the Francis formulae from the values of c given by
Smith amounts to 3^. The modified Francis formulae, says Smith, will give
results sufficiently exact, when great accuracy is not required, within the
limits of ft, from .5 ft. to 2 ft., I being not less than 3 ft.
MEASUREMEHT OF FLOWIHG WATER.
587
Q = discharge in cubic feet per second, I = length of weir in feet, 7i =effec-
tive head in feet, measured from the level of the crest to the level of still
water above the weir.
If Q' —. discharge in cubic, feet per minute, and V and hf are taken in
inches, the first of the above formulae reduces to Q' = Q.4l'h'%. From this
formula the following table is calculated. The values are sufficiently accu-
rate for ordinary computations of water-power for weirs without end con-
traction, that is, for a weir the full width of the channel of approach, and
are approximate also for weirs with end contraction when I = at least lO/i,
but about 6$ in excess of the truth when I = 4h.
Weir Table.
GIVING CUBIC FEET OF WATER PER MINUTE THAT WILL FLOW OVER A WEIR
ONE INCH WIDE AND FROM ^ TO 20% INCHES DEEP.
For other widths multiply by the width in inches.
fcin.
14 in.
%in.
y2 in.
%in.
%in.
%in.
in.
cu. ft.
cu. ft.
cu. ft.
cu. ft.
cu. ft.
cu. ft.
cu. ft.
cu. ft.
0
.00
.01
.05
.09
.14
.19
.26
.32
1
.40
.47
.55
.64
.73
.82
.92
1.02
2
1.13
1.23
1.35
1.46
1.58
1.70
1.82
1.95
3
2.07
2.21
2.34
2.48
2.61
2.76
2.90
3.05
4
3.20
3.35
3.50
3.66
3.81
3.97
4.14
4.30
5
4.47
• 4.64
4.81
4.98
5.15
5.33
5.51
5.69
6
5.87
6.06
6.25
6.44
6.62
6.82
7.01
7.21
7
7.40
7.60
7.80
8.01
8.21
8.42
8.63
8.83
8
9.05
9.26
9.47
9.69
9.91
10 13
10.35
10.57
9
10.80
11.02
11.25
11.48
11.71
11.94
12.17
12.41
10
12.64
12.88
13.12
13.36
13.60
13.85
14.09
14.34
11
14.59
14.84
15.09
15 34
15.59
15.85
16.11
16.36
12
16.62
16.88
17.15
17.41
17.67
17.94
18.21
18.47
13
18.74
19.01
19.29
19.56
19.84
20.11
20.39
20.67
14
20.95
21.23
21.51
21.80
22.08
23.37
22.65
22.94
15
< 23.23
23.52
23.82
24.11
24.40
24.70
25.00
25.30
16
25.60
25.90
26.20
26.50
26.80
27.11
27.42
27.72
17
28.03
28.34
28.65
28.97
29.28
29.59
29.91
30.22
18
30.54
30.86
31.18
31.50
31.82
3-2.15
32.47
32.80
19
33.12
33.45
33.78
34.11
34.44
34.77
35.10
35.44
20
35.77
36.11
36.45
36.78
37.12
37.46
37.80
38.15
For more accurate computations, the coefficients of flow of Hamilton
Smith, Jr., or of Bazin should be used. In Smith's hydraulics will be found
a collection of results of experiments on orifices and weirs of various shapes
made by many different authorities, together with a discussion of their
several formnlse. (See also Traut wine's Pocket Book.)
Uaziii's Experiments.— M. Bazin (Annales des Fonts et Chaussees,
Oct., 1888, translated by Marichal and Trautwine, Proc. Engrs. Club of Phila.,
Jan., 1890), made an extensive series of experiments with a sharp-crested
weir without lateral contraction, the air being admitted freely behind the
falling sheet, and found values of m varying from 0.42 to 0.50, with varia-
tions of the length of the weir from 19^ to 78% in., of the height of the crest
above the bottom of the channel from 0.79 to 2.46 ft., and of the head from
1.97 to 23.62 in. From these experiments he deduces the following formula :
Q =[o.425 + 0.21
in which Pis the height in feet of the crest of the weir above the bottom of
the channel of approach, L the length of the weir, H the head, both in feet,
and Q the discharge in cu. ft. per sec. This formula, says M. Bazin, is en-
tirely practical where errors of 2% to 3# are admissible. The following
table is condensed from M. Bazin's paper :
588
WATER-POWEB.
VALUES OP THE COEFFICIENT m IN THE FORMULA Q ss mLH VZgH* FOR A
SHARP-CRESTED WEIR WITHOUT LATERAL CONTRACTION ; THB Aw BEINA
ADMITTED FREELY BEHIND THIS FALLING SHEET.
Head,
B.
Height of Crest of Weir Above Bed of Channel.
Feet... 0.66
Inches 7.87
0.98
11.31
1.31
15.75
1.64
19.69
1.97!
23.62
m
0.449
0.442
0.438
0.436
0.435
0.486
0.438
0.441
0.444
0.448
0.451
0.454
0.457
0.460
0.463
0.466
8.62
31.50
8.28
39.88
4.92
59.07
656
78.76
m
0.448
0.439
0.434
0.430
0.426
0.423
0.422
0.422
0.421
0.421
0.421
0.421
0.421
0.421
0.421
0-421
00
00
m
0.4481
0.4391
0.4340
0.4291
0.4246
0.4215
0.4194
0.4181
0.4168
0.4156
0.4144
0.4134
0.4122
0.4112
0.4101
0.4093
Ft.
.164
.230
.295
.394
.525
.656
.787
.919
1.050
1.181
1.312
1.444
1.575
1.706
1.837
1.969
In.
1.97
2.76
3.54
4.72
6.30
7.87
9.45
11.02
12.60
14.17
15.75
17.32
18.90
20.47
22.05
23.62
m
0.458
0.455
0.457
0.462
0.471
0.480
0.488
0.496
m
0.453
0.448
0.447
0.448
0.453
0.459
0.465
0.472
0.478
0.483
0.489
0.494
m
0.451
0.445
0.442
0.442
0.444
0.447
0.452
0.457
0.462
0.467
0.472
0.476
0.480
0.483
0.487
0.490
m
0.450
0.443
0.440
0.438
0.438
0.440
0.444
0.448
0.452
0.456
0.459
0.463
0.467
0.470
0.473
0.476
m
0.449
0.441
0.436
0.433
0.431
0.431
0.432
0.433
0.436
0.438
0.440
0.442
0.444
0.446
0.448
0.451
m
0.449
0.440
0.436
0.432
0.429
0.428
0.428
0.429
0.480
0 432
0 433
0.435
0.436
0.438
0.439
0.441
m
0.448
0.440
0.435
0.430
0.427
0.425
0.424
0.424
0.424
0.424
0.424
0.425
0.425
0.426
0.427
0.427
A comparison of the results of this formula with those of experiments,
says M. Bazin, justifies us in believing: that, except in the unusual case of a
very low weir (which should always be avoided), the preceding table will
give the coefficient m in all cases within \%\ provided, however, that the ar-
rangements of the standard weir are exactly reproduced. It is especially
important that the admission of the air behind the falling sheet be perfectly
assured. If this condition is not complied with, m may vary within much
wider limits. The type adopted gives the least possible variation in tha
coefficient.
WATER-POWEB.
Power of a Fall of Water-OEfficlency.— The gross power of
a fall of water is the product of the weight of water discharged in a unit of
time into the total head, i.e., the difference of vertical elevation of the
upper surface of the water at the points where the fall in question begins
and ends. The term ** head " used in connection with water-wheels is the
difference in height from the surface of the water in the wheel-pit to the
surface in the pen-stock when the wheel is running.
If Q = cubic feet of water discharged per second, D = weight of a cubio
foot of water = 62.36 Ibs. at 60° F., H = total head in feet; then
DQH z= gross power in foot-pounds per second,
and DQH + 550 =.1134QH = gross horse-power.
~'H X 62.36
If Q' is taken in cubic feet per minute, H. P
33,000
.00189g'H.
A water-wheel or motor of any kind cannot utilize the whole of the head
H, since there are losses of head at both the entrance to and the exit from
the wheel. There are also losses of energy due to friction of the water in
its passage through the wheel. 1'he ratio of the power developed by the
wheel to the gross power of the fall is the efficiency of the wheel. For 75*
efficiency, net horse-power = .00142Q'H » ~— -.
MILL-POWER. 589
A head of water can be made use of in one or other of the following ways
viz. :
1st. By its weight, as in the water-balance and overshot-wheel.
2d. By its pressure, as in turbines and in the hydraulic engine, hydraulic
press, crane, etc.
3d. By its impulse, as in the undershot- wheel, and in the Pelton wheel.
4th. By a combination of the above.
Horse-power of a Running Stream.— The gross horse-power
is, H. P. ss QH X 62.30 •*• 550 = .1134QH, in which Q is the discharge in cubic
feet per second actually impinging on the float or bucket, and H - theoret-
ical head due to the velocity of the stream = |- = gj-^ « in which v is the
velocity in feet per second. If Q' be taken in cubic feet per minute,
H.P. a.wmQ'ff.
Thus, if the floats of an undershot-wheel driven by a current alone be 5
feet X 1 foot, and the velocity of stream = 210 ft. per minute, or 3)4 ft. per
sec., of which the theoretical head is .19 ft., Q = 5 sq. ft. X 210 =s 1050 cu. ft,
per minute ; H=s .19ft.; H.P. = 1050 X .19 X.00189 = ,877 H.P.
The wheels would realize only about .4 of this power, on account of friction
and slip, or .151 H.P., or about .03 H.T. per square foot of float, which is
equivalent to 83 sq. ft. of float per H. P.
Current motors. — A current motor could only utilize the whole power
of a running stream if it could take all the velocity out of the water, so that
it would leave the floats or buckets with no velocity at all; or in other words,
it would require the backing up of the whole volume of the stream until the
actual head was equivalent to the theoretical head due to the velocity of the
stream. As but a small fraction of the velocity of the stream can be taken
up by a current motor, its efficiency is very small. Current motors may be
used to obtain small amounts of power from large streams, but for large
powers they are not practicable.
Morse-power ofWater Flowing In a Tube.— The head due to
the velocity is ~- ; the head due to the pressure is - ; the head due to actual
height above the datum plane is h feet. The total head is the sum of these =
—. 4. ft, 4. JL^ in feet, in which v = velocity in feet per second,/ = pressure
in Ibs. per sq. ft., w « weight of 1 cu. ft. of water = 62.36 Ibs. lfp = pres-
sure in Ibs. per sq. in., — « 2.309p. In hydraulic transmission the velocity
w
and the height above datum are usually small compared with the pressure-
head. The work or energy of a given quantity of water under pressure =*
its volume in cubic feet X its pressure in Ibs. per sq. ft.; or if Q ss quantity
in cubic feet per second, and p = pressure in Ibs. per square inch, Wss
U4pQ, and the H. P. = = J2618p&
oou
Maximum Efficiency of a Long Conduit.— A. L. Adams and
R.C.(?einmelL (Eng'g News, May 4, 1893), show by mathematical analysis that
the -conditions for securing the maximum amount of power through a long
conduit of fixed diameter, without regard to the economy of water, is that
the draught from the pipe should be such that the frictional loss in the pipe
will be equal to one third of the entire static head.
Ittill-Power.— A "mill-power" is a unit used to rate a water-power for
the purpose of renting it. The value of the unit is different in different
localities. The following are examples (from Emerson):
Holyoke, Mass.— Each mill-power at the respective falls is declared to be
the right during 16 hours in a day to draw 38 cu. ft. of ^vater per second at
the upper fall when the head there is 20 feet, or a quantity proportionate to
the height at the falls. This is equal to 86.2 horse-power as a maximum.
Lowell, Mass.— The right to draw during 15 hours in the day so much water
as shall give a power equal to 25 cu. ft. a second at the great fall, when the
fall there is 30 feet. Equal to 85 H. P. maximum.
Lawrence, Mass.— The right to draw during 16 hours in a day so much
water as shall give a power equal to 30 cu. ft. per second when the head Is
85 feet. Equal to 85 H.P. maximum.
Minneapolis, Minn.— 30 cu. fc. of water per second with head of 22 feet.
Equal to 74.8 H.P.
Manchester, N. H.— Divide 725 by the number of feet of fall minus 1, and
590 WATER-POWER.
the quotient will be the number of cubic feet per second In that fall. For 20
feet fall this equals 38.1 cu. ft., equal to 86.4 H. P. maximum.
Cohoes, N. K— ** Mill-power " equivalent to the power given by 8 cu. ft.
per second, when the fall is 20 feet. Equal to 13.6 H. P., maximum.
Passaic, N. J.— Mill-power: The right to draw 8^ cu. ft. of water per sec.,
fall of 22 feet, equal to 21.2 horse-power. Maximum rental $700 per year for
each mill-power = $33.00 per H. P.
The horse-power maximum above given is that due theoretically to the
weight of water and the height of the fall, assuming the water-wheel to
have perfect efficiency. It should be multiplied by the efficiency of the
wheel, say 75# for good turbines, to obtain the H. P. delivered by the wheel.
Value of a Water-power.— In estimating the value of a water-
power, especially where such value is used as testimony for a plaintiff whose
water-power has been diminished or confiscated, it is a common custom for
the person making such estimate to say that the value is represented by a
sum of money which, when put at interest, would maintain a steam -plant
of the same power in the same place.
Mr. Charles T. Main (Trans. A. S. M. E. xiii. 140) points out that this sys-
tem of estimating is erroneous; that the value of a power depends upon a
great number of conditions, such as location, quantity of water, fall or head,
uniformity of flow, conditions which fix the expense of dams, canals, founda-
tions of buildings, freight charges for fuel, raw materials and finished prod-
net, etc. He gives an estimate of relative cost of steam and water-power
for a 500 H. P. plant from which the following is condensed:
The amount of heat required per H. P. varies with different kinds of busi-
ness, but in an average plain cotton-mill, the steam required for heating and
slashing is equivalent to about 25# of steam exhausted from the high-
pressure cylinder of a compound engine of the power required to run that
mill, the steam to be taken from the receiver.
The coal consumption per H. P. per hour for a compound engine is taken
at 1% Ibs. per hour, when no steam is taken from the receiver for heating
purposes. The gross consumption when 25# is taken from the receiver is
about 2.06 Ibs.
75g of the steam is used as in a compound engine at 1.75 Ibs. = 1.31 Ibs.
25% »* " high-pressure ?* 3.00 Ibs. = .75 "
iJioG ••
The running expenses per H. P. per year are as follows :
2.06 Ibs. coal per hour = 21.115 Ibs. for 10J4 hours or one day = 6503.42
Ibs. for 308 days, which, at $3.00 per long ton = $8 71
Attendance of boilers, one man <§)• $2.00, and one man © $1.25 = 2 00
" engine, •• '• " $3.50. 2 16
Oil, waste, and supplies. 80
The cost of such a steam-plant in New England and vicinity of 500
H. P. is about $65 per H. P. Taking the fixed expenses as 4£ on
engine, 5$ on boilers, and 2# on other portions, repairs at 2#, in-
terest at 5#, taxes at \\& on % cost, an insurance at y%% on exposed
portion, the total average per cent is about 12^$, or $65 X -12)^ = 813
Gross cost of power and low-pressure steam per H. P. $21 80
Comparing this with water-power, Mr. Main says : "At Lawrence the cost
of dam and canals was about $650,000, or $65 per H. P. The cost per H. P.
of wheel-plant from canal to river is about $45 per H. P. of plant, or about
$65 per H. P. used, the additional $20 being caused by making the plant
large enough to compensate for fluctuation of power due to rise and fall of
river. The total cost per H. P. of developed plant is then about $130 per H. P.
Placing the depreciation on the whole plant at 2& repairs at 1& interest at
5$, taxes and insurance at 1#, or a total of 9#, gives:
Fixed expenses per H. P. $130 X .09 = $11 TO
Running * (Estimated) 200
$1870
" To this has to be added the amount of steam required for heating pup.
poses, said to be about 25# of the total amount used, out in winter months
the consumption is at least 37^#. It is therefore necessary to have a boiler
plant of about 37^ of the size of the one considered witji the steam-plant,
TURBINE WHEELS. 591
costing about $20 X .375 = $7.50 per H. P. of total power used. The ex-
pense of running this boiler-plant is, per H. P. of the the total plant per year;
Fixed expenses 12^ on $7.50 , $0.94
Coal 3.26
Labor 1.23
Total ........................................... $5.43
Making a total cost per year for water-power^with the auxiliary boiler plant
$13.70 + $5. 43 = $19.13 which deducted from $21.80 make a difference in
favor of water-power of $2.67, or for 10,000 H. P. a saving of $«6,700 per
year.
" It is fair to say," says Mr. Main," that the value of this constant power is
a sum of money which when put at interest will produce the saving ; or if <o%
is a fair interest to receive on money thus invested the value would be
$26. 700 H- .06 = $445,000."
Mr. Main makes the following general statements as to the value of a
water-power : " The value of an undeveloped variable power is usually noth-
ing if its variation is great, unless it is to be supplemented by a steam-plant.
It is of value then only when the cost per horse-power for the double-plant
is less than the cost of steam-power under the same conditions as mentioned
for a permanent power, and its value can be represented in the same man-
ner as the value of a permanent power has been represented.
" The value of a developed power is as follows: If the power can be run
cheaper than steam, the value is that of the power, plus the cost of plant,
less depreciation. If it cannot be run as cheaply as steam, considering its
cost, etc., the value of the power itself is nothing, but the value of the plant
is such as could be paid for it new, which would bring the total cost of run-
ning down to the cost of steam-power, less depreciation."
Mr. Samuel Webber, Iron Age, Feb. and March, 1893, writes a series of
articles showing the development of American turbine wheels, and inci-
dentally criticises the statements of Mr. Main and others who have made
comparisons of costs of steam and of water-power unfavorable to the latter.
Hesays : ** They have based their calculations on the cost of steam, on large
compound engines of 1000 or more H. P. and 120 pounds pressure of steam
in their boilers, and by careful 10-hour trials succeeded in figuring down
steam to a cost of about $20 per H. P., ignoring the well-known fact that its
average cost in practical use, except near the coal mines, is from $40 to $50.
In many instances dams, canals, and modern turbines can be all completed
for a cost of $100 per H. P. ; and the interest on that, and the cost of attend-
ance and oil, will bring water-power up to but about $10 or $12 per annum;
and with a man competent to attend the dynamo in attendance, it can
probably be safely estimated at not over $15 per H. P."
TURBINE: WHIRLS.
Proportions of Turbines.— Prof. De Volson Wood discusses at
length the theory of turbines in his paper on Hydraulic Reaction Motors,
Trans. A. S. M. E. xiv. 266. His principal deductions which have an imme-
diate bearing upon practice are condensed in the following :
Notation.
Q = volume of water passing through the wheel per second,
7ii = head in the supply chamber above the entrance to the buckets,
7<2 = head in the tail-race above the exit from the buckets,
2i = fall in passing through the buckets.
H =• hi -f- Zi — /J2, the effective head,
/*! = coefficient of resistance along the guides,
fxa = coefficient of resistance along the buckets,
?-j = radius of the initial rim,
TO = radius of the terminal rim,
V =s velocity of the water issuing from supply chamber,
vl •= initial velocity of the water in the bucket in reference to the bucket,
va si terminal velocity in the bucket,
o> = angular velocity of fye wheel,
a = terminal angle between the guide and initial rim = CAB, Fig. 132,
i = angle between the initial element of bucket and initial rim =r EAD,
= GFIy the angle between the terminal rim and terminal element of
ucket.
eb, Fig. 133 = the arc subtending one gate opening,
va
the b
592
WATEB-POWER.
at = the arc subtending one bucket at entrance. (In practice a^ is large!
than a,)
«2 = gh, the arc subtending one bucket at exit,
K = lff normal section of passage, it being assumed that the passages
and buckets are very narrow,
fcj = bd, initial normal section of bucket,
fca = gi, terminal normal section,
wrj = velocity of initial rim,
w7-a = velocity of terminal rim,
e = HFI, angle between the terminal rim and actual direction of the
water at exit,
Y = depth of K. y, otcii, and y9 of 1T2, then
K = Ya sin a; K^ = 2/i a^ sin y^\ K% = 2/a«3 sin ya.
Fm. 132.
FIG. 133.
Three simple systems are recognized, rt < recalled outward flow; rj > ra,
called inward flow; r^ = r«, called parallel flow. The first and second may
be combined with the third, making a mixed system.
Value of v» (the quitting angle).— The efficiency is increased as y« de-
creases, and is greatest for y2 = 0. Hence, theoretically, the terminal ele-
ment of the bucket should be tangent to the quitting rim for best efficiency.
This, however, for the discharge of a finite quantity of water, would
require an infinite depth of bucket. In practice, therefore, this angle must
have a Unite value. The larger the diameter of the terminal rim the smaller
may be this angle for a given depth of wheel and given quantity of water
discharged. In practice y^ is from 10° to 20°.
In a wheel in which all the elements except ya are fixed, the velocity of
the wheel for best effect must increase as the quitting angle of the bucket
decreases.
Values of a. -f- y, must be less than 180°, but the best relation cannot be
determined by analysis. However, since the water should be deflected from
its course as much as possible from its entering to its leaving the wheel, the
angle a for this reason should be as small as practicable.
In practice, a cannot be zero, and is made from 20° to 30°.
The value r, = 1.4ra makes the width of the Srown for internal flow about
the same as for r, =ra \^ for outward flow, being approximately 0.3 of the
external radius.
Values O//AJ and f*a.— The frictional resistances depend upon the construc-
tion of the wheel as to smoothness of the surfaces, sharpness of the angles,
TURBINE WHEELS. 593
regularity of the curved parts, and also upon the speed it Is run. These
values cannot be definitely assigned beforehand, but Weisbach gives for
good conditions /xj = /xa = 0.05 to 0.10.
They are not necessarily equal, and /ttj may be from 0.05 to 0.075, and M*
from 0.06 to 0.10 or even larger.
Values of y^ must be less than 180° — a.
To be on the safe side, y, may be 20 or 30 degrees less than 180°-2o, giving
V1ral80°-2a-25 (say) =155-2o.
Then if a = 30°, yt « 95°. Some designers make y, 90°; others more, and
still others less, than that amount. Weisbach suggests that it be less, so
that the bucket will be shorter and friction less. This reasoning appears to
be correct for the inflow wheel, but not for the outflow wheel. In the Tre-
mont turbines, described in the Lowell Hydraulic Experiments, this angle
is 90°, the angle a 20°, and ya 10°, which proportions insured a positive
pressure in the wheel. Fourneyron made yt = 90°, and a from 30° to 33°,
which values made the initial pressure in the wheel near zero.
Form of Bucket.— The form of the bucket cannot be determined analytic-
ally. From the initial and terminal directions and the volume of the water
flowing through the wheel, the area of the normal sections may be found.
The normal section of the buckets will be :
*-£•<*•-£< *•-!• -
The depths of those sections will be : ,
n t, JL ;
"* a sin a* * m al sin yl * ^* ** a9 sin y9'^
The changes of curvature and section must be gradual, and the general
form regular, so that eddies and whirls shall not be formed. For the same
reason the wheel must be run with the correct velocity to secure the best
effect. In practice the buckets are made of two or three arcs of circles,
mutually tangential.
The Value of w.— So far as analysis indicates, the wheel may run at any
epeed; but in order that the stream shall flow smoothly from the supply
chamber into the bucket, the velocity V should be properly regulated.
If /utj =s /na = 0.10, ra -*- r, = 1.40, a = 25°, yx = 90°, y2 = 12°, the velocity of
the initial run for outward flow will be for maximum efficiency 0.614 of the
velocity due to the head, or wrj = 0.614 V2gH.
The velocity due to the head would be 4/2</H = 1.414 VgH.
For an inflow wheel for the case in_which r,a = 2ra», and the other dimen
sions as given above, w?*, =s 0.682 ^/2g H.
The highest efficiency of the Tremont turbine, found experimentally, was
0.79375, and the corresponding velocity, 0.62645 of that due to the head, and
for all velocities above and below this value the efficiency was less.
In the Tremont wheel a = 20° instead of 25°, and y? = 10° instead of 12°.
These would make the theoretical efficiency and velocity of the wheel some'
what greater. Experiment showed that the velocity might be considerably
larger or smaller than this amount without much diminution of the efficiency.
It was found that if the velocity of the initial (or interior) rim was not less
than 44# nor more than 75# of that due to the fall, the efficiency was 75* or
more. This wheel was allowed to run freely without any brake except its
own friction, and the velocity of the initial rim was observed to be
1.335 V2gH, half of which is 0.6675 V2gH. which is not far from the velocity
giving maximum effect; that is to say, when the gate is fully raised the coeffi-
cient of effect is a maximum when the wheel is moving with about half its
maximum velocity.
Number of Buckets. —Successful wheels have been made in which the dis-
tance between the buckets was as small as 0.75 of an inch, and others as
much as 2.75 inches. Turbines at the Centennial Exposition had buckets
from 4V6 inches to 9 inches from centre to centre. If too large they will not
work properly. Neither should they be too deep. Horizontal partitions
are sometimes introduced. These secure more efficient working in case the
gates are only partly opened. The form and number of buckets for com-
mercial purposes are chiefly the result of experience.
594 WATER-POWER.
Ratio of Radii.—Theory does not limit the dimensions of the wheel. In
practice,
for outward flow, ra -*• rt is from 1.25 to 1.50;
for inward flow, ra-5-rj is from 0.66 to 0.80.
It appears that the inflow-wheel has a higher efficiency than the outward-
flow wheel. The inflow- wheel also runs somewhat slower for best effect.
The centrifugal force in the outward-flow wheel tends to force the water
outward faster than it would otherwise flow ; while in the inward-flow wheel
it has the .contrary effect, acting as it does in opposition to the velocity in
the buckets.
It also appears that the efficiency of the outward-flow wheel increases
slightly as the width of the crown is less and the velocity for maximum
efficiency is slower ; while for the inflow-wheel the efficiency slightly in-
creases for increased width of crown, and the velocity of the outer rim at the
same time also increases.
Efficiency.— The exact value of the efficiency for a particular wheel must
be found by experiment.
It seems hardly possible for the effective efficiency to equal, much less
exceed, 8% and all claims of 90 or more per cent for these motors should be
discarded as improbable. A turbine yielding from 75# to 80£ is extremely
good. Experiments with higher efficiencies have been reported.
The celebrated Tremont turbine gave 79J4# without the " diffuser," which
might have added some 2$. A Jonval turbine (parallel flow) was reported
as yielding 0,75 to 0.90, but Morin suggested corrections reducing it to 0.63 to
0.71. Weisbach gives the results of many experiments, in which the effi-
ciency ranged from 50# to 84#. Numerous experiments give E — 0.60 to 0.65.
The efficiency, considering only the energy imparted to the wheel, will ex-
ceed by several per cent the efficiency of the wheel, for the latter will in-
clude the friction of the support and leakage at the joint between the sluice
and wheel, which are not included in the former ; also as a plant the resist-
ances and losses in the supply-chamber are to be still further deducted.
The Crowns. — The crowns may be plane annular disks, or conical, or
curved. If the partitions forming the buckets be so thin that they may be
discarded, the law of radial flow will be determined bv the form of the
crowns. If the crowns be plane, the radial flow (or radial component) will
diminish, for the outward flow-wheel, as the distance from the axis increases
—the buckets being full — for the angular space will be greater.
Prof. Wood deduces from the formulae in his paper the tables on page 595.
It appears fronVthese tables: 1. That the terminal angle, a, has frequently
been made too large in practice- for the best efficiency.
2. That the terminal angle, a, of the guide should be for the inflow less
than 10* for the wheels here considered, but when the initial angle of the
bucket is 90°, and the terminal angle of the guide is 5° 28', the gain of effi-
ciency is not 2f0 greater than when the latter is 25°.
3. that the initial angle of the bucket should exceed 90° for best effect for
outflow-wheels.
4. That with the initial angle between 60° and 120° for best effect on inflow
wheels the efficiency varies scarcely \%.
5. In the outflow-wheel, column (9) shows that for the outflow for best
effect the direction- of the quitting water in reference to the earth should be
nearly radial (from 76° to 97°), but for the inflo\y wheel the water is thrown
forward in quitting. This shows that the velocity of the rim should some-
what exceed the relative final velocity backward in the bucket, as shown in
columns (4) and (5).
6. In these tables the velocities given are in terms of V2gh, and the co-
efficients of this expression will be the part of the head which would produce
that velocity if the water issued freely. There is only one case, column (5),
where the coefficient exceeds unity, and the excess is so small it may be dis-
carded; and it may be said that in a properly proportioned turbine with the
conditions here given none of the velocities will equal that due to the head
in the supply-chamber when running at best effect.
7. The inflow turbine presents the best conditions for construction for
producing a given effect, the only apparent disadvantage being an increased
first cost due to an increased depth, or an increased diameter for producing
a given amount of work. The larger efficiency should, howevek , more than
neutralize the increased first cost.
TURBINE WHEELS.
595
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596
WATER-POWER.
Tests of Turbines.— Emerson says that in testing turbines it is a rare
thing to find two of the same size which can be made to do their best at the
same speed. The best speed of one of the leading wheels is invariably wide
from the tabled rate. It was found that a 54-in. Leffel wheel under 12 ft.
head gave much better results at 78 revolutions per minute than at 90.
Overshot wheels have been known to give 75$ efficiency, but the average
performance is not over 60$.
A fair average for a good turbine wheel maybe taken at 75#. In tests of 18
wheels made at the Philadelphia Water-works in 1859 and 1860, one wheel
gave less than 50# efficiency, two between 50^ and 60#, six between 60# and
70#, seven between 71 % and 77#, two 82#, and one 87.77$. (Emerson.)
Tests of Turbine "Wheels at the Centennial Exhibition.
1876. (From a paper by R. H. Thurston on The Systematic Testing of
Turbine Wheels iu the United States, Trans. A. S. M. E., viii. 359.)— In 1878
the judges at the International Exhibition conducted a series of trials of
turbines. Many of the wheels offered for tests were found to be more or
less defective in fitting and workmanship. The following is a statement of
the results of all turbines entered which gave an efficiency of over ?5£.
Seven other wheels were tested, giving results between 65$ and 75#.
Maker's Name, or Name the
Wheel is Known By.
5*
1
|.23
oS^
28'.
3 i2
.§3
cS^
|3
fl
3 tffl
|3
"§ 03
|S
I0w
!""
P
fesl
PUI
&
£
I11
Risdon
National • • * ••
87.68
8379
86.20
82.41
70.79
75.35
83.30
Thos Tait
82.13
70.40
66.35
55.00
Goldie & McCullough
81.21
71.01
55.90
Rodney Hunt Mach. Co
Tyler Wheel
78.70
79.59
7757
71.66
81.24
68.60
79.92
51.03
67.23
69.59
Knowlton & Dolan
E. T. Cope & Sons
77.43
76.94
74.25
*69.92
62.75
Barber & Harris
76.16
73.33
70.87
71.74
York Manufacturing Co. ......
W. F. Mosser & Co
75.70
75.15
74.89
67.08
71.90
67.57
70.52
62.06
66.04
The limits of error of the tests, says Prof. Thurston, were very uncertain ;
they are undoubtedly considerable as compared with the later work done in
the permanent flume at Holyoke— possibly as much as 4fo or 5£.
Experiments with " draught-uubes," or "suction-tubes," which were
actually ** diff users" in their effect, so far as Prof. Thurston has analyzed
them, indicate the loss by friction which should be anticipated in such
cases, this loss decreasing as the tube increased in size, and increasing aa
its diameter approached that of the wheel— the minimum diameter tried.
It was sometimes found very difficult to free the tube from air completely,
and next to impossible, during the interval, to control the speed with the
brake. Several trials were often necessary before the power due to the full
head could be obtained. The loss of power by gearing and by belting was
variable with the proportions and arrangement of the gears and pulleys,
length of belt, etc., but averaged not far from 30$ for a single pair of bevel-
gears, uncut and dry, but smooth for such gearing, and but 10$ for the same
gears, well lubricated, after they had been a short time in operation. The
amount of power transmitted was, however, small, and these figures are
probably much higher than those representing ordinary practice. Intro-
ducing a second pair— spur-gears— the best figures were but little changed,
although the difference between the case in which the larger gear was the
driver, and the case in which the small wheel was the driver, was perceiv-
able, and was in favor of the former arrangement. A single straight belt
gave a loss of but 2% or 3#, a crossed belt 6$ to 8#, when transmitting 14
TURBINE WHEELS. 597
horse-power with maximum tightness and transmitting power. A " quarter
turn '' wasted about 10$ as a maximum, and a "quarter twist " about 5%.
Dimensions of Turbines.— For dimensions, power, etc., of stand-
ard makes of turbines consult the catalogues of different manufacturers.
The wheels of different makers vary greatly in their proportions for any
given capacity.
The Pelton Water-wheel.— Mr. Ross E. Browne (Eng'g News, Feb.
20, 189.2) thus outlines the principles upon which this water-wheel is
constructed :
The function of a water-wheel, operated by a jet of water escaping from
a nozzle, is to convert the energy of the jet, due to its velocity, into useful
work In order to utilize this energy fully the wheel-bucket, after catching
the jet, must bring it to rest before discharging it, without inducing turbu-
lence or agitation of the particles.
This cannot be fully effected, and unavoidable difficulties necessitate the
loss of a portion of the energy. The principal losses occur as follows:
First, in sharp or angular diversion of the jet in entering, or in its course
through the bucket, causing impact, or the conversion of a portion of the
energy into heat instead of useful work. Second, in the so-called frictional
resistance offered to the motion of the water by the wetted surfaces of the
buckets, causing also the conversion of a portion of the energy into heat
instead of useful work, Third, in the velocity of the water, as it leaves the
bucket, representing energy which has not been converted into work.
Hence, in seeking a high efficiency: 1. The bucket-surface at the entrance
should be approximately parallel to the relative course of the jet, and
the bucket should be curved in such
a manner as to avoid sharp angular de-
flection of the stream. If, for example,
a jet strikes a surface at an angle and
is sharply deflected, a portion of the
water is backed, th
,
he smoothness of the
stream is disturbed, and there results
considerable loss by impact and other-
wise. The entrance and deflection in
the Pelton bucket are such as to avoid FIG. 134. Fia. 135.
these losses in the main. (See Fig. 136.)
2. The number of buckets should be small, and the path of the jet in the
bucket shorten other words, the total wetted surface should be small, as
the loss by friction will be proportional to this.
3. The discharge end of the bucket should be as nearly tangential to the
wheel periphery as compatible with the clearance of the bucket which
follows; and great differences of velocity in the parts of the escaping water
should be avoided. In order to bring the water to rest at the discharge end
of the bucket, it is shown, mathematically, that the velocity of the bucket
should be one half the velocity of the jet.
A bucket, such as shown in Fig. 135, will cause the heaping of more or less
dead or turbulent water at the point indicated by dark
shading. This dead water is subsequently thrown from
the wheel with considerable velocity, and represents o
large loss of energy. The introduction of the wedge in
the Pelton bucket (see Fig. 134) is an efficient means of
avoiding this loss.
A wheel of the form of the Pelton conforms closely in
construction to each of these requirements.
In a te_ « made by the proprietors of the Idaho mine,
Fir 136 near Grass Valley, Cal., the dimensions and results were
as foil /s : Main supply-pipe, 22 in. diameter, 6900 ft.
long, with a. head of 336^ feet above centre of nozzle. The loss by friction
in the pipe was 1.8 ft., reducing the effective head to 384.7 ft. The Pelton
wheel used in the t jst was 6 ft. in diameter and the nozzle was 1.89 in.
diameter. The work done was measured by a Prony brake, and the mean
of 13 tests showed a useful effect of 87.3#.
The Pelton wheel is also used as a motor for small powers. A test by
M. E. Cooley of a 12-inch wheel, with a %-inch nozzle, under 100 Ibs. pressure,
gave 1.9 horse-power. The theoretical discharge was .0935 cubic feet per
second, and the theoretical horse-power 2.45; the efficiency being 80 per
cent. Two other styles of water-motor tested at the same time each gave
efficiencies of 55 per cent.
598
WATER-POWER.
Pelion Water- wli eel Tables. (Abridged.)
The smaller figures under those denoting the various heads give the
spouting velocity of the water in feet per minute. The cubic-feet measure-
ment IK also based on the flow per minute.
Head
in ft.
Size of
Wheels.
6
in.
No.l
.05
1.67
684
12
in.
No. 2
18
in.
No. 3
18
in.
No. 4
24
in.
No. 5
3
ft.
ft.
5
ft.
6
ft.
20
2151.97
Horse-power.
Cubic feet....
Revolutions..
.12
3.91
342
.20
6.62
228
.37
11.72
228
.66
20.83
171
1.50
46.93
114
2.64
83.32
85
4.18
130.36
70
6.00
187.72
57
30
2635.62
Horse-power.
Cubic feet....
Revolutions..
.10
2.05
837
.23
4.79
418
.38
8.11
279
.69
14.36
279
1 22
25.51
209
2.76
57.44
139
4.88
102.04
104
7.69
159.66
83
11.04
229.76
69
40
3043.39
Horse-power.
Cubic feet. . . .
Revolutions..
.15
2.37
969
.21
2.64
1083
.35
5.53
484
.59
9.37
323
1.06
16.59
323
1.89
29.46
242
4.24
66.86
161
7.58
107.84
121
11.85
184. 36
96
16.96
265.44
. 80
50
3402.61
Horse-power.
Cubic feet....
Revolutions..
.49
6.18
541
.84
10.47
361
1.49
18.54
361
2.65
32.93
270
5.98
74.17
180
10.60
131.72
135
16.63
206.13
108-
23.93
296.70
90
60
3727.3?
Horse-power.
Cubic feet. . . .
Revolutions..
.28
2.90
1185
.65
6.77
592
1.10
11.47
395
1.96
20.31
395
3.48
36.08
296
7.84
81.25
197
13.94
144.32
148
21.77
225.80
118
31.36
325.00
98
70
4026.00
Horse-power.
Cubic feet. . . .
Revolutions..
.35
3.13
1281
.82
7.31
640
1.39
12.39
427
2.47
21.94
427
4.39
38.97
320
9.88
87.76
213
17.58
155.88
160
27.51
243.89
130
39.52
351.04
106
80
4303.99
Horse-power.
Cubic feet....
Revolutions..
.43
3.35
1368
1.00
7.82
684
1.70
13 25
456
3.01
23.46
456
5.36
41.66
342
12.04
93.84
228
21.44
166.64
171
33.54
260.73
137
48.16
375.36
114
90
4565.04
Horse-power.
Cubic feet....
Revolutions. .
.51
3.55
1452
1.20
8.29
726
2.03
14.05
484
3.60
24.88
484
6.39
44.19
363
14.40
99.52
242
25.59
176.75
181
40.04
276.55
145
57.60
398.08
121
100
4812.00
Horse-power.
Cubic feet....
Revolutions..
.60
3.74
1530
1.40
8.74
765
2.32
14.81
510
4.21
26.22
510
7.49
46.58
382
16.84
104.88
255
29.93
186.32
191
46.85
291.51
152
67.36
419.52
127
120
5271 .30
Horse-power.
Cubic feet. . . .
Revolutions..
.79
4.10
1677
1.84
9.57
838
3.12
16.21
559
5.54
28.72
559
9.85
51.02
419
22.18
114.91
279
39.41
204.10
209
61.66
319.33
16?
88.75
459.64
139
140
5693.65
Horse-power.
Cubic feet.,..
Revolutions..
.99
4.43
1812
1.22
4.73
1938
2.33
10.34
906
3.94
17.53
604
6.99
31.03
604
12.41
55.11
453
27.96
124.12
302
49.64
220.44
226
344! 92
181
111.85
496.48
151
160
6086.74
Horse-power.
Cubic feet....
Revolutions..
2.84
11.05
969
4.82
18.74
646
8.54
33.17
646
15.17
58.92
484
34.16
132.68
323
60.68
235.68
242
94. S4
368.73
193
136.65
530.75
161
180
6455.97
Horse power.
Cubic feet....
Revolutions. .
1.45
5.02
2049
3.39
11.72
1024
5.75
19.87
683
10.19
35.18
683
18.10
62.49
513
40.77
140.74
342
72.41
249.97
256
113.30
391.10
206
163.08
562.96
171
200
6805.17
Horse-power.
Cubic feet. . .
Revolutions..
1.70
5.29
2160
3.97
12.36
1080
6.74
20.94
720
11.93
37.08
720
21.20
65.87
540
47.75
148.35
360
84.81
263.49
270
132.70
412.25
216
191.00
593.40
180
250
7608.44
Horse-power.
Cubic feet....
Revolutions. .
2.38
5.92
2418
5.56
13.82
1209
9.42
23.42
806
16.68
41.46
806
29.63
73.64
605
66.74
165.86
403
118.54
294.59
302
185.47
460.91
241
266.96
663.45
202
POWER OP OCEAH WAVES. 599
Pelton Water-wheel Tables.— Continued.
Head
in ft.
Size of
Wheels.
6
in.
No.l
12
in.
No. 2
18
in.
No. 3
18
in.
No.l
24
in.
No. 5
3
ft.
4
ft.
5
ft.
6
ft.
300
8334.62
"~350
9002.43
rlorse-pow'r
Dubic feet...
Revolutions
3.13
6.48
2652
3.94
7.00
2865
7.31
15.13
1326
9.21
16.35
1432
12.38
25.66
884
15.61
27.71
955
21.93
45.42
884
38.95
80.67
663
87.73
181.69
442
155.83
322.71
331
196.38
348.57
358
243.82
504.91
265
307.25
545.36
285
350.94
726.76
221
442.27
785.00
238
lorse-pow'r
3ubic feet...
Devolutions
27.64
49.06
955
49.09
87.14
716
110.56
196.25
477
400
9624.00
Elorse-pow'r
3ubic feet...
Revolutions
4.82
7.49
3063
11.25
17.48
1531
19. o;
29.63
1021
33.77
52.45
1021
59.98
93.16
765
135.08
209.80
510
239.94
372.64
382
375.40
583.02
306
540.35
839.20
255
450
10207.79
Horse-pow'r
Cubic feet...
Revolutions
5.75
7.94
3249
13.43
18.54
1624
22.76
31.42
1083
40.29
55.63
1083
71.57
98.81
812
161.19
222.52
541
286.31
395.24
406
447.95
618.38
324
644.78
890.11
270
500
10759.96
Horse-pow'r
Cubic feet...
Revolutions
6.74
8.37
3426
15.73
19.54
1713
26.66
33.12
1142
47.20
58.64
1142
83.83
104.15
856
188.80
234.56
571
335.34
416.62
428
524.66
651.83
' 342
755.20
938.25
285
600
11786.94
650
12268.24
Horse-pow'r
Cubic feet...
62.04
64.24
1251
110.19
114.09
938
248.16
256.95
625
440.77
456.38
469
689.63
714.05
375
777.62
743.21
390
992.65
1027.80
31tt
1119.29
1069.77
325
Revolutions
Horse-pow'r
Cubic feet ..
69.95
66.86
1302
124.25
118.75
976
279.82
267.44
651
497.01
475.02
488
Revolutions
700
12731.34
~50~
13178.19
Horse-pow'r
Cubic feet...
Revolutions
78.18
69.38
1351
138.86
123.23
1013
312.73
277.54
675
555.46
492.95
506
869.06
771.26
405
1250.92
1110.16
337
•"
Horse-pow'r
Cubic feet...
86.70
71.82
1399
154.00
127.56
1049
346.83
287.28
699
616.03
510.25
524
963.82
798.33
419
1387.34
1149.13
319
Revolutions
i^:
....
800
13610.40
Horse-pow'i
Cubic feet...
95.52
74.17
1444
169.66
131.74
1083
382.09
296.70
722
678.66
526.99
542
1061.81
824.51
433
1528.36
1186.81
361
Revolutions
900
14436.00
Horse-pow'r
Cubic feet...
Revolutions
113.98
78.67
1532
202.45
139.74
1149
455.94
314.70
766
809.82
558.96
574
1267.02
874.53
459
1823.76
1258.81
383
1000
15216.89
Horse-pow'i
Cubic feet. .
133.50
82.93
1615
237.12
147,30
1210
534.01
331.72
807
948.48
589.19
605
1483.97
921.83
484
2136.04
1326.91
( 403
Revolutions
THE POWER OF OCEAN WAVES.
Albert W. Stahl, U. S. N. (Trans. A. S. M. E., xiii. 438), gives the following
formulae and table, based upon a theoretical discussion of wave motion:
The total energy of one whole wave-length of a wave Hfeet high, L feet
long, and one foot in breadth, the length being the distance between succes-
sive crests, and the height the vertical distance between the crest and the
trough, is E - 8LH* (l - 4.935 |^) foot-pounds.
The time required for each wave to travel through a distance equal to its
own length is P = A/ £-*$» seconds, and the number of waves passing any
600
WATER-POWER.
gO /5~l23
given point In one minute is JV = -- =» 60 ,|/ —-• Hence the total energy
of an indefinite series of such waves, expressed in horse-power per foot of
breadth, is
By substituting various values for H-*-L, within the limits of such values
actually occurring in nature, we obtain the following table of
TOTAL ENERGY OF DEEP-SEA WAVES IN TERMS OP HOUSE-POWER PER FOOT
OF BREADTH.
Ratio of
Length of
Waves to
Height of
Waves.
Length of Waves in Feet.
25
50
75
100
150
200
(300
400
50
40
30
20 •
15
10
5
.04
.06
.12
.25
.42
.98
3.80
.23
.86
.64
1.44
2.83
5.53
18.68
.64
1.00
1.77
3.96
6.97
15.24
51 48
1.31
2.05
8.64
8.13
14.31
31.29
105.68
342
5.65
10.02
21 79
39.43
86.22
291.20
7.43
11.59
20.57
45. 08
80.94
177.00
597.78
20.46
31.95
56.70
12G.70
223.06
487.75
1647. Gl
42.01
65.58
116.38
260.08
457.89
1001.25
3381.60
The figures are correct for trochoidal deep-sea waves only, but they give
a close approximation for any nearly regular series of waves in deep water
and a fair approximation for waves in shallow water.
The question of the practical utilization of the energy which exists iu
ocean waves divides itself into several parts :
1. The various motions of the water which may be utilized for power
purposes.
2. The wave motor proper. That is, the portion of the apparatus in direct
contact with the wat^r, and receiving and transmitting the energy thereof ;
ogether with the mechanism for transmitting this energy to the machinery
for utilizing the same.
. Regulating devices, for obtaining a uniform motion from the irregular
and more or less spasmodic action of the waves, as well as for adjusting the
apparatus to the state of the tide and condition of the sea.
4. Storage arrangements for insuring a continuous and uniform output of
power during a calm, or when the waves are comparatively small.
The motions that may be utilized for power purposes are the following:
1. Vertical rise and fall of particles at and near the surface. 2. Horizontal
to-and-fro motion of particles at and near the surface. 3. Varying slope of
surface of wave. 4. Impetus of waves rolling up the beach in the form of
breakers. 5. Motion of distorted verticals. All of these motions, except the
last one mentioned, have at various times been proposed to be utilized for
power purposes; and the last is proposed to be used in apparatus described
by Mr. Stahl.
The motion of distorted verticals is thus defined: A set of particles, origi-
nally in the same vertical straight line when the water is at rest, does not
remain in a vertical line during the passage of the wave; so that the line
connecting a set of such particles, while vertical and straight in still water,
becomes distorted, as well as displaced, during the passage of the wave, its
upper portion moving farther and more rapidly than its lower portion.
Mr. StahPs paper contains illustrations of several wave-motors designed
upon various principles. His conclusions as to their practicability is as fol-
lows: " Possibly none of the methods described in this paper may ever prove
commercially successful; indeed the problem may not be susceptible of a
financially successful solution. My own investigations, however, so far as I
have yet been able to carry them, incline me to the belief that wave-power
can and will be utilized on a paying basis.'1
Continuous Utilization of Tidal Power. (P. Decceur, Proc.
Inst. C. E. 1890.)— In connection with the training-walls to be constructed iu
PUMPS A^TD PUMPING ENGINES. 601
the estuary of the Seine, it is proposed to construct large basins, by means
of which the power available from the rise and fall of the tide could be util-
ized. The methou proposed is to have two basins separated by a bank rising
above high water, within which turbines would be placed. The upper basin
would be in communication with the sea during the higher one third of the
tidal range, rising, and the lower basin during the lower one third of the
tidal range, falling. If H be the range in feet, the level in the upper
basin would never fall below %H measured from low water, and the
level in the lower basin would never rise above *4H. The available head
varies between 0.53H and 0.807?, the mean value being %H. If S square feet
be the area of the lower basin, and the above conditions are fulfilled, a
quantity l/SSH cu. ft. of water is delivered through the turbines in ttie space
of 9*4 hours. The mean flow is, therefore, SH -7-99,900 cu. ft. per sec., and,
the mean fall being %}H, the available gross horse-power is about 1/30S'//2,
where Sf is measured in acres. This might be increased by about one third
if a variation of level in the basins amounting to \^H. were permitted. But
to reach this end the number of turbines would have to be doubled, the
mean head being reduced to %H, and it would be more difficult to transmit
a constant power from the turbines. The turbine proposed is of an improved
model designed to utilize a large flow with a moderate diameter. One has
been designed to produce 300 horse-power, with a minimum head of 5 ft. 3
in. at a speed of 15 revolutions per minute, the vanes having 13 ft. internal
diameter. The speed would be maintained constant by regulating sluices.
PUMPS AND PUMPING ENGINES.
Theoretical Capacity of a Pump.— Let Q' = cu. ft. per min.;
O' = Amer. gals, per min. = 7.4805^'; d = diam. of pump in inches; I =
stroke in inches; N = number of single strokes per min.
Capacity in cu. ft. per min. = Q' = ^ . -^L . .?"_ .oo04545AaaZ;
Capacity in gals, per min. Gf - . -~ .......... = .0034iVcW;
Capacity in gals, per hour ...................... =.204.ZV"d3Z.
Diameter required for a ) , _ 46 .g _ 17 <*.
given capacity per min. ja °'yj/ Jn " 17<15
If v = piston speed in feet per min., d =s 13.54 A/ ^ = 4.95<|/ .
If the piston speed is 100 feet per min.:
Nl = 1200, and d = 1.354 Vty = .495 V~G", Gf = 4.08d* per min.
The actual capacity will be from 60# to 95# of the theoretical, according to
the tightness of the piston, valves, suction-pipe, etc.
Theoretical Horse-power required to raise Water to a
given Height,— Horse-power =
Volume incu. ft. per min. X pressure per sq. ft. __ Weight X height of lift
33,000 ~ ~
Q'
in Ib
62.36$', P« 144p,p = .433H,
HP = ®'P = ®H X 144 X -483 - ®'H - G'H -
™ 33,000 33,000 ~~ 529.2 " 3958.7'
HP = WH - Q' X 62.36 X 2.309p _ Q'p _ G'p
38 33,000 ~~ 33,000 " 229.2 " 1714.5*
For the actual horse-po\yer required an allowance must be made for the
friction, slips, etc., of engine, pump, valves, and passages.
= cu. ft. per min.; Gf = gals, per min. ; W = wt. in Ibs. ; P = pressure
bs. per sq. ft.; p = pressure in Ibs. per sq. in.; H = height of lift in ft.;
62.36$', P« 144p,p = .433H, H = 2.309p, G' = 7.4805^.
602
tFATER-POWER.
Depth of Suction.— Theoretically a perfect pump will draw water
from a height of nearly 34 feet, or the height corresponding to a perfect
vacuum (14 7 Ibs. X 2.309 = 33.95 feet); but since a perfect vacuum cannot be
obtained, on account of valve-leakage, air contained in the water, and the
vapor of the water itself, the actual height is generally less than 30 feet.
When the water is warm the height to which it can be lifted by suction de-
^,.^00*10 rtvi a™»rmnt r»f HIP inf»rfifl.sftd t>rpssure of thevat)or. In Diimoiner hot
Temp.
F.
Absolute
Pressure
ofVapor,
Ibs. per
sq. in.
Vacuum
in
Inches of
Mercury.
Max.
Depth
of
Suction,
feet.
Temp.
F.
Absolute
Pressure
of Vapor,
Ibs. per
sq. in.
Vacuum
in
Inches of
Mercury.
Max.
Depth
of
Suction,
. feet.
102.1
126.3
141.6
153.1
162.3
170.1
176.9
1
2
3
4
5
6
7
27.88
25.85
23.83
21.78
19.74
17.70
15.67
31.6
29.3
27.0
24.7
22.3
20.0
17.7
182.9
188.3
193.2
197.8
202.0
205.9
209.6
8
9
10-
11
12
13
14
13.63
11.60
9.56
7.52
5.49
3.45
1.41
15.4
13.1
10.8
8.5
6.2
3.9
l.G
Amount of Water raised by a Single-acting Lift-pump.
—It is common to estimate that the quantity of water raised by a
single-acting bucket-valve pump per minute is equal to the number of
strokes in one direction per minute, multiplied by the volume traversed by
the piston in a single stroke, on the theory that the water rises in the pump
only when the piston or bucket ascends; but the fact is that the column of
water does not cease flowing when the bucket descends, but flows on con-
tinuously through the valve in the bucket, so that the discharge of the
pump, if it is operated at a high speed, may amount to nearly double that
calculated from the displacement multiplied by the number of single strokes
in one direction.
Proportioning the Steam-cylinder of a Direct-acting
Pump.— Let
A =-• area of steam-cylinder; a = area of pump-cylinder;
D = diameter of steam-cylinder; d = diameter of pump-cylinder;
P = steam-pressure, Ibs. persq. in.;p = resistance per sq. in. on pumps;
H = head ^ 2.309p; p = .433tf ;
work done in pump-cylinder
E = efficiency of the pump = work done by the steam.cylinde-r.
ap
A=EP< a~
A__p__ .433H.
a" EP" EP '
E is commonly taken at 0.7 to 0.8 for ordinary direct-acting pumps. For
the highest class of pumping-engines it may amount to 0.9. The steam-
pressure P is the mean effective pressure, according to the indicator-dia-
gram ; the water-pressure p is the mean total pressure acting on the pump
plunger or piston, including the suction, as could be shown by an indicator-
diagram of the water-cylinder. The pressure on the pump-piston is fre-
quently much greater than that due to the height of the lift, on account of
the friction of the valves and passages, which increases rapidly with velocity
of flow.
Speed of "Water through Pipes and Pump-passages.—
The speed of the water is commonly from 100 to 200 feet per minute. If 200
feet per minute is exceeded, the loss from friction may be considerable.
/ gallons per minute
The diameter of pipe required is 4.95|/ velocity in feet per minute'
For a velocity of 200 feet per minute, diameter =C35 x ^gallons permiu.
H- 2.309#P -; If E = 75*. H = 1.732P— .
PUMPS.
603
Sizes of Direct-acting Pumps.— The tables on this and the next
page are selected from catalogues of manufacturers, as representing the
two common types of direct-acting pump, viz., the single-cylinder and the
duplex. Both types are now made by most of the leading manufacturers.
Tlie Deane Single Boiler-feed or Pressure Pump.— Suitable
for pumping clear liquids at a pressure not exceeding 150 Ibs.
Sizes.
Capacity
^
£
ID
aj
at Given
1
•8
0
u |
Speed.
1 "E*
§
o|
03
03
'
E
c
w
$
&JD
_o
pH
o
®
"S
a
•
O
£j
qq
g
5
C5
QQ
O
3
2
5
.07
150
10
3/^
2^4
5
.09
150
13
4
2%
5
.10
150
15
4
2/^>
5
.11
150
16
4^4
3
5
.15
150
22
5
8^4
7
.25
125
31
51^3
3%
7
.33
125
42
7
8
.49
120
58
7
41^,
10
.69
100
69
7^j£
5
10
.85
100
85
8
5
12
1.02
100
102
10
6
12
1.47
100
147
12
7
12
2.00
100
200
14
8
12
2.61
100
261
Sizes of Pipes.
Tlie Beano Single Tank or Light-service Pump.— These
pumps will all stand a constant working pressure of 75 Ibs. on the water-
cylinders.
Sizes.
1
Capacity
CO
Sizes of Pipes.
.
E
at Given
Jj
0)
r}
1
fe
Speed.
.s
O
a
.S
1
°*
1
.s
a
•
&
i ">•>
It
n
|!
j«
Gallons
1
GQ
i
o
?
3
£
Width i
02
Exhaus
d
.2
• c;
s
02
Dischar
1
4
4
5
.27
130
35
33
9^
H
y
2
1^
5
4
7
.38
125
48
45^
15
34
1
3
2Jl2
5^4
51^6
7
.72
125
90
45^
15
*M
1
3
2^3
7L£
712
10
1.91
110
210
• 58
17
l
5
4
8
6
12
1.46
100
146
67
20^
i
1^2
4
4
6
n>
12
2.00
100
200
66
17
H
1
4
4
8
7
12
2 00
100
200
67
20^
i
1^2
5
4
8
8
12
2.61
100
261
68
30
i
1L^
5
5
10
8
12
2.G1
100
2G1
68^
30
1^13
2
5
5
8
10
12
4.08
100
408
68
20^
1
l^ij
8
8
10
10
12
4.08
100
408
68^
30
l^J
2
8
8
12
10
12
4.08
100
408
64
24
2
2^
8
8
10
12
12
5.87
100
587
68^
30
\\4,
2
8
8
12
12
12
5.87
10(?
587
64
28^
2/<w
2^>
8
8
10
12
18
8.79
70
616
95
25
W
2 "
8
8
12
12
18
8.79
70
616
95
28 Vo
2
2^
8
8
12
14
18
12.00
70
840
95
28^
2
2^
8
8
14
16
18
15.66
70
1093
95
34
2
2^
12
10
10
16
18
15.66
70
1096
95
34
2
2^
12
10
18
16
18
15.66
70
1096
97
34
3
31^
12
10
16
18
24
26.42
50
1321
115
40
2
2/^
14
12
18
18
24
26.42
50
1321
135
40
3
3^
14
12
G04
WATEfl-POWER.
Efficiency of Small Direct-acting Pumps.— Chas. E. Emery,
in Kepoi'is of Judges of Philadelphia Exhibition, 1876, Group xx., says: "Ex-
periments made with steam-pumps at the American Institute Exhibition of
mac ordinary steam-pumps rareiy require less man rw pouuas or steam
per hour for'each horse-power uti'lized in raising' water,.pquivalent to a duty
of only 15,000,000 foot-pounds per 100 pounds of coal. With larger steam-
pumps, particularly when they are proportioned for the work to be done,
the duty will be materially increased."
The Worthington Duplex Pump.
STANDARD SIZES FOR ORDINARY SERVICE.
>> '
3 O .
Sizes of Pipes for
««id
•° §
T3 o ^
Short Lengths.
E
t
u
O.-^ gj
2^
To be increased as
W)
Ail
3^3
flT3
3 g- a
length increases.
a
9
'E
.2 a
S'ba
fe"S •
£a5^
1
0>
o^
in
5"J8
cPc *
08
J2
ft ^S
<U £« 03
02
|
•~o
a> fe-g
lU
S^o
.
ft
£
CM
0
GO
1 =
1 1§
SB|
0^0
c
.&
0)
ft
1
1
*0
p
cSi|^
is£
its
•|
"co
a
!»
o
0)
o
£
s
bfl
'H,^
D- 3 3
^0^
5&£
c
eg
c3
^
.2
CJ
§
a.
2o2
.5S5
I
M
a
.2
Q
s
J
s
£
O
Q
OQ
w
CO
3
3
2
3
.04
100 to 250
8 to 20
2%
%
V6
\y.
!
4Jx>
2^4
4
.10
100 to 200
20 to 40
4
1,12
%
2
\\^
51/1
3J4
5
.20
100 to 200
40 to 80
5
M
\\^
2/^
1^
6
4
6
.33
100 to 150
70 to 100
5%
i
1J^
3
2
7^
41^
6
.42
100 to 150
85 to 125
6%
i/4
2
4
3
71^
5
6
.51
100 to 150
100 to 150
7
11^
2
4
3
714
4^£
10
.69
75 to 125
100 to 170
6%
i^
2
4
3
9
5/4
10
.93
75 to 125
135 to 230
?HJ
2
^Hj
4
3
10
6
10
1.22
75 to 125
180 to 300
gi^
2
gi^
5
4
10
7
10
1.66
75 to 125
245 to 410
9%
2
2^>
6
5
12
7
10
1.66
75 to 125
245 to 410
Q7/
i^
3 ~
6
5
14
7
10
1.66
75 to 125
245 to 410
97^
i^
3
6
5
12
8V£
10
2.45
75 to 125
365 to 610
12
^i
3
6
5
14
8J4
10
2.45
75 to 125
365 to 610
12
^
3
6
5
16
8V&
10
2.45
75 to 125
365 to 610
12
^a
3
6
5
gL£
10
2.45
75 to 325
365 to 610
12
3 i
31^
6
5
20 3
814
10
2.45
75 to 125
365 to 610
12
4
5
6
5
12
14
16
IOM
1014
10^4
10
10
10
3.57
3.57
3.57
75 to 125
7'5 to 125
75 to 125
530 to 890
530 to 890
530 to 890
1414
14H
i
3
3
3
8
8
8
7
7
18^
IOM
10
3.57
75 to 125
530 to 890
14^4
3 3
3J4
8
7
20
10^4
10
3.57
75 to 125
530 to 890
14^4
4
5
8
7
14
12
10
4.89
75 to 125
730 to 1220
17
~Hj
3
10
8
16
12
10
4.89
75 to 125
730 to 1220
17
2^4
3
10
8
18Vij
12
10
4.89
75 to 125
730 to 1220
17
3
31^
10
8
20
12
10
4.89
75 to 125
730 to 1220
17
4
5 "
10
8
18V<a
14
10
6.66
75 to 125
990 to 1660
3
31^
12
10
20
14
10
6.66
75 to 122
990 to 1660
19%
4
5
12
10
17
10
15
5.10
50 to 100
510 to 1020
14
3
3V*>
8
7
20
12
15
7.34
50 to 100
730 to 1460
17
4
5 "
12
10
20
15
15
11 47
50 to 100
1 1 4* tn 9 PQO
21
25
15
15
1L47
50 to 100 | 1145 to 2290
21
PUMPS.
Speed of Piston.— A piston speed of 100 feet per minute is commonly
assumed as correct in practice, but for short-stroke pumps this gives too
high a speed of rotation, requiring too frequent a reversal of the valves.
For long stroke pumps, 2 feet and upward, tin's speed may be considerably
exceeded, if valves and passages are of ample area.
Number of Strokes required to Attain a Piston Speed
from 50 to 125 Feet per Minute for Pumps having
Strokes from 3 to 18 Indies in Length*
03"S
si .
Length of Stroke in Inches.
<M ~
°.S g
3
4
5
6
7
8
10
12
15
18
is ®
£2 p<
Number of Strokes per Minute.
50
200
150
120
100
86
75
60
50
40
33
55
220
165
132
110
94
82.5
66
55
44
37
, 60
240
180
144
120
103
90
72
60
48
40
65
260
195
156
130
111
97.5
78
65
52
43
70
280
210
168
140
120
105
84
70
56
47
75
300
225
180
150
128
112.5
90
75
60
50
80
320
240
192
160
137
120
96
80
64
53
85
340
255
204
170
146
1-^7.5
102
85
68
57
90
360
270
216
180
154
135
108
90
72
60
95
380
285
228
190
163
142.5
114
95
76
63
100
400
300
240
200
171
150
120
100
80
67
105
420
315
252
210
180
157.5
126
JOS
84
70
110
440
330
264
220
188
165
132
110
88
73
115
460
345
276
230
197
172.5
138
115
92
77
120
480
360
288
240
206
180
144
120
90
80
125
500
375
300
250
214
187.5
150
125
100
83
Piston Speed of Pumpiug-engines. (John Birkinbine, Trans.
A. I. M. E , v. 451).)— In dealing with such a ponderous and unyielding sub-
stance as water there are many difficulties to overcome in making a pump
work with a high piston speed. The attainment of moderately high speed
is, however, easily accomplished. Well-proportioned pumping-engines of
large capacity, provided with ample water-ways and properly constructed
valves, are operated successfully against heavy pressures at a speed of 250 ft.
per minute, without "thug,1' concussion, or injury to the apparatus, and
there is no doubt that the speed can be still further increased.
Speed of "Water through Valves.— If areas through valves and
water passages are sufficient to give a velocity of 250 ft. per min. or less,
they are ample. The water should be carefully guided and not too abruptly
deflected. (F. W. Dean. Eng. News, Aug. 10, 1893.)
Boiler-feed Pumps.— Practice has shown that 100 ft. of piston speed
pei* minute is the limit, if excessive wear and tear is to be avoided.
The velocity of water through the suction-pipe must not exceed 200 ft.
per minute, else the resistance of the suction is too great.
The approximate size of suction-pipe, where the length does not exceed
25 ft. and there are not more than two elbows, may be found as follows :
7/10 of the diameter of the cylinder multiplied by 1/100 of the piston speed
in feet. For duplex pumps of small size, a pipe one size larger is usually
employed. The velocity of flow in the discharge-pipe should not exceed
500 ft. per minute. The volume of discharge and length of pipe vary so
greatly in different installations that where the water is to be forced more
than 50 ft. the size of discharge-pipe should be calculated for the particular
conditions, allowing no greater velocity than 500 ft. per minute. The size of
discharge-pipe is calculated in single-cylinder pumps from 250 to 400 ft. per
minute. Greater velocity is permitted in the larger pipes.
In determining the proper size of pump for a steam-boiler, allowances
must be made for a supply of water sufficient to cover all the demands of
engines, steam-heating, etc., up to the capacity of generator, and should not
be calculated simply according to the requirements of the engine. In prac-
tice engines use all the way from 12 up to 50, or more, pounds of steam per
H.P. per hour when being worked up to capacity. When an engine is over-
loaded or underloaded more water per H.P. will be required than when
operating at its rated capacity. The average run of horizontal tubular
£06
WATEK-POWER.
boilers will evaporate from 2 to 3 Ibs. of water per sq. ft. of heating-surface
per hour, but may be driven up to 6 Ibs. if the grate-surface is too large or
the draught too great for economical working.
Pump- Valves.— A. F. Nagle (Trans. A. S. M. E.,x. 521) gives a number
of designs with dimensions of double-beat or Cornish valves used in large
Dumping-engines, with a discussion of the theory of their proportions. The
following is a summary of the proportions of the valves described.
SUMMARY OP VALVE PROPORTIONS.
Location of Engine.
Diam. of Valve
in inches.
|||l
Ratio of Seat-
area to Inside Un-
balanced Area.
Pressure upon
Seat per sq. in.,
in Ibs.
g
Providence high-ser-
12
1 lb.
.
377 Ibs.
Good
Providence Cornish-
en^ine . . . •
16
reduced to
.66 lb.
1.28
12
680
Good
St. Louis Water Wks.
Milwaukee •* "
Chicago * "
4* U ««
»* U U
wood seats
Chicago Water Wks.
18
7
25
15
15
8
1.86
.40
1.41
1.31
1.16
.96
67
88
75
85
94
75
250
120
151
140
132
151
Some noise
j Some noise at
( high speed.
Noisy
*4
U
1
Mr. Nagle says : There is one feature in which the Cornish valves are
necessarily defective, namely, the lift must always be quite large, unless great
power is sacrificed to reduce it. It is undeniable that a small lift is prefer-
able to a great one, and hence it naturally leads to the substitution of
numerous small valves for one or several large ones. To what extreme re-
duction of size this view might safely lead must be left to the judgment of
the engineer for the particular case in hand, but certainly, theoretically, we
must adopt small valves. Mr. Corliss at one time carried the theory so
far as to make them only 1% inches in diameter, but from 3 to 4 inches is
the more common practice now. A small valve presents proportionately a
larger surface of discharge with the same lift than a larger valve, so that
whatever the total area of valve-seat opening, its full contents can be dis-
charged with less lift through numerous small valves than with one large
one.
Henry R. Worthington was the first to use numerous small rubber valves
in preference to the larger metal valves. These valves work well under all
the conditions of a city pumping-engine. A volute spring is generally used
to limit the rise of the valve.
In theLeavitt high-duty sewerage-engine at Boston (Am. Machinist, May
31, 1884), the valves are of rubber, %-inch thick, the opening in valve-seat
being 13}£ X 4U inches. The valves have iron face and back-plates, and
form their own ninges.
CENTRIFUGAL PUMPS.
Relation of Height of Lift to Velocity.— The height of lift
depends only on the tangential velocity of the circumference, every tangen-
tial velocity giving a constant height of lift— sometimes termed "head "—
whether the pump is small or large. The quantity of water discharged is in
proportion to the area of the discharging orifices at the circumference, or in
proportion to the square of the diameter, when the breadth is kept the same.
R. H. Buel (App. Cyc. Mech., ii, 606) gives the following:
Let Q represent the quantity of water, in cubic feet, to be pumped per
minute, h the height of suction in feet, h' the height of discharge in feet, and
d the diameter of suction-pipe, equal to the diameter of discharge-pipe, iu
CENTRIFUGAL PUMPS.
607
/ Q
feet; then, accord ing to Fink, d = 0.36 y /o i pi ' 0 feeing the accel
eration due to gravity.
If the suction takes place on one side of the wheel, the inside diameter of
the wheel is equal to 1.2d, and the outside to 2.4d. If the suction takes place
at both sides of the wheel, the inside diameter of the wheel is equal to 0.85d,
and the outside to 1.7d. Then the suction-pipe will have two branches, the
area of each equal to half the area of d. The suction-pipe should be as short
as possible, to prevent air from entering the pump. The tangential velocity
of the outer edge of wheel for the delivery Q is equal to 1.25 1/20 (h -f- hf)
feet per second.
The arms are six in number, constructed as follows : Divide the central
angle of 60°, which incloses the outer edges of the two arms, into any num-
ber of equal parts by drawing the radii, and divide the breadth of the wheel
in the same manner by drawing concentric circles. The intersections of the
several radii with the corresponding circles give points of the arm.
In experiments with AppohTs pump, a velocity of circumference of 500
ft. per min. raised the water 1 ft. high, and maintained it at that level
without discharging any; and double the velocity raised the water to foul
times the height, as the centrifugal force was proportionate to the squ&if
of the velocity; consequently,
500 ft. per min. raised the water 1 ft. without discharge.
1000 " *» " " " 4 " "
2000 " •' " " " 16 " " "
4000 " ^ " " " " 64 " " u
The greatest height to which the water had been raised \\ ithout discharge,
In the experiments with the 1-ft. pump, was 67.7 ft., with a velocity of 4153
ft. per min., being rather less than the calculated height, owing probably to
leakage with the greater pressure. A velocity of 1128 ft. per miu. raised the
water 5% ft. without any discharge, and the maximum effect from the
power employed in raising to the same height 5^ ft. was obtained at the
velocity of 1678 ft. per min., giving a discharge of 1400 gals, per miu. from
the 1-ft. pump. The additional velocity required to effect a discharge of
1400 gals, per min., through a 1-ft. pump working at a dead level without any
height of lift, is 550 ft. per min. Consequently, adding this number in each
case to the velocity given above, at which no discharge takes place, the fol-
lowing velocities are obtained for the maximum effect to be produced in
each case :
1050 ft. per min., velocity for 1 ft. height of lift.
1550 " " " *• 4 " " "
2550 " " " " 16 " •• ••
4550 •• •• " " 64 " '* **
Or, in general terms, the velocity in feet per minute for the circumference
of the pump to be driven, to raise the water to a certain height, is equal to
650 -f 500 I/height of lift in feet.
Lawrence Centrifugal Pumps9 Class B— For Lifts from
15 to 35 ft.
ll
Suction-
pipe, in.
fid
FS
|.|
5
if*
O£M c-
H.P. for
each foot
of lift.
it
P.
ji
It
§•5
cc
ft
.2 ft
ft
ji
£-L
w°°
jl
i*
3
4
5
6
8
6 "
6
8
i
2
3
4
5
6
8
25
70
100
250
450
700
1200
2000
.028
.05
.08
.15
.27
.36
.65
1.10
65
230
265
500
680
1032
1260
2460
10
12
15
18
24
30
36
10
12
15
18
24
30
36
10
12
15
18
24
30
36
3000
4200
7000
10000
18000
25000
35000
1.60
2.15
3.50
5.00
7.60
10.50
14.75
3000
6800
8840
10000
9000*
20000*
2200C*
* Without base.
The economical capacity corresponds to a flow not exceeding 10 ft. per
second in the delivery-pipe. Small pipes and high rate of flow cause a great
loss of power.
608
WATER-POWER.
Size of Pulleys, "Width of Kelts, and Revolutions per
Minute Necessary to Raise the Rated Quantity of Water
to Different Heights wit li Pumps of Class If.
JS
.2
S"3
c
«w'~
0 t^
~ JH
•S's
«w C
o ^
il
Rated
lantity of
ater.gals.
Height in Feet and Revolutions per Minute.
a
i
-2PH
£*
£
o£
6'
8'
10'
12'
16'
20'
25'
SO'
35'
&
~iu
5
5
3
70
520
590
665
720
835
930
1045
1125
1200
\y%
2
6
5
4
100
475
540
605
660
765
850
955
1025
1100
2
3
7
6
250
435
500
560
610
705
790
880
945
1000
3
4
10
7
7
450
400
465
520
570
655
730
815
880
945
4
5
14
11
8
700
355
410
454
595
575
640
715
765
8-25
5
6
16
11
9
1200
315
365
400
440
510
570
635
685
745
6
8
20
12
10
2000
234
270
300
330
385
425
475
500
555
8
10
22
12
10
3000
234
270
300
330
385
425
475
500
555
10
12
30
14
12
4200
160
185
200
220
255
285
318
340
360
19
15
36
16
15
7000
140
165
180
198
228
255
285
305
330
15
18
10
16
15
10000
125
145
160
173
200
225
250
270
290
13
24
18000
105
125
135
150
170
190
214
230
250 24
30
25000
95
106
118
130
148
165
185
204
215 30
36
35000
95
106
118
130
148
165
185
204
215 ;36
I
JEificiencies of Centrifugal and Reciprocating Punips.—
W. O. Webber (Trans. A. S. M. E., vii. 598) gives diagrams showing the
relative efficiencies of centrifugal and reciprocating pumps, from which the
following figures are taken for the different lifts stated :
Lift, feet:
2 5 10 15 20 25 30 35 40 50 60 80 100 120 160 200 240 280
Efficiency reciprocating pump:
30 .45 .55 .61 .66 .68 .71 .75 .77 .82 .85 .87 .90 .89 .88 .85
Efficiency centrifugal pump:
.50 .56 .64 .68 .69 .68 .66 .62 .58 .50 .40
The term efficiency here used indicates the value of W. H. P. -4- 1. H. P.,
or horse-power of the water raised divided by the indicated horse- power of
the steam -engiue,and does not therefore show the full efficiency of the pump,
but that of the combined pump and engine. It is, however, a very simple
way of showing the relative values of different kinds of pumping-engines
having their motive power forming a part of the plant.
The highest value of this term, given by Mr. Webber, is .9164 for a lift of
170ft.. and 3615 gals, per min. This was obtained in a test of the Leavitt
pumping-engine at Lawrence, Mass., July 24, 1879.
With reciprocating pumps, for higher lifts than 170 ft., the curve of effl
ciencies falls, and from 200 to 300 ft. lift the average value seems about;
.84. Below 170 ft. the curve also falls reversely and slowly, until at about 90
ft. its descent becomes more rapid, and at 35 ft. .727 appears the best
recorded performance. There are not any very satisfactory records below
this lift, but some figures are given for the yearly coal consumption and
total number of gallons pumped by engines in Holland under a 16-ft. lift,
from which an efficiency of .44 has been deduced.
With centrifugal pumps, the lift at which the maximum efficiency is ob-
tained is approximately 17 ft. At lifts from 12 to 18 ft. some makers of
large experience claim now to obtain from 65$ to 70$ of useful effect, but
.613 appears to be the best done at a public test under 14.7 ft. head.
The drainage-pumps constructed some years ago for the Haarlem Lake
were designed to lift 70 tons per min. 15 ft., and they weighed about 150
tons. Centrifugal pumps for the same work weigh only 5 tons. The weight
of a> centrifugal pump and engine to lift 10,000 gals, per min. 35 ft. high is
6 tons.
The pumps placed by Gwynne at the Ferrara Marshes, Northern Italy, in
1865, are, it is believed, capable of handling more water than other set of
pumping-engines in existence. The work performed by these pumps is the
lifting of 2000 tons per min.— over 600.000,000 gals, per 24 hours— on a mean
lift of about 10 ft. (maximum of 12.5 ft.). (See Engineering, 1876.)
The efficiency of centrifugal pumps seems to increase as the size of pump
DUTY TB1ALS OF PUMPING-ENGINES,
609
Increases, approximately as follows: A 2" pump (this designation meaning
always the size of discharge-outlet in inches of diameter), giving an effi-
ciency of 38#, a 3" pump 45#, and a 4" pump 52#, a 5" pump 60#, and a 6"
pump 64# efficiency.
Tests of Centrifugal Pumps,
W. O. Webber, Trans. A. S. M. E., ix. 237.
Maker.
An-
drews.
An-
drews.
An-
drews.
Heald
&
Sisco.
Heald
&
Sisco.
Heald
&
Sisco.
Berlin.
Schwartz-
kopff.
Size
Diam. discharge .
*' suction . . .
" disk
No. 9.
W
9%"
26"
191.9
1513.12
12.25
4.69
10.09
46.52
No. 9.
9^"
9M"
26"
195.5
2023.82
12.62
6.47
12.2
53.0
No. 9.
9!^"
9%"
26"
200.5
2499.33
13.08
8.28
14.38
57.57
No. 10.
10"
12"
30.5"
188.3
1673.37
12.33
5.22
8.11
64.5
No. 10.
10"
12"
30.5"
202.7
2044.9
12.58
6.51
10 74
60.74
No. 10.
10"
12"
30.5"
213.7
2371.67
13.0
7.81
14.02
55.72
No. 9.
w
10.3"
20.5"
500
1944.8
16.46
Rev. per minute.
Galls, per minute
Height in feet....
Water H.P
Dynamiter H.P.
Efficiency
11
73.1
Vanes of Centrifugal Pumps.— For forms of pump vanes, see
paper by W. O. Webber, Trans. A. S. M. E., ix. 228, and discussion thereon
by Profs. Thurston, Wood, and others.
The Centrifugal Pump used as a Suction Dredge.— The
Andrews centrifugal pump was used by Gen. Gillmore, U. S. A., in 1871, in
deepening the channel over the bar at the mouth of the St. John's River,
Florida. The pump was a No. 9, with suction and discharge pipes each 9
inches diam. It was driven at 300 revolutions per minute by belt from an
engine developing 26 useful horse-power.
Although 200 revolutions of the pump disk per minute will easily raise
3000 gallons of clear water 12ft. high, through a straight vertical 9 inch
pipe, 300 revolutions were required to raise 2500 gallons of sand and water
11 ft. high, through two inclined suction-pipes having two turns each, dis-
charged through a pipe having one turn.
The proportion of sand that can be pumped depends greatly upon its
specific gravity and fineness. The calcareous and argillaceous sands flow
more freely than the silicious, and fine sands are less liable to choke the
pipe than those that are coarse. When working at high speed, 50# to 55# of
sand can be raised through a straight vertical pipe, giving for every 10 cubic
yards of material discharged 5 to 5^ cubic yards of compact sand. With
the appliances used on the St. John's bar, the proportion of sand seldom
exceeded 45#, generally ranging from 30# to 35$ when working under the
most favorable conditions.
In pumping 2500 gallons, or 12.6 cubic yards of sand and water per minute,
there would therefore be obtained from 3.7 to 4.3 cubic yards of sand. Dur-
ing the early stages of the work, before the teeth under the drag had been
properly arranged to aid the flow of sand into the pipes, the yield was con-
siderably below this average. (From catalogue of Jos. Edwards & Co.,
Mfrs. of the Andrews Pump, New York.)
DUTY TRIALS OF PUMPING-ENGINES.
A committee of the A. S. M. E. (Trans., xii. 530) reported in 1891 on a
standard method of conducting duty trials. Instead of the old unit of
duty of foot-pounds of work per 100 Ibs. of coal used, the committee recom-
mend a new unit, foot-pounds of work per million heat-units furnished by
the boiler. The variations in quality of coal make the old standard unfit as
a basis of duty ratings. The new unit is the precise equivalent of 100 Ibs. of
coal in cases where each pound of coal imparts 10,000 heat-units to the
water in the boiler, or where the evaporation is 10,000 -*- 965.7 = 10.355 Ibs. of
water from and at 212° per pound of fuel. This evaporative result is readily
obtained from all grades of Cumberland bituminous coal, used in horizontal
return tubular boilers, and. in many cases, from the best grades of anthra-
cite coal.
610 WATER-POWER.
The committee also recommend that the work done be determined by
plunger displacement, after makiug a test for leakage, instead of by meas-
urement of. flow by weirs or other apparatus, but advise the use of such
apparatus when practicable for obtaining additional data. The following
extracts are taken from the report. When important tests are to be made
the complete report should be consulted.
The necessary data having been obtained, the duty of an engine, and other
Suantities relating to its performance, may be computed by the use of the
allowing formulae:
1 Dutr - Foot-pounds of work done
'uty - Total number of heat.units consumed x
(foofc.pounds).
C X 144
2. Percentage of leakage = • — ^ x 100 (per cent).
•A. X -" X -£•
3. Capacity = number of gallons of water discharged in 24 hours
A X L X N X 7.4805 X 24 AXLX NX 1.24675
D X 144 D
4. Percentage of total frictions,
I.H.P. -
(gallons).
-\
DX 60X33,000
or, in the usual case, where the length of the stroke and number of strokes
of the plunger are the same as that of the steam-piston, this last formula
becomes:
Percentage of total frictions = fl - j^^f £p ] X 100 (per cent).
In these formulae the letters refer to the following quantities:
A — Area, in square inches, of pump plunger or piston, corrected for area
of piston rod or rods;
P = Pressure, in pounds per square inch, indicated by the gauge on the
force main ;
p = Pressure, in pounds per square inch, correspond! '.ig to indication of the
vacuum-gauge on suction -main (or pressure-gauge, if the suction-
pipe is under a head). The indication of the vacuum-gauge, in
inches of mercury, may be converted into pounds by dividing it by
2.035;
s = Pressure, in pounds per square inch, corresponding to distance be-
tween the centres of the two gauges. The computation for this
pressure is made by multiplying the distance, expressed in feet, by
the weight of one cubic foot of water at the temperature of the
pump- well, and dividing the product by 144;
L = Average length of stroke of pump-plunger, in feet;
JV = Total number of single strokes of pump-plunger made during the trial;
As = Area of steam-cylinder, in square inches, corrected for area of piston-
rod. The quantity As X M.E.P., in an engine having more than ono
cylinder, is the sum of the various quantities relating to the respec-
tive cylinders;
Ls = Average length of stroke of steam -piston, in feet;
NS = Total number of single strokes of steam-piston during trial;
M.E.P. = Average mean effective pressure, in pounds per square inch,
measured from the indicator-diagrams taken from the steam-cylin-
der;
I.H.P. = Indicated horse-power developed by the steam-cylinder;
C = Total number of cubic feet of water which leaked by the pump-plunger
during the trial, estimated from the results of the leakage test;
D = Duration of trial in hours:
DUTY TRIALS OF PUMPING-EKGl^ES. 611
H = Total number of heat -units (B. T. IT.) consumed by engine = weight of
water supplied to boiler by main feed-pump X total heat of steam
of boiler pressure reckoned from temperature of main feed-water 4-
weight of water supplied by jacket-pump X total heat of steam of
boiler-pressure reckoned from temperature of jacket-water -f- weight
of any other water supplied X total heat of steam reckoned from its
temperature of supply. The total heat of the steam is corrected for
the moisture or superheat which the steam msy contain. No allow-
ance is made for water added to the feed-water, which is derived
from any source, except the engine or some accessory of the engine.
Heat added to the water by the use of a flue -heater at the boiler is
not to be deducted. Should heat be abstracted from the flue by
means of a steam reheater connected with the intermediate re-
ceiver of the engine, this heat must be included in the total quantity
supplied by the boiler.
Leakage Test of Pump.— The leakage of an inside plunger (the
only type which requires testing) is most satisfactorily determined by mak-
ing the test with the cylinder-head removed. A wide board or plank may
be temporarily bolted to the lower part of the end of the cylinder, so as to
hold back the water in the manner of a dam, and an opening made in the
temporary head thus provided for the reception of an overflow -pipe. The
plunger is blocked at some intermediate point in the stroke (or, if this posi-
tion is not practicable, at the end of the stroke), and the water from the
force main is admitted at full pressure behind it. The leakage escapes
through the overflow-pipe, and it is collected in barrels and measured. The
test should be made, if possible, with the plunger in various positions.
In the case of a pump so planned that it is difficult to remove the cylinder-
head, it may be desirable to take the leakage from one of the openings
which are provided for the inspection of the suction-valves, the head being
allowed to remain in place.
It is assumed that there is a practical absence of valve leakage. Exami-
nation for such leakage should be made, and if it occurs, and it is found to
be due to disordered valves, it should be remedied before making the plunger
test. Leakage of the discharge valves will be shown by water passing down
into the empty cylinder at either end when they are under pressure. Leak-
age of the suction-valves will be shown by the disappearance of water which
covers them.
If valve leakage is found which cannot be remedied the quantity of water
thus lost should also be tested. One method is to measure the amount of
water required to maintain a certain pressure in the pump cylinder when
this is introduced through a pipe temporarily erected, no water being al-
lowed to enter through the discharge valves of the pump.
Table of Data and Results.— In order that uniformity may be se-
cured, it is suggested that the data and results, worked out in accordance
with the standard method, be tabulated in the manner indicated in the fol-
lowing scheme :
DUTY TRIAL OF ENGINE.
DIMENSIONS.
1. Number of steam -cylinders
2. Diameter of steam-cylinders ins.
3. Diameter of piston-rods of steam-cylinders ins
4. Nominal stroke of steam-pistons , ft.
5. Number of water-plungers
6. Diameter of plungers ins.
7. Diameter of piston-rods of water-cylinders ins.
8. Nominal stroke of plungers ft.
9. Net area of steam-pistons — « ... sq. ins.
10. Net area of plungers sq. ins.
11. Average length of stroke of steam-pistons during trial ft.
12. Average length of stroke of plungers during trial ft.
(Give also complete description of plant.)
TEMPERATURES.
13. Temperature of water in pump-well degs.
14. Temperature of water supplied to boiler by main feed-pump., degs.
15. Temperature of water supplied to boiler from various other
sources.. degs.
612 WATER-POWER.
PEED-WATER.
16. Weight of water supplied to boiler by main feed-pump Ibs.
17. Weight of water supplied to boiler from various other sources. Ibs.
18. Total weight of feed-water supplied from all sources Ibs.
PRESSURES.
19. Boiler pressure indicated by gauge Ibs.
20. Pressure indicated by gauge on force main Ibs.
21 . Vacuum indicated by gauge on suction main ins.
22. Pressure corresponding to vacuum given in preceding line Ibs.
23. Vertical distance between the centres of the two gauges ins.
24. Pressure equivalent to distance between the two gauges Ibs.
MISCELLANEOUS DATA.
25. Duration of trial hrs.
26. Total number of single strokes during trial
27. Percentage of moisture in steam supplied to engine, or number
of degrees of superheating T % or deg,
28. Total leakage of pump during trial, determined from results of
leakage test Ibs.
29. Mean effective pressure, measured from diagrams taken from
steam-cylinders M.E.P.
PRINCIPAL RESULTS.
30. Duty ft. Ibs.
31. Percentage of leakage .....,£
32. Capacity gals.
33. Percentage of total friction %
ADDITIONAL RESULTS.
34. Number of double strokes of steam-piston per minute
35. Indicated horse-power developed by the various steam-cylinders I.H.P.
36. Feed- water consumed by the plant per hour Ibs.
37. Feed-water consumed by the plant per indicated horse-power
per hour, corrected for moisture in steam Ibs.
38. Number of heat units consumed per indicated horse-power
per hour B.T.U.
39. Number of heat units consumed per indicated horse-power
per minute B.T,U-
40. Steam accounted for by indicator at cut-off and release in the
various steam-cylinders Ibs.
41. Proportion which steam accounted for by indicator bears to
the feed-water consumption
42. Number of double strokes of pump per minute
43. Mean effective pressure, measured from pump diagrams ...... M.E.P.
44. Indicated horse-power exerted in pump-cylinders I.H.P.
45. Work done (or duty) per 100 Ibs. of coal ft. Ibs.
SAMPLE DIAGRAM TAKEN FROM STEAM-CYLINDERS.
(Also, if possible, full measurement of the diagrams, embracing pressures
at the initial point, cut-off, release, and compression ; also back pressure,
and the proportions of the stroke completed at the various points noted.)
SAMPLE DIAGRAM TAKEN FROM PUMP-CYLINDERS.
These are not necessary to the main object, but it is desirable to give
them.
DATA AND RESULTS OF BOILER TEST.
(In accordance with the scheme recommended by the Boiler-test Com-
mittee of the Society.)
VACUUM PUMPS— AIR-L.IFT PUMP.
Tlte Pulsometer.— In the pulsometer the water is raised by suction
into the pump-chamber by the condensation of steam within it, arid is then
forced into the delivery-pipe by the pressure of a new quantity of steam on
the surface of the water. Two chambers are used which work alternately,
one raising while the other is discharging.
Test of a Pulsometer.— A. test of a pulsometer is described by De Volson
Wood in Trans. A. S. M. E. xiii. It had a 3^-inch suction-pipe, stood 40 in.
high, and weighed 095 Ibs.
The steam-pipe was 1 inch in diameter. A throttle was placed about 2 feet
VACUUM PUMPS — AIR-LIFT PUMP.
613
from the pump, and pressure gauges placed on both sides of the throttle,
and a mercury well and thermometer placed beyond the throttle. The wire
drawing due to throttling caused superheating.
The pounds of steam used were computed from the increase of the tern
perature of the water in passing through the pump.
Pounds of steam X loss of heat = Ibs. of water sucked in X increase of temp.
Tha loss of heat in a pound of steam is the total heat in a pound of satu-
rated steam as found from ** steam tables " for the given pressure, plus the
heat of superheating, minus the temperature of the discharged water ; or
Ibs. water X increase of temp.
Pounds of steam = H - OASt - T. &
The results for the four tests are given in the following table :
Data and Results.
Number of Test.
1
2
3
4
Strokes per minute
71
60
57
64
Steam press. in pipe before throttl'g
Steam press, in pipe after throttl'g
114
19
110
30
127
43.8
104.3
26.1
Steam temp, after throttling,deg.F.
270.4
277
309.0
270.1
Steam am'nt of superheat'g.deg.F.
3.1
3.4
17.4
1.4
Steam used as det'd from temp., Ibs.
Water pumped Ibs
1617
404 786
931
186 362
1518
228 425
1019.9
248,053
Water temp. before entering pump,
75.15
80.6
76^3
70.25
Water temp., rise of
4.47
5.5
7.49
4.55
Water head by gauge on lift, ft
29.90
54.05
54.05
29.90
Water head by gauge on suction. . .
12.26
12.26
19.67
19.67
Water head by gauge, total (H)
42.16
66.31
73.72
49.57
Water head by measure, total (h)
32.8
57.80
66.6
41.60
Coeff. of friction of plant (h) H- (H)
0.777
0.877
0.911
0.839
Efficiency of pulsometer
0.012
0.0155
0.0126
0.0138
Effic. of plant exclusive of boiler. . .
00093
0.0136
0.0115
0.0116
Effic. of plant if that of boiler be 0.7
Duty,if 1 Ib.evaporates 10 Ibs. water
0.0065 0.0095
10,511,400| 13,391,000
0.0080
11,059,000
0.0081
12,036,300
Of the two tests having the highest lift (54.05 ft.), that was more efficient
'which had the smaller suction (12.26 ft.), and this was also the most efficient
of the four tests. But, on the other hand, the other two tests having the
same lift (29.9 ft.), that was the more efficient which had the greater suction
(19.67), so that no law in this regard was established. The pressures used,
19, 30, 43.8, 26.1, follow the order of magnitude of the total heads, but are
not proportional thereto. No attempt was made to determine what press-
ure would give the best efficiency for any particular head. The pressure used
was intrusted to a practical runner, and he judged that when the pump was
running regularly and well, the pressure then existing was the proper one
It is peculiar that, in the first test, a pressure of 19 Ibs. of steam should pro-
duce a greater number of strokes and pump over 50# more water than 26.1
Ibs., the lift being the same, as in the fourth experiment.
Chas. E. Emery in discussion of Prof. Wood's paper says, referring to
tests made by himself and others at the Centennial Exhibition in 1876 (see
Report of the Judges, Group xx.), that a vacuum-pump tested by him in
1871 gave a duty of 4.7 millions; one tested by J. F. Flagg, at the Cincinnati
Exposition in 1875, gave a maximum duty of 3.25 millions. < Several vacuum
and small steam-pumps, compared later on the same basis, were reported
to have given duties of 10 to 11 millions, the steam-pumps doing no better
than the vacuum-pumps. Injectors, when used for lifting water not re-
quired to be heated, have an efficiency of 2 to 5 millions; vacuum-pumps
vary generally between 3 and 10; small steam-pumps between 8 and 15 ;
larger steam-pumps, between 15 and 30, and pumping-engiues between 30
and 140 millions.
A very high record of test of a pulsometer is given in Eng'g. Nov. 24, 1893,
p. 639, viz. : Height of suction 11.27 ft. ; total height of lift, 102.6 ft. ; hori-
zontal length of delivery-pipe, 118 ft. ; quantity delivered per hour, 26,188
British gallons. Weight of steam used per H. P. per hour, 93.76 Ibs. ; work
614 WATER-POWER.
done per pound of steam 21,345 foot-pounds, equal to a duty of 21,345,000
foot-pounds pe • 100 Ibs. of coal, if 10 Ibs of steam were generated per
pound of coal.
The Jet-pump.— This machine works by means of the tendency of a
stream or jet of fluid to drive or carry contiguous particles of fluid along
with it. The water-jet pump, in its present form, was invented by Prof.
James Thomson, and first described in 1852. In some experiments on a
small scale as to the efficiency of the jet-pump, the greatest efficiency was
found to take place when the depth from which the water was drawn by the
suction-pipe was about nine tenths of the height from which the water fell
to form the jet ; the flow up the suction-pipe being in that case about one
fifth of that of the jet, and the efficiency, consequently, 9/10 X 1/5 = 0.18.
This is but a low efficiency; but it is probable that it may be increased by
improvements in proportions of the machine. (Rankine, S. E.)
Tlie Injector when used as a pump has a very low efficiency. (See
Injectors, under Steam-boilers.)
Air-lift Pump.— The air-lift pump consists of a vertical water-pipe
with its lower end submerged in a well, and a smaller pipe delivering air
into it at the bottom. The rising column in the pipe consists of air mingled
with water, the air being in bubbles of various sizes, and is therefore lighter
than a column of water of the same height; consequently the water in the
pipe is raised above the level of the surrounding water. This method of
raising water was proposed as early as 1797, by Loescher, of Freiberg, and
was mentioned by Collon in lectures in Paris in 1876, but its first practical
application probably was by Werner Siemens in Berlin in 1885. Dr. J. G.
Pohle experimented on the principle in California in 1886, and U. S. patents
on apparatus involving it were granted to Pohle and Hill in the same year.
A paper describing tests of the air-lift pump made by Randall, Browne and
Behr was read before the Technical Society of the Pacific Coast in Feb. 1890.
The diameter of the pump-column was 3 in., of the air-pipe 0.9 in., and
of the air-discharge nozzle % in. The air-pipe had four sharp bends and a
length of 35 ft. plus the depth of submersion.
The water was pumped from a closed pipe-well (55 ft. deep and 10 in. in
diameter). The efficiency of the pump was based on the least work theo-
retically required to compress the air and deliver it to the receiver. If the
efficiency of the compressor be taken at 70$, the efficiency of the pump and
compressor together would be 70# of the efficiency found for the pump
alone.
For a given submersion (h) and lift (I/), the ratio of the two being kept
within reasonable limits, (H) being not much greater than (ft), the efficiency
was greatest when the pressure in the receiver did not greatly exceed the
head due to the submersion. The smaller the ratio H •*• ft, the higher was
the efficiency.
The pump, as erected, showed the following efficiencies :
ForH-f-/i = 0.5 1.0 1.5 2.0
Efficiency = 50# 40# 30# 25£
The fact that there are absolutely no moving parts makes the pump
especially fitted for handling dirty or gritty water, sewage, mine water,
and acid or alkali solutions in chemical or metallurgical works.
In Newark, N. J., pumps of this type are at work having a total capacity
of 1,000,000 gallons daily, lifting water from three 8-in. artesian wells. The
Newark Chemical Works use an air-lift pump to raise sulphuric acid of 1.72°
gravity. The Colorado Central Consolidated Mining Co., in one of its mines
at Georgetown, Colo., lifts water in one case 250 ft., using a series of lifts.
For a full account of the theory of the pump, and details of the tests
above referred to, see Eng^g News, June 8, 1893.
THE HYDRAULIC RAM.
Efficiency.— The hydraulic ram is used where a considerable flow of
water with a moderate fall is available, to raise a small portion of that flow
to a height exceeding that of the fall. The following are rules given by
Eytelwein as the results of his experiments (from Rankine):
Let Q be the whole supply of water in cubic feet per second, of which q is
lifted to the height h above the pond, and Q — q runs to waste at the depth
H below the pond; L, the length of the supply-pipe, from the pond to the
waste-clack ; D, its diameter in feet; then
Volume of air vessel = volume of feed pipes
THE HYDEAULIC BAM.
615
= 1.12 — 0.2 y|/~ when — does not exceed 20.
Jd 11
1 •*- (l 4- J0£f / nearly, when — does not exceed 12.
D'Aubuisson gives
Clark, using five sixths of the values Riven by D'Aubuisson's formula, gives i
Ratio of lift to fall 4 6 8 10 12 14 16 18 20 22 24 26
Efficiency per cent 72 61 62 44 87 31 25 19 14 9 4 0
Prof. R. C. Carpenter (Eng'g Mechanics, 1894) reports the results of four
tests of a ram constructed by Rumsey & Co., Seneca Falls. The ram was
fitted for pipe connection for l^-inch supply and ^-inch discharge. The
supply-pipe used was l^j inches in diameter, about 50 feet long, with 3 elbows,
so that it was equivalent to about '05 feet of straight pipe, so far as resist-
ance is concerned. Each run was made with a different stroke for the waste
or clack-valve, the supply and delivery head being constant; the object of
the experiment was to find that stroke of clack-valve which would give the
highest efficiency.
Length of stroke, per cent
100
80
60
46
52
56
61
66
Supply head feet of water
5 67
5.77
5 58
5 65
Delivery head, feet of water
19.75
297
19.75
296
19.75
301
19.75
297.5
Total water supplied, pounds
1615
1567
1518
1455 5
64.9
66
74.9
70
The efficiency, 74.9, the highest realized, was obtained when the clack-valve
travelled a distance equal to 60# of its full stroke, the full travel being 15/16
of one inch.
Quantity of Water Delivered by the Hydraulic Ram.
(Chad wick Lead Works.)— From 80 to 100 feet conveyance, one seventh of
supply from spring can be discharged at an elevation five times as high as
the fall to supply the ram; or, one fourteenth can be raised and discharged
say ten times as high as the fall applied.
Water can be conveyed by a ram 3000 feet, and elevated 200 feet. The
drive-pipe is from 25 to 50 feet long.
The following table gives the capacity of several sizes of rams, the dimen-
sions of tho pipes to be used, and the size of the spring or brook to which
they are adapted:
Size of
Ram.
Quantity of Water
Furnished per
Min. by the Spring
or Brook to which
the Ram is
Adapted.
Caliber of
Pipes.
Weight of Pipe (Lead), if Wrought
Iron, then of Ordinary Weight.
1
&
Discharge.
Drive-pipe
for head
or fall not
over 10 ft.
Discharge-
pipe for not
over 50 ft.
rise.
Discharge-
pipe for
over 50 ft.
and not ex-
ceeding
100 ft. in
height.
No. 2
3
14 4
" 5
" 6
" 7
"10
Gals, per min.
% to 2
J* :: I
6 *• 14
12 u 25
20 " 40
25 •« 75
inch.
x
i*
4
inch.
P
per foot.
21bs.
3 "
5 "
8 "
13 "
13 "
21 "
per foot.
10 ozs.
12 "
12 "
lib. 4 "
2 "
3 "
7 "
per foot.
lib.
1 " 4 ozs.
1 " 4 oza
2 "
3 "
4 «*
8 "
616 WATER-POWER.
HYDRAULIC-PRESSURE TRANSMISSION.
Water under high pressure (700 to 2000 Ibs. per square inch and upward^
affords a very satisfactory method of transmitting power to a distance,
especially for the movemant of heavy loads at small velocities, as by cranes
and elevators. The system consists usually of one or more pumps capable
of developing the required pressure; accumulators, which are vertical cylin-
ders with heavily-weighted plungers passing through stuffing-boxes in the
upper end, by which a quantity of water may be accumulated at the pres-
sure to which the plunger Is weighted; the distributing-pipes; and the presses,
cranes, or other machinery to oe operated.
The earliest important use of hydraulic pressure probably was in the
Bramah hydraulic press, patented in 1796. Sir W. G. Armstrong in 1846 was
one of the pioneers in the adaptation of the hydraulic system to cranes. The
use of the accumulator by Armstrong led to the extended use of hydraulic
machinery. Recent developments and applications of the system are largely
due to Ralph Tweddell, of London, and Sir Joseph Whitworth. Sir Henry
Bessemer, in his patent of May 13, 1856, No. 1292, first suggested the use of
hydraulic pressure for compressing steel ingots while in the fluid state.
'The Gross Amount of Energy of the water under pressure stored
in the accumulator, measured in foot-pounds, is its volume in cubic feet X
its pressure in pounds per square foot. The horse-power of a given quantity
steadily flowing is H.P. = = .2618p£, in which Q is the quantity flowing
55(J
in cubic feet per second and p the pressure in pounds per square inch.
The loss of energy due to velocity of flow in the pipe is calculated as fol-
lows (R. GK Blaine, Eng'g, May 22 and June 5, 1891):
According to D'Arcy, every pound of water loses — — times its kinetic
energy, or energy due to its velocity, in passing along a straight pipe L feet
in length and D feet diameter, where A is a variable coefficient. For clean
cast-iron pipes it may be taken as A = .005 (l + jojj), or for diameter in
inches = d.
d= 16 1 2 3 456 7 8 9 10 12
A = .015 .01 .0075 .00667 .00625 .006 .00583 .00571 .00563 .00556 .0055 .00543
The loss of energy per minute is 60 X 62.36$ X -~- |~» and the horse-
power wasted in the pipe is W= •6363A^-p-)3> in which A varies with the
diameter as above, p = pressure at entrance in pounds per square inch.
Values of .6363A for different diameters of pipe in inches are:
d= ^ 1 2 3 4 5 6 7 8 9 10 12
.00954 .00636 .00477 .00424 .00398 .00382 .00371 .00363 .00358 .00353 .00350 .00345
Efficiency; of Hydraulic Apparatus.— The useful effect of a
direct hydraulic plunger or ram is usually taken at 93$. The following is
given as the efficiency of a ram with chain-and-pulley multiplying gear
properly proportioned and well lubricated:
Multiplying.... 2 to 1 4 to 1 6 to 1 8 to 1 lOtol 12 to 1 14 to 1 16 to 1
Efficiency^.... 80 76 72 67 63 59 54 50
With large sheaves, small steel pins, and wire rope for multiplying gear
the efficiency has been found as high as 66$ for a multiplication of 20 to 1.
Henry Adams gives the following formula for effective pressure in cranes
and hoists:
P = accumulator pressure in pounds per square inch;
m = ratio of multiplying power;
E = effective pressure in pounds per square inch, including all allowances
for friction;
E = P(.84 - .02m).
J. E. Tuit (Eng'g, June 15, 1888) describes some experiments on the fric-
tion of hydraulic jacks from 3*4 to 13%-inch diameter, fitted with cupped
leather packings. The friction loss varied from 5.6$ to 18.8$ according to
the condition of the leather, the distribution of the load on the ram, etc.
The friction increased considerably with eccentric loads. With hemp pack-
ing a plunger, 14-inch diameter, showed a friction loss of from 11.4$ to 3.4$,
the load being central, and from 15.0$ to 7.6$ with eccentric load, the per*
centage of loss decreasing in both cases with increase of load,
HYDRAULIC-PRESSURE TRANSMISSION. 617
Thickness of Hydraulic Cylinders.— From a table used by Sir
W. G. Armstrong we take the following, for cast-iron cylinders, for an in-
terior pressure of 1000 Ibs. per square inch:
Diam. of cylinder, inches.. 2 4 6 8 10 12 16 20 24
Thickness, inches.. 0.832 1.146 1.552 1.875 2.222 2.578 3.19 3.69 4.11
For any other pressure multiply by the ratio of that pressure to 1000.
These figures correspond nearly to the formula t = 0.175d -f 0.48, in which
t = thickness and d =•• diameter in inches, up to 16 inches diameter, but for
20 inches diameter the addition 0.48 is reduced to 0.19 and at 24 inches it
disappears. For formulae for thick cylinders see page 287, ante.
Cast iron should not be used for pressures exceeding 2000 Ibs. per square
inch. For higher pressures steel castings or forged steel should be used.
For working pressures of 750 Ibs. per square inch the test pressure should
be 2500 Ibs. per square inch, and for 1500 Ibs. the test pressure should not be
less than 3500 Ibs.
Speed of Hoisting by Hydraulic Pressure.— The maximum
allowable speed for warehouse cranes is 6 feet per second; for platform
cranes 4 feet per second; for passenger and wagon hoists, heavy loads, 2
feet per second. The maximum speed under any circumstances should
never exceed 10 feet per second.
The Speed of Water Through Valves should never be greater
than 100 feet per second.
Speed of Water Through Pipes.-— Experiments on water at 1600
Ibs. pressure per square inch flowing into a flanging-machine ram, 20-inch
diameter, through a J^-inch pipe contracted at one point to J^-inch, gave a
velocity of 114 feet per second in the pipe, and 456 feet at the reduced sec-
tion. Through a J^-inch pipe reduced to %-inch at one point the velocity
was 213 feet per second in the pipe and 381 feet at the reduced section In a
}£-inch pipe without contraction the velocity was 355 feet per second.
For many of the above notes the author is indebted to Mr. John Platt,
consulting engineer, of New York.
High-pressure Hydraulic Presses in Iron-works are de-
scribed by R. M. Daelen, of Germany, in Trans. A. I. M. E. 1892. The fol-
lowing distinct arrangements used in different systems of high-pressui3
hydraulic work are discussed and illustrated:
1. Steam-pump, with fly-wheel and accumulator.
2. Steam pump, without fly-wheel and with accumulator.
3. Steam-pump, without fly-wheel and without accumulator.
In these three systems the valve-motion of the working press is operated
In the high-pressure column. This is avoided in the following:
4. Single-acting steam-intensifier without accumulator.
5. Steam-pump with fly-wheel, without accumulator and with pipe-circuit.
6. Steam-pump with fly-wheel, without accumulator and without pipe-
circuit.
The disadvantages of accumulators are thus stated: The weighted plungers
which formerly served in most cases as accumulators, cause violent shocks
in the pipe-line when changes take place in the movement of the water,
so that in many places, in order to avoid bursting from this cause, the pipes
are made exclusively of forged and bored steel. The seats and cones of the
metallic valves are cut by the water (at high speed), and in such cases only
the most careful maintenance can prevent great losses of power.
Hydraulic Power in London.— The general principle involved
is pumping water into mains laid in the streets, from which service-pipes
are carried into the houses to work lifts or three-cylinder motors when
rotatory power is required. In some cases a small Pelton wheel has been
tried, working render a pressure of over 700 Ibs. on the square inch. Over 55
miles of hydraulic mains are at present laid (1892).
The reservoir of power consists of capacious accumulators, loaded to a
pressure of 800 Ibs. per square inch, thus producing the same effect as if
large supply-tanks were placed at 1700 feet above the street-level. The
water is taken from the Thames or from wells, and all sediment is removed
therefrom by filtration before it reaches the main engine-pumps.
There are over 1750 machines at work, and the supply is about 6,500,000
gallons per week.
It is essential that the water used should be clean. The storage-tank ex-
tends over the whole boiler-house and coal-store. The tank is divided, and
a certain amount of mud is deposited here. It then passes through the sur-
face condenser of the engines, and it is turned into a set of filters, eight in
Dumber. The body of the filter is a cast-iron cylinder, containing a layer of
618 WATER-POWEfc.
granular filtering material resting upon a false bottom; under this Is the dis-
tributing arrangement, affording passage for the air, and under this the real
bottom of the tank. The dirty water is supplied to the filters from an over-
head tank. After passing through the filters the clean effluent is pumped
into the clean-water tank, from which the pumping-engines derive their
supply. The cleaning of the filters, which is done at intervals of 24 hours, is
effected so thoroughly in situ that the filtering material never requires to be
removed.
The engine-house contains six sets of triple-expansion engines. The
cylinders are 15-inch, 22-inch, 36 inch X 24-inch. Each cylinder drives a
single plunger-pump with a 5-inch ram, secured directly to the cross-head,
the connecting-rod being double to clear the pump. The boiler-pressure is
150 Ibs. on the square inch. Each pump will deliver 300 gallons of water per
minute under a pressure of 800 Ibs. to the square inch, the engines making
about 61 revolutions per minute. This is a high velocity, considering the
heavy pressure; but the valves work silently and without perceptible shock.
The consumption of steam is 14.1 pounds per horse per hour.
The water delivered from the main pumps passes into the accumulators.
The rams are 20 inches in diameter, and have a stroke of 23 feet. They are
each loaded with 110 tons of slag, contained in a wrought-iron cylindrical
box suspended from a cross-head on the top of the ram.
One of the accumulators is loaded a little more heavily than the other, so
that they rise and fall successively; the more heavily loaded actuates a stop-
valve on the main steam-pipe. If the engines supply more water than is
wanted, the lighter of the two rams first rises as far as it can go; the other
then ascends, and when it has nearly reached the top, shuts off steam and
checks the supply of water automatically.
The mains in the public streets are so constructed and laid as to be per-
fectly trustworthy and free from leakage.
Every pipe and valve used throughout the system is tested to 2500 Ibs. per
square inch before being placed on the ground and again tested to a reduced
pressure in the trenches to insure the perfect tightness of the joints. The
jointing material used is gutta-percha.
The average rate obtained by the company is about 3 shillings per thou-
sand gallons. The principal use of the power is for intermittent work in cases
where direct pressure can be employed, as, for instance, passenger elevators,
cranes, presses, warehouse hoists, etc.
An important use of the hydraulic power is its application to the extin-
guishing of fire by means of Greathead's injector hydrant. By the use of
these hydrants a continuous fire-engine is available.
Hydraulic Riveting-machines.— Hydraulic riveting was intro-
duced in England by Mr. R. H. Tweddell. Fixed riveters were first used about
1868. Portable riveting-machines were introduced in 1872.
The riveting of the large steel plates in the Forth Bridge was done by small
portable machines working with a pressure of 1000 Ibs. per square inch. In
exceptional cases 3 tons per inch was used. (Proc. Inst. M. E., May, 1889.)
An application of hydraulic pressure invented by Andrew Higginson, of
Liverpool, dispenses with the necessity of accumulators. It consists of a
three-throw pump driven by shafting or worked by steam, and depends
partially upon the work accumulated in a heavy fly-wheel. The water in its
passage from the pumps and back to them is in constant circulation at a
very feeble pressure, requiring a minimum of power to preserve the tube of
water ready for action at the desired moment, when by the use ot a tap the
current is stopped from going back to the pumps, and is thrown upon the
§iston of the tool to be set in motion. The water is now confined, and the
riving-belt or steam-engine, supplemented by the momentum of the heavy
fly-wheel, is employed in closing up the rivet, or bending or forging the ob-
ject subjected to its operation.
Hydraulic Forging.— In the production of heavy forgings from
cast ingots of mild steel it is essential that the mass of metal should be
operated on as equally as possible throughout its entire thickness. When
employing a steam-hammer for this purpose it has been found that the ex-
ternal surface of the ingot absorbs a large proportion of the sudden impact
of the blow, and that a comparatively small effect only is produced on the
central portions of the ingot, owing to the resistance offered by the inertia
of the mass to the rapid motion of the falling hammer— a disadvantage that
is entirely overcome by the slow, though powerful, compression of the
hydraulic forging-press, which appears destined to supersede the steam-
hammer for the production of massive steel forgings.
HYDRAULIC-PRESSURE TRANSMISSION. 619
In the Allen forging-press the force-pump and the large or main cylinder
jf the press are in direct and constant communication. There are no inter-
mediate valves of any kind, nor has the pump any clack-valves, but it
simply forces its cylinder full of water direct into the cylinder of the press,
and receives the same water, as it were, back again on the return stroke.
Thus, when both cylinders and the pipe connecting them are full, the large
ram of the press rises and falls simultaneously with each stroke of the
pump, keeping up a continuous oscillating motion, the ram, of course,
travelling the shorter distance, owing to the larger capacity of the presa
cylinder. (Journal Iron and Steel Institute, 1891. See also illustrated article
in '* Modern Mechanism," page 668.)
For a very complete illustrated account of the development of the hy-
draulic forging-press, see a paper by R. H. Tweddell in Proc. Inst. C. E., vol.
cxvii. 1893-4.
Hydraulic Forging-press.— A 2000-ton forging-press erected at
the Couillet forges in Belgium is described in Eng. and M. Jour., Nov. 25, 1893.
The press is composed essentially of two parts— the press itself arid the
compressor. The compressor is formed of a vertical steam-cylinder and a
hydraulic cylinder. The piston-rod of the former forms the piston of the
latter. The hydraulic piston discharges the water into the press proper.
The distribution is made by a cylindrical balanced valve; as soon as the
pressure is released the steam-piston falls automatically under the action of
gravity. During its descent the steam passes to the other face of the piston
to reheat the cylinder, and finally escapes from the upper end.
When steam enters under the piston of the compressor-cylinder the pis-
ton rises, and its rod forces the water into the press proper. The pressure
thus exerted on the piston of the latter is transmitted through a cross-head
to the forging which is upon the anvil. To raise the cross-head two small
single-acting steam-cylinders are used, their piston-rods being connected to
the cross-head ; steam acts only on the pistons of these cylinders from below.
The admission of steam to the cylinders, which stand on top of the press
frame, is regulated by the same lever which directs the motions of the com-
pressor. The movement given to the dies is sufficient for all the ordinary
purposes of forging.
A speed of 30 blows per minute has been attained. A double press on the
same system, having two compressors and giving a maximum pressure of
6000 tons, has been erected in the Krupp works, at Essen.
The Aiken Intensifies (Iron Age, Aug. 1890.)— The object of the
machine is to increase the pressure obtained by the ordinary accumulator
which is necessary to operate powerful hydraulic machines requiring very
high pressures, without increasing the pressure carried in the accumulator
and the general hydraulic system.
The Aiken Intensifier consists of one outer stationary cylinder and one
inner cylinder which moves in the outer cylinder and on a fixed or stationary
hollow plunger. When operated in connection with the hydraulic bloom-
shear the method of working is as follows: The inner cylinder having been
filled with water and connected through the hollow plunger with the hydrau-
lic cylinder of the shear, water at the ordinary accumulator-pressure is ad-
mitted into the outer cylinder, which being four times the sectional area of
the plunger gives a pressure in the inner cylinder and shear cylinder con-
nected therewith of four times the accumulator-pressure— that is, if the ac-
cumulator-pressure is 500 Ibs. per square inch the pressure in the intensifier
will be 2000 Ibs. per square inch.
Hydraulic Engine driving an Air-compressor and a
Forging-hammer. (Iron Age, May 12, 1892.)'— The great hammer in
lerni, near Rome, is one of the largest in existence. Its falling weight
amounts to 100 tons, and the foundation belonging to it consists of a block
of cast iron of 1000 tons. The stroke is 16 feet 4% inches; the diameter of
the cylinder 6 feet 3J^ inches; diameterof piston-rod 13% inches; total height
of the hammer, 62 feet 4 inches. The power to work the hammer, as well as
the two cranes of 100 and 150 tons respectively, and other auxiliary appli-
ances belonging to it, is furnished by four air-compressors coupled together
and driven directly by water-pressure engines, by means of which the air is
compressed to 73.5 pounds per square inch. The cylinders of the water-
pressure engines, which are provided with a bronze lining, have a 13%-inch
bore. The stroke is 47^ inches, with a pressure of water on the piston
amounting to 264.6 pounds per square inch. The compressors are bored out
to 31^ inches diameter, and have 47%-inch stroke. Each of the four cylin-
ders requires a power equal to 280 horse-power. The compressed air is de-
620 FUEL.
livered into huge reservoirs, where a uniform pressure Is kept up by means
of a suitable water-column.
The Hydraulic Forging Plant at Bethlehem. Pa., is de-
scribed in a paper by R. W.Davenport, read before the [Society of Naval
Engineers and Marine Architects, 1893. It includes two hydraulic forging,
presses complete, with engines and pumps, one of 1500 and one of 4500 tons
capacity, together with two Whitworth hydraulic travelling forging-cranes
and other necessary appliances for each press; and a complete fluid-compres-
sion plant, including a press of 7000 tons capacity and a 125 ton hydraulic
travelling crane for serving it (the upper and lower heads of this press
weighing respectively about 135 and 120 tons).
A new forging- press has been designed by Mr. John Fritz, for the Bethle-
hem Works, of 14,000 tons capacity, to be run by engines and pumps of 15,000
horsepower. The plant is served by four open-hearth steel furnaces of a
united capacity of 120 tons of steel per heat.
Some References on Hydraulic Transmission — Reuleaux's
"Constructor;11 "Hydraulic Motors, Turbines, and Pressure-engines,'1 G.
Bodmer, London, 1889 ; Robinson's " Hydraulic Power and Hydraulic Ma-
chinery,'1 London, 1888 ; Colyer's "Hydraulic Stearn, and Hand-power Lift-
ing and Pressing Machinery," London, 1881. See also Engineering (London),
Aug. 1, 1884, p. 99, March 13, 1885, p. 262 ; May 22 and June 5, 1891, pp. 612,
665 ; Feb. 19, 1892, p. 25 ; Feb. 10, 1893, p. 170.
FUEL.
Theory of Combustion of Solid Fuel* vFrom Rankine, some-
what altered.)— The ingredients of every kind of fuel commonly used may
be thus classed: (1) Fixed or free carbon, which is left in the form of char-
coal or coke after the volatile ingredients of the fuel have been distilled
away. These ingredients burn either wholly in the solid state (C to CO2X or
part in the solid state and part in the gaseous state (CO -f O = CO3), the lat-
ter part being first dissolved by previously formed carbonic acid by the re-
action COj -j- C = 2CO. Carbonic oxide, CO, is produced when the supply
of air to the fire is insufficient.
(2) Hydrocarbons, such as olefiant gas, pitch, tar, naphtha, etc., all ot
which must pass into the gaseous state before being burned.
If mixed on their first issuing from amongst the burning carbon with a
large quantity of hot air, these inflammable gases are completely burned with
a transparent blue flame, producing carbonic acid and steam. When mixed
with cold air they are apt to be chilled and pass off unburned. When
raised to a red heat, or thereabouts, before being mixed with a sufficient
quantity of air for perfect combustion, they disengage carbon in fine pow-
der, and pass to the condition partly of marsh gas, and partly of free hydro-
gen; and the higher the temperature, the greater is the proportion of carbon
thus disengaged.
If the disengaged carbon is cooled below the temperature of ignition be«
fore coming in contact with oxygen, it constitutes, while floating in the gas,
smoke, and when deposited on solid bodies, soot.
But if the disengaged carbon is maintained at the temperature of ignition,
and supplied with oxygen sufficient for its combustion, it burns while float-
ing in the inflammable gas, and forms red, yellow, or white flame. The flame
from fuel is the larger the more slowly its combustion is effected. The
flame itself is apt to be chilled by radiation, as into the heating surface of a
steam-boiler, so that the combustion is not completed, and part of the gas
and smoke pass off unburned.
(3) Oxygen or hydrogen either actually forming water, or existing in
combination with the other constituents in the proportions which form water.
Such quantities of oxygen and hydrogen are to left be out of account in deter-
mining the heat generated by the combustion. If the quantity of water
actually or virtually present in each pound of fuel is so great as to make its
latent heat of evaporation worth considering, that heat is to be deducted
from the total heat of combustion of the fuel.
(4) Nitrogen, either free or in combination with other constituents. Thig
substance is simply inert.
(5) Sulphuret of iron, which exists in coal and is detrimental, as tending
to cause spontaneous combustion.
(6) Other mineral compounds of various kinds, which are also inert, and
form the ash left after complete combustion of the fuel, and also the rliukef
or glassy material produced by fusion of the ash, which tends to choxe the
grate.
FUEL.
621
Total Efeat of Combustion of Fuels. (Rankine.)— The follow-
ing table shows the total heat of combustion witb.oxygen of one pound of
each of the substances named in it, in British thermal units, and also in
Ibs. of water evaporated from 212°. It also shows*the weight of oxygen re-
quired to combine with each pound of the combustible and the weight of
air necessary in order to supply that oxygen. The quantities of heat are
given on the authority of MM. Favre and ttilbermann.
Combustible.
Lbs.Ox.y-
gen pev
Ib. Com-
bustible.
Lb. Air
(about).
Total Brit-
ish Heat-
units.
Evapora-
tive Power
from 212°
FM Ibs.
Hydrogen gas
8
IK
fi/7
36
6
12
153/7
62,032
4,400
14,500
21,344
from 21,700
to 19,000
10,000
64.2
4.55
15.0
22.1
from 22^
to 20
10.45
Carbon imperfectly burned so as
to make carbonic oxide..
Carbon perfectly burned so as to
make carbonic acid
Oiefiant gas, lib
Various liquid hydrocarbons, 1 Ib.
Carbonic oxide, as much as is made
by the imperfect combustion of
1 Ib. of carbon, viz., 2^g Ibs
IM
1
6
The imperfect combustion of carbon, making carbonicjoxide, produces
less than one third of the heat which is yielded by the complete combustion.
The total heat of combustion of any compound of hydrogen and carbon
is nearly the sum of the quantities of heat which the constituents would pro-
duce separately by their combustion. (Marsh-gas is an exception.)
In computing the total heat of combustion of compounds containing oxy-
gen as well as hydrogen and carbon, the following principle is to be
observed: When hydrogen and oxygen exist in a compound in the proper
proportion to form water (that is, by weight one part of hydrogen to eight
of oxygen), these constituents have no effect on the total heat of combus-
tion. ' If hydrogen exists in a greater proportion, only the surplus of hydro-
gen above that which is required by the oxygen is to be taken into account.
The following is a general formula (Dulong's) for the total heat of combus-
tion of any compound of carbon, hydrogen, and oxygen:
Let (7, H, and O he the fractions of one pound of the compound, which
consists respectively of carbon, hydrogen, and oxygen, the remainder being
nitrogen, ash, and other impurities. Let h be the total heat of combustion
of one pound of the compound in British thermal units. Then
h = 14,500 \ C+4.28(H- 40 }•
( , > 8 ' '
The following table shows the composition of those compounds which are
of importance, either as furnishing oxygen for combustion, as entering into
the composition, or as being produced by the combustion of fuel :
Names.
Symbol of
Chemical
Composition.
11}
gfi*
£°£
Chemical
Equivalent
by Weight.
Proportions
of Elements
by Volume.
^jr
N 77 -f O 23
H2 +O16
H3 +N14
C 12 + O 16
C 12 + O 32
C12 + H2
C 12-j-H 4
S 32 -f O 32
S 32 -f H 2
S 64 + C 12
100
18
17
28
44
14
16
64
34
76
N79H
H2 -
H3 -
C-
C-
C-
C-
-021
-0
-N
-0
hO2
^H2
-H4
H3O
NH3
CO
C03
CH2
CH4
S02
SH2
S|C
vJUeillall 6 V^omr*
Sulohuret of carbon — •
622
FUEL,
Since each Ib. of C requires 2% Ibs. of O to burn it to COa , and air contains
23% of O, by weight.. 2% -*- 0.83 or 11.6 Ibs. of air are required to burn 1 Ib. of C.
Analyses of Gases of Combustion.— The following are selected
from a large number of analyses of gases from locomotive boilers, to show
the range of composition under different circumstances (P. H. Dudley,
Trans. A. I. M. E , iv. 250):
Test.
C03
CO
O
N
1
18.8
2 5
2,5
81.fi
No smoke visible.
2
11.5
6
82.5
Old fire, escaping gas white, engine working hard.
8
8.5
8
83
Fresh fire, much black gas,
4
2.3
17.2
80.5
Old fire, damper closed, engine standing stilL
5
5.7
14.7
79. 6
: smoke white, engine working hard.
6
8.4
1.2
8.4
82
New fire, engine not working hard.
7
12
1
4.4
82.6
Smoke black, engine not working hard.
8
3.4
16.8
76.8
" dark, blower on, engine standing still.
9
6
13.5
81.5
" white, engine working hard.
In analyses on the Cleveland and Pittsburgh road, in every instance
when the smoke was the blackest, there was found the greatest percentage
of unconsumed oxygen in the product, showing that something besides the
mere presence for oxygen is required to effect the combustion of the volatile
carbon of fuels.
J. C. Hoadley (Trans. A. S. M. E., vi. 749) found as the mean of a great
number of analyses of flue gases from a boiler using anthracite coal :
C0a , 13.10 ; CO, 0.30 ; O, 11.94 ; N, 74.66.
The loss of heat due to burning O to CO instead of to CO2 was 2.13$. The
surplus oxjrgen averaged 113.3$ of the O required for the C of the fuel, the
average for different weeks ranging from 88.6$ to 137$.
Analyses made to determine the CO produced by excessively rapid firing
gave results from 2 54$ to 4.81$ CO and 5.12 to 8.01$ CO2 ; the ratio of C in
the CO to total carbon burned being from 43.80$ to 48.55$, and the number of
pounds of air supplied to the furnace per pound of coal being from 33.2 to
19.3 Ibs. The loss due to burning C to CO was from 27.84$ to 30.86 of the
full power of the coal.
Temperature of the Fire. (Rankine, S. E, p. 283.)— By temper,
ature of the fire is meant the temperature of the products of combustion at
the instant that the combustion is complete. The elevation of that temper-
ature above the temperature at which the air and the fuel are supplied to
the furnace may be computed by dividing the total heat of combustion of
one Ib. of fuel by the weight and by the mean specific heat of the whole
products of combustion, and of the air employed for their dilution under
constant pressure. The specific heat under constant pressure of these prod-
ucts is about as follows:
Carbonic-acid gas, 0.217; steam, 0475; nitrogen (probably), 0.245; air,
0.238; ashes, probably about 0.200. Using these data, the following results
are obtained for pure carbon and for olefiant gas burned, respectively, first,
in just sufficient air, theoretically, for their combustion, and, second, when
an equal amount of air is supplied in addition for dilution.
Fuel.
Products undiluted.
Products diluted.
Carbon.
Olefiant
Gas.
Carbon.
Olefiant
Gas.
21,300
31.86
0.248
7.9
271 0"
Total heat of combustion, per Ib.. .
Wt of products of combustion, Ibs.
Their mean specific heat . .....
14,500
13
0.237
3.08
4580°
21,300
16.43
0.257
4.22
5050°
14,500
25
0.238
5.94
2440°
Specific heat X weight
Elevation of temperature, F
[The above calculations are made on the assumption that the specific
heats of the gases are constant, but they probably increase with the in-
crease of temperature (see Specific Heat), in which case the temperature
would be less than those above given. The temperature would be further
CLASSIFICATION OP FUEL.
623
feduced by the heat rendered latent by the conversion Into steam of any
water present in the fuel.]
Rise of Temperature In Combustion of Oases. (Eng'g,
March 12 and April 2, 1886.)— It is found that the temperatures obtained
by experiment fall short of those obtained by calculation. Three theo-
ries have been given to account for this : 1. The cooling effect of the
sides of the containing vessel; 2. The retardation of the evolution of heat
caused by dissociation; 3. The increase of the specific heat of the gases at
very high temperatures. The calculated temperatures are obtainable only
on the condition that the gases shall combine instantaneously and simulta-
neously throughout their whole mass. This condition is practically impos-
sible in experiments. The gases formed at the beginning of an explosion
dilute the remaining combustible {gases and tend to retard or check the
combustion of the remainder.
CLASSIFICATION OF SOLID FUELS.
Gruner classifies solid fuels as follows (Eng'g and M'g Jour., July, 1874) :
Ratio — pr(
Name of Fuel. H
orO-f N*.
H
Pure cellulose
^portion <
Dharcoal
the Dry ]
0.28<§
.30 <g
.35 @
.40 (g
.50<§
.90 ra
of Coke or
yielded by
Pure Fuel.
^0.30
\ .35
\ .40
\ .50
\ .90
t .92
Wood (cellulose and encasing matter). ...
Peat and fossil fuel
7
6©5
5
4@!
1 <a 0.75
Lignite t or brown coal
The bituminous coals he divides into five classes as below:
)
Name of Type.
Elementary
Composition.
Ratio ~
0+N*.
Propor-
tion of
Coke
yielded
by Dis-
tilla-
Nature
and
Appear-
ance of
Coke.
Co
H.
0.
H
tion.
1. Long flaming dry )
coal,
75@80
5.5@4.5
19.5^15
4(^3
0.50®.60
j Pulveru-
I lent
2. Long flaming fat j
or coking coals, V
or gas coals, J
80,385
5.8©5
14.2@10
3@2
.60®.68
i Melted,
•< but
i friable.
' Melted;
3. Caking fat coals, )
some*
or blacksmiths' >
84@8£
5 ©4.5
11 @5.5
2<^l
.68®. 74
i what
coals, )
com-
pact. .
4. Short flaming fat)
! Melted;
or caking coals, V
coking coals, )
88©91
5.5@4.t
6.5®5.5
1
.74®. 82
very
com-
pact.
5, Lean or anthra- )
citic coals, J
90@93
4.5®4
5.5©3
1
.82®.90
j Pulveru
1 lent.
* The nitrogen rarely exceeds 1 per cent of the weight of the fuel.
t Not Including bituminous lignites, which resemble petroleums.
Rankine gives the following : The extreme differences in the chemical
composition and properties of different kinds of coal are very great. The
proportion of free carbon ranges from 30 to 93 per cent ; that of hydrocar-
bons of various kinds from 5 to 58 per cent ; that of water, or oxygen and
hydrogen in the proportions which form water, from an inappreciably
small quantity to 27 per cent ; that of ash, from 1}4 to 26 per cent.
The numerous varieties of coal may be divided into principal classes as
follows : 1, anthracite coal ; 2, semi- bituminous coal ; 3, bituminous coal ;
4, long tlaining or cannel coal ; 5, lignite or brown coal,
624 FUEL.
Diminution of H and O in Series from Wood to A n t hraeite
(Groves and Thorp's Chemical Technology, vol. i., Fuels, p. 58.)
Substance. Carbon, Hydrogen. Oxygen.
Woodyfibre 52.65 5.25 42.10
Peat from Vulcaire 59.57 5.96 8447
Lignite from Cologne 66.04 5.27 2869
Earthy brown coal 73.18 5.88 21.14
Coal from Belestat, secondary 75.06 5.84 19 10
Coal from Rive de Gier 89.29 5.05 5.66
Anthracite, Mayenne, transition formation 91.58 3.96 4.46
Progressive Change from Wood to Graphite.
(J. S. Newberry in Johnson's Cyclopedia.)
Wood Toss Li&~ loss Bitumi- T Anthra- T Graph-
wood. LOSS. nite L,oss.nouscoaLL,oss. cite Loss. it£
Carbon 49.1 18.65 30.45 12.35 18.10 3.57 14.53 1.42 13.11
Hydrogen... 6.3 3.25 3.05 1.85 1.20 0.93 0.27 0.14 0.13
Oxygen 44.6 24.40 20.20 18.13 2.07 1.32 0.65 0.65 0.00
100.0 4630 53.70 32.33 21.37 5.82 15.45 2.21 1334
Classification of Coals, as Anthracite, Bituminous, etc. —
Prof. Persifer Frazer (, Trans. A. I. M. E., vi, 430) proposes a classifica-
tion of coals according to their *' fuel ratio," that is, the ratio the fixed car-
bon bears to the volatile hydrocarbon.
In arranging coals under this classification, the accidental impurities, such
as sulphur, earthy matter, and moisture, are disregarded, and the fuel con-
stituents alone are considered.
Carbon Fixed Volatile
Ratio. Carbon. Hydrocarbon.
I. Hard dry anthracite. 100 to 12 100. to 92.31# 0. to 7.69#
II. Semi -anthracite 12 to 8 92.31to88.89 7.69toll.ll
III. Serni-bituminous. ... 8 to 5 88. 89 to 83. 33 11. 11 to 16. 67
IV. Bituminous 5 to 0 83.33to 0. 16.67tolOO
It appears to the author that the above classification does not draw the
line at the proper point between the semi-bituminous and the bituminous
coals, viz., at a ratio of C -*- V.H.C. = 5, or fixed carbon 83.33$, volatile hy-
drocarbon 16.67#, since it would throw many of the steam coals of Clearfield
and Somerset counties, Penn., and the Cumberland, Md., and Pocahontas,
Va., coals, which are practically of one class, and properly rated as
semi-bituminous coals, into the bituminous class. The dividing line be-
tween the semi -anthracite and semi-bituminous coals, C •*• V.H.C. = 8,
would place several coals known as semi-anthracite in the semi-bituminous
class. The following is proposed by the author as a better classification :
Carbon Ratio. Fixed Carbon. Vol. H.C.
I. Hard dry anthracite.. 100 to 12 100 to 92.31# 0 to 7.69#
II. Semi-anthracite 12 to 7 92.31 to 87.5 7. 69 to 12.5
til. Semi-bituminous 7 to 3 87.5 to 75 12.5 to 25
IV. Bituminous 3 to 0 75 to 0 25 to 100
Rhode Island Graphitic Anthracite.— A peculiar graphite is
found at Cranston, near Providence, R. I. It resembles both graphite and
anthracite coal, and has about the following composition (A. E. Hunt, Trans.
A. I. M. E., xvii., 678): Graphitic carbon, 78#; volatile matter, 2.60#; silica,
15.06$; phosphorus, .045#. It burns with extreme difficulty.
ANALYSES OF COALS.
Composition of Pennsylvania Anthracites. (Trans. A. I,
M. E., xiv., 706.)-Samples weighing 100 to 200 Ibs. were collected from Jots
of 100 to 200 tons as shipped to market, and reduced by proper methods to
laboratory samples. Thirty-three samples were analyzed by McCreath, giv-
ing results as follows. They show the mean character of the coal of the more
important coal-beds in the Northern field iu the vicinity of Wilkesbarre, in
the Eastern Middle (Lehigh) field in the vicinity of Hazleton, in the Westeru
ANALYSES OF COALS.
625
Middle field in the vicinity of Shenandoah, and in the Southern field between
Maucli Chunk and Tanmqua.
'
^
g^i
c
ll
il
s
cO
||
1|
M
1
3
2 s £§
jP
^
Of£B-°
0
Wharton...
E,. Middle
3.71
3.08
86.40
6.22
.58
3.44
28.07
Mammoth..
E. Middle
4.12
3.08
86.38
5.92
.49
3.45
27.99
Primrose . .
W. Middle
3.54
3.72
81.59
10.65
.50
4.36
21.93-
Mammoth .
W. Middle
3.16
3.72
81.14
11.08
.90
4.38
21.83
Primrose F
Southern
3.01
4.13
87.98
4.38
.50
4.48
21.32
Buck Mtn. .
W. Middle
3.04
3.95
82.66
9.88
.46
4.56
20.93
Seven Foot
W. Middle
3.41
3.98
80.87
11.23
.51
4.69
20.32
Mammoth .
Southern
3.09
4.28
83.81
8.18
.64
4.85
19.62
Mammoth .
Northern
3.42
4.38
83.27
8.20
.73
5.00
19.00
B. Coal Bed
Loyalsock
1.30
8.10
83.34
6.23
1.03
8.86
10.29
The above analyses were made of coals of all sizes (mixed). When coal is
screened into sizes for shipment the purity of the different sizes as regards
ash varies greatly. Samples from one mine gave results as follows:
Screened Analyses.
Name of Through Over Fixed
Coal. inches. inches. Carbon. Ash
Egg .......... 2.5 1.75 88.49 5.66
Stove ......... 1.75 1.25 83.67 1017
Chestnut ...... 1.25 .75 80.72 12 67
Pea ....... .... .75 .50 7905 14.66
Buckwheat... .50 .25 76.92 16.62
Bernice Basin, Pa., Coals.
Water. Vol. H.C. Fixed C. Ash. Sulphur.
Bernice Basin, Sullivan andi°tjf 3tf ' 8t2052 3£7 084
LycomingCos.; range of 8.. ^ g%
This coal is on the dividing-line between the anthracites and semi-anthra-
cites, and is similar to the coal of the Lykens Valley district.
More recent analyses (Trans. A. I. M. E., xiv. 721) give :
Water.' Vol. H.C. Fixed Carb. Ash. Sulphur.
Working seam ....... 065 9.40 83.69 5.34 0.91
60ft. below seam.... 3.67 15.42 71.34 8.97 0.59
The first is a semi-anthracite, the second a semi-bituminous.
Space Occupied by Anthracite Coal. (J. C. I. W., vol. iii.)— The
cubic contents of 2240 Ibs. of hard Lehigh coal is a little over 36 feet ; an
average Schuylkill W. A., 37 to 38 feet ; Shamokin, 38 to 39 feet; Lorberry,
nearly 41.
According to measurements made with Wilkesbarre anthracite coal from
the Wyoming Valley, it requires 32.2 cu. ft. of lump, 33.9 cu. ft. broken,
34.5 cu. ft. egg, 34.8 cu. ft. of stove, 35.7 cu. ft. of chestnut, and 36.7 cu. ft.
of pea, to make one ton of coal of 2240 Ibs. ; while it requires 28.8 cu. ft. of
lump, 30.3 cu. ft. of broken, 30.8 cu. ft. of egg, 31.1 cu. ft. of stove, 31.9 cu.
ft. of chestnut, and 32.8 cu. ft. of pea, to make one ton of 2000 Ibs.
Composition of Anthracite and Semi-bituminous Coals.
(Trans. A. I. M. E., vi. 430.)— Hard dry anthracites, 16 analyses by Rogers,
show a range from 94.10 to 82.47 fixed carbon, 1.40 to 9.53 volatile matter,
and 4.50 to 8.00 ash, water, and impurities. Of the fuel constituents alone,
the fixed carbon ranges from 98.53 to 89.63, and the volatile matter from 1.47
to 10.37, the corresponding carbon ratios, or C -*- Vol. H.C. being from 67.02
to 8.64.
Semi-anthracites.— 12 analyses by Rogers show a range of from 90.23 to
74.55 fixed carbon, 7.07 to 13.75 volatile matter, and 2.20 to 12.10 water, ash,
and impurities. Excluding the ash, etc., the range of fixed carbon is 92.75
to 84.42, and the volatile combustible 7.27 to 15.58, the corresponding carbon
ratio being from 12.75 to 5.41.
626
FUEL.
Semi-bituminous Coals.— 10 analyses of Penna. and Maryland coals give
fixed carbon 68.41 to 84.80, volatile matter 11.8 to 17.28, and ash, water, and
impurities 4 to 13.99. The percentage of the fuel constituents is fixed carbon
79.84 to 88.80, volatile combustible 11.20 to 20.16, and the carbon ratio 11.41 to
3.96.
American Semi-bituminous and Bituminous Coals.
(Selected chiefly from various papers in Trans. A. I. M. E.)
Moist-
ure.
Vol.
Hyd ro-
ar b on.
Fixed
Carbon
Ash.
Sul-
phur.
Penna. Semi-bituminous ;
Broad Top extremes of 5 . ...
( .79
13.84
78.46
6.00
.91
\ .78
17.38
76.14
4.81
.88
Somerset Co., extremes of 5
jl.27
11.89
14.33
18.51
77.77
65.90
6.63
10.62
0.66
3.08
Blair Co., average of 5
1.07
26.72
60.77
9.45
2.20
Cambria Co., average of 7, )
lower bed, B. f —
0.74
21.21
68.94
7.51
1.98
Cambria Co., 1, »
upper bed, C. f "
Cambria Co., South Fork, 1
1.14
17.18
15.51
73.42
78.60
6.58
5.84
1.41
Centre Co ,1
6.60
22 60
68.71
5.40
2^69
Clearfleld Co., average of 9, )
upper bed, C. f* "
0.70
23.94
69.28
4.62
1.42
Clearfield Co., average of 8, )
lower bed, D. \~*'
0.81
21.10
74.08
3.36
0.42
(0.41
20.09
66.69
2.65
0.43
Clearfield Co., range of 17 anal. .
1 to
to
to
to
to
(1.94
25.19
74.02
7.65
1.79
Bituminous :
Jefferson Co., average of 26
1.21
32.53
60.99
3.76
1.00
Clarion Co average of 7
1 97
38.60
54.15
4.10
1.19
Armstrong Co., 1
1 J8
42.55
49 69
4.58
2^00
Connellsville Coal
1.26
30.10
59^61
8.23
.78
Coke from ConnMlle (Standard)
.49
0.01
87.46
11.32
.69
1 03
36.49
59 05
2.61
81
Pittsburgh, Ocean Mine
.28
39.09
57.33
3.30
The percentage of volatile matter in the Kittaning lower bed B and the
Freeport lower bed D increases with great uniformity from east to west; thus*
Volatile Matter. Fixed Carbon.
Clearfield Co, bed D 20.09 to 25.19 68.73 to 74.76
" " " B 22.56 to 26.13 64.37 to 69.63
Clarion Co., " B 35.70 to 42.55 47.51 to 55.44
" D 37.15 to 40.80 51.39 to 56.36
Connellsville Coal and Coke. (Trans. A. I. M. E., xiii. 333.)—.
The Connellsville coal-field, in the southwestern part of Pennsylvania, is a
strip about 3 miles wide and 60 miles in length. The mine workings are
confined to the Pittsburgh seam, which here has its best development as to
size, and its quality best adapted to coke-making. It generally affords
from 7 to 8 feet of coal.
The following analyses by T. T. Morrell show about its range of composi-
tion :
Moisture. Vol. Mat. Fixed C. Ash. Sulphur. Phosph's.
Herold Mine .... 1.26 28.83 60.79 8.44 .67 .013
Kintz Mine 0.79 31.91 56.46 9.52 1.32 .02
In comparing the composition of coals across the Appalachian field, in the
western section of Pennsylvania, it will be noted that the Connellsville
variety occupies a peculiar position between the rather dry semi-bituminous
coals eastward of it and the fat bituminous coals flanking it on the west.
Beneath the Connellsville or Pittsburgh coal-bed occurs an interval of
from 400 to 600 feet of "barren measures," separating it from the lower
productive coal measures of Western Pennsylvania. The following tables
ANALYSES OF COALSo
627
Vol. Mat.
Fixed Carb.
Ash.
Sulphur.
3.45
89.06
5.81
0.30
15.52
74.28
9.29
0.71
22.35
68.77
5.96
1.24
31.38
60.30
7.24
1.09
33.50
61.34
3.28
0.86
37.66
54.44
5.86
0.64
show the great similarity in composition in the coals of these upper and
lower coal-measures iu the same geographical belt or basin.
Analyses from the Upper Coal-measures (Penna.) in a
Westward Order.
Localities. Moisture.
Anthracite 1.35
Cumberland, Md 0.89
Salisbury, Pa 1.66
Connellsville, Pa
Greensburg, Pa 1.02
Irwiu's, Pa, „ 1.41
Analyses from the Lower Coal-measures In a Westward
Order.
Localities. Moisture.
Anthracite 1.35
Broad Top 0.77
Bennington 1.40
Johnstown 1.18
Blairsville 0.92
Armstrong Co 0.96
Pennsylvania and Ohio Bituminous Coals. Variation
in Character of Coals of the same Beds in different Dis-
tricts.—From 50 analyses in the reports of the Pennsylvania Geological
Survey, the following are selected. They are divided into different groups,
and the extreme analysis in each group is given, ash and other impurities
being neglected, and the percentage in 100 of combustible matter being
alone considered.
Vol. Mat.
3.45
18.18
27.23
16.54
24.36
38.20
Fixed Carb.
89.06
73.34
61.84
74.46
62 22
52! 03
Ash.
5.81
6.69
6.93
5.96
7.69
5.14
Sulphur.
0 30
1.02
2.60
1.86
4.92
3.66
No. of
Analyses
Fixed
Carbon
Vol.
H. C.
Carbon
Ratio.
SVaynesburg coal-bed upper bench
5
Jefferson township, Greene Co
59.72
40 28
1 48
Hopewell township, Washington Co
Waynesburg coal-bed, lower bench.
9
53.22
46.78
1.13
Morgan township, Greene Co
Pleasant Valley, Washington Co
Sewickley coal-bed » ..
3
60.69
54.31
39.31
45.69
1.54
1.19
Whitely Creek Greene Co
64 39
35 61
1 80
Gray's Bank Creek, Greene Co
Pittsburgh coal-bed:
Upper bench, Washington Co
60.35
(60.87
39.65
39.13
1.52
1.65
Lower bench, u **....
5
I 59.11
j 63.54
40.89
36.46
1.20
1.74
3
j 50.97
J61.80
49.03
38.20
1.04
1.61
Frick & Co., Washington Co., average .
Lower bench, Greene Co
1
| 54 . 33
66.44
57.83
45.67
33.56
42.17
1.19
1.98
1.37
Somerset Co., semi-bituminous (showing
decrease of vol. mat. to the eastward).
Beaver Co., Pa
f 8
7
j 79.73
j 75.47
20.27
24.53
3.93
3.07
Diehl's Bank Georgetown
40.68
59 32
0 68
62.57
37.43
1 66
OHIO.
Pittsburgh coal-bed in Ohio:
61.45
38 55
1 59
Belmont Co., Ohio
Harrison Co., Ohio
j 63.46
166.14
J63.46
"J64.93
(60.92
36.54
33.86
36.54
35.07
39.08
.73
.95
.73
.85
.55
I 62.33
37.67
1.65
628
FUEL.
Analyses of Southern and Western Coals,
Moisture.
Vol. Mat.
Fixed C.
Ash.
Sul-
phur.
OHIO.
Hocking Valley
$ 5.00
32.80
53.15
9.05
0.44
MARYLAND.
( 7.40
95
29.20
19.13
60.45
72.70
2.95
6.40
0.93
0.78
VIRGINIA.
South of James River, 23 anal-
yses, range
Average of 23
1.23
j from 0.67
\ to 2.46
1.48
15.47
27.28
38.60
30 24
73.51
46.70
67.83
58 89
9.09
2.00
15.76
7 72
0.70
0.58
2.89
1 45
North of James Rixrer, eastern
outcrop,
Oarbonite or Natural Coke
Western outcrop, 11 analyses,
range
j 0.40
| 1.79
j 1.57
1 1.56
j from
1 to ..
18.60
23.96
9.64
14.26
21.33
30.50
26 06
71.00
59.98
79.93
81.61
54.97
70.80
63 75
10.00
14.28
8.86
2.24
3.35
22.60
10 06
0.23
Pocahontas Flat-top*
(Castner & Curran's Circular)
WEST VIRGINIA (New River.)
Quiunimont,t 3 analyses
Nuttalburgh t
j 0.52
1 0.62
from 0.76
' to 0.94
0.34
23.90
18.48
17.57
18.19
29.59
74.20
75.22
75.89
79.40
69.00
1,38
5.68
1.11
4.92
1,07
0.52
0.28
0.23
0.30
VIRGINIA and KENTUCKY.
Big Stone Gap Field, t 9 anal-
yses, range
KENTUCKY.
Pulaski Co., 3 analyses, range
Muhlenberg Co., 4 analyses,
range
Pike Co., Eastern Ky., 37 an-
1.35
j from 0.80
j to 2.01
(from 1.26
1 to 1.32
from 3. 60
to 7.06
from 1.80
to 1.60
25.35
31.44
36.27
35.15
39.44
30.60
38.70
26.80
41.00
70.67
54.80
63.50
60.85
52.48
58.80
53.70
67.60
50.37
2.10
1.73
8.25
1.23
5.52
3.40
6.50
3.80
7.80
0.08
0.56
1.72
0.40
1.00
0.79
3.16
0.97
0.03
Kentucky Cannel Coals, § 5 an-
alyses, range. ... ....
t from
f tO
40.2011
66.3011
59.80 coke
33.70 coke
8.81
4.80
0.96
1.32
TENNESSEE.
Scott Co., Range of several.^. .
Roane Co., Rockwood
H amilton Co. , Melville
Marion Co., Etna
j from 70
1 to 1.83
1.75
2.74
94
1.60
32.33
41.29
26.62
26.50
23.72
29.30
46.61
61.66
60.11
67.08
63.94
61.00
16.94
1.11
11.52
3.68
11.40
7.80-
3.37
0.77
1.49
91
1.19
Kelly Co Whiteside
1.30
21 80
74 20
2.70
GEORGIA.
Dade Co
1.20
23.05
60.50
15.16
0 84
ALABAMA.
Warren Field:
Jefferson Co., Birmingham..
" " Black Creek . .
Tuscaloosa Co
3.01
.12
1.59
42.76
26.11
38.33
48.30
71.64
54.64
3.21
2.03
5.45
2.72
.10
1 33
Cahaba Field, / Helena Vein .
Bibb Co l Coke Vein....
2.00
1.78
32.90
30.60
53.08
66.58
11.34
1.09
.68
.04
* Analyses of Pocahontas Coal by John Pattinson, F.C.S., 1889:
C. H. O. N. S. Ash. Water. Coke. °:
Lumps. . 86.51 4.44 4.95 0.66 0.61 1.54 1.29 78.8 21.2*
Small ... 83.13 4.29 5.33 0.66 0.56 4.63 1.40 79.8 20.2
t These coals are coked in beehive ovens, and yield from 63# to 64£ of coke.
JThis field covers about T-20 square miles in Virginia, and about 30 square
miles in Kentucky.
§ The principal use of the cannel coals is for enriching illuminating-gas.
II Volatile matter including moisture.
t Single analyses from Morgan, Rhea, Anderson, and Roane counties fall
within this range.
ANALYSES OF COALS.
629
Moisture.
Vol Mat.
Fixed C.
Ash.
Sul-
phur.
TEXAS.
Eagle Mine . . .
• 3 54
80 84
50 69
14 93
Sabinas Field, Vein I
1.91
20.04
62 71
15.35
" II
1.37
16.42
68.18
13.02
" III
0 84
29 35
50 18
19 63
it « (t jy^
0 45
21 6
45 75
29 1
31 *\
INDIANA.
Caking Coals.
Parke Co ....
4 50
• 45 50
45 50
4 50
2 35
45 25
51 60
0*80
Clay Co
7 00
39 70
47 30
6 00
3 50
45 00
46 00
2 50
Block Coals*
8 50
31 00
57 50
3 00
2 50
44 75
51 25
1 50
Daviess Co . ...
5 50
36 00
53 50
5 00
iLLINOIS.t
12 0
32 3
42 5
13 °
Seatonville
10 0
33 8
40 9
15 3
Christian Co. : Pana
Clinton Co. : Trenton
7.2
13 3
36.4
30 4
46.9
52 0
9K
• O
4 3
09
Fulton Co.: Cuba —
Grundy Co.: Morris.. .. ....
4.2
7 1
36.4
3° 1
48.6
49 7
10.8
11 1
Jackson Co. : Big Muddy
6 4
30 6
54 6
8 3
1 5
La Salle Co. : Streator
12.0
35.3
48 8
39
2 4
Logan Co.: Lincoln
8 4
35 0
44 5
12 1
Macon Co • Niantic
7 9
36 3
47 4
8 5
Macoupin Co.: Gillespie
Mt Olive
12.6
10 4
30.6
36 7
45.3
46 1
11.5
6 8
1.5
3 5
Staunton ....
6 3
57 1
°6 3
10 3
Madison Co. : Collinsville
Marion Co. : Centralia
McLean Co.: Pottstown ;...
Perry Co.: Du Quoin
9.3
8.3
4.6
11.3
29.9
34.0
35.5
30 3
40.8
45.5
45.5
49 9
16.1
8.0
14.4
8 5
3.9
09
San^amon Co. : Barclay
St. Clair Co. : St. Bernard
Vermilion Co * Danville....
10.8
14.4
11 0
27.3
30.9
32 6
44.8
4S.4
53 0
17.1
6.4
3 6
IA"
Will Co.: Wilmington
15.5
32.8
39.9
11.8
* Indiana Block Coal (J. S. Alexander, Trans. A. I. M. E., iv. 100).— The
typical block coal of the Brazil (Indiana) district differs in chemical coin-
position but little from the coking coals of Western Pennsylvania. The
physical difference, however, is .quite marked; the latter has a cuboid struc-
ture made up of bituminous particles lying against each other, so that under
the action of heat fusion throughout the mass readily takes place, while
block coal is formed of alternate layers of rich bituminous matter and a
charcoal-like substance, which is not only very slow of combustion, but so
retards the transmission of heat that agglutination is prevented, and the
coal burns away layer by layer, retaining its form until consumed.
An ultimate analysis of block coal from Sand Creek by E. T. Cox gave:
C, 72.94; H, 4.50; O, 11.77; N, 1.79; ash, 4.50; moisture, 4.50.
t The Illinois coals are generally high in moisture, volatile matter, sul-
phur and ash, and are consequently low in heating value. The range of
quality is a wide one. The Big Muddy coal of Jackson Co., which has a
high reputation as a steam coal, has, according to the analysis given above,
about 36$ of volatile matter in the total combustible, corresponding to the
coals of Western Pennsylvania and Ohio, while the Staunton coal has 68#,
ranking it among the poorer varieties of lignite. A boiler-test with this coal
(see p. 636, also Trans. A. S. M. E., v. 266) gave only 6.19 Ibs. water evapo-
rated from and at 212° per Ib. combustible. The Staunton coal is remarkable
for the high percentage of volatile matter, but, it is excelled in this respect by
630
FUEL.
Moisture
Vol. Mat
Fixed C,
Ash.
Sul-
phur.
IOWA.*
4.99.
35.27
25.37
34.37
Keb .
9.81
37.49
44.75
7 95
Flaglers .
9.84
40.16
37.69
12 31
9.18
40.42
39.58
10.82
MISSOURI.*
Brookfield
4.34
40.27
50.60
4.79
9.03
37.48
46 24
7 25
5.06
34.24
47.69
13 01
7 33
38 29
47.24
7 14
NEBRASKA.*
0.21
27.82
60.88
11.09
WYOMING.*
4.2
40.6
41.5
13 7
2.5
37.4
37 9
22 2
Goose Cr66k
9 7
40 2
46 3
3 8
13 92
36.78
42 03
7 27
.....
Deek Crock •
12 8
35 0
47 7
3 6
. •
Sheridan
6 04
42.37
35.57
16 02
COLORADO.:}:
Sunshine Colo, average
2.8
36.3
37.1
23 8
Newcastle " *'
1 7
37 95
48 6
11 6
ElMoro, " "
Crested Buttes u
1.32
1 10
38.23
23.20
55.86
72 60
3.59
3 10
UTAH (Southern).
Castledale • • • •
3 43
42 81
47 81 1
9 73
Cedar City
3.50
43.66
43. lit
5 95
OREGON.
15.45
41.55
34.95
8.05
2.53
17.27
44 15
32 40
6 18
1 37
Yaquina Bay
13 03
46 20
32.60
7 10
1 07
John Day River
4.55
40.00
48.19
7.26
60
6.54
34.45
52.41
5.95
.65
VANCOUVER ISLAND.
Comox Coal . . .
1.7
27.17
68.27
2.86
the Boghead coal of Linlitbgowshire, Scotland, an analysis of which by Dr.
Penny is as follows: Proximate— moisture 0.84; vol. 67.95; fixed C, 9.54, ash,
21.4; Ultimate— C,63. 94; H, 8.86; O, 4.70; N, 0.96; which is remarkable for the
high percentage of H.
* The analyses of Iowa, Missouri, Nebraska, and Wyoming coals are
selected from a paper on The Heating Value of Western Coals, by Wm.
Forsyth, Mech. Engr. of the C., B. & Q. R. R., Eng'g News, Jan. 17, 1895.
t Includes sulphur, which is very high. Coke from Cedar City analyzed :
Water and volatile matter, 1.42; fixed carbon, 76.70; ash, 16.61; sulphur, 5.27.
$ Colorado Coals.— The Colorado coals are of extremely variable com-
position, ranging all the way from lignite to anthracite. G. C. Hewitt
(Trans. A. I. M. E., xvii. 377) says : The coal seams, where unchanged
by heat and flexure, carry a lignite containing from 5$ to 20$ of water. In
the south-eastern corner of the field the same have been metamorphosed so
that in four miles the same seams are an anthracite, coking, and dry coal.
In the basin of Coal Creek the coals are extremely fat, and produce a hard,
bright, sonorous coke. North of coal basin half a mile of development
shows a gradual change from a good coking coal with patches of dry coal to
a dry coal that will barely agglutinate in a beehive oven. In another half
mile the same seam is dry. In this transition area, a small cross-fault
makes the coal fat for twenty or more feet on either side. The dry seams
also present wide chemical and physical changes in short distances. A soft
and loosely bedded coal has in a hundred feet become compact and hard
without the intervention of a fault. A couple of hundred feet has reduced
the water of combination from 12# to 5#.
Western Arkansas and Indian Territory. (H. M. Chance,
Trans. A. I. M. E. 1890.)— The Choctaw coal-field is a direct westward exten-
ANALYSES OF COALS.
631
sion of the Arkansas coal-field, but its coals are not like Arkansas coals, ex-
cept in the country immediately adjoining the Arkansas line.
The western Arkansas coals are dry semi-bituminous or semi-anthracitic
coals, mostly non-coking, or with quite feeble coking properties, ranging
from 14$ to 16$ in volatile matter, the highest percentage yet found, accord-
ing to Mr. Winslow's Arkansas report, being 17.655.
In the Mitchell basin, about 10 miles west from the Arkansas line, coal
recently opened shows 19$ volatile matter; the Mayberry coal, about 8 miles
farther west, contains 23$ volatile matter; and the Bryan Mine coal, about
the same distance west, shows 26$ volatile matter. About 30 miles farther
west, the coal shows from 38$ to 41^$ volatile matter, which is also about
the percentage in coals of the McAlester and Lehigh districts.
Western Lignites. (R. W. Raymond, Trans. A. I. M. E., vol. ii. 1873.)
C.
H.
N.
1.01
1.29
1.93
1.74
1.25
0.42
0.61
1.58
O.
S.
Mois-
ture.
4
Calorific
Power,
calories.
Monte Diabolo
Weber Canon, Utah
Echo Cafion Utah
59.72
64.84
69.84
64.99
69.14
56.24
55.79
67.67
67.58
5.08
4.34
3.90
3.76
4.36
3.38
3.26
4.66
7 40
15.69
15.52
10.99
15.20
9.54
21.82
19.01
12.80
13.42
14.42
3.92
1.60
0.77
1.07
1.03
0.81
0.63
0.92
0.63
2.08
8.94
9 41
9.17
11.56
8.06
13.28
16.52
3.08
5.18
14.68
5.64
3.00
3.40
1.68
6.62
4.05
4.18
9.28
5.77
3.80
5757
5912
6400
5738
6578
4565
4610
6428
7330
5602
Carbon Station, Wyo
Coos Bay, Oregon
Alaska
Baker Co., Ore
60.72
4.30
The calorific power is calculated by Dulong's formula,
8080C -f 34462(n - §),
x 0 /
deducting the heat required to vaporize the moisture and combined water,
that is, 537 calories for each unit of water. 1 calorie = 1.8 British thermal
units.
Analyses of Foreign Coals. (Selected from D. L. Barnes's paper
on American Locomotive Practice, A. S. C. E., 1893.)
Volatile
Matter.
Fixed
Carbon.
Ash.
Great Britain :
South Wales
8.5
88 3
3 2
6.2
92.3
1.5
Lancashire, Eng
Derbyshire, *'
Durham, "
Scotland
17.2
17.7
15 05
17 1
80.1
79.9
86.8
63.1
9 ***
IV. t
2.4
1.1
19.8
Semi-bit, coking coal.
Boghead cannel gas coal.
17 5
80 1
2 4
Semi-bit steam-coal
Staffordshire, Eng....
South America:
Chili, Conception Bay
" Chiroqui
Patagonia.
20.4
21.93
24.11
24 35
78.6
70.55
38.98
62 25
1.0
7.52
36.91
13.4
Brazil
40.5
57.9
1.6
Canada:
Nova Scotia ....
Cape Breton. . .
26.8
26.9
60.7
67.6
12.5
5.5
Australia
Australian lignite
Sydney, Soutli Wales..
Borneo .... .
15.8
14.98
26.5
64 .8
83.39
70.3
10.0
2.04
14.2
Van Diemen's Land
6.16
63.4
30.45
An analysis of Pictou, N. S., coal, in Trans. A. I. M. E., xiv. 560, is: Vol.,
?9.6.'i; carbon, 56.98; ash, 13.39; and one of Sydney, Cape Breton, coal is;
vol., 34.07; carbon, 61.43; ash, 4.50.
632 PtTEL.
Nixon's Navigation Welsh €oal is remarkably pure, and con-
tains not more than 3 to 4 per cent of ashes, giving 88 per cent of hard and
lustrous coke. The quantity of fixed carbon it contains would classify it
among the dry coals, but on account of its coke and its intensity of com-
bustion it belongs to the class of fat, or long-flaming coals.
Chemical analysis gave the following results: Carbon, 90.27; hydrogen,
4.39; sulphur, .69; nitrogen. .49; oxygen (difference), 4.16.
The analysis showed the following composition of the volatile parts: Car-
bon, 22.53; hydrogen, 34.96 ; O -f N + S, 42.51.
The heat of combustion was found to be, as a result of several experi-
ments, 8864 calories for the unit of weight. Calculated, according to its
composition, the heat of combustion would be 8805 calories = 15,849 British
thermal units per pound.
This coal is generally used in trial-trips of steam-vessels in Great Britain.
Sampling Coal for Analysis.— J. P. Kimball, Trans. A. I. M. E.,
Xii. 317, says : The unsuitable sampling of a coal-seam, or the improper
preparation of the sample in the laboratory, often gives rise to errors in de-
terminations of the ash so wide in range as to vitiate the analysis for all
practical purposes ; every other single determination, excepting moisture,
showing its relative part of the error. The determination of sulphur and
ash are especially liable to error, as they are intimately associated in the
slates.
Wm. Forsyth, in his paper on The Heating Value of Western Coals (Eng'g
News, Jan. 17, 1895), says : This trouble in getting a fairly average sample of
anthracite coal has compelled the Reading R. R. Co., in getting their samples,
to take as much as 300 Ibs. for one sample, drawn direct from the chutes, as
it stands ready for shipment.
The directions for collecting samples of coal for analysis at the C., B. & Q.
laboratory are as follows :
Two samples should be taken, one marked " average," the other •* select."
Each sample should contain about 10 Ibs., made up of lumps about the size
of an orange taken from different parts of the dump or car, and so selected
that they shall represent as nearly as possible, first, the average lot; second,
the best coal.
An example of the difference between an "average" and a "select"
sample, taken from Mr. ForsytlTs paper, is the following of an Illinois coal:
Moisture. Vol. Mat. Fixed Carbon. Ash.
Average 1.36 27.69 35.41 35.54
Select 1.90 34.70 48.23 15.17
The theoretical evaporative power of the former was 9.13 Ibs. of water
from and at 212° per Ib. of coal, and that of the latter 11.44 Ibs.
Relative Value of Fine Sizes of Anthracite.— For burning
on a grate coal-dust is commercially valueless, the finest commercial an-
thracites being sold at the following rates per ton at the mines, according
to an address by Mr. Eckley B. Coxe (1893):
Size. Ranjre of Size. Price at Mines.
Chestnut 1^ to % inch $2.75
Pea %to9/16 1.25
Buckwheat 9/1(5 to % 0.75
Rice %to3/16 0.25
Barley 3/16 to 2/32 0.10
But when coal is reduced to an impalpable dust, a method of burning it
becomes possible to which even {the finest of these sizes is wholly una-
dapted; the coal may be blown in as dust, mixed with its proper proportion
of air, and no grate at all i^ then required.
Pressed Fuel. (E. F. Loiseau, Trans. A. I. M. E., viii. 314.)— Pressed
fuel has been made from anthracite dust by mixing the dust with ten per
cent of its bulk of dry pitch, which is prepared by separating from tar at a
temperature of 572° F. the volatile matter it contains. The mixture is kept
heated by steam to 212°, at which temperature the pitch acquires its ce-
menting properties, and is passed between two rollers, on the periphery of
which are milled out a series of semi-oval cavities. The lumps of the mix-
ture, about the size of an egg, drop out under the rollers on an endless belt
•which carries them to a screen in eight minutes, which time is sufficient to-
cool the lumps, and they are then ready for delivery.
The enterprise of making the pressed fuel above described was not com-
mercially successful, on account of the low price of other coal. In France,
however, " briquettes " are regularly made of coal-dust (bituminous and
semi-bituminous),
RELATIVE VALUE OF STEAM COALS. 633
RELATIVE: VALUE OF STEAM COALS.
The heating value of a coal may be determined, with more or less approx-
imation to accuracy, by three different methods.
1st, by chemical analysis ; 2d. by combustion in a coal calorimeter ; 3d,
by actual trial in a steam-boiler. The first two methods give what may be
called the theoretical heating value, the third gives the practical value.
The accuracy of the first two methods depends on the precision of the
method of analysis or calorimetry adopted, and upon the care and skill of
the operator. The results of the third method are subject to numerous
sources of variation and error, and may be taken as approximately true
only for the particular conditions under which the test is made. Analysis
and calorimetry give with considerable accuracy the heating value which
may be obtained under the conditions of perfect combustion and complete
absorption of the heat produced. A boiler test gives the actual result under
conditions of more or less imperfect combustion, and of numerous and va-
riable wastes. It may give the highest practical heating value, if the condi-
tions of grate-bars, draft, extent of heating surface, method of firing, etc^
are the best possible for the particular coal tested, and it may give results
far beneath the highest if these conditions are adverse or unsuitable to the
coal.
The results of boiler tests being so extremely variable, their use for the
purpose of determining the relative steaming values of different coals has
frequently led to false conclusions. A notable instance is found in the
record of Prof. Johnson's tests, made in 1844, the only extensive series of
tests of American coals ever made. He reported the steaming value of the
Lehigh Coal & Navigation Co.'s coal to be far the lowest of all the anthra-
cites, a result which is easily explained by an examination of the conditions
under which he made the test, which were entirely unsuited to that coal.
He also reported a result for Pittsburgh coal which is far beneath that now
obtainable inevery-day practice, his low result being chiefly due to the use
of an improper furnace.
In a paper entitled Proposed Apparatus for Determining the Heating
Power of Different Coals (Trans. A. I. M. E., xiv. 727) the author described
and illustrated an apparatus designed to test fuel on a large scale, avoiding
the errors of a steam-boiler test. It consists of a fire-brick furnace enciosed
in a water casing, and two cylindrical shells containing a great number of
tubes, which are surrounded by cooling water and through which the gases
of combustion pass while being cooled. No steam is generated in the ap-
paratus, but water is passed through it and allowed to escape at a tempera-
ture below 200° F. The product of the weight of the water passed through
the apparatus by its increase in temperature is the measure of the heating
value of the fuel.
There has been much difference of opinion concerning the value of chemi-
cal analysis as a means of approximating the heating power of coal. It
was found by Scheurer-Kestnerand Meunier-Dollfus, in their extensive series
of tests, made in Europe in 1868, that the heating power as determined by
calorimetric tests was greater than that given to chemical analysis accord-
ing to Dulong's law.
Recent tests made in Paris by M. Mahler, however, show a much closer
agreement of analysis and calorimetric tests. A brief description of these
tests, translated from the French, may be found in an article by the authof
in The Mineral Industry, vol. i. page 97.
Dulong's law may be expressed by the formula,
Heating Power in British Thermal Units = 14,500C -|- 62,500 (H - 2.),*
in which C, H, and O are respectively the percentage of carbon, hydrogen,
and oxygen, each divided by 100. A study of M. Mahler's calorimetric tests
shows that the maximum difference between the results of these tests and
the calculated heating power by Dulong's law in any single case is only a
little over 3& and the results of 31 tests show that Dulong's formula gives an
average of only 47 thermal units less than the calorimetric tests, the
average total heating value being over 14,000 thermal units, a difference of
less than 4/10 of 1%.
* Mahler gives Dulong's formula with'Berthelot's figure for the heating
value of carbon, in British thermal units,'
Heating Power = 14,6500 + 62,025 (H - 1P + N) - 1^
634
Mahler's calorimetrlc apparatus consists of a strong- steel vessel or
" bomb" immersed in water, proper precaution being taken to prevent radi-
ation. One gram of the coal to be tested is placed in a platinum boat within
this bomb, oxygen gas is introduced under a pressure of 20 to 25 atmospheres,
and the coal ignited explosively by an electric spark. Combustion is com-
plete and instantaneous, the heat is radiated into the surrounding water,
weighing 2200 grams, and its quantity is determined by the rise in tempera-
ture of this water, due corrections being made for the heat capacity of the
apparatus itself. The accuracy of the apparatus is remarkable, duplicate
tests giving results varying only about 2 parts in 1000.
The close agreement of the results of calorimetric tests when properly
conducted, and of the heating power calculated from chemical analysis, in-
dicates that either the chemical or the calorimetric method may be ac-
cepted as correct enough for all practical purposes for determining the total
heating power of coal. The results obtained by either method may be
taken as a standard by which the results of a boiler test are to be com-
pared, and the difference between the total heating power, and the result of
the boiler test is a measure of the inefficiency of the boiler under the con-
ditions of any particular test.
In practice with good anthracite coal, in a steam-boiler properly propor-
tioned, and with all conditions favorable, it is possible to obtain in tha
sfeeam 80# of the total heat of combustion of the coal. This result was nearly
obtained in the tests at the Centennial Exhibition in 1876, in five different
boilers. An efficiency of 70# to 75# may easily be obtained in regular prac-
tice. With bituminous coals it is difficult to obtain as close an approach to
the theoretical maximum of economy, for the reason that some of the vola*
tile combustible portion of the coal escapes unburned, the difficulty increas*
ing rapidly as the content of volatile matter increases beyond 20#. With
most coals of the Western States it is with difficulty that as much as 60% or
65# of the theoretical efficiency can be obtained without the use of gas-pro-
ducers.
The chemical analysis heretofore referred to is the ultimate analysis, or
the percentage of carbon, hydrogen, and oxygen of the dry coal. It is found,
however, from a study of Mahler's tests that the proximate analysis, which
gives fixed carbon, volatile matter, moisture, and ash, may be relied on as
giving a measure of the heating value with a limit of error of only about 3#.
After deducting the moisture and ash, and calculating the fixed carbon as a
percentage of the coal dryland free from ash, the author has constructed the
following table :
APPROXIMATE HEATING VALUE OF COALS.
Percentage
F. C. in
Coal Dry
and Free
from Ash.
Heating
Value
B.T.U.
per Ib.
Cornb'le.
Equiv. Water
Evap. from
and at 212°
per Ib.
Combustible.
Percentage
F. C. in
Coal Dry
and Free
from Ash.
Heating
Value
B.T.U.
per Ib.
Cbmb'le.
Equiv. Water
Evap. from
and at 212°
per Ib.
Combustible.
100
97
94
90
87
80
72
14500
14760
15120
15480
15660
15840
15660
15.00
15.28
15.65
16.03
16.21
16.40
16.21
68
63
60
57
54
51
50
15480
15120
14580
14040
13320
12600
12240
16.03
15.65
15.09
14.53
13.79
13.04
12.67
Below 50# the law of decrease of heating-power shown in the table appar-
ently does not hold, as some cannel coals and lignites show much higher
heating-power than would be predicted from their chemical constitution.
The use of this table may be shown as follows:
Given a coal containing moisture 2#, ash 8#, fixed carbon 615?, and volatile
matter 29#, what is its probable heating value ? Deducting moisture and
ash we find the fixed carbon is 61/90 or 68# of the total of fixed carbon and
volatile matter. One pound of the coal dry and free from ash would, by the
table, have a heating value of 15,480 thermal units, but as the ash and moist-
ure, having no heating value, are 10# of the total weight of the coal, the
coal would have 90# of the table value, or 13,932 thermal units. This divided
by 906, the latent heat of steam at 212° gives an equivalent evaporation per
16, of coal Of J4.43 Ibs,
RELATIVE VALUE OF STEAM COALS.
The heating value that can be obtained in practice from this coal would
depend upon the efficiency of the boiler, and this largely upon the difficulty
of thoroughly burning its volatile combustible matter in the boiler furnace.
If a boiler efficiency of 65# could be obtained, then the evaporation per Ib. of
coal from and at 212° would be 14.42 X .65 = 9.37 Ibs.
With the best anthracite coal, in which the combustible portion is, say, 97#
fixed carbon and 3# volatile matter, the highest result that can be expected
in a boiler-test with all conditions favorable is 12.2 Ibs. of water evaporated
from and at 212° per Ib. of combustible, which is 80g of 15.28 Ibs. the theo-
retical heating-power. With the best semi-bituminous coals, such as Cum-
berland and Pocahontas, in which the fixed carbon is 80# of the total com-
bustible, 125 Ibs., or 76% of the theoretical 16.4 Ibs., may be obtained. For
Pittsburgh coal, with a fixed carbon ratio of 68#, 11 Ibs., or 69# of the theo-
retical 16.03 Ibs., is about the best practically obtainable with the best boilers
With some good Ohio coals, with a fixed carbon ratio of 60#, 10 Ibs., or 66#
of the theoretical 15.09 Ibs., has been obtained, under favorable conditions,
with a fire-brick arch over the furnace. With coals mined west of Ohio,
with lower carbon ratios, the boiler efficiency is not apt to be as high as 60$.
From these figures a table of probable maximum boiler-test results from
coals of different fixed carbon ratios may be constructed as follows:
Fixed carbon ratio 97 80 68 60 54 50
Evap. from and at 212° per Ib. combustible, maximum in boiler-tests:
12.2 12.5 11 10 8.3 7.0
Boiler efficiency, per cent 80 76 69 66 60 55
Loss, chimney, radiation, imperfect combustion, etc :
20 24 31 34 40 45
The difference between the loss of 20# with anthracite and the greater
losses with the other coals is chiefly due to imperfect combustion of the
bituminous coals, the more highly volatile coals sending up the chimney the
greater quantity of smoke and un burned hydrocarbon gases. It is a measure
of the inefficiency of the boiler furnace and of the inefficiency of heating-
surface caused by the deposition of soot, the latter being primarily caused
by the imperfection of the ordinary furnace and its uu suitability to the
proper burning of bituminous coal. If in a boiler-test with an ordinary fur-
nace lower results are obtained than those in the above table, it is an indica-
tion of unfavorable conditions, such as bad firing, wrong proportions of
boiler, defective draft, and the like, which are remediable. Higher results
can be expected only with gas-producers, or other styles of furnace espe-
cially designed for smokeless combustion.
Kind of Furnace Adapted for Different Coals. (From the
author's paper on "The Evaporative Power of Bituminous Coals,'1 Trans.
A. S. M. E., iv, 257.)— Almost any kind of a furnace will be found well
adapted to burning anthracite coals and semi-bituminous coals containing
less than 20# of volatile matter. Probably the best furnace for 'burning
those coals which contain between 20# and 40$ volatile matter, including the
Scotch, English, Welsh, Nova Scotia, and the Pittsburgh and Monongahela
river coals, is a plain grate-bar furnace with a fire-brick arch thrown over
it, for the purpose of keeping the combustion-chamber thoroughly hot. The
best furnace for coals containing over 40^ volatile matter will be a furnace
surrounded by fire-brick with a large combustion-chamber, and some spe-
cial appliance for introducing very hot air to the gases distilled from the
coal, or, preferably, a separate gas-producer and combustion-chamber, with
facilities for heating both air and gas before they unite in the combustion-
chamber. The character of furnace to be especially avoid* d in burning all
bituminous coals containing over 20$ of volatile matter is the ordinary fur-
nace, in which the boiler is set directly above the grate bars, and in which the
heating-surfaces of the boiler are directly exposed to radiation from the
coal on the grate. The question of admitting air above the grate is still un-
settled. The London Engineer recently said : "All on r experience, extending
over many years, goes to show that when the production of smoke is pre-
vented by special devices for admitting air, either there is an increase in the
consumption of fuel or a diminution in the production of steam. * * * The
best smoke -preventer yet devised is a good fireman."
Downward-draught Furnaces.— Recent experiments show that
with bituminous coal considerable saving may be made by causing the
draught to go downwards from the freshly-fired coal through the hot coal
on the grate. Similar good results are also obtained by the upward draught
by feeding the fresh coal under the bed of hot coal instead of on top. (See
Boilers.)
636
FUEL.
Calorlmetrlc Tests of American Coals,— From a number of
tests of American and foreign coals, made with an oxygen calorimeter, by
Geo. H. Barrus (Trans. A. S. M. E., vol. xiv. 816), the following are selected,
showing the range of variation:
Percentage
of Ash.
Total Heat
of Com-
bustion.
B. T. U.
Total Heat
reduced to
Fuel free
from Ash.
Semi- b ituminous.
George's Cr'k, Cumberl'd, Md.,10 tests
6.1
' 8.6
3.2
' 6.2
] 3.5
1 5.7
7.8
7.7
5.9
10.2
17.7
8.7
6.8
10.5
9.1
14,217
12,874
14,603
13,608
13,922
13,858
13,180
13,581
12,941
11,664
10,506
12,420
12,122
11,521
13,189
15,141
14,085
55,086
14,507
14,427
14.696
14,295
14,714
13,752
12,988
12,765
13,602
13,006
12,873
14,509
New River, Va.., 6 tests
Elk Garden, Va., 1 test
Welsh 1 test
Bituminous.
Youghiogheny, Pa., lump
44 " slack
Frontenac Kansas . . . .
Cape Breton (Caledonia)
Evaporative Power of* Bituminous Coals*
(Tests with Babcock & Wilcox Boilers, Trans. A. S. M. E., iv.
287.)
<M
n
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o.
of I?
r-j
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62
ai
£
Dura-
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i
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tion of
o
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O 4J
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Test.
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§*! -
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£"1
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p
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"52
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1
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w
1 Welsh
13J4 nrs
40
1679
7. 5
6.3
2.07
11.53
12.46
146
96
2. Anthracitescr'sl/5
Powelton, Pa.,
60
3126
8.8
17.6
4.32
11.32
12.42
272
448
Semi-bit. 4/5,
j
3. Pittsbg'h fine slack
4 hrs
33.7
1679
12.3
21.9
4.47
8.12
9.29
146
250
" 3d Pool lump
10 *«
43.5
2760
4.8
27.5
4.76
10.47
11.00
240
419
4. Castle Shannon, nr
i
Pittsb'gh, % nut,
U2J4h
69.1
4784
10.5
27.9
4.13
10.00
11.17
416
570
% lump,
^
d. 111. tk run of mine "
6 days.
1196
3.41
9 49
104
54
" Ind. block, " very
good "
[Sd'ys
1196
2.95
9.47
104
111
6. Jackson, O., nut ..
8 hrs.
48
3358
9.6
32.1
4.11
8.93
9.88
292
460
" Staunton, 111., nut..
8 "
60
3358
17.7
25.1
2.27
5.09
6.19
292
246
7. Renton screenings.
5h50m
21.2
1564
13.831.5
2.95
6.88
7.98
136
151
Wellington scr'gs..
6h30m
21.2
1564
18.327
2.93
7.89
9.66
136
150
Black Diam. scr'gs
5h 58m
21.2
1564
19.336.4
3.11
6.29
7.80
136
160
Seattle screenings.
6h24m
21.2
1564
18.481.3
2.91
6.86
7.92
136
•150
Wellington lump. .
6hl9m
21.2
1564
13.828.2
3.52
9.02
10.46
136
171
Cardiff lump.
fih 47 m
21 2
1564
11 726.7
3.69
10.07
11 40
136
189
" . 7h23m
21.2
1564
19.1 25.6
3.35
9.62
11.89
136
174
South Paine lump. 6 h 35 in
Seattle lump ..... 1 6 h 5m
21.2
21.2
1564
1564
13.928.9
9.534.1
3.53
3.57
8.961 10.41
7.68| 8.49
136
136
182
184
COKE.
637
Place of Test: 1. London, England; 2. Peacedale, B. I.; 3. Cincinnati, O. ;
4. Pittsburgh- Pa.; 5. Chicago, 111.; 6. Springfield, O.; 7. San Francisco,
Cal.
In all the above tests the furnace was supplied with a fire-brick arch for
preventing the radiation of heat from the coal directly to the boiler.
•Weathering of Coal. (I. P. Kimball, Trans. A. I. M. E., viii. 204.)-
The practical effect of the weathering of coal, while sometimes increasing
its absolute weight, is to diminish the quantity of carbon and disposable
hydrogen and to increase the quantity of oxygen and of indisposable hy-
drogen. Hence a reduction in the calorific value.
An excess of pyrites in coal tends to produce rapid oxidation and mechan-
ical disintegration of the mass, with development of heat, loss of coking
power, and spontaneous ignition.
The only appreciable results of the weathering of anthracite within the
ordinary limits of exposure of stocked coal are confined to the oxidation of
its accessory pyrites. In coking coals, however, weathering reduces and
finally destroys the coking power, while the pyrites are converted from the
state of bisulphide into comparatively innocuous sulphates.
Kichters found that at a temperature of 158° to 180° Fahr., three coals lost
in fourteen days an average of 3.6$ of calorific power. (See also paper by
R. P. Rothwell, Trans. A. I. M. E., iv. 55.)
COKE.
Coke is the solid material left after evaporating the volatile ingredients of
coal, either by means of partial combustion in furnaces called coke ovens,
or by distillation in the retorts of gas-works.
Coke made in ovens is preferred to gas coke as fuel. It is of a dark-gray
color, with slightly metallic lustre, porous, brittle, and hard.
The proportion of coke yielded by a given weight of coal is very different
for different kinds of coal, ranging from 0.9 to 0.35.
Being of a porous texture, it readily attracts and retains water from the
atmosphere, and sometimes, if it is kept without proper shelter, from 0.15 to
0.20 of its gross weight consists of moisture.
Analyses of Coke.
(From report of John R. Procter, Kentucky Geological Survey.)
Where Made.
Fixed
Carbon
Ash.
Sul-
phur.
Connellsville, Pa. (Average of 3 s
Chattanooga, Tenn. 4
Birmingham, Ala. " 4
P,ocahontas, Va. " 3
New River, W. Va. " 8
Big Stone Gap, Ky. "
imples)
88.96
80.51
87.29
92.53
92.38
93.23
9.74
16.34
10.54
5.74
7.21
5.69
0.810
1.595
1.195
0.597
0.562
0.749
M
*t
((
Experiments in Coking. CONNELLSVILLE REGION.
(John Fulton, Amer. Mfr., Feb. 10, 1893.)
0}
<v
fl .
73
Q)
o>
73
| .
^
<e
5 .
Per cent of Yield.
c
CM
O
i*
IS
03
&3
0>fl
|l
II
&
aaj
<D ®
^Sr«
*5 ®
23
co
^rC
,£
c fl
%
1- 0
i, ^
O
O
2
ry.
^* o
o ^
3
fe o
c80
H o
&
55
<1
^
H
S
h. m.
Ib.
Ib.
Ib.
Ib.
Ib.
1
67 00
12,420
99
385
7,518
7,903
00.80
3 10
60.53
63.63
35.57
2
68 00
11,090
90
359
6,580
6,939
00.81
3.24
59.33
62.57
36.62
3
45 00
9,120
77
272
5,418
5,690
00.84
2.98
59.41
62.39
36 77
4
45 00
9,020
74
349
5,334
5,683
00.82
3.87
59.13
63.00
36.18
41,650
340
1365
24,850
26,215
00.82
3.28
59.66
62.94
36.24
These results show, in a general average, that Connellsville coal carefully
coked in a modern beehive oven will yield 66.17$ of marketable coke, 2.30^
of small coke or braize, and 0.82% of ash.
638 FUEL.
The total average loss in volatile matter expelled from the coal in coking
amounts to 30.71$.
The modern beehive coke oven is 12 feet in diameter and 7 feet high at
crown of dome. It is used in making 48 and 72 hour coke.
In making these tests the coal was weighed as it was charged into the
oven- the resultant marketable coke, small coke or braize and ashes
weighed dry as they were drawn from the oven.
Coal W"asliiiigo— In making coke from coals that are high in ash ana
sulphur it is advisable to crush and wash the coal before coking it. A coal-
washing plant at Brookwood, Ala., has a capacity of 50 tons per hour. The
average percentage of ash in the coal during ten days' run varied from 14% to
21$ in the washed coal from 4.8$ to 8.1#, and in the coke from 6.1$ to 10.5$.
During three months the average reduction of ash was 60.9$. (Eng. and
Mining Jour., March 25, 1893.)
., , .
Recovery of By-products in Coke Manufacture.— In Ger-
many considerable progress has been made in the recovery of by-products.
The Hoffinan-Otto oven has been most largely used, its principal feature
being that it is connected with regenerators. In 1884 40 ovens on this
system were running, and in 1892 the number had increased to 1209.
A Hoffman-Otto oven in Westphalia takes a charge of 6J4 tons of dry coal
and converts it into coke in 48 hours. The product of an oven annually is
1025 tons in the Ruhr district, 1170 tons in Silesia, and 960 tons in the Saar dis-
trict The yield from dry coal is 75$ to 77% of coke, 2.5$ to 3$ of tar, and 1.1%
to 1.2$ of sulphate of ammonia in the Ruhr district; 65$ to 70$ of coke, 4$ to
4 5$ of tar, and 1$ to 1.25$ of sulphate of ammonia in the Upper Silesia region
and 68$ to 72$ of coke, 4$ to 4.3$ of tar and 1.8$ to 1 .9$ of sulphate of ammonia
in the Saar district. A group of 60 Hoffman ovens, therefore, yields annually
the folio wing:
Pokf> Tar Sulphate
Strict. Ct^; ££• Ammonia,
Ruhr 51,800 1860 780
Upper Silesia .......................... 48,000 3000 840
gjjar ................................. 40,500 2400 492
An oven which has been introduced lately into Germany in connection
with the recovery of by-products is the Semet-Solvay, which works hotter
than the Hoffman -Otto, and for this reason 73$ to 77$ of gas coal can be
mixed with 23$ to 27$ of coal low in volatile matter, and yet yield a good
coke. Mixtures of this kind yield a larger percentage of coke, but, on the
other hand, the amount of gas is lessened, and therefore the yield of tar and
ammonia is not so great.
The yield of coke by the beehive and the retort ovens respectively is
given as follows in a pamphlet of the Solvay Process Co.: Connellsville
coal : beehive, 66$, retort, 73$; Pocahontas : beehive, 62$, retort, 83$; Ala-
bama : beehive, 60$, retort, 74$. (See article in Mineral Industry -, vol. viii,,
1900.)
References: F. W. Luerman, Verein Deutscher Eisenhuettenleute 1891,
Iron Age, March 31, 1892 ; Amer. Mfr., April 28, 1893. An excellent series
of articles on the manufacture of coke, by John Fulton, of Johnstown, Pa.,
is published in the Colliery Engineer, beginning in January, 1893.
Making Hard Coke.— J. J. Fronheiser and C. S Price, of the Cam-
bria Iron Co., Johnstown, Pa., have made an improvement in coke manu-
facture by which coke of any degree of hardness may be turned out. It is
accomplished by first grinding the coal to a coarse powder and mixing it
with a hydrate of lime (air or water slacked caustic lime) before it is
charged into the coke-ovens. The caustic lime or other fluxing material
used is mechanically combined with the coke, filling up its cell-walls. It has
been found that about 5$ by weight of caustic lime mixed with the fine coal
gives the best results. However, a larger quantity of lime can be added to
coals containing more than 5$ to 7$ of ash. (Amer. Mfr.)
Generation of Steam from the Waste Heat and Oases of
Coke-ovens. (Erskine Ramsey, Amer. Mfr., Feb. 16, 1894.)— The gases
from a number of adjoining ovens of the beehive type are led into a long
horizontal flue, and thence to a combustion-chamber under a battery of
boilers. Two plants are in satisfactory operation at-Tracy City, Term., and
two at Pratt Mines, Ala.
A Bushel of Coal.— The weight of a bushel of coal in Indiana is 70 Ibs.,
in Penna. 76 Ibs.; in Ala., Colo., Ga., 111., Ohio, Tenn., and W. Va. it is SO Ibs.
A Bushel of Coke is almost uniformly 40 Ibs., but in exceptional
WOOD AS FUEL. 639
cases, when the coke is very light, 38, 36, and 33 Ibs. are regarded.as a bushel.
In others, from 42 to 50 Ibs. are given as the weight of a bushel ;* in this case
the coke would be quite heavy.
Products of tli e Distillation of Coal.— S. P. Sadler's Handbook
of Industrial Organic Chemistry gives a diagram showing over 50 chemical
products that are derived from distillation of coal. The first derivatives are
coal-gas, gas-liquor, coal-tar, and coke. From the gas-liquor are derived
ammonia and sulphate, chloride and carbonate of ammonia. The coal-tar
is split up into oils lighter than water or crude naphtha, oils heavier than
water — otherwise dead oil or .tar, commonly called creosote, — and pitch.
From the two former are derived a variety of chemical products.
From the coal-tar there comes an almost endless chain of known combina-
tions. The greatest industry based upon their use is the manufacture of
dyes, and the enormous extent to which this has grown can be judged from
the fact that there are over 600 different coal-tar colors in use, and many more
which as yet are too expensive for this purpose. Many medicinal prepara-
tions come from the series, pitch for paving purposes, and chemicals for
the photographer, the rubber manufacturers and tanners, as well as for
preserving timber and cloths.
The composition of the hydrocarbons in a soft coal is uncertain and quite
complex; but the ultimate analysis of the average coal shows that it ap-
proaches quite nearly to the composition of CH4 (marsh-gas). (W. H.
Blauvelt, Trans. A. I. M. E., xx. 625.)
WOOD AS FUEI,.
Wood, when newly felled, contains a proportion of moisture which varies
very much in different kinds and in different specimens, ranging between
30$ and 50$, and being on an average about 40$. After 8 or 12 months' ordi-
nary drying in the air the proportion of moisture is from 20 to 25$. This
degree of dry ness, or almost perfect dry ness if required, can be produced
by a few days' drying in an oven supplied with air at about 240° F. When
coal or coke is used as the fuel for that oven, 1 Ib. of fuel suffices to expel
about 3 Ibs. of moisture from the wood. This is the result of experiments
on a large scale by Mr. J. R. Napier. If air-dried wood were used as
fuel for the oven, from 2 to 2^ Ibs. of wood would probably be required to
produce the same effect.
The specific gravity of different kinds of wood ranges from 0.3 to 1.2.
Perfectly dry wood contains about 50$ of carbon, the remainder consisting
almost entirely of oxygen and hydrogen in the proportions which form
water. The coniferous family contain a small quantity of turpentine, which
is a hydrocarbon. The proportion of ash in wood is from \% to 5$. The
total heat of combustion of all kinds of wood, when dry, is almost ex-
nctly the same, and is that due to the 50$ of carbon.
The above is from Rankine; but according to the table by S. P. Sharpless
in Jour. 0. 1. W., iv. 36, the ash varies from 0.03$ to 1.20$ in American woods,
and the fuel value, instead of being the same for all woods, ranges from
3667 (for white oak) to 5546 calories (for long-leaf pine) = 6600 to 9883 British
thermal units for dry wood, the fuel value of 0.50 Ibs. carbon being 7272
B. T. U.
Heating; Value of Wood.— The following table is given in several
books of reference, authority and quality of coal referred to not stated.
The weight of one cord of different woods (thoroughly air-dried) is about
as follows :
Hickory or hard maple. . . . 4500 Ibs. equal to 1800 Ibs. coal. (Others give 2000.)
White oak 3850 " " 1540 " " " 1715.)
Beech, red and black oak.. 3250 " " 1300 " " •• 1450.)
Poplar, chestnut, and elm.. 2350 " " 940 •* * ** 1050.)
The average pine 2000 " "800 •* *• * 925.)
Referring to the figures in the last column, it is said :
From the above it is safe to assume that 214 Ibs. of dry wood are equal to
1 Ib. average quality of soft coal and that the full value of (he same weight
of different woods is very nearly the same — that is, a pound of hickory is
worth no more for fuel than a pound of pine, assuming both to be dry. It
is important that the wood be dry, as each 10$ of water or moisture in wood
will detract about 12$ from its value as fuel.
Taking an average wood of the analysis C 51$, H 6.5$, O 42.0$, ssh 0.5J6,
perfectly dry, its fuel value per pound, according to Dulong's formula. V c
640
FUEL.
[l4,500 C -f-*e2,000 (H -^ )], is 8170 British thermal units. If the wood, as
ordinarily dried in air, contains 25* of moisture, then the heating value of a
pound of such wood is three quarters of 8170 = 6127 heat-units, less the
heat required to heat and evaporate the y^ Ib. of water from the atmospheric
temperature, and to heat the steam made from this water to the tempera-
ture of the chimney gases, say 150 heat-units per pound to heat the water to
212°, 966 units to evaporate it at that temperature, and 100 heat-units to
raise the temperature of the steam to 420° F., or 1216 in all = 304 for y± Ib.,
which subtracted from the 6127, leaves 5824 heat-units as the net fuel value
of the wood per pound, or about 0.4 that of a pound of carbon.
Composition of Wood.
(Analysis of Woods, by M. Eugene Chevandier.)
Woods.
Composition.
Carbon.
Hydrogen.
Oxygen.
Nitrogen.
Ash.
Beech
Oak
49.36*
49.64
50.20
49.37
49.96
6.01*
5.92
6.20
6.21
5.96
42.69*
41.16
41.62
41.60
39.56
0.91*
1.29
1.15
0.96
0.96
1.06*
1.97
0.81
1.86
3.37
Birch . . ..
Poplar
Willow
49.70*
6.06*
41.30*
1.05*
1.80*
The following table, prepared by M. Violette, shows the proportion of
water expelled from wood at gradually increasing temperatures:
Temperature.
Water Expelled from 100 Parts of Wood.
Oak.
Ash.
Elm.
Walnut.
257° Fahr
15.26
14.78
16.19
21.22
27.51
33.38
15.32
17.02
36.94?
33.38
40.56
15.55
17.43
21.00
41.77?
36.56
302° Fahr
347° Fahr
32.13
35.80
44.31
392° Fahr
437° Fahr
The wood operated upon had been kept in store during two years. When
wood which has been strongly dried by means of artificial heat is left ex-
posed to the atmosphere, it reabsorbs about as much water as it contains
in its air-dried state.
A cord of wood = 4 X 4 X 8 = 128 cu. ft. About 56* solid wood and 44*
interstitial spaces. (Marcus Bull, Phila.. 1829. J. C. I. W., vol. i. p. 293.)
B. E. Fernow gives the per cent of solid wood in a cord as determined offi
cially in Prussia (J. C. I. WM vol. iii. p. 20):
Timber cords, 74.07* = 80 cu. ft. per cord;
Firewood cords (over 6" diam.), 69.44* = 75 cu. ft. per cord;
" Billet " cords (over 3" diam.), 55.55* = 60 cu. ft. per cord;
44 Brush" woods less than 3" diam., 18.52*; Roots, 37.00*.
CHARCOAL.
Charcoal is made by evaporating the volatile constituents of wood and
peat, either by a partial combustion of a conical heap of the material to be
charred, covered with a layer of earth, or by the combustion of a separate
portion of fuel in a furnace, in which are placed retorts containing the ma-
terial to be charged.
According to Peclet, 100 parts by weight of wood when charred in a heap
yield from 17 to 22 parts by weight of charcoal, and when charred in a
retort from 28 to 30 parts.
This has reference to the ordinary condition of the wood used in charcoal-
making, in which 25 parts in 100 consist of moisture. Of the remaining 75
parts the carbon amounts to one half, or 37^* of the gross weight of the
wood. Hence it appears that on an average nearly half of the carbon in the
CHARCOAL.
641
wood Is lost during the partial combustion in a heap, and about one quarter
during the distillation in a retort.
To char 100 parts by weight of wood in a retort, 12J4 parts of wood must
be burned in the furnace. Hence in this process the whole expenditure of
wood to produce from 28 to 30 parts of charcoal is 112}^ parts; so that if the
weight of charcoal obtained is compared with the whole weight of wood
expended, its amount is from 25% to 27%', and the proportion lost is on an
average 11 ^3 + 37^ = 0.3, nearly.
According to Peclet, good wood charcoal contains about 0.07 of its weight
of ash. The proportion of ash in peat charcoal is very variable, and is es-
timated on an average at about 0.18. (Rankine.)
Much information concerning charcoal may be found in the Journal of the
Charcoal-iron Workers' Assn., vols. i. to vi. From this source the following
notes have been taken:
Yield of Charcoal from a Cord of "Wood.— From 45 to 50
bushels to the cord in the kiln, and from 30 to 35 in the meiler. Prof. Egles-
ton in Trans. A. I. M. E., viii. 395, says the yield from kilns in the Lake
Champlain region is often from 50 to 60 bushels for hard wood and 50 for
soft wood ; the average is about 50 bushels.
The apparent yield per cord depends largely upon whether the cord is a
full cord of 128 cu. ft. or not.
In a four months' test of a kiln at Goodrich, Tenn., Dr. H. M. Pierce found
results as follows: Dimensions of kiln — inside diameter of base, 28 ft. 8 in.;
diam. at spring of arch, 26 ft. 8 in. ; height of walls, 8 ft. ; rise of arch, 5 ft. ;
capacity, 30 cords. Highest yield of charcoal per cord of wood (measured)
69.27 bushels, lowest 50.14 bushels, average 53.65 bushels.
No. of charges 12, length of each turn or period from one charging to
another 11 days. (J. C. I. W., vol. vi. p. 26.)
Results from Different Methods of Char coal -making.
Yield.
*"" n-<
02 *Q
0) +£
S*5
C'^'cS
Coaling Methods.
Character of Wood used.
p i
^ttl
O t,
t> £
0> ^rrj
^3 CJ 2
"S^ *
s*
fl*
GOJ= 0
|Sb
Odelstjerna's experiments
Birch dried at 230 F
35 Q
Mathieu's retorts, fuel ex-
cluded
I Air dry, av. good yel- )
•< low pine weighing V
( abt. 28 Ibs. per cu. ft. )
77.0
65.8
28.3
24.2
63.4
54.2
15.7
15.7
Mathieu's retorts, fuel in-
Swedish ovens, av. results
j Good dry fir and pine, ?
1 mixed.
81.0
27.7
66.7
13.3
Swedish ovens, av, results
Poor wood, mixed fir
and pine
70.0
25 8
62.0
13.3
Swedish meilers excep-
Fir and white-pine
72.2
24 7
59.5
13.3
wood mixed Av 25
Swedish meilers. av. results
Ibs. per cu. ft.
52.5
18 3
43.9
13.3
American kilns, av. results
American meilers, av. re-
( Av. good yellow pine )
•< weighing abt. 25 Ibs. V
54.7
22.0
45.0
17 5
sults
( per cu. ft. )
42.917.1
35 0
17.5
Consumption of Charcoal in HI a *t -furnaces per Ton of
Pig Iron ; average consumption according to census of 1880, 1.14 tons
charcoal per ton of pig. The consumption at the best furnaces is much
below this average. As low as 0 853 ton, is recorded of the Morgan furnace;
Bay furnace, 0.858; Elk Rapids. 0.884. (1892.)
Absorption .of "Water and of Oases toy Charcoal.— Svedlius,
in his hand-book for charcoal-burners, prepared for the Swedish Govern-
ment, says: Fresh charcoal, also reheated charcoal, contains scarcely
any water but when cooled it absorbs it very rapidly, so that after
twenty-four hours, it may contain 4% to 8% of water. After the lapse of a
few weeks the moisture of charcoal may not increase perceptibly, and may
be estimated at 10$ to 15#, or an average of 12#. A thoroughly charred
piece of charcoal ought, then, to contain about 84 parts carbon, 12 parts
ivater, 3 parts ash, and 1 part hydroeren.
642
FUEL.
Volumes.
Carbonic oxide .. 9.42
Oxygen 9.25
Nitrogen „. 6.50
M. Saussure, operating with blocks of fine boxwood charcoal, freshly
burnt, found that by simply placing such blocks in contact with certain
gases they absorbed them in the following proportion:
Volumes,
Ammonia 90-00
Hydrochloric-acid gas 85.00
Sulphurous acid 65.00
Sulphuretted hydrogen 55.00 Carburetted hydrogen. 5.00
Nitrous oxide (laughing-gas).. 40.00 Hydrogen 1.75
Carbonic acid. . ..... 35,00
It is this enormous absorptive power that renders of so much value a
comparatively slight sprinkling of charcoal over dead animal matter, as a
preventive of the escape of odors arising from decomposition.
In a box or case containing one cubic foot of charcoal may be stored
without mechanical compression a little over nine cubic feet of oxygen,
representing a mechanical pressure of one hundred and twenty-six pounds
to the square inch. From the store thus preserved the oxygen can be
drawn by a small hand-pump.
Composition of Charcoal Produced at Various Tempera*
tares. (By M. Violette.)
Temperature of Car-
bonization.
Composition of the Solid Product.
Carbon.
Hydro-
gen.
Oxygen.
Nitrogen
and Loss.
Ash.
Cent. Fahr.
150° 302°
200 392
250 482
300 592
350 662
432 810
1023 1873
Per cent.
47.51
51.82
65.59
73.24
76.64
81.64
81.97
Per cent.
6.12
3.99
4.81
4.25
4.14
4.96
2.30
Per cent.
46.29
43.98
28.97
21.96
18.44
15.24
14.15
Per cent.
0.08
0.23
0.63
0.57
0.61
1.61
1.60
Per cent.
47.51
39.88
32.98
24.61
22.42
15.40
15 30
The wood experimented on was that of black alder, or alder buckthorn,
which furnishes a charcoal suitable for gunpowder. It was previously
dried at 150 deg. C. = 302 deg. F.
MISCELLANEOUS SOLID FUELS.
Bust Fuel— Dust Explosions.— Dust when mixed in air burns with
such extreme rapidity as in some cases to cause explosions. Explosions of
flour-mills have been attributed to ignition of the dust in confined passages.
Experiments in England in 1876 on the effect of coal-dust in carrying flame in
mines showed that in a dusty passage the flame from a blown-out shot may
travel 50 yards. Prof. F. A. Abel (Trans. A. I. M. E. , xiii. 260) says that coal-
dust in mines much promotes and extends explosions, and that it may read-
ily be brought into operation as a fiercely burning agent which will carry
flame rapidly as far as its mixture with air extends, and will operate as an
explosive agent though the medium of a very small proportion of fire-damp
in the air of the mine. The explosive violence of the combustion of dust is
largely due to the instantaneous heating and consequent expansion of the
air. (See also paper on " Coal Dust as an Explosive Agent," by Dr. R W.
Raymond, Trans. A. I. M. E. 1894.) Experiments made in. Germany in 1893.
show that pulverized fuel may be burned without smoke, and with high
economy. The fuel, instead of being introduced into the fire-box in the
ordinary manner, is first reduced to a powder by pulverizers of any con-
struction. In the place of the ordinary boiler fire-box there is a combustion
chamber in the form of a closed furnace lined with fire-brick and provided
with an air-injector. The nozzle throws a constant stream of fuel into the
chamber, scattering it throughout the whole space of the fire-box. When
this powder is once ignited, and it is very readily done by first raising the
MISCELLAKEOUS SOLID FUELS. 643
lining to hi high temperature by an open fire, the combustion continues in
an intense arid regular manner under the action of the current of air which
carries it in. (Mfrs. Record, April, 1893.)
Records of tests with the Wegener powdered-coal apparatus, which is
now (1900) in use in Germany, are given in Eng. News, Sept. 16, 1897. Coal-
dust fuel is now extensively used in the United States in rotary kilns for
burning Portland cement.
Powdered luei was u*ed in the Crompton rotary puddling-furnace at
Woolwich Arsenal, England, in. 1873. (Jour. I. & S. I., i. 1873, p. 91.)
Peat or Turf, as usually dried in the air, contains from 25^ to 30$ of
water, which must be allowed for in estimating its heat of combustion. This
water having been evaporated, the analysis of M. Regnault gives, in 100
parts of perfectly dry peat of the best quality: C 58$, H 6#, O 32#, Ash 5#.
In some examples of peat the quantity of ash is greater, amounting to 7%
and sometimes to \\%.
The specific gravity of peat in its ordinary state is about 0.4 or 0.5. It can
be compressed by machinery to a much greater density. (Rankine.)
Clark (Steam-engine, i. 61) gives as the average composition of dried Irish
peat: C 59#, H 6£, O 30#, N 1.25#, Ash 4%.
Applying Dulong's formula to this analysis, we obtain for the heating value
of perfectly dry peat 10,260 heat-units per pound, and for air-dried peat con-
taining 25% of moisture, after making allowance for evaporating the water,
7391 heat-units per pound.
Sawdust as Fuel,— The heating power of sawdust is naturally the
same per pound as that of the wood from which it is derived, but if allowed
to get wet it is more like spent tan (which see below). The conditions neces-
sary for burning sawdust are that plenty of room should be given it in the
furnace, and sufficient air supplied on the surface of the mass. The same
applies to shavings, refuse lumber, etc. Sawdust is frequently burned in
saw-mills, etc., by being blown into the furnace by a fan-blast.
"Wet "Tan Bark as Fuel.— Tan, or oak bark, after having been used
In the processes of tanning, is burned as fuel. The spent tan consists of the
fibrous portion of the bark. According to M. Peclet, five parts of oak bark
produce four parts of dry tan; and the heating power of perfectly dry tan,
containing 15% of ash, is 6100 English units; whilst that of tan in an ordinary
State of dryness, containing 30# of water, is only 4284 English units. The
weight of water evaporated from and at 212° by one pound of tan, equiva-
lent to these heating powers, is, for perfectly dry tan, 5.46 Ibs., for tan with
30# moisture, 3.84 Ibs. Experiments by Prof. R. H. Thurston (Jour. Frank.
Inst., 1874) gave with the Crockett furnace, the wet tan containing 59# of
water, an evaporation from and at 212° F. of 4.24 Ibs. of water per pound
of the wet tan, and with the Thompson furnace an evaporation of 3.19 Ibs.
per pound of wet tan containing 55# of water. The Thompson furnace con-
sisted of six fire-brick ovens, each 9 feet X 4 feet 4 inches, containing 234
square feet of grate in all, for three boilers with a total heating surface of
2000 square feet, a ratio of heating to grate surface of 9 to 1. The tan was
fed through holes in the top. The Crockett furnace was an ordinary fire-
brick furnace, 6X4 feet, built in front of the boiler, instead of under it, the
ratio of heating surface to grate being 14.6 to 1. According to Prof. Thurs-
ton the conditions of success in burning wet fuel are the surrounding of the
mass so completely with heated surfaces and with burning fuel that it may
be rapidly dried, and then so arranging the apparatus that thorough com-
bustion may be secured, and that the rapidity of combustion be precisely
equal to and never exceed the rapidity of desiccation. Where this rapidity
or combustion is exceeded the dry portion is consumed completely, leaving
an uncovered mass of fuel which refuses to take fire.
Straw as Fuel. (Eng'g Mechanics, Feb., 1893, p. 55.)— Experiments in
Tlussia showed that winter- wheat straw, dried at 230° F., had the following
composition: C, 46.1; H, 5.6; N, 0.42; O, 43.7; Ash, 4.1. Heating value in
British thermal units: dry straw, 6290; with 6# water, 5770; with 10£ water,
5448. With straws of other grains the heating value of dry straw ranged
from 5590 for buckwheat to 6750 for flax.
Clark (S. E., vol. 1, p. 62) gives the mean composition of wheat and barley
straw as C, 36; H. 5; O, 38; O, 0.50; Ash, 4.75; water, 15.75, the two straws
varying less than \%. The heating value of straw of this composition, accord-
ing to Dulong's formula, and deducting the heat lost in evaporating the
water, is 5155 heat units. Clark erroneously gives it as 814 1 lieat units.
Bagasse as Fuel in Sugar Manufacture. --Bagasse is the name
given to refuse sugar-cane, after the juice has been extracted. Prof. L. A*
644 FUEL.
Becuel, in a paper read before the Louisiana Sugar Chemists' Association, in
1892, says: " With tropical cane containing 12.5$ woody fibre, a juice contain-
ing 16.13$ solids, and 83.37$ water, bagasse of, say, 66$ and 72$ mill extrac-
tion would have the following percentage composition:
Woody Combustible irrQx-
Fibre. Salts. Water.
66$bagasse 37 10 53
72$bagasse 45 9 46
"Assuming that the woody fibre contains 51$ carbon, the sugar and other
combustible matters an average of 42.1$, and that 12,906 units of heat are
generated for every ponnd of carbon consumed, the 66$ bagasse is capable
of generating 297,834 heat units per 100 Ibs. as against 345,200, or a difference
of 47,366 units in favor of the 72$ bagasse.
"Assuming the temperature of the waste gases to be 450° F., that of the
surrounding atmosphere and water in the bagasse at 86° F., and the quan-
tity of air necessary for the combustion of one pound of carbon at 24 Ibs.,
the lost heat will be as follows: In the waste gases, heating air from 86° to
450° F., and in vaporizing the moisture, etc., the 66$ bagasse will require
112,546 heat units, and 116,150 for the 72$ bagasse.
" Subtracting these quantities from the above, we find that the 66$ bagasse
will produce 185,288 available heat units per 100 Ibs., or nearly 24$ less than
the 72$ bagasse, which gives 229,050 units. Accordingly, one ton of cane of
2000 Ibs. at 66$ mill extraction will produce 680 Ibs. bagasse, equal to 1,259,958
available heat units, while the same cane at 72$ extraction will produce 560
Ibs. bagasse, equal to 1,282,680 units.
" A similar calculation for the case of Louisiana cane containing 10$ woody
fibre, and 16$ total solids in the juice, assuming 75$ mill extraction, shows
that bagasse from one ton of cane contains 1,573,956 heat units, from which
561,465 have to be deducted,
" This would make such bagasse worth on an average nearly 92 Ibs. coal
" per ton of cane ground. Under fairly good conditions, 1 Ib. coal will evap'
orate 7J4 Ibs. water, while the best boiler plants evaporate 10 Ibs. Therefore,
the bagasse from 1 ton or cane at 75$ mill extraction should evaporate from
689 Ibs. to 919 Ibs. of water. The juice extracted from such cane would un-
der these conditions contain 1260 Ibs. of water. If we assume that the
water added during the process of manufacture is 10$ (by weight) of the
juice made, the total water handled is 1410 Ibs. From the juice represented
in this case, the commercial massecuite would be about 15$ of the weight of
the original mill juice, or say 225 Ibs. Said mill juice 1500 Ibs., plus 10$,
equals 1650 Ibs. liquor handled; and 1650 Ibs., minus 225 Ibs., etmals 1425 Ibs.,
the quantity of water to be evaporated during the process of manufacture.
To effect a 7^-lb. evaporation requires 190 Ibs. of coal, and 142^ Ibs. for a 1O
Ib. evaporation.
" To reduce 1650 Ibs. of juice to syrup of, say, 27° Baume. requires the evap-
oration of 1170 Ibs. of water, leaving 480 Ibs. of syrup. If this work be ac-
complished in the open air, it will require about 156 Ibs. of coal at 7^ Ibs.
boiler evaporation, and 117 at 10 Ibs. evaporation.
" With a double effect the fuel required would be from 59 to 78 Ibs., and
with a triple effect, from 36 to 52 Ibs.
" To reduce the above 480 Ibs. of .syrup to the consistency of commercial
massecuite means the further evaporation of 255 Ibs. of water, requiring
the expenditure of 34 Ibs. coal at 7^ Ibs. boiler evaporation, and 25J^ Ibs.
with' a 10-lb. evaporation. Hence, to manufacture one ton of cane into sugar
and molasses, it will take from 145 to 190 Ibs. additional coal to do the work
by the open evaporator process; from 85 to 112 Ibs. with a double effect, and
only 7^ Ibs. evaporation in the boilers, while with 10 Ibs. boiler evaporation
the bagasse alone is capable of furnishing 8$ more heat than is actually re-
quired to do the work. With triple-effect evaporation depending on the ex-
cellence of the boiler plant, the 1425 Ibs. of water to be evaporated from the
juice will require between 62 and 86 Ibs. of coal. These values show that
from 6 to 30 Ibs. of coal can be spared from the value of the bagasse to run
engines, grind cane, etc.
"It accordingly appears," says Prof. Becuel, "that with the best boiler
plants, those taking up all the available heat generated, by using this heat
economically the bagasse can be made to supply all the fuel required by oui
sugar- houses."
PETKOLEUM.
645
PETROLEUM.
Products of tlie Distillation of Crude Petroleum.
Crude American petroleum of sp. gr. 0.800 may be split up by fractional
distillation as follows (Robinson's Gas and Petroleum Engines):
Temp, of
Distillation
Fahr.
Distillate.
Percent-
ages.
Specific
Gravity.
Flashing
Point.
Deg. F.
113°
Rhigolene. )
traces
590 to 625
113 to 140°
340 to 158°
158 to 248°
248°
to
347°
Chymogene. |
Gasolene (petroleum spirit). . .
Benzine, naphtha C, benzolene.
( Benzine, naphtha B
4 " " A
( Polishing oils. . .
1.5
10.
2.5
2.
.636 to .657
.680 to .700
.714 to .718
.725 to .737
'"i4"'
'"32"'
338° and )
Kerosene (lamp-oil)
50.
802 to 820
100 to 122
upwards, I
482°
Lubricating oil
15
850 to 915
230
Paraffine wax
2
Residue and Loss
16.
Lima Petroleum, produced at Lima, Ohio, is of a dark green
very fluid, and marks 48° Baum6 at 15° C. (sp. gr., 0.792).
The distillation in fifty parts, each part representing 2% by volume
the following results :
color,
Per Sp.
cent. Gr.
Per
cent
Sp.
. Gr.
Per
cent.
Sp.
Gr.
Per
cent
Sp. Per
. Gr. cent.
1?:
Per
cent.
Sp.
Gr.
2
0.680
18
0.720
34
0.764
50
0.802
68
0.820
88
0.815
4
.683
20
.728
36
.768
52j
I
70
.825
90
.815
6
.685
22
.730
38
.772
to
> .806
72
.830
S"
8
.690
24
.735
40
.778
58
>
73
.830
92)
10
.694
26
.740
42
.782
60
.800
76
.810
tot
3
12
.698
28
.742
44
,788
62
.804
78
.820
100 i
S
14
.700
30
.746
46
..792
64
.808
82
.818
<s
IS
.706
32
.760
48
.800
66
.812
86
.816
tf
RETURNS.
16 per cent naphtha, 70° Baum§. 6 per cent paraffine oil.
68 " burning oil. 10 " residuum.
The distillation started at 23° C., this being due to the large amount of
naphtha present, and when 60$ was reached, at a temperature of 310° C.,
the hydrocarbons remaining in the retort were dissociated, then gases
escaped, lighter distillates were obtained, and, as usual in such cases, the
temperature decreased from 310° C. down gradually to 200° C., until 75$ of
oil was obtained, and from this point the temperature remained constant
until the end of the distillation. Therefore these hydrocarbons in statu
mnriendi absorbed much heat. (Jour. Am. Chem. Soc.)
Value of Petroleum as Fuel.— Thos. Urquhart, of Russia (Proc.
Inst. M. E., Jan. 1889), gives the following table of the theoretical eyapora
tive power of petroleum in comparison with that of coal, as determined by
Messrs. Favre & Silbermann:
Fuel.
Specific
Gravity
at
32° F.,
Water
= 1.000.
Chem. Comp.
Heating-
power,
British
Thermal
Units.
Theoret.
Evap., Ibs.
Water per
Ib. Fuel,
from and
at 212° F.
C.
H.
O.
Penna. heavy crude oil
Caucasian light crude oil. .
" heavy " " ..
Petroleum refuse
Good English Coal, Mean
of 98 Samples
S. G.
0.886
0.884
0.938
0.928
1.380
p. c.
84.9
86.3
86.6
87.1
80.0
p. c.
13.7
13.6
12.3
11.7
5.0
p. c.
1.4
0.1
1.1
1.2
8.0
Units.
20,736
22,027
20,138 -
19,832
14,112
Ibs.
21.48
22.79
20.85
20.53
14.61
646 FUEL.
In experiments on Russian railways with petroleum as fuel Mr. TTrquhart
obtained an actual efficiency equal to 82% of the theoretical heating-value.
The petroleum is fed to the furnace by means of a spray-injector driven by
steam. An induced current of air is canied in around the injector-nozzle,
and additional air is supplied at the bottom of the furnace.
Oil vs. Coal as Fuel. (Iron Age, Nov. 2, 1893.)— Test by the Twin
City Rapid Transit Company of Minneapolis and St. Paul. This test showed
that with the ordinary Lima oil weighing 6 6/10 pounds per gallon, and
costing 2J4 cents per gallon, and coal that gave an evaporation of 7^ Ibs. of
water per pound of coal, the two fuels were equally economical when the
price of coal was $3.85 per ton of 2000 Ibs. With the same coal at $2.00 per
ton, the coal was 37# more economical, and with the coal at $4.85 per ton,
the coal was 20% more expensive than the oil. These results include the
difference in the cost of handling the coal, ashes, and oil.
In 1892 there were reported to the Engineers1 Club of Philadelphia some
comparative figures, from tests undertaken to ascertain the relative value
Of coal, petroleum, and gas.
Lbs. Water, from
and at 212° F.
J Ib. anthracite coal evaporated 9.70
1 Ib. bituminous coal 10.14
1 Ib. fuel oil, 36° gravity 16 48
1 cubic foot gas, 20 C. P 1.28
The gas used was that obtained in the destination of petroleum, having
about the same fuel-value as natural or coal-gas of equal candle-power.
Taking the efficiency of bituminous coal as a basis, the calorific energy of
petroleum is more than C0# greater than that of coal ; whereas, theoretically,
petroleum exceeds coal only about 45$— the one containing 14, 500 heat-units.
and the other 21,000.
Crude Petroleum vs. Indiana Block Coal for Steam-
raising at the South Chicago Steel Works. (E. C. Potter
Trans. A. I. M. E., xvii, bO?.)— With coal, 14 tubular boilers 1C ft. x 5ft. re-
quired 25 men to operate them ; with fuel oil, 6 men were required, a saving
of 19 men at $2 per day, or $38 per day.
For one week's work 2731 barrels of oil were used, against 848 tons of coal
required for the same work, showing 3.^2 barrels of oil to be equivalent to 1
ton of coal. With oil at 60 cents per barrel and coal at $2.15 per ton, the rel-
ative cost of oil to coal is as $1.93 to $2.15. No evaporation tests were
made.
Petroleum as a Metallurgical Fuel.— C. E. Felton (Trans. A. I.
M. E., xvii, 809) reports a series of trials with oil as fuel in steel-heating and
open-hearth steel-furnaces, and in raising steam, with results as follows : 1.
In a run of six weeks the consumption of oil, partly refined (the paraffine
and some of the naphtha being removed), in heating 14-inch ingots it) Siemens
furnaces was about 6^6 gallons per ton of blooms. 2. In melting in a 30-ton
open-hearth furnace 48 gallons of oil were used per ton of ingots. 3. In a
six weeks' trial with Lima oil from 47 to 54 gallons of oil were required per
ton of ingots. 4. In a six months' trial with Siemens heating-furnaces the
consumption of Lima oil was 6 gallons per ton of ingots. Under the most
favorable circumstances, charging hot ingots and running full capacity, 4J4
to 5 gallons per ton were required. 5. In raising steam in two 100-H.P0
tubular boilers, the feed- water being supplied at 160° F., the average evap-
oration was about 12 pounds of water per pound of oil, the best 12 hours0
work being 16 pounds.
In all of the trials the oil was vaporized in the Archer producer, an apparat*
us for mixing the oil and superheated steam, and heating the mixture to a
high temperature. From 0.5 Ib. to 0.75 Ib. of pea-coal was used per gallon
of oil in the oroducer itself.
FUEL GAS.
The following notes are extracted from a paper by W. J. Taylor on " The
Energy of Fuel " (Trans. A. I. M. E., xviii. 205):
Carbon Gas.— In the old Siemens producer, practically, all the heat of
primary combustion— that is, the burning of solid carbon to carbon monox-
ide, or about 30# of the total carbon energy— was lost, as little or no steam
was used in the producer, and nearly all the sensible heat of the gas was
dissipated in its passage from the producer to the furnace, which was usu-
ally placed at a considerable distance.
JModern practice has improved on this plan, by introducing steam with the
FUEL GAS. 64?
air blown into tW producer, and by utilizing the sensible heat of the gas in
the combustion-furnace. It ought to be possible to oxidize one out of every
four Ibs. of carbon with oxygen derived from water-vapor. The thermic
reactions in this operation are as follows:
Heat-units.
4 Ibs. C burned to CO (3 Ibs. gasified with air and 1 Ib. with water)
develop 17,600
1.5 Ibs. of water (which furnish 1.33 Ibs. of oxygen to combine with 1
Ib. of carbon) absorb by dissociation 10,333
The gas, consisting of 9.333 Ibs. CO, 0.167 Ib. H, and 13.39 Ibs. N, heated
600°, absorbs 3,748
Leaving for radiation and loss 3,519
17,600
The steam which is blown into a producer with the air is almost all con-
densed into finely-divided water before entering the fuel, and consequently
is considered as water in these calculations.
The 1.5 Ibs. of water liberates .167 Ib. of hydrogen, which is delivered to
the gas, and yields in combustion the same heat that it absorbs in the pro-
ducer by dissociation. According to this calculation, therefore, 60$ of the
heat of primary combustion is theoretically recovered by the dissociation of
steam, and, even if all the sensible heat of the gas be counted, with radia-
tion and other minor items, as loss, yet the gas must carry 4 x 14,500 —
(3748 -f 3519) = 50,733 heat-units, or 87$ of the calorific energy of the carbon.
This estimate shows a loss in conversion of 13$, without crediting the gas
with its sensible heat, or charging it with the heat required for generating
the necessary steam, or taking into account the loss due to oxidizing some
of the carbon to CO2. In good producer-practice the proportion of CO2 in
the gas represents from 4$ to 7% of the C burned to CO2, but the extra heat
of this combustion should be largely recovered in the dissociation of more
water-vapor, and therefore does not represent as much loss as it would indi-
cate. As a conveyer of energy, this gas has the advantage of carrying 4.46
Ibs. less nitrogen than would be present if the fourth pound of coal had
been gasified with air; and in practical working the use of steam reduces
the amount of clinkering in the producer.
Anthracite Gas,— In anthracite coal there is a volatile combustible
varying in quantity from 1.5$ to over 1%. The amount of energy derived
from the coal is shown in the following theoretical gasification made with
coal of assumed composition: Carbon, 85$; vol. HC, 5$; ash, 10$; 80 Ibs. car-
bon assumed to be burned to CO; 5 Ibs. carbon burned to COa; three fourths
of the necessary oxygen derived from air, and one fourth from water.
/ Products.—* »
Process. Pounds. Cubic Feet. Anal, by Vol.
80 Ibs. C burned to CO 186.66 2529.24 33.4
5 Ibs. C burned to COa 18.33 157.64 2.0
5 Ibs. vol. HC (distilled) 5.00 116.60 1.6
120 Ibs. oxygen are required, of which
30 Ibs. from H2O liberate H 3.75 712.50 9.4
90 Ibs. from air are associatied with N 301 .05 4064.17 53.6
514.79 758015 100.0
Energy in the above gas obtained from 100 Ibs. anthracite:
180 . 66 Ibs CO 807,304 heat-units.
5.00 " CH4 117,500 " v
3.75 " H 232,500 "
1,157,304
Total energy in gas per Ib 2,248
" 100 Ibs. of coal.. 1,349,500 . "
Efficiency of the conversion 86$.
The sum of CO and H exceeds the results obtained in practice. The sen-
Bible heat of the gas will probably account for this discrepancy, and, there-
fore, it is safe to assume the possibility of delivering at least 82$ of the
energy of the anthracite.
Bituminous Gas.— A theoretical gasification of 100 Ibs. of coal, con-
taining 55$ of carbon and 32$ of volatile combustible (which is above the
average of Pittsburgh coal), is made in the following table. It is assumed
that 50 Ibs. of C are burned to CO and 5 Ibs. to COa; one fourth of the 0 is
048 FUEL.
derived from steam and three fourths from air; the heat value of the
volatile combustible is taken at 20,000 heat-units to the pound. In comput-
ing volumetric proportions all the volatile hydrocarbons, fixed as well as
condensing, are classed as marsh-gas, since it is only by some such tenta-
tive assumption that even an approximate idea of the volumetric composi-
tion can be formed. The energy, however, is calculated from weight:
, Products. — ,
Process. Pounds. Cubic Feet. Anal, by Vol.
50 Ibs. C burned to..... CO 116.66 1580.7 27.8
5 Ibs. C burned to CO3 18.33 157.6 2.7
32 Ibs. vol. HC (distilled) 32.00 746.2 13.2
80 Ibs. O are required, of which 20 Ibs.,
derived from HaO, liberate ,H 2.5 475.0 8.3
60 Ibs. O, derived from air, are asso-
ciated with N 200.70 2709.4 47.8
370.19 5668.9 998
Energy in 116.66 Ibs. CO 504,554 heat-units.
44 " 32.00 Ibs. vol. HC.... 640,000 "
" " 2. 50 Ibs. H 155,000 "
1,299,554 "
Energy in coal 1,437,500 "
Per cent of energy delivered in gas 90.0
Heat-units in 1 Ib. of gas 3,484
Water-gas.— Water-gas is made in an intermittent process, by blowing
up the fuel-bed of the producer to a high state of incandescence (and in
some cases utilizing the resulting gas, which is a lean producer-gas), then
shutting off the air and forcing steam through the fuel, which dissociates
the water into its elements of oxygen and hydrogen, the former combining
with the carbon of the coal, and the latter being liberated.
This gas can never play a very important part in the industrial field, owing
to the large loss of energy entailed in its production, yet there are places
and special purposes where it is desirable, even at a great excess in cost per
unit of heat over producer-gas; for instance, in small high-temperature fur-
naces, where much regeneration is impracticable, or where the " blow-up "
gas can be used for other purposes instead of being wasted.
The reactions and energy required in the production of 1000 feet of water-
gas, composed, theoretically, of equal volumes of CO and H, are as follows:
500 cubic feet of H weigh 2.635 Ibs.
500 cubic feet of CO weigh 36.89 "
Total weight of 1000 cubic feet 39.525 Ibs.
Now, as CO is composed of 12 parts C to 16 of O, the weight of C in 36.89
Ibs. is 15.81 Ibs. and of O 21.08 Ibs. When this oxygen is derived from water
it liberates, as above, 2.635 Ibs. of hydrogen. The heat developed and ab-
sorbed in these reactions (roughly, as we will not take into account the en-
ergy required to elevate the coal from the temperature of the atmosphere
to say 1800°) is as follows:
Heat units.
2.635 Ibs. H absorb in dissociation from water 2.635 X 62,000.. = 163,370
15.81 Ibs. C burned to CO develops 15.81 X 4400 = 69,564
Excess of heat- absorption over heat-development = 93,806
If this excess could be made up from C burnt to CO2 without loss by radi-
ation, we would only have to burn an additional 4.83 Ibs. C to supply this
heat, and we could then make 1000 feet of water-gas from 20.64 Ibs. of car-
bon (equal 24 Ibs. of 85$ coal). This would be the perfection of gas-making,
as the gas would contain really the same energy as the coal; but instead, we
require in practice more than double this amount of coal, and do not deliver
more than 50$ of the energy of the fuel in the gas, because the supporting
heat is obtained in an indirect way and with imperfect combustion. Besides
this, it is not often that the sum of the CO and H exceed 90$, the balance be-
ing CO2 anO N. But water-gas should be made with much less loss of en-
ergy by burning the "blow-up" (producer) gas in brick regenerators, the
stored -up heat of which can be returned to the producer by the air used in
blowing-up.
The following table shows what may be considered average volumetric
FUEL GAS.
649
analyses, and the weight and energy of 1000 cubic feet, of the four types of
gases used for heating and illuminating purposes:
Natural
Gas.
Coal-
gas.
Water-
gas.
Producer-gas.
CO
0.50
2.18
92.6
0.31
6.0
46.0
40.0
4.0
45.0
45.0
2.0
Anthra.
27. 0
12.0
1.2
Bitu.
27.0
12.0
2.5
0.4
2.5
56.2
0.3
H
CH4
C,tU
co: :.:
0.26
3.61
0.34
0.5
1.5
0.5
1.5
32.0
735,000
4.0
2.0
0.5
1.5
45.6
322,000
2.5
57.0
0.3
N
o
Vapor .
Pounds in 1000 cubic feet.
Heat units in 1000 cubic feet
#-15.6
1,100,000
65.6
137,455
65.9
156,917
Natural Gas in Ohio and Indiana.
(Eng. and M. «/., April 21, 1894.)
Description.
Ohio.
Indiana.
Fos-
toria.
Findlay
St
Mary's.
Muncie.
Ander-
son.
Koko-
mo.
Mar-
ion.
Hydrogen
1.89
92.84
.20
.55
.20
.35
3.82
.15
1.64
93.35
.35
.41
.25
.39
3.41
.20
1.94
93.85
.20
.44
.23
.35
2.98
.21
2.35
92.67
.25
.45
.25
.35
3.53
.15
1.86
93.07
.47
.73
.26
.42
3.02
.15
1.42
94.16
.30
.55
.29
.30
2.80
.18
1.20
93.57
.15
.60
.30
.55
3.42
.20
Marsh-gas
defiant gas
Carbon monoxide..
Carbon dioxide —
Oxygen
Nitrogen
Hydrogen sulphide
Approximately 30,000 cubic feet of gas have the heating power of one
ton of coal.
Producer-gas from One Ton of Coal.
(W. H. Blauvelt, Trans. A. I. M. E., xviii. 614.)
Analysis by Vol.
Per
Cent.
Cubic Feet.
Lbs.
Equal to—
CO ...
H
25.3
9 2
33,213.84
12,077.76
2451.20
63.56
1050.51
63.56
Ibs. C+ 1400
.71bs.O.
CH4
3 1
4069.68
174 66
174 66
CH4.
C9H4
0.8
1,050.24
77.78
77.73
C2H4.
CO2 .-
3.4
4,463.52
519.02
141.54
C + 377.
44 Ibs. O.
JN (.by difference .
58.2
76,404.96
5659.63
7350.17
Air.
100.0
131,280.00
8945.85
Calculated upon this basis, the 131,280 ft. of gas from the ton of coal con-
tained 20,311,162 B.T.U., or 155 B.T.U. per cubic ft., or 2270 B.T.U. per Ib.
The composition of the coal from which this gas was made was as follows:
Water. 1.20$; volatile matter, 36. 22$; fixed carbon, 57.98$; sulphur, 0.70#;
ash, 3.78j£. One ton contains 1159.6 Ibs. carbon and 724.4 Ibs. volatile com-
bustible, the energy of which is 31,302,200 B.T.U. Hence, in the processes of
gasification and purification there was a loss of 35.2£ of the energy of the
coal.
The composition of the hydrocarbons in a soft coal is uncertain and quite
complex; but the ultimate analysis of the average coal shows that it ap-
proaches quite nearly to the composition of CH4 (marsh-gas).
Mr. Blauvelt emphasizes the following points as highly important in soft
coal producer-practice:
650 FUEL.
First. That a large percentage of the energy of the coal is lost when the
gas is made in the ordinary low producer and cooled to the temperature of
the air before being used. To prevent these sources of loss, the producer
should be placed so as to lose as little as possible of the sensible heat of the
gas, and prevent condensation of the hydrocarbon vapors. A high fuel-bed
should be carried, keeping the producer cool on top, thereby preventing the
breaking-down of the hydrocarbons and the deposit of soot, as well as keep-
ing the carbonic acid low.
Second. That a producer should be blown with as much steam mixed with
the air as will maintain incandescence. This reduces the percentage of
nitrogen and increases the hydrogen, thereby greatly enriching the gas.
The temperature of the producer is kept down, diminishing the loss of heat
by radiation through the walls, and in s large measure preventing clinkers.
'The Combustion of Producer-gas. (H. H. Campbell, Trans.
A. I. M. E., xix, 128.) — The combustion of the components of ordinary pro-
ducer-gas may be represented by the following formula:
C2H4 + 6O = 2COa + 2H2O; 2H + O = HaO;
CH4 + 40 = C02 + 2HaO; CO + O = COa.
AVERAGE COMPOSITION BY VOLUME OF PRODUCER- GAS: A, MADE WITH OPEN
GRATES, NO STEAM IN BLAST; B, OPEN GRATES, STEAM-JET IN BLAST. 10
SAMPLES OF EACH.
CO2. O. CaH4. CO. H. CH4. N.
A min 3.6 0.4 0.2 20.0 5.3 3.0 58.7
A max 5.6 0.4 0.4 24.8 8.5 5.2 64.4
A average... 4.84 0.4 0.34 22.1 6.8 3.74 61.78
B min 4.6 0.4 0.2 20.8 6.9 2.2 57.2
B max 6.0 0.8 0.4 24.0 9.8 3.4 62.0
B average... 5.3 0.54 0.36 22.74 8.37 2.56 60.13
The coal used contained carbon 82$, hydrogen 4.7$.
The following are analyses of products of combustion :
C02. O. CO. CH4. H. N.
Minimum 15.2 0.2 trace, trace. trace. 80.1
Maximum 17.2 1.6 2.0 0.6 2.0 83.6
Average 16.3 0.8 0.4 0.1 0.2 82.2
Use of Steam in Producers and in Boiler-furnaces. (R.
W. Raymond, Trans. A. I. M. E., xx. 635.)— No possible use of steam can
cause a gain of heat. If steam be introduced into a bed of incandescent
carbon it is decomposed into hydrogen and oxygen.
The heat absorbed by the reduction of one pound of steam to hydrogen is
much greater in amount than the heat generated by the union of the
oxygen thus set free with carbon, forming either carbonic oxide or carbonic
acid. Consequently, the effect of steam alone upon a bed of incandescent
fuel is to chill it. In every water-gas apparatus, designed to produce by
means of the decomposition of steam a fuel -gas relatively free from nitro-
gen, the loss of heat in the producer must be compensated by some reheat-
ing device.
This loss may be recovered if the hydrogen of the steam is subsequently
burned, to form steam again. Such a combustion of the hydrogen is con-
templated, in the case of fuel-gas, as secured in the subsequent use of that
gas. Assuming the oxidation of H to be complete, the use of steam will
cause neither gain nor loss of heat, but a simple transference, the heat
absorbed by steam decomposition being restored by hydrogen combustion.
In practice, it may be doubted whether this restoration is ever complete.
But it is certain that an excess of steam would defeat the reaction alto-
gether, and that there must be a certain proportion of steam, which per-
mits the realization of important advantages, without too great a net loss in
heat.
The advantage to be secured (in boiler furnaces using small sizes of
anthracite) consists principally in the transfer of heat from the lower side
of the fire, where it is not wanted, to the upper side, where it is wanted.
The decomposition of the steam below cools the fuel and the grate-bars,
whereas a blast of air alone would produce, at that point, intense combus-
tion (forming at first COa), to the injury of the grate, the fusion of part of
the fuel, etc.
The proportion of steam most economical is not easily determined. The
temperature of the steam itself, the nature of the fuel mixture, and .the use
or non-use of auxiliary air- supply, introduced into the gases above or
ILLUMINATING-GAS.
651
beyond the fire-bed, are factors affecting the problem. (See Trans.
A. I. M. E., xx. 625.)
Gas Analyses by Volume and by Weight.— To convert an an-
alysis of a mixed gas by volume into analysis by weight: Multiply the per-
centage of each constituent gas by the density of that gas (see p. 166). Divide
each product by the sum of the products to obtain the percentages by weight.
Gas-fuel for Small Furnaces,— E. P. Reichhelm (Am. Mach.,
Jan. 10, 1895) discusses the use of gaseous fuel for forge fires, for drop-
forging, in annealing-ovens and furnaces for melting brass and copper, for
case-hardening, muffle-furnaces, and kilns. Under ordinary conditions, in
such furnaces he estimates that the loss by draught, radiation, and the
heating of space not occupied by work is, with coal, 80$, with petroleum 70£,
and with gas above the grade of producer-gas 25£. He gives the following
table of comparative cost of fuels, as used in these furnaces :
Kind of Gas.
®.S 3
03 §
No. of Heat-
units in Fur-
naces after
Deducting
25£ Loss.
Average Cost
per 1,000 Ft.
0
Natural gas . .
1,000,000
675,000
646,000
690,000
313,000
377,000
185,000
150,000
306,365
750,000
506,250
484,500
517,500
234,750
282,750
138,750
112,500
229,774
Coal-gas 20 candle-power
$1.25
1.00
.90
.40
.45
.20
.15
.15
$2.46
2.06
1.73
1.70
1.59
1.44
1.33
.65
.73
.73
Gasolene gas 20 candle-power
Water-gas from coke
Water-gas from bituminous coal
Water-gas and producer-gas mixed. . . .
Producer-gas
Naphtha-gas, fuel 2>£ gals, per 1000 ft..
Coal, $4 per ton, per 1,000,000 heat-units utilized
Crude petroleum, 3 cts. per gal., per 1,000,000 he
at-units. .
Mr. Reichhelm gives the following figures from practice in melting brass
with coal and with naphtha converted into gas: 1800 Ibs. of metal require
1080 Ibs. of coal, at $4.65 per tou, equal to $2 51, or, say, 15 cents per 100 Ibs.
Mr. T.'s report : 2500 Ibs. of metal require 47 gals, of naphtha, at 6 cents per
gal., equal to $2.82, or, say, 11*4 cents per 100 Ibs.
ILLUMINATING-GAS.
Coal-gas is made by distilling bituminous coal in retorts. The retort
is usually a long horizontal semi-cylindrical or Q shaped chamber, holding
from 160 to 300 Ibs. of coal. The retorts are set in *' benches " of from
3 to 9, heated by one fire, which is generally of coke. The vapors distilled
from the coal are converted into a fixed gas by passing through the retort,
which is heated almost to whiteness.
The gas passes out of the retort through an " ascension-pipe " into a long
horizontal pipe called the hydraulic main, where it deposits a portion ol
the tar it contains; thence it goes into a condenser, a series of iron tubes
surrounded by cold water, where it is freed from condensable vapors, as
ammonia-water, then into a washer, where it is exposed to jets of water,
and into a scrubber, a large chamber partially filled with trays made of
wood or iron, containing coke, fragments of brick or paving-stones, which
are wet with a spray of water. By the washer and scrubber the gas is freed
from the last portion of tar and ammonia and from some of the sulphur
compounds. The gas is then finally purified from sulphur compounds by
passing it through lime or oxide of iron. The gas is drawn from the hy-
draulic main and forced through the washer, scrubber, etc., by an exhauster
or gas-pump.
The kind of coal used is generally caking bituminous, but as usually this
coal is deficient in gases of high illuminating power, there is added to it a
portion of cannel coal or other enricher.
The following table, abridged from one in Johnson's Cyclopedia, shows
the analysis, candle power, etc. , of ^oine gas coals and enrichers:
652
ILLUMIKATIKG-GAS.
Gas-coals, etc.
Vol. Matter.
1
'O
g
£
3
s »
ss-
^
5® 5
go.S
f-,
\*
-CO
5°
Coke per
ton of 2240
Ibs.
Gas purified 1
by 1 bush, of
lime,incu.ft.l
Ibs.
bush..
Pittsburgh, Pa
36.76
36.00
37.50
40.00
43.00
46.00
53.50
51.93
58.00
56.90
53.30
40.00
41.00
44.50
7.0?
6.00
5. GO
6.70
17.00
13.00
2.00
Westmoreland, Pa
Sterling, O
10,642
10,5-28
10,765
9,800
13,200
15,000
16.62
18.81
20.41
34.98
42.79
28.70
1544
1480
1540
1320
1380
1056
40
36
36
32
32
44
6420
3993
2494
2806
4510
Despard W Va
Petonia, W. Va
Grahamite, W. Va
The products of the distillation of 100 Ibs. of average gas-coal are about as
follows. They vary according to the quality of coal and the temperature of
distillation.
Coke, 64 to 65 Ibs.; tar, 6.5 to 7.5 Ibs.; ammonia liquor, 10 to 12 Ibs.; puri
fled gas, 15 to 12 Ibs.; impurities and loss, 4.5$ to3.5Jc.
The composition of the gas by volume ranges about as follows: Hydro-
gen, 38$ to 48$; carbonic oxide, 2$ to 14$; marsh-gas (Methane, CH4), 43$ to
31$; heavy hydrocarbons (CnHan, ethylene, propylene, benzole vapor, etc.),
7.5$ to 4.5$; nitrogen, \% to 3$.
In the burning of the gas the nitrogen is inert; the hydrogen and carbonic
oxide give heat but no light. The luminosity of the flame is due to the de-
composition by heat of the heavy hydrocarbons into lighter hydrocarbons
and carbon, the latter being separated in a state of extreme subdivision.
By the heat of the flame this separated carbon is heated to intense white-
ness, and the illuminating effect of the flame is due to the light of incandes-
cence of the particles of carbon.
The attainment of the highest degree of luminosity of the flame depends
upon the proper adjustment of the proportion of the heavy hydrocarbons
(with due regard to their individual character) to the nature of the diluent
mixed therewith.
Investigations of Percy F. Frankland show that mixtures of ethylene and
hydrogen cease to have any luminous effect when the proportion of ethy-
lene does not exceed 10$ of the whole. Mixtures of ethylene and carbonic
oxide cease to have any luminous effect when the proportion of the former*
does not exceed 20$, while all mixtures of ethylene and marsh-gas have more
or less luminous effect. The luminosity of a mixture of 10$ ethylene and 90$
marsh gas being equal to about 18 candles, and that of one of 20$ ethylene
and 80$ marsh- gas about 25 candles. The illuminating effect of marsh -gas
alone, when burned in an argand burner, is by no means inconsiderable.
For further description, see the Treatises on Gas by King. Richards, and
Hutrhes; also Appleton's Cyc. Mech., vol. i. p. 900.
"Water-gas. — Water-gas is obtained by passing steam through a bed of
coal, coke, or charcoal heated to redness or beyond. The steam is decom-
posed, its hydrogen being liberated and its oxygen burning the carbon ot
the fuel, producing carbonic-oxide gas. The chemical reaction is, C -f Ha(.)
= CO + 2H, or 2C -f 2H2O = C 4- CO2 -f 4H, followed by a splitting up ot
the CO2, making 2CO -f- 4H. By weight the normal gas CO -f 2H is com-
posed of C -f- O 4- H = 28 parts CO and 2 parts H, or 93.33$ CO and 6.67$ H;
12 + 16 + 2
by volume it is composed of equal parts of carbonic oxide and hydrogen.
Water-gas produced as above described has great heating- power, but no
illuminating- power. It may, however, be used for lighting by causing it to
heat to whiteness some solid substance, as is done in the Welsbach incan-
descent light.
An illuminating-)
gases or vapors, wh
products. A history of the development of modern illuminating water-gas
processes, together with a description of^the most recent forms of apparatus,
is given by Alex. C. Humphreys, in a paper on " Water-gas in the United
States," read before the Mechanical Section of the British Association for
Advancement of Science, in 1889. After describing many earlier patents, he
states that success in the manufacture of water-gas maybe said to date
g-gas is made from water-gas by adding to it hydrocarbon
which are usually obtained from petroleum or some of its
ANALYSES OF WATER-GAS AND COAL-GAS COMPARED. 653
from 1874, when the process of T. S. C. L9\ve was introduced. All the later
most successful processes are the modifications of Lowe's, the essential
features of which were " an apparatus consisting of a generator and super-
heater internally fired; the superheater being heated by the secondary
combustion from the generator, the heat so stored up in the loose brick of
the superheater being used, in the second part of the process, in the fixing
or rendering permanent of the hydrocarbon gases; the second part of the
process consisting in the passing of steam through the generator fire, and
the admission of oil or hydrocarbon at some point between the fire of the
generator and the loose filling of the superheater."
The water-gas process thus has two periods: first the ''blow, "during
which air is blown through the bed coal in the generator, and the partially
burned gaseous products are completely burned in the superheater, giving
up a great portion of their heat to the fire-brick work contained in it, and
then pass out to a chimney; second, the "run" during which the air blast
is stopped, the opening to the chimney closed, and steam is blown through
the incandescent bed of fuel. The resulting water-gas passing into the car-
buretting chamber in the base of the superheater is there charged with hy-
drocarbon vapors, or spray (such as naphtha and other distillates or crude
oil) and passes through the superheater, where the hydrocarbon vapors be-
come converted into fixed illuminating gases. From the superheater the
combined gases are passed, as in the coal-gas process, through washers,
scrubbers, etc., to the gas-holder. In this case, however, there is DO am-
monia to be removed.
The specific gravity of water-gas increases with the increase of the heavy
hydrocarbons which give it illuminating power. The following figures, taken
from different authorities, are given by F. H. Shelton in a paper on Water-
gas, read before the Ohio Gas Light Association, in 1894;
Candle-power ... 19.5 20. 22.5 24. 25.4 26.3 28.3 29.6 .30 to 31.9
Sp. gr. (Air=l).. .571 .630 .589 .60 to .67 .64 .602 .70 .65 .65 to .71
Analyses of Water-gas and Coal-gas Compared.
The following analyses are taken from a report of Dr. Gideon E. Moore
on the Granger Water-gas, 1885:
Composition by Volume.
Composition by Weight.
Water-gas.
Coal-gas.
Heidel-
berg.
Water-gas.
Coal-
gas.
Wor-
cester.
Lake.
Wor-
cester.
Lake.
Nitrogen
2.64
0.14
0.06
11.29
0.00
1.53
28.26
18.88
37.20
100.00
3.85
0.30
0.01
12.80
0.00
2.63
23.58
20.95
35.88
2.15
3.01
0.65
2.55
1.21
1.33
8.88
34.02
46.20
0.04402
0.00365
0.00114
0.18759
0.06175
0.00753
0.00018
0.20454
0.04559
0.09992
0.01569
0.05389
0.03834
0.07825
0.18758
0.41087
0.06987
1.00000
Carbonic acid —
Oxygen
Ethylene
Propylene
Benzole vapor —
Carbonic oxide . . .
Marsh-gas . . .
0.07077
0.46934
0.17928
0.04421
0.11700
0.37664
0.19133
0.04103
1.00000
Hydrogen
100.00
100.00
1.00000
Density : Theory.
Practice .
0.5825
0.5915
0.6057
0.6018
0.4580
B. T. U. from 1 cu.
ft. : Water liquid.
" vapor
650.1
597.0
688.7
646.6
642.0
577.0
Flame-temp
Av. candle-power.
5311. 2°F.
22.06
5281. 1°F.
26.31
5202. 9°F.
The heating values (B. T. U.) of the gases are calculated from the analysis
by weight, by using the multipliers given below (computed from results of
654
ILLUMINATING-GAS.
J. Thomsen), and multiplying the result by the weight of 1 cu, ft. of the gas
at 62° F., and atmospheric pressure.
The flame temperatures (theoretical) are calculated on the assumption of
complete combustion of the gases in air, without excess of air.
The candle-power was determined by photometric tests, using a pressure
of ^-iu. water-column, a caudle consumption of 120 grains of spermaceti
per hour, and a meter rate of 5 cu. ft. per hour, the result being corrected
for a temperature of 62° F. and a barometric pressure of 30 in. It appears
that the candle-power may be regulated at the pleasure of the person in
charge of the apparatus, the range of candle-power being from 20 to 29
candles, according to the manipulation employed.
Calorific Equivalents of Constituents of Illuminating-
gas.
Heat-units from 1 Ib.
Water Water
Liquid. Vapor.
Ethylene 21,524.4
Propylene 21,222.0 19,834.2
Benzole vapor.... 18,954.0 17,847.0
Heat-units from 1 Ib,
Water Water
Liquid. Vapor.
20,134.8 Carbonic oxide.. 4,395.6 4,395.6
- Marsh- gas 24,021.0 21,592.8
Hydrogen 61,524.0 51,804.0
Efficiency of a Water-gas Plant,— The practical efficiency of an
illuminating water-gas setting is discussed in a paper by A. G. Glasgow
(Proc. Am. Gaslight Assn., 18UO), from which the following is abridged :
The results refer to 1000 cu. ft. of unpurifled carburetted gas, reduced tc
60° F. The total anthracite charged per 1000 cu. ft. of gas was 33.4 Ibs., ash
and unconsumed coal removed 9.9 Ibs., leaving total combustible consumed
23.5 Ibs., which is taken to have a fuel-value of 14500 B. T. U. per pound, or
a total of 340,750 heat- units.
Composi-
tion by
Volume.
Weight
per
100 cu. ft.
Composi-
tion by
Weight.
Specific
Heat.
I. Carburetted
Water-gas.
fC02-f HaS..
C.&4. -
3.8
14.6
28.0
17.0
35.6
1.0
.465842
1.139968
2.1868
.75854
.1991404
.078596
.09647
.23607
.45285
.15710
.04124
.01627
.02088
.08720
.11226
.09314
.14041
.00397
co.'?.... .::
CH4.
H...
N
,
100.0
4.8288924
1.00000
.45786
II. Uncarburetted
gas.
COQ .
3.5
43.4
51.8
1.3
.429065
3.389540
.289821
.102175
.1019
.8051
.0688
.0242
.02205
.19958
.23424
.00591
CO
H
N
100.0
4.210601
1.0000
.46178
III. Blast products
escaping from -
superheater.
rcOa
17.4
3.2
79.4
2.133066
.2856096
6.2405221
.2464
.0329
.7207
.05342
.00718
.17585
o.a...
N
I
100.0
8.6591980
1.0000
.23645
IV. Generator
blast- gases.
rcoQ...
9.7
17.8
72.5
1.189123
1.390180
5.698210
.1436
.1680
.6884
.031075
.041647
.167970
CO...
N .
100.0
8.277513
1.0000
.240692
The heat energy absorbed by the apparatus is 23.5 X 14,500 = 340,750 heat-
units = A. Its disposition is as follows :
B, the energy of the CO produced;
C, the energy absorbed in the decomposition of the steam;
D, the difference between the sensible heat of the escaping
gases and that of the entering oil;
E, the heat carried off by the escaping blast products;
F, the heat lost by radiation from the shells:
EFFICIENCY OF A WATEfc-GAS PLAHT. 655
#, the heat carried away from the shells by convection (air-currents);
H, the heat rendered latent in the gasification of the oil;
/, the sensible heat in the ash and unconsumed coal recovered from the
generator.
The heat equation is A- B+C+D+E+ F+ G -f H+ I; A being
known. A comparison of the CO in Tables I and II show that-^ • , or 04.5%
of. the volume of carburetted gas is pure water-gas, distributed thus : COa ,
2.3#; CO, 28.0£; H, 33.4$; N, 0.8#; = 64.5#. 1 Ib. of CO at 60° F. = 13.531 cu.
ft. CO per 1000 cu. ft. of gas = 280 •*- 13.531 = 20.694 Ibs. Energy of the CO
= 20.694 X 4395.6 = 91,043 heat-units, = B. 1 Ib. of H at 60° F. = 189.2 cu.
ft. H per M of gas = 334-^-189.2 = 1.7653 Ibs. Energy of the H per Ib.
(according to Thomsen, considering the steam generated by its combustion
to be condensed to water at 75° F.) = 61,524 B.'T. U. In Mr. Glasgow's ex-
periments the steam entered the generator at 331° F. ; the heat required to
raise the product of combustion of 1 Ib. of H, viz., 8.98 Ibs. HaO, from water
at 75° to steam at 331° must therefore be deducted from Thomson's figure, or
61,524 - (8.98 X 1140.2) = 51,285 B. T. U. per Ib. of H. Energy of the H, then,
is 1.7653 X 51,285 = 90,533 heat-units, = C. The heat lost due to the sensible
beat in the illuminating-gases, their temperature being 1450° F., and that of
the entering oil 235° F., is 48.29 (weight) X .45786 sp. heat X 1215 (rise of tem-
perature) = 26,864 heat-units = D.
(The specific heat of the entering oil is approximately that of the issuing
gas.)
The heat carried off in 1000 cu. ft. of the escaping blast products is 86.592
(weight) X .23645 (sp. heat) X 1474° (rise of temp.) = 30,180 heat-units; the
temperature of the escaping blast gases being 1550° F., and that of the
entering air 76° F. But the amount of the blast gases, by registra-
tion of an anemometer, checked by a calculation from the analyses of the
blast gases, was 2457 cubic feet for every 1000 cubic feet of carburetted gas
made. Hence the heat carried off per M. of carburetted gas is 30,180 X
2.457 = 74,152 heat-units = E.
Experiments made by a radiometer covering four square feet of the shell
of the apparatus gave figures for the amount of heat lost by radiation
= 12,454 heat-units = F, and by convection = 15,696 heat-units = G.
The heat rendered latent by the gasefication of the oil was found by taking
the difference between all the heat fed into the carburetter and super-
heater and the total heat dissipated therefrom to be 12,841 heat-units = H.
The sensible heat in the ash and unconsumed coal is 9.9 Ibs. X 1500° X .25
(sp. ht.) = 3712 heat-units — I.
The sum of all the items B -f C + D + E + F+ G -f H+ 1= 327,295 heat-
units, which substracted from the heat energy of the combustible consumed,
340,750 heat-units, leaves 13,455 heat-units, or 4 percent, unaccounted for.
Of the total heat energy of the coal consumed, or 340,750 heat-units, the
energy wasted is the sum of items D, E, F, G, and I, amounting to 132,878
beat-units, or 39 per cent; the remainder, or 207,872 heat-units, or 61 per
cent, being utilized. The efficiency of the apparatus as a heat machine is
therefore 61 per cent.
Five gallons, or 35 Ibs. of crude petroleum were fed into the carburetter
per 1000 cu. ft. of gas made; deducting 5 Ibs. of tar recovered, leaves 30 Ibs.
X 20,000 = 600,000 heat-units as the net heating value of the petroleum used.
Adding this to the heating value of the coal, 340,750 B. T. U., gives 940,750
heat-units, of which there is found as heat energy in the carburetted gas, as
in the table below, 764,050 heat units, or 81 per cent, which is the commer-
cial efficiency of the apparatus, i.e., the ratio of the energy contained in
the finished product to the total energy of the coal and oil consumed.
The heating power per M. cu. ft. of
CO2 38.0
the carburetted gas is
CO2 35.0
C3H6* 146.0 X .117220 X 21222.0 = 363200 CO 434.0 X .078100 X 4395.6 = 148991
CO 280.0 X .078100 X 4395.6 = 96120 H 518.0 X .005594 X 61524.0 = 178277
CH4 170.0 X .044620 X 24021.0 = 182210 N 13.0
H 356.0 X .005594 X 61524.0 = 122520
N 10.0
The heating power per M. of the
uncarburetted gas is
1000.0 327268
1000.0 764050
* The heating value of the illuminants CnH2n is assumed to equal that
656 ILLUMINATING-GAS.
>
The candle-power of the gas is 31, or 6.2 candle-power per gallon of oil
used. The calculated specific gravity is .6355, air being 1.
For description of the operation of a modern carburetted water-gas
plant, see paper by J. Stelfox, Eng'g, July 20, 1894, p. 89.
Space required for a Water-gas Plant.— Mr. Shelton, taking
15 modern plants of the form requiring the most floor-space, figures the
average floor-space required per 1000 cubic feet of daily capacity as follows:
Water-gas Plants of Capacity Require an Area of Floor-space for
in 24 hours of each 1000 cu. ft. of about
100,000 cubic feet 4 square feet.
200,000 " " 3.5 " "
400,000 " " 2.75"
600,000 " " 2 to 2.5 sq.ft.
7 to 10 million cubic feet 1.25 to 1.5 sq. ft.
These figures include scrubbing and condensing rooms, but not boiler and
engine rooms. In coal-gas plants of the most modern and compact forms one
with 16 benches of 9 retorts each, with a capacity of 1,500,000 cubic feet per
24 hours, will require 4.8 sq. ft. of space per 1000 cu. ft. of gas, and one of 6
benches of 6 retorts each, with 300,000 cu. ft. capacity per 24 hours will re-
quire 6 sq. ft. of space per 1000 cu. ft. The storage-room required for the
gas-making materials is: for coal-gas, 1 cubic foot of room for every 232
cubic feet of gas made; for water-gas made from coke, 1 cubic foot of room
for every 373 cu. ft. of gas made; and for water-gas made from anthracite,
1 cu. ft. of room for every 645 cu. ft. of gas made.
The comparison is still more in favor of water-gas if the case is considered
of a water-gas plant added as an auxiliary to an existing coal-gas plant;
for, instead of requiring further space for storage of coke, part of that
already required for storage of coke produced and not at once sold can be
cut off, by reason of the water-gas plant creating a constant demand for
more or less of the coke so produced.
Mr. Shelton gives a calculation showing that a water-gas of .625 sp. gr.
would require gas-mains eight per cent greater in diameter than the same
quantity coal-gas of .425 sp. gr. if the same pressure is maintained at the
holder. The same quantity may be carried in pipes of the same diameter
if the pressure is increased in proportion to the specific gravity. With the
same pressure the increase of candle-power about balances the decrease of
flow. With five feet of coal-gas, giving, say, eighteen candle-power, 1 cubic
foot equals 3.6 candle-power; with water-gas of 23 candle-power, 1 cubic
foot equals 4.6 candle-power, and 4 cubic feet gives 18.4 candle-power, or
more than is given by 5 cubic feet of coal-gas. Water-gas may be made
from oven-coke or gas-house coke as well as from anthracite coal. A water-
gas plant may be conveniently run in connection with a coal-gas plant, the
surplus retort coke of the latter being used as the fuel of the former.
In coal-gas making it is impracticable to enrich the gas to over twenty
candle-power without causing too great a tendency to smoke, but water-gas
of as high as thirty candle-power is quite common. A mixture of coal-gas
and water-gas of a higher C.P. than 20 can be advantageously distributed.
Fuel-value of, Illuminating-gas.— E. Gr. Love (School of Mines
Qtly, January, 1892) describes F. W. Hartley's calorimeter for determining
the calorific power of gases, and gives results obtained in tests of the car-
buretted water-gas made by the municipal branch of the Consolidated Co.
of New York. The tests were made from time to time during the past two
years, and the figures give the heat-units per cubic foot at 60a F. and 30
inches pressure: 715, 692, 725, 732, 691, 738, 735, 703, 734, 730, 731, 727. Average,
721 heat units. Similar tests of mixtures of coal- and water-gases made by
other branches of the same company give 694, 715, 684, 692, 727, 665, 695, and
686 heat-units per foot, or an average of 694.7. ' The average of all these
tests was 710.5 heat-units, and this we may fairly take as representing the
calorific power of the illuminating gas of New York. One thousand feet of
this gas, costing $1.25, would therefore yield 710,500 heat-units, which would
be equivalent to 568,400 heat-units for $1.00.
The common coal-gas of London, with an illuminating power of 16 to 17
candles, has a calorific power of about 668 units per foot, and costs from 60
to 70 cents per thousand.
The product obtained by decomposing steam by incandescent carbon, as
effected iii the Motay process, consists of about 40# of CO, and a little over
50* of H.
FLOW OP GAS IN PIPES.
657
This mixture would have a heating-power of about 300 units per cubic foot,
and if sold at 50 cents per 1000 cubic feet would furnish 600,000 units for $1.00,
as compared with 568,400 units for $1.00 from illuminating gas at $1.25 per 1000
cubic feet. This illuminating-gas if sold at $1.15 per thousand would there-
fore be a more economical heating agent than the fuel-gas mentioned, at 50
cents per thousand, and be much more advantageous than the latter, in that
one main, service, and meter could be used to furnish gas for both lighting
and heating.
A large number of fuel-gases tested by Mr. Love gave from 184 to 470 heat-
units per foot, with an average of 309 units.
Taking the cost of heat from illuminating-gas at the lowest figure given
by Mr. Love, viz., $1.00 for 600,000 heat-units, it is a very expensive fuel, equal
to coal at $40 per ton of 2000 Ibs., the coal having a calorific power of only
12,000 heat-units per pound, or about 83% of that of pure carbon:
600,000 : (12,000 X 2000) :: $1 : $40.
FLOW OF GAS IN PIPES.
The rate of flow of gases of different densities, the diameter of pipes re-
quired, etc., are given in King's Treatise on Coal Gas, vol. ii. 374, as follows:
If d = diameter of pipe in inches,
Q = quantity of gas in cu. ft. per
hour,
I = length of pipe in yards,
h = pressure in inches of water,
« = specific gravity of gas, air be-
ing 1,
(1350)a/i'
h =
Molesworth gives Q = 1000J
J. P. Gill, Am. Gas-light Jour. 1894, gives Q = 1
This formula is said to be based on experimental data, and to make allow-
ance for obstructions by tar, water, and other bodies tending to check the
flow of gas through the pipe.
A set of tables. in Appleton's Cyc. Mech. for flow of gas in 2, 6, and 12 in.
pipes is calculated on the supposition that the quantity delivered varies
as the square of the diameter instead of as d 2 X ^ci, or ^d5.
These tables give a flow in large pipes much less than that calculated by
the formulae above given, as is shown by the following example. Length of
pipe 100 yds., specific gravity of gas 0.42, pressure 1-in. water-column
873
1116
Table in App. Cyc 1290
6-in. Pipe.
18,368
18,606
16,327
11,657
12-in. Pipe.
103,912
76,972
46,628
An experiment made by Mr. Clegg, in London, with a 4-in. pipe, 6 miles
long, pressure 3 in. of water, specific gravity of gas .398, gave a discharge
into the atmosphere of 852 cu. ft. per hour, after a correction of 33 cu. ft.
was made for leakage.
Substituting this value, 852 cu. ft., for Q in the formula Q = C Vd*h H- si,
we find C, the coefficient, = 997, which corresponds nearly with the formula
given by Molesworth.
658
ILLUMINATING-GAS.
Services for Lamps. (Molesworth.)
Lamps.
2
4
6
10...
Ft. from
Main.
... 40
... 40
... 50
...100
Require
Pipe- bore.
Lamps.
15....
20....
25 ...
30 ...
Ft. from
Main.
,... 130
.... 150
... 180
.. 200
Require
Pipe-bore.
1 in.
l^in.
(In cold climates no service less than % in. should be used.)
maximum Supply of Gas through Pipes in cii. ft. per
Hour, Specific Gravity being taken at ,4,5, calculated
from tne Formula Q = 1OOO V~d*h -*- si. (Molesworth.)
LENGTH OF PIPE = 10 YARDS.
Diameter
Pressure by the Water-gauge in Inches.
Inches.
.1
.2
.3
.4
.5
.6
31
64
187
365
638
1006
2066
.7
.8
.9
1.0
1 4
84
g
13
26
73
149
260
411
843
18
37
103
211
368
581
1192
22
46
126
258
451
711
1460
26
53
145
298
521
821
1686
29
59
162
333
582
918
1886
34
70
192
394
689
1082
2231
36
74
205
422
737
1162
2385
38
79
218
447
781
1232
2530
41
83
230
471
823
1299
2667
LENGTH OP PIPE = 100 YARDS.
Pressure by the Water-gauge in Inches.
.1
.2
.3
.4
.5
.75
1.0
1.25
1.5
2
2.5
H
8
12
14
17
19
23
26
29
32
36
42
%
23
32
42
46
51
63
73
81
89
103
115
1
47
67
82
94
105
129
149
167
183
211
236
1^4
82
116
143
165
184
225
260
291
319
368
412
l/'ll
130
184
225
260
290
356
411
459
503
581
049
2
267
377
462
533
596
730
843
943
1033
1193
1333
2^
466
659
807
932
1042
1276
1473
1647
1804
2083
2329
3
735
1039
1270
1470
1643
2012
2323
2598
2846
3286
3674
3^
1080
1528
1871
2161
2416
2958
3416
3820
4184
4831
5402
4
1508
813312613
3017
3373
4131
4770
5333
5842
6746
7542
LENGTH OP PIPE = 1000 YARDS.
fc
P
4
5
6
Pressure by the Water-gauge in Inches.
.5
.75
1.0
1.5
2.0
2.5
3.0
33
92
189
329
520
1067
1863
2939
41
113
231
403
636
1306
2282
3600
47
130
267
466
735
1508
2635
4157
58
159
327
571
900
1847
3227
5091
67
184
377
659
1039
2133
3727
5879
75
205
422
737
1162
2885
4167
6573
82
226
462
807
1273
2613
4564
7200
STEAM.
659
LENGTH OP PIPE = 5000 YARDS.
Diameter
of Pipe
in
Inches.
2
3
4
5
6
7
8
9
10
12
Pressure by the Water-gauge in Inches.
1.0
1.5
2.0
2.5
3.0
119
329
•78
1179
1859
2733
3816
5123
6667
10516
146
402
826
1443
2277
3347
4674
6274
8165
12880
169
465
955
1667
2629
3865
5397
7245
9428
14872
189
520
1067
1863
2939
4321
6034
8100
10541
16628
207
569
1168
2041
3220
4734
6610
8873
11547
18215
Mr. A. C. Humphreys says his experience goes to show that these tables
give too small a flow, but it is difficult to accurately check the tables, on ac-
count of the extra friction introduced by rough pipes, bends, etc. For
bends, one rule is to allow 1/42 of an inch pressure for each right-angle bend.
Where there is apt to be trouble from frost it is well to use no service of
less diameter than % in., no matter how short it may be. In extremely cold
climates this is now often increased to 1 in., even fora single lamp. The best
practice in the U. S. now condemns any service less than % in.
STEAM.
The Temperature of Steam in contact with water depends upon
the pressure under which it is generated. At the ordinary atmospheric
pressure (14.7 Ibs. per sq. in.) its temperature is 212° F. As the pressure is
increased, as by the steam being generated in a closed vessel, its tempera-
ture, and that of the water in its presence, increases.
Saturated Steam is steam of the temperature due to its pressure-
not superheated
Superheated Steam is steam heated to a temperature above that due
to its pressure.
Dry Steam is steam which contains no moisture. It may be either
saturated or superheated.
"Wet Steam is steam containing intermingled moisture, mist, or spray.
It has the same temperature as dry saturated steam of the same pressure.
Water introduced into the presence of superheated steam will flash into
vapor until the temperature of the steam is reduced to that due its pres-
sure. Water in the presence of saturated steam has the same temperature
as the steam. Should cold water be introduced, lowering the temperature
of the whole mass, some of the steam will be condensed, reducing the press-
ure and temperature of the remainder, until an equilibrium is established.
Temperature and Pressure of Saturated Steam.— The re-
lation between the temperature and the pressure of steam, according to
Regnault's experiments, is expressed by the formula (Buchanan's, as given
2938 16
by Clark) t = innQr77— i - 371.85, in which p is the pressure in pounds
o.iyyoo44 — log p
per square inch and t the temperature of the steam in Fahrenheit degrees.
It applies with accuracy between 120° F. and 446° F., corresponding to pres-
sures of from 1.68 Ibs. to 445 Ibs. per square inch. (For other formulae see
Wood's and Peabody's Thermodynamics.)
Total Heat of Saturated Steam (above 32° F.).— According to
Regnault's experiments, the formula for total heat of steam is H = 1091.7 +
.305(£ — 32°), in which t is temperature Fahr., and H the heat-units. (Ran-
kine and many others; Clark gives 1091.16 instead of 1091.7.)
Latent Heat of Steam.— The formula for latent heat of steam, as
given by Raukine and others, is L = 1091.7 — .695(£ - 32°). Clausius's for-
mula, in Fahrenheit units, as given by Clark, is L = 1092.6 - .708(£ - 32°).
660 STEAM.
The total heat in steam (above 32°) includes three elements:
1st. The heat required to raise the temperature of the water to the tem-
perature of the steam.
2d. The heat required to evaporate the water at that temperature, called
internal latent heat.
3d. The latent heat of volume, or the external work done by the steam in
making room for itself against the pressure of the superincumbent atmos-
phere (or surrounding steam if inclosed in a vessel).
The sum of the last two elements is called the latent heat of steam. In
Buel's tables (Weisbach, vol. ii., Dubois's translation) the two elements are
given separately.
Latent Heat of Volume ol Saturated Steam. (External
Work.)— The following formulas are sufficiently accurate for occasional use
within the given ranges of pressure (Clark, S. E.):
From 14.7 Ibs. to 50 Ibs. total pressure per square inch. . . 55.900 -f .07721.
From 50 Ibs. to 200 Ibs. total pressure per square inch.. .. 59.191 -f- .0655*.
Heat required to Generate 1 Ib. of Steam from water at 32° F.
Heat-unitSo
Sensible heat, to raise the water from 32° to 212° = . . . . 180.9
Latent heat, 1, of the formation of steam at 212° = . . . . 894.0
2, of expansion against the atmospheric
pressure, 2116.4 Ibs. per sq. ft.x26.36 cu. ft.
= 55,786 foot-pounds -t- 77t* = 71.7 965.7
Total heat above 32° F 1146.6
The Heat Unit, or British Thermal Unit.— The definition of
the heat-unit used in this work is that of Rankine, accepted by most modern
writers, viz., the quantity of heat required to raise the temperature of 1 Ib.
of water 1° F. at or near its temperature of maximum density (39.1° F.).
Peabody's definition, the heat required to raise a pound of water from 62°
to 63° F. is not generally accepted. (See Thurston, Trans. A. S. M. E.,
xiii. 351.)
Specific Heat of Saturated Steam.— The specific heat of satu-
rated steam is .305, that of water being 1; or it is 1.281, if that of air be 1.
The expression .305 for specific heat is taken in a compound sense, relating
to changes both of volume and of pressure which takes place in the eleva-
tion of temperature of saturated steam. (Clark, S. E.)
This statement by Clark is not strictly accurate. When the temperature
of saturated steam is elevated, water being present and the steam remain-
ing saturated, water is evaporated. To raise the temperature of 1 Ib. of
water 1° F. requires 1 thermal unit, and to evaporate it at 1° F. higher would
require 0.695 less thermal unit, the latent heat of saturated steam decreas-
ing 0.695 B.T.U. for each increase of temperature of 1° F. Hence 0.305 is
the specific heat of water and its saturated vapor combined.
When a unit weight of saturated steam is increased in temperature and in
pressure, the volume decreasing so as to just keep it saturated, the specific
heat is negative, and decreases as temperature increases. (See Wood,
Therm., p. 147; Peabody, Therm., p. 93.)
Density and Volume of Saturated Steam.— The density of
steam is expressed by the weight of a given volume, say one cubic foot; and
the volume is expressed by the number of cubic feet in one pound of steam.
Mr. Brownlee's expression for the density of saturated steam in terms of
X)'941
the pressure is D = /: , or log D = .941 logp-2.519, in which D is the den-
^ = ~~t or log v = 2.519 - .941 log p.
Relative Volume of Steam.— The relative volume of saturated
steam is expressed by the number of volumes of steam produced from one
STEAM. 661
volume of water, the volume of water being measured at the temperature
39° F. The relative volume is found by multiplying the volume in cu. ft. of
one Ib. of steam by the weight of a cu. ft. of water at 39* F., or 62.425 Ibs.
Gaseous Steam.— When saturated steam is superheated, or sur-
charged with heat, it advances from the condition of saturation into that of
gaseity. The gaseous state is only arrived at by considerably elevating the
temperature, supposing the pressure remains the same. Steam thus suffi-
ciently superheated is known as gaseous steam or steam gas.
Total Heat of Gaseous Steam.— Regnault found that the total
heat of gaseous steam increased, like that of saturated steam, uniformly
with the temperature, and at the rate of .475 thermal units per pound for
each degree of temperature, under a constant pressure.
The general formula for the total heat of gaseous steam produced from
1 pound of water at 32° F. is H = 1074.6 -f .475$. [This formula is for vapor
generated at 32°. It is not true if generated at 212°, or at any other tempera-
ture than 32°. (Prof. Wood.)]
The Specific Heat of Gaseous Steam is .475, under constant
pressure, as found by Reguanlt. It is identical with the coefficient of in-
crease of total heat for each degree of temperature. [This is at atmospheric
pressure and 212° F. He found it not true for any oilier pressure. Theory
indicates that it would be greater at higher temperatures. (Prof. Wood.)]
The Specific .Density of Gaseous Steam is .622, that of air being
1. That is to say, the weight of a cubic foot of gaseous steam is about five
eighths of that of a cubic foot of air, of the same pressure and temperature.
The density or weight of a cubic foot of gaseous steam is expressible by
the same formula as that of air, except that the multiplier or coefficient in
less in proportion to the less specific density. Thus,
' _ 2.7074p X .622 _ 1.684p
M-461 "~ *-r-461f
in winch Z>' is the weight of a cubic foot of gaseous steam, p the total pres-
sure per square inch, and t the temperature Fahrenheit.
Superheated Steam.— The above remarks concerning gaseous steam
are taken from Clark's Steam-engine. Wood gives for the total heat (above
32°) of superheated steam H - 1091.7 -f 0.48(2 - 32°).
The following is abridged from Peabody (Therrn., p. 115, etc.).
When far removed from the temperature of saturation, superheated steam
follows the laws of perfect gases very nearly, but near the temperature of
saturation the departure from those laws is too great to allow of calculations
by them for engineering purposes.
The specific heat at constant pressure, Cp, from the mean of three experi-
ments by Regnault, is 0.4805.
Values of the ratio of Cp to specific heat at constant volume:
Pressure p, pounds per square inch.. 5 50 100 200 300
Eatio Cp -f- Cv = k = 1.3351.332 1.330 1.324 1.316
Zeuner takes fc as a constant = 1 .333.
SPECIFIC HEAT AT CONSTANT VOLUME, SUPERHEATED STEAM.
Pressure, pounds per square inch 5 50 100 200 300
Specific heat Cv 0.351.348 .346 .344 .341
It is quite as reasonable to assume that Cv is a constant as to suppose that
Cp is constant, as has been assumed. If we take Cv to be constant, then Cp
will appear as a variable.
If p = pressure in Ibs. per sq. ft., v = volume in cubic feet, and T =
temperature in degrees Fahrenheit -f 460.7, then pv- 93.5 T — 971p±.
Total heat of superheated steam, H = 0.4805(2* - 10.38pi) 4- 857.2.
The Rationalization of Regnault's Experiments on
Steam. (J. McFarlane Gray, Proc. Inst. M. E., July, Ib89.)— The formulas
constructed by Regnault are strictly empirical, and were based entirely on
his experiments. They are therefore not valid beyond the range of temper-
atures and pressures observed.
Mr. Gray has made a most elaborate calculation, based not on experimenta
but on fundamental principles of thermodynamics, from which he deduces
foruvulse for the pressure and total heat of steam, and presents tables calcu-
662
STEAM.
lated therefrom which show substantial agreement with Regnault's figures.
He gives the following examples of steam-pressures calculated for temper*-
tures beyond the range of Regnault's experiments.
Temperature.
Pounds per
sq. in.
Temperature.
Pounds per
sq. in.
C.
Fahr.
C.
Fahr
230
240
250
260
280
300
320
446
464
482
500
536
572
608
406.9
488.9
579.9
691.6
940.0
1261.8
1661.9
340
360
380
400
415
427
644
680
716
752
779
800.6
2156.2
2742.5
3448.1
4300.2
5017.1
5659.9
These pressures are higher than those obtained by Regnault's formula,
which gives for 415° C. only 4067.1 Ibs. per square inch.
Table of the Properties of Saturated Steam.— In the table
of properties of saturated steam on the following pages the figures for tern*
perature, total heat, and latent heat are taken, up to 210 Ibs. absolute pres-
sure, from the tables in Porter's Steam-engine Indicator, which tables have
been widely accepted as standard by American engineers. The figures for
total heat, given in the original as from 0° F., have been changed to heat
above 32° F. The figures for weight per cubic foot and for cubic feet per
pound have been taken from Dwelshauvers-Dery's table, Trans. A. S. M. E.,
vol. xi., as being probably more accurate than those of Porter. The figures
for relative volume are from Duel's table, in Dubois's translation of Weis-
bach, vol. ii. The3r agree quite closely with the relative volumes calculated
from weights as given by Dwelshauvers. From 211 to 219 Ibs. the figures
for temperature, total heat, and latent heat are from Dwelshauvers' table ;
and from 220 to 1000 Ibs. all the figures are from BueFs table. The figures
have not been carried out to as many decimal places as they are in most of the
tables given by the different authorities ; but any figure beyond the fourth
significant figure is unnecessary in practice, and beyond the 'limit of error of
the observations and of the formulae from which the figures were derived.
of 1 Cubic Foot of Steam in Decimals of a Pound*
Comparison of Different Authorities.
Absolute
Pressure,
Ibs. per sq. in
Weight of 1 cubic foot
according to—
Absolute
Pressure,
Ibs. persq. in.
Weight of 1 cubic foot
according to—
Por-
ter.
Clark
Duel.
Dery.
Pea-
body,
Por-
ter.
Clark
Buel.
Dery.
.2724
.3147
.3567
.3983
.4400
Pea-
body
.2605
.3113
.3530
.3945
.4359
.4772
.5186
1
14.7
20
40
60
80
100
.0030
.03797
.0511
.0994
.1457
.19015
.23302
.003
.0380
.0507
.0974
.1425
.1869
.2307
.00303
.03793
.0507
.0972
.1424
.1866
.2303
,00299
.'6567'
.0972
.1422
.1862
.2296
.00299
.0376
.0502
.0964
.1409
.1843
.2271
120
140
160
180
200
220
240
.27428
.31386
.35209
.38895
.42496
.2738
.3162
.3590
.4009
.4431
.4842
.5248
.2735
.3163
.3589
.4012
.4433
.4852
.5270
There are considerable differences between the figures of weight and vol-
ume of steam as given by different authorities. Porter's figures are based
on the experiments of Fairbairn and Tate. The figures given by the other
authorities are derived from theoretical formulae which are believed to give
more reliable results than the experiments. The figures for temperature,
total heat, and latent heat as given by different authorities show a practical
agreement, all being derived from Regnault's experiments. See Peabody's
Tables of Saturated Steam; also Jacobus, Trans, A, S, M, E,, vol. xii., 593.
STEAM.
663
Properties of Saturated Steam.
rf.A
"
Total Heat
o>
Sl4
+*S
ffS
CC t- •
above 32° F.
K)
J •
*~! °s
3X3
<J
2 p,is
gi
Is •"*
"o^ II
3-2
O02
*"* S
O o
« j§'«
£X3
£ §
In the
In the
wt §
^Sf4
j£
«M »
2 «
E <S .
sxj >>
i«-S
Water
h
Steam
H
l°l
la
O^C 3
Isg1
^Eq
Heat-
Heat-
1 II W
K* 'S
"o fl
|s
>
5
units.
units.
2
&
>'~
fc
29.74
.089
32
0
1091.7
1091.7
208080
3333.3
.00030
29.67
.122
40
8.
1094.1
1086.1
154330
2472.2
.00040
29.56
.176
50
18.
1097.2
1079.2
107630
1724.1
.00058
29.40
.254
60
28.01
1100.2
1072.2
76370
1223.4
.00082
29.19
.359
70
38.02
1103.3
1065.3
54660
875.61
.00115
28.90
.502
80
48.04
1106.3
1058.3
39690
635.80
.00158
28.51
.692
90
58.06
1109.4
1051.3
29290
469.20
.00213
28.00
.943
100
68.08
1112.4
1044.4
21830
349.70
.00286
27.88
1
102.1
70.09
1113.1
1043.0
20623
334.23
.00299
25.85
2
126.3
94.44
1120.5
1026.0
10730
173.23
.00577
23.83
3
141.6
109.9
1125.1
1015.3
7325
117.98
.00848
21.78
4
153.1
121.4
1128.6
1007.2
5588
89.80
.01112
19.74
5
162.3
130.7
1131.4
1000.7
4530
72.50
.01373
17.70
6
170.1
138.8
1133.8
995.2
3816
61.10
.01631
15.67
7
176.9
145.4
1135.9
990.5
3302
53.00
.01887
13.63
8
182.9
151.5
1137.7
986.2
2912
46.60
.02140
11.60
9
188.3
156.9
1139.4
982.4
2607
41.82
.02391
9.56
10
193.2
161.9
1140.9
979.0
2361
37.80
.02641
7.52
11
197.8
166.5
1142.3
975.8
2159
84.61
.02889
5.49
12
202.0
170.7
1143.5
972.8
1990
31.90
.03136
3.45
13
205.9
174.7
1144.7
970.0
1846
29.58
.03381
1.41
14
209.6
178.4
1145.9
967.4
1721
27.59
.03625
Gauge
Pressure
Ibs. per
14.7
212
180.9
1146.6
965.7
1646
26.36
.03794
sq. in.
0.304
15
213.0
181.9
1146.9
965.0-
1614
25.87
.03868
1.3
16
216.3
185.3
1147.9
962.7
1519
24.33
.04110
2.3
17
219.4
188.4
1148.9
960.5
1434
22.98
.04352
3.3
18
222.4
191.4
1149 8
958.3
1359
21.78
.04592
4.3
19
225.2
194.3
1150.6
956.3
1292
S0.70
.04831
5.3
20
227.9
197.0
1151.5
954.4
1231
19.72
.05070
6.3
21
230.5
199.7
1152.2
952.6
1176
18.84
.05308
7.3
22
233.0
202.2
1153.0
950.8
1126
18.03
.05545
8.3
23
235.4
204.7
.7
949.1
1080
17.30
.05782
9.3
24
237.8
207.0
1154.5
947.4
1038
16.62
.06018
10.3
25
240.0
209.3
1155.1
945.8
998.4
15.99
.06253
11.3
26
242.2
211.5
.8
944.3
962.3
15.42
.06487
12.3
27
244.3
213.7
1156.4
942.8
928.8
14.88
.06721
13.3
28
246.3
215.7
1157.1
941.3
897.6
14.38
.06955
14.3
29
248.3
217.8
.7
939.9
868.5
13.91
.07188
15.3
80
250.2
219.7
1158.3
938.9
841.3
13.48
.07420
16.3
31
252.1
221.6
.8
937.2
815 8
13.07
.07652
17.3
32
254.0
223.5
1159.4
935.9
791.8
12.68
.07884
18.3
33
255.7
225.3
.9
934.6
769.2
12.32
.08115
19.3
34
257.5
227.1
1160.5
933.4
748.0
11.98
.08346
20.3
35
259.2
228.8
1161.0
932.2
727.9
11.66
.08576
21.3
36
260.8
230.5
1161.5 931.0
708.8
11.36
.08806
22.3
37
262.5
232.1
1162.0 929.8
690.8
11.07
.09035
664
STEAM.
Properties of Saturated Steam.
Total Heat
® ^
43 1
*4.5
ob ^ .
above 32° F.
k^ .
S *••-*
'*-' c3
3*£
WJ QQ
cS.0
fc'S
d ..-§
|| I'
QCO
®~~
^ «5'°
-S-s
In the
In the
tS"? §
>^[xj
.0
o|
&
-2^2
cE S
Water
Steam
43 '+a
> °0i
*^
+3 -M
t.
"3 aT 3
ft-5
h
H
gs5 ^
•-5,-jco
S-*
§^
.0
|||
s£
Heat-
Heat-
•§ HE
~~K* ts
r- 1 g
"££
o^
IT
units.
units.
tf
>'"
j*
23.3
38
264.0
233.8
1162.5
928.7
673.7
10.79
.09264
24.3
89
265.6
235.4
.9
927.6
657.5
10.53
.09493
25.3
40
267.1
236.9
1163.4
926.5
642.0
10.28
.09721
26.3
41
268.6
238.5
.9
925.4
627.3
10.05
.09949
27.3
42
270.1
240.0
1164.3
924.4
613.3
9.83
.1018
28.3
43
271.5
241.4
.7
923.3
599.9
9.61
.1040
29.3
44
272.9
242.9
1165.2
922.3
587.0
9.41
.1063
30.3
45
274.3
244.3
.6
921.3
574.7
9.21
.1086
31.3
46
275.7
245.7
1166.0
920.4
563.0
9.02
.1108
32.3
47
277.0
247.0
.4
919.4
551.7
8.84
.1131
33.3
48
278.3
248.4
.8
918.5
540.9
8.67
.1153
34.3
49
279.6
249.7
1167.2
917.5
530.5
8.50
.1176
35.3
50
280.9
251.0
.6
916.6
520.5
8.34
.1198
36.3
51
282.1
252.2
1168.0
915.7
510.9
8.19
.1221
37.3
52
283.3
253.5
.4
914.9
501.7
8.04
.1243
38.3
53
284.5
254.7
.7
914.0
492.8
7.90
.1266
39.3
54
285.7
256.0
1169.1
913.1
484.2
7.76
.1288
40.3
55
286.9
257.2
.4
912.3
475.9
7.63
.1311
41.3
56
288.1
258.3
.8
911.5
467.9
7.50
.1333
42.3
57
289.1
259.5
1170.1
910.6
460.2
7.38
.1355
43.3
58
290.3
260.7
.5
909.8
452.7
7.26
.1377
44.3
59
291.4
261.8
.8
909.0
445.5
7.14
.1400
45.3
60
292.5
262.9
1171.2
908.2
438.5
7.03
.1422
46.3
61
293.6
264.0
.5
907.5
431.7
6.92
.1444
47.3
62
294.7
265.1
.8
906.7
425.2
6.82
.1466
48.3
63
295.7
266.2
1172.1
905.9
418.8
6.72
.1488
49.3
64
296.8
267.2
.4
905.2
412.6
6.62
.1511
50.3
65
297.8
268.3
.8
904.5
406.6
6.53
.1533
51.3
66
298.8
269.3
1173.1
903 7
400.8
6.43
.1555
52.3
67
299.8
270.4
.4
903.0
395.2
6.34
.1577
53.3
68
300.8
271.4
.7
902.3
389.8
6.25
.1599
54.3
69
301.8
272.4
1174.0
901.6
384.5
6.17
.1621
55.3
70
302.7
273.4
.3
900.9
379.3
6.09
.1643
56.3
71
303.7
274.4
.6
900.2
374.3
6.01
.1665
57.3
72
304.6
275.3
.8
899.5
369.4
5.93
.1687
58.3
73
305.6
276.3
1175.1
898.9
364.6
5.85
.1709
59.3
74
306.5
277.2
.4
898.2
360.0
5.78
.1731
60.3
75
307.4
278.2
.7
897.5
355.5
5.71
.1753
61.3
76
308.3
279.1
1176.0
896.9
351.1
5.63
.1775
62.3
77
309.2
280.0
.2
896.2
346.8
5.57
.1797
63.3
78
310.1
280.9
.5
895.6
342.6
5.50
.1819
64.3
79
310.9
281.8
.8
895.0
338.5
5.43
.1840
65.3
80
311.8
282.7
1177.0
894.3
834.5
5.37
.1862
66.3
81
312.7
283.6
.3
893.7
330.6
5.31
.1884
67.3
82
313.5
284.5
.6
893.1
326.8
5.25
.1906
68.3
83
314.4
285.3
.8
892.5
323.1
5.18
.1928
69.3
84
315.2
286.2
1178.1
891.9
319.6
5.13
.1950
70.8
85
816.0
287.0
.3
891.3
815.9
5.07
.1971
STEAM.
665
Properties of Saturated Steam.
^ .
.
Total Heat
6^
*5 3
2.9
B*
1® •§
£s'
above 32° F.
M
-^ K
slU
a" .2
Za
R
*.g
2£
c$ a
In the
In the
eg • *=
<g.si 3
W 1 &
*t*
02
if
^
bflco
"3 4> J3
%Z
D.^3
Water
h
Steam
1^1
J*l
c3 O .3
ll
t& .
& 3 cc
fe
Heat-
Heat-
t* II PH
*o o
"33 £5
0~"
H
units.
units.
3
&
>'~
j*
71.3
86
316.8
287.9
1178.6
890.7
312.5
5.02
.1993
72.3
87
317.7
288.7
.8
890.1
309.1
4.96
.2015
73.3
88
318.5
289.5
1179.1
889.5
305.8
4.91
.2036
74.3
89
319.3
290.4
.3
888.9
302.5
4.86
.2058
75.3
90
320.0
291.2
.6
888.4
' 299.4
4.81
.2080
76.3
91
320.8
292.0
.8
887.8
296.3
4.76
.2102
77.3
92
321.6
292.8
1180.0
887.2
293.2
4.71
.2123
78.3
93
322.4
293.6
.3
886.7
290.2
4.66
.2145
79.3
94
323.1
294.4
.5
886.1
287.3
4.62
.2166
80.3
95
323.9
295.1
.7
885.6
284.5
4.57
.2188
81.3
96
324.6
295.9
1181.0
885.0
281.7
4.53
.2210
82.3
97
325.4
296.7
.2
884.5
279.0
4.48
.2231
83.3
98
326.1
297.4
.4
884.0
276.3
4.44
.2253
843
99
326.8
298.2
.6
883.4
273.7
4.40
.2274
85.3
100
3-27.6
298.9
.8
882.9
271.1
4.36
.2296
86.3
101
3-28.3
299 7
1182.1
882.4
268.5
4.32
.2317
87.3
102
3-29.0
300.4
.3
881.9
266.0
4.28
.2339
88.3
103
329.7
301.1
.5
881.4
263.6
4.24
.2360
89.3
104
330.4
301.9
.7
880.8
261.2
4.20
.2382
90.3
105
831.1
302.6
.9
880.3
258.9
4.16
.2403
91.3
106
331.8
303.3
1183.1
879.8
256.6
4.12
.2425
92.3
107
332.5
304.0
.4
879.3
254.3
4.09
.2446
93.3-
108
333.2
304.7
.6
878.8
252.1
4.05
.2467
94.3
109
333.9
305.4
.8
878.3
249.9
4.02
.2489
95.3
110
334.5
306.1
1184.0
877.9
247.8
3.98
.2510
96.3
111
335.2
306.8
.2
877.4
245.7
3.95
.2531
97.3
112
335.9
307.5
.4
876.9
243.6
3.92
.2553
98.3
113
336.5
308.2
.6
876.4
241.6
3.88
.2574
99.3
114
337.2
308.8
.8
875.9
239.6
3.85
.2596
100.3
115
337.8
309.5
1185.0
875.5
237.6
3.82
.2617
10.1.3
116
338.5
310.2
.2
875.0
235.7
3.79
.2638
102.3
117
339.1
810.8
.4
874.5
233.8
8.76
.2660
103.3
118
839.7
311.5
.6
874.1
231.9
3.73
.2681
104.3
119
340.4
312.1
.8
873.6
230.1
8.70
.2703
105.3
120
341.0
312.8
.9
873.2
228.3
8.67
.2724
106.3
121
841.6
313.4
1186.1
872.7
226.5
3.64
.2745
107.3
122
342.2
314.1
.3
872.3
224.7
3.62
.2766
108.3
123
342.9
314.7
.5
871.8
223.0
3.59
.2788
109.3
124
343.5
315.3
.7
871.4
221.3
3.56
.2809
110.3
125
344.1
316 0
.9
870.9
219.6
3.53
.2830
111.3
126
344.7
316.6
1187.1
870.5
. 218.0
8.51
.2851
112.3
127
345.3
317.2
.3
870.0
216.4
3.48
.2872
113.3
128
345.9
317.8
.4
869.6
214.8
3.46
.2894
114.3
129
346.5
318.4
.6
869.2
213.2
3.43
.2915
115.3
130
347.1
319.1
.8
868.7
211.6
3.41
.2936
116.3
131
347.6
319.7
1188.0
868.3
210.1
3.38
.2957
117.3
132
348.2
320.3
.2
867.9
208.6
3.36
.2978
118.3
133
348.8
320.8
.3
867.5
207.1
3.33
.3000
119.3
134
349.4
321.5
.5
867.0
205.7
3.31
.3021
666
6TEAM.
Properties of Saturated Steam,
"J
Total Heat
o5 +*
•^a
|s
|||
£+*
above 32° F.
^* ri
ijs
rfl
S*.Q
is-
fife
8*
sis
fgl
If
g-i-
In the
Water
h
In the
Steam
H
sT"!
lljj
<M
fljO
O "
jJtGQ
fjj
Js£
e GS
Heat-
Heat-
"^ II W
t-H "5 0
'o1""'
~
H
units.
units.
^
tfi>«
£.2
£:£
120.3
135
350.0
322.1
1188.7
866.6
204.2
3.29
.3042
121.3
136
350.5
322.6
.9
866.2
202.8
3.27
.8063
122.3
137
351.1
323.2
1189.0
865.8
201 4
3.24
.3084
123.3
138
351.8
323.8
.2
865.4
200.0
3.22
.3105
124.3
139
352;2
324.4
.4
865.0
198.7
3.20
.3126
125.8
140
852.8
325.0
.5
864.6
197.3
3.18
.3147
126.3
141
353.3
325.5
.7
864.2
196.0
3.16
.3169
127.3
142
353.9
326.1
.9
863.8
194.7
3.14
.3190
128.3
143
354,4
326.7
1190.0
863.4
193.4
3.11
.3211
129.3
144
355.0
327.2
.2
863.0
192.2
3.09
.3232
130.8
145
855.5
327.8
.4
862.6
190.9
3.07
.3253
131.8
146
356.0
328.4
.5
862.2
189.7
3.05
.3274
132.3
147
356.6
328.9
.7
861.8
188.5
3.04
.3295
133.3
148
357.1
329.5
.9
861.4
187.3
3.02
.8316
134.3
149
357.6
330.0
1191.0
861.0
186.1
3.00
.333?
135.3
150
358.2
330.6
.2
860.6
184.9
2.98
.3358
136.3
151
358.7
331.1
.3
860.2
183.7
2.96
.3379
137.3
152
359.2
331.6
.5
859.9
182.6
2.94
.3400
138.3
153
359.7
332.2
.7
859.5
181.5
2.92
.3421
139.3
154
360.2
382.7
.8
859.1
180.4
2.91
.3443
140.3
155
360.7
833.2
1192.0
858.7
179.3
2.89
.3463
141.3
156
361.3
333.8
.1
858.4
2.87
.3483
142.3
157
361.8
334.3
.3
858.0
177.0
2.85
.3504
143.3
158
362.3
334.8
.4
857.6
176.0
2.84
.3525
144.3
159
362.8
335.3
.6
857.2
174.9
2.82
.3546
145.8
160
363.3
335.9
.7
856.9
173.9
£.80
.3567
146.3
161
363.8
336.4
.9
856.5
172^9
2.79
.3588
147.3
162
364.3
836.9
1193.0
856.1
171.9
2.77
.3609
148.3
163
364.8
337.4
.2
855.8
171.0
2.76
.3630
149.3
164
365.3
337.9
.3
855.4
170.0
2.74
.3650
150.3
165
365.7
338.4
.5
855.1
169.0
2.72
.3671
151.3
166
366.2
338.9
.6
854.7
168.1
2.71
.3692
152.3
167
366.7
339.4
.8
854.4
167.1
2.69
.3713
153.3
168
367.2
339.9
.9
854.0
166.2
2.68
.3734
154.3
169
367.7
340.4
1194.1
653.6
165.3
2.66
.3754
155.3
170
368.2
340.9
.2
853.3
164.3
2.65
.8775
156.3
171
368.6
341.4
.4
852.9
163.4
2.63
.3796
157.3
172
369.1
341.9
.5
852.6
162.5
2.62
.8817
158.3
173
369.6
342.4
.7
852.3
161.6
2.61
.8838
159.3
174
370.0
342.9
.8
851.9
160.7
2.59
.8858
160.8
175
370.5
343.4
.9
851.6
159.8
2.58
.8879
161.3
176
371.0
343.9
1195.1
851.2
158.9
2.56
.8900
162.8
177
371.4
344.3
.2
850.9
158.1
2.55
.3921
163.3
178
371.9
344.8
.4
850.5
157.2
2.54
.3942
164.3
179
372.4
345.3
.5
850.2
156.4
2.52
.3962
165.3
180
372.8
345.8
.7
849.9
155.6
2.51
.3983
166.3
181
373.3
346.3
.8
849.5
154.8
2.50
.4004
167.3
183
873.7
346.7
.9
849.2
154.0
2.48
.4025
108.3
183
374.2
347.2
1196.1
848.9
153.2
2.47
.4046
STEAM.
Properties of Saturated Steam*
667
i
Total Heat
£ts
il
|.s
co ;-,
IIL
9 •
above 32° F.
kD
JJ tf>
Ife
3 a
SI
8s
Gauge Press
Ibs. per sq.
Absolute Pr
ure, Ibs. ]
square incl
Temperatur
Fahrenheit
In the
Water
h
Heat-
units.
In the
Steam
H
Heat-
units.
Latent Hea
= H-h.
Heat-unit;
Relative Vol
Vol . of wat
39° F.= 1.
S£
0
U
3 in
|f
?s
'SoQ
!®+3
£*
169.3
184
374.6
347.7
1196.2
848.5
152.4
2.46
.4066
170.3
185
375.1
348.1
.3
848.2
151.6
2.45
.4087
171.3
186
375.5
348.6
.5
847.9
150.8
2.43
.4108
172.3
187
375.9
349.1
.6
847.6
150.0
2.42
.4129
173.3
188
376.4
349.5
.7
847.2
149.2
2.41
.4150
174.3
189
376.9
350.0
.9
846.9
148.5
2.40
.4170
175.3
190
377 . 3
350.4
1197.0
846.6
147.8
2.39
.4191
176.3
191
377.7
350.9
.1
846.3
147.0
2.37
.4212
177.3
192
378.2
351.3
.3
845.9
146.3
2.36
.4233
178.3
193
378.6
351.8
.4
845.6
145.6
2.35
.4254
179.3
194
379.0
352.2
.5
845.3
144.9
2.34
.4275
180.3
195
379.5
352.7
.7
845.0
144.2
2.33
.4296
181.3
196
380.0
353.1
.8
844.7
143.5
2.32
.4317
185.3
197
380.3
353.6
.9
844.4
142.8
2.31
.4337
183.3
198
380.7
354.0
1198.1
844.1
142.1
2.29
.4358
184.3
199
381.2
354.4
.2
843.7
141.4
2.28
.4379
185.3
200
381.6
354.9
.3
843.4
140.8
2.27
.4400
186.3
201
382.0
355.3
.4
843.1
140.1
2.26
.4420
187.3
202
382.4
355.8
.6
842.8
139.5
2.25
.4441
188.3
203
382.8
356.2
.7
842.5
138.8
2.24
.4462
189.3
204
383.2
356.6
.8
842.2
138.1
2.23
.4482
190.3
205
383.7
357.1
1199.0
841.9
137.5
2.22
.4503
191.3
206
384.1
357.5
1
841.6
136.9
2.21
.4523
192.3
207
384.5
357.9
.2
841.3
136.3
2.20
.4544
193.3
208
384.9
358.3
.3
841 0
135.7
2.19
.4564
194.3
209
385.3
358.8
.5
840.7
135.1
2.18
.4585
195.3
210
385.7
359.2
.6
840.4
134.5
2.17
.4605
196.3
211
386.1
359.6
.7
840.1
ias.9
2.16
.4626
197,3
212
386.5
360.0
.8
839.8
133.3
2.15
.4646
198.3
213
386.9
360.4
.9
839.5
132.7
2.14
.4667
199.3
214
387.3
360.9
1200.1
839.2
132.1
2.13
.4687
200.3
215
387.7
361.3
.2
838.9
131.5
2.12
.4707
201.3
216
388.1
361.7
.3
838.6
130.9
2.12
.4728
202.3
217
388.5
362.1
.4
838.3
130.3
2.11
.4748
203.3
218
388.9
362.5
.6
838.1
129.7
2.10
.4768
204.3
219
389.3
362.9
.7
837.8
129.2
2.09
.4788
205.3
220
389.7
362.2*
1200.8
838.6*
128.7
2.06
.4852
215.3
230
393.6
366.2
1202.0
835.8
123.3
1.98
.5061
225.3
240
397.3
370.0
1203.1
833.1
118.5
1.90
.5270
235.3
250
400.9
373.8
1204.2
830.5
114.0
1.83
.5478
245.3
260
404.4
377.4
1205.3
827.9
109.8
1.76
.5686
255.3
270
407.8
380.9
1206.3
825.4
105.9
1,70
.5894
265.3
280
411.0
384.3
1207.3
823.0
102.3
1.64
.6101
275.3
290
414.2
387.7
1208.3
820.6
99.0
1.585
.6308
285.3
300
417.4
390.9
1209.2
818.3
95.8
1.535
.6515
335.3
350
432.0
406.3
1213.7
807.5
82.7
1.325
.7545
*The discrepancies nt 205.3 Ibs. gauge are due to the change from
Dwelshauvers-Dery's to BuePs figures.
668
STEAM.
Properties of Saturated Steam.
"" ®
Total Heat
®*>
^ .
s ='
1®^'
g'^
above 32° F.
^ rc
s «
*t^
9j*
II
B;rf|
03 25 '~
3 *§
go
In the
In the
Is „•;£
^ "~- c
te i ?
If-
^ ? H
6.2
?s"
s-g
0) V
Water
Steam
* s
+3 *
It
'o-S
p
h
Heat-
H
Heat-
1^1
« "W
§•5?
II
Is
0~
4 Pcfi
Hfe
units.
units.
M
(g>OT
l>to
g«M
385.3
400
444.9
419.8
1217.7
797.9
72.8
1.167
.8572
435.3
450
456.6
432.2
1221.3
789.1
65.1
1.042
.9595
485.3
500
467.4
443.5
1224.5
781.0
58.8
.942
1.062
535.3
550
477.5
454.1
1227.6
773.5
53.6
.859
1.164
585.3
600
486.9
464.2
1230.5
766.3
49.3
.790
1.266
635.3
650
495.7
473.6
1233.2
759.6
45.6
.731
1.368
685.3
700
504.1
482.4
1235.7
753.3
42.4
.680
1.470
735.3
750
512.1
490.9
1238.0
747.2
39.6
.636
1.572
785.3
800
519.6
498.9
1240.3
741.4
37.1
.597
1.674
835.3
850
526.8
506.7
1242.5
735.8
34.9
.563
1.776
885.3
900
533.7
514.0 '
1244.7
730.6
33.0
.532
1.878
935.3
950
540.3
521.3
1246.7
725.4
31.4
.505
1.980
985.3
1000
546.8
528.3
1248.7
720.3
30.0
.480
2.082
FLOW OF STEAM.
Flow of Steam through a Nozzle. (From Clark on the Steam-
engine.)— The flow of steam of a greater pressure into an atmosphere of a
less pressure increases as the difference of pressure is increased, until the
external pressure becomes only 58# of the absolute pressure in the boiler.
The flow of steam is neither increased nor diminished by the fall of the ex-
ternal pressure below 58#, or about 4/7ths of the inside pressure, even to th«
extent of a perfect vacuum. In flowing through a nozzle of the best form,
the steam expands to the external pressure, and to the volume due to this
pressure, so long as it is not less than 58$ of the internal pressure. For a/i
external pressure of 58#, and for lower percentages, the ratio of expansion
is 1 to 1.624. The following table is selected from Mr. Brownlee's data exem-
plifying the rates of discharge under a constant internal pressure, into
various external pressures:
Outflow of Steam ; from a Given Initial Pressure Into
Various Lower Pressures.
Absolute initial pressure in boiler, 75 Ibs. per sq. in.
Absolute
Pressure in
Boiler per
square
inch.
External
Pressure
per square
inch.
Ratio of
Expansion
in
Npzzle.
Velocity of
Outflow
at Constant
Density.
Actual
Velocity of
Outflow
Expanded.
Discharge
per square
inch of
Orifice per
minute.
Ibs.
Ibs.
ratio.
feet per sec.
feet p. sec.
Ibs.
75
74
1.012
227.5
230
16.68
75
72
1.037
386.7
401
28.35
75
70
1.063
490
521
35.93
75
65
1.136
660
749
48.38
75
61.62
1.198
736
876
53.97
75
60
1.219
765
933
56.12
75
50
1.434
873
1252
64
75
45
1.575
890
1401
65.24
75
j 43.46 )
| 58 p. cent f
1.624
890.6
1446.5
65.3
75
15
1.624
890.6
1446.5
65.3
75
0
1.624
890.6
1446.5
65.3
FLOW OF STEAM,
669
pressures is discharged into the atmos-
ng the
V ss the velocity of outflow in feet per second, as for steam of the initial
density ;
h = the height in feet of a column of steam of the given absolute initial
pressure of uniform density, the weight of which is equal to the pres-
sure on the unit of base.
The lowest initial pressure to which the formula applies, when the steam
is discharged into the atmosphere at 14.7 Ibs. per square inch, is (14.7 X
100/58 =) 25.37 Ibs. per square inch. Examples of the application of the
formula are given in the table below.
From the contents of this table it appears that the velocity of outflow into
the atmosphere, of steam above 25 Ibs. per square inch absolute pressure,
or 10 Ibs. effective, increases very slowly with the pressure, obviously be-
cause the density, and the weight to be moved, increase with the pressure.
An average of 900 feet per second may, for approximate calculations, be
taken for the velocity of outflow as for constant density, that is, taking the
volume of the steam at the initial volume.
Outflow of Steam into the Atmosphere.— External pressure
per square inch 14.7 Ibs. absolute. Ratio of expansion in nozzle, 1.624.
bsolute Initial
Pressure per
square inch.
elocity of Out- |
flow as at Ccn- 1
stant Density.
ctual Velocity
of Outflow
Expanded.
ischarge per
square inch of
Orifice per min
orse-power per
sq. in. of Orifice
if H. P. = 30
Ibs. per hour.
bsolute Initial
Pressure per
square inch.
elocity of Out-
flow as at Con-
stant Density.
ctual Velocity
of Outflow
Expanded.
ischarge per
square inch of
Orifice per
minute.
orse-power per
sq. in. of Orifice
if H. P. = 30
Ibs. per hour.
<
>
<
Q
E
<
>
<3
P
m
Ibs.
25.37
feet
p. sec.
863
feet
per sec.
1401
Ibs.
22.81
H.P.
45.6
Ibs.
90
feet
p. sec.
895
feet
per sec.
1454
Ibs.
77.94
H.P.
155.9
30
867
1408
26.84
53.7
100
898
1459
86.34
172.7
40
874
1419
35.18
70.4
115
902
1466
98.76
197.5
50
880
1429
44.06
88.1
135
906
1472
115.61
231.2
60
885
1437
52.59
105.2
155
910
1478
132.21
264.4
70
889
1444
61.07
122.1
165
912
1481
140.46
280.9
75
891
1447
65.30
130.6
215
919
1493
181.58
363.2
Napier's Approximate Rule.— Flow in pounds per second = ab-
solute pressure x area in square inches -*- 70. This rule gives results which
closely correspond with those in the above table, as shown below.
Abs. press., Ibs. p. sq. in. 25.37 40 60 75 100 135 165 215
Discharge per min., by
table,lbs ............... 22.8135.1852.5965.30 86.34 115.61 140.46 181.58
By Napier's rule ......... 21.74 34.29 51.43 64.29 85.71 115.71 141.43 184.29
Prof. Peabody, in Trans. A. S. M. E., xi, 187, reports a series of experi-
, . . .
ents on flow of steam through tubes y± inch in diameter, and *4, V& and
inch long, with rounded entrances, in which the results agreed closely with
Napier's formula, the greatest difference being an excess of the experimental
over the calculated result of 3.2#. An equation derived from the theory of
thermodynamics is given by Prof. Peabody, but it does not agree with the
experimental results as well as Napier's rule, the excess of the actual flow
being
..
Flour of Steam in Pipes.— A formula commonly used for velocity
of flow of steam in pipes is the same as Downing's for the flow of water in
• /Tr
smooth cast-iron pipes, viz., V '= 50/|/yA in which V ss velocity in feet
per second, L = length and D = diameter of pipe in feet, H = height in
£<aet of a. column of steam, of the pressure of the steam at the entrance*
670 STEAM.
which would produce a pressure equal to the difference of pressures at the
two ends of the pipe. (For derivation of the coefficient 50, see Briggs on
" Warming Buildings by Steam," Proc. Inst. C. E. 1882.)
If Q = quantity in cubic feet per minute, d = diameter in inches, L and .H
being in feet, the formula reduces to
Q = 4.7233&6, H = -0448, d
ence in pressure per square foot. Let w = density or weight per cubic foot
of steam at the pressure plt then the height of column equivalent to the
If W = weight of steam flowing in pounds per minute = Qwt and d is
taken in inches, L being in feet,
Velocity in feet per minute
For a velocity of 6000 feet per minute, d =
For a velocity of 6000 feet per minute, a steam-pressure of 100 Ibs. gauge,
or w =.264, and a length of 100 feet, d = - : - ; Pi - pa = -V. That is, a
Pi — Pi **
pipe 1 inch diameter, 100 feet long, carrying steam of 100 Ibs. gauge-pressure
at 6000 feet velocity per minute, would have a loss of pressure of 8.8 Ibs. per
sqaare inch, while steam travelling at the same velocity in a pipe 8.8 inches
diameter would lose only 1 Ib. pressure.
G. H. Babcock, in "Steam," gives the formula
w = t
In earlier editions of " Steam " the coefficient is given as 300,— evidently an
error,— and this value has been reprinted in Clark's Pocket-Book (1892 edi-
tion). It is apparently derived from one of the numerous formulas for flow
of water in pipes, the multiplier of L in the denominator being used for an
expression of the increased resistance of small pipes. Putting this formula
in the form W = CA/ W(Pl ~ ^2 — .$ in which c will vary with the diameter
of the pipe, we have,
For diameter, inches.... 1 2 3 4 6 9 12
Value of c 40.7 52.1 58.8 63 68.8 73.7 79.3
instead of the constant value 56.68, given with the simpler formula.
One of the most widely accepted formulae for flow of water is D'Arcy's,
/ iffy
V = CA/ TT* *n wk*ch c has values ranging from 65 for a J^-inch pipe up to
FLOW OF STEAM.
671
111.5 for 24 inch. Using D'Arcy's coefficients, and modifying his formula tc
make it apply to steam, to the form
Q =
wL
or W = (
we obtain,
For diameter, inches.... ^5
Value of c ................ 36.8
For diameter, inches.... 9
Value of c ................ 61.2
45.3 52.7 56.1
45678
57.8 58.4 59.5 60.1 60.7
10
61.8
12
62.1
14 16 18 20 22 24
62.3 62.6 62.7 62.9 63.2 63.2
In the absence of direct experiments these coefficients are probably as
accurate as any that may be derived from formulae for flow of water.
Loss of pressure in Ibs. per sq. in. = pl — p.t = ™,6 = 2 ,s.
Loss of Pressure due to Radiation as well as Friction.—
E. A. Rudiger (Mechanics, June 30, 1883) gives the following formulae and
tables for flow of steam in pipes. He takes into consideration the losses in
pressure due both to radiation and to friction.
Loss of power, expressed in heat-units due to friction, Hf = : „.
Loss due to radiation,
Hr = 0.262rW.
In which IF is the weight in Ibs. of steam delivered per hour, /the coeffi-
cient of friction of the pipe, Z the length of the pipe in feet, p the absolute
terminal pressure, d the diameter of the pipe in inches, and r the coefficient
of radiation. / is taken as from .0105 to .0175, and r varies as follows :
TABLE OF VALUES FOR 1*.
Absolute Pressure.
ripe uovermg.
40 Ibs.
65 Ibs.
90 Ibs.
115 Ibs.
437
555
620
684
2-inch cement composition . ;
146
178
193
209
2 asbestos
157
192
202
222
150
185
197
210
100
122
145
151
2 mineral wool. . • . • • • • .
61
76
85
93
2 hairfelt
48
58
66
73
The appended table shows the loss due to friction and radiation in a steam-
pipe where the quantity of steam to be delivered is 1000 Ibs. per hour, / =
1000 feet, the pipe being so protected that loss by radiation r = 64, and the
absolute terminal pressure being 90 Ibs.:
Diameter
of Pipe,
inches.
Loss by
Friction,
Hf.
Loss by
Radia-
tion,
Hr.
Total
Loss,
L.
Diam.
of Pipe,
inches.
Loss by
Friction,
Hf.
Loss by
Radia-
tion,
Hr.
Total
Loss,
L.
1
JVZ
1%
2
3*
197,531
64,727
26,012
12,035
6,173
2,023
813
16,768
20,960
25,152
29,344
33,536
41,920
50,304
214,300
85,687
51,164
41,379
39,709
43,943
51,117
¥*
5
6
7
8
376
193
63
25
12
6
58,688
67,072
83,840
100,608
117,376
134,144
59,064
67,265
83,903
100,623
117,388
134,150
672
STEAM.
If the pipes are carrying steam with minimum loss, then for same.r, I,
and PI the loss of pressure L for pipes of different diameters varies in»
versely as the diameters.
The general equation for the loss of pressure for the minimal loss from
friction and radiation is
_ 0.0007023 drip
W
The loss of pressure for pipes of 1 inch diameter for different absolute
terminal pressures when steam is flowing with minimal loss is expressed by
the formula L =CZ^/r2, in which the coefficient C has the following values,'
For 65 Ibs. abs. term, pressure C = 0.00089337
" 75 " " t4 " 0.00093G84
•• 90 " " " " 0.00099573
"100" •• " •• 0.00103132
" 115 " " M " 0.00108051
In order to find the loss of pressure for any other diameter, divide the l«sa
of pressure in a 1-inch pipe for the given terminal pressure by the given
diameter, and the quotient, will be the loss of pressure for that diameter.
The following is a general summary of the results of Mr. Rudiger's inves-
tigation :
The flow of steam in a pipe is determined in the same manner as the flow
of water, the formula for the flow of steam being modified only by substi-
tuting the equivalent loss of pressure, divided by the density of the steam,
for the loss of head.
The losses in the flow of steam are two in number— the loss due to the
friction of flow and that due to radiation from the sides of the pipe. The
sum of these is a minimum when the equivalent of the loss due to fric-
tion of flow is equal to one fifth of the loss of heat by radiation. For tt
greater or less loss of pressure — i.e., for a less or greater diameter of pipe
—the total loss increases very rapidly.
For delivering a given quantity of steam at a given terminal pressure,
with minimal total loss, the better the non-conducting material employed,
the larger the diameter of the steam-pipe to be used.
The most economical loss of pressure for a pipe of given diameter is equal
to the most economical loss of pressure in a pipe of 1 inch diameter for same
'conditions, divided by the diameter of the given pipe in inches.
The following table gives the capacity of pipes of different diameters, to
deliver steam at different terminal pressures through a pipe one half mile
long for loss of pressure of 10 Ibs., and a mean value of / = 0.0175. Let W
denote the number of pounds of steam delivered per hour :
Diameter
of Pipe,
inches.
Abs. Term. Pressure.
Diameter
of Pipe,
Abs. Term. Pressure.
65 Ibs.
80 Ibs.
100 Ibs.
inches.
65 Ibs.
80 Ibs
100 Ibs.
1
W
102
179
282
415
579
1,011
1,595
2,346
3,275
W
113
198
312
459
641
1,121
1,768
2 539
3!629
W
125
219
346
508
710
1,240
1,956
2,875
4,042
4U...
W
4,397
5,721
9,024
13,268
18,526
24,870
32,364
41,081
51,049
W
4,872
6,339
10,000
14,701
20,528
27,556
35,860
45,507
56,564
W
5,390
7,013
11,063
16,265
22,711
30,488
39,675
50,349
62,581
1/4 • ••
ST....::..
6
W±...
7
8
2
£?::•::::::::
9
10
11
3^
4
12
Resistance to Flow by Bends, Valves, etc. (From Briggs on
Warming Buildings by Steam.)— The resistance at the entrance to a tube
when no special bell-mouth is given consists of two parts. The head v* -*- 2g
is expended in giving the velocity of flow; and the head 0 505 - in over
FLOW OF STEAM. 673
coming the resistance ot the mouth of the tube. Hence the whole loss of
v*
head at the entrance is 1.505 — - . This resistance is equal to the resistance
of a straight tube of a length equal to about 60 times its diameter.
The loss at each sharp right-angled elbow is the same as in flowing
through a length of straight tube equal to about 40 times its diameter. For
a globe steam stop-valve the resistance is taken to be \y% times that of the
riprht-an^led elbow.
Sizes of Steam-pipes for Stationary Engines.— Authorities
on the steam-engine generally agree that steam-pipes supplying engines
should be of such size that the mean velocity of steam in them does not
exceed 6000 feet per minute, in order that the loss of pressure due to friction
may not be excessive. The velocity is calculated on the assumption that the
cylinder is filled at each stroke, In very long pipes, 100 feet and upward, it
is well to make them larger than this rule would give, and to place a large
steam receiver on the pipe near the engine, especially when the engine cuts
oif early in the stroke.
An article in Power, May, 1893, on proper area of supply-pipes for engines
gives a table showing the practice of leading builders. 'To facilitate corn
parison, all the engines have been rated in horse-power at 40 pounds mean
effective pressure. The table contains all the varieties of simple engines,
from the slide-valve to the Corliss, and it appears that there is no general
difference in the sizes of pipe used in the different types.
The .averages selected from this table are as follows:
lurmuid. ; at O<.L> u<* <o wu iai luu &LV Kyi oo
Formula (1) is: 1 H P. requires .1375 sq. in. of steam-pipe area.
Formula (2) is: Horse-power = 6cZ2. d = diam. of pipe in inches.
The factor .1375 in formula (1) is thus derived: Assume that the linear
velocity of steam in the pipe should not exceed 6000 feet per minute, then
pipe area = cyl. area X piston-speed -f- 6000 (a). Assume that the av. mean
effective pressure is 40 Ibs. per sq. in., then cyl. area X piston-speed X 40 -i-
33,000 = horse-power (6). Dividing (a) by (b) and cancelling, we have pipe
area-4-H.P. = .1375 sq. in. If we use 8000 ft. per min. as the allowable
velocity, then the factor .1375 becomes .1031; that is, pipe area -*- H.P. =
.1031, or pipe area X 9.7 = horse-power. This, however, gives areas of pipe
smaller than are used in the most recent practice. A formula which gives
results closely agreeing with practice, as shown in the above table is
Horse-power = 6d\ or pipe diameter =A/ S^i = .408 I/H.P.
DIAMETERS op CYLINDERS CORRESPONDING TO VARIOUS SIZES OF STEAM-
PIPES BASED ON PISTON-SPEED OF ENGINE OF 600 FT. PER MINUTE, AND
ALLOWABLE MEAN VELOCITY OF STEAM IN PIPE OF 4000, 6000, AND 8000
FT. PBR jilN. (6TEAM A^aUMElJ TO BE ADMITTED DURING FULL STROKE.]
Diam. of pipe, incnes 2 2^ 8 3^ 4 \Y2 5 6
Vel. 4000 5.2 6.5 7.7 9.0 10.3 11.6 12.9 15.5
" 6000 6.3 7.9 9.5 11.1 12.6 14.2 15.8 19.
" 8000 7.3 9.1 10.9 12.8 14.6 16.4 18.3 21.9
Horse-power, approx 20 31 45 62 80 100 125 180
Diam. of pipe, inches ? 8 9 10 11 12 13 14
Vel. 4000 .... 18.1 20.7 23.2 25.8 28.4 31.0 33.6 36.1
" 6000 22.1 25.3 28.5 31.6 34.8 37.9 41.1 44.3
" 8000 25.6 29.2 32.9 36.5 40.2 43.8 47.5 51.1
Horse-power, approx......... 245 320 406 500 606 718 845 981
Formula. Area of pipe = Area <* cylinder xplgton-n>eed
mean velocity of steam m pipe
For piston-speed of 600 ft. per min. and velocity in pipe of 4000, 6000, and
8000 ft. per min. area of pipe — respectively .15, .10, and .075 X area of cyl-
inder. Diam. of pipe = respectively .3873, .3162, and .2739 X diam. of cylin-
der. Reciprocals of these figures are 2.582, 3.162, and 3.651.
The first line in the above table may be used for proportioning exhaust-
674
STEAM.
.... in which a velocity not exceeding 4000 ft. per minute Is advisable.
The last line, approx. H.P. of engine, is based on the velocity of 6000 ft. per
min. in the pipe, using the corresponding diameter of piston, arid taking
H.P. = ^(diam. of piston in inches)3-
Sizes of Steam-pipes for Marine Engines.— In marine-engine
practice the steam -pipes are generally not as large as in stationary practice
for the same sizes of cylinder. Seaton gives the following rules:
Main Steam-pipes should be of such size that ihe mean velocity of flow
does not exceed 8000 ft. per min.
In large engines, 1000 to 2000 H.P., cutting off at less than half stroke, the
Bteam-pipe may be designed for a mean velocity of 9000 ft., and 10,000 ft.
for still larger engines.
In small engines and engines cutting later than half stroke, a velocity of
less than 8000 ft. per minute is desirable.
Taking 8100 ft. per min. as the mean velocity, S speed of piston in feet per
min., and D the diameter of the cyl.,
/ /)2 Q T) ,—
Diam. of main steam-pipe =A/ = — VS.
Y 8100 90
Stop and Throttle Valves should have a greater area of passages than the
area of the main steam-pipe, on account of the friction through the cir-
cuitous passages. The shape of the passages should be designed so as to
avoid abrupt changes of direction and of velocity of flow as far as possible.
Area of Steam Ports and Passages =
Area of piston X speed of piston in ft. per min.
6000
(Diam.)* X speed
7639
Opening of Port to Steam.— To avoid wire-drawing during admission the
area of opening to steam should be such that the mean velocity of flow does
not exceed 10,000 ft. per min. To avoid excessive clearance' the width of
port should be as short as possible, the necessary area being obtained by
length (measured at right angles to the line of travel of the valve). In
Sractice this length is usually 0.6 to 0.8 of the diameter of the cylinder, but
i long-stroke engines it may equal or even exceed the diameter.
Exhaust Passages and Pipes. — The area should be such that the mean
velocity of the steam should not exceed 6000 ft. per min., and the area
should be greater if the length of the exhaust-pipe is comparatively long.
The area of passages from cylinders to receivers should be such that the
velocity will not exceed 5000 ft. per min.
The following table is computed on the basis of a mean velocity of flow
of 8000 ft. per min. for the main steam-pipe, 10,000 for opening to steam,
and 6000 for exhaust. A = area of piston, D its diameter.
STEAM AND EXHAUST OPENINGS.
Piston-
speed,
ft. per min.
Diam. of
Steam -pipe
-*-Z>.
Area of
Steam-pipe
-*- A.
Diam. of
Exhaust
-*-£>.
Area of
Exhaust
-*- A.
Opening
to Steam
-*-A.
300
400
500
600
700
800
900
1000
0.194
0.224
0.250
0.274
0.296
0.316
0.335
0.353
0.0375
0.0500
0.0625
0.0750
0.0875
0.1000
0.1125
0.1250
0.223
0.258
0.288
0.316
0.341
0.365
0.387
0.400
0.0500
0.0667
0.0833
0.1000
0.1167
0.1333
0.1500
0.1667
0.03
0 04
0.05
0.06
0.07
0.08
0.09
0.10
STEAM FIFES.
Bursting-tests of Copper Steam-pipes. (From Report of Chief
Engineer Melville, U. S. N., for !8iW. )— Some tests were made at the New
York Navy Yard which show the unreliability of brazed seams in cop-
per pipes. Each pipe was 8 in. diameter inside and 3 ft. 1% in . long.
Both ends were closed by ribbed heads and the pipe was subjected to a hot-
water pressure, the temperature being maintained constant at 371* F, Three
STEAK-PIPES. 675
of the pipes were made of No. 4 sheet copper (" Stubbs " gauge) and the
fourth was made of No. 3 sheet.
The following were the results, in Ibs. per sq. in., of bursting-pressure:
Pipe number 1 2 3 4 4'
Actual bursting-strength 835 785 950 1225 1275
Calculated'* " . 1336 1336 1569 1568 1568
Difference 501 551 619 343 293
The theoretical bursting-pressure of the pipes was calculated by using the
figures obtained in the tests for the strength of copper sheet with a brazed
joint at 350° F. Pipes 1 and 2 are considered as having been annealed.
The tests of specimens cut from the ruptured pipes show the injurious
action of heat upon copper sheets; and that, while a white heat does not
change the character of the metal, a heat of only slightly greater degree
causes it to lose the fibrous nature that it has acquired in rolling, and a
serious reduction in its tensile strength and ductility results.
All the brazing was done by expert workmen, and their failure to make a
proven in the cases of many of the specimens, both of those cut from the
pipes and those made separately, which broke with a fibrous fracture.
Rule for Thickness of Copper Steam-pipes. (U. S. Super-
vising Inspectors of Steam Vessels.)— Multiply the working steam-pressure
in Ibs. per sq. in. allowed the boiler by the diameter of the pipe in inches,
then divide the product by the constant whole number 8000, and add .0625 to
the quotient; the sum will give the thickness of material required.
EXAMPLE.— Let 175 Ibs. = working steam-pressure per sq. in. allowed the
175 V 5
boiler, 5 in. = diameter of the pipe; then —5™- -f .0625 = .1718 -f inch,
oUUU
thickness required.
Reinforcing: Steam-pipes, (Eng., Aug. 11, 1893.)— In the Italian
Navy copper pipes above 8 in. diam. are reinforced by wrapping them with
a close spiral of copper or Delta-metal wire. Two or three independent
spirals are used for safety in case one wire breaks. They are wound at a
tension of about 1^ tons per sq. in.
Wire-wound Steam-pipes.— The system instituted by the British
Admiralty of winding all steam-pipes over 8 in. in diameter with 3/16-in.
copper wire, thereby about doubling the bursting-pressure, has within re-
cent years been adopted on many merchant steamers using high-pressure
steam, says the London Engineer. The results of some of the Admiralty
tests showed that a wire pipe stood just about the pressure it ought to have
stood when un wired, had the copper not been injured in the brazing.
Riveted Steel Steam-pipes have recently been used for high
pressures. See paper on A Method of Manufacture of Large Steam-pipes,
by Chas. H. Manning, Trans. A. S. M. E., vol. xv.
Valves in Steam-pipes. —Should a globe-valve on a steam-pipe have
the steam-pressure on top or underneath the valve is a disputed question.
With the steam-pressure on top, the stuffing-box around the valve-stem can-
not be repacked without shutting off steam from the whole line of pipe; on
the other hand, if the steam -pressure is on the bottom of the valve it all has
Mo be sustained by the screw-thread on the valve-stem, and there is danger
of stripping the thread.
A correspondent of the American Machinist, 1892, says that it is a very
uncommon thing in the ordinary globe-valve to have the thread give out,
Jmt by water-hammer and merciless screwing the seat will be crushed down
quite frequently. Therefore with plants where only one boiler is used he
advises placing the valve with the boiler-pressure underneath it. On plants
where several boilers are connected to one main steam-pipe he would re-
verse the position of the valve, then when one of the valves needs repacking
the valve can be closed and the pressure in the boiler whose pipe it controls
can be reduced to atmospheric by lifting the safety-v&lve. The repacking
can then be done without interfering with the operation of the other boilers
of the plant.
He proposes also the following other rules for locating valves: Place
valves with the stems horizontal to avoid the formation of a water-pocket.
Never put the junction-valve close to the boiler if the main pipe is above
the boiler, but put it on the highest point of the junction-pipe. If the other
676 STEAM.
plan Is followed, the pfpe fills with \vater whenever this boiler is stopped
and the others are running, and breakage of the pipe may cause serious re-
sults. Never let a junction-pipe run into the bottom of the main pipe, but
into the side or top. Always use an angle-valve where convenient, as there
is more room in them. Never use a gate valve under high pressure unless a
by-pass is used with'it. Never open a blow-off valve on a boiler a little and
then shut it; it is sure to catch the sediment and ruin the valve; throw it
well open before closing. Never use a globe-valve on an indicator-pipe. For
water, always use gate or angle valves or stop-cocks to obtain a clear pas-
sage. Buy if possible valves with renewable disks. Lastly, never let a man
go inside a boiler to work, especially if he is to hammer on it, unless you
break the joint between the boiler a^ ih« valve and put a plate of steel
between the flanges.
A Failure of a Brazed CWpper Steam-pipe on the British
steamer Prodano was investigated by Prof. J. O. Arnold. He found that
the brazing was originally sound, but that it had deteriorated by oxidation
of the zinc in the brazing alloy by electrolysis, which was due to the presence
of fatty acids produced by decomposition of the oil used in the engines.
A full account.of the investigation is given in The Engineer, April 15, 1898.
The "Steam I*oop'> is a system of piping by which water of con-
densation in steam-pipes is automatically returned to the boiler. In its
simplest form it consists of three pipes, which are called the riser, the hori-
zontal, and the drop-leg. When the steam-loop is used for returning to the
boiler the water of condensation and entrainment from the steam-pipe
through which the steam flows to the cylinder of an engine, the riser is gen-
erally attached to a separator; this riser empties at a suitable height into
the horizontal, and from thence the water of condensation is led into the
drop-leg, which is connected to the boiler, into which the water of condensa-
tion is fed as soon as the hydrostatic pressure in drop-leg in connection with
the steam-pressure in the pipes is sufficient to overcome the boiler-pressure.
The action of the device depends on the following principles: Difference of
pressure may be balanced by a water-column: vapors or liquids tend to flow
to the point of lowest pressure; rate of flow depends on difference of pres-
sure and mass; decrease of static pressure in a steam-pipe or chamber ia
proportional to rate of condensation; in a steam-current water will be car-
ried or swept along rapidly by friction. (Illustrated in Modern Mechanism,
p. 807.)
Loss from an Uncovered Steam-pipe* (Bjorling on Pumping-
engines.) — The amount of loss by condensation in a steam-pipe carried down
a deep mine-shaft has been ascertained by actual practice at the Clay Cross
Colliery, near Chesterfield, where there is a pipe 7!^ in. internal diam.. 1100
ft. long. The loss of steam by condensation was ascertained by direct
measurement of the water deposited in a receiver, and was found to be
equivalent to about 1 Ib. of coal per I.H.P. per hour for every 100 ft. of
steam-pipe; but there is no doubt that if the pipes had been in the upcast
shaft, and well covered with a good non-conducting material, the loss would
have been less. (For Steam-pipe Coverings, see p. 469, ante.)
THE HORSE-POWER OF A STEAM-BOILER. 677
THE STEAM-BOILER.
The Horse-power of a Steam-boiler.— The term horse power
has two meanings in engineering : first, an absolute unit or measure of the
rate of work, that is, of the work done in a certain definite period of time,
by a source of energy, as a steam-boiler, a waterfall, a current of air or
water, or by a prime mover, as a steam-engine, a water-wheel, or a wind-
mill. The value of this unit, whenever it can be expressed in foot-pounds
of energy, as in the case of steam-engines, water-wheels, and waterfalls, is
33,000 foot-pounds per minute. In the case of boilers, where the work done,
the conversion of water into steam, cannot be expressed in foot-pounds of
available energy, the usual value given to the term horse-power is the evap-
oration of 30 .lbs. of water of a temperature of 100° F. into steam at 70 Ibs.
pressure above the atmosphere. Both of these units are arbitrary; the first.
33,000 foot-pounds per minute, first adopted by James Watt, being considered
equivalent to the power exerted by a good London draught-horse, and the
30 lbs. of water evaporated per hour being considered to be the steam re-
quirement per indicated horse-power of an average engine.
The second definition of the term horse-power is an approximate measure
of the size, capacity, value, or " rating " of a boiler, engine, water-wheel, or
other source or conveyer of energy, by which measure it may be described,
bought and sold, advertised, etc. No definite value can be given to this
measure, which varies largely with local custom or individual opinion of
makers and users of machinery. The nearest approach to uniformity which
can be .arrived at in the term "horse- power," used in this sense, is to say
that a boiler, engine, water-wheel, or other machine, " rated1' at a certain
horse-power, should be capable of steadily developing that horse-power for
a long period of time under ordinary conditions of use and practice, leaving
to local custom, to the judgment of the buyer and seller, to written contracts
of purchase and sale, or to legal decisions upon such contracts, the interpre-
tation of what is meant by the term "ordinary conditions of use and
practice." (Trans. A. S. M. E., vol. vii. p. 226.)
The committee of the A. S. M. E. on Trials of Steam-boilers in 1884 (Trans.,
vol. vi. p. 265) discussed the question of the horse-power of boilers as follows:
The Committee of Judges of the Centennial Exhibition, to whom the trials
of competing boilers at that exhibition were intrusted, met with this same
problem, and finally agreed to solve it, at least so far as the work of that
committee was concerned, by the adoption of the unit, 30 lbs. of water evap-
orated into dry steam per hour from feed-water at 100° F., and under a
pressure of 70 lbs. per square inch above the atmosphere, these conditions
being considered by them to represent fairly average practice. The quan-
tity of heat demanded to evaporate a pound of water under these conditions
is 1110.2 British thermal units, or 1.1496 units of evaporation. The urnt of
power proposed is thus equivalent to the development of 33,305 heat units
per hour, or 34.488 units or evaporation. . . .
Your committee, after due consideration, has determined to accept the
Centennial Standard, the first above mentioned, and to recommend that in
all standard trials the commercial horse-power be taken as an evaporation
of 30 lbs. of water per hour from a feed-water temperature of 100° F. into
steam at 70 lbs. gauge pressure, which shall be considered to be equal to 34^
units of evaporation, that is, to 34^ lbs. of water evaporated from a feed-
water temperature of 212° F. into steam at the same temperature. This
standard is equal to 33,305 thermal units per hour.
It is the opinion of this committee that a boiler rated at any stated number
of horse-powers should be capable of developing that power with easy firing,
moderate draught, and ordinary fuel, while exhibiting good economy ; and
further, that the boiler should be capable of developing at least one third
more than its rated power to meet emergencies at times when maximum
economy is not the most important object to be attained.
Unit of Evaporation. — It is the custom to reduce results of boiler-
tests to the common standard of weight of water evaporated by the unit
weight of the combustible portion of the fuel, the evaporation being consid-
ered to have taken place at mean atmospheric pressure, and at the temper-
ature due that pressure, the feed-water being also assumed to have been
supplied at that temperature. This is, in technical language, said to be the
equivalent evaporation from and at the boiling point at atmospheric pres-
sure, or " from and at 212° F," This unit of evaporation, or one pound of
678 THE STEAM-BOILER.
water evaporated from and at 212°, is equivalent to 965.7 British thermal
units.
Measures for Comparing the Duty of Boilers.— The meas-
ure of the efficiency of a boiler is the number of pounds of water evaporated
per pound of combustible, the evaporation being reduced to the standard of
" from and at 212° ;" that is, the equivalent evaporation from feed- water at a
temperature of 212° F. into steam at the same temperature.
The measure of the capacity of a boiler is the amount of "boiler horse-
power " developed, a horse-power being defined as the evaporation of 30 Ibs.
of water per hour from 100° F. into steam at 70 Ibs. pressure, or 34J£ Ibs. per
hour from and at 212°.
The measure of relative rapidity of steaming of boilers is the number of
pounds of water evaporated per hour per square foot of water-heating sur-
face.
The measure of relative rapidity of combustion of fuel in boiler-furnaces
is the number of pounds of coal burned per hour per square foot of grate-
surface.
STEAM-BOILER PROPORTIONS.
Proportions of Orate and Heating Surface required for
a given Horse-power.— The term horse-power here means capacity
to evaporate 30 Ibs. of water from 100° F., temperature of feed-water, to
steam of 70 Ibs., gauge-pressure = 34.5 Ibs. from and at 212° F.
Average proportions for maximum economy for land boilers fired with
good anthracite coal:
Heating surface per horse-power 11.5 sq. ft.
Grate " '« " 1/3 **
Ratio of heating to grate surface .. 84.5 '*
Water evap'd from and at 212° per sq. ft. H.S. per hour 8 Ibs.
Combustible burned per H. P. per hour 8 **
Coal with 1/6 refuse, Ibs. per H.P. per hour 3.6 "
Combustible burned per sq. ft. grate per hour 9
Coal with 1/6 refuse, Ibs. per sq. ft. grate pe«* hour. . . . 10.8 **
Water evap'd from and at 212° per Ib. combustible... 11.5 ••
** " " ** " " " " coal (1/6 refuse) 9.6 "
The rate of evaporation is most conveniently expressed in pounds evapo-
rated from and at 21^° per sq. ft. of water-heating surface per hour, and the
rate of combustion in pounds of coal per sq. ft. of grate-surface per hour.
Heating-surface,— For maximum economy with any kind of fuel a
boiler should be proportioned so that at least one square foot of heating-
surface should be given for every 3 Ibs. of water to be evaporated from and
at 212° F. per hour. Still more liberal proportions are required if a portion
of the heating-surface has its efficiency reduced by: 1. Tendency of the
heated gases to short- circuit, that is, to select passages of least resistance
and flow through them with high velocity, to the neglect of other passages.
2. Deposition of soot from smoky fuel. 3. Incrustation. If the heating-sur-
faces are clean, and the heated gases pass over it uniformly, little if any
increase in economy can be obtained by increasing the heating-surface be-
yond the proportion of 1 sq. ft. to every 3 Ibs. of water to be evaporated, and
with all conditions favorable but little decrease of economy will take place
if the proportion is 1 sq. ft. to every 4 Ibs. evaporated; but in order to pro-
vide for driving of the boiler beyond its rated capacity, and for possible
decrease of efficiency due to the causes above named, it is better to adopt 1
sq. ft. to 3 Ibs. evaporation per hour as the minimum standard proportion.
Where economy may be sacrificed to capacity, as where fuel is very cheap,
it is customary to proportion the heating-surface much less liberally. The
following table shows approximately the relative results that may be ex-
pected with different rates of evaporation, with anthracite coal.
Lbs. water evapor'd from and at 212° per sq. ft. heating-surface per hour:
2 2.5 8 3.5 4 5 6 7 8 9 10
Sq. ft. heating-surface required per horse-power:
17.3 13.8 11.5 9.8 8.6 6.8 5.8 4.9 4.3 3.8 8.5
Ratio of heating to grate surface if 1/3 sq. ft. of G. S. is required per R.P.:
52 41.4 34.5 29.4 25.8 20.4 17.4 13.7 12.9 11.4 10.5
Probable relative economy:
100 100 100 95 90 85 80 75 70 65 60
Probable temperature of chimney gases, degrees F.:
450 450 450 518 585 652 720 787 855 922 990
STEAM-BOILER PROPORTIONS. 679
The relative economy will vary not only with the amount of heating-sur-
face per horse-power, but with the efficiency of that heating surface as
regards its capacity for transfer of heat from tne heated gases to the water,
which will depend on its freedom from soot and incrustation, and upon the
circulation of the water and the heated gases.
With bituminous coal the efficiency will largelydepend upon the thorough-
ness with which the combustion is effected in the furnace.
The efficiency with any kind of fuel will greatly depend upon the amount
of air supplied to the furnace in excess of that required to support com-
bustion. With strong draught and thin fires this excess may be very great,,
causing a serious loss of economy.
Measurement of Heating-surface.— Authorities are not agreed
as to the methods of measuring the heating-surface of steam-boilers. The
usual rule is to consider as heating-surface all the surfaces that are sur-
rounded by water on one side and by flame or heated gases on the other, but
there is a difference of opinion as to whether tubular heating-surface should
be figured from the inside or from the outside diameter. Some writers say,
measure the heating-surface alwaj^s on the smaller side — the fire side of the
tube in a horizontal return tubular boiler and the water side in a water-tube
boiler. Others would deduct from the heating-surface thus measured an
allowance for portions supposed to be ineffective on account of being cov-
ered by dust, or being out of the direct current of the gases.
It has hitherto been the common practice of boiler-makers to consider all
surfaces as heating-surfaces which transmit heat from the flame or gases
to the water, making no allowance for different degrees of effectiveness;
also, to use the external instead of the internal diameter of tubes, for
greater convenience in calculation, the external diameter of boiler-tubes
usually being made in even inches or half inches. This method, however,
is inaccurate, for the true heating-surface of a tube is the side exposed to
the hot gases, the inner surface in a fire-tube boiler and the outer surface
in a water-tube boiler. The resistance to the passage of heat from the hot
gases on one side of a tube or plate to the water on the other consists almost
entirely of the resistance to the passage of the heat from the gases into the
metal, the resistance of the metal itself and that of the wetted surface being
practically nothing. See paper by 0. W. Baker, Trans. A. S. M. E., vol. xix*
RULE for finding the heating-surface of vertical tubular boilers : Multiply
the circumference of the fire-box (in inches) by its height above the grate :
multiply the combined circumference of all the tubes by their length, and
to these two products add the area of the lower tube-sheet ; from this sum
subtract the area of all the tubes, and divide by 144 : the quotient is the
number of square feet of heating-surface.
RULE for finding the heating-surface of horizontal tubular boilers: Take
the dimensions in inches. Multiply two thirds of the circumference of the
shell by its length; multiply the siim of the circumferences of all the tubes
by their common length; to the sum of these products add two thirds of the
area of both tube-sheets; from this sum subtract twice the combined area of
all the tubes; divide the remainder by 144 to obtain the result in square feet.
RULE for finding the square feet of heating-surface in tubes : Multiply tbe
number of tubes by the diameter of a tube in inches, by its length in feet,
and by .2618.
Horse-power, Builder's Rating. Heating-surface per
Horse-power. — It is a general practice among builders to furnish about
12 square feet of heating-surface per horse-power, but as the practice is not
uniform, bids and contracts should always specify the amount of heating-
surface to be furnished. Not less than one third square foot of grate-surface
should be furnished per horse-power.
Engineering News, July 5, 1894, gives the following rough-and-ready rule*
for finding approximately the commercial horse-power of tubular or water-
tube boilers : Number of tubes X their length in feet X their nominal
diameter in inches -5- 50 = nLd -*- 50. The number of square feet of surface"
in the tubes is •—— = TTS^I an(* the horse-power at 12 square feet of surface1
1* O.O-4
of tubes per horse-power, not counting the shell, = nLd -?- 45.8. If 15 square
feet of surface of tubes be taken, it is nLd -*- 57.3. Making allowance for
the heating-surface in the shell will reduce the divisor to about 50.
Horse-power of Marine and Locomotive Boilers.— The
term horse-power is not generally used in connection with boilers in marine
practice, or with locomotives. The boilers are designed to suit the engines,
ami are rated by extent of grate and heating-surface only.
680
THE STEAM-BOILER.
Grate-surface.— The amount of grate-surface required per horse
power, and the proper ratio of heating-surface to grate-surface are ex-
tremely variable, depending chiefly upon the character of the coal and upon
the rate of draught. With good coal, low in ash, approximately equal results
may be obtained with large grate-surface and light draught and with small
grate-surface and strong draught, the total amount of coal burned per hour
being the same in both cases. With good bituminous coal, like Pittsburgh,
low in ash, the best results apparently are obtained with strong draught
and high rates of combustion, provided the grate-surfaces are cut down so
that the total coal burned per hour is not too great for the capacity of the
heating-surface to absorb the heat produced.
With coals high in ash, especially if the ash is easily fusible, tending to
choke the grates, large grate-surface and a slow rate of combustion are
required, unless means, such as shaking, grates, are provided to get rid of
the ash as fast as it is made.
The amount of grate-surface required per horse-power under various con-
ditions may be estimated from the following table :
14
w&
t* o
03 gj •>
£«*>£ •
jlsraa
m
' fc4 U
Pounds of Coal burned per square foot
of Grate per hour.
3£3£8
gaa
8
10
12
15
20
25
30
35 | 40
Sq. Ft. Grate per H. P.
Good coal
< 10
3.45
.43
.351 .28
.23
.17
.14
.11
.10
.09
and boiler,
i 9
3.83
.48
.38
.32
.25
.19
.15
.13
.11
.10
Fair coal or
boiler,
( 8.61
1 ?
4.
4.31
4.93
.50
.54
.62
.40
.43
.49
.33
.36
.41
.26
.29
.33
.20
.22
.24
.16
.17
.20
.13
.14
.17
.12
.13
.14
.10
.11
.12
Poor coal or
boiler,
\ l'g
I 5
5.
5.75
6.9
.63
.72
.86
.50
.58
.69
.42
.48
.58
.34
.38
.46
.25
.29
.35
.20
.23
.28
.17
.19
.23
.15
17
,22
.13
.14
.17
Lignite and
poor boiler,
[ 3.45
10.
1.25
1.00
.83
.67
.50
.40
.33
.29
.25
In designing a boiler for a given set of conditions, the grate-surfa.ce should
be made as liberal as possible, say sufficient for a rate of combustion of 10
Ibs. per square foot of grate for anthracite, and 15 Ibs. per square foot for
bituminous coal, and in practice a portion of the grate-surface may be
bricked over if it is found that the draught, fuel, or other conditions render
it advisable.
Proportions of Areas of Flues and other Gas-passages.
— Rules are usually given making the area of gas-passages bear a certain
ratio to the area of the grate-surface; thus a common rule for horizontal
tubular boilers is to mako the area over the bridge wall 1/7 of the grate-
surface, the flue area 1/8, and the chimney area 1/9.
For average conditions with anthracite coal and moderate draught, say a
:nate of combustion of 12 Ibs. coal per square foot of grate per hour, and a ratio
of heating to grate surface of 30 to 1, this rule is as good as any, but it is evi-
dent that if the draught were increased so as to cause a rate of combustion
of 24 Ibs., requiring the grate-surface to be cut down to a ratio of 60 to 1, the
areas of gas-passages should not be reduced in proportion. The amount
of coal burned per hour being the same under the changed conditions, and
there being no reason why the gases should travel at a higher velocity, the
actual areas of the passages should remain as before, but the ratio of the
area to the grate-surface would in that case be doubled.
Mr. Barrus states that the highest efficiency with anthracite coal Is
obtained when the tube area is 1/9 to 1/10 of the grate-surface, and with
bituminous coal when it is 1/6 to 1/7, for the conditions of medium rates of
combustion, such as 10 to 12 Ibs. per square foot of grate per hour, and 12
square feet of heating- surf ace allowed to the horse-power.
The tube area should be made large enough not to choke the draught, and
BO lessen the capacity of the boiler; if made too large the gases are apt to
select the passages of least resistance and escape from them at a high
velocity and high temperature.
This condition is very commonly found in horizontal tubular boilers where
PERFORMANCE OF BOILERS. 681
the gases go chiefly through the tipper rows of tubes; sometimes also in
vertical tubular boilers, where the gases are apt to pass most rapidly
through the tubes nearest to the centre.
Air-passages through Grate-bars.— The usual practice is, air-
opening = 30$ to 50% of area of the grate ; the larger the better, to avoid
stoppage of the air-supply by clinker; but with coal free from clinker much
smaller air-space may be used without detriment. See paper by F. A.
Scheffler, Trans. A. S. M. E., vol. xv. p. 503.
PERFORMANCE OF BOILERS.
The performance of a steam-boiler comprises both its capacity for gener-
ating steam and its economy of fuel. Capacity depends upon size, botb of
^rate-surface and of heating-surface, upon the kind of coal burned, upon
the draft, and also upon the economy. Economy of fuel depends upon tlie
completeness with which the coal is burned in the furnace, on the proper
regulation of the air-supply to the amount of coal burned, and upon the
thoroughness with which the boiler absorbs the heat generated in the
furnace. The absorption of heat depends on the extent of beating-sur-
face in relation to the amount of coal burned or of water evaporated, upon
the arrangement of the gas-passages, and upon the cleanness of the sur-
faces. The capacity of a boiler may increase with increase of economy
when this is due to more thorough combustion of the coal or to better regu-
lation of the air-supply, or it may increase at the expense of economy
when the increased capacity is due to overdriving, causing an increased
loss of heat in the chimney gases. The relation of capacity to econornv
is therefore a complex one, depending on many variable conditions.
Many attempts have been made to construct a formula expressing the rela-
tion between capacity, rate of driving, or evaporation per square foot of
heating-surface, to the economy, or evaporation per pound of combustible,
but none of them can be considered satisfactory, since they make the
economy depend only on the rate of driving (a few so-called ''constants,1*
however, being introduced in some of them for different classes of boilers,
kinds of fuel, or kind of draft), and fail to take into consideration the nu-
merous other conditions upon which economy depends. Such formulae are
Raukine's, Clark's, Emery's, Isherwood^s, Carpenter's, and Hale's. A dis-
cussion of them all may be found in Mr. R. S. Hale's paper on " Efficiency
of Boiler Heating Surface," in Trans. A. S. M. E., vol. xviii. p. 328. Mr.
Hale's formula takes into account the effect of radiation, which reduces the
economy considerably when the rate of driving is less than 3 Ibs. per square
foot of heating-surface per hour.
Selecting the highest results obtained at different rates of driving obtained
with anthracite coal in the Centennial tests (see p. 685), and the highest
results with anthracite reported by Mr. Barrus in his book on Boiler Tests,
the author has plotted two curves showing the maximum results which
may be expected with anthracite coal, the first under exceptional conditions
such as obtained in the Centennial tests, nnd the second under the best
conditions of ordinary practice. (Trans. A. S. M. E.,ixviii. 354). From these
curves the following figures are obtained.
Lbs. water evaporated from and at 212° per sq. ft. heating-surface per hour:
1.6 1.7 2 2.6 3 3.5 4 4.5 5 6 7 8
Lbs. water evaporated from and at 212° per Ib. combustible :
.Centennial. 11.8 11.9 12.0 12.1 12.05 12 11.85 11.7 11.5 1085 9.8 8.5
Barrus 11.4 11.5 11.5511.6 11.6 11.5 11.2 10.9 10.6 9.9 9.2 8.5
Avg. Cent'l 12.0 11.6 11.2 10.8 10.4 10.0 9.6 8.8 8.0 7.Q
JFhe figures in the last line are taken from a straight line drawn as nearly
as possible through the average of the plotting of all the Centennial tests.
The poorest results are far below these figures. It is evident that no formula
can be constructed that will express the relation of economy to rate of
driving as well as do the three lines of figures given above.
For semi-bituminous and bituminous coals the relation of economy to the
rate of driving no doubt follows the same general law that it does with
anthracite, i.e., that beyond a rate of evaporation of 3 or 4 Ibs. per sq. ft. of
heating-surface per hour there is a decrease of economy, but the figures
obtained in different tests will show a wider range between maximum and
average results on account of the fact that it is more difficult with bituminous
than with anthracite coal to secure complete combustion in the furnace.
682 THE STEAM-BOILER.
The amount of the decrease in economy due to driving at rates exceeding
4 Ibs. of water evaporated per square foot of heating-surface per hour
differs greatly with different boilers, and with the same boiler it may differ
with different settings and with different coal,, The arrangement and size
of the gas-passages seem to have an important effect upon the relation of
economy to rate of driving. There is a large field for future research to
determine the causes which influence this relation.
General Conditions which secure JEconomy of Steam-
"boilers.— In general, the highest results are produced where the tempera-
ture of the escaping gases is the least. An examination of this question is
made oy Mr. G. H. Barrus in his book on "Boiler Tests," by selecting those
tests made by him, six in number, in which the temperature exceeds the
average, that is, 375° F., and comparing with five tests in which the temper-
ature is less than 375°, The boilers are all of the common horizontal type,
and all use anthracite coal of either egg or broken size. The average flue
temperatures in the two series was 444° and 343° respectively, and the dif-
ference was 101°. The average evaporations are 10.40 Ibs. and 11.02 Ibs. re-
spectively, and the lowest result corresponds to the case of the highest flue
temperature. In these tests it appears, therefore, that a reduction of 101°
in the temperature of the waste gases secured an increase in the evaporation
of 6$. This result corresponds quite closely to the effect of lowering the
temperature of the gases by means of a flue-heater where a reduction of
107° was attended by an increase of 1% in the evaporation per pound of coal.
A similar comparison was made on horizontal tubular boilers using Cum-
berland coal. The average flue temperature in four tests is 450° and the
average evaporation is 11.34 Ibs. Six boilers have temperatures below 415°,
the average of which is 383°, and these give an average evaporation of 11.75
Ibs. With 67° less temperature of the escaping gases the evaporation is
higher by about 4%.
The wasteful effect of a high flue temperature is exhibited by other boilers
than those of the horizontal tubular class. This source of waste was shou n
to be the main cause of the low economy produced in those vertical boilers
which are deficient in heating-surface.
Relation between the Heating-surface and Grate-surface to obtain the
Highest Efficiency. — A comparison of three tests of horizontal tubular
boilers with anthracite coal, the ratio of heating, surf ace to grate-surface
being 36. 4 to 1, with three other tests of similar boilers, in which the ratio
was 48 to 1, showed practically no difference in the results. The evidence
shows that a ratio of 36 to 1 provides a sufficient quantity of heating-surface
to secure the full efficiency of anthracite coal where the rate of combustion
is not more than 12 Ibs. per sq. ft. of grate per hour.
In tests with bituminous coal an increase in the ratio from 36.8 to 42.8 se-
cured a small improvement in the evaporation per pound of coal, and a high
temperature of the escaping gases indicated that a still further increase
would be beneficial. Among the high results produced on common horizon-
tal tubular boilers using bituminous coal, the highest occurs where the ratio
is 53.1 to 1. This boiler gave an evaporation of 12.47 Ibs. A double-deck
boiler furnishes another example of high performance, an evaporation of
12.42 Ibs. having been obtained with bituminous coal, and in this case the
ratio is 65 to 1. These examples indicate that a much larger amount of
beating-surface is required for obtaining the full efficiency of bituminous
coal than for boilers using anthracite coal. The temperature of the escap-
ing gases in the same boiler is invariably higher when bituminous coal is
used than when anthracite coal is used. The deposit of soot on the surfaces
when bituminous coal is used interferes with the full efficiency of the sur-
face, and an increased area is demanded as an offset to the loss which this
deposit occasions. It would seem, then, that if a ratio of 36 to 1 is sufficient
for anthracite coal, from 45 to 50 should be provided when bituminous coal
is burned, especially in cases where the rate of combustion is above 10 or 12
Ibs. per sq. ft. of grate per hour.
The number of tubes controls the ratio between the area of grate-surface
and area of tube -opening. A certain minimum amount of tube-opening is
required for efficient work.
The best results obtained with anthracite coal in the common horizontal
boiler are in cases where the ratio of area of grate-surface to area of tube-
opening is larger than 9 to 1. The conclusion is drawn that the highest effi-
ciency with anthracite coal is obtained when the tube-opening is from 1/9 to
1/10 of the grate-surface.
PERFORMANCE OF BOILERS. 683
When bituminous coal is burned the requirements appear to be different.
The effect of a large tube opening does not seem to make the extra tubes
inefficient when bituminous coal is used. The highest result on any boiler of
the horizontal tubular class, fired with bituminous coal, was obtained where
the tube-opening was the largest. This gave an evaporation of 12.47 Ibs., the
ratio of grate-surface to tube- opening being 5.4 to 1. The next highest re-
sult was 12.42 Ibs., the ratio being 5.2 to 1. Three high results, averaging
12.01 Ibs., were obtained when the average ratio was 7.1 to 1. Without going
to extremes, the ratio to be desired when bituminous coal is used is that
which gives a tube-opening having an area of from 1/6 to 1/7 of the grate-
surface. This applies to medium rates of combustion of, say, 10 to 12 Ibs. per
sq. ft. of grate per hour, 12 sq. ft. of water-heating surface being allowed per
horse-power.
A comparison of results obtained from different types of boilers leads to
the general conclusion that the economy with which different types cf
boilers operate depends much more upon their proportions and the condi-
tions under which they work, than upon their type ; and, moreover, that
when these proportions are suitably carried out, and when the conditions
are favorable, the various types of boilers give substantially the same eco-
nomic result.
Efficiency of a Steam-boiler.— The efficiency of a boiler is the
percentage of the total heat generated by the combustion of the fuel
which is utilized in heating the water and in raising steam. With anthracite
coal the heating-value of the combustible portion is very nearly 14,500
B. T. U. per lb., equal to an evaporation from and at 212° of 14,500 -s- 966
as 15 Ibs. of water. A boiler which when tested with anthracite coal shows
an evaporation of 12 Ibs. of water per lb. of combustible, has an efficiency of
12 -5- 15 = 80#, a figure which is approximated, but scarcely ever quite
reached, in the best practice. With bituminous coal it is necessary to have
a determination of its heating-power made by a coal calorimeter before the
efficiency of the boiler using it can be determined, but a close estimate may
be made from the chemical analysis of the coal. (See Coal.)
The difference between the efficiency obtained by test and 100# is the sum
of the numerous wastes of heat, the chief of which is the necessary loss due
to the temperature of the chimney-gases. If we have an analysis and a
calorimetric determination of the heating-power of the coal (properly sam-
pled), and an average analysis of the chimney-gases, the amounts of the
several losses may be determined with approximate accuracy by the method
described below.
Data given :
1. ANALYSIS OF THE COAL. 2. ANALYSIS OP THE DRY CHIMNEY-
Cumberland Semi-bituminous. GASES, BY WEIGHT.
Carbon 80.55 C. O. N.
Hydrogen 4.50 COa = 13.6 = 3.71 9.89
Oxygen 2.70 CO = .2 = .09 .11
Nitrogen 1.08 O = 11.2 = .... 11.20
Moisture 2.92 N = 75.0 = ... .."... 75.00
Ash 8.25 •
100.0 3.80 21.20 75.00
100.00
Heating-value of the coal by Dulong's formula, 14,243 heat-units.
The gases being collected over water, the moisture in them is not deter-
mined.
3. Ash and refuse as determined by boiler-test, 10.25, or 2£ more than that
found by analysis, the difference representing carbon in the ashes obtained
in the boiler-test.
4. Temperature of external atmosphere, 60° F.
5. Relative humidity of air, 60£, corresponding (see air tables) to .007 lb. of
vapor in each lb. of air.
6. Temperature of chimney-gases, 560° F.
Calculated results :
The carbon in the chimney-gases being 3.8# of their weight, the total
weight of dry gases per lb. of carbon burned is 100 -r- 3.8 = 26.32 Ibs. Since
the carbon burned is 80.55 — 2 = 78.55# of the weight of 'the coal, the weight
of the dry gases per lb. of coal is 26.32 X 78.55 -*- 100 = 20.67 Ibs.
Each pound of coal furnishes to the dry chimney -gases .7855 lb. C, .0108N,
and (2 70 - —ty * 100 = .0214 lb. O; a total of .8177, say .82 lb. This sub-
684 THE STEvUr-BOILEH.
tracted from 20.6? Ibs. leaves 19.85 Ibs. as the quantity of dry air (not includ-
ing moisture) which enters the furnace per pound of coal, not counting the
air required to burn the available hydrogen, that is, the hydrogen minus one
eighth of the oxygen chemically combined in the coal. Each Ib. of coal
burned contained .045 Ib. H, which requires .045 X 8 — 36 Ib. O for its com-
bustion. Of this, .027 Ib. is furnished by the coal itself, leaving .333 Ib. to
come from the air. The quantity of air needed to supply this oxygen (air
containing 23# by weight of oxygen) is .333 -*- .23 = 1.45 Ib., which added to
the 19.85 Ibs. already found gives 21.30 Ibs. as the quantity of dry air sup-
plied to the furnace per Ib. of coal burned.
The air carried in as vapor is .0071 Ib. for each Ib. of dry air, or 21.3 X .0071
= 0.15 Ib. for each Ib. of coal. Each Ib. of coal contained .029 Ib. of mois-
ture, which was evaporated and carried into the chimney -gases. The .045 Ib.
Of H per Ib. of coal when burned formed .045 X 9 = .405 Ib. of H2O.
From the analysis of the chimney-gas it appears that .09 -j- 3.JSO = 2.3?# of
the carbon in the coal was burned to CO instead of to CO2.
We now have the data for calculating the various losses of heat, as follows,
for each pound of coal burned:
Heat-
units.
Per cent of
Heat-value
of the Coal.
20.67 Ibs. dry gas X (560° - 60°) X sp. heat 0 24 = 2480.4 17.41
.15 Ib. vapor in air X (560° - 60°) X sp. heat .48 = 36.0 0.25
.029 Ib. moisture in coal heated from t;0° to 212° •= 4.4 0.03
evaporated from and at 212°; .029 X 960 = 28.0 0.20
steam (heated from 212° to 560°) X 348 X .48 = 4.8 0 03
.405 Ib. H2O from H in coal X (153 4- 960 -f 31S X .4S) = 520.4 3.65
.0237 Ib. C burned to CO; loss by incomplete com-
bustion, .0237 X (14544 - 4451) = 239.2 1.68
.02 Ib. coal lost in ashes; .02 X 14544 = 5290. 9 2.04
Radiation and unaccounted for, by difference = 624.0 4.31
4228.1
Utilized in making steam, equivalent evaporation
10.37 Ibs. from and at 212° per Ib. of coal = 10,014.9 70.32
14,243.0 100.00
The heat lost by radiation from the boiler and furnace is not easily deter-
mined directly, especially if the boiler is enclosed in brickwork, or is pro-
tected by non-conducting covering. It is customary to estimate the heat
lost by radiation by difference, that is, to charge radiation with all the heat
lost which is not otherwise accounted for.
One method of determining the loss by radiation is to block off a portion
of the grate-surface and build a small fire on the remainder, and drive this
fire with just enough draught to keep up the steam-pressure and supply the
heat lost by radiation without allowing any steam, to lie discharged, weigh-
ing the coal consumed for this purpose during a test of several hours' dura-
tion.
Estimates of radiation by difference are apt to be greatly in error, as in
this difference are accumulated all the errors of the analyses of the coal
and of the gases. An average value of the heat lost by radiation from a
boiler set in brickwork is about 4 per cent. When several boilers are in a
battery and enclosed in a boiler-house the loss by radiation may be very
much less, since much of the heat radiated from the boiler is returned to it
in the air supplied to the furnace, which is taken from the boiler-room.
An important source of error in making a "heat balance" such as the
one above given, especially when highly bituminous coal is used, may be
due to the non-combustion of part of the hydrocarbon gases distilled from
the coal immediately after firing, when the temperature of the furnace may
be reduced below the point of ignition of the gases. Each pound of hydro-
gen which escapes burning is equivalent to a Joss of heat in the furnace of
62,500 heat-units.
In analyzing the chimney gases by the usual method the percentages of
the constituent gases are obtained by volume instead of by weight. To
reduce percentages by volume to percentages by weight, multiply the per-
centage by volume oi uucu &us oy us specific gravity as compared with air,
and divide each product by the sum of the products.
TESTS OF STEAM-BOILERS.
685
If O, CO, CO2 , and N represent the p^r cents by volume of oxygen car-
*onic oxide, carbonic acid, and nitrogen, respectively, in the gases of com-
bustion:
Lbs. of air required to burn ) _ 3.03? N
one pound of carbon | •*"" CO3 -f CO*
Eatio of total air to the theoretical requirement = — —
N - 3.782 O*
Lbs. of air per pound ) ( Lbs. of air per pound I v j Per cent of carbon
of coal f | of carbon | x < in coal.
Lbs. dry gas produced per pound of carbon = 31C°2 + 8O + 7(^° + N).
3(COj -p C/O)
TESTS OF STEAM-BOILERS.
Boiler-tests at the Centennial Exhibition, Philadel-
phia, 1876.— (See Reports and Awards Group XX, International Exhibi-
tion, Phila., 1876; also, Clark on the Steam-engine, vol. i, page 253.)
Competitive tests were made of fourteen boilers, using good anthracite
coal, one boiler, the Galloway, being tested with both anthracite and semi-
bituminous coal. Two tests were made with each boiler : one called the
capacity trial, to determine the economy and capacity at a rapid rate of
driving; and the other called the economy trial, to determine the economy
when driven at a rate supposed to be near that of maximum economy and
rated capacity. The following table gives the principal results obtained in
the economy trial, together with the capacity and economy figures of the
capacity trial for comparison.
Economy Tests.
Capacity
Tests.
36
8
S£
<s .
&
a
TJ i
Name
JTl
"3 ?
ifg
0
&
•a
si
S3 t>* 2
gib OQ
I
i
c3
2
02
*M
i!
Boiler.
ft
jl
§
xj
^
flj
o
1
I
O
g
^
u»
*u
lo
<D <B
C3 02
a
fe
>
s**>
$&
If
a
> .
0> p,
£^J
1
1
1
a
a
*§»§
O y
— g
0)
V
33 K
9£>
.§0 ^
A
2
1
g
i
02
St!l
jr
go
1
li
£9£
1
1
Ml
3
03
1
o
w
$**
Ibs.
p.ct
Ibs.
Ibs.
deg
£
deg
H.P.
H.P.
Ibs.
Root
34.6
9.1
10.4
2.25
12.094
393
41.4
119.8
148.6
10.441
Firmenich
64.3
12 0
10.4
1 68
11.988
415
32.6
57.8
68.4
11.064
30.6
6.8
11.3 1.87
11 923
333
9.4
47.0
69^3
11 163
Smith
45.8
13.1
11.12.42
11.906
411
is
99.8
125.0
11.925
Babcock & Wilcox
37.7
10.0
11.02.43
11.822
296
2^7
135.6
186.6
10.330
Galloway
23.7
9.6
11.1 3.68
11 583
303
'i."4
103.3
133.8
11.216
Do. semi-bit, coal
23.7
7.9
8.83.20
12.125
325
6!s
90.9
125.1
11.609
Andrews
15.6
8.0
10.32.32
11.039
420
71.7
42.6
58.7
9.745
Harrison
27 3
12.4
8.52.75
10.930
517
82 4
108 4
9 889
Wiegand
30.7
12.3
9.53.30
10^834
524
20 5
147^5
162!8
9^145
Anderson
17.5
9.7
9.32.64
10.618
417
15.7
98.0
132.8
9.568
Kelly
20.9
10.8
9.0 3.82
10.312
'5.6
81.0
99.9
8.397
Exeter
33 5
0 3
11.4 1.38
10.041
430
4.2
72 1
108 0
9 974
Pierce
14.0
8.0
11.04.41
374
5.2
51 .'7
67.8
9i 865
Rogers & Black . . .
19.0
8.6
9.93.43
9^613
572
2.1
45.7
67.2
9.429
Averages
.... 2.77
11.123
85.0
110.8
10.251
The comparison of the economy and capacity trials shows that an average
Increase in capacity of 30 per cent was attended by a decrease in economy
of 8 per cent, but the relation of economy to rate of driving varied greatly
in the different boilers. In the Kelly boiler an increase in capacity of 22 per
cent was attended by a decrease in economy of over 18 per cent, while the
Smith boiler with an increase of 25 per cent in capacity showed a slight
increase in economy.
686
THE STEAM-BOILER.
One of the most important lessqps gained from the above tests is that
there is no necessary relation between the type of a boiler and economy. Of
the five boilers that gave the best results, the total range of variation be-
tween the highest and lowest of the five being only 2.3%, three were water-
tube boilers, one was a horizontal tubular boiler, and the fifth was a com-
bination of the two types. The next boiler on the list, the Galloway, was an
internally fired boiler, all of the others being externally fired. The following
is a brief description of the principal constructive features of the fourteen
boilers:
o™, j 4-in. water-tubes, inclined 20° to horizontal ; reversed
Koot 1 draught.
Firmenich 3-in. water-tubes, nearly vertical; reversed draught.
Lowe Cylindrical shell, multitubular flue.
' Cylindrical shell, multitubular flue- -water-tubes in
side flues.
3^-in. water-tubes, inclined 15° to horizontal; re-
versed draught.
Cylindrical shell, furnace-tubes and water-tubes.
Smith ..................
Babcock & Wilcox ....
Galloway
Andrews ............. Square fire-box and double return multitubular flues.
slabs of cast-iron spheres, 8 in. in diameter; re-
versed draught.
j 4-in. water-tubes, vertical, with internal circulating
-j tubes
Anderson ............. . 3-in. flue-tubes, nearly horizontal; return circulation.
jr- 11 j 3-in. water-tubes, slightly inclined; each divided by
' ' 1 internal diaphragm to promote circulation.
Exeter ...... .. ......... 27 hollow rectangular cast-iron slabs.
Pierce ............... Rotating horizontal cylinder, with flue-tubes.
Rogers & Black ....... Vertical cylindrical boiler, with external water-tubes.
Tests of Tu bilious Boilers,— The following tables are given by S.
H. Leonard, Asst. Eugr. U. IS. N., in Jour. Am. Soc. Naval Enyrs. 1890. The
tests were made at different times by boards of U. S. Naval Engineers, ex-
cept thejiestofthelp^^
jj
Evaporation
.-S
.
from and at
Weights, Ibs.
Q
1
S
«?£
212° F.
.2
£
M
£l
03
3
w
too
K
fc •
1
5?
Type.
*O> Q.
j|
43
>..S
P_j
"c3 ^
3-3
3
II
a
1
g|
|L
w
t-S
||
^?
^a
G,
|
<
^O
xj
• r
<5^
W ^3 >
s_
qj
£^
^^
t!.
03
-H*
fi
(^
P4
H olf i-4
(2
£
«*
1
02
s
Belleville..
12.8
10.42
5.2
6.4
E 40,670
S 42,770
204
53.2
10.1
Nat1!.
111
B.
Herreshoff
j 9.3
1 25.8
10.23
8.68
3.1
8
9.1
23.8
E 2,945
S 3,050
96
38
14.8
4.8
1.8
Jet.
Jet.
120
195
A.
A.
Towne
j 4.3
1 24.5
13.4
6 77
2.7
8.2
10
30.4
E 1,380
S 1,640
172
56
21.8
8.1
2.6
Nat'l.
1.14
148
152
A.
A.
Ward.
i 7.9
1 15.5
10.77
10.01
1.7
3.2
5.8
11
E 1,682
Q 1 QQO
154
82
13.2
7.7
4.07
Nat1!.
Jet.
0
1?
A.
A.
/ 62.5
7.01
10
34.2
b i , you
26
1.3
Jet.
161
B.
Scotch
j 24.8
1 38
9.93
9.06
8.6
12.8
11
16.3
E 18,900
S 30,000
120
80
41.2
4.7
3.1
2.08
4.01
77
78
A.
A.
Locom^ive
torpedo,
j 98.3
1 120.8
;::::
17.1
20.05
30.5
36.2
S 34,990
47.7
33.3
31.3
1.8
1.2
3.13
4.95
125
128
B,
B.
Ward
55.04
8.44
9.47
32.1
E 26,533
26
12.3
1.3
1
160
B.
Thorny-
croft. (U.
S.S.Cush-
. ...
S 30,474
E 20.160
S 24,640
*31
10.3
8
245
B.
ing.)
j
* Approximate.
Per cent moisture in steam: Belleville, 6.31; Herreshoff (first test), 3,5
otch, 1st, 3.44; 24. 4.29; Ward, 11.6; others not given.
TESTS OF STEAM-BOILERS.
687
DIMENSIONS OF THE BOILERS.
No.
1
2
3
4
5
6
7
8
Length, ft. and in..
Width, " •*
Height," " "..
Space, cu. ft
Grate- area, sq. ft. .
Heating-surface,
sq. ft
8' 6"
7 0
11 0
645.5
34.1?
804
4' 9"
3 8
4 0
69.6
9
205
2' 6"
2 6
3 3
20 3
4.25
75
3' 2"
1 7
7 2
42.7
3.68
9' 0"
9 0
'572 .*5
31.16
727
16' 8
6 4
7 6
630.3
28
1116
10' 3"*
4 6 t
11 8
729.3
66.5
2490
10' 0"$
8 0$
560t
38.3
2375
Ratio H.S.--*-G ...
23.5
22
17.6
39.5
23.3
39.8
37.4
62
* Diameter, t Diam. of drum. $ Approximate.
The weight per I.H.P. is estimated on a basis of 20 Ibs. of water per hour
for all cases excepting the Scotch boiler, where 25 Ibs. have been used, as this
boiler was limited to 80 Ibs. pressure of steam.
The following approximation is made from the large table, on the assump-
tion that the evaporation varies directly as the combustion, and 25 Ibs. of
Coal per square foot of grate per hour used as the unit.
Type of Boiler.
Com
bustion.
Evapora-
tion per
cu. ft. of
Space.
Weight
per
I.H.P.
Weight
per sq. ft.
Heating-
surface.
Weight
per Ib.
Water
Evapo-
rated.
Belleville
0.50
0.50
2.02
2.10
2.50
1.00
0 95
0.72
0.60
0.90
1.00
1.20
1.12
0.87
1.30
Scotch
1.00
0 44
2.40
1.64
2.30
3.90
0.31
3.70
1.25
3.50
Ward ..
2.20
0.58
1.27
0.50
1.53
The Belleville boiler has no practical advantage over the Scotch either in
space occupied or weight. All the other tubulous boilers given greatly
exceed the Scotch in these advantages of weight and space.
Some High Rates of Evaporation.— Eng'g, May 9, 1884, p. 415.
Locomotive. Torpedo-boat.
Water evap. per sq. ft. H.S. per hour 12.57 13.73 12.54 20.74
" Ib. fuel from and at 212°. 8.22 8.94 8.37 7.04
Thermal units transf'd per sq. ft. of H.S. 12,142 13,263 12,113 20,034
Efficiency 586 .637 .542 .468
It is doubtful if these figures were corrected for priming,
Economy Effected by Heating the Air Supplied to
Boiler-furnaces. (Clark, S. E.)— Meimier and Scheurer-Kestner ob-
tained about 7% greater evaporative efficiency in summer than in winter,
from the same boilers under like conditions,— an excess which had been ex-
plained by the difference of loss by radiation and conduction. But Mr.
Poupardin, surmising that the gain might be due in some degree also to the
greater temperature of the air in summer, made comparative trials with
two groups of three boilers, each working one week with the heated air,
and the next week with cold air. The following were the several efficien-
cies:
FIRST TRIALS: THREE BOILERS; RONCHAMP COAL.
Water per Ib. of Water per Ib. of
Coal. Combustible.
With heated air (128° F.) 7.77 Ibs. 8.95 Ibs.
With cold air (69°.8) 7.33 " 8.63 "
Difference in favor of heated air ....0.41 " 0.32 "
SECOND TRIALS: SAME COAL; THREE OTHER BOILERS.
With heated air (120°.4 F.) 8.70 Ibs. 10.08 Ibs.
With cold air (75°.2) 8.09 " 9.34 "
Difference in favor of heated air 0.61 ** 0.74 u ;
688
THE STEAM-BOILER.
g
These results show economies in favor of heating the air of 6# and 7^|Jt.
Mr. Poupardin believes that the gain in efficiency is due chiefly to the
better combustion of the gases wtth heated air. It was observed that with
heated air the flames were much shorter and whiter, and that there was
notably less smoke from the chimney.
An extensive series of experiments was made by J. C. Hoadley (Trans.
A. S. M. E., vol. vi., 676) on a "Warm-blast Apparatus," for utilizing the
heat of the waste gases in heating the air supplied to the furnace. The ap-
paratus, as applied to an ordinary horizontal tu ular boiler 60 in. diameter,
21 feet long, with 65 3^-inch tubes, consisted of 240 2-inch tubes, 18 feet long,
through which the hot gases passed while the air circulated around them.
The net saving of fuel effected by the warm blast was from 10.7$ to 15.5% of
the fuel used with cold blast. The comparative temperatures averaged as
follows, in degrees F. :
Cold-blast Warm-blast
Boiler. Boiler.
Inheatoffire 2493 2793 300
Atbridgewall 1340 1600 260
In smoke box 373 375 2
Air admitted to furnace 32 332 300
Steam and water in boiler 300 300 0
Gases escaping to chimney 373 162 211
External air 32 32 0
With anthracite coal the evaporation from and at 212° per Ib. combustible
was, for the cold-blast boiler, days 10.85 Ibs., days and nights 10.51; and for
the warm-blast boiler, days 11.83, days and nights 11.03.
Results of Tests of Heine Water-tube Boilers with
Different Coals.
(Communicated by E. D. Meier, C.E., 1894.)
Difference.
1
2
3
4
5
6
7
8
•OS
^
..
a
J.§
2d Pool,
5
"§J
.5
£
Kind of Coal.
^2
Youghiogh-
c %
G"Z
•— p<
IB
's ^
eny.
&&
£&
i5
j§ §
H
§>%
§
&
o
o
1
Per cent ash
5.1
4.89
11.6
16.1
11.5
91.fi
12.8
Heating-surface, sq. ft . .
Grate-surface, sq. ft
2900
54
2040
44.8
2040
44.8
2300
50
12(30
21
3730
73.3
1168
27.9
2770
50
Ratio H S to G S
53.7
45 5
455
46
60
50.9
41 9
55 4
Coal per sq. ft. G.per hr.
24.7
23.5
22.7
35
33.7
26.2
27.7
36
Water per sq. ft. H.S.per
hr. from and at 21 2°....
5.03
5.14
5.24
5.56
4.26
4.28
4.86
5.08
Water evap. from and at
212° per Ib. coal
10.91
9.94
10.51
7.31
7.59
8.33
7.36
7.81
Per Ib. combustible
11.50
10.48
8.27
9.05
9.41
9.41
8.96
Temp, of chimney gases
530°
"400
567
571
609
707
Calorific value of fuel. . .
13,800
12,' 936
12,936
tO, 487
11,785
11,610
9,739
10,359
Efficiency of boiler per c.
77.0
74.3
78.5
67.2
62.5
69.3
73.0
^2.6
Tests Nos. 7 and 8 were made with the Hawley Down-draught Furnace,
the others with ordinary furnaces.
These tests confirm the statement already made as to the difficulty of
obtaining, with ordinary grate-furnaces, as high a percentage of the calo-
rific value of the fuel with the Western as with the Eastern coals.
Test No 3, 78.5$ efficiency, is remarkably good for Pittsburgh (Youghiogh-
eny) coal. If the Washington coal had given equal efficiency, the saving of
fuel would be 78-5^~ ^2-° _ 20 2#. The results of tests Nos. 7 and 8 indicate
<8.5
that the downward-draught furnace is well adapted for burning Illinois
coals.
BOILERS USING WASTE GASES. 689
maximum Boiler Efficiency with Cumberland Coal.—
About 12.5 Ibs. of water per Ib. combustible from and at 212° is about the
highest evaporation that can be obtained from the best steam fuels in the
United States, such as Cumberland, Pocahontas, and Clearfleld. In excep-
tional cases 13 Ibs. has been reached, and one test is on record (F. W. Dean,
Eng'g News, Feb. 1, 1894) giving 13.23 Ibs. The boiler was internally fired,
of the Belpaire type, 82 inches diameter, 31 feet long, with 160 3-inch tubes
W& feet long. Heating-surface, 1998 square feet; grate-surface,45 square feet,
reduced during the test to 30^ square feet. Double furnace, with fire-brick
arches and a long combustion -chamber. Feed-water heater in smoke-box.
The following are the principal results :
1st Test. 2d Test.
Dry coal burned per sq. ft. of grate per hour, Ibs 8.85 16.06
Water evap. per sq. ft. of heating-surface per hour, Ibs 1.63 3.00
Water evap. from and at 212° per Ib. combustible, in-
cluding feed- water heater 13.17 13.23
Water evaporated, excluding feed-water heater 12.88 12,90
Temperature of gases after leaving heater, F 360° 469°
BOILERS USING WASTE GASES.
Proportioning Boilers for Blast-Furnaces.— (F. W. Gordon,
Trans. A. I. M. E., vol. xii., 1883.)
Mr. Gordon's recommendation for proportioning boilers when properly set
for burning blast-furnace gas is, for coke practice, 30 sq. ft. of heating-sur-
face per ton of iron per 24 hours, which the furnace is expected to make,
calculating the heating-surface thus : For double-flued boilers, all shell-
surface exposed to the gases, and half the flue-surface; for the French type,
all the exposed surface of the upper boiler and half the lower boiler-
surface; for cylindrical boilers, not more than 60 ft. long, all the heating-
surface.
To the above must be added a battery for relay in case of cleaning, repairs,
etc., and more than one battery extra in large plants, when the water carries
much lime.
For anthracite practice add 50% to above calculations. For charcoal prac-
tice deduct 20%.
In a letter to the author in May, 1894, Mr. Gordon says that the blast-
furnace practice at the time when his article (from which the above extract
is taken) was written was very different from that existing at the present
time; besides, more economical engines are being introdused, so that less
than 30 sq. ft. of boiler-surface per ton of iron made in 24 hours may now be
adopted. He says further: Blast-furnace gases are seldom used for other
than furnace requirements, which of course is throwing away good fuel. In
this case a furnace in an ordinary good condition, and a condition where it
can take its maximum of blast, which is in the neighborhood of 200 to 225
cubic ft., atmospheric measurement, per sq. ft. of sectional area of hearth,
will generate the necessary H.P. with very small heating-surface, owing to
the high heat of the escaping gases from the boilers, which frequently is
1000 degrees.
A furnace making 200 tons of iron a day will consume about 900 H.P. in
blowing the engine. About a pound of fuel is required in the furnace per
pound of pig metal.
In practice it requires 70 cu ft. of air-piston displacement per Ib. of fuel
consumed, or 22,400 cu. ft. pel minute for 200 tons of metal in 1400 working
minutes per day, at, say, 10 Ibs. discharge-pressure. This is equal to 9*4 Ibs.
M.E.P. on the steam-piston of equal area to the blast-piston, or 900I.H.P. To
this add 20% for hoisting, pumping and other purposes for which steam is em-
ployed around blast-furnaces, and we have 1100 H.P., or say 5}^ H.P. per
ton of iron per day. Dividing this into 30 gives approximately 5£fj sq. ft. of
heating-surface of boiler per H.P.
Water-tube Boilers using Blast-furnace Gases.— D. S.
Jacobus (Trans. A. I. M. E., xvii. 50) reports a test of a water- tube boiler using
blast-furnace gas as fuel. The heating-surface was 2535 sq. ft. It developed
328 H.P. (Centennial standard), or 5.01 Ibs. of water from and at 212° per
sq. ft. of heating-surface per hour. Some of the principal data obtained
were as follows: Calorific value of 1 Ib. of the gas, 1413 B T.U., including
the effect of its initial temperature, which was 650° F. Amount of air used
to burn 1 Ib. of the gas = 0.9 Ib. Chimney draught, l^j in. of water. Area of
gas inlet, 300 sq. in.; of air inlet, 100 sq. in. Temperature of the chimney
690
THE STEAM-BOILER.
gases, 775° F. Efficiency of the boiler calculated from the temperatures
and analyses of the gases at exit and entrance, 61 #. The average analyses
were as follows, hydrocarbons being included in the nitrogen ;
By Weight.
By Volume.
At Entrance.
At Exit.
At Entrance.
At Exit.
CO2
10.69
.11
26.71
62.48
2.92
11.45
14.37
20.37
3.05
1.78
68.80
7.19
.76
7.95
7.08
.10
27.80
65.02
18.64
2.96
1.98
76.42
o
CO
C iii CO.
C in CO
Total C
No.l.
No. 2.
No. 3.
No. 4.
1026
1196
143
1380
19.9
13.6
13.6
16.7
52
87.2
10.5
82.8
3358
2159
1812
3055
3.3
1.8
12.7
2.2
5.9
6.24
3.76
6.34
7.20
4.31
8.34
Steam-boilers Fired with Waste Oases from Puddling
and Heating Furnaces.— The Iron Age, April 6, 1893, contains a report
of a number of tests of steam-boilers utilizing the waste heat from pud
dling and heating furnaces in rolling-mills. -The following principal data are
selected: In Nos. 1, 2, and 4 the boiler is a Babcock & Wilcox water-tube
boiler, and in No. 3 it is a plain cylinder boiler, 42 in. diam. and 26 ft. long.
No. 4 boiler was connected with a heating-furnace, the others with puddling
furnaces.
Heating-surface, sq. ft
Grate-surface, sq. ft...
Ratio H.S. to G.S
Water evap. per hour, Ibs
" ** per sq. ft. H.S. per hr., Ibs...
per Ib. coal from and at 212°.
*' '* comb. " " " "
In No. 2, 1 .38 Ibs. of iron were puddled per Ib. of coal.
In No. 3, 1.14 Ibs. of iron were puddled per Ib. of coal.
No. 3 shows that an insufficient amount of heating-surface was provided
for the amount of waste heat available.
RULES FOR CONDUCTING BOILER-TESTS,
Code of 1899.
(Reported by the Committee on Boiler Trials, Am. Soc. M. E.*)
I. Determine at the outset the specific object of the proposed trial,
whether it be to ascertain the capacity of the boiler, its efficiency as a
steam-generator, its efficiency and its defects under usual working condi-
tions, the economy of some particular kind of fuel, or the effect of changes
of design, proportion, or operation; and prepare for the trial accordingly.
II. Examine the boiler, both outside and inside; ascertain the dimensions
of grates, heating surfaces, and all important parts ; and make a full rec-
ord, describing the same, and illustrating special features by sketches.
II L Notice the general condition of the boiler and its equipment, and
record such facts in relation thereto as bear upon the objects in view.
If the object of the trial is to ascertain the maximum economy or capa-
city of the boiler as a steam-generator, the boiler and all its appurtenances
should be put in first-class condition. Clean the heating surface inside and
outside, remove clinkers from the grates and from the sides of the furnace.
Hemove all dust, soot, and ashes from the chambers, smoke-connections,
and flues. Close air-leaks in the masonry and poorly fitted cleaning-doors.
See that the damper will open wide and close tight. Test for air-leaks by
firing a few shovels of smoky fuel and immediately closing the damper, ob-
serving the escape of smoke through the crevices, or by passing the flame
of a candle over cracks in the brickwork.
* The code is here slightly abridged. The complete report of the Com-
mittee may be obtained in pamphlet form from the Secretary of the Ameri-
can Society of Mechanical Engineers, 12 West 31st St., New York.
RULES FOR CONDUCTING BOILER-TESTS. 691
IV. Determine the character of the coal to be used. For tests of the effi-
ciency or capacity of the boiler for comparison with other boilers the coal
should, if possible, be of some kind which is commercially regarded as a
standard. For New England and that portion of the country east of the
Allegheny Mountains, good anthracite egg coal, containing not over 10 per
cent, of ash, and semi-bituminous Clearfield (Pa.), Cumberland (Md.), and
Pocahontas (Va.) coals are thus regarded. West of the Allegheny Moun-
tains, Pocahontas (Va.) and New River (W. Va.) semi-bituminous, and
Youghiogheny or Pittsburg bituminous coals are recognized as standards.*
For tests made to determine the performance of a boiler with a partic-
ular kind of coal, such as may be specified in a contract for the sale of a
boiler, the coal used should not be higher in ash and in moisture than that
specified, since increase in ash and moisture above a stated amount is apt to
cause a falling off of both capacity and economy in greater proportion than
the proportion of such increase.
V. Establish the correctness of all apparatus used in the test for weighing
and measuring. These are :
1. Scales for weighing coal, ashes, and water.
2. Tanks or water-meters for measuring water. Water-meters, as a rule,
should only be used as a check on other measurements. For accurate work
the water should be weighed or measured in a tank.
8. Thermometers and pyrometers for taking temperatures of air, steam,
feed-water, waste gases, etc.
4. Pressure-gauges, draught-gauges, etc.
VI. See that the boiler is thoroughly heated before the trial to its usual
working temperature. If the boiler is -new and of a form provided with a
brick setting, it should be in regular use at least a week before the trial, so
as to dry and heat the walls. If it has been laid off and become cold, it
should be worked before the trial until the walls are well heated.
VII. The boiler and connections should be proved to be free from leaks
before beginning a test, and all water connections, including blow and
extra feed-pipes, should be disconnected, stopped with blank flanges, or
bied through special openings beyond the valves, except the particular pipe
through which water is to be fed to the boiler during the trial. During the
test the blow-off and feed pipes should remain exposed to view.
If an injector is used, it should receive steam directly through a felted
pipe from the boiler being tested.t .
If the water is metered after it passes the injector, its temperature should
be taken at the point where it leaves the injector. If the quantity is deter-
mined before it goes to the injector, the temperature should be determined
on the suction side of the injector, and if no change of temperature occurs
other than that clue to the injector, the temperature thus determined is
properly that of the feed- water. When the temperature changes between
the injector and the boiler, as by the use of a heater or by radiation, the
temperature at which the water enters and leaves the injector and that at
which it enters the boiler should all be taken. In that case the weight to be
used is that of the water leaving the injector, computed from the heat units
if not directly measured; and the temperature, that of the water entering
the boiler.
Let w — weight of water entering the injector;
x = " " steam " " " ;
hl = heat-units per pound of water entering injector;
7ia = ' " steam " " ;
Tz-3 = " " " " " water leaving "
* These coals are selected because they are about the only coals which
possess the essentials of excellence of quality, adaptability to various
kinds of furnaces, grates, boilers, and methods of firing, and wide distribu-
tion and general accessibility in the markets.
tin feeding a boiler undergoing test with an injector taking steam from
another boiler, or from the main steam-pipe from several boilers, the evap-
orative results may be modified by a difference in the quality of the steam
from such source compared with that supplied by the boiler being tested,
and in some cases the connection to the injector may act as a drip for the
main steam-pipe. If it is known that the steam from the main pipe is of
the same pressure and quality as that furnished by the boiler undergoing
the test, the steam may be taken from such main pipe.
692 THE STEAM-BOILER.
Then w-\-x — weight of water leaving injector,
7u — hi
x = w^ r1.
/ia — /ia
See that the steam-main is so arranged that water of condensation cannot
run back into the boiler.
VIII. Duration of the Test.— For tests made to ascertain either the max-
imum economy or the maximum capacity of a boiler, irrespective of the
particular class of service for which it is regularly used, the duration should
be at least ten hours of continuous running. If the rate of combustion ex-
ceeds 25 pounds of coal per square foot of grate-surface per hour, it may be
stopped when a total of 250 pounds of coal has been burned per square foot
of grate.
IX. Starting and Stopping a Test.— The conditions of the boiler and fur-
nace in all respects should be, as nearly as possible, the same at the end as
at the beginning of the test. The steam-pressure should be the same ; the
water-level the same ; the fire upon the grates should be the same in quan-
tity and condition ; and the walls, flues, etc., should be of the same tempera-
ture. Two methods of obtaining the desired equality of conditions of the
fire may be used, viz., those which were called in the Code of 1885 " the
Standard method " and "the alternate method," the latter being employed .
where it is inconvenient to make use of the standard method.*
X. Standard Method of Starting and Stopping a Test.— Steam being
raised to the working pressure, remove rapidly all the fire from the grate,
close the damper, clean the ash-pit, and as quickly as possible start a new
fire with weighed wood and coal, noting the time and the water-level t while
the water is in a quiescent state, just before lighting the fire.
At the end of the test remove the whole fire, which has been burned low,
clean the grates and ash-pit, and note the water-level when the water is in
a quiescent state, and record the time of hauling the fire. The water-level
should be as nearly as possible the same as at the beginning of the test. If
it is not the same, a correction should be made by computation, and not by
operating the pump after the test is completed.
XI. Alternate Method of Starting and Stopping a Test. — The boiler being
thoroughly heated by a preliminary run, the fires are to be burned low and
well cleaned. Note the amount of coal left on the grate as nearly as it can
be estimated; note the pressure of steam and the water-level. Note the
time, and record it as the starting-time. 'Fresh coal which has been weighed
should now be fired. The ash-pits should be thoroughly cleaned at once
after starting. Before the end of the test the fires should be burned low,
just as before the start, and the fires cleaned in such a manner as to leave a
bed of coal on the grates of the same depth, and in the same condition, as
at the start. When this stage is reached, note the time and record it as the
stopping-time. The water-level and steam-pressures should previously bo
brought as nearly as possible to the same point as at the start. If the water-
level is not the same as at the start, a correction should be made by com-
putation, and not by operating the pump after the test is completed.
XII. Uniformity of Conditions.— In all trials made to ascertain maximum
economy or capacity the conditions should be maintained uniformly con-
stant. Arrangements should be made to dispose of the steam so that the
rate of evaporation may be kept the same from beginning to end.
XIII. Keeping the Records. — Take note of every event connected with the
progress of the trial, however unimportant it may appeal-. Record the
time of every occurrence and the time of taking every weight and every
observation.
The coal should be weighed and delivered to the fireman in equal propor-
tions, each sufficient for not more than one hour's run, and a fresh portion
*The Committee concludes that it is best to retain the designations
" standard " and "alternate," since they have become widely known and
established in the minds of engineers and in the reprints in the Code of
1885. Many engineers prefer the " alternate " to the "standard " method
on account of its being less liable to error due to cooling of the boiler at the
beginning and end of a test.
tThe gauge-glass should not be blown out within an hour before the
water-level is taken at the beginning and end of a test, otherwise an error
in the reading of the water-level may be caused by a change in the tempera-
ture and density to the water in the pipe leading from the bottom of the
glass into the boiler.
RULES FOE CONDUCTING BOILER-TESTS. 693
should not be delivered until the previous one has all been fired. The time
required to consume each portion should be noted, the time being: recorded
at the instant of firing the last of each portion. It is desirable that at the
same time the amount of water fed into the boiler should be accurately
noted and recorded, including the height of the water in the boiler, and the
average pressure of steam and temperature of feed during the time. By
thus recording the amount of water evaporated by successive portions of
coal, the test may be divided into several periods if desired, and the degree
of uniformity of combustion, evaporation, and economy analyzed for each
period. In addition to these records of the coal and the feed-water, half-
hourly observations should be made of the temperature of the feed-water,
of the flue-gases, of the external air in the boiler-room, of the temperature
of the furnace when a furnace-pyrometer is used, also of the pressure of
steam, and of the readings of the instruments for determining the moisture
in the steam. A log should be kept on properly prepared blanks containing
columns for record of the various observations.
XIV. Quality of Steam.— The percentage of moisture in the steam should
be determined by the use of either a throttling or a separating steam-calo-
rimeter. The sampling-nozzle should be placed in the vertical steam-pipe
rising from the boiler. It should be made of £-inch pipe, and should extend
across the diameter of the steam-pipe to within half an inch of the opposite
side, being closed at the end and perforated with not less than twenty 1-inch
holes equally distributed along and around its cylindrical surface, but none
of these holes should be nearer than £ inch to the inner side of the steam-
pipe. The calorimeter and the pipe leading to it should be well covered
with felting. Whenever the indications of the throttling or separating
calorimeter show that the percentage of moisture is irregular, or occasion-
ally in excess of three per cent., the results should be checked by a steam-
separator placed in the steam-pipe as close to the boiler as convenient, with
a calorimeter in the steam-pipe just beyond the outlet from the separator.
The drip from the separator should be caught and weighed, and the per-
centage of moisture computed therefrom added to that shown by the calo-
rimeter.
Superheating should be determined by means of a thermometer placed in
a mercury-well inserted in the steam-pipe. The degree of superheating
should be taken as the difference between the reading of the thermometer
for superheated steam and the readings of the same thermometer for satu-
rated steam at the same pressure as determined i,by a special experiment,
and not by reference to steam-tables.
XV. Sampling the Coal and Determining its Moisture. — As each barrow-
load or fresh portion of coal is taken from the coal-pile, a represen-
tative shovelful is selected from it and placed in a barrel or box in a cool
place and kept until the end of the trial. The samples are then mixed and
broken into pieces not exceeding one inch in diameter, and reduced by the
process of repeated quartering and crushing until a final sample weighing
about five pounds is obtained, and the size of the larger pieces is such that
they will pass through a sieve with 4-inch meshes. From this sample two
one-quart, air-tight glass preserving-jars, or other air-tight vessels which
will prevent the escape of moisture from the sample, are to be promptly
filled, and these samples are to be kept f or , subsequent determinations of
moisture and of heating value and for chemical analyses. During the pro-
cess of quartering, when the sample has been reduced to about 100 pounds.
a quarter to a half of it may be taken for an approximate determination of
moisture. This may be made by placing it in a shallow iron pan, not over
three inches deep, carefully weighing it, and setting the pan in the hottest
place that can be found on the brickwork of the boiler-setting or flues,
keeping it there for at least 12 hours, and then weighing it. The determina-
tion of moisture thus made is believed to be approximately accurate for
anthracite and semi-bituminous coals, and also for Pittsburg or Youghio-
gheny coal ; but it cannot be relied upon for coals mined west of Pittsburg,
or for other coals containing inherent moisture. For these latter coals it is
important that a more accurate method be adopted. The method recom-
mended by the Committee for all accurate tests, whatever the character of
the coal, is described as follows :
Take one of the samples contained in the glass jars, and subject it to a
thorough air-drying, by spreading it in a thin layer and exposing it for
several hours to the atmosphere of a warm room, weighing it before and
after, thereby determining the quantity of surface moisture it contains.
694 THE STEAM-BOILER.
Then crush the whole of it by running it through an ordinary coffee-mifl
adjusted so as to produce somewhat coarse grains (less than ^ inch), thor-
oughly mix the crushed sample, select from it a portion of from 10 to 50
grams, weigh it in a balance which will easily show a variation as small as
1 part in 1000, and dry it in an air- or sand-bath at a temperature between
240 and 280 degrees Fahr. for one hour. Weigh it and record the loss, then
heat and weigh it again repeatedly, at intervals of an hour or less, until the
minimum weight has been reached and the weight begins to increase by
oxidation of a portion of the coal. The difference between the original and
the minimum weight is taken as the moisture in the air-dried coal. This
moisture test should preferably be ma.de on duplicate samples, and the
results should agree withim 0.3 to 0.4 of one per cent., the mean of the two
determinations being taken as the correct result. The sum of the percent-
age of moisture thus found and the percentage of surface moisture previ-
ously determined is the total moisture.
XVI. Treatment of Ashes and Refuse.— The ashes and refuse are to be
weighed in a dry state. If it is found desirable to show the principal char-
acteristics of the ash, a sample should be subjected to a proximate analysis
and the actual amount of incombustible material determined. For elabo-
rate trials a complete analysis of the ash and refuse should be made.
XVII. Calorific Tests and Analysis of Coal.— The quality of the fuel
should be determined either by heat test or by analysis, or by both.
The rational method of determining the total heat of combustion is to
burn the sample of coal in an atmosphere of oxygen gas, the coal to be
sampled as directed in Article XV of this code.
The chemical analysis of the coal should be made only by an expert
chemist. The total heat of combustion computed from the results of the
ultimate analysis may be obtained by the use of Dulong's formula (with
constants modified by recent determinations), viz.,
14,600 C -f 62,000 1 H - -—- \ -f 4COO S,
in which C, H, O, and S refer to the proportions of carbon, hydrogen, oxy-
gen, and sulphur respectively, as determined by the ultimate analysis.*
It is desirable that a proximate analysis should be made, thereby deter-
mining the relative proportions of volatile matter and fixed carbon. These
proportions furnish an indication of the leading characteristics of the fuel,
and serve to fix the class to which it belongs.
XVIII. Analysis of Flue-gases. — The analysis of the flue-gases is an
especially valuable method of determining the relative value of different
methods of firing or of different kinds of furnaces. In making these
analyses great care should be taken to procure average samples, since the
composition is apt vo vary at different points of the flue. The composition
is also apt to vary from minute to minute, and for this reason the drawings
of gas should last a considerable period of time. Where complete deter-
minations are desired, the analyses should be intrusted to an expert
chemist. For approximate determinations the Orsat or the Hem pel appa-
ratus may be used by the engineer.
For the continuous indication of the amount of carbonic acid present in
the flue-gases an instrument may be employed which shows the weight of
CO.j in the sample of gas passing through it.
XIX. Smoke Observations.— It is desirable to have a uniform system of
determining and recording the quantity of smoke produced where bitumin-
ous coal is used. The system commonly employed is to express the degree
of smokiness by means of percentages dependent upon the judgment of the
observer. The actual measurement of a sample of soot and smoke by some
form of meter is to be preferred.
XX. Miscellaneous. — In tests for purposes of scientific research, in which
the determination of all the variables entering into the test is desired,
certain observations should be made which are in general unnecessary for
ordinary tests. As these determinations are rarely undertaken, it is not
deemed advisable to give directions for making them.
XXI. Calculations of Efficiency. — Two methods of defining and calculat-
ing the efficiency of a boiler are recommended. They are:
* Favre and Silbermann give 14,544 B.T.U. per pound carbon; Berthelot,
14,647 B.T.U. Favre and Silbermann give 62,032 B.T.U. per pound hydrogen ;
Thomsen, 61,816 B.T.U.
RULES FOR CONDUCTING BOILER-TESTS/
695
Heat absorbed per Ib. combustible
1. Efficiency of the boiler = -7=- — .
Calorific value of 1 Ib. combustible
2. Efficiency of the boiler and grate =
Heat absorbed per Ib. coal
Calorific value of 1 Ib. coal
The first of these is sometimes called the efficiency based on combustible,
and the second the efficiency based on coal. The first is recommended as a
standard of comparison for all tests, and this is the one which is under-
stood to be referred to when the word "efficiency " alone is used without
qualification. The second, however, should be included in a report of a
test, together with the first, whenever the object of the test is to determine
the efficiency of the boiler and furnace together with the grate (or mechan-
ical stoker), or to compare different furnaces, grates, fuels, or methods of
firing.
The heat absorbed per pound of combustible (or per pound coal) is to be
calculated by multiplying the equivalent evaporation from and at 212 degrees
per pound combustible (or coal) by 965.7.
XXII. The Heat Balance.— An approximate "heat balance," may be in.
eluded in the report of a test when analyses of the fuel and of the chimney,
gases have been made. It should be reported in the following form:
HEAT BALANCE, OR DISTRIBUTION OF THE HEATING VALUE OF THE COM-
BUSTIBLE.
Total Heat Value of 1 Ib. of Combustible. B. T. U.
B. T. U.
Per
Cent.
1. Heat absorbed by the boiler = evaporation from and at
212 degrees per pound of combustible X 965.7
2. Loss due to moisture in coal = per cent of moisture re-
ferred to combustible -*- 100 X [(212 - t) + 966 -f
0.48(r-212)](£ = temperature of air in the boiler-
3. Loss due to moisture formed by the burning of hydro-
gen = per cent of hydrogen to combustible -4- 100 X 9
X [(212 — t) 4- 966 -\ 048(7"— 212)]
4.* Loss due to heat carried away in the dry chimney-gases
= weight of gas per pound of combustible X 0.24 X
(T t)
5.t Loss due to incomplete combustion of carbon
CO , percent. Gin combustible vx ,A1RA
C02 + C0 * 100
6. Loss due to unconsumed hydrogen and hydrocarbons,
to heating the moisture in the air, to radiation, and
unaccounted for. (Some of these losses may be sep-
arately itemized if data are obtained from which
Totals
100.00
* The weight of gas per pound of carbon burned may be calculated from
the gas analyses as follows:
Dry gas per pound carbon = - C°* +8^ + 7®9 4 — \ in which CO2, CO,
O, and N are the percentages by volume of the several gases. As the samp-
ling and analyses of the gases in the present state of the art are liable to
considerable errors, the result of this calculation is usually only an approxi-
mate one. The heat balance itself is also only approximate for this reason,
as well as for the fact that it is not possible to determine accurately the per-
centage of unburned hydrogen or hydrocarbons in the flue-gases.
The weight of dry gas per pound of combustible is found by multiplying
the dry gas per pound of carbon by the percentage of carbon in the combus-
tible, and dividing by 100.
t CO., and CO are respectively the percentage by volume of carbonic acid
and carbonic oxide in the flue-gases. The quantity 10,150 = number of heat-
units generated by burning to carbonic acid one pound of carbon contained
in carbonic oxide.
6950
THE STEAM-BOILER.
XXIII. Report of the Trial.— The data and results should be reported in
the manner given in either one of the two following tables [only the '• Shore
Form " of table is given here], omitting lines where the tests have not been
made as elaborately as provided for in such tables. Additional lines may be
added for data relating to the specific object of the test. The Short Form of
Report, Table No. 2, is recommended for commercial tests and as a conven-
ient form of abridging the longer form for publication when saving of space
is desirable. For elaborate trials it is recommended that the full log of the
trial be shown graphically, by means of a chart.
TABLE NO. 2.
DATA AND RESULTS OF EVAPORATIVE TEST,
Arranged in accordance with the Short Form advised by the Boiler Test
Committee of the American Society of Mechanical Engineers.
Code of 1899.
Made by on boiler, at to
determine . .
Kind of fuel
Method of starting and stopping the test ("stand-
ard " or " alternate," Arts. X and XI, Code)
Grate surface • • ....
sq ft
Water-heating surface
u
TOTAL QUANTITIES.
1 Date of trial
2 Duration of trial
hours
3 Weight of coal as fired *
Ibs.
4 Percentage of moisture in coal t
per cent.
5 Total weight of dry coal consumed. ...
Ibs
7 Percentage of ash and refuse in dry coal. ...
per cent
8 Total weight of water f^d to the boiler %
Ibs.
9. Water actually evaporated, corrected for moist-
9<z Factor of evaporation §....
10. Equivalent water evaporated into dry steam
from and at 212 degrees.] (Item 9 X Item 9a.)
HOURLY QUANTITIES.
11 Drv coal consumed per hour
»
12.' Dry coal per square foot of grate surface per
M
13. Water evaporated per hour corrected for qual-
tt
14. Equivalent evaporation per hour from and at
212 degrees j|
<4
15. Equivalent evaporation per hour from and at 212
degrees per square foot of water-heating sur-
face ||
«
* Including equivalent of wood used in lighting the fire, not including un°
burnt coal withdrawn from furnace at times of cleaning and at end of test.
One pound of wood is taken to be equal to 0.4 pound of coal, or, in case
greater accuracy is desired, as having a heat value equivalent to the evap-
oration of 6 pounds of water from and at 212 degrees per pound.
(6 X 965.7 = 5794 B. T.U.) The term "as fired " means in its actual con-
dition, including moisture.
•t This is the total moisture in the coal as found by drying it artificially, as
described in Art. XV of Code.
t Corrected for inequality of water-level and of steam-pressure at be-
ginning and end of test.
§ Factor of evaporation = ~ , in which H and h are respectively the
total heat in steam of the average observed pressure, and in water of the
average observed temperature of the feed.
1 The symbol "U. E.," meaning •' units of evaporation," may be con«
BULES FOR CONDUCTING BOILER-TESTS.
6956
AVERAGE PRESSURES, TEMPERATURES, ETC.
16 Steam pressure by gauge
Ibs. per sq. in.
deer
18. Temperature of escaping gases from boiler. . . .
19 Force of draft between damper and boiler
ins of water
20. Percentage of moisture in steam, or number of
per cent. or deg.
HORSE-POWER.
21. Horse- power developed. (Item 14 -*- 34J4-)^
*•*'* Builders' rated horse-power
H.P.
23. Percentage of builders' rated horse-power de-
per cent.
ECONOMIC RESULTS.
24. Water apparently evaporated under actual con-
ditions per pound of coal as fired. (Item
8 • Item 3 )
Ibs,
25. Equivalent evaporation from and at 212 degrees
per pound of coal as fired.| (Item 10-s-Item 3.)
26. Equivalent evaporation from and at 212 degrees
per pound of dry coal || (Item 10 -*- Item 5.). .
27. Equivalent evaporation from and at 212 degrees
per pound of combustible. [Item 10 -5- (Item
5 — Item 6) ]
it
(If Items 25, 26, and 27 are not corrected for
quality o£ steam, the fact should be stated.)
EFFICIENCY.
28. Calorific value of the dry coal per pound
29. Calorific value of the combustible per pound.. . .
30. Efficiency of boiler (based on combustible)**...
31. Efficiency of boiler, including grate (based on
dry coal)
B. T. U.
per cent.
COST OF EVAPORATION.
32. Cost of coal per ton of Ibs. delivered in
§
33. Cost of coal required for evaporating 1000 pounds
of water from and at 212 degrees. ...
$
veniently substituted for the expression ''Equivalent water evaporated into
dry steam from and at 212 degrees," its definition being given in a foot-note.
i Held to be the equivalent of 30 Ibs. of water evaporated from 100 degrees
Fahr. into dry steam at 70 Ibs. gauge-pressure.
** In all cases where the word "combustible " is used, it means the coal
without moisture and ash, but including all other constituents. It is the
same as what is called in Europe " coal-dry and free from ash.11
Factors of Evaporation.— The table on the following pages was
originally published by the author in Trans. A. S. M. E., vol. vi., 1884, under
the title, Tables for Facilitating Calculations of Boiler-tests. The table
gives the factors for every 3° of temperature of feed-water from 32° to 212U
F.. and for every two pounds pressure of steam within the limits of ordinary
working steam-pressures.
The difference in the factor corresponding to a difference of 3° tempera,
ture of feed is always either .0031 or .0032. For interpolation to find a factor
for a feed-water temperature between 32° and 212°, not given in the table,
take the factor for the nearest temperature and add or subtract, as the case
may be, .0010 if the difference is .0031, and .OOJ1 if the difference is .0032. As
in nearly all cases a factor of evaporation to three decimal places is accu-
rate enough, any error which may be made in the fourth decimal place by
interpolation is of no practical importance.
The tables used in calculating these factors of evaporation are those given
in Charles T. Porter's Treatise on the Richards' Steam-engine Indicator.
The formula is Factor = "" , in which H is the total heat of steam at the
observed pressure, and h the total heat of feed.- water of the observed
temperature.
696
THE STEAM-BOILER
Lbs.
Gauge-pressures.. ..0 +
Absolute pressures 15
10 +
25
20 +
35
30 +
15
40 +
55
45 +
60
50 +
65
52 +
67
54 +
69
56 +
71
Feed-water
Temperature
FACTORS OP EVAPORATION.
212° F.
1.0003 1.0088
1.0149
1.0197
1.0237 1.0254 1.0271 1.027711 .0283il. 0290
209
35 '1.0120
80
1.0228
68 861.03021.03091.0315
1.0321
206
66
51
1.0212
60
991.0317
34
40
4(
52
203
98
83
43
91
1.0331
49
65
72
78
84
200
1.0129
1.0214
75
1.0323
62
80
97
1.0403
1.0409
1.0415
197
60
46
1.0306
54
94
1.0412
1.0428
34
41
47
194
92
77
38
85
1.0425
4c
60
66
7'
78
191
1.0223
1.0308
69
1.0417
57
74
91
97
1.0503
1.0510
188
55
40
1.0400
48
88
1.0506
1.05221.0528
35
41
185
86
7
32
80
1.0519
37
54
60
66
72
182
1.0317
1.0403
63
1.0511
51
68
85
91
98
1.0604
179
49
34
95
42
82
1.0600
1.0616
1.0623
L0629
35
176
80
65
1.0526
74
1.0613
31
48
54
60
66
173
1.0411
97
57
1.0605
45
63
79
85
92
98
170
43
1.0528
89
36
76
94
1.0710
1.0717
1.0723
1.0729
167
rli
59
1.0620
68
1.0707
1.0725
42
48
54
60
164
1.0505
91
51
99
39
56
73
80
86
92
161
37
1.0622
82
1.0730
70
88
1.0804
1.0811
1.0817
1.0823
158
68
53
1.0714
62
1.0801
1.0819
36
42
48
54
155
99
84
45
93
33
50
67
73
80
86
152
1.0631
1.0716
76
1.0824
64
82
98
1.0905
1.0911
1.0917
149
62
47
1.0808
55
95
1.0913
1.0930
36
42
48
146
93
78
39
87
1.0926
44
61
67
7i
79
143
1.0724
1.0810
7C
1.0918
58
75
92
98
1.1005
1.1011
140
56
41
1.0901
49
89
1.1007
1.1023
1.1030
36
' 42
137
87
33
80
1.1020
38
55
61
67
73
134
1.0818
1.0903
64
1.1012
51
69
86
92
98
1.1104
131
49
34
95
43
83
1.1100
1.1117
1.1123
1.1130
36
.128
81
66
1.1026
74
1.1114
32
48
55
61
67
125
1.0912
97
57
1.1105
45
63
79
86
92
90
122
43
1.1028
89
36
76
94
1.1211
1.1217
1.1223
1.1229
119
74
59
1.1120
68
1.1207
1.1225
42
48
54
60
116
1.1005
90
51
99
39
56
73
79
86
92
113
36
1.1122
82
1.1230
70
88
1.1304
1.1310
1.1317
1.1328
110
68
53
1.1213
61
1.1301
1.1319
35
42
48
54
107
99
84
45
92
32
50
66
73
79
85
104
1 1130
1.1215
76
1.1323
63
81
98
1.1404
1.1410
1.1416
101
61
46
1.1307
55
94
1.1412
1.1429
35
41
47
98
92
rf
38
86
1.1426
43
60
66
7c
79
95
1.1223
1.1309
69
1.1417
57
75
91
97
1.1504
1.1510
92
55
40
1.1400
48
88
1.1506
1.1522
1.1529
35
41
89
86
71
31
79
1.1519
37
53
60
66
72
86
1.1317
1.1402
63
1.1510
50
68
84
91
97
1.1603
83
48
33
94
41
81
99
1.1616
1.1G22
1.1628
34
80
79
64
1.1525
73
1.1612
1.1630
47
53
59
65
77
1.1410
95
56
1.1604
44
61
78
84
90
96
74
41
1.152G
87
35
75
92
1.1709
1.1715
1.1722
1.1728
71
72
58
1.1618
66
1.1706
1.1723
40
46
53
59
68
1.1504
89
49
97
37
55
71
78
84
90
65
35
1.1620
80
1.1728
68
86
1.1802
1.1809
1.1815
1.1821
62
66
51
1.1711
59
99
1.1817
33
40
46
52
59
97
82
43
90
1.1830
48
64
71
77
83
56
1.1628
1.1713
74
1.1821
61
79
96
1.1902
1.1908
1 1914
53
59
44
1.1805
52
92
1.1910
1,1927
33
39
45
50
90
75
36
84
1.1923
41
58
64
70
76
47
1.1721
1.1806
67
1.1915
54
72
89
95
1.2001
1.2007
44
52
37
98
46
86
1.2003
1.20201.2026
32
39
41
83
68
1.1929
77
1.2017
34
51
57
64
70
38
1.1814
1 .1900
60
1.2008
48
65
82
88
95
.2101
85
45
31
91
39
79
96
1.2113 1.2119
1.2126
32
32
70
62
1.2022
70
1 2110
1.2128
44| 51
57
68
FACTORS OF EVAPORATION.
697
Bauge-press., Ibs. 58 +
Absolute Pressures.. 73.
S + | fl +
64 +
79
66 +
81
68 -f- 1 70+1 72 -f- j 74+1 76 -f-
83 1 85 1 87 1 89^1 91^
Feed-water
Temp.
FACTORS OF EVAPORATION.
212° F0
1.0295
1.0301
1.0307
1.0312
1.0318
1.0323
1.0329
1.0334
1.0339
1.0344
209
1.0327
33
38
44
49
55
60
65
70
75
206
58
64
70
75
81
86
91
97
1.0402
1.0407
203
90
96
1.0401
1.0407
1.0412
1.0418
1.0423
1.0428
33
38
200
1.0421
1.0427
33
38
44
49
54
59
65
69
197
53
58
64
70
75
80
86
91
96
1.0501
194
84
90
96
1.0501
1.0507
1,0512
1.0517
1.0522
1.0527
32
191
1.0515
1.0521
1.0527
33
38
43
49
54
59
64
188
47
53
58
64
69
75
80
85
90
95
185
78
84
90
95
1.0601
1.0606
1.0611
1.0616
1.0622
1.0626
182
1.0610
1.0615
1.0621
1.0627
32
37
43
48
53
58
179
41
47
521
58
63
69
74
79
84
89
176
72
78
84
89
95
1.0700
1.0705
1.0711
1.0716
1.0721
173
1.0704
1.0709
1.0715
1.0721
1.0726
32
37
42
47
52
170
35
41
46
52
57
63
68
73
78
83
167
66
72
78
83
89
94
99
1.08051.0810
1.0815
164
98
1.0803
1.0809
1.0815
1.0820
1.0825
1.0831
36 41
46
161
1.0829
35
40
46
51
57
62
67 72
77
158
60
66
72
77
83
88
93
981.0904
1.0908
155
92
97
1.0903
1.0909
1.0914
1.0919
1.0925
1.0930
35
40
152
1.0923
1.0929
34
40
45
51
56
61
66
71
149
54
60
66
71
77
82
87
92
97
1.1002
140
85
91
97
1.1002
1.1008
1.1013
1.1018
1.10241.1029
34
143
1.1017
1.1022
1.1028
34
39
44
50
55[ 60
65
140
48
54
59
65
70
76
81
86 91
96
137
79
85
91
96
1.1102
1.1107
1.1112
1.11171.1122
1.1127
134
1.1110
1.1116
1.1122
1.1127
33
38
43
49
54
59
131
42
47
53
59
64
69
75
80
85
90
128
73
79
84
90
95
1.1201
1.1206
1.1211
1.1216
1.1221
125
1.1204
1.1210
1.1215
1.1221
1.1226
32
37
42
47
52
122
35
41
47
52
58
63
68
73
78
83
119
66
72
78
83
89
94
99
1.1305
1.1310
1.1315
116
98
1.1303
1.1309
1.1315
1.1320
1.1325
1.1331
36
41
46
113
1.1329
34
40
46
51
57
62
67
72
77
110
60
66
71
77
82
88
93
98
1.1403
1.1408
107
91
97
1.1403
1.1408
1.1414
1.1419
1.1424
1.1429
34
39
104
1.1422
1.1428
34
39
45
50
55
60
65
70
101
53
59
65
70
76
81
86
92
97
1.1502
98
85
90
96
1.1502
1.1507
1.1512
1.1518
1.1523
1.1528
33
95
1.1516
1.1521
1.1527
33
38
43
49
54
59
64
92
47
53
58
64
69
75
80
85
90
95
89
78
84
89
95
1.1600
1.1606
1.1611
1.1616
1.1621
1.1626
86
1.1609
1.1615
1.1621
1.1626
32
37
42
47
52
57
83
40
46
52
57
63
68
73
78
83
88
80
71
77
83
88
94
99
1.1704
1.1710
1.1715
1.1720
77
1,1702
1 1708
1.1714
1.1719
1.1725
1.1730
35
41
46
51
74
34
39
45
51
56
61
67
72
77
82
71
65
70
76
82
87
92
98
1.1803
1.1808
1.1813
68
96
1 1802
1.1807
1.1813
1.1818
1.1824
1.1829
34
39
44
65
1.1827
33
38
44
49
55
60
65
70
75
62
58
64
69
75
80
86
91
96
1.1901
1.1906
59
89
95
1.1901
1.1906
1.1912
1.1917
1.1922
1.1927
32
37
56
1.1920
1.1926
32
37
43
48
53
58
63
68
53
51
57
63
68
74
79
84
89
94
99
50
82
88
94
99
1.2005
1.2010
1.2015
1.2021
1.2026
1.2031
47
1.2013
1.2019
1.2025
1.2030
36
41
46
52
57
62
44
44
50
56
61
67
72
78
83
88
93
41
76
81
87
93
98
1.2103
1.2109
1.2114
1.2119
1.2124
38
1.2107
1.2112
1.2118
1.2124
1.2129
34
40
45
50
55
35
38
43
49
55
60
65
71
76
81
86
32
69
75
80
86
91
97
1.2202
1.2207
1.2212
1.2217
698
THE STEAM-BOILER.
Gauge-pressures
lbs.,78 +
Absolute
Pressures, 93
80 +
95
82 +
97
84 +
99
86 +
101
88 +
103
90 +
105
92 +
107
94 +
109
96 +
111
98 h
113
FeTemplter| FACTORS OF EVAPORATION.
21-2
1.0349
1.0353
1.0358
1.0363
1.0367
1.0372
1.0376
1 .0381
1.0385
1.038911.0393
209
80
85
90
94
99
1.0403
1.0408
1.0412
1.0416
1. 0421 1 1.0425
206
1.0411
1.0416
1.0421
1.0426
1.0430
35
39
43
48
52
56
203
43
48
52
57
62
66
71
75
79
83
88
200
74
79
84
89
93
98
1.0502
1.0506
1.0511
1.0515
1.0519
197
1.0506
1.0511
1.0515
1.0520
1.0525
1.0539
33
38
42
46
50
194
37
42
47
51
56
60
65
69
73
78
82
191
69
73
78
83
87
92
96
1.0601
1.0605
1.0609
1.0613
188
1.0600
1.0605
1.0610
1.0614
1 .0619
1.0623
1.0628
32
36
40
45
185
31
36
41
46
50
55
59
63
68
72
76
182
63
68
72
77
81
86
90
95
99
1.0703
1.0707
179
94
99
1.0704
1.0708
1.0713
1.0717
1.0722
1.0726
1.0730
35
39
176
1.0725
1.0730
35
40
44
49
53
57
62
66
70
173
57
62
66
71
75
80
84
89
93
97
1.0801
170
88
93
98
1.C802
1.0807
1.0811
1.0816
1.0820
1.0824
1.0829
33
167
1.0819
1.0824
1.0829
34
38
43
47
51
56
60
64
164
51
56
60
65
69
74
78
83
87
91
95
161
82
87
92
96
1.0901
1.0905
1.0910
1.0914
1.0918
1.0923
1.0927
158
1.0913
1.0918
1.0923
1.0927
32
37
41
45
50
54
58
155
45
49
54
59
63
68
72
77
81
85
89
152
76
81
85
90
95
99
1.1004
1.1008
1.1012
1.1016
1.1021
149
1.1007
1.1012
1.1017
1.1021
1.1026
1.1030
35
39
43
48
52
146
88
43
48
53
57
62
66
70
75
79
83
143
70
74
79
84
88
93
97
1.1102
1.1106
1.1110
1.1114
140
1.1101
1.1106
1.1110
1.1115
1.1120
1.1124
1.1129
33
37
41
46
137
32
37
42
46
51
55
60
64
68
73
77
134
63
68
73
78
82
87
91
95
1.1200
1.1204
1.1208
J31
95
99
1.1204
1.1209
1.1213
1.1218
1.1222
1.1227
31
35
39
128
1.1226
1.1231
35
40
45
49
53
58
62
66
71
125
122
88
62
93
67
98
71
1.1302
76
1.1307
80
1.1311
85
1.1316
89
1.1320
93
1.1325
98
1.1329
1.1302
33
119
1.1320
1.1324
1.1329
34
38
43
47
51
56
60
64
116
51
55
60
65
69
74
78
83
87
91
95
113
82
87
91
96
1.1401
1.1405
1.1409
1.1414
1.1418
1.1422
1.1426
110
1.1418
1.1418
1.1422
1.1427
32
36
41
45
49
53
58
107
44
49
54
58
63
67
72
76
80
85
89
104
75
80
85
89
94
99
1.1503
1.1507
1.1512
1.1516
1.1520
101
1.1506
1.1511
1.1516
1.1521
1.1525
1.1530
34
38
43
47
51
98
38
42
47
52
56
61
65
70
74
78
82
95
69
74
78
83
87
92
96
1.1601
1.1605
1.1609
1.1613
92
1.1600
1.1605
1.1609
1.1614
1.1619
1.1623
1.1628
32
36
40
45
89
31
36
41
45
50
54
59
63
67
72
76
86
62
67
72
76
81
85
90
94
98
1.1703
1.1707
83
93
98
1.1703
1.1707
1.1712
1.1717
1.1721
1.1725
1.1730
34
38
80
1.1724
1.17'29
34
39
43
48
52
56
61
65
69
77
56
60
65
70
74
79
83
88
92
96
1.1800
74
87
91
96
1.1801
1.1805
1.1810
1.1814
1.1819
1.1823
1.1827
31
71
1.18181.1823
1.1827
32
36
41
45
50
54
58
62
68
49 54
58
63
68
72
81
85
89
94
65
80
85
89
94
99| 1.1903
1.1908
1.1912
1.1916
1 1920
1.1925
62
1.1911
1.1916
1.19*1
1.1925
1.1930 34
39
43
47
52
56
59
42
47
52
56
61
65
70
74
78
83
87
56
73
?8
83
87
92
96
1.2001
1.20051.2010
1.2014
1.2018
53
1.2004
1 2009
1.2014
1.2018
1.2023
1.2028
32
36
41
45
49
50
35
40
45
50
54
59
63
67
72
76
80
47
66
71
76
81
85
90
94
98
1.2103
1.2107
1.2111
44
98
1.2102
1.2107
1.2112
1.2116
1.2121
1.2125
1.2130
34
38
42
41
1.2129
33
38
43
47
52
56
61
65
69
73
38
60
64
69
74
78
83
87
92
96
1.2200
1.2204
85
91
96
1.2200
1.2205
1.2209
1.2214
1.2218
1.2223
1.2227
31
35
32
1.2222
1.2227
31
36
41
45
49
54
58
62
67
FACTORS OF EVAPORATION".
699
Gauge-pressures
Ibs. 100 -h
Absolute Press.
Ibs. 115.
105 +
120
110 +
125
115 +
130
120 +
135
125 +
140
130 +
145
135 +
150
140 +
155
145 +
160
150 +
165
Fe-remp!er FACTORS OF EVAPORATION.
212°
1.0397
1.0407
1.0417
1.0427
1.0436
1.0445
1.0453
1.0462 1.0470
1.04781.0486
209
1.0429
39
49
58
67
76
85
93
1.0501
1.0509
1.0517
206
60
70
80
89
99
1.0508
1.0516
1.0525
33
41
48
203
92
1.0502
1.0511
1.0521
1.0530
39
48
56
64
72
'80
200
1.0523
33
43
52
62
70
79
87
96
1.0604
1.0611
197
55
65
74
84
93
1 .0602
1.0610
1.0619
1.0627
35
43
194
86
96
1.0606
1.0615
1.0624
33
42
50
58
66
74
191
1.0617
1.0627
37
47
56
65
73
82
90
98
1.0706
188
49
59
69
78
87
96
1.0705
1.0713
1.0721
1.0729
37
185
80
90
1.0700
1.0709
1.0719
1.0727
36
44
53
61
68
182
1.0712
1.0722
31
41
50
59
67
76
84
92
1.0800
179
43
53
63
72
81
90
99
1.0807
1.0815
1.0823
31
176
74
84
94
1.0803
1.0813
1.0821
1.0830
39
47
55
62
173
1.0806
1.0816
1.0825
35
44
53
61
70
78
86
94
170
37
47
57
66
75
84
93
1.0901
1.0909
1.0917
1.0925
167
68
78
88
97
1.0907
1.0915
1.0924
32
41
49
56
164
1.0900
1.0910
1.0919
1.0929
38
47
55
64
72
80
88
161
31
41
51
60
69
78
87
95
1.1003
1 1011
1.1019
158
62
72
82
91
1.1000
1.1009
1.1018
1.1026
35
43
50
155
03
1.1003
1.1013
1.1023
32
41
49
58
66
74
82
152
1.1025
35
44
54
63
72
81
89
97
1.1105
1.1113
149
56
66
76
85
94
1.1103
1.1112
1.1120
1.1128
36
44
146
87
97
1.1107
1.1116
1.1126
34
43
51
60
68
75
143
1.1118
1.1129
38
48
57
66
74
83
91
99
1.1207
140
50
60
70
79
88
97
1.1206
1.1214
1.1222
1.1230
38
137
81
91
1.1201
1.1210
1.1219
1.1228
37
45
53
61
69
134
1.1212
1.1222
32
41
51
59
68
76
85
93
1.1300
131
43
53
63
73
82
91
99
1.1308
1.1316
1.1324
32
128
75
85
94
1.1304
1.1313
1.1322
1.1331
39
47
55
63
125
1.1306
1.1316
1.1326
35
44
53
62
70
78
86
94
122
37
47
57
66
75
84
93
1.1401
1.1409
1.1417
1.1425
119
68
78
88
97
1.1407
1.1415
1.1424
32
41
49
56
116
99
1.1409
1.1419
1.1429
38
47
55
64
72
80
88
113
1.1431
41
50
60
69
78
86
95
1.1503
1.1511
1.1519
110
62
72
82
91
1.1500
1.1509
1.1518
1.1526
34
42
50
107
93
1.1503
1.1513
1.1522
31
40
49
57
65
73
81
104
1.1524
34
44
53
62
71
80
88
97
1.1605
1.1612
101
55
65
75
84
94
1.1602
1.1611
1.1620
1.1628
36
43
98
86
96
1.1606
1.1616
1.1625
34
42
51
59
67
75
95
1 1618
1.1628
37
47
56
65
73
82
90
98
1.1706
92
49
59
68
78
87
96
1.1705
Iol713
1.1721
1.1729
37
89
80
90
1.1700
1.1709
1.1718
1.1727
36
44
52
60
68
86
1.1711
1.1721
31
40
49 58
67
75
83
91
99
83
42
52
62
71
80 89
98
1 . 1806
1.1815
1.1823
1.1830
80
73
83
93
1.1802
1.1812
1.1820
1.1829
37
46
54
61
77
1.1804
1.1814
1.1824
34
43
52
60
69
77
85
93
74
35
45
55
65
74
83
91
1.1900
1.1908
1.1916
1.1924
71
67
77
86
96
1.1905
1.1914
1.1922
31
39
47
55
68
98
1.1908
1.1917
1.1927
36
45
54
62
70
78
86
65
1.1929
39
49
58
67
76
85
93
1.2001
1.2009
1 .2017
ft
60
70
80
89
98
1.2007
1.2016
1.2024
32
40
48
59
91
1.2001
1.2011
1.2020
1.2029
38
47
55
63
71
79
56
1.2022
32
42
51
60
^69
78
86
94
1.2102
1.2110
63
68
63
73
82
91
l.£lOO
1.2109
1.2117
1.2126
34
41
50
84
94
1.2104
1.2113
1.2123
31
40
48
57
65
72
47
1.2115
1.2125
35
44
54
63
71
80
88
96
1.2203
44
46
56
66
76
85
94
1.2202
1.2211
1.2219
1.2227
35
41
77
87
97
1.2207
1.2216
1.2225
33
42
50
58
66
38
1.2208
1.2219
1.2228
38
47
56
64
73
81
89
97
35
40
50
59
69
78
87
95
1.2304
1.2312
1.2320
1.2328
32
71
81
90
1.23001.2309
1.2318
1.2326
35i 43
51
59
700 THE STEAM-BOILER.
STRENGTH OF STEAM-BOILERS. VARIOUS RULES
FOR CONSTRUCTION.
There is a great lack of uniformity in the rules prescribed by differ-
ent writers and by legislation governing the construction of steam-boilers
In the United States, boilers for merchant vessels must be constructed ac-
cording to the rules and regulations prescribed by the Board of Supervising
Inspectors of Steam Vessels; in the U. S. Navy, according to rules of the
Navy Department, and in some cases according to special acts of Congress.
On land, in some places, as in Philadelphia, the construction of boilers is
governed by local laws; but generally there are no laws upon the subject,
and boilers are constructed according to the idea of individual engineers and
boiler-makers. In Europe the. construction is generally regulated by strin-
gent inspection laws. The rules of the U. S. Supervising Inspectors of
Steam- vessels, the British Lloyd's and Board of Trade, the French Bureau
Veritas, and the German Lloyd's are ably reviewed in a paper by Nelson
Foley, M. Inst. Naval Architects, etc., read at the Chicago Engineering Con-
gress, Division of Marine and Naval Engineering. From this paper the fol-
lowing notes are taken, chiefly with reference to the U. S. and British rules',
(Abbreviations.— T. S., for tensile strength; El., elongation; Contr., con-
tract ion of area.)
Hydraulic Tests.— .Board of Trade, Lloyd's, and Bureau Veritas.—
Twice the working pressure.
United States Statutes.— One and a half times the working pressure.
Mr. Foley proposes that the proof pressure should be \y% times the work-
ing pressure -f one atmosphere.
Established Nominal Factors of Safety. —Board of Trade.—
4.5 for a boiler of moderate length and of the best construction and work-
manship.
Lloyd's.— Not very apparent, but appears to lie between 4 and 5.
United States Statutes. — Indefinite, because the strength of the joint is
not considered, except by the broad distinction between single and double
riveting.
Bureau Veritas: 4.4.
German Lloyd's: 5 to 4.65, according to the thickness of the plates.
Material for Riveting.— Board of Trade.— Tensile strength of
rivet bars between 26 and 30 tons, el. in 10" not less than 25%, and contr. of
area not less than 50#.
Lloyd's.— T. S., 26 to 80 tons; el. not less than 20# in 8". The material
must stand bending to a curve, the inner radius of which is not greater than
1^ times the thickness of the plate, after having been uniformly heated ta
a low cherry- red, and quenched in water at 82° F.
United States Statutes. — No special provision.
Rules Connected with Riveting.— Board of Trade.— The shead-
ing resistance of the rivet steel to be taken at 23 tons per square inch, 5 to
be used for the factor of safety independently of any addition to this factor
for the plating. Rivets in double shear to have only 1.75 times the single
section taken in the calculation instead of 2. The diameter must not be less
than the thickness of the plate and the pitch never greater than 8%". The
thickness of double butt-straps (each) not to be less than % the thickness of
the plate; single butt-straps not less than 9/8.
Distance from centre of rivet to edge of hole = diameter of rivet X 1J^.
Distance between rows of rivets
= 2 X diam. of rivet or = [(diam. X 4) -f 1] -t- 2, if chain, and
- y[(Pitch X 11) + (diam. X 4)] X (pitch -f diam. X 4) tf rf ^
Diagonal pitch = (pitch X 6 -f diam. X 4) ->- 10.
Lloyd's.— Rivets in double shear to have only 1.75 times the single section
taken in the calculation instead of 2. The shearing strength of rivet steel to
be taken at 85# of the T. S. of the material of shell plates. In any case
where the strength of the longitudinal joint is satisfactorily shown by ex-
periment to be greater than given by the formula, the actual strength may
be taken in the calculation.
United States Statutes. — No rules.
Material for Cyindrical Shells Subject to Internal Pres-
sure.— Board of Trade.— T. S I etween 27 and 32 tons. In the normal con-
dition, eL not less than 18£ in 10", but should be about 25* ; if annealed, not
STRENGTH OF STEAM-BOILERS. 701
less than 20%. Strips 2" wide should stand bending until the sides are
parallel at a distance from each other of not more than three times the
plate's thickness.
Lloyd's. — T. S. between the limits of 26 and 30 tons per square inch. El.
not less than 20% in 8". Test strips heated to a low cherry-red and plunged
into water at 82° F. must stand bending to a curve, the inner radius of
which is not greater than \y% times the plate's thickness.
U. S. Statutes.— Plates of W thick and under shall show a contr. of not
less than 50%; when over J£" and up to %", not less than 45# ; when over
%", not less than 40%.
Mr. Foley's comments : The Board of Trade rules seem to indicate a steel
of too high T. S. when a lower and more ductile one can be got : the lower
tensile limit should be reduced, and the bending test might with advantage
be made after tempering, and made to a smaller radius. Lloyd's rule for
quality seems more satisfactory, but the temper test is not severe. The
United States Statutes are not sufficiently stringent to insure an entirely
satisfactory material.
Mr. Foley suggests a material which would meet the following : 25 tons
lower limit in tension ; 25% in 8" minimum elongation ; radius for bending
test after tempering = the plate's thickness.
Shell-plate Form ulse.- Board of Trade: P= rx^^X8.
D = diameter of boiler in inches ;
P •=. working-pressure in Ibs. per square inch ;
t = thickness in inches ;
B = percentage of strength of joint compared to solid plate ;
T = tensile strength allowed for the material in Ibs. per square inch ;
F = a factor of safety, being 4.5, with certain additions depending on
method of construction.
.
t = thickness of plate in sixteenths ; B and D as before ; C = a constant
depending on the kind of joint.
When longitudinal seams have double butt-straps, C = 20. When longi-
tudinal seams have double butt-straps of unequal width, only covering on
one side the reduced section of plate at the outer line of rivets, C = 19.5.
When the longitudinal seams are lap-jointed, C = 18.5.
U. 8. Statutes.— Using same notation as for Board of Trade,
P = * * for single-riveting ; add 20% for double -riveting ;
where T is the lowest T. S. stamped on any plate.
Mr. Foley criticises the rule of the United States Statutes as follows ; The
rule ignores the riveting, except that it distinguishes between single and
double, giving the latter 20% advantage ; the circumferential riveting or
class of seam is altogether ignored. The rule takes no account of workman-
ship or method adopted of constructing the joints. The factor, one sixth,
simply covers the actual nominal factor of safety as well as the loss of
strength at the joint, no matter what its percentage ; we may therefore
dismiss it as unsatisfactory.
Rules for Flat Plates.— -Board of Trade; P = S_
P = working- pressure in Ibs. per square inch;
S = surface supported in square inches;
t — thickness in sixteenths of an inch;
C = a constant as per following table:
C = 125 for plates not exposed to heat or flame, the stays fitted with nuts
and washers, the latter at least three times the diameter of the stay
and % the thickness of the plate;
C = 187.5 for the same condition, but the washers % the pitch of stays in
diameter, and thickness not less than plate;
C = 200 for the same condition, but doubling plates in place of washers, the
width of which is % the pitch and thickness the same as the plate;
C ss 112.5 for the same condition, but the stays with nuts only;
(7 = 75 when exposed to impact of heat or flame and steam in contact with
the plates, and the stays fitted with nuts and washers three times the
Diameter of the stay and % the plate's thickness;
702 THE STEAM-BOILEB.
C = 67.5 for the same condition, but stays fitted with nuts only;
C = 100 when exposed to heat or flame, and water in C9ntact with the plates,
and stays screwed into the plates and fitted with nuts;
C = 66 for the same condition, but stays with riveted heads.
t7. S. Statutes.— Using same notation as for Board of Trade. P = * ,
where p = greatest pitch in inches, Pand t as above;
C =s 112 for plates 7/16" thick and under, fitted with screw stay-bolts
riveted over, screw stay-bolts and nuts, or plain bolt fitted
with single nut and socket, or riveted head and socket;
C = 120 for plates above 7/16", under the same conditions;
C = 140 for flat surfaces where the stays are fitted with nuts inside
and outside;
C = 200 for flat surfaces under the same condition, but with the addi-
tion of a washer riveted to the plate at least ^ plate's thick-
ness, and of a diameter equal :to% of the pitch of the stay-bolts.
N.B.— Plates fitted with double angle-irons and riveted to plate, with leaf
at least % the thickness of plate and depth at least J4 of pitch, would be
allowed the same pressure as determined by formula for plate with washer
riveted on.
N.B.— No brace or stay-bolt used in marine boilers to have a greater pitch
than 10^" on fire-boxes and back connections.
Certain experiments were carried out by the Board of Trade which showed
that the resistance to bulging does not vary as the square of the plate's
thickness. There seems also good reason to believe that it is not inversely
as the square of the greatest pitch. Bearing in mind, says Mr. Foley, that
mathematicians have signally failed to give us true theoretical foundations
for calculating the resistance of bodies subject to the simplest forms of
stresses,, we therefore cannot expect much from their assistance in the
matter of flat plates.
The Board of Trade rules for flat surfaces, being based on actual experi-
ment, are especially worthy of respect; sound judgment appears also to
have been used in framing them.
Furnace Formulae.— BOARD OF TRADE.— Long Furnaces.—
C X £2
P= — — — - - -, but not where L is shorter than (11. 5£ — 1), at which length
the rule for short furnaces comes into play.
P = working-pressure in pounds per square inch; t = thickness in inches;
D — outside diameter in inches; L = length of furnace in feet up to 10 ft.;
C = a constant, as per following table, for drilled holes :
C=99,000 for welded or butt-jointed with single straps, double-
riveted;
C = 88,000 for butts with single straps, single-riveted;
C = 99,000 for butts with double straps, single-riveted.
Provided always that the pressure so found does not exceed that given by
the following formulae, which apply also to short furnaces :
C x t
P = — ^— for all the patent furnaces named ;
p= 5 ~ when with Adamson rin*s-
C = 8,800 for plain furnaces;
C = 14,000 for Fox; minimum thickness 5/16", greatest %"; plain part
not to exceed 6" in length;
<7=s 13,500 for Morison: minimum thickness 5/16", greatest %"; plain
part not to exceed 6" in length;
C= 14,000 for Purves-Browu ; limits of thickness 7/16" and %"\ plain
part 9" in length;
C — 8,800 for Adamson rings; radius of flange next fire 1££".
U. S. STATUTES.— Long Furn aces.— Same notation.
89 600 X £2
P = — '-= - =: — , but L not to exceed 8 ft.
N.B.— If rings of wrought iron are fitted and riveted on properly around
:id to the flue in such a manner that the tensile stress on the rivets shall
STRENGTH OF STEAM-BOILERS. 703
q. in., the distance between the rings shall be taken
in the formulae.
?s, Pla
oy,oi'u x i"
lme = LXD
not exceed 6000 Ibs. per sq. in., the distance between the rings shall be taken
as the length of the flue in the formulae.
Short furnaces, Plain and Patent.— P, as before, when not 8 ft.
89,600 x t*
on==
_
C = 14,000 for Fox corrugations where D = mean diameter;
G = 14.000 for Purves-Brown where D = diameter of flue;
C = 5677 for plain flues over 16" diameter and less than 40", when
not over 3 ft. lengths.
Mr. Foley comments on the rules for long furnaces as follows: The Board
of Trade general formula, where the length is a factor, has a very limited
range indeed, viz.. 10 ft. as the extreme length, and 135 thicknesses — 12".
C y. t*
as the short limit. The original formula, P = — — , is that of Sir W.
Li X D
Fairbairn, and was, I believe, never intended by him to apply to short fur-
naces. On the very face of it, it is apparent, on the other hand, that if it is
true for moderately long furnaces, it cannot be so for very long ones. We
are therefore driven to the conclusion that any formula which includes
simple L as a factor must be founded on a wrong basis.
With Mr. Traill's form of the formula, namely, substituting (L -j- 1) for L,
the results appear sufficiently satisfactory for practical purposes, and in-
deed, as far as can be judged, tally with the results obtained from experi-
ment as nearly as could be expected. The experiments to which I refer
were six in number, and of great variety of length to diameter; the actual
factors of safety ranged from 4.4 to 6.2, the mean being 4.78, or practically
5. It seems to me, therefore, that, within the limits prescribed, the Board of
Trade formula may be accepted as suitable for our requirements.
The United States Statutes give Fairbairn's rule pure and simple, except
that the extreme limit of length to which it applies is fixed at 8 feet. As
far as can be seen, no limit for the shortest length is prescribed, but the
rules to me are by no means clear, flues and furnaces being mixed or not
well distinguished.
Material for Stays.— The qualities of material prescribed are as
follows:
Board of Trade.— The tensile strength to lie between the limits of 27 and
32 tons per square inch, and to have an elongation of not less than 20$ in
10". Steel stays which have been welded or worked in the fire should not
be used.
Lloyd's.— 26 to 30 ton steel, with elongation not less than 20# in 8".
U. 8. Statutes. — The only condition is that the reduction of area must not
be less than 40% if the test bar is over %" diameter.
Loads allowed on Stays.— Board of Trade.— 9000 Ibs. per square
inch is allowed on the net section, provided the tensile strength ranges from
27 to 32 tons. Steel stays are hot to be welded or worked in the fire.
Lloyd's.— For screwed and other stays, not exceeding 1^" diameter effec-
tive, 8000 Ibs. per square inch is allowed; for stays above 1}^", 9000 Ibs. No
stays are to be welded.
U. S. Statutes. — Braces and stays shall not be subjected to a greater stress
than 6000 Ibs. par square inch-
[Rankine, S. E., p. 459, says: " The iron of the stays ought not to be ex-
posed to a greater working tension than 3000 Ibs. on the square inch, in
order to provide against their being weakened by corrosion. This amounts
to making the factor of safety for the working pressure about 20." It is
evident, however, that an allowance in the factor of safety for corrosion may
reasonably be decreased with increase of diameter. W. K.]
C1 V d^ y t
\ Girders.— Board of Trade. P = w _ )p L> P = working pres-
sure in Ibs. per sq. in.; W = width of flarne-box in inches; L = length of
girder in inches; p = pitch of bolts in inches; D = distance between girders
from centre to centre in inches; d = depth of girder in inches; t = thick-
ness of sum of same in inches; C = a constant = 6600 for 1 bolt, 9900 for 2
or 3 bolts, and 11,220 for 4 bolts.
Lloyd's.— The same formula and constants, except that C = 11,000 for 4 or
5 bolts, 11,550 for 6 or 7, and 11,880 for 8 or more.
U. S. Statutes.— The matter appears to be left to the designers.
704 THE STEAM-BOILER.
Tube-riates.~J5oem* of Trade. P = t(D "jj*- D = least
horizontal distance between centres of tubes in inches; d = inside diameter
of ordinary tubes; t = thickness of tube-plate in inches; W= extreme
width of combustion-box in inches from front tube-plate to back of fire-
box, or distance between combustion-box tube-plates when the boiler is
double-ended and the box common to both ends.
The crushing stress on tube-plates caused by the pressure on the flame-
box top is to be limited to 10,000 Ibs. per square inch.
terial for Tubes.— Mr. Foley proposes the following: If iron, the
___ngation to be not less than 26% in 8" for the material before being
into strips; and after tempering, the test bar to stand completely closing
together. Provided the steel welds well, there does not seem to be any ob-
ject in providing tensile limits.
The ends should be annealed after manufacture, and stay-tube ends should
be annealed before screwing.
Holding-power of Boiler-tubes,— Experiments made in Wash-
ington Navy Yard show that wit h 2]4 in. brass tubes in no case was the holding-
power less, roughly speaking, than 6000 Ibs., while the average was upwards
of 20,000 Ibs. It was further shown that with these tubes nuts were super-
fluous, quite as good results being obtained with tubes simply expanded into
the tube-plate and fitted with a ferrule. When nuts were fitted it was shown
that they drew off without injuring the threads.
In Messrs. Yarrow's experiments on iron and steel tubes of 2" to 2*4"
diameter the first 5 tubes gave way on an average of 23,740 Ibs., which would
appear to be about % the ultimate strength of the tubes themselves. In all
these cases the hole through the tube-plate was parallel with a sharp edge
to it, and a ferrule was driven into the tube.
Tests of the next 5 tubes were made under the same conditions as the first
5, with the exception that in this case the ferrule was omitted, the tubes be-
ing simply expanded into the plates. The mean pull required was 15,270 Ibs.,
or considerably less than half the ultimate strength of the tubes.
Effect of beading the tubes, the holes through the plate being parallel and
ferrules omitted. The mean of the first 3, which are tubes of the same
kind, gives 26,876 Ibs. as their holding-power, under these conditions, as com-
pared with 23,740 Ibs. for the tubes fitted with ferrules only. This high
figure is, however, mainly due to an exceptional case where the holding-
power is greater than the average strength of the tubes themselves.
It is disadvantageous to cone the hole through the tube-plate unless its
sharp edge is removed, as the results are much worse than those obtained
with parallel holes, the mean pull being but 16,031 Ibs., the experiments be-
ing made with tubes expanded and ferruled but not beaded over.
In experiments on tubes expanded into tapered holes, beaded over and
fitted with ferrules, the net result is that the holding-power is, for the size
experimented on, about M of the tensile strength of the tube, the mean pull
being 28,797 Ibs.
With tubes expanded into tapered holes and simply beaded over, better
results were obtained than with ferrules; in these cases, however, the sharp
edge of the hole was rounded off, which appears in general to have a good
effect.
In one particular the experiments are incomplete, as it is impossible to
reproduce on a machine the racking the tubes get by the expansion of a
boiler as it is heated up and cooled down again, and it is quite possible,
therefore, that the fastening giving the best results on the testing-machine
may not prove so efficient in practice.
N.B.— It should be noted that the experiments were all made under the
cold condition, so that reference should be made with caution, the circum-
stances in practice being very different, especially when there is scale on
the tube-plates, or when the tube -plates are thick and subject to intense
heat.
Iron versus Steel Boiler-tubes. (Foley.) — Mr. Blechynden
prefers iron tubes to those of steel, but how far he would go in attributing
the leaky-tube defect to the use of steel tubes we are not aware. It appears,
however, that the results of his experiments would warrant him in going a
considerable distance in this direction. The test consisted of heating and
cooling two tubes, one of wrought iron and the other of steel. Both tubes
were 2% in. in diameter and .16 in. thickness of metal. The tubes were
STRENGTH OF STEAM-BOILERS. 705
put in the same furnace, made red-hot, and then dipped in water. The
length was gauged at a temperature of 46° F.
This operation was twice repeated, with results as follows :
Steel. Iron.
Original length . . . 55.495 in. 55.495 in.
Heated to 186° F. ; increase 052 " .048 "
Coefficient of expansion per degree F 0000067 .0000062
Heated red-hot and dipped in water; decrease .00? in. .003 in.
Second heating and cooling, decrease 031 in. .004 in.
Third heating and cooling, decrease 017 in. .006 in.
Total contraction ... .055 in. .013 in.
Mr. A. C. Kirk writes : That overheating of tube ends is the cause of the
leakage of the tubes in boilers is proved by the fact that the ferrules at
present used by the Admiralty prevent it. These act by shielding the tube
ends from the action of the flame, and consequently reducing evaporation,
and so allowing free access of the water to keep them cool.
Although many causes contribute, there seems no doubt that thick tube-
plates must bear a share of causing the mischief.
Rules for Construction of Boilers in Merchant Vessels
in tlie United States.
(Extracts from General Rules and Regulations of the Board of Supervising
Inspectors ot JSteam- vessels (as amended 1898).)
Tensile Strengtn of Plate* (Section 3.)— To ascertain the tensile
strength and other qualities of iron plate there shall be taken from each
sheet to be used in shell or other
parts of boiler which are subject to
tensile strain a test piece prepared
in form according to the following
diagram, viz.: 10 inches in length, 2
inches in width, cut out in the
centre in the manner indicated.
To ascertain the tensile strength
and other qualities of steel plate, there shall be taken from each sheet to be
used in shell or other parts of boiler which are subject to tensile strain a test-
piece prepared in form according to the following diagram:
The straight part in centre shall
be 9 inches in length and 1 inch in
width, marked with light prick-
punch marks at distances 1 inch
apart, as shown, spaced so as to
give 8 inches in length.
The sample must show when
tested an elongation of at least 25% in a length of 2 in. for thickness up to
J4 in., inclusive; in a length of 4 in. for over 14 to 7/16, inclusive; in a
length of 6 in., for all plates over 7/16 in. and under 1% in. thickness.
The reduction of area shall be the same as called for by the rules of the
Board. No plate shall contain more than M% of phosphorus and .04$ of
sulphur.
The samples shall also be capable of being bent to a curve, of which the
inner radius is not greater than 1^ times the thickness of the plates after
having been heated uniformly to a low cherry-red and quenched in water
of 82° F.
[Prior to 1894 the shape of test-piece for steel was the same as that for tron,
viz., the grooved shape. This shape has been condemned by authorities on
strength of materials for over twenty years. It always gives results which
are too high, the error sometimes amounting to 25 per cent. See pages 242,
243, ante; also, Strength of Materials, W. Kent, Van N. Science Series No. 41,
and Beardslee on Wrought-iron and Chain Cables.]
Ductility. (Section 6.)— To ascertain the ductility and other lawful
qualities, iron of 45,000 Ibs. tensile strength shall show a contraction of area
of 15 per cent, and each additional 1000 Ibs. tensile strength shall show 1
per cent additional contraction of area, up to and including 55,000 tensile
strength. Iron of 55,000 tensile strength and upwards, showing 25 per cent
reduction of area, shall be deemed to haVe the lawful ductility. All steel
plate of ]4 inch thickness and under shall show a contraction of area of not
less than 50 per cent. Steel plate over ^ inch in thickness, up to % inch in
706
THE STEAM-BOILER.
thickness, shall show a reduction of not less than 45 per cent. All steel plate
over % inch thickness shall show a reduction of not less than 40 per cent.
Bumped Heads of Boilers. (Section 17 as amended 1894.) —
Pressure Alloived on Bumped Heads. — Multiply the thickness of the plate
by one sixth of the tensile strength, and divide by six tenths of the radius to
which head is bumped, which will give the pressure per square inch of
steam allowed.
Pressure Allowable for Concaved Heads of Boilers.— Multiply the pressure
per square inch allowable for bumped heads attached to boilers or drums
convexly, by the constant .6, and the product will give the pressure per
square inch allowable in concaved heads.
The pressure on unstayed flat-heads on steam-drums or shells
of boilers, when flanged and made of wrought iron or steel or of cast steel,
shall be determined by the following- rule:
The thickness of plate in inches multiplied by one sixth of its tensile
strength in pounds, which product divided by the area of the head in square
inches multiplied by 0.9 will give pressure per square inch allowed. The
material used in the construction of flat-heads when tensile strength has
not been officially determined shall be deemed to have a tensile strength of
45,000 Ibs.
Table of Pressures allowable on Steam-boilers made of
Riveted Iron or Steel Plates.
(Abstract from a table published in Rules and Regulations of the U. S.
Board of Supervising Inspectors of Steam-vessels.)
Plates J4 mcn thick. For other thicknesses, multiply by the ratio of the
thickness to *4 inch.
°»
50,000 Tensile
Strength.
55,000 Tensile
Strength.
60.000 Tensile
Strength.
65,000 Tensile
Strength.
70,000 Tensile
Strength.
If-
|
•*!
o>
S
*1
2
•A!
e
3
•1
£
«j
c ^
M
•<j .2
%
<£
•*3j .2
S
•<i .2
cc
«3^ .2
2
O T3
2)
^
v^
^^
£
v.^
PH
PH
<?*
PH
it
PH
£* ^
PH
CJ
36
115.74
138.88
127.31
152.77
138.88
166.65
150.46
180.55
162.03
191.43
38
109.64
131.56
120.61
144.73
131.57
157.88
142.54
171.04
153.5
184.20
40
104.16
124.99
114.58
137.49
125
150
135.41
162.49
145.83
174.99
42
99.2
119.04
109.12
130.94
119.04
142 81
128.96
154.75
138.88
166.65
44
94.69
113.62
104.16
124.99
113.63
136.35
123.1
147.72
132.56
159.07
46
90.57
108.68
99.63
119.55
108.69
130.42
117.75
141.3
126.8
152.16
48
86.8
104.16
95.48
114.57
104.16
124.99
112.84
135.4
121.52
145.82
54
77.16
92.59
84.87
101.84
92.59
111.10
100.3
120.36
108.02
129.62
60
69.44
83.32
76.38
91.65
83.33
99.99
90.27
108.32
97.22
116.66
66
63.13
75.75
69.44
83.32
75.75
90.90
82.07
98.48
88.37
106.04
72
57.87
69.44
63.65
76.38
69 44
83.32
75.22
90.26
81.01
97.21
78
53.41
64.09
58.76
70 5
64.4
76.92
69.44
83.32
74.78
89.73
84
49.6
59.52
54.56
65.47
59.52
71.42
64.48
77.37
69.44
83.32
90
48.29
55.44
50.92
61.1
55.55
66.66
60.18
72.21
64.81
77.77
96
43.4
52.08
47.74
57.28
52.08
62.49
56.42
67.67
60.76
72.91
The figures under the columns headed " pressure " are for single-riveted
boilers. Those under the columns headed " 20# Additional" are for double-
riveted.
U. S. RULE FOR ALLOWABLE PRESSURES.
The pressure of any dimension of boilers not found in the table annexed
to these rules must be ascertained by the following rule:
Multiply one sixth of the lowest tensile strength found stamped on any
plate iu the cylindrical shell by the thickness (expressed in inches or part's
of an inch) of the thinnest plate in the same cylindrical shell, and divide by
the radius or half diameter (also expressed in inches), the quotient will b@
the pressure allowable per square inch of surface for single-riveting, to
which add twenty per centum for double-riveting when all the rivet-holes
in the shell of such boiler have been li fairly drilled " and no part of such
hole has been punched.
The author desires to express his condemnation of the above rule, and of
the tables derived from it, as giving too low a factor of safety. (See also
criticism by Mr. Foley, page 701, ante.)
STRENGTH OF STEAM-BOILERS.
707
If Pb = bursting-pressure, t = thickness, T= tensile strength, c = coef-
ficient of strength of riveted joint, that is, ratio of strength of the joint to
that of the solid plate, d = diameter, Pb = --T-» or if c be taken for double-
riveting at 0.7, then Pb =
d
By the U. S. rule the allowable pressure Pa =
X 1.20 =
whence
Pb = 3.5Pa; that is, the factor of safety is only 3.5, provided the "tensile
strength found stamped in the plate" is the real tensile strength of the
material. But in the case of iron plates, since the stamped T.S. is obtained
from a grooved specimen, it may be greatly in excess of the real T.S., which
would make the factor of safety still lower. According to the table, a boiler
40 in. diam., J4 in- thick, made of iron stamped 60,000 T.S., would be licensed
to carry 150 Ibs. pressure if double -riveted. If the real T.S. is only 50,000 Ibs.
nr^l" _ 437.5 ibs<>
the calculated bursting-strength would be
P_ 2tTc 2 X 50,000 X .25 X .70
= d = 40
and the factor of safety only 437.5-*- 150 = 2.91 !
The author's formula for safe working-pressure of externally -fired boilers
with longitudinal seams double-riveted, is P = — - — ; t— ——-;P = gauge-
pressure in Ibs. per sq. in. ; t = thickness and d = diam. in inches.
This is derived from the formula P = '-— -, taking c at 0.7 and / = 5 for
steel of 50,000 Ibs. T.S., or 6 for 60.000 Ibs. T.S.; the factor of safety being
increased in the ratio of the T.S., since with the higher T.S. there is greater
danger of cracking at the rivet-holes from the effect of punching and rivet-
ing and of expansion and contraction caused by variations of temperature.
For external shells of internally-fired boilers, these shells not being exposed
to the fire, with rivet-holes drilled or reamed after punching, a lower factor
of safety and steel of a higher T.S. may be allowable.
If the T.S. is 60,000, a working pressure P = — -5 — would give a factor of
safety of 5.25.
The following table gives safe working pressures for different diameter*
of shell and thicknesses of plate calculated from the author's formula.
Safe Working Pressures in Cylindrical Shells of Boilers,
Tanks, Pipes, etc., in Pounds per Square Inch.
Longitudinal seams double-riveted.
(Calculated from formula P= 14,000 X thickness -*- diameter.)
8 o ^
si!
Diameter in Inches.
oso1""1
ii3
24
30
36
38
40
42
44
46
48
50
52
i
36.5
29.2
24.3
23.0
21.9
20.8
19.9
19.0
18.2
17.5
16 8
2
72.9
58.3
48.6
46 1
43.8
41.7
39.8
38.0
36.5
35.0
33.7
3
109.4
87.5
72.9
69.1
65.6
62.5
59.7
57.1
54.7
52.5
50.5
4
145.8
116.7
97.2
92.1
87.5
83.3
79.5
76.1
72.9
70.0
67.3
5
182.3
145.8
121.5
115.1
109.4
104.2
99.4
95.1
91.1
87.5
84.1
6
218.7
175.0
145.8
138.2
131.3
125.0
119.3
114.1
109.4
105.0
101.0
7
255.2
204.1
170.1
161.2
153.1
145.9
139.2
133.2
127.6
122.5
117.8
8
291.7
233.3
194.4
184.2
175.0
166.7
159.1
152.2
145.8
140.0
134.6
9
328.1
262.5
218.8
207.2
196.9
187.5
179.0
171.2
164.1
157.5
151.4
10
364.6
291.7
243.1
230.3
218.8
208.3
198.9
190.2
182.3
175.0
168.3
11
401.0
3*0.8
267.4
253.3
240.6
229.2
218.7
2*09.2
200.5
192.5
185.1
12
437.5
350.0
291.7
276.3
262.5
250.0
238.6
228.3
218.7
210.0
201.9
13
473.9
379.2
316.0
299.3
284.4
270.9
258.5
247.3
337.0
227.5
218.8
14
410.4
408.3
340 3
322.4
306.3
291.7
278.4
266.3
255.2
245.0
235.6
15
546 9
437.5
364.6
345.4
328.1
312.5
298 3
285.3
273.4
266.5
252.4
16
583.3
466.7
388.9
368.4
350.0
333.3
318.2
304.4
291.7
280.0
269.2
708
THE STEAM-BOILER.
S3 .
§.§•§
Diameter in Inches.
IP
ei§
54
60
66
72
78
84
90
96
102
108
114
120
1
16.2
14.6
13.3
12.2
11.2
10.4
9.7
9.1
8.6
8.1
~rTr
7.3
2
32.4
29.2
26.5
24.3
22.4
20.8
19.4
18.2
17.2
16.2
15 4
14.6
3
48.6
43.7
39.8
36.5
33.7
31.3
29.2
27.3
25.7
24.3
23.0
21.9
4
64.8
58.3
53.0
48.6
44.9
41.7
38.9
36.5
34.3
32.4
30.7
29.2
5
81.0
72.9
66.3
60.8
56.1
52.1
48.6
45.6
42.9
40.5
38.4
36.5
6
97.2
87.5
79.5
72.9
67.3
62.5
58.3
54.7
51.5
48.6
40.1
43.8
7
113.4
102.1
92.8
85.1
78.5
72.9
68.1
63.8
60.0
56.7
53.7
51.0
8
129.6
116.7
106.1
97.2
89.7
83.3
77.6
72.9
68.6
64.8
61.4
58.3
9
145.8
131.2
119.3
109.4
101.0
93.8
87.5
82.0
77.2
72.9
69.1
65.6
10
162.0
145.8
132.6
121.5
112.P,
104.2
97.2
91.1
85.8
81.0
76.8
72.9
11
178.2
160.4
145.8
133.7
123.4
114.6
106.9
100.3
94.4
89.1
84.4
80.2
12
194.4
175.0
159.1
145.8
134.6
125.0
116.7
109.4
102.9
97.2
92.1
87.5
13
210.7
189.6
172.4
J58.0
145.8
135.4
126.4
118.5
111.5
105.3
99.8
94.8
14
226.9
204.2
185.6
170.1
157.1
145.8
136.1
127.6
120.1
113 4
107.5
102.1
15
243.1
218.7
198.9
182.3
168.3
156.3
145.8
136.7
128.7
121.5
115.1
109.4
16
259.3
233.3
212.1
194.4
179.5
166.7
155.6
145.8
137.3
129.6
122.8
116.7
Rules governing Inspection of Boilers in Philadelphia.
In estimating the strength of the longitudinal seams in the cylindrical
shells of boilers the inspector shall apply two formulae, A and B :
j Pitch of rivets — diameter of holes punched to receive the rivets _
* I pitch of rivets
percentage of strength of the sheet at the seam.
( Area of hole filled by rivet X No. of rows of rivets in seam X shear-
^ ing strength of rivet _
' i pitch of rivets X thickness of sheet X tensile strength of sheet
percentage of strength of the rivets in the seam.
Take the lowest of the percentages as found by formulae A and B and
apply that percentage as the " strength of the seam " in the following
formula C, which determines the strength of the longitudinal seams:
( Thickness of sheet in parts of inch X strength of seam as obtained
£< •< by formula A or B X ultimate strength of iron stamped on plates _
'* » internal radius of boiler in inches X 5 as a factor of safety
safe working pressure.
TABLE OP PROPORTIONS AND SAFE WORKING PRESSURES WITH FORMULA A
AND C, © 50,000 LBS., T.S.
Diameter of rivet
Diameter of rivet-hole.
%"
11/16"
11/16
H
13/16
13/16
%
15/16
Pitch of rivets
2"
2 1/16
gix
2 3/16
OL/!
Strength of seam, %
.656
.636
62
.60
58
Thickness of plate
y4»
5/16
%
7/16
K
Diameter cf boiler, in ...
Safe Working Pressure with Longitudinal Seams
Single-riveted.
24
137
165
193
220
242
30
109
132
154
176
194
32
102
124
144
165
182
84
96
117
136
155
171
86
91
110
129
147
161
38
86
104
122
139
153
40
82
99
116
132
145
44
74
91
105
120
132
48
68
83
96
110
121
54
60
73
86
98
107
60
55
66
77
88
97
STRENGTH OF STEAM-BOILERS.
70S
Diameter of rivet. .
5/»
11/16
%
13/16
7/r
Diameter of rivet-hole. . .
11/16"
M
13/16
15%
Pitch of rivets
3"
3U
Strength of seam, %
Thickness of plate
.77
5/16
I
7/16
73
H
Diameter of boiler, in ...
Safe Working Pressure with Longitudinal Seams,
Double-riveted.
24
160
198
235
269
305
30
127
158
188
215
243
32
119
148
176
202
228
34
112
140
166
190
215
36
106
132
156
179
203
38
101
125
148
170
192
40
96
119
141
161
183
44
87
108
128
147
166
48
79
99
118
135
152
54
70
88
104
120
135
60
64
79
94
108
122
Flues and Tubes for Steam-boilers.— (From Rules of U. S.
Supervising Inspectors. Steam-pressures per square inch allowable on
riveted and lap-welded flues made in sections. Extract from table in Rules
of U. S. Supervising Inspectors.)
T = least thickness of material allowable, D = greatest diameter in inches,
P = allowable pressure. For thickness greater than T with same diameter
P is increased in the ratio of the thickness.
Z) = in. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
T=in. .18 .20.21 .21 .22 .22 .23 .24 .25 .26 .27.28.29 30.31 .32 .33
P = lbs. 189184179174 172 158 152 147 143 139 1361341311^9126125122
D = in. 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
T= in. .34 .35 .36 .37 .38 .39 .40 .41 .42 .43 .44 .45 .46 .47 .48 .49 .50
P= Ibs. 121 120 119 117 116 115 115 114 112 112 110 110 109 109 108 108 107
For diameters not over 10 inches the greatest length of section allowable
is 5 feet; for diameters 10 to 23 inches, 3 feet; for diameters 23 to 40 inches, 30
inches. If lengths of sections are greater than these lengths, the allowable
pressure is reduced proportionately.
TheU. S. rule for corrugated flues, as amended in 1894, is as follows: Rule
II, Section 14. The strength of all corrugated flues, when used for furnaces
or steam chimneys (corrugation not less than 1^ inches deep and notexceed-
ing 8 inches from centres of corrugation), and provided that the plain parts
at the ends do not exceed 6 inches in length, and the plates are not less than
5/16 inch thick, when new, corrugated, and practically true circles, to be
calculated from the following formula:
14,000
X T = pressure.
T = thickness, in inches; D = mean diameter in inches.
Ribbed Flues. — The same formula is given for ribbed flues, with rib
projections not less than \% inches deep and not more than 9 inches
apart.
Flat Stayed Surfaces In Steam-boilers.— Rule II., Section 6, of
the rules of the U. S. Supervising Inspectors provides as follows:
No braces or stays hereafter employed in the construction of boilers
shall be allowed a greater strain than 6000 Ibs. per square inch of
section.
Clark, in his treatise on the Steam-engine, also in his Pocket-book, gives
the following formula: p = 40?fc -*- d, in which p is the internal pressure in
pounds per square inch that will strain the plates to their elastic limit, t is
the thickness of the plate in inches, d is the distance between two rows of
stay-bolts in the clear, and s is the tensile stress in the plate in tons of
2240 Ibs. per square inch, at the elastic limit. Substituting values of s
for iron, steel, and copper, 12, 14, and 8 tons respectively, we have t&e
following :
710
THE STEAM-BOILEK.
FORMULAE FOE ULTIMATE ELASTIC STRENGTH OF FLAT STAYED SURFACES,
Iron.
Steel.
Copper.
p — 5000-
p - 5700 t
p - 3300-
d
. PXd
d
t PXd
d
f PXd
Pitch of bolts
5000
5000*
57CO
d_5700£
3300
3300*
' P
P
( P
For Diameter of the Stay-bolts, Clark gives d' = .0024,4 /— ~,
in which d' = diameter of screwed bolt at bottom of thread, P = longitudi-
nal and P' transverse pitch of stay-bolts between centres, p = internal
pressure in Ibs. per sq. in. that will strain the plate to its elastic limit, s =
elastic strength of the stay-bolts in Ibs. per sq. in. Taking s = 12, 14, and 8
tons, respectively for iron, steel, and copper, we have
For iron, d' = .00069 |/PP^,;or if P = P', d' = .00069P Vp-
For steel, d' = .00064 4/PP'p, " " . ; d' = .00064P |/p;
For copper, d' = .00084 4/PP'p, " " d' = .00084P \/p.
In using these formulae a large factor of safety should be taken to allow
for reduction of size by corrosion. Thurston's Manual of Steam-boilers, p.
144, recommends that the factor be as large as 15 or 20. The Hartford
Steam Boiler Insp. & Ins. Co. recommends not less than 10.
Strength of Stays.— A. F. Yarrow (Engr., March 20, 1891) gives the
following results of experiments to ascertain the strength of water-space
stays :
Description.
Length
between
Plates.
Diameter of Stay over
Threads.
Ulti-
mate
Stress.
Hollow stays screwed into j
plates and hole expanded j
Solid stays screwed intoj
» plates and riveted over. (
4.75 in.
4. 64 in.
4. 80 in.
4. 80 in.
1 in. (hole 7/16 in. and 5/16 in.
1 in. (hole 9/16 in. and 7/16 in.
% in.
Ibs.
25,457
20,992
22,008
22,070
The above are taken as a fair average of numerous tests.
Stay-bolts in Curved Surfaces, as in Water-legs of Verti-
cal Boilers* — The rules of the U. S. Supervising Inspectors provide as
follows: All vertical boiler- furnaces constructed of wrought iron or steel
plates, and having a diameter of over 42 in. or a height of over 40 in. shall be
stayed with bolts as provided by § 6 of Rule II, for flat surfaces; and the
thickness of material required for the shells of such furnaces shall be de-
termined by the distance between the centres of the stay-bolts in the fur-
nace and not in the shell of the boiler; and the steam-pressure allowable
shall be determined by the distance from centre of stay-bolts in the furnace
and the diameter of such stay-bolts at the bottom of the thread.
The Hartford Steam-boiler Insp. & Ins. Co. approves the above rule (The
Locomotive, March, 1892) as far as it states that curved surfaces are to be
computed the same as flat ones, but prefers Clark's formulae for flat
stayed surfaces to the rules of the U. S. Supervising Inspectors.
Fusible-plugs.— Fusible-plugs should be put in that portion of the
heating-surface which first becomes exposed from lack of water. The rules
of the U. S. Supervising Inspectors specify Banca tin for the purpose. Its
melting-point is about 445° F. The rule says: All steamers shall have
inserted in their boilers plugs of Banca tin, at least %> in. in diameter at the
smallest end of the internal opening, in the following manner, to wit:
Cylinder- boilers with flues shall have one plug inserted in one flue of each
boiler; and also one plug inserted in the shell of each boiler from the inside,
immediately before the fire line and not less than 4 ft. from the forward
end of the boiler. All fire-box boilers shall have one ping inserted in the
crown of the back connection, or in the highest fire-surface of the boiler.
IMPROVED METHODS OF FEEDING COAL. 711
All upright tubular boilers used for marine purposes shall have a fusible
plug inserted in one of the tubes at a point at least 2 in. below the lower
gauge-cock, and said plug may be placed in the upper head sheet when
deemed advisable by the'local inspectors.
Steam-domes.— Steam domes or drums were formerly almost univer-
sally used on horizontal boilers, but their use is now generally discontinued,
as they are considered a useless appendage to a steam-boiler, and unless
properly designed and constructed are an element of weakness.
Height of Furnace.— Recent practice in the United States makes
the height of furnace much greater than it was formerly. With large sizes
of anthracite there is no serious objection to having the furnace as low as 12
to 18 in., measured from the surface of the grate to the nearest portion of
the heating surface of the boiler, but with coal containing much volatile
matter and moisture a much greater distance is desirable. With very vola-
tile coals the distance may be as great as 4 or 5 ft. Rankine (S. E., p. 457)
says: The clear height of the " crown " or roof of the furnace above the grate-
bars is seldom less than about 18 in., and often considerably more. In the
fire-boxes of locomotives it is on an average about 4 ft. The height of 18 in.
is suitable where the crown of the furnace is a brick arch. Where the crown
of the furnace, on the other hand, forms part of the heating-surface of the
boiler, a greater height is desirable in every case in which it can be
obtained; for the temperature of the boiler-plates, being much lower than
that of the flame, tends to check the combustion of the inflammable gases
which rise from the fuel. Asa general principle a high furnace is favorable
to complete combustion.
IMPROVED METHODS OF FEEDING COAT,,
Mechanical Stokers. (William R. Roney, Trans. A. S. M. E., vol.
xii.)— Median ical stokers have been used in England to a limited extent
since 1785. In that year one was patented by James Watt. It was a simple
device to push the coal, after it was coked at the front end of the grate,
back towards the bridge. It was worked intermittently by levers, and was
designed primarily to prevent smoke from bituminous coal. (See D. K.
Clark's Treatise on the Steam-engine.)
After the year 1840 many styles of mechanical stokers were patented in
England, but nearly all were variations and modifications of the two forms
of stokers patented by John Jukes in 1841, and by E. Henderson in 1843.
The Jukes stoker consisted of longitudinal fire-bars, connected by links,
so as to form an endless chain, similar to the familiar treadmill horse-power.
The small coal was delivered from a hopper on the front of the boiler, on to
the grate, which slowly moving from front to rear, gradually advanced the
fuel into the furnace and discharged the ash and clinker at the back.
The Henderson stoker consists primarily of two horizontal fans revolving
on vertical spindles, which scatter the coal over the fire.
Numerous faults in mechanical construction and in operation have limited
the use of these and other mechanical stokers. The first American stoker
was the Murphy stoker, brought out in 1878. It consists of two coal maga-
zines placed in the side walls of the boiler furnace, and extending back from
the boiler front 6 or 7 feet. In the bottom of these magazines are rectangu-
lar iron boxes, which are moved from side to side by means of a rack and
pinion, and serve to push the coal upon the grates, which incline at an angle
of about 35° from the inner edge of the coal magazines, forming a V-shaped
receptacle for the burning coal. The grates are composed of narrow parallel
bars, so arranged that each alternate bar lifts about an inch at Ihe lower
end, while at the bottom of the V, and filling the space between the ends of
the grate-bars, is placed a cast-iron toothed bar, arranged to be turned by a
crank. The purpose of this bar is to grind the clinker coming in contact
with it. Over this V-shaped receptacle is sprung a fire-brick arch.
In the Roney mechanical stoker the fuel to be burned is dumped into a
hopper on the boiler front. Set in the lower part of the hopper is a " pusher"
to which is attached the " feed-plate " forming the bottom of the hopper.
The " pusher,"" by a vibratory motion, carrying with it the " feed-plate,'1
gradually forces the fuel over the "dead-plate" and on the grate. The
grate-bars, in their normal condition form a series of steps, to the top step
of which coal is fed from the •' dead-plate." Each bar rests in a concave
seat in the bearer, and is capable of a rocking motion through an adjustable
angle. All the grate-bars are coupled together by a " rocker- bar." A vari-
able back-and-forth motion being given to the " rocker-bar," through a con-
714 THE STEAM-BOILER,
the grate and fire of the second, each furnace being charged with f resh fuel
when needed, the latter generally with a smokeless coal or coke : an irra-
tional and unpromising method.
Mr. C. F. White, Consulting Engineer to the Chicago Society for the Pre-
vention of Smoke, writes under date of May 4, 1893 :
The experience had in Chicago has shown plainly that it is perfectly easy
to equip steam-boilers with furnaces which shall burn ordinary soft coal in
such a manner that the making of smoke dense enough to obstruct the vision
shall be confined to one or two intervals of perhaps a couple of minutes'
duration in the ordinary day of 10 hours.
Gas-fired Steam-boilers.— Converting coal into gas in a separate
producer, before burning it under the steam-boiler, is an ideal method of
smoke-prevention, but its expense has hitherto prevented its general intro-
duction. A series of articles on the subject, illustrating a great number of
devices, by F. J. Rowan, is published in the Colliery Engineer, 1889-90. See
also Clark on the Steam-engine.
FORCED COMBUSTION IN STEAM-BOILERS.
For the purpose of increasing the amount of steam that can be generated
by a boiler of a given size, forced draught is of great importance. It is
universally used in the locomotive, the draught being obtained by a steam-
jet in the smoke-stack. It is now largely used in ocean steamers, especially
in ships of war, and to a small extent in stationary boilers. Economy of fuel
is generally not attained by its use, its advantages being confined to the
securing of increased capacity from a boiler of a given bulk, weight, or cost.
The subject of forced draught is well treated in a paper by James Howden,
entitled, "Forced Combustion in Steam-boilers" ^ection G, Engineering
Congress at Chicago, in 1893), from which we abstract the following:
Edwin A. Stevens at Bordentown, N. J., in 1827, in the steamer "North
America," fitted the boilers with closed ash-pits, into which the air of com-
bustion was forced by a fan. In 1828 Ericsson fitted in a similar manner the
steamer "Victory,'1 commanded by Sir John Ross.
Messrs. E. A. and R. L. Stevens continued the use of forced draught for
a considerable period, during which they tried three different modes of using
the fan for promoting combustion: 1, blowing direct into a closed ash-pit;
2, exhausting the base of the funnel by the suction of the fan: 3, forcing air
into an air-tight boiler-room or stoke-hold. Each of these three methods
was attended writh serious difficulties.
In the use of the closed ash-pit the blast-pressure would frequently force
the gases of combustion, in the shape of a serrated flame, from the joint
around the furnace doors in so great a quantity as to affect both the effi-
ciency and health of the firemen.
• The chief defect of the second plan was the great size of the fan required
to produce the necessary exhaustion. The size of fan required grows in a
rapidly increasing ratio as the combustion increases, both on account of the
greater air-supply and the higher exit temperature enlarging the volume of
the waste gases.
The third method, that of forcing cold air by the fan into an air-tight
boiler-room — the present closed stoke-hold system — though it overcame the
difficulties in working belonging to the two forms first tried, has serious
defects of its own, as it cannot be worked, even with modern high-class
boiler-construction, much, if at all, above the power of a good chimney
draught, in most boilers, without damaging them.
In 1875 John I. Thornycroft & Co., of London, began the construction of
torpedo-boats with boilers of the locomotive type, in which a high rate of
combustion was attained by means of the air-tight boiler-room, into which
air was forced by means of a fan.
Inl882H.B.M. ships , " Satellite " and " Conqueror " were fitted with this
system, the former being a small ship of 1500 I.H.P., and the latter an iron^
clad of 4500 I.H.P. On the trials with forced draught, which lasted from two
to three hours each, the highest rates of combustion gave 16.9 I.H.P. per
square foot of fire-grate in the "Satellite," and 13.41 I.H.P. in the " Con-
queror.'1
None of tne short trials at these rates of combustion were made without
injury to the seams and tubes of the boilers, but the system was adopted,
and it has been continued in the British Navy to this day (1893).
In Mr. Howden's opinion no advantage arising from increased combustion
over natural-draught rates is derived from using forced draught in a closed
ash-pit sufficient to compensate the disadvantages arising from difficulties
FUEL ECONOMIZERS. 715
in working, there being either excessive smoke from bituminous coal or
reduced evaporative economy.
In 1880 Mr. Howden designed an arrangement intended to overcome the
defects of both the closed ash-pit and closed stoke-hold systems.
An air-tight reservoir or chamber is placed on the front end of the boiler
and surrounding the furnaces. This reservoir, which projects from 8 to 10
inches from the end of the boiler, receives the air under pressure, which is
passed by the valves into the ash-pits and over the fires in proportions
suited to the kind of fuel used and the rate of combustion required. The
air nsed above the fires is admitted to a space between the outer and inner
furnace-doors, the inner having perforations and an air-distributing box
through which the air passes under pressure.
By means of the balance of air-pressure above and below the fires all
tendency for the fire to blow out at the furnace-door is removed.
By regulating the admission of the air by the valves above and below the
fires, the highest rate of combustion possible by the air-pressure used can
be effected, and in same manner the rate of combustion can be reduced to
far below that of natural draught, while complete and economical combus-
tion at all rates is secured.
A feature of the system is the combination of the heating of the air of
combustion by the waste gases with the controlled and regulated admission
of air to the furnaces. This arrangement is effected most conveniently by
passing the hot fire-gases after they leave the boiler through stacks of
vertical tubes enclosed in the uptake, their lower ends being immediately
above the smoke-box doors.
Installations on Howden's system have hitherto been arranged for a rate
of combustion to give at full sea-power an average of from 18 to 22 I.H.P.
per square foot of fire-grate with fire-bars from 5' 0" to 5' 6" in length.
It is believed that with suitable arrangement of proportions even SO
I.H.P. per square foot can be obtained.
For an account of recent uses of exhaust-fans for increasing draught, see
paper by W. R. Roney, Trans. A. S. M. E., vol. xv.
FUEI, ECONOMIZERS.
Green's Fuel Economizer.— Clark gives the following average re-
sults of comparative trials of three boilers at Wigan used with and without
economizers :
Without With
Economizers. Economizers.
Coal per square foot of grate per hour 21 . 6 21.4
Water at 1 00° evaporated per hour 73 . 55 79 . 32
Water at 212° per pound of coal 9.60 10.56
Showing that in burning equal quantities of coal per hour the rapidity of
evaporation is increased 9.3$ and the efficiency of evaporation W% by the
addition of the economizer.
The average temperatures of the gases and of the feed-water before and
after passing the economizer were as follows:
With 6-f t. grate. With 4-f t. grate.
Before. After. Before. After.
Average temperature of gases 649 340 501 312
Average temperature of feed- water. 47 157 41 137
Taking averages of the two grates, to raise the temperature of the feed-
water 100° the gases were cooled down 250°.
Performance of a Green Economizer with a Smoky Coal.
—The action of Green's Economizer was tested by M. W. Grosseteste for a
period of three weeks. The apparatus consists of four ranges of vertical
pipes, 6^ feet high, 3% inches in diameter outside, nine pipes in each range,
connected at top and bottom by horizontal pipes. The water enters all the
tubes from below, and leaves them from above. The system of pipes is en-
veloped in a brick casing, into which the gaseous products of combustion
are introduced from above, and which they leave from below. The pipes
are cleared of soot externally by automatic scrapers. The capacity for
water is 24 cubic feet, and the total external heating-surface is 290 square
feet. The apparatus is placed in connection with a boiler having 355 square
feet of surface.
This apparatus had been at work for seven weeks continuously without
having been cleaned, and had accumulated a J^-inch coating of soot and
716
THE STEAM-BOILER.
ash, when its performance, in the same condition, was observed for one
week. During the second week it was cleaned twice every day; but during
the third week, after having been cleaned on Monday morning, it was
worked continuously without further cleaning. A smoke-making coal was
used. The consumption was maintained sensibly constant from day to day.
GREEN'S ECONOMIZER.— RESULTS OF EXPERIMENTS ON ITS EFFICIENCY AS
AFFECTED BY THE STATE OF THE SURFACE. (W. GrOSSCteSte.)
TIME
(February and March).
Temperature of Feed-
water.
Temperature of Gas-
eous Products.
Enter-
ing
Feed-
heater.
Leav-
ing
Feed-
heater.
Differ-
ence.
Enter-
ing
Feed-
heater.
Leav-
ing
Feed-
heater.
Differ-
ence.
1st Week
Fahr.
73.5°
77 0
Fahr.
161.5°
230 0
196.0
181 4
178.0
170.6
169 0
172.4
Fahr.
88.0°
153.0
122.6
108.0
99.0
90.0
88.4
93.4
Fahr.
849°
882
831
871
952
889
901
Fahr.
261°
297
284"
309
329~
338
351
Fahr.
588°
585
547
562
623~
551
550
2d Week
3d Week — Monday
73.4
73.4
79.0
80.6
80.6
79.0
Tuesday
Wednesday
Thursday
Friday
Saturday
1st Week. 2d Week. 3d Week.
Coal consumed per hour 214 Ibs. 216 Ibs. 2131bs»
Water evaporated from 32° F. per hour. . 1424 1525 1428
Water per pound of coal 6.65 7.06 6.70
It is apparent that there is a great advantage in cleaning the pipes daily
—the elevation of temperature having been increased by it from 88° to 153*.
In the third week, without cleaning, the elevation of temperature relapsed
in three days to the level of the first week; even on the first day it was
quickly reduced by as much as half the extent of relapse. By cleaning the
pipes daily an increased elevation of temperature of 65° FM was obtained,
whilst a gain of 6# was effected in the evaporative efficiency.
INCRUSTATION AND CORROSION.
Incrustation and Scale.— Incrustation (as distinguished from
mere sediments due to dirty water, which are easily blown out, or gathered
up, by means of sediment-collectors) is due to the presence of salts in the
feed-water (carbonates and sulphates of lime and magnesia for the most
part), which are precipitated when the water is heated, and form hard de-
posits upon the boiler-plates. (See Impurities in Water, p. 551, ante.)
Where the quantity of these salts is not very large (12 grains per gallon,
say) scale preventives may be found effective. The chemical preventives
either form with the salts other salts soluble in hot water; or precipitate
them in the form of soft mud, which does not adhere to the plates, and can
be washed out from time to time. The selection of the chemical must de-
pend upon the composition of the water, and it should be introduced regu-
larly with the feed.
EXAMPLES.— Sulphate-of -lime scale prevented by carbonate of soda: The
sulphate of soda produced is soluble in water; and the carbonate of lime
falls down in grains, does not adhere to the plates, and may therefore be
blown out or gathered into sediment- collectors. The chemical reaction is:
Sulphate of lime -f Carbonate of soda = Sulphate of soda 4- Carbonate of lime
CaSO4 Na2COs NaaSO4 CaCO8
Sodium phosphate will decompose the sulphates of lime and magnesia:
Sulphate of lime 4- Sodium phosphate = Calcium phos. + Sulphate of soda.
CaSO4 Na3HPO4 CaHPO4 Na2SO4
Sul.of magnesia-f Sodium phosphate = Phosphate of magnesi$-|-Sul. of soda.
MgSO« Na,HP04 MgHPO4 Na8SO4
INCRUSTATION AND CORROSION. 717
Where the quantity of salts 'is large, scale preventives are not of much
use. Some other source of supply must be sought, or the bad water purified
before it is allowed to enter the boilers. The damage done to boilers by un-
suitable water is enormous.
Pure water may be obtained by collecting rain, or condensing steam by
means of surface condensers. The water thus obtained should be mixed
with a little bad water, or treated with a little alkali, as undiluted, pure
water corrodes iron; or, after each periodic cleaning, the bad may be used
for a day or two to put a skin upon the plates.
Carbonate of lime and magnesia may be precipitated either by heating the
water or by mixing milk of lime (Porter Clark process) with it, the water
being then filtered.
Corrosion may be produced by the use of pure water, or by the presence
of acids in the water, caused perhaps in the engine-cylinder by the action of
high-pressure steam upon the grease, resulting in the production of fatty
acids. Acid water may be neutralized by the addition of lime.
Amount of Sediment which may collect in a 100-H.P. steam-boiler,
evaporating 3000 Ibs. of water per hour, the water containing different
amounts of impurity in solution, provided that no water is blown off:
Grains of solid impurities per U. S. gallon:
5 10 20 30 40 50 60 70 80 90 100
Equivalent parts per 100,000:
8.57 17.14 34.28 51.42 68.56 85.71 102.85 120 137.1 154.3 171.4
Sediment deposited in 1 hour, pounds:
.257 .514 1.028 1.542 2.056 2.571 3.085 3.6 4.11 4.63 5.14
In one day of 10 hours, pounds:
2.57 5.14 10.28 15.42 20.56 25.71 30.85 36.0 41.1 46.3 51.4
In one week of 6 days, pounds:
15.43 30.85 61.7 92.55 123.4 154.3 185.1 216.0 246.8 277.6 308.5
If a 100-H.P. boiler has 1200 sq. ft. heating-surface, one week's running
without blowing off, with water containing 100 grains of solid matter per
gallon in solution, would make a scale nearly .02 in. thick, if evenly depos-
ited all over the heating- surf ace, assuming the scale to have a sp. gr. of
2.5 = 156 Ibs. per cu. ft.; .02 X 1200 X 156 X 1/12 = 312 Ibs.
Boiler-scale Compounds.— The Bavarian Steam-boiler Inspection
Assn. in 1885 reporfcod as follows:
Generally the unusual substances in water can be retained in soluble form
or precipitated as mud by adding caustic soda or lime. This is especially
desirable when the boilers have small interior spaces.
It is necessary to have a chemical analysis of the water in order to fully
determine the kind and quantity of the preparation to be used for tho
above purpose.
All secret compounds for removing boiler-scale should be avoided. (A list
of 27 such compounds manufactured and sold by German firms is then given
which have been analyzed by the association.)
Such secret preparations are either nonsensical or fraudulent, or contaia
either one of the two substances recommended by the association for re-
moving scale, generally soda, which is colored to conceal its presence, and
sometimes adulterated with useless or even injurious matter.
These additions as well as giving the compound some strange, fanciful
name, are meant simply to deceive the boiler owner and conceal from him
the fact that he is buying colored soda or similar substances, for which he ia
paying an exorbitant price.
The Chicago, Milwaukee & St. P. R. R. uses for the prevention of scale in
locomotive-boilers an alkaline compound consisting of 3750 gals, of water,
2600 Ibs. of 70# caustic soda, and 1600 Ibs. of 58# soda-ash (Eng. News, Dec. 5,
1891).
Mr. H. E. Smith, chemist of the Ry. Co., writes May, 1902, that this com-
pound was abandoned several years ago and commercial soda-ash, known
as "58° soda," containing about 9?# pure carbonate of soda, substituted in
the water in the locomotive tender tanks, where it dissolves and passes to
the boiler. Its action is to precipitate a portion of the scale forming solids
in a flocculent form so that they are kept loose and free from the metal un-
til they can be blown or washed out.
The amounts used vary according to the character of the water and are
based on the following rules : For calcium and magnesium sulphates and
718 THE STEAM BOILER.
chlorides, use soda-ash equal to the chemical equivalent of those com*
pounds present. For calcium and magnesium carbonates, the amount of
soda-ash to be used varies from nothing when sulphates or chlorides are
high, up to about one fifth the equivalent of the carbonates, when sulphates
and chlorides are low or absent. A few waters contain carbonate of soda
originally, and for these less soda-ash or none at all is necessary. It may
also be necessary to make some reduction in the dose of soda-ash when
large amounts of other alkali salts are present. In any case it is not desir-
able to use more than 2 Ibs. of soda-ash per 1000 gallons of .water, or more
than 10 Ibs. per 100 miles of locomotive run, on account of the foaming pro-
duced. The above rule assumes that the boilers are fairly clean and are
kept fairly free from sludge by blowing and washing out. On the C., M. &
St. P. Ry. boilers are usually washed once in 500 to 2000 miles run, accord-
ing to the character of the waters used.
In the upper Mississippi valley the majority of the waters are below 20 or
25 grains of incrusting solids per gallon, and the greater portion of this is
carbonates. For these the above treatment is very successful. From 25 to
60 grains, increasing difficulty is encountered on account of foaming pro-
duced by the large amounts of sludge and alkali, and above 50 grains, soda-
ash alone fails to keep the boilers clean in practical service.
Kerosene and. other Petroleum Oils ; Foaming.— Kerosene
has recently been highly recommended as a scale preventive. 8ee paper by
L. F. Lyne(Trans. A. S. M. E., ix. 247). The Am. Mack., May 22, 1890, says: Ker-
osene used in moderate quantities will not make the boiler foam ; it is recom-
mended and used for loosening the scale and for preventing the formation of
scale. The presence of oil in combination with other impurities increases the
tendency of many boilers to foam, as the oil with the impurities impedes the
free escape of steam from the water surface. The use of common oil not only
tends to cause foaming, but is dangerous otherwise. The grease appears to
combine with the impurities of the water, and when the boiler is at rest this
compound sinks to the plates and clings to them in a loose, spongy mass, pre-
venting the water from coming in contact with the plates, and thereby pro-
ducing overheating, which may lead to an explosion. Foaming may also
be caused by forcing the fire, or by taking the steam from a point over the
furnace or where the ebullition is violent; the greasy and dirty state of nevr
boilers is another good cause for foaming. Kerosene should be used at firs*
.in small quantities, the effect carefully noted, and the quantity increased if
necessary for obtaining the desired results.
R. C. Carpenter (Trans. A. S. M. E., vol. xi.) says: The boilers of the Stata
Agricultural College at Lansing, Mich., were badly incrusted with a hard
scale. It was fully three eighths of an inch thick in many places. The first
application of the oil was made while the boilers were being but little used,
,by inserting a gallon of oil, filling with water, heating to the boiling-point
and allowing the water to stand in the boiler two or three weeks before
removal. By this method fully one half the scale was removed during the
warm season and before the boilers were needed for heavy firing. The oil
was then added in small quantities when the boiler was in actual use. For
boilers 4 ft. in diam. and 12 ft. long the best results were obtained by the
use of 2 qts. for each boiler per week, and for each boiler 5 ft. in diam. 8 qts.
per week. The water used in the boilers has the following analysis : CaCO3,
206 parts in a million; MgCO3, 78 parts; Fe2CO3, 22 parts; traces of sulphates
and chlorides of potash and soda. Total solids, 325 parts in 1,000,000.
Tannate of Soda Compound.— T. T. Parker writes to Am. Mach.:
Should you find kerosene not doing any good, try this recipe: 50 Ibs. sal-soda,
35 Ibs. japonica; put the ingredients in a 50-gal. barrel, fill half full of water,
and run a steam hose into it until it dissolves and boils. Remove the hose,
fill up with water, and allow to settle. Use one quart per day of ten hours
for a40-H.P. boiler, and, if possible, introduce it as you do cylinder- oil to
your engine. Barr recommends tannate of soda as a remedy for scale com-
posed of sulphate and carbonate of lime. As the japonica yields the tannic
acid, I think the resultant equivalent to the tannate of soda.
Petroleum Oils heavier than kerosene have been used with good re-
sults. Crude oil should never be used. The more volatile oils it contains
make explosive gases, and its tarry constituents are apt to form a spongy
incrustation.
Removal of Hard Scale.— When boilers are coated with a hard
scale difficult to remove the addition of % Ib. caustic soda per horse-power,
and steaming for some hours, according to the thickness of the scale, jusfc
before cleaning, will greatly facilitate that operation, rendering the scale
INCRUSTATION AND CORROSION. 719
soft and loose. This should be done, "if possible, when the boilers are not
otherwise in use. (Steam.)
Corrosion in Marine Boilers. (Proc. Inst. M. E., Aug. 1884).— -The
investigations of the Committee on Boilers served to show that the internal
corrosion of boilers is greatly due to the combined action of air and sea-
water when under steam, and when not under steam to the combined action
of air and moisture upon the unprotected surfaces of the metal. There are
other deleterious influences at work, such as the corrosive action of fatty
acids, the galvanic action of copper and brass, and the inequalities of tem-
perature; these latter, however, are considered to be of minor importance.
Of the several methods recommended for protecting the internal surfaces
of boilers, the three found most effectual are: First, the formation of a
thin layer of hard scale, deposited by working the boiler with sea-water;
second, the coating of the surfaces with a thin wash of Portland cement,
particularly Wherever there are signs of decay ; third, the use of zinc slabs
suspended in tne water ana steam spaces.
As to general treatment for the preservation of boilers in store or when
laid up in the reserve, either of the two following methods is adopted, as
may be found most suitable in particular cases. First, the boilers are
dried as much as possible by airing-stoves, after which 2 to 3 cwt. of quick-
lime, according to the size of the boiler, is placed on suitable trays at the
bottom of the boiler and on the tubes. The boiler is then closed and made
as air-tight as possible. Periodical inspection is made every six months,
when if the lime be found slacked it is renewed. Second, the other
method is to fill the boilers up with sea or fresh water, having added soda
to it in the proportion of 1 Ib. of soda to every 100 or 120 Ibs. of water. The
sufficiency of the saturation can be tested by introducing a piece of clean
new iron and leaving it in the boiler for ten or twelve hours; if it shows
signs of rusting, more soda should be added. It is essential that the boilers
be entirely filled, to the complete exclusion of air.
Great care is taken to prevent sudden changes of temperature in boilers.
Directions are given that steam shall not be raised rapidly, and that care
shall be taken to prevent a rush of cold air through the tubes by too sud-
denly opening the smoke-box doors. The practice of emptying boilers by
blowing out is also prohibited, except in cases of extreme urgency. As a
rule the water is allowed to remain until it becomes cool before the boilers
are emptied.
Mineral oil has for many years been exclusively used for internal lubrica-
tion of engines, with the view of avoiding the effects of fatty acid, as this oil
does not readily decompose and possesses no acid properties.
Of all the preservative methods adopted in the British service, the use of
zinc properly distributed and fixed has been found the most effectual in
saving the iron and steel surfaces from corrosion, and also in neutralizing;
by its own deterioration the hurtful influences met with in water as ordina-
rily supplied to boilers. The zinc slabs now used in the navy boilers are 12
in. long, 6 in. wide, and *4 mcn thick; this size being found convenient for
general application. The amount of zinc used in new boilers at present is
one slab of the above size for every 20 I.H.P., or about one square foot of
zinc surface to two square feet of grate surface. Rolled zinc is found the
most suitable for the purpose. To make the zinc properly efficient as a
protector especial care must be taken to insure perfect metallic contact
between the slabs and the stays or plates to which they are attached. The
slabs should be placed in such positions that all the surfaces in the boiler
shall be protected. Each slab should be periodically examined to see that
its connection remains perfect, and to renew any that may have decayed;
this examination is usually made at intervals not exceeding three months.
Under ordinary circumstances of working these zinc slabs may be expected
to last in fit condition from sixty to ninety days, immersed in hot sea- water;
but in new boilers they at first decay more rapidly. The slabs are generally
secured by means of iron straps 2 in. wide and % inch thick, and long
enough to reach the nearest stay, to which the strap is firmly attached by
screw-bolts.
To promote the proper care of boilers when not in use the following order
has been issued to the French Navy by the Government: On board all ships
in the reserve, as well as those which are laid up, the boilers will be com-
pletely filled with fresh water. In the case of large boilers with large tubes
there will be added to the water a certain amounts of milk of lime, or a
solution of soda may be used instead. In the case of tubulous boilers with
small tubes milk of lime or soda may be added, but the solution will not be
720
THE STEAM-BOILER,.
so strong as in the case of the larger tube, so as to avoid any danger of
contracting the effective area by deposit from the solution ; but the strength
of the solution will be just sufficient to neutralize any acidity of the water.
(Iron Age, Nov. 2, 1893.)
Use of Zinc.— Zinc is often used in boilers to prevent the corrosive
action of water on the metal. The action appears to be an electrical one,
the iron being one pole of the battery and the zinc being the other. The
hydrogen goes to the iron shell and escapes as a gas into the steam. The
oxygen goes to the zinc.
On account of this action it is generally believed that zinc will always
prevent corrosion, and that it cannot be harmful to the boiler or tank.
Some experiences go to disprove this belief, and in numerous cases zinc has
not only been of no use, but has even been harmful. In one case a tubular
boiler had been troubled with a deposit of scale consisting chiefly of or-
ganic matter and lime, and zinc was tried as a preventive. The beneficial
action of the zinc was so obvious that its continued use was advised, with
frequent opening of the boiler and cleaning out of detached scale until all
the old scale should be removed and the boiler become clean. Eight or ten
months later the water-supply was changed, it being now obtained from
another stream supposed to be free from lime and to contain only organic
matter. Two or three months after its introduction the tubes and shell
were found to be coated with an obstinate adhesive scale, and composed of
zinc oxide and the organic matter or sediment of the water used. The
deposit had become so heavy in places as to cause overheating and bulging
of the plates over the fire. (The Locomotive.)
K fleet of Deposit on Flues. (Rankine.)— An external crust of a
carbonaceous kind is often deposited from the flame and smoke of the fur-
naces in the flues and tubes, and if allowed to accumulate seriously impairs
the economy of fuel. It is removed from time to time by means of scrapers
and wire brushes. The accumulation of this crust is the probable cause of
the fact that in some steamships the consumption of coal per indicated
horse-power per hour goes on gradually increasing until it reaches one and
a half times its original amount, and sometimes more.
Dangerous Steam-boilers discovered by Inspection.—
The Hartford Steam-boiler Inspection and Insurance Co. reports that its
inspectors during 1893 examined 163,328 boilers, inspected 66,698 boilers,
both internally and externally, subjected 7861 to hydrostatic pressure, and
found 597 unsafe for further use. The whole number of defects reported
was 122,893, of which 12,390 were considered dangerous. A summary is
given below. (The Locomotive, Feb. 1894.)
SUMMARY, BY DEFECTS, FOR THE YEAR 1893.
• NatureofDefects.
Deposit of sediment ..... 9,774
Incrustation and scale ... 1 8,369
Internal grooving ..... 1,249
Internal corrosion ....... 6,252
External corrosion ....... 8,600
Deftive braces and stays 1,966
Settings defective ........ 3,094
Furnaces out of shape. . . 4,575
Fractured plates ......... 3,532
Burned plates ............ 2,762
Blistered plates .......... 3,331
Defective rivets ......... 17,415
Defective heads ......... 1,357
548
865
148
39'
536
485
352
254
640
325
164
1,569
350
Nature of Defects.
Whole Dan-
No, gerous.
Leakage around tubes. ..21,211 2,909
Leakage at seams (M24
Water-gauges defective. 3,670
Blow outs defective 1,620
Deficiency of water . 204
Safety-valves overloaded 723
Safety-valves defective.. 942
Pressure-gauges def'tive 5,953
Boilers without pressure-
gauges 115
Unclassified defects 755
660
425
107
203
300
552
115
4
Total 122,893 12,390
The above-named company publishes annually a classified list of boiler-
explosions, compiled chiefly from newspaper reports, showing that from
200 to 300 explosions take place in the United States every year, killing from
200 to 300 persons, and injuring from 300 to 450. The lists are not pretended
to be complete, and may include only a fraction of the actual number of
explosions.
Steam-boilers as Magazines of Explosive Energy.- Prof.
R. H. Thurston (Trans. A. S. M. E., vol. vi.), in a paper with the above
title, presents calculations showing the stored energy in the hot water and
steam of various boilers. Concerning the plain tubular boiler of the
form and dimensions adopted as a standard by the Hartford Steam-boiler
SAFETY-VALVES. 721
Insurance Co., he says: It is 60 inches in diameter, containing 66 3-inch
tubes, and is 15 feet long. It has 850 feet of heating and 30 feet of grate
surface; is rated at 60 horse-power, but isoftener driven up to 75; weighs
9500 pounds, and contains nearly its own weight of water, but only 21
pounds of steam when under a pressure of 75 pounds per square inch,
which is below its safe allowance. It stores 52,000,000 foot-pounds of en-
ergy, of which but 4 per cent is in the steam, and this is enough to drive
the boiler just about one mile into the air, with an initial velocity of nearly
600 feet per second.
SAFETY-VALVES.
Calculation of Weight, etc., for Lever Safety-valves.
Let W = weight of ball at end of lever, in pounds;
w = weight of lever itself, in pounds;
V — weight of valve and spindle, in pounds;
L = distance between fulcrum and centre of ball, in inches;
1= " " valve, in inches;
g = " '* " " gravity of lever, in in.;
A = area of valve, in square inches;
P = pressure of steam, in Ibs. per sq. in., at which valve will open.
Then PA X I = W X L + ivX 9 + V X i;
whence P = —
w_PAl-wg-Vlm
L
T PAl - wg - VI
~w •
EXAMPLE.— Diameter of valve, 4"; distance from fulcrum to centre of ball,
86"; to centre of valve, 4"; to centre of gravity of lever, 15^j"; weight of
valve and spindle, 3 Ibs.; weight of lever, 7 Ibs.; required the weight of ball
to make the bio wing-off pressure »0 Ibs. per sq. in.; area of 4" valve = 12.56fl
sq. in. Then
w_PAl-wg- n _ 80 X 12.566 X 4 - 7 X 15^ - 3 X 4 __m i lbg
L 36
The following rules governing the proportions of lever- valves are given by
the U. S. Supervisors. The distance from the fulcrum to the valve-stem
must in no case be less than the diameter of the valve-opening; the length
of the lever must not be more than ten times the distance from the fulcrum
to the valve-stem; the width of the bearings of the fulcrum must not be
less than three quarters of an inch; the length of the fulcrum-link must not
be less than four inches; the lever and fulcrum-link must be made of
wrought iron or steel, and the knife-edged fulcrum points and the bearings
for these points must be made of steel and hardened ; the valve must be
guided by its spindle, both above and below the ground seat and above the
lever, through supports either made of composition (gun-metal) or bushed
with it; and the spindle must fit loosely in the bearings or supports.
Rules for Area of Safety-valves.
(Rule of U. S. Supervising Inspectors of Steam-vessels (as amended 1891).)
Lever safety-valves to be attached to marine boilers shall have an area of
not less than 1 sq. in. to 2 sq. ft. of the grate surface in the boiler, and the
seats of all such safety-valves shall have an angle of inclination of 45° to the
centre line of their axes.
Spring-loaded safety-valves shall be required to have an area of not less
than 1 sq. in. to 3 sq. ft. of grate surface of the boiler, except as hereinafter
otherwise provided for water-tube or coil and sectional boilers, and each
spring-loaded valve shall be supplied with a lever that will raise the valve
from its seat a distance of not less than that equal to one eighth the diam-
eter of the valve-opening, and the seats of all such safety-valves shall have
an angle of inclination to the centre line of their axes of 45°. All spring-
loaded safety-valves for water-tube or coil and sectional boilers required to
722 THE STEAM-BOILER.
carry a steam -pressure exceeding 175 Ibs. per square inch shall be required
to have an area of not less than 1 sq. in. to 6 sq ft. of the grate surface of
the boiler. Nothing herein shall be construed so as to prohibit the use of
two safety-valves on one water- tube or coil and sectional boiler, provided
the combined area of such valves is equal to that required by rule for one
such valve.
Rule in Philadelphia Ordinances : Bureau of Steam-
engine and Boiler Inspection.— Every boiler when fired sepa-
rately, and every set or series of boilers when placed over one fire, shall
have attached thereto, without the interposition of any other valve, two or
more safety-valves, the aggregate area of which shall have such relations to
the area of the grate and the pressure within the boiler as is expressed in
schedule A.
SCHEDULE A.— Least aggregate area of safety-valve (being the least sec-
tional area for the discharge of steam) to be placed upon all stationary boil-
ers with natural or chimney draught [see note a].
22.5g
~ P+8.62'
in which A is area of combined safety-valves in inches; G is area of grate in
square feet; Pis pressure of steam in pounds per square inch to be carried
in the boiler above the atmosphere.
The following table gives the results of the formula for one square foot of
grate, as applied to boilers used at different pressures:
Pressures per square inch:
10 20 30 40 50 60 70 80 90 100 110 120
Area corresponding to one square foot of grate:
1.21 0.79 0.58 0.46 0.38 0.33 0.29 0.25 0.23 0.21 0.19 0.17
[Note a.] Where boilers have a forced or artificial draught, the inspector
must estimate the area of grate at the rate of one square foot of grate- sur-
face for each 16 Ibs. of fuel burned on the average per hour.
Comparison of Various Rules for Area of Lever Safety-
valves. (From an article by the author in American Machinist, May x:4,
1894, with some alterations and additions.)— Assume the case of a boiler
rated at 100 horse-power; 40 sq. ft. grate; 1200 sq. ft. heating-surface; using
400 Ibs. of coal per hour, or 10 Ibs. per sq. ft. of grate per hour, and evapora-
ting 3600 Ibs. of water, or 3 Ibs. per sq. ft. of heating-surface per hour;
steam-pressure by gauge, 100 Ibs. What size of safety-valve, of the lever
type, should be required ?
A compilation of various rules for finding the area of the safety-valve disk,
from The Locomotive of July, 1892, is given in abridged form below, to-
gether with the area calculated by each rule for the above example.
Disk Area in sq. in,
U. S. Supervisors, heating-surface in sq. f t. -f- 25 * 48
English Board of Trade, grate-surface in sq. ft. -r- 2 20
Molesworth, four fifths of grate-surface in sq. f t 32
Thurston, 4 times coal burned per hour X (gauge pressure -j- 10) 14.5
Thurston, 1 0 X heating-surtace) •
' 2 gauge pressure + 10
Rankine, .006 x water evaporated per hour 216
Committee of U. S. Supervisors, .005 X water evaporated per hour 18
Suppose that, other data remaining the same, the draught were increased
so as to burn 13^& Ibs. coal per square foot of grate per hour, and the grate-
surface cut down to 30 sq. ft. to correspond, making the coal burned per
hour 400 Ibs., and the water evaporated 3600 Ibs., the same as before: then
the English Board of Trade rule and Molesworth's rule would give an area
of disk of only 15 and 24 sq. in., respectively, showing the absurdity of mak-
ing the area of grate the basis of the calculation of disk area.
Another rule by Prof. Thurston is given in American Machinist. Dec. 1877.
viz.:
Disk area = ^ max- wt- <>f water evap. per hour
gauge pressure -f 10
This gives for the example considered 16.4 sq. in.
* The edition of 1893 of the Rules of the Supervisors does not contain this
rule, but gives the rule grate-surface -*- 2.
SAFETY-YALVES. 723
One rule by Ranldne is 1/150 to 1/180 of the number of pounds of water
evaporated per hour, equals for the above case 27 to 20 sq. in. A communi-
tion in Power, July, 1890, gives two other rules:
1st. 1 sq. iu. disk area for 3 sq. ft. grate, which would give 13.3 sq. in.
2d. ^ sq. iu. disk area for 1 sq. ft. grate, which would give 30 sq. in.; but
if the grate-surface were reduced to 30 sq. ft. on account of increased
draught, these rules would make the disk area only 10 and 22.5 sq. in.,
respectively.
The Philadelphia rule for 100 Ibs. gauge pressure gives a disk area of 0.21
sq. in. for each sq. ft. of grate area, which would give an area of 8.4 sq. in.
for 40 sq. ft. grate, and only 6.3 sq. in. if the grate is reduced to 30 sq. ft.
According to the rule this aggregate area would have to be divided between
two valves. But if the boiler was driven by forced draught, then the in-
spector "must estimate the area of grate at 1 sq. ft. for each 16 Ibs. of fuel
burned per hour."
Under this condition the actual grate-surface might be cut down to 400 -4-
16 = 25 sq. ft., and by the rule the combined area of the two safety-valves
would be only 25 X 0.21 = 5.25 sq. in.
Nystrom's Pocket-book, edition of 1891, gives % sq. in. for 1 sq. ft. grate;
also quoting from Weisbach, vol. ii, 1/3000 of the heating-surface. This in
the case considered is 1200/3000 = .4 sq. ft. or 57.6 sq. in.
We thus have rules which give for the area of safety-valve of the same 100-
horse-power boiler results ranging all the way from 5.25 to 57.6 sq. in.
All of the rules above quoted give the area of the disk of the valve as the
thing to be ascertained, and it is this area which is supposed to bear some
direct ratio to the grate-surface, to the heating-surface, to the water evap-
orated, etc. It is difficult to see why this area has been considered even
approximately proportional to these quantities, for with small lifts the area
of actual opening bears a direct ratio, not to tne area of disk, but to the
circumference.
Thus for various diameters of valve :
Diameter 1 2 3 41 *» 6 7
Area .785 3.14 7.07 12.57 19.64 28.27 38.48
Circumference 3.14 6.28 9.42 12.57 15171 18.85 21.99
Circum. X lift of 0.1 in.... .31 .63 .94 1.26 1.57 1.89 2.20
Ratio to area .4 .2 .13 .1 .08 .067 .057
The apertures, therefore, are therefore directly proportional to the diam-
eter or to the circumference, but their relation to the area is a varying one.
If the lift = 14 diameter, then the opening would be equal to the area of
the disk, for circumference X M diameter = area, but such a lift is far
beyond the actual lift of an ordinary safety-valve.
A correct rule for size of safety-valves should make the product of the
diameter and the lift proportional to the weight of steam to be discharged.
A " logical " method for calculating the size of safety-valve is given in
The Locomotive, July, 1892, based on the assumption that the actual opening
should be sufficient to discharge all the steam generated by the boiler.
Napier's rule for flow of steam is taken, viz., flow through aperture of one
sq in. in Ibs. per second = absolute pressure -f- 70, or in Ibs. per hour = 51.43
X absolute pressure.
If the angle of the seat is 45°, as specified in the rules of the U. S. Super-
visors, the area of opening in sq. in. = circumference of the disk X the lift
X .71, .71 being the cosine of 45°; or diameter of disk X lift X 2.23.
A. Gr. Brown in his book on The Indicator and its Practical Working
(London, 1894) gives the following as the lift of the ordinary lever safety-
valve for 100 Ibs. gauge-pressure:
Diam. of valve.. 2 2*4 3 3^ 4 4^ 5 6 inches.
Rise of valve 0583 .0523 .0507 .0492 .0478 .0462 .0446 .0430 inch.
The lift decreases with increase of steam -pressure; thus fora 4-inch valve:
Abs. pressure, Ibs. 45 65 85 105 115 135 155 175 195 215
Gauge-press., Ibs.. 30 50 70 90 100 120 140 160 180 200
Rise, inch 1034 .0775 .06:20 .0517 .0478 .0413 .0365 .0327 .0296 .0270
The effective area of opening Mr. Brown takes at 70$ of the rise multiplied
by the circumference.
An approximate formula corresponding to Mr. Brown's figures for diam-
eters between 2^£ and 6 in. and gauge-pressures between 70 and 200 Ibs. is
Lift = (.0603 - 0031d) X abs ^assure* in which d ~ dittm' of valve in in'
724
THE STEAM-BOILER.
If we combine this formula with the formulae
Flow inlbs. per hour = area of opening in sq. in.x 51.43X abs. pressure, and
Area = diameter of valve X lift X 2.23, we obtain the following, which the
author suggests as probably a more correct formula for the discharging
capacity of the ordinary lever safety-valve than either of those above given.
Flow in Ibs. per hour = d(.0603 - .0031d) X 115 X 2.23 X 51.43 = d(795 - 41d).
From which we obtain :
Diameter, inches.... 1 \V% 2 2^ 3 3^ 4 5 6 7
Flow, Ibs. per hour.. 754 1100 1426 1733 2016 2282 2524 2950 3294 3556
Horse-power 25 37 47 58 67 76 84 98 110 119
the horse-power being taken as an evaporation of 30 Ibs. of water per hour.
If we solve the example, above given, of the boiler evaporating 3600 Ibs. of
water per hour by this table, we find it requires one 7-inch valve, or a 2^
and a 3-inch valve combined. The 7-inch valve has an area of 38.5 sq. in.,
and the two smaller valves taken together have an area of only 12 sq. in.;
another evidence of the absurdity of considering the area of disk as the
factor which determined the capacity of the valve.
It is customary in practice not to use safety-valves of greater diameter
than 4 in. If a greater diameter is called for by the rule that is adopted,
then two or more valves are used instead of one.
Spring-loaded Safety-valves.— Instead of weights, springs are
sometimes employed to hold down safety-valves. The calculations are
similar to those for lever safety-valves, the tension of the spring correspond-
ing to a given rise being first found by experiment (see Springs, page 347).
The rules of the U. S. Supervisors allow an area of 1 sq. in. of the valve
to 3 sq. ft. of grate, in the case of spring-loaded valves, except in water-tube,
coil, or sectional boilers, in which 1 sq. in. to 6 sq. ft. of grate is allowed.
Spring-loaded safety-valves are usually of the reactionary or ** pop " type,
in which the escape of the steam is opposed by a lip above the valve-seat,
against which the escaping steam reacts, causing the valve to lift higher
than the ordinary valve.
A. G. Brown gives the following for the rise, effective area, and quantity
of steam discharged per hour by valves of the " pop " or Richardson type.
The effective is taken at only 50$ of the actual area due to the rise, on account
of the obstruction which the lip of the valve offers to the escape of steam.
Dia. valve, in.
1
\y^
2
2^
3
3^
4
4^
5
6
Lift, inches.
.125
.150
.175
200
.225
.250
.275
.300
.325
.375
Area, sq. in.
.196
.354
.550
>85
1.061
1.375
1.728
2.121
2.553
3.535
Gauge-pres.,
Steam discharged per hour, Ibs.
30 Ibs.
474
856
1330
1897
2563
3325
4178
5128
6173
8578
50
669
1209
1878
2680
3620
4695
5901
7242
8718
1207G
70
861
1556
2417
3450
4660
6144
7596
9324
11220
15535
90
1050
1897
2947
4207
5680
7370
9260
11365
13685
18945
100
1144
2065
3208
4580
6185
8322
10080
12375
14895
20625
120
1332
2405
3736
5332
7202
9342
11735
14410
17340
24015
140
1516
2738
4254
6070
8200
10635
13365
16405
19745
27310
160
1696
3064
4760
6794
9175
11900
14955
18355
22095
30595
180
1883
3400
5283
7540
10180
13250
16595
20370
24520
33950
200
2062
3724
5786
8258
11150
14465
18175
*2310
26855
37185
If we take 30 Ibs. of steam per hour, at 100 Ibs. gauge-pressure = 1 H.P.,
we have from the above table:
Diameter, inches... 1 1^ 2 2^ 3 3^ 4 4l£ 5 6
Horse-power 38 69 107 153 206 277 336 412 496 687
A safety-valve should be capable of discharging a much greater quantity
of steam than that corresponding to the rated horse-power of a boiler, since
a boiler having ample grate surface and strong draught may generate more
than double the quantity of steam its rating calls for.
The Consolidated Safety-valve Co.'s circular gives the following rated
capacity of its nickel-seat " pop " safety-valves:
Size, in 1 114 ly2 2 2^ 3 3^ 4 4^ 5 5^
Boiler j from 8 10 20 35 60 75 100 125 150 175 200
H.P. 1 to 10 15 30 50 75 100 125 150 175 200 275
The figures in the lower line from 2 inch to 5 inch, inclusive, correspond to
the formula H.P. = 50(diameter - t inch).
THE INJECTOR.
725
THE INJECTOR.
Equation oi the Injector.
Let Sbe the number of pounds of steam used;
W the number of pounds of water lifted and forced into the boiler;
h the height in feet of a column of water, equivalent to the absolute
pressure in the boiler;
7i0 the height in feet the water is lifted to the injector;
t ! the temperature of the water before it enters the injector;
#2 the temperature of the water after leaving the injector;
H the total heat above 32° F. in one pound of steam in the boiler, in
heat-units;
L the lost work in friction and the equivalent lost work due to radia-
tion and lost heat;
778 the mechanical equivalent of heat.
Then
S[H - (f , - 320)] m mt _ ti}
i
7 to
An equivalent formula, neglecting Wh0 -f- L as small, is
- 32°)'
or S = \
[H — (ty — &>°)]d — .I851p'
in which d = weight of 1 cu. ft. of water at temperature £a; p = absolute
pressure of steam, Ibs. per sq. in.
The rule for finding the proper sectional area for the narrowest part of
the- nozzles is given as follows by Rankine, S. E. p. 477:
Area in square inches = cubic feet per hour gross feed-water.
800 I/pressure in atmospheres
An important condition which must be fulfilled in order that the injector
will work is that the supply of water must be sufficient to condense the
steam. As the temperature of the supply or feed -water is higher, the
amount of water required for condensing purposes will be greater.
The table below gives the calculated value of the maximum ratio of water
to the steam, and the values obtained on actual trial, also the highest admis-
sible temperature of the feed-water as shown by theory and the highest
actually found by trial with several injectors.
Gauge -
pres-
sure,
pounds
per
sq. in.
MAXIMUM RATIO WATER
TO STEAM.
Gauge -
pres-
sure,
pounds
per
sq. in.
MAXIMUM TEMPERATURE OF
FEED -WATER.
Calculated
from
Theory.
Actual Expe-
riment.
Theoretical.
Experrtal Results.
Temp,
discharge
180°.
Temp,
discharge
212°.
H.
P.
M.
S.
H.
P.
M.
10
20
30
40
50
60
70
80
90
100
36.5
25.6
20.9
17.87
16.2
14.7
13.7
12.9
12.1
11.5
30.9
22.5
19.0
15.8
13.3
11.2
12.3
11.4
19i9
17.2
15.0
14.0
11.2
11.7
11.2
21 is'
19.0
15.86
13.3
12.6
12.9
10
20
30
40
50
60
70
80
90
100
120
150
132°
134
134
132
131
130
130
131
132*
132*
134*
121*
142°
132
126
120
114
109
105
99
95
87
77
173°
162
156
150
143
139
134
129
125
117
107
135°
i40*
120°
m
130°
125
141*
141*
115
m
123
123
122
* Temperature of delivery above 212°. Waste-valve closed.
II, Hancock inspirator; P, Park injector; M, Metronolitan injector; S, Sel-
lers 1876 injector.
726 THE STEAM-BOILER.
Efficiency of the Injector.— Experiments at Cornell University,
described by Prof. R. C. Carpenter, in Cassier's Magazine, Feb. 1892, show
that the injector, when considered merely as a pump, has an exceedingly
low efficiency, the duty ranging from 161,000 to 2,752,000 under different cir-
cumstances of steam and delivery pressure. Small direct-acting pumps,
such as are used for feeding boilers, show a duty of from 4 to 8
million Ibs., and the best pumping-engines from 100 to 140 million. When
used for feeding water into a boiler, however, the injector has a thermal
efficiency of 100#, less the trifling loss due to radiation, since all the heat re-
jected passes into the water which is carried into the boiler.
The loss of work in the injector due to friction reappears as heat which is
carried into the boiler, and the heat which is converted into useful work in
the injector appears in the boiler as stored-up energy.
Although the injector thus has a perfect efficiency as a boiler-feeder, it is
nevertheless not the most economical means for feeding a boiler, since it
can draw only cold or moderately warm water, while a pump can feed
water which has been heated by exhaust steam which would otherwise be
wasted.
Performance of Injectors.— In Am. Mach., April 13, 1893, are a
number of letters from different manufacturers of injectors in reply to the
question: ** What is the best performance of the injector in raising or lifting
water to any height ?" St>me of the replies are tabulated below.
W. Sellers & Co.— 25.51 Ibs. water delivered to boiler per Ib. of steam; tem-
perature of water, 64°; steam pressure, 65 Ibs.
Schaeffer & Budenberg— 1 gal. water delivered to boile** for 0.4 to 0.8 Ib.
steam.
Injector will lift by suction water of
140° F. 136° to 133° 122° to 118° 113° to 107°
If boiler pressure is . 30 to 60 Ibs. 60 to 90 Ibs. 90 to 120 Ibs. 120 to 150 Ibs.
If the water is not over 80° FM the injector will force against a pressure 75
Ibs. higher than that of the steam.
Hancock Inspirator Co.:
Lift in feet 22 22 22 11
Boiler pressure, absolute, Ibs 75 . 8 54 . 1 95 . 5 75 . 4
Temperature of suction 34.9° 35.4° 47.3° 53.2°
Temperature of delivery 134° 117.4° 173.7° 131.1
Water fed per Ib. of steam, Ibs... 11.02 13.67 8.18 13.3
The theory of the injector is discussed in Wood's. Peabody's, and Ront-
gen's treatises on Thermodynamics. See also "Theory and Practice of the
Injector,1' by Strickland L. Kneass, New York, 1895.
Boiler-feeding Pumps.— Since the direct-acting pump, commonly
4 used for feeding boilers, has a very low efficiency, or less than one tenth
that of a good engine, it is generally better to use a pump driven by belt
from the main engine or driving shaft. The mqchanical work needed to feed
a boiler may be estimated as follows: If the combination of boiler and en-
gine is such that half a cubic foot, say 32 Ibs. of water, is needed per horse-
power, and the boiler-pressure is 100 Ibs. per sq. in., then the work of feed-
ing the quantity of water is 100 Ibs. X 144 sq. in. X ^ ft.-lbs. per hour = 120
ft. -Ibs. per min. = 120/33,000 = .0036 H.P., or less than 4/10 of \% of the
power exerted by the engine. If a direct-acting pump, which discharges its
exhaust steam into the atmosphere, is used for feeding, and it has only 1/10
the efficiency of the main engine, then the steam used by the pump will be
equal to nearly 4fo of that generated by the boiler.
The following table by Prof. D. S. Jacobus gives the relative efficiency of
steam and power pumps and injector, with and without heater, as used
upon a boiler with 80 Ibs. gauge-pressure, the pump having a duty of
10,000,000 ft.-lbs. per 100 Ibs. of coal when no heater is used ; the injector
heating the water from 60° to 150° F.
Direct-acting pump feeding water at 60°, without a heater 1 .000
Injector feeding water at 150°, without a heater 985
Injector feeding water through a heater in which it is heated from
150°to20e° .938
Direct-acting pump feeding water through a heater, in which it is
heated from 60° to 200° 879
Geared pump, run from the engine, feeding water through a heater,
in which it is heated from 60° to 200« , 868
FEED-WATER HEATERS.
727
FEED-WATER HEATERS.
Percentage of Saving- for Eacli Degree of Increase in Tem-
perature of Feed-water Heated by Waste Steam.
Initial
Temp.
Pressure of Steam in Boiler, Ibs. per sq. in. above
Atmosphere.
Initial
of
Feed.
0
20
40
60
80
100
120
140
160
180
200
Temp.
32°
.0872
.0861
.0855
.0851
.0847
.0844
.0841
.0839
.0837
.0835
.0833
32
40
.0878
.0867
.0861
.0856
.0853
.0850
.0847
.0845
.0843
.0841
.0839
40
50
.0886
.0875
.0868
.0864
.0860
.0857
.0854
.0852
.0850
.0848
.0846
50
60
.0894
.0883
.0876
.0872
.0867
.0864
.0862
.0859
.0856
.0855
.0853
60
70
.0902
.0890
.0884
.0879
.0875
.0872 .0869
.0867
.0864
.0862
.0860
70
80
.0910
.0898
.0891
.0887
.0883
.0879 .0877
.0874
.0872
.0870
.0868
80
90
.0919
.0907
.0900
.0895
.0888
.0887
.0884
.0883
.0879
.0877
.0875
90
100
.0927
.0915
.0908
.0903
.0899
.0895
.0892
.0890
.0887
.0885
.0883
100
110
.0936
.0923
.0916
.0911
.0907
.0903
.0900
.0898
.0895
.0893
.0891
110
120
.0945
.0932
.0925
.0919
.0915
.0911
.0908
.0906
.0903
.0901
.0899
120
130
.0954
.0941
.0934
.0928
.0924
.0920
.0917
.0914
.0912
.0909
.0907
130
140
.0963
.0950
.0943
.0937
.0932
.0929
.0925
.0923
.0920
.0918
.0916
140
150
.0973
.0959
.0951
.0946
.0941
.0937
.0934
.0931
.0929
.0926
.0924
150
160
.0982
.0968
.0961
.0955
.0950
.0946
.0943
.0940
.0937
.0935
.0933
160
170
.0992
.0978
.0970
.0964
.0959
.0955
.0952
.0949
.0946
.0944
.0941
170
180
.1002
.0988
.0981
.0973
.0969
.0965
.0961
.0958
.0955
.0953
.0951
180
190
.1012
.0998
.0989
.0983
.0978
.0974
.0971
.0968
.0964
.0962
0960
190
200
.1022
.1008
.0999
.0993
.0988
.0984
.0980
.0977
.0974
.0972
.0969
200
210
.1033
.1018
.1009
.1003
.0998
.0994
.0990
.0987
.0984
.0981
.0979
210
220
.1029
.1019
.1013
.1008
.1004
.1000
.0997
.0994
.0991
.0989
220
230
.1039
.1031
.1024
.1018
.1012
.1010
.1007
.1003
.1001
.0999
230
240
.1050
.1041
.1034
.1029
.1024
.1020
.1017
.1014
.1011
.1009
240
250
.1062
.1052
.1045
.1040
.-1035
.1031
.1027
.1025
.1022
.1019
250
An approximate rule for the conditions of ordinary practice is a saving
of \% is made by each increase of 11° in the temperature of the feed-water.
This corresponds to .0909$ per degree.
The calculation of saving is made as follows: Boiler-pressure, 100 Ibs.
gauge; total heat in steam above 32° = 1185 B.T.U. Feed- water, original
temperature 60°, final temperature 209° F. Increase in heat-units, 150.
Heat-units above 32° in feed -water of original temperature = 28. Heat-
units in steam above that in cold feed-water, 1185 - 28 = 1157. Saving by the
feed- water heater = 150/1157 = 18.96*. The same result is obtained by the
use of the table. Increase in temperature 150° X tabular figure .0864 =
12.96*. Let total heat of 1 Ib. of steam at the boiler-pressure = H\ total
heat of 1 Ib. of feed-water before entering the heater = /i,, and after pass-
ing through the heater = A9; then the saving made by the heater is ' ~ \
Strains Caused by Cold Feed- water. —A calculation is mad«
in The Locomotive of March, 1893. of the possible strains caused in the sec-
tion of the shell of a boiler by cooling it by the injection of cold feed-water.
Assuming the plate to be cooled 200° F., and the coefficient of expansion of
steel to be .0000067 per degree, a strip 10 in. long would contract .013 in., if it
were free to contract, To resist this contraction, assuming that the strip is
firmly held at the ends and that the modulus of elasticity is 29,000,000, would
require a force of 37,700 Ibs. per sq. in. Of course this amount of strain can-
not actually take place, since the strip is not firmly held at the ends, but is
allowed to contract to some extent by the elasticity of the surrounding
metal. But, says The Locomotive, we may feel pretty confident that in the
case considered a longitudinal strain of somewhere in the neighborhood of
8000 or 10,000 Ibs. per sq. in. may be produced by the feed-water striking
directly upon the plates; and this, in addition to the normal strain pro-
duced by the steam-pressure, is quite enough to tax the girth-seams beyond
their elastic limit, if the feed-pipe discharges anywhere near them. Hence
it is not surprising that the girth-seams develop leaks and cracks in 99
cases out of every 100 in which the feed discharges directly upon the fire-
sheets.
728
THE STEAM-BOILER.
STEAM SEPARATORS.
If moist steam flowing at a high velocity in a pipe has its direction sud-
denly changed, the particles of water are by their momentum projected in
their original direction against the bend in the pipe or wall of the chamber
in which the change of direction takes place. By making proper provision
for drawing off the water thu? separated the steam may be dried to a
greater or less extent.
For long steam-pipes a large drum should be provided near the engine
for trapping the water condensed in the pipe. A drum 3 feet diameter, 15
feet high, has given good results in separating the water of condensation of
a steam-pipe 10 inches diameter and 800 feet long.
Efficiency of Steam Separators.— Prof. R. C. Carpenter, in 1891,
made a series of tests of six steam separators, furnishing them with steam
containing different percentages of moisture, and testing the quality of
steam before entering and after passing the separator. A condensed table
of the principal results is given below.
Make of
Separator.
Test with Steam of about 1Q# of
Moisture.
Tests with Varying Moisture.
Quality of
Steam
before.
Quality of
Steam
after.
Efficiency
per cent.
Quality of
Steam
before.
Quality of
Steam
after.
Av'ge
Effi-
ciency.
B
A
D
C
E
F
87.0£
90.1
89.6
90.6
88.4
88.9
98. 8#
98.0
95.8
93.7
90.2
92.1
90.8
80.0
59.6
33.0
15.5
28.8
66.1 to 97. 5#
51.9 98
72.2 96.1
67.1 96.8
68.6 98.1
70.4 97.7
97.8 to 99#
97.9 99.1
95,5 98.2
93.7 98.4
79.3 98.5
84.1 97.9
87.6
76.4
71.7
63.4
36.9
28.4
Conclusions from the tests were: 1. That no relation existed between the
volume of the several separators and their efficiency.
2. No marked decrease in pressure was shown by any of the separators,
the most being 1.7 Ibs. in E.
3. Although changed direction, reduced velocity, and perhaps centrifugal
force are necessary for good separation, still some means must be provided
to lead the water out of the current of the steam.
The high efficiency obtained from B and A was largely due to this feature.
In B the interior surf aces, are corrugated and thus catch the water thrown
out of the steam and readily lead it to the bottom.
In A, as soon as the water falls or is precipitated from the steam, it comes
in contact with the perforated diaphragm through which it runs into the
space below, where it is not subjected to the action of the steam.
Experiments made by Prof. Carpenter on a " btratton " separator in 1894
showed that the moisture in the steam leaving tLe separator was less than
\% when that in the steam supplied ranged from 6% to 2] %.
DETERMINATION OF THE MOISTURE IN STEAM-
STEAM CALORIMETERS.
In all boiler-tests it is important to ascertain the quality of the steam,
i.e., 1st, whether the steam is "saturated" or contains the quantity
. of heat due to the pressure according to standard experiments; 2d, whether
the quantity of heat is deficient, so that the steam is wet; and 3d. whether
the heat is in excess and the steam superheated. The best method of ascer-
taining the quality of the steam is undoubtedly that employed by a com-
mittee which tested the boilers at the American Institute Exhibition of
1871-2, of which Prof. Thurston was chairman, i.e., condensing all the water
evaporated by the boiler by means of a surface condenser, weighing the
condensing water, a> d taking its temperature as it enters and as it leaves
the condenser; but this plan cannot always be adopted.
A substitute for this method is the barrel calorimeter, which with careful
operation and fairly accurate instruments may generally be relied on to
give results within two per cent -of accuracy (that is, a sample of steam
which gives the apparent result of 2jC of moisture may contain anywhere be
tween 0 and 4jQ. This calorimeter is described as follows: A sample of the
steam is taken by inserting a perforated i^-inch pipe into and through the
main pipe near the boiler, and led by a hose, thoroughly felted, to a barrel,
holding preferably 400 Ibs. of wateri which is set upon a platform scale and
DETERMINATION OF THE MOISTURE IN STEAM. 729
provided with a cock or valve for allowing the water to flow to waste, and
with a small propeller for stirring the water.
To operate the calorimeter the barrel is filled with water, the weight and
temperature ascertained, steam blown through the hose outside the barrel
until the pipe is thoroughly warmed, when the hose is suddenly thrust into
the water, and the propeller operated until the temperature of the water is
increased to the desired point, say about 110° usually. The hose is then
withdrawn quickly, the temperature noted, and the weight again taken.
An error of 1/10 of a pound in weighing the condensed steam, or an error
of y% degree in the temperature, will cause an error of over \% in the calcu-
lated percentage of moisture. See Trans. A. S. M. E.. vi. 293.
The calculation of the percentage of moisture is made as below:
Q = quality of the steam, dry saturated steam being unity.
H = total heat of 1 Ib. of steam at the observed pressure.
T = " " " " ** water at the temperature of steam of the ob-
served pressure.
h — '• " " " " condensing water, original.
hi= " " " " " " final.
W = weight of condensing water, corrected for water-equivalent of the
apparatus.
w = weight of the steam condensed.
Percentage of moisture = 1 — Q.
If Q is greater than unity, the steam is superheated, and the degrees of
superheating = 2.0833 (H - T) (Q - 1).
Difficulty of Obtaining a Correct Sample.— Recent experiments
by Prof. D. S. Jacobus, Trans. A. S. M. E., xvi. 1017, show that it is practi-
cally impossible to obtain a true average sample of the steam flowing in a
pipe. For accurate determinations all the steam made by the boiler should
be passed through a separator, the water separated should be weighed, and
a calorimeter test made of the steam just after it has passed the separator.
Coil Calorimeters.— Instead of the open barrel in which the steam
is condensed, a coil acting as a surface-condenser may be used, which is
placed in the barrel, the water in coil and barrel being weighed separately.
For description of an apparatus of this kind designed by the author, which
he has found to give results with a probable error not exceeding ^ Per cent
of moisture, see Trans. A. S. M. E., vi. 294. This calorimeter may be used
continuously, if desired, instead of intermittently. In this case a continu-
ous flow of condensing water into and out of the barrel must be established,
and the temperature of inflow and outflow and of the condensed steam
read at short intervals of time.
Throttling Calorimeter.— For percentages of moisture not ex-
ceeding 3 per cent the throttling calorimeter is most useful and convenient
and remarkably accurate. In this instrument the steam which reaches it
in a i^-inch pipe is throttled by an orifice 1/16 inch diameter, opening into a
chamber which has an outlet to the atmosphere. The steam in this cham-
ber has its pressure reduced nearly or quite to the pressure of the atmos-
phere. but the total heat in the steam before throttling causes the steam in
the chamber to be superheated more or less according to whether the
steam before throttling was dry or contained moisture. The only observa-
tions required are those of the temperature and pressure of the steam on
each side of the orifice.
The author's formula for reducing the observations of the throttling
calorimeter is as follows (Experiments on Throttling Calorimeters, Am.
•TT _ h — JffT1 _ f}
Mach., Aug. 4, 1892) : w = 100 X — - r ' , in wnich w = percent-
_L/
age of moisture in the steam; H — total heat, and L = latent heat of steam
in the main pipe; h = total heat due the pressure in the discharge side of
the calorimeter, = 1146.6 at atmospheric pressure; K= specific heat of su-
perheated steam; T— temperature of the throttled and superheated steam
in the calorimeter; t = temperature due the pressure in the calorimeter,
= 212° at atmospheric pressure.
Taking K at 0.48 and the pressure in the discharge side of the calorimeter
as atmospheric pressure, the formula becomes
w = ,00 x H
Li
From this formula the following table is calculated :
730 THE STEAM-BOILER.
MOISTURE IN STEAM— DETERMINATIONS BY THROTTLING CALORIMETER.
1
5t»§»"
°l7
ijh
be
0>
Q
Gauge-pressures.
5
10
20
30
40
50
60
70
75
80
85
90
Per Cent of Moisture in Steam.
0°
10°
20°
30«
40°
50°
60°
70°
0.51
0.01
0.90
0.39
1.54
1.02
.51
.00
2.06
1.54
1.02
.50
2.50
1.97
1.45
.92
.30
2.90
2.36
1.83
1.30
.77
.24
3.24
2.71
2.17
1.64
1.10
.57
.03
3.56
3.02
2.48
1.94
1.40
.87
.38
3.71
3.17
2.63
2.09
1.55
1.01
.47
3.86
3 32
2.77
2.23
1.69
1.15
.60
.06
.0542
3.99
3.45
2.90
2.35
1.80
1.26
.72
.17
4.13
3.58
3.03
2.49
1.94
1.40
.85
.31
.0535
.0539
Dif.p.detr
.0503
.0507
.0515
.0521
.0526
.0531
.0544
.0546
Degree of Super-
heating
T- 212°.
Gauge-pressures.
100
110
120
130
140
150
160
170
180
190
200
250
Per Cent of Moisture in Steam.
0°
10°
20°
30°
40°
50°
60°
70°
80°
90°
100°
110°
4.39
3.84
3.29
2.74
2.19
1.64
1.09
.55
.00
4.63
4.08
3.52
2.97
2.42
1.87
1.32
.77
.22
4.85
4.29
3.74
3.18
2.63
2.08
1.52
.97
.42
5.08
4.52
3.96
3.41
2.85
2.29
1.74
1.18
.63
5 29
4.73
4.17
3.61
3.05
2.49
1.93
1.38
.82
5.49
4.93
4.37
3.80
3.24
2.68
2.12
1.56
1.00
5.68
5.12
4.56
3.99
3.43
2.87
2.30
1.74
1.18
5.87
5.30
4.74
4.17
3.61
3.04
2.48
1.91
1.34
6.05
5.48
4.91
4.34
3.78
3.21
2.64
2.07
1 50
6.22
5.65
5.08
4.51
3.94
3.37
2.80
2.23
1.-66
6.39
5.82
5.25
4.67
4.10
3.53
2.96
2.38
1.81
7.16
6.58
6.00
5.41
4 83
4.25
3.67
3.09
2.51
.07
.26
.44
.61
.05
.78
.21
.94
.37
1.09
.52
1.24
.67
.10
1.93
1.34
.76
Dif.p.deg
.0549
.0551
.0554
.0556
.0559
.0561
.0564
.0566
.0568
.0570
.0572
.0581
Separating Calorimeters.— For percentages of moisture beyond
the range of the throttling calorimeter the separating calorimeter is used,
which is simply a steam separator on a small scale. An improved form of
this calorimeter is described by Prof. Carpenter in Power, Feb. 1893.
For fuller information on various kinds of calorimeters, see papers by
Prof. Peabody, Prof. Carpenter, and Mr. Barrus in Trans. A. S. M. E., vols.
x, xi, xii, 1889 to 1891; Appendix to Report of Com. on Boiler Tests,
A. S. M. E., vol. yi, 1884; Circular of Schaeffer & Budenberg, N. Y., "Calo-
rimeters, Throttling and Separating," 1894.
Identification of Dry Steam by Appearance of a Jet. —
Prof. Dentoii (Trans. A. S. M. E., vol. x.) found that jets of steam show un-
mistakable change of appearance to the eye when steam varies less than \%
from the condition of saturation either in the direction of wetness or super-
heating.
If a jet of steam flow from a boiler into the atmosphere under circumstances
such that very little loss of heat occurs through radiation, etc., and the jet
be transparent close to the orifice, or be even a grayish-white color, the
steam may be assumed to be so nearly dry that no portable condensing
calorimeter will be capable of measuring the amount of water in the steam.
If the jet be strongly white, the amount of water may be roughly judged up
to about 2#, but beyond this a calorimeter only can determine the exaot
amount of moisture.
CHIMNEYS.
731
A common brass pet-cock may be used as an orifice, but it should, if possi-
ble, be set into the steam-drum of the boiler and never be placed further
away from the latter than 4 feet, and then only when the intermediate reser-
voir or pipe is well covered.
Usual Amount of Moisture in Steam Escaping from a
Boiler. — In the common forms of horizontal tubular land boilers and
water-tube boilers with ample horizontal drums, and supplied with water
free from substances likely to cause foaming, the moisture in the steam
does not generally exceed 2f0 unless the boiler is overdriven or the water-
level is carried too high.
CHIMNEYS.
Chimney Draught Theory.— The commonly accepted theory of
chimney draught, based on Peclet's and Rankine's hypotheses (see Rankine,
S. E.), is discussed by Prof. De Volson Wood in Trans. A. S. M. E., vol. xi.
Peclet represented the law of draught by the formula
in which h is the " head,1' defined as such a height of hot gases as, if added1
to the column of gases in the chimney, would produce the
same pressure at the furnace as a column of outside air, of the
same area of base, and a height equal to that of the chimney;
u is the required velocity of gases in the chimney;
G a constant to represent the resistance to the passage of air
through the coal ;
I the length of the flues and chimney;
HI the mean hydraulic depth or the area of a cross-section divi-
ded by the perimeter;
/ a constant depending upon the nature of the surfaces over which
the gases pass, whether smooth, or sooty and rough.
Rankine's formula (Steam Engine, p. 288), derived by giving certain values
to the constants (so-called) in Peclet's formula, is
H - H =
in which H — the height of the chimney in feet;
TO = 493° F., absolute (temperature of melting ice);
TJ = absolute temperature of the gases in the chimney;
T2 = absolute temperature of the external air.
Prof. Wood derives from this a still more complex formula which gives,
the height of chimney required for burning a given quantity of coal per
second, and from it he calculates the following table, showing the height of
chimney required to burn respectively 24, 20, and 16 Ibs. of coal per square
foot of grate per hour, for the several temperatures of the chimney gases
given.
Chimney Gas.
Coal per sq. ft. of grate per hour, Ibs.
Outside Air.
T2
T!
Absolute.
Temp.
Fahr.
24
20
16
Height H, feet.
520°
700
239
250.9
157.6
67.8
absolute or
59° F
800
1000
339
539
172.4
149.1
115.8
100.0
55.7
48.7
1100
639
148.8
98.9
48.2
1200
739
152.0
100.9
49.1
1400
939
159.9
105.7
51.2
1600
1139
168.8
111.0
53.5
2000
1539
206.5
132.2
63.0
732
CHIMNEYS.
Rankine's formula gives a maximum draught when T = 2 l/lSr,, or 622° FM
when the outside temperature is 60°. Prof. Wood says: " This result is not
a fixed value, but departures from theory in practice do not affect the result
largely. There is, then, in a properly constructed chimney, properly work-
ing, a temperature giving a maximum draught,* and that temperature is not
far from the value given by Rankine, although in special cases it may be 50°
or 75° more or less.1'
All attempts to base a practical formula for chimneys upon the theoret-
ical formula of Peclet and Rankine have failed on account of the impos-
sibility of assigning correct values to the so-called " constants " G and /.
(See Trans. A. S. M. E., xi. 984.)
Force or Intensity of Draught.— The force of the draught is equal
to the difference between the weight of the column of hot gases iuside of the
chimney and the weight of a column of the external air of the same height.
It is measured by a draught-gauge, usually a U-tube partly filled with water,
one leg connected by a pipe to the interior of the flue, and the other open to
the external air.
If D is the density of the air outside, d the density of the hot gas inside,
in Ibs. per cubic foot, h the height of the chimney in feet, and .192 the factor
for converting pressure in Ibs. per sq. ft. into inches of water column, then
the formula for the force of draught expressed in inches of water is,
F= .1927i(Z> - d).
The density varies with the absolute temperature (see Rankine).
d = ^0.084; £> = 0.0807^,
T! T2
where TO is the absolute temperature at 32° F.. = 493., rt the absolute tem-
perature of the chimney gases and T% that of the external air. Substituting
these values the formula for force of draught becomes
,= .
To find the maximum intensity of draught for any given chimney, the
heated column being 600° F., and the external air 60°, multiply the height
above grate in feet by .0073, and the product is the draught in inches of water.
Height of Water Column Due to Unbalanced Pressure in
Chimney 1OO Feet High. (The Locomotive,
e >-.
Is s
Temperature of the External Air— Barometer, 14.7 Ibs. per sq. in.
s**^ S
H 0
0°
10°
20°
30°
40°
50°
60°
70°
80°
90°
100°
200
.453
.419
'.384
.353
.321
.292
.263
.234
.209
.182
.157
220
.488
.453
.419
.388
.355
.326
.298
.269
.244
.217
.192
240
.520
.488
.451
.421
.388
.359
.330
.301
.276
.250
.225
260
.555
.528
.484
.453
.420
.392
.363
.334
.309
.283
.257
280
.584
.549
.515
.482
.451
.422
.394
.365
.340
.313
.288
300
.611
.576
.541
.511
.478
.449
.420
.392
.367
.340
.315
320
.637
.603
.568
.538
.505
.476
.447
.419
.394
.367
.342
340
.662
.638
.593
.563
.530
.501
.472
.443
.419
.392
.367
300
.687
.653
.618
.588
.555
.526
.497
.468
.444
.417
.392
380
.710
.676
.641
.611
.578
.549
.520
.492
.467
.440
.415
400
.732
.697
.662
.632
.593
.570
.541
.513
.488
.461
.436
420
.753
.718
.684
.653
.620
.591
.563
.534
.509
.482
.457
440
.774
.739
.705
.674
.641
.612
.584
.555
.530
.503
.478
460
.793
.758
.724
.694
.660
.632
.603
.574
.549
.522
.497
480
.810
.776
.741
.710
.678
.649
.620
.591
.566
.540
.515
500
.829
.791
.760
.730
.697
.669
.639
.610
.586
.559
.534
-• mucii comusipn 10 students or tne rneory or cmmneys nas resuneu iroin
their understanding the words maximum draught to mean maximum inten-
sity or pressure of draught, as measured by a draught-gauge. It here means
maximum quantity or weight of gases passed up the chimney. The maxi-
mum intensity is found only with maximum temperature, but after the
temperature reaches about 622° F. the density of the gas decreases more
rapidly than its velocity increases, so that the weight is a maximum about
622° F., as shown by Rankine.— W. K.
CHIMNEYS.
733
For any other height of chimney than 100 ft. the height of water- column
is found by simple proportion, the height of water column being directly
proportioned to the height of chimney.
The calculations have been made for a chimney 100 ft. high, with various
temperatures outside and inside of the flue, and on the supposition that the
temperature of the chimney is uniform from top to bottom. This is the
basis on which all calculations respecting the draught-power of chimneys
have been made by Rankine and other writers, but it is very far from the
i ruth in most cases. The difference will be shown by comparing the read-
ing of the draught-gauge with the table given. In one case a chimney 122 ft.
high showed a temperature at the base of 320°, and at the top of 230°.
Box, in his " Treatise on Heat,'1 gives the following table :
DRAUGHT POWERS OF CHIMNEYS, ETC., WITH THE INTERNAL AIR AT 552°, AND
THE EXTERNAL AIR AT 62°, AND WITH THE DAMPER NEARLY CLOSED.
Height of
Chimney in
feet.
Draught
Power in ins.
of water.
Theoretical Velocity
in feet per second.
Height of
Chimney in
feet.'
Draught
Power in ins.
of water.
Theoretical Velocity
in feet per second.
Cold Air
Entering.
Hot Air
at Exit.
Cold Ail-
Entering.
Hot Air
at Exit.
10
20
30
40
50
60
70
.073
.146
.219
.292
.365
.438
.511
17.8
25.3
31.0
35.7
40.0
43.8
47.3
35.6
50.6
62.0
71.4
80.0
87.6
94.6
80
90
100
120
150
175
200
.585
.657
.730
.876
1.095
1.877
1.460
50.6
53.7
56,5
62.0
69.3
74.3
80.0
101.2
107.4
113.0
124.0
138.6
149.6
160.0
Kate of Combustion Due to Height of* Chimney.—
Trowbridge's "Heat and Heat Engines*1 gives the following table showing
the heights of chimney for producing certain rates of combustion per sq.
ft. of section of the chimney. It may be approximately true for anthracite
in moderate and large sizes, but greater heights than are given in the table
are needed to secure the given rates of combustion with small sizes of
anthracite, and for bituminous coal smaller heights will suffice if the coal
is reasonably free from ash — 5$ or less.
Lbs. of Coal
Lbs. of Coal
Lbs. of Coal
Burned per
Lbs. of Coal
Burned per
Burned per
Sq. Ft. of
Burned per
Sq. Ft. of
Heights
in
Hour per
Sq. Ft.
Grate, the
Ratio of
Heights
in
Hour per
Sq. Ft.
Grate, the
Ratio of
feet.
of Section
Grate to Sec-
feet.
of Section
Grate to Sec-
of
tion of
of
tion of
Chimney.
Chimney be-
Chimney.
Chimney be-
ing 8 to 1.
ing 8 to 1.
20
60
7.5
70
126
15.8
25
68
8.5
75
131
16.4
30
76
9.5
80
135
16.9
35
84
10.5
85
139
17.4
40
93
11.6
90
144
18.0
45
99
12.4
95
148
18.5
50
105
13.1
100
152
19.0
55
111
13.8
105
156
19.5
60
116
14.5
110
160
200
65
121
15.1
Thurston's rule for rate of combustion effected by a given Height of chim-
ney (Trans. A. S. M. E., xi. 991) is: Subtract 1 from twice the square root of
the height, and the result is the rate of combustion in pounds per square foot
of grate per hour, for anthracite. Or rate = 2 \/h - \, in which h is the
height in feet. This rule gives the following:
fc= 50 60 70 80 90 100 110 125 150 175 200
2 \li - 1 = 13.14 14.49 15.73 16.89 17.97 19 19.97 21.36 23.49 25.46 27.23
The results agree closely with Trowbridge's table given above, In prac-
734
CHIMNEYS.
tice the high rates of combustion for high chimneys given by the formula
are not generally obtained, for the reason that with high chimneys there are
usually long horizontal flues, serving many boilers, and the friction and the
interference of currents from the several boilers are apt to cause the inten^
sity of draught in the branch flues leading to each boiler to be much less
than that at the base of the chimney. The draught of each boiler is also
usually restricted by a damper and by bends in the gas-passages. In a bat-
tery of several boilers connected to a chimney 150 ft. high, the author found
a draught of %-inch water-column at the boiler nearest the chimney, and
only ^4-inch at the boiler farthest away. The first boiler was wasting fuel
from too high temperature of the chimney-gases, 9uO°, having too large a
grate-surface for the draught, and the last boiler was working below ita
rated capacity and with poor economy, on account of insufficient draught.
The effect of changing the length of the flue leading into a chimney 60 ft.
high and 2 ft. 9 in. square is given in the following table, from Box on
44 Heat":
Length of Flue in
feet.
Horse-power.
Length of Flue in
feet.
Horse-power.
50 .
100
200
400
600
107.6
100.0
85.3
70.8
62.5
800
1,000
1,500
2,000
3,000
56.1
51.4
43.3
38.2
31.7
The temperature of the gases in this chimney was assumed to be 552° F.,
and that of the atmosphere 62°.
High Chimneys not Necessary.— Chimneys above 150 ft. in height
are very costly, and their increased cost is rarely justified by increased e£
ficiency. In recent practice it has become somewhat common to build tyvo or
more smaller chimneys instead of one large one. A notable example is the
Spreckels Sugar Refinery in Philadelphia, where three separate chimneys are
used for one boiler-plant of 7500 H.P. The three chimneys are said to have
cost several thousand dollars less than a single chimney of their combined
capacity would have cost. Very tall chimneys have been characterized by
one writer as " monuments to the folly of their builders.1"
Heights of Chimney required for Different Fuels.— The
minimum height necessary varies with the fuel, wood requiring the least,
then good bituminous coal, and fine sizes o" anthracite the greatest. It
also varies with the character of the boiler— the smaller and more circuitous
the gas-passages the higher the stack required; also with the number of
boilers, a single boiler requiring less height than several that discharge
into a horizontal flue. No general rule can be given.
SIZE OF CHIMNEYS.
The formula given below, and the table calculated therefrom for chimneys
up to 96 in. diameter and 200 ft. high, were first published by the author
in 1884 (Trans. A. S. M. E. vi., 81). They have met with much approval
since that date by engineers who have used them, and have been frequently
published in boiler-makers' catalogues and elsewhere. The table is now
extended to cover chimneys up to 12 ft. diameter and 300 ft. high. The sizes
corresponding to the given commercial horse-powers are believed to be
ample for all cases in which the draught areas through the boiler-flues and
connections are sufficient, say not less than 20# greater than the area of the
chimney, and in which the draught between the boilers and chimney is not
checked by long horizontal passages and right-angled bends.
Note that the figures in the table correspond to a coal consumption of 5 Ibs.
of coal per horse-power per liour. This liberal allowance is made to cover
the contingencies of poor coal being used, and of the boilers being driven
beyond their rated capacity. In large plants, with economical boilers and
engines, good fuel and other favorable conditions, which will reduce tiia
maximum rate of coal consumption at any one time to less than 5 Ibs. per
H. P. per hour, the figures in the table may be multiplied by the ratio of 5 to
the maximum expected coal consumption per H.P. per hour. Thus, with
conditions which make the maximum coal consumption only 2.5 Ibs. per
hour, the chimney 300 ft. high X 12 ft. diameter should be sufficient for 6155
X 3 = 12,310 horse-power. The formula is based on the following data ;
SIZE OF CHIMNEYS.
735
• .
I ETC 3
gScM .3
Pill
35V
IS
*5ss s^is B3331
siii ills 1111
SSI E8S1
5S 28 :
$< ^
•03
S!
2S83
736 CHIMKEYS.
1. The draught power of the chimney varies as the square root of the
height.
2. The retarding of the ascending gases by friction may be considered as
equivalent to a diminution of the area of the chimney, or to a lining of the
chimney by a layer of gas which has no velocity. The thickness of this
lining is assumed to be 2 inches for all chimneys, or the diminution of area
equal to the perimeter X 2 inches (neglecting the overlapping of the corners
of the lining). Let D — diameter in feet, A = area, and E = effective area
In square feet.
For square chimneys, E = D* — -=-^= A — ^ ^A.
For round chimeys, E = £ (l)a - ~) =A- 0.591 |/Z
For simplifying calculations, the coefficient of |/Z may be taken as 0.6
for both square and round chimneys, and the formula becomes
E = A - 0.6 4/Z
3. The power varies directly as this effective area E.
4. A chimney should be proportioned so as to be capable of giving sufficient
draught to cause the boiler to develop much more than its rated power, in
case of emergencies, or to cause the combustion of 5 Ibs. of fuel per rated
horse-power of boiler per hour.
5. Tne power of the chimney varying directly as the effective area, E, and
as the square root of the height, H, the formula for horse-power of boiler for
a given size of chimney will take the form H.P. = CE \/H, in which C is a
constant, the average value of which, obtained by plotting the results
obtained from numerous examples in practice, the author finds to be 3.33.
The formula for horse-power then is
H.P. = 3.33# VH, or H.P. = 3.33U - .6 4/5) 4/Jff.
If the horse-power of boiler is given, to find the size of chimney, the height
being assumed,
For round chimneys, diameter of chimney = diam. of E-\- 4".
For square chimneys, side of chimney = ^E-}- 4".
If effective area E is taken in square feet, the diameter in inches is d =
13.54 yE + 4", and the side of a square chimney in inches is s = 12 \Sj5-\-4".
xn o TJ T> \ 2
If horse-power is given and area assumed, the height H = ( -1— w — ' ) •
In proportioning chimneys the height is generally first assumed, with due
consideration to the heights of surrounding buildings or hills near to the
proposed chimney, the length of horizontal flues, the character of coal to be
used, etc., and then the diameter required for the assumed height and
horse-power is calculated by ihe formula or taken from the table.
An approximate formula for chimneys above 1000 H.P. is H.P. :=
2^£ D2 VH. This gives the H.P. somewhat greater than the figures in the
table.
The Protection of TalT Chimney-shafts from Lightning.
— C. Molyneux and J. M. Wood (Industries, March 28, 1890) recommend for
tall chimneys the use of a coronal or heavy band at the top of the chimney,
with copper points 1 ft. in height at intervals of 2 ft. throughout the circum-
ference. The points should be gilded to prevent oxidation. The most ap-
proved form of conductor is a copper tape about % in. by % in. thick,
weighing 6 ozs. per ft. If iron is used it should weigh not less than 2J4 Ibs.
per ft. There must be no insulation, and the copper tape should be fastened
to the chimney with holdfasts of the same material, to prevent voltaic
action. An allowance for expansion and contraction should be made, say 1
in. in 40 ft. Slight bends in the tape, not too abrupt, answer the purpose.
For an earth terminal a plate of metal at least 3 ft. sq. and 1/16 in. thick
should be buried as deep as possible in a, damp spot. The plate should be of
the same metal as the conductor, to which it should be soldered. The best.
earth terminal is water, and when a deep well or other large body of water
is at hand, the conductor should be carried down into it. Right-angled
bends in the conductor should be avoided. No bend in it should be over 30".
SIZE OF CHIMNEYS.
737
Some Tall If rick Chimneys.
i
4>
w
Internal Diam.
Outside
Diameter.
Capacity by the
Author's
Formula.
i
&
H
H. P.
Pounds
Coal
pei-
hour.
1. Hallsbruckner Hiitte, Sax.
2. Townsend's, Glasgow.. ..
3. Tennant's, Glasgow
4. Dobson & Barlow, Bolton,
Eng
460
454
435.
36?^
350
335
282'9"
250
250
238
214
200
150
15.7'
'"iVe""
13' 2"
11
11
12
10
10
14
8
9
50" x 120"
33'
32
40
33'10"
30
28' 6"
16'
21
14
each
13,221
9,795
8,245
5,558
5,435
5,980
3,839
3,839
7,515
2,248
2,771
1,541
66,105
48,975
, 41,225
. 2?, 790
27,175
29,900
19,195
19,195
37,575
11,240
13,855
7,705
5. Fall River Irou Co., Boston
6. Clark Thread Co., Newark,
N J
7. Merrimac Mills, Low'l, Mass
8. Washington Mills, Law-
rence Mass . .
9. Amoskeag Mills, Manches-
ter N H
10. Narragansett E. L. Co.,
Providence R I
11. Lower Pacific Mills, Law-
rence Mass
12. Passaic Print Works, Pas-
saic N J
13. Edison Sta,B'klyn, Two e'ch
NOTES ON THE ABOVE CHIMNEYS.—!. This chimney is situated near
Freiberg, on the right bank of the Mulde, at an elevation of 219 feet above
that of the foundry works, so that its total height above the sea will be 711%
feet. The works are situated on the bank of the river, and the furnace-
gases are conveyed across the river to the chimney on a bridge, through a
pipe 3227 feet in length. It is built throughout of brick, and will cost about
$,40,000.— Mfr. and Bldr.
2. Owing to the fact that it was struck by lightning, and somewhat
damaged, as a precautionary measure a copper extension subsequently was
added to it, making its entire height 488 feet.
1, 2, 3, and 4 \vere built of these great heights to remove deleterious
gases from the neighborhood, as well as for draught for boilers.
5. The structure rests on a solid granite foundation, 55 X 30 feet, and
16 feet deep. In its construction there were used 1,700,000 bricks. 2000 tons
of stone, 2000 barrels of mortar, 1000 loads of sand, 1000 barrels of Portland
cement, and the estimated cost is $40,000. It is arranged for two flues, 9
feet 6 inches by 6 feet, connecting with 40 boilers, which are to be run in
connection with four triple-expansion engines of 1350 horse-power each.
6. It has a uniform batter of 2.85 inches to every 10 feet. Designed
for 21 boilers of 200 H. P. each. It is surmounted by a cast-iron cop-
ing which weighs six tons, and is composed of thirty-two sections,
which are bolted together by inside flanges, so as to present a smooth
exterior. The foundation is in concrete, composed of crushed lime-
stone 6 parts, sand 3 parts, and Portland cement 1 part. It is 40 feet
square and 5 feet doep. Two qualities of brick were used; the outer
portions were of the first quality North River, and the backing up was of
good quality New Jersey brick. Every twenty feet in vertical measurement
an iron ring, 4 inches wide and % to ^ inch thick, placed edgewise, was
built into the walls about 8 inches from the outer circle. As the chimney
starts from the base it is double. The outer wall is 5 feet 2 inches in thick-
ness, and inside of this is a second wall 20 inches thick and spaced off about
20 inches from main wall. From the interior surface of the main wall eight
buttresses are carried, nearly touching this inner or main flue wall in
order to keep it in line should it tend to sag. The interior wall, starting
with the thickness described, is gradually reduced until a height of about
90 feet is reached, when it is diminished to 8 inches. At 165 feet it ceases,
73b CHIMKEY8.
and the rest of the chimney is without lining. The total weight of the chinv
ney and foundation is 5000 tons. It was completed in September, 1888.
7. Connected to 12 boilers, with 1200 square feet of grate-surface. Draught-
gauge 1 9/16 inches.
8. Connected to 8 boilers, 6' 8" diameter X 18 feet Grate-surface 448
square feet.
9. Connected to 64 Manning vertical boilers, total grate surface 1810 sq. ft.
Designed to burn 18,000 Ibs. anthracite per hour.
10. Designed for 12,000 H. P. of engines; (compound condensing).
11. Grate-surface 434 square feet; H.P. of boilers (Galloway) about 2500.
13. Eight boilers (water-tube) each 450 H.P. ; 13 engines, each 300 H.P. Plant
designed for 36,000 incandescent lights. For the first 60 feet the exterior
wall is 28 inches thick, then 24 inches for 20 feet, 20 inches for 30 feet, 16
inches for 20 feet, and 12 inches for 20 feet. The interior wall is 9 inches
thick of fire-brick for 50 feet, and then 8 inches thick of red brick for the
next 30 feet. Illustrated in Iron Age, January 2, 1890.
A number of the above chimneys are illustrated in Power, Dec., 1890.
Chimney at Knoxville, Tenn., illustrated in Eng'gNetos, Nov. 2, 1893.
3 feet diameter, 120 feet high, double wall:
Exterior wall, height 20 feet, 30 feet, 80 feet, 40 feet;
44 " thickness 21^ in., 17 in., 13 in,, 814 in.;
Interior wall, height 85 ft., 35 ft., 29ft., 21ft.;
44 thickness 13^ in., 8J4 in., 4 in., 0.
Exterior diameter, 15' 6" at bottom ; batter, 7/16 inch in 12 inches from bot-
tom to 8 feet from top. Interior diameter of inside wall, 6 feet uniform to
top of interior wall. Space between walls, 16 inches at bottom, diminishing
to 0 at top of interior wall. The interior wall is of red brick except a lining
of 4 inches of fire-brick for 20 feet from bottom,
Stability Of Chimneys.— Chimneys must be designed to resist the
maximum force of the wind in the locality in which they are built, (see
Weak Chimneys, below). A general rule for diameter of base, of brick
chimneys, approved by many years of practice in England and the United
States, is to make the diameter of the base one tenth of the height. If the
chimney is square or rectangular, make the diameter of the inscribed circle
of the base one tenth of the height. The '* batter " or taper of a chimney
should be from 1/16 to *4 inch to the foot on each side. The brickwork
should be one brick (8 or 9 inches) thick for the first 25 feet from the top, in-
creasing 1& brick (4 or 4*4 inches) for each 25 feet from the top downwards.
If the inside diameter exceed 5 feet, the top length should be 1^ bricks; and
if under 3 feet, it may be ^ brick for ten feet.
(From Hie Locomotive, 1884 and 1886.) For chimneys of four feet in diam-
eter and one hundred feet high, and upwards, the best form is circular, with
a straight batter on the outside. A circular chimney of this size, in addition
to being cheaper than any other form, is lighter, stronger, and looks much
better and more shapely.
Chimneys of any considerable height are not built up of uniform thickness
from top to bottom, nor with a uniformly varying thickness of wall, but the
wall, heaviest of course at the base, is reduced by a series of steps.
Where practicable the load on a chimney foundation should not exceed two
tons per square foot in compact sand, gravel, or loam. Where a solid rock-
bottom is available for foundation, the load may be greatly increased. If
the rock is sloping, all unsound portions should be removed, and the face
dressed to a series of horizontal steps, so that there shall be no tendency to
slide after the structure is finished.
All boiler-chimneys of any considerable size should consist of an outer
stack of sufficient strength to give stability to the structure, and an inner
stack or core independent of the outer one. This core is by many engineers
extended up to a height of but 50 or 60 feet from the base of the chimney,
but the better practice is to run it up the whole height of the chimney; it
may be stopped off, say, a couple feet below the top, and the outer shell con-
tracted to the area of the core, but the better way is to run it up to about 8
or 12 inches of the top and not contract the outer shell. But under no cir-
cumstances should the core at its upper end be built into or connected with
the outei stack. This has been done in several instances by bricklayers, and
the result has been the expansion of the inner core which lifted the top of
the outer stack squarely up and ere eked the brickwork.
For a height of 100 feet we would make the outer shell in three steps, the
first 30 feet high, 16 inches thick, the second 30 feet high, 12 inches thick, the
SIZE OF CHIMNEYS. 739
third 50 feet high and 8 inches thick. These are the minimum thicknesses
admissible for chimneys of this height, and the batter should be not less
than 1 in 36 to give stability. The core should also be built in three steps,
each of which may be about one-third the height of the chimney, the lowest
12 inches, the middle 8 inches, and the upper step 4 inches thick. This will
insure a good sound core. The top of a chimney may be protected by a
cast-iron cap; or perhaps a cheaper and equally good plan is to lay the
ornamental part in some good cement, and plaster the top with the same
material.
Weak Chimneys.— James B. Francis, in a report to the Lawrence
Mfg. Co. in 1873 (Eng'g News, Au&. 28, 1880), gives some calculations con-
cerning the probable effects of wind on that company's chimney as then
constructed. Its outer shell is octagonal. The inner shell is cylindrical,
with an air-space between it and the outer shell; the two shells not being
bonded together, except at the openings at the base, but with projections in
the brickwork, at intervals of about 20 ft. in height, to afford lateral sup-
port by contact of the two shells. The principal dimensions of the chimney
are as follows :
Height above the surface of the ground 211 ft.
Diameter of the inscribed circle of the octagon near the ground . 15 •'
Diameter of the inscribed circle of the octagon near the top. . . , 10 ft.
Thickness of the outer shell near the base, 6 bricks, or 23^ in.
Thickness of the outer shell near the top, 3 bricks, or llj^ "
Thickness of the inner shell near the base, 4 bricks, or 15 "
Thickness of the inner shell near the top, 1 brick, or 3% "
One tenth of the height for the diameter of the base is the rule commonly
adopted. The diameter of the inscribed circle of the base of the Lawrence
Manufacturing Company's chimney being 15 ft., it is evidently much less
than is usual in a chimney of that height.
Soon after the chimney was built, and before the mortar had hardened, it
was found that the top had swayed over about 29 in. toward the east. This
was evidently due to a strong westerly wind which occurred at that time.
It was soon brought back to the perpendicular by sawing into some of the
joints, and other means.
The stability of the chimney to resist the force of the wind depends mainly
on the weight of its outer shell, and the width of its base. The cohesion of
the mortar may add considerably to its strength; but it is too uncertain to
be relied upon. The inner shell will add a little to the stability, but it may
be cracked by the heat, and its beneficial effect, if any, is too uncertain to
be taken into account.
The effect of the joint action of the vertical pressure due to the weight of
the chimney, and the horizontal pressure due to the force of the wind is to
shift the centre of pressure at the base of the chimney, from the axis to-
wrard one side, the extent of the shifting depending on the relative magni-
tude of the two forces. If the centre of pressure is brought too near the
side of the chimney, it will crush the brickwork on that side, and the chim-
ney will fall. A line drawn through the centre of pressure, perpendicular to
the direction of the wind, must leave an area of brickwork between it and
the side of the chimney, sufficient to support half the weight of the chim-
ney; the other half of the weight being supported by the brickwork on the
windward side of the line.
Different experimenters on the strength of brickwork give very different
results. Kirkaldy found the weights which caused several kinds' of bricks,
laid in hydraulic lime mortar and in Roman and Portland cements, to fail
slightly, to vary from 19 to 60 tons (of 2000 Ibs.) per sq. ft. If we take in this
case 25 tons per sq. ft., as the weight that would cause it to begin to fail, we
shall not err greatly. To support half the weight of the outer shell of the
chimney, or 322 tons, at this rate, requires an area of 12.88 sq. ft. of brick-
work. From these data and the drawings of the chimney, Mr. Francis cal-
culates that the area of 12.88 sq. ft. is contained in a portion of the chimney
extending 2. 428 ft. from one or its octagonal sides, and that the limit to
which the centre of pressure may be shifted is therefore 5.072 ft. from the
axis. If shifted beyond this, he says, on the assumption of the strength
of the brickwork, it will crush and the chimney will fall.
Calculating that the wind-pressure can affect only the upper 141 ft. of the
chimney, the lower 70 ft. being protected by buildings, he calculates that a
wind-pressure of 44 02 Ibs. per sq. ft. would blow the chimney down.
Bankiue, m a paper printed iu the transactions of the Institution of Engi*
740
CHIMNEYS.
neers, in Scotland, for 1867-68, says: "It had previously been ascertained
by observation of the success and failure of actual chimneys, and especially
of those which respectively stood and fell during the violent storms of 1856,
that, in order that a rc'^nd chimney may be sufficiently stable, its weight
should be such that a pressure of wind, of about 55 Ibs. per sq. ft. of a plane
surface, directly facing the wind, or 27l/& Ibs. per sq. ft. of the plane projec-
tion of a cylindrical surface, . . . shall not cause the resultant pressure
at any bed-joint to deviate from the axis of the chimney by more than one
quarter of the outside diameter at that joint,"
According to Eankine's rule, the Lawrence Mfg. Co/s chimney is adapted
to a maximum pressure of wind on a plane acting on the whole height of
18.80 Ibs. per sq. ft., or of a pressure of 21 .70 Ibs. per sq. ft. acting on the
uppermost 141 ft. of the chimney.
Steel Chimneys are largely coming into use, especially for tall chim-
neys of iron-works, from 150 to 300 feet in height. The advantages claimed
are: greater strength and safety; smaller space required; smaller cost, by
30 to 50 per cent, as compared with brick chimneys; avoidance of infiltra'
tion of air and consequent checking of the draught, common in brick chim-
neys. They are usually made cylindrical in shape, with a wide curved flare
for 10 to 25 feet at the bottom. A heavy cast-iron base-plate is provided, to
which the chimney is riveted, and the plate is secured to a massive founda-
tion by holding-down bolts. No guys are used. F. W. Gordon, of the Phila.
Engineering Works, gives the following method of calculating their resist-
ance to wind pressure (Pcwer, Oct. 1893) :
In tests by Sir William Fairbairn we find four experiments to determine
the strength of thin hollow tubes. In the table will be found their elements,
with their breaking strain. These tubes were placed upon hollow blocks,
and the weights suspended at the centre from a block fitted to the inside of
the tube.
I.
II.
III.
IV.
Clear
Span,
ft. in.
Thick-
ness Iron,
in.
Outside
Diame-
ter, in.
Sectional
Area,
in.
Breaking
Weight,
Ibs.
Breaking W't,
lbs.,byClarke'e
Formula,
Constant 1.2.
17
15 7^
23 5
23 5
.037
.113
.0631
.119
12
12.4
17.68
18.18
1.8901
4.3669
8.487
6.74
2,704
11,440
6,400
14,240
2,627
9,184
7,302
13,910
Edwin Clarke has formulated a rule from experiments conducted by him
during his investigations into the use of iron and steel for hollow tube
bridges, which is as follows :
Center break- ) ._ Area of material in sq.in. x Mean depth in in. X Constant
Ing load, in tons. ) ~~" Clear span in feet.
When the constant used is 1.2, the calculation for the tubes experimented
upon by Mr. Fairbairn are given in the last column of the table. D. 1C
Clark's " Rules, Tables, and Data," page 513, gives a rule for hollow tubes
as follows : W= 3.14D*TS -*-L. Ws: breaking weight in pounds in centre;
D = extreme diameter in inches; T= thickness in inches; L = length be-
tween supports in inches; S = ultimate tensile strength in pounds per sq. in.
, Taking S, the strength of a square inch of a riveted joint, at 35,000 Ibs.
1 per. sq. in., this rule figures as follows for the different examples experi-
mented upon by Mr. Fairbairn : I, 2870; II, 10,190; III, 7700; IV, 15,320.
This shows a close approximation to the breaking weight obtained by
experiments and that derived from Edwin Clarke's and D. K. Clark's rules.
We therefore assume that this system of calculation is practically correct,
and that it is eminently safe when a large factor of safety is provided, and
from the fact that a chimney may be standing for many years without
receiving anything like the strain taken as the basis of the calculation, viz.,
fifty pounds per square foot. Wind pressure at fifty pounds ?er square foot
may be assumed to be travelling in a horizontal direction, and be of the
same velocity from the top to the bottom of the stack. This is the extreme
assumption. If, however, the chimney is round, its effective area would be
only half of its diameter plane. We assume that the entire force may be
concentrated in the centre of the height of the section of the chimney
under Consideration.
SIZE OF CHIMNEYS.
741
Taking as an example a 125-foot iron chimney at Poughkeepsje, N. Y., the
average diameter of which is 90 inches, the effective surface in square feet
upon which the force of the wind may play will therefore be 7% times 125
divided by 2, which multiplied by 50 gives a total wind force of 23,437
pounds. The resistance of the chimney to breaking across the top of the
foundation would be 8.14 X 1682 (that is, diameter of base) X .25 X 35,000 -*•
<750 X4) = 258,486, or 10.6 times the entire force of the wind. We multiply
the half height above the joint in inches, 750, by 4, because the chimney is
considered a fixed beam with a load suspended on one end. In calculating
Its strength half way up, we have a beam of the same character. It is a
fixed beam at a line half way up the chimney, where it is 90 inches in diam-
eter and .187 inch thick. Taking the diametrical section above this line,
and the force as concentrated in the centre of it, or half way up from the
point under consideration, its breaking strength is: 8.14 X 902 X .187 X 35,000
-j- (381 X 4) = 109,220; and the force of the wind to tear it apart through its
cross-section, 7*4 X 62J4 x 50-5-2 =s 11,352, or a little more than one tenth of
the strength of the stack.
TheBabcock & Wilcox Co.'s book M Steam" illustrates a steel chimney
at the works of the Maryland Steel Co., Sparrow's Point, Md. It is 225 ft.
in height above the base, with internal brick lining 13' 9" uniform inside
diameter. The shell is 25 ft. diam. at the base, tapering in a curve to 17 ft.
25 ft. above the base, thence tapering almost imperceptibly to 14' 8" at the
top. The upper 40 feet is of ^-inch plates, the next four sections of 40 ft.
each are respectively 9/32, 5/16, 11/32, and % inch.
Sizes of Foundations for Steel Chimney s.
(Selected from circular of Phila. Engineering Works.)
HALF-LINED CHIMNEYS.
Diameter, clear, feet 8456 7 9 11
Height.feet 100 100 150 150 150 150 150
Least diameter foundation.. 15'9" 16'4" 20'4" 21'10" 22'7" 23'8" 24'8"
Least depth foundation 6' 6' 9' 8' 9' 10' 10'
Height, feet 125 200 200 250 275 300
Least diameter foundation 18'5" 28'8" 25' 29'8" 33'6" 36'
Least depth foundation V W 10> 12' 12' 14'
Weight of Sheet-iron Smoke-stacks per Foot.
(Porter Mfg. Co.)
Diam.,
Inches.
Thick-
ness
W.G.
Weight
per ft.
Diam.,
inches.
Thick-
ness
W.G.
Weight
per ft.
Diam.
inches.
Thick-
ness
W. G.
Weight
per ft.
10
12
14
16
20
22
24
Nou16
u
M
M
*4
M
7.20
8.66
9.58
11.68
18.75
15.00
16.25
26
28
80
10
12
14
16
No. 16
44
No. 14
44
M
U
17.50
18.75
20.00
9.40
11.11
13.69
15.00
20
22
24
26
28
30
No. 14
it
n
44
4(
18.33
20.00
21.66
23.33
25.00
26.66
Sheet-Iron Chimneys* (Columbus Machine Co.)
Diameter
Chimney,
inches.
Length
Chimney,
feet.
Thick-
ness
Iron,
B. W. G.
Weight,
Ibs.
Diameter
Chimney,
inches.
Length
Chimney,
feet.
Thick-
ness
Iron,
B. W. G
Weight,
Ibs.
10
15
20
22
24
26
28
20
20
20
80
40
40
40
No. 16
" 16
" 16
" 16
" 16
u 16
" 15
160
240
820
850
760
826
900
80
32
34
86
88
40
40
40
40
40
40
40
No. 15
" 15
u 14
" 14
" 12
" 12
960
1,020
1,170
1,240
1,800
1,890
742
THE STEAM-ENGINE.
THE STEAM-ENGINE.
Expansion of Steam. Isothermal and Adiabatic.— Accord-
ing to Mariotte's law, the volume of a perfect gas, the temperature being
kept constant, varies inversely as its pressure, or p QC -; pv - a constant.
The curve constructed from this formula is called the isothermal curve, or
curve of equal temperatures, and is a common or rectangular hyperbola.
The relation of the pressure and volume of saturated steam, as deduced
from Regnault's experiments, and as given in Steam tables, is approxi-
mately, according to Rankine (S. E., p. 403), for pressures not exceeding 120
lbs.,p<x — y, or p ex v~ l5, orpv*6 = pv = a constant. Zeuner has
found that the exponent 1.0646 gives a closer approximation.
When steam expands in a closed cylinder, as in an engine, according to
Rankine (S. E., p. 385), the approximate law of the expansion is p oc — — , or
p oc v~ 5°, orpv1%ln = a constant. The curve constructed from this for°
inula is called the adiabatic curve, or curve of no transmission of heat.
Peabody ;Therm., p. 112) says : "It is probable that this equation was
obtained by comparing the expansion lines on a large number of indicator-
diagrams. . . . There does not appear to be any good reason for using an
exponential equation in this connection, . . . and the action of a lagged steam-
engine cylinder is far from being adiabatic. . . . For general purposes the
hyperbola is the best curve for comparison with the expansion curve of an
indicator-card. . . ." Wolff and Denton, Trans. A. S. M. E., ii. 175, say:
41 From a number of cards examined from a variety of steam-engines in cm--
rent use, we find that the actual expansion line varies between the 10/9
adiabatic curve and the Mariotte curve.1'
Prof. Thurston (A. S. M. E., ii. 203), says he doubts if the exponent ever
becomes the same in any two engines, or even in the same engines at dif-
ferent times of the day and under varying conditions of the day.
Expansion of Steam according to ITIariotte's Law and
to the Adiabatic Lair. (Trans. A. S. M. E., ii. 156.)— Mariotte's law
pv =PIV i : values calculated from formula — '- = — (1 -f hyp log R), in which
Pi K
B = t'a -*-«!, j>] = absolute initial pressure, Pm = absolute mean pressure,
Vi =* initial volume of steam in cylinder at pressure p:, va = final volume of
steam at final pressure. Adiabatic law: pv1*' = plvl r; values calculated
from fprmula — = 10R ~ * - QR ~ ™'
Pi
Ratio of
Expan-
Ratio of Mean
to Initial
Pressure.
Ratio
of
Expan-
Ratio of Mean
to Initial
Pressure.
Ratio
of
Expan-
Ratio of Mean
to Initial
Pressure.
sion R.
Mar.
Adiab.
sion R.
Mar.
Adiab.
sion R.
Mar.
Adiab.
2.00
1.000
1.000
3.7
.624
.600
6.
.465
.438
1.25
.978
.976
38
.614
.590
6.25
.453
.425
1.50
.937
.931
3.9
.605
.580
65
.442
.413
1.75
.891
.881
4.
.597
.571
6.75
.431
.403
2.
.847
.834
4.1
.588
.562
7.
421
.393
2.2
.813
.798
4.2
.580
.554
7 25
.411
383
2.4
.781
.765
.3
.572
.546
75
.402
.374
2.5
.766
.748
.4
.564
.538
7.75
.393
.365
2.6
.752
.733
.5
.556
.530
8.
.385
.357
2.8
.725
.704
.6
.549
.523
8.25
.377
.349
3.
.700
.678
.7
.542
.516
8.5
.369
.342
3.1
.688
.666
.8
.535
.509
8.75
.362
.335
3.2
.676
.654
.9
.528
.502
9.
.355
.328
8.3
.665
.642
5.0
.522
.495
9.25
.349
.321
3.4
.654
.630
5 25
.506
.479
9.5
.342
.315
3.5
.644
.620
5.5
.492
.464
9.75
.336
.309
3.6
.634
.610
5.75
.478
.450
10.
.330
.303
MEAH AND TERMINAL ABSOLUTE PRESSURES. 743
Ifltean Pressure of Expanded Steam.— For calculations of
engines it is genets JJy assumed that steam expands according to Marietta's
law, the curve of the expansion line being a hyperbola. The mean pressure,
measured above vacuum, is then obtained from the formula
in which Pm is the absolute mean pressure, pj the absolute initial pressure
taken as uniform up to the point of cut-off, Pt the terminal pressure, and R
the ratio of expansion. If I = length of stroke to the cut-off, L = total stroke.
Pm =
and if R »
1 -f- hyp log R
t C»UVf 1JL Jlli — j J X 7» — *^J T> •
jL/ t K
Mean and Terminal Absolute Pressures.— JJIariotte>»
Li aw. — The values in the following table are based on Mariotse's law,
except those in ths last column, which give the mean pressure of superheated
steam, which, according to Rankine, expands in a cylinder according to
the law p QG v ~ H. These latter values are calculated from the formula
— = — =— = . R~™ may be found by extracting the square root of —
Pi K R
four times. From the mean absolute pressures given deduct the mean back
pressure (absolute) to obtain the mean effective pressure.
Rate
of
Expan-
sion.
Cut-
off.
Ratio of
Mean to
Initial
Pressure.
Ratio of
Mean to
Terminal
Pressure.
Ratio of
Terminal
to Mean
Pressure.
Ratio of
Initial
to Mean
Pressure.
Ratio of
Mean to
Initial
Dry Steam.
30
28
0.033
0.036
0.1467
0.1547
4.40
4 33
0.227
0.231
6.82
6.46
0.136
26
0 038
0.1638
4 26
0.235
6.11
24
0.042
0.1741
4.18
0.239
5.75
22
0 045
0 1860
4 09
0 244
5 38
80
18
0.050
0 055
0.1998
0 2161
4.00
3 89
0.250
0.256
5.00
4 63
0.186
16
0.062
0.2358
3 77
0.265
4.24
15
0 066
0.2472
3 71
0 269
4.05
*
14
0.071
0.2599
3 64
0 275
3.85
13.33
13
0.075
0.077
0.2690
0.2742
3.59
3 56
0.279
0.280
3.72
3.65
0.254
12
0 083
0 2904
3 48
0.287
3 44
11
0 091
0 3089
3 40
0 294
3 24
10
9
0.100
0.111
0.3303
0 3552
3.30
3 20
0.303
0 312
3.03
2 81
0.314
8
0.125
0 143
0.3849
0 4210
3.08
2 95
0.321
0 339
2.60
2 37
0.370
6.66
6.00
0.150
0 166
0.4347
0 4653
2.90
2 79
0.345
0 360
2. SO
2 15
0.417
5 71
0 175
0 4807
2 74
0 364
2 08
5.00
4 44
0.200
0 225
0.5218
0 5608
2.61
2 50
0.383
0 400
1.92
1 78
0.506
4.00
8 63
0.250
0 275
0.5965
0 6308
2.39
2 29
0.419
0 437
1.68
1 58
0.582
3.33
8 00
0.300
0 333
0.6615
0 6995
2.20
2 10
0.454
0 476
1.51
1 43
0.648
2.86
2 66
0.350
0 375
0.7171
0 7440
2.05
1 98
0.488
0 505
1.39
1 34
0.707
2.50
2.22
2.00
1.82
1.66
1 60
0.400
0.450
0.500
0.550
0 600
0 625
0.7664
0.8095
0.8465
0.8786
0.9066
0 9187
.91
.80
.69
.60
.51
47
0.523
0.556
0.591
0.626
0.662
0.680
1.31
1.24
1.18
1.14
1.10
1.09
0.756
0.800
0.840
8.874
0.900
1.54
1.48
0.650
0.675
0.9292
0.9405
1.43
1.39
0.699
0.718
1.07
1.06
0.926
744
THE STEAM-E^GINB.
Calculation of Ulean Effective Pressure, Clearance and
Compression Considered.— In the. above tables no account is taken
^ T __ j
Area of ABCD = Pl(l -f c)(l + hyp log
C = pcc(l -f hyp log
of clearance, which in actual
steam-engines modifies the ratio
of expansion and the mean pres-
sure ; nor of compression and
back-pressure, which diminish
the mean effective pressure. In
the following calculation these
elements are considered.
L = length of stroke, I = length
before cut-off, x = length of com-
pression part of stroke, c = clear-
ance, PJ = initial pressure, pb =
back pressure, pc = pressure of
clearance steam at end of com-
pression. All pressures are abso-
lute, that is, measured from a
perfect vacuum.
pb(x + c)(l + hyp log
D = (PI - Pc)c = p^ - pb(x -fc).
Area of A = ABCD - (B -f C -f D)
x) + pb(x -I- c)l -f hyp log
(lH- hyp log
- p^x + c)J
area of A
Mean effective pressure = - = - •
Lt
EXAMPLE.— Let L = 1, I = 0.25, x =• 0.25, c = 0.1, pl ss 60 Ibs., p^ ss 2 Ibs.
Area A = 60(.25 -f .l)(l -fhyp log -^-)
-2[(l-.25)4- .35 hyp log -^p] - 60 X .1
a= 21(1 + 1.145) - 2[.75 -}- 35 X 1.253] - 6
= 45.045 - 2.377 — 6 = 36.668 = mean effective pressure.
x'he actual indicator-diagram generally shows a mean pressure consider-
ably less than that due to the initial pressure and the rate of expansion. The
causes of loss of pressure are: 1. Friction in the stop-valves and steam-
pipes. 2. Friction or wire-drawing of the steam during admission and cut-
off, due chiefly to defective valve-gear and contracted steam-passages.
3. Liquefaction during expansion. 4. Exhausting btfore the engine has
completed its stroke. 5. Compression due to early closure of exhaust.
6. Friction in the exhaust-ports, passages, and pipes.
Re-evaporation during expansion of the steam condensed during admis-
sion, and valve-leakage after cut-off, tend to elevate the expansion line of
the diagram and increase the mean pressure.
If the theoretical mean pressure be calculated from the initial pressure
and the rate of expansion on the supposition that the expansion curve fol-
EXPANSION OF STEAM. 745
lows Mariotte's law, pv = a constant, and the necessary corrections are
made for clearance and compression, the expected mean pressure in practice
may be found by multiplying the calculated results by the factor in the
following table, according to Seaton.
Particulars of Engine. Factor.
Expansive engine, special valve-gear, or with a separate
cut-off valve, cylinder jacketed ....................... 0.94
Expansive engine having large ports, etc., and good or-
dinary valves, cylinders jacketed ....................... 0.9 to 0,92
Expansive engines with the ordinary valves and gear as
in general practice, and un jacketed ................... 0.8 to 0.85
Compound engines, with expansion valve to h.p. cylin-
der; cylinders jacketed, and with large ports, etc ...... 0.9 to 0.92
Compound engines, with ordinary slide-valves, cylinde/s
jacketed, and good ports, etc ............ ............... 0.8 to 0.85
Compound engines as in general practice in the merchant
service, with early cut-off in both cylinders, without
jackets and expansion-valves .......................... 0.7 to 0.8
Fast-running engines of the type and design usually fitted
in war-ships ............................................ 0.6 to 0.8
If no correction be made for clearance and compression, and the engine
is in accordance with general modern practice, the theoretical mean pres*
Burs may be multiplied by 0.96, and the product by the proper factor in the
table, to obtain the expected mean pressure.
Given the Initial Pressure and the Average Pressure, to
Find the Ratio of Expansion and the Period of Admis-
sion*
P ss initial absolute pressure in Ibs. per sq. in.;
£ = average total pressure during stroke m Ibs. per sq. in.;
*s length of stroke in inches;
I is period of admission measured from beginning of stroke!
C = clearance in inches;
=» actual ratio of expansion =z T^"- ••••••••«•(!)
To find average pressure p, taking account of clearance,
p «. *V + c) + P(! + c) hy P Jog R - Po
whence pL+Pcm P(l + c) (1 4- hyp log K) ;
fa-M
.. (8)
Given p and P, to find R and I (by trial and error).— There being two un-
known quantities R and I, assume one of them, viz., the period of admissio/i
i, substitute it in equation (3) and solve for R. Substitute this value of R in
the formula (1), or I = — ~~ - c, obtained from formula (1), and find I If
K
the result is greated than the assumed value of ?, then the assumed value of
the period of admission is too long; if less, the assumed value is too short.
Assume a new value of J, substitute it in formula (3) as before, and continue
by this method of trial and error till the required values of R and I are
obtained.
EXAMPLE.— P » 70, p »= 42.78, L =• 60'', c =« 3'-, to find i Assume I = 21 in,
hyp log R « Z-- - 1 » -• 8i'+8 -- 1 - 1.653 - 1 = .668?
hyp log R m .653, whence R ~ 1.9
746 THE STEAM-EKGIKE.
which is greater than the assumed value, 21 inches.
Now assume I = 15 inches :
hyp log R = - j£-j -- 1 » 1.204, whence K » 8.5;
I = — £> -- c = -— — 3=18 — 3 = 15 inches, the value assumed.
Therefore E = 3.5, and I = 15 inches.
Period of Admission Required for a Given Actual Ratio of Expansion:
I = ~^ - c, in inches ......... (4)
In percentage of stroke. I = 10<H-p.ctclearance _ p ct clearance. . (5)
Terminal pressure = ~j~ ~ = — ........ ...... (6)
Pressure at any other^Point of the Expansion.— Let L^ = length of stroke
up to the given point.
Pressure at the given point = - ...... , ...... (7)
LI-L -f- C
WORK OF STEAM IN A SINGLE: CYLINDER.
To facilitate calculations of steam expanded in cylinders the table on the
next page is abridged from Clark on the Steam-erigins. The actual ratios
of expansion, column 1, range from 1.0 to 8.0, for which the hyperbolic
logarithms are given in column 2. The 3d column contains the periods of
admission relative to the actual ratios of expansion, as percentages of the
stroke, calculated by formula (5) above. The 4th column gives the values
of the mean pressures relative to the initial pressures, the latter being taken
as 1, calculated by formula (2). In the calculation of columns 3 and 4, clear-
ance is taken into account, and its amount is assumed at ?$ of the stroke.
The final pressures, in the 5th column, are such as would be arrived at by
the continued expansion of the whole of the steam to the end of the stroke,
the initial pressure being equal to 1. They are the reciprocals of the ratios
of expansion, column 1. The 6th column contains the relative total per-
formances of equal weights of steam worked with the several actual ratios
of expansion; the total performance, when steam is admitted for the whole
of the stroke, without expansion, being equal to 1. They are obtained by
dividing the figures in column 4 by those in column 5.
The pressures have been calculated on the supposition that the pressure of
steam, during its admission into the cylinder, is uniform up to the point of
cutting off, arid that the expansion is continued regularly to the end of the
stroke. The relative performances have been calculated" without any allow-
ance for the effect of compressive action.
The calculations have been made for periods of admission ranging from
100$, or the whole of the stroke, to 6.4#, or 1/16 of the stroke. And though,
nominally, the expansion is 16 times in the last instance, it is actually only
8 times, as given in the first column. The great difference between the
nominal and the actual ratios of expansion is caused by the clearance,
which is equal to 7% of the stroke, and causes the nominal volume of steam
admitted, namely, 6.4#, to be augmented to 6.4 -f 7 = 13.4$ of the stroke, or,
say, double, for expansion. When the steam is cut off at 1/9, the actual
expansion is only 6 times; when cut off at 1/5, the expansion is 4 times;
when cut off at ^, the expansion is 2% times; and to effect an actual expan-
sion to twice the initial volume, the steam is cut off at 46V&* of the stroke,
not at half -stroke.
WORK OF STEAM IN A SINGLE CYLINDER. 74?
Expansive Working of Steam— Actual Ratios of Expan-
sion, with the Relative Periods ot Admission, Press-
ures, and Performance.
Steam-pressure 100 Ibs. absolute.
>f the stroke.
Clearance atjeach end of the cylinder 7%
(SINGLE CYLINDER.)
1
2
3
4
5
6
7
8
9
t.
«'ll
Efil-S
2*°>i
ill
if
•CUg
M «
$ II
fl £
•3 S
» u
£ "
* 1
IllL
^glH
3£OQ§
R-
£ *-— ' 9
S 0) =3 0
lal-s
0,-o^g.
Hil
° O-^!—~
|gS||
S o ®
«J
«4-( O '"
.3 £
H *
— OJ
1 fi
0 0<%*~>
*H8| +
I'Sfe
•se^i
3 O C
fysj
lll«H
o
•£ g.2 •
IcO
1-3
- *ii
osp
•aS'l
t^'i
l^ll
|S£Ja
I'HoM
1s«£
2 la
o s£
ffiifc^
5 ^-^
0^302
gQHJ^
«Ul5
^
w
b
<J M
2
•^
o>
&
1
.0000
100
1.000
1.000
1.000
58,273
34.0
4.05
1.1
.0953
90.3
.996
.909
.096
63,850
31.0
4.45
1.18
.1698
83.3
.986
.847
.164
67,836
29.2
4.78
1.23
.2070
80
.980
.813
.206
70,246
28.2
4.98
1.3
.2624
75.3
.969
.769
.261
73,513
26.9
5.26
1.39
.3293
70
.953
.719
.325
- 77,242
25.6
5.63
1.45
.3716
66.8
.942
.690
.365
79,555
24.9
5.87
1.54
.4317
62.5
.925
.649
.425
83,055
23.8
6.23
1.6
.4700
59 9
.913
.625
.461
85,125
23.3
6.47
1.75
.5595
54.1
.883
.571
.546
90,115
22.0
7.08
1.88
.6314
50
.860
.532
.616
94,200
21.0
7.61
2
.5931
46.5
.836
.5
.672
97,432
20.3
8.09
2.28
.8241
40
.787
.439
.793
104,466
19.0
9.23
2.4
.8755
37.6
.766
.417
1.837
107,050
18.5
9.71
2.65
.9745
33.3
.726
.377
1.925
112,2-20
17.7
10.72
2.9
1.065
29.9
.692
.345
2.006
116,885
16.9
11.74
3.2
1.163
26.4
.652
.313
2.083
121,386
16.3
12.95
3.35
.209
25
.637
.298
2.129
124,066
16.0
13.56
3.6
.281
22.7
.608
.278
8.187
127,450
15.5
14.57
3.8
.335
21.2
.589
.263
2.240
130,533
15.2
15.38
4
.386
19.7
.569
.250
2.278
132.770
14.9
16.19
4.2
.435
18.5
.551
.238
2.315
134,900
14.7
17.00
4.5
.504
16.8
.526
.222
2.370
138,130
14.34
18.21
4.8
.569
15.3
.503
.208
2.418
140,920
14.05
19.43
5
.609
14.4
.488
.200
2.440
142,180
13.92
20.23
5.2
.649
13.6
.476
.193
2.466
143,720
13.78
21.04
5.5
.705
12.5
.457
.182
2.511
146,325
13.53
22.25
5.8
.758
11.4
.438
.172
2.547
148,390
13.34
23.47
5.9
.775
11.1
.432
.169
2.556
148,940
13.29
23.87
6.2
.825
10.3
.419
.161
2.585
150,630
13.14
25.09
6.3
.841
10
.413
.159
2.597
151,370
13.08
25 49
6.6
.887
9.2
.398
.152
2.619
152,595
12.98
26.71
7
.946
8.3
.381
.143
2.664
155,200
12.75
28.33
7.3
.988
7.7
.369
.137
2.693
156,960
12.61
29.54
7.6
2.028
7.1
.357
.132
2.711
157,975
12.53
30.76
7.8
2.054
6.7
.348
.128
2.719
158,414
12.50
31.57
8
2.079
6.4
.342
.125
2.736
159,433
11.83
32.38
ASSUMPTIONS OP THE TABLE.— That the initial pressure is uniform; that
the expansion is complete to the end of the stroke; that the pressure in. ex-
pansion varies inversely as the volume; that there is no back-pressure of
exhaust or of compression, and that clearance is 1% of the stroke at each
end of the cylinder. No allowance has been made for loss of steam by cyl«
inder-condensation or leakage.
Volume of 1 Ib. of steam of 100 Ibs. pressure per sq. in., or 14,400
Ibs. per sq, ft 4.33 cu. ft.
Product of initial pressure and volume 62,352 ft.-lbs.
748
THE STEAM-ENGINE.
Though a uniform clearance of ?# at each end of the stroke has been
assumed as an average proportion for the purpose of compiling the table,
the clearance of C3Tlinders with ordinary slides varies considerably — say
from 5% to 10#. (With Corliss engines it is sometimes as low as 2%.) With
the clearance, ?#, that has been assumed, the table gives approximate re-
sults sufficient for most practical purposes, and more trustworthy than re-
sults deduced by calculations based on simple tables of hyperbolic loga-
rithms, where clearance is neglected.
Weight of steam of 100 Ibs. total initial pressure admitted for one stroke,
per cubic foot of net capacity of the cylinder, in decimals of a pound =
reciprocal of figures in column 9.
Total actual work done by steam of 100 Ibs. total initial pressure in one
stroke per cubic foot of net capacity of cylinder, in foot-pounds = figures
in column 7 -*- figures in column 9.
RULE 1: To find the net capacity of cylinder for a given .weight of steam
admitted for one stroke, and a given actual ratio of expansion. (Column 9
of table.)— Multiply the volume of 1 Ib. of steam of the given pressure by the
given weight in pounds, and by the actual ratio of expansion. Multiply the
product by 100, and divide by 100 plus the percentage of clearance. The
quotient is the net capacity of the cylinder.
RULE 2: To find the net capacity of cylinder for the performance of a
given amount of total actual work in one stroke, with a given initial press-
ure and actual ratio of expansion. — Divide the given work by the total
actual work done by 1 Ib. of stearn of the same pressure, and with the same
actual ratio of expansion; the quotient is the weight of steam necessary to
do the given work, for which the net capacity is found by Rule 1 preceding,
NOTE.— 1. Conversely, the weight of steam admitted per cubic foot of net
capacity for one stroke is the reciprocal of the cylinder-capacity per pound
of steam, as obtained by Rule 1.
2. The total actual work done per cubic foot of net capacity for one stroke
is the reciprocal of the cylinder-capacity per foot-pound of work done, as
obtained by Rule 2.
3. The total actual work done per square inch of piston per foot of the
stroke is 1 /144th part of the work done per cubic foot.
4. The resistance of back pressure of exhaust and of compression are to
be added to the net work required to be done, to find the total actual work.
APPENDIX TO ABOVE TABLE— MULTIPLIERS FOB NET CYLINDER-CAPACITY, AND
TOTAL ACTUAL. WORK DONE.
(For steam of other pressures than 100 Ibs. per square Inch.)
Total Pres-
sures per
square inch.
Multipliers.
Total Pres-
sures per
square inch.
Multipliers.
For Col. 7.
Total Work
by 1 Ib. of
Steam.
For Col. 9.
Capacity
of
Cylinder.
For Col. 7.
Total Work
by 1 Ib. of
Steam.
For Col. 9.
Capacity
of
Cylinder.
Ibs.
65
70
75
80
85
90
95
.975
.981
.986
.988
.991
.995
.998
1.50
.40
.31
.24
.17
.11
1.05
Ibs. -
100
110
120
130
140
150
160
1.000
1.009
1.011
1.015
1.022
1.025
1.031
1.00
.917
.843
.781
.730
.683
.644
The figures in the second column of this table are derived by multiplying
the total pressure per square foot of any given steam by the volume in
cubic feet of 1 Ib. of such steam, and dividing the product by 62,352, which
is The product in foot-pounds for steam of 100 Ibs. pressure. The quotient
is the multiplier for the given pressure.
The figures in the third column are the quotients of the figures in the
second column divided by the ratio of the pressure of the given steam to 100
Ibs.
Measures tor Comparing the Duty of Engines. — Capacity is
measured in horse powers, expressed by the initials, H.P.: 1 H.P. m 83.CKX?
ft.-lbs. per minute, = 550 ft.-lbs. per second, = 1,980,000 ft.-Jbs. per hour
WORK OF STEAM IK A SINGLE CYLINDER. 749
I ft.-lb. = a pressure of 1 Ib. exerted through a space of 1 ft. Economy is
measured, 1, m pounds of coal per horse-power per hour; 2, in pounds of
steam per horse-power per hour. The second of these measures is the more
accurate and scientific, since the engine uses steam and not coal, and it is
indepndent of the economy of the boiler.
In gas-engine tests the common measure Is the number of cubic feet
of gas (measured at atmospheric pressure) per horse-power, but as all gas
is not of the same quality, it is necessary for comparison of tests to give the
analj'sis of the gas. When the gas for one engine is made in one gas-pro-
ducer, then the number of pounds of coal used in the producer per hour per
horse-power of the engine is the proper measure of economy.
Economy, or duty of an engine, is also measured in the number of foot-
pounds of work done per pound of fuel. As 1 horse-power is equal to 1,980,-
000 ft.-lbs. of work in an hour, a duty of 1 Ib. of coal per H.P. per hour
would be equal to 1,980,000 ft.-lbs. per Ib. of fuel; 2 Ibs. per H.P. per hour
equals 990,000 ft.-lbs. per Ib. of fuel, etc.
The duty of pumping-engines is commonly expressed by the number ot
foot-pounds of work done per 100 Ibs. of coal.
When the duty of a pumping-engine is thus given, the equivalent number
of pounds of fuel consumed per horse-power per hour is found by dividing
198 by the number of millions of foot-pounds of duty. Thus a pumping-
engine giving a duty of 99 millions is equivalent to 198/99 = 2 Ibs. of fuel pel
horse-power per hour.
Efficiency Measured in Thermal Units per ITIliinto.™-
Some writers express the efficiency of an engine in terms of the number of
thermal units used by the engine per minute for each indicated horse-power,
instead of by the number of pounds of steam used per hour.
The heat chargeable to an engine per pound of steam is the difference be-
tween the total heat in a pound of steam at the boiler-pressure and that in
a pound of the feed-water entering the boiler. In the case of condensing*
engines, suppose we have a temperature in the hot-well of 101° F., corre-
sponding to a vacuum of 28 in. of mercury, or an absolute pressure of 1 Ib.
per sq. in. above a perfect vacuum : we may feed the water into the boiler
at that temperature. In the case of a non-condensing-engine, by using a por-
tion of the exhaust steam in a good feed- water heater, at a pressure a trifle
above the atmosphere (due to the resistance of the exhaust passages
through the heater), we may obtain feed-water at 212°. One pound of steam
used by the engine then would be equivalent to thermal units as follows :
Pressure of steam by gauge :
50 75 100 125 150 175 200
Total heat in steam above 32° :
1172.8 1179.6 1185.0 1189.5 1193.5 1197.0 1200.2
Subtracting 69.1 and 180.9 heat-units, respectively, the heat above 32° in
feed-water of 101° and 212° F., we have-
Heat given by boiler :
Feed at 101° 1103.7 1110.5 1115.9 1120.4 1124.4 1127.9 1131.1
Feed at 212° 991.9 998.7 1004.1 1008.6 1012.6 1016.1 1019.3
Thermal units per minute used by an engine for each pound of steam used
per indicated horse-power per hour :
Feed at 101° 18.40 18.51 18.60 18.67 18.74 18.80 18.85
Feed at 212° 16.53 16.65 16.74 16.81 16.88 16.94 16.99
EXAMPLES.— A triple-expansion engine, condensing, with steam at 175 Ibs.,
gauge and vacuum 28 in., uses 13 Ibs. of water per I. H.P. per hour, and a
high-speed non-condensing engine, with steam at 100 Ibs. gauge, uses 30
Ibs. How many thermal units per minute does each consume ?
Ans.— 13 X 18.80 = 244.4, and 30 x 16.74 = 502.2 thermal units per minute.
A perfect engine converting all the heat -energy of the steam into work
would require 83,000 ft.-lbs. * 778 = 42.4164 thermal units per minute per
indicated horse-power. This figure, 42.4164, therefore, divided by the num-
ber of thermal units per minute per I.H.P. consumed by an engine, gives its
efficiency as compared with an ideally perfect engine. In the examples
above, 42.4164 divided by 244.4 and by 502.2 gives 17.35$ and 8.45# efficiency,
respectively.
Total Work Done by One Pound of Steam expanded in
a Single Cylinder. (Column 7 of table.)— If 1 pound of water be con-
verted into steam of atmospheric pressure == 211(5.8 Ibs. per sq. ft., it occu-
pies a volume equal to 26,36 cu, ft. The work done is equal to 2116.8 Ibs.
750
THE STEAM-EXGINE.
X 26.36 ft. = 55,788 ft.-lbs. The heat equivalent of this work is (55,788 -f- 778
=)71.7 units. This is the work of 1 Ib. of steam of one atmosphere acting
on a piston without expansion.
The gross work thus done on a piston by 1 Ib. of steam generated at total
pressures varying from 15 Jbs. to 100 Ibs. per sq. in. varies in round numbers
from 56,000 to 62,000 ft.-lbs., equivalent to from 72 to 80 units of heat.
This work of 1 Ib. of steam without expansion is reduced by clearance
according to the proportion it bears to the net capacity of the cylinder. If
the clearance be 7# of the stroke, the work of a given weight of steam with-
out expansion, admitted for the whole of the stroke, is reduced in the ratio
of 107 to 100.
Having determined by this ratio the quantity of work of 1 Ib. of steam with-
out expansion, as reduced by clearance, the work of the same weight of steam
for various ratios of expansion may be found by multiplying it by the relative
performance of equal weights of steam, given in the 6th column of the table.
Quantity of Steam Consumed per Horse-power of* Total
Work per Hour. (Column 8 of table.)— The measure of a horse-power
is the performance of 33,000 ft.-lbs. per minute, or 1,980,000 ft.-lbs. per hour.
This work, divided by the work of 1 Ib. of steam, gives the weight of steam
required per horse-power per hour. For example, the total actual work
done in the cylinder by 1 Ib. of 100 Ibs. steam, without expansion and with
1% of clearance, is 58,273 ft.-lbs. ; and ^-~~ = 34 Ibs. of steam, is the weight
of steam consumed for the total work done in the cylinder per horse-power
per hour. For any shorter period of admission with expansion the weight
of steam per horse-power is less, as the total work of 1 Ib. of steam is more,
and may be found by dividing 1,980,000 ft.-lbs. by the respective total work
done; or by dividing 34 Ibs. by the ratio of performance, column 6 in the
table.
ACTUAL EXPANSIONS.
With Different Clearances and Cut-offs.
Computed by A. F. Nagle.
Cut-
Per Cent of Clearance.
off.
0
1
2
3
4
5
6
7
8
9
10
.01
100.00
50.5
34.0
25.75
20.8
17.5
15.14
13.38
12.00
10.9
10
.02
50.00
33.67
^5.50
<!0.60
17. b3
15.00
13.25
11.89
10.80
9.91
9.17
.03
33.33
25.25
20.40
17.16
14.86
13.12
11.78
10.70
9.82
9.08
8.46
.04
25.00
20.20
17.00
14.71
13.00
11.66
10.60
9.73
9.00
8.39
7.86
.05
20.00
16.83
14.57
12.87
11.55
10.50
9.64
8.92
8.31
7.79
7.33
.06
16.67
14.43
12.75
11.44
10.40
9.55
8.83
8.23
7.71
7.27
6.88
.07
14.28
12.6-4
11.33
10.30
9.46
8.75
8.15
7.64
7.20
6.81
6.47
.08
12.50
11.22
10.2
9.36
8.67
8.08
7.57
7.13
6.75
6.41
6.11
.09
11.11
10.10
Q O7
8.58
8.00
7.50
7.07
6.69
6.35
6.06
5.79
.10
10.00
9.18
8^50
7.92
7.43
7.00
6.62
6.30
6.00
5.74
5.50
.11
9.09
8.42
7.84
7.36
6.93
6.56
6.24
5.94
5.68
5.45
5.24
.12
8.33
7.78
7.29
6.86
6.50
6.18
5.89
5.63
5.40
5.19
5.00
.14
7.14
6.73
6.37
6.06
5.78
5.53
5.30
5.10
4.91
4.74
4.58
.16
6.25
5.94
5.67
5.42
5.20
5.00
4.82
4.65
4.50
4.36
4.23
.20
5.00
4.81
4.64
4.48
4.33
4.20
4.U8
3.96
3.86
3.76
3.67
.25
4.00
3.88
3.77
3.68
3.58
3.50
3.42
3.34
3.27
3.21
3.14
.30
3.33
3.26
3.19
3.12
3.06
3.00
2.94
2.90
2,84
2.80
2.75
.40
2.50
2.46
2.43
2.40
2.36
2.33
2.30
2.28
2.25
2.22
2.20
.50
2.00
1.98
1.96
1.94
1.92
1.90
1.89
1.88
.86
1.85
1.83
.60
1.67
1.66
1.65
1.64
1.63
1.615
1.606
1.597
.588
1.580
1.571
.70
1.43
1.42
1.42
1.41
1.41
1.400
1.395
1.390
.385
1.380
1.375
.80
1.25
1.25
1.244
1.241
1.238
1.235
1.233
1.230
.227
1.224
1.222
.90
1.111
1.11
1.109
1.108
1.106
1.105
1.104
1.103
.102
1.101
1.100
1.00
1.00
,00
1.000
1.000
1.000
1.000
1.000
1.000
.000
1.000
1.000
WORK OF STEAM IN A SINGLE CYLINDER. 751
Relative Efficiency of 1 lb. of Steam -with and without
Clearance; back pressure and compression not considered.
Mean total pressure ., = *« + «) + fg + e)hy|Mog. B - ft
Lt
Let P= 1; L = 100; I = 25; c = 7.
Whyp.tog.fl-r ' M + axljCT>_7
loo loo
If the clearance be added to the stroke, so that clearance becomes zero,
the same quantity of steam being used, admission I being then = I 4 c =
82, and stroke L+c= 107.
_
107 107
That is, if the clearance be reduced to 0, the amount of the clearance 7
being added to both the admission and the stroke, the same quantity of
steam will do more work than when the clearance is 7 in the ratio 707 : 637,
or 11 # more.
Back Pressure Considered.— If back pressure = .10 of P, this
amount has to be subtracted from p and^ giving p = .537, p^ = .607, the
work of a given quantity of steam used without clearance being greater
than when clearance is 7 per cent in the ratio of 607 : 537, or 13% more.
Effect of Compression.— By early closure of the exhaust, so that a
portion of the exhaust-steam is compressed into the clearance-space, much
of the loss due to clearance may be avoided. If expansion is continued
down to the back pressure, if the back pressure is uniform throughout the
exhaust-stroke, and if compression begins at such point that the exhaust-
steam remaining in the cylinder is compressed to the initial pressure at the
end of the back stroke, then the work of compression of the exhaust-steam
equals the work done during expansion by the clearance-steam. The clear-
ance-space being filled by the exhaust-steam thus compressed, no new steam
is required to fill the clearance-space for the next forward stroke, and the
work and efficiency of the steam used in the cylinder are just the same a.s if
tiiere were no clearance and no compression. When, however, there is a
drop in pressure from the final pressure of the expansion, or the terminal
pressure, to the exhaust or back pressure (the usual case), the work of com-
pression to the initial pressure is greater than the work done b3>- the expan-
sion of the clearance-steam, so that a loss of efficiency results. In this
case a greater efficiency can be attained by inclosing for compression a less
quantity of steam than that needed to fill the clearance-space with steam of
the initial pressure. (See Clark, S. E., p. 399, et seq.; also F. H. Ball, Trans.
A. S. M. E., xiv. 1067.) It is shown by Clark that a somewhat greater effi-
ciency is thus attained whether or not the pressure of the steam be carried
down by expansion to the back exhaust-pressure. As a result of calcula-
tions to determine the most efficient periods of compression for various
percentages of back pressure, and for various periods of admission, he gives
the table on the next page :
Clearance in JLow- and High-speed Engines. (Harris
Tabor, Am. Mac/i., Sept. 17, 1891.) — The construction of the high-speed
engine is such, with its relatively short stroke, that the clearance must be
much larger than in the releasing-valve type. The short-stroke engine is,
of necessity, an engine with large clearance, which is aggravated when a
variable compression is a feature. Conversely, the releasing-valve gear is,
from necessity, an engine of slow rotative 'speed, where great power is
obtainable from long stroke, and small clearance is a feature in its construc-
tion. In one case the clearance will vary from 8fa to 1% of the piston-dis-
placement, and in the other from 2# to 3$. In the case of an engine with a
clearance equalling 10$ of the piston-displacement the waste room becomes
enormous when considered in connection with an early cut-off. The system of
compounding reduces the waste due to clearance in proportion as the steam
is expanded to a lower pressure. The farther expansion is carried through
a train of cylinders the greater will be the reduction of waste due to clear-
ance. This is shown from the fact that the high-speed engine, expanding
752
THE STEAM-EKGINE.
steam much less than the Corliss, will show a greater gain when changed
from simple to compound than its rival under similar conditions.
COMPRESSION OF STEAM IN THE CYLINDER.
Best Periods of Compression; Clearance 7 per cent.
Cut-off in
Percent-
ages of
the
Stroke.
Total Back Pressure, in percentages of the total initial pressure.
2^
5
10
15
20
25
30
35
Periods of Compression, in parts of the stroke.
10*
15
20
25
30
35
40
45
50
55
60
65
70
75
65#
58
52
47
42
39
36
33
30
27
24
22
19
17
W%
52
47
42
39
35
32
30
27
24
22
20
17
16
44#
40
37
34
32
29
27
25
23
21
19
17
16
14
32%
29
27
26
25
23
21
20
18
17
15
15
14
13
23#
22
21
20
19
18
17
16
15
14
14
14
12
m
16
15
14
14
13
13
12
12
12
11
14%
13
13
12
12
11
11
10
10
9
12*
11
11
10
10
9
9
8
8
8
NOTES TO TABLE. — 1. For periods of admission, or percentages of back
pressure, other than those given, the periods of compression may be readily
found by interpolation.
2. For any other clearance, the values of the tabulated periods of com-
pression are to be altered in the ratio of 7 to the given percentage of
clearance.
Cylinder-condensation may have considerable effect upon the best point
of compression, but it has not yet (1893) been determined by experiment.
(Trans. A. S. M. E., xiv. 1078.)
Cylinder-condensation.— Rankine, S. E., p. 421, says : Conduction
of heat to and from the metal of the cylinder, or to and from liquid water
contained in the cylinder, has the effect of lowering the pressure at the be-
ginning and raising it at the end of the stroke, the lowering effect being on
the whole greater than the raising effect. In some experiments the quantity
of steam wasted through alternate liquefaction and evaporation in the
cylinder has been found to be greater than the quantity wnich performed
the work.
Percentage of Loss by Cylinder-condensation, taken at
Cut-off. (From circular of the Ashcroft Mfg. Co. on the Tabor
Indicator, 1889.)
Percentage of
Stroke completed
at Cut-oflf.
Percent, of Feed -water accounted
for by the Indicator diagram.
Percent, of Feed-water Consump-
tion due to Cylinder-condensat'u.
Simple
Engines.
Compound
Engines,
h.p. cyl.
Triple-ex-
pansion
Engines,
b.p. cyl.
Simple
Engines.
Compound
Engines,
h.p. cyl.
Triple-ex-
pansion
Engines,
h.p. cyl.
5
10
15
20
30
40
50
58
66
71
74
78
82
86
42
34
29
26
22
18
14
74
76
78
82
85
88
26
24
22
18
15
12
78
80
84
87
90
22
20
16
13
10
WORK OF STEAM Itf A SINGLE CYLINDER. 753
Theoretical Compared with Actual Water-consump-
tion, Single-cylinder Automatic Cut-off Engines. (From
the catalogue of the Buckeye Engine Co.)— The following table has been
prepared on the basis of the pressures that result in practice with a con-
stant boiler- pressure of 80 Ibs. and different points of cut-off, with Buckeye
engines and others with similar clearance. Fractions are omitted, except
in the percentage column, as the degree of accuracy their use would seem
to imply is not attained or aimed at.
Cut-off Part
of Stroke.
Mean
Effective
Pressure.
Total
Terminal
Pressure.
Indicated
Rate,
Ibs. Water,
perl.H.P.
per hour.
Assumed.
Act1! Rate.
Per ct. Loss.
.10
18
11
20
32
58
.15
27
15
19
27
41
.20
85
20
19
25
31.5
.25
42
25
20
25
25
.30
48
30
20
24
21.8
.35
53
85
21
25
19
.40
57
38
22
26
16.7
.45
61
43
23
27
15
.50
64
48
24
27
13.6
It will be seen that while the best indicated economy is when the cut-off
is about at .15 or .20 of the stroke, giving about 30 Ibs. M.E.P., and a termi-
nal 3 or 4 Ibs. above atmosphere, when we come to add the percentages due
to a constant amount of unindicated loss, as per sixth column, the most eco-
nomical point of cut-off is found to be about .30 of the stroke, giving 48 Ibs.
M.E.P. and 30 Ibs. terminal pressure. This showing agrees substantially
u?ith modern experience under automatic cut-off regulation.
Experiments on Cylinder-condensation.— Experiments by
Major Thos. English (Eng'y, Oct. 7, 1887, p. 386) wiih an engine 10 X 14 in.,
jacketed in the sides but not on the ends, indicate that the net initial con-
densation (or excess of condensation over re-evaporation) by the clearance
surface varies directly as the initial density of the steam, and inversely as
the square root of the number of revolutions per unit of time. The mean
results gave for the net initial condensation by clearance-space per sq. ft. of
surface at one rev. per second 6.06 thermal units in the engine when run
non-condensing and 5.75 units when condensing.
G. R. Bodmer (Eng'g, March 4, 1892, p. 299) says : Within the ordinary
limits of expansion desirable in one cylinder the expansion ratio has prac-
tically no influence on the amount of condensation per stroke, which for
simple engines can be expressed by the following formula for the weight
of water condensed [per minute, probably; the original does not state] :
S(T-t)
W — C~ 3/™' where T denotes the mean admission temperature, t the
mean exhaust temperature, 8 clearance-surface (square feet), N the num-
ber of revoluti6ns per second, L latent heat of steam at the mean admission
temperature, and O a constant for any given type of engine.
Mr. Bodmer found from experimental data that for high-pressure non-
jacketed engines O = about 0.11, for condensing non- jacketed engines 0.085
to 0.11, for condensing jacketed engines 0.085 to 0.053. The figures for jack-
eted engines apply to those jacketed in the usual way, and not at the ends.
C varies for different engines of the same class, but is practically con-
stant for any given engine. For simple high-pressure non-jacketed engines
it was found to range from 0.1 to 0.112.
Applying Mr. Bodmer's formula to the case of a Corliss non-jacketed non^
condensing engine, 4-ft. stroke, 24 in. diam , 60 revs, per min., initial pres-
sure 90 Ibs. gauge, exhaust pressure 2 Ibs., we have T - t = 112°, N= 1,
L = 880, 8 = 7 sq. ft.; and, taking C = .112 and W = Ibs. water condensed
112 V 112 V 7
per minute, W = * " = -09 H>- Per minute, or 5.4 Ibs. per hour. If
1 X ooU
the steam used per I.H.P. per hour according to the diagram is 20 Ibs., the
actual water consumption is 25.4 Ibs., corresponding to a cylinder condensa-
tion of 27£.
754
THE STEAM-ENGINE.
INDICATOR-DIAGRAM OF A SINGLE-CYLINDER
ENGINE.
Definitions,— The Atmospheric Line, AB, is a line drawn by the pencil
of the indicator when the connections with the engine are closed and both
sides of the piston are open to the atmosphere.
FIG. 138.
The Vacuum Line, OX, is a reference line usually drawn about 14 7/10
pounds by scale below the atmospheric line.
The Clearance Line, OY, is a reference line drawn at a distance from the
end of the diagram equal to the same percent of its length as the clearance
and waste room is of the piston-displacement.
The Line of Boiler-pressure, JK, is drawn parallel to the atmospheric
line, and at a distance from it by scale equal to the boiler-pressure shown
by the gauge.
The Admission Line, CD, shows the rise of pressure due to the admission
of steam to the cylinder by opening the steam-valve.
The Steam Line, DE, is drawn when the steam-valve is open and steam is
being admitted to the cylinder.
The Point of Cut-off, E, is the point where the admission of steam is
stopped by the closing of the valve. It is often difficult to determine the
exact point at which the cut-off takes place. It is usually located where the
outline of the diagram changes its curvature from convex to concave.
The Expansion Curve, Ef\ shows the fall in pressure as the steam in the
cylinder expands doing work.
The Point of Release, F, shows when the exhaust-valve opens.
The Exhaiist Line, FG, represents the change in pressure that takes
place when the exhaust-valve opens.
The Back-pressure Line, GH, shows the pressure against which the piston
acts during its return stroke.
The Point of Exhaust Closure, H, is the point where the exhaust-valve
closes. It cannot be located definitely, as the change in pressure is at first
due to the gradual closing of the valve.
The Compression Curve, HC, shows the rise in pressure due to the com-
pression of the steam remaining in the cylinder after the exhaust-valve has
closed.
The Mean Height of the Diagram equals its area divided by its length.
The Mean Effective Pressure is the mean net pressure urging the piston
forward = the mean height X the scale of the indicator-spring.
To find the Mean Effective Pressure from the Diagram. — Divide the
length, LB, into a number, say 10, equal parts, setting off half a part ati,
half a part at B, and nine other parts between; erect ordinates perpendicu-
lar to the atmospheric line at the points of division of LB, cutting the dia-
gram; add together the lengths of these ordinates intercepted between the
upper and lower lines of the diagram and divide by their number. Thig
INDICATED HORSE-POWER OF ENGINES. 755
gives the mean height, which multiplied by the scale of the indicator-spring
gives the M.E.P. Or find the area by a planimeter, or other means (see
Mensuration, p. 55), and divide by the length LB to obtain the mean height.
The Initial Pressure is the pressure acting on the piston at the beginning
of the stroke.
The Terminal Pressure is the pressure above the line of perfect vacuum
that would exist at the end of the stroke if the steam had not been released
earlier. It is found by continuing the expansion-curve to the end of the
diagram.
INDICATED HORSE-POWER OF ENGINES, SINGLE*
CYLINDER.
Indicated Horse-power I.H.P.=
,
oo,uOO
in which P = mean effective pressure in Ibs. per sq. in. ; L = length of stroke
in feet; « = area of piston in square inches. For accuracy, one half of the
sectional area of the piston-rod must be subtracted from the area of the
piston if the rod passes through one head, or the whole area of the rod if it
passes through both heads; n — No. of single strokes per rain. = 2 X No. of
revolutions.
I.H.P. = ' , in which S— piston speed in feet per minute.
o<5,U(JO
I.H.P. = ~]jj^fir.=* "ifo^ = .0000238Pid2n = .0000238Pd2S,
in which d = diam. of cyl. in inches. (The figures 238 are exact, since
7854 -f- 33 = 23.8 exactly.) If product of piston-speed X mean effective
pressure = 42,017, then the horse-power would equal the square of the
diameter in inches.
Handy Rule for Estimating the Horse-power of a
Single-cylinder Engine.— Square the diameter and divide by 2. This is
correct whenever the product of the mean effective pressure and the piston-
speed = ^ of 42,017, or, say, 21,000, viz., when M.E.P. = 30 and 8= 700;
when M.E.P. = 35 and 8= 600; when M.E.P. = 38.2 and S = 550; and when
M.E.P. = 42 and 8 = 500. These conditions correspond to those of ordinary
practice with both Corliss engines and shaft-erovernor high-speed engines.
Given Horse-power, Mean Effective Pressure, and
Piston-speed, to find Size of Cylinder.—
33-000p**tH-P-.
Diameter = 205|/ffi-. (Exact.)
Brake Horse-power is the actual horse-power of the engine as
measured at the fly-wheel by a friction-brake or dynamometer. It is the
indicated horse-Dower minus the friction of the engine.
Table for Roughly Approximating the Morse-power of
a Compound Engine from the Diameter of its Low-
pressure Cylinder.— The indicated horse-power of an engine being
y , in which P = mean effective pressure per sq. in., s = piston-speed in
ft. per min., and d = diam. of cylinder in inches; if s = 600 ft. permin.,
which is approximately the speed of modern stationary engines, and P = 35
Ibs., which is an approximately average figure for the M.E.P. of single-
cylinder engines, and of compound engines referred to the low-pressure
cylinder, then I.H.P. = ^d2; hence the rough-and-ready rule for horse-power
given above: Square the diameter in inches and divide by 2. This applies to
triple and quadruple expansion engines as well as to single cylinder and
compound. For most economical loading, the M.E.P. referred to the low-
pressure cylinder of compound engines is usually not greater than that of
simple engines; for the greater economy is obtained by a greater number of
expansions of steam of higher pressures, and the greater the number of
expansions for a given initial pressure the lower the mean effective pressure.
The f ollowing table gives approximately the figures of mean total and effec-
756
THE STEAM-ENGINE.
tive pressures for the different types of engines, together with the factor by
which the square of the diameter 'is to be multiplied to obtain the horse-
power at most economical loading, for a piston-speed of GOO ft. per minute.
Type of Engine.
Initial Abso-
lute Steam-
pressure.
Number of
Expan-
sions.
Terminal
Absolute
Press., Ibs.
lo £
soil!
•3 0-3 &
tfHSpH
Mean Total
Pressure,
Ibs.
Total Back
Pressure,
Mean, Ibs.
Mean Effec-
tive Pres-
sure, Ibs.
Piston-
speed, ft.
per min.
II X
ill
0 p,73
Non-conden sin g.
Single Cylinder.
Compound
Triple
100
120
160
5.
7.5
10.
20
16
16
.522
.402
.330
52.2
48.2
52.8
15.5
15.5
15.5
36.7
32.7
37.3
600
.524
.467
.533
Quadruple
•200
12.5
16
.282
56.4
15.5
40.9
"
.584
Condensing Engines.
Single Cylinder.
Compound
Triple
100
120
160
10.
15.
20.
10
8
8
.330
.247
.200
33.0
29.6
32.0
2
2
2
31.0
27.6
30.0
600
.443
.390
.429
Quadruple
200
25.
8
.169
33.8
2
31.8
ki
.454
For any other piston-speed than 600 ft. per mil}., multiply the figures in
the last column by the ratio of the piston-speed to 600 ft.
Nominal Horse-power.— The term " nominal horse-power" origi-
nated in the time of Watt, and was used to express approximately the power
of an engine as calculated from its diameter, estimating the mean pressure
in the cylinder at 7 Ibs. above the atmosphere. It has long been obsolete in
America, and is nearly obsolete in England.
Horse-power Constant of a given Engine for a Fixed
Speed = product of its area of piston in square inches, length of stroke in
feet, and number of single strokes per minute divided by 33,000, or ~^~
00,000
= C. The product of the mean effective pressure as found by the diagram
and this constant is the indicated horse-power.
Horse-power Constant of a given Engine for Varying
Speeds = product of its area of piston and length of stroke divided by
33,000. This multiplied by the mean effective pressure and by the number
of single strokes per minute is the indicated horse-power.
Horse-power Constant of any Engine of a given Diam-
eter of Cylinder, whatever the length of stroke = area of piston -t- 33,000
= square of the diameter of piston in inches X .0000238. A table of constants
derived from this formula is given below.
The constant multiplied by the piston-speed in feet per minute and by
the M.E.P. gives the I.H.P.
Errors of Indicators.— The most common error is that of the spring,
which may vary from its normal rating; the error may be determined by
proper testing apparatus and allowed for. But after making this correction,
even with the best work, the results are liable to variable errors which may
amount to 2 or 3 per cent. See Barrus, Trans. A. S. M. E., v. 310; Denton,
A. S. M. E., xi. 329; David Smith, U. S. N., Proc. Eng'g Congress, 1893,
Marine Division.
Indicator " Rigs," or Reducing-motions ; Interpretation of Diagrams for
Errors of Steam-distribution, etc. For these see circulars of manufacturers
of Indicators; also works on the Indicator.
Table of Engine Constants for Use in Figuring Horse-
power.— " Horse-power constant " for cylinders from 1 inch to 60 inches in
diameter, advancing by 8ths, for one foot of piston-speed per minute and one
pound of M.E.P. Find the diameter of the cylinder in the column at the
side. If the diameter contains no fraction the constant will be found in the
column headed Even Inches. If the diameter is not in even inches, follow
the line horizontally to the column corresponding to the required fraction.
INDICATED HORSE-POAVER OF .ENGINES.
757
The constants multiplied by tlie piston-speed and by the M.E.P. give the
horse-power.
Diameter
of
Cylinder.
Even
Inches.
+ Ys
or
.125.
+ H
or
.25.
+ %
or
.375.
*H
or
.5.
+ «
or
.625.
+ «
or
.75.
±%
or
.875.
1
.0000238
.0000301
.0000372
.0000450
.0000535
.0000628
.0000729
.0000837
2
.0000952
.0001074
.0001205
.0001342 .0001487
.0001640 .0001800
0001967
3
.0002142
.0002324
.0002514
.0002711 (.0002915
.0003127
0003347
.0003574
4
.0003808
.0004050
.0004299
.0004554 .0004819
.0005091
.0005370
.0005656
5
.0005950
.0006251
.0006560
.0006876 .0007199
.0007530
.0007869
.0008215
6
.0008568
.0008929
.0009297
.0009672 .0010055
.0010445
.0010844
.0011249
.0011662
.0012082
.0012510
.0012944 .0013387
.0013837
.0014295
.0014759
8
.0015232
.0015711
.00161981. 0016693! .0017195
.0017705
.0018222
.0018746
9
.0019278
.0019817
.0020363i .002091 6
.0021479
.0022048
.0022625
.0023209
10
.0023800
.0024398
.0025004
.0025618
.0026239
.0026867
.0027502
.0028147
11
.0028798
.0029456
.0030121
.0030794
.0031475
.0032163
.0032859
.0033561
12
.0034272
.0034990
.0035714
.0036447
.0037187
.0037934
.0038690
.0039452
13
.0040222
.0010999
.0041783
.0042576
.0043375
.0044182
.0044997
.0045819
14
.0046648
.0047484
.0048328
.0049181
.0050039
.0050906
.0051780
.0052661
15
.0053550
.0054446
.0055349
.0056261
.0057179
.0058105
.0059039
.0059979
16
.0060928
.0061884
.0062847
.0063817
.0064795
.0065780
.0066774
0067774
17
.0068782
.0069797
.0070819
.0071850
.0072887
.0073932
.0074985
.0076044
18
.0077112
.0078187
.0079268
.0080360
.0081452
.0082560
.0083672
.0084791
19
.0085918
.0087052
.0088193
.0089343
.0090499
.0091663
.009283f
.0094013
20
.0095200
.0096393
.0097594
.0098803
.0100019
.0101243
.0102474
.0103712
21
.0104958
.0106211
.0107472
.0108739
.0110015
.0111299
.0112589
.0113886
22
.0115192
.0116505
.0117825
.0119152
.0120487
.0121830
.0123179
.0124537
23
.0125902
.0127274
.0128654
.0130040
.0131435
.0132837
.0134247
.0135664
24
.0137088
.0138519
.0139959
.0141405
.0142859
.0144321
.0145789
.0147266
25
.0148750
.0150241
.0151739
.0153246
.0154759
.0156280
,0157809
.0159345
26
.0160888
.0162439
.0163997
.0165563
.0167135
.0168716
.0170304
.0171899
27
.0173502
.0175112
.0176729
.0178355
.0179988
.0181627
.0183275
.0184929
28
.0186592
.0188262
.0189939
.0191624
.0193316
.0195015
.0196722
.0198436
29
.0200158
.0201887
.020367,4
.0205368
.0207119
.0208879
.0210615
.0212418
30
.0214200
.0215988
.0217785
.0219588
.0221399
.0223218
.0225044
.02J6877
31
.0228718
.0230566
.0232422
.0234285
.0236155
.0238033
.0239919
.0241812
32
.0243712
.0245619
.0247535
.0249457
.0251387
.0253325
.0255269
.0257222
33
.0259182
.0261149
.0263124
.0265106
.0267095
.0269092
.0271097
.0273109
34
.0275128
.0277155
.0279189
.0281231
.0283279
.0285336
.0287399
.0289471
35
.0291550
.0293636
.0295729
.0297831
.0299939
.0302056
.0304179
.0306309
36
.0308448
.0310594
.0312747
.0314908
.0317075
.0319251
.0321434
.0323624
37
.0325822
.0328027
.0330239
.0332460
.0334687
.0336922
.0339165
.0341415
38
.0343672
.0345937
.0348209
.0350489
.0352775
.0355070
.0357372
.0359681
39
.0361998
.0364322
.0366654
.0368993
.0371339
.0373694
.0376055
.0378424
40
.0380800
.0383184
.0385575
.0387973
.0390379
.0392793
.0395214
.0397642
41
.0400078
.0402521
.0404972
.0407430
.0409895
.0412368
.0414849
.0417337
42
.0419832
.0422335
.0424845
.0427362
.0429887
.0432420
.0434959
.0437507
43
.0440062
.0442624
.0445194
.0447771
.0450355
.0452947
.0455547
.0458154
44
.0460768
.0463389
.0466019
.0468655
.0471299
.0473951
.0476609
.0479276
45
.0481950
.0484631
.0487320
.0490016
.0492719
.0495430
.0498149
.0500875
46
.0503608
.0506349
.0509097
.0511853
.0514615
.0517386
.0520164
.0522949
47
.0525742
.0528542
.0531349
.0534165
.0536988
.0539818
.0542655
.0545499
48
.0548352
.0551212
.0554079
.0556933
.0559835
.0562725
.0565622
.0568526
49
.0571438
.0574357
.0577284
.0580218
.0583159
.0586109
.0589065
.0592029
50
.0595000
.0597979
.0600965
.0603959
.0606959
.0609969
.0612984
.0616007
51
.0619038
.0622076
.0625122
.0628175
.0632235
.0634304
.0637379
.0640462
52
.0643552
.0646649
.0619753
.0652867
.0655987
.0659115
.0662250
.0665392
53
.0668542
.0671699
.0674864 '.0678036
.0681215
.0684402
.0687597
.0690799
54
.0694008
.0697225
.0700449!. 0703681
.0705293
.0710166
.0713419
0716681
55
.0719950
.0724226
.0726510 .0729801
.0733099
.0736406
.0739719
.0743039
56
.0746368
.0749704
.0753047 .0756398
.0759755
.0763120
.0766494
.0769874
57
.0773262
.0776657
.0780060 .0783476
.0786887
.0790312
.0793745
.0797185
58
.0800632
.0804087
.0807549 .0811019
.0814495
.0817980
.0821472
.0824971
59
.0828478
.0831992
.0835514 .0839043 .0842579
0846123
.0849675
.0853234
60
.0856800
.0860374
.0863955 .0867543 .0871139
.0874743
0878354
.0881973
THE STEAM-EXGINTE.
Horse-power per Pound Mean Effective Pressure.
Area in sq. in. X piston-speed
Fonnula, _
Diam. of
Cylinder,
inches.
Speed of Piston in feet per minute.
100
200
30O
40O
500
600
700
800
900
4
.0381
.0762
.1142
.1523
.1904
.2285
.2666
.3046
.3427
4^
.0482
.0964
.1446
.1928
.2410
.2892
.3374
.3856
.4338
5
.0595
.1190
.1785
.2380
.2975
.3570
.4165
.4760
.5355
$y>
.0720
.1440
.2160
.2880
.3600
.4320
.5040
.5760
.6480
6
.0857
.1714
.2570
.3427
.4284
.5141
.5998
.6854
.7711
6^
.1006
.2011
.3017
.4022
.5028
.6033
.7039
.8044
.9050
7
.1166
.2332
.3499
.4665
.5831
.6997
.8163
.9330
1.0496
T&
.1339
.2678
.4016
.5355
.6694
.8033
.8371
1.0710
1 2049
8
.15:23
.3046
.4570
.6093
.7616
.9139
1.0662
1.2186
1.3709
8^3
.1720
.3439
.5159
.6878
.8598
1.0317
1.2037
1.3756
1 . 5476
9
.1928
.3856
.5783
.7711
.9639
1.1567
1.3495
1.5422
1.7350
9^
.2148
.4296
.6444
.8592
1.0740
1.2888
1 5036
1.7184
1.9532
10
.2380
.4760
.7140
.9520
1.1900
1.4280
.1.6600
1 . 9040
2.1420
11
.2880
.5760
.8639
1.1519
1.4399
1.7279
2.0159
2.3038
2.5818
12
.3427
.6854
1.0282
1.3709
1.7136
2.0563
2.3990
2.7418
3.0845
13
.4022
.8044
I .2067
1.6089
2.0111
2.4133
2.8155
3.2178
3.6200
14
.4665
.9330
1.3994
1.8659
2.3324
2.7989
3.2654
3.7318
4.1983
15
.5355
.0710
1.6065
2.1420
2.6775
3.2130
3.7485
4 2840
4.8195
16
.6093
.2186
1.8278
2.4371
3.0464
3.6557
4.2650
4.8742
5.4835
17
.6878
.2756
1.9635
2.6513
3.3391
4.0269
4.6147
5.4026
6.1904
18
.7711
.5422
2.3134
3.0845
3 8556
4.6267
5.3978
6.1690
6.9401
19
.8592
.7184) 2.5775
3.4367
4.2959
5.1551
6.0143
6.8734
7.7326
20
.9520
.9040
2.8560
3.8080
4.7600
5.7120
6.6640 7.6160
8.5680
21
1.0496
2.0992
3.1488
4.1983
5.2479 6.2975
7.3471J 8.3966
9.4462
22
1.1519
2.3038
3.4558
4.6077
5.7596
6.9115
8.0634 9.2154
10.367
23
.2590
2.5180
3.7771
5.0361
6.2951
7.5541
8.8131
10.072
11.331
24
.3709
2.7418
4.1126
5.4835
6.8544
8.2253
9.5962
10.967
12.338
25
.4875
2.9750
4.4625
5.9500 7.4375
8.9250
10.413
11.900
13.388
26
.6089
3.2178
4.8266
6. 4355 | 8.0444
9.6f:34
11.262
12.871
14.480
27
.73M)
3.4700
5.2051
6.9101
8.6751
10.410
12.145
13.880
15.615
28
.8659
3.7318
5.5978
7.4637
9.3296
11.196
13.061
14.927
16.793
29
2.0016
4.0032
6.0047
8.006310.008
12.009
14.011
16.013
18.014
30
2.1420
4.2840
6.4260
8.5680 10.710
12.852
14.994
17.136
19.278
31
2.2872
4.5744
6.8615
9.1487H1.436
13.723
16.010
18.297
20.585
32
2.4371
4.8742
7.3114
9.7485
12 186
14.623
17.060
14.497
21.934
33
2.5918
5.1836
7.7755
10.367
12.959
15.551
18.143
20.735
23.026
34
2.7513
5.5026
8.2538
11.005
13.756
16.508
19.259
22.010
24.762
35
2.9155
5.8310
8.7465
11.662
14.578
17.493
20.409
23.324
26.240
36
3.0845
6.1690
9.2534
12.338
15.422
18.507
21.591
24.676
27.760
37
3.2582
6.5164
9.7747
13.033
16.291
19.549
22.808
26.066
29.324
38
3.4367
6.8734
10.310
13.7'47
17.184
20.620
24.057
27.494
30.930
39
3.6200
7.2400 10.860
14 480
18.100
21.720
25.340
28.960
32.580
40
3.8080
7.616011.424
15 232
19.040
22 848
26.656
30 464
34.272
41
4.0008
8.0016
12.002
16.003 20.004
24.005
28.005
32.006
36.007
42
4.1983
8.3866
12.585
16.783 20.982
25.180
29.378
33.577
37 . 775
43
4.4006
8.8012
13.202
17.602 22.003
26.404
30.804
35.205
39.606
44
4.6077
9.2154
13.823
18 431 23.038
27.646 32.254
36 861
41.469
45
4.8195
9.6390
14.459
19.278 24.098
28.917 33.737
38.556
43.376
46
5.03G1
10 072
15.108
20.144 25.180
30.216
35.253
40.289
45.325
47
5.2574
10.515
15.772
21.030
26.287
31.545
36.802
42.059
47.317
48
5.4835
10.967 16.451
21.934
27 418
32.901
38.385
43.868
49.352
49
5.7144
11.429
17.143
22.858
28.572
34.286
40.001
45.715
51.429
50
5.9500
11.900
17.850
23.800
29.750
35.700
41.650
47.600
53.550
51
6.1904
12.381
18.571
24.762
30.952
37.142
43.333
49.523
55.713
52
6.4355
1^.871
19.307
25.742
32.178
38.613
45.049
51.484
^7.920
53
6.6854
13.371
20.056
26.742
33.427
40.113
46.798
53.483
60.169
54
6.9401
13.8«0
20.820
27.760
34.700
41.640
48.581
55.521
62.461
55
7.1995
14.399
21.599
28.798
35.998
43 197
50.397
57.596
64.796
56
7.4637
14.927
22.391
29.855
37.318
44.782
52.246
59.709
67.173
57
7.7326
15.465
23.198
30.930
38.663
46.396
54.128
61.861
69.594
58
8.0063
16.013
24.019
32.025
40.032
48 038
56.044
64.051
72.057
59
8.2849
16.570
24.854
33.139
41.424
49.709 57.993
66.278
74.563
60 8.5680
17.136
25.704
34.272
42.840
51.408 [59.976
68.544 77.112
INDICATED HORSE-POWER OF ENGINES.
759
To draw the Clearance-line on the Indicator-diagram.
the actual clearance not being known. — The clearance-line may be obtained
approximately by drawing a straight line, cbad, across the compression
curve, first having drawn OX parallel to the atmospheric line and 14.7 Ibs.
below. Measure from a the distance ad, equal to c&, and draw YO perpen-
dicular to OX through d; then will TB divided by AT be the percentage of
<hr
Fia. 139.
clearance. The clearance may also be found from the expansion-line by
constructing a rectangle efkg, and drawing a diagonal gf to intersect the
line XO. This will give the point O, and by erecting a perpendicular to XO
we obtain a clearance-line OF.
Both these methods for finding the clearance require that the expansion
and compression curves be hyperbolas. Prof. Carpenter (Power, Sept.,
1893) says that with good diagrams the methods are usually very accurate,
and give results which check substantially.
The Buckeye Engine Co., however, say that, as the results obtained are
seldom correct, being sometimes too little, but more frequently too much,
and as the indications from the two curves seldom agree, the operation has
little practical value, though when a clearly defined and apparently undis-
torted compression curve exists of sufficient extent to admit of the applica-
tion of the process, it may be relied on to give much more correct results
than the expansion curve.
To draw the Hyperbolic Curve on the Indicator-dia-
gram.— Select any point /in the actual curve, and from this point draw a
line perpendicular to the line JB, meet- j 3 2 i M B
iag the latter in the point J. The line - : -
JB may be the line of boiler-pressure,
but this is not material ; it may be drawn
at any convenient height near the top of
diagram and parallel to the atmospheric
line. From J draw a diagonal to K, the
latter point being the intersection of
the vacuum and clearance lines; from J
draw IL parallel with the atmospheric
line. From L, the point of intersection
of the diagonal JK and the horizontal
line IL, draw the vertical line LM. The
point M is the theoretical point of cut-off, and LM the cut-off line. Fix
upon any number of points 1, 2, 3, etc., on the line JB, and from these points
draw diagonals to K, From the intersection of these diagonals with LM
draw horizontal lines, and from 1, 2, 3, etc , vertical lines. Where these lines
meet will be points in the hyperbolic curve.
Pendulum Indicator Rig.— Power (Feb. 1893) gives a graphical
representation of the errors m indicator-diagrams, caused by the use of in-
-piTP -J
7GO THE STEAM-EXGINE.
correct form of the pendulum rigging. Tt is shown that the " brumbo "
pulley on the pendulum, to which the cord is attached, does not gener-
ally give as good a reduction as a simple pin
attachment. When the end of the pendulum is
slotted, working in a pin on the crosshead, the
error is apt to be considerable at both ends of
the card. With a vertical slot in a plate fixed
to the crosshead, and a pin on the pendulum
working in this slot, the reduction is perfect,
when the cord is attached to a pin on the pen-
dulum, a slight error being introduced if the
brumbo pulley is used. With the connection
between the pendulum and the crosshead made
by means of a horizontal link, the reduction is
nearly perfect, if the construction is such that
the connecting link vibrates equally above and
FIG. 141. below the horizontal, and the cord is attached
by a pin. If the link is horizontal at mid-stroke
a serious error is introduced, which is magnified if a brumbo pulley also is
used. The adjoining figures show the two forms recommended.
Theoretical Water-consumption calculated from the
Indicator-card,— The following method is given by Prof. Carpenter
(Poiver, fcept. 1893): p = mean effective pressure, I = length of stroke in
feet, a = area of piston in square inches, a -*- 144 = area in square feet, c =
percentage of clearance to the stroke, b = percentage of stroke at point
where water rate is to be computed, n = number of strokes per minute,
60n = number per hour, w = weight of a cubic foot of steam having a pres-
sure as shown by the diagram corresponding to that at the point wherfc
water rate is required, w' = that corresponding to pressure at end of com-
pression.
(b I c\ n
mn y~MT*
1UU * J4i
Corresponding weight of steam per stroke in Ibs. =2 l(^ Q )~144W'
Volume of clearance = , . ....
14,400
Weight of steam in clearance = 14 4QO-
Total weight of ) _ z(&±f ^ _ *«"*' _ *<» |"(b . c}w _ cv/\%
steam per stroke) ~ 'V. 100 /144 14,400 14,400L
Total weight of steam i Wnia r . , , ,1
from diagram per hour f == 14^00 L(
The indicated horse-power is p I a n -*- 33,000. Hence the steara-consump
tion per hour per indicated horse- power is
plan
33,000
_ .
J
Changing the formula to a rule, we have: To find the water rate from the
Indicator diagram at any point in the stroke.
RULE. — To the percentage of the entire stroke which has been completed
by the piston at the point under consideration add the percentage of clear-
ance. Multiply this result by the weight of a cubic foot of steam, having a<
pressure of that at the required point. Subtract from this the product of
percentage of clearance multiplied by weight of a cubic foot of steam hav-
ing a pressure equal to that at the end of the compression. Multiply this
result by 137.50 divided by the mean effective pressure.*
NOTE.— This method only applies to points in the expansion curve or be-
tween cut-off and release.
* For compound or triple-expansion engines read: divided by the equiva-
lent mean effective pressure, on the supposition that all work is done in one
cylinder.
COMPOUKD ENGINES.
761
The beneficial effect of compression in reducing the water-consumption of
an engine is clearly shown by the formula. If the compression is carried to
such a poinL that it produces a pressure equal to that at the point under
consideration, the weight of steam per cubic foot is equal, and w — ?«'. In
this case the effect of clearance entirely disappears, and the formula
becomes — —(bw).
P
In case of no compression, w' becomes zero, and the water-rate =
Prof. Denton (Trans. A. S. M. E,, xiv. 1363) gives the following table of
theoretical water-consumption for a perfect Mariotte expansion with steam
at 150 Ibs. above atmosphere, and 2 Ibs. absolute back pressure :
Ratio of Expansion, r.
M.E.P., Ibs. persq. in.
Lbs. of Water per hour
per horse-power, W.
10
15
20
25
30
35
52.4
38.7
30.9
25.9
22.2
19.5
9.68
8.74
8.20
7.84
7.63
7.45
The difference between the theoretical water -consumption found by the
formula and the actual consumption as found by test represents " water not
accounted for by the indicator,1' due to cylinder condensation, leakage
througrh ports, radiation, etc.
Leakage of Steam.— Leakage of steam, except in rare instances, has
so In lie effect upon the lines of the diagram that it can scarcely be detected.
The only satisfactory way to determine the tightness of an engine is to take
it when not in motion, apply a full boiler-pressure to the valve, placed in a
closed position, and to the piston as well, which is blocked for the purpose at
some point away from the end of the stroke, and see by the eye whether
leakage occurs. The indicator-cocks provide means for bringing into view
steam which leaks through the steam-valves, and in most cases that which
leaks by the piston, and an opening made in the exhaust-pipe or observa-
tions at the atmospheric escape-pipe, are generally sufficient to determine
the fact with regard to the exhaust-valves.
The steam accounted for by the indicator should be computed for both
the cut-off and the release points of the diagram. If the expansion-line de-
parts much from the hyperbolic curve a very different result is shown at
one point from that shown at the other. In such cases the extent of the
loss occasioned by cylinder condensation and leakage is indicated in a much
more truthful manner at the cut-off than at the release. (Tabor Indicator
Circular.)
COMPOUND ENGINES.
Compound, Triple- and Quadruple-expansion Engines.
—A compound engine is one having two or more cylinders, and in which
the steam after doing work in the first or high-pressure cylinder completes
its expansion in the other cylinder or cylinders.
The term "compound" is commonly restricted, however, to engines in
which the expansion takes place in two stages only— high arid low pressure,
the terms triple-expansion and quadruple-expansion engines being used when
the expansion takes place respectively in three and four stages. The number
of cylinders may be greater than the number of stages of expansion, for
constructive reasons; thus in the compound or two-stage expansion engine
the low-pressure stage may be effected in two cylinders so as to obtain the
advantages of nearly equal sizes of cylinders and of three cranks at angles of
120°. In triple- expansion engines there are frequently two low-pressure
cylinders, one of them being placed tandem with the high-pressure, and the
other with the intermediate cylinder, as in mill engines with two cranks at
90°. In the triple-expansion engines of the steamers Campania and Lucania*
783
THE STEAM-ENGINE*
with three cranks at 120°, there are five cylinders, two high, one intermedi-
ate, and two low, the high-pressure cylinders being tandem with the low.
Advantages of Compounding,— The advantages secured by divid-
ing the expansion into two or more stages are twofold: 1. Reduction of wastes
of steam by cylinder-condensation, clearance, and leakage; 2. Dividing the
pressures on the cranks, shafts, etc., in large engines so as to avoid excessive
pressures and consequent friction. The diminished loss by cylinder-conden-
sation is effected by decreasing the range of temperature of the metal sur-
faces of the cylinders, or the difference of temperature of the steam at
admission and exhaust. When high-pressure steam is admitted into a single-
cylinder engine a large portion is condensed by the comparatively cold
metal surfaces; at the end of the stroke and during the exhaust the water
is re-evaporated, but the steam so formed escapes into the atmosphere or
into the condenser, doing no work; while if it is taken into a second
cylinder, as in a compound engine, it does work. The steam lost in the first
cylinder by leakage and clearance also does work in the second cylinder.
Also, if there is a second cylinder, the temperature of the steam exhausted
from the first cylinder is higher than if there is only one cylinder, and the
metal surfaces therefore are not cooled to the same degree. The difference
In temperatures and in pressures corresponding to the work of steam of
150 Ibs. gauge-pressure expanded 20 times, in one, two, and three cylinders,
is shown in the following table, by W. H. Weightman, Am. Mach.t July 28,
Single
Cyl-
inder.
Compound
Cylinders.
Triple-expansion
Cylinders.
Diameter of cylinders, in. .
60
33
1
5
165
86.11
53.11
366°
259°. 9
106.1
399
290
112.900
61
3.416
4
33
19.68
15.68
259°. 9
184°. 2
75 7
403
290
84,752
28
1
2.714
165
121.44
60.64
366°
293°. 5
72.5
269
238
64,162
46
2.70
2.714
60.8
44.75
22.35
293°. 5
234°. 1
59.4
268
238
63.817
61
4.741
2.714
22.4
16.49
12.49
234°. 1
184°. 2
49.9
264
238
53,773
Expansions
20
165
32.96
28.96
366°
184°. 2
181.8
800
322
455,218
Initial steam - pressures-
absolute — pounds
Mean pressures, pounds. .
Mean effective pressures,
pounds
Steam temperatures into
cylinders
Steam temperatures out of
the cylinders
Difference in temperatures
Horse-power developed. . .
Speed of piston
Total initial pressures on
pistons, pounds
" Woolf 99 and Receiver Types of Compound Engines.-
The compound steam-engine, consisting of two cylinders, is reducible to two
forms, 1, in which the steam from theli.p. cylinder is exhausted direct into
the 1. p. cylinder, as in the Woolf engine; and 2, in which the steam from the
h. p. cylinder is exhausted into an intermediate reservoir, whence the steam
is supplied to, and expanded in, the 1. p. cylinder, as in the " receiver-
engine."
If the steam be cut off in the first cylinder before the end of the stroke,
the total ratio of expansion is the product of the ratio of expansion in the
first cylinder, into the ratio of the volume of the second to that of the first
cylinder; that is, the product of the two ratios of expansion.
Thus, let the areas of the first and second cylinders be as 1 to 3^, the
strokes being equal, and let the steam be cut off in the first at ^stroke; then
Expansion in the 1st cylinder ......................................... 1 to 2
•* " 2d . " ......................... . ...............
Total or combined expansion, the product of the two ratios... 1 to 7
"Woolf Engine, without Clearance— Ideal Diagrams.—
The diagrams of pressure of an ideal Woolf engine are shown in Fig. 142, aa
they would be described by the indicator, according to the arrows. In these
diagrams pg is the atmospheric line, win the vacuum line, cd the admission
COMPOUND ENGINES.
763
line, dg the hyperbolic curve of expansion in the first cylinder, and gh the con-
secutive expansion-line of back pressure
for the return -stroke of the first piston,
and of positive pressure for the steam- /
stroke of the second piston. At the point
h, at the end of the stroke of the second
piston, the steam is exhausted into the
condenser, and the pressure falls to the
level of perfect vacuum, mn.
The diagram of the second cylinder,
below gh, is characterized by the absence
of any specific period of admission ; the
whole of the steam-line gh being expan-
sional, generated by the expansion of
the initial body of steam contained in
the first cylinder into the second. When
the return-stroke is completed, the
whole of the steam transferred from
the first is shut into the second cylin- F 142
der. The final pressure and volume of FlG" 1£-~; DIAGRMS
the steam in the second cylinder are the INDICATOR-DIAGRAMS.
same as if the whole of the initial steam had been admitted at once into the
second cylinder, and then expanded to the end of the stroke in the manner
of a single-cylinder engine.
The net work of the steam is also the same, according to both distributions.
Receiver-engine, without Clearance— Ideal Diagrams.—
In the ideal receiver-engine the pistons of the two cylinders are con-
nected to cranks at right angles to each other on the same shaft. The
receiver takes the steam exhausted from the first cylinder and supplies it to
the second, in which the steain is cut off and then expanded to the end of
the stroke. On the assumption that the initial pressure in the second cylin-
der is equal to the final pressure in the first, and of course equal to the pres-
sure in the receiver, the volume cut off in the second cylinder must be
equal to the volume of the first cylinder, for the second cylinder must admit
as much steam at each stroke as is discharged from the first cylinder.
In Fig. 143 cd is the line of admission and hg the exhaust-line for the first
5
FIG. 143.— RECEIVER-ENGINE, IDEAL
INDICATOR-DIAGRAMS.
FIG. 144. — RECEIVER ENGINE, IDEAL
DIAGRAMS REDUCED AND COMBINED.
cylinder; and dg is the expansion-curve and pq the atmospheric line. In
the region below the exhaust-line of the first cylinder, between it and the
line of perfect vacuum, ol, the diagram of the second cylinder is formed; hi,
the second line of admission, coincides with the exhaust-line hg of the first
cylinder, showing in the ideal diagram no intermediate fall of pressure, and
ik is the expansion-curve. The arrows indicate the order in which the dia-
grams are formed.
In the action of the receiver-engine, the expansive working of the steam,
though clearly divided into two consecutive stages, is, as in the Woolf
engine, essentially continuous from the point of cut-off in the first cylinder
to the end of the stroke of the second cylinder, where it is delivered to the
condenser; and the first and second diagrams may be placed together and
764
THE STEAM-ENGINE.
combined to form a continuous diagram. For this purpose take the second
diagram as the basis of the combined diagram, namely, hiklo, Fig. 144. The
period of admission, hi, is one third of the stroke, and as the ratios of the
cylinders are as 1 to 3, hi is also the proportional length of the first diagram
as applied to the second. Produce oh upwards, and set off oc equal to the
total height of the first diagram above the vacuum-line; and, upon the
shortened base 7a, and the height Tic, complete the first diagram with the
steam-line cd, and the expansion-line di.
It is shown by Clark (S. E., p. 432, et seq.) in a series of arithmetical cal-
culations, that the receiver-engine is an elastic system of compound engine,
in which considerable latitude is afforded for adapting the pressure in the
receiver to the demands of the second cylinder, without considerably dimin-
ishing the effective work of the engine. In the Woolf engine, on the
contrary, it is of much importance that the intermediate volume of space
between the first and second cylinders, which is the cause of an interme-
diate fall of pressure, should be reduced to the lowest practicable amount.
Supposing that there is no loss of steam in passing through the engine,
by cooling and condensation, it is obvious that whatever steam passes
through the first cylinder must also find its way through the second cylin-
der. By varying*, therefore, in the receiver-engine, the period of admission
in the second cylinder, and thus also the volume of steam admitted for each
stroke, the steam will be measured into it at a higher pressure and of a less
bulk, or at a lower pressure and of a greater bulk; the pressure and density
naturally adjusting themselves to the volume that the steam from the re-
ceiver is permitted to occupy in the second cylinder. With a sufficiently
restricted admission, the pressure in the receiver may be maintained at the
pressure of the steam as exhausted from the first cylinder. On the con-
trary, with a wider admission, the pressure in the receiver may fall or
"drop" to three fourths or even one naif of the pressure of the exhaust-
steam from the first cylinder.
(For a more complete discussion of the action of steam in the Woolf and
receiver engines, see Clark on the Steam-engine.)
Combined Diagrams of Compound Engines.— The only way
of making a correct combined diagram from the indicator-diagrams of the
several cylinders in a compound engine is to set off all the diagrams on the
same horizontal scale of volumes, adding the clearances to the cylinder ca-
pacities proper. When this is attended to, the successive diagrams fall ex-
actly into their right places relatively to one another, and would compare
properly with any theoretical expansion-curve. (Prof. A. B. W. Kennedy,
Proc. Inst. M. E., Oct. 1886.*
COMPOUKD EKGIHES.
This method of combining diagrams is commonly adopted, but there are
objections to its accuracy, since the whole quantity of steam consumed in
the first cylinder at the end of the stroke is not carried forward to the
second, but a part of it is retained in the first cylinder for compression. For
a method of combining diagrams in which compression is taken account of,
see discussions by Thomas Mudd and others, in Proc. Tnst. M. E., Feb.,
1887, p. 48. The usual method of combining diagrams is also criticised by
Frank H. Ball as inaccurate and misleading (Am. Mach., April 12, 1894;
Trans. A. S. M. E., xiv. 1405, and xv. 403).
Figure 145 shows a combined diagram of a quadruple-expansion engine,
drawn according to the usual method, that is, the diagrams are first reduced
in length to relative scales that correspond wiih the relative piston-displace-
ment of the three cylinders. Then the diagrams are placed at such distances
from the clearance-line of the proposed combined diagram as to correctly
represent the clearance in each cylinder.
Calculated Expansions and Pressures In Two-cylinder
Compound Engines* (James Tribe, Am. Mach., Sept. <£ Oct. 1891.)
TWO-CYLINDER COMPOUND NON-CONDKNSING.
Back pressure % Ib. above atmosphere.
Initial gauge-
pressure
100
110
120
130
140
150
160
170
175
Initial absolute
pressure
115
125
135
145
155
165
175
185
190
Total expansion .
7.39
7.84
8.41
9
9.61
10.24
10.89
11.56
11.9
Exp ansions in
each cylinder..
2.7
2.8
2.9
3
3.10
3.2
3.3
3.4
3.45
Hyp. log. plus 1.
1.993
2.029
2.064
2.098
2.131
2.163
2.193
2.223
2.238
Forward j High.
84.8
90.5
9U
101.4
106.5
111.5
116.3
120.9
123.3
pressures'! Low..
31.3
32.3
33.1
33.7
34.3
34.8
35.2
35.6
35.7
Back j High.
42.5
44.6
46.5
48.3
50
51.5
53
64.4
55
pressures"! Low..
15.5
15.5
15.5
15.5
15.5
15.5
15.5
15.5
15.5
Mean j Hieh
42.3
45.9
49.5
53.1
56.5
60
63.3
66.5
68.2
effective •< T JL '
pressures f
15.8
16.8
17.6
18.2
18.8
19.3
19.7
20.1
20.2
Ratio-c y I i n d e r
areas
2.67
2.73
2.81
2.91
3
3.11
3.21
3.31
3.37
TWO-CYLINDER COMPOUND CONDENSING.
Back pressure, 6.5 Ibs. above vacuum .
Initial gauge^pressures •
90
100
110
120
130
140
150
Initial absolute pressures. .....
Probable per cent of loss
Total expansions
Exps. in each cylinder
Hyp log plus 1
105
2.6
15.7
3.96
2.376
115
2.9
17
4.13
2.418
125
3.3
18.5
4.3
2.458
135
3.6
20
4.47
2.497
145
3.8
21.5
4.64
2.534
155
4.0
22.7
4.77
2.562
165
43
24.2
4.92
2.593
Mean forward j High
pressures 1 Low
62.9
15.25
67.3
15.55
71.4
15.9
75.4
16.2
79.3
16.5
83.2
16.75
87
17.05
Mean back j High
26.5
27.8
29
30.2
31.4
32.4
33.5
pressures ( Low ........
4.3
4.3
4.3
4.3
4.3
4.3
4.3
/e?.n JHigh .
36.4
39.5
42.4
45.2
47.9
50.8
53.5
effective K £o w
10.95
11.25
11.6
11.9
12.2
12.45
12.75
pressures (
Terminal ( High
pressures { Low
26.5
6.4
27.8
6.45
29.0
6.45
30.2
6.5
31.4
6.55
32.4
6.55
33 5
6.6
Initial pressure in 1. p. cyl
Ratio of cylinder areas
25.3
3.32
26.6
3.51
27.8
3.66
29
3.8
30.2
3.92
31.4
4.08
32.4
4.19
The probable percentage of loss, line 3, is thus explained: There is always
a loss of heat due to condensation, and which increases with the pressure of
steam. The exact percentage cannot be predetermined, as it depends
largely upon the quality of the non-conducting covering used on the cylin-
der, receiver, and pipes, etc., but will probably be about as shown.
Proportions of Cylinders in Compound Engines.— Authori-
ties differ as to the proportions by volume of the high and low pressure
cylinders v and V. Thus Grashof gives V+ v ~ 0.85 frJ Hrahak, 0.90 i/r/
766 THE STEAM-ENGINE.
Werner, Vr\ and Rankine, \/r*, r being the ratio of expansion. Busley
makes the ratio dependent on the boiler-pressure thus:
Lbs.persq.in 60 90 105 120
F-i-v...... = 34 4.5 5
(See Seaton's Manual, p. 95, etc., for analytical method; Sennett, p. 496,
etc.; Clark's Steam-engine, p. 445, etc; Clark, Rules, Tables, Data, p. 849, etc.)
Mr. J. McFarlane Gray states that he finds the mean effective pressure in
the compound engine reduced to the low-pressure cylinder to be approxi-
mately the square root of 6 times the boiler-pressure.
Approximate Horse-power of a Modern Compound
Marine-engine. (Seaton.)— The following rule will give approximately
the horse-power developed by a compound engine made in accordance with
modern marine practice. Estimated H.P. = D* X ^* B X S.
D — diameter of l.p. cylinder; p = boiler-pressure by gauge;
R = revs, per min.; 8 — stroke of piston in feet.
Ratio of Cylinder Capacity in Compound Marine Kn»
giiies. (Seaton.) — The low-pressure cylinder is the measure of the power
of a compound engine, for so long as the initial steam-pressure and rate of
expansion are the same, it signifies very little, so far as total power only is
concerned, whether the ratio between the low and high -pressure cylinders
is 3 or 4; but as the power developed should be nearly equally divided be-
tween the two cylinders, in order to get a good and steady working engine,
there is a necessity for exercising a considerable amount of discretion in
fixing on the ratio.
In choosing a particular ratio the objects are to divide the power evenly
and to avoid as much as possible " drop " and high initial strain.
If increased economy is to be obtained by increased boiler- pressures, the
rate of expansion should vary with the initial pressure, so that the pressure
at which the steam enters the condenser should remain constant. In this
case, with the ratio of cylinders constant, the cut-off in the high-pressure
cylinder will vary inversely as the initial pressure.
Let R be the ratio of the cylinders; r, the rate of expansion; pj the initial
pressure: then cut-off in high-pressure cylinder = R -*- r; r varies with plt
so that the terminal pressure pn is constant- and consequently r = P! -fr-pn;
therefore, cut-off in high-pressure cylinder = R X pn -J-PI.
Ratios of Cylinders as Found in Marine Practice.— The
rate of expansion may be taken at one tenth of the boiler-pressure (or about
one twelfth the absolute pressure), to work economically at full speed.
Therefore, when the diameter of the low-pressure cylinder does not exceed
100 inches, and the boiler-pressure 70 Ibs., the ratio of the low-pressure to
the high-pressure cylinder should be 3.5; for a boiler-pressure of 80 Ibs., 3.75;
for 90 Ibs., 4.0; for 100 Ibs., 4.5. If these proportions are adhered to, there
will be no need of an expansion -valve to either cylinder. If, however, to
avoid "drop,'1 the ratio be reduced, an expansion-valve should be fitted to
the high-pressure cylinder.
Where economy of steam is not of first importance, but rather a large
power, the ratio of cylinder capacities may with advantage be decreased,
so that with a boiler-pressure of 100 Ibs. it may be 3.75 to 4.
In tandem engines there is no necessity to divide the work equally. The
ratio is generally 4, but \* hen the steam-pressure exceeds 90 Ibs. absolute 4.5
is better, and for 100 Ibs. 5.0.
When the power requires that the 1. p. cylinder shall be more than 100 in.
diameter, it should be divided in two cylinders. In this case the ratio of the
combined capacity of the two 1. p. cylinders to that of the h. p. may be 3.0
for 85 Ibs. absolute. 3.4 for 95 Ibs., 3.7 for 105 Ihs.. and 4.0 for 115 Ibs.
Receiver Space in Compound Engines should be from 1 to
1.5 times the capacity of the high- pressure cylinder, when the cranks are at
an angle of from 90° to 120°. When the cranks are at 180° or nearly this,
the space may be very much reduced. In the case of triple-compound en-
gines, with cranks at 120°. and the intermediate cylinder leading the high-
pressure, a very small receiver will do. The pressure in the receiver should
never exceed half the boiler-pressure. (Seaton.)
COMPOUND ENGINE& 76?
Formula for Calculating the Expansion and the Work
of Steam In Compound Engines.
(Condensed from Clark on the " Steam-engine.")
a SB area of the first cylinder in square inches;
a' ss area of the second cylinder in square inches;
r =3 ratio of the capacity of the second cylinder to that of the first;
L s» length of stroke in feet, supposed to be the same for both cylinders;
I = period of admission to the first cylinder in feet, excluding clearance;
c = clearance at each end of the cylinders, in parts of the stroke, in feet;
L' = length of the stroke plus the clearance, in feet;
I' = period of admission plus the clearance, in feet ;
s =5 length of a given part of the stroke of the second cylinder, in feet;
P =s total initial pressure in the first cylinder, in Ibs. per square inch, sup-
posed to be uniform during admission;
P* = total pressure at the end of the given part of the stroke «;
p =s average total pressure for the whole stroke;
R - nominal ratio of expansion in the first cylinder, or L -4- Z;
R' = actual ratio of expansion in the first cylinder, or L'-*-l';
R" ss actual combined ratio of expansion, in the first and second cylinders
together;
n =s ratio of the final pressure in the first cylinder to any intermediate
fall of pressure between the first and second cylinders;
ji m ratio of the volume of the intermediate space in the Woolf engine,
reckoned up to, and including the clearance of, the second piston,
to the capacity of the first cylinder plus its clearance. The value
of N is correctly expressed by the actual ratio of the volumes as
stated, on the assumption that the intermediate space is a vacuum
when it receives the exhaust-steam f rom the first cylinder. In point
of fact, there is a residuum of unexhausted steam in the interme-
diate space, at low pressure, and the value of N is thereby prac-
tically reduced below the ratio here stated. N » n . — a.
tt> SB whole net work in one stroke, in foot-pounds.
Ratio of expansion in the second cylinder:
In the Woolf engine, .
i+y
In the receiver- engine, V!Ln*2r%
Total actual ratio of expansion = product of the ratios of the thrae con-
secutive expansions, in the first cylinder, in the intermediate space, and
in the second cylinder,
In the Woolf engine, R> ( r ~ -f A) .
In the receiver-engine, r -,
Combined ratio of expansion behind the pistons a -n rR' » #".
Work done in the two cylinders for one stroke, with a given cut-off and a
given combined actual ratio of expansion:
Woolf engine, w » aP(l'(\ -f hyp log R") - c];
Receiver engine, w » «pJV(l + hyp log 5") - c (l + ^|pO]»
when there is no intermediate fall of pressure.
When there is an intermediate fall, when the pressure falls to %, 26, ^ of
the final pressure in the 1st cylinder, the reduction of work is 0.2#, 1.0*, 4.6*
of that when there is no fall.
768 THE STEAM-ENGINE.
Total work in the two cylinders of a receiver-engine, for one stroke for
any intermediate fall of pressure,
EXAMPLE —Let a = 1 sq. in., P as 63 Ibs., V s= 2.42 ft., n =s 4, R" = 5.969,
c = .42 ft., r = 3, B' = 2.653;
w = 1 X 63[2.42(5/4 hyp log 5.969) - .42(1 4- 4 ^g^)] = 421.55 ft.-lbs.
Calculation of Diameters of Cylinders of a compound con-
densing engine of 2UOO H.P. at a speed of TOO feet per minute, with 100 Ibs.
boiler-pressure.
100 Ibs. gauge-pressure = 115 absolute, less drop of 5 Ibs. between boiler
and cylinder = 110 Ibs. initial absolute pressure. Assuming terminal pres-
sure in 1. p. cylinder = 6 Ibs., the total expansion of steam in both cylinders
= 110-*-6 = 18.33. Hyp log 18.33 = 2.909. Back pressure iu 1. p. cylinder,
3 Ibs. absolute.
The following formulae are used in the calculation of each cylinder :
H.P.X 3.1,000
(1) Area of cylinder = M.E.P. x piston-speed-
(2) Mean effective pressure = mean total pressure — back pressure.
(3) Mean total pressure =• terminal pressure X (1 -h hyp log R).
(4) Absolute initial pressure = absolute terminal pressure X ratio of ex-
pansion.
First calculate the area of the low-pressure cylinder as if all the work
were done in that cylinder.
From (3), mean total pressure = 6x(14- hyp log 18.33) = 23.454 Ibs.
From (sj), mean effective pressure = 23.454— 3 = 20.454 Ibs.
From (1), area of cylinder = 20 454 X '^OQ = 461° SCl' *ns* ~ 76*6 ins* diam*
If half the work, or 1000 H.P., is done in the 1. p. cylinder the M.E.P. will
be half (hat found above, or 10.227 Ibs., aud the mean total pressure 10.227 +
3 = 13.227 Ibs.
From (3), 1 -f hyp log R = 13.227 -*- 6 = 2.2045.
Hyp log R = 1.2045, whence R in 1. p. cyl. = 3.335.
From (4), 3.335X6 = 20.01 Ibs. initial pressure in 1. p. cyl. and terminal
pressure in h. p. cyl., assuming no drop between cylinders.
11U -i- MM = 18.33-^3.335 = 5.497, R in h. p. cyl.
From (3), mean total pres, in h. p. cyl. = 20.01 X (1 + hyp log 5.497) = 54.11.
From (2), 54.11 —20.01 = 34.10, M.E.P. in h. p. cyl.
From (!), area of h. p. cyl. = I(^*?TT^ = 1382 sq. ins. = 42 ins. diam.
t (JO X «4. 1
Cylinder ratio = 4G10 -f- 1382 =.- 3.336.
The area of the h. p. cylinder may be found more directly by dividing the
area of the 1. p. cyl. by the ratio of expansion in that cylinder. 4610 -*-
3.335 = 1382 sq. ins.
In the above calculation no account is taken of clearance, of compression,
of drop between cylinders, iiqr of area of piston-rods. It also assumes that
the diagram in eacli cylinder is the full theoretical diagram, with a horizontal
steam-line and a hyperbolic expansion line, with no allowance for round-
ing of the corners. To make allowance for these, the mean effective pres-
sure in each cylinder must be multiplied by a diagram factor, or the ratio
of the area of an actual diagram of the class of engine considered, with the
given initial and terminal pressures, to the area of the theoretical diagram.
Such diagram factors will range from 0.6 to 0.94, as in the table on p. 745.
Best Ratios of Cylinders.— The question what is the best ratio of
areas of the two cylinders of a compound engine is still (1901), a disputed
one, but there appears to be an increasing tendency in favor of large ratios,
even as great as 7 or 8 to 1, with considerable terminal drop in the high-
pressure cylinder. A discussion of the subject, together with a description
of a new method of drawing theoretical diagrams of multiple-expansion
engines, taking into consideration drop, clearance, and compression, will be
found ia a paper by Bert C. Ball, iu Trans. A. IS, M. En xxi. 1002,
TRIPLE-EXPANSIOK ENGINES. 769
TRIPLE-EXPANSION ENGINES.
Proportions of Cylinders.— H. H. Suplee, Mechanics, Nov. 1887,
gives the following method of proportioning cylinders of triple-expansion
engines:
As in the case of compound engines the diameter of the low-pressure
cylinder is first determined, being made large enough to furnish the entire
power required at the mean pressure due to the initial pressure and expan-
sion ratio given; and then this cylinder is only given pressure enough to per-
form one third of the work, and the other cylinders are proportioned so as to
divide the other two thirds between them.
Let us suppose that an initial pressure of 150 Ibs. is used and that 900 H.P.
is to be developed at a piston-speed of 800 ft. per min., a'.id that an expan-
sion ratio of Itt is to be reached with an absolute back pressure of 2 Ibs.
The theoretical M.E.P. with an absolute initial pressure of 150 -f 14.7 =s
164.7 Ibs. initial at 10 expansions is
/>(! 4- hyP log 16) _ 3,7726
16 • 1M<7 X TT
less 2 Ibs. back pressure, = 38.83 - 2 = 36.83.
In practice only about 0.7 of this pressure is actually attained, so that
36.83 X 0.7 =s 25.781 Ibs. is the M.E.P. upon which the engine is to be pro-
portioned.
To obtain 900 H.P. we must have 33,000 X 900 = 29,700.000 foot-pounds, and
this divided by the mean pressure (25.78) and by the speed in feet (800) will
give 1440 sq. in. for the area of the 1. p. cylinder, about equivalent to 43 j'n.
diam.
IN jw as one third of the work is to be done in the 1. p. cylinder, the M.E.P.
in it will be 25.78 -«- 3 = 8.59 Ibs.
The cut-off in the high-pressure cylinder is generally arranged to cut off
at 0.6 of the stroke, and so the ratio of the h. p. to the 1. p. cylinder is equal
to 16X0.6 = 9.6, and the h. p. cylinder will be 1440 -*- 9.6 = 150 sq. in. area, or
about 14 in. diameter, and the M.E.P. in the h. p. cylinder is equal to
9.6 X 8.59 = 82.46 Ibs.
If the intermediate cylinder Is made a mean size between the other two,
its size would be determined by dividing the area of the 1. p. cylinder by the
square root of the ratio between the low and the high; but in practice this is
found to give a result too large to equalize the stresses, so that instead the
area of the int. cylinder is found 1 y dividing the area of the 1. p. piston by
l.l times the square jroot of the ratio of 1. p. to h.p. cylinder, which in this
ca«^ is 1440 -*- (1.1 4/9.6) = 422.5 sq. in., or alittle more than 23 in. diam.
The choice of expansion ratio is governed by the initial pressure, and is
generally chosen so that the terminal pressure in the 1. p. cylinder shall be
about 10 Ibs. absolute.
Formulae for Proportioning Cylinder Areas of Triple-
Expansion Engines.— The following tormulae are based on the method
of first finding the cylinder areas that would be required if an ideal hyper-
bolic diagram were obtainable from each cylinder, with no clearance, com-
pression, wire-drawing, drop by free expansion in receivers, or loss by
cylinder condensation, assuming equal work to be done in each cylinder,
and then dividing the areas thus found by a suitable diagram factor, such as
those given on page 745, expressing the ratio which the area of an actual
diagram, obtained in practice from an engine of the type under considera-
tion, bears to the ideal or theoretical diagram. It will vary in different classes
of engine and in different cylinders of the same engine, usual values ranging
from 0.6 to 0.9. When any one of the three stages of expansion takes place
in two cylinders, the combined area of these cylinders equals the area found
by the formulae.
NOTATION.
pl = initial pressure in the high pressure cylinder.
pt = terminal " * low pressure
pb = back
pa = term, press, in h. p. cvl. and initial press, in intermediate cyl.
p3 = " " " int. " " 1. p. cyl.
Bj, .R2, R3, ratio of exp. in h. p. int. and 1. p cyls.
R = total ratio of exp. — R} x R^ x 7?3.
P = mean effec. press, of the combined ideal diagram, referred to the
1. p. cyl.
770
THE STEAM ENGINE.
P,, P2, -P» = ni. e. p. in the h. p., int., and 1. p, cyls.
HP = horse power of the engine = PLA3N -*- 33,000.
L = length of stroke in feet; N = number of single strokes per min.
AH Az, A*< areas (sq ins.) of h. p. int. and 1. p. cyls. (ideal).
W = work done in one cylinder per foot of stroke.
ra = ratio of A^ to A1 ; ra = ratio otA^toA^
F!, F2, Fa, diagram factors of h. p. int. and 1. p. cyl.
«i, «a, «ai areas (actual) of
Formuloe.
(1) R — pi -*-pt.
(2) P = pt(l f hyp. log. R) - pb.
(3) P3 = fcP.
(4) Hyp. log. P3 = (P8 - pf 4- pb) -*-ptm
(5) BjJR,, = R -j- P3; #! = P2 ^ ^'fl^T
(6) p3 = ?•>* x #3.
(7) pa =p3 x K2.
(8) PJ - pa x U,.
(9) P2 = 2>3(byp. log. R.j = P3#3.
(10) P, = p2(hyp log. P,) = P2R2.
(11) TT = 1 1, 000 HP + LN.
(12) 4, = TT-*-P,; ^a=TT-f-Pa; ^3=TT^P3.
(13) j-a = ^a -*- ^i = P! -f- P2 = R, or «a; ra = A3 -*- ^tj = P! -*- P8.
(14) aj = Al -*- P3 ; </a = J2 -»- P2; «3 = As-*r F3.
From these formulae the figures in the following tables have been
calculated:
THEORETICAL MEAN EFFECTIVE PRESSURES, CYLINDER RATIOS, ETC., OF TRIPLE
EXPANSION ENGINES.
Back pressure, 3 Ibs. Terminal pressure, 8 Ibs. (absolute).
Pi-
R.
P.
*v
&,.
B,. J?a.
or ra.
Pa.
P'2
P2.
A-
r*
120
15
26. G6
8.89
1.626
3.037
13.01
39.51
14.45
43.89
4.939
140
17.5
27.90
9.30
1.^12
3.197
13.70
43.79
15.92
50.89
5.472
160
20
28.97
9.66
1.790
3.343
14.32
47.86
17.29
57.76
5.980
180
22.5
29.91
9.97
1.861
3.477
14.89
51.77
18.55
64.5-2
6.471
200
25
30.75
10.25
1.928
3.601
15.42
55.54
19.76
71.16
6.942
220
27.5
31.51
10.50
1,990
3.718
15.91
59.16
20.90
77.69
7.397
240
30
32.21
10.74
2.049
3.826
16.39
62.72
22.00
84.16
7.839
Back pressure, 3 Ibs. Terminal pressure, 10 Ibs. (absolute).
Pi-
R.
P.
P>-
*,.
or ra.
P,.
P-z-
P2.
A.
r,.
120
12
31.85
10.62
.436
2.890
14.36
41.50
15.24
44.04
4.148
140
14
33.39
11.13
.511
3.044
15.11
45.99
16.82
51.20
4.600
160
16
34.73
11.58
.580
3.182
15.80
50.28
18.29
58.20
5.027
180
18
35.90
11.97
.643
3.310
16.43
54.38
19.66
65.09
5.439
200
20
36.96
12.32
.702
8.428
17.02
58.34
20.97
71.88
5.834
220
22
37.91
12.64
.757
3.538
17.57
62.15
22.20
78.54
6.215
240
24
38.78
12.93
.809
3.642
18.09
65.88
23.38
85.15
6.587
Given the required H.P. of an engine, its speed and length of stroke, and
the assumed diagram factors F^ PQ, F3 for the three cylinders, the areas of
the cylinders may be found by using formulae (11), (12), and (14), and the
values of P4, pa, and Pa in the above table.
TRIPLE-EXPANSION ENGINES.
A Common Rule for Proportioning the Cylinders of mul-
tiple-expansion engines is: for two-cylinder compound engines, the cylinder
ratio is the square root of the number of expansions, and for triple-expansion
engines the ratios of the high to the intermediate and of the intermediate
to the low are each equal to the cube root of the number of expansions, the
ratio of the high to the low being the product of the two ratios, that is, the
square of the cube root of the number of expansions. Applying this rule to
the pressures above given, assuming a terminal pressure (absolute) of 10 Ibs.
and 8 Ibs. respectively, we have, for triple-expansion engines:
Boiler-
pressure
(Absolute).
Terminal Pressure, 10 Ibs.
Terminal Pressure, 8 Ibs.
No. of Ex-
pansions.
Cylinder Ratios,
areas.
No. of Ex-
pansions.
Cylinder Ratios,
areas.
130
140
150
160
13
14
15
16
1 to 2. 35 to 5. 53
1 to 2. 41 to 5. 81
1 to 2. 47 to 6.08
1 to 2. 52 to 6. 35
16^4
18f?
20
1 to 2. 53 to 6. 42
1 to 2. 60 to 6. 74
1 to 2. 66 to 7. 06
1 to 2.71 to 7.37
The ratio of the diameters is the square root of the ratios of the areas, and
the ratio of the diameters of the first and third cylinders is the same as the
ratio of the areas of first and second.
Seaton, in his Marine Engineering, says: When the pressure of steam em-
ployed exceeds 115 Ibs. absolute, it is advisable to employ three cylinders,
through each of which the steam expands in turn. The ratio of the low-
pressure to high- pressure cylinder in this system should be 5, when the
eteam-pressure is 125 Ibs. absolute; when 135 Ibs. absolute, 5.4; when 145
Ibs. absolute, 5.8; when 155 Ibs. absolute, 6.2; when 165 Ibs. absolute, 6.6.
The ratio of low-pressure to intermediate cylinder should be about one half
that between low-pressure and high- pressure, as given above. That is, if
the ratio of 1. p. to h. p. is 6, that of 1. p. to int. should be about 3, and conse-
quently that of int. to h. p. about 2. In practice the ratio of int. to h. p. f
nearly 2.25, so that the diameter of the int. cylinder is 1.5 that of the h. p.
The introduction of the triple-compound engine has admitted of ships being
propelled at higher rates of speed than formerly obtained without exceeding
the consumption of fuel of similar ships fitted with ordinary compound
engines; in such cases the higher power to obtain the speed has been devel-
oped by decreasing the rate of expansion, the low-pressure cylinder being
only 6 times the capacity of the high-pressure, with a working pressure of
170 Ibs. absolute. It is now a very general practice to make the diameter of
the low pressure cylinder equal to the sum of the diameters of the h. p. and
int. cylinders; hence,
Diameter of int. cylinder = 1.5 diameter of h. p. cylinder;
Diameter of 1. p. cylinder = 2.5 diameter of h. p. cylinder.
In this case the ratio of 1. p. to h, p. is 6.25; the ratio of int. to h. p. is 2.25;
and ratio of 1. p. to int. is 2.78.
Ratios of Cylinders for Different Classes of Engines.
(Proc. Inst. M. E., Feb. 1887, p. 36.)— As to the best ratios for the cylinders
in a triple engine there seems to be great difference of opinion. Considera-
ble latitude, however, is due to the requirements of the case, inasmuch as
it would not be expecied that the same ratio would be suitable for an eco-
nomical land engine, where the space occupied and the weight were ©f
minor importance, as in a war-ship, where the conditions were reversed. In
the land engine, for example, a theoretical terminal pressure of about 7
Ibs. above absolute vacuum would probably be aimed at, which would give
a ratio of capacity of high pressure to low pressure of 1 to 8^ or 1 to
9; whilst in a war-ship a terminal pressure would be required of 12 to 13 Ibs.
which would need a ratio of capacity of 1 to 5; yet in both these instances
the cylinders were correctly proportioned and suitable to the requirements
of the case. It is obviously unwise, therefore, to introduce any hard-and-
fast rule.
Types <*f Three-stage Expansion Engines,— 1. Three cranks
at 120 deg. 2. Two cranks with 1st and 2d cylinders tandem. 3. Two
cranks with 1st and 3d cylinders tandem. The most common type is the
first, with cylinders arranged in the sequence high, intermediate, low,
772
THE STEAM-ENGINE.
Sequence of Cranks.- Mr. Wyllie (Proc. Inst. M. E., 1887) favors the
sequence high, low, intermediate, while Mr. Mudd favors high, intermediate,
low. The former sequence, high, low, intermediate, gave an approximately
horizontal exhaust-line, and thus minimizes the range of temperature and
the initial load; the latter sequence, high, intermediate, low, increased the
range and also the load.
Mr.
of the stroke; with the sequence high, intermediate, low, it was 5? percent,
In the former case the compression was just what was required to keep
the receiver-pressure practically uniform; in the latter case the compression
caused a variation in the receiver-pressure to the extent sometimes of
22J/6 Ibs.
Velocity of Steam through Passages in Compound
Engines. (1'roc. Inst. M. E , Feb. 1887.)— In the !SSS. Para, taking the area
of the cylinder multiplied by the piston-speed in feet per second and
dividing by the area of the port the velocity of the initial steam through
the high-pressure cylinder port would be about 100 feet per second; the ex-
haust would be about 90. In the intermediate cylinder the initial steam
had a velocity of about 180, and the exhaust of 120. In the low-pressure
cylinder the initial steam entered through the port with a velocity of 250,
and in the exhaust-port the velocity was about 140 feet per second.
QUADRUPLE-EXPANSION ENGINES.
H. H. Suplee (Trans. A. S. M. E., x. 583) states that a study of 14 different
quadruple-expansion engines, nearly all intended to be operated at a pres^
sure of 180 Ibs. per sq. in., gave average cylinder ratios of 1 to 2, to 3.78, to
7.70, or nearly in the proportions 1 , 2, 4, 8.
If we take the ratio of areas of any two adjoining cylinders as the fourth
root of the number of expansions, the ratio of the 1st to the 4th will be the
c*:be of the fourth root. On this basis the ratios of areas for different pres~
sures and rates of expansion will be as follows :
Gauge-
pressures.
Absolute
Pressures.
Terminal
Pressures.
Ratio of
Expansion.
Ratios of Areas
of Cylinders.
( 12
14.6
1 1.95 : 3.81 : 7.43
160 •
175
I10
ir.5
1 2.05:4.18: 8.55
1 8
21.9
1 2.16 : 4.68 : 10.12
(12
16.2
1 2.01 : 4.02: 8.07
180
195
|io
19.5
1 2.10:4.42: 9.28
1 8
24.4
1 2.22:4.94:10.98
(12
17.9
1 2.06 : 4.23 : 8.70
200
215
I10
21.5
1 2.15:4.64: 9.98
1 8
26.9
1 2.28:5.19:11.81
(12
19.6
1 2.10:4.43: 9.31
220
235
I10
23.5
1 2.20:4.85:10.67
I 8
29.4
1 : 2.33: 5.42: 12.62
Seaton says: When the pressure of steam employed exceeds 190 Ibs. abso-
lute, four cylinders should be employed, with the steam expanding through
each successively; and the ratio of 1. p to h. p. should be at least 7.5, and
if economy of fuel is of prime consideration it should be 8; then the ratio
of first intermediate to h. p. should be 1.8, that of second intermediate to
first int. 2, and that of 1. p. to second int. 2.2.
In a paper read before the North East Coast Institution of Engineers and
Shipbuilders, 1890, William Russell Cummins advocates the use of a four-
cylinder engine with four cranks as being more suitable for high speeds
than the three-cylinder three-crank engine. The cylinder ratios, he claims,
should be designed so as to obtain equal initial loads in each cylinder. The
ratios determined for the triple engine are 1, 2.04, 6.54, and for the quadru-
ple, 1, 2.08, 4.46, 10.47. He advocates long stroke, high piston-spfeed, 100 rev-
olutions per minute, and 250 Ibs. boiler-pressure, unjacketed cylinders, ancl
separate steam and exhaust valves.
QUADRUPLE-EXPANSION ENGINES.
Diameter* of Cylinders of Recent Triple-expansion
Engines, Chiefly Marine.
Compiled from several sources, 1890-1893.
Diam. in inches: H = high pressure, I — intermediate, L = low pressure.
H
;.*
L
H
I
L
H
I
L
H
*
L
3
5
7.5
8
13
16
25.6
41
38.5
22
36
J40
140
36
38
58
61.5
94
100
5 4
6.5
8
10.5
12
16.5
16.5
24.5
i8t
(31
23
23.5
38
38
61
60
28*
28 f
56
86
7
9
12.5
17
27
44
24
37
56
39
61
97
7.1
11.8
18.9
17
26.5
42
25
40
64
40
59
88
7.5
12
19
17
28
45
26
42
69
40
67
106
8
11.5
16
18
27
40
26
42.5
70
40
66
100
9
14.5
22.5
18
29
48
28
44
72
41
66
101
9.8
15.7
25.6
18
305
51
29%
44
70
41%
67
1069$
20
16
25
18.7
29.5
43 3
29.5
48
78
42
59
92
11
16
24
18%
23.6
35.4
30
48
77
43
66
92
11
18
25
19.7
29.6
47.3
32
46
70
43
68
110
11
18
30
20
30
45
32
51
82
43%
67
106^
11.5
11.5
18
17.5
28.5
30.5
20
32.5
J36
(36
32
33
54
58
82
88
45
32.5|
71
AQ
113
J85.7
12
19.2
30.7
20
33
5'j
33.9
55.1
84.6
32.5 f
DO
185.7
13
14
22
22.4
33.5
36
21
21
32
36
48
51
34
34
54
50
85
90
47
75
181. 5
181.5
14.5
15
24
24
39
39
21.7
2,1.9
33.5
34
49.2
57
34.5
34.5
51
57
85
93
37)
37 f
79
j98
|98
15
24.5
38
22
31
51
Where the figures are bracketed there are two cylinders of a kind. Two
28" = one 39.6", two 31 " = one 43.8", two 32.5" = one 46.0", two 36" = one
60.9", two 37" = one 52.3", two 40" = one 56.6", two 81.5" = one 115", two
85.7" = one 121", two 98" = one 140". The average ratio of diameters of
cylinders of all the engines in the above table is nearly 1 to 1.60 to 2.56 and
the ratio of areas nearly 1 to 2.56 to 6.55.
The Progress in Steam-engines between 1876 and 1893 is shown
in the following comparison of the Corliss engine at the Centennial Exhibi-
tion in 1876 and the Allis-Corliss quadruple-expansion engine at the Chicago
Exhibition.
1876.
Simple
2
40 in.
120 in.
30ft.
24 in.
125,440 Ibs.
36
1400 H.P.
2500 H. P.
1,360,; 88 Ibs.
Cylinders, number 4
diameter.... 24, 40, 60, 70 in.
" stroke..
Fly-wheel, diameter
width of face. . .
weight .
Revolutions per minute
Capacity, economical
maximum
Total weight
72 in.
30ft.
76 in.
136,000 Ibs.
60
2000 H.P.
3000 H.P.
650,000 Ibs.
The crank-shaft body or wheel-seat of the Allis engine has a diameter of
21 inches, journals 19 inches, and crank bearings 18 inches, with a total
length of 18 feet. The crank-disks are of cast iron «j,nd are 8 feet in diam-
eter. The crank-pins are 9 inches in diameter by 9 inches long.
A Donfole-taiittem Triple-expansion Engine, built by Watts,
Campbell & Co., Newark, N. J., is described in Am. Mach., April 26, 1894.
It is two three-cylinder tandem engines coupled to one shaft, cranks at 90°,
cylinders 21, 32 and 48 by 60 in. stroke, 65 revolutions per minute, rated H.P.
2000; fly-wheel 28 feet diameter, 12 ft. face, weight 174,000 Ibs.; main shaft
22 in. diameter at the swell; main journals 19 X 38 in.; crank-pins 9U X 10
in.; distance between centre lines of two engines 24 ft. 7J^ in.; Corliss
valves, with separate eccentrics for the exhausUvalves of the l,p, cylinder.
774
THE STEAM-ENGINE.
. ?§li
iiisSSSSS
<M -* 0>00<??0000000>i-<t~.-ioc
•adid I
o 9zjs I
•Ut 'a
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Ilillll :g :
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ot&l-Po-S^.aic
pli ilillif P
ii iiiiiiili II,
ECONOMIC PERFORMANCE OF STEAM-ENGINES. 775
ECONOMIC PERFORMANCE OF STEAM-ENGINES.
Economy of Expansive Working under Various Condi-
tions, Single Cylinder.
(Abridged from Clark on the Steam Engine.)
1. SINGLE CYLINDERS WITH SUPERHEATED STEAM, NONCONDENSING. — In-
side cylinder locomotive, cylinders and steam-pipes enveloped by the hot
gases in the smoke-box. Net boiler pressure 100 Ibs.; net maximum press-
ure in cylinders 80 Ibs. per sq. in.
Cut-off, per cent 20 25 30 35 40 50 60 70 80
Actual ratio of expansion 3.91 3.31 2.87 2.53 2.26 1.86 1.59 1.39 1.23
Water per I.H.P. per hour, .^r
Ibs 18.5 19.4 20 21.2 22.2 24.5 27 30 33
2. SINGLE CYLINDERS WITH SUPERHEATED STEAM, C9NDENSING.— The best
results obtained by Hirn, with a cylinder 23% X 67 in. and steam super-
heated 150° F., expansion ratio 3^4 to 4J^, total maximum pressure in cylin-
der 63 to 69 Ibs. were 15.63 and 15.69 Ibs of water per I.H.P. per hour.
3. SINGLE CYLINDERS OP SMALL SIZE, 8 OR 9 IN. DIAM., JACKETED, NON-
CONDENSING. — The best results are obtained at a cut-off of 20 per cent, with
75 Ibs. maximum pressure in the cylinder; about 25 Ibs. of water per I.H.P.
per hour.
4. SINGLE CYLINDERS, NOT STEAM-JACKETED, CONDENSING.— Best results.
Engine.
Cylinder,
Diam.
and
Stroke.
Cut-off.
Actual
Expan-
sion
Ratio.
Total
Maxi-
mum
Pressure
in Cylin-
der per
sq. in.
Water as
Steam
I.He.P.
per hour.
Corliss and Wheel ock . . .
Hirn, No. 6
ins.
18X48
23% X 67
per cent.
12.5
16.3
ratio.
6.95
5.84
Ibs.
104.4
61.5
Ibs.
19.58
19 93
Mair M
32 X 66
• 24.6
3 84
54 5
26 46
25 X 24
15.5
5.32
87.7
26.25
Dexter
26 X 36
18 3
4.46
80 4
23 86
Dallas
36 X 30
•JO Q
5.07
46.9
26.69
Gallatin
30.1 X 30
15.0
4.94
81.7
21.89
SAME ENGINES, AVERAGE RESULTS.
Long Stroke.
Inches.
Cut-off, Per cent.
Lbs.
Lbs.
Corliss and Wheelock. . .
18X48
12.5
104.4
19.58
Hirn
23% X 67
16.3
61.5
19.93
Short Stroke.
Bache
25 X 24
15 5
87.7
26 25
Dexter, Nos. 20, 21, 22, 23
26 X 36
{ 18.3 to 33.3 )
1 average 25 f
79.0
24.05
Dallas, Nos. 27, 28, 29....
36 X 30
j 13.3 to 26. 4 I
1 average 19.8 f
46.8
26.86
Gallatin, Nos, 24, 25, 22, f
26 f
30.1 X 30
j 12. 3 to 18. 5 )
J average 15.8 f
78.2
23.50
Feed- water Consumption of Different Types of Engines.
—The following tables are taken from the circular of the Tabor Indicator
(Ashcroft Mfg. Co., 1889). In the first of the two columns under Feed- water
required, in the tables for simple engines, the figures are obtained by
computation from nearly perfect indicator diagrams, with allowance for cyl-
inder condensation according to the table on page 752, but without allow-
ance for leakage, with back-pressure in the non-condensing table taken at 16
Ibs. above Zero, and in the condensing table at 3 Ibs. above zero. The com-
pression curve is supposed to be hyperbolic, and commences at 0.91 of the
return-stroke, with a clearance of 3£ of the piston-displacement.
Table No. 2 gives the feed-water consumption for jacketed compound-con-
776
THE STEAM- ENGINE.
densing engines of the best class. The water condensed in the jackets is
included in the quantities given. The ratio of areas of the two cylinders are
as 1 to 4 for 120 Ibs. pressure; the clearance of each cylinder is 3#; and the
cut off in the two cylinders occurs at the same point of stroke. The initial
pressure in the 1. p. cylinder is 1 Ib. per sq. in. below the back- pressure of the
n. p. cylinder. The average back pressure of the whole stroke in the 1. p.
cylinder is 4.5 Ibs. for 10% cut-off; 4.75 Ibs. for 20% cut-off; and 5 Ibs. for 30#
cut-off. The steam accounted for by the indicator at cut-off in the h. p.
cylinder (allowing a small amount for leakage) is .74 at 10* cut-off, .78 at
20%, and .82 at 30# cut-off. The loss by condensation between the cylinders
is such that the steam accounted for at cut-off in the 1. p. cylinder, ex-
pressed in proportion of that shown at release in the h. p. cylinder, is .85 at
10% cut-off, .87 at 20% cut-off, and .89 at 30$ cut-off.
The data upon which table No. 3 is calculated are not given, but the feed-
water consumption is somewhat lower than has yet been reached (1894), the
lowest steam consumption of a triple-exp. engine yet recorded being 11.7 Ibs.
TABLE No. 1.
FEED-WATER CONSUMPTION, SIMPLE ENGINES.
NON-CONDENSING ENGINES. CONDENSING ENGINES.
03
<D
Feed-water Re-
A
2"
Feed-water Re-
|
|
quired per I. H. P.
per Hour.
o
quired per I.H.P.
per Hour.
<D
£
«3,*
"S o> S ®
<D
£
2^
i "§}=«>
j§
0)
ft OJ
""•- Ee c3
1
S V
<5.£ | g1
^
c
J>
ii
*f*l
?'
|
o
bJDfl
si 1
4&
6
^
II
I
IS
§£«5
fill
-&
s
I
||
ll?t
*2
PH "
§,££
o
CW a"
CL^
o. 43 ^ JF1
6
"S 5
•5^3
a
w £ ~
f-1 o3 rn 2r
6
ll
Q
£* — t>0
K »
i
f*a
*£
o &£e3
&P.S.2
o3
•s A
*i2
0 ^<3
5^ p.£.2
&
8
HH
H
0
o
£*
I-H
S
0
60
8.70
37.26
40.95
\
60
14.42
18.22
20.00
70
12.39
30.99
33.68
70
16.96
17.96
19.69
80
16.07
27.61
29.88
b\
80
19.50
17.76
19.47
90
19.76
25.43
27.43
1
90
22.04
17.57
19.27
100
23.45
23.90
25.73
I
100
24.58
17.41
19.07
r
60
21.12
27.55
29.43
r
60
22.34
17.68
19.34
70
26.57
25.44
27.04
70
26.03
17 47
19.09
20 -1
80
32.02
21.04
25.68
10 J
80
29.72
17.30
18.89
1
90
37.47
23.00
24.57
90
33.41
17.15
18.70
I
100
42.92
22.25
23.77
L
100
37.10
17.02
18.56
60
30.47
27.24
29.10
r
60
29.00
17.93
19.51
70
37.21
25.76
27.43
70
33.65
17.75
19.27
so -
30
43.97
24.71
26.29
iaJ
80
38.28
17.60
19.09
90
50.73
23.91
25.38
90
42.92
17.45
18.91
100
57.49
23.27
24.68
I
100
47.56
17.32
18.74
60
37.75
27.92
29.63
r
60
34.73
18.58
20.09
70
45.50
26.66
28.18
70
40.18
18.40
19.85
40J-
80
53.25
25.76
27.17
20^
80
45.63
18.27
19.69
90
61.01
25.03
26.35
1
90
51.08
18.14
19.51
100
68.76
24.47
25.73
I
100
56.53
18.02
19.36
r
60
43.42
28.94
30.66
f
60
44. C6
20.19
21.64
i
70
51.94
27.79
29.31
1
70
50.81
20.04
21.41
30 i
80
60.44
26.99
28.38
30 4
80
57.57
19.91
21.25
' I
90
68.96
26.32
27.62
1
90
64.32
19.78
21.06
100
77.48
25.78
26.99
I
100
71.08
19.67
20.93
r
60
51.35
21.63
22.95
i
70
59.10
21.49
22.74
40^1
80
66.85
21.36
22.56
1
90
74.60
21.24
22.41
I
100
82.36
21.13
22.24
CALCULATED PERFORMANCES OF STEAM-ENGINES.
TABLE No. 2.
FEED-WATER CONSUMPTION FOB COMPOUND CONDENSING ENGINES.
Cut-off,
per cent.
Initial Pressure above
Atmosphere.
Mean Effective Press-
Atmosphere.
Feed-water
Required
per T.H.P. per
Hour, Lbs.
H.P. Cyl.,
Ibs.
L.P. Cyl..
Ibs.
H.P. Cyl.,
Ibs.
L.P Cyl,
Ibs.
• i
80
100
120
4.0
73
11.0
11.67
15.33
18.54
2.65
3.87
5.23
16.92
15.00
13.86
• 1
80
100
120
4.3
8.1
12.1
26.73
33.13
39.29
5.48
7.56
9.74
14.60
13.67
13.09
30 1
80
100
120
4.6
8.5
11.7
37.61
46.41
56.00
7.48
10.10
12.26
14.99
14.21
13.87
TABLE No. 3.
FEED-WATER CONSUMPTION FOR TRIPLE-EXPANSION CONDENSING ENGINES.
Cut-off,
per
Initial Pressure above
Atmosphere.
Mean Effective Pressure.,
Feed-water
Required
per I. H.P.
cent.
H.P. Cyl.,
Ibs.
I. Cyl.,
Ibs.
L.P. Cyl.,
Ibs.
H.P. Cyl.,
Ibs.
I. Cyl.,
Ibs.
L.P. Cyl..
Ibs.
per Hour,
Ibs.
(
120
37.8
1.3
38.5
17.1
6.5
12.05
30 •?
140
43.8
2.8
46 5
18.6
7.1
11.4 .
1
160
49.3
3.8
55.0
20.0
8.0
10.75
(
120
38.8
2.8
51.5
22.8
8.6
11.65
40 <
140
45.8
3.9
59.5
23.7
9.1
11.4
1
160
51.3
5.3
70.0
25.5
10.0
10.85
I
120
39.8
3.7
60.5
26.7
10.1
12.2
50 4
140
46.8
4.8
70.5
28.0
10.8
11.6
1
160
52.8
6.3
82.5
30.0
11.8
11.15
Most Economical Point of Cut-off in Steam-engines.
(See paper by Wolff and Denton, Trans. A. S. M. E., vol. ii. p. 147-281; also,
Ratio of Expansion at Maximum Efficiency, R. H. Thurston, vol. ii. p. 128.)
—The problem of the best ratio of expansion is not one of economy of con-
sumption of fuel and economy of cost of boiler alone. The question of
interest on cost of engine, depreciation of value of engine, repairs of engine,
etc., enters as well; for as we increase the rate of expansion, and thus,
within certain limits fixed by the back-pressure and condensation of steam,
decrease the amount of fuel required and cost of boiler per unit of work,
we have to increase the dimensions of the cylinder and the size of the en-
gine, to attain the required power. We thus increase the cost of the engine,
etc,, as we increase the rate of expansion, while at the same time we de-
crease the fuel consumption, the cost of boiler, etc. So that there is in
every engine some point of cut-off, determinable by calculation and graphi-
cal construction, which will secure the greatest efficiency for a given expen-
diture of money, taking into consideration the cost of fuel, wages of engineer
and firemen, interest on cost, depreciation of value, repairs to and insurance
of boiler and engine, and oil, waste, etc., used for engine. In case of freight-
carrying vessels, the value of the room occupied by fuel should be consid-
ered in estimating the cost of fuel.
Sizes and Calculated Performances of Vertical High*
speed Engines.— The following tables are taken from a circular of the
Field Engineering Co., New York, describing the engines made by the Lake
Erie Engineering Works, Buffalo, N. Y. The engines are fair representatives
of the type now coming largely into use for driving dynamos directly with-
out belts. The tables were calculated by E. F. Williams, designer of the
engines. They are here somewhat abridged to save space:
778
THE STEAM-ENGINE.
Simple Engines— Non-condensing:.
*l
°~
I'l
5-s
Stroke, inches.
Revs, per Min-
ute.
H.P. when
Cutting off
at 1/5 stroke.
H.P. when
Cutting off
at J4 stroke.
H.P. when
Cutting off
at ^ stroke.
Dimen-
sions of
Wheels.
diam. face
JS
1
5,
1
1
Exhaust-pipe, j
70
Ibs.
80
Ibs.
90
Ibs.
70
Ibs.
80
Ibs.
90
Ibs.
70
Ibs.
80
Ibs.
90
Ibs.
Ft.
In.
3*
&
&
18
22
a*
10
12
14
16
18
20
24
28
32
34
370
318
277
246
222
181
158
138
120
112
20
27
41
53
66
95
119
179
221
269
25
32
49
64
80
115
144
216
267
325
30
39
60
96
138
173
261
322
392
~35~
26
34
52
67
84
120
151
227
281
342
31
41
62
81
100
144
181
272
336
409
36
47
71
93
116
1C6
208
313
386
470
32
41
63
82
302
146
183
276
340
414
37
48
74
96
120
172
215
324
400
487
43
56
85
111
138
198
248
373
460
560
4
4^
5'9"
6'8"
»
10
11'8"
13'4"
14'2"
4
5
°&
11
15
19
28
34
41
1
aya
P
6
7
8
3
V
P
6
7
8
9
10
Mean
Ratio
Termi
(abc
Cyl.cc
Steam
pei-
eff. press.lb.
of expans'n.
nal pressure
ut) Ibs.
24
29
30.5
36.5
42
37
43.5
50
NOTE. — The
nominal -power
rating of the en-
gines is at 80 Ibs.
gauge pressure,
steam cut-off at
14 stroke.
5
4
3
17.9
26
32.9
20
26
30
22.3
26
27.4
22.4
24
31.2
25
24
29.0
27.6
24
27.9
29.8
21
32
33.3
21
31.4
36.8
21
30
)ndensat1n, %
L per I.H.P.
hour Ibs.
Compound Engines — Non-condensing — High - pressure
. Cylinder and Receiver Jacketed.
Diam.
Cylinder,
inches.
Stroke, inches.
Revolutions per
Minute.
H.P. when cutting
off at J4 Stroke
in h.p. Cylinder.
H.P. when cutting
off at m Stroke
in h.p. Cylinder .
H.P. when cutting
off at y% Stroke
in h.p. Cylinder.
Cyl.
Ratio,
8fc:l.
Cyl.
Ratio,
4J4: 1.
Cyl.
Ratio,
%:l.
Cyl.
Ratio,
4^:1.
Cyl.
Ratio,
3^:1.
Cyl.
Ratio,
4^:1.
PL,'
w
Pi
W
P4
hj
80
Ibs.
90
Ibs.
130
Ibs.
150
Ibs.
80
Ibs.
90
Ibs.
130
Ibs.
150
Ibs.
80
Ibs.
90
Ibs.
130
Ibs.
150
Ibs.
79
101
159
196
281
340
461
623
803
1030
1508
1973
94
&
&
18
20
24«^
2S!i
6J4
9
10H
12
13V6
15^3
18^
2Qyz
22y2
w
12
18H
15*
&
28^
33J^
38
43
52
60
10
12
14
16
18
20
24
28
32
34
42
48
370
318
277
246
222
185
158
138
120
112
93
80
7
9
14
18
26
32
43
57
74
94
138
180
15
19
28
37
53
65
88
118
152
194
285
374
19
24
36
47
68
84
112
151
194
249
385
477
32
40
60
78
112
139
186
249
321
412
603
789
23
29
43
57
81
100
135
180
232
297
436
570
31
39
58
76
109
135
181
242
312
400
587
767
35
45
67
87
125
154
206
277
357
457
670
877
46
59
87
114
164
202
271
363
468
601
880
1151
44
56
83
109
156
192
258
346
446
572
838
1096
55
70
104
136
195
241
323
433
558
715
1048
1370
64
81
121
158
226
279
374
502
647
829
1215
1589
Mean effec. press... Ibs
Ratio of expansion
Cyl. condensation, #...
Ter. press, (about) .Ibs.
Loss from expanding
below atmosphere, %
St. per I.H.P. p. hr.lbs.
3.3
6.8
8.7
14.4
10.4
14.0
16
21
20
25
29
36
Wt
18M
10J4
13%
6M
VA
14
7.3
34
55
14
7.7
15
42
16
7.9
17
47
16 12
9 92
3 5
29 133.3
12
10.4
0
27.7
13
10.5
0
28.7
13
12
0
25.4
10
14
0
30
10
15.5
0
26.2
11
14.6
0
21
11
17.8
0
20
The original table contains figures of horse-power, etc., for 110 and 120 Ibs.,
cylinder ratio of 4 to 1 ; and J40 Ibs., ratio 4J^ to 1.
CALCULATED PERFORMANCES OF STEAM-ENGINES. 779
Compound-engines— Condensing— Steam-jacketed,
Diam.
Cylinder,
Inches.
Stroke, inches.
Revolutions per
Minute.
H.P.when cutting
off at 14 Stroke
in h.p. Cylinder.
H.P. when cutting
off at ^ Stroke
in h.p. Cylinder.
H.P. when cutting
off at m Stroke
in h.p. Cylinder.
R<2
8fc
fl.
tio,
• 1
Cyl.
Ratio,
4 : 1.
Cyl.
Ratio,
3^6 : 1.
Cyl.
Ratio,
4 : 1.
Cyl.
Ratio,
3^: 1.
Cyl.
Ratio,
4 : 1.
AH*
w
fc
W
AJ
80
Ibs.
110
ibs.
115
Ibs.
125
Ibs.
80
Ibs.
110
Ibs.
115
Ibs.
125
Ibs.
80
Ibs.
110
Ibs.
115
Ibs.
125
Ibs.
6
H
J3
12^
14
17
19
21
26
30
6^6
8*
13H
22}J
28^
33
12
18fc
IP
£
38 2
43
52
60
10
12
14
16
18
20
24
28
32
34
42
48
370
318
277
246
222
185
158
138
120
112
93
80
44
56
83
109
156
192
258
346
446
572
838
1096
59
76
112
147
210
260
348
467
602
772
1131
1480
53
67
100
131
187
231
310
415
535
686
1006
1316
62
78
116
152
218
269
361
484
624
801
1174
1534
55
70
104
136
195
241
323
433
558
715
1048
1370
70
90
133
174
250
308
413
554
714
915
1341
1757
68
87
129
169
242
298
400
536
691
887
1299
1699
75
95
141
185
265
327
439
588
758
972
1425
1863
70
90
133
174
250
308
413
554
714
915
1341
1757
97
123
183
239
343
423
568
761
981
1258
1844
2411
95
120
179
234
335
414
555
744
959
1230
1801
2356
106
134
200
261
374
462
619
830
1070
1S?'3
2012
2632
Mean effec. press.. Ibs.
Ratio of Expansion . . .
Cyl. condensation, %. . .
St. perl.H.P. p. hr.lbs.
20
27
24
28
25
32
31
34
32
44
43
48
13*
16M
10
im
6%
8M
18
17.3
18
16.6
20
16.6
20
15.2
15
17.0
15
16.4
18
16.3
18
15.8
12
17.5
12
17.0
14
16.8
14
16.0
The original table contains figures for 95 Ibs., cylinder ratio 3J^ to 1; and
120 Ibs , ratio 4 to 1.
Triple-expansion Engines, Non-condensing,— Receiver
only Jacketed.
Diameter
Cylinders,
0
1
00
Horse-power
when Cutting
off at 42 per
cent of Stroke
Horse-power
when Cutting
off at 50 pei-
cent of Stroke
Horse-power
when Cutting
off at 67 per
cent of Stroke
me es.
.2®
in First Cylin-
in First Cylin-
in First Cylin-
jg
3 3
der.
der.
der.
H. P.
I. P.
L. P.
m
I8
180 Ibs.
200 Ibs.
180 Ibs.
200 Ibs.
180 Ibs.
200 Ibs,
4%
7*
12
10
370
55
64
70
84
95
108
8*
13*
12
318
70
81
90
106
120
137
gi/
iovl
14
277
104
121
133
158
179
204
•j-rx
12
19
16
246
136
158
174
207
234
267
9
18
222
195
226
250
296
335
382
10
16 2
25
20
185
241
279
308
366
414
471
18
24
158
323
374
413
490
555
632
13
22
33}J
28
138
433
502
554
657
744
848
15
38
120
558
647
714
847
959
1093
17
27
43
34
112
715
829
915
1089
1230
1401
20
33
52
42
93
1048
1215
1341
1592
1801
2053
23*
38
60
48
80
1370
1589
1754
2082
2356
2685
Mean effective press. , Ibs.
25
29
32
38
43
49
No of expansions .
16
13
10
Per cent cyl. condens —
14
12
10
Steam p. I.H.P. p.hr., Ibs.
Lbs. coal at 8 Ib. evap. Ibs.
20.76
2.59
19.36
2.39
19.25
2.40
17.00
2.12
17.89
2.23
17.20
2.15
780
THE STEAM-ENGINE.
Triple-expansion Engines— Condensing— Steam*
Jacketed.
Diameter
Horse- po\ver
when Cut-
Horse-power
when Cut-
Horse-power
when Cut-
Horse-power
when Cut-
Cylinders,
|
£
—
ting off at J4
Stroke in
ting off at y§
Stroke in
ting off at y%
Stroke in
ting off at 24
Stroke in
me es.
o
a
Fin
st Cylin-
First Cylin-
First Cylin-
First Cylin-
of
o 35
s 3
der.
der.
der.
der.
^
.
f*4
"S.2
120
140
160
120 140
160
120
140
160
120
140
160
W
HH
OD
S"
Ibs.
Ibs.
.Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs.
Ibs
Ibs.
Ibs.
4%
7U
12
10
370
35
42
48
44
58
59
57
72
84
81
97
110
5V4
8J^
13V£
12
318
45
53
62
56
67
76
73
92
107
104
123
140
10^
16J^
14
2VV
67
79
92
83
100
112
108
137
159
154
183
208
T^
12
19
16
246
87
103
120
109
131
147 141
180
208
201
289
272
9
141^
22U
18
22*
125
148
172
156
187
211 203
257
299
289
343
390
10
16
25
20
185
154
183
212
192
231
260 250
317
368
356
423
481
18
28V6
24
158
206
245
284
258
310
348 335
426
494
477
568
645
13 °
22
33U
28
138
277
329
381
346
415
407 450
571
663
640
761
865
15
32
120
357
424
491
446
535
602 580
736
854
825
98!
1115
17
27
43
34
112
458
543
629
572
686
772 744
944
1095
1058
1258
1430
20
83
52
42
93
670
796
922
838
1006 1131 1089
1383
1605
1551
1844
209(5
23^
38
60
48
80
8771041
1206
1096
1316 1480 1454
1808
2099
2028
2411
2740
Mean effec. press., Ibs.
16' 19
22
20
24
27; 26
33
38.3
37
44
50
No. of expansions —
26.8
20.1
13.4
8.9
Percent cyl. condens.
19
19
19
16 16
16 12
12
12
8
8
8
St.p.I.H.P.p. hr.,lbs.
14.7
13.9
13.3
14.3
13.98
13.214.3
13.6
13.0
15.7
14.9
14.2
Coal at 8 Ib. e vap., Ibs.
1.8
1.73
1.66
1.78
1.74
1.651.78
1.70
1.62
1.96
1.86
1.77
of Engine to be used where Exhaust-steam is
needed for Heating.— In many factories more or less of the steam
exhausted from the engines is utilized for boiling, drying, heating, etc.
Where all the exhaust-steam is so used the question of economical use of
steam in the engine itself is eliminated, and the high-pressure simple engine
is entirely suitable. Where only part of the exhaust-steam is used, and the
quantity so used varies at different times, the question of adopting a simple,
a condensing, or a compound engine becomes more complex. ThiR problem
is treated by C. T. Main in Trans. A. S. M. E., vol. x. p. 48. He shows that
the ratios of the volumes of the cylinders in compound engines should vary
according to the amount of exhaust-steam that can be used for heating. A
case is given in which three different pressures of steam are required or
could be used, as in a worsted dye-house: the high or boiler pressure for
the engine, an intermediate pressure for crabbing, and low-pressure for
boiling, drying, etc. If it did not make too much complication of parts in
the engine, the boiler-pressure might be used in the high-pressure cylinder,
exhausting into a receiver from which steam could be taken for running
small engines and crabbing, the steam remaining in the receiver passing
into the intermediate cylinder and expanded there to from 5 to 10 Ibs. above
the atmosphere and exhausted into a second receiver. From this receiver
is drawn the low-pressure steam needed for drying, boiling, warming mills,
etc., the steam remaining in receiver passing into the condensing cylinder.
Comparison of the Economy of Compound and Single-
cylinder Corliss Condensing Engines, each expanding
about Sixteen Times. (D. S. Jacobus, Trans. A. S. M. E., xii. 943.)
The engines used in obtaining comparative results are located at Stations
I. and II. of the Pawtucket Water Co.
The tests show that the compound engine is about 30£ more economical
than the single-cylinder engine. The dimensions of the two engines are as
follows: Single 20" X 48"; compound 15" and 30*4" X 30". The steam
used per horse-power per hour was: single 20.35 Ibs., compound 13.73 Ibs.
Both of the engines are steam-jacketed, practically on the barrels only
with steam at full boiler-pressure, viz. single 106.3 Ibs., compound 127.5 Ibg.
PERFORMANCES OF STEAM-ENGINES. 781
The steam -prsssure in the case of the compound engine is 127 Ibs., or 21
Ibs. higher than for the single engine. If the steam-pressure be raised this
amount in the case of the single engine, and the indicator-cards be increased
accordingly, the consumption for the single-cylinder engine would be 19.97
Ibs. per hour per horse-power.
Two-cylinder vs. Three-cylinder Compound Engine.—
A Wheelock triple-expansion engine, built for the Merrick Thread Co.,
Holyoke, Mass., is constructed so that the intermediate cylinder may be cut
out of the circuit and the high-pressure and low-pressure cylinders run as a
two -cylinder compound, using the same conditions of initial steam -pressure
and load. The diameters of the cylinders are 12, 16, and 24£f inches, the
stroke of the first t\vo being 36 in. and that of the low-pressure cylinder 48
in. The results of a test reported by S. M. Green and G. I. Rockwood, Trans.
A. S. M. E., vol. xiii. 647, are as follows: In Ibs. of dry steam used per I.H.P.
per hour, 12 and 24^f in. cylinders only used, two tests 13.06 and 12.76 Ibs.,
average 12.91. All three cylinders used, two tests 12.67 and 12.90 Ibs., average
12.79. The difference is only \%, and would indicate that more than two cylin-
ders are unnecessary in a compound engine, but it is pointed out by Prof.
Jacobus, that the conditions of the test were especially favorable for the
two-cylinder engine, and not relatively so favorable for the three cylinders.
The steam-pressure was 142 Ibs. and'the number of expansions about 25.
(See also discussion on the Rockwood type of engine, Trans. A. S. M. E., vol.
xvU
Inflect of Water contained in Steam on the Efficiency of
the Steam-engine. (From a lecture by Walter C. Kerr, before the
Franklin Institute, 1891.) — Standard writers make little mention of the effect
of entrained moisture on the expansive properties of steam, but by common
consent rather than any demonstration they seem to agree that moisture
produces an ill effect simply to the percentage amount of its presence.
That is, 5% moisture will increase the water rate of an engine 5#.
Experiments reported in 1893 by R. C. Carpenter and L. S. Marks, Trans.
A. S. M. E., xv., in which water in varying quantity was introduced into the
steam-pipe, causing the quality of the steam to ranee from 99$ to 58$ dry,
showed that throughout the range of qualities used the consumption of dry
steam per indicated horse-power per hour remains practically constant, and
indicated that the water was an inert quantity, doing neither good nor harm.
Relative Commercial Economy of Best Modern Types of
Compound and Triple-expansion Engines. (J. E. Denton,
American Machinist, Dec. 17, 1891.) — The following table and deductions
show the relative commercial economy of the compound and triple type for
the best stationary practice in steam plants of 500 indicated horse-power.
The table is based on the tests of Prof. Schroter, of Munich, of engines built
at Augsburg, and those of Geo. H. Barrus on the best plants of America, and
of detailed estimates of cost obtained from several first-class builders.
Trip motion, or Corliss engines of [^Vbv^asureS? ! 13'6 14'°
th« t.wm-rvmmrmnd-rpofiivfii- non. H.-t1., by measurement.
the twin-compound-receiver con-
densing type, expanding 16 times.
Boiler pressure 120 Ibs.
Trip motion, or Corliss engines of
the triple-expansion four-cylin-
der-receiver condensing type, ex-
panding 22 times. Boiler pressure,
150 Ibs.
Lbs. coal per hour per
H.P., assuming 8.5 Ibs. J- 1.60 1.65
actual evaporation. )
Lbs. water per hour per I 12 *
H.P., by measurement, r1<5'5
Lbs. coal per hour per )
H.P., assuming 8.5 Ibs. V 1.48 1.50
actual evaporation. )
The figures in the first column represent the best recorded performance
(1891), and those in the second column the probable reliable performance.
The table on the next page shows the total annual cost of operation, with
coal at $4.00 per ton, the plant running 300 days in the year, for 10 hours and
for 24 hours per day.
Increased cost of triple-expansion plant per horse-power, including
boilers, chimney, heaters, foundations, piping and erection $4.50
Taking the total cost of the plants at $33.50, $36.50 and $41 per horse-
power respectively, the figures in the table imply that the total annual sav-
ing is as follows for coal at $4 per ton:
1. A compound 500 horse-power plant costs $18,250, and saves about $1630
for 10 hours1 service, and $4885 for 24 hours1 service, per year over a single
plant costing $16,750. That is, the compound saves its extra cost in 10-hour
service in about one year, or in 24-hour service in four months.
782
THE STEAM-EHGINE.
2. A triple 500 horse-power plant costs $20,500, and saves about $114 per
year in 10-hour service, or $826 iu 24-hour service, over a compound plant,
thereby saving its extra cost in 10-hour service in about 19% years, or in
24-hour service in about 2% years.
Hours running per day
10
24
Expense for coal. Compound plant
Per H.P.
$9.90
Per H.P.
$28.50
Expense for coal. Triple plant
9 00
25 92
Annual saving of triple plant in fuel
0.90
2 60
Annual interest at 5# on $4.50
$0.23
$0.23
Annual depreciation at 5# on $4.50
Annual extra cost of oil, 1 gallon per 24-hour
day, at $0.50, or 15# of extra fuel cost
0.23
0.15
0.23
0.36
Annual extra cost of repairs at 3% on $4.50 per
24 hours
0 06
0 14
$0.67
$0.96
Annual saving per H.P
$0.23
$1.64
Highest Economy of Pumping Engines. 1900. (Eng. News*
Sept. 27, 1900.)
Name of Builder.
E. P. Allis Co.
Nordberg Mfg.
Co.
ChestnutHill,
Boston.
St. Louis
(No. 10).
Wildwood, Pa.
Expansions .
Triple.
Triple.
Quadruple.
Cyls. diam. and stroke, in
Plungers, diam., in
30, 56, 87 x 66
42
17.5
187.4
13.8
801.6
30
140.35
157,052,500 *
10.335
196.08 *
21.63*
6.71
42
34, 62, 92 x 72
29*
16.43
130.2
14.04
801.6
15
292.11
158,077,324
10.676
201.96
21.003
3.16
23.4
14*' '
36.5
199.9
13.11
712
6
504.06
162,948,824
12.26
185.96
22.81
6.12
24
Steam pressure, Ibs. per sq. in.
Vacuum Ibs. per sq. in
Total head ft ...
Duty per million B.T.U
Dry steam per I.H.P. hour, Ibs.
B.T.U. per I.H.P. per min
Thermal efficiency, per cent...
Friction pel cent
Ratio of expansion, about
* These figures do not include the heat saved by the economizer; including
this they are 163,912,300; 187.8; 22.58. The Nordberg engine had a series of
feed-water heaters taking steam respectively from the exhaust, from the
low-pressure cylinder, and from the third, second, and first receivers. The
feed- water was thereby treated successively to 105°, 136°, 193°, 260°, and
311° F. The coal consumption of the Chestnut Hill engine was 1.062 Ibs.
per I.H.P. per hour, including the coal used by the fan, stoker, and econo-
mizer engines. This is the lowest figure yet recorded.
Steam Consumption of Sulzer Compound and Triple-
expansion Engines with Superheated Steam.
The figures on the next page were furnished to the author (Aug., 1902)
by Sulzer Bros., Winterthur, Switzerland. They are the results of official
tests by Prof. Schroter of Munich, Prof. Weber of Zurich, and other emi-
nent engineers.
PERFORMANCES OF STEAM-ENGINES.
783
S. — A, B, C, D, tandem engines at electrical stations' A, Frank-
fort a/M.; B, Zurich; C, Mannheim; Z>, Mayence. E, F, tandem engine
with intermediate superheater: E, Metallwarenfabrik. Geislingen, Wiirtem-
berg; F, Neue Baumwoll-Spinnerei, Hof, Bavaria. G, H, engines at electri-
cal stations, Berlin1 G, Moabit station, horizontal 4-cyl.; H, Louisenstrasse,
4-cyl. vertical.
COMPOUND ENGINES.
Location (see Note).
Itoc-t-o i OOC+-CH Normal Power,
Cn O Cn O O o TTTP
Dimensions
of
Cylinders,
Inches.
30.5 and
49.2X59.1
26 . 8 and
43.3X51.2
oo | Revs, per Minute.
I
il
a
i— i
130
132
122
108
02
-8*
I1
356
428
482
455
Vacuum, Inches of
Mercury.
PH'
w
i— 5
Steam Consump-
tion in Pounds.
Efficiency
PH*
Si
jK
13.3
12.05
12.42
PH*
Wjj
«i
|
tt
feW
PH
|
««H
O
° I
if
f*&
*s
A
26.4
26.4
26.6
26.8
850
842
1719
14.90
13.52
13.24
21.30
19.48
18.72
0.895
0.891
0.939
0.851
0.842
0.903
O.C04
B
1167
13.10
13.77
19.72
0.951
C
800
to
1000
24 and
40.4X51.2
83
136
134
135
135
132
134
357
356
356
547
533
545
28
28
27,6
28
27.8
27.2
481
750
1078
515
788
1100
13.00
13.10
14.10
11.32
11.52
11.88
14.68
14.14
14.95
12.70
12.38
12.50
21.30
20.35
21.30
18.69
17.90
17.92
0.886
0.926
0.932
0.894
0.931
0.951
0.830
0.877
0.892
0.824
0.875
0.902
D
950
to
1150
26 and
42.3X51.2
do., non-cor
86
id'g
130
129
132
136
358
358
496
527
28.2
28
28.3
1076
1316
1071
1021
14.10
14.50
11.73
15.37
14.82
15.10
12.33
16.30
21.25
21.55
17.70
23.40
0.951
0.960
0.951
0.943
0.902
0.915
0.903
0.893
E
F
400
to
500
1000
to
1200
17.7 and
30.5X35.4
26.9 and
47.2X66.9
no
65
135
135
127
127
128
577
554
655
664
572
26.4
26.4
27.2
27.2
27.1
519
347
788
797
788
10.80
10.35
9.91
9.68
10.70
Intern
supei
temp
at en
l.p. c
aediate 1 349° F.
-heating, 1 331° F.
. of steam I
trance of ^
yl
1 3
07° F.
TRIPLE -EXPANSION ENGINES.
.
£
B
n
o
gr, -M
3
9
^ 3
0
Dimensions of
o d
1 •
QQ
PH'
§ °
Normal P
I.H.P.
Cylinders,
Incnes.
Revoluti
per M
-1
'3
P
Vacuum,
Inches
feteam Co
I.H.P. P
Pounds.
G
3000
32J,47i 58X59
85
188
606
28
2860
8.97
190
397
274
2880
11.28
H
3000
34,49.61X51
83*
189
613
27
2908
9.41
196
381
264
3040
11.57
784 THE STEAM-ENGINE.
Relative Economy of Compound Non-condensing *En-
gines under Variable Loads.— F. M. Rites, in a paper on the Steam
istribution in a Form of Single-acting Engine (Trans. A. S. M. E., xiii. 537),
discusses an engine designed to meet the following problem : Given an
extreme range of conditions as to load or steam -pressure, either or both, to
fluctuate together or apart, violently or with easy gradations, to construct
an engine whose economical performance should be as good as though the
engine were specially designed for a momentary condition— the adjustment
to be complete and automatic. In the ordinary non- condensing compound
engine with light loads the high-pressure cylinder is frequently forced to
supply all the power and in addition drag along with it the low-pressure
piston, whose cylinder indicates negative work. Mr. Rites shows the
peculiar value of a receiver of predetermined tolume which acts as a clear-
ance chamber for compression in the high-pressure cylinder. The Westing-
house compound single-acting engine is designed upon this principle. The
following results of tests of one of these engines rated at 175 H.P. for most
economical load are given :
WATER RATES UNDER VARYING LOADS, LBS. PER H.P. PER HOUR.
Horse-power 210 170 140 115 100 80 50
Non-condensing 22.6 21.9 22.2 22.2 22.4 24.6 28.8
Condensing 18.4 18.1 18.2 18.2 18.3 18.3 20.4
Efficiency of Non-condensing Compound Engines. (W.
Lee Church, Am. Mack., Nov. 19, 1891.) — The compound engine, non-con-
densing, at its best performance will exhaust from the low-pressure cylin-
der at a pressure 2 to 6 pounds above atmosphere. Such an engine will be
limited in its economy to a very short range of power, for the reason that
its valve-motion will not permit of any great increase beyond its rated
power, and any material decrease below its rated power at once brings the
expansion curve in the low-pressure cylinder below atmosphere. In other
words, decrease of load tells upon the compound engine somewhat sooner,
arid much more severely, than upon the non-compound engine. The loss
commences the moment the expansion line crosses a line parallel to the
atmospheric line, and at a distance above it representing the mean effective
pressure necessary to carry the f fictional load of the engine. When expan-
sion falls to this point the low-pressure cylinder becomes an air-pump over
more or less of its stroke, the power to drive which must come from the
high-pressure cylinder alone. Under the light loads common in many
industries the low-pressure cylinder is thus a positive resistance for the
greater portion of its stroke. A careful study of this problem revealed the
functions of a fixed intermediate clearance, always in communication with
the high-pressure cylinder, and having a volume bearing the same ratio to
that of the high-pressure cylinder that the high-pressure cylinder bears to
Uie low-pressure. Engines laid down on these Hues have lully confirmed
the judgment of the designers.
The effect of this constant clearance is to supply sufficient steam, to the
low-pressure cylinder under light loads to hold its expansion curve up to
atmosphere, and at the same time leave a sufficient clearance volume in the
high-pressure cylinder to permit of governing the engine on its compression
under lignt loads.
Economy of Engines under Varying Loads. (From Prof.
W. C. Uawin's lecture before the Society of Arts, London, 1892.)— The gen-
eral result of numerous trials with large engines was that with a constant
load an indicated horse-power should be obtained with a consumption of
1^ pounds of coal per indicated horse-power for a condensing engine, and
1% pounds for a non-condensing engine, figures which correspond to about
194 pounds to 2J4 pounds of coal per effective horse-power. It was much more
difficult to ascertain the consumption of coal in ordinary every-day work,
but such facts as were known showed it was more than on trial.
In electric-lighting stations the engines work under a very fluctuating
load, and the results are far more unfavorable. An excellent Willans non-
condensing engine, which on full-load trials worked with under 2 pounds
per effective horse-power hour, in the ordinary daily working of the station
used 7J4 pounds per effective H.P. hour in 1886, which was reduced to 4.3
pounds in 1890 and 3.8 pounds in 1891. Probably in very few cases were the
engines at electric-light stations working under a consumption of 4J4 pounds
per effective H.P. hour. In the case of small isolated motors working with
a fluctuating load, still more extravagant results were obtained.
PERFORMANCES OF STEAM-ENGINES. 785
ENGINES IN ELECTRIC CENTRAL STATIONS.
Year 1886. 1890. 1892.
Coal used per hour per effective H.P 8.4 5.6 4.9
" " '' indicated " 6.5 4.35 3.8
At electric-lighting: stations the load factor, viz., the ratio of the average
load to the maximum, is extremely small, and the engines worked under
very unfavorable conditions, which largely accounted for the excessive fuel
consumption at these stations.
In steam-engines the fuel consumption has generally been reckoned on
the indicated horse-power. At full-power trials this was satisfactory
enough, as the internal friction is then usually a small fraction of the total.
Experiment has, however, shown that the internal friction is nearly con-
stant, and hence, when the engine is lightly loaded, its mechanical efficiency
is greatly reduced. At full load small engines have a mechanical efficiency
of 0.8 to 0.85, and large engines might reach at least 0.9, but if the internal
friction remained constant this efficiency would be much reduced at low
powers. Thus, if an engine working at 100 indicated horse power had an effi-
ciency of 0.85, then when the indicated horse-power fell to 50 the effective
horse-power would be 35 horse-power and the efficiency only 0.7. Similarly,
at 25 horse-power the effective horse-power would be 10 and the efficiency
Experiments on a Corliss engine at Creusot gave the following results :
Effective power at full load 1.0 0.75 0.50 0.25 0.125
Condensing, mechanical efficiency 0.82 0.79 0.74 0.63 0.48
Nou condensing, " " 0.86 0.83 0.78 0.67 0.52
At light loads the economy of gas and liquid fuel engines fell off even
more rapidly than in steam-engines. The engine friction was large and
nearly constant, and in some cases the combustion was also less perfect at
light loads. At the Dresden Central Station the gas-engines were kept
working at nearly their full power by the use of storage-batteries. The
results of some experiments are given below :
rakeload,per
cent of full
Power.
Gas-engine, cu. ft.
of Gas per Brake
H.P. per hour.
Petroleum Eng.,
Lbs.of Oil per
B.H.P. per hr.
Petroleum Eng.,
Lbs. of Oil per
B.H.P. per hr.
100
22 2
0.96
0.88
75
23.8
1.11
0.99
59
28.0
1.44
1.20
20
40.8
2.38
1.82
&M
66.3
4.25
3.07
Steam Consumption of Engines of Various Sizes.— W. C.
Unwin (Cassier's Magazine, 1894) gives a table showing results of 49 tests of
engines of different types. In non-condensing simple engines, the steam
consumption ranged from 65 Ibs. per hour in a 5-horse-power engine to 22
Ibs. in a 134-H.P. Harris-Corliss engine. In non condensing compound en-
fines, the only type tested was the Willans, which ranged from 27 Ibs. in a
0 H.P. slow-speed engine, 122 ft. per minute, with steam-pressure of 84 Ibs.
to 19.2 Ibs. in a 40-H.P. engine, 401 ft. per minute, with steam-pressure 165
Ibs. A Willans triple-expansion non-condensing engine, 39 H.P., 172 Ibs.
pressure, and 400 ft. piston speed per minute, gave a consumption of 18.5 Ibs.
In condensing engines, nine tests of simple engines gave results ranging only
from 18.4 to 22 Ibs., and, leaving out a beam pumping-engine running at slow
speed (240 ft. per minute) and low steam -pressure (45 Ibs.), the range is only
from 18.4 to 19.8 Ibs. In compound-condensing engines over 100 H.P., in 13
tests the range is from 13.9 to 20 Ibs. In three triple-expansion engines the
figures are 11.7, 12 2, and 12.45 Ibs., the lowest being a Sulzer engine of 360
H.P. In marine compound engines, the Fusiyama and Colchester, tested
by Prof. Kennedy, gave steam consumption of 21.2 and 21.7 Ibs.; and the
Meteor and Tartar triple-expansion engines gave 15.0 and 19.8 Ibs.
Taking the most favorable results which can be regarded as not excep-
tional, it appears that in test trials, with constant and full load, the expen-
diture of steam and coal is about as follows:
Per Indicated Horse- Per Effective Horse
power Hour. power Hour.
Kind of Engine. * * > / » v
Coal, Steam, Coal, Steam,
Ibs. Ibs. Ibs. Ibs.
Non-condensing 1.80 16.5 2.00 18.0
Condensing 1.50 13.5 1.75 15.8
786
THE STEAM-ENGINE.
These may be regarded as minimum rallies, rarely surpassed by the most
efficient machinery, and only reached with very good machinery in the
favorable conditions of a test trial.
Small Engines and Engines with Fluctuating Loads are
usually very wasteful of fuel. The following figures, illustrating their low
economy, are given by Prof. TJnwin, Cassier's Magazine, 1894.
COAL CONSUMPTION PER INDICATED HORSE -POWER IN SMALL ENGINES.
In Workshops in Birmingham, Eng.
Probable I. H.P. at full load... 12 45 60 45
Average I.H.P. during obser-
vation 2.96 7.37 8.2 8.6
Coal per I.H.P. per hour dur-
ing observation, Ibs 36.0 21.25 22.61 18.13
75 60 60
23.64 19.08 20.08
11.68 9.53 8.50
It is largely to replace such engines as the above that power will be dis-
•ibuted from central stations.
tributed J
Steam Consumption in Small Engines.
Tests at Royal Agricultural Society's show at Plymouth, Eng. Engineer-
ing, June 27, 1890.
Diam. of
Per Brake H.P.,
I
Rated H.P.
Com-
pound or
Cylinders.
Stroke,
Max.
Steam-
per hour.
IT;?
Simple.
h.p.
l.p.
pressure.
Coal.
Water.
££P
5
simple
7
10
75
12.12
78.1 Ibs.
6.1 Ib.
3
compound
3
6
6
110
4.82
42.03 "
8.72"
2
simple
4*
7K
75
11.77
89.9 u
7.64"
Steam-consumption of Engines at Various Speeds.
(Profs. Denton and Jacobus, Trans. A. S. M. E., x. 722)— 17 X 30 in. engine,
non-condensing, fixed cut-off, Meyer valve.
STEAM-CONSUMPTION, LBS. PER I.H.P. PER HOUR.
Figures taken from plotted diagram of results.
Revs, per min .....
8
39
20
30
29.5
33
24
29.3
29
32
32
29
28.4
30.8
40
28.7
28
29.8
48
28.5
27.5
29.2
56
28 3
27.1
28.8
72 88
28 27.7
26.3 25.6
28.7 ....
STEAM-CONSUMPTION OP SAME ENGINE; FIXED SPEED, 60 RKVS. PER MIN.
Vary ing cut -off compared with throttling- engine for same horse-power
and boiler-pressures:
Cut-off , fraction of stroke 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8
Boiler-pressure, 90 Ibs... 29 27.5 27 27 27.227.828.5 .........
60 Ibs... 39 34.2 32.2 31.5 31.4 31.6 32.234.136.5 39
THROTTLING -ENGINE, % CUT-OFF, FOR CORRESPONDING HORSE -POWERS.
Boiler-pressure, 901bs... 42 37 33.831.5 29.8 ............. . ...
601bs ....... 50.1 49 46.8 44.6 41 ...............
Some of the principal conclusions from this series of tests are as follows :
1. There is a distinct gain in economy of steam as the speed increases for
y<^ y%, and J4 cut-off at 90 Ibs. pressure. The loss in economy for about 14
cut-off is at the rate of 1/12 Ib. of water per H.P. for each decrease of a
revolution per minute from 86 to 26 revolutions, and at the rate of % Ib. of
water below 26 revolutions. Also, at all speeds the y± cut-off is more eco-
nomical than either the }fa or y% cut-off.
2. At 90 Ibs. boiler-pressure and above ^ cut-off, to produce a given H.P.
requires about 20# less steam than to cut off at % stroke and regulate by the
throttle.
3. For the same conditions with 60 Ibs. boiler-pressure, to obtain, by
throttling, the same mean effective pressure at % cut-off that is obtained by
PERFORMANCES OF STEAM-ENGINES. 787
cutting off about ^, requires about 30# more steam than for the latter
condition.
High Piston-speed in Engines. (Proc. Inst. M. E., July, 1883, p.
321).— The torpedo boat is an excellent example of the advance towards
high speeds, and shows what can be accomplished by studying lightness
and strength in combination. In running at 22% knots an hour, an engine
with cylinders of 16 in. stroke will make 480 revolutions per minute, which
gives 1280 ft. per minute for piston-speed; and it is remarked that engines
running at that high rate work much more smoothly than at lower speeds,
and that the difficulty of lubrication diminishes as the speed increases.
A High-speed Corliss Engine.— A Corliss engine, 20x42 in., has
been running a wire -rod mill at the Trenton Iron Co.'s works since 1877, at
160 revolutions or 1120 ft. piston-speed per minute (Trans. A. S. M. E., ii.
72). A piston-speed of 1200 ft. per min. has been realized ID locomotive
practice.
The Limitation of Engine-speed. (Chas. T. Porter, in a paper
on the Limitation of Engine-speed, Trans. A. S. M. E., xiv. 806.)— The
practical limitation to high rotative speed in stationary reciprocating steam-
engines is not found in the danger of heating or of excessive wear, nor, as
is generally believed, in the centrifugal force of the fly-wheel, nor in the
tendency to knock in the centres, nor in vibration. He gives two objections
to very high speeds: First, that " engines ought not to be run as fast as
they can be ;" second, the large amount of waste room in the port, which
is required for proper steam distribution. In the important respect of
economy of steam, the high-speed engine has thus far proved a failure.
Large gain was looked for from high speed, because the loss by condensa-
tion on a given surface would be divided into a greater weight of steam, but
this expectation has not been realized. For this unsatisfactory result we
have to lay the blame chiefly on the excessive amount of waste room. The
ordinary method of expressing the amount of waste room in the percentage
added by it to the total piston displacement, is a misleading one. It should
be expressed as the percentage which it adds to the length of steam admis-
sion. For example, if the steam is cut off at 1/5 of the stroke, 8% added by
the waste room to the total piston displacement means 40% added' to the
volume of steam admitted. Engines of four, five and six feet stroke may
properly be run at from 700 to 800 ft. of piston travel per minute, but for
ordinary sizes, says Mr. Porter, 600 ft. per minute should be the limit.
Influence of the Steam-jacket.— Tests of numerous engines with
and without steam-jackets show an exceeding diversity of results, ranging
all the way from 30# saving down to zero, or even in some cases showing an
actual loss. The opinionsof engineers at this date (1894) is also as diverse as
the results, but there is a tendency towards a general belief that the jacket is
not as valuable an appendage to an engine as was formerly supposed. An ex-
tensive resume of facts and opinions on the steam-jacket is given by Prof.
Thurston, in Trans. A. S. M. E., xiv. 462. See also Trans. A. S. M. E., xiv.
873 and 1340; xiii. 176; xii. 426 and 1340; and Jour. F. I., April, 1891, p. 276.
The following are a few statements selected from these papers.
The results of tests reported by the research committee on steam-jackets
appointed by the British Institution of Mechanical Engineers in 1886, indi-
cate an increased efficiency due to the use of the steam-jacket of from \% to
over 30#, according to varying circumstances.
Sennett asserts that 'kit has been abundantly proved that steam-
jackets are not only advisable but absolutely necessary, in order that high
rates of expansion may be efficiently carried out and the greatest possible
economy of heat attained."
Isherwood finds the gain by its use. under the conditions of ordinary
practice, as a general average, to be about 20$ on small and 8% or 9% on
large engines, varying through Intel-mediate values with intermediate sizes,
it being understood that the jacket has an effective circulation, and that
both heads and sides are jacketed.
Professor Unwin considers that " in all cases and on all cylinders the
jacket is useful: provided, of course, ordinary, not superheated, steam is
used; but the advantages may diminish to an amount not worth the interest
on extra cost.1'
Professor Cotterill says: Experience shows that a steam-jacket is advan-
tageous, but the amount to be gained will vary according to circumstances.
In many cases it may be that the advantage is small. Great caution is
necessary in drawing conclusions from any special set of experiments on
the influence of jacketing:.
788 THE STEAM-ENGINE.
Mr. E. D. Leavitt has expressed the opinion that, in his practice, steam.
jackets produce an increase of efficiency of from 15$ to 20$.
In the Pawtucket pumping engine, 15 and 30^ X 30 in., 50 revs, per min.,
steam-pressure 125 Ibs. gauge, cut-off J4 m n-P- and % in l.p. cylinder, the
barrels only jacketed, the saving by the jackets was from 1$ to 4$.
The superintendent of the Holly Mfg. Co. (compound pumping-engines)
says: "In regard to the benefits derived from steam-jackets on our steam-
cylinders, I am somewhat of a skeptic. From data taken on our own en-
gines and tests made I am yet to be convinced that there is any practical
value in the steam-jacket." ..." You might practically say that there
is no difference."
Professor Schroter from his work on the triple-expansion engines at Augs-
burg, and from the results of his tests of the jacket efficiency on a small
engine of the Sulzer type in his own laboratory, concludes: (1) The value
of the jacket may vary within very wide limits, or even become nega-
tive. (2) The shorter the cut-off the greater the gain by the use of a
jacket. (3) The use of higher pressure in the jacket than in the cylinder
produces an advantage. The greater this difference the better. (4) The
high-pressure cylinder may be left unjacketed without great loss, but the
others should always be jacketed.
The test of the Laketon triple-expansion pumping-engine showed a gain
of 8.3# by the use of the jackets, but Prof. Denton points out (Trans. A. .S
M. E., xiv. 1412) that all but 1.9$ of the gain was ascribable to the greater
range of expansion used with the jackets.
Test of* a Compound Condensing Engine with and with-
out Jackets at different Loads. (K. C. Carpenter, Trans. A. S.
M. E., xiv. 428.)— Cylinders 9 and H5 in.x!4 in. stroke; 112 Ibs. boiler-pressure;
rated capacity 100 H.P. ; 265 revs, per min. Vacuum, 23 in. From the results
of several tests curves are plotted, from which the following principal figures
are taken.
Indicated H.P ......... 30 40 50 60 70 80 90 100 110 120 125
Steam per I.H.P. per hour:
With jackets, Ibs ..... 22.6 21.4 20.3 19.6 19 18.7 18.6 18.9 19.5 20.4 21.0
Without jackets, Ibs .............. 22. 20.519.6 19.2 19.1 19.3 20.1 ....
Saving by jacket, p. c ............. 10.9 7.3 4.6 3.1 1.0-1.0-1.5 ....
This table gives a clue to the great variation in the apparent saving due to
the steam-jacket as reported by different experimenters. With this par-
ticular engine it appears that when running at its most economical rate of
100 H.P., without jackets, very little saving is made by use of the jackets.
When running light the jacket makes a considerable saving, but when over-
loaded it is a detriment.
At the load which corresponds to the most economical rate, with no steam
in jackets, or 100 H.P., the use of the jacket makes a saving of only 1$; but
at a load of 60 H.P. the saving by use of the jacket is about 11$, and the
shape of the curve indicates that the relative advantage of the jacket would
be still greater at lighter loads than 60 H.P.
Counterbalancing Engines.— Prof. Unwin gives the formula for
counterbalancing vertical engines:
(1)
in which Wi denotes the weight of the balance weight and p the radius to
its centre of gravity, W^ the weight of the crank-pin and half the weight of
the connecting-rod, and r the length of the crank. For horizontal engines:
to
in which W« denotes the weight of the piston, piston-rod, cross-head, and
the other half of the weight of the connecting-rod.
The American Machinist, commenting on these formulae, says: For hori-
zontal engines formula (2) is often used; formula (1) will give a counter-
balance too light for vertical engines. We should use formula (2) for
computing the counterbalance for both horizontal and vertical engines,
excepting locomotives, in which the counterbalance should be heavier.
PERFORMANCES OF STEAM-EKGIKES.
789
Preventing Vibrations of FJngines.— Many suggestions hava
been made for remedying the vibration and noise attendant on the working
of the big engines which are employed to run dynamos. A plan which has
given great satisfaction is to build hair-felt into the foundations of the
engine. An electric company has had a 90-horse-power engine removed
from its foundations, which were then taken up to the depth of 4 feet. A
layer of felt 5 inches thick was then placed on the foundations and run up 2 feet
on all sides, and on the top of this the brickwork was built up.— Safety Valve.
Steam-engine Foundations Embedded in Air.— In the sugar-
refinery of Claus Spreckels, at Philadelphia, Fa., the engines are distributed
practically all over the buildings, a large proportion of them being on upper
floors. Some are bolted to iron beams or girders, and are consequently
innocent of all foundation. Some of these engines ran noiselessly and satis-
factorily, while others produced more or less vibration and rattle. To cor-
rect the latter the engineers suspended foundations from the bottoms of the
engines, so that, in looking at them from the lower floors, they were literally
hanging in the air.— Iron Age, Mar. 13, 1890.
Cost of Coal for Steam-power.— The following table shows the
amount and the cost of coal per day and per year for various horse-powers,
from 1 to 1000, based on the assumption of 4 Ibs. of coal being used per hour
per horse-power. It is useful, among other things, in estimating the saving
that may be made in fuel by substituting more economical boilers and
engines for those already in use. Thus with coal at $3.00 per ton, a saving
of $9000 per year in fuel may be made by replacing a steam plant of 1000
H.P., requiring 4 Ibs. of coal per hour per horse-power, with one requiring
only 2 Ibs.
Coal Consumption, at 4 Ibs,
per H.P. per hour ; 10 hours a
$1.50.
$2.00.
$3.00.
$4.00.
day 5 300 days in a Year.
e-power,
Lbs.
Long Tons.
Short
Tons.
Per
Short Ton.
Per
Short Ton.
Per
Short Ton.
Per
Short Ton.
Cost in
Cost in
Cost in
Cost in
w
K
Dollars.
Dollars.
Dollars.
Dollars.
Per
Per
Per
Per
Per
Day.
Day.
Year.
Day.
Year
Per
Per
Per
Per
Per
Per
Per
Per
Day.
Year
Day.
Year.
Day.
Year.
Day.
Year
l
40
.0179
5.357
.02
6
.03
9
.04
12
.06
18
.08
24
10
400
.1786
63.57
.20
60
.30
90
.40
120
.60
180
.80
240
1,000
.4464
133.92
.50
150
.75
225
1.00
300
1.50
450
2.00
600
60
2,000
.8928
267.85
1.00
300
1.50
450
2.00
600
3.00
900
4.00
1,200
75
3,000
1.3393
401.78
1.50
450
2.25
675
3.00
900
4.50
1,350
6.00
1,800
100
4,000
1.7857
535.71
2.00
600
3.00
900
4.00
1,200
6.00
1,800
8.00
2,400
150
6,000
2.6785
803.56
3.00
900
4.50
1,350
6.00
1,800
9.00
2700
12.00
3,600
200
8,000
3.5714
1,071.42
4.00
1,200
6.00
1,800
8.00
2,400
12.00
3,600
16.00
4,800
250
300
10,000
12,000
4.4642
53571
1,339.27
1,607.13
6.00
6.00
1,500
1,800
7.50
9.00
2,250
2,700
10.00
12.00
3,000
3,600
15.00
18.00
4,500
5,400
20.00
24.00
6,000
7,200
350
14,000
6.2500
1,874.98
7.00
2,100
10.50
3,150
14.00
4,200
21.00
6,200
28.00
8,400
400
16,000
7.1428
2,112.84
8.00
2,400
12.00
3,600
16.00
4,800
24.00
7,200
32.00
9,600
450
18,000
8.0356
2,410.69
9.00
2,700
13.50
4,050
1800
5,400
27.00
8,100
36.00
10,800
500
20,000
8.9285
2,678.55
10.00
3,000
15.00
4,500
20.00
6,000
30.00
9,000
40.00
12,000
600
24,000
10.7142
3,214.26
12.00
3,600
18.00
5,400
24.00
7,200
36.00
10,800
48.00
14,400
700
800
900
28,000
32,000
36,000
12.4999
14.2856
16.0713
3,749.97
4,285.68
4,821.39
14.00
16.00
18.00
4,200
4,800
5,400
21.00
24.00
27.00
6,300
7,200
8,100
28.00
32.00
36.00
8,400
9,600
10,80<:
42.00
48.00
54.00
11,600
12,400
14,200
56.00
64.00
72.00
16,800
19,200
21,600
1,000
40,000
17.8570
5,357.10
20.00
6,000
30.00
9,000
40.00
12,000
60.00
18,000
80.00
24,000
Storing Steam Heat.— There is no satisfactory method for equalizing
the load on the engines and boilers in electric-light stations. Storage-batteries
have been used, but they are expensive in first cost, repairs, and attention.
Mr. Halpin, of London, proposes to store heat during the day in specially
constructed reservoirs. As the water in the boilers is raised to 250 Ibs. pres-
sure, it is conducted to cylindrical reservoirs resembling English horizontal
boilers, and stored there for use when wanted. In this way a comparatively
small boiler-plant can be used for heating the water to 860 Ibs. pressure all
through the twenty-four hours of the day, arid the stored water may be
drawn on at any time, according to the magnitude of the demand The
790
THE STEAM-ENGIHE.
steam-engines are to be worked by the steam generated by the release of
pressure from this water, and the valves are to be arranged in such a way
that the steam shall work at 130 Ibs. pressure. A reservoir 8 ft. in diameter
and 30 ft. long, containing 84,000 Ibs. of heated water at 250 Ibs. pressure,
would supply 5250 Ibs. of steam at 130 Ibs. pressure. As the steam consump-
tion of a condensing electric -light engine is about 18 Ibs. per horse-power
hour, such a reservoir would supply 286 effective horse-power hours. In
1878, in France, this method of storing steam was used on a tramway.
M. Francq, the engineer, designed a smokeless locomotive to work by steam-
power supplied by a reservoir containing 400 gallons of water at 220 Ibs.
pressure. The reservoir was charged with steam from a stationary boiler
at one end of the tramway.
Cost of Steam-power. (Chas. T. Main, A. S. M. E., x. 48.)— Estimated
costs in New England in 1888, per horse-power, based on engines of 1000 H.P.
Compound .Condens- *™5S*'
Engine, ing Engine.
1. Cost engine and piping, complete $25.00 $20.00 $17.50
2. Engine-house 8.00 7.50 7.50
8. Engine foundations 7.00 5.50 4.50
,4. Total engine plant 40.00 83.00 29.50
6. Depreciation, 4% on total cost 1 .60 1 .32 1.18
6. Repairs, 2% " " " 0.80 0.66 0.59
7. Interest, 5g «* •» •' 2.00 1.65 1.475
8. Taxation, 1.5£ on % cost 0.45 0.371 0.333
9. Insurance on engine and house 0.165 0. 1 38 0. 125
10. Total of lines 5, 6, 7, 8, 9 5.015 4.139 3.702
11. Cost boilers, feed-pumps, etc... , 9.33 13.33 16.00
12. Boiler-house 2.92 4.17 5.00
13. Chimney and flues 6.11 7.30 8.00
14. Total boiler-plant o... "isTse 24.80 29.00
15. Depreciation, 5# on total cost... 0.918 1.240 1.450
16. Repairs, 2* •* " " 367 .496 .580
17. Interest, 5% " «* " 918 1.240 1.450
18. Taxation, 1.5£ on % cost 207 .279 .326
19. Insurance, 0.5# on total cost 092 .124 .145
20. Total of lines 15 to 19 2.502 3.379 3.951
21. Coal used per I.H.P. per hour, Ibs 1.75 2.50 3.00
22. Cost of coal per I.H.P. per day of 10*4 cts. cts. cts.
hours at $5.00 per ton of 2240 Ibs 4.00 5.72 6.86
23. Attendance of engine per day 0.60 0.40 0.35
24. 4t " boilers " " 0.53 0.75 0.90
25. Oil, waste, and supplies, per day 0.25 0.22 0,20
26. Total daily expense 5~38~ To9 8.31
27. Yearly running expense. 308 days, per
I.H;P ..!.... .$16.570 $21.837 $25.595
28. Total yearly expense, lines 10, 20, and 27.. 24.087 29.355 83.248
29. Total yearly expense per I.H.P. for power
if 50# of exhaust-steam is used for heat-
ing 12.597 14.907 16.663
80. Total if all ex.-steam is used for heating. . . 8.624 7.816 7.700
When exhaust-steam or a part of the receiver-steam is used for heating, or
if part of the steam in a condensing engine is diverted from the condenser,
and used for other purposes than power, the value of such steam should
be deducted from the cost of the total amount of steam generated iu order
to arrive at the cost properly chargeable to power. The figures in lines 29
KOTARY STEAM-ENGINES. 791
and 30 are based on an assumption made by Mr. Main of losses of heat
amounting to 25£ between the boiler and the exhaust-pipe, an allowance
which is probably too large.
See also two papers by Chas. E. Emery on " Cost of Steam Power,1' Trans.
A. S. C. E., vol. xii, Nov. 1883, and Trans. A. I. E. E.t vol. x, Mar. 1893.
ROTARY STEAM-ENGINES.
Steam Turbines.— The steam turbine is a small turbine wheel which
runs with steam as the ordinary turbine does with water. (For description
of the Parsons and the Dow steam turbines see Modern Mechanism, p. 5398,
etc.) The Parsons turbine is a series of parallel-flow turbines mounted side
by side on a shaft; the Dow turbine is a series of radial outward-flow tur-
bines, placed like a series of concentric rings in a single plane, a stationary
guide-ring being between each pair of movable rings. The speeds of the
steam turbines enormously exceed those of any form of engine with recip-
rocating piston, oreven of the so-called rotary engines. The three- and four-
cylinder engines of the Brotherhood type, in which the several cylinders
are usually grouped radially about a common crank and shaft, often exceed
1000 revolutions per minute, and have been driven, experimentally, above
2000; but the steam turbine of Parsons makes 10,000 and even 20,000 revolu-
tions, and the Dow turbine is reputed to have attained 25,000. (See Trans.
A. S. M. E., vol. x. p. 680, and xii.- p. 888; Trans. Assoc. of Eng'g Societies,
vol. viii. p. 583; Eng'g, Jan. 13, 1888, and Jan. 8, 1892; Eng'g Neivs, Feb. 27,
1892.) A Dow turbine, exhibited in 1889, weighed 68 IDS., and developed 10
H.P., with a consumption of 47 Ibs. of steam per H.P. per hour, the steam
pressure being 70 Ibs. The Dow turbine is used to spin the fly-wheel of the
Howell torpedo. The dimensions of the wheel are 13.8 in. diam., 6.5 in.
width, radius of gyration 5.57 in. The energy stored in it at 10,000 revs,
per min. is 500,000 ft.-lbs.
The De Laval Steam Turbine, shown at the Chicago exhibition,
1893, is a reaction wheel somewhat similar to the Pelton water-wheel. The
steam jet is directed by a nozzle against the plane of the turbine at quite a
small angle and tangentially against the circumference of the medium
periphery of the blades. The angle of the blades is the same at the side of
admission and discharge. The width of the blade is constant along the
entire thickness of the turbine.
The steam is expanded to the pressure of the surroundings before arriv-
ing at the blades. This expansion takes place in the nozzle, and is caused
simply by making its sides diverging. As the steam passes through this
channel its specific volume is increased in a greater proportion than the
cross section of the channel, and for this reason its velocity is increased,
and also its momentum, till the end of the expansion at the last sectional
area of the nozzle. The greater the expansion in the nozzle the greater its
velocity at this point. A pressure of 75 Ibs. and expansion to an absolute
pressure of one atmosphere give a final velocity of about 2625 ft. per second.
Expansion is carried further in this steam turbine than in ordinary steam-
engines. This is on account of the steam expanding completely during its
work to the pressure of the surroundings.
For obtaining the greatest possible effect the admission to the blades must
be free from blows and the velocity of discharge as low as possible. These
conditions would require in the steam turbine an enormous velocity of
-as high as 1300 to 1650 ft. per second. The centrifugal force,
periphery ___ 0_ ^
nevertheless, puts a limit to the use of very high velocities. In the 5 horse-
power turbine the velocity of periphery is 574 ft. per second, and the num-
ber of revolutions 30,000 per minute.
However carefully the turbine may be manufactured it is impossible, on
account of unevenness of the material, to get its centre of gravity to corre-
spond exactly to its geometrical axle of revolution; and however small this
difference may be, it becomes very noticeable at such high velocities. De
Laval has succeeded in solving the problem by providing the turbine with a
flexible shaft. This yielding shaft allows the turbine at the high rate of
speed to adjust itself and revolve around its true centre of gravity, the
centre line of the shaft meanwhile describing a surface of revolution.
In the gearing-box the speed is reduced from 30,000 revolutions to 3000
by means of a driver on the turbine shafts, which sets in motion a cog-
wheel of 10 times its own diameter. These gearings are provided with spiral
cogs placed at an angle of about 45°.
For descriptions of the most recent forms of steam turbines, see circulars
of the Westinghouse Machine Co., Pittsburg, Pa., and the De Laval Steam
792 THE STEAM-EKGINE.
Turbine Co., Trenton, N. J.; also paper by Dr. R. H. Thurston in Trans.
A. S. M. E., vol. xxii., p. 170.
Rotary Steam-engines, other than steam turbines, have been
invented by the thousands, but not one has attained a commercial success,
„,, — „„«.!,, ~« ™,, ~t c.^«r,ni> The possible advantages, such as saving of
)tary engine are overbalanced by its w
in use, however, for special purposes, $
r^aixi ^G-^ng.aiiGo c*^i o^cmJ fflftHs for Sawmill* in ™hinh atoo™ *w>™
not a matter of importance.
DIMENSIONS OF PARTS OF ENGINES.
The treatment of this subject by the leading authorities on the steam-en-
gine is very unsatisfactory, being a confused mass of rules and formulae
based partly upon theory and partly upon practice. The practice of builders
shows an exceeding diversity of opinion as to correct dimensions. The
treatment given below is chiefly the result of a study of the works of Rankine,
Seaton, Unwin, Thurston, Marks, and Whitham, and is largely a condensa-
tion of a series of articles by the author published in the American Met"
chinist, in 1894, with many alterations and much additional matter. In or-
der to make a comparison of many of the formulas they have been applied
to the assumed cases of six engines of different sizes, and in some cases
this comparison has led to the construction of new formulae.
Cylinder. (Whitham.)— Length of bore = stroke -f breadth of piston-
ring — % to y% in ; length between heads == stroke + thickness of piston -j-
sum of clearances at both ends; thickness of piston = breadth of ring -f-
thickness of flange on one side to carry the ring -f- thickness of follower-
plate.
Thickness of flange or follower. ... % to J^ in. $4 in. 1 in.
For cylinder of diameter 8 to 10 in. 36 in. 60 to 100 in.
Clearance of Piston. (Seaton.)— The clearance allowed varies with
the size of the engine from % to % in. for roughness of castings and 1/16 to
^ in. for each working joint. Naval and other very fast-running engines
have a larger allowance. In a vertical direct acting engine the parts which
wear so as to bring the piston nearer the bottom are three, viz., the shaft
journals* the crank-pin brasses, and Diston-rod gudgeon-brasses.
^Thickness of Cylinder. (Thurston.) — For engines of the older
types and under moderate steam-pressures, some builders have for many
years restricted the stress to about 2550 Ibs. per sq. in.
t = ajo,D -f- 6 (I)
1s a common proportion; £, D, and 6 being thickness, diam., and a constant
added quantity varying from 0 to ^ in., all in inches; pt is the initial unbal-
anced steam-pressure per sq. in. In this expression 6 is made larger for
horizontal than for vertical cylinders, as, for example, in large engines 0.5
in the one case and 0.2 in the other, the one requiring re-boring more than
the other. The constant a is from 0.0004 to 0.0005: the first value for verti-
cal cylinders, or short strokes; the second for horizontal engines, or for
long strokes.
Tniclmess or Cylinder and Its Connections for marine
Engines. (Seaton).— D = the diam. of the cylinder in inches: p = load on
the safety-valves in Ibs. per sq. in.; /, a constant multiplier = thickness of
barrel 4- .25 in.
Thickness of metal of cylinder barrel or liner, not to be less than p x D -*•
8000 when of cast iron.* (2)
Thickness of cylinder-barrel = ^H- 0.6 in. ......... (8)
" " liner = 1.1 X/. • • • • • (4)
Thickness of liner when of steei p X D -*- 6000 -f- 0.5
metal of steam-ports =0.6 x/.
valve-box sides = 0 . 65 X /.
* When made of exceedingly good material, at least twice melted, the
thickness may be 0.8 of that given by the above rules.
DIMENSIONS OF PARTS OF ENGINES.
793
Naickness of metal of valve-box covers = 0.7 X f*
" cylinder bottom = 1.1 X /, if single thickness.
" = 0.65 X /, if double "
" covers =1.0 X /, if single "
" " =0.6 x/, if double **
cylinder flange
cover-flange
valve-box"
. ,
=1.4 X /.
=1.3 X /.
- =1.0 X /.
door-flange =0.9 X /.
face over ports = 1.2 X /.
** = 1 .0 x /,
false-face
— .i . v, x /, when there is a f al se-f ao«.
= 0.8 X /, when cast iron.
= 0.6 X /, when steel or bronze.
Whitham gives the following from (Afferent authorities:
t = 0.03 I/Dp.
Tredgold : t -.
.5)p
1900
(5)
(6)
(7)
Weisbach: t = 0.8 -f- 0.00033pD. ........ (8^
Seaton : t = 0.5 -f 0.0004pD (9)
Haswell- 5 * = 0.0004pD-f- ^ (vertical); (10)
' (£ = 0.0005pD-fj4 (horizontal) (11)
Whitham recommends (6) where provision is made for the reboring, and
where ample strength and rigidity are secured, for horizontal or vertical
cylinders of large or small diameter; (9) for large cylinders using steam
under 100 Ibs. gauge -pressure, and
t = 0.003D yp for small cylinders. ...... (12)
Marks gives t = 0.00028pD. (13)
This is a smaller value than is given by the other formulae quoted; but
Marks says that it is not advisable to make a steam -cylinder less than 0.75
in. thick under any circumstances.
The following table gives the calculated thickness of cylinders of engines
of 10, 30, and 50 in. diam., assuming p the maximum unbalanced pressure on
the piston = 100 Ibs. per sq. in. As the same engines will be used for calcu-
lation of other dimensions, other particulars concerning them are here
given for reference.
DIMENSIONS, ETC., OP ENGINES.
Engine No... •
1 and 2
3 and 4.
5 and 6.
Indicated horse-power I.H.P.
50
10
450
30
1250
50
Stroke, feet L
1 .... 2
2^ .... 5
4 .... 8
Revs, per min r
Piston speed, ft. per min S
250 ... 125
500
130 ... 65
650
90 .... 45
700
Area of piston, sq. in . a
78.54
706.86
1963.5
Mean effective pressure M.E.P.
Max. total unbalanced press P
Max. total per sa. in n
42
7854
100
32.3
70,686
100
30
196,350
100
794
THE STEAM-ENGINE.
THICKNESS OP CYLINDER
BY FORMULA.
1 and 2.
3 and 4.
5 and 6.
(1) .OQQipD -f 0.5, short stroke...
(1) .OOOSpD -f- 0.5, long stroke ....
(2) 00033pZ>
.90
1.00
.33
1.70
2.00
.99
2.50
3.00
1 67
(3) 0002pD + 06 . . ...,
.80
1.40
1.66
(5) 0001pZ>-{- 15 \^D
.57
1.12
1.56
(6) 03 VDp
.95
1.64
2 12
.66
1.71
2.76
^ 1900 ^
(8) 00033/>Z> -f- 0.8 . ,
1.13
1.79
2.45
(9) 0004p D -f- 0 5 .
.90
1.70
2.50
(10) 0004pZ) -4- % (vertical)
.53
1.33
2.13
(11) '.0005pD + Ys (horizontal)
(12) .003D Vp (small engines)
(13) QOQ2$pD
.63
.30(?)
1.63
*'.84(?)
2.63
Average of first eleven
.76
1.48
2.26
The average corresponds nearly to the formula t = .00037 Dp + 0.4 in. A
convenient approximation is t = .0004Z)p -f 0.3 in., which gives for
Diameters 10 20 30 40 50 60 in.
Thicknesses 70 1.10 1.50 1.90 2.30 2. 70 in.
The last formula corresponds to a tensile strength of cast iron of 12,500
Ibs., with a factor of safety of 10 and an allowance of 0.3 in. for reboring.
Cylinder-heads* — Thurston says : Cylinder-heads may be given a
thickness, at the edges and in the flanges, exceeding somewhat that of the
cylinder. An excess of not less than 25% is usual. It may be thinner in the
middle. Where made, as is usual in large engines, of two disks with inter-
mediate radiating, connecting ribs or webs, that section which is safe
against shearing is probably ample. An examination of the designs of
experienced builders, by Professor Thurston, gave
(2)
(3)
D being the diameter of that circle in which the thickness is taken.
Thurston also gives t = .005D |/p_-f 0.25
Marks gives t = O.Q03Z) \/p
He also says a good practical rule for pressures under 100 Ibs. per sq. in. is
to make the thickness of the cylinder-heads 1*4 times that of the walls; and
applying this factor to his formula for thickness of walls« or .00028p/>, we
have
t .= .00035j?D (4)
Whitham quotes from Seaton,
t =
pD -f- 500
2000
, which is equal to .0005pZ> -f .25 inch.
(5)
Seaton's formula for cylinder bottoms, quoted above, is
«=!.!/, in which/ = .0002pD + .85 inch, or t = .00022pD -f .93. . (C)
Applying the above formulae to the engines of 10, 30, and 50 inches diame-
ter, with maximum unbalanced steam-pressure of 100 Ibs. per sq. in., we
Cylinder diameter, inches =10 30 50
(1) t = .00033Dp_-f- .25
(2) t = .005Z) Vp + .25
(3) t = .003D Vp
(4) t = . 00035 Dp
(5) t = .0005Z)p + .25
(6) t = .Om-Wp + .93
.53
.75
.30
.35
.75
3.15
1.25
1.75
.90
1.05
1.75
1.59
1.82
2.75
1.50
1.75
2.75
2.03
Average of 6. ............... J65 1.38 2.10
DIMENSIONS OF PARTS OF ENGINES. 79&
The average is expressed by the formula t = .00036Z)p -f .81 inch.
Meyer's " Modern Locomotive Construction," p. 24, gives for locomotive
cylinder-heads for pressures up to 120 Ibs.:
For diameters, in ........ 19 to 22 16 to 18 14 to 15 11 to 18 9 to 10
Thickness, in ............ \y± 1 1 % %
Taking the pressure at 120 Ibs. per sq. in., the thicknesses 1^ in. and % in.
for cylinders 22 and 10 in. diam., respectively, correspond to the formula
t = .00035 Dp -f .33 inch.
Web-stiffened Cylinder-covers,— Seaton objects to webs for
stiffening cast-iron cylinder-covers as a source of danger. The strain on
the web is one of tension, and if there should be a nick or defect in the
outer edge of the web the sudden application of strain is apt to start a
crack. He recommends that high-pressure cylinders over 24 in. and low-
pressure cylinders over 40 in. diam. should have their covers cast hollow,
with two thicknesses of metal. The depth of the cover at the middle should
be about J4 the diam. of the piston for pressures of 80 Ibs. and upwards,
and that of the low-pressure cylinder-cover of a compound engine equal to
that of the high-pressure cylinder. Another rule is to make the depth at
the middle not less than 1.8 times the diameter of the piston-rod. In the
British Navy the cylinder-covers are made of steel castings,^ to 1*4 in.
thick, generally cast without webs, stiffness being obtained by their form,
which is often a series of corrugations.
Cylinder-head Bolts.— Diameter of bolt-circle for cylinder-head =»
diameter of cylinder -f- 2 X thickness of cylinder -f- 2 X diameter of bolts.
The bolts should not be more than 6 inches amrt (Whitham).
Marks gives for number of bolts b = *^?*P = .0001571^, in which c =
ouuuc c
area of a single bolt, p =r boiler-pressure in Ibs. per sq. in.; 5000 Ibs. is taken
&B the safe strain per sq. in. on the nominal area of the bolt.
Seaton says: Cylinder-cover studs and bolts, when made of steel, should
be of such a size that the strain in them does not exceed 5000 Ibs, per sq. in.
When of less than % inch diameter it should not exceed 4500 Ibs. per sq. in.
When of iron the strain should be 20$ less.
Thurston says : Cylinder flanges are made a little thicker than the cylin*
der, and usually of equal thickness with the flanges of the heads. Cylinder-
bolts should be so closely spaced as not to allow springing of the' flanges
and leakage, say, 4 to 5 times the thickness of the flanges. Their diameter
should be proportioned for a maximum stress of not over 4000 to 5000 Ibs.
per square inch.
If D =i diameter of cylinder, n = maximum steam-pressure, 6 = number
of bolts, 8 1= size or diameter of each bolt, and 5000 Ibs. be allowed per sq,
in. of nominal area of the bolt, .7851E>2p — 3927^2 . whence 6sa = .0002Z>3p;
b = .0002^-; s = .OUUDA/£. For the three engines we have:
Diameter of cylinder, inches. ....... 10 80 60
Diameter of bolt-circle, approx.... 13 85 57.5
Circumference of circle, approx.... 40.8 110 180
Minimum No. of bolts, circ. •*• 6 ..... 7 18 30
J/I
Diam, of bolts, s = .01414PJ ...... %in. 1.00 1.89
The diameter of bolt for the 10-inch cylinder is 0.54- tn. by the formula,
but % inch is as small as should be taken, on account of possible overstrain
by the wrench in screwing up the nut.
The Piston* Details of Construction of Ordinary Pis«
tons* (Seaton.) — Let D be the diameter of the piston in inches, p the effec-
tive pressure per square inch on it, x a constant multiplier, found as follows:
# = x VP + I.
796 THE STEAM-ENGIKE.
The thickness of front of piston near the boss =; C.2 X X
** •* " " rim = 0.17xa?.
•* back " = 0.18X0.
boss around the rod =0.3 X x.
flange inside packing-ring = 0 . 23 X x.
•* " at edge = 0.25 x x.
•• packing-ring = 0.15 X r
«• Junk-ring at edge ^ 0.23 X x.
* •• inside packing-ring = 0.21 x x.
«• •« at bolt-holes = 0.35 x x.
•• metal around piston edge = 0.25 x x.
The breadth of packing-ring = 0.63 X x.
" depth of piston at centre = 1.4 X x.
" lap of junk-ring on the piston = 0.45 X x.
" space between piston body and packing-ring =0.3 X x.
" diameter of junk-ring bolts ~ 0.1 X x -f 0.25 in.
-* pitch " := 10 diameters.
" number of webs in the piston = CD -f- 20) -f- 12.
" thickness " " " s=0.18x#.
Marks gives the approximate rule: Thickness of piston-head== \/ld, in
tfhich I — length of stroke, and d — diameter of cylinder in inches. Whit-
ham says in a horizontal engine the rings support the piston, or at least a
part of it, under ordinary conditions. The pressure due to the weight of
the piston upon an area equal to 0.7 the diameter of the cylinder X
breadth of ring-face should never exceed 200 Ibs. per sq. in. He also gives
a formula niuch used in this country: Breadth of ring-face = 0.15 X diam-
eter of cylinder.
For our engines we have diameter «....«. 10 80 50
Thickness of piston -head.
Marks, VTb\ long stroke 8.81 5.48 7.00
Marks, " ; short stroke 8.94 6.51 8.32
Seaton, depth at centre = lAx .., 4.80 9.80 15.40
Seatou, breadth of ring = .6&r 1.89 4.41 6.93
Whitham, breadth of ring = .157) 1.50 4.50 7.50
Diameter of Piston Packing- Hugs. — These are generally
turned, before they are cut, about J4 inch diameter larger than the cylinder,
for cylinders up to 20 inches diameter, and then enough is cut out of the ring
to spring them to the diameter of the cylinder. For larger cylinders the
rings are turned proportionately larger. Seaton recommends an excess
of \% of the diameter of the cylinder.
Cross-section of the Rings.— The thickness Is commonly made
l/30th of the diam. of cyl. -f % inch, and the width = thickness -f- *& inch.
For an eccentric ring the mean thickness may be the same as for a ring of
uniform thickness, and the minimum thickness = % the maximum.
A circular issued by J. H. Dunbar, manufacturer of packing -rings,
Youngstown, O., says: Unless otherwise ordered, the thickness of rings will
be made equal to .03 X their diameter. This thickness has been found
to be satisfactory in practice. It admits of the ring being made about 3/16"
to the foot larger than the cylinder, and has, when new, a tension of about
two pounds per inch of circumference, which is ample to prevent leakage,
if -the surface of the ring and cylinder are smooth.
As regards the width of rings, authorities *4 scatter" from very narrow to
very wide, the latter being fully ten times the former. For instance, Unwin
gives W= d .014 4- .08. Whitham 's formula is W s= d .15. In both for.
mulse W is the width of the ring in inches, and d the diameter of the cylinder
in inches. Unwin's formula makes the width of a 20" ring W = 20 X .014
-f ,08 = .86", while Whitham's Is 20 X .15 se 3" for the same diameter of
ring. There is much less difference in the practice of engine-builders In this
respect, but there is still room for a standard width ot ring. It is believed
that for cylinders over 16" diameter %" is a popular and practical width,
and ^" for cylinders of that size and under.
Fit of Piston-rod into Piston* (Seaton.)— The most convenient
and reliable practice is to turn the piston-rod end with a shoulder of 1/16
inch tor small engines, and ^ inch for large ones, make tiie taper 8 in. to
DIMENSIONS OF PARTS OF ENGINES, ?97
the foot until the section of the rod Is three fourths of that of the body, then
turn the remaining part parallel; the rod should then fit into the piston so
as to leave ^ inch between it and the shoulder for large pistons, and 1/16 in.
for small. The should ar prevents the rod from splitting the piston, and
allows of the rod being turned true after long wear without encroaching on
the taper.
The piston is secured to the rod by a nut, and the size of the rod should
be such that the strain on the section at the bottom of the thread does not
exceed 5500 Ibs. per sq. in. for iron, 7000 Ibs. for steel. The depth of this nut
need not exceed the diameter which would be found by allowing these
strains. The nut should be locked to prevent its working loose,
Diameter of Piston-rods.— Unwin gives
in which D is the cylinder diameter in inches, p is the maximum unbalanced
pressure in Ibs. per sq. in., and the constant b = 0.0167 for iron, and b —
U.0144 for steel. Thurston, from an examination of a consideiable number
of rods in use, gives
- — , nearly (2)
(L in feet, D and d in inches), in which a = 10,000 and upward in the various
types of engines, the marine screw engines or ordinary fast engines on
shore given the lowest values, while "low-speed engines " being less
liable to accident from shock give a = 15,000, often.
Connections of the piston-rod to the piston and to thecrosshead should
have a factor of safety of at least 8 or 10. Marks gives
d" = 0.0179D j/p, for iron; for steel d" » 0.0105D Vp\ . . (8)
4 . 4
and d" «= 0.03901 tf D'Wp, for iron; for steel d" =s 0.03525 VlW»p, (4)
in which I is the length of stroke, all dimensions in inches. Deduce the
diameter of piston-rod by (3), and if this diameter is less than 1/12J, then use
(4).
Seaton gives: Diameter of piston-rod = Piameterof cylinder ^
The following are the values of Fi
Naval engines, direct-acting Fsz 60
" return connnecting-rod, 2 rods F = 80
Mercantile ordinary stroke, direct-acting F = 50
*' long F= 48
very long " .F=45
medium stroke, oscillating F = 45
NOTE.— Long and very long, as compared with the stroke usual for the
power of engine or size of cylinder.
In considering an expansive engine p, the effective pressure should be
taken as the absolute working pressure, or 15 Ibs. above that to which the
boiler safety-valve is loaded; for a compound engine the value of p for the
high-pressure piston should be taken as the absolute pressure, less 15 Ibs.,
or the same as the load on the safety-valve; for the medium-pressure the
load may be taken as that due to half the absolute boiler-pressure: and for
the low-pressure cylinder the pressure to which the escape- valve is loaded
-f- 15 Ibs., or the maximum absolute pressure, which can be got in the re-
ceiver, or about 25 Ibs. It is an advantage to make all the rods of a com-
pound engine alike, and this is now the rule.
Applying the above formulas to the engines of 10, 30, and 50 in. diameter,
both short and long stroke, we have;
798
THE STEAM-ENGINE.
Diameter of Piston-rods,
Diameter of Cylinder, inches ...
1(
}
3(
)
M
1
Stroke, inches
12
24
30
60
48
95
Unwin,iron, .0167 D Vp
Unwin, steel, .0144Z) Vjp
1.67
1.44
1.67
1.44
5.01
4.32
5.01
4.32
8.35
7.20
8.35
7 20
Thurston ,| / — — {- : — (L in feet).
Thurston same with M ~~ 15 000. .....
1.13
1 4fl
3.12
q QQ
5.10
6 OK
Marks iron, 0179Z) Vp
Marks iron .03901 \ ' DH^p
1.79
5.37
5.37
8.95
8.95
Marks, steel, .0105D 1/p. . . . .
1.35
1.91
3.70
5.13
6.04
8.54
Marks, steel, .03525 \/ D'Wp
D
Seaton, naval engines, — yp
Seaton, land engine,-™-^
(1.05)
1.22
1.67
1.73
2 22
(3.15)
3.34
5.01
4.72
6.67
(5.25)
5.46
8.35
7.72
11 11
J
8.74
The figures in brackets opposite Marks' third formula would be rejected-
since they are less than $& of the stroke, and the figures derived by his
fourth formula would be taken instead. The figure 1.79 opposite his first
formula would be rejected for the engine of 24-inch stroke.
An empirical formula which gives results approximating the above aver-
ages is d" - .013 VDlp.
The calculated results from this formula, for the six engines, are, respec'
tively, 1.42, 1.88, 3.90, 5.61, 6.37, 9.01.
Piston-rod Guides,— The thrust on the guide, when the connecting-
rod is at its maximum angle with the line of the piston-rod, is found from
the formula: Thrust = total load on piston x tangent of maximum angle
of connecting-rod = p tan 0. This angle, 0, is the angle whose sine = half
stroke of piston -5- length of connecting-rod.
Ratio of length of connecting-rod to stroke 2 2^£ 3
Maximum angle of connecting-rod with line of
piston-rod . 14° 29' 11° 33' 9° 36'
Tangent of the angle . .258 .204 .169
Secant of the angle 1.0327 1.0206 1.014
Seaton says: The area of the guide-block or slipper surface on which the
thrust is taken should in no case be less than will admit of a pressure of 400
Ibs. on the square inch; and for good working those surfaces which take the
thrust when going ahead should be sufficiently large to prevent the maxi-
mum pressure exceeding 100 Ibs. per sq. in. When the surfaces are kept
well lubricated this allowance may be exceeded.
Thurston says: The rubbing surfaces of guides are so proportioned that
if Fbe their relative velocity in feet per minute, and p be the intensity of
pressure on the guide in Ibs. per sq. in., pV < 60,000 and pV > 40,000.
The lower is the safer limit; but for marine and stationary engines it is
allowable to take p = 60,000 -5- F. According to Rankine, for locomotives,
44800
p = , where p is the pressure in Ibs. per sq. in. and Fthe velocity of
rubbing in feet per minute. This includes the sum of all pressures forcing
the two rubbing surfaces together.
Some British builders of portable engines restrict the pressure between
the guides and cross-heads to less than 40, sometimes 35 Ibs. per square inch.
For a mean velocity of 600 feet per minute, Prof. Thurston's formulas
give, p < 100, p > 66.7; Rankine's gives p = 72.2 Ibs. per sq. in.
DIMENSIOHS OF PABTS OF EHGIHES. 799
Whitham gives,
A = area of slides in square inches
in which P = total unbalanced pressure, pl = pressure per square inch
on piston, d = diameter of cylinder, pQ = pressure allowable per square inch
on slides, and n = length of connecting-rod -*- length of crank. This is
equivalent to the formula, A = P tan 0 -j- p0. For n = 5, PJ = 100 and p0
= 80, A = .2004d2. For the three engines 10, 30 and 50 in. diain., this would
give for area of slides, A — 20, 180 and 500 sq. in., respectively. Whitham
says: The normal pressure on the slide may be as high as 500 Ibs. per sq. in.,
but this is when there is good lubrication and freedom from dust. Station-
ary and marine engines are usually designed to carry 100 Ibs. per sq. in.,
and the area in this case is reduced from 50$ to 60$ by grooves. In locomo-
tive engines the pressure ranges from 40 to 50 Ibs. per sq. in. of slide, on ac-
count of the inaccessibility of the slide, dirt, cinder, etc.
There is perfect agreement among the authorities as to the formula for
area of the slides, A = P tan 0 -*- p0; but the value given to pn, the allow*
able pressure per square inch, ranges all the way from 35 Ibs. to 500 Ibs.
Tlie Connecting-rod, Ratio of length of connecting-rod to length
of stroke.— Experience has led generally to the ratio of 2 or 2^ to 1, the
latter giving a long and easy-working rod, the former a rather short, but
yet a manageable one (Thurston). Whitham gives the ratio of from 2 to 4J^,
and Marks from 2 to 4.
Dimensions of the Connecting-rod.— The calculation of the diameter of
a connecting-rod on a theoretical basis, considering it as a strut subject to
both compressive and bending stresses, and also to stress due to its inertia,
in high-speed engines, is quite complicated. See Whitham, Steam-engine
Design, p. 217; Thurston, Manual of S. E., p. 100. Empirical formulas are aa
follows: For circular rods, largest at the middle, D = diam. of cylinder, I =
length of connecting-rod in inches, p = maximum steam-pressure per sq. in.
(1) Whitham, diam. at middle, d" - 0.0272 V Dl Vp.
(2) Whitham, diam. at necks, d" = 1.0 to 1.1 X diam. of piston-rod.
(3) Sennett, diam. at middle, d" = — \/p.
55
(4) Sennett, diam. at necks, d" — — \/p.
60
(5) Marks, diam., d" = 0.0179D Vp. if diam. is greater than 1/24 length.
(6) Marks, diam., d" — 0.02758 V Dl Vp if diam. found by (5) is less than
1/24 length.
(7) Thurston, diam. at middle, d" = a \/DL \/p -f- C, D in inches, L in
feet, a = 0.15 and C = ^ inch for fast engines, a = 0.08 and C = % inch for
moderate speed.
(8) Seaton says: The rod may be considered as a strut free at both ends,
and, calculating its diameter accordingly,
diameter at middle =
where R = the total load on piston P multiplied by the secant of the maxi-
mum angle of obliquity of the connecting-rod.
For wrought iron and mild steel a is taken at 1/3000. The following are
the values of r in practice:
Naval engines — Direct-acting r = 9 to 11;
" Return connecting-rod r = 10 to 13, old;
*' " -r = 8 to 9, modern;
" " Trunk r= 11. 5 to 13.
Mercantile *' Direct-acting, ordinary r = 12.
" long stroke r = 13 to 16.
(9) The following empirical formula is given by Seaton as agreeing closely
with good modern practice:
Diameter of connecting-rod at middle = 4/5T-*- 4, ' E = length of rod in
inches, and K= 0.03 ^effective load on piston in pounds.
800
THE STEAM-ENGINE.
The diam. at the ends may be 0.875 of the diam. at the middle.
Seaton's empirical formula when translated into terms of D andp is the
same as the second one by Marks, viz., d" = 0.02758 ^ Dl \/p~. WhithanVs
(1) is also practically the same.
(10) Taking Seaton's more complex formula, with length of connecting-
rod = 2.5 X length of stroke^and r = 12 and^ 16, respectively, it reduces to:
Diam. at middle = .02294 |/P and .02411 4/P for short and long stroke en-
gines, respectively.
Applying the above formulas to the engines of our list, we have
Diameter of Connecting-rods.
Diameter of Cylinder, inches
1
0
3
3
5
0
Si roke, inches
12
24
30
60
48
96
Length of connecting-rod 1
30
60
75
150
120
240
(3) d" — Vp ~ .0182Z) yp
1 82
1 82
5 46
5 46
9 09
9 09
(5) d" 0179Z) yp
1 79
5.37
8.95
(6) d" - .02758|/Z)J \/p
2.14
5.85
9.51
(7) d" = 0.1oVDLyp + %...,
2.87
7.00
11.11
(7) d" = O.OS|/DI, Vp + %
(9) d" = .03 VP.
(10) d" = .02294 1/P; .02411 yp.
2.67
2.03
2.54
2.67
2.14
7.97
6.09
5.65
7.97
6.41
13.29
10.16
8.75
13.29
10.68
Average
2.24
2.26
6.38
6.27
10.52
10.26
Formulae 5 and 6 (Marks), and also formula 10 (Seaton), give the larger
diameters for the long-stroke engine; formulas 7 give the larger diameters
for the short-stroke engines. The average figures show but little difference
in diameter between long- and short-stroke engines; this is what might be
expected, for while the connecting-rod, considered simply as a column,
would require an increase of diameter for an increase of length, the load
remaining the same, yet in an engine generally the shorter the connecting-
rod the greater the number of revolutions, and consequently the greater the
strains due to inertia. The influences tending to increase the diameter
therefore tend to balance each other, and to render the diameter to some
extent independent of the length. The average figures correspond nearly
to the simple formula d" — .021 D \/p. The diameters of rod for the three
diameters of engine by this formula are, respectively, 2.10, 6.30, and 10.50 in.
Since the total pressure on the piston P = .7854Z)2p, the formula is equiva-
lent to d' = .0237 yp.
Connecting-rod Ends.— For a connecting-rod end of the marine
type, where the end is secured with two bolts, each bolt should be propor-
tioned for a safe tensile strength equal to two thirds the maximum pull or
thrust in the connecting-rod.
The cap is to be proportioned as a beam loaded with the maximum pull
of the connecting-rod, and supported at both ends. The calculation should
be made for rigidity as well as strength, allowing a maximum deflection of
1/100 inch. For a strap-and-key connecting-rod end the strap is designed for
tensile strength, considering that two thirds of the pull on the connecting-
rod may come on one arm. At the point where the metal is slotted for the
key and gib, the straps must be thickened to make the cross-section equal
to that of the remainder of the strap. Between the end of the strap and the
slot the strap is liable to fail in double shear, and sufficient metal must be
provided at the end to prevent such failure.
The breadth of the key is generally one fourth of the width of the strap,
and the length, parallel to the strap, should be such that the cross-section
will have a shearing strength equal to the tensile strength of the section of
the strap. The taper of the key is generally about % inch to the foot.
DIMENSIONS OF PARTS OP ENGINES. 801
Tapered Connecting-rods,— In modern high-speed engines it is
customary to make the connecting-rods of rectangular instead of circular
section, the sides being parallel, and the depth increasing regularly from
the crosshead end to the crank-pin end. According to Grashof , the bending
action on the rod due to its inertia is greatest at 6/10 the length from the
crosshead end, and, according to this theory, that is the point at which the
section should be greatest, although in practice the section is made greatest
at the crank-pin end.
Professor Thurston furnishes the author with the following rule for tapered
connecting-rod of rectangular section: Take the section as computed by the
formula dn = 0.1 1' DL Vp + 3/4 for a circular section,, and for a rod 4/3 the
actual length, placing the computed section at 2/3 the length from the small
end, and carrying the taper straight through this fixed section to the large
end. This brings the computed section at the surge point and makes it
heavier than the rod for which a tapered form is not required.
Taking the above formula, multiplying L by 4/3, and changing it to I in
inches, it becomes d = 1/30 V Dl Vp -f 3/4". Taking a rectangular section
of the same area as the round section whose diameter is dt and making the
depth of the section h = twice the thickress £, we have ,7854d8 ^ht — 2£2,
whence t = .Q27d = .0209 V Dl Vp -f .47", which is the formula for the thick-
ness or distance between the parallel sides of the rod. Making the depth at
the crosshead end = 1.5t, and at 2/3 the length = 2t, the equivalent depth at
the crank end is 2.25L Applying the formula to the short-stroke engines of
our examples, we have
10
30
50
13
80
43
80
75
120
Thickness, t — .0209 \ f Dl Vp -f- .4? —
1 61
8.60
5.59
2.42
5 41
8 39
Depth at crank end, 2%t
8.62
8.11
12.58
The thicknesses f, found by the formula t = .0209 \ Dl Vp -f- .47, agree
closely with the more simple formula t = .01D Vp -f- .60", the thicknesses
calculated by this formula being respectively 1.6, 3.6, and 5.6 inches.
Tlie Crank-pin.— A crank pin should be designed (1) to avoid heating,
(2) for strength, (3) for rigidity. The heating of a crank-pin depends on the
pressure on its rubbing- surf ace, and on the coefficient of friction, which
latter varies greatly according to the effectiveness of the lubrication. It also
depends upon the facility with which the heat produced may be carried
away: thus it appears that locomotive crank-pins may be prevented to some
degree from overheating by the cooling action of the air through which theTJ
pass at a high speed.
Marks gives I = . 000024? ./pIM*
Whitham gives I = 0.9075/ Q~, (2)
In which I = length of crank-pin journal in inches, / = coefficient of friction,
which may be taken at .08 to .05 for perfect lubrication, and .08 to .10 for im-
perfect; p — mean pressure in the cylinder in pounds per square inch; D
— diameter of cylinder in inches; N = number of single strokes per minute;
I.H.P. = indicated horse-power; L = length of stroke in feet. These
formulae are independent of the diameter of the pin, and Marks states as a
general law, within reasonable limits as to pressure and speed of rubbing,
the longer a bearing is made, for a given pressure and number of revolutions,
the cooler it will work; and its diameter Las no effect upon its heating.
Both of the above formulae are deduced empirically from dimensions of
crank-pins of existing marine engines. Marks says that about- one-fourth
the length required for crank-pins of propeller engines will serve for the pins
of side-wheel engines, and one tenth for locomotive engines, making: the
#02 XHE STEAM-EKGIKB.
formula for locomotive crank-pins I = .00000247/pJVD*. or if » = 250, /
= .06, and N = 600, I = .013D2.
Whitham recommends for pressure per square inch of projected area, for
naval engines 500 pounds, for merchant engines 400 pounds, for paddle-wheel
engines 800 to 900 pounds.
Thurston says the pressure should, in the steam-engine, never exceed 500
or 600 pounds per square inch for wrought-iron pins, or about twice that
figure for steel. He gives the formula for length of a steel pin, in inches.
I = PR -i- 600,000, ....... , . (3)
in which P and R are the mean total load on the pin in pounds, and the
number of revolutions per minute. For locomotives, the divisor may be
taken as 500,000. Where iron is used this figure should be reduced to 300,000
and 250,000 for the two cases taken. Pins so proportioned, if well made and
well lubricated, may always be depended upon to run cool; if not well
formed, perfectly cylindrical, well finished, and kept well oiled, no crank-pin
can be relied upon. It is assumed above that good bronze or white-metal
bearings are used.
Thurston also says : The size of crank -pins required to prevent heating of
the journals may be determined with a fair degree of precision by either of
the f ormulee given below :
PN
cv>an Buren' 1866)
The first two formulae give what are considered by their authors fair work-
ing proportions, and the last gives minimum length for iron pins. (V —
velocity of rubbing-surface in feet per minute.)
Formula (1) was obtained by observing locomotive practice in which great
liability exists of annoyance by dust, and great risk occurs from inaccessi-
bility while running, and (2) by observation of crank-pins of naval screw-
engines. The first formula is therefore not well suited: for marine practice.
Steel can usually be worked at nearly double the pressure admissible with
iron running at similar speed.
Since the length of the crank-pin will be directly as the power expended
upon it and inversely as the pressure, we may take it as
in which a Is a constant, and L the stroke of piston, in feet. The values of
the constant, as obtained by Mr. Skeel, are about as follows: a = 0.04 where
water can be constantly used; a = 0.045 where water is not generallv used;
a = 0.05 where water is seldom used; a = 0.06 where water is never needed.
Unwin gives
(8
in which r = crank radius in inches, a = 0.8 to a = 0.4 for iron and for marine
engines, and a = 0.066 to a = 0.1 for the case of the best steel and for loco-
motive work, where it is often necessary to shorten up outside pins as much
as possible.
J. B. Stanwood (Eng'g, June 12, 1891), in a table of dimensions of parts of
American Corliss engines from 10 to 30 inches diameter of cylinder, gives
sizes of crank-pins which approximate closely to the formula
«s.275D"-f .5 in.; d = .25D" ........ (9)
By calculating lengths of iron crank-pins for the engines 10, 30, and 50 inches
diameter, long and snort stroke, by the several formulae above given, it is
found that there is a great difference in the results, so that one formula in
certain cases gives a length three times as great as another. Nos. (4), (" , and
(6) give lengths much greater than the others. Marks (1), Whitham (2),
Thurston (7), I = .06 1.H.P. -H £, and Unwin (8), I = 0.4 1.H.P. •*- r, give re-
sults which agree more closely.
DIMENSIONS OF PARTS OF ENGINES.
803
The calculated lengths of iron crank-pins for the several cases by formulas
(1), (2), (7), and (8) are as follows:
Length of Crank-pins.
Diameter of cylinder D
10
1
250
50
7,854
42
3,299
2.18
2.59
3.00
3.33
2.50
10
2
125
50
7,854
42
3,299
.09
.30
.50
.67
.25
30
2^
130
450
70,686
32.3
22,832
8.17
9.34
10.80
12.0
9.0
30
5
65
450
70,686
32.3
22,832
4.08
4.67
5.40
6.0
4.5
50
4
90
1,250
196,350
30
58,905
14.18
16.22
18.75
20.83
15.62
50
8
45
1,250
196.350
30
58,905
7.09
8.11
9.38
10.42
7.81
Stroke .i (ft.)
Revolutions per minute ...... R
Horse-power . I.H.P.
Maximum pressure • IDS
Mean pressure oer cent of max
Mean pressure P
Length of crank-pin . . .
(1) Whitham, 1 = .9075 X .05 I.H.P. •*• L.
(2) Marks, 1 = 1.038 X .05 I.H.P.-*- L.
(7) Thurston, I = .06 I.H.P. -*-£
(8) Unwin, 1 = .4 I H.P. -*- r
^8) ** 1— 3 1 H.P -*-r
Average
2.72
1.36
9.86
4.93
17.12
8.56
T TT T>
(8) Unwin bost steel Z =* 1-' • *---°
.83
1.37
.42
.69
3.0
4.95
1.5
2.47
5.21
8.84
2.61
4.42
PR
The calculated lengths for the long-stroke engines are too low to prevent
excessive pressures. See ** Pressures on the Crank-pins," below.
The Strength of the Crank-pin is determined substantially as is
that of the crank. In overhung cranks the load is usually assumed as
carried at its extremity, and, equating its moment with that of the resist-
ance of the pin,
and d
in which d = diameter of pin in inches, P = maximum load on the piston,
t = the maximum allowable stress on a square inch of the metal. For iron
it may be taken at 9000 Ibs. For steel the diameters found by this formula
may be reduced 10#. (Thurston.)
Unwin gives the same formula in another form, viz.:
d=a A7~
the last form to be used when the ratio of length to diameter is assumed.
For wt-ought iron, t = 6000 to 9000 Ibs. per sq. in.,
».0947 to .0827;
=p = .0291 to .0238.
For steel, t ~ 9000 to 13,000 Ibs. per sq. In.,
/n y^i
4/~ » .0827 to .0723; |/ ^ =s .0238 to .0194.
Whitham gives d = 0.0827 tfPl = 2.1058//^-^~£l for strength, and
0.0405 fyPl* for rigidity, and recommends that the diameter be calculated
pressure (one third of the length from the free end).
804 THE STEAM-ENGIKE.
Marks, calculating the diameter for rigidity, gives
d - 0.066 Vpl
0.94
p = maximum steam-pressure in pounds per square inch, D •= diameter of
cylinder in inches, L = length of stroke in feet, N= number of single strokes
per minute. He says there is no need of an investigation of the strength of
a crank-pin, as the condition of rigidity gives a great excess of strength.
Marks's formula is based upon the assumption that the whole load may be
concentrated at the outer end, and cause a deflection of .01 inch at that
point.
It is serviceable, he says, for steel and for wrought iron alike.
Using the average lengths of the crank-pins already found, we have the
following for our six engines :
Diameter of Crank-pins.
10
10
30
30
50
50
Stroke ft
1
2
5
4
8
2.72
1 .36
Q n/»
4 93
17 12
8.56
3/5.1PZ
Unwin u = A / •• ............ . .
2 29
1 82
7 34
5 82
12 40
9 84
Marks, d — .066 typPD*
1.39
.85
6.44
3.78
12.41
7.3ft
Pressures on the Crank-pins.— If we take the mean pressure upon
the crank-pin = mean pressure on piston, neglecting the effect of the vary •
ing angle of the connecting-rod, we have the following, using the average
lengths already found, and the diameters according to Unwin and Marks:
Engine No ...
1
2
3
4
5
6
Diameter of cylinder inches . . .
10
1
3,299
6.23
3.78
530
873
10
2
3,299
236
1.16
1,398
2,845
30
2^
22,832
72.4
63.5
315
360
30
5
22,832
28.7
18.6
796
1,228
50
4
58,905
212.3
212.5
277
277
50
8
58,905
84.2
63.3
700
930
Stroke feet ... .
Mean pressure on pin, pounds
Projected area of piu, Unwin
44 ** " ** Marks
Pressure per square inch, Unwin
44 *' 4* *k Marks
The results show that the application of the formulae for length and diam-
eter of crank-pins give quite low pressures per square inch of projected
area for the short-stroke high-speed engines of the larger sizes, but too high
pressures for all the other engines. It is therefore evident that after calcu-
lating the dimensions of a crank-pin according to the formulae given that the
results should be modified, if necessary, to bring the pressure per square
inch down to a reasonable figure.
In order to bring the pressures down to 500 pounds per square inch, we
divide the mean pressures by 500 to obtain the projected area, or product
of length by diameter. Making / = 1.5d for engines Nos. 1, 2, 4 and 6, the
revised table for the six engines is a* follows :
Engine, No 1 2 3 4 5 6
Length of crank-pin, inches 8.15 3.15 9.86 8.37 17.12 13.30
Diameter of crank-pin 2.10 2.10 7.34 5.58 12.40 8.87
Crosshead-pin or Wrist-pin.— /Whitham says the bearing surface
for the wrist-piu is found by the formula for crank-pin design. Seaton says
the diameter at the middle must, of course, be sufficient to withstand the
bending action, and generally from this cause ample surface is provided for
good working; but in any case the area, calculated by multiplying the diam-
eter of the journal by its length, should be such that the pressure does not
exceed 1200 Ibs. per sq. in., taking the maximum load on the piston as the
total pressure on it,
For small engines witb the gudgeon shrunk into the jaws of the connect
DIMENSIONS OF PARTS OF ENGINES. 805
ing-rod, and working: in brasses fitted into a recess in the piston-rod end and
secured by a wrought- iron cap and two bolts, Seaton gives:
Diameter of gudgeon = 1.25 X diam. of piston-rod.
Length of gudgeon as 1.4 X diam. of piston-rod.
length by
ased.
length of
crosshead-pin 0.25 to 0.3 diam. of piston, and diam. = 0.18 to 0.2 diam. of
piston. Since he gives for diarn. of piston-rod 0.14 to 0.17 diam. of piston,
his dimensions for diameter and length of crosshead-pin are about 1.25 and
1 .8 diam. of piston-rod respectively. Taking the maximum allowable press-
ure at 1200 Ibs. per sq. in. and making the length of the crosshead-pin =?
4/3 of its diameter, we have d =s V P-»- 40, 1 as \TP •*• 30, in which P = max-
imum total load on piston in Ibs., d ss diam. and I as length of pin in inches.
For the engines of our example we havei
Diameter of piston, inches ...................... 10 80 50
Maximum load on piston, Ibs. .................. 7854 70,686 196,350
Diameter of crosshead-pin, inches ........ ...... 2.22 6.66 11.08
Length of crosshead-pin, inches.... ......... 8.96 8.86 14.77
Stanwood's rule gives diameter, inches ....... 1.8 to 2 6.4 to 6 9.0 to 10
Stanwood's rule gives length, inches ............ 3.5 to 8 7, 6 to 9 12.5 to 15
Stan wood's largest dimensions give pressure
per sq. in., Ibs . . ........................... 1809 1829 1309
Which pressures aro greater than the maximum allowed by Seaton.
The Cranlt-arm.— The crank>arm is to be treated as a lever, so that
if a is the thickness in direction parallel to the shaft-axis and b its breadth
at a section x inches from the crank-pin centre, then, bending moment M
at that section = Px^ P being the thrust of the connecting-rod, and / the
safe strain per square inch,
«X 6*
-
If a crank-arm were constructed so that 6 varied as ]/x (as given by the
above rule) it would be of such a curved form as to be inconvenient to man-
ufacture, and consequently it is customary in practice to find the maxi-
mum value of b and draw tangent lines to the curve at the points ; these
lines are generally, for the same reason, tangential to the boss of the crank-
arm at the shaft.
The shearing strain is the same throughout the crank-arm; and, conse-
quently, is large compared with the bending strain close to the crank -pin ;
and so it is not sufficient to provide there only for bending strains. The
section at this point should be such that, in addition to what is given by the
calculation from the bending moment, there is an extra square inch for
every 8000 Ibs. of thrust on the connecting-rod (Seaton).
The length of the boss h into which the shaft is fitted is from 0.75 to 1.0
of the diameter of the shaft D, and its thickness e must be calculated from
the twisting strain PL. (L = length of crank.)
For different values of length of boss h, the following values of thickness
of boss e are given by Seaton:
When h ss Z), then e = 0.35 D; if steel, 0.8.
h =s 0.9 D, then e = 0.38 D, if steel, 0.32.
h =s 0.8 D, then e = 0.40 D, if steel, 0.33.
h = 0.7 D. then e == 0.41 D, if steel, 0.34.
The crank-eye or boss into which the pin is fitted should bear the same
relation to the pin that the boss does to the shaft.
The diameter of the shaft-end onto which the crank is fitted should be
1.1 X diameter of shaft.
Thurston says: The empirical proportions adopted by builders will com-
monly be found to fall well within the calculated safe margin. These pro-
portions are, from the practice of successful designers, about as follows :
For the wrought-iron crank, the hub is 1.75 to 1.8 times the least diameter
of that part of the shaft carrying full load; the eye is 2.0 to 2.25 the diame-
ter of the inserted portion of the pin, and their depths are, for the hub, 1.0
to 1.2 the diameter of shaft, and for the eye, 1.25 to 1.5 the diameter of pin.
808
THE STEAM-ENGINE.
The web Is made 0.7 to 0.75 the width of adjacent hub or eye, and is given a
depth of 0.6 to 0.6 that of adjacent hub or eye.
For the cast-iron crank the hub and eye are a little larger, ranging in
diameter respectively from 1.8 to 2 and from 2 to 2.2 times the diameters of
shaft and pin. The flanges are made at either end of nearly the full depth
of hub or eye. Cast-iron has, however, fallen very generally into disuse.
The crank-shaft is usually enlarged at the seat of the crank to about 1.1
its diameter at the Journal. The size should be nicely adjusted to allow for
the shrinkage or forcing on of the crank. A difference of diameter of one
fifth of 1#, will usually suffice ; and a common rule of practice gives an
allowance of but one half of this, or .001.
The formulas given by different writers for crank-arms practically agree,
since they all consider the crank as a beam loaded at one end and fixed at
the other. The relation of breadth to thickness may vary according to the
taste of the designer. Calculated dimensions for our six engines are as f ol
lows :
Dimensions of Crank-arms*
Diam. of cylinder, ins.. .
10
10
30
30
50
50
Stroke £, ins
12
24
30
60
48
96
Wax. pressure on pin P,
7854
7854
70,686
70686
196 350
196,350
Diam. crank-pin d
2.10
2.10
7.34
5.58
12.40
8.87
Vl.H.P.
U.74
3.46
7.70
9.70
12.55
15.82
Diam.shaft,a/4/ ^ D
(a = 4.69, 5.09 and 5.22)..
Length of boss, .SD
2.19
2.77
6.16
7.76
10.04
12.65
Thickness of boss, AD. .
1.10
1.39
3.08
3.88
5.02
6.32
Diam. of boss, 1.8D
4.93
6.23
13.86
17.46
22.59
28.47
Length crank-pin eye, .8d
Thickness of crank-pin
1.76
1.76
5.87
4.46
9.92
7.10
eye, Ad
088
.88
2.94
2.23
4.46
3.55
Max. mom. Tat distance
}£S — }£D from centre
of pin, inch-lbs ...
37, 149
80,661
788,149
1,848,439
3,479,322
7,871,671
Thickness of crank-arm
a ss .75D
2.05
2.60
5.78
7.28
9.41
11.87
Greatest breadth,
bst Y 9000a
Min.mom. T0 at distance
d from centre of pin=Pd
3.48
16,493
4.55
16,493
9.54
528,835
13.0
394,428
15.7
2,434,740
21.0
1,741,625
Least breadth,
/ 6 TO
2.32
2.06
7.81
6.01
13.13
9.89
6» = Y 9000a
The Shaft. -Twisting Resistance.— From the general formula
for torsion, we have: T= ^- d*S = .19635^35, whence d = I/ ^— , in which
T — tprsional moment in inch-pounds, d = diameter in inches, and S = the
shearing resistance of the material in pounds per square inch.
If a constant force P were applied to the crank-pin tcngentially to its path,
the work done per minute would be
PXiX ^X B = 33,000 XLH.P.,
in which L m length of crank in inches, and R = revs, per min., and the
I H P
mean twisting moment T = ' ' ' X 63,025. Therefore
R
*/5.1!T 3/321,427I.H.P. /
y Tm v — B3~;
DIMENSIONS OF PARTS OF ENGINES.
807
This may take the form
• X -F, or d =
In which .Fand a are factors that depend on the strength of the material
and on the factor of safety. Taking S at 45,000 pounds per square inch for
wrought iron, and at 60,000 for steel, we have, for simple twisting by a uni-
form tangential force,
Factor of safety =
Iron F =
Steel Fs
5
35.7
26.8
6
42.8
32.1
8
57.1
42.8
10
71.4
53.5
5
o = 3.3
a = 3.0
6 8 10
8.5 3.85 4.15
3.18 3.5 8.77
Unwin, taking for safe working strength of wrought iron 9000 Ibs., steel
13,500 Ibs., and cast iron 4500 Ibs., gives a = 3.294 for wrought iron, 2.877 for
steel, and 4. 15 for cast iron. Thurston, for crank-axles of wrought iron,
gives a = 4.15 or more.
Seaton says: For wrought iron, /, the safe strain per square inch, should
not exceed 9000 Ibs., and when the shafts are more than 10 inches diameter,
8000 Ibs. Steel, when made from the ingot and of good materials, will ad-
mit of a stress of 12,000 Ibs. for small shafts, and 10,000 Ibs. for those above
10 inches diameter.
The difference in the allowance between large and small shafts is to com-
pensate for the defective material observable in the heart of large shafting,
owing to the hammering failing to affect it.
3 / T TT p
The formula d m a |/ - ' _' -' assumes the tangential force to be uniform
and that it is the only acting force. For engines, in which the tangential
force varies with the angle between the crank and the conneoting-rod, and
with the variation in steam-pressure in the cylinder, and also is influenced
by the inertia of the reciprocating parts, and in which also the shaft may be
subjected to bending as well as torsion, the factor a must be increased, to
provide for the maximum tangential force and for bending.
Seaton gives the following table showing the relation between the maxi-
mum and mean twisting moments of engines working under various condi-
tions, the momentum of the moving parts being neglected, which is allow-
able:
Description of Engine.
Steam Cut-off
at
Max.
Twist
Divided
by
Mean
Twist.
Mome't
Cube
Root
of the
Ratio.
Single-crank expa
M
Two-cylinder exp
it
M
Three-cylinder coi
opposite one aro
0.2
0.4
0.6
0.8
0.2
0.3
0.4
0.5
0.6
0.7
0.8
h.p. 0.5, l.p. 0.66
4* 44
<
i
J.625
J.125
.835
.698
.616
.415
.298
.256
.270
.329
.357
.40
1.26
1.38
.29
.22
.20
.17
.12
.09
.08
.08
.10
1. 11
1.12
1.08
nsive, cranks at 90* .
M
M
M
M
M
npound, cranks 120°.
1. p. cranks j
ther, and h.p. midway j
Seaton also gives the following rules for ordinary practice for ordinary
two-cylinder marine engines:
Diameter of the tunnel-shafts
• /I. H.P
•i/-r:
THlT
808 THE STEAM-EHGIHE.
Compound engines, cranks at right angles:
Boiler pressure 70 Ibs., rate of expansion 6 to 7, F = 70, a = 4.19.
Boiler pressure 80 Ibs., rate of expansion 7 to 8, F = 72, a = 4.16.
Boiler pressure 90 Ibs., rate of expansion 8 to 9, F = 75, a = 4.22.
Triple compound, three cranks at 120 degrees:
Boiler pressure 150 Ibs., rate of expansion 10 to 12, F r= 62, a = 3.96.
Boiler pressure 160 Ibs., rate of expansion 11 to 13, F = 64, a — 4.
Boiler pressure 170 Ibs., rate of expansion 12 to 15, F = 67, a = 4.06.
Expansive engines, cranks at right angles, and the rate of expansion 5,
boiler-pressure 60 Ibs., F - 90, a = 4.48.
Single-crank compound engines, pressure 80 Ibs., F = 96, a — 4.58.
For the engines we are considering it will be a very liberal allowance for
ratio of maximum to mean twisting moment if we take it as equal to the
ratio of the maximum to the mean pressure on the piston. The factor a,
then, in the formula for diameter of the shaft will be multiplied by the cube
root of this ratio, 01^/^=1.34, A/~ = 1.45, W&A/TJr * 1-49 for the
I/ 32.3
., ~ ., Tr
42 I/ 32.3 \ 30
10, 30, and 50-in. engines, respectively. Taking a = 3.5, which corresponds
to a shearing strength of 60,000 and a factor of safety of 8 for steel, or to
45,000 and a factor of 6 for iron, we have for the new coefficient a, in the
* /T H P
formula d, = 04 A /~-^— *, the values 4.69, 5.08, and 5.22, from which we
obtain the diameters of shafts of the six engines as follows:
Engine No 12345 6
Diam.ofcyl 10 10 30 30 50 50
Horse-power, I.H.P 50 50 450 450 1250 1250
Revs, per min., R -JLUL: !_••••• 25° 125 13° 65 90 45
Diam. of shaftd ssaa//1^?:.... 2.74 3.46 7.67 9.70 12.55 15.82
These diameters are calculated for twisting only. When the shaft is also
subjected to bending strain the calculation must be modified as below :
Resistance to Bending.— The strength of a circular-section shaft
to resist bending is one halt' of that to resist twisting. If B is the bending
moment in inch-lbs., and d the diameter of the shaft in inches,
/ Is the safe strain per square inch of the material of which the shaft is
composed, and its value may be taken as given above for twisting (Seaton).
Equivalent Twisting Moment.— When a shaft is subject tc
both twisting and bending simultaneously, the combined strain on any sec-
tion of it may be measured by calculating what is called the equivalent
twisting moment; that is, the two strains are so combined as to be treated
as a twisting strain only of the same magnitude and the size of shaft cal-
culated accordingly. Rankine gave the following solution of the combined
action of the two strains.
If T = the twisting moment, and B — the bending moment on a section of
a shaft, then the equivalent twisting moment T\-= B-\- ^B^ -f- T2.
Seaton says: Crank-shafts are subject always to twisting, bending, and
shearing strains; the latter are so small compared with the former that
they are usually neglected directly, but allowed for indirectly by means of
the factor/.
The two principal strains vary throughout the revolution, and the maxi-
mum equivalent twisting moment can only be obtained accurately by a
series of calculations of bending and twisting moments taken at fixed inter-
vals, and from them constructing a curve of strains.
Considering the engines of our examples to have overhung cranks, the
maximum bending moment resulting from the thrust of the connecting rod
on the crank-pin will take place when the engine is passing its centres
(neglecting the effect of the inertia of the reciprocating parts), and it will
be the product of the total pressure on the piston by the distance between
DIMENSIONS OF PARTS OF ENGINES.
809
f wo parallel lines passing through the centres of the crank-pin and of the
shaft bearing, at right angles to their axes; which distance is equal to
££ length of crank-pin bearing -f length of hub -f/^ length of shaft-bearing -|-
any clearance that may be allowed between the crank and the two bearings.
For our six engines we may take this distance as equal to ^ length of
crank-pin -J- thickness of crank-arm -f 1.5 X the diameter of the shaft as
already found by the calculation for twisting. The calculation of diameter
is then sfs below:
Engine No.
1
2
3
4
5
6
Diam. of cyl., in. .
Horse-power
10
50
250
7,854
6.32
49,637
47,124
118,000
10
50
125
7.854
7.94
62,361
94,«48
175,000
30
450
130
70,686
22.20
1,569,222
1,060,290
3,463,000
30
450
65
70,686
26.00
1,837,836
2,120,580
4,647,000
50
1250
90
196,350
36.80
7,225,680
4,712,400
15,840,000
50
1250
45
196,350
42.25
8,295,788
9,424,800
20,850,00(1
Revs, per min.. . .
Max. press, on pis,P
Leverage,* L in . „ . .
Bd.mo.PI,=JBin.-lb
Twist, mom. T.
Equiv.Twist. mom.
(approx.)
* Leverage = distance between centres of crank-pin and shaft bearing =
Having already found the diameters, on the assumption that the shafts
were subjected to a twisting moment Tpnly, we may find the diameter for
resisting combined bending and twisting by multiplying the diameters
already found by the cube roots of the ratio TI -t- T, or
1.40 1.27 1.46 1.34 1.64 1.36
Gi ving corrected -diameters dj =... 3.84 4.39 11.35 12.99 20.58 21.52
By plotting these results, using the diameters of the cylinders for abscissas
and diameters of the shafts for ordinates, we find that for the long-stroke
engines the results lie almost in a straight line expressed by the formula,
diameter of shaft = .43 X diameter of cylinder; for the short-stroke engines
the line is slightly curved, but does not diverge far from a straight line
whose equation is, diameter of shaft = .4 diameter of cylinder. Using these
two formulas, the diameters of the shafts will be 4.0, 4.3, 12.0, 12.9, 20.0, 21.5.
J. B. Stan wood, in Engineering, June 12, 1891, gives dimensions of shafts
of Corliss engines in American practice for cylinders 10 to 30 in. diameter.
The diameters range from 4 15/16 to 14 15/ 16, following precisely the equation,
diameter of shaft = yz diameter of cylinder - 1/16 inch.
Fly-wheel Shafts.— Thus far we have considered the shaft as resist-
ing the force of torsion and the bending moment produced by the pressure
on the crank-pin. In the case of fly-wheel engines the shaft on the opposite
side of the bearing from the crank- pin has to be designed with reference to
the bending moment caused by the weight of the fly wheel, the weight of
the shaft itself, and the strain of the belt. For engines in which there is an
outboard bearing, the weight of fly-wheel and shaft being supported by
two bearings, the point of the shaft at which the bending moment is a
maximum may be taken as the point midway between the two bearings or
at the middle of the fly-wheel hub, and the amount of the moment is the
product of the weight supported by one of the bearings into the distance
from the centre of that bearing to the middle point of the shaft. The shaft
is thus to be treated as a beam supported at the ends and loaded in the
middle. In the case of an overhung fly-wheel, the shaft having only one
bearing, the point of maximum moment should be taken as the middle of
the bearing, and its amount is very nearly the product of half the weight
of the fly- wheel and the shaft into the distance from the middle of its hub
from the middle of the bearing. The bending moment should be calculated
and combined with the twisting moment as above shown, to obtain the
equivalent twisting moment, and the diameter necessary at the point of
maximum moment calculated therefrom.
In the case of our six engines we assume that the weights of the fly-
wheels, together with the shaft, are double the weight of fly-wheel rim
obtained from the formula* W= 785,40° ~^j^ (given under Fly-wheels);
810
THE STEAM-ENGIKE.
that the shaft is supported by an outboard bearing, the distance between
the two bearings being 24£, 5, and 10 feet for the 10-in., 30-in., and 50-iu.
engines, respectively. The diameters of the fly-wheels are taken such
that their rim velocity will be a little less than 6000 feet per minute.
EngineNo 13345 6
Diam. of cyl., inches 10 30 30 30 50 50
Diam. of fly-wheel, ft 7.5 15 14.5 29 21 42
Revs, per rnin ... 250 125 130 65 90 45
Half wt.fly-wh1! and shaft,lb. 268 536 5,963 11,936 26,884 52,7(59
Lever arm for max. mom., in. 15 15 30 30 60 60
Max. bending moment, in.-lb. 4020 8040 179,040 358,0801,583,070 3,166,140
As these are very much less than the bending moments c&fculated from
the pressures on the crank -pin, the diameters already found are sufficient
for the diameter of the shaft at the fly-wheel hub.
In the case of engines with heavy band fly-wheels and with long fly wheel
shafts it is of the utmost importance to calculate the diameter of the shaft
with reference to the bending moment due to the weight of the fly-wheel
and the shaft.
B. H. Coffey (Power, October, 1892) gives the formula for combined bend-
ing and twisting resistance, Ttl = .196d3& in which 7\ = B -\- |/Z?a_|_ya; T
being the maximum, not the 'mean twisting moment; and finds empirical
working values for .1968 as below. He says: Four points should be consid-
ered in determining this value: First, the nature of the material; second,
the manner of applying the loads, with shock or otherwise; third, the ratio
of the bending moment to the tcrsional moment — the bending moment in a
revolving shaft produces reversed strains in the material, which tend to rup-
ture it; fourth, the size of the section. Inch for inch, large sections are
weaker than small ones. He puts the dividing line between large and small
sections at 10 in. diameter, and gives the following safe values of S X .196 for
steel, wrought iron, and cast iron, for these conditions.
VALUE OF S X .196.
Ratio.
Heavy Shafts
with Shock.
Light shafts with
Shock. Heaw
Shafts No Shock.
Light Shafts
No Shock.
BtoT.
Steel.
Wro't
Iron.
Cast
Iron.
Steel.
Wro't
Iron.
Cast
Iron.
Steel.
Wro't
Iron.
Cast
Iron.
880
785
715
655
3 to 10 or less
3 to 5 or less
1 to 1 or less .
1045
941
855
784
880
785
715
655
440
393
358
328
1566
1410
1281
1176
1320
1179
1074
984
660
589
537
492
2090
1882
1710
1568
1760
1570
1430
1310
B greater than T. .
Mr. Coffey gives as an example of improper dimensions the fly-wheel
shaft of a 1500 H.P. engine at Willimantic, Conn., which broke while the en-
gine was running at 425 H.P. The shaft was 17 ft. 5 in. long between centres
of bearings, 18 in. diam. for 8 ft. in the middle, and 15 in. diam. for the re-
niainder, including the bearings. It broke at the base of the fillet connect-
ing the two large diameters, or 56}^ in. from the centre of the bearing. He
calculates the mean torsional moment to be 446,654 inch -pounds, and the
maximum at twice the mean; and the total weight on one bearing at 87,530
Ibs., which, multiplied by 56J^ in., gives 4,945,445 in.-lbs. bending moment at
the fillet. Applying the formula T^ = B -f- \/B* -f- IT3, gives for equivalent
twisting moment 9,971,045 in.-lbs. Substituting this value in the formula
7\ = .196, Sd3 gives for 5 the shearing strain 15,070 Ibs. per sq. in., or if the
metal had a shearing strength of 45,000 Ibs., a factor of safety of only 3.
Mr. Coffey considers that 6000 Ibs. is all that should be allowed for S under
these circumstances. This would give d — 20.35 in. If we take from Mr.
Coffey's table a value of .1968 = 1100, we obtain d» = 9000 nearly, or d = 20.8
in., instead of 15 in., the actual diameter.
Length of Shaft-bearings.— There is as great a difference of
opinion among writers, and as great a variation in practice concerning length
of journal-bearings, as there is concerning crank-pins. The length of a
DIMENSIONS OF PARTS OF ENGINES. 811
journal being determined from considerations of its heating, the ooserva-
tions concerning heating of crank-pins apply also to shaft-bearings, and the
formulae for »ength of crank-pins to avoid heating may also be used, using
for the total load upon the bearing the resultant of all the pressures brought
upon it, by the pressure on the crank, by the weight of the fly-wheel, and by
the pull of the belt. After determining this pressure, however, we must
resort to empirical values for the so-called constants of the formulae!, really
variables, which depend on the power of the bearing to carry away heat,
and upon the quantity of heat generated, which latter depends on the pres-
sure, on the number of square feet of rubbing surface passed over in a
minute, and upon the coefficient of friction. This coefficient is an exceed-
ingly variable quantity, ranging from .01 or less with perfectly polished
journals, having end-play, and lubricated by a pad or oil-bath, to .10 or more
with ordinary oil-cup lubrication.
For shafts resisting torsion only, Marks gives for length of bearing I =
.0000247/p.ZVD2, in which /is the coefficient of friction, p the mean pressure
in pounds per square inch on the piston, IV the number of single strokes per
minute, and D the diameter of the piston. For shafts under the combined
stress due to pressure on the crank-pin, weight of fly-wheel, etc., he gives
the following: Let Q = reaction at bearing due to weight, 8 = stress due
steam pressure on piston, and Rj.= the resultant force; for horizontal engines,
/?! = YQ* -f- Sa, for vertical engines R: = Q -f S, when the pressure on the
crank is in the same direction as the pressure of the shaft on its bearings,
and R! = Q - S when the steam pressure tends to lift the shaft from its
bearings. Using empirical values for the work of friction per square inch
of projected area, taken from dimensions of crank-pins in marine vessels,
he finds the formula for length of shaft-journals I = .0000325/2?! 2V, and
recommends that to cover the defects of workmanship, neglect of oiling,
and the introduction of dust, / be taken at .16 or even greater. He says
that 500 Ibs. per sq. in. of projected area may be allowed for steel or wrought-
iron shafts in brass bearings with good results if a less pressure is not attain-
able without inconvenience. Marks says that the iise of empirical rules that
do not take account of the number of turns per minute has resulted in bear-
ings much too long for slow-speed engines and too short for high-speed
engines.
Whitham gives the same formula, with the coefficient .00002575.
Thurston says that the maximum allowable mean intensity of pressure
PV
<nay be, for all cases, computed by his formula for journals, I = — OOQrf» or
P(F"-h20)
by Rankine's, I = -, in which P is the mean total pressure in pounds,
Fthe velocity of rubbing surface in feet per minute, and d the diameter of
the shaft in inches. It must be borne in mind, he says, that the friction work
on the main bearing next the crank is the sum of that due the action of the
piston on the pin, and that due that portion of the weight of wheel and
shaft and of pull of the belt which is carried there. The outboard bearing
carries practically only the latter two parts of the total. The crank-shaft
journals will be made longer on one side, and perhaps shorter on the other,
than that of the crank-pin, in proportion to the work falling upon each, i.e.,
to their respective products of mean total pressure, speed of rubbing sur-
faces, and coefficients of friction.
Unwin says: Journals running at 150 revolutions per minute are often
only one diameter long. Fan shafts running 150 revolutions per minute have
journals six or eight diameters long. The ordinary empirical mode of pro-
portioning the length of journals is to make the length proportional to the
diameter, and to make the ratio of length to diameter increase with the
speed. For wrought-iron journals:
Revs, per min. = 50 100 150200 250 500 1000 ^ = . 00422 -fl.
Length -*- diam. = 1.2 1.4 1.6 1.8 2.0 3.0 5.0.
Cast-iron journals may have I -*• d = 9/10, and steel journals I -f- d = 1^,
of the above values.
Unwin gives the following, calculated from the formula I = — \ in
which r is the crank radius in inches, and H.P. the horse-power transmitted
to the crank- pin. * -
812 THE STEAM-ENGINE.
THEORETICAL JOURNAL LENGTH IN INCHES.
Load on
Journal
in
pounds.
Revolutions of Journal per minute.
50
100
200
300
500
1000
1,000
2,000
4,000
5,000
10,000
15,000
20,000
30,000
40,000
50,000
.2
.4
.8
1.0
2.
3.
4.
6.
8.
10.
.4
.8
1.6
2.
4.
6.
8.
12.
16.
20.
.8
1.6
3.2
4.
8.
12.
16.
24.
32.
40.
1.2
2.4
4.8
6.
12.
18.
24.
36.
2.
4.
8.
10.
20.
30.
40.
4.
8.
16.
20.
40.
• •••
• •• •
Applying these different formluae to our six engines, we have:
1
2
3
4
5
6
Diam. cyl
10
10
30
30
50
50
Horse -power
50
50
450
450
1,250
1,250
Revs, per min ,
250
125
130
65
90
45
Mean pressure on crank-pin = S
Half wt. of fly-wheel and shaft = Q..
Resultant press, on bearing
3,299
268
3,299
536
23,185
5,968
23,185
11,936
58,905
26,470
58,905
52,940
fQ*7&BJ&
Diam. of shaft journal
3,310
3 84
3,335
4 39
23,924
11 35
26,194
12 99
64,580
20 58
79,200
21 52
Length of shaft journal:
Marks, 1 = .OOOOSSS/tf^/^lO)
Whitham, I = .00005 15/£,.R(/=. 10).
PV
Thurston \
5.38
4.27
3 61
2.71
2.15
1 82
20.87
16.53
14 00
11.07
8.77
7 43
37.78
29.95
25 36
23.17
18.35
15 55
ou' 60,OOOcT"
B-HoM-qS?
Unwin, I = (.004R -f l)<i
5.22
7 68
2.78
6 59
21.70
17 °5
10.85
•fC OC
35.16
°7 99
22.47
25 39
, 0.4 H.P.
Unwin, 1 — —
3 33
1 60
12 00
6 00
20 83
10 42
r
Average
4.92
2.99
17.05
10.00
29.54
19.22
If we divide the mean resultant pressure on the bearing by the projected
area, that is, by the product of the diameter and length of the journal, using
the greatest and smallest length out of the seven lengths for each Journal
given above, we obtain the pressure per square inch upon the bearing, as
follows:
Engine No
1
2
3
4
5
6
Pressure per sq. in., shortest journal.
Longest journal
259
112
455
115
176
97
336
1^3
151
83
353
145
Average journal
175
254
124
202
106
191
Journal of length = diam
173
155
1V5
Many of the formulae give for the long-stroke engines a length of journal
less than the diameter, but such short journals are rarely used in practice.
The last line in the above table has been calculated ou the supposition that
DIMENSIONS OF PARTS OP ENGINES. 813
fche Journals of the long-strofc^ engines are made of a length equal to the
diameter.
In the dimensions of Corliss engines given by J. B. Stan wood (Eng., June
12. 1891), the lengths of the journals for engines of diam. of cyl. 10 to 20 in.
*re the same as the diam. of the cylinder, and a little more than twice the
diam. of the journal. For engines above 20 in. diam. of cyl. the ratio of
tength to diam. is decreased so that an engine of 30 in. diam. has a journal
26 in. long, its diameter being 14££ in. These lengths of journal are greater
than those given by any of the formulas above quoted.
There thus appears to be a hopeless confusion in the various formulae for
length of shaft journals, but this is no more than is to be expected from the
variation in the coefficient of friction, and in the heat-conducting power of
journals in actual use, the coefficient varying from .10 (or even .16 as given
by Marks) down to .01, according to the condition of the bearing surfaces
PV
and the efficiency of lubrication. Thurston's formula, I = -, reduces to
j
the form I = .000004363PJ?, in which P = mean total load on journal, and
ft = revolutions per minute. This is of the same form as Marks' and
Whituam's formulae, in which, if /the coefficient of friction be taken at .10,
the coefficients of PR are, respectively, .0000065 and .00000515. Taking the
mean of these three formulae, we have I = .0000053P.fi, if / = .10 or I =
.000053/P/? for any other value of /. The author believes this to be as safe
a formula as any for length of journals, with the limitation that if it brings
a result of length of journal less than the diameter, then the length should
be made equal to the diameter. Whenever with / = .10 it gives a length
which is inconvenient or impossible of construction on account of limited
space, then provision should be made to reduce the value of the coefficient
of friction below .10 by means of forced lubrication, end play, etc., and to
carry away the heat, as by water-cooled journal-boxes. The value of P
should be taken as the resultant of the mean pressure on the crank, and the
load brought on the bearing by the weight of the shaft, fly-wheel, etc., as
calculated by the formula already given, viz., Rl = |/<2a + S3 for horizontal
engines, and RI = Q -j- S for vertical engines.
For our six engines the formula I = .0000053P# gives, with the limitation
for the long-stroke engines that the length shall not be less than the diam-
eter, the following:
EngineNo .......... . .......... 128456
Length of journal .................... 4.39 4.39 16.48 13.99 30.80 21.52
Pressure per square inch on journal. . 196 173 128 155 102 171
frank -GliaftM with Centre-crank and Double-crank
Arms* — In centre-crank engines, one of the crank-arms, and its adjoining
journal, called the after journal, usually transmit the power of the engine
to the work to be done, and the journal resists both twisting and bending
moments, while the other journal is subjected to bending moment only.
For the after crank-journal the diameter should be calculated the same as
for an overhung crank, using the formula for combined bending and twist-
ing moment, T, = J3 -f- |/#2 -f T2, in which Tl is the equivalent twisting
moment, B the bending moment, and T the twisting moment. This value
3 /E i rrt
of !T, is to be used in the formula diameter = A / -lif. The bending mo'
w s
ment is taken as the maximum load on piston multiplied by one fourth ot
the length of the crank-shaft between middle points of the two journal
bearings, if the centre crank is midway between the bearings, or by one
half the distance measured parallel to the shaft from the middle of the
crank-pin to the middle of the after bearing. This supposes the crank-
shaft to be a beam loaded at its middle and supported at the ends, but
Whitham would make the bending moment only one half of this, consider-
ing the shaft to be a beam secured or fixed at the ends, with a point of con-
traflexure one fourth of the length from the end. The first supposition is
the safer, but since the bending moment will in any case be much less than
the twisting moment, the resulting diameter will be but little greater than
if WhithanVs supposition is used. For the forward journal, which is sub-
8/10 27?
Jeeted to bending moment only, diameter of shaft =* A/ l±ZTf in which B
W w
814
THE STEAM-ENGIKB.
is the maximum bending moment and 8 the safe shearing strength of the
metal per sqnare inch.
For our six engines, assuming them to be centre-crank engines, and con^
sidering the crank-shaft to be a beam supported at the ends and loaded in
the middle, and assuming lengths between centres of shaft bearings as
given below, we have:
Engine No
1
8
8
4
ft
6
Length of shaft, assumed,
inches L
20
7,854
39,270
47,124
101,000
3.98
3.68
24
7,854
49,637
94,248
156,000
4.60
3.99
48
70,686
848,232
1,060,290
2,208,000
11.15
10.28
60
70,686
1.060,290
2,120,580
3,430,000
13.00
11.16
76
196,350
3,729,750
4,712,400
9,740,000
18.85
16.82
96
196,350
4,712,400
9,424,800
15,240,000
21 .20
18.18
Max. press, on crank-pin, P
Max. bending moment,
B = y±PL, inch-lbs
Twisting moment T . .
Equiv. twisting moment,
B -f 4/B2 -{- Ta
Diameter of after journal,
ff |3/^
V 8000
Diam. of forward journal,
rfi-//1"0*...
V 8000
The lengths of the journals would be calculated in the same manner as in
the case of overhung cranks, by the formula I = .000053/PK, in which P is
the resultant of the mean pressure due to pressure of steam on the piston,
and the load of the fly-wheel, shaft, etc., on each of the two bearings.
Unless the pressures are equally divided between the two bearings, the
calculated lengths of the two will be different; but it is usually customary
to make them both of the same length, and in no case to make the length
less than the diameter. The diameters also are usually made alike for the
two journals, using the largest diameter found by calculation.
The crank-pin for a centre crank should be of the same length as for an
overhung crank, since the length is determined from considerations of
heating, and not of strength. The diameter also will usually be the same,
since it is made great enough to make the pressure per square inch on the
projected area (product of length by diameter) small enough to allow of
free lubrication, and the diameter so calculated will be greater than is re«
quired for strength.
Crank-shaft witli Two Cranks coupled at 90°. — If the
whole power of the engine is transmitted through the after journal of the
after crank-shaft, the greatest twisting moment is equal to 1.414 times the
maximum twisting moment due to the pressure on one of the crank-pins,
[f T — the maximum twisting moment produced by the steam-pressure on
one of the pistons, then Tj the maximum twisting moment on the after part
of the crank-shaft, and on the line-shaft, produced when each crank makes
an angle of 45° with the centre line of the engine, is 1.414T". Substituting
this value in the formula for diameter to resist simple torsion, viz., d =
*5A
3/5.1 X1.414T
or d = 1 .932 A/ — , in which T is
J_ii±, we have d =
the maximum twisting moment produced by one of the pistons, d = diam-
eter in inches, and S = safe working shearing strength of the material.
For the forward journal of the after crank, and the after journal of the
forward crank, the torsional moment is that due to the pressure of steam
on the forward piston only, and for the forward journal of the forward
crank, if none of the power of the engine is transmitted through it, the
torsional moment is zero, and its diameter is to be calculated for bending
moment only.
For Combined Torsion and Flexure.— Let #x = bending mo-
ment on either journal of the forward crank due to maximum pressure on
DIMENSIONS OF TARTS OF ENGINES. 815
forward piston, 1?2 = bending moment on either journal of the after crank
due to maximum pressure on after piston, Tj = maximum twisting moment
on after journal of forward crank, and T2 = maximum twisting moment on
after journal of after crank due to pressure on the after piston.
Then equivalent twisting moment on after journal of forward crank ss Bl
_
On forward journal of after crank = #a -f- VBf -f 2\a.
On after journal of after crank = B* -f- V-#22 -f- (2\ + 2,)*.
These values of equivalent twisting moment are to be used in the formula
3 / e i rp
for diameter of journals d = A/ — — . For the forward journal of the
S
forward crank-shaft d = j/!i£&,
v s
It is customary to make the two journals of the forward crank of om.
diameter, viz., that calculated for the after journal.
For a Three-cylinder Engine with cranks at 120*, the greatest
twisting moment on the after part of the shaft, if the maximum pressures
on the three pistons are equal, is equal to twice the maximum pressure on
any one piston, and it takes place when two of the cranks make angles of
30° with the centre line, the third crank being at right angles to it. (For de-
monstration, see WhithanTs " Steam-engine Design,11 p. 252.) For combined
torsion and flexure the same method as above given for two crank engines
is adopted for the first two cranks; and for the third, or after crank, if all
the power of the three cylinders is transmitted through it, we have the
equivalent twisting moment on the forward journal = B3 4- t^i'-KSFi-l-ZV*,
and on the after journal = B3 -f \'&z* -f- (2\ 4- 2'8 + T3)a, B3 and T8 being
respectively the bending and twisting moments due to the pressure on the
third piston.
Crank » shafts for Triple-expansion Marine Engines,
according to an article in The Engineer, April 25, 1890, should be made
larger than the formulae would call for, in order to provide for the stresses
due to the racing of the propeller in a sea-way, which can scarcely be cal-
culated. A kind of unwritten law has sprung up for fixing the size of a
crank-shaft, according to which the diameter of the shaft is made about
0.45D, where D is the diameter of the high-pressure cylinder. This is for
solid shafts. When the speeds are high, as in war-ships, and the stroke
short, the formula becomes 0 4D, even for hollow shafts.
The Valve-stein or Valve-rod.— The valve-rod should be designed
to move the valve under the most unfavorable conditions, which are when
the stem acts by thrusting, as a long column, when the valve is unbalanced
(a balanced valve may become unbalanced by the joint leaking) and when it
is imperfectly lubricated. The load on the valve is the product of the ar°a
into the greatest unbalanced pressure upon it per square inch, and the co-
efficient of friction may be as high as 20^. The product of this coefficient
and the load is the force necessary to move the valve, which equals the
maximum thrust on the valve-rod. From this force the diameter of the
valve- rod may be calculated by Hodgkinson's formula for columns. An
empirical formula given by Seaton is: Diam. of rod = d =A/-jr » in which
I = length and 6 = breadth of valve, in inches; p = maximum absolute
pressure on the valve in Ibs. per sq in., and Fa, coefficient whose values are,
for iron: long rod 10,000, short 12,000; for steel: long rod 12,000, short 14,500.
Whitham gives the short empirical rule: Diam. of valve-rod = 1/30 diam.
of cyl. = ^ diam of piston-rod.
8ize of Slot-link. (Seaton.)— Let D be the diam. of the valve rod
/j&JT.
~y 12,000*
then Diameter of block-pin when overhung 0 D.
" secured at both ends = 0.76 x D.
•* eccentric-rod pins ss 0.7 x D.
guspension-rod pins ss 0.56 X D.
«• pin when overhung « 0.76 x D.
816 THE STEAM-ENGINE.
Breadth of link ss 0.8 to 09 X D.
length of block = 1.8 to 1.6 X D.
Thickness of bars of link at middle = 0.7 X D.
If a single suspension rod of round section, its diameter = 0.7 X D.
If two suspension rods of round section, their diameter = 0.55 X D.
Size of Double-bar Links.— When the distance between centres of
eccentric pins = 0 to 8 times -throw of eccentrics (throw = eccentricity =
half -travel of valve at full gear) D as before :
Depth of bars = 1.25 x D -f % in.
Thickness of bars *' =0.5 x D -j- y± in.
Length of sliding-block = 2.5 to 3 X D.
Diameter of eccentric-rod pins = 0.8 x D -j- Y± in.
" centre of sliding-block = 1.3 x D.
When the distance between eccentric -rod pins = 5 to 5^ times throw of
eccentrics:
Depth of bars = 1 .25 X D -f- ^ in.
Thickness of bars =0.5 X D -\- 1A in.
Length of sliding-block = 2.5 to 3 X D.
Diameter of eccentric-rod pins = 0.75 X D.
Diameter of eccentric bolts (top end) at bottom of thread = 0.42 X D when "
)f iron, and 0.38 x D when of steel.
The Eccentric. — Diam. of eccentric-sheave = 2.4 x throw of eccentric
•4- 1.3 X diam. of shaft. D as before
Breadth of the sheave at the shaft .................. = 1 .15 X D -f- 0.65 inch
Breadth of the sheave at the strap .................. = D -+- 0.6 inch.
Thickness of metal around the shaft .............. = 0.7 X D + 0.5 inch*
Thickness of metal at circumference .... ........... = 0.6 X D -4- 0.4 inch.
Breadth of key ...................................... = 0.7 X D -f- 0.5 inch.
Thickness of key ............................... .. = 0.25 X D -f 0.5 inch.
Diameter of bolts connecting parts of strap ........ = 0.6 X D -{- 0.1 inch.
THICKNESS OP ECCENTRIC-STRAP.
When of bronze or malleable cast iron:
Thickness of eccentric-strap at the middle ......... = 0.4 X D -f- 0.6 inch.
" sides ........... = 0.3 X D -f- 0.5 inch.
When of wrought iron or cast steel:
Thickness of eccentric-strap at the middle .......... =0.4 X D -f 0.5 inch.
" " " sides ............ = 0.27 X D -j- 0.4 inch
Tlie Eccentric-rod.— The diameter of the eccentric-rod in the body
and at the eccentric end may be calculated in the same way as that of the
connecting-rod, the length being taken from centre of strap to centre of
pin. Diameter at the link end = 0.8Z) -f 0.2 inch.
This is for wrought-iron; no reduction in size should be made for steel.
Eccentric-rods are often made of rectangular section.
Reversins-gear should be so designed as to have more than sufficient
strength to withstand the strain of both the valves and their gear at the
same time under the most unfavorable circumstances; it will then have the
stiffness requisite for good working.
Assuming the work done in reversing the link-motion, TF, to be only that
due to overcoming the friction of the valves themselves through their whole
travel, then, if T be the travel of valves in inches; for a compound engine
Tflxbxp\ r/l'
- 12 \ 5 / + 12V
I1, bl andp1 being length, breadth and maximum steam-pressurs on valve
of the second cylinder; and for an expansive engine
To provide for the friction of link-motion, eccentrics and other gear, and
for abnormal conditions of the same, take the work at one and a half times
the above amount.
FLY-WHEELS. 817
To find the strain at any part of the gear having motion when reversing,
divide the work so found by the space moved through by that part in feet;
the quotient is the strain in pounds; and the size may be found from the
ordinary rules of construction for any of the parts of the gear. (Seaton.)
Engine-frame* or Bed-plates.— No definite rules for the design
of engine- frames have been given by authors of works on the steam-engine.
The proportions are left to the designer who uses " rule of thumb," or
copies from existing engines. F. A. Halsey (Am. Mach., Feb. 14, 1895) has
made a comparison of proportions of the frames of horizontal Corliss
engines of several builders. The method of comparison is to compute from
the measurements the number of square inches in the smallest cross-sec-
tion of the frame, that is, immediately behind the pillow-block, also to
compute the total maximum pressure upon the piston, and to divide the
latter quantity by the former. The result gives the number of pounds
pressure upon the piston allowed for each square inch of metal in the
frame. He finds that the number of pounds per square inch of smallest
section of frame ranges from 217 for a 10 X 30-in. engine up to 575 for a
28 X 48-inch. A 30 X 60-inch engine shows 350 Ibs., and a 32-inch engine
which has been running for many years shows 667 Ibs. Generally the
strains increase with the size of the engine, and more cross-section of metal
is allowed with relatively long strokes than with short ones.
From the above Mr. Halsey formulates the general rule that in engines
of moderate speed, and having strokes up to one and one-half times the
diameter of the cylinder, the load per square inch of smallest section
should be for a 10-inch engine 300 pounds, which figure should be increased
for larger bores up to 500 pounds for a 30- inch cylinder of same relative
stroke. For high speeds or for longer strokes the load per square inch
should be reduced.
FLY -WHEELS.
The function of a fly-wheel is to store tip and to restore the periodical fluc-
tuations of energy given to or taken from an engine or machine, and thus
to keep approximately constant the velocity of rotation. Rankine calls the
quantity — ~ the coefficient of fluctuation of speed cr of unsteadiness, in
%J&<3
which E0 is the mean actual energy, and &E the excess of energy received or
of work performed, above the mean, during a given interval. The ratio of
the periodical excess or deficiency of energy AE'to the whole energy exerted
in one period or revolution General Morin found to be from 1/6 to J4 for
single-cylinder engines using expansion; the shorter the cut-off the higher
the value. For a pair of engines with cranks coupled at 90° the value of the
ratio is about *4, and for three engines with cranks at 120°, 1/12 of its value
for single cylinder engines. For tools working at intervals, such as punch-
ing, slotting and plate-cutting machines, coining-presses, etc., AS is nearly
equal to the whole work performed at each operation.
A fly-wheel reduces the coefficient ^r to a certain fixed amount, being
JW60
about 1/32 for ordinary machinery, and 1/50 or 1/60 for machinery for fine
purposes.
If in be the reciprocal of the intended value of the coefficient of fluctua-
tion of speed, A£ the fluctuation or energy, I toe moment of inertia of the
fly-wheel alone, and a0 its mean angular velocity, 1 = m^ 9 '• As the rim of
CtO
a fly-wheel is usually heavy in comparison with the arms, I may be faken
to equal PFr2, in which W = weight of rim in pounds, and r the radius of the
wheel; then W = "^j- = ?~^» if v be the velocity of the rim in feet per
second. The usual mean radius of the fly-wheel in steam-engines is from
three to five times the length of the crank. The ordinary values of the prod
«ct m.gr, the unit of time being the second, He between 1000 and 2000 feet.
<Abridged from Rankine, S, E., p. 62.)
Thurston gives for engines with automatic valve-gear W = 250.001
•— ^ , in which A = area of piston in square inches, S = stroke in feet, p a
mean steam -pressure in Ibs. per sq. in., R = revolutions per minute, D = omV
gide diameter of wheel in feet. Thurstou also gives for ordinary forms at
818 THE STEAM-ENGINE.
non-condensing engine with a ratio of expansion between 3 and 5, W*s
•^L in which a ranges from 10,000,000 to 15,000,000, averaging 12,000,000.
i
For gas-engines, in which the charge is fired with every revolution, the Amer-
ican Machinist gives this latter formula, with a doubled, or 24,000,000.
Presumably, if the charge is fired every other revolution, a should be again
doubled.
Rankine (" Useful Rules and Tables," p. 247) gives W = 475,000 wl^ , fa
which V is the variation of speed per cent, of the mean speed. Thurston's
first rule above given corresponds with this if we take Fat 1.9 per cent.
Hartnell (Proc. Inst., M. E. 1882, 427) says: The value of V, or tne
variation permissible in portable engines, should not exceed 3 per cent, with
an ordinary load, and 4 per cent when heavily loaded. In fixed engines, for
ordinary purposes, V = 2J4 to 3 per cent. For good governing or special
purposes, such as cotton- spinning, the variation should not exceed 1}$ to 2
per cent.
F. M. Rites (Trans. A. S. M. E., xiv. 100) develops anew formula for weight
Q \s T TT T> /"«
of rim, viz., W= — JjpjyT"1'' and wefenfc of rim per horse-power = j^^, in
which Ovaries from 10,000,000,000 to 20, 000,000,000; also using the latter value
of C, he obtains for the energy of the fly-wheel -~ = r— ^—^QQ — =
--' .
The limit of variation of speed with such a weight of wheel from excess of
power per fraction of revolution is less than .0023.
The value of the constant C given by Mr. Rites was derived from practice
of the Westinghouse single-acting engines used for electric-lighting. F.or
double-acting engines in ordinary service a value of C = 5,000,000,000 would
probably be ample.
From these formulae it appears that the weight of the fly-wheel for a given
horse-power should vary inversely with the cube of the revolutions and the
square of the diameter.
J. B. Stanwood (J0n0'0i June 12, 1891) says: Whenever 480 feet is the
lowest piston-speed probable for an engine of a certain size, the fly-wheel
weight for that speed approximates closely to the formula
W. 700,000^.
W = weight in pounds, d = diameter of cylinder in inches, s = stroke in
inches, D = diameter of wheel in feet, R = revolutions per minute, corre
spending to 480 feet piston -speed.
In a Ready Reference Book published by Mr. Stanwood, Cincinnati, 1892,
he erives the same formula, with coefficients as follows: For slide-valve en-
gines, ordinary duty, 350,000; same, electric-lighting, 700,000; for automatic
high-speed engines, 1,000,000; for Corliss engines, ordinary duty 700,000,
electric-lighting 1,000,000.
Thurston's formula above given, W = ^^, with a = 12,000,000, when re-
K*D*
duced to terms of d and s in inches, becomes W = 785,400—-—.
If we reduce it to terms of horse-power, we have I.H.P. 00 ..„ >
00,000
in which P ss mean effective pressure. Taking this at 40 Ibs., we obtain
r TT p
W = 5,000,000,000^^:. If mean effective pressure = 80 Ibs., then JF =
6,666,000,0;
Emil Theiss (Am. Mach., Sept. 7 and 14, 1893) gives the following values
or d, the coefficient of steadiness, which is the reciprocal of what Rankiiic
calls the coefficient of fluctuation :
FLY-WHEELS.
819
For engines operating-
Hammering and crushing machinery „. «= I
Pumping and shearing machinery « d =s 20 to 30
Weaving and paper-making machinery d = 40
Milling machinery .. d = 50
Spinning machinery d s= 50 to 100
Ordinary driving-engines (mounted on bed-plate),
belt transmission d = 35
Gear-wheel transmission d = 50
Mr. Theiss's formula for weight of fly-wheel in pounds is W= i X V9' — '—\
where d is the coefficient of steadiness, V the mean velocity of the fly-
wheel rim in feet per second, n the number of revolutions per minute, i =:
a coefficient obtained by graphical solution, the values of which for dif-
ferent conditions are given in the following table. In the lines under " cut-
off,1' p means " compression to initial pressure," and O " no compression ":
VALUES OP i. SINGLE-CYLINDER NON-CONDENSING ENGINES.
Piston-
speed, ft.
per min.
Cut-off, 1/6.
Cut-off, H-
Cut-off, U.
Cut-off,^.
Comp.
P
o
Comp.
P
O
Comp.
P
220,760
188,510
165,210
0
201,920
170,040
146,610
Comp.
P
193,340
174,630
O
182,840
167,860
200
400
600
800
272,690
240,810
194,670
158,200
218,580
187,430
145,400
108,690
242.010
208,200
168.590
162,070
209,170
179,460
136,460
135,260
SINGLE-CYLINDER CONDENSING ENGINES.
*«'«
2-eS
03 0> .
SH
200
400
600
Cut-Off, ^.
Cut-off, 1/6.
Cut-off, M.
Cut-off, }£.
Cut-off, &
Comp.
P
0
Comp.
P
0
Comp.
P
0
Comp.
P
O
Comp.
P
O
1567990
265,560
194,550
148,780
176,560
117,870
140,090
234,160
174,380
173,660
118,350
204,210
164,720
167,140
133,080
189,600
174,630
161,830
151,680
172,690
TWO-CYLINDER ENGINES, CRANKS AT 90°.
&4
111
Cut-off, 1/6.
Cut-off, y±.
Cut-off, }£>
Cut-off, 1$.
Comp.
P
0
Comp.
P
0
Comp.
P
0
Comp.
P
0
200
400
600
800
71,980
70,160
70,040
70,040
[ Mean
j 60,140
59,420
57,000
57,480
60,140
IMean
54,340
49,272
49,150
49,220
J Mean
f 50,000
87,930
35,500
I Mean
j 36,950
THREE-CYLINDER ENGINES, CRANKS AT 120°.
o*.S
s*?
Kl&
200
800
Cut-off, 1/6.
Cut-off, H-
Cut-off, &
Cut-off, H-
Comp.
P
O
Comp.
P
O
Comp.
P
O
Comp.
P
0
33,810
30,190
32,240
81,570
33,810
35,140
35,500
33,810
34,540
36,470
33,450
32,850
35,260
33,810
32,370
32,370
As a mean value of * for these engines we may use 33,810.
820 THE STEAM-ENGINE.
Centrifugal Force in Fly-wheels.— Let W — weight of rim in
pounds; R = mean radius of rim iu feet; r = revolutions per minute, g =
32.16; v = velocity of rim in feet per second = 2irRr-*- 60.
Centrifugal force of whole rim = F^ 8|? = ^J^f1'- = .000341 WRr*.
gK oWOg
The resultant, acting at right angles to a diameter of half of this force,
tends to disrupt one half of the wheel from the other half, and is resisted by
the section of the rim at each end of the diameter. The resultant of half the
Q
radial forces taken at right angles to the diameter is 1 -*- J^TT = - of the sum
of these forces; hence the total force F is to be divided by 8 X 2 X 1.5708
= 6.2832 to obtain the tensile strain on the cross-section of the rim, or, total
strain on the cross-section = S = .00005427 WRr*. The weight Wt of a
rim of cast iron 1 inch square in section is Z-nR X 3.125 = 19.635.R pounds,
whence strain per square inch of sectional area of rim = Si = .0010656A'2* a
= .0002664£>2r2 = .0000270 F2, in which D = diameter of wheel in feet, and V
As velocity of rim in feet per minute. &, = .0972i;2, if v is taken in feet per
second.
For wrought iron Si = .0011366#2r2 = .0002842JW = .0000288F2.
For steel St = .0011593.RV2 = . 0002901 Z)2r2 = .0000294 F2,
For wood Si = .0000888.R2?-* = .0000222ZAr2 = .00000225 V 2,
The specific gravity of the wood being taken at 0.6 = 37.5 Ibs. per cu. ft.,
or 1/12 the weight of cast iron.
Example.— Required the strain per square inch in the rim of a cast-iron
wheel 30 ft. diameter, 60 revolutions per minute.
Answer. 152 X 602 X .0010656 = 863.1 Ibs.
Required the strain per square inch in a cast-iron wheel-rim running a
mile a minute. Answer. .000027 X 52802 = 752.7 Ibs.
In cast-iron fly-wheel rims, on account of their thickness, there is difficulty
in securing soundness, and a tensile strength of 10,000 Ibs. per sq. in. is as
much as can be assumed with safety. Using a factor of safety of 10 gives a
maximum allowable strain in the rim of 1000 Ibs. per sq. in., which corre-
sponds to a rim velocity of 6085 ft. per minute.
For any given material, as cast iron, the strength to resist centrifugal force
depends only on the velocity of the rim, and not upon its bulk or weight.
Chas. E. Emery (Cass. Mag., 1892) says: By calculation half the strength
of the arms is available to strengthen the rim, or a trifle more if the fly-
wheel centres are relatively large. The arms, however, are subject to trans-
verse strains, from belts and from changes of speed, and there is, moreover,
no certainty that the arms and rim will be adjusted so as to pull exactly
together in resisting disruption, so the plan of considering the rim by itself
and making it strong enough to resist disruption by centrifugal force within
safe limits, as is assumed in the calculations above, is the safer way.
It does not appear that fly-wheels of customary construction should be
..nsafe at the comparatively low speeds now in common use if proper
materials are used in construction. The cause of rupture of fly-wheels that
have failed is usually either the " running away " of the engine, such as may
be caused by the breaking or slackness of a governor-belt, or incorrect
design or defective materials of the fly-wheel.
Chas. T. Porter (Trans. A. S. M. E., xiv. 808) states that no case of the
bursting of a fly-wheel with a solid rim in a high-speed engine is known. He
attributes the bursting of wheels built in segments to insufficient strength
of the flanges and bolts by which the segment* are held together. (See also
Thnrston, " Manual of the Steam-engine. " Part II, page 413, etc.)
Arms of Fly-wlieels and Pulleys, — Professor Torrey (Am.
Mack., July 30, 1891) gives the following formulafor arms of elliptical cross-
section of cast-iron wheels :
W = load in pounds acting on one arm; 8 = strain on belt in pounds per
inch of width, taken at 56 for single and 112 for double belts; v = width of
belt in inches; n = number of arms; L = length of arm in feet; b = breadth
of arm at hub; d = depth of arm at hub, both in inches : W = — •
b = — — . The breadth of the arm is its least dimension = minor axis of
tAJCt'
the ellipse, and the deoth the major axis. This formula is based on a factor
of safety of 10,,
FLY-WHEELS. 821
In using the formula, first assume some depth for the arm, and calculate
the required breadth to go with it. If it gives too round an arm, assume
tiie depth a little greater, and repeat the calculation. A second trial will
almost always give a good section.
The size of the arms at the hub having been calculated, they may be
somewhat reduced at the rim end. The actual amount cannot be calculated,
as there are too many unknown quantities. However, the depth and
breadth can be reduced about one third at the rim without danger, and this
will give a well-shaped arm.
Pulleys are often cast in halves, and bolted together. When this is done
the greatest care should be taken to provide sufficient metal in the bolts.
This is apt to be the very weakest point in such pulleys. The combined area
of the bolts at each joint should be about 28/100 the cross-section of the pul
ley at that point. (Torrey.)
Unwin gives d m 0.6337 y ~^~ for single belts ;
'~BD
d = 0.798 |/ ~^- for double belts;
D being the diameter of the pulley, and B the breadth of the rim, both in
inches. These formulae are based on an elliptical section of arm in which
6 = OAd or d = 2.56 on a width of belt = 4/5 the width of the pulley rim,
a maximum driving force transmitted by the belt of 56 Ibs. per inch of width
for a single belt and 112 Ibs. for a double belt, and a safe working stress of
cast iron of 2250 Ibs. per square inch.
If in Torrey's formula we make b = 0.4d, it reduces to
Example. —Given a pulley 10 feet diameter; 8 arms, each 4 feet long; face,
36 inches wide; belt, 30 inches: required the breath and depth of the arm at
the hub. According to Unwin,
* /~BD s /36 X 120
d = 0.6337 y — = 0.633// g — = 5.16 for single belt, b = 2.06;
3 /BD 3 /36 X 120
d = 0.798 A/ — - 0.798 j/ — g = 6.50 for double belt, 6 = 2.60.
1VT
According to Torrey, if we take the formula b = —- and assume d -.= 5
and 6,5 inches, respectively, for single and double belts, we obtain b = 1.08
a:id 1.33, respectively, or practically only one half of the breadth according
to Unwin, and, since transverse strength is proportional to breadth, an arm ]
only one half as strong. i
Torrey's formula is said to be based on a factor of safety of 10, but this '
factor can be only apparent and not real, since the assumption that the
strain on each arm is equal to the strain on the belt divided by the number
of arms, is, to say the least,- inaccurate. It would be more nearly correct to
say that the strain of the belt is divided among half the number of arms.
Unwin makes the same assumption in developing his formula, but says it is
only in a rough sense true, and that a large factor of safety must be allowed.
He therefore takes the low figure of 2250 Ibs. per square inch for the safe
working strength of cast iron. Unwin says that his equations agree well
Y/ith practice.
Diameters of Flywlieels for Various Speeds.— If 6000 feet
per minute be the maximum velocity of rim allowable, then 6000 = irRD, in
which R = revolutions per minute, and D = diameter of wheel in feet,
822
THE STEAM-ENGINE.
MAXIMUM DIAMETER OF FLY-WHEEL ALLOWABLE FOR DIFFERENT NUMBERS
OF REVOLUTIONS.
!
Revolutions
per minute.
Assuming Maximum Speed of
5000 feet per minute.
Assuming Maximum Speed
of 6000 feet per minute.
Circum. ft.
Diam. ft.
Circum. ft.
Diam. ft.
40
125
39.8
150.
47.7
50
100
31.8
120.
38.2
60
83.3
26.5
100.
31.8
70
71.4
22.7
85.72
27.3
80
62.5
19.9
75.00
23.9
90
55.5
17.7
66.66
21.2
100
50.
15.9
60.00
19.1
120
41.67
13.3
50.00
15.9
140
35.71
11.4
42.86
13.6
160
31.25
9.9
37.5
11.9
180
27.77
8.8
33.33
10.6
200
25.00
8.0
30.00
9.6
220
22.73
7.2
27.27
8.7
240
20.83
6.6
25.00
8.0
260
19.23
6.1
23.08
7.3
280
17.86
5.7
21.43
6.8
300
16.66
5.3
20.00
6.4
350
14.29
4.5
17.14
5.5
400
12.5
4.0
15.00
4.8
450
11.11
3.5
13.33
4.2
500
10.00
3.2
12.00
3.8
Strains in the Rims of Fly-band Wheels Produced by
Centrifugal Force. (James B. Stanwood, Trans. A. S. M. E., xiv. 251.)
—Mr. Stanwood mentions one case of a fly-band wheel where the periphery
velocity on a 17' 9" wheel is over 7500 ft. per minute.
In band saw-mills the blade of the saw is operated successfully over
wheels 8 and 9 ft. in diameter, at a periphery velocity of 9000 to 10,000 ft. per
minute. These wheels are of cast iron throughout, of heavy thickness, with
a large number of arms.
In shingle-machines and chipping-machines where cast-iron disks from 2 to
5 ft. in diameter are employed, with knives inserted radially, the speed is
frequently 10,000 to 11,000 ft. per minute at the periphery.
If the rim of a fly-wheel alone be considered, the tensile strain in pounds
per square inch of the rim section is T = — - nearly, in which V — velocity
in feet per second; but this strain is modified by the resistance of the arms,
which prevent the uniform circumferential expansion of the rim, and induce
a bending as well as a tensile strain. Mr. Stanwood discusses the strains in
band-wheels due to transverse bending of a section of the rim between a
pair of arms.
When the arms are few in number, and of large cross-section, the ring
will be strained transversely to a greater degree than with a greater number
of lighter arms. To illustrate the necessary rim thicknesses for various
rim velocities, pulley diameters, number of arms, etc., the following table
is given, based upon the formula
(JL _ 1)'
V F2 10/
in which t = thickness of rim in inches, d = diameter of pulley in inches,
N — number of arms, V = velocity of rim in feet per second, and F = the
greatest strain in pounds per square inch to which any fibre is subjected.
The value otFis taken at 6000 Ibs. per sq. in.
FLY-WHEELS.
823
Thickness of Kims in Solid Wheels.
Diameter of
Pulley in
inches.
Velocity of
Rim in feet per
second.
Velocity of
Rim in feet per
minute.
No. of
Arms.
Thickness in
inches.
24
24
48
108
108
50
88
88
184
184
8,000
5,280
5,280.
11,040
11,040
6
6
6
16
36
2/10
15/32
15/16
If the limit of rim velocity for all wheels be assumed to be 88 ft. per sec-
ond, equal to 1 mile per minute, F = 6000 Ibs., the formula becomes
._.476d . „. d
.67A2
= 0.7-
When wheels are made in halves or in sections, the bending strain may
be such as to make t greater than that given above. Thus, when the joint
comes half way between the arms, the bending action is similar to a beam
supported simply at the ends, uniformly loaded, and t is 50^ greater. Then
the formula becomes
or for a fixed maximum rim velocity of 88 ft. per second and F = 6000 Ibs.,
t = " ' . In segmental wheels it is preferable to have the joints opposite
the arms. Wheels in halves, if very thin rims are to be employed, should
have double arms along the line of separation,
Attention should be given to the proportions of large receiving and tight-
ening pulleys. The thickness of rim for a 48-in. wheel (shown in table) with
a rim velocity of 88 ft. per second, is 15/16 in. Many wrecks have been
caused by the failure of receiving or tightening pulleys whose rims have bees
too thin. Fly-wheels calculated for a given coefficient of steadiness are fre-
quently lighter than the minimum safe weight. This is true especially of
large wheels. A rough guide to the minimum weight of wheels can be de-
duced from our formulae. The arms, hub, lugs, etc., usually form from one
quarter to one third the entire weight of the wheel. If b represents the
of a wheel in inches, the weight of the rim (considered as a simple annular
ring) will be w = .&>dtb Ibs. If the limit of speed is 88 ft. per second, then
for solid wheels t = 0.7d -s- N2. For sectional wheels (joint between arms)
t = 1.05d -f- JV«. Weight of rim for solid wheels, iv - .57d*b -s- N* in pounds.
Weight of rim in sectional wheels with joints between arms, w = Md^b -*-
N* in pounds. Total weight of wheel: for solid wheel, W = .76^6 -5- N* to
.86du6 -5- .ZV2, in pounds. For segmental wheels with joint between arms,
W = 1.05rf»6 -?- N* to 1.8da6 -s- N*, in pounds.
(This subject is further discussed by Mr. Stanwood, in vol. xv., and by
Prof. Gaetano Lanza, in vol. xvi., Trans. A. S. M. E.)
A Wooden It im Fly-wheel* built in 1891 for a pair of Corliss en-
gines at the Amoskeag Mfg. Co/s mill, Manchester, N. H., is described by
C. H. Manning in Trans. A. S. M. E., xiii. 618. It is 30 ft. diam. and 108 in. face.
The rim is 12 inches thick, and is built up of 44 courses of ash plank, 2, 3,
and 4 inches thick, reduced about ^ inch in dressing, set edgewise, so as to
break joints, and glued and bolted together. There are two hubs and two
sets of arms, 12 in each, all of cast iron. The weights are as follows:
Weight (calculated) of ash rim 31,855 Ibs.
** of 24 arms (foundry 45,020) 40,349 "
" «" 2hubs( " 35,030) 31,394^: «*
Counter-weights in 6 arms 664
Total, excluding bolts and screws 104,262 ± "
Ihe wheel was tested at 76 revs, per min., being a surface speed of nearly
7200 feet per minute.
824 THE STEAM-ENGINE.
Mr. Manning discusses the relative safety of cast iron and of wooden
wheels as follows: As for safety, the speeds being the same in both
cases, the hoop tension in the rim per unit of cross-section would be directly
as the weight per cubic unit; and its capacity to stand the strain directly as
the tensile strength per square unit; therefore the tensile strengths divided
by the weights will give relative values of different materials. Cast iron
weighing 450 Ibs. per cubic foot and with a tensile strength of 1,440,000 Ibs.
per square foot would give a value of 1,440,000-^-450= 3200, whilst ash, of
which the rim was made, weghing 34 Ibs. per cubic foot, and with 1,152,000
Ibs. tensile strength per square foot, gives a result 1,152,000 -=- 34 = 33,882,
and 33, 882 -f- 3200 = 10.58, or the wood-rimmed pulley is ten times safer
than the cast-iron when the castings are good. This would allow the wood-
rimmed pulley to increase its speed to 1/10.58 =3.25 times that of a sound
cast-iron one with equal safety.
Wooden Fly-wbeel of the Willimantic Linen Co. (Illus-
trated in Power, March, 1893.) — Rim 28 ft. diaui., 110 in. face. The rim is
carried upon three sets of arms, one under the centre of each belt, with 12
arms in each set.
The material of the rim is ordinary whitewood, % in. in thickness, cut into
segments not exceeding 4 feet in length, and either 5 or 8 inches in width.
These were assembled by building a complete circle 13 inches in width, first
with the 8 inch inside and the 5-inch outside, and then beside it another cir-
cle with the widths reversed, so as to break joints. Each piece as it was
added was brushed over with glue and nailed with three-inch wire nails to
the pieces already in position. The nails pass through three and into the
fourth thickness. At the end of each ann four 14-inch bolts secure the
rim, the ends being covered by wooden plugs glued and driven into the face
of the wheel.
Wire-wound Fly-wheels for Extreme Speeds. (Eng'g News,
August 2, 1890.)— The power required to produce the Mannesmann tubes is
very large, varying from 2000 to 10,000 H.P., according to the dimensions of
the tube. Since this power is only needed for a short time (it takes only 30
to 45 seconds to convert a bar 10 to 12 ft. long and 4 in. in diameter into a
tube), and then some time elapses before the next bar is ready, an engine of
1200 H.P. provided with a large fly-wheel for storing the energy will supply
power enough for one set of rolls. These fly-wheels are so large and run at
such great speeds that the ordinary method of constructing them cannot be
followed. A wheel at the Mannesmann Works, made in Komotau, Hungary,
in the usual manner, broke at a tangential velocity of 125 ft. per second.
The fly-wheels designed to hold at more than double this speed consist of a
cast-iron hub to which two steel disks, 20 ft. in diameter, are bolted; around
the circumference of the wheel thus formed 70 tons of No. 5 wire are wound
under a tension of 50 Ibs. In the Mannesmann Works at Landore, Wales,
such a wheel makes 240 revolutions a minute, corresponding to a tangential
velocity of 15,080 ft. or 2.85 miles per minute.
THE SLIDE-VALVE.
Definitions.— Travel = total distance moved by the valve.
Throiv of the Eccentric = eccentricity of the eccentric = distance from the
centre of the shaft to the centre of the eccentric disk = y% the travel of the
valve. (Some writers use the term *' throw " to mean the whole travel of
the valve.)
Lap of the valve, also called outside lap or steam-lap = distance the outer
or steam edge of the valve extends beyond or laps over the steam edge of
the port when the valve is in its central position.
Inside lap, or exhaust-Jap — distance the inner or exhaust edge of the
valve extends beyond or laps over the exhaust edge of the port when the
valve is in its central position. The inside lap is sometimes made zero, or
even negative, in which latter case the distance between the edge of the
valve and the edge of the port is sometimes called exhaust clearance, or
inside clearance.
Lead of the valve r= the distance the steam-port is opened when the engine
is on its centre and the piston is at the beginning of the stroke.
Lead-angle = the angle between the position of the crank when the valve
begins to be opened and its position when the piston is at the beginning of
the stroke.
The valve is said to have lead when the steam-port opens before the pirton
SLIDE-VALVE.
825
begins its stroke. If the piston begins its stroke before the admission of
gtearn begins the valve is said tr have negative lead, and its amount is the
lap of the edge of the valve over the edge of the port at the instant when
the piston stroke begins.
Lap-angle = the angle through which the eccentric must be rotated to
cause the steam edge to travel from its central position the distance of the
lap.
Angular advance of the eccentric = lap-angle -J- lead angle.
Linear advance = lap -|- lead.
greatest port-opening. (Halsey on Slide-valve Gears.) Draw a circle of
diameter fh = travel of valve. From O the centre set off Oa = lap and ab
= lead, erect perpendiculars Ge, etc, bd; then ec is the lap-angle and cd the
lead-angle, measured as arcs. Set off fg = cd, the lead-angle, then Og is
the position of the crank for steam admission. Set off 2ec-\-cd from h to i\
then Oi is the crank-angle for cut-off, and/fc-*-//i is the fraction of stroke
completed at cut-off. Set off Ol = exhaust -lap and draw lm; em is the
exhaust-lap angle. Set off hn = ec + cd — em, and On is the position of
crank at release. Set off fp = ec •+• cd+ em, and Op is the position of crank
for compression, fo -+-fh is the fraction of stroke completed at release, and
]iq -L. hf is the fraction of the return stroke completed when compression
begins; O/i, the throw of the eccentric, minus Oa the lap, equals ah the
maximum port-opening.
If a valve has neither lap nor lead, the line joining the centre of the eccen-
i Cut-off
LJ Port—
j* Lap >| j Opening.
\L
Fio. 146.
trie disk and the centre of the shaft being at right angles to the line of the
crank, the engine would follow full stroke, admission of steam beginning at
the beginning of the stroke and ending at the end of the stroke.
Adding lap to the valve enables us to cut off steam before the end of the
stroke; the eccentric being advanced on the shaft an amount equal to the
lap-angle enables steam to be admitted at the beginning of the stroke, as
826
THE STEAM-ENGINE.
before lap was added, and advancing it a further amount equal to the lead
angle causes steam to be admitted before the beginning of the stroke.
Having given lap to the valve, and having advanced the eccentric on the
shaft from its central position at right angles to the crank, through the
angular advance = lap-angle and lead-angle, the four events, admission,
cut-off, release or exhaust-opening, and compression or exhaust-closure,
take place as follows: Admission, when the crank lacks the lead-angle of
having reached the centre; cut-off, when the crank lacks two lap-angles and
one lead-angle of having reached the centre. During the admission of
steam the crank turns through a semicircle less twice the lap-angle. The
greatest port-opening is equal to half the travel of the valve less the lap.
Therefore for a given port-opening the travel of the valve must be in-
creased if the lap is increased. When exhaust-lap is added to the valve it
delays the opening of the exhaust and hastens its closing by an angle of
rotation equal to the exhaust- lap angle, which is the angle through which
the eccentric rotates from its middle position while the exhaust edge of the
valve uncovers its lap. Release then takes place when the crank lacks one
lap-angle and one lead-angle minus one exhaust-lap angle of having reached
the centre, and compression when the crank lacks lap-angle -j- lead-angle -f-
exhaust-lap angle of having reached the centre.
The above discussion of the relative position of the crank, piston, and
valve for the different points of the stroke is accurate only with a connect-
ing-rod of infinite length.
For actual connecting-rods the angular position of the rod causes a
distortion of the position of the valve, causing the events to take place too
late in the forward stroke and too early in the return. The correction of
this distortion may be accomplished to some extent by setting the valve so
as to give equal lead on both forward and return stroke, and by altering
the exhaust-lap on one end so as to equalize the release arid compression.
F. A. Halsey, in his Slide-valve Gears, describes a method of equalizing the
cut-off without at the same time affecting the equality of the lead. In
designing slide-valves the effect of angularity of the connecting-rod should
be studied on the drawing-board, and preferably by the use of a model.
Sweet's Valve-diagram.— To find outside and inside lap of valve
for different cut-offs and compressions (see Fig. 147): Draw a circle whose
FIQ. 147.— Sweet's Valve-diagram.
diameter equals travel of valve. Draw diameter BA and continue to A1,
BO that the length AA* bears the same ratio to XA as the length of con-
necting-rod does to length of engine-crank. Draw small circle K with a
radius equal to lead. Lay off AC so that ratio of AC to AB — cut-off in
parts of the stroke. Erect perpendicular CD. Draw DL tangent to K\
draw XS perpendicular to DL\ XS is then outside lap of valve.
To find release and compression: If there is no inside lap, draw FE
through X parallel to DL. F and E will be position of crank for release
and compression. If there is an inside lap, draw a circle about JXT, in which
radius XY equals inside lap. Draw HG tangent to this circle and parallel
to DL', then H and G are crank position for release and compression.
Draw HN and MG, then AN is piston position at release and AM piston
position at compression, AB being considered stroke of engine.
To make compression alike on each stroke it is necessary to increase the
inside lap on crank end of valve, and to decrease by the same amount the
THE SLIDE-VALVE.
82?
Inside lap on back end of valve. To determine this amount, through M with
a radius MM1 = AA*, draw arc M P, from P draw PT perpendicular to AB,
then TM is the amount to be added to inside lap on crank end, and to be
deducted from inside lap on back end of valve, inside lap being XY.
For the Bilgram Valve Diagram, see Halsey on Slide-valve Gears.
The Zeuiier Valve-diagram is given in most of the works on the
steam-engine, and in treatises on valve-gears, as Zeuner's, Peabody's, and
dead centre
P/
FIG. 148.— Zeuner's Valve-diagram.
Spangler's. The following is condensed from Holmes on the Steam-engine:
Describe a circle, with radius OA equal to the half travel of the valve.
From O measure off OB equal to the outside lap, and BC equal to the lead.
When the crank- pin occupies the dead centre A, the valve has already
moved to the right of its central position by the space OB + BC. From C
erect the perpendicular CE and join OE. Then will OE be the position
occupied by the line joining the centre of the eccentric with the centre of
the crank-shaft at the commencement of the stroke. On the line OE as
diameter describe the circle OCE ; then any chords, as Oe, OE, Oe', will
represent the spaces travelled by the valve from its central position when
the crank-pin occupies respectively the positions opposite to D, E, and F.
Before the port is opened at all the valve must have moved from its central
position by an amount equal to the lap OB. Hence, to obtain the space by
which the port is opened, subtract from each of the arcs Oe, OE, etc., a
length equal to OB This is represented graphically by describing from
centre O a circle with radius equal to the lap OB ; then the spaces fe, gE,
etc., intercepted between the circumferences of the lap-circle Bfe' and the
valve-circle OCE, will give the extent to which the steam-port is opened.
At the point fc, at which the chor I Ok is common to both valve and lap
circles, it is evident that the valve fcas moved to the right by the amount of
the lap, and is consequently just on the point of opening the steam-port.
Hence the steam is admitted before the commencement of the stroke, when
the crank occupies the position OH, and while the portion HA of the revo-
328 THE STEAM-ENGINE.
lution still remains to be accomplished. When the crank-pin reaches the
position At that is to say, at the ^mmencement of the stroke, the port is
already opened by the space OC - OB = BC, called the lead. From this
point forward till the crank occupies the position OE the port continues to
open, but when the crank is at OE the valve has reached the furthest limit
of its travel to the right, and then commences to return, till when in the
position OF the edge of the valve just covers the steam-port, as is shown
by the chord Oe\ being again common to both lap and valve circles. Hence
when the crank occupies the position OF the cut-off takes place and the
steam commences to expand, and continues to do so till the exhaust opens.
For the return stroke the steam-port opens again at Hf and closes at F'.
There remains the exhaust to be considered. When the line joining the
centres of the eccentric and crank-shaft occupies the position opposite to
OG at right angles to the line of dead centres, the crank is in the line OP at
right angles to OE ; and as OP does not intersect either valve-circle the
valve occupies its central position, and consequently closes the port by the
amount of the inside lap. The crank must therefore move through such
an angular distance that its line of direction OQ must intercept a chord on
the valve-circle OX" equal in length to the inside lap before the port can be
opened to the exhaust. This point is ascertained precisely in the same
manner as for the outside lap, namely, by drawing a circle from centre O,
with a radius equal to the inside lap; this is the small inner circle in the
figure. Where this circle intersects the two valve-circles we g^t four points
which show the positions of the crank when the exhaust opens and closes
during each revolution. Thus at Q the valve opens the exhaust on the side
of the piston which we have been considering, while at R the exhaust closes
and compression commences and continues till the fresh steam is read-
mitted at H.
Thus the diagram enables us to ascertain the exact position of the crank
when each critical operation of the valve takes place. Making a resume of
these operations of one side of the piston, we have: Steam admitted before
the commencement of the stroke at H. At the dead centre A the valve is
already opened by the amount BC. At E the port is fully opened, and
valve has reached one end of its travel. At F steam is cut off, consequently
admission lasted f rom H to F. At P valve occupies central position, and
ports are closed both to steam and exhaust. At Q exhaust opened, conse-
quently expansion lasted from F to Q. At K exhaust opened to maximum
extent, and valve reached the end of its travel to the left. At R exhaust
closed, and compression begins and continues till the fresh steam is admitted
at H.
PROBLEM.— The simplest problem which occurs is the following : Given
the length of throw, the angle of advance of the eccentric, and the laps of
the valve, find the angles of the crank at which the steam is admitted and
cut off and the exhaust opened and closed. Draw the line OE, representing
the half -travel of the valve or the throw of the eccentric at the given angle
of advance with the perpendicular OG. Produce OE to K. On OE and OK
as diameters describe the two valve -circles. With centre and radii equal to
the given laps describe the outside and inside lap-circles. Then the inter-
section of these circles with the two valve-circles give points through which
the lines OH, OF, OQ, and OR can be drawn. These lines give the required
positions of the crank.
Numerous other problems will be found in Holmes on the Steam-engine,
including problems in valve-setting and the application of the Zeuner dia-
gram to link motion and to the Meyer valve-gear.
Port Opening.— The area of port opening should be such that the ve-
locity of the steam in passing through it should not exceed 6000 ft. per min.
The ratio of port area to piston area will then vary with the piston-speed as
follows:
F°rftPeeer°minStOD' [ 10° 20° 30° 40° 50° 60° 70° 80° 90° 10°° 12°°
Port area^ piston J. ^ 033 Q5 >06? >Q83 ^ <10? tl33 ,15 >167 o
For a velocity of 6000 ft. per min.,
_ . sq. of diam. of cyl. X piston- speed
Port area = ^ 7639 T*
The length of the port opening may be equal to or something less than the
diameter of the cylinder, and the width = area of port opening H- its length.
The bridge between steam and exhaust ports should be wide enough to
prevent a leak of steam into the exhaust due to overtravel of the valve.
THE SLIDE-VALVE.
829
Auchincloss gives: Width of exhaust port = width of steam port -f
y% travel of valve - width of bridge.
Lead. (From Peabody's Valve-gears.)— The lead, or the amount that
the valve is open when the engine is on a dead point, varies, with the type
and size of the engine, from a very small amount, or even nothing, up to %
of an inch or more. Stationary-engines running at slow speed may have
from 1/64 to 1/16 inch lead. The effect of compression is to fill the waste
space at the end of the cylinder with steam; consequently, engines having
much compression need less lead. Locomotive-engines haying the valves
controlled by the ordinary form of Stephenson link-motion may have
a small lead when running slowly and with along cut-off, but when at speed
with a short cut-off the lead is at least J4 inch; and locomotives that have
valve-gear which gives constant lead commonly have J4 i«ch lead. The
lead angle is the angle the crank makes with the line of dead points at
admission. It may vary from 0° to 8°.
Inside Lead.— Weisbach (vol. ii. p. 296) says: Experiment shows that
the earlier opening of the exhaust ports is especially of advantage, and in
the best engines the lead of the valve upon the side of the exhaust, or the
inside lead; is 1/25 to 1/15; i.e., the slide-valve at the lowest or highest posi-
tion of the piston has made an opening whose height is 1/25 to 1/15 of the
whole throw of the slide-valve. The outside lead of the slide-valve or the
lead on the steam side, on the other hand, is much smaller, and is often
only 1/100 of the whole throw of the valve.
Effect of Changing Outside Lap, Inside Lap, Travel
and Angular Advance. (Thurston.)
Admission
Expansion
Exhaust
Compression
Incr.
O.L.
is later,
ceases sooner
occurs earlier,
continues longer
is unchanged
begins at
same point
Incr.
I.L.
unchanged
begins as before,
continues longer
occurs later,
ceases earlier
begins sooner,
continues longer
Incr.
begins sooner,
begins later,
begins later,
begins later,
T.
continues longer
ceases sooner
ceases later
ends sooner
Incr.
A. A.
begins earlier,
period unaltered
begins sooner,
per. the same
begins earlier,
per. unchanged
begins earlier,
P3r. the same
Zeuner gives the following relations (Weisbach-Dubois, vol. ii. p. 307):
If 8 = travel of valve, p ='maximum port opening;
L = steam-lap, I = exhaust-lap;
R = ratio of steam-lap to half travel = — , L = — X S;
r = ratio of exhaust lap to half travel = -— , I = £ ;
.53'
If
*%i ~+» * a * *» — j — p«
, = angle HOP between positions of crank at admission and at cut-off,
and ft = angle QOR between positions of crank at release and at
, , sin (180° - a) 1x/sin (180° - 0
compression, then R = V* : — ^-. ; r = }£• : — 7-73 — .
sin Jx<jja sin j^>p
Ratio of Lap and of Port-opening to Valve-travel .—The
table on page 831, giving the ratio of lap to travel of valve and ratio of travel
to port opening, is abridged from one given by Duel in Weisbach-Dubois,
vol. ii. It is calculated from the above formulae Intermediate values may
be found by the formul®, or with sufficient accuracy by interpolation from
the figures in the table. By the table on page 830 the crank-angle may be
found, that is, the angle between its position when the engine is on the
centre and its position at cut-off, release, or compression, when these are
known in fractions of the stroke. To illustrate the use of the tables the
following example is given by Buel: width of port = 2.2 in.; width of port
opening = width of port -f 0.3 in.; overtravel = 2.5 in.; length of connect-
ing-rod = %y% times stroke ; cut-off = 0.75 of stroke ; release = 0.95 of
stroke ; lead-angle, 10°, From the first table we find crank-angle = U4,&
830
THE STEAM-ENGLffE.
add lead-angle, making 124.6.° From the second table, for angle between
admission and cut-off, 125°, we have ratio of travel to port-opening = 3.72,
or for 124.6° = 3.74, which, multiplied by port-opening 2.5, gives 9.45 in
travel. The ratio of lap to travel, by the table, is .2324, or 9.45 X .2324 = 2.2
in. lap. For exhaust-lap we have, for release at .95, crank-angle =151.3;
add lead-angle 10° = 161.3°. From the second table, by interpolation, ratio
of lap to travel = .0811, and .0811 X 9.45 = 0.77 in., the exhaust-lap.
Lap-angle = V* (180° — lead- angle — crank- angle at cut-off);
' = yz (180° - 10 - 114.6) = 27.7°.
Angular advance = lap -angle -f lead-angle = 27.7 + 10 = 37.7°.
Exhaust lap-angle = crank-angle at release 4- lap-angle 4- lead-angle — 180°;
= 151.3 -f 27.T -j- 10 - 180° = 9°.
Crank-angle at com- )
pression measured >• = 180° - lap-angle — lead-angle — exhaust lap-angle;
on return stroke j
= 180 - 27.7 - 10 - 9 = 133.3° ; corresponding, by
table, to a piston position of .81 of the return stroke; or
Crank-angle at compression = 180° — (angle at release — angle at cut- off)
4- lead- angle;
s 180 - (151.3- 114.6) -f 10 = 133,3°.
The positions determined above for cut-off and release are for the forward
stroke of the piston. On the return stroke the cut-off will take place at
.
the same angle, 114.6°, corresponding by table to 66.6£ of the return
stroke, instead of 75#. By a slight adjustment of the angular advance
and the length of the eccentric rod the cut-off can be equalized. The
Crank Angles for Connecting-rods of Different Length.
. FORWARD AND RETURN STROKES.
'raction of
troke from
imencement.
Ratio of Length of Connecting-rod to Length of Stroke.
2
' ^
3
3^
4
5
Infi-
nite.
For.
For.
Ret.
For.
Ret.
For.
Rei.
For.
Ret.
For.
Ret.
For.
Ret.
or
^6
Ret.
.01
10.3
13.2
10.5
12.8
10.6
12.6
10.7
12.4
10.8
12.3
~10.9
12.1
11.5
.02
14.6
18.7
14.9
18.1
15.1
17.8
15.2
17.5
15.3
17.4
15^5
17.1
16.3
.03
17.9
22.9
18.2
22.2
18.5
21.8
18.7
21.5
18.8
21.3
19 0
21.0
19.9
.04
20.7
26.5
21.1
25.7
21.4
25.2
21.6
24.9
21.8
24.6
22.0
24.3
23.1
.05
23 2
29.6
23.6
28.7
24.0
28.2
24.2
27.8
24.4
27.5
24.7
27.2
25.8
.10
33ll
41.9
33.8
40.8
34.3
40.1
34.6
39.6
34.9
39.2
85.2
38.7
36.9
.15
41
51.5
41.9
50.2
42.4
49.3
42.9
48.7
43.2
48.3
43.6
47.7
45.6
.20
48
59.6
48.9
58.2
49.6
57.3
50.1
56.6
50.4
56.2
50.9
55.5
53.1
.25
54.3
66.9
55.4
65.4
56.1
64.4
56.6
63.7
57.0
63.3
57.6
62.6
60.0
.30
60.3
73.5
61.5
72.0
62.2
71.0
62.8
70.3
63.3
69.8
63.9
69.1
66.4
.35
66.1
79 8
67.3
78.3
68.1
77.3
68.8
76.6
69 2
76.1
69.9
75.3
72.5
.40
71.7
85.8
73.0
84.3
73.9
83.3
74.5
82.6
75.0
82.0
75.7
81.3
78.5
.45
77.2
91.5
78.6
90.1
79.6
89.1
80.2
88.4
80.7
87.9
81.4
87.1
84.3
.50
82.8
97.2
84.3
95.7
85.2
94.8
85.9
94.1
86.4
93.6
87.1
92.9
90.0
.55
88.5
102.8
89.9
101.4
90.9
100.4
91.6
99.8
92.1
99.3
92.9
98. C
95.7
.60
94.2
108.3
95.7
107.0
96.7
106.1
97.4
105.5
98.0
105.0
98.7
104.3
101.5
.65
100.2
113.9
101.7
112.7
102.7
111.9
103.4
111.2
103.9
110.8
104.7
110.1
107.5
.70
106.5
119.7
108.0
118.5
109.0
117.8
109.7
117.2
110.2
116.7
110.9
116.1
113.6
.75
113.1
125.7
114.6
124.6
115.6
123.9
116.3
123.4
116.7
123.0
117.4
122.4
120.0
.80
120.4
132
121.8
181.1
122.7
130.4
123.4
129.9
123.8
129.6
124.5
129.1
126.9
.85
128.5
139
129.8
138.1
130.7
137.6
131.3
137.1
131.7
136.8
132.3
136.4
134.4
.90
138.1
146.9
139.2
146.2
139.9
145.7
140.4
145.4
140.8
145.1
141.3
144.8
143.1
.95
150.4
156.8
151.3
156.4
151.8
156.0
152.2
155.8
152.5
155.6
152.8
155.3
154.2
.96
153.5
159.3
154.3
158.9
154.8
158.6
155.1
158.4
155.4
158.2
155.7
158.0
156.9
.97
157.1
162.1
157.8
161.8
158.2
161.5
158.5
161.3
158.7
161.2
159.0
161.0
160.1
.98
161.3
165.4
161.9
165.1
162.2
164.9
162.5
164.8
162.6
164.7
162.9
164.5
163.7
.99
166.8
169.7
167.2
169.5
167.4
169.4
167.6
169.3
167.7
169.2
167.9
169.1
168.5
1.00
180
180
180 [180
180
180
180
180
180
180
180
180
180
THE SLIDE-VALVE.
831
Relative Motions of Cross-head and Crank.— If L = length
of connecting-rod, R = length of crank, 0 = angle of crank with centre line
of engine, D = displacement of cross-head from the beginning of its stroke,
3 = E(l - cos 0) -f- L - Ml? - R3 sin* 9.
Lap and Travel of Valve.
?f
p
.4769
.4699
.4619
.4532
.4435
.4330
.4217
.4096
.3967
s.
5
13-S w
^_J1
58.70
43.22
33.17
26.27
21.34
17.70
14.93
12.77
11.06
9.68
8.55
ofcg
2 55^.2 < «" .;
TSOSca 0£
w- «- -.
c o<J o ft
85°
90
95
100
105
110
115
120
125
130
.3378
.3214
.3044
.2868
.2687
.2500
.2309
.2113
1 of Valve
Port-open-
7.61
6.83
6.17
5.60
5.11
4.69
4.32
4.00
3.72
3.46
flOfc£
fill
|$p«
**"gS
z^S
135°
140
145
150
155
160
165
170
175
180
P.
o®
fl
.1913
.1710
.1504
.1294
.1082
.0868
.0653
.0436
.0218
.0000
! of Valve
Port-open-
3.24
3.04
2.86
2.70
2.55
2.42
2.30
2.19
2.09
2.00
PERIODS OF ADMISSION, OR CUT-OFF, FOR VARIOUS
LAPS AND TRAVELS OF SLIDE-VALVES.
The two following tables are from Clark on the Steam-engine. In the first
table are given the periods of admission corresponding to travels of valve
of from 12 in. to 2 in., and laps of from 2 in. to % in., with % in. and y% in. of
lead. With greater leads than those tabulated, the steam would be cut off
earlier than as shown in the table.
The influence of a lead of 5/16 in. for travels of from 1% in. to 6 in., and
laps of from y% in. to 1J4 in., as calculated for in the second table, is exhibited
by comparison of the periods of admission in the table, for the same lap and
travel. The greater lead shortens the period of admission , and increases the
range for expansive working.
Periods of Admission* or Points of Cnt-otf. for Given
Travels and Laps of Slide-valves.
<W *
I
Periods of Admission, or Points of Cut off, for the following
Laps of Valves in inches.
;•£
*
2
IK
%
1x4
1
%
H
%
K
%
in.
in.
£
%
%
%
*
%
%
%
%
%
12
88
90
93
95
96
97
98
98
99
99
10
IX
82
87
89
92
95
96
97
98
98
99
8
Ixj
72
78
84
88
92
94
95
96
98
98
6
Ix;
50
62
71
79
86
89
91
94
96
97
IX
43
56
68
77
85
88
91
94
96
97
5
IX
32
47
61
72
82
86
89
92
95
97
IX
14
35
51
66
78
83
87
90
94
96
£
IX
17
39
57
72
78
83
88
92
95
gix
IX
20
44
63
71
79
84
90
94
3
?x
23
50
61
71
79
86
91
2V6
LX
27
43
57
70
80
88
p
xi
33
§2
70
81
832
THE STEAM-ENGIKE.
Periods of Admission, or Points of Cut-off, for given
Travels and Laps of Slide-valves.
Constant lead, 5/16.
Travel .
I
,ap.
Inches.
^
%
%
H
1
Ifc
m
1%
IK
•JR/
19
1%
39
1%
47
17
2
55
34
61
42
14
2^4
65
50
30
ORX
68
55
38
13
OJL/
71
59
45
27
gKX
74
63
49
36
12
234
76
67
56
43
26
2%
78
70
59
47
32
11
3
80
73
62
50
38
23
81
74
65
55
44
30
10
QIX
83
76
68
59
48
34
22
SI
84
85
78
80
71
73
62
64
51
53
40
45
29
34
9
20
3%
4^
4V6
4%
5
t*
86
87
87
88
89
90
92
93
94
95
61
82
83
84
86
87
89
90
92
93
75
76
78
79
81
83
85
87
89
91
66
68
70
72
76
79
81
83
86
88
57
60
63
66
70
73
76
78
82
85
49
52
55
58
63
67
70
73
78
82
38
42
46
49
56
61
65
67
73
78
26
32
36
40
47
54
58
62
68
74
9
19
25
29
37
45
51
56
63
69
Diagram for Port-opening, Cut-off, and Lap,— The diagram
on the opposite page was published in Power, Aug., 1893. It shows at a
glance the relations existing between the outside lap, steam port-opening,
and cut-off in slide valve engines.
In order to use the diagram to find the lap, having given the cut-off and
maximum port-opening, follow the ordinate representing the latter, taken
on the horizontal scale, until it meets the oblique line representing the given
cut-off. Then read off this height on the vertical lap scale. Thus, with a
port-opening of 1% inch and a cut-off of .50, the intersection of the two lines
occurs on the horizontal 3. The required lap is therefore 3 in.
If the cut off and lap are given, follow the horizontal representing the
latter until it meets the oblique line representing the cut-off. Then vertically
below this read the corresponding port-opening on the horizontal scale.
If the lap and port-opening are given, the resulting cut-off may be ascer-
tained by finding the point of intersection of the ordinate representing the
port-opening with the horizontal representing the lap. The oblique line
passing through the point of intersection will give the cut-off.
If it is desired to tate lead into account, multiply the lead in inches by the
numbers in the following table corresponding to the cut-off, and deduct the
result from the lap as obtained from the diagram:
Cut-off.
Multiplier.
Cut-off.
Multiplier.
.20
4.717
.60
1.358
.25
3.731
.625
1.288
.30
3.048
.65
1.222
.33
2.717
.70
1.103
.375
2.381
.75
1.000
.40
2.171
.80
0.904
.45
1.930
.85
0.815
.50
1.706
.875
0.772
.55
1.515
.90
0.731
THE SLIDE-VALVE.
Cutoff
.25 .30 .35 .375.40 .45 .50
4-4 lit
.55
/
.685
1234
Maximum Steam Port opening in Inches.
DIAGRAM FOR SLIDE VALVES.
FIG. 149.
834 THE STEAM-ENGINE.
Piston-valve,— The piston-valve is a modified form of the slide-valva
The lap, lead, etc., are calculated in the same manner as for the common
slide-valve. The diameter of valve and amount of port-opening are calcu-
lated on the basis that the most contracted portion of the steam-passago
between the valve and the cylinder should nave an area such that th«
Telocity of steam through it will not exceed 6000 ft. per minute. The area
of the opening around the circumference of the valve should be about double
the area of the steam-passage, since that portion of the opening that is
opposite from the steam-passage is of little effect.
Setting tbe Valves of an Engine.— The principles discussed
above are applicable not only to the designing of valves, but also to adjust-
ment of valves that have been improperly set; but the final adjustment of
the eccentric and of the length of the rod depend upon the amount of lost
motion, temperature, etc., and can be effected only after trial. After the
valve has been set as accurately as possible when cold, the lead and lap for
the forward and return strokes being equalized, indicator diagrams should
be taken and the length of the eccentric-rod adjusted, if necessary, to eoi~
rect slight irregularities.
To Put an Engine on its Centre.— Place the engine in a posi-
tion where the piston will have nearly completed its outward stroke, and
opposite some point on the cross-head, such as a corner, make a mark upon
the guide. Against the rim of the pulley or crank-disk place a pointer and
mark a line with it on the pulley. Then turn the engine over the centre until
the cross-head is again in the same position on its inward stroke. This will
bring the crank as much below the centre as it was above it before. With the
pointer in the same position as before make a second mark on the pulley-
rim. Divide the distance between the marks in two and mark the middle
point. Turn the engine until the pointer is opposite this middle point, and
it will then be on its centre. To avoid the error that may arise from tbe
looseness of crank-pin and wrist-pin bearings, the engine should be turned
a little above the centre and then be brought up to it, so that the crank- pin
will press against the same brass that it does when the first two marks are
made.
Link-motion. — Link-motions, of which the Stephenson link is the
most commonly used, are designed for two purposes: first, for reversing the
motion of the engine, and second, for varying the point of cut-off by varying
the travel of the valve. The Stephenson link-motion is a combination of
two eccentrics, called forward and back eccentrics, with a link connecting
the extremities of the eccentric- rods; so that by varying the position of
the link the valve-rod may be put in direct connection with either eccentric,
or may be given a movement controlled in part by one and in j>art by the
other eccentric. When the link is moved by the reversing lever into a posi-
tion such that the block to which the valve-rod is attached is at either end
of the link, the valve receives its maximum travel, and when the link is in
mid-gear the travel is the least and cut-off takes place early in the stroke.
In the ordinary shifting-link with open rods, that is, not crossed, the lead
of the valve increases as the link is moved from full to mid-gear, that is, as
the period of steam admission is shortened. The variation of lead is equa-
lized for the front and back strokes by curving the link to the radius of the
eccentric-rods concavely to the axles. With crossed eccentric-rods the lead
decreases as the link is moved from full to mid-gear. In a valve-motion
with stationary link the lead is constant. (For illustration see Clark's Steam-
engine, vol. ii. p. 22.)
The linear advance of each eccentric is equal to that of the valve in full
gear, that is, to lap -J- lead of the valve, when the eccentric-rods are attached
to the link in such position as to cause the half -travel of the valve to equal
the eccentricity of the eccentric.
The angle between the two eccentric radii, that is, between lines drawn
from the centre of the eccentric disks to the centre of the shaft equals 180°
less twice the angular advance.
Buel, in Appleton's Cyclopedia of Mechanics, vol. ii. p. 316, discusses the
Stephenson link as follows: " The Stephenson link does not give a perfectly
correct distribution of steam; the lead varies for different points of cut-off.
The period of admission and the beginning of exhaust are not alike for botk
ends of the cylinder, and the forward motion varies from the backward.
" The correctness of the distribution of steam by Stephenson's link-motion
depends upon conditions which, as much as the circumstances will permit,
ought to be fulfilled, namely: 1. The link should be curved in the arc of a
circle whose radius is equal to the length of the eccentric- rod. 2. The
THE SLIDE-VALVE.
835
eccentric-rods ought to belong; the longer they are in proportion to the
eccentricity the more symmetrical will the travel of the valve be on both
sides of the centre of motion. 3. The link ought to be short. Each of its
points describes a curve in a vertical plane, whose ordinates grow larger the
farther the considered point is from the centre of the link; and as the hori-
zontal motion only is transmitted to the valve, vertical oscillation will cause
irregularities. 4. The link-hanger ought to be long. The longer it is the
nearer will be the arc in which the link swings to a straight line, and thus
the less its vertical oscillation. If the link is suspended in its centre, the
curves that are described by points equidistant on both sides from the centre
are not alike, and hence results the variation between the forward and back-
ward gear. If the link is suspended at its lower end, its lower half will have
less vertical oscillation and the upper half more. 5. The centre from which
the link-hanger swings changes its position as the link is lowered or raised,
and also causes irregularities. To reduce them to the smallest amount the
arm of the lifting-shaft should be made as long as the eccentric-rod, and the
centre of the lifting-shaf t should be placed at the height corresponding to
the central position of the centre on which the link-hanger swings."
All these conditions can never be fulfilled in practice, and the variations
in the lead and the period of admission can be somewhat regulated in an
artificial way, but for one gear only. This is accomplished by giving differ-
ent lead to the two eccentrics, which difference will be smaller tbe longer the
eccentric-rods are and the shorter the link, and by suspending *he link not
exactly on its centre line but at a certain distance from it, giving what is
called'" the offset."
For application of the Zeuner diagram to link-motion, see Holmes on the
Steam-engine, p. 290. See also Clark's Railway Machinery (1855), Clark's
Steam-engine, Zeuner's and Auchincloss's Treatises on Sli(]e-valve Gears,
and Halsey's Locomotive Link Motion. (See page 859a.)
The following rules are given by the American Machinist for laying out a
link for an upright slide-valve engine. By the term radius of link is meant
the radius of the lint-arc a&, Fig. 150, drawn through the centre of the slot;
FIG. 150.
this radius is generally made equal to the distance from the centre of shaft
to centre of the link-block pin P when the latter stands midway of its travel.
The distance between the centres of the eccentric-rod pins e^ e2 should not
be less than 2*4 times, and, when space will permit, three times the throw of
the eccentric. By the throw we mean twice the eccentricity of the eccentric.
The slot link is generally suspended from the end next to the forward eccen-
tric at a point in the fink-arc prolonged. This will give comparatively a
small amount of slip to the link-block when the link is in forward gear; but
this slip will be increased wben the link is in backward gear, This increase
836 THE STEAM-E^GIKE.
of slip is, however, considered of little importance, because marine engines,
as a rule, work but very little in the backward gear. When it is necessary
that the motion shall be as efficient in backward gear as in forward gear,
then the link should be suspended from a point midway between the two
eccentric-rod pins; in marine engine practice this point is generally located
on the link-arc; for equal cut-offs it is better to move the point of suspen-
sion a small amount towards the eccentrics.
For obtaining the dimensions of the link in inches : Let L denote the
length of the valve, B the breadth, p the absolute steam-pressure per sq.
in., and R a factor of computation used as below; then R = .01 4/L xB Xp.
Breadth of the link = R x 1.6
Thickness T of the bar = R x .8
Length of sliding-block < = R x 2.5
Diameter of eccentric-rod pins .., = (R x .7) -f- %
Diameter of suspension-rod pin = (R x .6) + *A
Diameter of suspension- rod pin when overhung.. = (R x .8) -j- J4
Diameter of block -pin when overhung = .Z? -f- J4
Diameter of block-pin when secured at both ends = (R X .8) -f- M
The length of the link, that is, the distance from a to 6, measured on a
straight line joining the ends of the link-arc in the slot, should be such as to
allow the centre of the link-block pin P to be placed in a line with the eccen-
tric-rod pins, leaving sufficient room for the slip of the block. Another type
of link frequently used in marine engines is the double -bar link, and this
type is again divided into two classes: one class embraces those links which
have the eccentric-rod ends as well as the valve-spindle end between the
bars, as shown at B (with these links the travel of the valve is less than
the throw of the eccentric); the other class embraces those links, shown at
C, for which the eccentric-rods are made with fork-ends, so as to connect to
studs on the outside of the bars, allowing the block to slide to the end of the
link, so that the centres of the eccentric-rod ends and the block-pin are in
line when in full gear, making the travel of the valve equal to the throw of
the eccentric. The dimensions of these links when the distance between
the eccentric-rod pins is 2% to 2££ times the throw of eccentrics can be
found as follows:
Depth of bars = (R x 1.25)4-^"
Thickness of bars = (R x .5)-f$I"
Diameter of centre of sliding-block = R x 1.8
When the distance between the eccentric-rod pins is equal to 3 or 4 times
the throw of the eccentrics, then
Depth of bars = (R X 1.25)-f-%"
Thickness of bars..., = (R X .5)-f J4"
All the other dimensions may be found by the first table. These are em-
pirical rules, and the results may have to be slightly changed to suit given
conditions. In marine engines the eccentric-rod ends for all classes of links
have adjustable brasses. In locomotives the slot-link is usually employed,
and in these the pin-holes have case-hardened bushes driven into the pin-
holes, and have no adjustable brasses in the ends of the eccentric-rods. The
link in B is generally suspended by one of the eccentric-rod pins; and the
link in C is suspended by one of the pins in the end of the link, or by one of
the eccentric-rod pins. (See note on Locomotive Link Motion in Appendix.
P. 1077.)
Eldridge in Power, Sep. 1893. See also Henthorn on the Corliss engine.
Rules for laying down the centre lines of the Joy valve-gear are given iu
American Machinist, Nov. 13, 1890. For Joy's " Fluid- pressure Reversing-
Talve, " see Sng'g, May 25, 1894.
GOVERNORS.
Pendulum or Fly-ball Governor.— The inclination of the arms
of a revolving pendulum to a vertical axis is such that the height of the
point of suspension h above the horizontal plane in which the centre of
gravity of the balls revolve (assuming the weight of the rods to be small
GOVERNORS. 837
compared with the weight of the balls) bears to the radius r of the circle
described by the centres of the balls the ratio
h _ weight _ w __ gr
r ~~ centrifugal force ~~ wv* ~~ va*
gr
which ratio is independent of the weight of the balls, v being the velocity
of the centres of the balls in feet per second.
If T = number of revolutions of the balls in 1 second, v = 2nrT = or, in
which a = the angular velocity, or 2irT, and
grr9 g 0.8146. 9.775.
h = — j- = * , or h = feet = -=- inches,
g being taken at 32.16. If N = number of revs, per minute, h = — ==-
inches
Fot» revolutions per minute 40 45 50 60 75
The height in inches will be 21.99 17.38 14.08 9.775 6.256
Number of turns per minute required to cause the arms to take a given
angle with the vertical axis: Let I = length of the arm in inches from the
centre of suspension to the centre of gyration, and a the required angle;
then
jvr= A/ >3o19° = 187.6,4 A—! — = 187.CJ /— •
\ I cos a \ I cos a \ h
used. From the balls of a common governor whose collective weight is A
let there be hung by a pair of links of lengths equal to the pendulum arms
a load B capable of sliding on the spindle, having its centre of gravity in
the axis of rotation. Then the centrifugal force is that due to A alone, and
the effect of gravity is that due to A -f- 25; consequently the altitude for a
given speed is increased in the ratio (A -f 21?) : A, as compared with that of
a simple revolving pendulum, and a given absolute variation in altitude pro-
duces a smaller proportionate variation in speed than in the common gover-
nor. (Rankine, S. E., p. 551.)
For the weighted governor let I = the length of the arm from the point of
suspension to the centre of gravity of the ball, and let the length of the sus-
pending-link, ll = the length of the portion of the arm from the point of
suspension of the arm to the point of attachment of the link; G = the weight
of one ball, Q = half the weight of the sliding weight, h = the height of the
governor from the point of suspension to the plane of revolution of the
balls, a = the angular velocity = 2nTt Tbeing the number of revolutions per
second; then a = V*™(l + * |); k-=!|«(1 + «1S) in feet, or
35190/" 21 O \
h = '—^ ( 1 + — l ~ ) in inches, N being the number of revolutions per
minute.
For various forms of governor sfee App. Cycl. Mech., vol. ii. 61, and Clark's
Steam-engine, vol. ii. p. 65.
To Change the Speed of an Engine Having a Fly-ball
Governor,— A slight difference in the speed of a governor changes the
position of its weights from that required for fnll load to that required for
no load. It is evident therefore that, whatever the speed of the engine, the
normal speed of the governor must be that for which the governor was de-
signed ; i.e., the speed of the governor must be kept the same. To change the
speed of the engine the problem is to so adjust the pulleys which drive the
governor that the engine at its new speed shall drive it just as fast as it was
driven at its original speed. In order to increase the engine-speed we must
decrease the pulley upon the shaft of the engine, i.e., the driver, or increase
that on the governor, i.e., the driven, in the proportion that the speed of tbe
engine is to be increased.
838 THE STEAM-ENGINE.
Fly-wheel or Shaft Governors.— At the Centennial Exhibition
in 1876 there were shown a few steam-engines in which the governors wert
contained in the fly-wheel or band-wheel, the fly-balls or weights revolving
around the shaft in a vertical plane with the wheel and shifting the eccen-
tric so as automatically to vary the travel of the valve and the point of cut-
off. This form of governor has since come into extensive use, especially for
high-speed engines. In its usual form two weights are carried on arms the
ends of which are pivoted to two points on the pulley near its circum-
ference, 180° apart. Links connect these arms to the eccentric. The
eccentric is not rigidly keyed to the shaft but is free to move trans-
versely across it for a certain distance, having an oblong hole which allows
of this movement. Centrifugal force causes the weights to fly towards the
circumference of the wheel and to pull the eccentric into a position of min-
imum eccentricity. This force is resisted by a spring attached to each arm
which tends to pull the weights towards the shaft and shift the eccentric to
the position of maximum eccentricity. The travel of the valve is thus
varied, so that it tends to cut off earlier in the stroke as the engine increases
its speed. Many modifications of this general form are in use. For discus-
sions of this form of governor see Hartnell, Proc. Inst. M. E., 1882, p. 408;
Trans. A. S. M. E., ix. 300; xi. 1081 ; xiv. 9,'; xv. 929 ; Modern Mechanism,
p. 399; Whitham's Constructive Steam Engineering; J. Begtrup,.4m. Macli.,
Oct. 19 and Dec. 14, 1893, Jan. 18 and March 1, 1894.
Calculation of Springs lor Shaft-governors. (Wilson Hart-
nell, Proc. Inst. M. E., Aug. 1882.)— The springs for shaft-governors may be
conveniently calculated as follows, dimensions being in inches:
Let W = weight of the balls or weights, in pounds;
TI and ra = the maximum and minimum radial distances of the centre
of the balls or of the centre of gravity of the weights;
li and Z3 = the leverages, i.e., the perpendicular distances from the cen-
tre of the weight-pin to a line in the direction of the centrifugal force
drawn through the centre of gravity of the weights or balls at radii
TI and ra;
mi and ma = the corresponding leverages of the springs;
Ci and Ca = the centrifugal forces, for 100 revolutions per minute, at
radii rj and?-a;
P! and Pa = the corresponding pressures on the spring;
(It is convenient to calculate these and note them down for reference.)
C8 and C4 = maximum and minimum centrifugal forces;
8 = mean speed (revolutions per minute);
Si and St = the maximum and minimum number of revolutions per
minute;
P. and P4 = the pressures on the spring at the limiting number of revo«
lutions (Stands,,);
P4 - P$ = D — the difference of the maximum and minimum pressures
on the springs;
V = the percentage of variation from the mean speed, or the sensitive-
ness;
t = the travel of the spring;
u = the initial extension of the spring;
v = the stiffness in pounds per inch;
w = the maximum extension = u + t.
The mean speed and sensitiveness desired are supposed to be given. Then
Sl = s-|£ sa = s+f<r,
Cl = 0.28 X TI X W\ C* = 0.28 X ra X W\
P4
—s.
V
It is usual to give the spring-maker the values of P* and of v or w. To
ensure proper space being provided, the dimensions of the spring should be
CONDENSERS, AIR-PUMPS, ETC. 839
calculated by the formulae for strength and extension of springs, and the
least length of the spring as compressed be determined.
P _L P t
The governor-power = ^ * X ^
With a straight centripetal line, the governor-power
For a preliminary determination of the governor-power it may be taken
as equal to this in all cases, although it is evident that with a curved cen-
tripetal line it will be slightly less. The difference D must be constant for
the same spring, however great or little its initial compression. Let the
spring be screwed up until its minimum pressure is 2^. Then to find the
speed PQ = P§ + D,
The speed at which the governor would be isochronous would bo
lOOi
Suppose the pressure on the spring with a speed of 100 revolutions, at the
maximum and minimum radii, was 200 Ibs. and 100 Ibs., respectively, then
the pressure of the spring to suit a variation from 95 to 105 revolutions will
be 100 X (^,)2 = 90-2 and 200 X (^5)* = 220.5. That is, the increase
of resistance from the minimum to the maximum radius must be 220 - 90 =
130 Ibs.
The extreme speeds due to such a spring, screwed up to different press-
ures, are shown in the following table:
Revolutions per minute, balls shut
80
90
V)
100 110
19(\
Pressure on springs, balls shut .
64
81
90
100 121
144
180
130
130
130 130
130
Pressure on springs, balls open fully
191
°11
ooo
230 251
274
Revolutions per minute, balls open fully
98
10'?
105
107 112
11?
Variation, per cent of mean speed
10
fi
5
3 1
-1
1
The speed at which the governor would become isochronous is 114.
Any spring will give the right variation at some speed ; hence in experi-
menting with a governor the correct spring may be found from any wrong
one by a very simple calculation. Thus, if a governor with a spring whose
stiffness is 50 Ibs. per inch acts best when the engine runs at 95, 90 being its
proper speed, then 50 X (=5) = 45 Ibs. is the stiffness of spring required.
To determine the speed at which the governor acts best, the springs may
be screwed up until it begins to " hunt " and then slackened until the gov-
ernor is as sensitive as is compatible with steadiness.
CONDENSERS. AIR-PUMPS CIRCULATING-
PUMPS, ETC.
The J/et Condenser* (Chiefly abridged from Seaton's Marine Engi-
neering.>-The jet condenser is now uncommon in marine practice, being
generally supplanted by the surface condenser. It is commonly used where
fresh water is available for boiler feed. With the jet condenser a vacuum of 24
in. was considered fairly good, and 25 in. as much as was possible with most
condensers; the temperature corresponding to 24 in. vacuum, or 3 Ibs. pressure
absolute, is 140°. In practice the temperature in the hot-well varies from 110°
to 120°, and occasionally as much as 130° is maintained. To find the quantity
of injection-water per pound of steam to be condensed: Let T* = tempera-
ture of steam at the exhaust pressure; TQ = temperature or the cooling-
840 THE STEAM-EKGIKE.
water; T* = temperature of the water after condensation, or of the hot-well;
Q — pounds of the cooling- water per Ib. of steam condensed; then
1114° -f Q.STj - T2
Tt — TQ
Another formula is: Q = —^ , in which W is the weight of steam con-
flensed, H the units of heat given up by 1 Ib. of steam in condensing, and
H the rise in temperature of the cooling- water.
This is applicable both to jet and to surface condensers. The allowance made
for the injection- water of engines working in the temperate zone is usually
27 to 30 times the weight of steam, and for the tropics 80 to 35 times ; 30
times is sufficient for ships which are occasionally in the tropics, and this is
what was usual to allow for general traders.
Area of injection orifice = weight of injection- water in Ibs. per min. -f- 650
to 780.
A rough rule sometimes used is: Allow one fifteenth of a square inch for
every cubic foot of water condensed per hour.
Another rule: Area of injection orifice = area of piston H- 250.
The volume of the jet condenser is from one fourth to one half of that of
the cylinder. It need not be more than one third, except for very quick-
running engines.
Ejector Condensers.— For ejector or injector condensers (Bulkley's,
Schutte's, etc.) the calculations for quantity of condensing-water is the same
as for jet condensers.
The Surface Condenser— Cooling Surface.— Peclet found that
with cooling water of an initial temperature of 68° to 77°, one sq. ft. of copper
plate condensed 21.5 Ibs. of steam per hour, while Joule states that 100 Ibs.
per hour can be condensed. In practice, with the compound engine, brass
condenser-tubes, 18 B.W.G thick, 13 Ibs. of steam per sq. ft. per hour, with
the cooling-water at an initial temperature of 60°, is considered very fair
work when the temperature of the feed- water is to be maintained at 120°.
It has been found that the surface in the condenser may be half the heating
surface of the boiler, and under some circumstances considerably less than
this. In general practice the following holds good when the temperature of
sea- water is about 60° :
Terminal pres., Ibs., abs.... 30 20 15 12^ 10 8 6
Sq. ft. per I.H.P 3 2.50 2.25 2.00 1.80 1.60 1.50
For ships whose station is in the tropics the allowance should be increased
by 20$. and for ships which occasionally visit the tropics 10$ increase will
give satisfactory results. If a ship is constantly employed in cold climates
10% less suffices.
Wbitbam (Steam-engine Design, p. 283, also Trans. A. S. M. E., ix. 431)
gives the following: S = -=—, = - , in which S = condensing-surface in sq.
CK( JL i — t)
ft.; TI = temperature Fahr. of steam of the pressure indicated by the
vacuum-gauge; t = mean temperature of the circulating water, or the
arithmetical mean of the initial and final temperatures; L = latent heat of
saturated steam at temperature 2\; k — perfect conductivity of 1 sq. ft. of
the metal used for the condensing-surface for a range of 1° F. (or 557 B.T.U.
per hour for brass, according to Isherwood's experiments); c = fraction de-
noting the efficiency of the condensing surface; W = pounds of steam con-
densed per hour. ..From experiments by Loring and Emery, on U.S.S. Dallas.
c is found to be 0.323, and ck = 180; making the equation S = isnrr _ ^-
Whitham recommends this formula for designing engines having indepen-
dent circulating- pumps. When the pump is worked by the main engine the
value of 8 should be increased about 10#.
Taking Tt at 135° F., and L = 1020, corresponding to 25 in. vacuum, and t
1020TF 17W
for summer temperatures at 75°, we have: S = 1g0(135 _ y^ = JJJQ*
For a mathematical discussion of the efficiency of surface condensers see
a paper by T. E. Stanton in Proc. Inst. C. E,, cxxxyi, June 1899, p. 321.
Condenser Tuoes are generally made of solid-drawn brass tubes, and
tested both by hydraulic pressure and steam. They are usually made of a
composition of 68# of best selected copper and 32$ of best SUesian spelter.
CONDENSERS, AIR-PUMPS, ETC.
841
The Admiralty, however, always specify the tubes to be made of 70£ of best
selected copper and to have \% of tin in the composition, and test the tubes
to a pressure of 300 Ibs. per sq. in. (Seaton.)
The diameter of the condenser tubes varies from */£ inch in small conden-
sers, when they are very short, to 1 inch in very large condensers and long
tubes. In the mercantile marine the tubes are, as a rule, % inch diameter
externally, and 18 B.W.G. thick (0.049 inch); and 16 B.W.G. (0.065), under
some exceptional circumstances. In the British Navy the tubes are also,
as a rule, % mcn diameter, and 18 to 19 B.W.G. thick, tinned on both sides;
when the condenser is made of brass the.Admiralty do not require the tubes
to be tinned. Some of the smaller engines have tubes % inch diameter, and
19 B.W.G. thick. The smaller the tubes, the larger is the surface which
can be got in a certain space.
In the merchant service the almost universal practice is to circulate the
water through the tubes.
Whitham says the velocity of flow through the tubes should not be less
than 400 nor more than 700 ft. per min.
Tube-plates are usually made of brass. Rolled-brass tube -plates
should be from 1.1 to 1.5 times the diameter of tubes in thickness, depending
on the method of packing. When the packings go completely through the
plates the latter, but when only partly through the former, is sufficient.
Hence, for M-inch tubes the plates are usually % to 1 inch thick with glands
and tape-packings, and 1 to 1J4 inch thick with wooden ferrules.
The tube-plates should be secured to their seatings by brass studs and
nuts, or brass screw-bolts; in fact there must be no wrought iron of any
kind inside a condenser. When the tube-plates are of large area it is advis-
able to stay them by brass-rods, to prevent them from collapsing.
Spacing of Tubes, etc,— The holes for ferrules, glands, or india-
rubber are usually J4 inch larger in diameter than the tubes; but when ab-
solutely necessary the wood ferrules may be only 3/32 inch thick.
The pitch of tubes when packed with wood ferrules is usually J4 mch
more than the diameter of the ferrule-hole. For example, the tubes are
generally arranged zigzag, and the number which may be fitted into a
square foot of plate is as follows:
Pitch of
Tubes.
No. in a
sq. ft.
Pitch of
Tubes.
No. in a
sq. ft.
Pitch of
Tubes.
No. in a
sq.ft.
V
1 1/16"
W
172
150
137
1 5/32"
1 3/16"
1 7/32"
128
121
116
1 9/32"
1 5/16"
110
106
99
Quantity of Cooling Water.— The quantity depends chiefly upon
its initial temperature, which in Atlantic practice may vary from 40° in the
winter of temperate zone to 80° in subtropical s^as. To raise the tempera-
ture to 100° in the condenser will require three times as many thermal units
in the former case as in the latter, and therefore only one third as much
cooling- water will be required in the former case as in the latter.
TI = temperature of steam entering the condenser;
IT0 = " circulating-water entering the condenser;
!Ta = ** leaving the condenser;
T9 = " water condensed from the steam;
Q = pounds of circulating water per Ib. of steam condensed
- 11 14 + 0.37*1 - T3
T2~TQ
It is usual to provide pumping power sufficient to supply 40 times the
weight of steam for general traders, and as much as 50 times for ships sta-
tioned in subtropical seas, when the engines are compound. If the circulat-
ing-pump is double-acting, its capacity may be 1/53 in the former and 1/42
in the latter case of the capacity of the low-pressure cylinder.
Air-pump.— The air-pump in all condensers abstracts the water con-
densed and the air originally contained in the water when it entered the
boiler. In the case of jet-condensers it also pumps out the water of con-
densation and the air which it contained. The size of the pump is calculated
from these conditions, making allowance for efficiency of the pump.,
842
THE STEAM-ENGIHE.
Ordinary sea-water contains, mechanically mixed with it, 1/20 of its vol-
ume of air when under the atmospheric pressure. Suppose the pressure in
the condenser to be 2 Ibs. and the atmospheric pressure 15 Ibs., neglecting
the effect of temperature, the air on entering the condenser will be expanded
to 15/2 times its original volume; so that a cubic foot of sea-water, when it
has entered the condenser, is represented by 19/20 of a cubic foot of water
and 15/40 of a cubic foot of air.
Let q be the volume of water condensed per minute, and Q the volume of
sea- water required to condense it; and let Ta be the temperature of the
condenser, and Tj that of the sea-water.
Then 19/20 (q -f; Q) will be the volume of water to be pumped from the
condenser per minute,
and ^q + Q) X y* 46J! the quantity of air.
If the temperature of the condenser be taken at 120°, and that of sea-
water at 60°, the quantity of air will then be AlS(q -f Q), so that the total
volume to be abstracted will be
•95(g -f- Q) + .418(3 + Q) = U'68(g + Q).
If the average quantity of injection-water be taken at 26 times that con-
densed, q -j- Q will equal 27g. Therefore, volume to be pumped from the
condenser per minute = 37g, nearly.
In surface condensation allowance must be made for the water occasion-
ally admitted to the boilers to make up for waste, and the air contained in
it, also for slight leak in the joints and glands, so that the air-pump is made
about half as large as for jet-condensation.
The efficiency of a single-acting air-pump is generally taken at 0.5, and
that of a double-acting pump at 0.35. When the temperatur of the sea is
60°, and that of the (jet) condenser is 120°, Q being the volume of the cooling
water and q the volume of the condensed water in cubic feet, and n the
number of strokes per minute,
The volume of the single-acting pump = 2.7
The volume of the double-acting pump = 4( ^' /•
The following table gives the ratio of capacity of cylinder or cylinders to
that of the air-pump; in the case of the compound engine, the low-pressure
cylinder capacity only is taken.
Description of Pump.
Description of Engine.
Ratio.
Single-acting vertical . ..
U it
it (i
it U
Double-acting horizontal..
«t ti
« c«
Jet-cone
Surface
Jet
Surface
Surface
Jet
Surface
Jet
Surface
Surface
tensing, expansion \y%
"32
" " 3
** nrmrmrmnrl
to 2.
to 2.
to 5.
to 5.
6 to 8
8 to 10
10 to 12
12 to 15
15 to 18
10 to 13
13 to 16
16 to 19
19 to 24
24 to 28
ti
tt
14
it
expansion 1%
3S
" 3
compound
to 2.
to 2.
to 5
to 5
The Area through Valve-seats and past the valves should not be
less than will admit the full quantity of water for condensation at a velocity
not exceeding 400 ft. per minute. In practice the area is generally in
excess of this.
- 1000 square inches.
- 800 square inches.
S! -*- 35 inches.
its speed in ft. per min.
James Tribe (Am. Mach., Oct. 8, 1891) gives the following rule for air-
Area through foot-valves = D* X S-
Area through head- valves = D2 X S-
Diameter of discharge-pipe = D X
Ds* diam. of air-pump in inches, S
CONDENSERS, AIR-PUMPS, BTO. 843
bumps used with jet-condensers: Volume of single-acting air-pump driven
v*y main engine = volume of low-pressure cylinder in cubic feet, multiplied
by 3.5 and divided by the number of cubic feet contained in one pound of
exhaust-steam of the given density. For a double-acting air-pump the
same rule will apply, but the volume of steam for each stroke of the pump
will be but one half. Should the pump be driven independently of the
engine, then the relative speed must be considered. Volume of jet-con-
5 inser = volume of air-pump x 4. Area of injection valve = vol. of air-
v^mp in cubic inches -^ 520.
Circulating-pump.— Let Q be the quantity of cooling water in cubic
?£t, n the number of strokes per minute, and /S the length of stroke in feet.
Capacity of circulating-pump = Q -+- n cubic feet.
Diameter " •« = 13.55|/ • v inches.
The following table gives the ratio of capacity of steam- cylinder or cylin*
c ^rs to that of the circulating-pump :
Description of Pump, Description of Engine. Ratio.
Single-acting. Expansive V& to 2 times. 13 to 16
" 3 to 5 " SO to 25
Compound. 25 to 30
Double " Expansive 1J4 to 2 times. 25 to 30
•• " 3 to 5 " 86 to 46
Compound. 46 to 56
The c»ear area through the valve-seats and past the valves should be such
that the mean velocity of flow does not exceed 450 feet per minute. The
flow through the pipes should not exceed 500 ft. per min. in small pipes and
600 in large pipes.
For Centrifugal Circulating -pumps, the velocity of flow in the inlet and
outlet pipes should not exceed 400 ft. per min. The diameter of the fan- wheel
is from 2^ to 3 times the diam. of the pipe, and the speed at its periphery
450 to 500 ft. per min. If W = quantity of water per minute, in American
gallons, d = diameter of pipes in inches, jR = revolutions of wheel per min.,
W 1700
-— — - ; diam. of fan-wheel = not less than -^-. Breadth of blade at
£4
fcip = gg-r. Diam. of cylinder for driving the fan ^ about 2.8 Vdiam. of pipe,
and its stroke = 0.28 X diam. of fan.
Feed-pumps for Marine Engines.— With surface-condensing
engines the amount of water to be fed by the pump is the amount condensed
from the main engine plus what may be needed to supply auxiliary engines
and to supply leakage and waste. Since an accident may happen to the
surface-condenser, requiring the use of jet-condensation, the pumps of
engines fitted with surface-condensers must be sufficiently large to do duty
under such circumstances. With jet-condensers and boilers using salt water
the dense salt water in the boiler must be blown off at intervals to keep the
density so low that deposits of salt will not be formed. Sea-water contains
about 1/32 of its weight of solid matter in solution. The boiler of a surface-
condensing engine may be worked with safety when the quantity of salt is
four times that in sea- water. If Q = net quantity of feed- water required in
a given time to make up for what is used as steam, n = number of times the
saltness of the water in the boiler is to that of sea- water, then the gross feed-
water = r Q. In order to be capable of filling the boiler rapidly each
n — i
feed-pump is made of a capacity equal to twice the gross feed-water. Two
feed-pumps should be supplied, so that one may be kept in reserve to be
used while the other is out of repair. If Q be the quantity of net feed- water
in cubic feet, I the length of stroke of feed-pump in feet, and n the num-
ber of strokes per minute,
Diameter of each feed-pump plunger in inches = A/* X. •
844
THE STEAM-EKGINE.
If W be the n«& feed-water in pounds,
Diameter of each feed-pump plunger in inches :
An Evaporative Surface Condenser built at the Virginia Agri
cultural College is described by James H. Fitts (Trans. A. S. M. E., xiv. 690).
It consists of two rectangular end-chambers connected by a series of hori-
zontal rows of tubes, each row of tubes immersed in a pan of water.
Through the spaces between the surface of the water in each pan and the
bottom of the pan above air is drawn by means of an exhaust-fan. At the
top of one of the end-chambers is an inlet for steam, and a horizontal dia-
phragm about midway causes the steam to traverse the upper half of the
tubes and back through the lower. An outlet at the bottom leads to the air-
pump. The condenser, exclusive of connection to the exhaust-fan, occupies
a floor space of 5' 4}&" x 1' 9%", and 4' 1J4" high. There are 27 rows of
tubes, 8 in some and 7 in others; 210 tubes in all. The tubes are of brass,
No. 20 B.W.G., %" external diameter and 4' 9^£" in length. The cooling sur-
face (internal) is 176.5 sq. ft. There are 27 cooling pans, each 4' 9J^" X 1' 9%",
and 1 7/16" deep. These pans have galvanized iron bottoms which slide
into horizontal grooves J4" wide and *4" deep, planed into the tube-sheets.
The total evaporating surface is 234.8 sq. ft. Water is fed to every third pan
through small cocks, and overflow-pipes feed the rest. A wood casing con-
nects one side with a 30" Buffalo Forge Co.'s disk- wheel. This wheel is
belted to a S" x 4" vertical engine. The air-pump is 5%" diameter with a
6" stroke, is vertical and single-acting.
The action of this condenser is as follows: The passage of air over the
water surfaces removes the vapor as it rises and thus hastens evaporation.
The heat necessary to produce evaporation is obtained from the steam in the
tubes, causing the steam to condense. It was designed to condense 800 Ibs.
steam per hour and give a vacuum of 22 in., with a terminal pressure in the
cylinder of 20 Ibs. absolute.
Results of tests show that the cooling- water required is practically equal in
amount to the steam used by the engine. And since consumption of steam
is reduced by the application of a condenser, its use will actually reduce the
total quantity of water required. From a curve showing the rate of evapora-
tion per square foot of surface in still air, and also one showing the rate
when a current of air of about 2300 ft. per min. velocity is passed over its
surface, the following approximate figures are taken:
Temp.
F.
Evaporation, Ibs. per
sq. ft. per hour.
Temp.
Evaporation, Ibs. per
sq. ft. per hour.
Still Air.
Current.
Still Air.
Current.
IOC*
110
120
130
0.2
0.25
0.4
0.6
1.1
1.6
2.5
3.5
140°
150
160
170
0.8
1.1
1.5
2.0
5.0'
6.7
9.5
The Continuous Use of Condensing-water is described in a
series of articles in Power, Aug. -Dec., 1892. It finds its application in situa-
tions where water for ondensing purposes is expensive or difficult to obtain.
In San Francisco J. . H. Stut cools the water after it has left the hot-
well by means of a system of pans upon the roof. These pans are shallow
troughs of galvanized iron arranged hi tiers, on a slight incline, so that the
water flows back and forth for 1500 or 2000 ft., cooling by evaporation and
radiation as it flows. The pans are about 5 ft. in width, and the water as it
flows has a depth of about half an inch, the temperature being reduced from
about 140° to 90°. The water from the hot-well is pumped up to the highest
point of the cooling system and allowed to flow as above described, discharg-
ing finally into the main tank or reservoir, whence it again flows to the con-
denser as required. As the water in the reservoir lowers from evaporation, an
auxiliary feed from the city mains to tLe condenser is operated, thereby
keeping the amount of water in circulation practically constant. An accu-
mulation of oil from the engines, with dust from the surrounding streets,
makes a cleaning necessary about once in six weeks or two months. It is
found by comparative trials, running condensing and non-condensing, that
COHDENSERS, AIR-PUMPS, ETC. 845
about 50# less water is taken from the city mains when the whole apparatus
is in use than when the engine is run non-condensing. 22 to 23 in. of vacuum
are maintained. A better vacuum is obtained on a warm day with a brisk
breeze blowing than on a cold day with but a slight movement of the air.
In another plant the water from the hot- well is sprayed from a number of
fountains, and also from a pipe extending around its border, into a large
pond, the exposure cooling it sufficiently for the obtaining of a good vacuum
by its continuous use .
In the system patented by Messrs. See, of Lille, France, the water is dis-
charged from a pipe laid in the form of a rectangle and elevated above a
TDond through a series of special nozzles, by which it is projected into a fine
cpray. On coming into contact with the air in this state of extreme divi-
sion "the water is cooled 40° to 50°, with a loss by evaporation of only one
tenth of its mass, and produces an excellent vacuum. A 3000-H.P. cooler
upon this system has been erected at Lannoy, one of 25CO H.P. at Madrid, and
one of 1200 H.P. at Liege, as well as others at Roubaix and Tourcoing. The
system could be used upon a roof if ground space were limited.
In the ** self-cooling" system of H. R. Worthington the injection-water is
taken from a tank, and after having passed through the condenser is dis-
charged in a heated condition to the top of a cooling tower, where it is scat-
tered by means of distributing-pipes and trickles down through a cellular
structure made of 6-in. terra-cotta pipes, 2 ft. long, stood on end. The
water is cooled by a blast of air furnished by a disk fan at the bottom of the
tower and the absorption of heat caused by a portion of the water being
vaporized, and is led to the tank to be again started on its circuit. (En<j\j
News, March 5, 1896.)
In the evaporative condenser of T. Ledward & Co. of Brockley, London,
the water trickles over the pipes of the large condenser or radiator, and by
evaporation carries away the heat necessary to be abstracted to condense
the steam inside. The condensing pipes are fitted with corrugations
mounted with circular ribs, whereby the radiating or cooling rurface is
largely increased. The pipes, which are cast in sections about 76 in. long by
3V£ in. bore, have a cooling surface of 26 sq. ft., wbich is found sufficient
under favorable conditions to permit of the condensation of 20 to 30 Ibs.
of steam per hour when producing a vacuum of 13 Ibs. per sq. in, In a
condenser of this type at Rixdorf, near Berlin, a vacuum ranging from 24
to 26 in. of mercury was constantly maintained during the hottest weather
of August. The initial temperature of the cooling-water used in the appara-
tus under notice ranged from 80° to 85° F., and the temperature in the sun,
to which the condenser was exposed, varied each day from 100° to 115° F.
During the experiments it was found that it was possible to run one engine
under a load of 100 horse-power and maintain the full vacuum without the
use of any cooling-water at all on the pipes, radiation afforded by the pipes
alone sufficing to condense the steam for this power.
In Klein's condensing water-cooler, the hot water coming from the con-
denser enters at the top of a wooden structure about twenty feet in height,
and is conveyed into a series of parallel narrow metal tanks. The water
overflowing from these tanks is spread as a thin film over a series of wooden
partitions suspended vertically about 3^ inches apart within the tower.
The upper set of partitions, corresponding to the number of metal tanks,
reaches half-way down the tower. From there down to the well is sus-
pended a second set of partitions placed at right angles to the first set. This
impedes the rapidity of the downflow of the water, and also thoroughly
mixes the water, thus affording a better cooling. A fan-blower at the base of
the tower drives a strong current of air with a velocity of about twenty feet
per second against the thin film of water running down over the partitions.
It is estimated that for an effectual cooling two thousand times more air
than water must be forced through the apparatus. With such a velocity
the air absorbs about two per cent of aqueous vapor. The action of the
strong air-current is twofold: first, it absorbs heat from the hot water by
being itself warmed by radiation; and, secondly, it increases the evapora-
tion, which process absorbs a great amount of heat. These two cooling
effects are different during the different seasons of the year. During the
winter months the direct cooling effect of the cold air is greater, while
during summer the heat absorption by evaporation is the more important
factor. Taking all the year round, the effect remains very much the same.
The evaporation is never so great that the deficiency of water would not
be supplied by the additional amount of water resulting from the condensed
steam, while in very cold winter months it may be necessary to occasionally
rid the cistern of surplus water. It was found that the vacuum obtained by
846 THE STEAM-ENGIHE.
this continual use of the same condensing-water varied during the year
between 2? .5 and 28.7 inches. The great saving of space is evident from
the fact that only the five-hundredth part of the floor-space is required as
if cooling tanks or ponds were used. For a 100-horse-power engine the
floor-space required is about four square yards by a height of twenty feet.
For one horse-power 3.6 square yards cooling-surface is necessary. The
vertical suspension of the partitions is very essential. With a ventilator 50
inches in diameter and a tower 6 by 7 feet and 20 feet high, 10,500 gallons of
water per hour were cooled from 104° F. to 68° F. The following record
was made at Mannheim, Germany: Vacuum in condenser, 28.1 inches; tem-
perature of condensing-water entering at top of tower, 104° to 108° F.;
temperature of water leaving the cooler, 66.2° to 71.6° F. The engine was
of the Sulzer compound type, of 120 horse-power. The amount of power
necessary for the arrangement amounts to about three per cent of the total
horse-power of the engine for the ventilator, and from one and one half to
three per cent for the lifting of the water to the top of the cooler, the total
being four and one half to six per cent.
A novel form of condenser has been used with considerable success in
Germany and other parts of the Continent. The exhaust-steam from the
engine passes through a series of brass pipes immersed in water, to which
it gives up its heat. Between each section of tubes a number of galvanized
disks are caused to rotate. These disks are cooled by a current of air
supplied by a fan and pass down into the water, cooling it by abstract-
ing the heat given out by the exhaust-steam and carrying it up where it is
driven off by the air-current. The disks serve also to agitate the water and
thus aid it in abstracting the heat from the steam. With 85 per cent
vacuum the temperature of the cooling water was about 130° F., and a
consumption of water for condensing is guaranteed to be less than a pound
for each pound of steam condensed. For an engine 40 in. X 50 in., 70 revo-
lutions per minute, 90 Ibs. pressure, there is about 1150 sq. ft. of condensing-
surface. Another condenser, 1600 sq. ft. of condensing-surface, is used for
three engines, 32 in. X 48 in., 27 in. x 40 in., and 30 in. X 40 in., respectively.
— The Steamship.
The Increase of Power that may be obtained by adding a condenser
giving a vacuum of 26 inches of mercury to a non-condensing engine maybe
approximated by considering it to be equivalent to a net gain of 12 pounds
mean effective pressure per square inch of piston area. If A — area of piston
in square inches, S = piston-speed in ft. per minute, then ^ QOQ = ^^ = H.P.
made available by the vacuum. If the vacuum = 13.2 Ibs. per sq. in. = 27.9
in. of mercury, then H.P. = -45-4-2500.
The saving of steam for a given horse-power will be represented approxi-
mately by the shortening of the cut-off when the engine is run with the
condenser. Clearance should be included in the calculation. To the mean
effective pressure non-condensing, with a given actual cut-off, clearance
considered, add 3 Ibs. to obtain the approximate mean total pressure, con-
densing. From tables of expansion of steam find what actual cut-off will
give this mean total pressure. The difference between this and the original
actual cut-off, divided by the latter and by 100, will give the percentage of
saving.
The following diagram (from catalogue of H. R. Worthington) shows the
percentage of power that may be gained by attaching a condenser to a non-
condensing engine, assuming that the vacuum is 12 Ibs. per sq. in. The dia-
gram also shows the mean pressure in the cylinder for a given initial pres-
sure and cut-off, clearance and compression not considered.
The pressures given in the diagram are absolute pressures above a vacuum.
To find the mean effective pressure produced in an engine-cylinder with 90
Ibs. gauge ( = 105 Ibs. absolute) pressure, cut-off at *4 stroke: find 105 in the
left-hand or initial-pressure column, follow the horizontal line to the right
until it intersects the oblique line that corresponds to the y± cut-off, and read
the mean total pressure from the row of figures directly above the point of
intersection, which in this case is 63 Ibs. From this subtract the mean abso-
lute back pressure (say 3 Ibs. for a condensing engine and 15 Ibs. for a non-
read on the lower scale the figures that correspond in position to 48 Ibs. in
the upper row, in this case 25$. As the diagram does not take into consid-
eration clearance or compression., the results are only approximate*
GAS, PETROLEUM, AtfD HOT-AIR ENGINES. 847
-off. SoTs ?61T6T* & It T' W 4 "5 4
I 1 1 I I I Abs'olu'te Nlean'Pressure in Pounds/
40 /SO7 60/70 80/90/100/110 120 130 140 150/160
FIG. 151.
Evaporators and Distillers are used with marine engines for the
purpose of providing fresh water for the boilers or for drinking purposes.
Weir's Evaporator consists of a small horizontal boiler, contrived so as
to be easily taken to pieces and cleaned. The water in it is evaporated by
the steam from the main boilers passing through a set of tubes placed in its
bottom. The steam generated in this boiler is admitted to the low-
pressure valve-box, so that there is no loss of energy, and the water con-
densed in it is returned to the main boilers.
In Weir's Feed-heater the feed- water before entering the boiler is heated
lip very nearly to boiling-point by means of the waste water and steam
from the low-pressure valve-box of a compound engine.
GAS, PETROLEUM, AND HOT-AIR ENGINES.
Gas-engines.— For theory of the gas-engine, see paper by Dugald
Clerk, Proc. lust. C. E. 1882, vol. Ixix.; and Van Nostrand's Science Series,
No. 62. See also Wood's Thermodynamics. Three standard works on gas-
engines are " A Practical Treatise on the * Otto ' Cycle Gas-engine," by Wm.
Norris: " A Text-book on Gas, Air, and Oil Engines," by Bryan Donkin; and
44 The Gas and Oil Engine," by Dugald Clerk (6th edition, 1896).
In the ordinary type of single-cylinder gas-engine (for example the Otto)
known as a four-cycle engine one ignition of gas takes place in one end of
the cylinder every two revolutions of the fly-wheel, or every two double
strokes. The following sequence of operations takes place during four con-
secutive strokes: (a) inspiration during an entire stroke; (6) compression
during the second (return) stroke; (c) ignition at the dead-point, and expan-
sion during the third stroke; (a) expulsion of the burnt gas during the fourth
(return) stroke. Beau de Rochas in 1862 laid down the law that there «"•
848 GAS, PETROLEUM, AND HOT-AIR ENGINES.
four conditions necessary to realize the best results from the elastic force
of gas: (1) The cylinders should have the greatest capacity with the smallest
circumferential surface; (2) the speed should be as high as possible; (3) the
cut-off should be as early as possible; (4) the initial pressure should be as
high as possible. In modern engines it is customary for ignition to take
place, not at the dead point, as proposed by Beau de Rochas, but somewhat
later, when the piston has already made part of its forward stroke. At first
sight it might be supposed that this would entail a loss of power, but experi-
ence shows that though the area of the diagram is diminished, the power
registered by the friction-brake is greater. Stalling is also made easier by
this method of working. (The Simplex Engine, Proc. Inst. M. E. 1889.)
In the Otto engine the mixture of gas and air is compressed to about 3
atmospheres. When explosion takes place the temperature suddenly rises
to somewhere about 2900° F. (Robinson.)
The two great sources of waste in gas-engines are: 1. The high tempera-
ture of the rejected products of combustion ; 2. Loss of heat through the
cylinder walls t® the water-jacket. As the temperature of the water-jacket
is increased the efficiency of the engine becomes higher.
With ordinary coal-gas the consumption may be taken at 20 cu. ft. per
hour per I.H.P., or 24 cu. ft. per brake H.P. The consumption will vary with
the quality of the gas. When burning Dowson producer-gas the consump-
tion of anthracite (\Velsh) coal is about 1.3 Ibs. per I.H.P. per hour for
ordinary working. With large twin engines, 100 H.P., the consumption is
reduced to about 1.1 Ib. The mechanical efficiency or B.H.P. -*- I.H.P. in
ordinary engines is about 85^; the friction loss is less in larger engines.
Efficiency of the Gas-engine* (Thurston on Heat as a Form of
Energy.)
Heat transferred into useful work 17£
to the jacket- water 52
" lost in the exhaust-gas 16
'* " by conduction and radiation 15
- 83*
This represents fairly the distribution of heat in the best forms of gas-
engine. The consumption of gas in the best engines ranges from a mini-
mum of 18 to 20 cu. ft. per I.H.P. per hour to a maximum exceeding in the
smaller engines 25 cu. ft. or 30 cu. ft. In small engines the consumption per
brake horse-power is one third greater than these figures.
The report of a test of a 170 -H.P. Crossley (Otto) gas-engine in England,
1892, using producer-gas, shows a consumption of but .85 Ib. of coal per H.P.
hour, or an absolute combined efficiency of 21. 3# for the engine and pro-
ducer. The efficiency of the engine alone is in the neighborhood of 25#.
The Taylor gas-producer is used in connection with the Otto gas-engine
at the Otto Gas-engine Works in Philadelphia. The only loss is due to
radiation through the walls of the producer and a small amount of heat
carried off in the water from the scrubber. Experiments on a 100-H.P,
engine show a consumption of 97/100 Ib. of carbon per I.H.P. per hour. This
result is superior to any ever obtained on a steam-engine. (Iron Age, 1893.)
Tests of the Simplex Gas-engine. (Proc. Inst. M. E. 1889.)—
Cylinder 7% X 15% in., speed 160 revs, per min. Trials were made with town
gas of a heating value of 607 heat-units per cubic foot, and with Dowson
gas, rich in CO, of about 150 heat-units per cubic foot.
Town Gas. Dowson Gas.
123 1 23
Effective H.P 6.'?0 8.67 9.28 7/12 3.61 5.26
Gas per H.P. per hour, cu. ft.. 21.55 20.12 20.73 88.03 114.85 97.88
Water per H.P. per hour, Ibs. 54.7 44.4 43.8 58.3
Temp, water entering, F 51° 51° 51° 48°
" effluent 135° 144° 172° 144°
The gas- volume is reduced to 32° F. and 30 in barometer. A 50-H.P. engine
working 35 to 40 effective H.P. with Dowson generator consumed 51 Ibs.
English anthracite per hour, equal to 1.48 to 1.3 Ibs. per effective H.P. A 16-
H.P. engine working 12 H.P. used 19.4 cu. ft. of gas per effective H.P.
A 320-H.P. Gas-engine.- The flour-mills of M. Leblanc, at Pantin,
France, have been provided with a 320-horse-power fuel-gas engine of the
Simplex type. With coal-gas the machine gives 450 horse-power. There is
one cylinder, 34.8 in, diain. ; the piston-stroke is 40 in. ; and the speed 100 revs.
GAS-EKGIKES.
849
per min. Special arrangements have been devised m order to keep the
different parts of the machine at appropriate temperatures. The coal used
is 0.812 lb. per indicated or 1 .03 Ib. per brake horse-power. The water used
is 8M gallons per brake horse-power per hour.
Test of an Otto Gas-engine. (Jour. F. I., Feb. 1890, p. 115.)— En-
gine 7 H.P. nominal; working capacity of cylinder .2594 cu. ft.; clearance
space .1796 cu. ft.
.
Temperature of gas supplied . . 62 . 2
" " " exhaust... 774.3
" " entering water 50.4
" " exit water .... 89.2
Pressure of gas, in. of water, . 3.0<
Revolution per min., av'ge ---- 161. o
Explosions missed per min.,
average ....................
Mean effective pressure, Ibs.
per sq. in .......... ......
Horse-power, indicated ....... 4.94
Work per explosion, foot-
pounds
6.8
59.
4.!
.2204.
Explosions per minute ........ 74.
Gas per I.H.P. per hour, cu. ft. 23.4
Heat-units. Per cent.
Transferred into work ......... 22.84
Taken by jacket- water ........ 49 . 94
" " exhaust .............. 27.22
Composition of the gas:
By Volume. By Weight.
C02 ............ 0.50# 1.923*
CoH4 ........... 4.32 10.520
O ............ 1.00 2.797
CO ............. 5.33 15.419
CH4 ........... 27.18 38.042
H ............. 51.57 9.021
N ............. 9.06 22.273
99.96
99.995
Te»t of the Clerli Gas-engine. (Proc. Inst. C. E. 1882, vol. Ixix.)—
Cylinder 6 x 12 in., 150 revs, per min.; mean available pressure, 70.1 Ibs., 9
I.H.P.; maximum pressure, 220 Ibs. per sq. in. above atmosphere; pressure
before ignition, 41 Ibs. above atm.; temperature before compression, 60° F.,
after compression, 313° F.; temperature after ignition calculated from pres-
sure, 2800° F.; gas required per I.H.P. per hour, 22 cu. ft.
More Recent Tests of gas-engines, 1898, have given higher economical re-
sults than those above quoted. The gas-consumption (city gas) has been as
low as 15 cu. ft. per I.H.P. per hour, and the efficiency as high as 27# of the
heating value of the gas. The principal improvement in practice has been
the use of much higher compression of the working charge.
Combustion of the Gas in the Otto Engine.— John Imray, in
discussion of Mr. Clerk's paper on Theory of the Gas-engine, says: The
change which Mr. Otto introduced, and which rendered the engine a success,
was that, instead of burning in the cylinder an explosive mixture of gas and
air, he burned it in company with, and arranged in a certain way in respect
of, a large volume of incombustible gas which was heated by it, and which
diminished the speed of combustion. W. B. Bpusfield, in the same discus-
sion, says: In the Otto engine the charge varied from a charge which was
an explosive mixture at the point of ignition to a charge which was merely
an inert fluid near the piston. When ignition took place there was n explo-
sion close to the point of ignition that was gradually communicated through-
out the mass of the cylinder. As the ignition got farther away from the
primary point of ignition the rate of transmission became slower, and if the
engine were not worked too fast the ignition should gradually catch up to
the piston during its travel, all the combustible gas being thus consumed.
This theory of slow combustion is, however, disputed by Mr. Clerk, who
holds that the whole quantity of combustible gas is ignited in an instant.
Temperatures and Pressures deTel oped in a Gas-engine.
(Clerk on the Gas-engine.) — Mixtures of air and Oldhain coal-gas. Temper-
ature before explosion, 17° C.
Mixture.
Gas.
1vol.
1 ||
1 ;»
1 "
1 "
1 "
1
Air.
14 vols.
13 "
12 "
11 "
9 ••
7
6
5
4
Max. Press
above Atmos.,
lbs.*per sq. in.
Temp, of Explo-
sion calculated
from observed
Pressure.
Theoretical
Temp, of Explo-
sion if all Heat
were evolved.
40.
806° C.
1786° C.
51.5
1033
1912
60.
1202
2058
61.
1220
2228
78.
1557
2670
87.
1733
3334
90.
1792
3808
91.
1812
....
80.
1595
....
Use of Carfouretted Air in Gas-engines.— Air passed over
850 GAS, PETROLEUM, AND HOT-AIR EKGIKES.
gasoline or volatile petroleum spirit of low sp. gr., 0.65 to 0.70, liberatei
some of the gasoline, and the air thus saturated with vapor is equal in heat-
ing or lighting power to ordinary coal-gas. It may therefore be used as a
fuel for gas-engines. Since the vapor is given off at ordinary temperatures
gasoline is very explosive and dangerous, and should be kept in an under-
ground tank out of doors. A defect in the use of carburetted air for gas-
engines is that the more volatile products are given off first, leaving an oily
residue which is often useless. Some of the substances in the oil that are
taken up by the air are apt to form troublesome deposits and incrustations
when burned in the engine cylinder.
The Otto Gasoline-engine. (Eng'g Neius, May 4, 1893.)— It is
claimed that where but a small gasoline-engine is used and the gasoline
bought at retail the liquid fuel will be on a par with a steam-engine using 6
Ibs. of coal per horse -power per hour, and coal at $3.50 per ton, and will
besides save all the handling of the solid fuel and ashes, as well as the at-
tendance for the boilers. As very few small steam-engines consume less
than 6 Ibs. of coal per hour, this is an exceptional showing for economy. At
8cts. per gallon for gasoline and 1/10 gal. required per H.P. per hour, the
cost per H.P. per hour will be 0.8 cent.
Gasoline-engines are coming into extensive use (1898). In these engines
the gasoline is pumped from an underground tank, located at some distance
outside the engine-room, and led through carefully soldered pipes to the
working cylinder. In the combustion chamber the gasoline is sprayed into
a current of air, by which it is vaporized. The mixture is then compressed
and ignited by an electric spark. At no time does the gasoline come in con-
tact with the air outside of the engine, nor is there any flame or burning
gases outside of the cylinder.
"•Naphtha-engines are in use to some extent in small yachts and
launches. The naphtha is vaporized in a boiler, and the vapor is used ex-
pansively in the engine-cylinder, as steam is used; it is then condensed and
returned to the boiler. A portion of the naphtha vapor is used for fuel un-
der the boiler. According to the circular of the builders, the Gas Engine
and Power Co. of New York, a 2-H.P. engine requires from 3 to 4 quarts of
naphtha per hour, and a 4-H.P. engine from 4 to 6 quarts. The chief advan-
tages of the naphtha-engine and boiler for launches are the saving of weight
and the quickness of operation. A 2-H.P. engine weighs 200 Ibs., a 4-H.P. 300
Ibs. It takes only about two minutes to get under headway. (Modern
Mechanism, p. 270.)
Hot-air (or Caloric) Engines.— Hot-air engines are used to some
extent, but their bulk is enormous compared with their effective power. For
an account of the largest hot-air engine ever built (a total failure) see
Church's Life of Ericsson. For theoretical investigaton, see Rankine's
Steam-engine and Rontgen's Thermodynamics. For description of con-
structions, see Appleton's Cyc. of Mechanics and Modern Mechanism, and
Babcock on Substitutes forSteam, Trans. A. S. M. E., vii., p. 693.
Test of a Hot-air Engine (Robinson).— A vertical double-cylinder
(Caloric Engine Co.'s) 12 nominal H.P. engine gave 20.19 I.H.P. in the work-
ing cylinder and 11.38 I.H.P. in the pump, leaving 8.81 net I.H.P.; while the
effective brake H.P. was 5.9, giving a mechanical efficiency of 67$. Con-
sumption of coke, 3.7 Ibs. per brake H.P. per hour. Mean pressure on
pistons 15.37 Ibs. per square inch, and in pumps 15.9 Ibs., the area of working
cylinders being twice that of the pumps. The hot air supplied was about
1160° F. and that rejected at end of stroke about 890° F.
The Priestman Petroleum-engine. (Jour. Frank. Inst., Feb.
1893 )— The following is a description of the operation of the engine: Any
ordinary high-test (usually 150° test) oil is forced under air-pressure to an
atomizer, where the oil is met by a current of air and broken up into atoms
and sprayed into a mixer, where it is mixed with the proper proportion of
supplementary air and sufficiently heated by the exhaust from the cylinder
passing around this chamber. The mixture is then drawn by suction into
the cylinder, where it is compressed by the piston and ignited by an electric
spark, a governor controlling the supply of oil and air proportionately to
the work performed. The burnt products are discharged through an ex-
haust-valve which is actuated by a cam. Part of the air supports the com-
bustion of the oil, and the heat generated by the combustion of the oil
expands the air that remains and the products resulting from the explosion,
and thus develops its power from air that it takes in while running. In
Other words, the engine exerts its power by inhaling air, heating that air,
and expelling the products of combustion when done with. In the largest
engines only the 1/250 part of a pint of oil is used at any one time, and in
EFFICIENCY OF LOCOMOTIVES.
851
the smallest sizes the fuel is prepared in correct quantities varying from
1/7000 of a pint upward, according to whether the engine is running on light
or full duty. The cycle of operations is the same as that of the Otto gas-
engine.
Trials of a 5-H.P. Priestman Petroleum-engine. (Prof.
W. C. Unwin, Proc. Inst. C. E. 1892.)— Cylinder, 8^ X 12 in., making normally
200 revs, per min. Two oils were used, Russian and American. The more
important results were given in the following table:
Trial V.
Full
Power.
Trial I.
Full
Power.
Trial IV.
Full
Power.
Trial II.
Half
Power.
Trial III.
Light.
Oil used -1
Day-
Russo-
Russo-
Russo-
Russo-
Brake H.P
light.
7.722
lene.
6.765
lene.
6.882
lene.
3.62
lene.
I H P . ...
9.369
7.408
8.332
4 70
0 889
Mechanical efficiency...
0.824
0.91
0.876
0.769
Oil used per brake H.P.
0.842
0.946
O.S88
1.381
Oil used per indicated
H P hour Ib ...
0.694
0 864
0 81G
1 063
5 734
Lb. of air per Ib. of oil. .
Mean explosion pressure,
Ibs per sq in
33.4
151.4
31.7
134.3
43.2
128.5
21.7
48.5
10.1
9.6
Mean compression pres-
sure, Ibs. per sq. in
Mean terminal pressure,
Ibs. per sq. in
35.0
35.4
27.6
23.7
26,0
25.5
14.8
15.6
6.0
To compare the fuel consumption with that of a steam-engine, 1 Ib. of
oil might be taken as equivalent to 1^ Ibs. of coal. Then the consumption
in the oil-engine was equivalent, in Trials I., IV., arid V., to 1.42 Ibs., 1.48 Ibs.,
and 1.2Glbs. of coal per brake horse-power per hour. From Trial IV. the
following values of the expenditure of heat were obtained:
Per cent.
Useful work at brake... 13.31
Engine friction 2.81
Heat shown on indicator-diagram , 16.12
Rejected in jacket -water 47.54
" in exhaust -gases , , 26.72
Radiation and unaccounted for 9.61
Total... 99.99
LOCOMOTIVES.
ttesistaii.ee of Trains.— Resistance due to Speed—Various formulae
and tables for the resistance of trains at different speeds on a straight level
track have been given by different writers. Among these are tne following:
By George R. Henderson (Proc. Engrs. Club of Phila., 1886):
R = 0.0015(1 +«•-*• 650),
in which R = resistance in Ibs. per ton of 2240 Ibs. and v = speed in miles per
hour.
Speed in miles per hour:
5 10 15 20 25 30 35 40 45 50 55
Resistance in pounds per ton of 2000 Ibs. :
3.1 3.4 4. 4.8 5.8 7.1 8.6
By D. L. Barnes (Eng. Mag.), June, 1894 :
Speed, miles per hour 50
Resistance, pounds per gross ton . 12
60
10.2 12.1 14.3 16.8 19.2
12.4
70
13.5
100
20
852 LOCOMOTIVES.
By Engineering News, March 8, 1894 :
Resistance in Ibs. per ton of 2000 Ibs. = Y^v + 4.
Speed 5 10 15 20 25 30 35 40 45 50 CO 70 80 90 100
Resistance.. 3J4 4.5 5% 7 8J4 9.5 10% 12 13)4 14.5 17 19.5 22 24.5 27
By Baldwin Locomotive Works :
Resistance in Ibs. per ton of 2000 Ibs. = 3 -f v -*- 6.
Speed 5 10 15 20 25 30 35 40 45 50 55 60 70 80 90 100
Resistance.. 3.8 4.7 5.5 6.3 7.2 8 8.8 9.7 10.5 11.3 12.2 13 14.7 16.3 18 19.7
The resistance due to speed varies with the condition of the track, the
number of cars in a train, and other conditions.
For tables showing that the resistance varies with the area exposed to the
resistance and friction of the air per ton of loads, see Dashiell, Trans. A. S.
M. E., vol. xiii. p. 371.
P. H. Dudley (Bulletin International Ry. Congress, 1900, p. 1734) shows
that the condition of the track is an important factor of train resistance
which has not hitherto been taken account of. The resistance of heavy
trains on the N. Y. Central R. R. at 20 miles an hour is only about 3J*> Ibs per
ton on smooth 80-lb. 5J4-in. rails. The resistance of an 80-car freight train,
60,000 Ibs. per car, as given by indicator cards, at speeds between 15 and 25
miles per hour is represented by the formula R = 1 4- l/s V^ in which R = re-
sistance in Ibs. per ton and V = miles per hour.
Resistance due to Grade. —The resistance due to a grade of 1 ft. per mile
is, per ton of 2000 Ibs., 2000 X r^z = 0.3788 Ib. per ton, or if Kg - resistance
0/*OvJ
in Ibs. per ton due to grade and G = ft. per mile, Rg = 0.3788(7.
If the grade is expressed as a percentage of the length, the resistance is 20
Ibs per ton for each per cent of grade.
Resistance due to Curves.— Mr. Henderson gives the resistance due to
curvature as 0.5 Ib. per ton of 2000 Ibs. per degree of the curve. (For defini-
tion of degrees of a railroad curve see p. 53.)
If c is the number of degrees. Re the resistance in Ibs. per ton, = 0.5c. The
Baldwin Locomotive Works take the approximate resistance due to each
degree of curvature as that due to a straight grade of \y% ft- per mile. This
corresponds to Re — 0.5682c.
Resistance due to Acceleration.— This may be calculated by means of the
ordinary formulae for acceleration, as follows :
Let Vl = velocity in ft. per second at the beginning of a mile run.
F9 = velocity at the end of the mile.
*^(F2 — Fj) = average velocity during the mile.
T - 5280 -j- i^(F2 - FI) = time in seconds required to run the mile.
w = weight of the train in Ibs. W = weight in tons.
f = resistance in Ibs. due -to acceleration = ^-^ — -
_ w (F9 - F!>« nn-oo9TW17 T^2
3T2 X 10,560 ~ .OOo88<lF( J 2 - F,)'.
S = increase of speed in miles per hour ; (F2 - F^2 = -S2 X (22/15)2.
Ra = resistance in Ibs. per ton = ..01265/Sa.
Total Resistance. — The total resistance in Ibs. per ton of 2000 Ibs. due to
speed, to grade, to curves, and to acceleration is the sum of the resistances
calculated above. Taking the Baldwin Locomotive Works' rules for speed
and curvature, we have
Rt= (3+ |-) + 0.3788<? -f 0.5682c + .012G5S2,
in which Rt is the resistance in Ibs. per ton of 2000 Ibs., v - speed in miles per
hour, O = grade in ft. per mile, c = degrees of curvature, S = rate of in-
crease of speed in miles per hour in a run of one mile.
Resistance due to Friction.— In the above formula no account
has been taken of the resistance to tbe friction of the working parts of the
engine, nor to the friction of the engine and tender on curves due to the
rigid wheel bases. No satisfactory formula can be given for these resist-
ances Mr. Henderson takes them as being proportional to the tractive
power, so that, if the total tractive power be P, the effective tractive is ul\
TBACTIVE POW^K OF A LOCOMOTIVE. 853
and the resistance (1 - u)P, the value of the coefficient u being probably
about 0.8.
The Baldwin Locomotive Works in their "Locomotive Data" take the
total resistance on a straight level track at slow speeds at from 6 to 10 Ibs.
per ton, and in a communication printed in the fourth edition (1898) of this
Pocket-book, p. 1076, say : " We know that in some cases, for instance in
mine construction, the frictional resistance has been shown to be as much as
60 Ibs. per ton at slow speed. The resistance should be approximated to
suit the conditions of each individual case, and the increased resistance due
to speed added thereto."
Holmes on thp Steam-engine, p. 142, says : " The frictional resistance
to uniform motion of the whole train, including the engine and tender, is
usually expressed by giving the direct pull in pounds necessary in order to
propel each ton's weight of the train along a level line at slow speed. The
pull varies with the condition of the line, the state of the surface of the rails,
the state of the rolling stock, and the speed. If M be the speed in miles per
hour, and T the weight of the train in tons [2240 Ibs.] exclusive of engine
and tender, the resistance to uniform motion may be expressed by the
formula
R= [6 + 0.3(M- 10) T].
If Tl be the weight of the engine and tender, the corresponding resistance is
RI = [12 f 0.3(M - 10)7'J,
which expression includes the friction of the mechanism of the engine.
Holmes also says that a strong side wind by pressing the tires of the
wheels against the rails may increase the frictional resistance of the train by
as much as 20 per cent.
Hauling Capacity due to Adhesion.— The limit of the hauling
capacity of a locomotive is the adhesion due to the weight on the driving
wheels. Holmes gives the adhesion, in English practice, as equal to 0.15 of
the load on the driving wheels in ordinary dry weather, but only 0.07 in
damp weather or when the rails are greasy. In American practice it is gener-
ally taken as from 1/4 to 1/5 of the load on the drivers. The hauling capacity
at slow speed on a track of different grades may be calculated by the fol-
lowing formula:
Let T — tons of 2000 Ibs., locomotive and train, per 1000 Ibs. load on
drivers, a = the reciprocal of the coefficient of adhesion, g = the per cent
of grade, R = the frictional resistance in Ibs. per ton. Then T *° ""
From this formula the following table has been calculated :
Grade Per Cent, 0 0.5 1 1.5 2 $.5 3 3.5 4 5 6 7
Tons Hauling Capacity per 1000 Ibs. Weight on Drivers.
Fora = 4, R= 6.. 42 15.6 9.2 6.9 5.4 4.5 3.8 3.3 2.9 2.4 2.0 1.7
a = 5, R = 8.. 25 11.1 7.2 5.3 4.2 3.4 2.9 2.6 2.3 1.9 1.6 1.4
a = 5, 12 = 10. 20 10. 6.7 5. 4. 3.3 2.9 2.5 2.2 1.8 1.5 I 3
Tractive Power of a locomotive.— Single Expansion.
Let P = tractive power in Ibs.
p = average effective pressure in cylinder in Ibs. per sq. in.
8 = stroke of piston in inches.
d — diameter of cylinders in inches.
D = diameter of driving-wheels in inches. Then
_ d*pS
~~ 4jrD '''' D '
The average effective pressure can be obtained from an indicator-dia-
gram, or by calculation, when the initial pressure and ratio of expansion are
known, together with the other properties of the valve-motion. The sub-
joined table from " Auchincloss " gives the proportion of mean effective
pressure to boiler-pressure above atmosphere for various proportions of
cut-off.
854
LOCOMOTIVES,
Stroke,
Cut off at—
M.E.P.
(Boiler-
pres. = 1).
Stroke,
Cut of at-
(M.E.P.
Boiler -
pres. = 1).
Stroke,
Cut off at—
M.E.P.
(Boiler-
pres. = 1).
.1
.15
.333 = YB
.5='fc£
.625 = %
79
.125 = ^
.2
.375 = %
.55
.666 = %
82
.15
.24
.4
.57
.7
35
.175
.28
.45
.62
.75 =%
89
.2
.32
.5=^
.67
.8
93
.25 = ^
,4
.55
.72
.875 = 7/8
98
.3
.46
These values were deduced from experiments with an English locomotive
by Mr. Gooch. As diagrams vary so much from different causes, this table
will only fairly represent practical cases. It is evident that the cut-off must
be such that the boiler will be capable of supplying sufficient steam at the
given speed.
Compound Locomotives.— The Baldwin Locomotive Works give the fol-
lowing formulae for compound engines of the Vauclain four-cylinder type :
C*S x
D D
T = tractive power in Ibs.
C = diam. of high-pressure cylinder in ins.
c— u '• low " " •' "
P = boiler pressure in Ibs.
S = stroke of piston in ins.
D = diam. of driving-wheels in ins. „
For a two-cylinder or cross-compound engine it is only necessary to cpn-
tsider the high-pressure cylinder, allowing a sufficient decrease in boiler
pressure to compensate for the necessary back-pressure. The formula is
C*S x %p
D
Efficiency of the Mechanism of a Locomotive.— Frank C.
Wagner (Proc. A. A. A. S., 1900, p. 140) gives an account of some dynamom-
eter tests which indicate that in ordinary freight service the power used
to drive the locomotive and tender and to overcome the friction of the mech-
anism is from 10£ to 35# of the total power developed in the steam-cylinder.
In one test the weight of th,e locomotive and tender was 16# of the total
weight of the train, while the power consumed in the locomotive and tender
was from 30$ to 33$ of the indicated horse-power.
The Size of Locomotive Cylinders is usually taken to be such
that the engine will just overcome the adhesion of its wheels to the rails
under favorable circumstances.
The adhesion is taken by a committee of the Am. Ry. Master Mechanics'
Assn. as 0.25 of the weight on the drivers for passenger engines, 0.24 for
freight, and 0.22 for switching engines ; and the mean effective pressure in
the cylinder, when exerting the maximum tractive force, is taken at 0.85 of
the boiler -pressure.
Let W = weight on drivers in Ibs. ; P = tractive force in Ibs., = say 0.25 W;
Pi = boiler-pressure in Ibs. per sq. in.;p = mean effective pressure, = 0.85pj ;
cL = diam. of cylinder, S = length of stroke, and D = diam. of driving-
wheels, all in inches. Then
Whence
D
'.=»sV^
= 0.542
Von Borries's rule for the diameter of the low-pressure cylinder of a com-
2ZD
pound locomotive is da = — ^-,
LOCOMOTIVES. 855
where d = diameter of l.p. cylinder in inches;
D = diameter of driving-wheel in inches;
p = mean effective pressure per sq. in., after deducting internal
machine friction;
h = stroke of piston in inches;
Z — tractive force required, usually 0.14 to 0.16 of the adhesion.
The value of p depends on the relative volume of the two cylinders, and
from indicator experiments may be taken as follows:
ria<;<? of Fne-ine Ratio of Cylinder p in percentage p for Boiler-presa
Volumes. of Boiler-pressure. ure of 176 Ibs.
Large-tender eng's 1 : 2 or 1 : 2.05 42 74
Tank-engines l:2orl:2.2 40 71
Horse-power of a Locomotive.— For each cylinder the horse-
power is H.P. = pLaN-+- 33,000, in which p = mean effective pressure, L
= stroke in feet, a = area of cylinder = ^d2, N = number of single strokes
per minute, LN = piston speed, ft. per min. Let M = speed of train in miles
per hour, S = length of stroke in inches, and D = diameter of driving-wheel
in inches. Then LN = M x 88 x 2S -*- itD. Whence for the two cylinders
the horse-power is
2 x p x yyrd* x 1765? x M _ pcPSM
wD x 33,000 ~ 375D '
Tlie Size of Locomotive Boilers. (Forney's Catechism of the
Locomotive.)— They should be proportioned to the amount of adhesive
weight and to the speed at which the locomotive is intended to work. Thus
a locomotive with a great deal of weight on the driving-wheels could pull a
heavier load, would have a greater cylinder capacity than one with little
adhesive weight, would consume more steam, and therefore should have a
larger boiler.
The weight and dimensions of locomotive boilers are in nearly all cases
determined by the limits of weight and space to which they are necessarily
confined. It may be stated generally that within these limits a locomotive
boiler cannot be made too large. In other words, boilers for locomotives
should always be made as large as is possible under the conditions that de-
termine the weight and dimensions of the locomotives. (See also Holmes on
the Steam-engine, pp. 371 to 377 and 383 to 389, and the Report of the Am. Ry.
M. M. Assn. for 1897, pp. 218 to 232.)
Holmes gives the following from English practice :
Evaporation, 9 to 12 Ibs. of water from and at 212°.
Ordinary rate of combustion, 65 Ibs. per sq. ft. of grate per hour.
Ratio of grate to heating surface, 1 : 60 to 90.
Heating surface per Ib. of coal burnt per hour, 0.9 to 1.5 sq. ft.
Qualities Essential for a Free-steaming Locomotive*
(From a paper by A. E. Mitchell, read before the N. Y. Railroad Club ;
Eng'g News, Jan. 24, 1891.)— Square feet of boiler-heating surface for bitu-
minous coal should not he less than 4 times the square of the diameter in
inches of a cylinder 1 inch larger than the cylinder to be used. One tenth
of this should be in the fire-box. On anthracite locomotives more beating-
surface is required in the fire-box, on account of the larger grate-area
required, but the heating-surface of the flues should not be materially
decreased.
Wootten's Locomotive. (Clark's Steam-engine ; see also Jour.
Frank. lust. 1891, and Modern Mechanism, p. 485.)— J. E. Wootten designed
and constructed a locomotive boiler for the combustion of anthracite and
lignite, though specially for the utilization as fuel of the waste produced in
the mining and preparation of anthracite. The special feature of the engine
is the fire-box, which is made pf great length and breadth, extending clear
over the wheels, giving a grate-area of from 64 to 85 sq. ft. The draught
diffused over these large areas is so gentle as not to lift the fine panicles of
the fuel. A number of express-engines having this type of boiler are engaged
on the fast trains between Philadelphia and Jersey City. The fire-box shell
is 8 ft. 8 in. wide and 10 ft. 5 in. long ; the fire-box is 8x9^ ft., making 76 sq.
ft. of grate-area. The grate is composed of bars and water-tubes alternately.
The regular types of cast-iron shaking grates are also used. The height of
the fire-box is only 2 ft. 5 in. above the grate. The grate is terminated by
a bridge of fire-brick, beyond which a combustion-chamber, 27 in. long,
leads to the flue-tubes, about 184 in number, 1% in. diam. The cylinders are
856
LOCOMOTIYES.
21 in. diam., w'th a stroke of 22 inches. The driving-wheels, four-coupled,
are 5 "ft. 8 in. diam. The engine weighs 44 tons, of which 29 tons are on driv-
ing wheels. The heating-surface of the fire-box is 135 sq. ft., that of the
flue-tubes is 983 sq. ft.; together, 1117 sq. ft., or 14.7 times the grate-area.
Hauling 15 passenger-cars, weighing with passengers 360 tons, at an average
speed of 42 miles per hour, over ruling gradients of 1 in 89, the engine con-
sumes 62 Ibs. of fuel per mile, or 34^ Ibs. per sq. ft. of grace per hour.
Grate-surface, Smoke-stacks, antl Exhaust-nozzles for
Locomotives. (Am. Mack., Jan. 8, 1891.)— For grate-surface for anthra-
cite coal: Multiply the displacement in cubic feet of one piston during a
stroke by 8.5; the product will be the area of the grate in square feet.
For bituminous coal : Multiply the displacement in feet of one piston
during a stroke by 6^; the product will be the grate-area in square feet for
engines with cylinders 12 in. in diameter and upwards. For engines with
smaller cylinders the ratio of grate-area to piston-displacement should be 7^
to 1, or even more, if the design of the engine will admit this proportion.
The grate-areas in the following table have been found by the foregoing
rules, and agree very closely with the average practice :
Smoke-stacks.— The internal area of the smallest cross-section of the stack
Bhould be 1/17 of the area of the grate in soft-coal-burning engines.
A. E. Mitche)!, Supt. of Motive Power of the N. Y. L. E. & W. R. R., says
that recent practice varies from this rule. Some roads use the same size of
stack, 13^ in. diam. at throat, for all engines up to 20 in. diam. of cylinder.
The area of the orifices in the exhaust-nozzles depends on the quantity and
quality of the coal burnt, size of cylinder, construction of stack, and the
condition of the outer atmosphere. It is therefore impossible to give rules
for computing the exact diameter of the orifices. All that can be done is to
five a rule by which an approximate diameter can be found. The exact
iameter can only be found by trial. Our experience leads us to believe that
the area of each orifice in a double exhaust-nozzle should be equal to 1/400
part of the grate-surface, and for single nozzles 1/200 of the grate-surface.
These ratios have been used in finding the diameters of the nozzles given in
the following table. The same sizes are often used for either hard or soft
coal-burners.
Double
Single
Size of
Cylinders,
in inches.
Grate-area
for Anthra-
cite Coal, in
sq. in.
Grate-area
for Bitumin-
ous Coal, in
sq. in.
Diameter
of Stacks,
in inches.
Nozzles.
Nozzles.
Diam. of
Orifices, in
Diam. of
Orifices, in
inches.
inches.
12 X 20
1591
1217
§y
2
2 13/16
13 X 20
1873
1432
10}^
2^3
3
14X20
2179
1666
11!4
2 5/16
3M
15 X 22
2742
2097
12^
2 9/16
3 11/16
16 X 24
3415
2611
14
2%
4 1/16
17X24
3856
2948
15
3 1/16
4 5/16
18 X 24
4321
3304
15%
3M
4%
19X24
4810
3678
16V6
3 7/16
4 13/16
20 X 24
5337
4081
55"
3%
5 1/16
Exhaust-nozzles ill Locomotive Rollers*— A committee of
the Am. Ry. Master Mechanics' Assn. in 1890 reported that they had, after
two years of experiment and research, come to the conclusion that, owing
to the great diversity in the relative proportions of cylinders and boilers,
together with the difference in the quality of fuel, any rule which does not
recognize each and all of these factors would-be worthless.
The committee was unable to devise any plan to determine the size of the
exhaust-nozzle in proportion to any other part of the engine or boiler, and
believes that the best practice is for each user of locomotives to adopt a
nozzle that will make steam freely and fill the other desired conditions, best
determined by an intelligent use of the indicator and a check on the fuel
account. The conditions desirable are : That it must create draught enough
on the fire to make steam, and at the same time impose the least possible
amount of work on the pistons in the shape of back pressure. It should be
largo enough to produce a nearly uniform blast without lifting or tearing
SIZE, WEIGHT, TRACTIVE POWER, ETC,
85?
the fire, and be economical in its use of fuel. The Annual Report of the As-
sociation for 1896 contains interesting data on this subject.
Fire-brick Arches in Locomotive Fire-boxes.— A com-
mittee of the Am. Ry. Master Mechanics' Assn. in 1890 reported strongly in
favor of the use of brick arches in locomotive fire-boxes. They say : it is
the unanimous opinion of all who use bituminous coal and brick arch, that
it is most efficient in consuming the various gases composing black smoke,
and by impeding and delaying their passage through the tubes, and ming-
ling and subjecting them to the heat of the furnace, greatly lessens the
volume ejected, and intensifies combustion, and does not in the least check
but rather augments draught, with the consequent saving of fuel and in-
creased steaming capacity that might be expected from such results. This
in particular when used in connection with extension front.
Size, Weight, Tractive Power, etc., of Different Sizes of
Locomotives. (J. G. A. Meyer. Modern Locomotive Construction, Am.
Mach., Aug. 8, 1885.)— The tractive power should not be more or less than
the adhesion. In column 3 of each table the adhesion is given, and since the
adhesion and tractive power are expressed by the same number of pounds,
these figures are obtained by finding the tractive power of each engine, for
this purpose always using the small diarneter of driving-wheels given in
column 2. The weight on drivers is shown in column 4, which is obtained by
multiplying the adhesion by 5 for all classes of engines. Column 5 gives the
weights on the trucks, and these are based upon observations. Thus, the
weight on the truck for an eight-wheeled engine is about one half of that
placed on the drivers.
For Mogul engines we multiply the total weight tm drivers by the decimal
.2, and the product will be the weight on the truck.
For ten-wheeled engines the total weight on the drivers, multiplied by the
decimal .32, will be equal to the weight on the truck.
And lastly, for consolidation engines, the total weight on drivers multi-
plied by the decimal .16, will determine the weight on the truck.
In column 6 the total weight of each engine is given, which is obtained by
adding the weight on the drivers to the weight on the truck. Dividing the
EIGHT-WHEELED LOCOMOTIVES.
TEN-WHEELED ENGINES.
G
'£
TJ
>
•%
Hi
1
§
>
'S
1
i
ll
ill
s!
(5
5
Q
I
£
fc'~
5
P
1
2
4^
1 2
*0
v ,£
|
G
O
0
i
honll
L
*O
§
§
G
0
11
III
||
2®
Jl
•o
*
bD
JL
f
1
.s^|£
p?t
11
•|l
1
I
1
||
S3§H
i££*>
i
2
~8~
4
5
6
7
i
~2~
~8~
4
~6
6
i
in.
in.
Ibs.
Ibs.
Ibs.
Ibs.
in.
in.
Tbs"
Ibs.
Ibs.
Ibs.
10X20
45-51
4000
20000
10000
30000
533
12X18
39-43
5981
29907
9570
39477
797
11x22
45-51
5324 26620
13310
39930
709
13x18
41-45 | 6677
33387
10683
44070
890
12x22
48-54
5940 29700
14850
44550
792
14x20
43-47 8205
41023
13127
54150
1093
13X22
49-57
6828 34140
17070
51210
910
15X22
45-50
9900 49500
15840
65340
1320
14X24
55-61
7697 38485
19242
57727
1026
16X24
48-54111520
57600
18432
76032
1536
15X24
55-66
8836 44180
22090
66270
1178
17X24
51-56 12240
61200
19584
80784
1632
16X24
58-66
9533 47665
23832
71497
1271
18X24
51-5613722 68611
21955
90566
1829
17X24
60-66
10404S 52020
26010
78030
1387
19X24
54-60 14440
72200
23104
95304
1925
18X24
61-66
11472 57360
28680
86040
1529
MOGUL ENGINES.
CONSOLIDATION ENGINES.
in.
in.
Ibs.
Ibs.
Ibs.
Ibs.
in.
in.
Ibs.
Jbs.
Ibs.
Ibs.
11x16
35-40
4978
24891
4978
29869
663
14x16
36-38
7840
39200
6272
45472
1045
12X18
36-41
6480
32400
6480
38880
864
15X18
36-38
10125
50625
8100
58725
1350
13X18
37-42
7399
36997
7399
44396
986
20x24
48-50
18000
90000
14400
104400
2400
14X20
39-43
9046
45230
9046
54276
1206
22X24
50--52
00909
104544
16727
121271
2787
15X22
42-47
10607
53035
10607
63642
1414
16X24
45-51
12288
61440
12288
73738
1638
17X24
49-54
12739
63697
12739
76436
1698
18X24
51-56
13722
68611
13722
82333
1829
19x24
54-60
14440! 72200
14440
86640
1925
858 LOCOMOTIVES.
adhesion given in column 3 by 7^ gives the tons of 2000 Ibs. that the engine
is capable of hauling on a straight and level track, column 7. at slow speed
The weight of engines given in these tables will be found to agree gen-
erally with the actual weights of locomotives recently built, although it
must not be expected that these weights will agree in every case with the
actual weights, because the different builders do not build the engines alike.
The actual weight on trucks for eight-wheeled or ten-wheeled engines will
not differ much from those given in the tables, because these weights depend
greatly on the difference between the total and rigid wheel-base, and these
are not often changed by the different builders. The proportion between
the rigid and total wheel-base is generally the same.
The rule for finding the tractive power is :
j Square of dia. of \ v j Mean effect, steam ) J stroke )
1 piston in inches f • 1 press, per sq. in. f 1 in feet j
Diameter of wheel in feet. ~ = tractlve P°wer'
Leading American Types of Locomotive for Freight and
Passenger Service.
1. The eight-wheel or "American" passenger type, having four coupled
driving-wheels and a four-wheeled truck in front.
2. The " ten- wheel " type, for mixed traffic, having six coupled drivers and
a leading four-wheel truck.
3. The "Mogul1' freight type, having six coupled driving-wheels and a
pony or two-wheel truck in front.
4. The " Consolidation " type, for heavy freight service, having eight
coupled driving-wheels and a pony truck in front.
Besides these there is a great variety of types for special conditions of
service, as four-wheel and six- wheel switching-engines, without trucks; the
Forney type used on elevated railroads, with four coupled wheels under the
engine and a four-wheeled rear truck carrying the water-tank and fuel;
locomotives for local and suburban service with four coupled driving-wheels,
with a two-wheel truck front and rear, or a two-wheel truck front and a
four-wheel truck rear, etc. "Decapod11 engines for heavy freight service
have ten coupled driving-wheels and a two-wheel truck in front.
O O A n O .O o n«
O O OB O O O n F
O O O Qc O O O n n«
O O n n° O O O O o H
Classification of Locomotives (Penna. R. R. Co., 1900).— Class
A, two pairs of drivers and no truck. Class B, three pairs of drivers and no
truck. Class C, four pairs of drivers and no truck. Class D, two pairs of
drivers and four-wheel truck. Class E, two pairs of drivers, four-wheel
truck, and trailing wheels. Class F, three pairs of driving-wheels and two-
wheel truck. Class G, three pairs of drivers and four-wheel truck. Class H,
" Consolidation.'1
Steam-distribution for Hign-gpeed Locomotives.
(C. H. Quereau, Eng'g News, March 8, 1894.)
Balanced Valves.— Mr. Philip Wallis, in 1886, when Engineer of Tests for
the C., B. & Q. R. R., reported that while 6 H.P. was required to work un-
balanced valves at 40 miles per hour, for the balanced valves 2.2 H.P. only
was necessary.
STEAM-DISTKIBUTIOK FOR LOCOMOTIVES. 859
Effect of Speed on Average Cylinder-pressure.— Assume that a locomotive
has a train in motion, the reverse lever is placed in the running notch, and
the track is level: by what is the maximum speed limited ? The resistance
of the train and the load increase, arid the power of the locomotive de-
creases with increasing speed till the resistance and power are equal, when
the speed becomes uniform. The power of the engine depends on the
average pressure in the cylinders. Even though the cut-off and boiler-
pressure remain the same, this pressure decreases as the speed increases;
because of the higher piston-speed and more rapid valve-travel the steam
has a shorter time in which to enter the cylinders at the higher speed. The
following table, from indicator-cards taken from a locomotive at varying
speeds, shows the decrease of average pressure with increasing speed:
Miles per hour 46 51 51 53 54 57 60 66
Speed, revolutions 224 248 248 258 263 277 292 321
Average pressure per sq. in. :
Actual 51.5 44.0 47.3 43.0 41.3 42.5 37.3 36.3
Calculated 46.5 46.5 44.7 43.8 41.6 39.5 35.9
The " average pressure calculated " was figured on the assumption that
the mean effective pressure would decrease in the same ratio that the speed
increased. The main difference lies in the higher steam-line at the lower
speeds, and consequent higher expansion-line, showing that more steam
entered the cylinder. The back pressure and compression-lines agree quite
closely for all the cards, though .they are slightly better for the slower
speeds. That the difference is not greater may safely be attributed to the
large exhaust-ports, passages, and exhaust tip, which is 5 in. diameter.
These are matters of great importance for high speeds. .
Boiler-pressure.— Assuming that the train resistance increases as the speed
after about 20 miles an hour is reached, that an average of 50 Ibs. per sq.
in. is the greatest that can be realized in the cylinders of agiven engine at 40
miles an hour, and that this pressure furnishes just sufficient power to keep
the train at this speed, it follows that, to increase the speed to 50 miles, the
mean effective pressure must be increased in the same proportion. To in-
crease the capacity for speed of any locomotive its power must be increased,
and at least by as much as the speed is to be increased. One way to accom-
plish this is to increase the boiler-pressure. That this is generally realized,
is shown by the increase in boiler-pressure in the last ten years. For twenty-
three single-expansion locomotives described in the railway journals this
year the steam-pressures are as follows: 3, 160 Ibs.: 4, 165 Ibs.; 2, 170 Ibs.:
18, 180 Ibs,; 1.190 Ibs.
Valve-travel. — An increased average cylinder-pressure may also be
obtained by increasing the valve-travel without raising the boiler-pressure,
and better results will be obtained by increasing both. The longer travel
gives a higher steam-pressure in the cylinders, a later exhaust-opening,
later exhaust-closure, and a larger exhaust-opening — all necessary for high
speeds and economy. I believe that a 20-in. port and 6^-in. (or even 7-in.)
travel could be successfully used for high-speed engines, and that frequently
by so doing the cylinders could be economically reduced and the counter-
balance lightened. Or, better still, the diameter of the drivers increased,
securing lighter counterbalance and better steam-distribution.
Size of Drivers.— Economy will increase with increasing diameter of
drivers, provided the work at average speed does not necessitate a cut-off
longer than one fourth the stroke. The piston-speed of a locomotive with
62-in. drivers at 55 miles per hour is the same as that of one with 68-in.
drivers at 61 miles per hour.
Steam-ports.— The length of steam-ports ranges from 15 in. to 23 in., and
has considerable influence on the power, speed, and economy of the loco-
motive. In cards from similar engines the steam-line of the card from the
engine with 23-in. ports is considerably nearer boiler-pressure than that of
the card from the engine with l?*4-in. ports. That the higher steam-line is
due to the greater length of steam-port there is little room for doubt. The
23-in. port produced 531 H.P. in an 18^-in. cylinder at a cost of 23.5 Ibs of
indicated water per I. H.P. per hour. The 17J4 in. port, 424 H.P., at the rate
of 22.9 Ibs. of water, in a 19-in. cylinder.
Allen Valves.— There is considerable difference of opinion as to the advan-
tage of the Allen ported- valve (See Eng. News, July 6, 1893.)
Speed of Railway Trains.— In 1834 the average speed of trains on
the Liverpool and Manchester Railway was twenty miles an hour; in 1838 it
LOCOMOTIVES.
was twenty-five miles an hour. But by 1840 there were engines on the Great
Western Railway capable of running fifty miles an hour with a train, and
eighty miles an hour without. (Trans. A. S. M. E., vol. xiii., 363.)
The limitation to the increase of speed of heavy locomotives seems at
present to be the difficulty of counterbalancing the reciprocating parts. The
unbalanced vertical component of the reciprocating parts causes the pres-
sure of the driver on the rail to vary with every revolution. Whenever the
speed is high, it is of considerable magnitude, and its change in direction is
so rapid that the resulting effect upon the rail is not inappropriately called
a "hammer blow.1' Heavy rails have been kinked, and bridges have been
shaken to their fall under the action of heavily balanced drivers revolving
at high speeds. The means by which the evil is to be overcome has not yet
been made clear. See paper by W. F. M. Goss, Trans. A. S. M. E., vol. xvi.
Engine No. 999 of the New York Central Railroad ran a mile in 32 seconds
equal to 112 miles per hour, May 11, 1893.
Speed in miles \ _ circum. of driving-wheels in in. X no. of rev, per min. X 60
per hour f - ' 63,360
= diam, of driving-wheels in in. X no. of rev. per min. X .003
(approximate, giving result 8/10 of 1 per cent too great),
Formulae for Curves. (Baldwin Locomotive Works.)
Approximate Formula for Radius. Approximate Formula for Swing.
.7646 IF WT 0
<f
o
o
R = radius of min. curve in feet. W = rigid wheel base,
P=play of driving-wheels in T = total
decimals of 1 ft. R = radius of curve.
W— rigid wheel-base in feet. S = swing on each side of centre."
Performance of a High-speed locomotive.— The Baldwin
compound locomotive No. 1027, on the Phila. & Atlantic City Ry., in July and
August, 1897, made a record of which the following is a summary:
On July 2d a train was placed in service scheduled to make the run
between the terminal cities in 1 hour. Allowing 8 minutes for ferry from
Philadelphia to Camden, the time for the 55^> miles from the latter point to
Atlantic City was 52 minutes, or at the rate of 64 miles per hour. Owing to
the inability of the ferry-boats to reach Camden on time, the train always
left late, the average detention being upwards of 2 minutes. This loss was
invariably made up, the train arriving at Atlantic City ahead of time, 2
minutes on an average, every day. For the 52 days the train ran, from July
2d to August 31st, the average time consumed on the run was 48 minutes,
equivalent to a uniform rate of speed from start to stop of 69 miles per hour.
On July 14th the run from Camden to Atlantic City was made in 46^ min.,
an average of 71.6 miles per hour /<>r the total distance. On 22 days the
train consisted of 5 cars and on 30 days it was made up of 6, the weight of
cars being as follows : combination car, 57,200 Ibs. ; coaches, each, 59,200 Ibs. ;
Pullman car, 85,500 Ibs.
diameter of tubes, 1% in.; number of tubes, 278; length of fire-box, 113% in.;
width of fire-box, 96 in.; heating-surface of fire-box, 136.4 sq. ft.; heating-
surface of tubes, 1614.9 sq. ft.; total heating-surface, 1835.1 sq. ft.; tank
capacity, 4000 gallons; boiler-pressure, 200 Ibs. per sq, in.; total weight of
engine and tender, 227,000 Ibs.; weight on drivers (about), 78,600 Ibs.
Locomotive Link Motion.— Mr. F. A. Halsey, in his work on
"Locomotive Link Motion," 1898, shows that the location of the eccentric-
rod pins back of the link-arc and the angular vibrations of the eccentric-
rods introduce two errors in the motion which are corrected by the angular
LOCOMOTIVE LLtfK MOTION.
8595 •
vibration of the connecting-rod and by locating the saddle-stud back of the
link-arc. He holds that it is probable ' that the opinions of the critics of the
locomotive link motion are mistaken ones, and that it comes little short of
all that can be desired for a locomotive valve motion. The increase of lead
from full tto mid gear and the heavy compression at mid gear are both
advantages and not defects. The cylinder problem of a locomotive is en-
tirely different from that of a stationary engine. With the latter the
problem is to determine the size of the cylinder and the distribution of
steam to drive economically a given load at a given speed. With locomotives
the cylinder is made of a size which will start the heaviest train which the
adhesion of the locomotive will permit, and the problem then is to utilize
that cylinder to the best advantage at a greatly increased speed, but under
a greatly reduced mean effective pressure.
Negative lead at full gear has been used in the recent practice of some
railroads. The advantages claimed are an increase in the power of the
engine at full gear, since positive lead offers resistance to the motion of the
piston ; easier riding; reduced frequency of hot bearings; and a slight gain
in fuel economy. Mr. Halsey gives the practice as to lead on several roads
as follows, showing great diversity :
Full Gear
Forward, in.
Full Gear
Back, in.
Reversing
Gear, in.
New York, New Haven &
Hartford
1/16 pos.
14 neg.
J4 pos.
Maine Central
0
/4 n<^g
Illinois Central
1/32 pos.
abt. 3/16
1/16 neg.
9/64 neg.
5/16 pos.
Chicago Great Western
Chicago & Northwestern
0
3/16 neg
0
3/16 to 9/16
J4 pos.
The link-chart of a locomotive built in 1897 by the Schenectady Locomotive
Works for the Northern Pacific Ry. is as follows:
Lead.
Valve Open.
Cut-off.
Forward
Stroke, in.
Rearward
Stroke, in.
Forward
Stroke, in.
Real-ward
Stroke, in.
Forward
Stroke, in.
Rearward
Stroke, in.
i ft.
+ 1/32
3/32
^
5/32 s.
5/32
5/32 f .
i &*
+ $!
fo
5/32 s.
5/32
5/32 f .
1 %
1 7/16
1 1/16
23/32
5/16
$»
1 %
1 7/16
1 1/16
5/16
. fa
22 9/16
21
19
16
13
10
8
6
4
22%
21
19
16
13^
10
8
6
4 1/16
Cylinders 20 x 26 in., driving-wheels 69 in., six coupled wheels, main rods
! 126J^ in., radius of link 40 in., lap 1*4 in., travel 6 in., Allen valve.
DIMENSIONS OF SOME LARGE AMERICAN
LOCOMOTIVES, 1893.
The four locomotives described below were exhibited at the Chicago
Exposition in 1893. The dimensions are from Engineering News, June, 1893.
The first or Decapod engine, has ten-coupled driving-wheels. It is one of
the heaviest and most powerful engines ever built for freight service. The
Philadelphia & Reading engine is a new type for passenger service, with four-
coupled drivers. The Rhode Island engin-e has six drivers, with a 4-wheel
leading truck and a 2-wheel trailing truck. These three engines have all
compound cylinders. The fourth is a simple engine, of the standard Ameri-
can 8-wheel type, 4 driving-wheels, and a 4-wheel truck in front. This
engine holds the world's record for speed (1893) for short distances, having
run a mile m 32 seconds.
860
LOCOMOTIVES.
Baldwin.
N. Y., L. E.
&
W. R. R.
Decapod
Freight.
Baldwin.
Phila.
&
Read. R. R
Express
Passenger.
Rhode Isl.
Locomoti'e
Works.
Heavy
Express.
N. Y. C. &
H. R. R.
Empire
State
Express,
No. 999.
Running-gear :
Driving-wheels, diam
Truck '4 "
Journals, driving-axles...
44 truck- 4 ...
44 tender- 44 ...
\Vlieel-base :
Driving . . .
4 ft. 2 in.
2 44 6 l4
9 xlOin.
5 xlO kk
41/3 x 9 44
18 ft. 10 in
6 ft. 6 in.
4 " 0 44
8K>xl2in.
6'^xlO '4
4^2 x 8 44
6 ft. 10 in.
6 ft. 6 in.
2 " 9 kk
8 x'8%in.
5^x10 "
41/4 x 8 4'
13 ft 6 in.
7 ft. 2 in.
3 " 4 ';
6*4x10 "'
4V x 8 "
8 ft. 6 in,
Total engine
27 44 3 "
23 44 4 k*
29 44 9*4 "
23 44 11 k4
41 tender
16 44 8 44
16 44 0 i4
15 44 0 "
15 ft. 2J4 '4
4 4 engine and ten der. . .
Wt. in working-order:
On drivers
53 " 4 "-
170 000 Ibs
47 44 3 4k
82 TOO Ibs
50 44 6% "
88 500 Ibs.
47 " 8^ "
84 000 Ibs.
On truck-wheels
29,500 44
47,000 4i
54,500 "
40,000 4k
192,500 44
129,700 "
143,000 44
124,000 "
Tender 44
117 500 44
80,573 4l
75,000 44
80,000 u
Engine and tender, loaded
Cylinders :
h p (2)
310,000 44
16x28 in
210,273 44
13 x 24 in
218,000 44
one 21 x 26
204,000 44
19x24 in.
1 p (2).
27x28 44
22 x 24 '4
one 31 x -^6
Distance centre to centre.
Piston-rod diam .
7ft. 544
4 in.
7 ft. 4^4 in.
3V|> in
7 ft. 1 in.
3^j in
6 ft. 5 in.
3% in.
Connecting-rod, length...
Steam-ports . . ...
9' 8 7/16"
28J^ x 2 in
8ft. 0^ in.
24xl^> in.
10- ft. 3J4 in.
li^ x 20 and
8 ft. \\fa in.
Exhaust-ports
28^x8 4'
24x4J^ 4'
3x20 in.
2^x18 44
Slide-valves, out. lap, h.p.
44 out lap 1 p
1J4 in.
1 in.
1 in.
44 in lap h p
/8
(neg ) % in
1/10 in
" in lap 1 p
None
44 max. travel..
44 lead h p
6 in.
1/16 in.
5 in.
6*4 in.
3/32 44
% in.
44 lead Ip
5/16 44
3/ "
Boiler — Type
Straight
Straight
Wagon top
Wagon top
Diam. of barrel inside
Thickness of barrel-plates
Height from rail to centre
line
Length of smoke-box
Working steam-pressure..
Firebox type .
6 ft. 2J4 in.
8ft. 0 in.
5 44 7% 44
180 Ibs.
Wootten
4 ft. 814 in.
' ' 180 ibs'. "
Wootten
5 ft. 2 in.
8 ft. 11 in.
6 " 1 "
200 Ibs.
Radial sta}*
4 ft. 9 in.
9/16 in.
7 ft. 11J4 in,
4 « g lk
190 Ibs.
Buchanan
Length inside
10' 11 9/16"
9 ft. 6 in.
10 ft. 0 in.
9 ft. (fyd in.
'Width • 44
8 ft. 2J4 in.
2 4k 9% <4
3 '4 4% "4
Depth at front
Thickness of side plates . .
44 4' back plate. . .
Thickness of crown-sheet.
44 4t tube 44 .
Grate-area
5/16 in.
5/16 44
89 6 sq ft
5/16 in.
5/16 44
5/1 6- "
76 8 sq ft
6 44 10% ki
5/1 6 in.
28 sq ft.
6 '4 1J4 "
5/16 in.
5/16 tk
30 7 sq. ft.
Stay-bolts, diam., \y% in . .
Tubes — iron
pitch ,4)4 in.
354
4 in.
272
4 in.
268
Pitch...
2-^ in
2 1/16 in
2% in.
Diam , outside
2 44
IVo in
2 kk
2 in.
Length betw'n tube-plates
Heating-surface :
Tubes, exterior
Fire-box
11 ft, 11 in.
2,208.8 ft.
2343 44
10 ft. 0 in.
1,262 sq. ft.
173 4t 44
12 ft. 8% in.
12 ft. 0 in.
l,697sq.ft
233 " 44
Miscellaneous :
Exhaust-nozzle diam
5 in
514 in
Smokestack,smal'st diam.
44 height from
rail to top
1 ft. 6 44
15 44 6^ 44
1 ft. 6 in.
14 ft. 0% in.
1 ft. 3 in.
15 44 2 44
1 ft,23l4 in.
14 44 10 44
DIMENSIONS OF AMERICAN" LOCOMOTIVES. 861
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862
LOCOMOTIVES.
Dimensions of Some American Locomotives.— The table on
page 861 is condensed from one given by D. L. Barnes, in his paper on
" Distinctive Features and Advantages of American Locomotive Practice,"
Trans. A.S.C.E., 1893. The formula from which column marked "Ratio ol
cylinder- power to weight available for adhesion11 is calculated as follows:
2 X cylinder area X boiler-pressure X stroke
Weight on drivers X diameter of driving-wheel*
(Ratio of cylinder-power of compound engines cannot be compared with
that of the single-expansion engines.)
Where the boiler-pressure could not be determined from the description
of the locomotives, as given by the builders and operators of the locomotives,
it has been assumed to be 160 Ibs. per sq. in. above the atmosphere.
For compound locomotives the figures in the last column of ratios are
based on the capacity of the low-pressure cylinders only, the volume of the
high-pressure being omitted. This has been done for the purpose of com-
parison, and because there is no accurate simple way of comparing the
cylinder-power of single-expansion and compound locomotives.
Dimension* of Standard Locomotives on the N. IT. ۥ &,
H. R. R. and Penna. R. R., 1882 and 1893.
C. H. Quereau, Eng'g News, March 8/1894.
N. Y. C. & H. R. R.
Pennsylvania R. R.
Through
Passenger.
Through
Freight.
Through
Passenger.
Through
Freight.
1882,
1893.
1882.
1893.
1882.
1893.
1882.
1893.
Grate surface, sq. ft
Heating surface, sq. ft. .
17.87
1353
50
70
150
17X24
5M
1/16
%
1%
Am.
27.3
1821
58
78,86
180
19X24
5^
1/16
0
18
JM
Am.
17.87
1353
50
64
150
17X24
5M
1/16
%
1/16Z
15fc
W
Am.
29.8
1763
58
67
160
19X26
5%
1/16
%
3/32Z
18
$i
Mog.
17.6
1057
50
62
125
17X24
5
1/16
^
16
A^
Am.
33.2
1583
57
78
175
18^X24
ih
1
Mel
17%
is
Am.
23.
1260
54
50
125
•20X24
5
ijm
16
n 1M
Cons.
31.5
1498
60
50
140
20X24
5
1/16
&
16
1%
Cons.
Driver, diam., in
Steam- pressure, Ibs . ,
Cylin., diam. and stroke.
Valve-travel, ins
Lead at full gear, ins
Outside lap
Inside lap or clearance . .
Steam-ports, length
44 " width
Type of engine
Indicated Water Consumption of Single and Compound
Locomotive Engines at Varying Speeds.
C. H. Quereau, Eng'g News, March 8, 1894.
Two-cylinder Compound.
Single-expansion.
Revolu-
tions.
Speed,
miles per
hour.
Water
per I.H.P.
per hour.
Revolu-
tions.
Miles per
Hour.
Water.
100 to 150
150 " 200
200 " 250
250 " 275
21 to 31
31 " 41
41 " 51
51 " 56
18.33 Ibs.
18.9 "
19. 7 "
21.4 "
151
219
253
307
321
31
45
52
63
66
21.70
20.91
20.52
20.23
20.01
It appears that the compound engine is the more economical at low speeds,
the economy decreasing as the speed increases, nnd that the single engine
increases in economy with increase of speed within ordinary limits, becom-
ing more economical than the compound at speeds of more than 50 miles
per hour.
The C., B. & Q. two-cylinder compound, which was about 30# less eco-
nomical than simple engines of the same class when tested in passenger
service, has since been shown to be 15* more economical in freight service
Card No.
Revs.
Miles
per hour.
I.H.P.
Card No.
Revs.
Miles,
per hour.
1
160
37.1
648.3
V
304
70.5
2
260
60.8
728
8
296
68.6
3
190
44
551
9
300
69.6
4
250
58
891
10
304
70.5
5
260
60
960
11
340
78.9
6
298
69
983
12
310
71.9
ADVANTAGES OF COMPOUNDING. 863
than the best single-expansion engine, and 29# more economical than the
average record of 40 simple engines of the same class on the same division.
Indicator-tests of a Locomotive at High Speed. (Locomo-
tive Eng'g, June, 1893.) — Cards were taken by Mr. Angus Sinclair on the
locomotive drawing the Empire State Express.
RESULTS OP INDICATOR-DIAGRAMS.
I.H.P.
977
972
1,045
1,059
1,120
1,026
The locomotive was of the eight-wheel type, built by the Schenectady
Locomotive Works, with 19 X 24 in. cylinders, 78-in. drivers, and a large
boiler and fire-box. Details of important dimensions are as follows :
Heating-surface of fire-box, 150.8 sq. ft.; of tubes, 1670.7 sq. ft.; of boiler.
1821.5 sq ft. Grate area, 27.3 sq. ft. Fire-box: length, 8 ft.; width, 3 ft. 4%
in. Tubes, 268; outside diameter, 2 in. Ports: steam, 18 X 11A in. ; exhaust,
18 X 2%in. Valve-travel, 5^ in. Outside lap, 1 in.; inside lap, 1/64 in.
Journals: driving-axle, 8^ X 10^ in.; truck-axle, 6 X 10 in.
The train consisted of four coaches, weighing, with estimated load, 340,000
Ibs. The locomotive and tender weighed in working order 200,000 Ibs,,
making the total weight of the train about 270 tons. During the time that
the engine was first lifting the train into speed diagram No. 1 was taken. It
shows a mean cylinder-pressure of 59 Ibs. According to this, the power
exerted on the rails to move the train is 6553 Ibs., or 24 Ibs. per ton. The
speed is 37 miles an hour. When a speed of nearly 60 miles an hour was
reached the average cylinder-pressure is 40.7 Ibs., representing a total
traction force of 4520 Ibs., without making deductions for internal friction.
If we deduct \Q% for friction, it leaves 15 Ibs. per ton to keep the train going
at the speed named. Cards 6, 7, and 8 represent the work of keeping the
train running 70 miles an hour. They were taken three miles apart, when
the speed was almost uniform. The average cylinder-pressure for the three
cards is 47.6 Ibs. Deducting 10# again for friction, this leaves 17.6 Ibs. per
ton as the power exerted in keeping the train up to a velocity of 70 miles.
Throughout the trip 7 Ibs. of water were evaporated per Ib. of coal. The
work of pulling the train from New York to Albany was done on a coal con-
sumption of about 3^ Ibs. per H.P. per hour. The highest power recorded
was at the rate of 1120 H.P.
Locomotive-testing Apparatus at the Laboratory of
Purdue IJniyersity. ( W. F. M. Goss, Trans. A. S. M. E., vol. xiv. 826.)—
The locomotive is mounted with its drivers upon supporting wheels which
are carried by shafts turning in fixed bearings, thus allowing the engine to
be run without changing its position as a whole. Load is supplied by four
friction-brakes fitted to the supporting shafts and offering resistance to the
turning of the supporting wheels. Traction is measured by a dynamometer
attached to the draw-bar. The boiler is fired in the usual way, and an
exhaust-blower above the engine, but not in pipe connection with 'it, carries
off all that may be given out at the stack.
A Standard Method of Conducting Locoi „ _
by a Committee of the A. S. M. E. in vol. xiv. of the Transactions, page 1312.
A Standard Method of Conducting Locomotive-tests is given in a report
"Waste of Fuel in Locomotives.— In American practice economy
of fuel is necessarily sacrificed to obtain greater economy due to heavy
train-loads. D. L. Barries, in Eng. Mag., June, 1894, gives a diagram showing
the reduction of efficiency of boilers due to high rates of combustion, from
which the following figures are taken:
Lbs. of coal per sq. ft. of grate per hour 12 40 80 120 160 200
Per cent efficiency of boiler 80 75 67 59 51 43
A rate of 12 Ibs. is given as representing stationary-boiler practice, 40 Ibs.
is English locomotive practice, 120 Ibs. average American, and 200 Ibs. max-
imum American, locomotive practice.
Advantages of Compounding.— Report of a Committee of the
American Railway Master Mechanics' Association on Compound Locomotives
(Am. Mach., July 3, 1890) gives the following summary of the advantages
gained by compounding: (a) It has achieved a saving in the fuel burnt
averaging 18# at reasonable boiler-pressures, with encouraging possibilities
864 LOCOMOTIVES.
of further improvement in pressure and in fuel and water economy. (6) It
has lessened the amount of water (dead weight) to be hauled, so that (c) the
tender and its load are materially reduced in weight, (d) It has increased
the possibilities of speed far beyond 60 miles per hour, without unduly
straining the motion, frames, axles, or axle-boxes of the engine, (e) It has
increased the haulage-power at full speed, or, in other words, has increased
the continuous H.P. developed, per given weight of engine and boiler. (/) In
some classes has increased the starting-power, (g) It has materially lessened
the slide-valve friction per H.P. developed, (h) It has equalized or distrib-
uted the turning force on the crank-pin, over a longer portion of its path,
which, of course, tends to lengthen the repair life of the engine, (i) In the
two-cylinder type it has decreased the oil consumption, and has even done
so in the Woolf four-cylinder engine. ( j) Its smoother and steadier draught
on the fire is favorable to the combustion of all kinds of soft coal; and the
sparks thrown being smaller and less in number, it lessens the risk to prop-
erty from destruction by fire, (fc) These advantages and economies are
gained without having to improve the man handling the engine, less being
left to his discretion (or careless indifference) than in the simple engine. (/)
Valve-motion, of every locomotive type, can be used in its best working and
most effective position, (m) A wider elasticity in locomotive design is per-
mitted; as, if desired, side-rods can be dispensed with, or articulated engines
of 100 tons weight, with independent trucks, used for sharp curves on moun-
tain service, as suggested by Mallet and Brunner.
Of 27 compound locomotives in use on the Phila. and Reading Railroad (in
1892), 12 are in use on heavy mountain grades, and are designed to be the
equivalent of 22 X 24 in. simple consolidations; 10 are in somewhat lighter
service and correspond to 20 X 24 in. consolidations; 5 are in fast passenger
service. The monthly coal record shows:
Class of Engine. No. ^Econom"6*
Mountain locomotives 12 25# to 30#
Heavy freight service 10 12# to Yt%
Fast passenger 5 9# to 1 \%
(Report of Com. A. R. M. M. Assn. 1892.) For a description of the various
types of compound locomotive, with discussion of their relative merits, see
paper by A. Von Borries, of Germany, The Development of the Compound
Locomotive, Trans. A. S. M. E. 1893, vol. xiv., p. 1172.
Counterbalancing Locomotives.- The following rules, adopted
by different locomotive- builders, are quoted in a paper by Prof. Lanza
(Trans. A. S. M. E., x. 302):
A. " For the main drivers, place opposite the crank-pin a weight equal to
one half the weight of the back end of the connecting-rod plus one half the
weight of the front end of the connecting-rod, piston, piston-rod, and cross-
head. For balancing the coupled wheels, place a weight opposite the crank-
pin equal to one half the parallel rod plus one half of the weights of the
front end of the main-rod, piston, piston-rod, and cross-head. The centres
of gravity of the above weights must be at the same distance from the
axles as the crank-pin."
B. The rule given by D. K. Clark : " Find the separate revolving weights
of crank-pin boss, coupling-rods, and connecting-rods for each wheel, also
the reciprocating weight of the piston and appendages, and one half the
connecting-rod, divide the reciprocating weight equally between each wheel
and add the part so allotted to the revolving weight on each wheel: the
sums thus obtained are the weights to be placed opposite the crank-pin, and
at the same distance from the axis. To find the counterweight to be used
when the distance of its centre of gravity is known, multiply the above
weight by the length of the crank in inches and divide by the given dis-
tance." This rule differs from the preceding in that the same weight is
placed in each wheel.
sx'(»-?)
C. ** TF=* • £ — — , in which S = one half the stroke, G = distance
from centre of wheel to centre of gravity in counterbalance, w — weight at
crank-pin to be balanced, W = weight in counterbalance, / = coefficient of
friction so called, = 5 in ordinary practice. The reciprocating weight is
found by adding together the weights of the piston, piston-rod, cross-head,
and one half of the main rod. The revolving weight for the main wheel is
found by adding together the weights of the crank-pin hub, crank-pin, one
PETROLEUM-BURNING LOCOMOTIVES, 865
fcalf of the main rod, and one half of each parallel-rod connecting to this
wheel; to this add the reciprocating weight divided by the number of
wheels. The revolving weight for the remainder of the wheels is found in
the same manner as for the main wheel, except one half of the main rod is
not added. The weight of the crank-pin hub and the counterbalance does
not include the weight of the spokes, but of the metal inclosing them. This
calculation is based for one cylinder and its corresponding wheels."
D. " Ascertain as nearly as possible the weights of crank-pin, additional
weight of wheel boss for the same, add side rod, and mam connections,
piston-rod and head, with cross-head on one side: the sum of these multi-
plied by the distance in inches of the centre of the crank-pin from the centre
of the wheel, and divided by the distance from the centre of the wheel to
the common centre of gravity of the counterweights, is taken for the total
counterweight for that side of the locomotive which is to be divided among
the wheels on that side."
E. " Balance the wheels of the locomotive with a weight equal to the
weights of crank-pin, crank-pin hub, main and parallel rods, brasses, etc.,
plus two thirds of the weight of the reciprocating parts (cross-head, piston
and rod and packing)."
F. " Balance the weights of the revolving parts which are attached to
each wheel with exactness, and divide equally two thirds of the weights of
the reciprocating parts between all the wheels. One half of the main rod is
computed as reciprocating, and the other as revolving weight."
See also articles on Counterbalancing Locomotives, in E. R. <& Eng. Jour.*
this subject.
Maximum Safe Load for Steel Tires on Steel Rails.
(A. S. M. E., vii., p. 786.)— Mr. Chanute's experiments led to the deduction
that 12,000 Ibs. should be the limit of load for any one driving-wheel. Mr.
Angus Sinclair objects to Mr. Chanute's figure of 12,000 Ibs., and says that
a locomotive tire which has a light load on it is more injurious to the rail
than one which has a heavy load. In English practice 8 and 10 tons are
safely used. Mr. Oberlin Smith has used steel castings for cam-rollers 4 in.
diam. and 3 in. face, which stood well under loads of from 10,000 to 20,000
Ibs. Mr. C. Shaler Smith proposed a formula for the rolls of a pivot-bridge
which may be reduced to the form : Load = 1760 X face X 1/diam., all in
Ibs. and inches.
See dimensions of some large American locomotives on pages 860 and 861.
On the " Decapod " the load on each driving-wheel is 17,000 Ibs., and on
"No. 999," 21 ,000 Ibs.
Narrow-gauge Railways in Manufacturing Works.—
A tramway of 18 inches gauge, several miles in length, is in the works of
the Lancashire and Yorkshire Railway. Curves of 13 feet radius are used.
The locomotives used have the following dimensions (Proc. Inst. M. E., July,
1888): The cylinders were 5 in. diameter with 6 in. stroke, and 2 ft. 3J4 in.
centre to centre. The wheels were 16*4 in. diameter, the wheel-base
2 ft. 9 in. ; the frame 7 ft. 4*4 in. long, and the extreme width of the engine
3 feet. The boiler, of steel, 2 ft. 3 in. outside diameter and 2 ft. long between
tube-plates, containing 55 tubes of 1% in. outside diameter; the fire-box, of
iron and cylindrical, 2 ft. 3 in. long and 17 in. inside diameter. The heating-
surface 10.42 sq. ft. in the fire-box and 36.12 in the tubes, total 46.54 sq. ft.;
the grate-area, 1.78 sq. ft. ; capacity of tank, 26^ gallons; working-pressure,
170 Ibs. per sq. in.; tractive power, say, 1412 Ibs., or 9.22 Ibs. per Ib. of effec-
tive pressure per sq. in. on the piston. Weight, when empty, 2.80 tons;
when full and in working order, 3.19 tons.
For description of a system of narrow-gauge railways for manufactories,
see circular of the C. W. Hunt Co., New York.
ILight Locomotives.— For dimensions of light ocomotives used for.
mining, etc., and for much valuable information concerning them, see cata-
logue of H. K. Porter & Co., Pittsburgh.
Petroleum-burning Locomotives* (From Clark's Steam-en-
gine.)—The combustion of petroleum refuse in locomotives has been success
fully practised by Mr. Thos. Urquhart, on the Grazi and Tsaritsin Railway,
Southeast Russia. Since November, 1884, the whole stock of 143 locomotives
under his superintendence has been fired with petroleum refuse. The oil is
Injected from a nozzle through a tubular opening in the back of the fire-box,
by means of a jet of steam, with an induced current of air.
866 LOCOMOTIVES.
A brickwork cavity or " regenerative or accumulative combustion -cham-
ber " is formed in the fire-box, into which the combined current breaks as
spray against the rugged brickwork slope. In this arrangement the brick-
work is maintained at a white heat, and combustion is complete and smoke-
less. The form, mass, and dimensions of the brickwork are the most im-
portant elements in such a combination.
Compressed air was tried instead of steam for injection, but no appreciable
Deduction in consumption of fuel was noticed.
The heating-power of petroleum refuse is given as 19,832 heat-units,
equivalent to the evaporation of 20.53 Ibs. of water from and at 212° F., or to
17.1 Ibs. at 8^ atmospheres, or 125 Ibs. per sq. in., effective pressure. The
highest evaporative duty was 14 Ibs. of water under 8% atmospheres per Ib.
of the fuel, or nearly 82% efficiency.
There is no probability of any extensive use of petroleum as fuel Tor loco-
motives in the United States, on account of the unlimited supply of coal and
the comparatively limited supply of petroleum. Texas oil is now (1902) used
in locomotives of the Southern Pacific Railway.
Fireless locomotive.— The principle of the Francq locomotive is
that it depends for the supply of steam on its spontaneous generation from
a body of heated water in a reservoir. As steam is generated and drawn
off the pressure falls; but by providing a sufficiently large volume of water
beated to a high temperature, at a pressure correspondingly high, a margin
of surplus pressure may be secured, and means may thus be provided for
supplying the required quantity of steam for the trip.
The fireless locomotive designed for the service of the Metropolitan Rail-
way of Paris has a cylindrical reservoir having gegmental ends, about 5 ft.
7 in. in diameter, 26J4 ft. in length, with a capacity of about 620 cubic feet.
Four fifths of the capacity is occupied by water, which is heated by the aid
of a powerful jet of steam supplied from stationary boilers. The water is
heated until equilibrium is established between the boilers and the reser-
voir. The temperature is raised to about 390° F., corresponding to 225 Ibs.
per sq. in. The steam from the reservoir is passed through a reducing-
valve, by which the steam is reduced to the required pressure. It is then
passed through a tubular superheater situated within the receiver at the
upper part, and thence through the ordinary regulator to the cylinders.
The exhaust-steam is expanded to a low pressure, in order to obviate noise
of escape. In certain cases the exhaust-steam is condensed in closed
vessels, which are only in part filled with water. In the upper free space a
pipe is placed, into which the steam is exhausted. Within this pipe another
pipe is fixed, perforated, from which cold water is projected into the sur-
rounding steam, so as to effect the condensation as completely as may be.
The heated water falls on an inclined plane, and flows off without mixing
with the cold water. The condensing water is circulated by means of a
centrifugal pump driven by a small three -cylinder engine.
In working off the steam from a pressure of 225 Ibs. to 67 Ibs., 530 cubic
feet of water at 390° F.iis sufficient for the traction of the trains, for working
the circulating-pump for the condensers, for the brakes, and for electric-
lighting of the train. At the stations the locomotive takes from 2200 to 3300
Ibs. of steam— nearly the same as the weight of steam consumed during the
run between two consecutive charging stations. There is 210 cubic feet of
condensing water. Taking the initial temperature at 60° F., the tempera-
ture rises to about 180° F. after the longest runs underground.
The locomotive has ten wheels, on a baso 24 ft. long, of which six are
coupled, 4)4 ft- in diameter. The extreme wheels are on radial axles. The
cylinders are 23^ in. in diameter, with a stroke of 23^ in.
The engine weighs, in working order, 53 tons, of which 36 tons are on the
coupled wheels. The speed varies from 15 miles to 25 miles per hour. The
trains weigh about 140 tons.
Compressed-air Locomotives.— For an account of the Mekarski
system of compressed-air locomotives see page 510 ante.
SHAFTING.
867
SHAFTING.
(See also TORSIONAL STRENGTH; also SHAFTS OF STEAM-ENGINES.)
For diameters of shafts to resist torsional strains only, Molesworth gives
3/pT
d = A/ — :, in which d = diameter in inches, P = twisting force in pounds
applied at the end of a lever-arm whose length is I in inches, K = a coeffi-
cient whose values are, for cast iron 1500, wrought iron 1700, cast steel 3200,
gun-bronze 460, brass 425, copper 380, tin 220, lead 170. The value given for
cast steel probably applies only to high-carbon steel.
Thurston gives:
r
For head shafts well
supported against •
springing (bearings close
to pulleys or gears):
For line shafting, .
hangers 8 ft. apart:
For transmission sim-
ply, no pulleys:
- d*K. d _ /
.--^-, d-y
r5 H-p-. for cold-rolled
R iron.
, for cold-rolled iron.
H.P. -.
•, for cold-rolled iron.
H.P. = horse-power transmitted, d = diameter of shaft in inches, R = rev-
olutions per minute.
3 /100 H P
J. B. Francis gives for turned-iron shafting d = |/ — ^— *.
Jones and Laughlins give the same formulae as Prof. Thurston, with the
following exceptions: For line shafting, hangers 8 ft. apart:
cold-rolled iron, H.P. = , d =
For simply transmitting power and short counters:
turned iron, H.P. = ,rf
cold-rolled iron, H.P. = , d =
30 H.P.
R '
They also give the following notes: Receiving and transmitting pulleys
should always be placed as close to bearings as possible; and it is good prac-
tice to frame short " headers " between the main tie-beams of a mill so as
to support the main receivers, carried by the head shafts, with a bearing
close to each side as is contemplated in the formulae. But if it is preferred,
or necessary, for the shaft to span the full width of the " bay " without in-
868
SHAFTING.
termediate bearings, or for the pulley to be placed away from the bearings
towards or at the middle of the bay, the size of the shaft must be largely
increased to secure the stiffness necessary to support the load without un-
due deflection. Shafts may not deflect more than 1/80 of an inch to each
foot of clear length with safety.
To find the diameter of shaft necessary to carry safely the main pulley at
the centre of a bay: Multiply the fourth power of the diameter obtained by
above formulae by the length of the " bay," and divide this product by the
distance from centre to centre of the bearings when the shaft is supported
as required by the formula. The fourth root of this quotient will be the
diameter required.
The following table, computed by this rule, is practically correct and safe.
in.
2
Diameter of Shaft necessary to carry the Load at the Centre of
a Bay, which is from Centre to Centre of Bearings
2J4 ft. 3 ft.
4ft. 5ft. 6ft. I 8ft. 10ft.
As the strain upon a shaft from a load upon it is proportional to the
product of the parts of the shaft multiplied into each other, therefore,
should the load be applied near one end of the span or bay instead of at the
centre, multiply the fourth power of the diameter of the shaft required to
carry the load at the centre of the span or bay by the product of the two
parts of the shaft when the load is near one end, and divide this product by
the product of the two parts of the shaft when the load is carried at the
centre. The fourth root of this quotient will be the diameter required.
The shaft in a line which carries a receiving-pulley, or which carries a
transmitting-pulley to drive another line, should always be considered a
head -shaft, and should be of the size given by the rules for shafts carrying
main pulleys or gears.
Deflection of Shafting* (Pencoyd Iron Works.)— As the deflection
of steel and iron is practically alike under similar conditions of dimensions
and loads, and as shafting is usually determined by its transverse stiffness
rather than its ultimate strength, nearly the same dimensions should be
used for steel as for iron.
For continuous line-shafting it is considered good practice to limit the"
deflection to a maximum of 1/100 of an inch per foot of length. The weight
of bare shafting in pounds = 2.6d2Z/ = W, or when as fully loaded with
pulleys as is customary in practice, and allowing 40 Ibs. per 'inch of width
for the vertical pull of the belts, experience shows the load in pounds to be
about 13d2!/ = W. Taking the modulus of transverse elasticity at 26,000,000
Ibs., we derive from authoritative formulae the following:
L m ^873^ d = |/~, for bare shafting;
L = V 176d*, d = A/r==i for shafting carrying pulleys,fetc. ;
Y 1 <o
L being the maximum distance in feet between bearings for continuous
shafting subjected to bending stress alone, d = diam. in inches.
The torsional stress is inverselv proportional to the velocity of rotation,
while the bending stress will not be reduced in the same ratio. It is there*
fore impossible to write a formula covering the whole problem and sufft-
HORSE-POWER AT DIFFERENT SPEEDS.
869
ciently simple for practical application, but the following rules are correct
within the range of velocities usual in practice.
For continuons shafting so proportioned as to deflect not more than 1/100
of an inch per foot of length, allowance being made for the weakening
effect of key-seats,
d = //50H'^, L = V 720d«, for bare shafts;
d = //iOHtR, L = V 140d«, for shafts carrying pulleys, etc.
d = diam. in inches, L = length in feet, R = revs, per min.
The following table (by J. B. Francis) gives the greatest admissible dis-
tances between the hearings of continuous shafts subject to no transverse
strain except from their own weight, as would be the case were the power
given off from the shaft equal on all sides, and at an equal distance from
the hanger-bearings.
Distance between
Bearings, in ft.
Diam. of Shaft, Wrought-iron Steel
in inches. Shafts. Shafts.
2 15.46 15.89
3 17.70 18.19
4 19.48 20.02
5 2C.99 21.57
Distance between
Bearings, in ft.
Diam. of Shaft, Wrought-iron Steel
in inches. Shafts. Shafts.
6 22.30 22.92
7 23.48 24.13
8 24.55 25.23
9 25.53 ' 26.24
These conditions, however, do not usually obtain in the transmission of
power by belts and pulleys, and the varying circumstances of each case
render it impracticable to give any rule which would be of value for univer-
sal application.
For example, the theoretical requirements would demand that the bear-
ings be nearer together on those sections of shafting where most power
is delivered from the 'shaft, while considerations as to the location and
desired contiguity of the driven machines may render it impracticable to
separate the driving-pulleys by the intervention of a hanger at the theo-
retically required location. (Joshua Rose.)
Horse-power Transmitted by Turned Iron Shafting at
Different Speeds.
As PRIME MOVER OR HEAD SHAFT CARRYING MAIN DRIVING- PULLEY OR GEAR,
WELL SUPPORTED BY BEARINGS. Formula : H.P. = d3B -*- 125.
Number of Revolutions per Minute.
S oi
60
80
100
125
150
175
200
225
250
275
300
Ins.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
2.6
3.4
4.3
5.4
6.4
7.5
8.6
9.7
10.7
11.8
12.9
2
3.8
5.1
6.4
8
9.6
11.2
12.8
14.4
16
17.6
19.2
5.4
7.3
8.1
10
12
14
16
18
20
22
24
giz
7.5
10
12.5
15
18
22
25
28
31
34
37
23^
10
13
16
20
24
28
32
36
40
44
48
g'
13
17
20
25
30
35
40
45
50
55
60
3J4
16
22
27
34
40
47
54
61
67
74
81
3J4
20
27
34
42
51
59
68
76
85
93
102
3M
25
33
42
52
63
73
84
94
105
115
126
4
30
41
51
64
76
89
102
115
127
140
153
43
58
72
90
108
126
144
162
180
198
216
5
60
80
100
125
150
175
200
225
250
275
300
80
106
133
166
199
233
266
299
333
366
400
870
SHAFTING.
As SECOND MOVERS OR LINE-SHAFTING, BEARINGS 8 tff . APART.
Formula : H.P. = d*R -*• 90.
i"s«
si
Number of Revolutions per Minute.
100
125
150
175
200
225
250
275
300
325
350
Ins.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
6
7.4
8.9
10.4
11.9
13.4
14.9
16.4
17.9
19.4
20.9
1%
7.3
9.1
10.9
12.7
14.5
16.3
18.2
20
21.8
23.6
25.4
2
8.9
11.1
13.3
15.5
17.7
20
22.2
24.4
26.6
28.8
31
10.6
13.2
15.9
18.5
21.2
23.8
26.5
29.1
31.8
34.4
37
2J4
12.6
15.8
19
22
25
28
31
35
38
41
44
2&£
15
18
22
26
29
33
37
41
44
48
52
2Vij>
17
21
26
30
34
39
43
47
52
56
60
234
23
29
34
40
46
52
58
64
69
75
81
3
30
37
45
52
60
67
75
82
90
97
105
3M
38
47
57
66
76
85
95
104
114
123
133
31^
47
59
71
83
95
107
119
131
143
155
167
334
58
73
88
102
117
132
146
162
176
190
205
4
71
89
ior
125
142
160
178
196
213
231
249
FOR SIMPLY TRANSMITTING POWER.
Formula : H.P. = d*R -*- 50.
• ^
jNi
ft 55
Number of Revolutions per Minute.
100
125
150
175
200
233
267
300
333
367
400
Ins.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
6.7
8.4
10.1
11.8
13.5
15.7
17.9
20.3
22.5
24.8
27.0
J5X
8.6
10.7
12.8
15
17.1
20
22.8
25.8
28.6
31.5
34.3
1%
10.7
13.4
16
18.7
21.5
25
28
32
36
39
43
1%
13.2
16.5
19.7
23
26.4
31
35
39
44
48
5a
2
16
20
24
28
32
37
42
48
53
58
64
gl£
19
24
29
33
38
44
51
57
63
70
76
2M
22
28
34
39
45
52
60
.68
75
83
90
2«i
27
33
40
47
53
62
70
79
88
96
105
2^&
31
39
47
54
62
73
83
93
104
114
125
234
41
52
62
73
83
97
111
125
139
153
167
3
54
67
81
94
108
126
144
162
180
198
216
3^
68
86
103
120
137
160
182
205
228
250
273
3^
85
107
128
150
171
200
228
257
285
313
342
Horse
(-power Transmitted by Cold-rolled Iron Shafting
at Different Speeds.
As PRIME MOVER OR HEAD SHAFT CARRYING MAIN DRIVING-PULLEY OR
GEAR, WELL SUPPORTED BY BEARINGS. Formula : H.P. = d*R •*- 75.
Number of Revolutions per Minute.
Q x
60
80
100
125
150
175
200
225
250
275
300
Ins.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
ji^
2.7
3.6
4.5
5.6
6.7
7.9
9.0
10
11
12
13
134
4.3
5.6
7.1
8.9
10.6
12.4
14.2
16
18
19
21
2
6.4
8.5
10.7
13
16
19
21
24
26
29
32
9
12
15
19
23
26
30
34
38
42
46
21^
12
17
21
26
31
36
41
47
52
57
62
234
16
22
27
35
41
48
55
62
70
76
82
3
21
29
36
45
54
63
72
81
90
98
108
3^4
27
36
45
57
68
80
91
103
114
126
136
8gB
34
45
57
71
86
100
114
129
142
157
172
33a
42
56
70
87
105
123
140
158
174
193
210
4
51
69
85
106
128
149
170
192
212
244
256
73
97
121
151
182
212
243
273
302
333
364
EOE8E-POWER AT DIFFERENT SPEEDS.
871
As SECOND MOVERS OR LINE-SHAFTING, BEARINGS 8 FT. APART.
Formula : H.P. = d*R -*• £0.
s £
Number of Revolutions per Minute.
,3*8 *
5 02
100
125
150
175
200
225
250
275
300
325
350
Ins.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
6.7
8.4
10.1
11.8
13.5
15.2
16.8
18.5
20.2
21.9
23.6
1%
8.6
10.7
12.8
15
17.1
19.3
21.5
23.6
25.7
28.9
31
1%
10.7
13.4
16
18.7
21.5
24.2
26.8
29.5
32.1
34.8
39
1%
13.2
16.5
19.7
23
26.4
29.6
32.9
36.2
39.5
42.8
46
2
16
20
24
28
32
36
40.
44
48
52
56
19
24
29
33
38
43
48
52
57
62
67
2M
22
28
34
39
45
50
56
61
68
74
80
2?«
27
33
40
47
53
60
67
73
80
86
91
J>L£
31
39
47
54
62
69
78
86
93
101
109
2M
41
52
62
73
83
93
104
114
125
135
145
3
54
67
81
94
108
121
134
148
162
175
189
68
86
103
120
137
154
172
188
205
222
240
3^1
85
107
128
150
171
192
214
235
257
278
300
FOR SIMPLY TRANSMITTING POWER AND SHORT COUNTERS.
Formula : H.P. = d*R -*- 30.
Number of Revolutions per Minute.
5 02
100
125
150
175
200
233
267
300
333
367
400
Ins.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
H.P.
6.5
8.1
9.7
11.3
13
15.2
17.4
19.5
21.7
23.9
26
]RZ
8.5
10.7
12.8
15
17
19.8
22.7
25.5
28.4
31
34
l/^
11.2
14
16.8
19.6
22.5
26
30
33
37
41
45
]S£
14.2
17.7
21.2
24.8
28.4
33
38
42
47
52
57
1%
18
22
27
31
35
41
47
53
59
65
71
1%
22
27
33
38
44
51
58
65
72
79
87
2
26
33
40
46
53
62
71
80
88
97
106
32
40
47
55
63
73
84
95
105
116
127
2^4
38
47
57
66
76
89
101
114
127
139
152
2%
44
55
66
77
88
103
118
133
148
163
178
21*3
52
65
78
91
104
121
138
155
172
190
207
2%
69
84
99
113
138
161
184
207
231
254
277
3
90
112
135
157
180
210
240
270
300
330
360
SPEED OF SHAFTING.— Machine shops 120 to 180
Wood-working 250 to 300
Cotton and woollen mills 300 to 400
There are in some factories lines 1000 ft. long, the power being applied al
the middle.
Hollow Shafts*— Let d be the diameter of a solid shaft, and c?jC?a the
external and internal diameters of a hollow shaft of the same material.
Then the shafts will be of equal torsional strength when d3 = * ~ — - .
of*
A 10-inch hollow shaft with internal diameter of 4 inches will weigh 16$ less
than a solid 10-inch shaft, but its strength will be only 2.56# less. If the hole
were increased to 5 inches diameter the weight would be 2o% less than that
of the solid shaft, and the strength 6.25$ less.
Table for Laying Out Shafting.— The table on the opposite page
(from the Stevens Indicator, April, 1892) is used by Wm. Sellers & Co. to
facilitate the laying out of shafting.
The wood-cuts at the head of this table show the position of the hangers
and position of couplings, either for the case of extension in both directions
from a central head-shaft or extension in one direction from that head-shaft.
TAB1Z FOE LAYING OUT SHAFTING.
si
II
•S9qoui
•sm 'xog ao 'Sui
?
•3-43
a o 03
^
S llllife
§ 11121^
p.S S <^s *3^-^
oSg^^,,
^{M <K.S JH'S »-.
^ ft w O S-^BQ
I
S
I
NNafl
*SJ«*
,.gs§-s
tilts"
S8??2*j
;««o^^S
<M W Oi W OJCC
» ^
C3OJ OOOOrt*
PROPORTIONS OF PULLEYS. 873
PULLEYS.
Proportions of Pulleys. (See also Fly-wheels, pages 820 to 823.)—
Let n = number of arms, D = diameter of pulley, S = thickness of belt, t =
thickness of rim at edge, T = thickness in middle, B = width of rim, /3 =
width of belt, h = breadth of arm at hub, ftj = breadth of arm at rim, e =
thickness of arm at hub e: = thickness of arm at rim, c = amount of crown-
ing; dimensions in inches.
B — width of rim . . .
Unwin.
9/8 (84-04^
Reuleaux.
9/86 to 5/4^
t — thickness at edge of rim
0 7£ -f- 005D -J
T— " " middle of rim.
2t + c
l/5ft to y±h
h = breadth of arm at hub J
For single A / BD
belts = .6337 j/ n
For double 1 /~BD
belts = .798y ~^T
W' B D
4 + 4 "*" 2071
0 8ft
e = thickness of arm at hub. ....
e1 — ** *' ** " rim
0.34ft
0.4ft,
0.5ft
0 5ftj
n = number of arms, for a )
single set, > "
«+^
^x2f)
,
T - 1 Anp>th nf hub $ nofc less than 2-5s> I B for sin.-arm pulleys.
L - length of hub .............. ^ is Qf fcen y^ ^ 2B tl double_^m u*
M= thickness of metal in hub ..................... ft to %ft
c = crowning of pulley .............. 1/245
The number of arms is really arbitrary, and may be altered if necessary.
(Unwin.)
Pulleys with two or three sets of arms may be considered as two or three
separate pulleys combined in one, except that the proportions of the arms
should be 0.8 or 0.7 time that of single-arm pulleys. (Reuleaux.)
EXAMPLE.— Dimensions of a pulley 60" diam., 16" face, for double belt W
thick.
Solution by.... nftftt e el t T L M c
Unwin ......... 9 3.79 2.53 1.52 1.01 .65 1.97 10.7 3.8 .67
Reuleaux ..... 4 5.0 4.0 2.5 2.0 1.25 16 5
The following proportions are given in an article in the Amer. Machinist,
authority not stated:
ft = .0625D -f .5 in., h^ = .041) -f- 3125 in., e = .G25D -J- .2 in., et = .016D -f
.125 in.
These give for the above example: ft = 4.25 in., ftj = 2.71 in., e = 1.7 in.
ex = 1.09 in. The section of the arms in all cases is taken as elliptical.
The following solution for breadth of arm is proposed by the author-.
Assume a belt pull of 45 Ibs. per inch of width of a single belt, that the
whole strain is taken in equal proportions on one half of the arms, and that
the arm is a beam loaded at one end and fixed at the other. We have the
formula for a beam of elliptical section fP — .0982 — j— , in which P = the
load, R = the modulus of rupture of the cast iron, 6 = breadth, d = depth,
and I = length of the beam, and/ = factor of safety. Assume a modulus
of rupture of 36.000 Ibs., a factor of safety of 10, and an additional allow-
ance for safety in taking I — y2 the diameter of the pulley instead of ^D
less the radius of the hub.
Take d — ft, the breadth of the arm at the hub, and 6 = e = 0.4ft, the
thickness. We then have fP = 10 X -^5 = 900- = 3585 *^4/J\ whence
-
h _ A/g^2 = .633/7— , which is practically the same as the value
y tJ5o5?t \ 11
reached by Unwin from a different set of assumptions.
874
PULLEYS.
Convexity of Pulleys.— Authorities differ. Morin gives a rise equal
to 1/10 of the face; Molesworth, 1/24; others from % to 1/96. Scott A.
Smith says the crown should not be over ^ inch for a 24-inch face. Pulleys
for shifting belts should be u straight,11 that is, without crowning.
CONE OR STEP
To find the diameters for the several steps of a pair of cone-pulleys:
1. Crossed Belts.— -Let D and d be the diameters of two pulleys con
nected by a crossed belt, L = the distance between their centres, and /3 =.
the angle either half of the belt makes with a line joining the centres of the
pulleys : then total length of belt = (D -f d)£ + (D -f d)~ + 2L cos /3.
-* loO
2L
; /, cosjS =
The length of
the belt is constant when D -f d is constant; that is, in a pair of step-
pulleys the belt tension will be uniform when the sum of the diameters of
each opposite pair of steps is constant. Crossed belts are seldom used for
cone-pulleys, on account of the friction between the rubbing parts of the
belt.
To design a pair of tapering speed-cones, so that the belt may fit
equally tight in all positions : When the belt is crossed, use a pair of equal
and similar cones tapering opposite ways.
2. Open Belts.— When the belt is uncrossed, use a pair of equal and
similar conoids tapering opposite ways, and bulging in the middle, accord-
ing to the following formula: Let L denote the distance between the axes
of the conoids; R the radius of the larger end of each; r the radius of the
smaller end; then the radius in the middle, ra, is found as follows:
R-\-r - (R-r)*
2 "•" Q.28L '
(Rankine.)
If DO = the diameter of equal steps of a pair of cone-pulleys, D and d =r
the diameters of unequal opposite steps, and L = distance between the
D -f d , (D - d)<>
axes, D0 = —~ f- r2 566L'
If a series of differences of radii of the steps, R — r, be assumed, then
for each pair of steps ~^r = r0 - ^ ~g^ •, and the radii of each may be
computed from their half sum and half difference, as follows :
r> -R + r . R — r R + r R — r
T~ + ~~2~; ~~1T ~~2~~-
A. J. Frith (Trans. A. S. M. E., x. 298) shows the following application of
Rankine's method: If we had a set of cones to design, the extreme diame-
ters of which, including thickness of belt, were 40" and 10", and the ratio
desired 4, 3, 2, and 1, we would make a table as follows, L being 100":
Trial
Sum of
D-fd.
Ratio.
Trial Diameters.
Values of
\D — d)2
Amount
to be
Added.
Corrected Values.
D
d
12,561,
D
d
50
50
50
50
4
3
2
1
40
37.5
33.333
25
10
12.5
16.666
25
.7165
.4975
.2212
.0000
.0000
.2190
.4953
.7165
40
37.7190
33.8286
25.7165
10
12.7190
17.1619
25.7165
The above formulae are approximate, and they do not give satisfactory
results when the difference of diameters of opposite steps is large and when
the axes of the pulleys are near together, giving a large belt-angle. The
following more accurate solution of the problem is given by C. A, Smith
(Trans. A. S. M. E., x. 269) (Fig 152):
Lay off the centre distance C or EF, and draw the circles 7^ and d, equal
to the first pair of pulleys, which are always previously determined by
known conditions. Draw HI tangent to the circles Dj and dt. From 5,
midway between E apd F, erecl the perpendicular BG, making the length
COKE OR STEP PULLEYS.
875
BG = 3UC. With G as a centre, draw a circle tangent to HI. Generally
this circle will be outside of the belt-line, as in the cut, but when C is short
and the first pulleys D! and dt are large, it will fall on the inside of the belt-
line The belt-line of any other pair of pulleys must be tangent to the cir-
cle G" hence any line, as JKor LM, drawn tangent to the circle <?, will give
FIG. 152.
the diameters D2, dt or D3, d3 of the pulleys drawn tangent to these lines
from the centres E and F.
The above method is to be used when the belt-angle A does not exceed
18°. When it is between 18° and 30° a slight modification is made. In that
case, in addition to the point G, locate another point ra on the line BG .298 C
above B. Draw a tangent line to the circle (r, making an angle of 18° to the
line of centres EF, and from the point m draw an arc tangent to this tan-
gent line. All belt-lines with angles greater than 1 3° are tangent to this arc.
The following is the summary of Mr. Smith's mathematical method:
A — angle in degrees between the centre line and the belt of any pair of
pulleys;
a = .314 for belt-angles less than 18°, and .298 for angles between 18°
and 30° ;
B° = an angle depending on the velocity ratio;
C = the centre distance of the two pulleys;
D, d = diameters of the larger and smaller of the pair of pulleys;
E° — an angle depending on B° ;
L = the length of the belt when drawn tight around the pulleys;
r = D -f- d, or the velocity ratio (larger divided by smaller).
\ij uiii ^a. — jj-p; , v*1/ "° - r 4-1 '
(3) Sin E° = sin B°(cos A - D ^ ) ?
B* — E° when sin E° is positive; = B° 4- E° when sin E° is negative;
(5) d = 2Cs™^ = .3183(L - 2C) when A - 0 and r = 1;
(6) D = rd;
(7) L = 2Ccos A -f- .01745d[180 + (r - 1)(90 + A)].
Equation (1) is used only once for any pair of cones to obtain the constant
cos A, by the aid of tables of sines and cosines, for use in equation (3).
876 BELTING.
BELTING.
Theory of Belts and Bands.— A pulley Is driven by a belt by
means of the friction between the surfaces in contact. Let 2\ be the tension
on the driving side of the belt, 2'2 the tension on the loose side; then S, = Tt
— !T2 , is the total friction between the band and the pulley, which is equal to
the tractive or driving force. Let/ = the coefficient of friction, 6 the ratio
of the length of the arc of contact to the length of the radius, a = the angle
of the arc of contact in degrees, e — the base of the Naperian logarithms
= 2.71828, m = the modulus of the common logarithms = 0.434295. The
following formulae are derived by calculus (Rankine's Mach'y & Millwork,
p. 351 ; Carpenter's Exper. Eng'g, p. 173):
!.7288/ =
Zi
If the arc of contact between the band and the pulley expressed in turns
and fractions of a turn = n, Q = 2/m; e*e = io2-7288/w; that is, e& is the
natural number corresponding to the common logarithm 2.7288/n.
The value of the coefficient of friction / depends on the state and material
of the rubbing surfaces. For leather belts on iron pulleys, Morin found
/ = .56 when dry, .36 when wet, .23 when greasy, and . 15 when oily. In calcu-
lating the proper mean tension for a belt, the smallest value, / = .15, is
to be taken if there is a probability of the belt becoming wet with oil. The
experiments of Henry R. Towne and Robert Briggs, however (Jour. Frank.
Inst., 1868). show that such a state of lubrication is not of ordinary occur-
rence; and that in designing machinery we may in most cases safely take
/ = 0.42. Reuleaux takes / = 0.25. The following table shows the values of
the coefficient 2.728H/, by which n is multiplied in the last equation, corre-
sponding to different values of /; also the corresponding values of various
ratios among the forces, when the arc of contact is half a circumference :
/=0.15 0.25 0.42 0.56
!8/ = 0.41 0.68 1.15 1.53
Let 0 = TT and n = J^, then
2\-f-!T2 = 1.603 2.188 3.758 6.821
T, +8 = 2.66 1 84 1.36 1.21
2\ -f T2 -T- 2S = 2.16 1.34 0.86 0.71
In ordinary practice it is usual to assume T3 = S; Tt = 25; Tj -f- T9 -*•
2S = 1.5. This corresponds to/ = 0.22 nearly.
For a wire rope on cast iron / maybe taken as 0.15 nearly; and if the
groove of the pulley is bottomed with gutta-percha, 0.25. (Rankine.)
Centrifugal Tension of Belts.— When a belt or band runs at a
high velocity, centrifugal force produces a tension in addition to that exist-
ing when the belt is at rest or moving at a low velocity. This centrifugal
tension diminishes the effective driving force.
Rankine says : If an endless band, of any figure whatsoever, runs at a
given speed, the centrifugal force produces a uniform tension at each cross-
section of the band, equal to the weight of a piece of the band whose length
is twice the height from which a heavy body must fall, in order to acquire
the velocity of the band. (See Cooper on Belting, p. 101.)
If Tc = centrifugal tension;
V = velocity in feet per second;
g — acceleration due to gravity = 32.2;
W = weight of a piece of the belt 1 ft. long and 1 sq. in. sectional area,—
Leather weighing 56 Ibs. per cubic foot gives W = 56 -*- 144 ss .888.
BELTING PRACTICE, 877
Belting Practice. Handy Formula: for Belting. — Since
in the practical application of the above formulae the value of the coefficient
of friction must be assumed, its actual value varying within wide limits (15%
to 135$), and since the values of Tt and T^ also are fixed arbitrarily, it is cus-
tomary in practice to substitute for these theoretical formulae more simple
empirical formulae and rules, some of which are given below.
Let d = diam. of pulley in inches; nd = circumference;
V = velocity of belt in ft. per second; v = vel. in ft. per minute;
a = angle of the arc of contact;
L = length of arc of contact in feet = irda •+• (12 X 360);
F = tractive force per square inch of sectional area of belt;
w = width in inches; t = thickness;
S = tractive force per inch of width = F-*- 1 ;
rpm. = revs, per minute; rps. = revs, per second = rpm. •*• 60.
s. = $ X ^ . .00,363* x rpnx =
~ x rpm.; = .2618d x rpm.
florse-power, H.P. - - * - = -
If F = working tension per square inch = 275 Ibs., and t = 7/32 inch, 8
60 Ibs. nearly, then
H.P. = ^ = .mrw = .000476MK* X rpm. = w ^m'- • (D
If F £z 180 Ibs. per square inch, and t = 1/6 inch, 8 = 30 Ibs., then
H.P. = ££ = .056F«, = .000238«,d X rpm. = '"' ^g""' . . (2)
If the working strain is 60 Ibs. per inch of width, a belt 1 inch wide travel-
ling 550 ft. per minute will transmit 1 horse-power. If the working strain is
30 Ibs. per inch of width, a belt 1 inch wide, travelling 1100 ft. per minute,
will transmit 1 horse-power. Numerous rules are given by different writers
on belting which vary between these extremes. A rule commonly used is :
1 inch wide travelling 1000 ft. per min. =: I.H.P.
H.P. .£= =.06K«,= . OMMBiKi X rpm. = |^'. . . (3)
This corresponds to a working strain of 33 Ibs. per inch of width.
Many writers give as safe practice for single belts in good condition a
working tension of 45 Ibs. per inch of width. This gives
For double belts of average thickness, some writers say that the trans-
mitting efficiency is to that of single belts as 10 to 7, which would give
H.P. of double belts = ^ = .1169 Vw = MQ51wd X rpm. = ™d * ^f1"' . (5)
olo 1JOU
Other authorities, however, make the transmitting-power of double belts
twice that of single belts, on the assumption that 'the thickness of a double-
belt is twice that of a single belt.
Rules for ho''se-power of belts are sometimes based on the number of
square feet of surface of the belt which pass over the pulley in a minute.
Sq. ft. per min. = wv •+• 12. The above formulae translated into this form
give:
(1) For 8 = 60 Ibs. per inch wide ; H.P. ss 46 sq. ft. per minute.
(2) " 8 ss 30 " ** H.P. = 92 " "
(3) - 8 = 83 " •* •• H.P. = 83 " "
(4) " S«=45 " * •* H.P. = 61 «* «
(W^fiisWJ" •• •* H.P. =48 * " (double belt*
878
BELTING.
The above formulae are all based on the supposition that the arc of con.
tact is 180° For other arcs, the transmitting power is approximately pro«
portiohal to the ratio of the degrees of arc to 180°.
Some rules base the horse-power on the length of the arc of contact in
feet. Since L = ^^ and H P. = |^ = J^x g X rpm. X ^ we
Sw
obtain by substitution H.P. = 1050Q xLx rpm., and the five formulae then
take the following form for the several values of S:
H.P
wL X rpm. wL X rpm.
- ~ 1 ~~
275
H.F. (double belt) =
550
ivL X rpm.
257
wL X rpm. wL X rpm.
500 ( '' 367 W;
(5).
None of the handy formulae take into consideration the centrifugal ten-
sion of belts at high velocities. When the velocity is over 3000 ft. per min-
ute the effect of this tension becomes appreciable, and it should be taken
account of as in Mr. Nagle's formula, which is given below.
Horse-power of a Leather Belt One Inch wide, (NAGLE.)
Formula: H.P. = CVtw(S - .012 F2) -* 550.
For /= .40, a = ISO9, C = .715, w = 1.
LACED BELTS, S = 275.
RIVETED BELTS, S = 400.
0 o
2 o
'" V
K^CC
Thickness in inches = t.
£»J8
Thickness in inches ^ t.
8&
'en '
1/7
1/6
3/16
7/32
1/4
5/16
1/3
I8-
7/32
1/4
5/16
1/3
3/8
7/16
1/2
££
.143
.167
.187
.219
.250
.312
.333
££
,219
.250
.312
.333
.375
.437
.500
10
.51
.59
.63
.73
.84
1.05
1.18
15
1.69
1.94
2.42
2.58
2.91
3.39
3.87
15
.75
.88
1.00
1.16
1.32
1.66
1.77
20
2.24
2.57
3.21
3.42
3.85
4.49
5.13
20
1.00
1.17
1-32
1.54
1 .75
2 19
2.34
25
2.79
3.19
3.98
4.25
4.78
5.57
6.37
25
1.23
1.43
1.61
1.88
2.16
2.69
2.86
30
3.31
3.79
4.74
5.05
5.67
6.62
7.58
30
1.47
1.72
1.93
2.25
2.58
3.22
3.44
35
3.82
4.37
5.46
5.83
6.56
7.65
8.75
35
1.69
1.97
2.22
2.59
2.96
3.70
3.94
40
4.33
4.95
6.19
6.60
7.42
8.66
9.90
40
1.90
2.22
2.49
2.90
3.32
4.15
4.44
45
4.85
5.49
6.86
7.32
8.43
9 70
10.98
45
2.09
2.45
2.75
3.21
3.67
4.58
4.89
50
5.26
6.01
7.51
8.02
9 02
10.5212.03
50
2.27
2.65
2.98
3.48
3.98
4.97
5.30
55
5.68
6.50
8.12
8.66
9.74
11.3613.00
55
2.44
2.84
3.19
3.72
4.26
5.32
5.69
60
6.09
6.C6
8.70
9.28
10.43
12.1713.91
60
2.58
3.01
3.38
3.95
4.51
5.64
6.02
65
6.45
7.37
9.22
9.83
11.06
12.90 14.75
65
2.71
3.16
3:55
4.14
4.74
5.92
6.32
70
6.78
7.75
9 69
10.33
11.62
13.56J15.50
70
2.81
3.27
3.68
4.29
4.91
6.14
6.54
75
7.09
8.11
10.13
10.84
12.16
14.18'l6.21
75
2.89
3.37
3.79
4.42
5.05
6.31
6.73
80
7.36
8.41
10 51
11.21
12.61
14.71J16.81
80
2.94
3.43
3.86
4.50
5.15
6.44
6.86
85
7.58
8.66
10.82
11.55
13.00
15.1617.32
85
2.97
3.47
3.90
4.55
5.20
6.50
6.93
90
7.74
8.85
11.06
11.80
13.27
15.4817.69
90
2.97
3.47
3.90
4.55
5.20
6.50
6.93
100
7.96
9.10
11.37
12.13
13.65
15.92 18.20
The H.P. becomes a maximum
The H.P. becomes a maximum at
at 87. 41 ft. per sec, = 5245 ft. p. min.
105.4 ft. per sec. = 6324 ft. per min.
In the above table the angle of subtension, a, is taken at 180°.
Should it be.. .. I 900|1000|1100I120on300jl400|1500|1600|1700ll80«>j200e
Multiply above values by | .65 | .70 I .75 ( .79 | .83 j .87 | .91 | .94 | .97 [ 1 ll .03
A. F. Nagle's Formula (Trans. A. S. M. EM voi. ii.,
Tables published in 1882.)
1881, p. 91.
550
C as 1 - l
a = degrees of belt contajt;
/ = coefficient of friction;
w as width in inches;
t 3= thickness in inches;
V = velocity in feet per second;
S = stress upon belt per square inch*
WIDTH OF BELT FOR A GIVEST HORSE-POWER. 879
Taking S at 275 Ibs. per sq. in. for laced belts and 400 Ibs. per sq. in. for
lapped and riveted belts, the formula becomes
H.P. = CVtiv(.bO - .0000218 F«) for laced belts;
H.P. = CF*w;(.727 - .0000218 F2) for riveted belts.
VALUES OP
1 - 10 --00758/a. <NAGLE.)
12 §
Degrees of contact = a.
11 o
90°
100°
110°
120°
130<»
140°
150°
160°
170°
180°
200°
.15
,210
.230
.250
.270
.288
.307
.325
.342
.359
.376
.408
.20
.270
.295
.319
.342
.864
.386
.408
.428
.448
.467
.503
.25
.325
.854
.581
.407
.432
.457
.480
.503
.524
.544
.582
30
.376
.408
.438
.467
.494
.520
.544
.567
.590
.610
.649
.35
.423
.457
.489
.520
.548
.575
.600
.624
.646
.667
.705
.40
.467
.502
.536
.567
.597
.624
.649
.673
.695
.715
.753
.45
.507
.544
.579
.610
.640
.667
.692
.715
.737
.757
.792
.55
.578
.617
.652
.684
.713
.739
.763
.785
.805
.822
.853
.60
.610
.649
.684
.715
.744
.769
.792
.813
.832
.848
.877
1.00
.792
.825
.853
.877
.897
.913
.9 .'7
.937
.947
.956
.969
The following table gives a comparison of the formulae already given for
the case of a belt one inch wide, with arc of contact 180°.
Horse-power of a Belt One Inch wide, Arc of Contact 180°.
COMPARISON OP DIFFERENT FORMULAE.
£S
£ B
£S
««.S
°.a
Form. 1
H.P. -
Form. 2
H.P. =
Form. 3
H.P. =
Form. 4
H.P. =
Form. 5
dbl.belt
Nagle's Form.
7/32"single belt
*&
Sd
tM ft
WV
ivv
wv
ivv
1VV
3J5.J
><*
|«i
s|
550
1100
iooo'
733
"513"
Laced.
Riveted
10
600
50
1.09
.55
.60
.82
1.17
.73
1.14
20
1200
100
2.18
1.09
1.20
1.64
2.34
1.54
2.24
30
1800
150
3.27
1.64
1.80
2.46
3.51
2.25
3.31
40
2400
200
4.36
2.18
a. 40
3.27
4.68
2.90
4.33
50
3000
250
5.45
2.73
3.00
4.09
5.85
3.48
5.26
60
3600
300
6.55
3.27
8.60
4.91
7.02
3.95
6.09
70
4200
350
7.63
3.82
4.20
5.73
8.19
4.29
6.78
80
4800
400
8.73
4.36
4.80
6.55
9.36
4.50
7.36
90
5400
450
9.82
4.91
5.40
7.37
10.53
4.55
7.74
100
6000
500
10.91
5.45
6.00
8.18
11.70
4.41
7.96
110
6600
550
4.05
7 97
120
7200
600
3.49
7.75
Width of Belt for a Given Horse-power.— The width of beH
required for any given horse-power may be obtained by transposing tiie for
mulae for horse-power so as to give the value of w. Thus:
550 H.P. 9.17 H.P. 2101 H.P. 275 H.P.
•«,•
From formula .(1),
From formula (2), w :
From formula (8), w •
From formula (4), w -.
From formula (5),* w =s
* For double belts.
v
1100 H.P.
v
1000 H.P.
v
733H.P.
1 :
V
513 H.P.
18.33 H.P.
16.67 H.P.
--
12.22 H.P.
8.56 H.P.
V
d xrpm.
_ 4202 H.P.
" d X rpm. :
_ 8820 HP.
~~ d X rpm.
_ SSOO H.P.
~" d X rpm.
1960 H.P. _
d X rpm. ~~ L X rpm.*
. 630 H.P.
L X rpm.*
. 600 H.P.
L x rpm.*
360 H.P.
"LX
257H.P.
880
BELTIKG.
Many authorities use formula (1) for double belts and formula (2) or (3) fof
single belts.
a or divide
To obtain the width by Nagle's formula, w
the given horse-power by the figure in the table corresponding to the given
thickness of belt and velocity in feet per second.
The formula to be used in any particular case is largely a
matter of judgment. A single belt proportioned according to formula (1),
if tightly stretched, and if the surface is in good condition, will transmit the
horse- power calculated by the formula, but one so proportioned is objec-
tionable, first, because it requires so great an initial tension that it is apt to
Btretch, slip, and require frequent restretching and relacing; and second,
because this tension will cause an undue pressure on the pulley -shaft, and
therefore an undue loss of power by friction. To avoid these difficulties,
formula (2), (3), or (4,) or Mr. Nagle's table, should be used; the latter espe-
cially m cases in which the velocity exceeds 4000 ft. per min.
Taylor's Rules for Belting. -F. W. Taylor (Trans. A. S. M. E.,
xv. 204) describes a nine years1 experiment on belting in a machine-shop,
giving results of tests of 42 belts running night and day. Some of these
belts were run on cone pulleys and others on shifting, or fast-and-loose, pul-
leys. The average net working load on the shifting belts was only 4/10 of
that of the cone belts.
The shifting belts varied in dimensions from 39 ft. 7 in. long, 3.5 in. wide,
.25 in. thick, to 51 ft. 5 in. long, 6.5 in. wide, .37 in. thick. The cone belts
varied in dimensions from 24 ft. 7 in. long, 2 in. wide, .25 in. thick, to 31 ft.
10 in. long, 4 in. wide, .37 in. thick.
Belt-clamps were used having spring-balances between the two pairs c*
clamps, so that the exact tension to which the belt was subjected was
accurately weighed when the belt was first put on, and each time it was
tightened.
The tension under which each belt was spliced was carefully figured so as
to place it under an initial strain— while the belt was at rest immediately
after tightening— of 71 Ibs. per inch of width of double belts. This is equiv-
alent, in the case of
Oak tanned and fulled belts, to 192 Ibs. per sq. in. section;
Oak tanned, not fulled belts, to 229 " " " " "
Semi-raw-hide belts, to 253 *• " " " "
Raw-hide belts, to 284 " ** " " "
From the nine years' experiment Mr. Taylor draws a number of conclu-
sions, some of which are given in an abridged form below.
In using belting so as to obtain the greatest economy and tke most satis-
factory results, the following rules should be observed:
Oak Tanned
and Fulled
Leather Belts.
Other Types of
Leather Belts
and 6- to 7-ply
Rubber Belts.
A double belt, having an arc of contact of
180°, will give an effective pull on the face
of a pulley per inch of width of belt of
Or, a different form of same rule:
The number of sq.-ft. of double Belt passing
around a pulley per minute required to
transmit one horse-power is
35 Ibs.
80 sq. ft.
30 Ibs.
90 sq ft.
Or : The number of lineal feet of double-
belting 1 in. wide passing around a pulley
per minute required to transmit one horse-
power is
950 ft.
1100 ft.
Or : A double belt 6 in. wide, running 4000 to
5000 ft. per min., will transmit
30 H.P.
25 H.P.
The terms "initial tension," "effective pull," etc., are thus explained by
Mr. Taylor : When pulleys upon which belts are tightened are at rest, both
strands of the belt (the upper and lower) are under the same stress per in
of width. By " tension," " initial tension," or " tension while at rest,11 we
TAYLOR'S RULES FOR BELTING. 881
mean the stress per in. of width, or sq. in. of section, to which one of the
Strands of the belt is tightened, when at rest. After the belts are in motion
and transmitting power, the stress on the slack side, or strand, of the belt
becomes less, while that on the tight side— or the side which does the pull-
ing—becomes greater than when the belt was at rest. By the term " total
load " we mean the total stress per in. of width, or sq. in. of section, on the
tight side of belt while in motion.
The difference between the stress on the tight side of the belt and its slack
Ride, while in motion, represents the effective force or pull which is trans-
mitted from one pulley to another. By the terms "working load,1' " net
working load,11 or "effective pull," we mean the difference in the tension
of the tight and slack sides of the belt per in. of width, or sq. in. section,
while in motion, or the net effective force that is transmitted from one pul-
ley to another per in. of width or sq. in. of section.
The discovery of Messrs. Lewis and Bancroft (Trans. A. S. M. E., vii. 749)
that the "sum of the tension on both sides of the belt does not remain
constant," upsets all previous theoretical belting formulae.
The belt speed for maximum economy should be from 4000 to 4500 ft. per
minute.
The best distance from centre to centre of shafts is from 20 to 25 ft.
Idler pulleys work most satisfactorily when located on the slack side of
the belt about one quarter wa3^ from the driving-pulley.
Belts are more durable and work more satisfactorily made narrow and
thick, rather than wide and thin.
It is safe and advisable to use: a double belt on a pulley 12 in. diameter or
larger; a triple belt on a pulley 20 in. diameter or larger; a quadruple belt
on a pulley 30 in. diameter or larger.
As belts increase in width they should also be made thicker.
The ends of the belt should be fasteneu together by splicing and cement-
ing, instead of lacing, wiring, or using hooks or clamps of any kind.
A V-splice should be used on triple and quadruple belts and when idlers
are used. Stepped splice, coated with rubber and vulcanized in place, is best
for rubber belts.
For double belting the rule works well of making the splice for all belts
up to 10 in. wide, 10 in. long; from 10 in. to 18 in. wide the splice should be
the same width as the belt, 18 in. being the greatest length of splice required
for double belting.
Belts should be cleaned and greased every five to six months.
Double leather belts will last well when repeatedly tightened under a
Btrain (when at rest) of 71 Ibs. per in. of width, or 240 Ibs per sq. in. section.
They will not maintain this tension for any length of time, however.
Belt-clamps having spring-balances between the two pairs of clamps
should be used for weighing the tension of the belt accurately each time it
is tightened.
The stretch, durability, cost of maintenance, etc., of belts proportioned
(A) according to the ordinary rules of a total load of 111 Ibs. per inch of
width corresponding to an effective pull of 65 Ibs. per inch of width, and (B)
according to a more economical rule of a total load of 54 Ibs., corresponding
to an effective pull of 26 Ibs. per inch of width, are found to be as follows:
When it is impracticable to accurately weigh the tension of a belt in tight-
ening it, it is safe to shorten a double belt one half inch for every 10 ft. of
length for (A) and one inch for every 10 ft. for (B), if it requires tightening.
Double leather belts, when treated with great care and run night and day
at moderate speed, should last for 7 years (A); 18 years (B).
The cost of all labor and materials used in the maintenance and repairs of
double belts, added to the cost of renewals as they give out, through a term
of years, will amount on an average per year to 3?# of the original cost of
the belts (A); 14* or less (B).
In figuring the total expense of belting, and the manufacturing cost
chargeable to this account, by far the largest item is the time lost on the
machines while belts are being relaced and repaired.
The total stretch of leather belting exceeds 6# of the original length.
The stretch during the first six months of the life of belts is 36# of their
entire stretch (A); 15# (B).
A double belt will stretch 47/100 of 1% of its length before requiring to be
tightened (A); 81/100 of \% (B).
The most important consideration in making up tables and rules for the
use and care of belting is how to secure the minimum of interruptions to
manufacture from this source.
888 BELTING.
The average double belt (A), when running night and day in a machine-
shop, will cause at least 26 interruptions to manufacture during its life, or 5
interruptions per year, but with (B) interruptions to manufacture will not
average ofteuer for each belt than one in sixteen months.
The oak-tanned and fulled belts showed themselves to be superior in all
respects except the coefficient of friction to either the oak-tanned^not fulled,
the semi-raw-hide, or raw-hide with tanned face.
Belts of any width can be successfully shifted backward and forward on
tight and loose pulleys. Belts running between 5000 and 6000 ft. per min.
and driving 300 H.P. are now being daily shifted on tight and loose pulleys,
to throw lines of shafting in and out of use.
The best form of belt-shifter for wide belts is a pair of rollers twice the
width of belt, either of which can be pressed onto the flat surf ace of the
belt on its slack side close to the driven pulley, the axis of the roller making
an angle of 75° with the centre line of the belt.
writers. A very commonly used rule is, one horse-power may be transmitted
by a single belt 1 in. wide running x ft. per min., substituting for x various
values, according to the ideas of different engineers, ranging usually from
550 to 1100.
The practical mechanic of the old school is apt to swear by the figure
600 as being thoroughly reliable, while the modern engineer is more apt to
use the figure 1000. Mr. Taylor, however, instead of using a figure from 550
to 1100 for a single belt, uses 950 to 1100 for double belts. If we assume that
a, double belt is twice as strong, or will carry twice as much power, as a
single belt, then he uses a figure at least twice as large as that used in
modern practice, and would make the cost of belting for a given shop twice
as large as if the belting were proportioned according to the most liberal of
the customary rules.
This great difference is to some extent explained by the fact that the
problem which Mr. Taylor undertakes to solve is quite a different one from
that which is solved by the ordinary rules with their variations. The prob-
lem of the latter generally is, •* How wide a belt must be used, or how nar-
row a belt may be used, to transmit a given horse-power ?" Mr. Taylor's
problem is: " How wide a belt must be used so that a given horse-power
may be transmitted with the minimum cost for belt repairs, the longest life
to the belt, and the smallest loss and inconvenience from stopping the
machine while the belt is being tightened or repaired ?'*
The difference between the old practical mechanic's rule of a l-in.-wide
single belt, 600 ft. per min., transmits one horse-power, and the rule com-
monly used by engineers, in which 1000 is substituted for 600, is due to the
belief of the engineers, not that a horse-power could not be transmitted by
the belt proportioned by the older rule, but that such a proportion involved
undue strain from overtightening to prevent slipping, which strain entailed
too much journal friction, necessitated frequent tightening, arid decreased
the length of the life of the belt.
Mr. Taylor's rule substituting 1100 ft. per min. and doubling the belt is a
further step, and a long one, in the same direction. Whether it will be taken
in any case by engineers will depend upon whether they appreciate the ex-
tent of the losses due to slippage of belts slackened by use under overstrain,
and the loss of time in tightening and repairing belts, to such a degree as to
induce them to allow the first cost of the belts to be doubled in order to
avoid these losses.
It should be noted that Mr. Taylor's experiments were made on rather
narrow belts, used for transmitting power from shafting to machinery, and
his conclusions may not be applicable to heavy and wide belts, such aa
engine fly-wheel belts.
MISCELLANEOUS NOTES ON BELTING.
Formulae are useful for proportioning belts and pulleys, but they furnish
no means of estimating how much power a particular belt may be trans-
mitting at any given time, any inore than the size of the engine is a measure
of the load it is actually drawing, or the known strength of a horse is a
measure of the load on the wagon. The only reliable means of determining
the power actually transmitted is some form of dynamometer. (See Trans.
A. S. M. E., vol. x'ii. p. 707.)
MISCELLANEOUS NOTES ON BELTING. 883
If we Increase the thickness, the power transmitted ought to increase in
proportion; and for double belts we should have half the width required for
a single belt under the same conditions. With large pulleys and moderate
velocities of belt it is probable that this holds good. With small pulleys,
however, when a double belt is used, there is not such perfect contact
between the pulley-face and the belt, due to the rigidity of the latter, and
more work is necessary to bend the belt-fibres than when a thinner and
more pliable belt is used. The centrifugal force tending to throw the belt
from the pulley also increases with the thickness, and for these reasons the
width of a double belt required to transmit a given horse-power when used
with small pulleys is generally assumed not less than seven tenths the
width of a single belt to transmit the same power. (Flather on " Dynamom-
eters and Measurement of Power.1")
F. W. Taylor, however, finds that great pliability is objectionable, and
favors thick belts even for small pulleys: The power consumed in bending
the belt around the pulley he considers inappreciable. According to Kan-
kine's formula for centrifugal tension, this tension is proportional to the
sectional area of the belt, and hence it does not increase with increase of
thickness when the width is decreased in the same proportion, the sectional
area remaining constant.
Scott A. Smith (Trans. A. S. M. E., x. 765) says: The best belts are made
from all oak-tanned leather, and curried with the use of cod oil and tallow,
all to be of superior quality. Such belts have continued in use thirty to
forty years when used as simple driving-belts, driving a proper amount of
power, and having had suitable care. The flesh side should not be run to
the pulley-face, for the reason that the wear from contact with the pulley-
should come on the grain side, as that surface of the belt is much weaker
in its tensile strength than the flesh side; also as the grain is hard it is more
enduring for the wear of attrition; further, if the grain is actually worn off,
then the belt may not suffer in its integrity from a ready tendency of the
hard grain side to crack.
The most intimate contact of a belt with a pulley comes, first, in the
smoothness of a pulley-face, including freedom from ridges and hollows left
by turning-tools; second, in the smoothness of the surface and evenness in
the texture or body of a belt; third, in having the crown of the driving and re-
ceiving pulleys exactly alike,— as nearly so as is practicable in a commercial
sense; fourth, in having the crown of pulleys not over %" for a 24" face, that
is to say, that the pulley is not to be over J4" larger in diameter in its centre;
fifth, in having the crown other than two planes meeting at the centre;
sixth, the use of any material on or in a belt, in addition to those necessarily
used in the currying process, to keep them pliable or increase their tractive
quality, should wholly depend upon the exigencies arising in the use of
belts; non-use is safer than over-use; seventh, with reference to the lacing
of belts, it seems to be a good practice to cut the ends to a convex shape by
using a former, so that there may be a nearly uniform stress on the lacing
through the centre as compared with the edges. For a belt 10" wide, the
centre of each end should recede 1/10".
Lacing of Belts.— In punching a belt for lacing, use an oval punch,
the longer diameter of the punch being parallel with the sides of the belt.
Punch two rows of holes in each end, placed zigzag. In a 8-in. belt there
should be four holes in each end— two in each row. In a 6-inch belt, seven
holes— four in the row nearest the end. A 10-inch belt should hare nine
holes. The edge of the holes should not come nearer than % of an inch from
the sides, nor % of an inch from the ends of the belt. The second row should
be at least 1% inches from the end. On wide belts these distances should
be even a little greater.
Begin to lace in the centre of the belt and take care to keep the ends
exactly in line, and to lace both sides with equal tightness. The lacing
should not be crossed on the side of the belt that runs next the pulley. In
taking up belts, observe the same rules as putting on new ones.
Setting a Belt on Quarter-twist.— A belt must run squarely on to
tne pulley. To connect With a belt two horizontal shafts at right angles
with each other, say an engine-shaft near the floor with a line attached to
the ceiling, will require a quarter-turn. First, ascertain the central point
on the face of each pulley at the extremity of the horizontal diameter where
the belt will leave the pulley, and then set that point on the driven pulley
plumb over the corresponding point on the driver. This will cause the belt
to run squarely on to each pulley, and it will leave at an angle greater or
less, according to the size of the pulleys and their distance from each other.
884 BELTING.
In quarter-twist belt*, In order that the belt may remain on the pulleys,
the central plane on each pulley must pass through the point of delivery of
the other pulley. This arrangement does not admit of reversed motion.
To find the Length of Belt required for two given
Pulleys. — When the length cannot be measured directly by a tape-line,
ihe following approximate rule may be used : Add the diameter of the two
pulleys together, divide the sum by 2, and multiply the quotient by 3^, and
add the product to twice the distance between the centres of the shafts.
(See accurate formula below.)
To find the Angle of the Arc of Contact of a Belt.— Divide
the difference between the radii of the two pulleys in inches by the distance
between their centres, also in inches, and in a table of natural sines find the
angle most nearly corresponding with the quotient. Multiply this angle by
2, and add the product to 180° for the angle of contact with the larger
pulley, or subtract it from 180° for the smaller pulley.
Or, let R = radius of larger pulley, r = radius of smaller;
i = distance between centres of the pulleys;
a = angle whose sine is (R — r) -*- L.
Arc of contact with smaller pulley = 180° — 2a;
' larger pulley = 180° -f 2a.
To find the Length of Belt in Contact with the Pulley.—
For the larger pulley, multiply the angle a, found as above, by .0349, to the
product add 3.1416, and multiply the sum by the radius of the pulley. Or
length of belt in contact with the pulley
= radius X (IT -f .0349a) = radius X w(l + j^).
For the smaller pulley, length = radius X (7r-.0349a)= radius X w(l - ^) •
The above rules refer to Open Belts. The accurate formula for length
of an open belt is,
Length =: irtf(l -f ^) + wr(l -^) +2L cos <*
= R(ir -f .0349a) -f- r(v - .0349a) -f- 2L cos a,
in which R = radius of larger pulley, ?• = radius of smaller pulley,
L = distance between centres of pulleys, and a = angle whose sine is
(R- r) + L; cos a = VL* - (R - r)a -*- L.
.For Crossed Belts the formula is
Length of belt = irfl(l + ~Q) + *r(l + ^) + 2L cos 0,
= (R + r) X (w -f .0349/3) -f 2L cos /3,
in which /5 = angle whose sine is (R -f- r) -*- L ; cos j3 = \/L? — (R -f *')2 •*• £•
To find the Length of Belt when Closely Rolled. -The sum
of the diameter of the roll, and of the eye in inches, X the number of turrit
made by the belt and by .1309, = length of the belt in feet
To find the Apprpximate Weight of Belts —Multiply the
length of belt, in feet, by the width in inches, and divide the product by 13
for single, and 8 for double belt.
Relations of the Size and Speeds of Driving and Driven
Pulleys. — The driving pulley is called the driver, D, and the driven pulley
the driven, rt. If the number of teeth in gears is used instead of diameter, m
these calculations, number of teeth must be substituted wherever diametol
occurs. R = revs, per min. of driver, r = revs, per min. of driven.
D = dr -*- R;
^Diam. of driver = diam. of driven x revs, of driven -*- revs, of driver.
d = DR -*- r;
Diam. of driven = diam. of driver x revs, of driver -*- revs, of driven.
R= drn-D;
Revs, of driver = revs, of driven x diam. of driven •*• diam. of driver.
•
MISCELLANEOUS NOTES ON BELTING.
885
r = DR -f- d\
Revs, of driven = revs, of driver x diam. of driver -*- diam. of driven.
Evils of Tight Belts. (Jones and Laughlins.)— Clamps with powerful
screws are often used to put on belts with extreme tightness, and with most
injurious strain upon the leather. They should be very judiciously used for
horizontal belts, which should be allowed sufficient slackness to move with a
loose undulating vibration on the returning side, as a test that they have no
more strain imposed than is necessary simply to transmit the power.
On this subject a New England cotton-mill engineer of large experience,
says: I believe that three quarters of the trouble experienced in broken pul-
leys, hot boxes, etc., can be traced to the fault of tight belts. The enormous
and useless pressure thus put upon pulleys must in time break them, if tfiey
are made in any reasonable proportions, besides wearing out the whole out-
fit, and causing heating and consequent destruction of the bearings. Below
are some figures showing the power it takes in average modern mills with
first-class shafting, to drive the shafting alone :
'Whrklck
Shafting Alone.
'WVi/"\lck
Shafting Alone.
Mill,
No.
Load,
H.P.
Horse-
power.
Per cent
of whole.
Mill,
No.
Load,
H.P.
Horse-
power.
Per cent
of whole.
1
199
51
25.6
5
759
172.6
22.7
2
472
111.5
23.6
6
235
84.8
36.1
3
486
134
27.5
7
670
262.9
39.2
4
677
190
28.1
8
677
182
26.8
These may be taken as a fair showing of the power that is required in
many of our best mills to drive shafting. It is unreasonable to think that all
-that power is consumed by a legitimate amount of friction of bearings
and belts. I know of no cause for such a loss of power but tight belts. These,
when there are hundreds or thousands in a mill, easily multiply the friction
on the bearings, and would account for the figures.
Sag oi" Belts.— In the location of shafts that are to be connected with
each other by belts, care should be taken to secure a proper distance one
from the other. This distance should be such as to allow of a gentle sag to
the belt when in motion.
A general rule may be stated thus: Where narrow belts are to be run over
small pulleys 15 feet is a good average, the belt having a sag of l^to 2 inches.
For larger belts, working on larger pulleys, a distance of 20 to 25 feet does
well, with a sag of 2^ to 4 inches.
For main belts working on very large pulleys, the distance should be 25 to
30 feet, the belts working well with a sag of 4 to 5 inches.
If too great a distance is attempted,the belt will have an unsteady flapping
motion, which will destroy both the belt and machinery.
Arrangement of Belts and Pulleys.— If possible to avoid it, con-
nected shafts should never be placed one directly over the other, as in such
case the belt must be kept very tight to do the work. For this purpose belts
should be carefully selected of well-stretched leather.
It is desirable that the angle of the belt with the floor should not exceed
45°. It is also desirable to locate the shafting and machinery so that belts
should run off from each shaft in opposite directions, as this arrangement
will relieve the bearings from the friction that would result when the belts all
pull one way on the shaft.
In arranging the belts leading from the main line of shafting to the
counters, those pulling in an opposite direction should be placed as near
each other as practicable, while those pulling in the same direction should be
separated. This can often be accomplished by changing the relative posi-
tions of the pulleys on the counters. By this procedure much of the friction
on the journals may be avoided.
If possible, machinery should be so placed that the direction of the belt
motion shall be from the top of the driving to the top of the driven pulley,
when the sag will increase the arc of contact.
The pulley should be a little wider than the belt required for the work.
886 BELTING.
The motion of driving should run with and not against the laps of the belts.
Tightening or guide pulleys should be applied to the slack side of belts and
near the smaller pulley.
Jones & Laughlins, in their Useful Information, say: The diameter of the
pulleys should be as large as can be admitted, provided they will not pro-
duce a speed of more than 4750 feet of belt motion per minute.
They also say: It is better to gear a mill with small pulleys and run them
at a high velocity, than with large pulleys and to run them slower. A mill
thus geared costs less and has a much neater appearance than with large
heavy pulleys.
M. Arthur Achard (Proc. Inst. M. E., Jan. 1881, p. 62) says: When the belt
is wide a partial vacuum is formed between the belt and the pulley at &
high velocity. The pressure is the~ greater than that computed from the
tensions in the belt, and th3 resistance to slipping is greater. This has the
advantage of permitting a greater power to be transmitted by a given belt,
and of diminishing the strain on the shafting.
On the other hand, some writers claim that the belt entraps air between
itself and the pulley, which tends to diminish the friction, and reduce the
tractive force. On this theory some manufacturers perforate the belt with
numerous holes to let the air escape.
Care of Belts.— Leather belts should be well protected against water,
loose stearn, and all other moisture, with which they should not come in con-
tact. But where such conditions prevail fairly good results are obtained by
using a special dressing prepared for the purpose of water-proofing leather,
though a positive water-proofing material has not yet been discovered.
Belts made of coarse, loose-fibred leather will do better service in dry and
warm places, but if damp or moist conditions exist then the very finest and
firmest leather should be used. (Fayerweather & Ladew.)
Do not allow oil to drip upon the belts. It destroys the life of the leather.
Leather belting cannot safely stand above 11C° of heat.
Strength of Belting.— The ultimate tensile strength of belting does
not generally enter as a factor in calculations of power transmission.
The strength of the solid leather in belts is from 2000 to 5000 Ibs. per square
inch; at the lacings, even if well put together, only about 1000 to 1500. If
riveted, the joint should have half the strength of the solid belt. The work-
ing strain on the driving side is generally taken at not over one third of the
strength of the lacing, or from one eighth to one sixteenth of the strength
of the solid belt. Dr. Hartig found that the tension in practice varied from
80 to 532 Ibs. per square inch, averaging: 273 Ibs.
Adhesion Independent of Diameter. (Schultz Belting Co.)—
1. The adhesion of the belt to the pulley is the same — the arc or number of
degrees of contact, aggregate tension or wreight being the same— without
reference to width of belt or diameter of pulley.
2. A belt will slip just as readily on a pulley four feet in diameter as it will
on a pulley two feet in diameter, provided the conditions of the faces of the
pulleys, the arc of contact, the tension, and the number of feet the belt
travels per minute are the same in both cases.
3. To obtain a greater amount of power from belts the pulleys may be
covered with leather; this will allow the belts to run very slack and give 25#
more durability.
Endless Belts,— If the belts are to be endless, they should be put on
and drawn together by *' belt clamps " made for the purpose. If the belt is
made endless at the belt factory, it should never be run on to the pulleys, lest
the irregular strain spring the belt. Lift out one shaft, place the belt on the
pulleys, and force the shaft back into place.
Belt I>ata«— A fly-wheel at the Amoskeag Mfg. Co., Manchester, N. H.,
30 feet diameter, 110 inches face, running 61 revs, per min., carried two heavy
double-leather belts 40 inches wide each, and one 24 inches wide. The engine
indicated 1950 H.P., of which probably 1850 H.P. was transmitted by the
belts. The belts were considered to be heavily loaded, but not overtaxed.
(30 X 3.14 X 104 X 61) H- 1850 = 323 ft. per min. for 1 H.P. per inch 'of width.
Samuel Webber (Am. Mach., Feb. 22, 1894) reports a case of a belt 30
inches wide, % inch thick, running for six years at a velocity of 3900 feet per
minute, on to a pulley 5 feet diameter, and transmitting 556 H.P. This gives
a velocity of 210 feet per minute for 1 H.P. per inch of width. By Mr. Nagle's
table of riveted belts this belt would be designed for 332 H.P. By Mr. Taylor's
rule it would be used to transmit only 123 H.P0
The above may be taken as examples of what a belt may be made to do, but
they should not be used as precedents in designing. It is not stated how much
power was lost by the journal friction due to over-tightening of these belts.
TOOTHED-WHEEL GEARING. 887
Belt Dressings.— We advise that no belt dressing should be used ex-
cept when the belt becomes dry and husky, and in such instances we recom-
mend the use of a dressing. Where this is not used beef tallow at blood,
warm temperature should be applied and then dried in either by artificial
heat or the sun. The addition of beeswax to the tallow will be of some ser-
vice if the belts are used in wet or damp places. Our experience convinces
us that resin should never be used on leather belting. (Fayerweather &
Ladew.)
foot oil applied. Frequent applications of such oils to a new belt render the
leather soft and flabby, thus causing it to stretch, and making it liable to
run out of line. A composition of tallow and oil, with a little resin or bees-
wax, is better to use. Prepared castor-oil dressing is good, and may be
applied with a brush or rag while the belt is running. (Alexander Bros.)
Cement for Cloth or Leather. (Moles worth.)— 16 parts gutta-
percha, 4 india-rubber, 2 pitch, 1 shellac, 2 linseed-oil, cut small, melted to-
gether and well mixed.
Rubber Belting.— The advantages claimed for rubber belting are
perfect uniformity in width and thickness; it will endure a great degree of
heat and cold without injury; it is also specially adapted for use in damp or
wet places, or where exposed to the action of steam; it is very durable, and
has great tensile strength, and when adjusted for service it has the most per-
fect hold on the pulleys, hence is less liable to slip than leather.
Never use animal oil or grease on rubber belts, as it will greatly injure and
soon destroy them.
Rubber belts will be improved, and their durability increased, by putting
on with a painter's brush, and letting it dry, a composition made of equal
parts of red lead, black lead, French yellow, and litharge, mixed with boiled
linseed-oil and japan enough to make it dry quickly. The effect of this will
be to produce a finely polished surface. If, from dust or other cause, the
belt should slip, it should be lightly moistened on the side next the pulley
with boiled linseed-oil. (From circulars of manufacturers.)
The best conditions are large pulleys and high speeds, low tension and re-
duced width of belt. 4000 ft. per min. is not an excessive speed on proper
sized pulleys.
H.P. of a 4-ply rubber belt = (length of arc of contact on smaller pulley
in ft. X width of belt in ins. X revs, per min.) -*- 325. For a 5-ply belt mul-
tiply by 134 for a 6-ply by % fora 7-ply by 2, for an 8-ply by 2^. When
the proper weight of duck is used a 3- or 4-ply rubber belt is equal to a single
leather belt and a 5- or 6-ply rubber to a double leather belt. When the
arc of contact is 180°, H.P. of a 4-ply belt = width in ins. X velocity in ft.
per min. •*• 650. (Boston Belting Co.)
GEARING-.
TOOTHED- WHEEL GEARING*
Pitch, Pitch-circle, etc.— If two cylinders with parallel axes are
pressed together and one ot them is rotated on its axis, it will drive the other
by means of the friction between the surfaces. The cylinders may be con-
sidered as a pair of spur-wheels with an infinite number of very small teeth.
If actual teeth are formed upon the cylinders, making alternate elevations
and depressions in the cylindrical surfaces, the distance between the axes
remaining the same, we have a pair of gear-wheels which will drive one an-
other by pressure upon the faces of the teeth, if the teeth are properly
shaped. In making the teeth the cylindrical surface may entirely disap-
pear, but the position it occupied may still be considered as a cylindrical
surface, which is called the " pitch-surface," and its trace on the end of the
wheel, or on a plane cutting the wheel at right angles to its axis, is called
the " pitch-circle " or *' pitch-line." The diameter of this circle is called the
pitch -diameter, and the distance from the face of one tooth to the corre-
sponding face of the next tooth on the same wheel, measured on an arc of
the pitch-circle, is called the " pitch of the tooth," or the circular pitch.
If two wheels having teeth of the same pitch are geared together so that
their pitch-circles touch, it is a property of the pitch-circles that their diam-
eters are proportional to the number of teeth in the wheels, and vice vertaf
888
GEARING.
thus, if one wheel is twice the diameter (measured on the pitch-circle) of the
other, it has twice as many teeth. If the teeth are properly shaped the
linear velocity of the two wheels are equal, and the angular velocities, or
speeds of rotation, are inversely proportional to the number of teeth and to
the diameter. Thus the wheel that has twice as many teeth as the other
will revolve just half as many times in a minute.
The "pitch," or distance measured on an arc of the pitch-circle from the
face of one tooth to the face of the next, consists of two parts— the " thick-
ness" of the tooth and the "space" between it and the next tooth. The
space is larger than the thickness by a small amount called the "back-
lash," which is allowed for imperfections of workmanship. In finely cut
gears the backlash may be almost nothing.
The length of a tooth in the direc-
tion of the radius of the wheel is
called the "depth," and this is di-
vided into two parts: First, the
"addendum," the height of the tooth
above the pitch line; second, tlie
"dedendum," the depth below the
pitch line, which is an amount equal
to the addendum of the mating gear.
The depth of the space is usually
given a little "clearance" to allow
for inaccuracies of workmanship,
especially in cast gears.
Referring to Fig. 153, pi, pi are the
_ pitch-lines, al the addendum-line, rl
l?T/a <KO the root-line or dedendum-line, cl
the clearance-line, and b the back-
lash. The addendum and dedendum are usually made equal to each other.
. , ., , No. of teeth 3.1416
Diametral pitch =
Circular pitch^ =
diam. of pitch-circle in inches '
diam. X 3.1416 3.1416
circular pitch'
No. of teeth diametral pitch*
Some writers use the term diametral pitch to mean
circular pitch
3.1416 "
diam.
No. of teeth "
-, but the first definition is the more common and the more
convenient. A wheel of 12 in. diam. at the pitch-circle, with 48 teeth is 48/12
= 4 diametral pitch, or simply 4 pitch, The circular pitch of the same
, .. 12X3.1416 wor 3.1416
wheel is -^ = .7854, or — - — = .7854 in.
48 4
Relation of Diametral to Circular Pitch.
Diama-
tral
Pitch.
Circular
Pitch.
Diame-
tral
Pitch.
Circular
Pitch.
Circular
Pitch.
Diame-
tral
Pitch.
Circular
Pitch.
Diame-
tral
Pitch.
1
3. 142 in.
11
.286 in.
3
1.047
15/16
3.351
1^2
2.091
12
.262
2/^3
1.257
7k
3.590
2
1.571
14
.224
2
1.571
13/16
3.867
2*4
1.396
16
.196
1%
1.676
5*
4.189
gi^j
1.257
18
.175
1%
1.795
11/16
4.570
23^
1.142
20
.157
%
1.933
%
5.027
3
1.047
22
.143
l^>
2.094
9/16
5.585
3^3
.898
24
.131
7/16
2.185
^
6.283
4
.785
26
.121
2.285
7/16
7.181
5
.628
28
.112
5/16
2.394
8.378
6
.524
30
.105
2.513
5/16
10.053
7
.449
32
.098
3/16
2.646
M
12.566
8
.393
36
.087
Ys
2.793
3/16
16.755
9
.349
40
.079
1/16
2.957
i£
25.133
10
.314
I 48
.065
3.142
1/16
50.266
.. ,
S.nce c,rcular p,tch =
diam. X 3.1416
,.
duun. =
circ.
No ofteeth
which always brings out the diameter as a number w
pitch x No. of teeth
3.1416 -,
ith an inconvenient
TOOTHED-WHEEL GEARING.
889
fraction If the pitch is in even inches or simple fractions of an inch. By the
diametral-pitch system this inconvenience is avoided. The diameter may
be in even inches or convenient fractions, and the number of teeth is usually
an even multiple of the number of inches in the diameter.
Diameter of Pitch-line of Wheels from 10 to 100 Teeth
of 1 in. Circular Pitch.
.A
&l
1.2
^
Z 0)
la
el
Z o>
I.S
If
jfi
& o>
1.2
of
£ V
is
$
5
H
5
^H
5
P
j5
EH
S
H
5
10
3.183
26
8.276
41
13.051
56
17.825
71
22.600
86
27.375
11
3.501
27
8.594
42
13.369
57
18.144
72
22.918
87
27.693
12
3.820
28
8.913
43
13.687
58
18.462
73
23.286
88
28.011
13
4.138
29
9.231
44
14.006
59
18.781
74
23.555
89
28.329
14
4.456
30
9.549
45
14.324
60
19.099
75
23.873
90
28.648
15
4.775
31
9.868
46
14.642
61
19.417
76
24.192
91
28.966
16
5.093
32
10.186
47
14.961
62
19.735
77
24.510
92
29.285
17
5.411
33
10.504
48
15.279
63
20.054
78
24.828
93
29.603
18
5.730
34
10.823
49
15.597
64
20.372
79
25.146
94
29.921
lu
6.048
35
11.141
50
15.915
65
20.690
80
25.465
95
30.239
20
6.366
36
11.459
51
16.234
66
21.008
81
25.783
96
30.558
21
6.685
37
11.777
52
16.552
67
21.327
82
26.101
97
30.876
22
7.003
38
12.096
53
16.870
68
21.645
83
26.419
98
31.194
33
7.321
39
12.414
54
17.189
69
21.963
84
26.738
99
31.512
24
7.639
40
12.732
55
17.507
70
22.282
85
27.056
100
31.831
25
7.958
For diameter of wheels of any other pitch than 1 in., multiply the figures
in the table by the pitch. Given the diameter and the pitch, to find the num-
ber of teeth. Divide the diameter by the pitch, look in the table under
diameter for the figure nearest to the quotient, and the number of teeth will
be found opposite.
Proportions of Teeth. Circular Pitch = 1.
1.
2
3.
4.
5.
6.
.30
.35
'.65
!485
.515
.03
.65
Depth of tooth above pitch-line. . .
" '* below pitch-line...
.35
.40
70
.30
.40
.60
.70
.10
.45
.55
.10
.37
.43
.73
.80
.07
.47
.53
.06
.47
.33
!66
.75
!45
.55
.10
.45
.30
.40
!70
.'475
.525
.05
.70
Total depth of tooth
.75
.05
.45
.54
.09
Clearance at root .
Thickness of tooth
Width of space
Backlash
7.
8.
9.
10.*
Depth of tooth above pitch-line. . .
<k •» ** below pitch-line...
Working depth of tooth
.25 to .33
.35 to .42
.30
.35+. 08"
.318
.369
.637
.687
.04 to .05
.48 to .5 |
.52 to .5 1
.0 to .04
1-r-P
1.157-r-P
2H-P
2.157-f-P
.157-r-P
1.51-^-Pto
1.57-h-P
1.57-r-PtO
1.63-*-P
0 to 0 6-^P
Total depth of tooth
.6 to .75
.65+. 08"
.48 to .485
.52 to .515
.04 to ,03
.48-. 03"
.52+. 03"
.04+. 06"
Width of space
Backlash
* In terms of diametral pitch.
AUTHORITIES.— 1. Sir Wm. Fairbairn. 2, 3. Clark, R. T. D.; "used by en-
gineers in good practice.11 4. Molesworth. 5, 6. Coleman Sellers : 5 for
cast, 6 for cut wheels. 7, 8. Unwin. 9, 10. Leading American manufacturers
of cut gears.
The Chordal Pitch (erroneously called "true pitch" by some
authors) is the length of a straight line or chord drawn from centre to
centre of two adjacent teeth. The term is now but little used.
890
GEARING.
Chordal pitch = diam. of pitch-circle X sine of ^ of teeth« Chordal
pitch of a wheel of 10 in. pitch diameter and 10 teeth, 'lO X sin 18° = 3.0902
in. Circular pitch of same wheel = 3.1416. Chordal pitch is used with chain
or sprocket wheels, to conform Co the pitch of the chain.
Formulas for Determining the Dimensions of Small Gears.
(Brown & Sharpe Mfg. Co.)
P = diametral pitch, or the number of teeth to one inch of diameter of
pitch- circle;
*
D — whole diaTTietftr » ...»T.
ILarger
jy — number of teeth .. .-...
Wheel.
These wheels
run
d' — diameter of pitch-circle
together.
d — whole diameter
Smaller
n — number of teeth
Wheel
a = distance between the centres of the two wheels;
b = number of teeth in both wheels;
t = thickness of tooth or cutter on pitch-circle;
s = addendum;
£>"= working depth of tooth;
/ = amount added to depth of tooth for rounding the corners and for
clearance;
D"4- f = whole depth of tooth;
* = 3.1416.
P' = circular pitch, or the distance from the centre of one tooth to the
centre of the next measured on the pitch-circle.
Formulae for a single wheel:
P tf+2.
D'
D
P
DXN .
0
D" 2'
1 P'
— ^1ftSP'»
P- D '
P ^'
IV+2 '
2V
P
IV « PD';
N = PD-
f ^.
~ P " 7T
D'
D
P- jy,
IT
-P'
2; S ~ N ~" J
« 1 / ^ f 4
t ^ § «>A(
F^P*
p=-^;
P '
f ~10'
<=^=
S-TJ — p\i
T-g0/"~'361
Formulae for a pair of wheels:
JV =
nv a
JVT.
v '
6v
PD>V
PD>V
JVF.
w *
wv
bV
The following
man Sellers. (
proportions of gear wheels are recommended by frof. Cole«
Indicator, April, 1892.)
TOOTHED-WHEEL GEARING.
891
Proportions of Gear-wheel*.
Inside of Pitch-line.
Width of Space.
Diametral
Pitch.
Circular
Pitch.
Outside of
Pitch-line.
PX.3
For Cast or
Cut Bevels
or for Cast
Spurs.
PX .4
For Cut
Spurs.
PX .35
For Cast
Spurs or
Bevels.
P X .525
For Cut
Bevels or
Spurs.
PX.51
Y±
.075
.100
.088
J31
.128
12
.2618
.079
.105
.092
.137
.134
10
.31416
.094
.126
.11
.165
.16
%
.113
.150
.131
.197
.191
8
.3927
.118
.157
.137
.206
.2
7
.4477
.134
.179
.157
.235
.228
Hi
.15
.20
.175
.263
.255
6
.5236
.157
.209
.183
.275
.267
9/16
.169
.225
.197
.295
.287
%
.188
.25
.219
.328
.319
5
.62832
.188
.251
.22
.33
.32
<K
.225
.3
.263
.394
.383
4
.7854
.236
.314
.275
.412
.401
%
.263
.35
.307
.459
.446
1
.3
.4
.35
.525
.51
3
1.0472
.314
.419
.364
.55
.534
1&
.338
.45
.394
.591
.574
2%
1.1424
.343
.457
.40
.6
.583
IN
.375
.5
.438
.656
.638
2H
1.25664
.377
.503
.44
.66
.641
1%
.413
.55
.481
.722
.701
ji^j
.45
.6
.525
.783
.765
2
1.5708
.471
.628
.55
.825
.801
1%
.525
.7
.613
.919
.893
2
.6
.8
.7
1.05
1.02
%
2.0944
.628
.838
.733
1.1
.068
2^4
.675
.9
.788
1.181
.148
2i2
.75
1.0
.875
1.313
.275
2%
.825
1.1
.963
1.444
.403
3
.9
1.2
1.05
1.575
.53
1
3.1416
.942
1,257
1.1
1.649
.602
3H
.975
1.3
1.138
1.706
.657
3^
1.05
1.4
1.225
1.838
.785
Thickness of rim below root = depth of tooth.
Width of Teeth.— The width of the faces of teeth is generally made
from 2 to 3 times the circular pitch — from 6.28 to 9.42 divided by the diam-
etral pitch. There is no standard rule for width.
The following sizes are given in a stock list of cut gears in " Grant's
Gears: "
6
WA and 2
Diameter pitch 3
Face, inches 3 and 4 2j
The Walker Company give:
Circular pitch, in. .
Face, in 1*4
8 12 16
and 1^ % and 1 ^ and %
Rules for Calculating the Speed of Gears and Pulleys.—
The relations of the size and speed of driving and driven gear wheels are
the same as those of belt pulleys. In calculating for gears, multiply or
divide by the "diameter of the pitch-circle or by the number of teeth, as
may be required. In calculating for pulleys, multiply or divide by their
diameter in inches.
If D = diam. of driving wheel, d = diam. of driven, R = revolutions per
minute of driver, r — revs, per min. of driven.
R = rd -*- D; r — RL > -*- d\ D = dr •+- R' d — DR -f- r.
If N = number of teeth of driver and n — number of teeth of driven,
2V =s nr •+• R\ n = NR -*•?•; R =s rn -t- N\ r = RN-*~ n.
892 GEARING.
' To find the number of revolutions of the last wheel at the end of a train
of spur-wheels, all of which are in a line and mesh into one another, when
the revolutions of the first wheel and the number of teeth or the diameter
of the tirst and last are given: Multiply the revolutions of the first wheel by
its number of teeth or its diameter, and divide the product by the number
, of teeth or the diameter of the last wheel.
"•* To find the number of teeth in each wheel for a train of spur-wheels,
each to have a given velocity: Multiply the number of revolutions of the
driving-wheel by its number of teeth, and divide the product by the number
of revolutions each wheel is to make.
To find the number of revolutions of the last wheel in a train of wheels
and pinions, when the revolutions of the first or driver, and the diameter,
the teeth, or the circumference of all the drivers and pinions are given:
Multiply the diameter, the circumference, or the number of teeth of all the
driving-wheels together, and this continued product by the number of revo-
lutions of the first wheel, and divide this product by the continued product
of the diameter, the circumference, or the number of teeth of all the driven
wheels, and the quotient will be the number of revolutions of the last wheel.
EXAMPLE. — 1. A train of wheels consists of four wheels each 12 in. diameter
of pitch-circle, and three pinions 4, 4, and 3 in. diameter. The large wheels
are the drivers, and the first makes 36 revs, per min. Required the speed
of the last wheel.
2. What is the speed of the first large wheel if the pinions are the drivers,
the 3-in. pinion being the first driver and making 36 revs, per min. ?
Milling Cutters for Interchangeable Gears.— The Pratt &
Whitney Co. make a series of cutters for cutting epicycloidal teeth. The
number of cutters to cut from a pinion of 12 teeth to a rack is 24 for each
pitch coarser than 10. The Brown & Sharpe Mfg. Co. make a similar series,
and also a series for involute teeth, in which eight cutters are made for
each pitch, as follows:
No ............. 1. 2. 3. 4. 5. 6. 7. 8.
Will cut from 135 55 35 26 21 17 14 12
to Rack 134 54 34 25 20 16 13
FORMS OF THE TEETH.
In order that the teeth of wheels and pinions may run together smoothly
and with a constant relative velocity, it is necessary that their working
faces shall be formed of certain curves called odontoids. The essential
property of these curves is that when two teeth are in contact the common
normal to the tooth curves at their point of contact must pass through the
pitch-point, or point of contact of the two pitch-circles. Two such curves
are in common use — the cyloid and the involute.
The Cycloidal Tooth.— In Fig. 154 let PL andpZ be the pitch-circles
of two gear-wheels; GO and yc are two equal generating-circles, whose radii
should be taken as not greater than one half of the radius of the smaller
pitch-circle. If the circle gc be rolled to the left on the larger pitch-circle
PL, the point O will describe an epicycloid, oefgh. If the other generating-
circle GC be rolled to the right on PL, the point 0 will describe a hypocy-
cloid oabcd. These two curves, which are tangent at O, form the two parts
of a tooth curve for a gear whose pitch-circle is PL. The upper part oh is
called the face and the lower part od is called the flank, If the same circles
be rolled on the other pitch-circle p£, they will describe the curve for a tooth
of the gear pi, which will work properly with the tooth on PL.
The cycloidal curves may be drawn without actually rolling the generat-
ing-circle, as follows: On the line PL, from O, step off and mark equal dis-
tances, as 1, 2, 3, 4, etc. From 1, 2, 3, etc., draw radial lines toward the centre
of PL, and from 6, 7, 8, etc., draw radial lines from the same centre, but be-
yond PL. With the radius of the generating-circle, and with centres suc-
cessively placed on these radial lines, draw arcs of circles tangent to PL at
1 2 3, 6 7 8, etc. With the dividers set to one of the equal divisions, as O14
FORMS OF THE TEETH.
893
step off la and 6e; step off two such divisions on the circle from 2 to b, and
from 7 to/; three such divisions from 3 to c, and from 8 to g\ and so on, thus
locating the several points abcdH and efgk, and through these points draw
the tooth curves.
The curves for the mating tooth on the other wheel may be found in like
manner by drawing arcs of the generating-circle tangent at equidistant
points on the pitch-circle pi.
The tooth curve of the face oh is limited by the addendum-line r or rlt
FIG. 154.?
and that of the flank oH by the root curve R or JF?t. E and r represent the
root and addendum curves for a large number of small teeth, and R^r the
like curves for a small number of large teeth. The form or appearance of
the tooth therefore varies according to the number of teeth, while the pitch
circle and the generating-circle may remain the same.
In the cycloidal system, in order that a set of wheels of different diam-
eters but equal pitches shall all correctly work together, it is necessary that
the generating-circle used for the teeth of all the wheels shall be the same,
and it should have a diameter not grea ter than half the diameter of the pitch-
line of the smallest wheel of the set. The customary standard size of the
generating-circle of the cycloidal system is one having a diameter equal to
the radius of the pitch-circle of a wheel having 12 teeth. (Some gear-
makers adopt 15 teeth.) This circle gives a radial flank to the teeth of a
wheel having 12 teeth. A pinion of 10 or even a smaller number of teeth
can be made, but in that case the flanks will be undercut, and the tooth will
not be as strong as a tooth with radial flanks. If in any case the describing
circle be half the size of the pitch-circle, the flanks will be radial; if it be
less, they will spread out toward the root of the tooth, giving a stronger
form; but if greater, the flanks will curve in toward each other, whereby the
teeth become weaker and difficult to make.
In some cases cycloidal teeth for a pair of gears are made with the gener-
ating-circle of each gear,Qiaving a radius equal to half the radius of its pitch-
circle. In this case each of the gears will have radial flanks. This method
makes a smooth working gear, but a disadvantage is that the wheels are
not interchangeable with other wheels of the same pitch but different num-
bers of teeth.
394
GEARIKQ.
The racK in the cycloidal system is equivalent to a wheel with an infinite
number of teeth. The pitch is equal to the circular pitch of the mating
gear. Both faces and flanks are cycloids formed by rolling the generating-
circle of the mating gear-wheel on each side of the straight pitch-line of
the rack.
FIG. 155,
Another method of drawing the cycloidal curves is shown in Fig. 155. It
is known as the method of tangent arcs. The generating-circles, as before,
are drawn with equal radii, the length of the radius being less than half the
radius of pi, the smaller pitch-circle. Equal divisions 1, 2, 3, 4, etc., are
marked off on the pitch circles and divisions of the same length stepped off
on one of the generating-circles, as oabc, etc. From the points 1, 2, 3, 4, 5 on
the line po, with radii successively equal to the chord distances oa, ob, oc,
od, oe, draw the five small arcs F. A line drawn through the outer edges of
these small arcs, tangent to them all, will be the hypocycloidal curve for the
flank of a tooth below the pitch-line pi. From the points 1, 2, 3, etc., on the
line ol, with radii as before, draw the small arcs G. A line tangent to these
arcs will be the epicycloid for the face of the same tooth for which the flank
curve has already been drawn. In the same way, from centres on the line
P0, and oL, with the same radii, the tangent arcs J7 and K may be drawn,
which will give the tooth for the gear whose pitch-circle is PL.
If the generating-circle had a radius just one half of tlu radius of pi, the
bypocycloid F —Id be a straight line, and the flank of the tooth would
have been radial.
Tlie Involute Tooth.— In drawing the involute tooth curve, the
angle of obliquity, or the angle which a common tangent to the teeth, when
they are in contact at the pitch-point, makwj with a line joining the centres
of the wheels, is first arbitrarily determined. It is customary to take it at 15°.
The pitch-lines pi and PL being drawn in contact at O, the line of obliquity
AB is drawn through O normal to a common tangent to the tooth curves, or
at the given angle of obliquity to a common tangent to the pitch-circles. In
PORMS OF THE TEETH.
895
the cut the angle is 20°. From the centres of the pitch-circles draw circles c
and d tangent to the line AB. These circles are called base-lines or base-
circles, from which the involutes F and K are drawn. By laying off conven-
ient distances, 0, 1,2, 3, which should each be less than 1/10 of the diameter
of the base-circle, small arcs can be drawn with successively increasing
radii, which will form the involute. The involute extends from the points F
FIG. 156.
and K down to their respective base-circles, where a tangent to the invo-
lute becomes a radius of the circle, and the remainders of the tooth curves,
as G and .H, are radial straight lines.
In the involute system the customary standard form of tooth is one
having an angle of obliquity of 15° (Brown and Sharpe use 14J/a°), an adden-
dum of about one third the circular pitch, and a clearance of about one
eighth of the addendum. In this system the smallest gear of a set has 12
teeth, this being the smallest number of teeth that will gear together when
made with this angle of obliquity. In gears with less than 30 teeth the
points of the teeth must be slightly rounded over to avoid interference (see
Grant's Teeth of Gears). All involute teeth of the same pitch and with the
same angle of obliquity work smoothly together. The rack to gear with an
involute-toothed wheel has straight faces on its teeth, which make an angle
with the middle line of the tooth equal to the angle of obliquity, or in the
standard form the faces are inclined at an angle of 30° with each other.
To draw the teeth of a rack which is to gear with an involute wheel (Fig.
157).— Let AB be the pitch-line of the rack and AI=H'=thQ pitch. Through
FIG. 157.
the pitch-point /draw EF at the given angle of obliquity. Draw AE and
I'F perpendicular to EF. Through E and F draw lines EGG' and FH par-
allel to the pitch-line. EGG' will be the addendum-line and H^the flank-
line. From /draw IK perpendicular to AB equal to the greatest addendum
in the set of wheels of the given pitch and obliquity plus an allowance for
clearance equal to ^ of the addendum. Through K, parallel to AB, draw
the clearance-line. The fronts of the teeth are planes perpendicular to EF,
and the backs are planes inclined at the same angle to AB in the contrary
direction. The outer half of the working face AE may be slightly curved.
Mr. Grant makes it a circular arc drawn from a centre on the pitch-line
GEARING.
with a radius = 2.* inches divided by the diametral pitch, or .67 in. x cir«
cular pitch.
To Draw an Angle of 15° without using a Protractor.— From C, on the
line AC, with radius AC, draw
an arc AB, and from A, with
the same radius, cut the arc at
B. Bisect the arc BA by draw-
ing small arcs at D from A and B
as centres, with the same radius,
which must be greater than one
half of AB. Join DC, cutting BA
at E. The angle EGA is 30°. Bi-
sect the arc AE in like manner,
arid the angle FCA will be 15°.
A property of involute-toothed
wheels is that the distance between
the axes of a pair of gears may be
altered to a considerable extent
without interfering with their ac-
tion. The backlash is therefore
variable at will, and may be ad-
FIG. 158.
justed by moving the wheels farther from or nearer to each other, and may
thus be adjusted so as to be no greater than is necessary to prevent jam-
ming of the teeth.
Tlie relative merits of cycloidal and involute-shaped teeth are still a sub-
ject of dispute, but there is an increasing tendency to adopt the involute
tooth for all purposes.
Clark (R. T. D., p. 734) says : Involute teeth have the disadvantage of
being too much inclined to the radial line, by which an undue pressure is
exerted on the bearings.
Unwin (Elements of Machine Design, 8th ed., p. 265) says : The obliquity
of action is ordinarily alleged as a serious objection to involute wheels. Its
importance has perhaps been overrated.
George B. 'Grant (Am. Much., Dec. 26, 1885) says :
1. The work done by the friction of an involute tooth xs always less than
the same work for any possible epicycloidal tooth.
2. With respect to work done by friction, a change of the base from a
gear of 12 teeth to one of 15 teeth makes an improvement for the epicycloid
of less than one half of one per cent.
3. For the 12-tooth system the involute has an advantage of 1 1/5 per
cent, and for the 15-tooth system an advantage of % per cent.
4. That a maximum improvement of about one per cent can be accom-
plished by the adoption of any possible non -interchangeable radial flank
tooth in preference to the 12-tooth interchangeable system.
5. That for gears of very few teeth the involute has a decided advantage.
6. That the common opinion among millwrights and the mechanical pub^
lie in general in favor of the epicycloid is a prejudice that is founded on
long-continued custom, and not on an intimate knowledge of the properties
of that curve.
Wilfred Lewis (Proc. Engrs. Club of Phila., vol. x., 1893) says a strong
reaction in favor of the involute system is in progress, and he believes that
an involute tooth of 22^° obliquity will finally supplant all other forms.
Approximation toy Circular Arcs. — Having found the form of
the actual tooth-curve on the drawing-board, circular arcs maybe found by
trial which will give approximations to the true curves, and these may be
FIG. 159.
FORMS OF THE TEETH.
897
used In completing the drawing and the pattern of the gear-wheels. The
root of the curve is connected to the clearance by a fillet, which should be
as large aspossible to give increased strength to the tooth, provided it is not
large enough to cause interference.
Molesworth gives the following method of construction by circular arcs :
From the radial line at the edge of the tooth on the pitch-line, lay off the
line f/lTat an angle of 75° with the radial line; on this line will be the cen-
tres of the root AB and the point EF. The lines struck from these centres
are shown in thick lines. Circles drawn through centres thus found will
give the lines in which the remaining centres will be. The radius DA for
striking the root AB is = pitch -f the thickness of the tooth. The radius
CE for striking the point of the tooth EF — the pitch.
George B. Grant says : It is sometimes attempted to construct the curve
by some handy method or empirical rule, but such methods are generally
worthless.
Stepped. Gears, - -Two gears of the same pitch and diameter mounted
side by side on the same shaft will act as a single gear. If one gear is keyed
on the shaft so that the teeth of the two wheels are not in line, but the
teeth of one wheel slightly in advance of the other, the two gears form a
stepped gear. If mated with a similar stepped gear on a parallel shaft the
number of teeth in contact will be twice as great as in an ordinary gear,
which will increase the strength of the gear and its smoothness of action.
Twisted Teeth.— If a great number of very thin gears were placed
together, one slightly in advance of the other, they would still act as a
stepped gear. Continuing the subdivision until the
flnickness of each separate gear is infinitesimal, the
aces of the teeth instead of being in steps take the
form of a spiral or twisted surface, and we have a
twisted gear. The twist may take any shape, and if it is
in one direction for half the width of the gear and in the
opposite direction for the other half, we have what is
known as the herring-bone or double helical tooth. The
obliquity of the twisted tooth if twisted in one direction
causes an end thrust on the shaft, but if the herring-
bone twist is used, the opposite obliquities neutralize
each other. This form of tooth is much used in heavy
rolling-mill practice, where great strength and resistance
to shocks are necessary. They are frequently made of
steel castings (Fig. 100). The angle of the tooth with a
line parallel to the axis of the gear is usually 30°.
Spiral Gears.— If a twisted gear has a uniform twist it becomes a
spiral gear. The line in which the pitch-surface intersects the face of the
tooth is part of a helix drawn on the pitch-surface. A spiral wheel may be
made with only one helical tooth wrapped around the cylinder several
times, in which it becomes a screw or worm. If it has two or three teeth
so wrapped, it is a double- or triple-threaded screw or worm. A spiral -gear
meshing into a rack is used to drive the table of some forms of planing-
machine.
Worna-gearlng.— When the axes of two spiral gears are at right
' angles, and a wheel of one, two, or three threads works with a larger wheel
of many threads, it becomes a worm-gear, or endless screw, the smaller
Fio. 161.
wheel or driver being called the worm, and the larger, or driven wheel, the
worm-wheel. With this arrangement a high velocity ratio may be obtained
with a single pair of wheels. For a one-threaded wheel the velocity ratio is
898
GEARING.
the number of teeth in the worm- wheel. The worm and wheel are com-
monly so constructed that the worm will drive the wheel, but the wheel will
not drive the worm.
To find the diameter of a worm-wheel at the throat, number of teeth and
pitch of the worm being given: Add 2 to the number of teeth, multiply the
sum by 0.3183, and by the pitch of the worm in inches.
To find the number of teeth, diameter at throat and pitch of worm being
given: Divide 3.1416 times the diameter by the pitch, and subtract 2 from
the quotient.
In Fig. 161 ab is the diam. of the pitch-circle, cd is the diam. at the throat.
EXAMPLE.— Pitch of worm y± in., number of teeth 70, required the diam.
at the throat. (70 f 2) X .3183 X .25 = 5.73 in.
Teetli of Bevel- wheels* (Rarikine's Machinery and Millwork.)^
The teeth of a bevel -wheel have acting surfaces of the conical kind, gen-
erated by the motion of a line traversing the apex of the conical pitch-
surface, while a point in it is carried round the traces of the teeth upon a
spherical surface described about that apex.
The operations of drawing the traces of the teeth of bevel-wheels exactly,
whether by involutes or by rolling curves, are in every respect analogous to
those for drawing the traces of the teeth of spur-wheels; except that in the
case of bevel- wheels all those operations are to be performed on the surface
of a sphere described about the apex, instead of on a plane, substituting
poles for centres and great circles for straight lines.
In consideration of the practical difficulty, especially in the case of large
wheels, of obtaining an accurate spherical surface, and of drawing upon it
when obtained, the following approximate method, proposed originally by
Tredgold, is generally used:
Let O, Fig. 162, be the common apex of the pitch-cones, OBI, OB'I, of a
pair of bevel-wheels; OC, OC', the axes of those cones; Ol their line of con-
tact. Perpendicular to OI draw
AIA', cutting the axes in A, A'\
make the outer rims of the patterns
and of the wheels portions of the
cones ABI, A'B'I, of which the nar-
row zones occupied by the teeth will
be sufficiently near for practical pur-
poses to a spherical surface described
about 0. As the cones ABI, A'B'I
cut the pitch -cones at right angles in
the outer pitch- circles IB, IB', they
may be called the normal cones. To
find the traces of the teeth upon the
normal cones, draw on a flat surface
circular arcs, ID, ID', with the radii
AI, A'l; those arcs will be the de-
velopments of arcs of the pitch -
circles IB, IB' when the conical sur-
faces ABI, A'B'I are spread out flat. Describe the traces of teeth for the
developed arcs as for a pair of spur-wheels, then wrap the developed arcs
on the normal cones, so as to make them coincide with the pitch-circles, and"
trace the teeth on the conical surfaces.
AF:
Co.; and "Teeth of Gears,1' by George B. Grant', Lexington, Mass. The
student may also consult Rankine's Machinery and Millwork, Reuleaux's
Constructor, and Unwinds Elements of Machine Design. See also article on
Gearing, by C. W. MacCord in App. Cyc. Mech., vol. ii.
Annular and Differential Gearing. (S. W. Balch., Am. Mach.,
Aug. 24, 1893.)— In internal gears the sum of the diameters of the describing
circles for faces and flanks should not exceed the difference in the pitch
diameters of the pinion and its internal gear. The sum may be equal to this
difference or it may be less; if it is equal, the faces of the teeth of each
wheel will drive the faces as well as the flanks of the teeth of the other
wheel. The teeth will therefore make contact with each other at two points
at the same time.
Cycloidal tooth-curves for interchangeable gears are formed with describ-
ing circles of about ^ the pitch diameter of the smallest gear of the series.
To admit two such circles between the pitch-circles of the pinion and internal
EFFICIENCY OF GEARING.
899
gear the number of teeth in the internal gear should exceed the number in
the pinion by 12 or more, if the teeth are of the customary proportions and
curvature used in interchangeable gearing.
Very often a less difference is desirable, and the teeth may be modified in
several ways to make this possible.
.First. The tooth curves resulting from smaller describing circles may be
employed. These will give teeth which are more rounding and narrower at
their tops, and therefore not as desirable as the regular forms.
Second. The tips of the teeth may be rounded until they clear. This is a
cut-and-try method which aims at modifying the teeth to such outlines as
smaller describing circles would give.
Third. One of the describing circles may be omitted and one only used,
which may be equal to the difference between the pitch -circles. This will
permit the meshing of gears differing by six teeth. It will usually prove
inexpedient to put wheels in inside gears that differ [by much less than 12
teeth.
If a regular diametral pitch and standard tooth forms are determined on,
the diameter to which the internal gear-blank is to be bored is calculated by
subtracting 2 from the number of teeth, and dividing the remainder by the
diametral pitch.
The tooth outlines are the match of a spur-gear of the same number of
teeth and diametral pitch, so that the spur gear will fit the internal gear as
a punch fits its die, except that the teeth of each should fail to bottom in .
the tooth spaces of the other by the customary clearance of one tenth the
thickness of the tooth.
Internal gearing is particularly valuable when employed in differential
action. This is a mechanical movement in which one of the wheels is
mounted on a crank so that its centre can move in a circle about the centre
of the other wheel. Means are added to the device which restrain the wheel
on the crank from turning over and confine it to the revolution of the crank.
The ratio of the number of teeth in the revolving wheel compared with
the difference between the two will represent the ratio between the revolv-
ing wheel and the crank-shaft by which the other is carried. The advan-
tage in accomplishing the change of speed with such an arrangement, as
compared with ordinary spur-gearing, lies in the almost entire absence of
friction and consequent wear of the teeth.
But for the limitation that the difference between the wheels must not be
too small, the possible ratio of speed might be increased almost indefinitely,
and one pair of differential gears made to do the service of a whole train of
wheels. If the problem is properly worked out with bevel-gears this limita-
tion may be completely set aside, and external and internal bevel-gears,
differing by but a single tooth if need be, made to mesh perfectly with each
other.
Differential bevel-gears have been used with advantage in mowing-ma-
chines. A description of their construction and operation is given by Mr.
Balch in the article from which the above extracts are taken.
EFFICIENCY OF GEARING.
An extensive series of experiments on the efficiency of gearing, chiefly
worm and spiral gearing, is described by Wilfred Lewis in Trans. A. S. M. E.,
vii. 273. The average results are shown in a diagram, from which the fol-
lowing approximate average figures are taken :
EFFICIENCY OP SPUR, SPIRAL, AND WORM GEARING.
Gearing.
Pitch.
Velocity at Pitch line in feet per mm.
3
10
40
100
200
45°
30
20
15
10
7
5
.90
.81
.75
.67
.61
.51
.43
.34
.935
.87
.815
.75
.70
.615
.53
.43
.97 '
.93
.89
.845
.805
.74
.72
.60
.98
.955
.93
.90
.87
.82
.765
.70
.985
.965
.945
.92
.90
.86
.815
.765
Spiral pinion
tt it
41 U
Spiral pinion or worm
900
GEARING.
The experiments showed the advantage of spur-gearing over all oth*r
kinds in both durability and efficiency. The variation from the mean results
rarely exceeded 5# in either direction, so long as no cutting occurred, but
the variation became much greater and very irregular as soon as cutting
began. The loss of power varies with the speed, the pressure, the tempera-
ture, and the condition of the surfaces. The excessive friction of worm and
spiral gearing is largely due to thee nd thrust on the collars of the shaft.
This may be considerably reduced by roller-bearings for the collars.
When two worms with opposite spirals run in two spiral worm-gears that
also work with each other, and the pressure on one gear is opposite that on
the other, there is no thrust on the shaft. Even with light loads a worm
will begin to heat and cut if run at too high a speed, the limit for safe work-
ing being a velocity of the rubbing surfaces of 200 to 300 ft. per minute, the
former being preferable where the gearing has to work continuously. The
wheel teeth will keep cool, as they form part of a casting haying a large
radiating surface; but the worm itself is so small that its heat is dissipated
slowly. Whenever the heat generated increases faster than it can be con-
ducted and radiated away, the cutting of the worm may be expected to be-
gin. A low efficiency for a worm-gear means more than the loss of power,
since the power which is lost reappears as heat and may cause the rapid
destruction of the worm.
Unwin (Elements of Machine Design, p. 294) says : The efficiency is greater
the less the radius of the worm. Generally the radius of the worm = 1.5 to
3 times the pitch of the thread of the worm or the circular pitch of the
worm-wheel. For a one- threaded worm the efficiency is only 2/5 to J4;
for a two-threaded worm, 4/7 to 2/5; for a three- threaded worm, % to %.
Since so much work is wasted in friction it is not surprising that the wear
is excessive. The following table gives the calculated efficiencies of worm-
wheels of 1, 2, 3, and 4 threads and ratios of radius of worm to pitch of teeth
of from 1 to 6, assuming a coefficient of friction of 0.15 :
No. of
Radius of Worm -j- Pitch.
1
1*4
1&
w
2
2«
3
4
6
1
.50
.44
.40
.36
.33
.28
.25
.20
.14
2
.67
.62
.57
.53
.50
.44
.40
.33
.25
3
.75
.70
.67
.63
.60
.55
.50
.43
.33
4
.80
.76
.73
.70
.67
.62
.57
.50
.40
STRENGTH OF GEAR-TEETH.
The strength of gear-teeth and the horse-power that may be transmitted
by them depend upon so many variable and uncertain factors that it is not
surprising that the formulas and rules given by different writers show a
wide variation. In 1879 John H. Cooper (Jour. Frank. Inst., July, 1879)
found that there were then in existence about 48 well-established rules for
horse-power and working strength, differing from each other in extreme
cases about 500#. In 1886 Prof. Win. Harkness (Proc. A. A. A. S. 1886),
from an examination of the bibliography of the subject, beginning in 1796,
found that according to the constants and formulae used by various authors
there were differences of 15 to 1 in the power which could be transmitted
by a given pair of gearsd wheels. The various elements which enter into
the constitution of a formula to represent the working strength of a toothed
wheel are the following: 1. The strength of the metal, usually cast iron, which
is an extremely variable quantity. 2. The shape of the tooth, and espec-
ially the relation of its thickness at the root or point of least strength to the
pitch and to the length. 3. The point at which the load is taken to be ap-
plied, assumed by some authors to be at the pitch-line, by others at the
extreme end, along the whole face, and by still others at a single outer
corner. 4. The consideration of whether che total load is at any time re-
ceived by a single tooth or whether it is divided between two teeth, 5. The
influence of velocity in causing a tendency to break the teeth by shock. 6.
The factor of safety assumed to cover all the uncertainties of the other ele-
ments of the problem.
STRENGTH OF GEAR-TEETH.
901
Prof. Harkness, as a result of his investigation, found that all the formulae
on the subject might be expressed in one of three forms, viz.:
Horse-power = CTpf, or CPp2, or CVp*f\
in which C is a coefficient, V •= velocity of pitch-line in feet per second, p =
pitch in inches, and/ = face of tooth in inches.
From an examination of precedents he proposed the following formula
for cast-iron wheels:
H.P.=
0.910Fp/
4/1 + 0.65 V
He found that the teeth of chronometer and watch movements were sub-
ject to stresses four times as great as those which any engineer would dare
to use in like proportion upon cast-iron wheels of large size.
It appears that all of the earlier rules for the strength of teeth neglected
the consideration of the variations in their form; the breaking strength, as
said by Mr. Cooper, being based upon the thickness of the teeth at the pitch-
line or circle, as if the thickness at the root of the tooth were the same in
all cases as it is at the pitch-line.
Wilfred Lewis (Proc. Eng'rs Club, Phila., Jan. 1893; Am. Mack., June 22.
1893) seems to have been the first to use the form of the tooth in the con-
struction of a working formula and table. He assumes that in well-con-
structed machinery the load can be more properly taken as well distributed
across the_ tooth than as concentrated in one corner, but that it cannot be
safely taken as concentrated at a maximum distance from the root less
than the extreme end of the tooth. He assumes that the whole load is
taken upon one tooth, and considers the tooth as a beam loaded at one end,
and from a series of drawings of teeth of the involute, cycloidal, and radial
flauk systems, determines the point of weakest cross-section of each, and
the ratio of the thickness at that section to the pitch. He thereby obtains
the general formula,
W~ spfy;
in which W is the load transmitted by the teeth, in pounds ;s is the safe
working stress of the material, taken at 8000 Ibs. for cast iron, when the
working speed is 100 ft. or less per minute; p =: pitch;/ = face, in inches;
y = a factor depending on the form of the tooth, whose value for different
cases is given in the following table:
Factor for Strength, y.
Factor for Strength, y.
No of
rso. or
Teeth.
Involute
20° Obli-
quity.
Involute
15° and
Cycloidal
Radial
Flanks.
Teeth.
Involute
20° Obli-
quity.
Involute
15° and
Cycloidal
Radial
Flanks.
12
.078
.067
.052
27
.111
.100
.064
13
.083
.070
.053
30
.114
102
.065
14
.088
.072
.054
34
.118
.104
.066
15
.092
.075
.055
38
.122
.107
.067
16
.094
.077
.056
43
126
.110
.068
17
.096
.080
.057
50
•30
.112
.069
18
.098
.083
.058
60
134
.114
.070
19
.100
.087
.059
75
.138
.116
.071
20
.102
.090
.060
100
.142
.118
.072
21
.104
.092
.061
150
146
.120
.073
23
.106
.094
.062
300
.150
122
.074
25
.108
.097
.063
Rack.
.154
.124 j .075
SAFE WORKING STRESS, s, FOR DIFFERENT SPEEDS.
Speed of Teeth in
ft. per minute.
100 or
less.
COO
300
600
900
1200
1800
2400
Ca st iron
8000
6000
4800
4000
3000
2400
2000
1700
Steel
20000
15000
12000
10000
7500
6000
5000
4300
902 GEARING.
The values of s in the above table are given by Mr. Lewis tentatively, in
the absence of sufficient data upon which to base more definite values, but
they have been found to give satisfactory results in practice.
Mr. Lewis gives the following example to illustrate the use of the tables;
Let it be required to find the working strength of a 12-toothed pinion of 1-
inch pitch, 2J^-inch face, driving a wheel of 60 teeth at 100 feet or less per
minute, and let the teeth be of the 20-degree involute
form. In the formula TF— spfy we have for a cast-iron
pinion s = 8000, pf = 2.5, and1 y ='.078; and multiplying these
I values together, we have W — 1560 pounds. For the wheel
we have y = .134 and W = 2080 pounds.
The cast-iron pinion is, therefore, the measure of
Strength; but if a steel pinion be substituted we have
S = 20,000 and W = 3900 pounds, in which combination
the wheel is the weaker, and it therefore becomes the
measure of strength.
For bevel-wheels Mr. Lewis gives the following, refer-
ring to Fig. 168: D = large diameter of bevel; d =
small diameter of bevel; p — pitch at large diameter;
n = actual number of teeth; / = face of beve^, N = for-
Flo. 163. mative number of teeth = n X secant a, or the number
corresponding to radius R ; y = factor depending upon
shape of teeth and formative number N ; W = working load on teeth.
7)3 - c*3 f d
W = spfy ^ __ , ; or, more simply, W = spfy-j:,
which gives almost identical results when d is not less than % D, as is the
case in good practice.
In Am. Mach., June 22, 1893, Mr. Lewis gives the following formulae for
the working strength of the three systems of gearing, which agree very
closely with those obtained by use of the table:
For involute, 20° obliquity, W = spf (.154 - — ) ;
/ 684 \
For involute 15°, and cycloidal, W = spf^ .124 - - — J ;
For radial flank system, W = spf (^.075 — — — j ;
in which the factor within the parenthesis corresponds to y in the general
formula. For the horse-power transmitted, Mr. Lewis's general formula
W = spfy, = 33<OOQ H'Pt, may take the form H.P. = -§^, in which v =
>er minute; or since v — dir >
eter in inches and rpm. = re
Wv __ spfy XdX rpm. _
velocity in feet per minute; or since v = dn X rpm. -*- 12 = .2618d X rpm.,, in
which d = diameter in inches and rpm. = revolutions per minute,
rpu,
It must be borne in mind, however, that in the case of machines which
consume power intermittently, such as punching and shearing machines,
the gearing should be designed with reference to the maximum load JF",
which can be brought upon the teeth at any time, and not upon the average
horse-power transmitted.
Comparison of the Harkness and Lewis Formulas.—
Take an average case in which the safe working strength of the material,
s = 6000, v = 200 ft. per min., and y = .100, the value in Mr. Lewis's table
for an involute tooth of 15° obliquity, or a cycloidal tooth, the number of
teeth in the wheel being 27.
if Fis taken in feet per second.
Prof. Harkness gives H,P.= ^'91QFp/ - If the F in the denominate*
STREHGTH OF GEAR-TEETH.
903
be taken at 200 . . uO = 3}£ feet per second, |/l-f 0.65F = ^3.167=1.78,
910
and H.P. = j-^g^P/ = .571p/F, or about 52% of the result given by Mr. Lewis's
formula. This is probably as close an agreement as can be expected, since
Prof. Harkness derived his formula from an investigation of ancient prece-
dents and rule-of-thumb practice, largely with common cast gears, while
Mr, Lewis's formula was derived from considerations of modern practice
with machine-moulded and cut gears.
Mr. Lewis takes into consideration the reduction in working strength of a
tooth due to increase in velocity by the figures in his table of the values of
the safe working stress s for different speeds. Prof. Harkness gives expres-
sion to the same reduction by means of the denominator of his formula,
y 1-+ 0.65 F. The decrease in strength as computed by this formula is
somewhat less than that given in Mr. Lewis's table, and as the figures given
in the table are not based on accurate data, a mean between the values given
by the formula and the table is probably as near to the true value as may
?oe obtained from our present knowledge. The following table gives the
values for different speeds according to Mr. Lewis's table and Prof. Hark-
ness's formula, taking for a basis a working stress s, for cast-iron 8000, and
for steel 20,000 Ibs. at speeds of 100 ft. per minute and less:
v = speed of teeth, ft. per min. .
F = " ** ft. per sec..
100
1%
200
3^
300
5
600
10
900
15
1200
20
1800
30
2400
40
teafe stress s, cast-iron, Lewis. ..
Relative do., s-f-8000.
— 1 •*- Vl -J-0.65F
8000
1
.6930
8000
8000
20000
20000
6000
.75
.5621
.811
6438
6200
15500
15000
4800
.6
.4850
.700
5600
5200
13000
12000
4000
.5
.3650
.526
4208
4100
10300
10000
3000
.375
.3050
.439
3512
3300
8100
7500
2400
.3
.2672
.385
3080
2700
6800
6000
2000
.25
.2208
.318
2544
2300
5700
5000
1700
.2125
.1924
.277
2216
2000
4900
4300
Relative val c -*- 693 . . .
Si — 8000 X (c -1- .693) ...... .
Mean of s and sl9 cast-iron = s2 .
:* " *• for steel = s3.
Safe stress for steel, Lewis
Comparing the two formulae for the case of s
speed of 100 ft. per min., we have
Harkness: H.P. = 1 •
8000, corresponding to a
i-|-0.65F X o910Fp/ = .695 X .91 X V%pf = 1.05Jp/*
Lewis:
H.P.:
_
33,000 ~ 550 : 550
In which y varies according to the shape and number of the teeth.
For radial-flank gear with 12 teeth y =r .052; 24.24pfy = 1.260»/ ;
For 20° involute, 19 teeth, or 15° inv., 27 teeth y = .100; 24.24pfy = 2.424p/;
For 20° involute, 300 teeth y = .150; 24.34pjfy = 3.636p/.
Thus the weakest-shaped tooth, according to Mr. Lewis, will transmit 20
per cent more horse-power than is given by Prof. Harkness's formula, in
which the shape of the tooth is not considered, and the average-shaped
tooth, according to Mr. Lewis, will transmit more than double the horse-
power given by Prof. Harkness's formula.
Comparison of Other Formulae.— Mr. Cooper, in summing up
his examination, selected an old English rule, which Mr. Lewis considers as
a passably correct expression of good general averages, viz. : X — 2000p/,
X = breaking load of tooth in pounds, p = pitch. / = face. If a factor of
safety of 10 be taken, this would give for safe working load W = 200/>/.
George B. Grant, in his Teeth of Gears, page 33, takes the breaking load
at 3500p/, and, with a factor of safety of 10, gives W = 350p/.
Nystrom's Pocket-Book, 20th ed., 1891, says : " The strength and durability
of cast-iron teeth require that they shall transmit a force of 80 Ibs. per inch
of pitch and per inch breadth of face." This is equivalent to W = 80p/, or
only 40# of that given by the English rule.
F. A. Halsey (Clark's Pocket Book) gives a table calculated from the
formula H.P. = pfd X rpm. -*- 850.
Jones & Laughlins give H.P. = pfd X rpm. -f- 550.
These formulae transformed give TF= 128p/and W = 218p/, respectively
904 GEARING.
Unwin, on the assumption that the load acts on the corners of the teeth,
derives a formula p = K Vw, in which K is a coefficient derived from ex-
isting wheels, its values being : for slowly moving gearing not subject to
much vibration or shock 1C =.04; in ordinary mill-gearing, running at
greater speed and subject to considerable vibration, K = .05; and in wheels
subjected to excessive vibration and shock, and in mortise gearing, K— .06.
Reduced to the form W — Cpf, assuming that/ = 2p, these values of K give
W = 262p/, 200»/, and 139p/, respectively.
Unwin also gives the following formula, based on the assumption that the
pressure is distributed along the edge of the tooth: p = i
where X"t = about .0707 for iron wheels and ,0848 for mortise wheels when
the breadth of face is not less than twice the pitch. For the case of / = 2p
and the given values of -K"j this reduces to W = 200pf and W = 139p/,
respectively.
Box, in his Treatise on Mill Gearing, gives H.P. = , in which n
= number of revolutions per minute. This formula differs from the more
modern formulae in making the H.P. vary as p2/, instead of as p/, and in
this respect it is no doubt incorrect.
Making the H.P. vary as Vdii or as Vv , instead of directly as v, makes
the velocity a factor of the working strength as in the Harkness and Lewis
Vv 1
formulae, the relative strength varying as - , or as /- , which for different
velocities is as follows :
Speed of teeth in ft. per min.,v = 100 200 300 600 900 1200 1800 2400
Relative strength = 1 .707 .574 .408 .333 .289 .236 .204
Showing a somewhat more rapid reduction than is given by Mr. Lewis.
For the purpose of comparing different formulae they may in general be
reduced to either of the following forms :
H.P. = Cpfv, H.P. = Cjpfd X rpm., W = cp/,
in which p = pitch, / = face, d = diameter, all in inches ; v = velocity in
feet per minute, rpm. revolutions per minute, and (7, (7j and c coefficients.
The formulae for transformation are as follows :
HP- -
33000 ~~ 126,050
'• = 33,0000p/; p/=«^ = **'
= , = = „ =
v dx rpm. Cv dd X rpm. c
.2618(7; c = 33,000(7; C = 3.82(7, , = 5-^; c = 126,050CX.
In the Lewis formula (7 varies with the form of the tooth and with the
speed, and is equal to sy-*- 33,000, in which y and s are the values taken from
the table, and c = sy.
910
In the Harkness formula C varies with the speed and is equal to .,- ^
(V being in feet per second), = — '
Vl-f-Ollv.
In the Box formula C varies with the pitch and also with the velocity,
and equals ^ ^ rpm' = .02345 J^. c = 33,OOOC =* 774 -£-
~ -
For v = 100 ft. per miu. C = 77 Ap ; for v = 600 ft. per minute c =31. 6p.
In the other formulae considered (7, d , and c are constants. Reducing
the several formulae to the form W = cp/, we have the following :
FEICTIONAL GEARING. 905
COMPARISON OP DIFFERENT FORM ju& FOR STRENGTH OF GEAR-TEETH.
Safe working pressure per inch pitch and per inch of face, or value of c in
formula W = cpf:
v = 100 ft. v = 600 ft.
per min. per min.
Lewis: Weak form of tooth, radial flank, 12 teeth. .. c = 416 208
Medium tooth, inv. 15°, or cycloid, 27 teeth., c = 800 400
Strong form of tooth, inv. 20°, 300 teeth ...... c— 1200 600
Harkness: Average tooth ............................ c— 347 184
Box: Tooth of 1 inch pitch .......................... c— 77.4 31.6
" " 3 inches pitch ............ ............ c = 232 95
Various, in which c is independent of form and speed: Old English
rule, c = 200; Grant, c = 350; Nystrom, c = 80; Halsey, c = 128; Jones &
Laughlins, c = 218; Unwin, c = 262, 200, or 139, according to speed, shock,
and vibration.
The value given by Nystrom and those given by Box for teeth of small
pitch are so much smaller than those given by the other authorities that they
may be rejected as having an entirely unnecessary surplus of strength. The
values given by Mr. Lewis seem to rest on the most logical basis, the form of
the teeth as well as the velocity being considered; and since they are said to
have proven satisfactory in an extended machine practice, they may be con-
sidered reliable for gears that are so well made that the pressure bears
along the face of the teeth instead of upon the corners. For rough ordi-
nary work the old English rule W = 200p/ is probably as good as any, ex-
cept that the figure 200 may be too high for weak forms of tooth and for
high speeds.
The formula W= 200p/ is equivalent to H.P. = ' = -, of
H.P. = .0015873p/ef X rpm. = .006063p/v.
Maximum Speed of Gearing.— A. Towler, Eng'g, April 19, 1889,
p. 388, gives the maximum speeds at which it was possible under favorable
conditions to run toothed gearing safely as follows:
Ft, per min.
Ordinary cast-iron wheels ....................................... 1800
Helical " " " ....................................... 2400
Mortise u •' " ........................................ 2400
Ordinary cast-steel wheels ............................... . ........ 2600
Helical " " " ........................................ 30CO
Special cast-iron machine-cut wheels .......................... 3000
Prof. Coleman Sellers (Stevens Indicator, April, 1892) recommends that
gearing be not run over 1200 ft. per minute, to avoid great noise. The
Walker Company, Cleveland, O., say that 2200 ft. per min. for iron gears and
3000 ft. for wood and iron (mortise gears) are excessive, and should be
avoided if possible. The Corliss engine at the Philadelphia Exhibition (187<5)
had a fly-wheel 30 ft. in diameter running 35 rpm. geared into a pinion 12 ft.
diam. The speed of the pitch-line was 3300 ft. per min.
A Heavy Macliine-cut Spur-gear was made in 1891 by the
Walker Company, Cleveland, O., for a diamond mine in South Africa, with
dimensions as follows: Number of teeth, 192; pitcn diameter, 30' 6.66"; face,
30"; pitch, 6"; bore, 27"; diameter of hub, 9' 2"; weight of hub, 15 tons; and
total weight of gear, 66^ tons. The rirn was made in 12 segments, the joints
of the segments being fastened with two bolts each. The spokes were bolted
to the middle of the segments and to the hub with four bolts in each end.
Frictioiial Gearing.— In frictional gearing the wheels are toothless,
and one wheel drives the other by means of the friction between the two
surfaces which are pressed together. They may be used where the power
to be transmitted is not very great; when the speed is so high that toothed
wheels would be noisy; when the shafts require to be frequently put into
and out of gear or to have their relative direction of motion reversed; or
when it is desired to change the velocity-ratio while the machinery is in mo-
tion, as in the case of disk friction-wheels for changing the feed in machine
tools.
Let P = the normal pressure in pounds at the line of contact by which
two wheels are pressed together, T = tangential resistance of the driven
wheel at the line of contact, / = the coefficient of friction, V — the velocity
of the pitch surface in feet per second, and H.P. = horse-power ; then
T may be equal to or Jess than fP\ H.P. = TV-*- 550. The value of/ for
906
HOISTING.
metal on metal may be taken at .15 to .20; for wood on metal, .25 to .30; and
for wood on compressed paper, .20. The tangential driving force T may be
as high as 80 Ibs. per inch width of face of the driving surface, but this is ac-
companied by great pressure and friction on the journal-bearings.
In frictional grooved gearing circumferential wedge-shaped grooves are
cut in the faces of two wheels in contact. If P = the force pressing the
wheels together, and N = the normal pressure on all the grooves, P = JN
(sin a +/ cos a), in which 2a = the inclination of the sides of the grooves,
and the maximum tangential available force T — fN. The inclination of the
sides of the grooves to a plane at right angles to the axis is usually 30°.
Frictional Grooved Gearing.— A set of friction-gears for trans-
mitting 150 H.P. is on a steam- dredge described in Proc. Inst. M. E., July,
1888. Two grooved pinions of 54 in. diam., with 9 grooves of 1% in. pitch and
angle of 40° cut on their face, are geared into two wheels of 127^ in diam.
similarly grooved. The wheels can be thrown in and out of gear by levers
operating eccentric bushes on the large wheel-shaft. The circumferential
speed of the wheels is about 500 ft. per min. Allowing for engine-friction,
if half the power is transmitted through each set of gears the tangential
force at the rims is about 3960 Ibs., requiring, if the angle is 40° and the co-
efficient of friction 0.18, a pressure of 7524 Ibs. between the wheels and
pinion to prevent slipping.
The wear of the wheels proving excessive, the gears were replaced by spur-
gear wheels and brake-wheels with steel brake-bands, which arrangement
has proven more durable than the grooved wheels. Mr. Daniel Adamson
states that if the frictional wheels had been run at a higher speed the results
would have been better, and says they should run at least 30 ft. per second.
HOISTING AND CON /EYING.
Approximate Weight and Strength of Cordage. (Boston
and Lockport Block Co.)— See also pages 339 to 345.
Size in
Circum-
ference.
Size in
Diam-
eter.
Weight of
100ft.
Manila,
in Ibs.
Strength
of Manila
Rope,
in Ibs.
Size in
Circum-
ference.
Size in
Diam-
eter.
Weight of
100 ft.
Manila,
in Ibs.
Strength
of Manila
Rope,
in Ibs.
inch.
inch.
inch.
inch.
2
%
13
4,000
19/16
72
22,500
2^
13/16
16
20
5,000
6,250
5
iff
80
97
25,000
30,250
2^4
%
24
7,500
6 2
2
113
36,000
3
1
28
9,000
133
42,250
3/4
1 1/16
33
10,500
7
2J4
153
49,000
3^
1/^3
38
12,250
74^
2/^
184
56,250
3%
1/4
45
14,000
8
2&x
211
64,000
4
1 5/16
51
16,000
8/>is
g7£
236
72,250
4/4
1%
58
18,062
9
3
262
81,000
4H
U|
65
20,250
Working Strength of Blocks
Regular Mortise-blocks Single and Wide
Double, or Two Double Iron-
strapped Blocks, will hoist about—
inch.
P
6
7
8
9
10
12
14
Ibs.
250
350
600
1,200
2,000
4,000
10,000
16,000
(B. & L. Block Co.)
,~~ Mortise and Extra Heavy
Single and Double, or Two Double,
Iron-strapped Blocks, will hoist
about —
Ibs.
2,000
6,000
12,000
24,000
36,000
inch.
8
10
12
14
16
18
20
50,000
90,000
Where a double and triple block are used together, a certain extra propor-
tioned amount of weight can be safely bpisted, as larger hooks are used.
PROPORTIONS OF HOOKSo
907
Comparative Efficiency in Chain-blocks both in
Hoisting and. Lowering.
(Tests by Prof. R. H. Thurston, Hoisting, March, 1892.)
WORK OF HOISTING.
WORK OF LOWERING.
Load of 2000 Ibs.
Load* of 2000 Ibs., lowered 7 ft. in each case.
•g
a
£
Exclusive of Factor of Time.
Inclusive of
Time.
0
«
1^
S3
£ '
€
1
•d
*>£
..
&*
e
•S
£f
P
* s
^
K~
o 3
•* s *
g^5
S
g£
Number
q
H^
F
S's
Velocit
S-S
I!
I8
PH
h*
f
D'd £
> fl 53
3 §.»•
js&o
s*
rt
|1
*|
!
20.50
79.50
1 00
32.50
8.00
227.
1,816
1.00
0.75
1.000
2
68.00
32.00
40
62.44
14.00
436.
6,104
3.32
1.20
.186
3
69.00
31.00
39
30 00
92.30
196.
18,090
10.00
1.50
.050
4
71.20
28.80
36
28.00
92.60
168.
15,556
8.60
2.50
.035
5
73.96
26.04
33
48. 0(
73.30
17.5
1,282
0.71
2.80
.380
g
75.66
24.34
31
53.00
56.60
370.
20,942
11.60
1.80
.036
7
77.00
23.00
29
44.30
55.00
310.
17,050
9.40
2.75
.029
8
81.03
18.97
24
61.00
48.50
426.
20,000
11.60
3.75
.018
No. 1 was Weston's triplex block; No. 3, Weston's differential; No. 4,
Weston's imported. The others were from different makers, whose names
are not given. All the blocks were of one-ton capacity.
Proportions of Hooks.— The following formulae are given by
Henry R. Towne, in his Treatise on Cranes, as a result of an extensive
experimental and mathematical investi-
gation. They apply to hooks of capaci-
ties from 250 Ibs. to 20,000 Ibs. Each size
of hook is made from some commercial
size of round iron. The basis in each
case is, therefore, the size of iron of
which the hook is to be made, indicated
by 4 in the diagram. The dimension D
is arbitrarily assumed. The other di-
mensions, as given by the formulae, are
those which, while preserving a proper
bearing-face on the interior of the hook
for the ropes or chains which may be
passed through it, give the greatest re-
sistance to spreading and to ultimate '
rupture, which the amount of material
in the original bar admits of. The sym-
bol A is used to indicate the nominal ca-
pacity of the hook in tons of 2000 Ibs.
The formulae which determine the lines
of the other parts of the hooks of the
several sizes are as follows, the measure-
ments being all expressed in inches:
D = .5 A -|- 1.25
ft = .64 A + 1.60
F = .33 A -J- .85
FIG. 164.
G = .75D.
O - .363 A -f .66
Q = .64 A + 1.60
H= 1.084
1=1.834
J= 1.204
K = 1.134
L = 1.054
M = .504
N= .855- .16
U= .8664
The dimensions 4 are necessarily based upon the ordinary merchant sizes
of round iron. The sizes which it has been found best to select are the
following:
Capacity of hook:
% Y± M 11^ 234568 10 tons.
Dimension 4:
% 11/16 ft 11/16 IK 1% \H 2 % % 2%
908 HOISTING.
Experiment has shown that hooks made according to the above formula
will give way first by opening of the jaw, which, however, will not occur
except with a load much in excess of the nominal capacity of the hook.
This yielding of the hook when overloaded becomes a source of safety, as it
constitutes a signal of danger which cannot easily be overlooked, and which
must proceed to a considerable length before rupture will occur and the
load be dropped.
POWER OF HOISTING-ENGINES.
Horse-power required to raise a Load at a Given
TT _ Gross weight in Ibs
Speed. — H.P. = -- 33000 - '~' X speed m ft- Per mm- To this add
25$ to 50# for friction, contingencies, etc. The gross weight includes the
weight of cage, rope, etc. In a shaft with two cages balancing each other
use the net load -f- weight of one rope, instead of the gross weight.
To find the load which a given pair of engines will start.— Let A = area
of cylinder in square inches, or total area of both cylinders, if there are two;
P = mean effective pressure in cylinder in Ibs. per sq. in.; S = stroke of
cylinder in inches; C = circumference of hoisting-drum in inches; L — load
lifted by hoisting- rope in Ibs.; F— friction, expressed as a diminution of
the load. Then L = AI?S - F.
c
An example in ColVy Engr., July, 1891, is a pair of hoisting-engines 24" X
40", drum 12 ft. diam., average steam-pre.ssure in cylinder = 59.5 Ibs.; A =
904.8; P= 59.5; 8 = 40; C— 452.4. Theoretical load, not allowing for friction,
AP2S -f- C = 9589 Ibs. The actual load that could just be lifted on trial was 7988
Ibs., making friction loss F = 1001 Ibs., or 20 -f- per cent of the actual load
lifted, or 16%# of the theoretical load.
The above rule takes no account of the resistance due to inertia of the
load, but for all ordinary cases in which the acceleration of speed of the
cage is moderate, it is covered by the allowance for friction, etc. The re-
sistance due to inertia is equal to the force required to give the load the
velocity acquired in a given time, or, as shown in Mechanics, equal to the
product of the mass by the acceleration, or R = — — , in which R = resist-
ance in Ibs. due to inertia; W = weight of load in Ibs. ; V= maximum veloc-
ity in feet per second; T *= time in seconds taken to acquire the velocity V\
g = 32.16.
Effect of Slack Rope upon Strain in Hoisting. -A series of
tests with a dynamometer are published by the Trenton Iron Co., which
show that a dangerous extra strain may be caused by a few inches of slack
rope. In one case the cage and full tubs weighed 11,800 Ibs. ; the strain when
the load was lifted gently was 11,525 Ibs.; with 3 in. of slack chain it was
19.0-25 Ibs , with 6 in. slack 25,750 Ibs.. and with 9 in. slack 27,950 Ibs.
Limit of Depth for Hoisting.— Taking the weight of a cast-steel
hoisting-rope of l£| inches diameter at 2 Ibs. per running foot, and its break-
ing strength at 84,000 Ibs., it should, theoretically, sustain itself until 42,000
feet long before breaking from its own weight. But taking the usual factor
of safety of 7, then the safe working length of such a rope would be only
6000 feet. If a weight of 3 tons is now hung to the rope, which is equivalent
to that of a cage of moderate capacity with its loaded cars, the maximum
length at which such a rope could be used, with the factor of safety of 7, is
3000 feet, or
2o? -f- 6000 = ; .-. x = 3000 feet.
This limit may be greatly increased by using special steel rope of higher
strength, by using a smaller factor of safety, and by using taper ropes.
(See paper by H. A. Wheeler, Trans. A. I. M. E., xix. 107.)
Large Hoisting Records.— At a colliery in North Derbyshire dur-
ing the first week in June, 1890, 6309 tons were raised from a depth of 509
yards, the time of winding being from 7 a.m. to 3.30 p.m.
At two other Derbyshire pits, 170 and 140 yards in depth, the speed of
winding and changing has been brought to such perfection that tubs are
drawn and changed three times in one minute. (Proc. Inst. M. EM 1890.)
POWER 01 HOISTIXG-ENGINES. yOU
At the Nottingham Colliery near Wilkesbarre, Pa., in Oct. 1891, 70,152 tons
were shipped in 24.15 days, the average hoist per day being 1318 mine cars.
The depth of hoist was 470 feet, and all coal came from one opening. The
engines were fast motion, 22 X 48 inches, conical drums 4 feet 1 inch long, 7
feet diameter at small end and 9 feet at large end. (Eng^g Neivs, Nov. 1891.)
Pneumatic Hoisting. (H. A. Wheeler, Trans. A. 1. M. E., xix. 107.)-
A pneumatic hoist was installed in 1876 at Epinac, France, consisting of two
continuous air-tight iron cylinders extending from the bottom to the top of
the shaft. Within the cylinder moved a piston from which was hung the
cage. It was operated by exhausting the air from above the piston, the
lower side being open to the atmosphere. Its use \ras discontinued on ac-
count of the failure of the mine. Mr. Wheeler gives a description of the sys-
tem, but criticises it as not being equal on the whole to hoisting by steel ropes.
Pneumatic hoisting-cylinders using compressed air have been used at
blast-furnaces, the weighted piston counterbalancing the weight of the cage,
and the two being connected by a wire rope passing over a pulley-sheave
above the top of the cylinder. In the more modern furnaces steam-engine
hoists are generally used.
Counterbalancing of Winding-engines. (H. W. Hughes, Co-
lumbia Coll. Qly.) — Engines running unbalanced are subject to enormous
variations in the load; for Jet W — weight of cage and empty tubs, say 6270
Ibs.; c — weight of coal, say 4480 Ibs,; r = weight of hoisting rope, say 6000
Ibs. ; r' = weight of counterbalance rope hanging down pit, say 6000 Ibs. The
weight to be lifted will be:
If weight of rope is unbalanced. If weight of rope is balanced.
At beginning of lift:
- W or 10, 480 Ibs. W+c+r- (PF-f r'),
or
4480
Ibs.
At end of lift:
TT-f c — (W+ r) or minus 1520 Ibs. W+ c + r' — (W-\- r)t
That counterbalancing materially affects the size of winding-engines is
shown by a formula given by Mr. Robert Wilson, which is based on the fact
that the greatest work a winding-engine has to do is to get a given mass into
a certain velocity uniformly accelerated from rest, and to raise a load the
distance passed over during the time this velocity is being obtained.
Let W — the weight to be set in motion: one cage, coal, number of empty
tubs on cage, one winding rope from pit head-gear to bottom,
and one rope from banking level to bottom.
v — greatest velocity attained, uniformly accelerated from rest;
g = gravity = 32.2;
t = time in seconds during which v is obtained;
L = unbalanced load on engine;
R = ratio of diameter of drum and crank circles;
P = average pressure of steam in cylinders;
N= number of cylinders;
S = space passed over by crank-pin during time t ;
C = %, constant to reduce angular space passed through by crank, to
the distance passed through by the piston during the time £;
A = area of one cylinder, without margin for friction. To this an ad-
dition for friction, etc., of engine is to be made, varying from 10
to 30# of A.
1st. Where load is balanced,
At middle of lift:
j (g
PNSC.
2d. Where load is unbalanced:
The formula is the same, with the addition of another term to allow for
the variation in the lengths of the ascending and descending ropes. In this
910
HOISTING.
ft, = reduced length of rope in t attached to ascending cage;
h9 — increased length of rope in t attached to descending cag
w = weight of rope per foot in pounds. Then
- Kg) -Ha*)-
PNSC.
Applying the above formula when designing new engines, Mr. Wilson
found that 30 inches diameter of cylinders would produce equal results, when
balanced, to those of the 36-inch cylinder in use, the latter being unbal-
anced.
Counterbalancing may be employed in the following methods :
(a) Tapering Rope.— At the initial stage the tapering rope enables us to
wind from greater depths than is possible with ropes of uniform section.
The thickness of such a rope at any point should only be such as to safely
bear the load on it at that point.
With tapering ropes we obtain a smaller difference between the initial and
final load, but the difference is still considerable, and for perfect equaliza-
tion of the load we must rely on some other resource. The theory of taper
ropes is to obtain a rope of uniform strength, thinner at the cage end where
the weight is least, and thicker at the drum end where it is greatest.
(6) The Counterpoise System consists of a heavy chain working up and
down a staple pit, the motion being obtained by means of a special small
drum placed on the same axis as the winding drum. It is so arranged that
the chain hangs in full length down the staple pit at the commencement of
the winding; in the centre of the run the whole of the chain rests on the
bottom of the pit, and, finally, at the end of the winding the counterpoise
has been rewound upon the small drum, and is in the same condition as it
was at the commencement.
(c) Loaded-wagon System. — A plan, formerly much employed, was to
have a loaded wagon running on a short incline in place of this heavy chain;
the rope actuating this wagon being connected in the same manner as the
above to a subsidiary drum. The incline was constructed steep at the com-
mencement, the inclination gradually decreasing to nothing. At the begin-
ning of a wind the wagon was at the top of the incline, and during a portion
of the run gradually passed down it till, at the meet of cages, no pull was
exerted on the engine— the wagon by this time being at the bottom. In the
latter part of the wind the resistance was all against the engine, owing to
its having to pull the wagon up the incline, and this resistance increased
from nothing at the meet of cages to its greatest quantity at the conclusion
of the lift.
(d) The Endless-rope System is preferable to all others, if there is suffi-
cient sump room and the shaft is free from tubes, cross timbers, and other
impediments. It consists in placing beneath the cages a tail rope, similar
in diameter to the winding rope, and, after conveying this down the pit, it i*
attached beneath the other cage.
(e) Flat Ropes Coiling on Reels. — This means of winding allows of a cer-
tain equalization, for the radius of the coil of (ascending rope continues to
increase, while that of the descending one continues to diminish. Conse-
quently, as the resistance decreases in the ascending load the leverage
Increases, and as the power increases in the other, the leverage diminishes.
The variation in the leverage is a constant quantity, and is equal to the
thickness of the rope where it is wound on the drum.
By the above means a remarkable uniformity in the load may be ob-
tained, the only objection being the use of flat ropes, which weigh heavier
and only last about two thirds the time of round ones.
(/) Conical Drums. — Results analogous to the preceding may be obtained
by using round ropes coiling on conical drums, which may either be smooth,
with the successive coils lying side by side, or they may be provided with a
spiral groove. The objection to these forms is, that perfect equalization is
not obtained with the conical drums unless the sides are very steep, and con-
sequently there is great risk of the rope slipping ; to obviate this, scroll
drums were proposed. They are, however, very expensive, and the lateral
displacement of the winding rope from the centre line of pulley becomes
very great, owing to their necessary large width.
(g) The Koepe System of Winding,— An iron pulley with a siugle circular
groove takes the place of the ordinary drum. The winding rope passes
from one cage, over its head-gear pulley, round the drum, and, after pass
CRANES. 911
ing over the other head-gear pulley, is connected with the second cage. The
wind ing rope thus encircles about half the periphery of the drum in the
same manner as a driving-belt on an ordinary pulley. There is a balance
rope beneath the cages, passing round a pulley in the sump; the arrange-
in -nt may be likened to an endless rope, the two cages being simply points
of attachment.
CRANES.
Classification, of Cranes* (Henry R. Towne, Trans. A. S. M. E., iv.
288. Revised in Hoisting, published by The Yale & Towne Mfg. Co.)
A Hoist is a machine for raising and lowering weights. A Crane is a
hoist with the added capacity of moving the load in a horizontal or lateral
direction.
Cranes are divided into two classes, as to their motions, viz., Rotary and
Rectilinear, and into four groups, as to their source of motive power, viz.:
Hand.— When operated by manual power.
Power. — When driven by power derived from line shafting.
Steam, Electric, Hydraulic, or Pneumatic.— When driven by an engine or
motor attached to the crane, and operated by steam, electricity, water, or
air transmitted to the crane from a fixed source of supply.
Locomotive. — When the crane is provided with its own boiler or other
generator of power, and is self-propelling ; usually being capable of both
rotary and rectilinear motions.
, Rotary and Rectilinear Cranes are thus subdivided :
ROTARY CRANES.
(1) Swing-cranes. — Having rotation, but no trolley motion.
(2) Jib-cranes. — Having rotation, and a trolley travelling on the jib.
(3) Column-cranes.— Identical with the jib-cranes, but rotating around a
fixed column (which usually supports a floor above).
(4) Pillar-cranes. — Having rotation only; the pillar or column being sup-
ported entirely from the foundation.
(5) Pillar Jib-cranes. — Identical with the last, except in having a jib and
trolley motion.
(6) Derrick-cranes.— Identical with jib-cranes, except that the head of the
mast is held in position by guy- rods, instead of by attachment to a roof or
ceiling.
(7) Walking-cranes.— Consisting of a pillar or jib-crane mounted on wheels
and arranged to travel longitudinally upon one or more rails.
(8) Locomotive-cranes.— Consisting of a pillar crane mounted on a truck,
and provided with a steam-engine capable of propelling and rotating the
crane, and of hoisting and lowering the load.
RECTILINEAR CRANES.
(9) Bridge-cranes.— Having a fixed bridge spanning an opening, and a
trolley moving across the bridge.
(10) Tram-cranes.— Consisting of a truck, or short bridge, travelling lon-
gitudinally on overhead rails, and without trolley motion.
(11) Travelling-cranes.— Consisting of a bridge moving longitudinally on
overhead tracks, and a trolley moving transversely on the bridge.
(12) Gantries.— Consisting of an overhead bridge, carried at each end by a
trestle travelling on longitudinal tracks on the ground, and having a trolley
moving transversely on the bridge.
(13) Rotary Bridge-cranes.— Combining rotary and rectilinear movements
and consisting of a bridge pivoted at one end to a central pier or post,
and supported at the other end on a circular track ; provided with a trolley
moving transversely on the bridge.
For descriptions of these several forms of cranes see Towne's "Treatise
on Cranes."
Stresses in Cranes.— See Stresses in Framed Structures, p. 440, ante.
Position of the Inclined Brace in a Jib-crane.— The most
economical arrangement is that in which the inclined brace intersects the
jib at a distance from the mast equal to four fifths the effective radius of
the crane. (Hoisting.)
A. Large Travelling-crane, designed and built by the Morgan
Engineering Co., Alliance, O., for the 12-inch-gnn shop at the Washington
Navy Yard, is described in American Machinist, June 12, 1890. Capacity,
150 net tons; distance between centres of inside rails, 59 ft. 6 in.; maximum
cross travel, 44 ft. 2 in.; effective lift, 40 ft.; four speeds for main hoist, 1, 2.
912 HOISTIKG.
4, and 8 ft. per min.; loads for these speeds, 150, 75, 3?^, and 18% tons respec-
tively; traversing speeds of trolley on bridge, 25 and 50 ft. per minute;
speeds of bridge on main track, 30 and 60 ft. per minute. Square shafts are
employed for driving.
A 150-ton Pillar-crane was erected in 1893 on Finnieston Quay,
Glasgow. The jib is formed of two steel tubes, each 39 in. diam. and 90 ft.
long. The radius of sweep for heavy lifts is 65 ft. The jib and its load are
counterbalanced by a balance-box weighted with 100 tons of iron and steel
punchings. In a test a 130- ton load was lifted at the rate of 4 ft. per minute,
and a complete revolution made with this load in 5 minutes. Eng'g News,
July 20, 1893.
Compressed-air Travelling-cranes. —Compressed-air overhead
travelling-cranes have been built by the Lane & Bodley Co., of Cincinnati.
They are of 20 tons nominal capacity, each about 50 ft. span and 400 ft. length
of travel, and are of the triple-motor type, a pair of simple reversing-engines
being used for each of the necessary operations, the pair of engines for the
bridge and the pair for the trolley travel being each 5-inch bore by 7-inch
stroke, while the pair for hoisting is 7-inch bore by 9-inch stroke. Air is
furnished by a compressor having steam and air cylinders each 10-in. diam.
and 12-in. stroke, which with a boiler-pressure of about 80 pounds gives an air-
pressure when required of somewhat over 100 pounds. The air -compressor
is allowed to run continuously without a governor, the speed being regulated
by the resistance of the air in a receiver. From a pipe extending from the
receiver along one of the supporting trusses communication is continuously
maintained with an auxiliary receiver on each traveller by means of a one-
inch hose, the object of the auxiliary receiver being to provide a supply of
air near the engines for immediate demands and independent of the hose
connection, which may thus be of small dimension. Some of the advantages
said to be possessed by this type of crane are: simplicity; absence of all mov-
ing parts, excepting those required for a particular motion when that motion
is in use; no danger from fire, leakage, electric shocks, or freezing; ease of
repair; variable speeds and reversal without gearing; almost entire absence
of noise; and moderate cost.
Quay-cranes.— An illustrated description of several varieties of sta-
tionary and travelling cranes, with results of experiments, is given in a
paper on Quay-cranes in the Port of Hamburg by Chas. Nehls, Trans. A. S.
C. E., Chicago Meeting, 1893.
Hydraulic Cranes, Accumulators, etc.— See Hydraulic Press-
ure Transmission, page 616, ante.
Electric Cranes.— Travelling-cranes driven by electric motors have
largely supplanted cranes driven by square shafts or flying-ropes. Each of
the three motions, viz., longitudinal, traversing and hoisting, is usually ac-
complished by a separate motor carried upon the crane.
COAL-HANDLING MACHINERY.
The following notes and tables are supplied by the Link-Belt Engineer-
ing Co. of Philadelphia, Pa.:
In large boiler-houses coal is usually delivered from hopper-cars into
a track-hopper, about 10 feet wide, and 12 to 16 feet long. A feeder
set under the track-hopper feeds the coal at a regular rate to a crusher,
which reduces it to a size suitable for stokers.
After crushing, the coal is elevated or conveyed to overhead storage-bins.
Overhead stprage is preferred for several reasons:
1. To avoid expensive wheeling of coal in case of a breakdown of the
coal-handling machinery.
2. To avoid running the coal-handling machinery continuously.
3. Coal kept under cover indoors will not freeze in winter and clog the
supply-spouts to the boilers.
4. It is often cheaper to store overhead than to use valuable ground-
space adjacent to the boiler-house.
5. As distinguished from vault or outside hopper storage, it is cheaper
to build steel bins and supports than masonry pits.
COAL-HANDLING MACHINERY. 9J2</>
Weight of Overhead Bins.— Steel bins of approximately rectangu-
lar cross-section, say 10 X 10 feet, will weigh, exclusive of supports, about
one-sixth as much as the contained coal. Larger bins, with sloping bottoms,
may weigh one-eighth as much as the contained coal. Bag bottom bins of
the Berquist type will weigh about one-twelfth as much as the contained
coal, not including posts, and about one-ninth as much, including posts.
Supply-pipes from Bins.— The supply-pipes from overhead bins
to the boiler-room floor, or to the stoker-hoppers, should not be less than
12 inches in diameter. They should be fitted at the top with a flanged
casting and a cut-off gate, to permit removal qf the pipe when the boilers
are to be cleaned or repaired.
Types of Coal Elevators.— Coal elevators consist of buckets of
various shapes attached to one or more strands of link-belting or chain,
or to rubber belting. The buckets may either be attached continuously
or at intervals. The various types are as follows:
Continuous bucket elevators consist usually of one strand of chain and
two sprocket-wheels with buckets attached continuously to the chain.
Each bucket after passing the head wheel acts as a chute to direct the
flow from the next bucket. This type of elevator will handle the larger
sizes of coal. It runs at slow speeds, usually from 90 to 175 feet per min-
ute, and has a maximum capacity of about 120 tons per hour.
Centrifugal discharge elevators consist usually of a single strand of chain,
with the buckets attached thereto at intervals. They are used to handle
the smaller sizes of coal in small quantities. They run at high speeds,
usually 34 to 40 revolutions of the head wheel per minute, and have a
capacity up to 40 tons per hour.
Perfect discharge elevators consist of two strands of chain, with buckets
at intervals between them. A pair of idlers set under the head wheels
cause the buckets to be completely inverted, and to make a clean delivery
into the chutes at the elevator head. This type of elevator is useful in
handling material which tends to cling to the buckets. It runs at slow
speeds, usually less than 150 feet per minute. The capacity depends on
the size of the buckets.
Combined Elevators and Conveyors are df the following types:
Gravity discharge elevators, consisting of two strands of chain, with spaced
V-shaped buckets fastened between them. After passing the head wheels
the buckets act as convey or -flights and convey the coal in a trough to
any desired point. This is the cheapest type of combined elevator and
conveyor, and is economical of power. A machine carrying 100 tons of
coal per hour, in buckets 20 inches wide, 10 inches deep, and 24 inches long,
spaced 3 feet apart, requires 5 H. P. when loaded and 1}^ H.P. when empty
for each 100 feet of horizontal run, and % H.P. for each foot of vertical lift.
Rigid bucket-carriers consist of two strands of chain with a special bucket
rigidly fastened between them. The buckets overlap and are so shaped
that they will carry coal around three sides of a rectangle. The coal is
carried to any desired point and is discharged by completely inverting
the bucket over a turn-wheel.
Pivoted bucket- carriers consist of two strands of long pitch steel chain to
which are attached, in a pivotal manner, large malleable iron or steel buckets
so arranged that their adjacent lips are close together or overlap. Over-
lapping buckets require special devices for changing the lap at the corner
turns. Carriers in tvhich the buckets do not overlap should be fitted with
auxiliary pans or buckets, arranged in such a manner as to catch the spill
which falls between the lips at the loading point, and so shaped as to return
the spill to the buckets at the corner turns. Pivoted bucket carriers will
carry coal around four sides of a rectangle, the buckets being dumped on
the horizontal run by striking a cam suitably placed. Carriers of this type
are economical of power, but are costly and of relatively low capacity.
Coal Conveyors. — Coal conveyors are of four general types, viz.,
scraper or flight, bucket, screw, and belt conveyors.
The flight conveyor consists of a trough of any desired cross-section and
a single or double strand of chain carrying scrapers or flights of approxi-
mately the same shape as the trough. The flights push the coal ahead
of them in the trough to any desired point, where it is discharged through
openings in the bottom of the trough.
For short, low-capacity conveyors, malleable link hook-joint chains
are used. For heavier service, malleable pin-joint chains, steel link chains,
9126
COAL-HANDLING MACHINERY.
or monobar, are required For the heaviest service, two strands of steel
link chain, usually with rollers, are used.
Flight conveyors are of three types: plain scraper, suspended flight,
and roller flight
In the plain scraper conveyor, the flight is suspended from the chain
and drags along the bottom of the trough. It is of low first cost and is
useful where noise of operation is not objectionable. It has a maximum
capacity of about 30 tons per hour, and requires more power than either
of the other two types of flight conveyors.
Suspended flight conveyors use one or two strands of chain. The flights
are attached to cross-bars having wearing-shoes at each end. These wear-
ing-shoes slide on angle-iron tracks on each side of the conveyor trough. The
flights do not touch the trough at any point. This type of conveyor is
used where quietness of operation is a consideration. It is of higher first
cost than the plain scraper conveyor, but requires one-fourth less power
for operation. It is economical up to a capacity of about 80 tons per hour.
The roller flight conveyor is similar to the suspended flight, except that
the wearing-shoes are replaced by rollers. It is highest in first cost of
all the flight conveyors, but has the advantages of low power consump-
tion (one-half that of the scraper), low stress in chain, long life of chain,
trough, and flights, and noiseless operation. It has an economical maxi-
mum capacity of about 120 tons per hour.
The following formula gives approximately the horse-power at the head
wheel required to operate flight conveyors:
H.P. = (ATL + BWS) -4- 1000.
7* = tons of coal per hour; L = length of conveyor in feet, centre to
centre; W = weight of chain, flights, and shoes (both runs) in pounds;
S — speed in feet per minute; A and B constants depending on angle of
incline from horizontal. See example below.
Values of A and B.
Angle ,
Deg.
A
B
Angle,
Deg.
A
B
Angle,
Deg.
A
B
0
2
4
6
8
.343
.378
.40
.44
.47
.01
.01
.01
.01
.01
10
14
18
22
26
.50
.57
.63
.69
.74
.01
.01
.009
.009
.009
30
34
38
42
46
.79
.84
.88
.92
.95
.009
.008
.008
.007
.007
For suspended flight conveyors take B as 0.8, and for roller flights as 0.6 ,
of the values given in the table.
Weight of Chain in Pounds per Foot.
LINK-BELTING.
MONOBAR.
Chain
No.
Pitch of Flights,
Inches.
Chain
No.*
Pitch of Flights, Inches.
12
18
24
36
12
18
24
36
48
54
72
2 4
2 3
O OA
2 2
612
3 9
3 6
3 5
88
2 8
2'.7 2'.Q
2.5'
618
3.0
2.8
2.7
85
3.1
2.8:2.7
2.6
818
5.7
5.5
5.3
103
4 6
4.4
4.3
4.2
824
4. 9
4.7
4.6
108
4 9
4.7i4.4
4.1
1018
11.5
16.7
10.4
110
5.6
5.2
4 9
4.7
1024
9.6
9.07
8.8
114
6 3
6.05.9
5.7j
1224
14.7
14.04
13.8
122
8,1
7.7
7.4
7.2,
1236
ii.8
11.34
124
8.9
8.4
8.2
7.9
1424
-20 . r>
i9.7
19.4
* In monobar the first one or two figures in the number of the chain
denote the diameter of the chain in eighths of an inch. The last two fig-
ures denote the pitch in inches.
COAL-HANDLING MACHINERY.
912c
PIN CHAINS.
ROLLER CHAINS.
No.
Pitch of Flights,
Inches.
No.
Pitch of Flights, Inches.
12
18
24
36
12
18
'24
36
720
730
825
5.9
6.9
9.6
5.0
6.6
9.3
5.4
6.4
9.1
5.3
6.3
8.9
1112
1113
1130
7.7
9.5
10.5
6.9
8.8
9.5
6.2
8.0
9.0
5.7
7.5
7.8
Weight of Flights with Wearing-shoes and Bolts.
Suspended Flights.
Size, Inches.
Steel.
Malleable
Iron.
Size.
Weight, Lbs.
4X 10
3.5
4.3
6X14
12.37
4X12
3.9
4.7
8X19
15.55
5X10
4.1
5.2
10X24
25.57
5X12
4.6
5.7
10X30
29.37
5X15
5.8
5.9
10X36
33.17 '
6X18
8.1
9.2
10X42
34.97
8X18
10.1
12.7
8X20
11.0
13.4
8X24
12.6
14.4
10X24
15.2
17.4
EXAMPLE. — Required the H.P. for a monobar conveyor 200 ft. centre
to centre, carrying 100 tons of coal per hour, up a 10° incline at a speed
of 100 feet per minute. Conveyor has No. 818 chain arid 8X19 suspended
flights, spaced 18 inches apart.
„ _, _ .5 X 100 X 200 + .008(400 X 5.7 + 267 X 15.55) X 100 _ .
1000
The following table shows the conveying capacities of various sizes of
nights at 100 feet per minute in tons of 2000 Ibs. per hour. The values
are true for continuous feed only.
Size
of
Flight.
Horizontal Conveyors.
Inclined Conveyors.
Flight
Every
16".
Flight
Every
18".
Flight
Every
24".
Pounds
Coal
per
Flight.
10°
Flights
Every
24".
20°
Flights
Every
24".
30°
Flights
Every
24".
6X14
8X19
10X24
10X30
10X36
10X42
Tons.
69.75
Tons.
62
130
Tons.
46.5
97.5
172.5
220
268
315
31
65
115
147
179
210
Tons.
40.5
78
150
184
225
264
Tons.
31.5
62
120
146
177
210
Tons.
22.5
52
90
116
142
167
Bucket Conveyors.— Rigid bucket-carriers are used to convey
large quantities of coal over a considerable distance when there is no
intermediate point of discharge. These conveyors are made with two
strands of steel roller chain. They are built to carry as much as 10 tons
of coal per minute. -
WIRE-ROPE HAULAGE.
Screw Conveyors. — Screw conveyors consist of a helical steel
flight, either in one piece or in sections, mounted on a pipe or shaft, and
running in a steel or wooden trough. These conveyors are made from 4 to
18 inches in diameter, and in sections 8 to 12 feet long. The speed ranges
from 20 to 60 revolutions per minute and the capacity from 10 to 30 tons
of coal per hour. It is not advisable to use this type of conveyor for coal,
as it will only handle the smaller sizes and the flights are very easily dam-
aged by any foreign substance of unusual size or shape.
Belt Conveyors. — Rubber or cotton belt conveyors are used for
handling coal, grain, sand, or other finely divided material. They com-
bine a high carrying capacity with low power consumption, but are rela-
tively high in first cost.
In some cases the belt is flat, the material being fed to the belt at it i
centre in a narrow stream. In the majority of cases, however, the bel ;
is troughed by means of idler pulleys set at an angle from the horizontal
and placed at intervals along the length of the belt. Rubber belts aro
very often made more flexible for deep troughing by removing some oir
the layers of cotton from the belt and substituting therefor an extra thick-
ness of rubber.
Belt conveyors may be used for elevating materials up to about 23°
incline. On greater inclines the material slides back on the belt and spills.
With many substances it is important to feed the belt steadily if the con-
veyor stands at or near the limiting angle. If the flow is interrupted
the material may slide back on the belt.
Belt conveyors are run at any speed from 200 to 800 feet per minute,
and are made in widths varying from 12 inches to 60 inches.
Capacity of Belt Conveyors In Tons of Coal per Hour.
Width
of
Belt,
Ins.
Velocity of Belt, Feet per Minute.
300
350
31.5
42.8
56
70.8
87.5
126
197
283
400
450
500
550
49.5
67.4
88
111
137.5
198
307
446
600
12
14
16
18
20
24
30
36
27
36.7
48
60.7
75
108
168.7
243
36
49
64
81
100
144
225
324
40.5
55.2
72
91.2
112.5
162
253
365 $
45
61.3
80
101
125
180
281
405
54
73.6
96
135
150
216
338
486
For materials other than coal, the figures in the above table should
be multiplied by the coefficients given in the table below:
Material.
Coefficient.
Material.
Coefficient.
A h (dam )
0 86
Earth
1.4
P t
1 76
Sand
1.8
Clay
1.26
Stone (crushed)
2.0
Coke
0.60
; :
Carrying"bands or Belts, used for the purpose of sorting coal and
removing impurities, are sometimes made of ar» endless length of woven
wire, or of two or three endless chains, carrying steel plates varying in width
from 6 inches to 14 inches. (Proc. Inst. M. E., July, 1890.)
Grain-elevators. — American Grain-elevators are described in a
paper by E Lee Heidenreich, read at the International Engineering Con-
gress at Chicago (Trans. A. S. C. E., 1893). See also Trans. A. S. M. E., vn,
660.
WIRE-ROPE HAULAGE.
Methods for transporting coal and other products by means of wire rope,
though varying from each other in detail, may be grouped in five classes;
I. The Self-acting or Gravity Inclined Plane.
II. The Simple Engine-plane.
WIRE-ROPE HAULAGE. 913
III. The Tail-rope System.
IV. The Endless- rope System
V. The Cable Tramway.
The following brief description of these systems is abridged from a
pamphlet on Wire-rope Haulage, by Wm. Hildenbrand, G.E., published by
John A. Roebling's Sons Co., Trenton, N. J.
I. The Self-acting Inclined Plane.— The motive power for the
self-acting inclined plane is gravity; consequently this mode of transport-
ing coal finds application only in places where the coal is conveyed from a
higher to a lower point and. where the plane has sufficient grade for the
loaded descending cars to raise the empty cars to an upper level.
At the head of the plane there is a drum, which is generally constructed
of wood, having a diameter of seven to ten feet. It is placed high enough
to allow men and cars to pass under it. Loaded cars coming from the pit
are either singly or in sets of two or three switched on the track of the
plane, and their speed in descending is regulated by a brake on the drum.
Supporting rollers, to prevent the rope dragging on the ground, are
fnerally of wood, 5 to 6 inches in diameter and 18 to 24 inches long, with
• to %-inch iron axles. The distance between the rollers varies from 15 to
feet, steeper planes requiring less rollers than those with easy grades.
Considering only the reduction of friction and what is best for the preserva-
tion of rope, a general rule may be given to use rollers of the greatest
possible diameter, and to place them as close as economy will permit.
The smallest angle of inclination at which a plane can be made self-acting
will be when the motive and resisting forces balance each other. The
motive forces are the weights of the loaded car and of the descending rope.
The resisting forces consist of the weight of the empty car and ascending
rope, of the rolling and axle friction of the cars, and of the axle friction of
the supporting rollers. The friction of the drum, stiffness of rope, and
resistance of air may be neglected. A general rule cannot be given, because
a change in the length of the plane or in the weight of the cars changes the
proportion of the forces; also, because the coefficient of friction, depending
on the condition of the road, construction of the cars, etc., is a very uncer-
tain factor.
For working a plane with a %-inch steel rope and lowering from one to
four pit cars weighing empty 1400 Ibs. and loaded 4000 Ibs., the rise in 100
feet necessary to make the plane self-acting will be from about 5 to 10 feet,
decreasing as the number of cars increase, and increasing as the length of
plane increases.
A gravity inclined plane should be slightly concave, steeper at the top
than at the bottom. The maximum deflection of the curve should be at an
inclination of 45 degrees, and diminish for smaller as well as for steeper
Inclinations.
II. The Simple Engine-plane,— The name '* Engine-plane " is
given to a plane on which a load is raised or lowered by means of a single
wire rope and stationary steam-engine. It is a cheap and simple method of
conveying coal underground, and therefore is applied wherever circum-
stances permit it.
Under ordinary conditions such as prevail in the Pennsylvania mine
region, a train of twenty-five to thirty loaded cars will descend, with reason-
able velocity, a straight plane 5000 feet long on a grade of 1% feet in 100,
while it would appear that 2*4 feet in 100 is necessary for the same number
of empty cars. For roads longer than 5000 feet, or when containing sharp
curves, the grade should be correspondingly larger.
III. The Tail-rope System.— Of all methods for conveying coal
underground by wire rope, the tail-rope system has found the most applica-
tion. It can be applied under almost any condition. The road may be
straight or curved, level or undulating, in one continuous line or with side
branches. In general principle a tail-rope plane is the same as an engine-
plane worked in both directions with two ropes. One rope, called the " main
rope," serves for drawing the set of full cars outward; the other, called
the " tail-rope," is necessary to take back the empty set, which on a level
or undulating road cannot return by gravity. The two drums may be
located at the opposite ends of the road, and driven by separate engines,
but more frequently they are on the same shaft at one end of the plane.
In the first case each rope would require the length of the plane, but in the
second case the tail rope must be twice as long, being led from the drum
around a sheave at the other end of the plane and back again to its starting-
914 HOISTINO.
point. When the mam rope draws a set of full cars out, the tail-rope drum
runs loose on the shaft, and the rope, being attached to the rear car, un-
winds itself steadily. Going in, the reverse takes place. Each drum is
provided with a brake to check the speed of the train on a down grade and
prevent its overrunning the forward rope. As a rule, the tail rope is
strained less than the main rope, but in cases of heavy grades dipping out-
ward it is possible that the strain in the former may become as large, or
even larger, than in the latter, and in the selection of the sizes reference
should be had to this circumstance.
IV. The Endless-rope System.— The principal features of this
system are as follows:
1. The rope, as the name indicates, is endless.
2. Motion is given to the rope by a single wheel or drum, and friction is
obtained either by a grip-wheel or by passing the rope several times around
the wheel.
3. The rope must be kept constantly tight, the tension to be produced by
artificial means. It is done in placing either the return-wheel or an extra
tension wheel on a carriage and connecting it with a weight hanging over a
pulley, or attaching it to a fixed post by a screw which occasionally can be
shortened.
4. The cars are attached to the rope by a grip or clutch, which can take
hold at any place and let go again, starting and stopping the train at will,
without stopping the engine or the motion of the rope.
5. On a single-track road the rope works forward and backward, but on a
double track it is possible to run it always in the same direction, the full
cars going on one track and the empty cars on the other.
This method of conveying coal, as a rule, has not found as general an in-
troduction as the tail-rope system, probably because its efficacy is not so
apparent and the opposing difficulties require greater mechanical skill and
more complicated appliances. Its advantages are, first, that it requires
one third less rope than the tail-rope system. This advantage, however,
is partially counterbalanced by the circumstance that the extra tension in
the rope requires a heavier size to move the same load than when a main
and tail rope are used. The second and principal advantage is that it is
possible to start and stop trains at will without signalling to the engineer.
On the other hand, it is more difficult to work curves with the endless sys-
tem, and still more so to work different branches, and the constant stretch
of the rope under tension or its elongation under changes of temperature
frequently causes the rope to slip on the wheel, in spite of every att'ention,
causing delay in the transportation and injury to the rope.
V. "Wire-rope Tramways.— The methods of conveying products on
a suspended rope tramway find especial application in places where a mine
is located on one side of a river or deep ravine and the loading station on
the other. A wire rope suspended between the two stations forms the track
on which material in properly constructed "carriages" or "buggies" is
transported. It saves the construction of a bridge or trestlework, and is
practical for a distance of 2000 feet without an intermediate support.
There are two distinct classes of rope tramways:
1. The rope is stationary, forming the track on which a bucket holding
the material moves forward and backward, polled by a smaller endless
wire rope.
. 2. The rope is movable, forming itself an endless line, which serves at
/ the same time as supporting track and as pulling rope.
Of these two the first method has found more general application, and is
especially adapted for long spans, steep inclinations, and heavy loads. The
second method is used for long distances, divided into short spans, and is
only applicable for light loads which are to be delivered at regular intervals.
For detailed descriptions of the several systems of wire-rope transporta-
tion, see circulars of John A. Roebling's Sons Co., The Trenton Iron Co., and
other wire-rope manufacturers. See also paper on Two-rope Haulage
Systems, by R. Van A. Norris, Trans. A. S. M. E., xii. 626.
In the Bleichert System of wire-rope tramways, in which the track rope is
stationary, loads of 1000 pounds each and upward are carried. While the
average spans on a level are from 150 to 200 feet, in crossing rivers, ravines,
etc., spans up to 1500 feet are frequently adopted. In a tramway on this
system at Granite, Montana, the total length or the line is 9750 feet, with a
fall of 1225 feet. The descending loads, amounting to a constant weight of
about 11 tons, develop over 14 horse-power, which is sufficient to haul the
empty buckets as well as about 50 tons of supplies per day up the line, and
SUSPENSION CABLEWAYS OR CABLE HOISTS. 915
also to run the ore crusher and elevator. It is capable of delivering 250
tons of material in 10 hours.
Suspension Cableways or Cable Hoist-conveyors.
(Trenton Iron Co.)
In quarrying, rock-cutting, stripping, piling, dam-building, and many
other operations where it is necessary to hoist and convey large individual
loads economically, it frequently happens that the application of a system
of derricks is impracticable, by reason of the limited areaof their efficiency
and the room which they occupy.
To meet such conditions cable hoist-conveyors are adapted, as they can be
operated in clear spans up to 1500 feet, and in lifting individual loads up to
15 tons. Two types are made— one in which the hoisting and conveying are
done by separate running ropes, and the other applicable only to inclines,
in which the carriage descends by gravity, and but one running rope is re-
quired. The moving of the carriage in the former is effected by means of
an endless rope, and these are commonly known as "endless-rope" hoist-
conveyors to distinguish them from the latter, which are termed "inclined "
hoist-conveyors.
The general arrangement of the endless-rope hoist-conveyors consists of a
main cable passing over towers, A frames or masts, as may be most conve-
nient, and anchored firmly to the ground at each end, the requisite tension
in the cable being maintained by a turnbuckle at one anchorage.
Upon this cable travels the carriage, which is moved back and forth over
the line by means of the endless rope. The hoisting is done by a separate
rope, both ropes being operated by an engine specially designed for the
Eurpose, which may be located at either end of the line, and is constructed
i such a way that the hoist ing- rope is coiled up or paid out automatically
as the carriage is moved in and out. Loads may be picked up or discharged
at any point along the line. Where sufficient inclination can be obtained in
the main cable for the carriage to descend by gravity, and the loading and
unloading is done at fixed points, the endless rope can be dispensed with.
The carriage, which is similar in construction to the carriage used in the
endless-rope cableways, is arrested in its descent by a stop-block, which
may be clamped to the main cable at any desired point, the speed of the
descending carriage being under control of a brake on the engine-drum.
Stress in Hoisting-ropes on Inclined Planes*
(Trenton Iron Co.)
fej
o|
5 II
fe*1
•si
.all
S--3
•sl
all
£88
£ <3
$£|
Isl
<D o3
US
111
Q) O ®
.CCO.N
•a!
111
K"s
%a
a§|-g
* 1
*n
g|o
XI
^1
«}£'o
ft.
ft.
ft.
5
2° 52'
140
55
28° 49'
1003
110
47° 44'
1516
10
5° 43'
240
60
30° 58'
1067
120
50° 12'
1573
15
8° 32'
336
65
33° 02'
1128
130
52° 26'
1620
20
11° 10'
432
70
35° 00'
1185
140
54° 28'
1663
25
14° 03'
527
75
36° 53'
1238
150
56° 19'
1699
30
16° 42'
613
80
38° 40'
1287
160
58° 00'
1730
35
19° 18'
700
85
40° 22'
1332
170
59° 33'
1758
40
21° 49'
782
90
42° 00'
1375
180
60° 57'
1782
45
24° 14'
860
95
43° 32'
1415
190
62° 15'
1804
50
26° 34'
933
100
45° 00'
1450
200
63° 27'
1822
' The above table is based on an allowance of 40 Ibs. per ton for rolling fric-
tion, but an additional allowance must be made for stress due to the weight
of the rope proportional to the length of the plane. A factor of safety of 5
to 7 should be taken.
In hoisting the slack-rope should be taken up gently before beginning the
lift, otherwise a severe extra strain will be brought on the rope.
A Double-suspension Cableway, carrying loads of 15 tons, erected near
Williamsport, Pa., by the Trenton Iron Co., is described by E. G. Spilsbury
in Trans. A. I. M. E. xx. 766. The span is 733 feet, crossing the Susquehanna
River. Two steel cables, each 2 in. diam., are used. On these cables runs a
carriage supported on four wheels and moved by an endless cable 1 inch in
diam. The load consists of a cage carrying c. railroad-car loaded with lum-
910
HOISTIKG.
ber, the latter weighing about 12 tons. The power is furnished by a 50-H.P.
engine, and the trip across the river is made in about three minutes.
A hoisting cableway on the endless-rope system, erected by the Lidger-
wood Mfg. Co., at the Austin Dam, Texas, had a single span 1350 ft. in
length, with main cable 2J/6 in. diam., and hoisting-rope 1% in. diam. Loads
of 7 to 8 tons were handled at a speed of 600 to 800 ft. per minute.
Another, of still longer span, 1650 ft., was erected by the same company at
Holyoke, Mass., for use in the construction of a dam. The main cable is
the Elliott or locked wire cable, having a smooth exterior. In the construc-
tion of the Chicago Drainage Canal twenty cableways, of 700 ft. span and 8
tons capacity, were used, the towers travelling on rails.
Tension required to Prevent Slipping of Rope on Drum*
(Trenton Iron Co.)— The amount of artificial tension to be applied in an
endless rope to prevent slipping on the driving-drum depends on the char-
acter of the drum, the condition of the rope and number of laps which it
makes. If Tand S represent respectively the tensions in the taut and slack
lines of the rope; TF, the necessary weight to be applied to the tail-sheave;
J?, the resistance of the cars and rope, allowing for friction; n, the number
of half-laps of the rope on the driving-drum; and/, the coefficient of fj*io
tion, the following relations must exist to prevent slipping:
r=Se/n7r, W=T+S, and R = T - S\
from which we obtain
in which e = 2.71828, the base of the Naperian system of logarithms.
The following are some of the values of/ :
Dry. Wet. Greasy.
Wire-rope on a grooved iron drum 120 .085 .070
Wire-rope on wood-filled sheaves 235 .170 .140
Wire-rope on rubber and leather filling.. .495 .400 .205
The importance of keeping the rope dry is evident from, these figures.
efnir i |
The values of the coefficient , corresponding to the above values
efmr _ !
of/, for one up to six half-laps of the rope on the driving-drum or sheaves,
are as follows:
n = Number of Half -laps on Driving-wheel.
1
2
3
4
5
6
.070
9.130
4.623
8.141
2.418
1.999
1.729
.065
7.536
3.833
2.629
2.047
1.714
1.505
.120
5.345
2.777
1.953
.570
.358
.232
.140
4.623
2.418
1.729
.416
.249
.154
.170
3.833
2.047
1.505
.268
.149
.085
.205
3.212
1.762
1.338
.165
.083
.043
.235
2.831
1.592
1.245
.110
.051
.024
.400
1.795
1.176
1.047
.013
.004
.001
.495
1.538
1.093
1.019
.004
.001
When the rope is at rest the tension is distributed equally on the two lines
of the rope, but when running there will be a difference in the tensions of
the taut and slack lines equal to the resistance, and the values of T and 3
may be readily computed from the foregoing formulae.
Taper Ropes of Uniform Tensile Strength.— The true form
of rope is not a regular taper but follows a logarithmic curve, the girth
rapidly increasing toward the upper end. Mr. Chas. D. West gives the fol-
lowing formula, based on a breaking strain of 80.000 Ibs. per sq. in. of the
rope, core included, and a factor of safety of 10: log G = F/3680 -4- log <?, in
which F = length in fathoms, and G and g the girth in inches at any two
sections .F fathoms apart. The girth g is first calculated fora safe strain
of 8000 Ibs. per sq. in., and then G is obtained by the formula. For a
mathematical investigation see The Engineer, April, 1880, p. 267.
TRANSMISSION OF POWER BY WIRE ROPE.
917
TRANSMISSION OP POWER BY WIRE ROPE.
The following notes have been furnished to the author by Mr. Wm. Hewitt,
Vice-President of the Trenton Iron Co. (See also circulars of the Trenton
Iron Co. and of the John A. Roebling's Sons Co., Trenton, N. J. ; "Trans-
mission of Power by Wire Ropes," by A. W. Stahl, Van Nostrand's Science
Series, No. 28; and Reuleaux's Constructor.)
The force transmitted should not exceed the difference between the
elastic limit of the wires and the bending stress as determined by the fol-
lowing tables, taking the elastic limit of tempered steel, such as is used in
the best rope, at 57,000 Ibs. per sq. in., and that of Swedish iron at half this,
or 28,500 Ibs. (The el. Jim. of fine steel wires may be higher than 57,000 Ibs.)
. Elastic Limit of Wire Ropes.
7- Wire Rope.
Diam. of
Wires.
Aggregate
Area of Wires.
Elastic Limit.
Steel.
Elastic Limit.
Iron.
diam., in.
ins.
sq. in.
Ibs.
Ibs.
VA,
.038
.025862
1,474
737
5/16
.035
.040409
2.303
1,152
%
.042
.058189
3.317
1,659
7/16
.049
.079201
4,514
2,257
H
.055
.099785
5,688
2,844
9/16
.0625
.128855
7,345
3,672
%
.070
.161635
9,213
4,607
11/16
.076
.190532
10,860
5,430
ft£
.083
.227246
12,953
6,477
%
.097
.310373
17,691
8,846
1
.111
.406430
23,167
11,583
19-Wire Rope.
M
.017
.025876
5/16
.021
.039485
%
.024
.051573
The elastic limit of 19- wire
7/16
K
.029
.033
.075299
.097504
rope may be taken the same
as for 7-wire rope since the
9/16
.0375
.125909
ultimate strength of the
%
.042
.157941
wires is 7 to 10 per cent
11/16
.046
.189453
greater.
m&
.050
.223839
%
• .058
.301198
1
.067
.401925
The working tension may be greater, therefore, as the bending stress is
less; but since the tension in the slack portion of the rope cannot be less
than a certain proportion of the tension in the taut portion, to avoid
slipping, a ratio exists between the diameter
of sheave and the wires composing the rope,
corresponding to a maximum safe working
tension. This ratio depends upon the nurn- <
ber of laps that the rope makes about the
sheaves, and the kind of filling in the rims, or
the character of the material upon which the
rope tracks.
The sheaves (Fig. 165) are usually of
cast iron, and are made as light as possible
consistent with the requisite strength. Vari-
ous materials have been used for filling the
bottom of the groove, such as tarred oakum,
jute yarn, hard wood, India-rubber, and
leather. The filling which gives the best S
satisfaction, however, in ordinary transmis- ,
sions consists of segments of leather and *
blocks of India-rubber soaked in tar and *IG- lbo-
packed alternately in the groove. Where the working tension is very
Section
of Rim.
Section I
of Arm. I
918 TRANSMISSION OF POWER BY WIRE ROPE.
great, however, the wood filling is to be preferred, as in the case of long-dis
tar>ce transmissions where the rope makes several laps about the sheaves
and is run at a comparatively slow speed.
The Bending Stress is determined by the formula
k =
Ea
2.06(# -f- d) -f- C'
fc = bending stress in Ibs.; E = modulus of elasticity — 28,500,000 ; a = ag-
gregate area of wires, sq. ins.; R = radius of bend; d = diam. of wires, ins.
For 7-wirerope d = 1/9 diam. of rope; C = 27.54.
" 19-wire " d = 1/15 " " " ; C = 45.9.
From this formula the tables below have been calculatedr
Bending Stresses, 7-wire Rope.
Diam. Bend.
*4
36
48
411
556
800
1,377
2,178
3,070
4,486
6,278
8,008
10,392
16,465
24,492
34 721
60
73
84
96
108
13O
133
Diam. Rope'
14
9/32
5/16
1%
ft
L
V/s
IjJ
810
1,095
1,569
2,692
4,243
5,962
8,701
545
7S8
1,060
1,822
2,878
4,053
5,915
8,267
10,535
13,655
21,585
330
447
642
1,106
1,751
2,470
3,613
5,060
6,459
8,388
13,309
19,824
28,144
38,472
275
373
537
925
1,465
2,067
3,025
4,238
5,412
7,032
11,168
16,651
23,661
32,374
42,962
55,595
236
321
461
794
1,259
1,777
2.601
3,646
4,657
6,053
9,650
14,354
20,411
27,945
37,110
48,054
207
281
404
696
1,104
1,558
2,282
3,199
4,087
5,314
8,449
12,613
17,986
24,582
32,661
42,314
184
250
359
620
982
1,387
2,032
2,849
3,641
4,735
7,532
11,249
16,011
21,942
29,164
37,799
166
225
324
558
885
1,250
1,831
2,569
3,283
4,270
6,795
10,151
14,453
19,814
26,344
34,155
151
205
294
508
806
1,138
1,667
2,339
3,059
3,888
6,189
9,249
13,172
18,062
24,021
31,151
Bending Stresses, 19- Wire Rope.
Diam. Bend
13
34
36
48
60
73
84
96
108
180
Diam. Rope.
Y4 '
965
495
338
250
200
167
144
126
112
101
5/16
1,774
920
621
468
376
314
270
236
210
189
%
2,620
1,366
924
698
561
469
403
353
314
283
7/16
4,546
2,389
1,620
1,226
986
824
708
621
553
498
ii
6,609
3,495
2,376
1,800
1,448
1,212
1,042
913
813
738
9/16
5,089
3,468
2,630
2,118
1,773
1,525
1,338
1,191
1,074
H
7,095
4,847
3,680
2,967
2,485
2,137
1,876
1,671
1,506
11716
9,257
6,201
4,818
3,886
3,257
2,802
2.459
2,191
1,976
11,807
8,101
6,165
4,977
4,173
3,591
3,153
2,809
2,534
%
18,183
12,528
9,556
7,724
6,481
5,583
4,886
4,371
3,943
1
27,612
19,113
14,614
11,830
9,937
8,566
7,528
6,714
6,059
' i^
26,566
20,357
16,500
13,872
11,966
10,523
9,387
8,474
' (§
35 683
27,400
22,239
18,713
16,153
14,209
12,682
11,452
0
48,109
37,028
30,096
25,350
•21,897
19,272
17,209
15.545
y
61,238
47,229
38,436
32,403
28,008
24,662
22,030
19,906
59.094
48,152
40,629
35,140
30 957
27,664
25,005
3/
74,565
60,844
49,919
44,476
39,203
35,048
31,689
3
90,325
73,795
62,379
54,022
47,639
42,606
38,534
2/8
88,409
74,795
64,814
57,183
51,160
46,285
214
92,203
81,428
72,908
66,002
2H>
99,951
90,540
TRANSMISSION OF POWER BY WIRE ROPE.
919
Horse-Power Transmitted. -The general formula for the amount
of power capable of being transmitted is as follows:
H.P. = [cd2 - .000006 (w + 9i + 0a)]v;
in which d = diameter of the rope in inches, v = velocity of the rope in feet
per second, w = weight of the rope, g^ = weight of the terminal sheaves
and shafts, <72 = weight of the intermediate sheaves and shafts (all in Ibs.),
and c = a constant depending on the material of the rope, the filling in the
grooves of the sheaves, and the number of laps about the sheaves or drums,
a single lap meaning a half-lap at each end. The values of c for one up to
six laps for steel rope are given in the following table:
c = for steel rope on
Number of Laps about Sheaves or Drums.
1
2
3
4
5
6
5.61
6.70
9.29
8.81
9.93
11.95
10.62
11.51
12.70
11.65
12.26
12.91
12.16
12.66
12.97
12.56
12.83
13,00
Wood
Rubber and leather . . . .
The values of c for iron rope are one half the above.
When more than three laps are made, the characte'r of the surface in
contact is immaterial as far as slippage is concerned.
From the above formula we have the general rule, that the actual horse-
power capable of being transmitted by any wire rope approximately equals
c limes the square of the diameter of the rope in inches, less six millionths
the entire weight of all the moving parts, multiplied by the speed of the rope,
in feet per second.
Instead of grooved drums or a number of sheaves, about which the rope
makes two or more laps, it is sometimes found more desirable, especially
•where space is limited, to use grip-pulleys. The rim is fitted with a con-
tinuous series of steel jaws, which bite the rope in contact by reason of the
pressure of the same against them, but as soon as relieved of this pressure
they open readily, offering no resistance to the egress of the rope.
In the ordinary or " flying " transmission of power, where the rope makes
a single lap about sheaves lined with rubber and leather or wood, the ratio
between the diameter of the sheaves and the wires of the rope, correspond-
ing to a maximum safe working tension, is : For 7-wire rope, steel, 76.9; iron,
157.8. For 12-wire rope, steel, 59.3; iron, 122.6. For 19-wire rope, steel, 44.5;
iron, 93.1.
Diameters of Minimum Sheaves in Indies, Corresponding
to a Maximum Safe Working Tension.
Diameter
Steel.
Iron.
of Rope.
In.
7-Wire.
12-Wire.
19- Wire.
7-Wire.
12-Wire.
19 Wire.
5|
19
15
11
39
31
23
5/16
24
19
14
49
38
29
%
29
22
17
59
46
35
7/16
34
26
19
69
54
41
K
38
30
22
79
61
47
9/16
43
33
25
89
69
52
%
48
37
28
99
77
58
11/16
53
41 '
31
109
84
64
k
58
44
34
119
92
70
%
67
52
39
138
107
81
1
77
59
45
158
123
93
I
Assuming the sheaves to be of equal diameter, and of the sizes in the
^bove table, the horse-power that may be transmitted by a steel rope making
& single lap on wood-filled sheaves is given in the table on the next page,
920 TRANSMISSION OF POWER BY WIRE ROPE.
The transmissioiTof greater horse-powers than 250 is impracticable with
filled sheaves, as the tension would be so great that the filling would
quickly cut out, and the adhesion on a metallic surface would be insufficient
where the rope makes but a single lap. In this case it becomes necessary
to use the Reuleaux method, in which the rope is given more than one lap,
as referred to below, under the caption " Long-distance Transmissions."
Horse-power Transmitted by a Steel Rope on Wood-filled
Sheaves.
Diameter
Velocity of Rope in Feet per Second.
of Rope.
In.
10
20
30
40
50
60
70
80
90
100
H
4
8
13
17
21
25
28
32
37
40
5/16
7
13
20
20
33
40
44
51
57
62
%
10
19
28
38
47
56
64
73
80
89
7/16
13
26
38
51
63
75
88
99
109
121
H
17
34
51
67
83
99
115
130
144
159
9/16
22
43
65
86
106
128
147
167
184
203
%
27
53
79
104
130
155
179
203
225
247
11/16
32
63
9.-)
126
157
186
217
245
%
38
• 76
103
150
186
223
7X
52
104
156
206
1
68
135
202
The horse-power that may be transmitted by iron ropes is one half of the
above.
This table gives the amount of horse-power transmitted by wire ropes
under maximum safe working tensions. In using wood-lined sheaves, there-
fore, it is well to make some allowance for the stretching of the rope, and
to advocate somewhat heavier equipments than the above table would give;
that is, if it is desired to transmit 20 horse-power, for instance, to put in a
plant that would transmit 25 to 30 horse-power, thus avoiding the necessity
of having to take up a comparatively small amount of stretch. On rubber
and leather filling, however, the amount of power capable of being trans-
mitted is 40 per cent greater than for wood, so that this filling is generally
used, and in this case no allowance need be made for stretch, as such
sheaves will likely transmit the power given by the table, under all possible
deflections of the rope.
Under ordinary conditions, ropes of seven wires to the strand, laid about
a hemp core, are best adapted to the transmission of power, but conditions
often occur where 12- or 19-wire rope is to be preferred, as stated below.
Deflections of the Rope. — The tension of the rope is measured by
the amount of sag or deflection at the centre of the span, and the deflection
corresponding to the maximum safe working tension is determined by the
following formulae, in which S represents the span in feet:
Steel Rope. Iron Rope.
Def. of still rope at centre, in feet . . . h = .000045* h = .00008S2
driving " " " .... 7i, = .000025S2 Ti^.OOOOSS2
" slack " " •*.... 7i2=.0000875S2 fta= .000175S2
Limits of Span.— On spans of less than sixty feet, it is impossible to
splice the rope to such a degree of nicety as to give exactly the required de-
flection, and as the rope is further subject to a certain amount of stretch, it
becomes necessary in such oases to apply mechanical means for producing
the proper tension, in order to avoid frequent splicing, which is very objec-
tionable ; but care should always be exercised in using such tightening
devices that they do not become the means, in unskilled hands, of over-
straining the rope. The rope also is more sensitive to every irregularity in
the sheaves and the fluctuations in the amount of power transmitted, and
is apt to sway to such an extent beyond the narrow limits of the required
deflections as to cause a jerking motion, which is very injurious. For this
reason on very short spans it is found desirable to use a considerably
heavier rope than that actually required to transmit the power; or in
other words, instead of a 7-wire rope corresponding to the conditions of
maximum tension, it is better to use a 19-wire rope of the same size wires,
and to run this under a tension considerably below the maximum. In this
way is obtained the advantages of increased weight and less At retch, without
TRANSMISSION OF POWER BY WIRE ROPE. 921
having to use larger sheaves, while the wear will be greater in proportion to
the increased surface.
In determining the maximum limit of span, the contour of the ground
and the available height of the terminal sheaves must be taken into con.
sideration. It is customary to transmit the power through the lower portion
of the rope, as in this case the greatest deflection in this portion occurs
when the rope is at rest. When running, the lower portion rises and the
upper portion sinks, thus enabling obstructions to be avoided which other-
wise would have to be removed, or make it necessary to erect very high
towers. The maximum limit of span in this case is determined by the max-
imum deflection that may be given to the upper portion of the rope when
running, which for sheaves of 10 ft. diameter is about 600 feet.
Much greater spans than this, however, are practicable where the contour
of the ground is such that the upper portion of the rope may be the driver,
and there is nothing to interfere with the proper deflection of the under
portion. Some very long transmissions of power have been effected in this
way without an intervening support, one at Lockport, N. Y., having a clear
span of 1700 feet.
Long-distance Transmissions.— When the distance exceeds the
limit for a clear span, intermediate supporting sheaves are used, with plain
grooves (not filled), the spacing and size of which will be governed by the
contour of the ground and the special conditions involved. The size of these
sheaves will depend on the augle of the bend, gauged by the tangents to the
curves of the rope at the points of inflection. If the curvature due to this
angle and the working tension, regardless of the size of the sheaves, as deter-
mined by the table on the next page, is less than that of the minimum
sheave (see table p. 919) the intermediate sheaves should not be smaller
than such minimum sheave, but if the curvature is greater, smaller inter-
mediate sheaves may be used.
In very long transmissions of power, requiring numerous intermediate
supports, it is found impracticable to run the rope at the high speeds main-
tained in " flying transmissions." The rope therefore is run under a higher
working tension, made practicable by wrapping it several times about
grooved terminal drums, with a lap about a sheave on a take-up or counter-
weighted carriage, which preserves a constant tension in the slack portion.
Inclined Transmissions.— When the terminal sheaves are not on
che same elevation, the tension at the upper sheave will be greater than that
at the lower, but this difference is so slight, in most cases, that it may be
ignored. The span to be considered is the horizontal distance between the
sheaves, and the principles governing the limits of span will hold good in
this case, so that for vory steep inclinations it becomes necessary to resort
to tightening devices for maintaining the requisite tension in the rope. The
limiting case of inclined transmissions occurs when one wheel is directly
above the other. The rope in this case produces no tension whatever on
the lower wheel, while the upper is subject only to the weight of the rope,
which is usually so insignificant that it may be neglected altogether, and
oti vertical transmissions, therefore, mechanical tension is an absolute ne-
cessity.
Bending Curvature of "Wire Ropes.— The curvature due to
any bend in a wire rope is dependent on the tension, and is not always the
same as the sheave in contact, but may be greater, which explains how it is
that large ropes are frequently run around comparatively small sheaves
without detriment, since it is possible to place these so close that the bend-
ing angle on each will be such that the resulting curvature will not over-
strain the wires. This curvature may be ascertained from the formula
and table on the next page, which give the theoretical radii of curvature in
inches for various sizes of ropes and different angles for one pound tension
in the rope. Dividing these figures by the actual tension in pounds, gives
the radius of curvature assumed by the rope in cases where this exceeds the
curvature of the sheave. The rigidity of the rope or internal friction of
the wires and core has not been taken into account in these figures, but the
effect of this is insignificant, and it is on the safe side to ignore it. By the
"angle of bend " is meant, the angle between the tangents to the curves of
the rope at the points of inflection. When the rope is straight the angle is
180°. For angles less than 160° the radius of curvature in most cases will be
less than that corresponding to the safe working tension, and the proper
size of sheave to use in such cases will be governed by the table headed
"Diameters of Minimum Sheaves Corresponding to a Maximum Safe
Woi-king Tension '"en page 919.
922
llOPE-DUIVIKU
Radius of Curvature of Wire Hopes in Inches for
1-lb. Tension.
Formula : R = E8*n -*- 5.25£ cos J£0 ; in which R — radius of curvature;
E = modulus of elasticity = 28,500,000; 6 = diameter of wires; n = no.
of wires ; 6 = angle of bend; t = working stress (Ibs. and ins.).
Divide by stress in pounds to obtain radius in inches.
Diam.
of wire.
160°
165°
170°
172°
174°
176°
178°
g,f y*
4,226
5,623
8,421
10,949
14,593
21,884
43,762
0
%
11,090
14,753
22,095
26,731
35,628
53.429
1 06,84 J
H
22,274
29,633
45,412
54,417
72,530
108,767
217,50
o> .
%
43,184
57,451
86,040
102,688
136,809
205,251
410,44v
r
71,816
95,541
.143.085
175,182
233,492
350,150
700,193
&
1/^i
112,763
150,016
224,667
280,607
374,010
560.872
1,121,574
^
k. l/^
169,135
225,012
336,982
427,689
570,050
854,858
1,709,456
<D
r ^
12,914
17,179
25,727
31,125
41,485
62,212
124,405
ff
%
29,762
39,594
59,297
75,988
101,282
151,884
303.723
f£
%
62,313
82,899
124,151
157,570
210,018
314,948
629,800
o; *
%
116,239
154,641
231,593
291,917
389,085
583,479
1,164.099
r
1
199,323
265,173
397,129
497,998
663,767
995,390
1,990.478
(6
l^g
320,556
4-26,459
638,674
797,697
1,063,217
1,594,422
3,188,359
ti-
^*
504,402
671,041
1,004,965
1,215,817
1,620,513
2,430,151
4,859,561
ROPE-DRIVING.
The transmission of power by cotton or manila ropes is a competitor with
gearing and leather belting when the amount of power is large, or the dis-
tance between the power and the work is comparatively great. The follow-
ing is condensed from a paper by C. W. Hunt, Trans. A. S. M. E., xii. 230 :
But few accurate data are available, on account of the long period re-
quired in each experiment, a rope lasting from three to six years. Installa-
tions which have been successful, as well as those in which the wear of the
rope was destructive, indicate that 200 Ibs. on a rope one inch in diameter
is a safe and economical- working strain When the strain is materially
increased, the wear is rapid.
In the following equations
C = circumference of rope in inches ; g — gravity ;
D = sag of the rope in inches ; H — horse-power ;
F = centrifugal force in pounds; L — distance between pulleys in feet;
P — pounds per foot of rope ; w = working strain in pounds;
R = force in pounds doing useful work ;
S = strain in pounds on the rope at the pulley;
T = tension in pounds of driving side of the rope ;
t = tension in pounds on slack side of the rope ;
v = velocity of the rope in feet per second ;
W = ultimate breaking strain in pounds.
W = 720C2 ; P = .032(72 ; w r= 2OC2.
This makes the normal working strain equal to 1/36 of the breaking
strength, and about 1/25 of the strength at the splice. The actual strains
are ordinarily much greater, owing to the vibrations in running, as well as
from imperfectly adjusted tension mechanism.
For this investigation we assume that the strain on the driving side of a
rope is equal to 200 Ibs. on a rope one inch in diameter, and an equivalent
strain for other sizes, and that the rope is in motion at various velocities of
from 10 to 140 ft. per second.
The centrifugal force of the rope in running over the pulley will reduce
ftOPE-DRIVIHG. 923
the amount of force available for the transmission of power. The centrifu-
gal force F = Pv* -j- g.
At a speed of about 80 ft. per second, the centrifugal force increases faster
than the power from increased velocity of the rope, and at about 140 ft. per
second equals the assumed allowable tension of the rope. Computing this
force at various speeds and then subtracting it from the assumed maximum
tension, we have the force available for the transmission of power. The
whole of this force cannot be used, because a certain amount of tension on
the slack side of the rope is needed to give adhesion to the pulley. What
tension should be given to the rope for this purpose -is uncertain, as there
are no experiments which give accurate data. It is known from considerable
experience that when the rope runs iu a groove whose sides are1 inclined
toward each other at an angle of 45° there is sufficient adhesion when the
ratio of the tensions T-r- 1 = 2.
For the present purpose, T can be divided into three parts: 1. Tension
doing useful work; 2. Tension from centrifugal force; 3. Tension to balance
the strain for adhesion.
The tension t can be divided into two parts: 1. Tension for adhesion;
2. Tension from centrifugal force.
It is evident, however, that the tension required to do a given work should
not be materially exceeded during the life of the rope.
There are two methods of putting ropes on the pulleys; one in which the
ropes are single and spliced on, being made very taut at first, and less so as
the rope lengthens, stretching until it slips, when it is respliced. The other
method is to wind a single rope over the pulley as many turns as needed to
obtain the necessary horse power and put a tension pulley to give the neces-
sary adhesion and also take up the wear. The tension t required to trans-
mit the normal horse-power for the ordinary speeds and sizes of rope is com-
puted by formula (1), below. The total tension T on the driving side of the
rope is assumed to be the same at all speeds. The centrifugal force, as well
as an amount equal to the tension for adhesion on the slack side of the rope,
must be taken from the total tension T to ascertain the amount of force
available for the transmission of power.
It is assumed that the tension on the slack side necessary for giving
adhesion is equal to one half the force doing useful work on the driving side
of the rope; hence the force for useful work is R = — — ^ — • ; and the ten-
o
sion on the slack side to give the required adhesion is }&(T — F). Hence
«>
The sum of the tensions Tand t is not the same at different speeds, as the
equation (1) indicates.
As F varies as the square of the velocity, there is, with an increasing
speed of the rope, a decreasing useful force, and an increasing total tension,
tt on the slack side.
With these assumptions of allowable strains the horse-power will be
Transmission ropes are usually from 1 to 1^ inches in diameter. A com-
putation of the horse-power for four sizes at various speeds and under
ordinary conditions, based on a maximum strain equivalent to 200 Ibs. for a
rope one inch in diameter, is given in Fig. 166. The horse-power of other
sizes is readily obtained from these. The maximum power is transmitted,
under the assumed conditions, at a speed of about 80 feet per second.
The wear of the rope is both internal and external ; the internal is caused
by the movement of the fibres on each other, under pressure in bending
over the sheaves, and the external is caused by the slipping and the wedg-
ing in the grooves of the pulley. Both of these causes of wear are, within
the limits of ordinary practice, assumed to be directly proportional to the
speed. Hence, if we assume the coefficient of the wear to be fc, the wear
will be fcv, in which the wear increases directly as the velocity, but the
horse-power that can be transmitted, as equation (2) shows, will not vary at
the same rate.
The rope is supposed to have the strain T constant at all speeds on the
driving side, and in direct prooortion to the area of the cross-section; hence
924
ROPE-DRIVIHG.
the catenary of the driving side is not affected by the speed or by the diam-
eter of the rope.
The deflection of the rope between the pulleys on the slack side varies
with each change of the load or change of the speed, as the tension equation
(1) indicates.
The deflection of the rope is computed for the assumed value of T and C
ROPE DRIVING.
Horse Power of manilla
rope at various speeds.
10 20 30 40 50 60
Velocity of Driving Rope in feet per second.
FIG. 166.
PL*
by the parabolic formula S = -^ + PD, S being the assumed strain T on
the driving side, and t, calculated by equation (1), on the slack side. The
tension t varies with the speed.
Horse-power of Transmission Rope at Various Speeds*
Computed from formula (2), given above.
«M
°*
|i
Speed of the Rope in feet per minute.
l*sj
?§£§
llfiS
1500
2000
2500
3000
3500
4000
4500
5000
6000
7000
8000
f8
1%
2
1.45
2.3
3.3
4.5
5.8
9.2
13.1
18
23.2
1.9
3.2
4.3
5.9
7.7
12.1
17.4
23.7
30.8
2.3
3.6
5.2
7.0
9.2
14.3
20.7
28.2
36.8
2.7
4.2
5.8
8.2
10.7
16.8
23.1
32.8
42.8
3
4.6
6.7
9.1
11.9
18.6
26.8
36.4
47.6
3.2
5.0
7.2
9.8
12.8
20.0
28.8
39.2
51.2
3.4
5.3
7.7
10.8
13.6
21.2
30.6
41.5
54.4
3.4
5.3
7.7
10.8
13.7
21.4
30.8
41.8
54 8
3.1
4.9
7.1
9.3
12.5
19.5
28.2
37.4
50
2.2
3.4
4.9
6.9
8.8
13.8
19.8
27.6
35.2
0
0
0
0
0
0
0
0
0
20
24
30
36
42
54
60
72
84
The following notes are from the circular of the C. W. Hunt Co., New
York :
For a temporary installation, when the rope is not to be long in use, it
might be advisable to increase the work to double that given in the table.
For convenience in estimating the necessary clearance on the driving and
on the slack sides, we insert a table showing the sag of the rope at different
speeds when transmitting the horse-power given in the preceding table.
When at rest the sag is not the same as when running, being greater on the
driving and less on the slack sides of the rope. The sag of the driving side
when transmitting the normal horse -power is the same no matter what size
of rope is used or what the speed driven at, because the assumption is that
the strain on the rope shall be the same at all speeds when transmitting the
SAG OF THE HOPE BETWEEN PULLEYS.
925
assumed horse-power, but on the slack side the strains, and consequently
the sag, vary with the speed of the rope and also with the horse -power.
The table gives the sag for three speeds. If the actual sag is less than given
in the table, the rope is strained more than the work requires.
This table is only approximate, and is exact only when the rope is running
at its normal speed, transmitting its full load and strained to the assumed
amount. All of these conditions are varying in actual work, and the table
must be used as a guide only.
Sag of the Rope between Pulleys.
Distance
between
Pulleys
in feet.
Driving Side.
Slack Side of Rope.
All Speeds.
80 ft. per sec.
60 ft. per sec.
40 ft. per sec.
40
60
80
100
120
140
160
Ofeet 4 inches
0 " 10 "
Ofeet 7 inches
1 " 5 "
Ofeet 9 inches
1 " 8 "
0 feet 11 inches
1 " 11 "
2 " 0 "
2 " 11 "
5 •• 8 *'
6 " 3 "
7 u 4 i.
5 " 1 "
9 " 3 "
11 " 3 "
14 " 0 "
The size of the pulleys has an important effect on the wear of the rope —
the larger the sheaves^ the less the fibres of the rope slide on each other, and
consequently there is less internal wear of the rope. The pulleys should not
be less than forty times the diameter of the rope for economical wear, and
as much larger as it is possible to make them. This rule applies also to the
idle and tension pulleys as well as to the main driving-pulley.
The angle of the sides of the grooves in which the rope runs varies, with
different engineers, from 45° to 60°. It is very important that the sides of
these grooves should be carefully polished, as the fibres of the rope rubbing
on the metal as it comes from the lathe tools will gradually break fibre by
fibre, and so give the rope a short life. It is also necessary to carefully avoid
all sand or blow holes, as they will cut the rope out with surprising rapidity.
Much depends also upon the arrangement of the rope on the pulleys, es-
pecially where a tension weight is used. Experience shows that the
increased wear on the rope from bending the rope first in one direction and
then in the other is similar to that of wire rope. At mines where two cages
are used, one being hoisted and one lowered by the same engine doing the
same work, the wire ropes, cut from the same coil, are usually arranged so
that one rope is bent continuously in one direction and the other rope is bent
first in one direction and then in the other, in winding on the drum of the
engine. The rope having the opposite bends wears much more rapidly than
the other, lasting about three quarters as long as its mate. This difference
in wear shows in manila rope, both in transmission of power and in coal-
hoisting. The pulleys should be arranged, as far as possible, to bend the
rope in one direction.
TENSION ON THE SLACK PART OF THE ROPE.
Speed of
Elope, in feet
per second.
Diameter of the Rope and Pounds Tension on the Slack Rope.
M
%
H
'H
1
1J4
I*
w
. 2
20
30
40
50
60
70
80
90
10
14
15
16
18
19
81
24
27
29
31
33
36
39
43
48
40
42
45
49
53
59
64
70
54
56
60
65
71
78
85
93
71
74
79
85
93
101
111
122
110
115
123
132
145
158
173
190
162
170
181
195
214
236
255
279
216
226
240
259
285
310
340
372
283
296
315
339
373
406
445
487
926
ROPE-DRIVING.
For large amounts of power it is common to use a number of ropes lying
side by side iu grooves, each spliced separately. For lighter drives some
engineers use one rope wrapped as many times around the pulleys as is
necessary to get the horse-power required, with a tension pulley to take up
the slack as the rope wears when first put in use. The weight put upon this
tension pulley should be carefully adjusted, as the overstraining of the rope
from this cause is one of the most common errors in rope driving. We
therefore give a table showing the proper strain on the rope for the various
sizes, from which the tension weight to transmit the horse-power in the
tables is easily deduced. This strain can be still further reduced if the
horse-power transmitted is usually less than the nominal work which the
rope was proportioned to do, or if the angle of groove in the pulleys is
acute.
DIAMETER OF PULLEYS AND WEIGHT OF ROPE.
Diameter of
Rope,
in inches.
Smallest Diameter
of Pulleys, in
inches.
Length of Rope to
allow for Splicing,
in feet.
Approximate
Weight, in Ibs. per
foot of rope.
H
20
6
.12
7&
24
6
.18
%
30
7
.24
%
36
8
.32
1
42
9
.49
54
10
.60
JL^
60
12
.83
1%
72
13
1.10
2
84
14
1.40
With a given velocity of the driving-rope, the weight of rope required for
transmitting a given horse-power is the same, no matter what size rope is
adopted. The smaller rope will require more parts, but the weight will be
the same.
Miscellaneous Notes on Rope-driving.— W. H. Booth commu-
nicates to the Amer. Machinist the following data from English practice with
cotton ropes. The calculated figures are based on a total allowable tension
on a 1%-inch rope of 600 Ibs., and an initial tension of 1/10 the total allowed
stress, which corresponds fairly with practice.
Diameter of rope 1M" W W W W Wd' 2"
Weight per foot, Ibs 5 .6 .72 .844 .98 1.125 1.3
Centrifugal tension = F2 divided by 64 53 44 38 33 28 25
for F= 80 ft. per sec., Ibs. 100 131 145 170 193 228 256
Total tension allowable 300 360 430 500 600 675 780
Initial tension 30 36 43 50 60 67 78
Net working tension at 80 ft. velocity 170 203 242 280 347 380 446
Horse-power per rope ' 24 28 34 41 49 54 63
The most usual practice in Lancashire is summed up roughly in the fol-
lowing figures: 1%-inch cotton ropes at 5000 ft. per minute velocity = 50 H. P.
per rope. The most common sizes of rope now used are 1% and 1% in. The
maximum horse-power for a given rope is obtained at about 80 to 83 feet
per second. Above that speed the power is reduced by centrifugal tension.
At a speed of 2500 ft. per minute four ropes will do about the same work as
three at 5000 ft. per min.
Cotton ropes do not require much lubrication iu the sense that it is re-
quired by ropes made of the rough fibre of manila hemp. Merely a slight
surface dressing is all that is required. For small ropes, common in spin-
ning machinery, from ^ to % inch diameter, it is the custom to prevent the
fluffing of the ropes on the surface by a light application of a mixture of
black-lead and molasses,— but enly enough should be used to lay the fibres,—
city " of hemp rope in
J practice, that is, the horse -power transmitted per square inch of
cross-section for each foot of linear velocity per minute, .004 to .002, the
cross-section being taken as that due to the full outside diameter of the
rope. For a 1%-in. rope, with a cross-section of 2.405 ?q. in., at a velocity of
5000 ft. per min,, this gives a horse-power of from 24 to 48, as against 41.8
by Mr. Hunt's table and 49 by Mr. Booth's.
MISCELLANEOUS NOTES ON ROPE-DRIVING 927
Reuleaux gives formulae for calculating sources of loss in hemp-rope
transmission due to (1) journal friction, (2) stiffness of ropes, and (3) creep
of ropes. The constants in these formulae are, however, uncertain from
lack of experimental data. He calculates an average case giving loss of
power due to journal friction = 4g, to stiffness 7.8$, and to creep 5#, or 16.8#
in all, and says this is not to be considered higher than the actual loss.
Spencer Miller, in a paper entitled " A Problem in Continuous Hope-driv-
ing " (Trans. A. 8. C. E., 1897), reviews the difficulties which occur in rope-
driving, with a continuous rope from a large to a small pulley. He adopts
the angle of 45° as a minimum angle to use on the smaller pulley, and
recommends that the larger pulley be grooved with a wider angle to a degree
such that the resistance to slipping is equal in both wheels. By doing this
the effect of the tension weight is felt equally throughout all the slack
strands of the rope-drive, hence the tight ropes pull equally. It is shown
that when the wheels are grooved alike the strains in the various ropes may
differ greatly, and to such a degree that danger is introduced, for while one-
half the tension weight should represent the maximum strain on the slack
rope, it is demonstrated in the paper that the actual maximum strain may
be even four or six times as great.
In a drive such as is recommended, with a wide angle in the large sheave
with the larger arc of contact, the conditions governing the ropes are the
same as if the wheels were of the same diameter; and where the wheels are
of the same diameter, with a proper tension weight, the ropes pull alike. It
is claimed that by widening the angle of the large sheave not only is there
no power lost, but there is actually a great gain in power transmitted. An
example is given in which it is shown that in that instance the power trans-
mitted is nearly doubled. Mr. Miller refers to a 250-horse-power drive which
lias been running ten years, the large pulley being grooved 60° and the
smaller 45°. This drive was designed to use a l*4-in. inanila rope, but the
grooves were made deep enough so that a %-in. rope would not bottom. In
order to determine the value of the drive a common %-in. rope was put in.
at first, and lasted six years, working under a factor of safety of only 14.
He recommends, however, the employment in continuous rope-driving of a
factor of safety of not less than 20.
The Walker Company adopts a curved form of groove instead of one with
straight sides inclined to each other at 45°. The curves are concave to the
rope. The rope rests on the sides of the groove in driving and driven pul-
leys. In idler pulleys the rope rests on the bottom of the groove, which is
semicircular. The Walker Company also uses a "differential" drum for
heavy rope-drives, in which the grooves are contained each in a separate
ring which is free to slide on the turned surface of the drum in case one rope
pulls more than another.
A heavy rope-drive on the separate, or English, rope system is described
and illustrated in Power, April, 1892. It is in use at the India Mill at Darwen,
England. This mill was originally driven by gears, but did not prove success-
ful, and rope-driving was resorted to. The 85,000 spindles and preparation
are driven by a 2000-horse-power tandem compound engine, with cylinders
23 and 44 inches in diameter and 72-inch stroke, running at 54 revolutions
per minute. The fly-wheel is 30 feet in diameter, weighs G5 tons, and is
arranged with 30 grooves for 1%-inch ropes. These ropes lead off to receiv-
ing-pulleys upon the several floors, so that each floor receives its power direct
from the fly-wheel. The speed of the ropes is 5089 feet per minute, and five
7-foot receivers are used, the number of ropes upon each being proportioned
to the amount of power required upon the several floors. Lambeth cotton
ropes are used. (For much other information on this subject see " Rope«
Driving," by J. J. Flather, John Wiley & Sons, 1895.)
928
PRICTIOtf AND LUBRICATION.
FRICTION AND LUBRICATION.
Friction is defined by Rankine as that force which acts between two
bodies at their surface of contact so a? to resist their sliding on each other,
and which depends on the force with which the bodies are pressed together.
Coefficient of Friction.— The ratio of the force required to slide a
body along a horizontal plane surface to the weight of the body is called the
coefficient of friction. It is equivalent to the tangent of the angle of repose,
which is the angle of inclination to the horizontal of an inclined plane on
which the body will just overcome its tendency to slide. The angle is usually
denoted by 0, and the coefficient by f.f= tan 0.
Friction of Rest and of 'Motion.— The force required to start a
body sliding is called the friction of x'est, and the force required to continue
its sliding after having started is called the friction of motion.
Rolling Friction is the force required to roll a cylindrical or spheri-
cal body'on a plane or on a curved surface. It depends on the nature of the
surfaces and on the force with which they are pressed together, but is
essentially different from ordinary, or sliding, friction.
Friction of Solids.— Rennie's experiments (1829) on friction of solids,
usually urilubricated and dry, led to the following conclusions:
1. The laws of sliding friction differ with the character of the bodies
rubbing together.
2. The friction of fibrous material is increased by increased extent of
surface and by time of contact, and is diminished by pressure and speed.
3. With wood, metal, and stones, within the limit of abrasion, friction
varies only with the pressure, and is independent of the extent of surface,
time of contact and velocity.
4. The limit of abrasion is determined by the hardness of the softer of the
two rubbing parts.
5. Friction is greatest with soft and least with hard materials.
6. The friction of lubricated surfaces is determined by the nature of the
lubricant rather than by that of the solids themselves.
Friction of Rest. (Rennie.)
Pressure,
Ibs.
per square
inch..
Values of /.
Wrought iron on
Wrought Iron.
Wrought on
Cast Iron.
Steel on
Cast Iron.
Brass on
Cast Iron.
187
224
336
448
560
672
784
.25
.27
.31
.38
.41
Abraded
"
.28
.29
.33
.37
.37
.38
Abraded
.30
.33
.35
.35
.36
.40
Abraded
.23
.22
.21
.21
.23
.23
.23
Law of Unlubricated Friction.— A. M. Wellington, Eng'g News*
April 7, 1888, states that the most important and the best determined of all
the laws of unlubricated friction may be thus expressed:
The coefficient of unlubricated friction decreases materially with velocity,
is very much greater at minute velocities of 0 -f, falls very rapidly with
minute increases of such velocities, and continues to fall much less rapidly
with higher velocities up to a certain varying point, following closely the
laws which obtain with lubricated friction.
Friction of Steel Tires Sliding on Steel Rails. (Westing'
house & Galton.)
Speed, miles per hour 10 15 25 38 45 50
Coefficient of friction 0.110 .087 .080 .051 .04T .040
, Adhesion, Ibs. per ton (2240 Ibs,) 246 195 179 128 114 90
FRICTION
929
Rolling Friction Is a consequence of the Irregularities of form and
the roughness of surface of bodies rolling one over the other. Its laws
are not yet definitely established in consequence of the uncertainty which
exists in experiment as to how much of the resistance is due to roughness of
surface, how much to original and permanent irregularity of form, and how
much to distortion under the load. (Thurston.)
Coefficients of Rolling Friction.— If R = resistance applied at
the circumference of the wheel, W — total weight, r = radius of the wheel,
and / = a coefficient, R = fW-+- r. f is very variable. Coulomb gives .06
for wood, .005 for metal, where W is in pounds and r in feet. Tredgold
made the value of /for iron on iron .002.
For wagons on soft soil Morin found/ = .065, and on hard smooth roads
.02.
A Committee of the Society of Arts (Clark, R. T. D.) reported a loaded
omnibus to exhibit a resistance on various loads as below:
Pavement Speed per hour. Coefficient. Resistance.
Granite. 2.8? miles. .007 17.41 per ton.
Asphalt...., 3.56 " .0121 27.14
Wood 3.34 " .0185 41.60 "
Macadam, gravelled 3.45 " .0199 44.48 **
granite, new.. 3.51 " .0451 101.09 "
Thurston gives the value of /for ordinary railroads, .003, well-laid railroad
track, .002; best possible railroad track, .001.
The few experiments that have been made upon the coefficients of rolling
friction, apart from axle friction, are too incomplete to serve as a basis for
practical rules. (Trautwine).
Laws of Fluid Friction.— For all fluids, whether liquid or gaseous,
the resistance is (1) independent of the pressure between the masses in
contact; (2) directly proportional to the area of rubbing-surface; (3) pro-
portional to the square of the relative velocity at moderate and high speeds,
and to the velocity nearly at low speeds; (4) independent of the nature of
the surfaces of the solid against which the stream may flow, but dependent
to some extent upon their degree of roughness; (5) proportional to the den-
sity of the fluid, and related in some way to its viscosity. (Thurston.)
The Friction of Lubricated Surfaces approximates to that of solid fric-
tion as the journal is run dry, and to that of fluid friction as it is flooded
with oil.
Angles of Repose and Coefficients of Friction of Build*
ing Materials. (From Rankine's Applied Mechanics.)
9.
/ = tan 0.
1
tan0*
Dry masonry and brickwork. .
Masonry and brickwork with
damp mortar ...
31° to 35°
.6 to .7
.74
1.67 to 1.4
1 35
92°
about 4
2 5
Iron on stone .
35* to 16%°
.7 to 3
1 43 to 3 3
Timber on timber
26^° to 11H°
.5 to 2
2 to 5
" " metals . . ...
31° to 11J£0
6 to 2
1 67 to 5
14° to 8U°
.25 to . 15
4 to 6 67
Masonry on dry clay ..
27°
.51
1 96
** " moist clay
Earth on earth
18^°
14° to 45°
.33
25 to 1 0
3.
4 to 1
" *' dry sand, clay,
and mixed earth
Earth on earth, damp clay —
** 4t ** wet clay
" " •• shingle and
gravel
21° to 37°
45°
17°
39° to 48°
.38 to .75
1.0
.31
.81
2.63 to 1.38
1
3.23
1.23 to 0.9
Friction of Motion.— The following is a table of the angle of repose
0, the coefficient of friction / = tan 0, and its reciprocal, 1 -f-/, for the ma-
terials of mechanism— condensed from the tables of General Morin {1831),
and other sources, as given by Rankine:
930
FEICTIOK AND LUBRICATION.
No.
Surfaces.
0.
/.
I-*-/.
1
2
3
4
5
6
7
Wood on wood, dry ....
" " " soaped..
Metals on oak, dry
' wet
" soapy.. .
" " elm, dry
Hemp on oak, dry
14° to 26J^°
\\Y2° to 2°
2W/2° to 31°
13^° to 14°
iw
Iiy2° to 143
28°
.25 to .5
.2 to .04
.5 to .6
.24 to .26
.2
.2 to .25
.53
4 to 2
5 to 25
2 to 1.67
4.17 to 3. 85
5
5 to 4
1.89
g
18J^°
.33
3
9
Leather on oak
15° to 19V£°
.27 to .38
3. 7 to 2 86
10
11
12
" " nietals, dry..
" " *' wet..
' greasy
29^°
20°
13°
Q1/O
.56
.36
.23
•JK
1.79
2.78
4.35
6R7
14
15
16
Metals on metals, dry. ..
" " "• wet...
Smooth surfaces, occa-
sionally greased •
°7S
8^° toll0
i6M°
4° to 4^°
.15 to .2
.3
.07 to .08
6.67 to 5
3.33
14.3 to 12.5
17
18
Smooth surfaces, con-
tinuously greased
Smooth surfaces, best
results
3°
1<%° to 2°
.05
.03 to .036
20
19
Bronze on lignum vitse,
constantly wet . .
3° ?
.05?
Coefficients of Friction of Journals. (Morin.)
Lubrication.
Material.
Unguent.
Intermittent.
Continuous.
Cast iron on cast iron . . .. •!
Oil, lard tallow.
Unctuous and wet.
.07 to .08
.14
.03 to .
054
Cast iron on bronze j
Oil, lard, tallow.
Unctuous and wet.
.07 to .08
.16
.03 to .
054
Cast iron on lignum- vitSB
Oil, lard.
.02
Wrought iron on cast iron |_
" " bronze . . }
Oil, lard, tallow.
.07 to .08
.03 to .
054
Iron on lignum vitge -j
Oil, lard.
Unctuous.
.11
.19
Bronze on bronze «
Olive -oil.
Lard.
.10
.09
Prof. Thurston says concerning the above figures that much better results
are probably obtained in good practice with ordinary machinery. Those
here given are so greatly modified by'variations of speed, pressure, and tem-
perature, that they cannot be taken as correct for general purposes.
Average Coefficients of Friction. Journal of cast iron in bronze
bearing; velocity 720 feet per minute; temperature 70° F.; intermittent
feed through an oil-hole. (Thurston on Friction and Lost Work.)
Pressures, pounds per square inch.
uus.
8
16
32
48
Sperm, lard, neat's-foot,etc.
Olive, cotton -seed, rape, etc.
.159
.160
to
.250
.283
.138
.107
to
.192
.245
.086
.101
to
.141
.168
.077 to
.079 "
.144
.131
Cod and menhaden
.248
"
.278
.124
44
.167
.097
**
.102
.081 "
.122
Mineral lubricating-oils. . . .
.154
**
.261
.145
M
.233
.086
.178 .094 "
.222
With fine steel journals running in bronze bearings and continuous lubri-
cation, coefficients far below those above given are obtained. Thus with
sperm-oil the coefficient with 50 Ibs. per square inch pressure was .0034; with
200 Ibs., .0051; with 300 Ibs . .0057. •
FRICTION 931
For very low pressures, as in spindles, the coefficients are much higher.
Thus Mr. Woodbuiy found, at a temperature of 100° and a velocity of 600
feet per minute,
Pressures, Ibs. per sq. in 1 2 3 4 5
Coefficient 38 .27 .22 .18 .17
These lrig.» coefficients, however, and the great decrease in the coefficient
at increased pressures are limited as a practical matter only to the smaller
Pressures which exist especially in spinning machinery, where the pressure
; so light and the film of oil so thick that the viscosity of the oil is an import-
ant part of the total frictional resistance.
Experiments on Friction of a Journal Lubricated by an
Oil-bath (reported by the Committee on Friction, Froc. Inst. M. E.,
Nov. 1883) show that the absolute friction, that is, the absolute tangential
force per square inch of bearing, required to resist the tendency of the brass
to go round with the journal, is nearly a constant under all loads, within or-
dinary working limits. Most certainly it does not increase in direct proper
tiori to the load, as it shoul.l do according to the ordinary theory of solid
friction. The results of these experiments seem to show that the friction of
a perfectly lubricated journal follows the laws of liquid friction much more
closely than those of solid friction. They show that under these circum-
stances the friction is nearly independent of the pressure per square inch,
and that it increases with the velocity, though at a rate not nearly so rapid
us the square of the velocity.
The experiments on friction r.t different temperatures indicate a great
diminution in tb<» friction as the temperature rises. Thus in the case of
lard-oil, taking £ ^speed of 450 revolutions per minute, the coefficient of fric-
tion at a temperature of 120° is only one third of what it was at a tempera-
ture of 60.
The journal was of steel, 4 inches diameter and 6 inches long, and a gun-
metal brass, embracing somewhat less than half the circumference of the
journal, rested on its upper side, on which the load was applied. When the
bottom of the journal was immersed in oil, and the oil therefore carried
under the brass by rotation of the journal, the greatest load carried with
rape-oil was 573 Ibs. per square inch, and with mineral oil 625 Ibs.
In experiments with ordinary lubrication, the oil being fed in at the cen-
tre of the top of the brass, and a distributing groove being cut in the brass
parallel to the axis of the journal, the bearing would not run cool with only
100 Ibs. per square inch, the oil being pressed out from the bearing-surface
and through the oil-hole, instead of being carried in by it. On introducing
the oil at the sides through two parallel grooves, the lubrication appeared
to be satisfactory, but the bearing seized with 380 Ibs. per square inch.
When the oil was introduced through two oil-holes, one near each end of
the brass, and each connected with a curved groove, the brass refused to
take its oil or run cool, and seized with a load of only 200 Ibs. per square
inch.
With an oil-pad under the journal feeding rape-oil, the bearing fairly car-
ried 551 Ibs. Mr. Tower's conclusion from these experiments is that the
friction depends on the quantity and uniformity of distribution of the oil,
and may be anything between the oil-bath results and seizing, according to
the perfection or imperfection of the lubrication. The lubrication may be
very small, giving a coefficient of 1/100; but it appeared as though it could
not be diminished and the friction increased much beyond this point with-
out imminent risk of heating and seizing. The oil-bath probably represents
the most perfect lubrication possible, and the limit beyond which friction
cannot be reduced by lubrication ; and the experiments show that with speeds
of from 100 to 200 feet per minute, by properly proportioning the bearing-
surface to the load, it is possible to reduce the coefficient of friction to as low
as 1/1000. A coefficient of 1/1500 is easily attainable, and probably is fre-
quently attained, in ordinary engine-bearings in which the direction of the
force is rapidly alternating and the oil given an opportunity to get between
the surfaces, while the duration of the force in one direction is not sufficient
to allow time for the oil film to be squeezed out.
Observations on the behavior of the apparatus gave reason to believe that
with perfect lubrication the speed of minimum friction was from 100 to 150
feet per minute, and that this speed of minimum friction tends to be higher
with an increase of load, and also with less perfect lubrication. By the
speed of minimum friction is meant that speed in approaching which from
rest the f fiction aittiittislitis, autl above which the friction increases.
932
FRICTIOK AKB LUBRICATION.
Coefficients of Friction of Journal with Oil-bath.— Ab.
stract of results of Tower's experiments on friction (Proc. Inst. M. E., Nov.
1883). Journal, 4 in. diam., 6 in. long; temperature, 90° F.
Lubricant in Bath.
Nominal Load, in pounds per square inch.
625
520 | 415
310
205
153 j 100
Lard-oil :
Coefficients of Friction.
.0009
.0017
.0014
.0022
seiz'd
.0012
.0021
.0016
.0027
.0015
.0021
.0009
.0016
.0012
.002
.0014
.0029
.0022
.004
.0011
.0019
.0008
.0016
.0014
.0024
.0056
.0068
.0099
0099
.0020
.0042
.0034
.0066
.0016
.0027
.0014
.0024
.0021
.0035
.0098
.0077
.0105
0078
.0027
.0052
.0038
.0083
.0019
0037
.002
.004
.0042
.009
.0076
.0151
.003
.0064
.004
.007
.004
.007
.0125
.0152
.0099
.0133
471 " **
Mineral grease :
.001
.002
471 " "
Sperm-oil :
157ft permin... .;
471 " "
Rape-oil :
(573 Ib.)
.001
.001
.0015
.0012
.0018
Mineral-oil :
157 ft. per min 0 . . .
471 " " :.
Rape-oilfed by syphon lubricator:
157 ft. per min
314 "
Rape-oil, pad under journal:
1 57 ft. per min
314 "
.OC13
Comparative friction of different lubricants under same circumstances,
temperature 90°, oil-bath:
Sperm-oil 100 per cent.
Rape-oil 106
Mineraloil 129
Lard 135 percent.
Olive-oil 135
Mineral grease 217 "
Coefficients of Friction of Motion and of Rest of a
Journal.— A cast-iron journal in steel boxes, tested by Prof. Thurston at
a speed of rubbing of 150 feet per minute, with lard and with sperm oil,
gave the following:
100
.008
Pressures per sq. in., Ibs 50
Coeff.. with sperm 013
** lard 02 .0137
The coefficients at starting were:
With sperm 07 .135
With lard 07 .11
250
.005
.0085
500
.004
.0053
750
.0043
.0066
1000
.009
.0125
.14
.11
.15
.10
.185
.12
.18
.12
The coefficient at a speed of 150 feet per minute decreases with increase
of pressure until 500 Ibs. per sq. in. is reached; above this it increases. The
coefficient at rest or at starting increases with the pressure throughout the
range of the tests.
Value of Anti-friction Metals. (Denton.)— The various white
metals available for lining brasses do not afford coefficients of friction
lower than can be obtained with bare brass, but they are less liable to
"overheating,1' because of the superiority of such material over bronze in
ability to permit of abrasion or crushing, without excessive increase of
friction.
Thurston (Friction aud Lost Work) says that gun-bronze, Babbitt, and
other soft white alloys have substantially' the same friction; in other words,
the friction is determined by the nature of the unguent and not by that of
the rubbing-surfaces, when the latter are in good order. The soft metals
run at higher temperatures than the bronze. This, however, does not nec-
essarily indicate a serious defect, but simply deficient conductivity. The
value of the white alloys for bearings lies mainly in their ready reduction
to a smooth surface after any local or general injury by alteration of either
surface or form.
MORIN'S LAWS OF FRICTION. 933
Cast-iron for Bearings. (Joshua Rose.)— Cast iron appears to be a*
exception to the general rule, that the harder the metal the greater the
resistance to wear, because cast iron is softer in its texture and easier to
cut with steel tools than steel or wrought iron, but in some situations it is
far more durable than hardened steel; thus when surrounded by steam it
will wear better than will any other metal. Thus, for instance, experience
has demonstrated that piston-rings of cast iron will wear smoother, better,
and equally as long as those of steel, and longer than those of either
wrought iron or brass, whether the cylinder in which it works be composed
of brass, steel, wrought iron, or cast iron; the latter being the more note-
worthy, since two surfaces of the same metal do not, as a rule, wear or
work well together. So also slide-valves of brass are not found to wear so
long or so smoothly as those of cast iron, let the metal of which the seating
is composed be whatever it may; while, on the other hand, a cast iron slide-
valve will wear longer of itself and cause less wear to its seat, if the latter
is of cast iron, than if of steel, wrought iron, or brass.
Friction of Metals under Steam-pressure.— The friction of
brass upon iron under steam-pressure is double that of iron upon iron.
(G. H. Babcock, Trans. A. S. M. E., i. 151.)
Morin's "Laws of Friction."—!. The friction between two bodies
is directly proportioned to the pressure; i.e., the coefficient is constant for
all pressures.
2. The coefficient and amount of friction, pressure being the same, is in-
dependent of the areas in contact.
3. The coefficient of friction is independent of velocity, although static
friction (friction of rest) is greater than the friction of motion.
Eng^q News, April 7, 1888, comments on these "laws" as follows : From
1831 till about 1876 there was no attempt worth speaking of to enlarge our
knowledge of the laws of friction, which during all that period was assumed
to be complete, although it was really worse than nothing, since it was for
the most part wholly false. In the year first mentioned Morin began a se-
ries of experiments which extended over two or three years, and which
resulted in the enunciation of these three " fundamental laws of friction,"
no one of which is even approximately true.
For fifty years these laws were accepted as axiomatic, and were quoted as
such without question in every scientific work published during that whole
period. Now that they are so thoroughly discredited it has been attempted
to explain away their defects on the ground that they cover only a very lim-
ited range of pressures, areas, velocities, etc., and that Morin himself only
announced them as true within the range of his conditions. It is now clearly
established that there are no limits or conditions within which any one of
them, even approximates to exactitude, and that there are many conditions
under which they lead to the wildest kind of error, while many of the con-
stants were as inaccurate as the laws. For example, in Morin's " Table of
Coefficients of Moving Friction of Smooth Plane Surfaces, perfectly lubri-
cated," which may be found in hundreds of text-books now in use. the coeffi-
cient of wrought iron on brass is given as .075 to .103, which would make the
rolling friction of railway trains 15 to 20 Ibs. per ton instead of the 3 to 6 Ibs.
which it actually is.
General Morin, in a letter to the Secretary of the Institution of Mechanical
Engineers, dated March 15, 1879, writes as follows concerning.his experiments
on friction made more than forty years before: '* The results furnished by my
experiments as to the relations between pressure, surface, and speed on the
one hand, and sliding friction on the other, have always been regarded by
myself, not as mathematical laws, but as close approximations to the truth,
within the limits of the data of the experiments themselves. The same holds,
in my opinion, for many other laws of practical mechanics, such as those of
rolling resistance, fluid resistance, etc."
Prof. J. E. Denton (Stevens Indicator, July, 1890) says: It has been gen-
erally assumed that friction between lubricated surfaces follows the simple
law that the amount of the friction is some fixed fraction of the pressure be-
tween the surfaces, such fraction being independent of the intensity of the
pressure per square inch and the velocity of rubbing, between certain limits
of practice, and that the fixed fraction referred to is represented by the co-
efficients of friction given by the experiments of Morin or obtained from ex-
perimental data which represent conditions of practical lubrication, such as
those given in Webber's Manual of Power.
By the experiments of Thurston, Woodbury, Tower, etc., however, it
appears that the friction between lubricated metallic surfaces, such as ma-
934 FRICTION" AND LUBRICATION.
chine bearings, is not directly proportional to the pressure, is not indepen-
dent of the speed, and that the coefficients of Morin and Webber are about
tenfold too great for modern journals.
Prof. Denton offers an explanation of this apparent contradiction of au-
thorities by showing, with laboratory testing machine data, that Moriu's
laws hold for bearings lubricated by a restricted feed of lubricant, such as
is afforded by the oil-cups common to machinery; whereas the modern ex-
periments have been made with a surplus feed or superabundance of lubri-
cant, such as is provided only in railroad- car journals, and a few special
cases of practice.
That the low coefficients of friction obtained under the latter conditions
are realized in the case of car journals, is proved by the fact that the tem-
perature of car-boxes remains at 100° at high velocities; and experiment shows
that this temperature is consistent only with a coefficient of friction of a
fraction of one per cent. Deductions from experiments on train resistance
also indicate the same low degree of friction. But these low co-efficients do
hot account for the internal friction of steam-engines as well as do the co
efficients of Morin and Webber.
In American Machinist, Oct. 23, 1890, Prof. Denton says: Morin's measure-
ment of friction of lubricated journals did not extend to light pressures.
They apply only to the conditions of general shafting and engine work.
He clearly understood that there was a frictional resistance, due solely to
the viscosfty of the oil, and that therefore, for very light pressures, the laws
which he enunciated did not prevail.
He applied his dynamometers to ordinary shaft-journals without special
preparation of the rubbing- surf aces, and without resorting to artificial
methods of supplying the oil.
Later experimenters have with few exceptions devoted themselves exclu-
sively to the measurement of resistance practically due to viscosity alone.
They have eliminated the resistance to which Morin confined his measure-
ments, namely, the friction due to such contact of the rubbing-surfaces as
Erevail with a very thin film of lubricant between comparatively rough sur-
ices.
Prof. Denton also says (Trans. A. S. M. E., x. 518): " I do not believe there
is a particle of proof in any investigation of friction ever made, that Morin's
laws do not hold for ordinary practical oil-cups or restricted rates of feed."
Laws of Friction of well-lubricated Journals.— John
Goodman (Trans. Inst. C. E. 1886, Eny\j J\rews, Apr. 7 and 14, 1888), review-
ing the results obtained from the testing-machines of Thurston, Tower, and
Stroudley, arrives at the following laws:
LAWS OP FRICTION: WELL- LUBRICATED SURFACES.
(Oil-bath.)
1. The coefficient of friction with the surfaces efficiently lubricated is from
1/6 to 1/10 that for dry or scantily lubricated surfaces.
2. The coefficient of friction for moderate pressures and speeds varies ap-
proximately inversely as the normal pressure; the frictional resistance va-
ries as the area in contact, the normal pressure remaining constant.
3. At very low journal speeds the coefficient of friction is abnormally
high; but as the speed of sliding increases from about 10 to 100 ft. per min.,
the friction diminishes, and again rises when that speed is exceeded, varying
approximately as the square root of the speed.
4. The coefficient of friction varies approximately inversely as the temper-
ature, within certain limits, namely, just before abrasion takes place.
The evidence upon which these laws are based is taken from various mod-
ern experiments. That relating to Law 1 is derived from the "First Report
on Friction Experiments," by Mr. Beauchamp Tower.
Method of Lubrication.
Coefficient of
Friction.
Comparative
Friction.
Oil-bath
.00139
1.00
.0098
7.06
Pad under journal
.0090
6.48
With a load of 293 Ibs. per sq. in. and a journal speed of 314 ft. per min.
Mr. Tower found the coefficient of friction to be .0016 with an oil-bath, and
LAWS OF FRICTION.
935
.0097, or six times as much, with a pad. The very low coefficients ob-
tained by Mr. Tower will be accounted for by Law 2, as he found that the
frictional resistance per square inch under varying loads is nearly constant,
as below:
Load in Ibs. per sq. in 529 468
Frictional resist, per sq. in. .416 .514
415
.498
363
.472
310
.464
258
.438
205
.43
153 100
.458 .45
The frictional resistance per square inch is the product of the coefficient
of friction into the load per square inch on horizontal sections of the brass.
Hence, if this product be a constant, the one factor must vary inversely as
the other, or a high load will give a low coefficient, and vice versa.
For ordinary lubrication, the coefficient is more constant under varying
loads; the frictional resistance then varies directly as the load, as shown by
Mr. Tower in Table VIII of his report (Proc. Inst. M. E. 1883).
With respect to Law 3, A. M. Wellington (Trans. A. S. C. E. 1884), in ex-
periments on journals revolving at very low velocities, found that the friction
was then very great, and nearly constant under varying conditions of the
lubrication, load, and temperature. But as the speed increased the friction
fell slowly and regularly, and again returned to the original amount when
the velocity was reduced to the same rate. This is shown in the following
table:
Speed, feet per minute:
0+ 2.16 3.33 4.86 8.82 21.42 35.37 53.01 89.28 106.02
Coefficient of friction:
.118 .094 .070 .069 .055 .047 .040 .035 .030 .026
It was also found by Prof. Kimball that when the journal velocity was in-
creased from 6 to 110 ft. per minute, the friction was reduced 70$; in another
case the friction was reduced 67$ when the velocity was increased from 1'to
100ft. per minute; but after that point was reached the coefficient varied
approximately with the square root of the velocity.
The following results were obtained by Mr. Tower:
Feet per minute. . .
209
262
314
366
419
471
Nominal Load
per sq. in.
Coeff.^of friction..
.0010
.0013
.0014
.0012
.0014
.0015
.0013
.0015
.0017
.0014
.0017
.0019
.0015
.0018
.0021
.0017
.002
.0024
520 Ibs.
468 "
415 •«
The variation of friction with temperature is approximately intheinvers(
rr«l'~ * -ample, Mr. Tower's results, at 262 ft. per minute
me variation or rricuon witn t
ratio, Law 4. Take, for example
•se
Temp. F.
Observed 0044
Calculated 00451
110°
100°
.0051
.00518
90°
.006
.00608
.0073
.00733
70°
.0092
.00964
60°
.0119
.01252
This law does not hold good for pad or siphon lubrication, as then the co-
efficient of friction diminishes more rapidly for given increments of tern-
perature, but on a gradually decreasing scale, until the normal temperature
has been reached; this normal temperature increases directly as the load
per sq. in. This is shown in the following table taken from Mr. Stroudley's
experiments with a pad of rape oil:
Temp F
105°
110°
115°
120°
125°
130°
135°
140°
145°
Coefficient
.022
.0180
.0160
.0140
.0125
.0115
.0110
.0106
.0102
Decrease of coeff..
.0040
.0020
0020
.0015
.0010
.0005
.0004
.0002
In the Gal ton -Westi nghouse experiments it was found that with velocities
below 100 ft. per min., and with low pressures, the fricrional resistance
varied directly as the normal pressure; but when a velocity of 100 ft. per
min. was exceeded, the coefficient of friction greatly diminished; from the
same experiments Prof. Kennedy found that the coefficient of friction for
high pressures was sensibly less than for low.
Allowable Pressures on Bearing-surfaces. (Proc. Inst. M. E.,
May, 1888.)— The Committee on Friction experimented with a steel ring of
930 FRICTION AND LUBRICATION".
rectangular section, pressed between two cast-iron disks, the annular bear
ing-surfaces of which were covered with gun-metal, and were 12 in. inside
diameter and 14 in. outside. The two disks were rotated together, and the
steel ring was prevented from rotating by means of a lever, the holding
force of which was measured. When oiled through grooves cut in each face
of the ring and tested at from 50 to 130 revs, per min., it was found that a
pressure of 75 Ibs. per sq. in. of bearing-surface was as much as it would
bear safely at the highest speed without seizing, although it carried 90 Ibs.
per sq. in. at the lowest speed. The coefficient of friction is also much
higher than for a cylindrical bearing, and the friction follows the law of the
friction of solids much more nearly than that of liquids. This is doubtless
due to the much less perfect lubrication applicable to this form of bearing
compared with a cylindrical one. The coefficient of friction appears to be
about the same with the same load at all speeds, or, in other words, to be
independent of the speed; but it seems to diminish somewhat as the load is
increased, and may be stated approximately as 1/20 at 15 Ibs. per sq. in.,
diminishing to 1/30 at 75 Ibs. per sq. in.
The high coefficients of friction are explained by the difficulty of lubricat~
ing a collar-bearing. It is similar to the slide-block of an engine, which can
carry only about one tenth the load per sq. in. that can be carried by the
crank-pins.
In experiments on cylindrical journals it has been shown that when a
cylindrical journal was lubricated from the side on which the pressure bore,
100 Ibs. per sq. in. was the limit of pressure that it would carry; but when it
came to be lubricated on the lower side and was allowed to drag the oil in
with it, 600 Ibs. per sq. in. was reached with impunity; and if the 600 Ibs. per
sq. in., which was reckoned upon the full diameter of the bearing, came to
be reckoned on the sixth part of the circle that was taking the greater pro-
portion of the load, it followed that the pressure upon that part of the circle
amounted to about 1200 Ibs. per sq. in.
In connection with these experiments Mr. Wicksteed states that in drill-
ing-machines the pressure on the collars is frequently as high as 336 Ibs. per
sq. in., but the speed of rubbing in this case is lower than it was in any of
the experiments of the Research Committee. In machines working very
slowly and intermittently, as in testing-machines, very much higher pres-
sures are admissible.
Mr. Adamson mentions the case of a heavy upright shaft carried upon a
small footstep-bearing, where a weight of at least 20 tons was carried on a
shaft of 5 in. diameter, or, say, 20 sq. in. area, giving a pressure of 1 ton per
sq. in. The speed was 190 to 200 revs, per min. It was necessary to force the
oil under the bearing by means of a pump. For heavy horizontal shafts,
such as a fly-wheel shaft, carrying 100 tons on two journals, his practice for
getting oil into the bearings was to flatten the journal along one side
throughout its whole length to the extent of about an eighth of an inch in
\vidth for each inch in diameter up to 8 in. diameter; above that size rather
Jess flat in proportion to the diameter. At first sight it appeared alarming
to get a continuous flat place coming round in every revolution of a heavily
loaded shaft; yet it carried the oil effectually into the bearing, which ran
much better in consequence than a truly cylindrical journal without a flat
side.
In thrust-Tbearings on torpedo-boats Mr. Thornycroft allows a pressure of
never more than 50 Ibs. per sq. in.
Prof. Thurston (Friction and Lost Work, p. 240) says 7000 to 9000 Ibs,
pressure per square inch is reached on the slow-working and rarely moved
pivots of swing bridges.
Mr. Tower says (Proc. Inst. M. E., Jan. 1884): In eccentric-pins of punch-
in)? and shearing-machines very high pressures are sometimes used without
seizing. In addition to the alternation in the direction, the pressure is ap-
Elied for only a very short space of time in these machines, so that the oil
as no time to be squeezed out.
In the discussion on Mr. Tower's paper (Proc. Inst. M. E. 1885) it was
stated that it is well known from practical experience that with a constant
load on an ordinary journal it is difficult and almost impossible to have more
than 200 Ibs. per square inch, otherwise the bearing would get hot and the
oil go out of it; but when the motion was reciprocating, so that the load was
alternately relieved from the journal, as with crank-pins and similar jour-
nals, much higher loads might be applied than even 700 or 800 Ibs. per square
inch.
FRICTION OF CAR-JOURNAL BRASSES. 937
Mr. Goodman (Proc. Inst. C. E. 1886) found that the total frictional re-
sistance is materially reduced by diminishing the width of the brass.
The lubrication is most efficient in reducing the friction when the brass
subtends an angle of from 1^0° to 60°. The film is probably at its best be-
tween the angles 80° and 110°.
In the case of a brass of a railway axle-bearing where an oil-groove is cut
along its crown and an oil-hole is drilled through the top of the brass into it,
the wear is invariably on the off side, which is probably due to the oil escap-
ing as soon as it reaches the crown of the brass, and so leaving the off side
almost dry, where the wear consequently ensues.
In railway axles the brass wears always on the forward side. The same ob-
servation has been made in marine-engine journals, which always wear in
exactly the reverse way to what they might be expected. Mr. Stroudley
thinks this peculiarity is due to a film of lubricant being drawn in from the un-
der side of the journal to the aft part of the brass, which effectually lubri-
cates and prevents wear on that side; and that when the lubricant reaches
the forward side of the brass it is so attenuated down to a wedge shape that
there is insufficient lubrication, and greater wear consequently follows.
Prof. J. E. Denton (Am. Mack., Oct. 30, 1890) says: Regarding the pres-
sure to which oil is subjected in railroad car-service, it is probably more severe
than in any other class of practice. Car brasses, when used bare, are so im-
perfectly fitted to the journal, that during the early stages of their use the
area of bearing may be but about one square inch. In this case the pressure
per square inch is upwards of 6000 Ibs. But at the slowest speeds of freight
service the wear of a brass is so rapid that, within about thirty minutes the
area is either increased to about three inches, and is thereby able to relieve
the oil so that the latter can successfully prevent overheating of the journal,
or else overheating takes place with any oil. and measures of relief must be
taken which eliminate the question of differences of lubricating power
among the different lubricants available. A brass which has been run about
fifty miles under 5000 Ibs. load may have extended the area of bearing-surface
to about three square inches. The pressure is then about 1700 Ibs. per square
inch. It may be assumed that this is an average minimum area for car-ser-
vice where no violent and unmanageable overheating has occurred during the
use of a brass for a short time. This area will very slowly increase with any
lubricant.
C. J. Field (Power, Feb. 1893) says: One of the most vital points of an en-
gine for electrical service is that of main bearings. They should have a sur-
face velocity of not exceeding 350 feet per minute, with a mean bearing-
pressure per square inch of projected area of journal of not more than 80
Ibs. This is considerably within the safe limit of cool performance and easy
operation. If the bearings are designed in this way, it would admit the use
of grease on all the main wearing-surface, which in a large type of engines
for this class of work we think advisable.
Oil-pressure In a Bearing.— Mr. Beauchamp Tower (Proc. Inst.
M. E , Jan. 1885) made experiments with a brass bearing 4 inches diameter
by 6 inches long, to determine the pressure of the oil between the brass and
the journal. The bearing was half immersed in oil, and had a total load of
8008 Ibs. upon it. The journal rotated 150 revolutions per minute. The
pressure of the oil was determined by drilling small holes in the bearing at
different points and connecting them by tubes to a Bourdon gauge. It was
found that the pressure varied from 310 to 625 Ibs. per square inch, the great-
est pressure being a little to the " off " side of the centre line of the top of
the bearing, in the direction of motion of the journal. The sum of the up-
ward force exerted by these pressures for the whole lubricated area was
nearly equal to the total pressure on the bearing. The speed was reduced
from 150 to 20 revolutions, but the oil-pressure remained the same, showing
that the brass was as completely oil-borne at the lower speed as at the
higher. The following was the observed friction at the lower speed:
Nominal load, Ibs. per square inch ... 443 333 211 89
Coefficient of friction 00132 .00168 .00247 .0044
The nominal load per square inch is the total load divided by the product of
the diameter and length of the journal. At the same low speed of 20 revo-
lutions per minute it was increased to 676 Ibs. per square inch without any
signs of heating or seizing.
Friction of Car-journal Brasses. (J. E. Denton, Trans. A. S. M-
E., xji. 405.)— A new brass dressed with an emery-wheel, loaded with 5000 Ibs.,
may have an actual bearing-surface on the journal, as shown by the polish
938 FRICTION AKD LUBRICATION.
of a portion of the surface, of only 1 square inch. With this pressure of 5000
Ibs. per square inch, the coefficient of friction may be 6$, and the brass may
be overheated, scarred and cut but, on the contrary, it may wear down evenly
to a smooth bearing, giving a highly polished area of contact of 3 square
inches, or more, inside of two hours of running, gradually decreasing the
pressure per square inch of contact, and a coefficient of friction of less than
0.5$. A reciprocating motion in the direction of the axis is of importance
in reducing the friction. With such polished surfaces any oil will lubricate,
and the coefficient of friction then depends on the yiscosity of the oil. With
a pressure of 1000 Ibs per square inch, revolutions from 170 to 320 per minute,
and temperatures of 75° to 113° F. with both sperm and parraffine oils, a co-
efficient of as low as 0.11$ has been obtained, the oil being fed continuously
by a pad.
Experiments on Overheating of Bearings.— Hot Boxes.
(Denton.)— Tests with car brasses loaded from 1100 to 4500 Ibs. per square
inch gave 7 cases of overheating out of 32 trials. The tests show how purely
a matter of chance is the overheating, as a brass which ran hot at 5000 Ibs.
load on one day would run cool on a later date at the same or higher pres-
sure. The explanation of this apparently arbitrary difference of behavior is
that the accidental variations of the smoothness of the surfaces, almost in-
finitesimal in their magnitude, cause variations of friction which are always
tending to produce overheating, and it is solely a matter of chance when
these tendencies preponderate over the lubricating influence of the oil.
There is no appreciable advantage shown by sperm-oil, when there is no ten-
dency to overheat — that is, paraffine can lubricate under the highest pres-
sures which occur, as well as sperm, when the surfaces are within the condi-
tions affording the minimum coefficients of friction.
Sperm and other oils of high heat-resisting qualities, like vegetable oil and
petroleum cylinder stocks, only differ from the more volatile lubricants,
like paraffine, in their ability to reduce the chances of the continual acci-
dental infinitesimal abrasion producing overheating.
The effect of emery or other gritty substance in reducing overheating of a
bearing is thus explained :
The effect of the emery upon the surfaces of the bearings is to cover the
latter with a series of parallel grooves, and apparently after such grooves
are made the presence of the emery does not practically increase the friction
over the amount of the latter when pure oil only is between the surfaces.
The infinite number of grooves constitute a very perfect means of insuring
a uniform oil supply at every point of the bearings. As long as grooves in
ihe journal match with those in the brasses the friction appears to amount
to only about 10$ to 15$ of the pressure. But if a smooth journal is placed
between a set of brasses which are grooved, and pressure be applied, the
journal crushes the grooves and becomes brazed or coated with brass, and
then the coefficient of friction becomes upward of 40$. If then emery is
applied, the friction is made very much less by its presence, because the
grooves are made to match each other, and a uniform oil supply prevails at
every point of the bearings, whereas before the application of the emery
many spots of the latter receive no oil between them.
Moment of Friction and Work of Friction of Sliding-
surfaces, etc.
Moment of Fric- Energy lost by Friction
tion, inch-lbs. in ft.-lbs. per min.
Flat surfaces fWS
Shafts and journals VzfWd .2618/JFdn
Flat pivots %fWr .349/JFm
Collar-bearing KfW**l ~ **| .349/TFn ^ ~ ^°
Conical pivot %/TFr cosec a -349/Wrn cosec a
Conical journal ~AfWr sec a -349/TFru sec a
Truncated-cone pivot %fW^ T TI .349/PF^-^
?"«j sin a *2 >3i1-1 **
Hemispherical pivot fWr .5236/ JFni
Tractrix, or Schiele's " anti-
friction " pivot fWr ,5236/JFm
PIVOT-BEARINGS. 939
In the above / = coefficient of friction ;
W — weight on journal or pivot in pounds;
r = radius, d = diameter, in inches;
S = space in feet through which sliding takes place;
ra = outer radius, r} = inner radius;
n = number of revolutions per minute;
a = the half-angle of the cone, i.e., the angle of the slope
with the axis.
To obtain the horse-power, divide the quantities in the last column by
33,000. Horse-power absorbed by friction of a shaft =
The formula for energy lost by shafts and journals is approximately true
for loosely fitted bearings. Prof. Thurston shows that the correct formula
varies according to the character of fit of the bearing; thus for loosely
fitted journals, if U — the energy lost,
2/7rr .MISfWdn ,. , .,
U = — J - Wn inch-pounds = - J t oot-lbs.
Vi +/2 Vi+/2
For perfectly fitted journals U = 2MfnrWn inch-lbs. = .3325/PFdn, ft.-lbs,
For a bearing in which the journal is so grasped as to give a uniform
pressure throughout, U = fw*rWn inch-lbs. = AllZfWdn, ft.-lbs.
Resistance of railway trains and wagons due to friction of trains:
f X 2240
Pull on draw-bar = - — - — pounds per gross ton,
K
in which R is the ratio of the radius of the wheel to the radius of journal.
A cylindrical journal, perfectly fitted into a bearing, and carrying a total
load, distributes the pressure due to this load unequally on the bearing, the
maximum pressure being at the extremity of the vertical radius, while at
the extremities of the horizontal diameter the pressure is zero. At any
point of the bearing-surface at the extremity of a radius which makes an
angle 0 with the jertical radius the normal pressure is proportional to cos 0.
If p = normal pressure on a unit of surface, w = total load on a unit of
length of the journal, and r — radius of journal,
w cos d
w cos 0 = i.otrp, p = — .
1 . 577*
PIVOT-BEARINGS.
The Schiele Curve.— W. H. Harrison, in a letter to the Am. Machin-
ist, 1891, says the Schiele curve is not as good a form for a bearing as the
segment of a sphere. He says: A mill-stone weighing a ton frequently
bears its whole weight upon the flat end of a hard-steel pivot 1^" diameter,
or one square inch area of bearing; but to carry a weight of 3000 Ibs. he
advises an end bearing about 4 inches diameter, made in the form of a seg-
ment of a sphere about ^ inch in height. The die or fixed bearing should
be dished to fit the pivot. This form gives a chance for the bearing to
adjust itself, which it does not have when made flat, or when made with the
Schiele curve. If a side bearing is necessary it can be arranged farther up
the shaft. The pivot and die should be of steel, hardened; cross-gutters
should be in the die to allow oil to flow, and a central oil-hole should be
made in the shaft.
The advantage claimed for the Schiele bearing is that the pressure is uni-
formly distributed over its surface, and that it therefore wears uniformly.
Wilfred Lewis (Am. Mach., April 19, 1894) says that its merits as a thrust-
bearing have been vastly overestimated; that the term "anti-friction1'
applied to it is a misnomer, since its friction is greater than that of a flat
step or collar of the same diameter. He advises that flat thrust-bearings
should always be annular in form, having an inside diameter one half of
the external diameter,
Friction of a Flat Pivot-bearing.— The Research Committee
on Friction (Proc. Inst. M. E. 1891) experimented on a step-bearing, flat-
ended, 3 in. diam., the oil being forced into the bearing through a hole in
Its centre and distributed through two radial grooves, insuring thorough
lubrication. The step was of steel and the bearing of manganese-bronze.
940 tfUlCTIOK AND LUBRICATION.
At revolutions per min 50 128 194 290 353
The coefficient of friction varied j .0181 .0053 .0051 .0044 .0053
between I and .0221 .0113 .0102 .0178 .0167
With a white-metal bearing at 128 revolutions the coefficient of friction
was a little larger than with the manganese-bronze. At the higher speeds
the coefficient of friction was less, owing to the more perfect lubrication, as
shown by the more rapid circulation of the oil. At 128 revolutions the
bronze bearing heated and seized on one occasion with a load of 260 pounds
and on another occasion with 300 pounds per square inch. The white-metal
bearing under similar conditions heated and seized with a load of 240
pounds per square inch. The steel footstep on manganese-bronze was after-
wards tried, lubricating with three and with four radial grooves; but the
friction was from one and a half times to twice as great as with only the two
grooves. (See also Allowable Pressures, page 936.)
Mercury-bath Pivot.— A nearly frictipnless step-bearing may be
obtained by floating the bearing with its superincumbent weight upon mer-
cury. Such an apparatus is used in the lighthouses of La Heve, Havre. It
is thus described in Eng'g, July A, 1893, p. 41:
The optical apparatus, weighing about 1 ton, rests on a circular cast-iron
table, which is supported by a vertical shaft of wrought iron 2.36 in.
diameter.
This is kept in position at the top by a bronze ring and outer iron support,
and at the bottom in the same way, while it rotates on a removable steel
pivot resting in a steel socket, which is fitted to the base of the support. To
the vertical shaft there is rigidly fixed a floating cast-iron ring 17.1 in. diam-
eter and 11.8 in. in depth, which is plunged into and rotates in a mercury
bath contained in a fixed outer drum or tank, the clearance between the
vertical surfaces of the drum and ring being only 0.2 in., so as to reduce as
much as possible the volume of mercury (about 220 Ibs.), while the horizon-
tal clearance at the bottom is 0.4 in.
BALL-BEARINGS, FRICTION ROLLERS, ETC.
A. H. Tyler (Eng'g, Oct. 20, 1893, p. 483), after experiments and com-
parison with experiments of others arrives at the followiug*conclusions:
That each ball must have two points of contact only.
The balls and race must be of glass hardness, and of absolute truth.
The balls should be of the largest possible diameter which the space at
disposal will admit of.
Any one ball should be capable of carrying the total load upon the bearing.
Two rows of balls are always sufficient.
A ball-bearing requires no oil, and has no tendency to heat unless over-
loaded.
Until the crushing strength of the balls is being neared, the frictional re-
sistance is proportional to the load.
The frictional resistance is inversely proportional to the diameter of the
balls, but in what exact proportion Mr. Tyler is unable to say. Probably it
varies with the square.
The resistance is independent of the number of balls and of the speed.
No rubbing action will take place between the balls, and devices to guard
against it are unnecessary, and usually injurious.
The above will show that the ball-bearing is most suitable for high speeds
and light loads. On the spindles of wood-carving machines some make as
much as 30,000 revolutions per minute. They run perfectly cool, and never
have any oil upon them. For heavy loads the balls should not be less than
two thirds the diameter of the shaft, and are better if made equal to it.
Ball-bearings have not been found satisfactory for thrust-blocks, for
the reason apparently that the tables crowd together. Better results have
been obtained from coned rollers. A combined system of rollers and balls
is described in Entfg, Oct. 6, 1893, p. 429.
Friction-rollers. —If a journal instead of revolving on ordinary
bearings be supported on friction -rollers the force required to make the jour-
nal revolve will be reduced in nearly the same proportion that the diameter
of the axles of the rollers is less than the diameter of the rollers themselves.
In experiments by A. M. Wellington with a journal 3J/g in. diam. supported
on rollers 8 in. diam., whose axles were 1% iu. diam., the friction in starting
from rest was J4 the friction of an ordinary 3^-in. bearing, but at a car
speed of 10 miles per hour it was ^ that of the ordinary bearing. The ratio
of the diam. of the axle to diam. of roller was 1%: 8, or as 1 to 4.6.
FRICTION OF STEAM-ENGINES. 941
Bearings for Very High Rotative Speeds. (Proc. Inst. M. E.,
Oct. 1888, p. 482.)— In the Parsons steam-turbine, which has a speed of as
high as 18,000 rev. per min., as it is impossible to secure absolute accuracy
of balance, the bearings are of special construction so as to allow of a certain
very small amount of lateral freedom. For this purpose the bearing is sur-
rouudel by two sets of steel washers 1/16 inch thick and of different diam-
eters, the larger fitting close in the casing and about 1/3^ inch clear of the
bearing, and the smaller fitting close on the bearing and about 1/32 inch
clear of the casing. These are arranged alternately, and are pressed
together by a spiral spring. Consequently any lateral movement of the
bearing causes them to slide mutually against one another, and by their
friction to check or damp any vibrations that may be set up in the spindle.
The tendency of the spindle is then to rotate about its axis of mass, or prin-
cipal axis as it is called; and the bearings are thereby relieved from exces-
sive pressure, and the machine from undue vibration. The finding of the
centre of gyration, or rather allowing the turbine itself to find its own
centre of gyration, is a well-known device in other branches of mechanics:
as in the instance of the centrifugal hydro-extractor, where a mass very
much out of balance is allowed to find its own centre of gyration; the faster
it ran the more steadily did it revolve and the less was the vibration. An-
other illustration is to be found in the spindles of spinning machinery,
which run at about 10,000 or 11,000 revolutions per minute: they are made
of hardened and tempered steel, and although of very small dimensions, the
outside diameter of the largest portion or driving whorl being perhaps not
more than 114 in., it is found impracticable to run them at that speed in
what might be called a hard-and-fast bearing. They are therefore run with
some elastic substance surrounding the bearing, such as steel springs, hemp,
or cork. Any elastic substance is sufficient to absorb the vibration, and
permit of absolutely steady running.
FRICTION OF STEAM-ENGINES.
Distribution of the Friction of Engines.— Prof . Thurston in
his " Friction and Lost Work," gives the following:
1. 2. 3.
Mainbearings 47.0 35.4 85.0
Piston and rod 32.9 25.0 21.0
Crank-pin 6.8 5.1| 1Q n
Cross-head and wrist-pin 5.4 4.1 f
Valve and rod 2.5 26. 4J 00 n
Eccentric strap. 5.3 4. Of ass-
Link and eccentric 9.01
Total
100.0 100.0 100.0
No. 1, Straight-line, 6" X 12", balanced valve ; No. 2, Straight-line, 6" X 12",
unbalanced valve; No. 3, 7" X 10", Lansing traction locomotive valve-gear.
Prof. Thurston's tests on a number of different styles of engines indicate
that the friction of any engine is practically constant under all loads.
(Trans. A. S. M. E., viii. 86; ix. 74.)
In a Straight-line engine, 8" X 14", I.H.P. from 7.41 to 57.54, the friction H.
P. varied irregularly between 1.97 and 4.02, the variation being independent
of the load. With 50 H.P. on the brake the I.H.P. was only 52.6, the friction
being only 2.6 H.P., or about 5g.
In a compound condensing-engine, tested from 0 to 102.6 brake H.P., gave
I.H.P. from 14.92 to 117.8 H.P., the friction H.P. varying only from 14.92 to
17.42. At the maximum load the friction was 15.2 H.P., or 12.9$.
The friction increases with increase of the boiler-pressure from 30 to 70
Ibs., and then becomes constant. The friction generally increases with in-
crease of speed, but there are exceptions to this rule.
Prof. Denton (Stevens Indicator, July, 1890), comparing the calculated
friction of a number of engines with the friction as determined by measure-
ment, finds that in one case, a 75-ton ammonia ice-machine, the friction of
the compressor, 17^ H.P., is accounted for by a coefficient of friction of 7>#5
on all the external bearings, allowing 6$ of the entire friction of the machine
for the friction of pistons, stuffing-boxes, and valves. In the case of the
Pawtucket pumping-engine, estimating the friction of the external bearings
with a coefficient of friction of 6$ and that of the pistons, valves, and stuff-
ing-boxes as in the case of the ice-machine, we have the total friction
distributed as follows :
942 FRICTIOK AKD LtJBRICATIOK.
Horse- Per cent
power, of Whole.
Crank-pins and effect of piston-thrust on main shaft . . 0.71 11.4
Weight of fly- wheel and main shaft 1.95 32.4
Steam-valves 0.23 3.7
Eccentric 0.07 1.2
Pistons 0.43 7.2
Stuffing-boxes, six altogether 0.72 11.3
Air-pump 2.10 32 . 8
Total friction of engine with load 6.21 100.0
Total friction per cent of indicated power ... 4.27
The friction of this engine, though very low in proportion to the indicated
power, is satisfactorily accounted for by Morin's law used with a coefficient
of friction of 5#. In both cases the main items of friction are those due to
the weight of the fly-wheel and main shaft and to the piston-thrust on
crank-pins and main-shaft bearings. In the ice-machine the latter items
are the larger owing to the extra crank-pin to work the pumps, while
in the Pawtucket engine the former preponderates, as the crank-thrusts are
partly absorbed by the pump-pistons, and only the surplus effect acts on
the crank -shaft.
Prof. Denton describes in Trans. A. S. M. E., x. 392, an apparatus by
which he measured the friction of a piston packing- ring. When the parts
of the piston were thoroughly devoid of lubricant, the coefficient of friction
was found to be about 7£gf; with an oil-feed of one drop in two minutes the
coefficient was about 5$; with one drop per minute it was about 3$. These
rates of feed gave unsatisfactory lubrication, the piston groaning at the
ends of the stroke when run slowly, and the flow of oil left upon the surfaces
was found by analysis to contain about 50$ of iron. A feed of two drops per
minute reduced the coefficient of friction to about \%, and gave practically
perfect lubrication, the oil retaining its natural color and purity.
LUBRICATION.
Measurement of the Durability of Lubricants* (J. E. Den.
ton, Trans. A. S. M. E., xi. 1013.)— Practical differences of durability of lubri-
cants depend not on any differences of inherent ability to resist being "worn
out " by rubbing, but upon the rate at which they flow through and away
from the bearing-surfaces. The conditions which control this flow are so
delicate in their influence that all attempts thus far made to measure dura-
bility of lubricants may be said to have failed to make distinctions of lubri-
cating value having any practical significance. In some kinds of service the
limit to the consumption of oil depends upon the extent to which dust or other
refuse becomes mixed with it, as in railroad-car lubrication and in the case
of agricultural machinery. The economy of one oil over another, so far as
the quality used is concerned — that is, so far as durability is concerned— is
simply proportional to the rate at which it can insinuate itself into and flow
out of minute orifices or cracks. Oils will differ in their ability to do this,
first, in proportion to their viscosity, and, second, in proportion to the ca-
pillary properties which they may possess by virtue of the particular ingre-
dients used in their composition. Where the thickness of film between rub-
bing-surfaces must be so great that large amounts of oil pass through,
bearings in a given time, and the surroundings are such as to permit oil to
be fed at high temperatures or applied by a method not requiring a perfect
fluidity, it is probable that the least amount of oil will be used when the vis-
cosity is as great as in the petroleum cylinder stocks. When, however, the
oil must flow freely at ordinary temperatures and the feed of oil is
restricted, as in the case of crank-pin bearings, it is not practicable to feed
such heavy oils in a satisfactory manner. Oils of less viscosity or of a
fluidity approximating to lard-oil must then be used.
Relative Value of Lubricants. (J. E.Denton, Am. Mach., Oct. 30,
1890.)— The three elements which determine the value of a lubricant are the
cost due to consumption of lubricants, the cost spent for coal to overcome
the frictional resistance caused by use of the lubricant, and the cost due to
the metallic wear on the journal ami the brasses.
The Qualifications of a Good Lubricant, as laid down by
W. H. Bailey, in Proc. Inst. C. E., vol. xlv., p. 37^ are: 1. Sufficient body to
keep the surfaces free from contact under maximum pressure. 2. The
LUBKICATIOK. 943
greatest possible fluidity consistent with the foregoing condition. 3. 'itie
lowest possible coefficient of friction, which in bath lubrication would be for
fluid friction approximately. 4. The greatest capacity for storing and car-
rying a\yay heat. 5, A high temperature of decomposition. 6. Power to
resist oxidation or the action of the atmosphere. 7. Freedom from corrosire
ac ioa on the metals upon which used.
Amount of Oil needed to Run an Engine.— The Vacuum Oil
Co. in 1892, in response to an inquiry as to cost of oil to run a 1000-H.P.
Corliss engine, wrote: The cost of running two engines of equal size of the
same make is not always the same. Therefore while we could furnish
figures showing what it is costing gome of our customers having Corliss
engines of 1000 H.P., we could only give a general idea, which in itself
might be considerably out of the way as to the probable cost of cylinder-
and engine-oils per year for a particular engine. Such an engine ought to
run readily on less than 8 drops of 600 W oil per minute. If 3000 drops are
figured to the quart, and 8 drops used per minute, it would take about
two and one half barrels (52.5 gallons) of 600 W cylinder- oil, at 65 cents per
fallon, or about $85 for cylinder-oil per year, running 6 days a week and 10
ours a day. Engine-oil would be even more difficult to guess at what the
cost would be, because it would depend upon the number of cups required
on the engine, which varies somewhat according to the style of the engine.
It would doubtless be safe, however, to calculate at the outside that not
more than twice as much engine-oil would be required as of cylinder-oil.
The Vacuum Oil Co. in 1892 published the following results of practice
with " 600 W " cylinder-oil:
rwii« omYinmind f>n^in« 5 20 and 33 X 48; 83 revs, per min. ; 1 drop of oil
Corliss compound engine, -j per min to 1 drop in two minutes
" triple exp. 20, 33, and 46 X 48; 1 drop every 2 minutes.
~ „. _ A llan i * j 20 and 36 X 36; 143 revs, per min. ; 2 drops of oil
1 per min., reduced afterwards to 1 drop per min.
P M * % 1 15 X 25 X 16; 240 revs, per min.; 1 drop every 4
| minutes.
Results of tests on ocean-steamers communicated to the author by Prof.
Denton in 1892 gave: for 1200-H.P. marine engine, 5 to 6 English gallons (6 to
7.2 U. S. gals.) of engine-oil per 24 hours for "external lubrication; and for a
1500-H.P. marine engine, triple expansion, running 75 revs, per min., 6 to 7
English gals, per 24 hours. The cylinder-oil consumption is exceedingly
variable,— from 1 to 4 gals, per day on different engines, including cylinder-
oil used to swab the piston-rods.
Quantity of Oil used on a locomotive Crank-pin.— Prof.
Denton, Trans. A. S. M. E., xi. 10:20, says: A very economical case of practical
oil-consumption is when a locomotive main crank-pin consumes about six
cubic inches of oil in a thousand miles of service. This is equivalent to a
consumption of one milligram to seventy square inches of surface rubbed
over.
The Examination of Lubricating-oils. (Prof. Thos. B. Still-
man, Stevens Indicator, July, 1890.) — The generally accepted conditions of
a good lubricant are as follows:
1. " Body " enough to prevent the surfaces, to which it is applied, from
coming in contact with each other. (Viscosity.)
2. Freedom from corrosive acid, either of mineral or animal origin.
3. As fluid as possible consistent with " body."
4. A minimum coefficient of friction.
5. High "flash" and burning points.
6. Freedom from all materials liable to produce oxidation or " gumming."
The examinations to be made to verify the above are both chemical and
mechanical, and are usually arranged in the following order :
1. Identification of the oil, whether a simple mineral oil, or animal oil, or
a mixture. 2. Density. 3. Viscosity. 4. Flash-point. 5. Burning -point.
6. Acidity. 7. Coefficient of friction. 8. Cold test.
Detailed directions for making all of the above tests are given in Prof.
Stillnmn's Article. See also tstillman's Engineering Chemistry, p. 366.
Notes on Specifications for Petroleum Lubricants, (C.
M. Everest, Vice-Pres. Vacuum Oil Co., Proc. Engineering Congress, Chicago
World's Fair, 1893.)— The specific gravity was the first standard established
for determining quality of lubricating oils, but it has long since been dis-
carded as a conclusive test of lubricating quality. However, as the specific
gravity of a particular petroleum oil increases the viscosity also increases.
94:4 FRICTION AKD LUBKICATIOST.
The object of the fire test of a lubricant, as well as its flash test, is 1 he pre-
vention of danger from fire through the use of an oil that will evolve in-
flammable vapors. The lowest fire test permissible is 300°, which gives a
liberal factor of safety under ordinary conditions.
The cold test of an oil, i.e., the temperature at which the oil will congeal,
should be well below the temperature at which it is used; otherwise the co-
efficient of friction \yould be correspondingly increased.
Viscosity, or fluidity, of an oil is usually expressed in seconds of time in
which a given quantity of oil will flow through a certain orifice at the tem-
perature stated, comparison sometimes being made v.ith water, sometimes
with sperm-oil, and again with rape seed oil. It seems evident that within
limits the lower the viscosity of an oil (without a too near approach to metal-
lic contact of the rubbing surfaces) the lower will be the coefficient of fric-
tion. But we consider that each bearing in a mill or factory would probably
require an oil of different viscosity from any other hearing in the mill, in
order to give its lowest coefficient of friction, and that slight variations in the
condition of a particular bearing would change the requirements of that
bearing; and further, that when nearing the '• danger point " the question of
viscosity alone probably does not govern.
The requirement of the New England Manufacturers' Association, that
an oil shall not lose over 5fe of its volume when heated to 140° Fahr. for 12
hours, is to prevent losses by evaporation, with the resultant effects.
The precipitation test gives no indication of the quality of the oil itself, as
the free carbon in improperly manufactured oils can be easily removed.
It is doubtful whether oil buyers who require certain given standards of
laboratory tests are better served than those who do not. Some of the
standards are so faulty that to pass them an oil manufacturer must supply
oil he knows to be faulty ; and the requirements of the best standards can
generally be met by products that will give inferior results in actual service.
Penna. R. R. Specifications for Petroleum Products,
19OO. — Five different grades of petroleum products will be used.
The materials desired under this specification are the products of the
distillation and refining of petroleum unmixed with any other sub-
stances.
150° Fire-test Oil.— This grade of oil will not be accepted if sample (1) is
not "water-white" in color; (2) flashes below 130° Fahrenheit; (3) burns
below 151° Fahrenheit; (4) is cloudy or shipment has cloudy barrels when
received, from the presence of glue or suspended matter; (5) becomes
opaque or shows cloud when the sample has been 10 minutes at a tempera-
ture of 0° Fahrenheit.
300° Fire- test Oil.— This grade of oil will not be accepted if sample (1) is
not "water-white1' in color; (2) flashes below 249° Fahrenheit; (3) burns
below 298° Fahrenheit; (4) is cloudy or shipment has cloudy barrels when
received, from the presence of glue or suspended matter; (5) becomes
opaque or shows cloud when the sample has been 10 minutes at a tempera-
ture of 32° Fahrenheit; (6) shows precipitation when some of the sample is
heated to 450° F. The precipitation test is made by having about two fluid
ounces of the oil in a six-ounce beaker, with a thermometer suspended in
the oil, and then heating slowly until the thermometer shows the required
temperature. The oil changes color, but must show no precipitation.
Paraffine and Neutral Oils.— These grades of oil will not be accepted if
the sample from shipment (1) is so dark in color that printing with long-
primer type cannot be read with ordinary daylight through a layer of the
oil ^ inch thick ; (2) flashes below 298° F. ; (3) has a gravity at 60° F., below 24°
or above 35° Baume; (4) from October 1st to May 1st has a cold test above
10° F., and from May 1st to October 1st has a cold test above 32° F.
The color test is made by having a layer of the oil of the prescribed thick-
ness in a proper glass vessel, and then putting the printing on one side of the
vessel and reading it through the layer of oil with the back of the observer
toward the source of light.
Well Oil.— This grade of oil will not be accepted if the sample from
shipment (1) flashes, from May 1st to October 1st, below 298° F., or,
from October 1st to May 1st, below 249° F.; (2) has a gravity at 60° F.,
below 28° or above 31° Bairthe; (3) from October 1st to May 1st has
a cold test above 10° F., and from May 1st to October 1st has
a cold test above 32° F.; (4) shows any precipitation when 5 cubic
centimetres are mixed with 95 c. c. of gasoline. The precipitation test
is to exclude tarry and suspended matter. It is made by putting 95 c.c. of
88° B gasoline, which must not be above 80° F. in temperature, into a 100 c. c.
SOLID LUBRICANTS.
945
graduate, then adding the prescribed amount of oil and shaking thoroughlyt
Allow to stand ten minutes. With satisfactory oil no separated or precip-
itated material can be seen.
500° Fire-test Oil.— This grade of oil will not be accepted if sample from
shipment (1) flashes below 494° F.; (2) shows precipitation with gasoline
when tested as described for well oil.
Printed directions for determining flashing and burning tests and for
making cold tests and taking gravity are furnished by the railroad com-
pany.
Penna. R. R. Specifications for Lubricating Oils (1894).
(In force 1902.)
Constituent Oils.
Parts by volume.
Extra lard-oil
1
4
~E~
Extra No 1 lard-oil
1
1
4
1
1
2
1
2
1
1
1
4
1
1
2
1
2
1
5JO° fire-test oil
1
Paraffine oil ....
Well oil
1
Used for
A
B
CL
C2
<?3
2>i
D2
D*
A, freight cars; engine oil on shifting-engines; miscellaneous greasing in
foundries, etc. B, cylinder lubricant on marine equipment and on station-
ary engines. C, engine oil; all engine machinery; engine and tender truck
boxes; shafting and machine tools; bolt cutting; general lubrication except
cars. D, passenger-car lubrication. E, cylinder lubricant for locomotives,
d, DI, for use in Dec., Jan., and Feb.; C2, D2, in March, April, May, Sept.,
Oct., and Nov.; C3, Z)3. in June, July, and August. Weights per gallon, A,
7.4 Ibs.; B, C, D, E, 7. 5 Ibs.
Soda Mixture for Machine Tools. (Penna. R. R. 1894.)— Dissolve
5 Ibs. of common sal-soda in 40 gallons of water and stir thoroughly. When
needed for use mix a gallon of this solution with about a pint of engine oil.
Used for the cutting parts of machine tools instead of oil.
SOLID LUBRICANTS.
Graphite in a condition of powder and used as a solid lubricant, so
called, to distinguish it from a liquid lubricant, has been found to do well
where the latter has failed. .
Rennie, in 1829, says : " Graphite lessened friction in all cases where it
was used." General Morin. at a later date, concluded from experiments
that it could be used with advantage under heavy pressures; and Prof.
Thurston found it well adapted for use under both light and heavy pressures
when mixed with certain oils. It is especially valuable to prevent abrasion
and cutting under heavy loads and at low velocities.
Soapstone, also called talc and steatite, in the form of powder and
mixed with oil or fat, is sometimes used as a lubricant. Graphite or soap-
stone, mixed with soap, is used on surfaces of wood working against either
iron or wood.
Fibre-graphite. — A new self-lubricating bearing known as fibre-
graphite is described by John H. Cooper in Trans. A. S. M. E., xiii. 374, as
the invention of P. H. Holmes, of Gardiner, Me. This bearing material is
composed of selected natural graphite, which has been finely divided and
freed from foreign and gritty matter, to which is added wood-fibre or other
growth mixed in water in various proportions, according to the purpose to
be served, and then solidified by pressure in specially prepared moulds ;
after removal from which the bearings are first thoroughly dried, then satu-
rated with a drying oil. and finally subjected to a current of hot, dry air for
the purpose of oxidizing the oil, and hardening the mass. When finished,
they may be " machined " to size or shape with the same facility and means
employed on metals. (Holmes Fibre-Graphite Mfg. Co., Philadelphia.)
Meiaiine is a solid compound, usually containing graphite, made in the
form of small cylinders which are fitted permanently into holes drilled in
the surface of the bearing. The bearing thus fitted runs without any other
lubrication. (North American Metaline Co., Long Island City, N. Y.)
946 THE FOUNDRY.
THE FOUNDRY.
CUPOLA PRACTICE.
The following notes, with the accompanying table, are taken from an
article by Simpson Bolland in American Machinist, June 30, 1892. The table
shows heights, depth of bottom, quantity of fuel on bed, proportion of fuel
and iron in charges, diameter of main blast-pipes, number of tuyeres, blast-
Eressure, sizes of blowers and power of engines, and melting capacity per
our, of cupolas from 24 inches to 84 inches in diameter.
Capacity of Cupola.— The accompanying table will be of service in deter-
mining the capacity of cupola needed for the production of a given quantity
of iron in a specified time.
First, ascertain the amount of iron which is likely to be needed at each
cast, and the length of time which can be devoted profitably to its disposal;
and supposing that two hours is all that can be spared for that purpose, and
that ten tons is the amount which must be melted, find in the column, Melt-
ing Capacity per hour in Pounds, the nearest figure to five tons per hour,
which is found to be 10,760 pounds per hour, opposite to which in the column
Diameter of Cupolas, Inside Lining, will be found 48 inches ; this will be the
size of cupola required to furnish ten tons of molten iron in two hours.
Or suppose that the heats were likely to average 6 tons, with an occasional
increase up to ten, then it might not be thought wise to incur the extra ex-
pense consequent on working a 48-inch cupola, in which case, by following
the directions given, it will be found that a 40-inch cupola would answer the
purpose for 6 tons, but would require an additional hour's time for melting
whenever the 10 ton heat came along.
The quotations in the table are not supposed to be all that can be melted
in the hour by some of the very best cupolas, but are simply the amounts
which a common cupola under ordinary circumstances may be expected to
melt in the time specified.
Height of Cupola.— By height of cupola is meant the distance from the
base to the bottom side of the charging hole.
Depth of Bottom of Cupola.— Depth of bottom is the distance from the
sand-bed, after it has been formed at the bottom of the cupola, up to the
under side of the tuyeres.
All the amounts for fuel are based upon a bottom of 10 inches deep, and
any departure from this depth must be met by a corresponding change in
the quantity of fuel used on the bed ; more in proportion as the depth is
increased, and less when it is made shallower.
Amount of Fuel Required on the Bed.— The column " Amount of Fuel re-
quired on Bed, in Pounds" is based on the supposition that the cupola is a
straight one all through, and that the bottom is 10 inches deep. If the bot-
tom be more, as in those of the Colliau type, then additional fuel will be
needed.
The amounts being given in pounds, answer for both coal and coke, for,
should coal be used, it would reach about 15 inches above the tuyeres ; the
same weight of coke would bring it up to about 22 inches above the tuyeres,
which is a reliable amount to stock with.
First Charge of Iron. — The amounts given in this column of the table are
safe figures to work upon in every instance, yet it will always be in order,
after proving the ability of the bed to carry the load quoted, to make a slow
and gradual increase of the load until it is fully demonstrated just how much
burden the bed will carry.
Succeeding Charges of Fuel and Iron.— In the columns relating to succeed-
ing charges of fuel and iron, it will be seen that the highest proportions are
not favored, for the simple reason that successful melting with any greater
proportion of iron to fuel is not the rule, but, rather, the exception. When-
ever we.see that iron has been melted in prime condition in the proportion
of 12 pounds of iron to one of fuel, we may reasonably expect that the talent,
material, and cupola have all been up to the highest degree of excellence.
Diameter of Main Blast-pipe.— The table gives the diameters of main
blast-pipes for all cupolas from 24 to 84 inches diameter. The sizes given
opposite each cupola are of sufficient area for all lengths up to 100 feet.
CUPOLA PRACTICE.
947
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948 THE FOUNDRY.
Tuyeres for Cupola. — Two columns are devoted to the number and sizes of
tuyeres requisite for the successful working of each cupola ; one gives the
number of pipes 6 inches diameter, and the other gives the number and
dimensions of rectangular tuyeres which are their equivalent in area.
From these two columns any other arrangement or disposition of tuyeres
may be made, which shall answer in their totality to the areas given in the
table.
When cupolas exceed 60 inches in diameter, the increase in diameter
should begin somewhere above the tuyeres. This method is necessary in all
common cupolas above 60 inches, because it is not possible to force the blast
to the middle of the stock, effectively, at any greater Jiameter.
On no consideration must the tuyere area be reduced; thus, an 84-inch
cupola must have tuyere area equal to 31 pipes 6 inches diameter, or 16 flat
tuyeres 16 inches by 13^ inches.
If it is found that the given number of flat tuyeres exceed in circumference
that of the diminished part of the cupola, they can be shortened, allowing
the decreased length to be added to the depth, or they may be built in on
end; by so doing, we arrive at a modified form of the Blakeney cupola.
Another important point in this connection is to arrange the tuyeres in
such a manner as will concentrate the fire at the melting-point into the
smallest possible compass, so that the metal in fusion will have less space
to traverse while exposed to the oxidizing influence of the blast.
To accomplish this, recourse has been had to the placing of additional
rows of tuyeres in some instan es— the "Stewart rapid cupola" having
three rows, and the " Colliau cupola furnace " having two rows, of tuyeres.
Blast-pressure.— Experiments show that about 30,000 cubic feet of air are
consumed in melting a ton of iron, which would weigh about 2400 pounds,
or more than both iron and fuel. When the proper quantity of air is sup-
plied, the combustion of the fuel is perfect, and carbonic-acid gas is the
result. When the supply of air is insufficient, the combustion is imperfect,
and carbonic-oxide gas is the result. The amount of heat evolved in these
two cases is as 15 to 4*4, showing a loss of over two thirds of the heat by im-
perfect combustion.
It is not always true that we obtain the most rapid melting when we are
forcing into the cupola the largest quantity of air. Some time is required
to elevate the temperature of the air supplied to the point that it will enter
into combustion. If more air than this is supplied, it rapidly absorbs heat,
reduces the temperature, and retards combustion, and the fire in the cupola
may be extinguished with too much blast.
Slag in Cupolas. — A certain amount of slag is necessary to protect the
molten iron which has fallen to the bottom from the action of the blast; if
it was not there, the iron would suffer from decarbonization.
When slag from any cause forms in too great abundance, it should be led
away by inserting a hole a little below the tuyeres, through which it will
find its way as the iron rises in the bottom,
In the event of clean iron and fuel, slag seldom forms to any appreciable
extent in small heats ; this renders any preparation for its withdrawal un-
necessary, but when the cupola is to be taxed to its utmost capacity it is
then incumbent on the melter to flux the charges all through the heat, car-
rying it away in the manner directed.
The best flux for this purpose is the chips from a white marble yard.
About 6 pounds to the ton of iron will give good results when all is clean.
When fuel is bad, or iron is dirty, or both together, it becomes imperative
that the slag be kept running all the time.
Fuel for Cupolas. — The best fuel for melting iron is coke, because it re-
quires less blast, makes hotter iron, and melts faster than coal. When coal
must be used, care should be exercised in its selection. All anthracites
which are bright, black, hard, and free from slate, will melt iron admirably.
The size of the coal used affects the melting to an appreciable extent, and,
for the best results, small cupolas should be charged with the size called
"egg,Ma still larger grade for medium-sized cupolas, and what is called
" lump " will answer for all large cupolas, when care is taken to pack it
carefully on the charges.
Charging a Cupola.— Chas. A. Smith (Am. Mach., Feb. 12, 1891) gives
the following : A 28-in. cupola should have from 300 to 400 pounds of coke
on bottom bed; a 36-in. cupola, 700 to 800 pounds; a 48-in. cupola, 1500 Ibs.;
and a 60-in« cupola should have one ton of fuel on bottom bed. To every
pound of fuel on the bed, three, and sometimes four pounds of metal can be
added with safety, if the cupola has proper blast; in after-charges, to every
CUPOLA PEACTICE.
949
pound of fuel add 8 to 10 pounds of metal; any well-constructed cupola will
stand ten.
F. P. Wolcott (Am. Mack., Mar. 5, 1891) gives the following as the practice
of the Colwell Iron-works, Carteret, N. J.: " We melt daily from twenty to
forty tons of iron, with an average of 11.2 pounds of iron to one of fuel. In
a 36-in. cupola seven to nine pounds is good melting, but in a cupola that
lines up 48 to 60 inches, anything less than nine pounds shows a defect in
arrangement of tuyeres or strength of blast, or in charging up."
" The Moulder's Text-book,1' by Thos. D. West, gives forty-six reports in
tabular form of cupola practice in thirty States, reaching from Maine to
Oregon.
Cupola Charges in Stove-foundries. (Iron Age, April 14, 1892.)
No two cupolas are charged exactly the same. The amount of fuel on the
bed or between the charges differs, while varying amounts of iron are used
in the charges. Below will be found charging-lists from some of the prom-
inent stove-foundries in the country :
Ibs.
A— Bed of fuel, coke . . 1,500
First charge of iron 5,000
All other charges of iron . . 1 ,000
First and second charges
of coke, each 200
Ibs.
Four next charges of coke,
each 150
Six next charges of coke, each 120
Nineteen next charges of coke,
each 100
Thus for a melt of 18 tons there would be.5120 Ibs. of coke used, giving a
ratio of 7 to 1. Increase the amount of iron melted to 24 tons, and a ratio of
8 pounds of iron to 1 of coal is obtained.
Ibs.
Second and third charges of
fuel 130
All other charges of fuel, each 100
Ibs.
B-Bed of fuel, coke 1,600
First charge of iron 1,800
First charge of fuel 150
All other charges of iron,
each 1,000
For an 18 ton melt 5060 Ibs. of coke would be necessary, giving a ratio of
7.1 lbs> of iron to 1 pound of coke.
Ibs.
All other charges of iron . . .
All other charges of coke. . .
Ibs.
2,000
, 150
C— Bed of fuel, coke 1,600
First charge of iron 4,000
First and second charges
of coke 200
In a melt of 18 tons 4100 Ibs. of coke would be used, or a ratio of 8.5 to 1.
Ibs. I Ibs.
B-Bed of fuel, coke 1,800 All charges of coke, each 200
First charge of iron 5,600 J All other charges of iron 2,900
In a melt of 18 tons, 3900 Ibs. of fuel would be used, giving a ratio of 9.4
pounds of iron to 1 of coke. Very high, indeed, for stove-plate.
Ibs. I Ibs.
E— Bed of fuel, coal 1,900 I All other charges of iron, each 2,000
First charge of iron 5,000 I All other charges of coal, each 175
First charge of coal 200 |
In a melt of 18 tons 4700 Ibs. of coal would be used, giving a ratio of 7.7
Ibs. of iron to 1 Ib. of coal.
These are sufficient to demonstrate the varying practices existing among
different stove-foundries. In all these places the iron was proper for stove-
plate purposes, and apparently there was little or no difference in the kind
of work in the sand at the different foundries.
Results of Increased Driving. (Erie City Iron-works, 1891.)—
May— Dec. 1890: 60-in. cupola, 100 tons clean castings a week, melting 8 tons
per hour; iron per pound of fuel, 7J^ Ibs. ; percent weight of good castings to
iron charged, 75%. Jan. -May, 1891 : Increased rate of melting to llj^ tons per
hour; iron per Ib. fuel, 9^; per cent weight of good castings, 75; one week,
1314 tons per hour, 10.3 Ibs. iron per Ib. fuel; per cent weight of good cast-
ings, 75.3. The increase was made by putting in an additional row of tuyeres
and using stronger blast, 14 ounces. Coke was used as fuel. (W. O. Webber.
Trans. A. S. M. E. xii. 1045.)
950
THE FOUHDRY.
Buffalo Steel Pressure-Mowers. Speeds and Capacities
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^.s a
1<&
1
OJ 3J
•^ >»s
<K.^ p.
m
CO
A
PH
02
s
0
£
0}
s
0
4
4
20
8
4732
1545
666
9
5030
1647
717
5
6
25
8
4209
2321
773
10
4726
2600
867
6
8
30
8
3660
3093
951
10
4108
3671
1067
7
14
35
8
3244
4218
1486
30
3842
4777
1668
8
18
40
8
2948
5425
2199
10
3310
6082
2469
9
26
45
10
2785
7818
3203
12
3260
8598
3523
10
36
55
10
2195
11295
4938
12
2413
12378
5431
11
45
65
12
1952
16955
7707
14
2116
18357
8353
11J<<2
55
72
12
1647
22607
10276
14
1797
25176
11144
12
75
84
12
1625
25836
11744
14
1775
28019
12736
In the table are given two different speeds and pressures for each size of
blower, and the quantity of iron that may be melted, per hour, with each.
In all cases it is recommended to use the lowest pressure of blast that will do
the work. Run up to the speed given for that pressure, and regulate quan-
tity of air by the blast-gate. The tuyere area should be at least one ninth
of the area of cupola in square inches, with not less than four tuyeres at
equal distances around cupola, so as to equalize the blast throughout. Va-
riations in temperature affect the working of cupolas materially, hot
weather requiring increase in volume of air.
(For tables of the Sturtevant blower see pages 519 and 520.)
Loss in Melting Iron in Cupolas.— G. O. Vair, Am. Mach.,
March 5, 1891, gives a record of a 45-in. Colliau cupola as follows:
Ratio of fuel to iron, 1 to 7.42.
Good castings 21,314 Ibs.
New scrap 3,005 '*
Millings 200 "
Lossofmetal 1,481 "
Amount melted 26,000 Ibs.
Loss of metal, 5.69#. Ratio of loss, 1 to 17.55.
Use of Softeners in Foundry Practice, (W. Graham, Iron Age,
June 27, 1889.) — In the foundry the problem is to have the right proportions
of combined and graphitic carbon in the resulting casting; this is done by
getting the proper proportion of silicon. The variations in the proportions
of silicon afford a reliable and inexpensive means of producing a cast iron
of any required mechanical character which is possible with the material
employed. In this way, by mixing suitable irons in the right proportions,
a required grade of casting can be made more cheaply than by using irons
in which the necessary proportions are already found.
If a strong machine casting were required, it would be necessary to keep
the phosphorus, sulphur, and manganese within certain limits. Professor
Turner found that cast iron which possessed the maximum of the desired
qualities contained, graphite, 2.59$; silicon, 1.42$; phosphorus, 0.39#; sul-
phur, 0.06#; manganese, 0.58$.
A strong casting could not be made if there was much increase in the
amount of phosphorus, sulphur, or manganese. Irons of the above percent-
ages of phosphorus, sulphur, and manganese would be most suitable for this
purpose, but they could be of different grades, having different percentages
of silicon, combined and graphitic carbon. Thus hard irons, mottled and
white irons, and even steel scrap, all containing low percentages of silicon
and high percentages of combined carbon, could be employed if an iron
haying a large amount of silicon were mixed with them in sufficient amount.
This would bring the silicon to the proper proportion and would cause the
combined carbon to be forced into the graphitic State, and the resulting
SHRINKAGE OF CASTINGS.
951
casting would be soft. High-silicon irons used in this way are called " soft-
eners. "
The following are typical analyses of softeners:
Ferro-silicon.
Softeners, American.
Scotch
Irons, No. 1.
Foreign.
American.
Well-
ston.
Globe
Belle-
fonte.
Eg-
linton
Colt-
ness.
3.59
Silicon
10.55
1.84
0.52
3.86
0.04
0.03
9.80
0.69
1.12
1.95
0.21
0.04
12.08
0.06
1.52
0.76
0.48
Trace
10.34
0.0?
1.92
0.52
0.45
Trace
6.67
2i57
0^50
Trace
5.89
0.30
2.85
1.00
1.10
0.02
3 to 6
0.25
3.
0.53
0.35
0.03
2.15
0.21
3.76
2.80
0.62
0.03
Combined C..
Graphitic C .
Manganese . .
Phosphorus. .
Sulphur
1.70
0.85
0.01
(For other analyses, see pages 371 to 373.)
Ferro-silicons contain a low percentage of total carbon and a high per-
centage of combined carbon. Carbon is the most important constituent of
cast iron, and there should be about 3.4$ total carbon present. By adding
ferro-silicon which contains only 2% of carbon the amount of carbon in the
resulting mixture is lessened.
Mr. Keep found that more silicon is lost during the remelting of pig of
over 10$ silicon than in remelting pig iron of lower percentages of silicon.
He also points out the possible disadvantage of using ferro-silicons contain-
ing as high a percentage of combined carbon as 0.70$ to overcome the bad
effects of combined carbon in other irons.
The Scotch irons generally contain much more phosphorus than is desired
in irons to be employed in making the strongest castings. It is a mistake to
mix with strong low -phosphorus irons an iron that would increase the
amount of phosphorus for the sake of adding softening qualities, when soft-
ness can be produced by mixing irons of the same low phosphorus.
(For further discussion of the influence of silicon see page 365.)
Shrinkage of Castings. — The allowance necessary for shrinkage
varies for different kinds of metal, and the different conditions under which
they are cast. For castings where the thickness runs about one inch, cast
under ordinary conditions, the following allowance can be made:
For cast-iron, ^ inch per foot. For zinc, 5/16 inch per foot.
" brass, 3/16 " * tin, 1/12 " " "
" steel, % ' aluminum, 3/16 *'
" mal. iron, % ' Britannia, 1/32 "
Thicker castings, under the same cond tions, will shrink less, and thinner
ones more, than this standard. The qual ty of the material and the manner
of moulding and cooling will also make a difference.
Numerous experiments by W. J. Keep (see Trans. A. S. M. E., vol. xvi.)
showed that the shrinkage of cast iron of a given section decreases as the
percentage of silicon increases, while for a given percentage of silicon the
shrinkage decreases as the section is increased. Mr. Keep gives the follow-
ing table showing the approximate relation of shrinkage to size and per-
centage of silicon:
Sectional Area of Casting.
Percentage
of
Silicon.
K"o
V D
1" X 2"
2" D
3" D
4" D
Shrinkage in Decimals of an inch per foot of Length.
1.
1.5
2.
2.5
3.
3.5
.183
.171
.159
.147
.135
.123
.158
.145
.133
.121
.108
.095
.146
.133
.121
.108
.095
.082
.130
.117
.104
.092
.077
.065
.113
.098
.085
.073
.059
.046
.102
.087
.074
.060
.045
.032
952
THE FOUNDRY.
Mr. Keep also gives the following " approximate key for regulating foun-
dry mixtures" so as to produce a shrinkage of J4 in. per ft. in castings of
different sections:
Size of casting 14 1 2 3 4 in. sq.
Silicon required, per cent 3.25 2.75 2.25 1.75 1.25 percent.
Shrinkage of a i^-in. test-bar. .125 .135 .145 .155 .165 in. per ft.
Weight of Castings determined from Weight of Pattern.
(Rose's Pattern-maker's Assistant.)
Will weigh when cast in
A Pattern weignmg une f ouna,
made of —
Cast
Iron.
Zinc.
Copper.
Yellow
Brass.
Gun-
metal.
Mahogany — Nassau
Ibs.
10 7
Ibs.
in d
Ibs.
12 8
Ibs.
199
Ibs.
•JO K
12 9
12 7
15 3
14 6
15
'* Spanish
8 5
8 2
10 1
9 7
9 9
Pine red . .
1° 5
12 1
14 9
149
1 4 ft
44 white
16 7
16 1
19 8
19 0
19 5
14 1
13 6
16 7
16 0
16 5
Moulding Sand, (From a paper on "The Mechanical Treatment of
Moulding Sand," by Walter Bagshaw, Proc. Inst. M. E. 1891.)— The chemical
composition of sand will affect the nature of the casting, no matter what
treatment it undergoes. Stated generally, good sand is composed of 94 parts
silica, 5 parts alumina, and traces of magnesia and oxide of iron. Sand con-
taining much of the metallic oxides, and especially lime, is to be avoided.
Geographical position is the chief factor governing the selection of sand ;
and whether weak or strong, its deficiencies are made up for by the skill of
the moulder. For this reason the same sand is often used for both heavy and
light castings, the proportion of coal varying according to the nature of the
casting. A common mixture of facing-sand consists of six parts by weight
of old sand, four of new sand, and one of coal-dust. Floor-sand requires
only half the above proportions of new sand and coal-dust to renew it. Ger-
man founders adopt one part by measure of new sand to two of old sand;
to which is added coal-dust in the proportion of one tenth of the bulk for
large castings, and one twentieth for small castings. A few founders mix
street-sweepings with the coal in order to get porosity when the metal in
the mould is likely to be a long time before setting. Plumbago is effective in
preventing destruction of the sand; but owing to its refractory nature, it
must not be dusted on in such quantities as to close the pores and pi-event
free exit of the gases. Powdered French chalk, soapstone, and other sub-
stances are sometimes used for facing the mould; but next to plumbago, oak
charcoal takes the best place, notwithstanding its liability to float occasion-
ally and give a rough casting.
For the treatment of sand in the moulding-shop the most primitive method
is that of hand-riddling and treading. Here the materials are roughly pro-
portioned by volume, and riddled over an iron plate in a flat heap, where
the mixture is trodden into a cake by stamping with the feet; it is turned
over with the shovel, and the process repeated. Tough sand can be obtained
in this manner, its toughness being usually tested by squeezing a handful
into a ball and then breaking it; but the process is slow and tedious. Other
things being equal, the chief characteristics of a good moulding-sand are
toughness and porosity, qualities that depend on the manner of mixing as
well as on uniform ramming.
Toughness of Sand,— In order to test the relative toughness, sand
mixed in various ways was pressed under a uniform load into bars 1 in. sq.
and about 12 in. long, and each bar was made to project further and
further over the edge of a table until its end broke off by its own weight.
Old sand from the shop floor had very irregular cohesion, breaking at all
lengths of projections from }& in. to 1^ in. New sand in its natural state
held together until an overhang of 2% in. was reached. A mixture of old
sand, new sand, and coal-dust
Mixed under rollers broke at 2 to 2*4 in. of overhang.
" in the centrifugal machine " " 2 '* 2*4 " " "
" through a riddle ,„, " •' 1% " 2>| " " "
SPEED OF CUTTING-TOOLS IN LATHES, ETC. 953
Sho"ring as a mean of the tests only slight differences between the last
three methods, but in favor of machine-work. In many instances the frac-
tures were so uneven that minute measurements were not taken.
Dimensions of Foundry Ladles.— The following table gives the
dimensions, inside the lining, of ladles from 25 Ibs. to 16 tons capacity. All
the ladles are supposed to have straight sides. (Am. Mack., Aug. 4, 1892.)
Capacity.
Diam.
Depth.
Capacity.
Diam.
Depth.
16 tons
in.
54
in.
56
a* ton ..,
in,
20
in.
20
14 **
52
53
i2 «*
17
17
12 «*
49
50
?! **
13i£
13^£
XO '*
46
48
800 pounds
lli|
31^
8 «•
43
44
250 **
11
8 **
39
40
200 "
10 4
10^
4 *'
3 **
84
31
35
32
150 "
100 a
9
8
2 *'
27
28
75 *
7
7v
1U"
24V£
25
50 u
6v
82
22
85 "
fcf?
6
THE MACHINE-SHOP,
SPEED OF CUTTING-TOOLS IN L VTMES. RIILLING
MACHINES, ETC.
Relation of diameter of rotating tool or piece, number of revolutions,
and cutting-speed :
Let d — diam. of rotating piece in inches, n = No. of revs, per min.;
8 as speed of circumference in feet per minute;
3.823
d '
3.82S
n
Approximate rule : No. of revs, per min. = 4 X speed in ft. per mm. -+-
diam. in inches.
Speed of Cut for Lathes and Planers* (Prof. Coleman Sellers,
Stevens' Indicator, April, ]892.)— Brass may be turned at high speed like
wood.
Bronze.— A. speed of 18 feet per minute can be used with the soft alloys-
say 8 to 1, while for hard mixtures a slow speed is required— say 6 feet per
minute.
Wrought Iron can be turned at 40 feet per minute, but planing-machines
that are used for both cast and forged iron are operated at 18 feet per
minute.
Machinery Steel.— Ordinary, 14 feet per minute; car-axles, etc., 9 feet per
minute.
•Wheel Tires.— 6 feet per minute; the tool stands well, but many prefer
to run faster, say 8 to 10 feet, and grind the tool more frequently.
Lathes.— The speeds obtainable by means of the cone-pulley and the back
gearing are in geometrical progression from the slowest to the fastest. In
a well-proportioned machine the speeds hold the same relation through all
the steps. Many lathes have the same speed on the slowest of the cone and
the fastest of the back-gear speeds.
The Speed of Counter-shaft of the lathe is determined by an assumption
of a slow speed with the back gear, say 6 feet per minute, on the largest
diameter that the lathe will swing.
EXAMPLE.— A 30-inch lathe will swing 30 Inches =, say, 90 inches circumfer-
ence = 7' 6"; the lowest triple gear should give a speed of 5 or 6 per minute.
In turning or planing, if the cutting-speed exceed 30 ft. per minute, so
much heat will be produced that the temper will be drawn from the tool.
The speed of cutting is also governed by the thickness of the shaving, and
by the hardness and tenacity of the metal which is being cut; for instance,
in cutting mild steel, with a traverse of % in. per revolution or stroke, and
with a shaving about % in. thick, the speed of cutting must be reduced to
about 8 ft. per minute. A good average cutting-speed for wrought or cast
954
THE MACHINE-SHOP.
Iron Is 20 ft. per minute, whether for the lathe, planing, shaping, or slotting
machine. (Proc. Inst. M. E., April, 1883, p. 248.)
Table of Cutting-speeds.
Diameter,
inches.
Feet per minute.
5 | 10 | 15 | SO | 25 | 80
85 | 40 | 45 | 50
Revolutions per minute.
H
76.4
152.8
229.2
305.6
382.0
458.4
534.8 611.2
687.6
764.0
%
50.9
101.9
153.8
203.7
254.6
305.6
356.5 407.4
458.3
509.3
L&
88.2
76.4
114.6
152.8
191.0
229.2
267.4 305.6
343.8
382.0
%
30.6
61.1
91.7
122.2
152.8
183.4
213.9 244.5
275.0
305.6
S/
25.5
50.9
76.4
101.8
127.3
152.8
178.2
203.7
229.1
254.6
y»
21.8
43.7
65.5
87.3
109.1
130.9
152.8
174.6
196.4
218.3
1
19.1
38.2
57.3
70.4
95.5
114.6
133.7
152.8
171.9
191.0
1&
17.0
34.0
50.9
67.9
84.9
101.8
118.8
135.8
152.8
169.7
]g
15.3
30.6
45.8
61.1
76.4
91.7
106.9
122.2
137.5
152.8
13 9
27.8
41.7
55.6
69.5
83.3
97.2
111.1
125.0
138.9
JL£
12.7
25.5
38.2
50.9
63.6
76.4
89.1
101.8
114.5
127.2
m
10.9
21.8
82.7
43.7
54.6
65.5
76.4
87.3
98.2
109.2
2
9.6
19.1
28.7
38.2
47.8
57.3
66.9
76.4
86.0
95.5
2*4
8.5
17.0
25.5
31.0
42.5
50.9
59.4
67.9
76.4
84.9
2^2
7.6
15.3
22 9
30.6
38.2
45.8
53.5
61.1
68.8
76.4
2M
6.9
13.9
20.8
27.8
34.7
41.7
48.6
55.6
62.5
69.5
8
6.4
12.7
19.1
25.5
31.8
38.2
44.6
50.9
57.3
63.7
3^
5.5
10.9
16.4
21.8
27.3
32.7
38.2
43.7
49.1
54.6
4
4.8
9.6
14.3
19.1
23.9
28.7
83.4
38.2
43.0
47.8
4^
4.2
8.5
12.7
17.0
21.2
25.5
29.7
34.0
38.2
42.5
5
3.8
7.6
11.5
15.3
19.1
22.9
26.7
30.6
34.4
38.1
6^
3.5
6.9
10.4
13.9
17.4
20.8
24.3
27.8
31.2
34.7
6
3.2
6.4
9.5
12.7
15.9
19.1
22.3
25.5
28.6
31.8
7
2.7
5.5
8.2
10.9
13.6
16.4
19.1
21.8
24.6
27.3
8
2.4
4.8
7.2
9.6
11.9
14.3
16.7
19.1
21.5
23.9
9
2.1
4.2
6.4
8.5
10.6
12.7
14.8
17.0
19.1
21.2
10
.9
3.8
5.7
7.6
9.6
11.5
13.3
15.3
17.2
19.1
11
.7
8.5
5.2
6.9
8.7
10.4
12.2
13.9
15.6
17.4
12
.6
8.2
4.8
6.4
8.0
9.5
11.1
12.7
14.3
15.9
13
.5
2.9
4.4
5.9
7.3
8.8
10.3
11.8
13.2
14.7
14
.4
2.7
4.1
5.5
6.8
8.2
9.5
10.9
12.3
13.6
15
.3
2.5
8.8
5.1
6.4
7.6
8.9
10.2
11.5
12.7
16
.2
2.4
8.6
4.8
6.0
7.2
8.4
9.5
10.7
11.9
18
.1
2.1
8.2
4.2
6.8
6.4
7.4
8.5
9.5
10.6
20
.0
1.9
8.9
3.8
4.8
5.7
6.7
7.6
8.6
9.6
22
.9
1.7
2.6
8.5
4.3
5.2
6.1
6.9
7.8
8.7
24
.8
1.6
2.4
8.2
4.0
4.8
6.6
6.4
7.2
8.0
£6
.7
1.6
2.2
2.9
8.7
4.4
6.1
5.9
6.6
7.3
28
.7
1.4
2.0
2.7
8.4
4.1
4.8
5.5
6.1
6.8
80
.6
1.3
1.9
2.5
8.2
8.8
4.5
5.1
57
6.4
86
.5
1.1
1.6
2.1
2.7
8.2
8.7
4.2
4.8
5.3
42
.5
.9
1.4
1.8
2.3
2.7
8.2
8.6
4.1
4.5
48
.4
.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
54
.4
.7
1.1
1.4
1.8
2.1
2.5
2.8
3.2
3.5
60
.3
.6
1.0
1.3
1.6
1.9
2.2
2.5
2.9
3.2
Speed of Cutting with Turret loathes.— Jones & Lamson Ma-
chine Co. give the following cutting-speeds for use with their flat turret
lathe on diameters not exceeding two inches:
Ft. per minute.
( Tool steel and taper on tubing 10
Threading 1 *c- -*-1
[ Machinery .
f Very soft steel
fCut which reduces the stock to }
! Cut which reduces the stock to *, . .. _ 0. .
j Cut which reduces the stock to % of its original diam. . 30 to 35
( Cut which reduces the stock to 15/16 of its original diam. 40 to 45
Turning very soft machinery steelt light cut and cool work..;. ..... 50 to 60
Turning
steel
j of its original diam . .
{ of its original diam. .
15
20
20
25
GEA1UKG Otf LATHES. 955
Forms of Metal-cutting Tools* — " Hutte," the German Engi-
neers1 Pocket-book, gives the following cutting-angles for using least power:
Top Rake. Angle of Cutting-edge.
Wroughtiron 8° 51«
Castiron.... 4* 61°
BronEe..... 4° 66*
The American Machinist comments on these figures as follows : We are
not able to give the best nor even the generally used angles for tools,
because these vary so much to suit different circumstances, such as degree
of hardness of the metal being cut, quality of steel of which the tool is
made, depth of cut, kind of finish desired, etc. The angles that cut with
the least expenditure of power are easily determined by a few experiments,
but the best angles must be determined by good judgment, guided by expe-
rience. In nearly all cases, however, we think the best practical angles are
greater than those given.
For illustrations and descriptions of various forms of cutting-tools, see
articles on Lathe Tools in App. Cyc. App. Mech.t vol. ii., and in Modern
Mechanism.
Cold Chisels,— Angle of cutting-faces (Joshua Rose): For cast steel,
about 65 degrees; for gun-metal or brass* about 50 degrees; for copper and
soft metals, about 80 to 35 degrees.
Rule for Gearing Lathes for Screw-cutting:. (Garyin Ma-
chine Go.) — Read from the lathe index the number of threads per inch cut
by equal gears, and multiply it by any number that will give for a product
a gear on the index; put this gear upon the stud, then multiply the number
of threads per inch to be cut by the same number, and put the resulting gear
upon the screw.
EXAMPLE.— To cut llj^ threads per inch. We find on the index that 48 into
48 cuts 6 threads per inch, then 6 X 4 = 24, gear on stud, and 11 w X 4 = 46,
gear on screw. Any multiplier may be used so long as the products include
gears that belong with the lathe. For instance, instead of 4 as a multiplier
we may use 6. Thus, 6 X 6 = 36, gear upon stud, and 11J4 X 6 = 69, gear
upon screw.
Rules for Calculating Simple and Compound Gearing
where there is no Index. (Am Mach.) — If the Jathe is simple-
geared, and the stud runs at the same speed as the spindle, select some gear
for the screw, and multiply its number of teeth by the number of threads
per inch in the lead-screw, and divide this result by the number of threads
per inch to be cut. This will give the number of teeth in the gear for the
stud. If this result is a fractional number, or a number which is not among
the gears on hand, then try some other gear for the screw. Or, select the
gear for the stud first, then multiply its number of teeth by the number of
threads per inch to be cut, and divide by the number of threads per inch on
the lead-screw. This will give the number of teeth for the gear on the
screw. If the lathe is compound, select at random all the driving-gears,
multiply the numbers of their teeth together, and this product by the num-
ber of threads to be cut. Then select at random all the driven gears except
one; multiply the numbers of their teeth together, and this product by the
number of threads per inch in the lead-screw. Now divide the first result by
the second, to obtain the number of teeth in the remaining driven gear. Or,
select at random all the driven gears. Multiply the numbers of their teeth
together, and this product by the number of threads per inch in the lead-
screw. Then select at random all the driving-gears except one. Multiply
the numbers of their teeth together, and this result by the number of threads
per inch of the screw to be cut. Divide the first result by the last, to obtain
the number of teeth in the remaining driver. When the gears on the com-
pounding stud are fast together, arid cannot be changed, then the driven one
has usually twice as many teeth as the other, or driver, in which case in the
calculations consider the 'lead-screw to have twice as many threads per inch
as it actually nas, and then ignore the compounding entirely. Some lathes
are so constructed that the stud on which the first driver is placed revolves
only half as fast as the spindle. This can be ignored in the calculations by
doubling the number of threads of the lead-screw. If both the last condi-
tions are present ignore them in the calculations by multiplying the numbei
of threads per inch in the lead-screw by four. If the thread to be cut is a
fractional one, or if the pitch of the lead-screw is fractional, or if both are
fractional, then reduce the fractions to a common denominator, and use
the numerators of these fractions as if thev eaualled the pitch of the screw
956
THE MACHIKE-SHOP.
to be cut, and of the lead-screw, respectively. Then use that part of the ruld
given above which applies to the lathe in question. For instance, suppose
it is desired to cut a thread of 25/32-inch pitch, and the lead-screw has 4
threads per inch. Then the pitch of the lead-screw will be J4 inch, which is
equal to 8/32 inch. We now have two fraction, 25/32 and 8/32, and the two
screws will be in the proportion of 25 to 8, and the gears can be figured by
the above rule, assuming the number of threads to be cut to be 8 per inch,
and those on the lead-screw to be 25 per inch. But this latter number may
be further modified by conditions named above, such as a reduced speed of
the stud, or fixed compound gears. In the instance given, if the lead-screw
had been 2*4 threads per inch, then its pitch being 4/10 inch, we have the
fractions 4/10 and 25/32, which, reduced to a common denominator, are
64/160 and 125/1 60, and the gears will be the same as if the lead-screw had 125
threads per inch, and the screw to be cut 64 threads per inch.
On this subject consult also *' Formulas in Gearing," published by Brown
& Sharpe Mfg. Co., and Jamieson's Applied Mechanics.
Change-gears for Screw-cutting I, at lies. — There is a lack of
uniformity among lathe-builders as to the change-gears provided for screw-
cutting. W. R. Macdonald, in Am. Mack., April 7, 1892, proposes the follow-
ing series, by which 33 whole threads (not fractional) may be cut by changes
of only nine gears:
1
Spindle.
Whole Threads.
20
80
40
50
60
70
110
ieo
130
20
30
40
50
60
70
110
120
130
'is"
24
30
36
42
66
72
78
8
'16
20
24
28
4*
48
52
6
9
12
15
18
21
33
36
39
4 4/5
7 1/5
9 3/5
14*2/5
16 4/5
26 2/5
28 4/5
31 1/5
4
6
8
10
14
22
24
26
3 3/7
5 1/7
6 6/7
8 4/7
10 2/7
18* 6/7
20 4/7
22 3/7
2 2/11
3 3/11
4 4/11
5 5/11
6 6/11
77/11
2
3
4
5
6
7
11
"is"
1 11/13
2 10/13
3 9/13
4 8/13
5 7/13
6 6/13
10 2/13
11 1/13
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
28
30
33
36
39
42
44
48
52
66
72
78
13 1/11
14 2/11
Ten gears are sufficient to cut all the usual threads, with the exception of
perhaps ll^t, the standard pipe-thread; in ordinary practice any fractional
thread between 11 and 12 will be near enough for the customary short pipe-
thread; if not, the addition of a single gear will give it.
In this table the pitch of the lead-screw is 12, and it may be objected to as
too fine for the purpose. This may be rectified by making the real pitch 6
or any other desirable pitch, and establishing the proper ratio between the
lathe spindle and the gear-stud.
Metric Screw-threads may be cut on lathes with inch-divided lead-
ing-screws by the use of change wheels with 50 and 127 teeth; lor 127
centimetres = 50 inches (127 X 0.3937 = 49.9999 in.).
Rule for Setting the Taper in a Lathe. (Am. Jfacft.)— No
rule ca.i be given which will produce exact results, owing to the fact that
the centres enter the work an indefinite distance. If it were not for this cir-
cumstance the following would be an exact rule, and it is an approximation
as it is. To find the distance to set the centre over: Divide the difference in
the diameters of the large and small end of the taper by 2, and multiply this
quotient by the ratio which the total length of the shaft bears to the length
of the tapered portion. Example: Suppose a shaft three feet long is to har I
a taper turned on the end one foot long, the large end of the taper being two
inches and the small end one inch diameter. ~ • X - = 1% inches.
Electric Drilling-machines -Speed of Drilling Holes in
Steel Plates. (Proc. Inst. M. E., Aug. 1887, p. 329.)-In drilling holes in
the shell of the S.S. "Albania," after a very small amount of practice the
men working the machines drilled the %-inch holes in the shell with great
rapidity, doing the work at the rate of one hole every 69 seconds, inclusive of
the time occupied in altering the position of the machines by means of differ-
ential pulley-blocks, which were not conveniently arranged as slings foi
this purpose. Repeated trials of these drilling-machines have also shown
that, when using electrical energy in both holding-on magnets and motor
MILLING-CUTTERS,
95?
amounting to about % H.P., they have drilled holes of 1 inch diameter
through \\% inch thickness of solid wrought iron, or through \% inch of mild
steel in two plates of 13/16 inch each, taking exactly 1% min. for each hole.
Speed of Drills. (Morse Twist-drill and Machine Company.)— The fol-
lowing table gives the revolutions per minute for drills from 1/J6 in. to 2 in.
diameter, as usually applied:
Diameter
of
Drills, in.
Speed for
Wrought
Iron and
Steel.
Speed
for
Cast
Iron.
Speed
for
Brass.
Diameter
of
Drills, in.
Speed for
Wrought
Iron and
Steel.
Speed
for
Cast
Iron.
Speed
for
Brass.
1/16
1712
2383
3544
1 1/16
72
108
180
H
855
1191
1772
l^f
68
102
170
f
571
397
794
565
1181
855
1 3/16
1*4
64
58
97
89
161
150
5/16
318
452
684
1 5/16
55
84
143
3/
265
377
570
]5^>
53
81
136
7/16
227
323
489
1 7/16
50
77
130
L£
183
267
412
l/^
46
74
122
9/16
163
238
367
1 S>/16
44
71
117
%
147
214
330
i!N*
40
66
113
11/16
133
194
300
1 11/16
38
63
109
M
112
168
265
1M
37
61
105
13/16
103
155
244
1 13/16
36
59
101
15/16
96
89
144
134
227
212
1 15/16
33
32
55
53
98
95
1
76
115
191
2
31
51
92
One inch to be drilled in soft cast iron will usually require: for *4-in.
drill, 160 revolutions; for J^-in. drill, 140 revolutions; for %-in. drill, 100
revolutions; for 1 -in. drill, 95 revolutions. These speeds should seldom be
exceeded. Feed per revolution for M-in. drill. .005 inch; for U-in. drill.
.007 inch; for %-in. drill .010 inch.
The rates of feed for twist drills are thus given by the same company:
Diameter of drill 1/16 % % ^ % * 1 1^
'Revs, per inch depth of hole. 125 125 120 to 140 1 inch feed per min!
MILLING-CUTTERS.
George Addy, (Proc. Inst. M. E., Oct. 1890, p. 537), gives the following:
Analyses of Steel.— The following are analyses of milling-cutter
blanks, made from best quality crucible cast steel and from self -hardening
41 Ivanhoe " steel :
Carbon
Silicon
Phosphorus
Manganese t
Sulphur 0.02
Tungsten
Iron, by difference 98.29
Crucible Cast Steel,
per cent.
1.2
0.112
0.018
0.36
Ivanhoe Steel,
per cent.
1.67
0.252
0.051
2.557
0.01
4.65
90.81
100.000 100.000
The first analysis is of a cutter 14 in. diam., 1 in. wide, which gave very
good service at a cutting-speed of 60 ft. per min. Large milling-cutters are
sometimes built up, the cutting-edges only being of tool steel. A cutter 22 in.
diam. by 5J4 in. wide has been made in this way, the teeth being clamped
between two cast-iron flanges. Mr. Addy recommends for this form of
tooth one with a cutting-angle of 70°, the face of the tooth being set 10° back
of a radial line on the cutter, the clearance -angle being thus 10°. At the
Clarence Iron-works, Leeds, the face of the tooth is set 10° back of the radial
line for cutting: wrought iron and 20° for steel.
Pitcli of Teeth.— For obtaining a suitable pitch of teeth for milling-
, cutters of various diameters there exists no standard rule, the pitch being
usually decided in an arbitrary manner, according to individual taste.
958 THE MACHINE-SHOP.
For estimating the pitch of teeth in a cutter of any diameter from 4 in. to 15
in., Mr. Addy has worked out the following rule, which he has found capa-
ble of giving good results in practice:
Pitch in inches = V(diam. in inches X 8) X 0.0625 = .177 i/diam.
J. M. Gray gives a rule for pitch as follows: The number of teeth in a
milling-cutter ought to be 100 times the pitch in inches; that is, if there
were 27 teeth, the pitch ought to be 0.27 in. The rules are practically the
same, for if d = diam., n = No. of teeth, p = pitch, c = circumference, c —
pn\ d = ^ = ^— = 31.83p2; p = |/.0314d = .177 Vd\ No. of teeth, n, =
7T 7T
3.14d-^-p.
Number of Teeth in Mills or Cutters. (Joshua Rose.)— The teeth
of cutters must obviously be spaced wide enough apart to admit of the emery-
wheel grinding one tooth without touching the next one, and the f ront faces
of the teeth are always made in the plane of a line radiating from the axis of
the cutter. In cutters up to 3 in. in diam. it is good practice to provide 8
teeth per in. of diam., while in cutters above that diameter the spacing
may be coarser, as follows:
Diameter of cutter, 6 in.; number of teeth in cutter, 40
" 7 " " " " " " 45
" 8 " " " " " " 50
Speed of Cutters.— The cutting speed for milling was originally fixed
very low; but experience has shown that with the improvements now in
use it may with advantage be considerably increased, especially with cutters
of large diameter. The following are recommended as safe speeds for cut-
ters of 6 in. and upwards, provided there is not any great depth of material
to cut away:
Steel. Wrought iron. Cast iron. Brass.
Feet per minute 36 48 60 120
Feed, inch per min... *4 1 1% 2%
Should it be desired to remove any large quantity of material, the same
cutting-speeds are still recommended, but with a finer feed. A simple rule
for cutting-speed is: Number of revolutions per minute which the cutter
spindle should make when working on cast iron = 240, divided by the diam-
eter of the cutter in inches.
Speed of Milling-cutters. (Proc. Inst. M. E., April, 1883, p. 248.)—
The cutting-speed which can be employed in milling is much greater than
that which can be used in any of the ordinary operations of turning in the
lathe, or of planing, shaping, or slotting. A milling-cutter with a plentiful
supply of oil, or soap and water, can be run at from 80 to 100 ft. per min.,
when cutting wrought iron. The same metal can only be turned in a lathe,
with a tool-holder having a good cutter, at the rate of 30 ft. per min., or at
about one third the speed of milling. A milling-cutter will cut cast steel at
the rate of 25 to 30 ft. per min.
The following extracts are taken from an article on speed and feed of
milling-cutters in Eng'g, Oct. 22, 1891: Milling-cutters are successfully em-
ployed on cast iron at a speed of 250 ft. per min. ; on wrought iron at from
80 ft. to 100 ft. per min. The latter materials need a copious supply of good
lubricant, such as oil or soapy water. These rates of speed are not ap-
proached by other tools. The usual cutting-speeds on the lathe, planing,
shaping, and slotting machines rarely exceed about one third of those given
above, and frequently average about a fifth, the time lost in back strokes not
being reckoned.
The feed in the direction of cutting is said by one writer to vary, in ordi-
nary work, from 40 to 70 revs, of a 4-in. cutter per in. of feed. It must always
to an extent depend on the character of the work done, but the above gives
shavings of extreme thinness. For example, the circumference of a 4-in.
cutter being, say, 12^ in., and having, say, 60 teeth, the advance corre-
sponding to the passage of one cutting-tooth over the surface, in the coarser
of the above-named feed-motions, is 1/40 X 1/60 = 1/2400 in.; the finer feed
gives an advance for each tooth of only 1/70 X 1/60 = 1/4200 in. Such fine
feeds as these are used only for light finishing cuts, and the same author-
ity recommends, also for finishing, a cutter about 9 in. in circumference, or
nearly 3 in. in diameter, which should be run at about 60 revs, per min. to
cut tough wrought steel, 120 for ordinary cast iron, about 80 for wrought
MILLING-MACHINES. 959
Iron, and from 140 to 160 for the various qualtities of gun-metal and brass.
With cutters smaller or larger the rates of revolution are increased or
diminished to accord with the following table, which gives these rates of
cutting-speeds and shows the lineal speed of the cutting-edge:
Steel. Wrought Iron. Cast Iron. Gun-metal. Brass.
Feet per minute... 45 60 90 105 120
These speeds are intended for very light finishing cuts, and they must be
reduced to about one half for heavy cutting.
The following results have been found to be the highest that could be at-
tained in ordinary workshop routine, having due consideration to economy
and the time taken to change and grind the cutters when they become dull:
Wrought iron— 36 ft. to 40 ft. per min.; depth of cut, 1 in.; feed, % in. per
min. Soft mild steel— About 30 ft. per min.; depth of cut, J4 *"•; feed, %
in. per min. Tough gun-metal— 80 ft. per min. ; depth of cut, ^ in. ; feed, %
in. per min. Cast-iron gear-wheels— 26J4 ft. per min.; depth of cut, $& in.;
feed, % in. per min. Hard, close-grained cast iron— 30 ft. per min.; depth
of cut, 2^6 in.; feed, 5/16 in. per min. Gun-metal joints, 53 ft. per min.;
depth of cut, 1% in. ; feed, % in. per min. Steel-bars — 21 ft. per min. ; depth
of cut, 1/32 in.; feed, % in. per min.
A stepped milling-cutter, 4 in. in diam. and 12 in. wide, tested under two
conditions of speed in the same machine, gave the following results: The
cutter in both instances was worked up to its maximum speed before it gave
way, the object being to ascertain definitely the relative amount of work
done by a high speed and a light feed, as compared with a low speed and a
heavy cut. The machine was used single-geared and double-geared, and in
both cases the width of cut was 10^ in.
Single-gear, 42 ft. per min.; 5/16 in. depth of cut; feed, 1.3 in. per min. =
4.16 cu. in. per min. Double-gear, 19 ft. per min.; %in. depth of cut; feed,
% in. per min. = 2.40 cu. in. per min.
Extreme Results with Milling-machines. — Horace L.
Arnold (Am. Mack., Dec. 28, 1893) gives the following results in flat-surface
milling, obtained in a Pratt & Whitney milling-machine : The mills for the
flat cut were 5" diam., 12 teeth, 40 to 50 revs, and 4%j" feed per min. One
single cut was run over this piece at a feed of 9" per min., but the mills
showed plainly at the end that this rate was greater than they could endure.
At 50 revs, for these mills the figures are as follows, with 4%" feed: Surface
speed, 64 ft., nearly; feed per tooth, 0.00812": cuts per inch, 123. And with
9" feed per min.: Surface speed, 64 ft. per min.; feed per tooth, 0.015"; cuts
per inch, 66%.
At a feed of 4%" per min. the mills stood up well in this job of cast-iron
surfacing, while with a 9" feed they required grinding after surfacing one
piece; in other words, it did not damage the mill-teeth to do this job with
123 cuts per in. of surface finished, but they would not endure 66% cuts per
inch. In this cast-iron milling the surface speed of the mills does not seem
to be the factor of mill destruction: it is the increase of feed per tooth that
prohibits increased production of finished surface. This is precisely the re-
verse of the action of single-pointed lathe and planer tools in general: with
such tools there is a surface-speed limit which cannot be economically ex-
ceeded for dry cuts, and so long as this surface-speed limit is not reached,
the cut per tooth or feed can be made anything up to the limit of the driv-
ing power of the lathe or planer, or to the safe strain on the work itself,
which can in many cases be easily broken by a too great feed.
In wrought metal extreme figures were obtained in one experiment made
in cutting key ways 5/16" wide by *&" deep in a bank of 8 shafts 1J4" diam.
at once, on a Pratt & Whitney No. 3 column milling-machine. The 8 mills
were successfully operated with 45 ft. surface speed and 19^ in. per min.
feed; the cutters were 5" diam., with 28 teeth, giving the following figures,
in steel: Surface speed, 45 ft. per min.; feed per tooth, 0.02024"; cuts per
inch, 50, nearly. Fed with the revolution of mill. Flooded with oil, that is,
a large stream of oil running constantly over each mill. Face of tooth
radial. The resulting key way was described as having a heavy wave or
cutter-mark in the bottom, and it was said to have shown no signs of being
heavy work on the cutters or on the machine. As a result of the experiment
it was decided for economical steady work to run at 17 revs., with a feed of
4" per min., flooded cut, work fed with mill revolution, giving the following
figures: Surface speed, 22& ft. per min.; feed per tooth, 0,0084"; cuts per
inch, 119.
960 THE MACHINE-SHOP.
An experiment in milling a wrought-iron connecting-rod of a locomotive
on a Pratt & Whitney double-head milling-machine is described in the Iron
Age, Aug. 27, 1891. the amount of metal removed at one cut measured 3^
in. wide by 1 3/16 in. deep in the groove, and across the top y& in. deep by 4%
in. wide. This represented a section of nearly 4]^ sq. in. This was done at
the rate of 1% in. per min. Nearly 8 cu. in. of metal were cut up into chips
every minute. The surface left by the cutter was very perfect. The cutter
moved in a direction contrary to that of ordinary practice; that is, it cut
down from the upper surface instead of up from the bottom.
milling "with" or "against" the Feed.— Tests made with
the Brown & Sharpe No. 5 milling-machine (described by H. L. Arnold, in
Am. Mach., Oct. 18, 1894) to determine the relative advantage of running
the milling-cutter with or against the feed—" with the feed " meaning that
the teeth of the cutter strike on the top surface or "scale" of cast-iron
work in process of being milled, and "against The feed " meaning that the
teeth begin to cut in the clean, newly cut surface of the work and cut up-
wards toward the scale — showed a decided advantage in favor of running
the cutter against the feed. The result is directly opposite to that obtained
in tests of a Pratt & Whitney machine, by experts of the P. & W. Co.
In the tests with the Brown & Sharpe machine the cutters used were 6
inches face by 4^ and 3 inches diameter respectively, 15 teeth in each mill,
42 revolutions per minute in each case, or nearly 50 feet per minute surface
speed for the 4^-inch and 33 feet per minute for the 3-inch mill. The revo-
lution marks were 6 to the inch, giving a feed of 7 inches per minute, and a
cut per tooth of .011". When the machine was forced to the limit of its
driving the depth of cut was 11/32 inch when the cutter ran in the " old "
way, or against the feed, and only % inch when it ran in the " new " way,
or with the feed. The endurance of the milling-cutters was much greater
when they were run in the " old " way.
Spiral Milling-cutters.— There is no rule for finding the angle of
the spiral; from 10° to 15° is usually considered sufficient; if much greater
the end thrust on the spindle will be increased to an extent not desirable for
some machines.
Milling-cu tters with Inserted Teeth.— When it is required to
use milling-cutters of a greater diameter than about 8 in., it is preferable to
insert the teeth in a disk or head, so as to avoid the expense of making
solid cutters and the difficulty of hardening them, not merely because of
the risk of breakage in hardening them, but also on account of the difficulty
in obtaining a uniform degree of hardness or temper.
Milling • machine versus Planer. — For comparative data of
work done by each see paper by J. J. Grant, Trans. A. S. M. E., ix. 259. He
says : The advantages of the milling machine over the planer are many,
among which are the following : Exact duplication of work; rapidity of pro-
duction— the cutting being continuous; cost of production, as several
machines can be operated by one workman, and he not a skilled mechanic;
and cost of tools for producing a given amount of work.
POWER REQUIRED FOR MACHINE TOOLS.
Resistance Overcome in Cutting Metal. (Trans. A. S. M. E.,
viii. 308.) — Some experiments made at the works of William Sellers & Co.
showed that the resistance in cutting steel in a lathe would vary from
180,000 to 700,000 pounds per square inch of section removed, while for
cast iron the resistance is about one third as much. The power required to
remove a given amount of metal depends on the shape of the cut and on
the shape and the sharpness of the tool used. If the cut is nearly square in
section, the power required is a minimum; if wide and thin, a maximum.
The dulness of a tool affects but little the power required for a heavy cut.
Heavy Work on a Planer.— Wm. Sellers & Co. write as follows
to the American Machinist : The 120" planer table is geared to run 18 ft. per
minute under cut, and 72 feet per minute on the return, which is equivalent,
without allowance for time lost in reversing, to continuous cut of 14.4 feet
per minute. Assuming the work to be 28 feet long, we may take 14 feet as
the continuous cutting speed per minute, the .8 of a foot being much more
than sufficient to cover time loss in reversing and feeding. The machine
carries four tools. At y^' feed per tool, the surface planed per hour would
be 35 square feet. The section of metal cut at «%" depth would be .75" X
,125" X 4 = .375 square inch, which would require approximately 30,000 jfeg.
POWER REQUIRED FOR MACHINE TOOLS. 961
pressure to remove it. The weight of metal removed per hour would be
14 X 12 x .375 X .26 x 60 = 1082.8 Ibs. Our earlier form of 36" planer has
removed with one tool on %" cut on work 200 Ibs. of metal per hour, and
the 120" machine has more than five times its capacity. The total pulling
power of the planer is 45,000 Ibs.
Horse-power Required to Run Lathes. (J. J. Flather, Am.
Mach., April 23, 1891.)— The power required to do useful work varies with
the depth and breadth of chip, with the shape of tool, and with the nature
and density of metal operated upon; and the power required to run a ma-
chine empty is often a variable quantity.
For instance, when the machine is new, and the working parts have not
become worn or fitted to each other as they will be after running a few
months, the power required will be greater than will be the case after the
running parts have become better fitted.
Another cause of variatiofi of the power absorbed is the driving-belt; a
tight belt will increase the friction, hence to obtain the greatest efficiency
of a machine we should use wide belts, and run them just tight enough to
prevent slip. The belts should also be soft and pliable, otherwise power is
consumed in bending them to the curvature of the pulleys.
A third cause is the variation of journal-friction, due to slacking up or
tightening the cap-screws, and also the end-thrust bearing screw.
Hartig's investigations show that it requires less total power to turn off a
given weight of metal in a given time than it does to plane off the same
amount; and also that the power is less for large than for small diameters.
The following table gives the actual horse-power required to drive a lathe
empty at varying numbers of revolutions of main spindle.
HORSE-POWER FOR SMALL LATHES.
Without Back Gears.
With Back Gears.
Remarks.
Revs, of
Spindle
per min.
H.P.
required
to drive
empty.
Revs, ot
Spindle
per min.
H.P.
required
to drive
empty.
132.72
219.08
365.00
.145
.197
.310
14.6
24.33
38.42
.126
.141
.274
20" Fitchburg lathe.
47.4
125.0
188
.159
.259
.339
4.84
12.8
19 2
.132
.187
.230
Smallla the (13^"), Chenr
nitz. Germany. New
machine.
54. G
122
183
.206
.339
.455
6.61
14.8
22.1
.157
.206
.249
V%" lathe do. New
machine.
18.8
54.6
82.2
.086
.210
.326
2.31
6.72
10.8
.035
.063
.087
26" lathe do.
If H.P.o = horse-power necessary to drive lathe empty, and N= number
of revolutions per minute, then the equation for average small lathes is
H.P.o = 0.095 -f 0.0012AT.
For the power necessary to drive the lathes empty when the back gears
are in, an average equation for lathes under 20" swing is
H.P.o = 0.10 + O.OOQN.
The larger lathes vary so much in construction and detail that no general
rule can be obtained which will give, even approximately, the power re-
quired to run them, and although the average formula shows that at least
0.095 horse-power is needed to start the small lathes, there are many Amer-
ican lathes under 20" swing working on a consumption of less than ,0*
horse-power.
962
THE MACHINE-SHOP.
The amount of power required to remove metal in a machine is determine
able within more accurate limits.
Referring to Dr. Hartig's researches, H.P.j = CW, where C is a constant,
and W the weight of chips removed per hour.
Average values of C are .030 for cast-iron, .032 for wrought-iron, .047 for
steel.
The size of lathe, and, therefore, the diameter of work, has no apparent
effect on the cutting power. If the lathe be heavy, the cut can be increased,
and consequently the weight of chips increased, but the value of C appears
to be about the same for a given metal through several varying sizes of
lathes.
HORSE-POWER REQUIRED TO REMOVE CAST IRON IN A 20-iNCH LATHE.
(J. J. Hobart.)
VD
• '~>
.2
•S 03
i 0)
v >
*£
4*
6
1
.2 a
^
H
*-> o
• S
&1
1
f^
&
"§ U
^
gfl
PH D
Ra
a
Q«M
^'d
Wo
p<2 .
g
>
°
Tool used.
o-2 o5
O ai
o jj
5 §
w
.2*
1
t~;3
0 S
§£3
tfiD'og
fcC'cgrfl
*0
1
,0
fl
£» o
12
0> P.M
2* §3
§
<P
a
> OS S
4)-S
> o
> crS
>. S &
'c3 ^
O
55
<«1
O
<3
^
<J
>
1
22
Side tool
37.90
.125
.015
.342
13.30
.025
2
15
Diamond
30.50
.125
.015
.218
10.70
.020
3
17
42.61
.125
.015
.352
14.95
.023
4
2
Left - hand round
nose
26.29
.125
.015
.237
9.22
.026
5
4
Square -faced tool
25.82
.015
.125
.255
9.06
028
6
1
25.27
.048
.048
.200
10.89
.018
7
1
"
25.64
.125
.015
.246
8.99
.027
The above table shows that an average of .26 horse-power is required to
turn off 10 pounds of cast-iron per hour, from which we obtain the average
value of the constant C — .024.
Most of the cuts were taken so that the metal would be reduced y±" in
diameter; with a broad surface cut and a coarse feed, as in No. 5, the power
required per pound of chips removed in a given time was a maximum; the
least power per unit of weight removed being required when the chip was
square, as in No. 6.
HORSE-POWER REQUIRED TO REMOVE METAL IN A 29-INCH LATHE.
(R. H. Smith.)
M
.2
'O
^
Number of E
periments.
Metal.
1 Cutting- speed
ft. per min
Depth of Cut,
Average Brea
of Cut, in.
Avereage H.l
required to ]
move Metal.
Average poun
Metal remov
per hour.
Value of C
4
Cast iron
12.7
.05
.046
.105
5.49
.019
4
Cast iron
11.1
.135
.046
.217
12.96
.017
2
Cast iron
12.85
.04
.038
.098
3.66
.027
4
Wrought iron
9.6
.03
.046
.059
2.49
.023
4
Wrought iron
9.1
.06
.046
.138
4.72
.029
4
2
Wrought iron
Wrought iron
7.9
9.35
.14
.045
.046
.038
.186
.092
9.56
2.99
.019
.031
4
Steel
6.00
.02
.046
.043
1.03
.042
4
Steel
5.8
.04
.046
.085
2.00
.042
4
Steel
5.1
.06
.046
.108
2.64
.040
POWER REQUIRED FOR MACHIHE TOOLS. 963
The small values of C, .017 and .019, obtained for cast iron are probably
due to two reasons : the iron was soft and of fine quality, known as pulley
metal, requiring less power to cut; and, as Prof. Smith remarks, a lower
cutting-speed also takes less horse-power.
Hardness of metals and forms of tools vary, otherwise the amount of
chips turned out per hour per horse-power would be practically constant, the
higher cutting-speeds decreasing but slightly the visible work done.
Taking into account these variations, the weight of metal removed per
hour, multiplied by a certain constant, is equal to the power necessary to do
the work.
This constant, according to the above tests, is as follows :
Cast Iron. Wrought Iron. Steel.
Hartig 030 .032 .047
Smith 023 .028 .042
Hobart 024
Average 026 .030 .044
The power necessary to run the lathe empty will vary from about .05 to .2»
H.P., which should be ascertained and added to the useful horse-power, to
obtain the total power expended.
Power used by Machine-tools. (R. E. Dinsmore, from the Elec-
trical World.)
1. Shop shafting 2 3/16" X 180 ft. at 160 revs., carrying ?" pulleys
from 6" diam. to 36", arid running 20 Idle machine belt 1.32 H.P.
2. Lodge-Davis upright back- geared drill-press with t& le, 28"
swing, drilling %" hole in cast iron, with a feed of 1 u. per
minute 0.78 H.P.
3. Morse twist-drill grinder No. 2, carrying 2" X 6" wheels t 3200
revs 0. 29 H.P.
4. Pease planer 30" X 36", table 6 ft., planing cast iron, c\
deep, planing 6 sq. in. per minute, at 9 reversals ...
5. Shaping-machine 22" stroke, cutting steel die, 6" stroke
1.06 H.P.
deep, shaping at rate of 1.7 square inch per minute 0.37 H.P.
6. Engine-lathe 17" swing, turning steel shaft 2%" diam., cut u/16
deep, feeding 7. 92 inch per minute, 0.43 H.P.
7. Engine-lathe 21" swing, boring cast-iron hole 5" diam., cut 3/16
diam., feeding 0.3" per minute 0.23 H.P.
8. Sturtevant No. 2, monogram blower at 1800 revs, per minute,
no piping 0.8 H.P.
9. Heavy planer 28" X 28" X 14 ft. bed, stroke 8", cutting steel,
22 reversals per minute 3.2 H.P.
The table on the next page compiled from various sources, principally
from Hartig's researches, by Prof. J. J. Flather (Am. Mach., April 12, 1894),
may be used as a guide in estimating the power required to run a given
machine; but it must be understood that these values, although determined
by dynamometric measurements for the individual machines designated,
are not necessarily representative, as the power required to drive a machine
itself is dependent largely on its particular design and construction. The
character of the work to be done may also affect the power required to ;
operate; thus a machine to be used exclusively for brass work may be
speeded from 10$ to 15$ higher than if it were to be used for iron work of
similar size, and the power required will be proportionately greater.
Where power is to be transmitted to the machines by means of shafting
and countershafts, an additional amount, varying from 30$ to 50$ of the total
power absorbed by the machines, will be necessary to overcome the friction
of the shafting.
Horse-power required to drive Shafting.— Samuel Webber,
in his " Manual of Power " gives among numerous tables of power required
to drive textile machinery, a table of results of tests of shafting. A line of
2J4" shafting, 342 ft. long, weighing 4098 Ibs , with pulleys weighing 5331 Ibs.,
or a total of 9429 Ibs., supported on 47 bearings, 216 revolutions per minute,
required 1.858 H.P. to drive it. This gives a coefficient of friction of 5.52$.
In seventeen tests the coefficient ranged from 3.34# to 11.4$, averaging
5.73$.
964:
THE MACHINE-SHOP.
Horse -power Required to Drive Machinery*
Name of Machine.
Observed Horse-power.
Total
Work.
Running Light.
Small screw-cutting lathe 13J^" swing, B. G.
Screw-cutting lathe 17^" B G
0.41
0.867
0.47
0.462
0.53
0.91
0.16
0.24
0.63
1.14
0.24
0 84
1.47
0.62
0.41
1.33
1.24
0.53
0.67
1.08
0.28
0.44
0.95
0.28
0.66
0.18
0.28
0 93
1.52
7.12
4.41
0.79
4.12
2.70
4.24
3.03
4.63
5.00
3.20
6.91
3.23
5.64
0.96
0.49
3.68
2.11
2.73
2.25
2.00
2.45
1.55
3.11
0.56
0.18;0.15*-0.34t
0.207; 0.16-0.466
0.12; 0.12 to 0.31
O.C5; 0.03 to 0.33
0.187;0.12to0.66
0.37; 0.39 to 0.81
0.23 to 3. 40
0.086 to 0.26
0.07; 0.07 to 0.1 2
0.21 ; 0.01 to 0.47
0.26; 0.15 to 0.73
0.12; 0.12 to 0.40
0.27
0.60
0.39
0.15; 0.15 to 0.43
0.62
0.62
0.44; 0.1*-0.44t
0.30; 0.12*-0.80t
0.46
0.09; 0.05 to 0.25
0.22; 0.15 to 0.65
0.57; 0.43 to 0.94
0.01; 0.003-0.13
0.26; 0.26 to 0.55
0.10
0.11
0.12; 0.10-0.12*;
0.10to0.25t
0 37
0.67
1.00
0.16
0.61
.54
3.35
1 42
1.25
0. 74$-0. 17§
1.45
4.18
0.70
1.16
0.19
0.34
1.67; 0.65 to 2.0
1.42
0.61
2.17
1.30
2.00
0.32
0.24
0.40
Screw-cutting lathe 20"~(Fitchburg), B. G
Screw-cutting lathe 26", B. G
Lathe 80" face plate, will swing 108", T G
Large facing lathe, will swing 68". T. G .
Wheel lathe 60" swing
Small shaper (stroke 4", traverse II")
Small shaper, Richards (9^j" X 22")
Shaper (15" stroke Gould & Eberhardt).
Large shaper, Richards (29" X 91")
Crank planer (capacity 23" X 27" X 28J^" stroke). .
Planer (capacity 36 '' X 36" X 1 1 feet)
Large planer (capacity 76" X 76" X 57 feet
Small drill press
Upright slot drilling mach. (will drill 2W diam.).. . .
Medium drill press
Large drill press
Radial drill 6 feet swing
Radial drill 8J^ feet swing
Radial drill press
Slotter (8" stroke)
Slotter (9^j" stroke)
Slotter (15" stroke) * •
Universal milling mach (Brown & Sharpe No. 1).. . .
Milling machine (13" cutter-head, 12 cutters)
Small head traversing milling machine (cutter-head
11" diameter 16 cutters)
Gear cutter will cut 20" diameter
Horizontal boring machine for iron, 22^" swing. . . .
Hydraulic shearing machine
Large plate shears — knives 28" long, 3" stroke
Large punch press, over-reach 28", 3" stroke, 1J^"
stock can be punched
Small punch and shear combed, 7J4" knives, 1 }$' str.
Circular saw for hot iron (30^" diameter of saw). . .
Plate-bending rolls, diam. of rolls 13", length 9J4 ft.
Wood planer 13^j" (rotary knives, 2 hor'l 2 vert. . . .
Wood planer 24" (rotary knives)
Wood planer 17^" (rotary knives).
Wood planer 28" (rotary knives)
Wood planer 28" (Daniel's pattern). ,
Wood planer and matcher (capacity 14^ X 4%"). . .
Circular saw for wood (23" diameter of saw) . .
Circular saw for wood (35" diameter of saw)
Band saw for wood (34" band wheel)
Wood-mortising and boring machine
Hor'l wood-boring and mortising machine, drill 4"
diam., mortise 8% deep X HJij" long
Tenon and mortising machine
Tenon and mortising machine
Tenon and mortising machine
Edge-molder and shaper. (Vertical spindle)
Wood-molding mach. (cap. 7J4 X 2^»). Hor. spindle
Grindstone for tools, 31" diam., 6" face. Velocity
680 ft. per minute
Grindstone for stock, 42"xl2". Vel. 1680 ft. permin.
Emery wheel 11*4" diameter X V^'. Saw grinder. .
* With back gears, t Without back gears. \ For surface cutters. § With
side cutters. B. G., back-geared. T. G.. triple-geared.
ABRASIVE PROCESSES.
965
Horse-power consumed In Machine-shops.— How much
power is required to drive ordinary machine-tools? and how many men can
be employed per horse-power? are questions which it is impossible to answer
by any fixed rule. The power varies greatly according to the conditions in
each shop. The following table given by J. J. Flather in his work on .Dyna-
mometers gives an idea of the variation in several large works. The percen-
tage of the total power required to drive the shafting varies from 15 to 80,
and the number of men employed per total H.P. varies from 0.62 to 6.04.
Horse-power; Friction; Men Employed*
Horse-power.
1
1
1
I*
C .
<D
•£
fl
H
W
Kind
"O .
_ be
?i
£
ft •
JSft
Name of Firm.
of
3|?
U£
-2.2
S*T*
£«
Work.
13 ij
0) y»
"£?
o
S
|£
3
h%
2$
%£
£
"o
$'
o
i
tf
&
I
6
0
Lane & Bodley
E. &W. W.
58
132
9 97
J A Fay & Co
W W
100
15
85
15
300
1 00
3 53
Union Iron Works
E , M. M.
400
95
S0f>
23
1600
4 00
5.24
Frontier Iron & Brass W'ks
M. E., etc.
25
8
17
32
150
6.00
8-82
Taylor Mfg Co
E.
95
230
9 49
Baldwin Loco ^V^orks
2500
2000
500
80
4100
1 64
8 20
W. Sellers & Co. (one de-
. H. M.
M. T.
102
180
41
75
61
105
40
41
300
432
2.93
2.40
4.87
4.11
Pond Machine Tool Co —
Pratt & Whitney Co
12C
725
ft (H
Brown & Sharpe Co
it
230
900
3 91
Yale & Towne Co
C. & L.
135
67
68
49
700
5 11
10.25
Ferracute Machine Co
P. &D.
35
11
24
31
90
2.57
3.75
T B Wood 's Sons
P. & S.
12
3C
9 5(
Bridgeport Forge Co
Singer Mfg Co
H. F.
S. M.
150
1300
75
75
50
130
3500
.86
9 69
1.73
Howe Mfg Co
350
1500
4 98
Worcester Mach. Screw Co
M.S.
40
80
2.00
Hartford "
'*
40(
100
300
25
250
0.62
0.83
Nicholson File Co
F.
35(
40(
1 14
Averages
346.4
38.6$
818.3
2.96
5.13
Abbreviations: E., engine; W.W., wood -working machinery; M. M., min-
ing machinery; M. E., marine engines; L., locomotives; H. M., heavy ma-
chinerv; M. T., machine tools; C. & L., cranes and locks; P. & D., presses
and dies; P. & S., pulleys and shafting; H. F., heavy forgings; S. M., sewing'
machines; M. S., machine-screws: F., files.
J. T. Henthorn states (Trans. A. S. M. E., vi. 462) that in print-mills which
he examined the friction of the shafting and engine was in 7 cases belov*
20$ and in 35 cases between 20$ and 30$, in 11 cases from 30$ to 35$ and in 2
cases above 35$, the average being 25. 9$. Mr. Barrus in eight cotton-mills
found the range to be between 18$ and 25.7$, the average being 22$. Mr.
Flather believes that for shops usfng heavy machinery the percentage of
power required to drive the shafting will average from 40$ to 50$ of the total
power expended. This presupposes that under the head of shafting are
included elevators, fans, and blowers.
ABRASIVE PROCESSES.
Abrasive cutting is performed by means of stones, sand, emery, glass,
corundum, carborundum, crocus, rouge, chilled globules of iron, and in some
cases by soft, friable iron alone. (See paper by John Richards, read before
the Technical Society of the Pacific Coast, Am. Mach.t Aug. 20, 1891, and
Eng. & M. Jour., July 25 and Aug. 15, 1891.)
966 THE BTACHIKF-SHUF.
The ** Cold Saw."— For sawing any section of iron while coiu ch*
cold saw is sometimes used. This consists simply of a plain soft steel or
iron disk without teeth, about 42 inches diameter and 3/16 inch thick. The
velocity of the circumference is about 15,000 feet per minute. One of these
«aws will saw through an ordinary steel rail cold in about one minute. In
this saw the steel or iron is ground off by the friction of the disk, and is not
cut as with the teeth of an ordinary saw. It has generally been found more
profitable, however, to saw iron with disks or band-saws fitted with cutting-
teeth, which run at moderate speeds, and cut the metal as do the teeth of a
milling-cutter.
Reese's Fusing-disk.— Reese's fusing-disk is an application of the
cold saw to cutting iron or steel in the form of bars, tubes, cylinders, etc.,
in which the piece to be cut is made to revolve at a slower rate of speed
than the saw. By this means only a small surface of the bar to be cut is
presented at a time to the circumference of the saw. The saw is about the
same size as the cold saw above described, and is rotated at a velocity of
about 25,000 feet per minute. The heat generated by the friction of this saw
againsfr the small surface of the bar rotated against it is so great that the
particles of iron or steel in the bar are actually fused, and the "sawdust "
welds as it falls into a solid mass. This disk will cut either cast iron, wrought
Iron, or steel. It will cut a bar of steel \% inch diameter in one minute, in-
cluding the time of setting it in the machine, the bar being rotated about
200 turns per minute.
Cutting Stone with Wire.— A plan of cutting stone by means of a
wirn cord has been tried in Europe. While retaining sand as the cutting
agent, M. Paulin Gay, of Marseilles, has succeeded in applying it by mechan-
ical means, and as continuously as formerly the sand-blast and band-saw,
with both of which appliances his system — that of the " helicoidal wire
cord "—has considerable analogy. An engine puts in motion a continuous
wire cord (varying from five to seven thirty-seconds of an inch in diameter,
according to the work), composed of three mild-steel wires twisted at a cer-
tain pitch, that is found to give the best results in practice, at a speed of
from 15 to 17 feet per second.
The Sand-blast.— In the sand-blast, invented by B. F. Tilghman, of
Philadelphia, and first exhibited at the American Institute Fair, New York,
in 1871, common sand, powdered quartz, emery, or any sharp cutting mate-
rial is blown by a jet of air or steam on glass, metal, or other comparatively
brittle substance, by which means the latter is cut, drilled, or engraved
To protect those portions of the surface which it is desired shall not be
abraded it is only necessary to cover them with a soft or tough material,
such as lead, rubber, leather, paper, wax, or rubber-paint. (See description
in App. Cyc. Mech.; also U. S. report of Vienna Exhibition, 1873, vol. iii. 316.)
A " jet of sand " impelled by steam of moderate pressure, or even by the
blast of an ordinary fan, depolishes glass in a few seconds; wood is cut quite
rapidly; and metals are given the so-called "frosted" surface with great
rapidity. With a jet issuing from under 300 pounds pressure, a hole was
cut through a piece of corundrum 1J4 inches thick in 25 minutes.
The sand-blast has been applied to the cleaning of metal castings and
sheet metal, the graining of zinc plates for lithographic purposes, the frost-
ing of silverware, the cutting of figures on stone and glass, and the cutting
of devices on monuments or tombstones, the recutting of files, etc. The
time required to sharpen a worn-out 14-inch bastard file is about four
minutes. About one pint of sand, passed through a No. 120 sieve, and four
horse-power of 60-lb. steam are required for the operation. For cleaning
castings compressed air at from 8 to 10 pounds pressure per square inch is
employed. Chilled -iron globules instead of quartz or flint-sand are used
with good results, both as to speed of working and cost of material, when
the operation can be carried on under proper conditions. With the expen-
diture of 2 horse-power in compressing air, 2 square feet of ordinary
scale on the surface of steel and iron plates can be removed per minute.
The surface thus prepared is ready for tinning, galvanizing, plating, bronz-
ing, painting, etc. By continuing the operation the hard skin on the surface
of castings, which is so destructive to the cutting edges of milling and
other tools, can be removed. Small castings are placed in a sort of slowly
rotating barrel, open at one or both ends, through which the blast is
directed downward against them as they tumble over and over. No portion
of the surface escapes the action of the sand. Plain cored work, such as
valve-bodies, can be cleaned perfectly both inside and out. 100 Ibs. of cast-
ings can be cleaned in from 10 to 15 minutes with a blast created by 2 hors*-
EMERY-WHEELS AXD GRINDSTOHES.
967
power. The same weight of small forgings and stampings can be scaled in
from 20 to 30 minutes.— Iron Age, March 8, 1894.
EIVERY-WHEELS AND GRINDSTONES.
The Selection of Emery-wheels.— A pamphlet entitled " Emery-
wheels, their Selection and Use," published by the Brown & Sharpe Mfg.
Co., after calling attention to the fact that too much should not be expected
of one wheel, and commenting upon the importance of selecting the proper
wheel for the work to be done, says :
Wheels are numbered from coarse to fine; that is, a wheel made of No.
60 emery is coarser than one made of No. 100. Within certain limits, and
other things being equal, a coarse wheel is less liable to change the tem-
perature of the work and less liable to glaze than a fine wheel. As a rule,
the harder the stock the coarser the wheel required to produce a given
finish. For example, coarser wheels are required to produce a given sur-
face upon hardened steel than upon soft steel, while finer wheels are re-
quired to produce this surface upon brass or copper than upon either
hardened or soft steel.
Wheels are graded from soft to hard, and the grade is denoted by the
letters of the alphabet, A denoting the softest grade. Awheel is- soft or
hard chiefly 011 account of the amount and character of the material com.
bined in its manufacture with emery or corundum. But other character-
istics being equal, a wheel that is composed of fine emery is more compact
and harder than one made of coarser emery. For instance, a wheel of No.
100 emery, grade B, will be harder than one of No. 60 emery, same grade.
The softness of a wheel is generally its most important characteristic. A
soft whael is less apt to cause a change of temperaturfe in the work, or to
become glazed, than a harder one. It is best for grinding hardened steel,
cast-iron, brass, copper, and rubber, while a harder or more compact wheel
is better for grinding soft steel and wrought iron. As a rule, other things
being equal, the harder the stock the softer the wheel required to produce
a given finish.
Generally speaking, a wheel should be softer as the surface in contact
with the work is increased. For example, a wheel 1/16-inch face should be
harder than one J^-inch face. If a wheel is hard and heats or chatters, it
can often be made somewhat more effective by turning off a part of its
cutting surface; but it should be clearly understood that while this will
sometimes prevent a hard wheel from heating or chattering the work, such
a wheel will not prove as economical as one of the full width and proper
grade, for it should be borne in mind that the grade should always bear the
proper relation to the width. (See the pamphlet ref erred to for other in-
formation. See also lecture by T. Dunkin Paret, Pres't of The Tanite Co.,
on Emery-wheels, Jour. Frank. Inst., March, 1890.)
Speed of Emery- wli eels. —The following speeds are recommended
by different makers :
OJ
q_, o>
OJ3
11
P
±
P
f*
4
5
6
7
8
9
Revolutions per minute.
!l
2.2
0)^
2 <u
3|
10
12
14
16
18
20
22
24
26
30
36
Revolutions per minute.
1*
&
_|«_
19,000
12,500
9,500
7,600
6,400
4,800
3,800
3,200
2,700
2,400
2,150
'j*
A y>
_1
So
<-> SO
CT3r_
c8 fl o>
&2Z
8*
§3
I*
*M
|3
M
1,950
1,600
1,400
1,200
1.Q50
950
875
800
750
675
550
*<3
»fl ®
«K
g§s
Os£
#
**
W
2,200~~
1,850
1,600
1,400
1,250
1,100
1,000
925
825
785
550
2,160
1,800
1,570
1,350
1,222
1,080
1,000
917
2,200
1,800
1,600
1,400
1,250
1,100
1,000
925
600
500
400
14,400
10,800
8,640
7,200
5,400
4,320
3,600
3,080
2,700
2,400
12,000
10,000
8,500
7,400
5,450
4,400
3,600
3,150
2,750
2,450
7,400*
5,400
4,400
3,600
3,200
2,700
2,400
733
611
" We advise the regular speed of 5500 feet per minute." (Detroit Emery-
wheel Co.)
" Experience has demonstrated that there is no advantage in running
968
THE MACHIKE-SHOP.
solid emery-wheels at a higher rate than 5500 feet per minute peripheral
speed.'' (Springfield E. W. Mfg. Co.)
" Although there is no exactly defined limit at which a wheel must be run
to render it effective, experience has demonstrated that, taking into account
safety, durability, and liability to heat, 5500 feet per minute at the periphery
gives the best results. All first-class wheels have the number of revolutions
necessary to give this rate marked on their labels, and a column of figures
in the price-list gives a corresponding rate. Above this speed all wheels
are unsafe. If run much below it they wear away rapidly in proportion to
what they accomplish." (Northampton E. W. Co.)
Grades of Emery.— The numbers representing the grades of emery
run from 8 to 120, and the degree of smoothness of surface they leave ma^
be compared to that left by files as follows:
8 and 10 represent the cut of a wood rasp.
16 ' 20 *' * " a coarse rough file,
24 * 30 ** " * an ordinary rough file.
36 * 40 «• " * a bastard file.
46 * 60 u •• * a second-cut file.
70 • 80 " " • a smooth
90 " 100 •• " • a superfine "
120 F and FF " " ' a dead-smooth file.
Speed of Polishing-wheels.
Wood covered with leather, about 7000 ft. per minute
44 a hair brush, about 2500 revs, tor larges
" 1W' to 8" diam., hair 1" to \W long, ab. 4500 " " smallest
Walrus-hide wheels, about 8000 ft. per*minute
Rag-wheels, 4 to 8 in. diameter, about 7000 " " "
Safe Speeds for Grindstones and Emery-wheels.— G. T>
Hiscox (Iron Age, April 7, 1892), by an application of the formula for centrif-
ugal force in fly-wheels (see Fly-wheels), obtains the figures for strains in
grindstones and emery-wheels which are given in the tables below. His
formulae are:
Stress per sq. in. of section of a grindstone = (.7071 D X N)* X .0000795
' " " " " an emery-wheel = (.7071D X N)* X 00010226
D = diameter in feet, N = revolutions per minute.
He takes the weight of sandstone at .078 Ib. per cubic inch, and that of an
emery-wheel at 0.1 Ib. per cubic inch; Ohio stone weighs about .081 Ib. and
Huron stone about .089 Ib. per cubic inch. The Ohio stone will bear a speed
at the periphery of 2500 to 3000 ft. per min., which latter should never bd
exceeded. The Huron stone can be trusted up to 4000 ft., when property
clamped between flanges and not excessively wedged in setting. Apart
from the speed of grindstones as a cause of bursting, probably the majority
of accidents have really been caused by wedging them on the shaft and over-
wedging to true them. The holes being square, the excessive driving oJ
wedges to true the stones starts cracks in the corners that eventually run
out until the centrifugal strain becomes greater than the tenacity of tin
remaining solid stone. Hence the necessity of great caution in the use oJ
wedges, as well as the holding of large quick-running stones between large
flanges and leather washers.
Strains in Grindstones.
LIMIT OF VELOCITY AND APPROXIMATE ACTUAL STRAIN PER SQUARE INCH o»
SECTIONAL AREA FOR GRINDSTONES OF MEDIUM TENSILE STRENGTH.
Diam-
eter.
Revolutions per minute.
100
150
200
250
300
350
400
feet.
2
p
3*
ff
6
7
Ibs.
1.58
2.47
3.57
4.86
6.35
8.04
9.93
14.30
19.44
Ibs.
3.57
5.57
8.04
10.93
14.30
18.08
22.34
32.17
Ibs.
6.35
9.88
14.28
19.44
27.37
32.16
Ibs.
9.93
15.49
22.34
30.38
Ibs.
14.30
22.29
32.16
Ibs.
18.36
28.64
Ibs.
25.42
39.75
Approximate breaking strain tev
times the strain for size opposite
the bottom figure in each column.
EMERY-WHEELS AND GRINDSTONES.
9G9
The figures at the bottom of columns designate the limit cf velocity (in
revolutions per minute), at the head of the columns for stones of the diam-
eter in the first column opposite the designating figure.
A general rule of safety for any size grindstone that has a compact and
strong grain is to limit the peripheral velocity to 47 feet per second.
There is a large variation in the listed speeds of emery-wheels by different
makers— 4000 as a minimum and 5600 maximum feet per minute, while
others claim a maximum speed of 10,000 feet per minute as the safe speed
of their best emery-wheels. Rim wheels and iron centre wheels are special-
ties that require the maker's guarantee and assignment of speed.
Strains in Kmery-wlieels.
ACTUAL, STRAIN PER SQUARE INCH OF SECTION IN EMERY-WHEELS AT THE
VELOCITIES AT HEAD OF COLUMNS FOR SIZES IN FIRST COLUMN.
r M
SD
-•£
.s «
P.S
4
6
8
10
12
14
16
18
20
22
24
26
30
36
Revolutions per minute.
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
22.67
51.13
90.71
141.90
27.43
61.86
109.76
171.71
32.64
73.62
130.62
38.31
86.40
153.30
'18.40
24.80
32.57
41.41
50.98
61.81
73.62
86.36
115.04
165.64
*32!72
43.90
57.65
73.62
90.23
109.41
130.88
152.85
22.67
35.47
51.12
68.70
90.24
115.03
141.22
171.23
32.65
51.08
73.62
99.21
130.31
165.65
44.45
69.51
100.21
134.65
177.80
58.05
90.81
130.88
175.60
73.47
114.94
165.65
Diam
Revs, per
min.
in.
2800
3000
4
6
8
44.43
100.21
177.80
51.12
115.03
Joshua Rose (Modern Machine-shop Practice) says: The average speed of
grindstones in workshops may be given as follows:
Circumferential Speed of Stone.
For grinding machinists' tools, about 900 feet per minute.
carpenters' " 600 " " "
The speeds of stones for file-grinding, and other similar rapid grinding is
thus given in the "Grinders1 List."
Diam. ft 8 7^ 7 6^ 6 5U 5 4U 4 3V£ 3
Revs, per min. 135 144 154 166 180 196 216 240 270 308 360
The following table, from the Mechanical World, is for the diameter of
stones and the number of revolutions they should run per minute (not to be
exceeded), with the diameter of change of shift-pulleys required, varying
each shift or change 2Hj inches, 2J4 inches, or 2 inches in diameter for each
reduction of 6 inches in the diameter of the stone.
Diameter
Revolutions
Shift of Pulleys, in inches.
of Stone.
per minute.
2*£
2*4
2
ft. in.
8 0
135
40
36
32
7 6
144
37*6
33%
30
7 0
•154
35
31*1
28
6 6
166
32*£
29*4
26
6 0
180
30
27
24
5 6
196
27*£
24%
22
5 0
216
25
22*<£
20
4 6
240
22*£
20*4
18
4 0
270
20
18
16
3 6
306
17*4j
15%
14
3 0
360
15
13*|
12
1
2
3
4
5
970
THE MACHINE-SHOP.
Columns 3, 4, and 5 are given to show that if we start an 8-foot stone with,
say, a countershaft pulley driving a 40-inch pulley on the grindstone spindle,
and the stone makes the right number (135) of revolutions per minute, the
reduction in the diameter of the pulley on the grinding-stone spindle, when
the stone has been reduced Q inches in diameter, will require to be also re-
duced %*4 inches in diameter, or to shift from 40 inches to 3?^ inches, and so
on similarly for columns 4 and 5. Any other suitable dimensions of pulley
may be used for the stone when eight feet in diameter, but the number of
inches in each shift named, in order to be correct, will have to be propor-
tional to the numbers of revolutions the stone should run, as given in column
2 of the table.
Varieties of Grindstones.
(Joshua Rose.)
FOR GRINDING MACHINISTS' TOOLS.
Name of Stone.
Kind of Grit.
Texture of Stone.
Color of Stone.
Nova Scotia,
Bay Chaleur (New 1
Brunswick), f
Liverpool or Melling.
All kinds, from
finest to coarsest
Medium to finest
Medium to fine
All kinds, from
hardest to softest
Soft and sharp
Soft, with sharp
grit
Blue or yellowish
gray
Uniformly light
blue
Reddish-
FOR WOOD-WORKING TOOLS.
Wickersley
Liverpool or Melling.
Bay Chaleur (New l
Brunswick), f
Huron, Michigan . . .
Medium to fine
Medium to fine •!
Medium to finest
Fine
Very soft
Soft, with sharp
grit
Soft and sharp
Soft and sharp
Grayish yellow
Reddish
Uniform light blue
Uniform light blue
FOR GRINDING BROAD SURFACES, AS SAWS OR IRON PLATES.
Newcastle
Coarse to med^n
The hard ones
Yellow
Independence
Coarse
Hard to medium
Grayish white
Massillon
Coarse
Hard to medium
Yellowish white
TAP DRILLS.
Taps for Machine-screws. (The Pratt & Whitney Co.)
Approx.
Diameter,
Wire
No. of Threads
Approx.
Diameter,
Wire
No. of Threads
fractions
Gauge.
to inch.
fractions
Gauge.
to inch.
of an inch.
of an inch.
No. 1
60,72
No. 13
20, 24
2
48, 56, 64
H
14
16, 18, 20, 22, 24
3
40, 48, 56
15
18, 20, 24
7/64
4
32. 36, 40
17/64
16
16, 18, 20. 22
5
30,' 32, 36, 40
9/32
18
16, 18, 20
9/64
6
30, 32, 36, 40
19
16, 18, 20
7
24, 30, 32
5/16
20
16, 18, 20
5/32
8
24, 30. 32, 36, 40
22
16, 18
9
24, 28, 30, 32
%
24
14, 16, 18
3/16
10
20, 22, 24, 30, 32
26
16
11
22, 24
28
16
7/32
12
20, 22, 24
30
16
The Morse Twist Drill and Machine Co. gives the following table showing
the different sizes of drills that should be used when a suitable thread is to
be tapped in a hole. The sizes given are practically correct.
TAP DlilLLS.
971
ril
T
Tf« Tf <N«OO
--
a
i
a? -a
a |
35O«O«O?O*3«O«OU
.
lTJ 00 J^ »W\Oi O
/-' S9CIO \O XSJI- \OS NflO'-t i-< 5C V*lO CO l^" \90OS O T^H"
"-i Off\r-i I- i~t ^^H Oi 1-1 IO\C* t-H OJI MK7* r-l C» I>\O» ^ CO
m
02 .
g^ : :?°?° : :S2
OOQOOOC30?O«O«O?OOOCOT
*ot • .we* • ^ • •
-c «-H O> O> T-I T-< . «OO
972
THE MACHINE-SHOP.
TAPER BOLTS, PINS, REAMERS, ETC.
Taper Bolts for Locomotives.— Bolt-threads, U. S. standard
except stay-bolts and boiler-studs, V threads, 12 per inch; valves, cocks, and
plugs, V threads, 14 per inch, and J^-inch taper per 1 inch. Standard 'bolt
taper 1/16 inch per foot.
Taper Reamers.— The Pratt & Whitney Co. makes standard taper
reamers for locomotive work taper 1/16 inch per foot from J4 inch diam.;
4 in. length of flute to 2 in. diam. ; 18 in. length of flute, diameters advancing
by 16ths and 32ds. P. & W. Co.'s standard taper pin reamers taper 14 in.
per foot, are made in 14 sizes of diameters, 0.135 to 1.009 in.; length of flute
1 5/16 in. to 12 in.
DIMENSIONS OF THE PRATT & WHITNEY COMPANY'S REAMERS FOR MORSE
STANDARD-TAPER SOCKET.
No.
Diameter
Small End,
inches.
Diameter
Large End,
inches.
Gauge
Diarn..la'ge
end, inches
Gauge
L'ngth,
inches.
Length
Flute,
inches.
Total
L'ngth.
Taper
per foot,
inches.
1
2
3
4
5
6
0.365
0.573
0.779
1.026
1.486
2.nr
0.525
0.749
0.982
1.283
1.796
2.566
0.475
0.699
0.93(5
1.231
1.746
2.500
35/16
4
5
7M
00 Oi Ut £>. CO CO
$y±
10 4
I2K
0.600
0.602
0.602
0.023
0.630
9.686
5
6
7
8
9
10
.289
.341
.409
.492
.591
.706
19/64
11/32
13/32
H
19/32
23/32
&
&
1
m
1%
534
¥
Standard Steel Taper-pins.— The following sizes are made by
The rratt & Whitney Co.:
Number:
0 1234
Diameter large end:
.156 .172 .193 .219 .250
Approximate fractional sizes:
5/32 11/64 3/16 7/32 %
Lengths from
& 9* 9£ K K
To* 1 114 1M 1% 2
Diameter small end of standard taper-pin reamer:t
.135 .146 .162 .183 .208 .240 .279 .331 .398 .482 .581
Standard Steel Mandrels. (The Pratt & Whitney Co.)— These
mandrels are made of tool-steel, hardened, and ground true on their cen-
tres. Centres are also ground to true 60° cones. The ends are of a form
best adapted to resist injury likely to be caused by driving. They are
slightly taper. Sizes, y± in. diameter by 3% in. long to 3 in. diam. by 14% in.
long, diameters advancing by 16ths.
PUNCHES AND JDIES, PRESSES, ETC.
Clearance between Punch and Die.— For computing the amount
of clearance that a die should have, or, in other words, the difference in
siz-1 between die and punch, the general rule is to make the diameter of
die hole equal to the diameter of the punch, plus 2/10 the thickness of the
piate. Or, D = d -f- .2f, in which D = diameter of die-hole, d = diameter of
punch, and t = thickness of plate. For very thick plates some mechanics
p efer to make the die-hole a little smaller than called for by the above rule.
For ordinary boiler-work the die is made from 1/10 to 3/10 of the thickness
of 'he plate larger than the diameter of the punch; and some boiler-makers
advocate making the punch fit the die accurately. For punching nuts, the
punHi fits in the die. (Am. Machinist.)
Kennedy's Spiral Punch. (The Pratt & Whitney Co.)— B. Martell,
Chief Surveyor of Lloyd's Register, reported tests of Kennedy's spiral
punches in which a %-inch spiral punch penetrated a %-inch plate at a pres-
sure of 22 to 25 tons, while a flat punch required 33 to 35 tons. Steel boiler-
plates punched with a flat punch gave an average tensile strength of 58,579
* Lengths vary by y±" each size,
vze overlaps smaller one about y%"
t Taken y%" from extreme end. Each
Taper y^' to the foot.
FOECIKG AND SHRINKING FITS. 973
Ibs. per square inch, and an elongation in two inches across the hole of 5.2£,
while plates punched with a spiral punch gave 63,929 Ibs., and 10. 6# elonga-
tion.
The spiral shear form is not recommended for punches for use in metal of
a thickness greater than the diameter of the punch. This form is of great.
est benefit when the thickness of metal worked is less than two thirds the
diameter of punch.
Size of Blanks used in the Drawing-press. Oberlin Smith
(Jour. Frank. Inst., Nov. 1886) gives three methods of finding the size of
blanks. The first is a tentative method, and consists simply in a series of
experiments with various blanks, until the proper one is found. This is for
use mainly in complicated cases, and when the cutting portions of the die
and punch can be finally sized after the other work is done. The second
method is by weighing the sample piece, and then, knowing the weight of
the sheet metal per square inch, computing the diameter of a piece having
the required area to equal the sample in weight. The third method is by
computation, and the formula is x = Vd* -f 4dh for sharp-cornered cup,
where x = diameter of blank, d = diameter of cup, h = height of cup. For
round-cornered cup where the corner is small, say radius of corner less than
J4 height of cup, the formula is x = ( 1/d2 -f- 4dh) — r, about; r being the
radius of the corner. This is based upon the assumption that the thickness
of the metal is not to be altered by the drawing operation.
Pressure attainable by the Use of the Drop-press. (R. H.
Thurston, Trans. A. S. M. E., v. 53.)— A set of copper cylinders was prepared,
of pure Lake Superior copper; they were subjected to the action of presses
of different weights and of different heights of fall. Companion specimens
of copper were compressed to exactly the same amount, and measures were
obtained of the loads producing compression, and of the amount of work
done in producing the compression by the drop. Comparing one with the
other it was found that the work done with the hammer was 90# of the work
which should have been done with perfect efficiency. That is to say, the
work done in the testing-machine was equal to 90# of that due the weight of
the drop falling the given uisiance.
, Weight of drop X fall X efficiency
Formula: Mean pressure m pounds = compression
For pressures per square inch, divide by the mean area opposed to crush-
ing action during the operation.
Flow of Metals. (David Townsend, Jour. Frank. Inst., March, 1878.)
—In punching holes 7/16 inch diameter through iron blocks 1% inches thick,
it was found that the core punched out was only 1 1/16 inch thick, and its
volume was only about 32# of the volume of the hole. Therefore, 68# of the
metal displaced by punching the hole flowed into the block itself, increasing
its dimensions.
FORCING AND SHRINKING FITS.
Forcing Fits of Pins and Axles by Hydraulic Pressure.
--A 4-inch axle is turned .015 inch diameter larger than the hole into which
it is to be fitted. They are pressed on by a pressure of 30 to 35 tons. (Lec-
ture by Coleman Sellers, 1872.)
For forcing the crank-pin into a locomotive driving-wheel, when the pin-
hole is perfectly true and smooth, the pin should be pressed in with a pres-
sure of 6 tons for every inch of diameter of the wheel fit. When the hole is
not perfectly true, which may be the result of shrinking the tire on the
wheel centre after the hole for the crank-pin has been bored, or if the hole is
not perfectly smooth, the pressure may have to be increased to 9 tons for
every inch of diameter of the wheel-fit. (Am. Machinist.)
Shrinkage Fits.— In 1886 the American Railway Master Mechanics'
Association recommended the following shrinkage allowances for tires of
standard locomotives. The tires are uniformly heated by gas-flames, slipped
over the cast-iron centres, and allowed to cool. The centres are turned to
the standard sizes given below, and the tires are bored smaller by the
amount of the shrinkage designated for each:
Diameter of centre, in.... 38 44 50 56 62 66
Shrinkage allowance, in.. .040 .047 .053 .060 .066 .070
This shrinkage allowance is approximately 1/fiO inch per foot, or 1/960. A
common allowance is 1/1000. Taking the modulus of elasticity of steel at
974 THE MACHINE-SHOP.
30,000,000, the strain caused by shrinkage would be 30,000 Ibs. per square
inch, less an uncertain amount due to compression of the centre.
SCREWS, SCREW-THREADS, ETC.*
Efficiency of a Screw.— Let a = angle of the thread, that is, the
angle whose tangent is the pitch of the screw divided by the circumference
of a circle whose diameter is the mean of the diameters at the top and
bottom of the thread. Then for a square thread
Efficiency = l-/tan«
1 -\-f cotan a
in which / is tlie coefficient of friction. (For demonstration, see Cotterill and
Slade, Applied Mechanics, p. 146.) Since cotan = 1 -r- tan, we may substitute
for cotan a the reciprocal of the tangent, or if p = pitch, and c = mean cir-
cumference of the screw,
'-'£
Efficiency = .
EXAMPLE.— Efficiency of square-threaded screws of J^ in. pitch.
Diameter at bottom of thread, in .... 1 2 3 4
41 top " " " .... 1^ 2^ 3^ 4^
Mean circumference" " "....3.927 7.069 10.21 13. 3D
Cotangent a = c -J- p =7.854 14.14 20.42 26.70
Tangent a = p -*- c = .1273 .0707 .0490 .0375
Efficiency if /= .10 = 55.3* 41.2* 32.7* 27.2*
" "/=.15 = 45* 31.7* 24.4* 19.9*
The efficiency thus increases with the steepness of the pitch.
The above formulae and examples are for square-threaded screws, and
consider the friction of the screw-thread only, and not the friction of the
collar or step by which end thrust is resisted, and which further reduces the
efficiency. The efficiency is also further reduced by giving an inclination to
the side of the thread, as in the V-threaded screw. For discussion of this
subject, see paper by Wilfred Lewis, Jour. Frank. Inst. 1880; also Trans.
A. S. M. E., vol. xii. 784.
Efficiency of Screw-bolts.— Mr. Lewis gives the following approx-
imate formula for ordinary screw-bolts (V threads, with collars): p =
Eitch of screw, d = outside diameter of screw, F = force applied at circum-
srence to lift a unit of weight, E = efficiency of screw. For an average
case, in which the coefficient of friction may be assumed at .15,
For bolts of the dimensions given above, J^-in. pitch, and outside diam*
eters 1^, 2^, 3^, and 4^ in., the efficiencies according to this formula
would be, respectively, .25, .167, .125, and .10.
James McBride (Trans. A. S. M. E.. xii. 781) describes an experiment with
an ordinary 2-in. screw-bolt, with a V thread, 4^ threads per inch, raising
a weight of 7500 Ibs., the force being applied by turning the nut. Of the
power applied 89.8* was absorbed by friction of the nut on its supporting
washer and of the threads of the bolt in the nut. The nut was not faced,
and had the flat side to the washer.
Prof. Ball in his " Experimental Mechanics " says: "Experiments showed
in two cases respectively about % and % of the power was lost."
Trautwine says: " In practice the friction of the screw (which under
heavy loads becomes very great) make the theoretical calculations of but
little value."
Weisbach says: " The efficiency is from 19* to 30*."
Efficiency of a Differential Screw.— A correspondent of the
American Machinist describes an experiment with a differential screw-
punch, consisting of an outer screw 2 in. diam., 3 threads per in., and an
inner screw \% in. diam., 3^ threads per inch. The pitch of the outer screw
* For U. S. Standard Screw-threads, see page 204. *
KEYS. 975
boing ^ In. and that of the inner screw 2/7 in., tno ^unch would ad-
vance in one revolution ^£ — 2/7 = 1/21 in. Experiments were made to de-
termine the force required to punch an 11/16-in. hole in iron *4 in. thick, the
force being applied at the end of a lever-arm of 47% in. The leverage would
be 47% X 27T X 21 = 6300. The mean force applied at the end of the lever
was 95 Ibs., and the force at the punch, if there was no friction, would be
6300 X 95 = 598,500 Ibs. The force required to punch the iron, assuming a
shearing resistance of 50,000 Ibs. per sq. in., would be 50,000 X 11/16 X «• X
V± = 27,000 Ibs., and the efficiency of the punch would be 27,000 -5- 598,500 =
only 4.5$. With the larger screw only used as a punch the mean force at
the end of the lever was only 82 Ibs. The leverage in this case was 47% X
2ir X 3 = 900, the total force referred to the punch, including friction, 900 x
82 = 73,800, and the efficiency 27,000 H- 73,800 = 36. 7$. The screws were of
tool-steel, well fitted, and lubricated with lard-oil and plumbago.
Powell's New Screw-thread.— A. M. Powell (Am. Mach., Jan. 24,
1895) has designed a new screw-thread to replace the square form of thread,
giving the advantages of greater ease in making fits, and provision for k< take
up " in case of wear. The dimensions are the same as those of square-
thread screws, with the exception that the sides of the thread, instead of
being perpendicular to the axis of the screw, are inclined 14^° to such per-
pendicular; that is, the two sides of a thread are inclined 29° to each other.
The formulae for dimensions of the thread are the following: Depth of
thread = ^ -*- pitch; width of top of thread = width of space at bottom =
.3707 -r- pitch; thickness at root of thread = width of space at top = .6293 -f-
pitch. The term pitch is the number of threads to the inch.
PROPORTIONING PARTS OF MACHINES IN A
OF SIZES.
(Stevens Indicator, April, 1892.)
The following method was used by Coleman Sellers while at William Sellers
& Co/s to get the proportions of the parts of machines, based upon the
size obtained in building a large machine and a small one to any series of
machines. This formula is used in getting up the proportion-book and ar-
ranging the set of proportions from which any machine can be constructed
of intermediate size between the largest and smallest of the series.
Rule to Establish Construction Formulae.— Take difference
between the nominal sizes of the largest and the smallest machines that
have been designed of the same construction. Take also the difference be-
tween the sizes of similar parts on the largest and smallest machines se-
lected. Divide the latter by the former, and the result obtained will be a
" factor, " which, multiplied by the nominal capacity of the intermediate
machine, and increased or diminished by a constant " increment," will give
the size of the part required. To find the " increment :" Multiply the nomi-
nal capacity of some known size by the factor obtained, and subtract the
result from the size of the part belonging to the machine of nominal ca-
pacity selected.
EXAMPLE.— Suppose the size of a part of a 72-in. machine is 3 in., and the
corresponding part of a 42-in. machine is 1%, or 1.875 in.: then 72 — 42 =
30, and 3 in. - 1% in. = \VS in. = 1.125. 1.125 H- 30 = .0375 = the " factor,"
and .0375 X 42 = 1.575. Then 1.875 - 1.575 = .3 = the "increment " to be
added. Let D = nominal capacity; then the formula will read: x =
D X .0375 + .3.
Proof: 42 X .0375 -f .3 = 1.875, or 1%, the size of one of the selected parts,
Some prefer the formula: aD 4- c = if, in which D = nominal capacity in
inches or in pounds, c is a constant increment, a is the factor, and x = the
part to be found.
KBITS.
Sizes of Keys for Mill-gearing. (Trans. A. S. M. E., xiii. 229.)— E.
G. Parkhurst's rule : Width of key =' % diam. of shaft, depth = 1/9 diam. of
Shaft; taper ^ in. to the foot.
Custom in Michigan saw-mills : Keys of square section, side = ^ diam. of
shaft, or as nearly as may be in even sixteenths of an inch.
J. T. Hawkins's rule : Width = ^ diam. of hole; depth of side abutment
in shaft = ^ diam. of hole.
W. S. Huson's rule : J^-inch key for 1 to 1*4 in. shafts, 5/16 key for 1J4 to
1^ in. shafts, % in. key for 1^ to 1% in. shafts, and so on. Taper % in. to
the foot. Total thickness at large end of splice, 4/5 width of key.
976
THE MACHINE-SHOP.
Unwin (Elements of Machine Design) gives : Width = y±d -\- ^ in. Thick
ness = %d -f ^ in., in which d = diam. of shaft in inches. When wheels or
Sulleys transmitting only a small amount of power are keyed on large shafts,
e says, these dimensions are excessive. In that cas^, if H.P. = horse-
power transmitted by the wheel or pulley, N = revs, per min, P = force
acting at the circumference, in Ibs., and R = radius of pulley in inches, take
3/100 H.P. */PR
= /Y ~~N or Y 630"'
Prof. Coleman Sellers (Stevens Indicator, April, 1892) gives the following :
The size of keys, both for shafting and for machine tools, are the propor-
tions adopted by William Sellers & Co., and rigidly adhered to during a pe-
riod of nearly forty years. Their practice in making keys and fitting them
is, that the keys shall always bind tight sidewise, but riot top and bottom;
that is, not necessarily touch either at the bottom of the key-seat in the
shaft or touch the top of the slot cut in the gear-wheel that is fastened to
the shaft ; but in practice keys used in this manner depend upon the fit of
the wheel upon the shaft being a forcing fit, or a fit that is so tight as to re-
quire screw-pressure to put the wheel in place upon the shaft.
Size of Keys for Shafting.
Diameter of Shaft, in. Size of Key, in.
\Y± 17/16 111/16 5/16 x %
115/16 23/16 7/16 x ^
27/16 9/16 x %
211/16 215/16 33/16 37/16 11/16 x %
3 15/16 4 7/16 4 15/16 13/16 x %
57/16 515/16 67/16 15/16x1
6 15/16 7 7/16 7 15/16 8 7/16 8 15/16.. 1 1/16 xljg
Length of key-seat for coupling = \y% X nominal diameter of shaft.
Size of Keys for Machine Tools.
Diam. of Shaft, in.
15/16 and under .
Size of Key,
-.in^q<
Diam. of Shaft, in.
4 to 5 7/16
Size of Key,
in. sq.
13/16
1 tol 3/16
:..... 3/i6
5^ to 6 15/16...
15/16
1*4 to 1 7/16
7 to 8 15/16...
1 1/16
l^i to 1 11/16
. 5/16
9 to 10 15/16.
. 1 3/16
1% to 2 3/16
7/16
11 to 12 15/16 ..
1 5/10
2^ to 2 11/16
9/16
13 to 14 15/16
1 7/lt
WA to 3 15/16...
.. 11/16
John Richards, in an article in Gassier"1 s Magazine, writes as follows: There,
are two kinds or system of keys, both proper and necessary, but widely dif-
ferent in nature. 1. The common fastening key, usually made in width one
fourth of the shaft's diameter, and the depth five eighths to one third the
width. These keys are tapered and fit on all sides, or, as it is commonly de-
scribed, " bear all over." They perform the double function in most cases
of driving or transmitting and fastening the keyed-on member against
movement endwise on the shaft. Such keys, when properly made, drive
as a strut, diagonally from corner to corner.
2. The other kind or class of keys are not tapered ar-il fit on their sides
only, a slight clearance being left on the back to insure against wedge action
or radial strain. These keys drive by shearing strain.
For fixed work where there is no sliding movement such keys are com-
monly made of square section, the sides only being planed, so the depth is
more than the width by so much as is cut away in finishing or fitting.
For sliding bearings, as in the case of drilling-machine spindles, the depth
should be increased, and in cases where there is heavy strain there should
be two keys or feathers instead of one.
The following tables are taken from proportions adopted in practical use.
Flat keys, as in the first table, are employed for fixed work when the
parts are to be held not only against torsional strain, but also against move-
ment endwise ; and in case of heavy strain the strut principle being the
strongest and most secure against movement when there is strain each way,
as in the case of engine cranks and first movers generally. The objection*
HOLDING-POWER OF KEYS AND SET-SCREWS. 97?
to the system for general use are, straining the work out of truth, the care
and expense required in fitting, and destroying the evidence of good or bad
fitting of the keyed joint. When a wheel or other part is fastened with a
tapering key of this kind there is no means of knowing whether the work is
well fitted or not. For this reason such keys are not employed by machine-
tool-makers, and in the case of accurate work of any kind, indeed, cannot
be, because of the wedging strain, and also the difficulty of inspecting com-
pleted work.
T. DIMENSIONS OP FLAT KEYS, IN INCHES,
Diam. of shaft....
Breadth of keys
Depth of keys . . . ,
5/16
3/16
r/ie
\l 9/32 5/
4 5
1 IX
% 11/16
6
1%
13/16
II. DIMENSIONS OP SQUARE KEYS, IN INCHES.
Diam. of shaft
Breadth of keys...
Depth of keys
1
5/32
3/16
1M
7/32
9/32
5/16
%•
s/s
2
7/16
2lf/32
3
17/32
9/16
9/16
11/16
III. DIMENSIONS OP SLIDING FEATHER-KEYS, IN INCHES.
Diam. of shaft
Breadth of keys. .
Depth of keys
5^16
7/16
5/16
7/16
3^
9/16
P. Pryibil furnishes the following table of dimensions to the Am. Machin
ist. He says : On special heavy work and very short hubs we put in two
keys in one shaft 90° apart. With special long hubs, where we cannot use
keys with noses, the keys should be thicker than the standard.
Diameter of Shafts,
inches.
Width,
inches.
Thick-
ness, in.
Diameter of Shafts,
inches.
Width,
inches.
Thick-
ness, in.
% tol 1/16
3/16
3/16
3 7/16 to 3 11/16
%
%
lj| to 1 5/16
5/16
M
r!6 to 4 3/16
1
11/16
1 7/16 to 1 11/16
1 15/16 to 2 3/16
ft
5/16
6 to 4 11/16
to 5%
1M
15/16
2 7/16 to 2 11/16
%
\A
to 6%
^X
1
2 15/16 to 3 3/16
•%
9/16
to 7%
1%
1^
Keys longer than 10 inches, say 14 to 16", 1/16" thicker; keys longer than
10 inches, say 18 to 20", ^" thicker; and so on. Special short hubs to have
two keys.
For description of the Woodruff system of keying, see circular of the
Pratt & Whitney Co. ; also Modern Mechanism, page 455.
HOLDING-POWER OF KEYS AND SET-SCREWS.
Tests of the Holding-power of Set-screws In Pulleys.
|G. Lanza, Trans. A. S. M. E., x. 230.)— These tests were made by using a
pulley fastened to the shaft by two set-screws with the shaft keyed to the
holders; then the load required at the rim of the pulley to cause it to slip
was determined, and this being multiplied by the number 6.037 (obtained by
adding to the radius of the pulley one-half the diameter of the wire rope,
and dividing the sum by twice the radius of the shaft, since there were two
set-screws in action at a time) gives the holding-power of the set-screws.
The set-screws used were of wrought-iron, % of an inch in diameter, and ten
threads to the inch; the shaft used was of steel and rather hard, the set-
screws making but little impression upon it. They were set up with a
force of 75 Ibs. at the end of a ten-inch monkey-wrench. The set-screws
used were of four kinds, marked respectively A, B, C, and D. The results
were as follows :
978 DYNAMOMETERS.
A, ends perfectly flat, 9/16-in. diameter, 1412 to 2294 Ibs. ; average 2064.
B, radius of rounded ends about ^ inch, 2747 " 3079 " " 2912.
C, " " " " " y± " 1902 " 3079 " " 2573.
D ends cup-shaped and case-hardened, 1962 " 2958 " 2470.
REMARKS.— A. The set-screws were not entirely normal to the shaft ; hence
they bore less in the earlier trials, before they had become flattened by
wear.
B. The ends of these set-screws, after the first two trials, were found to
be flattened, the flattened area having a diameter of about y± inch.
C. The ends were found, after the first two trials, to be flattened, as in B.
D. The first test held well because the edges were sharp, then the holding-
power fell off till they had become flattened in a manner similar to B, when
the holding-power increased again.
Tests of the Holding-power of" Keys. (Lanza.)— The load
was applied as in the tests of set-screws, the shaft being firmly keyed to the
holders. The load required at the rim of the pulley to shear the keys was
determined, and this, multiplied by a suitable constant, determined in a sim-
ilar way to that used in the case of set-screws, gives us the shearing strength
per square inch of the keys.
The keys tested were of eight kinds, denoted, respectively, by the letters
A, B, C, D, E, F, G and H, and the results were as follows : A, B, D and F,
each 4 tests; E, 3 tests ; C, G, and H, each 2 tests.
A, Norway iron, 2" X W X 15/32", 40,184 to 47,760 Ibs.; average, 42,726.
BT refined iron, 2" X V±" X 15/32", 36,482 " 39,254; " 38,059.
C, tool steel, 4" X M" X 15/32", 91,344 & 100,056.
D, machinery steel, 2" X J4" X 15/32", 64,630 to 70,186; " 66.875.
E, Norway iron, \W X %" X 7/16", 36,850 k' 37,222; " 37,036.
F, cast-iron, 2" X H" X 15/32", 30,278 " 36,944; " 33,034.
G, cast-iron, iyB" X %" X 7/16", 37,222 & 38,700.
H, cast-iron, 1" X W X 7/16", 29,814 & 38,978.
In A and B some crushing took place before shearing. In E, the keys be-
ing only 7/16 in. deep, tipped slightly in the key- way. In H, in the first test,
there was a defect in the key-way of the pulley.
DYNAMOMETERS.
Dynamometers are instruments used for measuring power. They are of
several classes, as : 1. Traction dynamometers, used for determining the
power required to pull a car or other vehicle, or a plough or harrow.
2. Brake or absorption dynamometers, in which the power of a rotating
shaft or wheel is absorbed or converted into heat by the friction of a brake;
and, 3. Transmission dynamometers, in which the power in a rotating shaft
is measured during its transmission through a belt or other connection to
another shaft, without being absorbed.
Traction Dynamometers generally contain two principal parts:
(1) A spring or series of springs, through which the pull is exerted, the exten-
sion of the spring measuring the amount of the pulling force ; and (2) a paper-
covered drum, rotated either at a uniform speed by clockwork, or at a speed
•proportional to the speed of the traction, through'gearing, on which the ex-
' tension of the spring is registered by a pencil. From the average height of
the diagram drawn by the pencil above the zero-line the average pulling
force in pounds is obtained, and this multiplied by the distance traversed,
in feet, gives the work done, in foot-pounds. The product divided by the
time in minutes and by 33,000 gives the horse-power.
The Prony brake is the typical form of absorption dynamometer.
(See Fig. 167, from Flather on Dynamometers and the Measurement of
Power.)
Primarily this consists of a lever connected to a revolving shaft or pulley
in such a manner that the friction induced between the surfaces in contact
will tend to rotate the arm in the direction in which the shaft revolves. This
rotation is counterbalanced by weights P, hung in the scale-pan at the end
of the lever. In order to measure the power for a given number of revolu-
tions of pulley, we add weights to the scale-pan and screw up on bolts 66,
until the friction induced balances the weights and the lever is maintained
THE ALDEK ABSORPTION-DYNAMOMETER. 979
In its horizontal position while the revolutions of shaft per minute remain
constant.
For small powers the beam is generally omitted— the friction being mea-
sured by weighting a band or strap thrown over the pulley. Ropes or cords
are often used for the same purpose.
Instead of hanging weights in a scale-pan, as in Fig. 167, the friction may be
weighed on a platform-scale; in this
case, the direction of rotation being
the same, the lever-arm will be on the
opposite side of the shaft.
In a modification of this brake, the
brake-wheel is keyed to the shaft,
and its rim is provided with inner
flanges which form an annular trough
for the retention of water to keep the
pulley from heating. A small stream
of water constantly discharges into
tlte trough and revolves with the T?IQ 157
pulley— tr - centrifugal force of the
particles or water overcoming the action of gravity; a waste-pipe with its
end flattened is so placed in the trough that it acts as a scoop, and removes
all surplus water. The brake consists of a flexible strap to which are fitted
blocks of wood forming the rubbing-surface; the ends of the strap are con-
nected by an adjustable bolt-clamp, by means of which any desired tension
may be obtained.
The horse -power or work of the shaft is determined from the following:
Let W = work of shaft, equals power absorbed, per minute;
P = unbalanced pressure or weight in pounds, acting on lever-arm
at distance £,;
L = length of lever-arm in feet from centre of shaft;
V = velocity of a point in feet per minute at distance L, if arm were
allowed to rotate at the speed of the shaft;
N = number of revolutions per minute;
H.P. = horse-power.
Then will W - PV - ZnLNP.
Since H.P. = PV -*- 33,000, we have H.P. = ZirLNP -4- 33,000.
If L = —, we obtain H.P. = ££-. 33 -*-2»r is practically 5 ft. 3 in., a value
air 1000
often used in practice for the length of arm.
If the rubbing-surface be too small, the resulting friction will show great
irregularity— probably on account of insufficient lubrication— the jaws be-
<ng allowed to seize the pulley, thus producing shocks and sudden vibra-
tions of the lever-arm.
Soft woods, such as bass, plane-tree, beech, poplar, or maple are all to be
preferred to the harder woods for brake-blocks. The rubbing-surface should
be well lubricated with a heavy grease.
The Aide ii Absorption-dynamometer. (G. I. Alden, Trans.
A. S. M. E., vol. xi. 958; also xii, 700 and xiii. 429.)— This dynamometer is a
friction-brake, which is capable in quite moderate sizes of absorbing large
powers with unusual steadiness and complete regulation. A smooth cast-
iron disk is keyed on the rotating shaft. This is enclosed in a cast-iron
shell, formed of two disks and a ring at their circumference, which is free
to revolve on the shaft. To the interior of each of the sides of the shell is
fitted a copper plate, enclosing between itself and the side a water-tight
space. Water under pressure from the city pipes is admitted into each of
these spaces, forcing the copper plate against the central disk. The
chamber enclosing the disk is filled with oil. To the outer shell is fixed a
weighted arm, which resists the tendency of the shell to rotate with the
shaft, caused by the friction of the plates against the central disk. Four
brakes of this type, 56 in. diam., were used in testing the experimental
locomotive at Purdue University (Trans. A. S. M. E., xiii. 429). Each was
designed for a maximum moment of 10,500 foot-pounds with a water-press-
ure of 40 Ibs. per sq. in.
The area in effective contact with the copper plates on either side is rep-
resented by an annular surface having its outer radius equal to 28 inches,
and its inner radius equal to 10 inches. The apparent coefficient of friction
between the plates and the disk was 3}££.
980
DYNAMOMETERS.
W. W. Beaumont (Proc. Inst. C. E. 1889) has deduced a formula by means
of which the relative capacity of brakes can be compared, judging from the
amount of horse-power ascertained by their use.
If W= width of rubbing-surface on brake-wheel in inches; V — vel. of
point on circum. of wheel in feet per minute; K = coefficient; then
K = WV -*- H.P.
Capacity of Friction-brakes.— Prof. Flather obtains the values
of K given in the last column of the subjoined table :
Horse-power.
1
»•£
*u
tf
Brake-
pulley.
Length of Arm.
Design of Brake.
Value of K.
flgj
"1^3
D O
£ ~
Diameter,
in feet.
21
19
20
40
33
150
24
180
475
125 I
250 f
40|
1.25 f
150
148.5
146
180
150
150
142
100
76.2
290 /
250 f
3221
290 C
7
7
10.5
10.5
10
12
24
24
24
13
5
5
5
5
5
9
6
5
7
4
4
33"
33.38"
32.19"
32"
32"
Royal Ag. Soc., compensating
785
858
802
741
749
282
1385
209
84.?
McLaren, compensating
4 4 water-cooled an d comp
Garrett, " "
it 41 it U
Schoenheyder, water-cooled
38.31"
126.1"
191"
63"
27%"
Balk
Gately & Kletsch, water-cooled . ...
Webber, water-cooled
Westinghouse, water-cooled
465
817
44 it
The above calculations for eleven brakes give values of K varying from
84 7 to 1385 for actual horse-powers tested, the average being K = 655.
Instead of assuming an average coefficient, Prof. Flather proposes the
following :
Water-cooled brake, non-compensating, K = 400; W = 400 H.P. -f- V.
Water-cooled brake, compensating, K = 750; W = 750 H.P. -*- V.
Non-cooling brake, with or without compensating device, K = 900;
W - 900 H.P. -*- V.
Transmission Dynamometers are of various forms, as the
Batchelder dynamometer, in which the power is transmitted through a
" train-arm " of bevel gearing, with its modifications, as the one described
by the author in Trans. A. I. M. E., viii. 177, and the one described by
Samuel Webber in Trans. A. S. M. E., x. 514; belt dynamometers, as the
Tatham; the Van Winkle dynamometer, in which the power is transmitted
from a revolving shaft to another in line with it, the two almost touching,
through the medium of coiled springs fastened to arms or disks keyed to
the shafts; the Brackett and the Webb cradle dynamometers, used for
measuring the power required to run dynamo-electric machines. Descrip-
tions of the four last named are given in Flather on Dynamometers.
Much information on various forms of dynamometers will be found in
Trans. A. S. M. E., vol. vii. to xv., inclusive, indexed under Dynamometers
OPERATIONS OF A REFRIGERATIXG-MACHINF . 981
ICE-MAKING OR REFRIGERATING MACHINES.
References.— An elaborate discussion of the therm odynamic theory of
the action of the various fluids used in the production of cold was published by
M. Ledoux in theAnnales des Mines, and translated in Van Nostrand^s Maga-
zine in 1879. This work, revised and additions made in the light of recent ex-
perience by Professors Denton, Jacobus, and Riesenberger, was reprinted in
1892. (Van Nostrand's Science Series, No. 46.) The work is largely mathe-
matical, but it also contains much information of immediate practical value,
from which some of the matter given below is taken. Other references are
Wood's Thermodynamics, Chap. V., and numerous papers by Professors
'Wood, Denton, Jacobus, and Linde in Trans. A. S. M. E., vols. x. toxiv.;
Johnson's Cyclopaedia, article on Refrigerating-machines; also Eng'g, June
18, July 2 and 9, 1886; April 1, 1887; June 15, 1888; July 31, Aug. 28, 1889; Sept.
11 and Dec. 4, 1891 ; May 6 and July 8, 1892. For properties of Ammonia and
Sulphur Dioxide, see papers by Professors Wood and Jacobus, Trans. A. S.
M. E., vols. x. and xii.
For illustrated articles describing refrigerating-machines, see Am. Mack.,
May 29 and June 26, 1890, and Mfrs. Record, Oct. 7, 1892; also catalogues of
builders, as Frick & Co., Waynesboro, Pa. ; De La Vergne Refrigerating-ma-
chine Co., New York; and others.
Operations of a Refrigerating-macliine.— Apparatus designed
for refrigerating is based upon the following series of operations:
Compress a gas or vapor by means of some external force, then relieve it
of its heat so as to diminish its volume; next, cause this compressed gas or
vapor to expand so as to produce mechanical work, and thus lower its tem-
perature. The absorption of heat at this stage by the gas, in resuming its
original condition, constitutes the refrigerating effect of the apparatus.
A re frigerat ing-machine is a heat-engine reversed.
From this similarity between heat-motors and freezing-machines it results
that all the equations deduced from the mechanical theory of heat to deter-
mine the perfoi nance of the first, apply equally to the second.
The efficiency depends upon the difference between the extremes of tem-
perature.
The useful effect of a refrigerating-machine depends upon the ratio
between the heat-units eliminated and the work expended in compressing
and expanding.
This result is independent of the nature of the body employed.
Unlike the heat-motors, the freezing-machine possesses the greatest effi-
ciency when the range of temperature is small, and when the final tempera-
ture is elevated.
If the temperatures are the same, there is no theoretical advantage in em-
ploying a gas rather than a vapor in order to produce cold.
The choice of the intermediate body would be determined by practical
considerations based on the physical characteristics of the body, such as the
greater or less facility for manipulating it, the extreme pressures required
for the best effects, etc.
Air offers the double advantage that it is everywhere obtainable, and that
we can vary at will the higher pressures, independent of the temperature of
the refrigerant. But to produce a given useful effect the apparatus must
be of larger dimensions than that required by liquefiable vapors.
The maximum pressure is determined by the temperature of the con-
denser and the nature of the volatile liquid: this pressure is often very high.
When a change of volume of a saturated vapor is made under constant
pressure, the temperature remains constant. The addition or subtraction of
heat, which produces the change of volume, is represented by an increase or
a diminution of the quantity of liquid mixed with the vapor.
On the other hand, when vapors, even if saturated, are no longer in con-
tact with their liquids, and receive an addition of heat either through com-
pression by a mechanical force, or from some external source of heat, they
comport themselves nearly in the same way as permanent gases, and be-
come superheated.
It results from this property, that refrigerating-machines using a liquefi-
able gas will afford results differing according to the method of working,
982 ICE-MAKIKG OR REFRIGERATIHG MACHINES.
and depending upon the state of the gas, whether it remains constantly sat-
urated, or is superheated during a part of the cycle of working.
The temperature of the condenser is determined by local conditions. The
interior vvill exceed by 9° to 18° the temperature of the water furnished to
the exterior. This latter will vary from about 52° F., the temperature of
water from considerable depth below the surface, to about 95° F., the tem-
perature of surface-water in hot climates. The volatile liquid employed in
the machine ought not at this temperature to have a tension above that
which can be readily managed by the apparatus.
On the other hand, if the tension of the gas at the minimum temperature
is too low, it becomes necessary to give to the compression-cylinder large
dimensions, in order that the weight of vapor compressed by a single stroke
of the piston shall be sufficient to produce a notably useful effect.
These two conditions, to which may be added others, such as those de-
pending upon the greater or less facility of obtaining the liquid, upon the
dangers incurred in its use, either from its inflammability or unhealthful-
ness, and finally upon its action upon the metals, limit the choice to a smalK
number of substances.
The gases or vapors generally available are: sulphuric ether, sulphurous
oxide, ammonia, methylic ether, and carbonic acid.
The following table, derived from Regnault, shows the tensions of the
vapors of these substances at different temperatures between — 22° and 4-
104°.
Pressures and Boiling-points of Liquids available for
Use in Refrigerating-machines.
Temp, of
Ebullition.
Tension of Vapor, in Ibs. per sq. in., above Zero.
Deg.
Fahr.
Sul-
phuric
Ether.
Sulphur
Dioxide.
Ammonia.
Methylic
Ether.
Carbonic
Acid.
Pictet
Fluid.
— 40
10 22
— 31
13 23
-22
5 56
16.95
11 15
- 13
7 23
21 51
13 85
251 6
- 4
1.30
9.27
27.04
17.06
292.9
13.5
5
1.70
11.76
33.67
20.84
340.1
16.2
14
2.19
14.75
41.58
25.27
393.4
19.3
S3 .
2.79
18.31
50.91
30.41
453.4
?2.9
32
3.55
22.53
61.85
36.34
520.4
26.9
41
4.45
27.48
74.55
43.13
594.8
31.2
50
5.54
33.26
89.21
50.84
676.9
36.2
59
6.84
39.93
105.99
59 56
766.9
41.7
68
8.38
47.62
125.08
69.35
864.9
48.1
77
10.19
56.39
146.64
80.28
971.1
55.6
86
12.31
66.37
170.83
92.41
1085.6
64 J.
95
14 76
77 64
197 83
1207 9
73 2
104
17.59
90.32
227.76
1338.2
82.9
The table shows that the use of ether does not readily lead to the produc-
tion of low temperatures, because its pressure becomes then very feeble.
Ammonia, on the contrary, is well adapted to the production of low tem-
peratures.
Methylic ether yields low temperatures without attaining too great pres-
sures at the temperature of the condenser. Sulphur dioxide readily affords
temperatures of — 14 to — 5, while its pressure is only 3 to 4 atmospheres
at the ordinary temperature of the condenser. These latter substances then
lend themselves conveniently for the production of cold by means of
mechanical force.
The "Pictet fluid" is a mixture of 97# sulphur dioxide and Sf* carbonic
acid. At atmospheric pressure it affords a temperature 14° lower than
sulphur dioxide.
Carbonic acid is as yet (1895) in use but to a limited extent, but the rela-
tively greater compactness of compressor that it requires, and its inoffensive
THE AMMOKIA ABSOKPTION-MACHIKE. 983
character, are leading to its recommendation for service on shipboard, where
economy of space is important.
Certain ammonia plants are operated with a surplus of liquid present dur-
ing compression, so that superheating is prevented. This practice is known
as the "cold system " of compression.
Nothing definite is known regarding the application of methylic ether or
of the petroleum product chymogene in practical refrigerating service. The
inflammability of the latter and the cumbrousness of the compressor
required are objections to its use.
" Ice-melting Effect."— It is agreed that the term "ice-melting
effect" means the cold produced in an insulated bath of brine, on the as-
sumption that each 142.2 B.T.U.* represents one pound of ice, this being the
latent heat of fusion of ice, or the heat required to melt a pound of ice at
32° to water at the same temperature.
The performance of a machine, expressed in pounds or tons of " ice-melt-
ing capacity," does not mean that the refrigerating-machine would make
the same amount of actual ice, but that the cold produced is equivalent to
the effect of the melting of ice at 32° to water of the same temperature.
In making artificial ice the water frozen is generally about 70° F. when sub-
mitte'd to the refrigerating effect of a machine ; second, the ice is chilled from
]-2° to 20° below its freezing-point; third, there is a dissipation of cold, from
the exposure of the brine tank and the manipulation of the ice-cans: there-
fore the weight of actual ice made, multiplied by its latent heat of fusion,
142.2 thermal units, represents only about three fourths of the cold produced
in the brine by the refrigerating fluid per I.H.P. of the engine driving the
compressing-pumps. Again, there is considerable fuel consumed to operate
the brine-circulating pump, the condensing-water and feed-pumps, and to
reboil, or purify, the condensed steam from which the ice is frozen. This
fuel, together with that wasted in leakage and drip water, amounts to about
one half that required to drive the main steam-engine. Hence the pounds
of actual ice manufactured from distilled water is just about half the equiv-
alent of the refrigerating effect produced in the brine per indicated horse-
power of the steam-cylinders.
When ice is made directly from natural water by means of the " plate
system," about half of the fuel, used with distilled water, is saved by avoid-
ing the rebelling, and using steam expansively in a compound engine.
Ether-machines, used in India, are said to have produced about 6
Ibs. of actual ice per pound of fuel consumed.
The ether machine is obsolete, because the density of the vapor of ether,
at the necessary working-pressure, requires that the compressing-cylinder
shall be about 6 times larger than for sulphur dioxide, and 17 times largev
than for ammonia.
Air-machines require about 1.2 times greater capacity of compiess-
ing cylinder, and are, as a whole, more cumbersome than ether machines,
but they remain in use on ship-board. In using air the expansion must take
place in a cj7linder doing work, instead of through a simple expansion-cock
which is used with vapor machines. The work done in the expansion-cylin-
der is utilized in assisting the compressor.
Ammonia Compression -machines.— "Cold " vs. "Dry "Systems
of Compression. — In the "cold" system or "humid" system some of the
ammonia entering the compression-cylinder is liquid, so that the heat de-
veloped in the cylinder is absorbed by the liquid and the temperature of the
ammonia thereby confined to the boiling-point due to the condenser-pres-
sure. No jacket is therefore required about the cylinder.
In the " dry M or u hot" system all ammonia entering the compressor is
gaseous, and the temperature becomes by compression several hundred de-
grees greater than the boiling-point due to the condenser-pressure. A water-
jacket is therefore necessary to permit the cylinder to be properly lubri-
cated.
Relative Performance of Ammonia Compression- and
Absorption-machines, assuming no Water to be fin-
trained with the A in in o ii i a -» us in the Condenser. (Denton
and Jacobus, Trans. A. S. M. E., xiii.) — It is assumed in the calculation for
both machines that 1 Ib. of coal imparts 10,000 B.T.U. to the boiler. The
* The latent heat of fusion of ice is 144 thermal units (Phil. Mag., 1871,
xli., 182); but it is customary to use H2. (Prof, Wood. Trans, A, S. M, E,,
984 ICE-MAKITCG OR REFRIGERATING MACHINES.
condensed steam from the generator of the absorption-machine is assumed
to be returned to the boiler at the temperature of the steam entering the
generator. The engine of the compression-machine is assumed to exhaust
through a feed-water heater that heats the feed-water to 212° F. The engine
is assumed to consume 26J4 Ibs. of water per hour per horse-power. The
figures for the compression- machine include the effect of friction, which is
taken at 15% of the net work of compression.
Condenser.
Refrigerat-
ing Coils.
Pounds of Ice-melting Effect
per Ib. of Coal.
O D
O i—!
ft
I
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Compress.
Machine.
Absorption-
machine.*
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969
59.0
106.0
5
33.7
59.0
39.8
74.6
38.3
33.9
967
59.0
106.0
5
33.7
130.0
39.8
74.6
39.8
35.1
931
59.0
106.0
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16.9
59.0
23.4
43.9
36.3
31.5
1000
86.0
170.8
5
33.7
86.0
25.0
46.9
35.4
28.6
988
86.0
170.8
5
33.7
130.0
25.0
46.9
36.2
29.2
966
86.0
170.8
-22
16.9
86.0
16.5
30.8
33.3
26.5
1025
86.0
170.8
-22
16.9
130.0
16.5
30.8
34.1
27.0
1002
104 0
227.7
5
33.7
104.0
19.6
36.8
33.4
25.1
1002
104.0
227 7
-22
16.9
101.0
13.5
25.3
31.4
23.4
1041
Tlie Ammonia Absorption-machine comprises a generator
which contains a concentrated solution of ammonia in water; this gener-
ator is heated either directly by a fire, or indirectly by pipes leading from a
steam-boiler. The condenser communicates with the upper part of the gen-
erator by a tube; it is cooled externally by a current of cold water. The
cooler or brine-tank is so constructed as to utilize the cold produced; the up-
per part of it is in communication with the lower part of the condenser.
An absorption-chamber is filled with a weak solution of ammonia; a tube
puts this chamber in communication with the cooling-tank.
The absorption-chamber communicates with the boiler by two tubes: one
leads from the bottom of the generator to the top of the chamber, the other
leads from the bottom of the chamber to the top of the generator. Upon
the latter is mounted a pump, to force the liquid from the absorption -cham-
ber, where the pressure is maintained at about one atmosphere, into the gen-
erator, where the pressure is from 8 to 12 atmospheres.
To work the apparatus the ammonia solution in the generator is first
heated. This releases the gas from the solution, and the pressure rises.
When it reaches the tension of the saturated gas at the temperature of the
condenser there is a liquefaction of the gas, and also of a small amount of
steam. By means of a cock the flow of the liquefied gas into the refrigerat-
ing-coils contained in the cooler is regulated. It is here vaporized by ab-
sorbing the heat from the substance placed there to be cooled. As fast as it
is vaporized it is absorbed by the weak solution in the absorbing-chamber.
Under the influence of the heat in the boiler the solution is unequally sat-
urated, the stronger solution being uppermost.
The weaker portion is conveyed by the pipe entering the top of the absorb-
ing-chamber, the flow being regulated by a cock, while the pump sends an
equal quantity of strong solution from the chamber back to the boiler.
* 5# of water entrained in the ammonia will lower the economy of the ab-
sorption-machine about 15$ to 20$ below the figures given in the table.
SULPHUR-DIOXIDE MACHINES.
985
The working of the apparatus depends upon the adjustment and regula-
tion of the flow of the gas and liquid; by these means the pressure is varied,
and consequently the temperature in the cooler may be controlled.
The working is similar to that of compression-machines. The absorption-
chamber fills the office of aspirator, and the generator plays the part of
compressor.
The mechanical force producing exhaustion is here replaced by the affinity
of water for ammonia gas; and the mechanical force required for compres-
sion is replaced by the heat which severs this affinity and sets the gas at
liberty.
(For discussion of the efficiency of the absorption system, see Ledoux's
work; paper by Prof. Linde, and discussion on the same by Prof. Jacobus,
Trans. A. S. M. E., xiv. 1416, 1436; and papers by Denton and Jacobus,
Trans. A. S. M. E. x. 792; xiii. 507.
Sulphur-Dioxide Machines.— Results of theoretical calculations
are given in a table by Ledoux showing an ice-melting capacity per
hour per "
ranging
pressure of the vapor
retical results do not represent the actual. It is necessary to take into ac-
count the loss occasioned by the pipes, the waste spaces in the cylinder, loss
of time in opening of the valves, the leakage around the piston and valves,
the reheating by the external air, and finally, when the ice is being made,
the quantity of the ice melted in removing the blocks from their moulds.
Manufacturers estimate that practically the sulphur-dioxide apparatus using
water at 55° or 60° F. produces 56 Ibs. of ice, or about 10,000 heat-units, per
hour per horse-power, measured on the driving-shaft, which is about 5Sj2 of
the theoretical useful effect. In the commercial manufacture of ice about
7 Ibs. are produced per pound of coal. This includes the fuel used for re-
boiling the water, which, together with that wasted by the pumps and lost
by radiation, amounts to a considerable portion of that used by the engine.
Prof. Denton says concerning Ledoux's theoretical results: The figures
given are higher than those obtained in practice, because the effect of
superheating of the gas during admission to the cylinder is not considered.
This superheating may cause an increase of work of about 25$. There are
other losses due to superheating the gas at the brine-tank, and in the pipe
leading from the brine-tank to the compressor, so that in actual practice a
sulphur-dioxide machine, working under the conditions of an absolute
pressure in the condenser of 56 Ibs. per sq. in. and the corresponding tem-
perature of 77° F., will give about 22 Ibs. of ice-melting capacity per pound
of coal, which is about 60$ of the theoretical amount neglecting friction, or
70$ including friction. The following tests, selected from those made by
Prof. Schroter on a Pictet ice-machine having a compression-cylinder 11.3
in. bore and 24.4 in. stroke, show the relation between the theoretical and
actual ice-melting capacity.
No. of
Test.
Temp, in degrees Fahr.
corresponding to
pressure of vapor.
Ice-melting capacity per pound of coal,
assuming 3 Ibs. per hour per H.P.
Condenser.
Suction.
Theoretical
friction
included.*
Actual.
Per cent loss due to
cylinder sup er-
h eating, or differ-
ence between
cols. 4 and 5.
11
12
13
14
77.3
76.2
75.2
80.6
28.5
14.4
-2.5
-15.9
41.3
31.2
23.0
16.6
33.1
24.1
17.5
10.1
19.9
22.8
23.9
39.2
Tlie Refrigerating Coils of a Pictet ice-machine described by
Ledoux had 79 sq. ft. of surface for each 100,000 theoretic negative heat-units
produced per hour. The temperature corresponding to the pressure of the
dioxide in the coils is 10.4° F., and that of the bath (calcium chloride solu-
tion) in which they were immersed is 19.4°.
* Friction taken at figure observed in the test, which ranged from 23# to
26# of the work of the steam-cylinder.
986 ICE-MAKING OR REFKIGERATING MACHIKES.
Ammonia Compression-machines.— Ammonia gas possesses the advantage or affording about three times the useful
effect of sulphur dioxide for the same volume described by the piston.
The perfection of ammonia apparatus now renders it so convenient and reliable that no practical advantaf 3 results from the
lower pressures afforded by sulphur dioxide.
The results of the calculations for ammonia are given in the table below :
PERFORMANCE OF AMMONIA COMPRESSION-MACHINES.
Gas superheated during compression as in ordinary practice. Temperature of condenser, 64.4° Fahr. Pressure in condenser,
117.44 Ibs per sq. in. (Ledoux.)
BJ
1
ooo
The theoretical results for ammonia are higher than the actual, for the same reasons that have been stated for sulphur dioxide.
In the case of ammonia the action of the cvlinder-walls in superheating the entering vapor has been determined experimentally by
Prof. Denton, and the amount found to agree with that indicated by theory. In these experiments the ammonia circulated m a
75-ton refrigerating machine was measured directly by means of a special meter, so that in addition to determining the effect or
superheating, the latent heats can be calculated at the suction and condenser pressure.
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AMMONIA COMPRESSIOH-MACHINES.
987
988 ICE-MAKIHG OR REFtUGEKATIKG MACHINES.
The following is a comparison of the theoretical ice-melting capacity of an
ammonia compression machine with that obtained in some of Prof.
Schroter's tests on a Linde machine having a compression-cylinder 9.9 in.
bore and 16.5 in. stroke, and also in tests by Prof. Den ton on a machine
having two single-acting compression cylinders 12 in. X 30 in.:
No.
Temp, in Degrees F.
Corresponding to
Pressure of Vapor.
Ice-melting Capacity per Ib. of Coal,
assuming 3 Ibs per hour per
Horse-power.
of
Test.
Condenser.
Suction.
Theoretical,
Friction * in-
cluded.
Actual.
Per Cent
of Loss Due to
Cylinder
Superheating.
& r i
72.3
26.6
50.4
40.6
19.4
1 j 2
70.5
14.3
37.6
80.0
20.2
1 • 3
69.2
0.5
29.4
22.0
25.2
£ 1 4
68.5
-11.8
22.8
16.1
29.4
o (24
84.2
15.0
27.4
24.2
11.7
"3 < 26
82.7
- 3.2
21.6
17.5
19.0
0 (25
84.6
-10.8
18.8
14.5
2-2.9
Refrigerating Machines using Vapor of Water. (Ledoux.)
— In these machines, sometimes called vacuum machines, water, at ordi-
nary temperatures, is injected into, or placed in connection with, a chamber
in which a strong vacuum is maintained. A portion of the water vaporizes,
the heat to cause the vaporization being supplied from the water not vapor-
ized, so that the latter is chilled or frozen to ice. If brine is used instead of
pure water, its temperature may be reduced below the freezing-point of
water. The water vapor is compressed from, say, a pressure of one tenth
of a pound per square inch to one and one half pounds, and discharged into
a condenser. It is then condensed and removed by means of an ordinary
air-pump. The principle of action of such a machine is the same as that of
volatile-vapor machines.
A theoretical calculation for ice-making, assuming a lower temperature-
of 32° F., a pressure in the condenser of iJJ Ibs. per square inch, and a coal
consumption of 3 Ibs. per I.H.P. per hour, gives an ice-melting effect of 34.5
Ibs. per pound of coal, neglecting friction. Ammonia for ice-making condi-
tions gives 40.9 Ibs. The volume of the compressing cylinder is about 150
times the theoretical volume for an ammonia machine for these conditions.
Relative Efficiency of a Refrigerating Machine.— The effi-
ciency of a refrigerating machine is sometimes expressed as the quotient ef
the quantity of heat received by the ammonia from the brine, that is, the
quantity of useful work done, divided by the heat equivalent of the mechan-
ical work done in the compressor. Thus in column 1 of the table of perform-
ance of the 75-ton machine (page 998) the heat given by the brine to the
ammonia per minute is 14,776 B.T.U. The horse-power of the ammonia cylin-
der is 65.7, and its heat equivalent = 05.7 X 33, 000 -j- 778 = 2786 B.T.U. Then
14. 776 -r- 2786 = 5.304, efficiency. The apparent paradox that the efficiency
is greater than unity, which is impossible in any machine, is thus explained.
The working fluid, as ammonia, receives heat from the brine and rejects
heat into the condenser. (If the compressor is jacketed, a port ion is rejected
into the jacket-water.) The heat rejected into the condenser is greater than
that received from the brine; the difference (plus or minus a small difference
radiated to or from the atmosphere) is heat received by the ammonia from
the compressor. The work to be done by the compressor is not the mechan-
ical equivalent of the refrigeration of the brine, but only that necessary to
supply the difference between the heat rejected by the ammonia into the con-
denser and that received from the brine. If cooling water colder than the
brine were available, the brine might transfer its heat directly into the cool-
ing water, and there would be no need of ammonia or of a compressor; but
* Friction taken at figures observed in the tests, which r_.,jge from 14# to
0# of the work of the steam-cylinder.
EFFICIENCY OF REFKIGEKATIKG-MACHItfES.
eince such cold water is not available, the brine rejects its heat into the
colder ammonia, and then the compressor is required to heat the ammonia
to such a temperature that it may reject heat into the cooling water.
The efficiency of a refrigerating plant referred to the amount of fuel
consumed is
j Pounds circulated per hour ) - . . ..
•< X specific heat X range S-SfJ^Sf'I Suid
of temperature ( c" Bid-
Ice-melting capacity [
per pound of fuel, j
142.2 X pounds of fuel used per hour.
The ice -melting capacity is expressed as follows:
Tons (of 2000 Ibs.)
ice-melting ca-
pacity per 24 hours
I-
( 24 X pounds
•< X specific heat
f X range of temp.
of brine circulated per hour.
142.2 X 2000
The analogy between a heat-engine and a refrigerating-inachine is as fol-
lows: A steam-engine receives heat from the boiler, converts a part of it
into mechanical work in the cylinder, and throws away the difference into
the condenser. The ammonia in a compression refrigerating-machine re-
ceives heat from the brine-tank or cold-room, receives an additional amount
of heat from the mechanical work done in the compression -cylinder, and
throws away the sum into the condenser. The efficiency of the steam-engine
= work done -f- heat received from boiler. The efficiency of the refrigerat-
ing-machine = heat received from the brine-tank or cold-room -5- heat re-
quired to produce the work in the compression-cylinder. In the ammonia
vom vv aier
I i «.
Compressor
209° 239°
"10° 3°
Brine Tank
Condenser
82°
v fil°
Ammonia
Coils
| 1
85°
1*° Inlet
Warm Water from compression. Heat received
Heat rejected from brine
DIAGRAM OF AMMONIA COMPRESSION MACHINE.
' Heat received
from compression.
Jjso-
"Force Pump
DIAGRAM OF AMMONIA ABSORPTION MACHINE.
absorption-apparatus, the ammonia receives heat from the brine-tank and
additional heat from the boiler or generator, and rejects the sum into the
condenser and into the cooling water supplied to the absorber. The effi-
ciency c= heat received from the brine -5- heat received from the boiler.
990 ICE-MAKING OR REFRIGERATING MACHINES.
TEST-TRIALS OF REFRIGERATING-MACHINES.
(G. Linde, Trans. A. S. M. E., xiv. 1414.)
The purpose of the test is to determine the ratio of consumption and pro-
duction, so that there will have to be measured both the refrigerative effect
and the heat (or mechanical work) consumed, also the cooling water. The
refrigerative effect is the product of the number of heat-units (Q) abstracted
To — T
from the body to be cooled, and the quotient — — — ; in which Tc = abso-
lute temperature at which heat is transmitted to the cooling water, and T =
absolute temperature at which heat is taken from the body to be cooled.
The determination of the quantity of cold will be possible with the proper
exactness only when the machine is employed during the test to refrigerate
circulating air, nor from the manufacture of a certain quantity of ice, nor
from a calculation of the fluid circulating within the machine (for instance,
the quantity of ammonia circulated by the compressor). Thus the refrig-
eration of brine will generally form the basis for tests making any pretension
to accuracy. The degree of refrigeration should not be greater than neces-
sary for allowing the range of temperature to be measured with the neces-
sary exactness; a range of temperature of from 5° to o° Fahr. will suffice.
The condenser measurements for cooling water and its temperatures will
be possible with sufficient accuracy only with submerged condensers.
The measurement of the quantity of brine circulated, and of the cooling
water, is usually effected by water-meters inserted into the conduits. If the
necessary precautions are observed, this method is admissible. For quite
precise tests, however, the use of two accurately gauged tanks must be ad
vised, which are alternately filled and emptied.
To measure the temperatures of brine and cooling water at the entrance
and exit of refrigerator and condenser respectively, the employment of
specially constructed and frequently standardized thermometers is indis-
pensable; no less important is the precaution of using at each spot simul-
taneously two thermometers, and of changing the position of one such
thermometer series from inlet to outlet (and vice versa) after the expiration
of one half of the test, in order that possible errors may be compensated.
It is important to determine the specific heat of the brine used in each
instance for its corresponding temperature range, as small differences in the
composition and the concentration may cause considerable variations.
As regards the measurement of consumption , the programme will not have
any special rules in cases where only the measurement of steam and cooling
water is undertaken, as will be mainly the case for trials of absorption-ma-
chines. For compression-machines the steam consumption depends both
on the quality of the steam-engine and on that of the ref rigerating-machine,
while it is evidently desirable to know the consumption of the former sep-
arately from that of the latter. As a rule steam-engine and compressor are
coupled directly together, thus rendering a direct measurement of the power
absorbed by the ref rigerating-machine impossible, and it will have to suffice
to ascertain the indicated work both of steam-engine and compressor. By
further measuring the work for the engine running empty, and by compar-
ing the differences in power between steam-engine and compressor resulting
for wide variations of condenser-pressures, the effective consumption of
work Le for the refrigerating-machine can be found very closely. In gen-
eral, it will suffice to use the indicated work found in the steam-cylinder,
especially as from this observation the expenditure of heat can be directly
determined. Ordinarily the use of the indicated work in the compressor-
cylinder, for purposes of comparison, should be avoided; firstly, because
there are usually certain accessory apparatus to be driven (agitators, etc.),
belonging to the refrigerating-machine proper; and secondly, because the
external friction would be excluded.
Heat Balance. — We possess an important aid for checking the cor-
rectness of the results found in each trial by forming the balance in each
case for the heat received and rejected. Only such tests should be re-
garded as correct beyond doubt which show a sufficient conformity in the
heat balance. It is true thai in certain instances it may not be easy to
account fully for the transmission of heat between the several Darts of the
machine and its environment by radiation and convection, t>-t generally
TEMPERATURE RAHGE. 991
(particularly for compression -machines) it will be possible to obtain for the
heat received and rejected a balance exhibiting small discrepancies only.
Report of Test. — Reports intended to be used for comparison with
the figures found for other machines will therefore have to embrace at least
the following observations :
Refrigerator:
Quantity of brine circulated per hour . .
Brine temperature at inlet to refrigerator
Brine temperature at outlet of refrigerator t
Specific gravity of brine (at 64° Fahr.)
Specific heat of brine
Heat abstracted (cold produced) Qe
Absolute pressure in the refrigerator
Condenser :
Quantity of cooling water per hour ...
Temperature at inlet to condenser
Temperature at outlet of condenser t
Heat abstracted Qt
Absolute pressure in the condenser
Temperature of gases entering the condenser
ABSORPTI ON - MACHINE.
Still :
Steam consumed per hour
Abs. pressure of heating steam.
Temperature of condensed
steam at outlet
Heat imparted to still Q'e
Absorber :
Quantity of cooling water per
hour
Temperature at inlet
Temperature at outlet
Heat removed
Pump for Ammonia Liquor:
Indicated work of steam-engine
Steam-consumption for pump..
Thermal equivalent for work of
COMPRESSION-MACHINE.
Compressor :
Indicated work Lt
Temperature of gases at inlet..
Temperature of gases at exit. .
Steam-engine :
Feed- water per hour
Temperature of feed-water
Absolute steam-pressure before
steam-engine
Indicated work of steam-engine
Le
Condensing water per hour
Temperature of da
Total sum of losses by radiation
and convection ± Q9
Heat Balance ;
Qe + ALc = Ql ± Q9.
pump ALp
Total sum of losses by radiation
and convection ± Q3
Heat Balance :
Qe+Q'e = Q, + Q9 ± Q3.
For the calculation of efficiency and for comparison of various tests, the
actual efficiencies must be compared with the theoretical maximum of effi-
/ Q \ T
ciency \^rf-) max. = — — corresponding to the temperature range.
Temperature Range. — As temperatures (T and Tc) at which the
heat is abstracted in the refrigerator and imparted to the condenser,it is cor
rect to select the temperature of the brine leaving the refrigerator and thai
of the cooling water leaving the condenser, because it is in principle impos-
sible to keep the refrigerator pressure higher than would correspond to the
lowest brine temperature, or to reduce the condenser pressure below that
corresponding to the outlet temperature of the cooling water.
Prof. Linde shows that the maximum theoretical efficiency of a com-
pression-machine may be expressed by the formula
Q T
AL ~ Tc- T1
in which Q = quantity of heat abstracted (cold produced);
AL = thermal equivalent of the mechanical work expended;
L = the mechanical work, and A = 1 -*- 778;
T = absolute temperature of heat abstraction (refrigerator) ;
To = " *' " rejection (condenser).
If u = ratio between the heat equivalent of the mechanical work AL, and
the quantity of heat Q' which must be imparted to the motor to produce
the work Z/, then
992 ICE-MAKING OR REFRIGERATING MACHINES.
AL
Q'
Tc-T
It follows that the expenditure of heat Q' necessary for the production of
the quantity of cold Q in a compression -machine will be the smaller, the
smaller the difference of temperature Tc — T.
Uletering tlte Ammonia, — For a complete test of an ammonia re-
frigerating-machine it is advisable to measure the quantity of ammonia cir-
culated, as was done in the test of the 75-ton machine described by Prof.
Denton. (Trans. A. S. M. E., xii. 326.)
PROPERTIES OF SULPHUR DIOXIDE AND
AMMONIA OAS.
Ledoux's Table for Saturated Sulphur-dioxide Gas.
Heat-units expressed in B.T.U. per pound of sulphur dioxide.
V 0
1
ta &i
1 fa.
0 g
*$
si, ,
S O
>§ .
s-S&I
Hiss
3!>ni
Jf
•^H^*
t2"Ss
"^fl-
'oii^ ^
H*-
d>— ' .1~1
wjf*
o|gw
'•*•' o *•
S^|l
««*
£3 •*-=>
£££•-§ s
^o§J!
5o.S
III/"
lo>|
gg8
II
ill
E S
35
fit8
aSC^
§
•j
H
W
S
tiT
a
i— i
q
Q
Deg. F.
Lbs.
B.T.U.
B.T.U.
B.T.U.
B.T.U.
B.T.U.
Cu. ft.
Lbs.
-22
5.56
157.43
-19.56
176.99
13.59
163.39
13.17
.076
-13
7.23
158.64
—16.30
174.95
13.83
161.12
10.27
.097
- 4
9.27
159.84
-13.05
172.89
14.05
15&84
8.12
.123
5
11.76
161.03
- 9.79
170.82
14.26
156.56
6.50
.153
14
14.74
162.20
- 6.53
168.73
14.46
154.27
5.25
.190
23
18.31
163.36
- 3.27
166.63
14.66
151.97
4.29
.232
32
22.53
164.51
0.00
164.51
14.84
149.68
3.54
.282
41
27.48
165.65
3.27
162.38
15.01
147.37
2.93
.340
50
33.25
166.78
6.55
160.23
15.17
145.06
2.45
.407
59
39.93
167.90
9.83
158.07
15.32
142.75
2.07
.483
68
47.61
168.99
13.11
155.89
15.46
140.43
1.75
.570
77
56.39 "
170.09
16.39
153.70
15.59
138.11
1.49
.669
86
66.36
171.17
19.69
151.49
15.71
135.78
1.27
.780
95
77.64
172.24
22.98
149.26
15.82
133.45
1.09
.906
104
90.31
173.30
26.28
147.02
15.91
131.11
91
1.046
Density of Liquid Ammonia. (D'Andreff, Trans. A. S. M. EM
x. 641.)
At temperature C -10 -5 0 5 10 15 20
F +14 23 32 41 50 59 68
Density 6492 .6429 .6364 .6298 .6230 .6160 .6089
These may be expressed very nearly by
8 = 0.6364 - 0.0014<° Centigrade;
8 = 0.6502 - 0.000777T0 Fahr.
Latent Heat of E vat oration of Ammonia. (Wood, Trans,
A.. S. M. E., x. 641.)
Tie = 555.5 - 0.613^ - 0.000219T2 (in B.T.U., Fahr. deg.);
Ledoux found he = 583.33 - 0.5499T - 0.00011732^.
For experimental values at different temperatures determined by Prof.
Denton, see Trans. A. S. M. E., xii. 356. For calculated values, see
vol. x. 646.
Density of Ammonia Gas.— Theoretical, 0.5894; experimental,
0.596. Renault (Trans. A. S. 31. E., x. 633).
Specific Bleat of Liquid Ammonia. (Wood, Trans. A. S. M. E ,
x 645 )— The specific heat is nearly constant at different temperatures, and
about equal to that of water, or unity. From 0° to 100° F., it is
c — 1.096 - .001221, nearly.
In a later paper by Prof. Wood (Trans. A.S. M. E., xii. 136) he gives a higher
value, viz. , c ~ 1 . 12136 -f 0 . 000438T,
PROPERTIES OF AMMONIA VAPOR.
993
i. A. Elleau and Wm. D. Ennis (Jour. Franklin Inst., April, 1898) give the
sults of nine determinations, made between 0° and 20° C., which range
LiUaeKing ana oiun (sun. uvui. octe/tce, ui, «u, *wj uutaiiieu v.uuv. _. —
Wood deduced from thermodynamic equations c = 1.093 at — 34° F. or
- 38° C., and Ledoux in like manner finds c = 1.0058 -f- .0036582° C. Elleau
and Ennis give Ledoux's equation with a new constant derived from their
experiments, thus c = 0.9834 -f- 0.0036582° C.
Properties of the Saturated Vapor of Ammonia.
(Wood's Thermodynamics.)
emperature.
Pressure,
Absolute.
Heat of
Vaporiza-
tion, ther-
mal units.
Volume
of Vapor
per lb.,
cu. ft.
Volume
of Liquid
perlb.,
cu. ft.
Weight
of a cu.
ft. of
Vapor.
Ibs.
»egs.
Abso-
lute, F.
Lbs.per
sq. ft.
Lbs.per
sq. in.
- 40
420.66
1540.7
10.69
579.67
24.372
.0234
.0410
- 35
425.66
1773.6
12.31
576.69
21.319
.0236
.0468
- 30
430.66
2035.8
14.13
573.69
18.697
.0237
.0535
- 25
435.66
2329.5
16.17
570.68
16.445
.0238
.0608
- 20
440.66
2657.5
18.45
567.67
14.507
.0240
.0689
- 15
445.66
3022.5
20.99
564.64
12.834
.0242
.0779
- 10
450.66
3428.0
23.80
561.61
11.384
.0243
.0878
- 5
455.66
3877.2
26.93
558.56
10.125
.0244
.0988
0
460.66
4373.5
30.37
555.50
9.027
.0246
.1108
h 5
465.66
4920.5
34.17
552.43
8.069
.0247
.1239
- 10
470.66
5522.2
38.34
549.35
7.229
.0249
.1383
- 15
475.66
6182.4
42.93
546.26
6.492
.0250
.1544
- 20
480.66
6905.3
47.95
543.15
5.842
.0252
.1712
- 25
485.66
7695.2
53.43
540.03
5.269
.0253
.1898
- 30
490.66
8556.6
59.41
536.92
4.763
.0254
.2100
- 35
495.66
9493.9
65.93
533.78
4.313
.0256
.2319
- 40
500.66
10512
73.00
530.63
3.914
.0257
.2555
- 45
505.66
11616
80.66
527.47
3.559
.0259
.2809
- 50
510.66
12811
88.96
524.30
3.242
.0261
.3085
- 55
515.66
14102
97. y3
521.12
2.958
.0263
.3381
- 60
520.66
15494
107.60
517.93
2.704
.0265
.3698
- 65
525.66
16993
118.03
514.73
2.476
.0266
.4039
- TO
530.66
18605
129.21
511.52
2.271
.0268
.4403
- 75
535.66
20336
141.25
508.29
2.087
.0270
.4793
- 80
540.66
22192
154.11
505.05
.920
.0272
.5208
- 85
545.66
24178
167.86
501.81
.770
.0273
.5650
- 90
550.66
26300
18.2.8
498.11
.632
.0274
.6128
- 95
555.66
28565
198.37
495.29
.510
.0277
.6623
-100
560.66
3098C
215.14
492.01
.398
.0279
.7153
-105
565. r)6
33550
232.98
488.72
.296
.0281
.7716
-no
570.66
36284
251.97
485.42
.203
.0283
.8312
-115
575.66
39188
272.14
482.41
.119
.0285
.8937
-120
580.66
42267
293.49
478.79
.045
.0287
.9569
-126
585.66
45528
316.16
475.45
0.970
.0289
1.0309
- 150
590.66
48978
340.42
472.11
0.905
.0291
1.1049
-135
595.66
52626
365.16
468.75
0.845
.0293
1.1834
-140
€00.66
56483
392 22
465.39
0.791
.0295
1.2642
-145
605.66
60550
420.49
462.01
0.741
.0297
1.3495
- 150
610.66
64833
450.20
458.62
0.695
.0299
1.4388
-155
615.66
69341
481.54
455.22
0.652
.0302
1.5337.
-160
e-.'o.ee
74086
514.40
451.81
0.613
.0304
1.6343
-165
625.66
79071
549.04
448.39
0.577
.0306
1.7333
Specific Heat of Ammonia Vapor at the Saturation
Point. (Wood, Trans. A. S. M.'E., x. 644.)— For the range of temperatures
ordinarily used in engineering practice, the specific heat of saturated am-
monia is negative, and the saturated vapor will condense with adiabatic ex-
pansion, and the liquid will evaporate with the compression of the vapor,
and when all is vaporized will superheat.
Regnault (Rel. des. Exp., ii. 162) gives for specific heat of ammonia-gas
0.50836. (Wood, Trans. A. S. M. E., xii. 133.)
994 ICE-MAKIHG OR REFRIGERATING MACHINES.
Properties of Brine used to absorb Refrigerating Effect
of Ammonia* (J. E. Denton, Trans. A. S. M. E., x. 799.)— A solution of
Liverpool salt in well-water having a specific gravity of 1.17, or a weight
per cubic foot of 73 Ibs., will not sensibly thicken or congeal at 0° Fahren^
heit.
The mean specific heat between 39° and 16° Fahr. was found by Denton to
be 0.805. Brine of the same specific gravity has a specific heat of 0.805 at
65° Fahr., according to Naumann.
Naumann's values are as follows (Lehr- und Handbuch der Thermochemie,
1882):
Specific heat 791 .805* .863 .895 .931 .962 .978
Specific gravity. 1.187 1.170 1.103 1.072 1.044 1.023 1.012
* Interpolated.
Chloride-of-calcium solution has been used instead of brine. Ac-
cording to Naumann , a solution of 1.0255 sp. gr. has a specific heat of .957.
A solution of 1.163 sp. gr. in the test reported in Eng'g, July 22, 1887, gave a
specific heat of .827.
ACTUAL PERFORMANCES OF ICE-MAKING
MACHINES.
The table given on page 996 is abridged from Denton, Jacobus, and Riesen-
berger's translation of Ledoux on Ice-making Machines. The following
shows the class and size of the machines tested, referred to by letters in the
table, with the names of the authorities:
Class of Machines.
Authority.
Dimensions of Compres-
sion-cylinder in inches.
Bore.
Stroke.
A. Ammonia cold-compression..
B. Pictet fluid dry-compression.
C Bell-Golem an air
Schrpter.
j Renwick &
( Jacobus.
Denton.
9.9
11.3
28.0
10.
12.0
16.5
24.4
23.8
18.0
30.0
E. Ammonia dry-compression . .
F. Ammonia absorption
Performance of a 75-ton Ammonia Compression-
machine. (J. E. Denton, Trans. A. S. M. E., xii, 326.)— The machine had
two single-acting compression cylinders 12" X 30", and one Corliss steam -
cylinder, double-acting, 18" X 36". It was rated by the manufacturers as a
50-ton machine, but it showed 75 tons of ice-refrigerating effect per 24 hours
during the test.
The most probable figures of performance in eight trials are as follows :
Ammonia
Brine
a^
^-Sg
^|S
'S'o.i
6
cS
3
Pressures,
Ibs. above
Tempera-
tures,
£||
%^*
-co^ ^
9 .87.
2^ §30
o w
3-24
1
H
Atmosphere.
Degrees F.
>»&>*3
>>i*+^ <DO_,
o « co e£-
8a?§>;
^ ^^^
CM
T ^vSZ"
o .
1
Con-
densing
Suc-
tion.
Inlet.
Outlet.
0
Ilill
W
v o-g u §
|§£8,&
P;
o«|i
|*Si
.2.2
1
151
28
36.76
28.86
70.3
22.60
0.80
.0
1.0
8
161
27.5
36.36
28.45
70.1
22.27
1.09
.0
1.0
7
147
13.0
14.29
2.29
42.0
16.27
0.83
.70
1.6Q
4
152
8.2
6.27
2 .03
36.43
14.10
1.1
.93
1.92
6
105
7.6
6.40
-2.22
37.20
17.00
2.00
.91
1.88
2
135
15.7
4.62
3.22
27.2
13.20
1.25
2.59
2 57
The principal results in four tests are given in the table on page 998. The
fuel economy under different conditions of operation is shown in the fol-
lowing table :
PERFORMANCES Otf ICE-MAKING MACHINES. 995
v-i u* _i *- Condensing Press-
gggg ure, Ibs.
Sue tion -pressure,
Ibs.
Pounds of Ice-melting Effect with
Engines—
B.T.U. per Ib. of Steam
with Engines—
Non-con-
densing.
Non-com-
pound Con-
densing.
Compound
Con-
densing.
Non-condens-
ing.
Condensing.
1
66
640
366
923
591
|
gg
i
ii
Il
I'l
28
7
28
7
24
14
34.5
22
2.90
1.69
4.16
2.65
30
17.5
43
27.5
3.61
2.11
5.18
3.31
37.5
21.5
54
34.5
4.51
2.58
6.50
4.16
393
240
591
376
513
300
725
470
The non -condensing engine is assumed to require 25 Ibs. of steam per
horse-power per hour, the non-compound condensing 20 Ibs., and the com-
densing 16 Ibs., and the boiler efficiency is assumed at 8.3 Ibs. of water per
Ib. coal under working conditions. The following conclusions were derived
from the investigation :
1. The capacity of the machine is proportional, almost entirely, to the
weight of ammonia circulated. This weight depends on the suction-
pressure and the displacement of the compressor-pumps. The practical
suction-pressures range from 7 Ibs. above the atmosphere, with which a
temperature of 0° F. can be produced, to 28 Ibs. above the atmosphere, with
which the temperatures of refrigeration are confined to about 28° F. At the
lo>ver pressure only about one half as much weight of ammonia can be cir-
culated as at the upper pressure, the proportion being about in accordance
with the ratios of the absolute pressures, 22 and 42 Ibs. respectively. For each
cubic foot of piston-displacement per minute a capacity of about one sixth
of a ton of " refrigerating effect " per 24 hours can be produced at the lower
pressure, and of about one third of a ton at the upper pressure. No other
elements practically affect the capacity of a machine, provided the cooling-
surface in the brine-tank or other space to be cooled is equal to about
36 sq. ft. per ton of capacity at 28 Ibs. back pressure. For example, a differ-
ence of 100% in the rate of circulation of brine, while producing a propor-
tional difference in the range of temperature of the latter, made no practical
difference in capacity.
The brine-tank was 10J^ X 13 X 10% ft., and contained 8000 lineal feet of
1-in. pipe as cooling-surface. The condensing-tank was 12 X 10 X 10ft., and
contained 5000 lineal feet of 1-in. pipe as cooling-surface.
2. The economy in coal-consumption depends mainly upon both the suc-
tion-pressures and condensing-pressures. Maximum economy, with a given
type of engine, where water must be bought at average city prices, is
obtained at 28 Ibs. suction -pressure and about 150 Ibs. condensing-pressure.
Under these conditions, for a non-condensing steam-engine, consuming coal
at the rate of 3 Ibs. per hour per I. H.P. of steam-cylinders, 24 Ibs. of ice-
refrigerating effect are obtained per Ib. of coal consumed. For the same
condensing-pressure, and with 7 Ibs. suction-pressure, which affords tem-
peratures of 0° F., the possible economy falls to about 14 Ibs. of ^ refrigerat-
ing effect " per Ib. of coal consumed. The condensing-pressure is determined
by the amount of condensing-water supplied to liquefy the ammonia in the
condenser. If the latter is about 1 gallon per minute per ton of refrigerating
effect per 24 hours, a condensing-pressure of 150 Ibs. results, if the initial tem-
perature of the water is about 56° F. Twenty-five per cent less water causes
the condensing-pressure to increase to 190 Ibs. The work of compression is
thereby increased about 20#, and the resulting "economy" is reduced to
about 18 Ibs. of " ice effect " per Ib. of coal at 28 Ibs. suction-pressure and
11.5 at 7 Ibs. If, on the other hand, the supply of water is made 3 gallons
per minute, the condensiug-pressure may be confined to about 105 Ibs. The
work of compression is thereby reduced about 25$, and a proportional increase
of economy results. Minor alterations of economy depend on the initial
temperature of the condensing-water and variations of latent heat, but these
are confined within about 5# of the gross result, the main element of control
being the work of compression, as affected by the back pressure and con-
densing-pressure, or both. If the steam-engine supplying the motive power
may use a condenser to secure a vacuum, an increase of economy of 25# is
available over the above figures, making the Ibs. of " ice effect" per Ib. of
996 ICE-MAKING OR REFRIGERATING MACHINES.
coal for 150 Ibs. condensing-pressure and 28 Ibs. suction -pressure 30.0, and
for 7 Ibs. suction-pressure, 17.5. It is, however, impracticable to use a con-
denser in cities where water is bought. The latter must be practically
f ree of cost to be available for this purpose. In this case it may be assumed
that water will also be available for condensing the ammonia to obtain as
low a condensing-pressure as about 100 Ibs., and the economy of the refrig-
erating-machine becomes, for 28 Ibs. back-pressure, 43.0 Ibs. of "ice effect ""
per Ib. of coal, or for 7 Ibs. back-pressure, 27.5 Ibs. of ice effect per lb.
of coal. If a compound condensing-engine can be used with a steam-con-
sumption per hour per horse-power of 16 Ibs. of water, the economy of the
refrigerating-machine may be 25$ higher than the figures last named, mak-
ing for 28 Ibs. back pressure a refrigerating effect of 54.0 Ibs. per lb. of coal,
and for 7 Ibs. back pressure a refrigerating effect of 34.0 Ibs. per lb. of coal.
Actual Performance of Ice-making Machines.
• JU
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185| 55
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44.9
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40.63
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50.3
4
126, 22
68
-12
0
- 5
44.8
15.5
19.5
9.0
16.14
42.9
29.1
44.7
5
200 42
95
14
28
23
45.0
24.1
10.5
16.5
19.07
36.0
28.5
77.0
6
136 60
72
80
44
37
45.2
17.9
10.7
29.8
46.29
28.5
19.9
56.8
7
131
45
71
18
28
28
45.1
18.0
12.1
21.6
83.23
31.3
21 9
56.4
8
126
24
68
- 9
0
- 6
44.7
15.6
18.0
99
17.55
41.1
28.8
46.1
9
117
41
64
13
28
23
45.0
16.4
13.5
20.0
33.77
33 1
22.9
50.6
10
130
60
70
31
43
37
31.7
12.0
14.8
19.5
45.01
35.2
23.8
52.0
11
57
21
77
28
43
37
57.0
21.5
22.925.6
33.07
39.9
22.2
24.1
12
56
15
76
14
28
23
56.8
20.6
22.9
17.9
24.11
41.3
24.0
23.1
13
55
10
75
- 2
14
9
57.1
18.5
24.0
11.6
17.47
42.2
25.2
20.4
14
60
7
81
-16
0
- 6
57.6
15.7
25.7
5.7
10.14
54.5
38.5
16.8
15
91
15
104
14
28
23
59 8
27.2
16.9
15.7
16.05
36.2
23.1
31.5
1Q
61
22
81
31
44
37
57.3
21 6
14.0
28.1
36.19
38.4
22.5
26.8
17
59
16
80
16
28
23
57.5
20.5
12.8
19.3
26.24
34.6
25.0
25.6
18
59
7
79
-16
0
- 6
57.8
15.9
21.1
6.8
11.93
47.5
33.4
18.0
19
54
22
75
31
43
37
35.3
12.4
22.3
17.0
38.04
39.5
22.6
22.6
20
89
16
103
16
28
28
42.9
19.9
14 7
11.9
16.68
37.7
27.0
32.7
21
62
6
82
—17
0
- 5
34.8
9.9
24.3
3.5
9.86
54.2
39.5
17.7
22
59
15
65*
—53*
63 2
83 2
21 9
10.3
3 42
71.7
56.9
26 6
23
175
54
81*
-40*
93.4
88:i
32 .'l
4.9
3.0
80.
63.
89 2
24
166
43
84
15
"37
"28
58 1
85.0
22.7
73.9
24.16
32.8
11.7
65.9
25
167
23
85
-11
6
2
57.7
72.6
18.6
37.9
14.52
37.4
22.7
57.6
26
162
28
83
- 3
14
2
57.9
73.6
19.346.5
17.55
34.9
18.6
59.9
27
176
42
88
14
36
2858.9
88.6
19 774.4
23.31
30.5
13.5
70.5
28
152
40
79
13
21
16|....
....142.2
20.1
47.8
* Temperature of air at entrance and exit of expansion-cylinder.
t On a basis of 3 Ibs. of coal per hour per H.P. of steam -cylinder of com-
pression-machine and an evaporation of 11.1 Ibs. of water per pound of
combustible from and at 212° F. in the absorption-machine.
t Per cent of theoretical with no friction.
§ Loss due to heating during aspiration of gas in the compression-cylinder
and to radiation and superheating at brine-tank.
H Actual, including resistance due to inlet and exit valves.
PERFORMANCES OF ICE-MAKING MACHINES. 997
In class A, a German machine, the ice-melting capacity ranges from 46. 29
to 16.14 Ibs. of ice per pound of coal, according as the suction pressure
varies from about 45 to 8 Ibs. above the atmosphere, this pressure being the
condition which mainly controls the economy of compression-machines.
These results are equivalent to realizing from 72% to f>7# of theoretically per-
fect performances. The higher per cents appear to occur with the higher
suction-pressures, indicating a greater loss from cylinder-heating (a phe-
nomenon the reverse of cylinder condensation in steam-engines), as the
range of the temperature of the gas in the compression-cylinder is
greater.
In E, an American compression-machine, operating on the " dry system,"
the percentage of theoretical effect realized ranges from 69.5$ to 62. 6$.
The friction losses are higher for the American machine. The latter's higher
efficiency may be attributed, therefore, to more perfect displacement.
The largest " ice-melting capacity " in the American machine is 24.16 Ibs.
This corresponds to the highest suction-pressures used in American practice
for such refrigeration as is required in beer-storage cellars using the direct-
expansion system. The conditions most nearly corresponding to American
brewery practice in the German tests are those in line 5, which give an " ice-
melting capacity " of 19.07 Ibs.
For the manufacture of artificial ice, the conditions of practice are those
of lines 3 and 4, and lines 25 and 26. In the former the condensing pressure
used requires more expense for cooling water than is common in American
practice. The ice-melting capacity is therefore greater in the German ma-
chine, being 22.03 and 16.14 Ibs. against 17.55 and 14.52 for the American
apparatus.
CLASS B. Sulphur Dioxide or Pictet Machines. — No records are available
for determination of the "ice-melting capacity" of machines using pure
sulphur dioxide. This fluid is in use in American machines, but in Europe
it has given way to the " Pictet fluid," a mixture of about 97$ of sulphur
dioxide and 3% of carbonic acid. The presence of the carbonic acid affords
a temperature about 14 Fahr. degrees lower than is obtained with pure sul-
phur dioxide at atmospheric pressure. The latent heat of this mixture has
never been determined, but is assumed to be equal to that of pure sulphur
dioxide.
For brewery refrigerating conditions, line 17, we have 26.24 Ibs. "ice-
melting capacity," and for ice-making conditions, line 13, the "ice-melt-
ing capacity" is 17.47 Ibs. These figures are practically as economical
as those for ammonia, the per cent of theoretical effect realized ranging
from 65.4 to 57.8. At extremely low temperatures, —15° Fahr., lines 14 and
18, the per cent realized is as low as 42.5.
C'yliiider-licating. — In compression-machines employing volatile
vapors the principal cause of the difference between the theoretical and the
practical result is the heating of the ammonia, by the warm cylinder walls,
during its entrance into the compressor, thereby expanding it, so that to
compress a pound of ammonia a greater number of revolutions must be
made by the compressing-pumps than corresponds to the density of the
ammonia-gas as it issues from the brine-tank.
Tests of Ammonia Absorption-macliine used in storage-ware-
houses under approaches to the New York and Brooklyn Bridge. (Eng'g,
July 22, 1887.)— The circulated fluid consisted of a solution of chloride of cal-
cium of 1.163 sp. gr. Its specific heat was found to be .827.
The efficiency of the apparatus for 24 hours was found by taking the
product of the cubic feet of brine circulating through the pipes by the aver-
age difference in temperature in the ingoing and outgoing currents, as
observed at frequent intervals by the specific heat of the brine (.827) and its
weight per cubic foot (73.48). The final product, applying all allowances for
corrections from various causes, amounted to 6,218,816 heat-units as the
amount abstracted in 24 hours, equal to the melting of 43,565 Ibs. of ice in
the same time.
The theoretical heating-power of the coal used in 24 hours was 27,000,000
heat-units; hence the efficiency of the apparatus was 23#. This is equivalent
to an ice-melting effect of 16.1 Ibs. per Ib. of coal having a heating value of
10,000 B.T.U. per Ib.
A test of a 35-ton absorption -machine in New Haven, Conn., by Prof.
Denton (Trans. A. S. M. E,, x. 792), gave an ice-melting effect of 20.1 ibs. per
Ib. of coal on a basis of boiler economy equivalent to 3 Ibs. of steam per
l.H.P. in a good non-condensing steam-engine. The ammonia was worked
between 138 and 23 Ibs. pressure above the atmosphere.
998 ICE-MAKING OR REFRIGERATING MACHINES.
Performance of a 75-ton Refrigerating-machtne.
Maximum Capacity and
Economy at 28 Ibs.
Back Pressure.
Maximum Capacity and
Economy at Zero,
Brine, and 8 Ibs.
Back Pressure.
Maximum Capacity and
Economy for Zero,
Brine, 13 Ibs. Back
.Pressure.
Maximum Capacity and
Economy at 27.5 Ibs.
Back Pi'essure.
Av. high ammonia press, above atmos
Av. back ammonia press, above atmos
Av. temperature brine inlet
Av temperature brine outlet
151 Ibs.
28 "
36.76°
28 86°
152 Ibs.
8.2 "
6.27°
2 03°
147 Ibs.
13 "
14.29°
2 29°
161 Ibs.
27.5 >k
*28 45°
Av range of temperature ..
7.9°
4 24°
12.00°
7.91°
Lbs. of brine circulated per minute
Av temp condensing-water at inlet
2281
44.65°
2173
56 65°
943
46.9°
2374
54 00°
Av. temp, condensing-water at outlet
Av. range of temperature
83.66°
39.01°
85.4°
28.75°
85.46°
38.56°
82.86°
28.80°
Lbs. water circulated p. min. thro' cond'ser
Lbs. water per min. tli rough jackets
442
25
315
44
257
40
601.5
14
Range of temp 'rature in jackets
24.0°
16.2°
16.4°
29.1°
Lbs. ammonia circulated per min
*28.17
14.68
16.67
28.32
Probable temperature of liquid ammonia,
entrance to brine-tank
*71 . 3°
*68°
*63 7°
76.7°
Temp, of amm. corresp. to av. back press.
Av. temperature of gas leaving brine-tanks
Temperature of gas entering compressor..
Av. temperature of gas leaving compressor
Av. temp, of gas entering condenser
Temperature due to condensing pressure. .
Heat given ammonia:
By brine, B T.U. per miniute. . .
+14°
34.2°
*39°
213°
200°
84.5°
14776
- 8°
14.7°
25°
263°
218°
84.0°
7186
- 5°
3 0°
10.13°
239°
209°
82.5°
8824
11°
29.2°
34°
221°
168°
88.0°
14647
By compressor, B.T.U. per minute
By atmosphere, B.T.U. per minute. . . .
Total heat rec. by amm., B.T.U. per min.
Heat taken from ammonia:
By condenser B.T U per min
2786
140
17702
17242
2320
147
0653
9056
2518
167
11409
9910
3020
141
17708
17359
By jackets, B.T.U. per min
By atmosphere, B.T.U. per min ...
Total heat rej. by amm., B.T.U. per min. . .
Dif. of heat rec'd and rej., B.T.U. per min.
% work of compression removed by jackets.
Av. revolutions per min
608
182
18033
330
22#
58 09
712
338
10106
453
J31*
656
250
10816
407
26$
57 88
406
252
18017
309
18*
58.89
Mean eff. press, steam-cyl., Ibs. per sq. in. .
Mean eff. press, amm.-cyl., Ibs. per sq. in . .
Av. H. P. steam-cylinder
32.5
65.9
85.00
27.17
53.3
71.7
27.83
59.86
73.6
32.97
70.54
88.63
Av. H.P. ammonia-cylinder
65.7
54.7
59.37
71.20
Friction in per cent of steam H.P
Total cooling water, gallons per min. per
ton per 24 hours
23.0
0.75
24.0
1 185
20.0
0.797
19.67
0.990
Tons ice-melting capacity per 24 hours
Lbs. ice-refrigerating eff. per Ib. coal at 3
Ibs per H P per hour
74.8
24.1
36.43
14.1
44.64
17 27
74.56
23 37
Cost coal per ton of ice-refrigerating effect
at $4 per ton
$0.166
$0.283
$0,231
$0.170
Cost water per ton of ice-refrigerating effect
at $1 per 1000 cu. ft . . .
$0.128
$0.200
$0.136
$0.169
Total cost of 1 ton of ice-refrigerating eff...
$0.294
$0.483
$0.467
$0.339
Figures marked thus (*) are obtained by calculation; all other figures are
obtained from experimental data ; temperatures are in Fahrenheit degrees,
ARTIFICIAL ICE-MANUFACTURE.
999
Ammonia Compression-machine.
ACTUAL RESULTS OBTAINED AT THE MUNICH TESTS.
(Prof. Lincle, Trans. A. S. M. E., xiv. 1419.)
No of Test
1
2
3
4
5
Temp, of refrig- [ Inlet, deg. F
erated brine ) Outlet, t deg. F...
43.194
37.054
28.344
22.885
13.952
8.-; 71
-0.279
-5.879
28.251
23.072
Specific heat of brine
0.861
0.851
0.843
0.83?
0.851
8uantity of brine circ. per h., cu. ft.
1,039.38
908.84 633.89
414.98
800.93
old produced, B.T.U. per hour
342,909
263,950
172,776
121,474
220,284
Quant, of cooling water per h., c. ft.
338.76
260.83
187.506
139.99
97.76
I.H.P. in steam-engine cylinder (Le).
15.80
16.47
15.28
14.24
21.61
Cold pro- ) Per I.H.P. in comp.-cvl.
24,813
18,471
12,770
10,140
11,151
duced per v Per I.H.P. in steam-cyl.
21.703
16,026
11,307
8,530
10,194
h., B.T.U. ) Per Ib. of steam
1,100.8
785.6
564.9
435.82
512.12
Means for Applying the Cold. (M. C. Bannister, Liverpool
Eng'g Soc'y, 1890j— The most useful means for applying the cold to various
uses is a saturated solution of brine or chloride of magnesium, which
remains liquid at 5° Fahr. The brine is first cooled by being circulated in
contact with the refrigerator-tubes, and then distributed through coils of
pipes, arranged either in the substances requiring a reduction of tempera-
ture, or in the cold stores or rooms prepared for them; the air coming in
contact with the cold tubes is immediately chilled, and the moisture in the
air deposited on the pipes. It then falls, making room for warmer air, and
so circulates until the whole room is at the temperature of the brine in the
pipes.
In a recent arrangement for refrigerating made by the Linde British Re-
frigeration Co., the cold brine is circulated through a shallow trough, in
which revolve a number of shafts, each geared together, and driven by me-
chanical means. On the shafts are fixed a number of wrought-iron disks,
partly immersed in the brine, wThich cool them down to the brine tempera-
ture as they revolve; over these disks a rapid circulation of air is passed by
a fan, being cooled by contact with the plates; then it is led into the cham-
bers requiring refrigeration, from which it is again drawn by the same fan;
thus all moisture and impurities are removed from the chambers, and de-
posited in the brine, producing the most perfect antiseptic atmosphere yet
invented for cold storing; while the maximum efficiency of the brine tem-
perature was always available, the brine being periodically concentrated by
suitable arrangements.
Air has also been used as the circulating medium. The ammonia-pipes
refrigerate the air in a cooling-chamber, and large wooden conduits are used
to convey it to and return it from the rooms to be cooled. An advantage of
this system is that by it a room may be refrigerated more quickly than by
brine-coils. The returning air deposits its moisture in the form of snow on
the ammonia-pipes, which is removed by mechanical brushes.
ARTIFICIAL ICE-MANUFACTURE.
Under summer conditions, with condensing water at 70°, artificial ice-ma-
chines use ammonia at about 190 Ibs. above the atmosphere condenser-
pressure, and 15 Ibs. suction-pressure.
In a compression type of machine the useful circulation of ammonia,
allowing for the effect of cylinder- heating, is about 13 Ibs. per hour per in-
dicated horse-power of the steam cylinder. This weight of ammonia pro-
duces about 32 Ibs. of ice at 15° from water at 70°. If the ice is made from
distilled water, as in the "can system," the amount of the latter supplied
by the boilers is about 33$ greater than the weight of ice obtained. This
excess represents steam escaping to the atmosphere, from the re-boiler and
steam-condenser, to purify the distilled water, or free it from air; also, the
loss through leaks and drips, and loss by melting of the ice in extracting it
from the cans. The total steam consumed per horse-power is, therefore,
about 32 X 1.33 = 43,0 Ibs. About 7.0 Ibs. of this covers the steam -consump-
tion of the steam-engines driving the brine circulating-pumps, the several
1000 ICE-MAKtlTG OR HEllUGEKATIHG MACHINES.
cold-water pumps, and leakage, drips, etc. Consequently, the main steam«
engine must consume 36 Ibs. of steam per hour per I.H.P., or else live steam
must be condensed to supply the required amount of distilled water. There
is, therefore, nothing to be gained by using steam at high rates of expansion
in the steam-engines, in making artificial ice from distilled water. If the
cooling water for the ammonia-coils and steam-condenser is not too hard for
use in the boilers, it may enter the latter at about 175° F., by restricting the
quantity to l^fj gallons per minute per ton of ice. With good coal 8^3 Ibs. Q£
feed -water may then be evaporated, on the average, per Ib. of coal.
The ice made per pound of coal will then be 32 -r- (43.0 -s- 8.5) = 6.0 Ibs.
This corresponds with the results of average practice.
If ice is manufactured by the "plate system," no distilled water is used
for freezing. Hence the water evaporated by the boilers may be reduced to
the amount which will drive the steam-motors, and the latter may use steam
expansively to any extent consistent with the power required to compress
the ammonia, operate the feed and filter pumps, and the hoisting machinery.
The latter may require about 15$ of the power needed for compressing the
ammonia.
If a compound condensing steam-engine is used for driving the com-
pressors, the steam per indicated steam horse-power, or per 32 Ibs. of net
ice, may be 14 Ibs. per hour. The other motors at 50 Ibs. of steam per horse-
power will use 7.5 Ibs. per hour, making the total consumption per steam
horse-power of the compressor 21.5 Ibs. Taking the evaporation at 8 Ibs.,
the feed-water temperature being limited to about 110°, the coal per horse-
power is 2.7 Ibs. per hour. The net ice per Ib. of coal is then about 32-^-2.7 =
11.8 Ibs. The best results with "plate-system1' plants, using a compound
Steam-engine, have thus far afforded about 1CJ4 Ibs. of ice per Ib. of coal.
In the " plate system1' the ice gradually forms, in from 8 to 10 days, to a
thickness of about 14 inches, on the hollow plates, 10 X 14 feet in area, in
which the cooling fluid circulates.
In the *' can system " the water is frozen in blocks weighing about 300 Ibs.
each, and the freezing is completed in from 40 to 48 hours. The freezing-
tank area occupied by the tk plate system" is, therefore, about twelve
times, and the cubic contents about four times as much as required in the
•* can system."
The investment for the "plate" is about one-third greater than for the
"can " system. In the latter system ice is being drawn throughout the 24
hours, arid the hoisting: is done by hand tackle. Some "can " plants are
equipped with pneumatic hoists and on large hoists electric cranes are used
to advantage. In the "plate system" the entire daily product is drawn,
cut, and stored in a few hours, the hoisting being performed by power.
The distribution of cost is as follows for the two systems, taking the cost
for the "can " or distilled-water system as 100, which represents an actual
cost of about $1.25 per net ton:
Can System. Plate System.
rioisting and storing ice . 14.2 2.8
Engineers, firemen, and coal-passer 15.0 13.9
Coal at $3.50 per gross ton 42.2 20.0
Water pumped directly from a natural source
at 5 cts. per 1000 cubic feet 1.3 2.6
Interest and depreciation at 10$ 24.6 32.7
Repairs 2.7 3.4
100.00 75.4
A compound condensing engine is assumed to be used by the " plate sys-
tem."
Test of the New York Hygeia Ice-making- Plant.— (By
Messrs. Hupfel, Grisvvold, and Mackenzie; Stevens Indicator, Jan. 1894.)
The final results of the tests were as follows:
Net ice made per pound of coal, in pounds 7.12
Pounds of net ice per hour per horse-power 37.8
Net ice manufactured per day (12 hours) in tons — 97
Av. pressure of ammonia-gas at condenser, Ibs. per sq. in. ab. atmos. 135.2
Average back pressure of amm.-gas, Ibs. per sq. in. above atmos.. . . 15.8
Average temperature of brine in freezing-tanks, degrees F 19 7
Total number of cans filled per week 4389
Ratio of cooling-surface of coils in briue-tank to can-surface 7 to 10
MARINE ENGINEERING. 1001
Ratio of brine in tanks to water in cans 1 to 1.2
Ratio ot circulating water at condensers to distilled water 26 to 1
Pounds of water evaporated at boilers per pound of coal 8.085
Total horse-power developed by compressor-engines 444
Percentage of ice lost in removing from cans 2.2
APPROXIMATE DIVISION OP STEAM IN PER CENTS OF TOTAL AMOUNT.
Compressor-engines 60 . 1
Live steam admitted directly to condensers 19. 7
Steam for pumps, agitator, and elevator engines , 7.6
Live steam for reboiling distilled water. , 6.5
Steam for blowers furnishing draught at boilers 5.6
Sprinklers for removing ice from cans 0.5
The precautions taken to insure the purity of the ice are thus described:
The water which finally leaves the condenser is the accumulation of the
exhausts from the various pumps and engines, together with an amount of
live steam injected into it directly from the boilers. This last quantity is
used to make up any deficit in the amount of water necessary to supply the
ice-cans. This water on leaving the condensers is violently reboiled, and
afterwards cooled by running through a coil surface-cooler. It then passes
through an oil-separator, after which it runs through three charcoal-filters
and deodorizers, placed in series and containing 28 feet of charcoal. It next
passes into the supply-tank in which there is an electrical attachment for
detecting salt. Nitrate-of-silver tests are also made for salt daily. From
this tank it is fed to the ice-cans, which are carefully covered so that the
water cannot possibly receive any impurities.
MARINE ENGINEERING-.
Rules for Measuring Dimensions and Obtaining Ton*
nage of Vessels, (Record of American & Foreign Shipping. American
Bureau of Shipping, N. Y. 1890.)— The dimensions to be measured as follows:
I. Length. L.— From the fore side of stem to the after side of stern-post
measured at middle line on the upper deck of all vessels, except those hav-
ing a continuous hurricane-deck extending right fore and aft, in which the
length is to be measured on the range of deck immediately below the hurri-
cane-deck.
Vessels having clipper heads, raking forward, or receding stems, or rak^
ing stern-posts, the length to be the distance of the fore side of stem from
aft-side of stern-post at the deep-load water-line measured at middle line.
(The inner or propeller-post to be taken as stern-post in screw-steamers.
II. Breadth, B.— To be measured over the widest frame at its widest part;
in other words, the moulded breadth.
III. Depth, D.— To be measured at the dead-flat f rame and at middle line
of vessel. It shall be the distance from the top of floor-plate to the upper
side of upper deck-beam in all vessels except those having a continuous
hurricane-deck, extending right fore and aft, and not intended for the
American coasting trade, in which the depth is to be the distance from top
of floor-plate to midway between top of hurricane deck-beam and the top
of deck-beam of the deck immediately below hurricane-deck.
In vessels fitted with a continuous hurricane deck, extending right fore
and aft. and intended for the American coasting trade, the depth is to be
the distance from top of floor-plate to top of deck-beam of deck immedi-
ately below hurricane-deck.
Rule for Obtaining Tonnage,— Multiply together the length,
breadth, and depth, and their product by .75; divide the last product by 100;
the quotient will be the tonnage. — - — -^ — '• — = tonnage.
The U, S. Custom-house Tonnage I,aw, May 6, 1864, provides
that "the register tonnage of a vessel shall be her entire internal cubic
capacity in tons of 100 cubic feet each." This measurement includes all the
space between upper decks, however many there may be. Explicit direc-
tions for making the measurements are given in the law.
The Displacement of a Vessel (measured in tons of 2240 Ibs.) is
the weight of the volume of water which it displaces. For sea- water it is
equal to the volume of the vessel beneath the water-line, in cubic feet,
divided by 35, which figure is the number of cubic feet of sea-water at 60»
1002 MARINE ENGINEERING.
F. in a ton of 2240 Ibs. For fresh water the divisor is 35.93. The U. 8. reg-
ister tonnage will equal the displacement when the entire internal cubio
capacity bears to the displacement the ratio of 100 to 35.
The displacement or gross tonnage is sometimes approximately estimated
as follows: Let L denote the length in feet of the boat, B its extreme
breadth in feet, and D the mean draught in feet; the product of these three
dimensions will give the volume of a parallelopipedon in cubic feet. Put-
ting V for this volume, we have V = L X B X D.
The volume of displacement may then be expressed as a "percentage of
the volume F", known as the " block coefficient." This percentage varies for
different classes of ships. In racing yachts with very deep keels it varies
from 22 to 33; in modern merchantmen from 55 to 75; for ordinary small
boats probably 50 will give a fair estimate. The volume of displacement in
cubic feet divided by 35 gives the displacement in tons.
Coefficient of Fineness,— A term used to express the relation be-
tween the displacement of a ship and the volume of a rectangular prism or
box whose lineal dimensions are the length, breadth, and draught of the
ship.
Coefficient of fineness = ^ B wlD being the displacement in tons
of 35 cubic feet of sea-water to the ton, Lthe length between perpendiculars,
B the extreme breadth of beam, and W the mean draught of water, all in
feet.
Coefficient of "Water-lines,— An expression of the relation of the
displacement to the volume of the prism whose section equals the midship
section of the ship, and length equal to the length of the ship.
Coefficient of water-lines = area of tomerwter section x g Seat°D
gives the following values:
Coefficient Coefficient of
of Fineness. Water-lines.
Finely-shaped ships ............................. 0.55 0.63
Fairly-shaped ships ............................. 0.61 0.67
Ordinary merchant steamers for speeds of 10 to
11 knots ...... . .............................. 0.65 0.72
Cargo steamers, 9 to 10 knots ................... 0.70 0.76
Modern cargo steamers of large size ............ 0.78 0.83
Resistance of Snips.— The resistance of a ship passing through
water may vary from a number of causes, as speed, form of body, displace*
ment, midship dimensions, character of wetted surface, fineness of lines,
etc. The resistance of the water is twofold : 1st. That due to the displace*
ment of the water at the bow and its replacement at the stern , with the
consequent formation of waves. 2d. The friction between the wetted sur-
face of the ship and the water, known as skin resistance. A common ap«
proximate formula for resistance of vessels is
Resistance = speed2 x ^displacement2 x a constant, or R = S*D$ X <7.
If D = displacement in pounds, 8 = speed in feet per minute, R = resist-
ance in foot-pounds per minute, R = CS*D$. The work done in overcom-
ing the resistance through a distance equal to S is R X S = CfiPZ^; and
it' E is the efficiency of the propeller and machinery combined, the indicated
horse-power I.H.P. =
If 8 = speed in knots, D = displacement in tons, and Ca constant which
includes all the constants for form of vessel, efficiency of mechanism, etc.,
TRP
I.H.P.
The wetted surface varies as the cube root of the square of the displace-
ment; thus, let L be the length of edge of a cube just immersed, whose dis-
placement is D and wetted surface W. Then D = £3 or L = ^Dt and
W - 5 X L2 SB 5 x( |/I>)a. That is, W varies as Di
MARINE ENGINEERING.
1003
Another approximate formula is
area of immersed midship section X ffl
K " """'
I.H.P. :
The usefulness of these two formulae depends upon the accuracy of the
so-called "constants " C and K, which vary with the size and form of the
ship, and probably also with the speed. Seaton gives the following, which
taay be taken roughly as the values of C and K under the conditions ex-
pressed:
General Description of Ship.
Speed,
knots.
Value
of 0.
Value
of K.
15 to 17
240
620
" 300 " "
15 " 17
190
500
it it tt
13 " 15
240
650
it ti «(
11 •* 13
260
700
Jhips over 300 feet long, fairly shaped
11 13
240
650
9 11
260
700
jihips over 250 feet long, finely shaped
13 15
200
580
11 13
240
660
ii it it
9 11
260
700
11 13
220
620
9 11
250
680
11 12
220
600
9 11
240
640
Ships over 200 feet long, fairly shaped . .
9 11
220
620
Ships under 200 feet long, finely shaped
11 12
200
550
10 11
210
580
it «i tt
9 10
230
620
Ships under 200 feet long, fairly shaped
9 10
200
600
Coefficient of Performance of Vessels. -The quotient
^/(displacement)2 X (speed in knots)3
tons of coal in 24 hours
gives a quotient of performance which represents the comparative cost of
propulsion in coal expended. Sixteen vessels with three-stage expansion-
engines in 1890 gave an average coefficient of 14,810, the range being from
12,1 50 to 16,700.
In 1881 seventeen vessels with two-stage expansion-engines gave an aver-
Uge coefficient of 11,710. In 1881 the length of the vessels tested ranged from
260 to 320, and in 1890 from 295 to 400. The speed in knots divided by the
square root of the length in feet in 1881 averaged 0.539; and in 1890, 0.579;
ranging from 0.520 to 0.641. (Proc. Inst. M E., July, 1891, p. 329.)
Defects of the Common Formnla for Resistance.— Modern
experiments throw doubt upon the truth of the statement that the resistance
varies as the square of the speed. (See Robt. Mansers letters in Engineer-
ing, 1891 ; also his paper on The Mechanical Theory of Steamship Propulsion,
read before Section G of the Engineering Congress, Chicago, 1893.)
Seaton says: In small steamers the chief resistance is the skin resistance
In very fine steamers at high speeds the amount of power required seems
excessive when compared with that of ordinary steamers at ordinary speeds.
In torpedo-launches at certain high speeds the resistance increases at a
lower rate than the square of the speed.
In ordinary sea-going and river steamers the reverse seems to be the case.
Rankine's Formula for total resistance of vessels of the " wave-
line" type is:
R = ALBV*(l -f 4 sin' 0 + sin* 0),
in which equation 0 is the mean angle of greatest obliquity of the stream-
lines, A is a constant multiplier, B the mean wetted girth of the surface ex-
posed to friction, L the length in feet, and V the speed in knots. The power
demanded to impel a ship is thus the product of a constant to be determined
by experiment, the area of the wetted surface, the cube of the speed, and the
1004
MARINE ENGINEERING.
quantity in the parenthesis, which is known as the "coefficient of augmen-
tation." The last term of the coefficient may be neglected in calculating the
resistance of ships as too small to be practically important. In applying the
formula, the mean of the squares of the sines of the angles of maximum
obliquity of the water-lines is to be taken for sin2 0, and the rule will then
read thus:
To obtain the resistance of a ship of good form, in pounds, multiply the
length in feet by the mean immersed girth and by the coefficient of augmen-
tation, and then take the product of this "augmented surface,11 as Rankine
termed it, by the square of the speed in knots, and by the proper constant
coefficient selected from the following:
For clean painted vessels, iron hulls ........ A = .01
For clean coppered vessels .......... ....... A = .009 to .008
For moderately rough iron vessels ......... A = -Oil -f
The net, or effective, horse -power demanded will be quite closely obtained
by multiplying the resistance calculated, as above, by the speed in knots and
dividing by 326. The gross, or indicated, power is obtained by multiplying
the last quantity by the reciprocal of the efficiency of the machinery and
propeller, which usually should be about 0.6. Rankine uses as a divisor in
this case 200 to 260.
The form of the vessel, even when designed by skilful and experienced
naval architects, will often vary to such an extent as to cause the above con-
stant coefficients to vary somewhat; and the range of variation with good
forms is found to be from 0.8 to 1.5 the figures given.
For well-shaped iron vessels, an approximate formula for the horse-power
^ in which s is tne " augmented surface." The ex-
required is H.P.
8V3
pression 57-=- has been called by Rankine the coefficient of propulsion. In
tl.r.
the Hudson River steamer " Mary Powell," according to Thurston, this
coefficient was as high as 23,500.
The expression
Jti..r.
has been called the locomotive performance. (See
...
Rankine's Treatise on Shipbuilding, 1864; Thurston's Manual of the Steam-
engine, part ii. p. 16; also paper by F. T. Bowles, U.S.N., Proc. U. S. Naval
Institute, 1883.)
Rankine's method for calculating the resistance is said by Seaton to give
more accurate and reliable results than those obtained by the older rules,
but it is criticised as being difficult and inconvenient of application.
Dr. Kirk's Method.— This method is generally used on the Clyde.
The general idea proposed by Dr. Kirk is to reduce all ships to so definite
and simple a form that they may be easily compared; and the magnitude of
certain features of this form shall determine the suitability of the ship for
speed, etc.
The form consists of a middle body, which is a rectangular parallelepiped,
and fore body and after body, prisms having isosceles triangles for bases,
as shown in Fig. 168.
G
H
F
K
L
FIG. 168.
This is called a block model, and is such that its length is equal to that of
the ship, the depth is equal to the mean draught, the capacity equal to the
displacement volume, and its area of section equal to the area of im-
MARINE ENGINEERING. 1005
mersed midship section. The dimensions of the block model may be obtained
as follows:
Let AG = HB = length of fore- or after-body = F;
GH = length of middle body = M\
KL = mean draught = H\
___ area of immersed midship section „
XX =- KL •**'
Volume of block = (F+M)X # X H;
Midship section = B X H ;
Displacement in tons = volume in cubic ft. -f- 35.
AH = AG + GH=F+M=: displacement X 35 + (B X H).
The wetted surface of the block is nearly equal to that of the ship of the
s&me length, beam and draught; usually 2% to 5% greater. In exceedingly
fine hollow-line ships it may be 8# greater.
Area of bottom of block = (F+M)XB',
Area of sides = 2M X H.
= 4^A
Area of sides of ends = 4.F« -f- x H\
Tangent of half angle of entrance = ^~ = — .
From this, by a table of natural tangents, the angle of entrance may be
obtained :
Angle of Entrance Fore-body in
of the Block Model, parts of length.
Ocean-going steamers, 14 knots and upward. 18° to 15° .3 to .36
" 12 to 14 knots ......... 21 to 18 .26 to .3
cargo steamers, 10 to 12 knots.. 30 to 22 .22 to .26
E. R. Mumford's Method of Calculating Wetted Surfaces
is given in a paper by Archibald Denny, Eng"g, Sept. 21, 1894. The following
is his formula, which gives closely accurate results for medium draughts,
beams, and finenesses:
8 = (L X D X 1.7) + (L X B X C),
in which S = wetted surface in square feet;
L = length between perpendiculars in feet;
D = middle draught in feet;
B = beam in feet;
C = block coefficient.
The formula may also be expressed in the form 8 = L(1.7D -f- BC).
In the case of twin-screw ships having projecting shaft-casings, or in the
case of a ship having a deep keel or bilge keels, an addition must be made
for such projections. The formula gives results which are in general much
more accurate than those obtained by Kirk's method. It underestimates
the surface when the beam, draught, or block coefficients are excessive; but
the error is small except in the case of abnormal forms, such as stern-wheel
steamers having very excessive beams (nearly one fourth the length), and
also very full block coefficients. The formula gives a surface about 6# too
smali for such forms.
To Find the Indicated Horse-power from the Wetted
Surface. (Seaton.)— in ordinary cases the horse-power per 100 feet of
wetted surface may he found by assuming that the rate for a speed of 10
knots is 5, and thar the quantity varies as the cube of the speed. For exam-
ple: To find the numuer of I.H.P. necessary to drive a ship at a speed of 15
knots, having a wetted skin ef block model of 16,200 square feet:
The rate per 100 feet = (15/10)» X 5 = 16.875.
Then I.H.P. required = 16.875 X 162 = 2734.
1006
MARINE ENGINEERING.
When the ship is exceptionally well-proportioned, the bottom quite clean,
and the efficiency of the machinery high, as low a rate as 4 I.H.P. per 100
feet of wetted skin of block model may be allowed
The gross indicated horse-power includes the power necessary to over-
come the friction and other resistance of the engine itself and the shafting,
and also the power lost in the propeller. In other words, I.H.P. is no meas-
ure of the resistance of the ship, and can only be relied on as a means of
deciding the size of engines for speed, so long as the efficiency of the engine
and propeller is known definitely, or so long as similar engines and propellers
are employed in ships to be compared. The former is difficult to obtain,
and it is nearly impossible in practice to know how much of the power shown
in the cylinders is employed usefully in overcoming the resistance of the
ship. The following example is given to show the variation in the efficiency
of propellers:
Knots. I.H.P.
H.M.S. " Amazon," with a 4-bladed screw, gave 12.064 with 1940
H.M.S. u Amazon," with a 2-bladed screw, increased pitch,
and less revolutions per minute 12.396 " 1663
H.M.S. " Iris," with a 4-bladed screw 16.577 " 7503
H.M.S. "Iris," with 2-bladed screw, increased pitch, less
revolutions per knot 18.587 " 7556
Relative Horse-power Required for Different Speeds of
Vessels. (Horse-power for 10 knots — 1.) — The horse-power is taken usually
to vary as the cube of the speed, but in different vessels and at different
speeds it may vary from the 2.8 power to the 3.5 power, depending upor the
lines of the vessel and upon the efficiency of the engines, the propeller, etc.
•o"*
u
02^
HPCC
S2>8
£2-9
S3
S3'i
£3-2
£3-3
S3-4
S3'6
4
6
8
10
12
14
16
18
20
22
24
26
28
30
.0769
.0701
.0640
.0584
.0533
.0486
.0444
.0405
.239
.227
.216
.205
.195
.185
.176
.167
.535
.524
.512
.501
.490
.479
.468
.458
1.
1.
1.
1.
1.
1.
1.
1.
1.666
1.697
1.728
1.760
1.792
1.825
1.859
1.893
2.565
2.653
2.744
2.838
2.935
3.036
3.139
3.247
3.729
3.908
4.096
4.293
4.500
4.716
4.943
5.181
5.185
5.499
5.832
6.185
6.559
6.957
7.378
7.824
6.964
7.464
8.
8.574
9.189
9.849
10.56
11.31
9.095
9.841
10.65
11.52
13^49
14.60
15.79
11.60
12.67
13.82
15.09
16.47
17.98
19.62
21.42
14.52
15.97
17.58
19.34
21.28
23.41
25.76
28.34
17.87
19.80
21.95
24.33
26,97
29.90
33.14
36.73
21.67
24.19
27.
30.14
33.63
37.54
41.90
46.77
EXAMPLE IN USE OF THE TABLE.— A certain vessel makes 14 knots speed
with 587 I.H.P. and 16 knots with 900 I.H.P. What I.H.P. will be required at
18 knots, the rate of increase of horse-power with increase of speed remain-
ing constant ? The first step is to find the rate of increase, thus: 14X : 16^ ::
587 : 900.
x log 16 - x log 14 = log 900 - log 587;
#(0.204120 - 0.146128) = 2.954243 - 2.768638,
tvhence x (the exponent of S in formula H.P. ccSx) — 3.2.
From the table, for S3'2 and 16 knots, the I H.P. is 4.5 times the I.H.P. at
10 knots, .'. H.P. at 10 knots = 900 ~ 4.5 = 200.
From the table, forS3'2 and 18 knots, the I.H.P. is 6.559 times the I.H.P. at
10 knots: /. H.P. at 18 knots = 200 X 6.559 = 1312 HP.
Resistance per Horse-power for Different Speeds. (One
horse-power — 33,000 Ibs. resistance overcome through 1 ft. in 1 min.) — The
resistances per horse-power for various speeds are as follows: For a speed of
1 knot, or 6080 feet per hour = 101^ ft. per min., 33,000 -s- 101^ = 325.658 Ibs.
per horse-power; and for any other speed 325.658 Ibs. divided by the speed
in knots; or for
1 knot 325. 66 Ibs.
2 knots 162. 83 "
3 " 108.55 "
4 •* 81.41 "
* " 65.13 "
6 knots 54. 28 Ibs.
7 *' 46.52 "
8 " 40.71 t4
9 " 36.18 4t
10 " 32.57 "
11 knots 29. 61 Ibs.
12 " 27.14 "
13 " 25.05 "
14 " 23.26 "
15 *' 21.71 "
16 knots 20. 35 Ibs.
17 " 19.16 "
18 " 18.09 "
19 " 17.14 "
20 " 16.28 "
MAKIKE EXGINEERIHG.
1007
Results of Trials of Steam-vessels of Various Sizes.
(From Beaton's Marine Engineering.)
d
4
d
d
rJf
00 SH
1
s.s.
14 Africa."
P.S.
"Mary Powell"
cci
-a
R.M.P.S.
" Connaught."
Length, perpendiculars. ...
90' 0"
10' 6"
2' 6"
29.73
24?
903
45' 0"
12° 40'
0.481
22.01
460
50.9
4.78
223
556?
171' 9"
18' 9"
6' 9H"
280
99
3793
72' 00"
11° 30'
0.576
15.3
798
21.04
5.87
192
445
130' 0"
21' 0"
8' 10"
370
148
3754
42' 6"
23° 50'
0.608
10.74
371
9.88
7.97
172.8
495
286' 0"
34' 3"
6' 0"
800
200
8222
143' 0"
13° 21'
0.489
17.20
1490
18.12
3.56
293.7
683
230' 0"
29' 0"
13' 6"
1500
340
10,075
79' 6"
17° 0"
0.671
10.04
503
5.00
4.90
266
6'JO
3-27' 0"
35' 0"
13' 0"
1900
336
15,782
129' 0''
11° 26'
0.605
17.8
4751
30.00
5.32
182
399
Breadth, extreme
Mean draught water
Displacement (tons) . .
Area Immersed mid. section —
M . Wetted skin
M -2 " Length fore-body
2^° ! Angle of entrance .
Displacement X 35
Length X Imm. mid area""
Indicated horse-power
I.H.P. per 100 ft. wetted skin ....
I.H.P. per 100 ft. wetted skin, re-
duced to 10 knots
D§X -S3
I.H.P. "
Immersed mid area X S*
I.H.P.
H.M.S.
" Active."
ofcc
&'£
Ms
Hi
S.S.
"Garonne."
5/j «8
K$
a*
R.M.S.S.
" Britannic."
Length, perpendiculars
270' 0"
42' 0"
18' 10"
3057
632
16,008
101' 0"
18° 44'
0.629
14.966
4015
25.08
7.49
75.8
527.5
300' 0"
46' 0"
18' 2"
3290
700
18,168
135' 6"
16° 16'
0.548
18.573
7714
42.46
6.634
183.7
581.4
300' 0"
46' 0"
18' 2"
3290
700
18,168
135' 6"
16° 16'
0.548
15.746
3958
21.78
5.58
218.2
690.5
370' 0"
41' 0"
18' 11"
4635
656
22,633
123' 0"
16° 4'
0.668
13.80
2500
11.04
4.20
292
689
392 0"
39 0"
21' 4"
5767
738
26,235
118' 0"
16° 30'
0.698
12.054
1758
6.7
3.83
320
735
450' 0"
45' 2'-'
23' 7"
8500
926
32,578
129' 0*
17° 16'
0.714
15.045
4900
15.04
4.43
289.3
642.5
Breadth extreme .... . .
Displacement (tons) .
-03 f Wetted skin
.gs
g S J Length fore-body
CQ ^ [ Angle of entrance. ......
Displacement X 85
Length X Imm. mid area
Speed (knots)
Indicated horse-power
I.H.P. per 100 ft. wetted skin. . . .
I.H.P. per 100 ft. wetted skin, re-
duced to 10 knots.
7)§XS»
I.H.P. "
Immersed mid area X S*
I.H.P.
1008
MARIHB EKGIHEERIHG.
Results of Progressive Speed Trials in Typical Vessels.
(Eng'g, April 15, 1892, p. 463.)
*j
|
1
o-oi
g
5 si
o
^^"PO
*~/3
|s
*~ ~ 2
la
LI
o
a° *-
ss
^r*
03 S
^6
o j-f «
'O .
C .
g,
& **' 0
'S'u
P-'o
W o
^0
s 1 *
o
&
1
- CO
§HO*
£
- 15
4
Length ' in f pfttA
135
230
265
300
360
375
525
Bread
h " "
14
27
41
43
60
65
63
Draught (mean
Displaf^nifint. (
) on trial
5' 1"
103
8' 3"
735
16' 6"
2800
16' 2"
3330
23' 9"
7390
25' 9"
9100
21' 3"
11550
I H P
mknnf
«_
110
450
700
bOO
1000
1500
2000
'* 14 *'
260
1100
2100
2400
3000
4000
4600
18 "
87'0
2500
6400
6000
7500
9000
10000
it
20 "
1130
3500
10000
9000
11000
12500
14500
Speed
Ratio of
speed3
10
1.
Ratio of H.P. =
1
1
1
1
1
1
1
14
2.744
it *i
2.36
2.44
3
3
3
2.67
2.3
18
5.838
" " =
7.91
5.56
9.14
7.5
7.5
6.
5
20
8.
" " =
10.27
7.78
14.14
11.25
11
8.42
7.25
Admiralty coeff . f 10 knots,
ni N/.Q3 1 14 "
200
232
181
203
284
259
279
255
380
347
290
298
255
304
*> 18 "
1 47
1 QO
181
917
OQC
989
9Q7
I.H.P.
I 18
1 20 "
156
186
159
198
276
278
281
The figures for I.H.P. are " round." The " Medusa's " figures for 20 knots
are from trial on Stokes Bay, and show the retarding effect of shallow water.
The figures for the other ships for 20 knots are estimated for deep water.
More accurate methods than those above given for estimating the
horse-power required for any proposed ship are: 1. Estimations calculated
from the results of trials of 4k similar" vessels driven at " corresponding"
speeds; " similar " vessels being those that have the same ratio of length to
breadth and to draught, and the same coefficient of fineness, and " corre-
sponding" speeds those which are proportional to the square roots of
the lengths of the respective vessels. Froude found that the resistances of
such vessels varied almost exactly as wetted surface x (speed)2.
2. The method employed by the British Admiralty and by some Clyde
shipbuilders, viz., ascertaining the resistance of a model of the vessel, 12 to
20 ft. long, in a tank, and calculating the power from the results obtained.
Speed on Canals* — A great loss of speed occurs when a steam- vessel
passes from open water into a more or less restricted channel. The average
speed of vessels in the Suez Canal in 1882 was only 5J4 statute miles per hour.
(Eng'g. Feb. 15, 1884, p. 139.)
Estimated Displacement, Horse-power, etc. -The table on
the next page, calculated by the author, will be found convenient for mak-
Sng approximate estimates. 2
The figures in 7th column are calculated by the formula H.P. = S3D^ -r- c,
in which c = 200 for vessels under 200 ft. long when C— .65, and 210
when C = .55; c — 200 for vessels 200 to 400 ft. long when C = .75, 220 when
C = .65, 240 when C - .55; c = 280 for vessels over 400 ft. long when C = .75,
250 when C .= .65, 260 when C = .55.
The figures in the 8th column are based on 5 H.P. per 100 sq. ft. of wetted
surface.
The diameters of screw in the 9th column are from formula D ~
3.31 I/I.H.P., and in the 10th column from formula D = 2.71 |/l7lLPT
To find the diameter of screw for any other speed than 10 knots, revolu-
tions being 100 per minute, multiply the diameter given in the table by the
5th root of the cube of the given speed -j- 10. For any other revolutions per
minute than 100, divide by the revolutions and multiply by 100.
To find the approximate horse-power for any other speed than 10 knots,
multiply the horse-power given in the table by the cube of the ratio of the
given speed to 10, or by the relative figure from table on p. 1006.
MARINE ENGINEERING.
1009
Intimated Displacement, Horse-power, etc., of Steam-
vessels of Various Sizes.
j*«
fi
fijfi
LBDx C
Wetted Surface
L(1.7D + BC)
Sq. ft.
Estimated Horse-
power at 10 knots.
Diam. of Screw for 10
knots speed and 100
revs, per minute.
Calc.
from Dis-
placem't.
Calc. from
Wetted
Surface.
35
tons.
If Pitch =
Diam.
If Pit^h =
1.4 Diam.
12
3
1.5
.55
.85
48
4.3
2.4
4.4
3.6
1AJ
3
1.5
.55
1.13
64
5.2
3.2
4.6
3.8
16 1
4
2
.65
2.38
96
8.9
4.8
5.1
4.2
3
1.5
.55
1.41
80
6.0
4.0
4.7
3.9
20 1
4
2
.65
2.97
120
10.3
6.0
5.3
4.3
0/t (
3.5
1.5
.55
1.98
104
7.5
5.2
5
4.1
24 j
4.5
2
.65
4-21
152
12.6
7.6
5.5
4.5
4
2
.55
3.77
168
11.5
8.4
5.4
4.4
30
5
2.5
.65
6.96
224
18.2
11.2
5.9
4.8
40 ]
4.5
6
2
2.5
.55
.65
5.66
11.1
235
326
15.1
24.9
11.8
16.3
5.7
6.3
4.7
5.2
KftJ
6
3
.55
14.1
420
27.8
21.0
6.4
5.4
50 i
8
3.5
.65
26
558
43.9
27.9
7.1
5.8
8
3.5
.55
26.4
621
42.2
31.1
7.0
5.7
60 1
10
4
.65
44.6
798
62.9
39.9
7.6
6.2
^ i
10
4
.55
44
861
59.4
43.1
7.5
6.1
'°i
12
4.5
.65
70.2
1082
85.1
54.1
8.1
6.6
eft]
12
4.5
.55
67.9
1140
79.2
57.0
7.9
6.5
80 i
14
5
.65
104.0
1408
111
70 4
8.5
7.0
13
5
.55
91.9
1408
97
70.4
8.3
6.8
90 1
16
6
.65
160
1854
147
92.7
9
7.3
i
13
5
.55
102
1565
104
78.3
8.4
6.9
100^
15
5.5
.65
153
1910
143
95.5
8.9
7.3
1
17
6
.75
219
2295
202
115
9.6
7.8
14
5.5
.55
145
2046
131
102
8.8
7.2
120 -j
16
6
.65
214
2472
179
124
9.4
l.G
18
6.5
.75
301
2946
250
147
10
8.2
(
16
6
.55
211
2660
169
133
9.2
7.4
140-J
18
6.5
.65
306
3185
227
159
9.8
8.0
|
20
7
.75
420
3:66
312
188
10.5
8.5
j
17
6.5
.55
278
3264
203
163
9.6
7.8
160-^
19
7
.65
395
3880
269
194
10.1
8.3
j
21
7.5
.75
540
4560
368
228
10.8
8.8
20
7
.55
396
4122
257
206
10.1
8.2
180-
22
7.5
.65
552
4869
337
243
10.6
8.7
24
8
.75
741
5688
455
284
11.3
9.2
22
.55
484
4800
257
240
10.1
8.2
200-
25
8
.65
743
5970
373
299
10.8
8.8
28
9
.75
1080
7260
526
363
11.6
9.5
l
28
8
.55
880
7250
383
363
10.9
8.9
250^
32
10
.65
1486
9450
592
473
11.9
9.7
J
36
12
.75
2314
11850
875
593
12.8
10.5
32
10
.55
1509
10380
548
519
11.7
9.6
300 \
36
12
.65
2407
13140
806
657
12.6
10.4
}
40
14
.75
3600
17140
1175
857
13.6
11.1
*(
38
12
.55
2508
14455
769
723
12.5
10.2
350-
42
14
.65
3822
17885
1111
894
13.5
11.0
46
16
.75
5520
21595
1562
1080
14.4
11.8
(
44
14
.55
3872
19200
1028
960
13.3
10.8
400^
48
16
.65
5705
23360
1451
1168
14.2
11.6
1
52
18
.75
8023
27840
2006
1392
15.2
12.4
50
16
.55
5657
24515
1221
1226
13.7
11.2
450 1
54
18
.65
8123
29565
1616
1478
14.5
11.9
I
58
20
.75
11157
34875
2171
1744
15.4
12.6
52
18
.55
7354
29600
1454
1480
14.2
11.6
500-
56
20
.65
10400
35200
1966
1760
15.1
12.4
1
60
22
.75
14143
41200
2543
2060
15.9
13.0
56
20
.55
9680
36245
1747
1812
14.7
12.0
550-1
60
22
.65
13483
42735
2266
2137
15 5
12.7
|
64
24
.75
18103
49665
2998
2483
16.4
13.4
I
60
22
.55
12446
42900
2065
2145
15.2
12.5
600X
64
24
.65
17115
50220
2656
2511
15.4
13.1
j
68
26
.75
22731
58020
3489
2901
16.9
13.8
1010 MARINE ENGINEERING.
THE SCREW-PROPEI^ER,
The " pitch " of a propeller is the distance which any point in a blade,
describing a helix, will travel in the direction of the axis Curing one revolu-
tion, the point being assumed to move around the axis. The pitch of a
propeller with a uniform pitch is equal to the distance a propeller will
advance during one revolution, provided there is no slip. In a case of this
kind, the term "pitch" is analogous to the term "pitch of the thread" of
an ordinary single-threaded screw.
Let P = pitch of screw in feet, R = number of revolutions per second,
V — velocity of stream from the propeller = P x -B, v = velocity of the ship
in feet per second, V — v = slip, A = area in square feet of section of stream
from the screw, approximately the area of a circle of the same diameter,
A X V = volume of water projected astern from the ship in cubic feet per
second. Taking the weight of a cubic foot of sea-water at 64 Ibs., and the
force of gravity at 32, we have from the common formula for force of accel-
eration, viz.: F= MJ- — — y, or F = — vt , when t = 1 second, vt being
the acceleration.
64A.V
Thrust of screw in pounds = 0. (F - v) = 2AT(V — v).
Bra
Rankine (Rules, Tables, and Data, p. 275) gives the following: To calculate
the thrust of a propelling instrument (jet, paddle, or screw) in pounds,
multiply together the transverse sectional area, in square feet, of the stream
driven astern by the propeller; the speed of the stream relatively to the snip
in knots; the real slip, or part of that speed which is impressed on that
stream by the propeller, also in knots; and the constant 5.06 for sea-water,
or 5.5 for fresh water. If /S = speed of the screw in knots, s = speed of ship
in knots, A = area of the stream in square feet (of sea-water),
Thrust in pounds = A X 8(8 - s) X 5.66.
Tlie real slip is the velocity (relative to water at rest) of the water pro-
jected sternward; the appat -en t slip is the difference between the speed of
the ship and the speed of the screw; i.e., the product of the pitch of the
screw by the number of revolutions.
This apparent slip is sometimes negative, due to the working of the screw
in disturbed water which has a forward velocity, following the ship. Nega-
tive apparent slip is an indication that the propeller is not suited to the
ship.
The apparent slip should generally be about 8# to 10# at full speed in well-
formed vessels with moderately fine lines; in bluff cargo boats it rarely
exceeds 5$.
The effective area of a screw is the sectional area of the stream of water
laid hold of by the propeller, and is generally, if not always, greater than
the actual area, in a ratio which in good ordinary examples is 1.2 or there-
abouts, and is sometimes as high as 1.4; a fact probably due to the stiffness
of the water, which communicates motion laterally amongst its particles.
(Rankine's Shipbuilding, p. 89.)
Prof. D. S. Jacobus, Trans. A. S. M. E., xi. 1098, found the ratio of the ef-
fective to the actual disk area of the screws of different vessels to be as
follows :
Tug-boat, with ordinary true-pitch screw ............................... 1 .42
** . " screw having blades projecting backward ................ 57
Ferryboat " Bergen," with or- \ at speed of 12.09 stat. miles per hour. 1.53
dinary true-pitch screw 1 ' "13.4 " " ** " 1.48
Steamer " Homer Ramsdell," with ordinary true-pitch screw ........... 1 20
Size of Screw.— Seaton says: The size of a screw depends on so many
things that it is very difficult to lay down any rule for guidance, and much
must always be left to the experience of the designer, to allow for all the
circumstances of each particular case. The following rules are given for
ordinary cases. (Seaton and Rounthwaite's Pocket-book):
1Q1QQ &
P = pitch of propeller in feet = ' - in which S = speed in knots,
xv(10J — X)
R = revolutions per minute, and x — percentage of apparent slip.
For a slip of 10*, pitch =
THE SCREW PROPELLER.
1011
/ I.H.P.
• — 7T /
A I / T* V K \
\ / ( X ]
V >. 100 '
« diameter of propeller «=
in the table below. If K = 20, D = 20000,
, K being a coefficient given
I.H.P.
Total developed area of blades =
' ' ', in which C is a coefficient
to be taken from the table.
Another formula for pitch, given in Seaton's Marine Engineering, is
C 3 /T ft "P
C 3 /
= J? A/
™
which C = 737 for ordinary vessels, and 660 for slow-
speed cargo vessels with full lines.
Thickness of blade at root =
-r X &, in which d
diameter of tail
shaft in inches, n — number of blades, b = breadth of blade in inches where
it joins the boss, measured parallel to the shaft axis; k = 4 for cast iron, 1.5
for cast steel, 2 for gun-metal, 1.5 for high-class bronze.
Thickness of blade at tip: Cast iron .04D -4- .4 in. ; cast steel .037) -f- .4 in.;
gun-metal .03Z) -f- -2 in. ; high-class bronze .02D-J-. 3 in., where D = diameter
of propeller in feet.
Propeller Coefficients.
L-
= ,
?«i
$
S
1
Description of Vessel.
ill
p a S
III
1
*0
DO
ill
gtfl
§02
d
Jj
p'CrQ
Si
5
1 o,
1
>
CO
p
Bluff cargo boats
8-10
One
4
17 -17 5
19 -17.5
Cast iron
Cargo, moderate lines. . .
10-13
4
18 -19
17 -15.5
Pass, and mail, fine lines.
13-17
44
4
19.5-20.5
15 -13
C. I. or S.
" " " very fine.
13-17
17-22
Twin
One
4
4
20.5-21-5
21 -22
14.5-12.5
12.5-11
G. M. or B
44 it i» 4* 44
17-22
Twin
3
22 -23
10.5- 9
44 " 4t
Naval vessels, " "
16-22
"
4
21 -22.5
11.5-10.5
it 44 it
44 44 it 44
16-22
M
3
22 -23.5
8.5- 7
it (4 ti
Torpedo-boats, " "
20-26
One
3
25
7- 6
B. or F. S.
C. I., cast iron; G. M., gun-metal; B., bronze; S., steel; F. S., forged steel.
From the formulae D - 20000 1/ -(p ' ' and P = ~^-|/ ' ^ ', if P = S
and R = 100, we obtain D = 1^00 X I.HJR = 8.31
If P = 1.4D and ^ = 100, then D = ^145.8 X I.H.P. = 2.71-^I.H.P.
From these two formulae the figures for diameter of screw in the table on
page 1009 have been calculated. They may be used as rough approximations
to the correct diameter of screw for any given horse-power, for a speed of
10 knots and 100 revolutions per minute.
For any other number of revolutions per minute multiply the figures in
the table by 100 and divide by the given number of revolutions. For any
other speed than 10 knots, since the I.H.P. varies approximately as the cube
of the speed, and the diameter of the screw as the 5th root of the I.H.P.,
multiply the diameter given for 10 knots by the 5th root of the cube of one
tenth of the given speed. Or, multiply by the following factors:
For speed of knots:
4 5 6 7 8 9 11 12 13 14 15 16
AS -s- 10)3
= .577
.736 .807 .875 .9391.0591.1161.1701.2241.2751.387
1012
HARINE ENGINEERING.
Speed:
17 18 19 20 21 22 23 24 25 26 27 38
&(S -*- 10)3
= 1.375 1.423 1.470 1.515 1.561 1.605 1.648 1.691 1.733 1.774 1.815 1.855
For more accurate determinations of diameter and pitch of screw, the
formulge and coefficients given by Seaton, quoted above, should be used.
Efficiency of the Propeller,— According to Rankine, if the slip of
the water be s, its weight W^ the resistance /?, and the speed of the ship v,
W*.
g '
Wsv
9
This impelling action must, to secure maximum efficiency of propeller, be
effected by an instrument which takes hold of the fluid without shock or
disturbance of the surrounding mass, and, by a steady acceleration, gives it
the required final velocity of discharge. The velocity of the propeller over-
coming the resistance R would then be
and the work performed would be
the first of the last two terms being useful, the second the minimum lost
work; the latter being the wasted energy of the water thrown backward.
The efficiency is
and this is the limit attainable with a perfect propelling instrument, which
limit is approached the more nearly as the conditions above prescribed are
the more nearly fulfilled. The efficiency of the propelling instrument is
probably rarely much above 0.60, and never above 0.80.
In designing the screw-propeller, as was shown by Dr. Froude, the best
angle for the surface is that of 45° with the plane of the disk; but as all
parts of the blade cannot be given the same angle, it should, where practi-
cable, be so proportioned that the " pitch-angle at the centre of effort"
should be made 45°. The maximum possible efficiency is then, according
to Froude, 77#.
In order that the water should be taken on without shock and discharged
with maximum backward velocity, the screw must have an axially increas-
ing pitch.
The true screw is by far the more usual form of propeller, in all steamers,
both merchant and naval. (Thurston, Manual of the Steam-engine, part ii.i,
p. 176.)
The combined efficiency of screw, shaft, engine, etc., is generally taken
at 50$. In some cases it may reach QOfo or 65$. Rankine takes the effective
H.P. to equal the I.H.P. •+- 1.63.
Pitch-ratio and Slip for Screws of Standard Form.
Pitch-ratio.
Real Slip of
Screw.
Pitch ratio.
Real Slip of
Screw
.8
15.55
1.7
21.3
.9
16.22
1.8
21.8
.0
16.88
1.9
22.4
.1
17.55
2.0
22.9
.2
18.2
2.1
23.5
.8
18.8
2.2
24.0
.4
19.5
2.3
24.5
.5
20.1
2.4
25.0
1.6
20.7
2.5
25.4
THE PADDLE-WHEEL. 1013
Results of Recent Researches on the efficiency of screw-propel-
lers are summarized by S. W. Baruaby, in a paper read before section G of
the Engineering Congress, Chicago, 1893. He states that the following gen-
eral principles have been established:
(a) There is a definite amount of real slip at which, and at which only,
maximum efficiency can be obtained with a screw of any given type, and
this amount varies with the pitch-ratio. The slip-ratio proper to a given
ratio of pitch to diameter has been discovered and tabulated for a screw
of a standard type, as below (see table on page 1012):
(ft) Screws of large pitch-ratio, besides being less efficient in themselves,
add to the resistance of the hull by an amount bearing some proportion to
their distance from it, and to the amount of rotation left in the race.
(c) The best pitch-ratio lies probably between 1.1 and 1.5.
(d) The fuller the lines of the vessel, the less the pitch-ratio should be.
(e) Coarse-pitched screws should be placed further from the stern than
fine-pitched ones.
(/) Apparent negative slip is a natural result of abnormal proportions of
propellers.
(g) Three blades are to be preferred for high-speed vessels, but when the
diameter is unduly restricted, four or even more may be advantageously
employed.
(h) An efficient form of blade is an ellipse having a minor axis equal ta
four tenths the major axis.
(i) The pitch of wide-bladed screws should increase from forward to aft,
but a uniform pitch gives satisfactory results when the blades are narrow,
and the amount of the pitch variation should be a function of the width of
the blade.
(/) A considerable inclination of screw-shaft produces vibration, and wjth
right-handed twin-screws turning outwards, if the shafts are inclined at
all, it should be upwards and outwards from the propellers.
For results of experiments with screw-propellers, see F. C. Marshall, Proc.
Inst. M. E. 1881; R. E. Froude, Trans. Institution of Naval Architects, 1886;
G. A. Calvert, Trans. Institution of Naval Architects 1887; and S. W. Bar-
naby, Proc. Inst. Civil EngYs 1890, vol. cii.
One of the most important results deduced from experiments on model
screws is that they appear to have practically equal efficiencies throughout
a wide range both in pitch-ratio and in surf ace -ratio; so that great latitude
is left to the designer in regard to the form of the propeller. Another im-
portant feature is that, although these experiments are not a direct guide to
the selection of the most efficient propeller for a particular ship, they sup-
ply the means of analyzing the performances of screws fitted to vessels, and
of thus indirectly determining what are likely to be the best dimensions of
screw for a vessel of a class whose results are known. Thus a great ad-
vance has been made on the old method of trial upon the ship itself, which
was the origin of almost every conceivable erroneous view respecting the
screw-propeller. (Proc. Inst. M. E., July, 1891.)
THE PADDLE- WHEEL.
Paddle-wheels with Radial Floats. (Seaton's Marine En-
gineering.)—The effective diameter of a radial wheel is usually taken from
the centres of opposite floats; but it is difficult to say what is absolutely
that diameter, as much depends on the form of float, the amount of dip,
and the waves set in motion by the wheel. The slip of a radial wheel is
from 15 to 30 per cent, depending on the size of float.
T TT -p
Area of one float = ' X C.
D is the effective diameter in feet, and C is a multiplier, varying from
0 25 in tugs to 0.175 in fast-running light steamers.
The breadth of the float is usually about 14 its length, and its thickness
about ^ its breadth. The number of floats varies directly with the diam-
eter, and there should be one float for every foot of diameter.
(For a discussion of the action of the radial wheel, see Thurston, Manual
of the Steam-engine, part ii., p, 182.)
Feathering Paddle - wheels. (Seaton.) — The diameter of a
feathering-wheel is found as follows : The amount of slip varies from 12 to
20 per cent, although when the floats are small or the resistance great it
1014 MAR1*TE EKGIKEERIKG.
is as high as 25 per cent; a well-designed wheel on a well-formed ship should
not exceed 15 per cent under ordinary circumstances.
If K is the speed of the ship in knots, S the percentage of slip, and R the
revolutions per minute,
Diameter of wheel at centres = .
o.l4 X R
The diameter, however, must be such as will suit the structure of the
ship, so that a modification may be necessary on this account, and the
revolutions altered to suit it.
The diameter will also depend on the amount of " dip " or immersion of
float.
When a ship is working always in smooth water the immersion of the top
edge should not exceed y% the breadth of the float; and for general service
at sea an immersion of ^ the breadth of the float is sufficient. If the ship
is intended to carry cargo, the immersion when light need not be more than
2 or 3 inches, and should not be more than the breadth of float when at the
deepest draught; indeed, the efficiency of the wheel falls off rapidly with
the immersion of the wheel.
I FT "P
Area of one float = ' X C.
C is a multiplier, varying from 0.3 to 0.35; D is the diameter of the wheel
to the float centres, in feet.
The number of floats ±= ^(D -f- 2).
The breadth of the float = 0.35 x the length.
The thickness of floats — 1/12 the breadth.
Diameter of gudgeons = thickness of float.
Seaton and Rounthwaite's Pocket-book gives:
60
Number of floats = — ^.
VR
where R is number of revolutions per minute.
Area of one float (in square feet) = ^/
where N = number of floats in one wheel.
For vessels plying always in smooth water K = 1200. For sea-going
steamers K = 1400. For tugs and such craft as require to stop and start
frequently in a tide-way K — 1600.
It will be quite accurate enough if the last four figures of the cube
(D X #)3 be taken as ciphers.
For illustrated description of the feathering paddle-wheel see Seaton 's
Marine Engineering, or Seaton and Rounthwaite's Pocket-book. The diam-
eter of a feathering -wheel is about one half that of a radial wheel for equal
efficiency. (Thurston.)
[Efficiency of Paddle-wheels.— Computations by Prof. Thurston
of the efficiency of propulsion by paddle-wheels give for light river steamers
with ratio of velocity of the vessel, v, to velocity of the paddle -float at
centre of pressure, V, or — , = -, with a dip = 3/20 radius of the wheel, and
a slip of 25 per cent, an efficiency of .714 ; and for ocean steamers with
the same slip and ratio of — , and a dip = J£ radius, an efficiency of .685.
JET-PROPULSION.
Numerous experiments have been made in driving a vessel by the
reaction of a jet of water pumped through an orifice in the stern, but
they have all resulted in commercial failure. Two jet- propulsion steamers,
the " Waterwitch," 1100 tons, and the "Squirt," a small torpedo-boat,
were built by the British Government. The former was tried in 1867, and
gave an efficiency of apparatus of only 18 per cent. The latter gave a speed
of 12 knots, as against 17 knots attained by a sister-ship having a screw and
equal steam-power. The mathematical theory of the efficiency of the jet
was discussed by Rankine in The Engineer ', Jan. 11, 1867, and he showed that
the greater the quantity of water operated on by a jet-propeller, the greater
RECENT PRACTICE IK MARINE ENGINES. 1015
is the efficiency. In defiance both of the theory and of the results of earlier
experiments, and also of the opinions of many naval engineers, more than
$200,000 were spent in 1888-90 in New York upon two experimental boats, the
** Prima Vista " and the " Evolution,'1 in which the jet was made of very small
size, in the latter case only %-inch diameter, and with a pressure 'of 2500
Ibs. per square inch. As had been predicted, the vessel was a total failure.
(See "article by the author in Mechanics, March, 1891.)
The theory of the jet-propeller is similar to that of the screw-propeller.
If A = the area of the jet in square feet, Fits velocity with reference to the
orifice, in feet per second, v = the velocity of the ship in reference to the
earth, then the thrust of the jet (see Screw-propeller, ante) \z^AV(V — v).
The work done on the vessel is 2AV(V— v)v, and the work wasted on the
rearward projection of the jet is }& X 2AV(V - v)3. The efficiency is
2v
Thls exPression
F = v, that is, when the velocity of the jet with reference'to the earth, or
V — V, = 0; but then the thrust of the propeller is also 0. The greater the
value of Fas compared with v, the less the efficiency. For F = 20v, as was
proposed in the " Evolution," the efficiency of the jet would be less than 10
per cent, and this would be further reduced by the friction of the pumping
mechanism and of the water in pipes.
The whole theory of propulsion may be summed up in Rankine's words:
"That propeller is the best, other things being equal, which drives astern
the largest body of water at the lowest velocity.1'
It is practically impossible to devise any system of hydraulic or jet propul-
sion which can compare favorably, under these conditions, with the screw
or the paddle-wheel.
Reaction of a Jet.— If a jet of water issues horizontally from a ves-
sel, the reaction on the side of the vessel opposite the orifice is equal to the
weight of a column of water the section of which is the area of the orifice,
and the height is twice the head.
The propelling force in jet-propulsion is the reaction of the stream issuing
from the orifice, and it is the same whether the jet is discharged under
water, in the open air, or against a solid wall. For proof, see account of
trials by C. J. Everett, Jr., given by Prof. J. Burkitt Webb, Trans. A. S. M.
E.,xii. 904.
RECENT PRACTICE IN MARINE ENGINES.
(From a paper by A. Blechynden on Marine Engineering during the past
Decade, Proc. Inst. M. E., July, 1891.)
Since 1881 the three-stage-expansion eneine has become the rule, and the
boiler-pressure has been increased to 160 Ibs. and even as high as 200 Ibs.per
square inch. Four-stage-expansion engines of various forms have also been
adopted.
Forced Draught has become the rule in all vessels for naval service,
and is comparatively common in both passenger and cargo vessels. By this
means it is possible considerably to augment the power obtained from a
given boiler; and so long as it is kept within certain limits it need result in
no injury to the boiler, but when pushed too far the increase is sometimes
purchased at considerable cost.
In regard to the economy of forced draught, an examination of the ap-
pended table (page 1018) will show that while the mean consumption of coal
in those steamers working under natural draught is 1.578 Ibs. per indicated
horse-power per hour, it is only 1.336 Ibs. in those fitted with forced draught. '-
This is equivalent to an economy of 15#. Part of this economy, however,
may be due to the other heat-saving appliances with which the latter
steamers are fitted.
Bollem.— As a material for boilers, iron is now a thing of the past,
though it seems probable that it will continue yet awhile to be the material
for tubes. Steel plates can be procured at 132 square feet superficial area
and l^jj inches thick. For purely boiler work a punching-machine has be-
come obsolete in marine-engine work.
The increased pressures of steam have also caused attention to be directed
to the furnace, and have led to the adoption of various artifices in the shape
of corrugated, ribbed, and spiral flues, with the object of giving increased
.strength against collapse without abnormally increasing the thickness of
the plate. A thick furnace- plate is viewed by many engineers with great
1016 MARINE
suspicion; and the advisers of the Board of Trade have fixed the limit of
thickness for furnace-plates at % inch ; but whether this limitation will
stand in the light of prolonged experience remains to be seen. It is a fact
generally accepted that the conditions of the surfaces of a plate are far
greater factors in its resistance to the transmission of heat than either the
material or the thickness. With a plate free from lamination, thickness
being a mere secondary element, it would appear that a furnace-plate might
be increased from ^ inch to % inch thickness without increasing its resist-
ance more than \y&. So convinced have some engineers become of the
soundness of this view that they have adopted flues % inch thick.
Piston-valves.— Since higher steam -pressures have become common,
piston-valves have become the rule for the high-pressure cylinder, and are
not unusual for the intermediate. When well designed they have the great
advantage of being almost free from friction, so far as the valve itself is
concerned. In the earlier piston-valves it was customary to fit spring
rings, which were a frequent source of trouble and absorbed a large amount
of power in friction ; but in recent practice it has become usual to fit spring-
less adjustable sleeves.
For low-pressure 'cylinders piston-valves are not in favor; if fitted with
spring rings their friction is about as great as and occasionally greater than
that of a well-balanced slide-valve; while if fitted with springless rings there
is always some leakage, which is irrecoverable. But the large port-clear-
ances inseparable from the use of piston -valves are most objectionable;
and with triple engines this is especially so, because with the customary
late cut-off it becomes difficult to compress sufficiently for insuring econo-
my and smoothness of working when in " full gear,1' without some special
device.
Steam-pipes.— The failures of copper steam-pipes on large vessels
have drawn serious attention both to the material and the modes of con-
struction of the pipes. As the brazed joint is liable to be imperfect, it is
proposed to substitute solid drawn tubes, but as these are not made of large
sizes two or more tubes may be needed' to take the place of one brazed tube.
Reinforcing the ordinary brazed tubes by serving them with steel or copper
wire, or by hooping them at intervals with steel or iron bands, has been
tried and found to answer perfectly.
Auxiliary Supply of Fresh "Water— Evaporators.— To make
up the losses of water due to escape of steam from safety-valves, leakage at
glands, joints, etc., either a reserve supply of fresh water is carried in tanks,
or the supplementary feed is distilled from sea-water by special apparatus
provided for the purpose. In practice the distillation is effected by passing
steam, say from the first receiver, through a nest of tubes inside a still or
evaporator, of which the steam-space is connected either with the second
receiver or with the condenser. The temperature of the steam inside the
tubes being higher than that of the steam either in the second receiver or in
the condenser, the result is that the water inside the still is evaporated, and
passes with the rest of the steam into the condenser, where it is condensed
and serves to make up the loss. This plan localizes the trouble of the de-
posit, and frees it from its dangerous character, because an evaporator can-
not become overheated like a boiler, even though it be neglected until it
salts up solid; and if the same precautions are taken in working the evapo-
rator which used to be adopted with low-pressure boilers when they were
fed with salt water, no serious trouble should result.
"Weir's Feed-water Heater.— The principle of a method of heating
feed -water introduced by Mr. James Weir and widely adopted in the
marine service is founded 011 the fact that, if the feed -water as it is drawn
from the hot-well be raised in temperature by the heat of a portion of steam
introduced into it from one of the steam-receivers, the decrease of the coal
necessary to generate steam from the water of the higher temperature bears
a greater ratio to the coal required without feed-heating than the power
which would be developed in the cylinder by that portion of steam would
bear to the whole power developed when passing all the steam through all
the cylinders. Suppose a triple-expansion engine were working under the
following conditions without feed-heating: boiler-pressure 150 Ibs.; I.H.P. in
high-pressure cylinder 398, in intermediate and low-pressure cylinders to-
gether 790, total 1188. The temperature of hot-well 100° F. Then with feed-
heating the same engine might work as follows: the feed might be heated to
220° F., and the percentage of steam from the first receiver required to heat
it would be 10.9#; the I.H.P. in the h.p. cylinder would be as before 398, and
in the three cylinders it would be 1103, or 93# of the power developed without
RECENT PRACTICE IN MARINE ENGINES. 1017
feed-heating. Meanwhile the heat to be added to each pound of the feed-water
af 250° F. for converting it into steam would be 1005 units against 1125 units
jdth feed at 100° F., equivalent to an expenditure of only 89. 4# of the heat
required without feed-heating. Hence the expenditure of heat in relation
to power would be 89.4 -*- 93.0 = 96.4#, equivalent to a heat economy of 3.6#.
If the steam for heating can be taken from the low-pressure receiver, the
economy is about doubled.
Passenger Steamers fitted with Turin Screws.
i i -Ji
%
£££
Cylinders, two sets
.
g
Vessels.
*3
A a .2
. +5 JSJ2
in all.
, 3 cr
||
ti ®
fc?£s
5
«* tf *
8 g
SU
1
Diameters.
Stro.
S*&
1*
Feet
Feet
Inches
In.
Lbs.
I.H.P.
City of New York j.
525
63^
45, 71, 113
60
150
20,000
" " Paris \ ' '
Majestic (_
565
58
43, 68, 110
60
180
18,000
Teutonic I ' '
Normannia
500
57V
40, 67, 106
66
160
11 500
463^
55>J
41, 66, 101
66
160
12500
Empress of India )
" " Japan V
" China j
440
51
32, 51, 82
54
160
10,125
Orel
415
48
34 54 85
51
160
10000
Scot
460
34J4, 57^, 92
60
170
11,656
Comparative Results of Working of Marine lEiigines,
1872, 1881, and 1891.
Boilers, Engines, and Coal.
1872.
1881.
1891.
Boiler-pressure Ibs per sq in .
52.4
77.4
158 5
Heating-surface per horse-power, sq. ft
Revolutions per minute, revs
4.410
55.67
3.9)7
59.76
3.275
63.75
Piston-speed, feet per min
376
467
529
Coal per horse-power per hour, Ibs
2.110
1.828
1 522
Weignt of Three - stage - expansion Engines in Nine
Steamers in Relation to Indicated Horse-power and
to Cylinder-capacity.
1
Weight of
Machinery.
Relative Weight of Machinery.
Type of
Per Indicated Horse-
S«i
as'*>
DQ
c 3
£s
3
power.
?*"•"§•-
l^il
Machinery.
*0
d
'K
f§
H
rs o
§
a Q,«M o
ffi1
Engine-
room.
Boiler-
room.
Total
tons.
tons.
tons.
Ibs.
Ibs.
Ibs.
tons.
tons.
1
681
662
1343
226
220
446
1.30
3.75
Mercantile
2
638
619
1257
259
251
510
1.46
4.10
*'
3
134
128
262
207
198
405
1.23
3.23
•*
4
38.8
46.2
85
170
203
373
1.29
3.30
**
5
719
695
1414
167
162
329
1.41
3.44
M
6
75.2
107.8
183
141
202
343
1.37
3.37
it
7
44
61
105
77
108
185
1.21
2.72 1
Naval
horizontal
8
73.5
109
182.5
78
116
194
1.11
2.78
do.
9
262
429
691
62.5
102
165
0.82
2.70 -j
Naval
vertical
i018
MARIiTB EKGIKEERIKG.
WWKW W WH MM
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M'Hl
^uan
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MtlOtJ
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jo '!}j *bs aad £;3£^2^S^S^i£i^?3t""?-3S!5S£HrtSSS
•8^a3 jo -i}j
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k
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oc
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C?c* w(NOJOJ»**Je<i<?Jw<?i<Ncc'NT-ii-i(NO*i--iTHC}THrt^r-ir-ia<i<N
F«.W
•UTUI aad •%
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h
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Propel
_*i
8-as
111
ill
3S22
W
«a
I
1019
jdimensions, Indicated Horse - power, and Cylinder*
eapaeity of Three -stage -expansion Engines in Nine
Steamers.
02
1
"i
a) a
O CD
<t> o
71)02
Cylinders.
II
3.9
,If
TJ£
!l
£&
T3'o
Heating-sur-
face.
|OQ
£
•S3
»(
EH
Diameters.
Stroke
3S
4> CD
tf *
III
M
? |
e^ O
51
Total.
Per
I.H.P.
ins.
ins.
revs.
Ibs.
I.H.P.
cu.ft.
sq. ft.
sq. ft.
i
2
Single
40 66 100
39 61 97
66
64.5
67.8
160
160
6751
5525
522
436
17,640
15,107
2.62
2.73
3
'*
23 38 61
42
83
160
1450
109
3,973
2.73
4
"
17 26U 42
24
90
150
510
30
1,403
2.75
5
Twin
32 54 82
54
88
160
9625
508
20,193
2.10
6
k*
15 24 38
27
113
150
1194
55
3,200
2.68
7
Single
20 30 45
24
191
145
1265
36.3
2,227
1.76
8
Twin
18^ 29 43
24
182.5
140
2105
66.2
3,928
1.87
9
"
33^ 49 74
39
145
150
9400
319
15,882
1.62
CONSTRUCTION OF BUILDINGS.*
(Extract from the Building Laws of the City of New "York, 1893.)
Walls of Warehouses, Stores, Factories, and Stables.—
25 feet or less in width between walls, not less than 12 in. to height of 40 ft.;
If 40 to 60 ft. in height, not less than 16 in. to 40 ft., and 12 in. thence to top:
60 to 80 " " " " " 20 " 25 " 16
75 to 85 " * " *« «• 24 •' SO ft. ; 20 in. to 60 ft., and 16 in.
to top;
85 to 100 ft. in height, not less than 28 in. to 25 ft.; 24 in. to 50 ft.: 20 in'
to 75 ft., and 16 in. to top;
Over 100 ft. in height, each additional 25 ft. in height, or part thereof, next
above the curb, shall be increased 4 inches in thickness, the upper 100
feet remaining the same as specified for a wall of that weight.
If walls are over 25 feet apart, the bearing-walls shall be 4 inches thicker
than above specified for every 12J^ feet or fraction thereof that said walla
are more than 25 feet apart.
Strength, of Floors, Roofs, and Supports.
Floors calculated to bear
safely per sq. ft., in addition
to their own weight.
Floors of dwelling, tenement, apartment-house or hotel, not
less than TOlbs.
Floors of office-building, not less than 100 "
public-assembly building, not less than 120 **
u store, factory, warehouse, etc., not less than... .... 150 **
Roofs of all buildings, not less than 60 *'
Every floor shall be of sufficient strength to bear safely the weight to be
imposed thereon, in addition to the weight of the materials of which the
floor is composed,
Columns and Posts.— The strength of all columns and posts shall
be computed according to Gordon s formulae, and the crushing weights in
pounds, to the square incl of section, for the following-named materials,
shall be taken as the coefficients in said formulae, namely: CasC iron, 80,000;
* The limitations of space fo»bi T any extended treat m nt of this subject.
Much valuable information upon it will be found in Trautwiiie's Civil Engi-
neer's Pocket-book, and in Kidder's Architect's an L Builder's Pocket-book.
The latter in its preface mentions the following works of reference: " Notes
on Bui) ding Construction," 3 vols., Rivingtons, publishers, Boston; "Building
Superintendence," by T. M.' Clark (J. R. Osgood & Co., Boston.); "The
American House Carpenter," by R. G. Hal field ; ** Graphical Analysis of
ing Mortars and Cements," by Fred. T. Hodgson; "Foundations and Con-
crete Works." and "Art of Building," by E. Dobsou, Weale's Series, London.
J. H. woodbury; "House Drainage and Water Service," Dy james t7.
Bayles; " The Builder's Guide and Estimator's Price-book," and "Plaster-
ing Mortars and Cements,'1 by Fred. T. Hodgson; "Foundations arid Con-
crete Works." and '* Art of Building," by E. Dobson, Weale's Series, London,
1020 COKSTKUCTIOK OF BUILDIKGS.
wrought or rolled iron, 40,000; rolled steel, 48,000; white pine and spruce,
8500; pitch or Georgia pine, 5000; American oak, 6000. The breaking strength
of wooden beams and girders shall be computed according to the formulae
in which the constants for transverse strains for central load shall be as
follows, namely: Hemlock, 400; white pine, 450; spruce, 450; pitch or Georgia
pine, 550; American oak, 550; and for wooden beams and girders carrying a
uniformly distributed load the constants will be doubled. The factors of
safety shall be as one to four for all beams, girders, and other pieces subject
to a transverse strain; as one to four for all posts, columns, and other
vertical supports when of wrought iron or rolled steel; as one to five for
other materials, subject to a compressive strain; as one to six for tie-
rods, tie-beams, and other pieces subject to a tensile strain. Good, solid,
natural earth shall be deemed to safely sustain a load of four tons to the
superficial foot, or as otherwise determined by the superintendent of build-
ings, and the width of footing-courses shall be at least sufficient to meet this
requirement. In computing the width of walls, a cubic foot of brickwork
shall be deemed to weigh 115 Ibs. Sandstone, white marble, granite, and
other kinds of building-stone shall deemed to weigh 160 Ibs. per cubic foot.
The safe-bearing load to apply to good brickwork shall be taken at 8 tons
per superficial foot when good lime mortar is used, 11^ tons per superficial
foot when good lime and cement mortar mixed is used, and 15 tons per sup-
erficial foot when good cement mortar is used.
Fire-proof Buildings— Iron and Steel Columns.— All cast-
iron, wrought-iron, or rolled-steel columns shall be made true and smooth
at both ends, and shall rest on iron or s^eel bed-plates, and have iron or
steel cap-plates, which shall also be made true, All iron or steel trimmer-
beams, headers, and tail-beams shall be suitably framed and connected to-
gether, and the iron girders, columns, beams, trusses, and all other ironwork
of all floors and roofs shall be strapped, bolted, anchored, and connected to-
gether, and to the walls, in a strong and substantial mariner. Where beams
are framed into headers, the angle-irons, which are bolted to the tail-beams,
shall have at least two bolts for all beams over 7 inches in depth, and three
bolts for all beams 12 inches and over in depth, and thece bolts shall not bi
less than % inch in diameter. Each one of such angles or knees, when bolte< \
to girders, shall have the same number of bolts as stated for the other leg.
The angle-iron in no case shall be less in thickuess-than the header or trim-
mer to which it is bolted, and the width of angle in no case shall be less than
one third the depth of beam, excepting that no angle-knee shall be less than
2*4 inches wide, nor required to be more than 6 inches wide. All wrought-
iron or rolied-steel beams 8 inches deep and under shall have bearings equal
to their depth, if resting on a wall; 9 to 12 inch beams shall have a bearing
of 10 inches, and all beams more than 12 inches in depth shall have bearings
of not less than 12 inches if resting on a wall. Where beams rest on iron
supports, and are properly tied to the same, no greater bearings shall be re-
quired than one third of the depth of the beams. Iron or steel floor-beams
shall be so arranged as to spacing and length of beams that the load to be
supported by them, together with the weights of the materials used in the
construction of the said floors, shall not cause a deflection of the said beams
of more than 1/30 of an inch per linear foot of span; and they shall be tied
together at intervals of not more than eight times the depth of the beam.
Under the ends of all iron or steel beams, where they rest on the walls, a
stone or cast-iron template shall be built into the walls. Said template shall
be 8 inches wide in 12 -inch walls, and in all walls of greater thickness said
template shall be 12 inches wide; and such templates, if of stone, shall not be
in any case less than 2^£ inches in thickness, and no template shall be less
than 12 inches long.
No cast-iron post or column shall be used in any building of a less average
thickness of shaft than three quarters of an inch, nor shall it have an un-
supported length of more than twenty times its least lateral dimensions or
diameter. No wrought-iron or rolled-steel column shall have an unsupported
length of more than thirty times its least lateral dimension or diameter, nor
shall its metal be less than one fourth of an inch in thickness.
Lintels, Bearings and Supports.— All iron or steel lintels shall
have bearings proportionate to the weight to be imposed thereon, but no
lintel used to span any opening more than 10 feet in width shall have a bear-
ing less than 12 inches at each end, if resting on a wall; but if resting on an
iron post, such lintel shall have a bearing of at least 6 inches at each end,
by the thickness of the wall to be supported
Strains on drders and Rivets.— Rolled iron or steel beam gir-
STRENGTH OF FLOORS. 1021
ders, or riveted iron or steel plate girders used as lintels or as girders,
carrying a wall or floor or both, shall be so proportioned that the loads
which may come upon them shall not produce strains in tension or com-
pression upon the flanges of more than 12,000 Ibs. for iron, nor more than
15,000 Ibs. for steel per square inch of the gross section of each of such
flanges, nor a shearing strain upon the web-plate of more than 6000 Ibs. per
square inch of section of such web-plate, if of iron, nor more than 7000
pounds if of steel; but no web-plate shall be less than y± inch in
thickness. Rivets in plate girders shall not be less than % inch in diameter,
and shall not be spaced more than 6 inches apart in any case. They shall be
so spaced that their shearing strains shall not exceed 9000 Ibs. per square
inch, on their diameter, multiplied by the thickness of the plates through
which they pass. The riveted plate girders shall be proportioned upon the
supposition that the bending or chord strains are resisted entirely by the
upper and lower flanges, and that the shearing strains are resisted "entirely
by the web-plate. No part of the web shall be estimated as flange area, nor
more than one half of that portion of the angle-iron which lies against the
web. The distance between the centres of gravity of the flange areas will
be considered as the effective depth of the girder.
The building laws of the City of New York contain a great amount of de-
tail in addition to the extracts above, and penalties are provided for viola-
tion. See An Act creating a Department of Buildings, etc., Chapter 275,
Laws of 1892. Pamphlet copy published by Baker, Voorhies & Co., New
York.
JJIAX1MUM LOAD ON FLOORS.
(Eng'g, Nov. 18, 1892. p. 644.)— Maximum load per square foot of floor
surface due to the weight of a dense crowd. Considerable variation is
apparent in the figures given by many authorities, as the following table
shows:
Authorities. *£&£&
French practice, quoted by Trautwine and Stoney 41
HatfieldO* Transverse Strains," p. 80) 70
Mr. Page, London, quoted by Trautwine 84
Maximum load on American highway bridges according to
Waddell's general specifications 100
Mr. Nash, architect of Buckingham Palace 120
Experiments by Prof. W. N. Kernot, at Melbourne j U3 1
Experiments by Mr. B. B. Stoney (" On Stresses," p. 617) ... 147.4
The highest results were obtained by crowding a number of persons pre-
viously weighed into a small room, the men being tightly packed so as to
resemble such a crowd as frequently occurs on the stairways and platforms
of a theatre or other public building.
STRENGTH OF FLOORS.
(From circular of the Boston Manufacturers' Mutual Insurance Co.)
The following tables were prepared by C. J. H. Woodbury, for determining
safe loads on floors. Care should be observed to select the figure giving the
greatest possible amount and concentration of load as the one which may
be put upon any beam or set of floor-beams; and in no case should beams be
subjected to greater loads than those specified, unless a lower factor of
safety is warranted under the advice of a competent engineer.
Whenever and wherever solid beams or heavy timbers are made use of in
the construction of a factory or warehouse, they should not be painted, var-
nished or oiled, filled or encased in impervious concrete, air-proof plastering,
or metal for at least three years, lest fermentation should destroy them by
what is called '* dry rot."
It is, on the whole, safer to make floor-beams in two parts, with a small
open space between, so that proper ventilation may be secured, even if the
outside should be inadvertently painted or filled.
These tables apply to distributed loads, but the first can be used in respect
to floors which may carry concentrated loads by using half the figure given
in the table, since a beam will bear twice as much load when evenly distrib-
uted over its length as it would if the load was concentrated in the centre
of the span.
The weight of the floor should be deducted from the figure given in the
table, in order to ascertain the net load which may be placed upon any floor.
The weight of spruce may be taken at 36 Ibs. per cubic foot, and that of
Southern pine at 48 Ibs. per cubic foot.
1022 CONSTRUCTION OF BUILDINGS.
Table I was computed upon a working modulus of rupture of Southern
pine at 2160 Ibs., using a factor of safety of six. It can also be applied to
ascertaining the strength of spruce beams if the figures given in the table
are multiplied by 0.78; or in designing a floor to be sustained by spruce
beams, multiply the required load by. 1.28, and use the dimensions as given
by the table.
Theses tables are computed for beams one inch in width, because the
strength of beams increases directly as the width when the beams are broad
enough not to cripple.
EXAMPLE. — Required the safe load per square foot of floor, which may be
safely sustained by a floor on Southern pine 10 X 14 inch beams, 8 feet on
centres, and 20 feet span. In Table I a 1 X 14 inch beam, 20 feet span, will
sustain 118 Ibs. per foot of span; and for a beam 10 inches wide the load
would be 1180 Ibs. per foot of span, or 147^ Ibs. per square foot of floor for
Southern-pine beams. From this should be deducted the weight of the floor,
which would amount to 17J4 Ibs. per square foot, leaving 130 Ibs. per square
foot as a safe load to be carried upon such a floor. If the beams are of
spruce, the result of 147^j Ibs. would be multiplied by 0.78, reducing the load
to 115 Ibs. The weight of the floor, in this instance amounting to 16 Ibs.,
would leave the safe net load as 90 Ibs. per square foot for spruce beams.
Table II applies to the design of floors whose strength must be in excess
of that necessary to sustain the weight, in order to meet the conditions of
delicate or rapidly moving machinery, to the end that the vibration or dis-
tortion of the floor may be reduced to the least practicable limit.
In the table the limit is that of load which would cause a bending of the
beams to a curve of which the average radius would be 1250 feet.
This table is based upon a modulus of elasticity obtained from observa-
tions upon the deflection of loaded storehouse floors, and is taken at 2,000,000
Ibs. for Southern pine;, the same table can be applied to spruce, whose
modulus of elasticity is taken as 1,200,000 Ibs., if six tenths of the load for
Southern pine is taken as the proper load for spruce; or, in the matter of
designing, the load should be increased one and two thirds times, and the
dimension of timbers for this increased load as found in the table should be
used for spruce.
It can also be applied to beams and floor-timbers which are supported at
each end and in the middle, remembering that the deflection of a beam
supported in that manner is only four tenths that of a beam of equal span
which rests at each end; that is to say, the floor-planks are two and one
half times as stiff, cut two bays in length, as they would be if cut only one
bay in length. When a floor-plank two bays in length is evenly loaded,
three sixteenths of the load on the plank is sustained by the beam at each
end of the plank, and ten sixteenths by the beam under the middle of the
plank; so that for a completed floor three eighths of the load would be sus-
tained by the beams under the joints of the plank, and five eighths of the load
by the beams under the middle of the plank: this is the reason of the impor-
tance of breaking joints in a floor-plank every three feet in order that each
beam shall receive an identical load. If it were not so, three eighths of the
whole load upon the floor would be sustained by every other beam, and five
eighths of the load by the corresponding alternate beams.
Repeating the former example for the load on a mill floor on Southern-
pine beams 10 X 14 inches, and 20 feet span, laid 8 feet on centres: InVTable
II a 1 X 14 inch beam should receive 61 Ibs. per foot of span, or 75 Ibs. per
sq. ft. of floor, for Southern-pine beams. Deducting the weight of the floor,
17J4 Ibs. per sq. ft., leaves 57 Ibs. per sq. ft. as the advisable load.
If the beams are of spruce, the result of 75 Ibs. should be multiplied by 0.6,
reducing the load to 45 Ibs. The weight of the floor, in this instance amount-
ing to 16 Ibs., would leave the net load as 29 Ibs. for spruce beams.
If the beams were two spans in length, they could, under these conditions,
support two and a half times as much load with an equal amount of deflec-
tion, unless such load should exceed the limit of safe load as found by Table
I, as would be the case under the conditions of this problem.
Mill Columns.— Timber posts offer more resistance to fire than iron
pillars, and have generally displaced them in millwork. Experiments
made on the testing-machine at the U. S. Arsenal at Watertown. Mass.,
show that sound timber posts of the proportions customarily used in mill-
work yield by direct crushing, the strength being directly as the area at the
smallest part. The columns yielded at about 4500 Ibs. per square inch, con-
firming the general practice of allowing 600 Ibs. per square inch, as a safe
load. Square columns are one fourth stronger than round ones of the same
diameter.
STRENGTH OF FLOORS.
1023
I. Safe "Distributed Loads upon Southern -pane Beams
One Ineli in Width.
(C. J. H. Woodbury.)
(If the load is concentrated at the centre of the span, the beams will sus<
tain half the amount as given in the table.)
1
a
&
02
Depth of Beam in inches.
2
3
4
5
0|7|8
9 | 10
11
12
13
14
15
16
Load in pounds per foot of Span.
5
6
8
9
10
11
12
13
14
15
16
*7
18
19
20
21
22
23
24
25
38
27
20
15
86
60
44
34
27
22
154
107
78
60
47
38
32
27
240
167
122
94
74
60
50
42
36
31
27
346
240
176
135
107
86
71
60
51
44
38
34
30
470
32?
240
184
145
118
97
82
70
60
52
46
41
36
614
427
314
240
190
154
127
107
90
78
68
60
53
47
43
38
778
540
397
304
240
194
161
135
115
99
86
76
67
60
54
49
44
960
667
490
375
296
240
198
167
142
123
107
94
83
74
66
60
54
50
45
807
593
454
359
290
240
202
172
148
129
113
101
90
80
73
66
60
55
50
46
705
540
427
346
286
240
205
176
154
135
120
107
96
86
78
71
65
60
55
828
634
501
406
335
282
240
207
180
158
140
!25
112
101
92
84
77
70
65
735
581
470
389
327
278
240
209
184
163
145
130
118
10?
97
89
82
75
667
540
446
375
320
276
240
211
187
167
150
135
122
112
102
94
86
759
614
508
474
364
314
273
240
217
190
170
154
139
127
116
107
98
II. Distributed Loads upon Southern-pine Beams suffi>
cient to produce Standard Limit of Deflection.
(C. J. H. Woodbury.)
C
9
I
Vi
Depth of Beam in inches.
Deflection,
inches.
0
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Load in pounds per foot of Span.
o
6
7
8
9
10
11
•jo
13
14
15
16
17
18
19
20
21
22
23
24
25
3
9
10
7
5
4
23
16
12
9
7
6
44
31
23
14
11
9
77
53
39
30
24
19
16
13
11
122
85
62
48
38
30
25
21
18
16
14
182
126
93
71
56
46
38
32
27
23
20
18
16
259
180
132
101
80
65
54
45
38
33
29
25
22
20
18
247
181
139
110
89
73
62
53
45
40
35
31
27
25
22
20
241
185
146
118
98
82
70
60
53
46
41
37
33
30
27
24
22
240
190
154
127
107
91
78
68
60
53
47
43
38
35
32
29
27
25
305
241
195
161
136
116
100
87
76
68
60
54
49
44
40
37
34
81
301
244
202
169
144
124
108
95
84
75
68
61
55
50
46
42
39
300
248
208
178
153
133
117
104
93
83
75
68
62
57
52
48
301
253
215
186
162
147
126
112
101
91
83
75
69
63
58
.0300
.0432
.0588
.0768
.0972
.1200
.1452
.1728
.2028
.2352
.2700
.3072
.3468
.3888
.4332
.4800
.5292
.5808
.6348
.6919
.7500
1024 ELECTRICAL
ELECTRICAL ENGINEERING.
STANDARDS OF MEASUREMENT.
C.G.S. (Centimetre, Gramme, Second) or u Absolute''
System of Physical Measurements :
Unit of space or distance = 1 centimetre, cm.;
Unit of mass = 1 gramme, gm. ;
Unit of time = 1 second, s.;
Unit of velocity = space -4- time = 1 centimetre in 1 second;
Unit of acceleration = change of 1 unit of velocity in 1 second ;
Acceleration due to gravity, at Paris, = 981 centimetres in 1 second;
1 002204fi
Unit of force = 1 dyne = ~- gramme = — - — Ib. = .000002247 Ib.
9bl «7Ol
A dyne is that force which, acting on a mass of one gramme during one
second, will give it a velocity of one centimetre per second. The weight of
one gramme in latitude 40° to 45° is about 980 dynes, at the equator 973 dynes,
and at the poles nearly 984 dynes. Taking the value of g, the acceleration
due to gravity, in British measures at 32.185 feet per second at Paris, and the
metre = 39.37 inches, we have
1 gramme = 32.185 X 12 -*• .3937 = 981. 00 dynes.
Unit of work = 1 erg = 1 dyne-centimetre = .00000007373 foot-pound ;
Unit of power = 1 watt = 10 million ergs per second,
= .7373 foot-pound per second,
= ^~ = j^j of 1 horse -power = .00134 H.P.
C.G.S. Unit of magnetism = the quantity which attracts or repels an
equal quantity at a centimetre's distance with the force of 1 dyne.
C.G.S. Unit of electrical current = the current which, flowing through a
length of 1 centimetre of wire, acts with a force of 1 dyne upon a unit of
magnetism distant 1 centimetre from every point of the wire. The ampere,
the commercial unit of current, is one tenth of the C.G.S. unit.
The Practical Units used in Electrical Calculations are:
Ampere, the unit of current strength, or rate of flow, represented by /.
Volt, the unit of electro-motive force, electrical pressure, or difference of
potential, represented by E.
Ohm, the unit of resistance, represented by R.
Coulomb (or ampere- second), the unit of quantity, Q.
Ampere-hour = 3600 coulombs, Q'.
Watt (ampere-volt, or volt -ampere), the unit of power, P.
Joule (volt-coulomb), the unit of energy or work, W.
Farad, the unit of capacity, represented by C.
Henry, the unit of inductance, represented by L.
Using letters to represent the units, the relations between them may be
expressed by the following formulae, in which t represents one second and
T one hour:
/=!, Q = It, Q' = 1T, 0=j|, W=QE, P=IE.
As these relations contain no coefficient other than unity, the letters may
represent any quantities given in terms of those units. For example, if E
represents the number of volts electro- motive force, and K the number of
ohms resistance in a circuit, then their ratio E -t- R will give the number of
amperes current strength in that circuit.
The above six formulae can be combined by substitution or elimination,
so as to give the relations between any of the quantities. The most impor-
tant of these are the following :
O = IU C=i, W= IEt = ^t = I*Rt = Pt,
K Hi -tt
E E* W OE
, E=IR. * = , Ji.JW.*.
STANDARDS OF MEASUREMENT. 1025
The definitions of these units as adopted at the International Electrical
Congress at Chicago in 1893, and as established by Act of Congress of the
United States, July 12, 1894, are as follows:
The ohm is substantially equal to 109 (or 1,000,000,000) units or resistance
of the C.G.S. system, and is represented by the resistance offered to an un-
varying electric current by a column of mercury at 32° F., 14.4521 grammes
in mass, of a constant cross-sectional area, and of the length of 100.3 centi-
metres.
The ampere is 1/10 of the unit of current of the C.G.S. system, and is the
practical equivalent of the unvarying current which when passed through
a solution of nitrate of silver in water in accordance with standard speci-
fications deposits silver at the rate of .001118 gramme per second.
The volt is the electro-motive force that, steadily applied to a conductor
whose resistance is one ohm, will produce a current of one ampere, and is
practically equivalent to 1000/1434 (or .6974) of the electro-motive force be-
tween the poles or electrodes of a Clark's cell at a temperature of 15° C.,
and prepared in the manner described in the standard specifications.
The coulomb is the quantity of electricity transferred by a current of one
ampere in one second.
The farad is the capacity of a condenser charged to a potential of one
volt by one coulomb of electricity.
The joule is equal to 10,COO,000 units of work in the C.G.S. system, and is
Tactically equivalent to the energy expended in one second by an ampere
in an ohm.
The watt is equal to 10,000,000 units of power in the C.G.S. system, and is
practically equivalent to the work done at the rate of one joule per second.
The henry is the induction in a circuit when the electro-motive force in-
duced in this circuit is one volt, while the inducing current varies at the rate
of one ampere per second.
The ohm, volt, etc., as above defined, are called the "international " ohm,
volt, etc., to distinguish them from the " legal " ohm, B.A. unit, etc.
The value of the ohm, determined by a committee of the British Associa-
tion in 1863, called the B.A. unit, was the resistance of a certain Apiece of
copper wire. The so-called "legal" ohm, as adopted at the International
Congress of Electricians in Paris in 1884, was a correction of the B.A. unit,
and was defined as the resistance of a column of mercury 1 square millimetre
in section and 106 centimetres long, at a temperature of 32° F.
1 legal ohm = 1.0112 B.A. units, 1 B.A. unit = 0.9889 legal ohm;
1 international ohm = 1.0136 *« " 1 *' " = 0.9866 int. ohm;
1 »•"••.« 1.0023 legal ohm, 1 legal ohm = 0.9977 "
DERIVED UNITS.
1 megohm = 1 million ohms;
1 microhm = 1 millionth of an ohm;
1 milliampere = 1/1000 of an ampere;
1 micro-farad = 1 millionth of a farad.
RELATIONS OF VARIOUS UNITS.
P1
iu
I ampere = 1 coulomb per second;
1 volt-ampere =1 watt = 1 volt-coulomb per second;
( = .7373 foot-pound per second,
1 watt , •< = .0009477 heat-units per second (Fahr.),
f = 1/746 of one horse-power;
( = .7373 foot-pound,
1 joule ..... K — work done by one watt in one second,
C = .0009477 heat-unit;
1 British thermal unit = 1055.2 joules;
1 kilowatt, or 1000 watts = 1000/746 or 1.3405 horse-powers;
1 kilowatt-hour, ( = 1.3405 horse-power hours,
1000 volt-ampere hours, < = 2,654,200 foot-pounds,
1 British Board of Trade unit, ( = 341'3 heat-units;
j = 746 warts = 746 volt-amperes,
1 horse-power -j _ 33^000 foot-pounds per minute.
The ohm, ampere, and volt are defined in terms of one another as follows:
Ohm the resistance of a conductor through which a current of one ampere
will pass when the electro-motive force is one volt. Ampere, the quantity
of current which will flow through a resistance of one ohm when the electro-
motive force is one volt. Volt, the electro-motive force required to cause a
current of one ampere to flow through a resistance of one ohm.
1026
ELECTRICAL EHGIHEERIKG.
sfi1
'~ i *•«
0) P.O)
a • ft
jFp;
|WE
(Jji>-00
sss
.I
. .
55=
•- • L
C fl t-
S »
itac-
|^s
2&&
Kilogram
Metre =
;lls ^
f!
'
5 .
® .2
te.
pe
m
t.-l
Hflj
W
n Oth
Val
I
o'ofco"
os c5
W °8
FLOW OF WATER AKD ELECTRICITY.
1027
ing,
Table
Units of tne ]Haguetic Circuit.— (See Electro-magnels, page 1052.)
For Methods of making Electrical Measurements, Test-
ig, etc., see Munroe & Jamieson's Pocket-Book of Electrical Rules,
ibles, and Data; S. P. Thompson's Dynamo-Electric Machinery; Carhart &
Patterson's Electrical Measurements; and works on Electrical Engineering.
Equivalent Electrical and Mechanical Units.— H. Ward
Leonard published in The Electrical Engineer, Feb. 25, 1895, a table of useful
equivalents of electrical and mechanical units, from which the table on page
1026 is taken, with some modifications.
ANALOGIES BETWEEN THE FLOW OF WATER AND
ELECTRICITY.
WATER. ELECTRICITY.
Head, difference of level, in feet. ) Volts; electro-motive force; differ-
Difference of pressure, Ibs. per sq. in. J ence of potential; E. or E.M.F.
Ohms, resistance, R. Increases di-
rectly as the length of the conductor
or wire and inversely as its sectional
area, R op I -*• s. It varies with the
nature of the conductor.
Amperes; current; current strength;
Resistance of pipes, apertures, etc.,
increases with length of pipe, with
contractions, roughness, etc.; de-
creases with increase of sectional
area.
Rate of flow, as cubic ft. per second,
gallons per minute, etc., or volume
divided by the time. In the mining
regions sometimes expressed
"miners' inches."
Quantity, usually measured in cubic 1
ft. or gallons, but is also equivalent I
to rate of flow X time, as cu. ft. per j"
second for so many hours.
Work, or energy, measured in foot-
pounds; product of weight of fall-
ing water into height of fall; in
pumping, product of quantity in
cubic feet into the pressure in Ibs.
per square foot against which the
water is pumped.
Power, rate of work. Horse-power =
ft.-lbs. of work in 1 inin. -*- 33,000.
In water flowing in pipes, rate of
flow in cu. ft. per second X resist-
ance to the flow in Ibs. per sq. ft.
-r-550.
intensity of current; rate of now;
1 ampere = 1 coulomb per second.
volts , E
Amperes
i-T-
ohms
= ~;E=IR.
iere-hour = 3600 coulombs.
Joule, volt-coulomb, W, the unit of
work, = product of quantity by the
electro-motive force = volt-ampere-
second. 1 joule =.7373 foot-pound.
If C (amperes) = rate of flow, and
E (volts) = difference of pressur**
between two points in a circuit,
energy expended = lEt, — I^Rt.
Watt, unit of power, P, = volts X
amperes, = current or rate of flow
X difference of potential.
1 watt = .7373 foot-pound per second
= 1/746 of a horse-power.
ELECTRICAL RESISTANCE.
Laws of Electrical Resistance.— The resistance, R, of any con-
ductor varies directly as its length, I, and inversely as its sectional area, s,
or R QC I -T- s.
If r = the resistance of a conductor 1 unit in length and 1 square unit in
sectional area, R = rl -f- s. The common unit of length for electrical calcu-
lations in English measure is the foot, and the unit of area of wires is the
circular mil = the area of a circle 0.001 in. diameter. 1 mil-foot = 1 foot
long 1 circ.-mil area.
Resistance of 1 mil -foot of soft copper wire at 51° F. = 10 international
ohms.
EXAMPLE. — What is the resistance of a wire 1000 ft. long, 0.1 in. diam.?
0.1 in. diam. = 10,000 circ. mils.
R = rl -*- s = 10 X 1000 -*- 10,000 = 1 ohm.
Specific resistance, also called resistivity, is the resistance of a material of
unit length and section as compared with the resistance of soft copper.
Conductivity is the reciprocal of specific resistance, or the relative con-
ducting power compared with copper taken at 100.
1028
ELECTRICAL ENGIKEER1HG.
Relative Conductivities of Different Metals at 0° and
100° C. (Matthiessen.)
Metals.
Conductivities.
Metals.
Conductivities.
At 0° C.
" 32° F.
At 100° C.
" 212° F.
At 0° C.
" 32° F.
At 100° C
" 212° F.
Silvpr hard ....
100
99.95
77.96
29.02
23.72
18.00
16.80
71.56
70.27
55.90
20.67
16.77
Tin...
Lead
12.36
8,32
4.76
4.62
1.60
1.245
8.67
5.86
3.33
3.26
""61878"
Copper, hard. . . .
Gold, hard
Zinc, pressed —
Cadmium
Arsenic
Antimony
Mercury, pure. .
Bismuth
Platinum, soft. ..
Iron, soft
Electrical Conductivity of Different Metals and Alloys.
The following figures of electrical conductivity are given by Lazare Weiler
Pure silver 100
Pure copper 100
Telegraphic silicious bronze . . 98
Alloy of y% copper, yz silver. . 86 . 65
Pure gold "i8
Silicide of copper, 4% Si 75
Telephonic silicious bronze. . . 35
Pure zinc 29.9
Brass with 35$ of zinc 21.5
Phosphor tin.... 17.7
Alloy of % gold, ^ silver 16.12
Swedish iron 16
Pure Banca tin 15.45
Aluminum bronze (10$) 12.6
Siemens steel 12
Pure platinum 10.6
Copper with 10$ of nickel 10.6
Pure lead 888
Bronze with 20$ of tin 8.4
Pure nickel 7 89
Phosphor-bronze, 10$ tin 6.5
Antimony 3.88
' Conductivity of Aluminum.— J. W. Richards (Jour. Frank. Inst.,
Mar. 1897) gives for hard-drawn aluminum of purity 98.5, 99.0, 99.5, and 99.75$
respectively a conductivity of 55, 59, 61, and 63 to 64$, copper being 100$.
The Pittsburg Reduction Co. claims that its purest aluminum has a con-
ductivity of over 64.5$. (Eng'g News, Dec. 17, 1896.)
German Silver.— The resistance of German silver depends on its com-
position. Matthiessen gives it as nearly 13 times that of copper, with a tem-
perature coefficient of .0004433 per degree C. Weston, however (Proc.
Electrical Congress 1893. p. 179), has found copper-nickel-zinc alloys (German
silver) which had a resistance of nearly 28 times that of copper, and a tem-
perature coefficient of about one half that given by Matthiessen.
Conductors and Insulators in Order of tlieir Value.
CONDUCTORS.
All metals
Well-burned charcoal
Plumbago
Acid solutions
Saline solutions
Metallic ores
Animal fluids
Living vegetable substances
Moist earth
Water
INSULATORS (NON-CONDUCTORS
Dry air Ebonite
Shellac Gutta-percha
Paraffin India-rubber
Amber Silk
Resins Dry paper
Sulphur Parchment
Wax Dry leather
Jet Porcelain
Glass Oils
Mica
According to Culley, the resistance of distilled water is 6754 million times
as great as that of copper. Impurities in water decrease its resistance.
Resistance Varies with Temperature.— For every degree Cen-
tigrade the resistance of copper increases about 0.4%, or for every degree F.
0.2222#. Thus a piece of copper \\ire having a lesistance of 10 ohms at 32°
would have a resistance of 11.11 ohms at 82° F.
The following table shows the amount of resistance cf a few substances
used for various electrical purposes by which 1 ohm is increased by a rise of
temperature of 1° C.
ELECTRICAL RESISTANCE.
^ 00021
Platinum silver 00031
German s.iver (see above). . . . „ .00044
Gold, silver 00065
Cast iron 00080
Copper 00400
Annealing.— Resistance is lessened by annealing. Matthiessen gives
the following relative conductivities for copper and silver, the comparison
being made with pure silver at 100° C.:
Metal. Temp. C. Hard. Annealed. Ratio.
Copper ............ 11° 95.81 97.83 1 to 1.027
Silver ............. 14.6° 95.36 103.33 1 to 1.084
Dr. Siemens compared the conductivities of copper, silver, and brass with
the following results. Ratio of hard to annealed :
Copper ........ 1 to 1.058 Silver ....... 1 to 1.145 Brass ------- 1 to 1.180
Standard of Resistance of Copper Wire. (Trans. A. I. E. E.,
Sept. and Nov. 1890.)— Maithiessen's standard is: A hard -drawn copper wire
1 metre long, weighing 1 gramme, has a resistance of 0.1469 B. A. unit at 0° C.
Relative conducting power (Matthiessen): silver, 100; hard or unannealed
copper, 99.95; soft or annealed copper, 102.21. Conductivity of copper at
other temperatures than 0° C., Cf = C0(l - .00387* + .000009009**).
The resistance is the reciprocal of the conductivity, and is
pt _ #fl(i 4. .00387* 4- .00000597*2).
The shorter formula Rt = R0(l -f- .004060 is commonly used.
A committee of the Am. Inst. Electrical Engineers recommend the follow-
ing as the most correct form of the Matthiessen standard, taking 8.89 as the
sp. gr. of pure copper :
A soft copper wire 1 metre long and 1 mm. diam. has an electrical resist-
ance of .02057 B.A. unit at 0° C. From this the resistance of a soft copper
wire 1 foot long and .001 in. diani. (mil-foot) is 9.720 B.A. units at 0° C.
Standard Resistance at 0° C. B.A. Units. Legal Ohms,
Moure-millimetre, soft copper .......... 02057 .02034 .02029
Cubic centimetre " " .......... 000001616 .000001598 .000001593
Mil-foot " " ......... 9.720 9.612 9.590
1 mil-foot, of soft copper at 10°.22 C. or 50°.4 F. . . 10 9. 977
" " " " " 5°5 " ° 1
. . . .
15°.5 " 59°.9 F... 10.20 10.175
23°.9 " 75° F... 10.53 10.505
For tables of the resistance of copper ivire, see pages 218 to 220, also
pp. 1034, 1035.
Taking Matthiessen's standard of pure copper as 100#, some refined metal
has exhibited an electrical conductivity equivalent to 103$.
Matthiessen found that impurities in copper sufficient to decrease its
density from 8.94 to 8.90 produced a marked increase of electrical resistance.
DIRECT ELECTRIC CURRENTS.
Ohm's Law.— This law expresses the relation between the three fun-
damental units of resistance, electrical pressure, and current. It is :
electrical pressure T E E
Current = — — ; J= — ; whence E = JR. and R = •=-.
resistance R' I
In terms of the units of the three quantities,
Amperes = T° S : volts = amperes X ohms; ohms = VO S -.
ohms amperes
EXAMPLES: Simple Circuits.— -1. If the source has an effective electrical
pressure of 100 volts, and the resistance is two ohms, what is the current ?
r E 100 ,
I - jjj- — -y = 50 amperes.
2. What pressure will give a current of 50 amperes through a resistance of
2 ohms ? #=7# = 50X2 = 100 volts.
3. What resistance is required to obtain a current of 50 amperes when the
pressure is 100 volts ? R = E -*- 1 = 100 -f- 50 = 2 ohms.
Ohm's law applies equally to a complete electrical circuit and to any
part thereof.
Series Circuits.— If conductors are arranged one after the other they
1030 ELECTRICAL ENGINEERING.
are said to be in series, and the total resistance of the circuit is the sum of
the resistances of its several parts. Let A, Fig.
170, be a source of current, such as a battery or
generator, producing a difference of potential or
2 \r3 E. M. F. of 120 volts, measured across a6, and let
the circuit contain four conductors whose resist*
ances, rj, r2, r3, ?*4, are 1 ohm each, and three
other resistances, #,, /?2, 7?3, each 2 ohms. The
-,-- total resistance is 10 ohms, and by Ohm's law
FIG. 1<U. the current / = E 4- R = 120 -*- 10 = 12 amperes.
This current is constant throughout the circuit, and a series circuit
is therefore one of constant current. The drop of potential in the
whole circuit from a aror.nd to b is 120 volts, or E = RI. The drop in any
po-rtion depends on the resistance of that portion; thus from a to Rl the re-
sistance is 1 ohm, the constant current 12 amperes, and the drop 1 X 12
= 12 volts. The drop in passing through each of the resistances Rlt J?a, R3
is 2 x 12 = 24 volts
Parallel, Divided, or Multiple Circuits.— Let B, Fig. 171, be
a generator producing an E. M. F. of 220 volts across the terminals ab. The
current is divided, so that part flows
through the main wires ac and part
through the "shunt" s, having a resist-
ance of 0.5 ohm. Also the current has
three paths between c and d, viz , through
the three resistances in parallel Ri,R*, #3,
of 2 ohms each. Consider that the resist-
5 "2 g h ance of the wires is so small that it may
be neglected. Let the conductances of
FIG. 171. the four paths be represented by Cs, Cj,
C2, <73. The total conductance is Cs •+ Cj
-f C2 + f 3 = C and the total resistance R = 1 -*- C. The conductance of
each path is the reciprocal of its resistance, the total conductance is the sum
of the separate conductances, and the resistance of the combined or " par-
allel " paths is the reciprocal of the total conductance.
J? = 1~4~ (o^5 + 2~ + ~:f 4~~5") = 1-*- 3-5 = 0.286 ohm.
The current I = E -f- R = 770 amperes.
Conductors in Series and Parallel.— Let the resistances in
parallel be the same as in Fig. 171, with the additional resistance of 0.1 ohm
in each of the six sections of the main, wires, ac, bd, etc., in series. The
voltage across ab being 220 volts, determine the drop in voltage at the
several points, the total current, and the current through each path. The
problem is somewhat complicated. It may be solved as follows : Consider
first the points eg ; here there are two paths for the current, efyh and eg.
Find the resistance and the conductance of each and the total resistance
(the reciprocal of the joint conductance) of the parallel paths. Next con-
sider the points cd ; here there are two paths— one through e and the other
through cd. Find the total resistance as before. Finally consider the points
ab ; here there are two paths— one through c, the other through s. Find the
conductances of each and their sum. The product of this sum and the volt-
age at ab will be the total amperes of current, and the current through any
path will be proportional to the conductance of that path. The resistances,
B, and conductances, C, of the several paths are as follows •
R C
Ra of efR3hg = 0.1 -K2 + 0.1 =.- 2.2 0.4545
RofeRrf = 2 0.5
= 1.048 0.9545
Rd of ce + dg + R° = 1.248 0.8013
Re of cRid =2 0.5
Joint Rf = 0.7687 1.3013
Rg of ac + M + Rf - 0.9687 1 .0332
Rhots = C.5 2
Joint Rg + Rh = 0.330 3.0333
ELECT1UC CUKREHTS. 1031
Total current = 220 x 3.0332 = 667.3 amperes.
CurreDt through s = 220 x 2 = 440 amp. ; through c = 227.3 amp.
" " cRid = 227.3 x 0.5 -s- 1.3013 = 87.34 amp.
' " " e= 227.3 x 0.8013 -*- 1.3013 *= 139.96 "
41 " eR?g = 139.96 x 0.5 -s- 0.9545 = 73.31 "
" /#3 = 139.96 x 0.4545 -*- 0.9545 = 66.65 "
The drop in voltage in any section of the line is found by the formula
E - Rl, R being the resistance of that section and 1 the current in it. As
the R of each section is 0.1 ohm we find E for ac and bd each = 22.7 volts,
for ce and d</ each 14.0 volts, and for e/and gh each 6.67 volts. The voltage
across cd is 220 — 2 x 22.7 = 174.6 volts; across eg, 174.6 — 2 x 14.0 = 14G.(\
and across //i 146.6 — 2 x 667 = 133.3 volts. Taking these voltages and the
resistances R^R^, each 2 ohms, we find from 7= E -f- R the current
through each of these resistances 87.3, 73.3, and 66.65 amperes, as before.
Internal Resistance.— In a simple circuit we have two resistances,
that of the circuit R and that of the internal parts of the source of electro-
motive force, called internal resistance, r. The formula of Ohm's law when
the internal resistance is considered is I — E -f- (R -f- '')•
Power of the Circuit.— The power, or rate of work, in watts =
current in amperes X electro -motive force in volts = I X E. Since 1= E^-R^
watts = E2 -*- R = electro-motive force2 •*- resistance.
EXAMPLE.— What H.P. is required to supply 100 lamps of 40 ohms resist-
ance each, requiring an electro-motive force of 60 volts ?
The number of volt-amperes for each lamp is -^- = -— - , 1 volt-ampere =
602
.00134 H.P.; therefore — x 100 x .00134 = 12 H.P. (electrical) very nearly.
Electrical, Brake, and Indicated Horse-power.— The power
given out by a dynamo = volts x amperes -5- 1000 = kilowatts, kw. Volts x
amperes -i- 746 = electrical horse-power, E.H.P. The power put into a
dynamo shaft by a direct-connected engine or other prime mover is called
the shaft or brake horse-power, B.H.P. If e1 is the efficiency of the
dynamo, B.H.P. = E.H.P. H-CJ. If e2 is the mechanical efficiency of the
engine, the indicated horse-power, I.H.P. = brake H.P. -f ea = E.H.P. •*•
elfXeieand e2 each = 91^, I.H.P. = E.H.P. X 1.194 = kw. x 1.60. In direct-
connected units of 250 kw. or less the rated H.P. of the engine is commonly
taken as 1.6 x the rated kw. of the generator.
Electric motors are rated at the H.P. given out at the pulley or belt. H.P.
of motor = E.H.P. supplied -*- efficiency of motor.
Heat Generated by a Current.— Joule's law shows that the heat
developed in a conductor is directly proportional, 1st, to its resistance; 2d,
to the square of the current strength; and 3d, to the time during which the
current flows, or H = I*Rt. Since / = E -*- Rt
I*Rt = f IRl = Elt = EJ>t = %£.
JK £6 K
Or, heat = current2 x resistance X time
= electro-motive force X current X time
= electro-motive force2 x time -f- resistance.
Q = quantity of electricity flowing = It = (Et -f- R).
a. — EQ; or'heat = electro-motive force x quantity.
The electro-motive force here is that causing the flow, or the difference in
potential between the ends of the conductor.
The electrical unit of heat, or "joule " = 107 ergs = heat generated in one
second by a current of 1 ampere flowing through a resistance of one ohm =
.239 gramme of water raised 1° C. H = I*Rt X .239 gramme calories =
I*Rt x .0009478 British thermal units.
In electric lighting the energy of the current is converted into heat in the
lamps. The resistance of the lamp is made great so that the required
Quantity of heat may be developed, while in the wire leading to and from
the lamp the resistance is made as small as is commercially practicable, so
that as little energy as possible may be wasted in heating the wire.
Heating of Conductors, (From Kapp's Electrical Transmission
• of Energy.)— It becomes a matter of great importance to determine before-
1032 ELECTRICAL EHGINEEEING.
hand what rise in temperature is to be expected in each given case, and if
that rise should be found to be greater than appears safe, provision must be
made to increase the rate at which heat is carried off. This can generally
be done by increasing the superficial area of the conductor. Say we have
one circular conductor of 1 square inch area, and find that with 1000 amperes
flowing it would become too hot. Now by splitting up this conductor into
10 separate wires each one tenth of a square inch cross-sectional area, we
have not altered the total amount of energy transformed into heat, but we
have increased the surface exposed to the cooling action of the surrounding
air in the ratio of 1 : t/10, and therefore the ten thin wires can dissipate more
than three times the heat, as compared with the single thick wire.
Prof. Forbes states that an insulated wire carries a greater current without
overheating than a bare wire if the diameter be not too great. Assuming
the diameter of the cable to be twice the diam. of the conductor, a greater
current can be carried in insulated wires than in bare wires up to 1.9 inch
diam. of conductor. If diam. of cable = 4 times diarn. of conductor, this is
the case up to 1.1 inch diam. of conductor.
Heating of Bare "Wires. — The following formulae are given by
Kennelly:
72
T - -3 X 90,000 + *; d - 4
T => temperature of the wire and t that of the air, in Fahrenheit degrees;
7 = current in amperes, d = diameter of the wire in mils.
If we take T - t = 90° F., ^/90 = 4.48, then
d = 10 |//2 and / = |/rf3 •*- 1,000.
This latter formula gives for the carrying capacity in amperes of bare
wires almost exactly the figures given for weather-proof wires in the Fire
Underwriters' table except in the case of Nos. 18 and 16, B. & S. gauge,
for which the formula gives 8 and 11 ampere -, respectively, instead of 5
and 8 amperes, given in the table.
Heating of Coils. — The rise of temperature in magnet coils due to
the passage of current through the wire is approximately proportional to
the watts lost in the coil per unit of effective radiating surface, thus:
t being the temperature rise in degrees Fahr. ; S, the effective radiating
surface; and k a coefficient which varies widely, according to conditions.
In electromagnet coils of small size and power, k may be as large as 0.015.
Ordinarily it ranges from 0.012 down to 0.005; a fair average is 0.007.
The more exposed the coil is to air circulation, the larger is the value of k;
the larger the proportion of iron to copper, by weight, in the core and
winding, the thinner the winding with relation to its dimension parallel
witTi the magnet core, and the larger the "space factor" of the winding,
the larger will be the value of k. The space factor is the ratio of the actual
copper cross-section of the whole coil to the gross cross-section of copper,
insulation, and interstices.
See also the discussion of magnet windings under Electromagnets, p. 1050.
Fusion of Wires. — W. H. Preece gives a formula for the current re-
quired to fuse wires of different metals, viz., 7 = ac$» in which d is the
diameter in inches and a a coefficient whose value for different metals t is as
follows: Copper, 10244; aluminum, 7585; platinum, 5172; German silver,
5230; platinoid, 4750; iron, 3148; tin, 1462; lead, 1379; alloy of 2 lead and
1 tin, 1318.
ELECTRIC CURRENTS.
1033
Allowable Carrying Capacity of Copper Wires.
(Fire Underwriters' Rules.)
Amperes.
Amperes
B. &S.
Circular
Circular
Gauge.
Mils.
Rubber-
Weather-
Mils.
Rubber
Weather-
Covered.
proof.
Covered
proof.
18
1,624
3
5
200,000
200
300
16
2,583
6
8
300,000
270
400
14
4,107
12
16
400,000
330
500
12
6,530
17
23
500,000
390
590
10
10,380
24
32
600,000
450
680
8
16,510
33
46
700,000
500
760
6
26,250
46
65
800000
550
840
5
33,100
54
77
900,000
600
920
4
41,740
65
92
1,000,000
650
1,000
3
52,630
76
110
1,100,000
690
1,080
2
66,370
90
131
.200.000
730
1,150
1
83,690
107
156
,300,000
770
1.220
0
105,500
127
185
.400,000
810
1,290
00
133,100
150
220
1,600,000
890
1,430
000
167,800
177
262
1,800,000
970
1,550
0000
211,600
210
312
2,000,000
1,050
1,670
For insulated aluminum wire the safe-carrying capacity is 84 per cent of
that of copper wire with the same insulation.
Underwriters' Insulation. — The thickness of insulation required
by the rules of the National Board of Fire Underwriters varies with the size
of the wire, the character of the insulation- and the voltage. The thickness
of insulation on rubber- covered wires carrying voltages up to 600 varies from
-3% inch for a No. 18 B. & S. gauge wire to i inch for a wire of 1.000 000 cir-
cular mils. Weather-proof insulation is required to be slightly thicker.
For voltages of over 600 the insulation is required to be at least 1/16 inch
thick for all sizes of wire under No. 8 B. & S. gauge, and to be at least 3/32
inch thick for all sizes greater than No. 0000 B. & S. gauge.
Copper- wire Table.— The table on pages 1034 and 1035 is abridged
from one computed by the Committee on Units and Standards of the Ameri-
can Institute of Electrical Engineers (Trans. Oct. 1893).
ELECTRIC TRANSMISSION, DIRECT CURRENTS.
Cross-section of Wire Required for a Given Current.—
Let R = resistance of a given line of copper wire, in ohms'
r = "1 mil-foot of copper;
L = length of wire, in feet;
e = drop in voltage between the two ends;
/ = current, in amperes;
A = sectional area of wire, in circular mils;
then I = ^; R = -j\ R = r^ whence A = -^ .
The value of r for soft copper wire at 75° F. is 10.505 international ohms.
For ordinary drawn copper wire the value of 10.8 is commonly taken, cor-
responding to a conductivity of 97.2 per cent.
For a circuit, going and return, the total length is 2L, and the formula
becomes./! = 21.6/L •*• e, L here being the distance from the point of supply
to the point of delivery.
If E is the voltage at the generator and a the per cent of drop in the line,
2160/L
then e = Ea •*• 100, and A = — —^ — .
2160PL
If P = the power in watts, = El, then I = w , and A
MI
If Pk= the power in kilowatts, A
aE*
1034
ELECTEJCAL
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ELECTRIC CURRENTS.
1035
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1036
ELECTRICAL ENGINEERING.
If Lm =* the distance in miles, and Ac the area in circular inches,
Ac = 6405 PkLm •*- aE2. If As= area in square inches As — 5030 PkLm
•+• aJ?2. When the area in circular mils has been determined by either
of these formulae reference should be made to the table of Allowable Capacity
of Wires, to see if the calculated size is sufficient to avoid overheating. For
all interior wiring the rules of the National Board of Fire Underwriters should
be followed. See Appendix to Vol. II of Crocker's Electric Lighting.
Weight of Copper for a Given Power. — Taking the weight of
a mil-foot of copper at .000003027 lb.. the weight of copper in a circuit of
length 2L and cross-section A, in circ. mils, is 0.000006054LA Ibs., = W.
Substituting for A its value 2160PL -*- aE2 we have
W = 0.0130766PL2 •*• aE2] P in watts, L in ft.
W = 13.0766 PkL2 -f- aE2; Pk in kilowatts, L in ft.
W = 364,556,000 PkL2m + a#2; Pk in kilowatts, Lm in miles.
The weight of copper required varies directly as the power, transmitted ;
inversely as the percentage of drop or loss; directly as the square of the
distance; and inversely as the square of the voltage.
From the last formula the following table has been calculated.
WEIGHT OF COPPER WIRE TO CARRY 1000 KILOWATTS' WITH 10# LOSS.
Distance
in miles.
1 5 10 20 50 100
Volts.
500
1,000
2,000
5,000
10,000
20,000
40,000
60,000
Weight in Ibs.
145,822
36,456
9,114
1,458
365
91
3,645,560
911,390
227,848
36,456
9,114
2,278
570
3,645,560
911,390
145,822
36,456
9,114
2,278
1,013
3,645,560
593,290
145,822
36,456
9,114
4,051
3,645,560
911,390
227,848
56,962
25,316
3,645,560
911,390
227,848
101,266
In calculating the distance, an addition of about 5 per cent should be
made for sag of the wires.
•pi
Short-circuiting. — From the law I = 5- it is seen that with any
• ">
pressure JS,the current 7 will become very great if R is made very small. In
short-circuiting the resistance becomes small and the current therefore
great. Hence the dangers of short-circuiting a current.
Economy of Electric Transmission. — Lord Kelvin's rule for
the most economical section of conductor is that for which the annual
interest on capital outlay is equal to the annual cost of energy wasted.
Tables have been compiled by Professor Forbes and others in accordance
with modifications of this rule. For a given entering horse-power the ques-
tion is merely one as to what current density, or how many amperes per
square inch of conductor, should be employed. Kelvin's rule gives about
393 amperes per square inch, and Professor Forbes's tables give a current
density of about 380 amperes per square inch as most economical.
Bell (Electric Transmission of Power) shows that while Kelvin's rule cor-
rectly indicates the condition of minimum cost in transmission for a given
current and line, it omits many practical considerations and is inapplicable
to most power transmission work. Each plant has to be considered on its
merits and very various conditions are likely to determine the line loss in
different cases. Several cases are cited by Bell to show that neither Kel-
vin's law nor any modification of it is a safe guide in determining the proper
allowance for loss of energy in the line.
Wire Tables. — The tables on the following page show the relation
between load, distance, and "drop" or loss by voltage in a two- wire circuit
of any standard size of wire. The tables are based on the formula
(21.6/L)-7- A =Drop in volts.
1 = current in amperes, L = distance in feet from point of supply to point
of delivery. The factors / and L are combined in the table, in the com-
pound factor "ampere feet."
WIRE TABLES.
1037
WIRE TABLE
RELATION BETWEEN LOAD, DISTANCE, Loss, AND SIZE OF
CONDUCTOR.
Table I.-110-volt and 22O-volt Two- Wire Circuits.
NOTE. — The numbers in the body of the tables are Ampere- Feet; i.e.,
Amperes X Distance (length of one wire) in feet. See examples on next page.
Wire Sizes ;
B. & S. Gauge.
Line Loss in Percentage of the Rated Voltage; and Power
Loss in Percentage of the Delivered Power.
110V.
220V.
1
H
2
3
4
5
6
8
10
0000
21,55032,32543,100
64,650
86,200
107,750
129,300
172,400
215,500
000
17,08025,62034,160
51,240
68,320
85,400
102,480
136,640
170,800
00
13,55020,32527,100
40,650
54,200
67,750
81,300
108,400
135,500
0000
0
10,750
16,125
21,500
32,250
43,000
53,750
64,500
86,000
107,500
000
1
8,520
12,780
17,040
25,560
34,080
42,600
51,120
68,160
85,200
00
2
6,750
10,140
13,520
20,280
27,040
33,800
40,560
54,080
67,600
0
3
5,360
8,040
10,720
16,080
21,440
26,800
32,160
42,880
53,600
1
4
4,250
6,375
8,500
12,750
17,000
21,250
25,500
34,000
42,500
2
5
3,370
5,055
6,740
10,110
13,480
16,850
20,220
26,960
33,700
3
6
2,670
4,005
5,340
8,010
10,680
13,350
16,020
21,360
26,700
4
7
2,120
3,180
4,240
6,360
8,480
10,600
12,720
16,960
21,200
5
8
1,680
2,520
3,360
5,040
6,720
8,400
10,800
13,440
16,800
6
9
1,330
1,995
2,660
3,990
5,320
6,650
7,980
10,640
13,300
7
10
1,055
1,582
2,110
3,165
4,220
5,275
6,330
8,440
10,550
8
11
838
1,257
1,675
2,514
3,350
4,190
5,028
6,700
8,380
9
12
665
997
1,330
1,995
2,660
3,320
3,990
5,320
6,650
10
13
527
790
1,054
1,580
2,108
2,635
3,160
4,215
5,270
11
14
418
627
836
1,254
1,672
2,090
2,508
3,344
4,180
12
332
498
665
997
1,330 1,660
1,995
2,660
3,325
14
209
313
418
627
836 1,045
1,354
1,672
2,090
Table II.— 500, 1000, and 20OO Volt Circuits.
Wire Sizes ;
B. & S. Gauge.
Line Loss in Percentage of the Rated Voltage ; and
Power Loss in Percentage of the Delivered Power.
500V.
1000 V.
2000 V.
1
H
2
2*
3
4
5
0000
0
97,960
146,940
195,920
244,900
293,880
391,840
489,800
000
1
77,690
116,535
155,380
194,225
233,970
310,760
388,450
00
2
61,620
92,430
123,240
154,050
184,860
246,480
308,100
0000
0
3
48,880
73,320
97,760
122,200
146,640
195,420
244,400
000
1
4
38,750
58,125
77,500
96,875
116,250
155,000
193,750
00
2
5
30,760
46,140
61,520
76,900
92,280
123,040
153,800
0
3
6
24,370
36,555
48,740
60,925
73,110
97,480
121,850
1
4
7
19,320
28,980
38,640
48,300
57,960
77,280
96,600
2
5
8
15,320
22,980
30,640
38,300
45,960
61,280
76,600
3 | 6
9
12,150
18,225
24,300
30,375
36,450
48,300
60,750
4
7
10
9,640
14,460
19,280
24,100
28,920
38,560
48,200
5
8
11
7,640
11,460
15,280
19,100
22,920
30,560
38,200
6
9
12
6,060
9,090
12,120
15,150
18,180
24,240
30,300
7
10
13
4,805
7,207
9,610
12,010
14,415
19,220
24,025
8
11
14
3,810
5,715
7,620
9,525
11,430
15,220
19,050
9
12
3,020
4,530
6,040
7,550
9,060
12,080
15,100
10
13
2,395
3,592
4,790
5,985
7,185
9,580
11,975
11
14
1,900
2,850
3,800
4,750
5,700
7,600
9,500
12
1,510
2,265
3,020
3,775
4,530
6,040
7,550
14
950
1,425
1,900
2,375
2,850
3,800
4,750
1038
ELECTRICAL EKGHSTEERIKG.
EXAMPLES IN THE USE OF THE WIRE TABLES. — !. Required the
maximum load in amperes at 220 volts that can be carried 95 feet by No. 6
wire without exceeding 1^ drop.
Find No. 6 in the 220- volt column of Table I; opposite this in the \Y$
column is the number 4005, which is the ampere-feet. Dividing this by the
required distance (95 feet), gives the load, 42.15 amperes.
Example 2. A 500-volt line is to carry 100 amperes 600 feet with a drop
not exceeding 5% ; what size of wire will be required?
The ampere-feet will be 100X600 = 60,000. Referring to the 5% column
of Table II, the nearest number of ampere-feet is 60,750, which is opposite
No. 3 wire in the 500-volt column.
These tables also show the percentage of the power delivered to a line
that is lost in non-inductive alternating-current circuits. Such circuits are
obtained when the load consists of incandescent lamps and the circuit wires
lie only an inch or two apart, as in conduit wiring.
Efficiency of Long-distance Transmission, (F. R. Hart,
Power, Feb. 189'2.)— The mechanical efficiency of a system is the ratio of the
power delivered to the dynamo-electric machines at one end of the line to
the power delivered by the electric motors at the distant end. The com
mercial efficiency of a dynamo or motor varies with its load. Under the
most favorable conditions we must expect a loss of say 9# in the dynamo
and 9# in the motor. The loss in transmission, due to fall iu electrical pres-
sure or "drop " in the line, is governed by the size of the wires, the other
conditions remaining the same. For a long-distance transmission plant
this will vary from b% upwards. With a loss of 5# in the line the total
efficiency of transmission will be slightly under 79#. With a loss of \Q% in
the line it will be slightly under 75$. We may call 80# the practical limit of
the efficiency with the apparatus of to-day. The methods for long-distance
transmission may be divided into three general classes : (1) continuous cur-
rent; (2) alternating current; and (3) regenerating or "motor-dynamo'1
systems.
There are many factors which govern the selection of a system. For each
problem considered there will be found certain fixed and certain unfixed
conditions. In general the fixed factors are: (1) capacity of source of
power; (2) cost of power at source; (3) cost of power by othfirmeans at point
of delivery; (4) danger considerations at motors; (5) operating condition**;
(6) construction conditions (length of line, character of country, etc.). The
partly fixed conditions are: (7) power which must be delivered, i.e., the effi-
ciency of the system; (8) size and number of delivery units. The variable
conditions are: (9) initial voltage; (10) pounds of copper on line; (11) origi-
nal cost of all apparatus an d construction; (12) expenses, operating (fixed
charges, interest, depreciation, taxes, insurance, etc.); (13) liability of trouble
and stoppages; (14) danger at station and on line; (15) convenience in oper-
ating, making changes, extensions, etc.
The relative advantages of different systems vary with each particular
transmission problem, but in a general way may be tabulated as below:
System.
Advantages.
Disadvantages.
( Low voltage.
Safety, simplicity.
Expense for copper.
( High voltage.
Economy, simplicity.
Danger; difficulty of
building machines.
3-wire.
Low voltage on machines
and saving in copper.
Not saving enough in
copper for long dis-
tances. Necessity for
" balanced " system.
Multiple-wire.
Low voltage at machines
and saving in copper.
Single phase.
Economy of copper.
Cannot start under load.
Low efficiency.
Multiphase.
Economy of copper, syn-
chronous speed unnec-
essary ; applicable to
very long distances.
Requires more than two
wires.
Motor-dynamo.
High-voltage transmis-
sion. Low-voltage de-
livery.
Expensive.
Low efficiency.
TABLE OF ELECTRICAL HORSE-POWERS.
1039
TABLE OF ELECTRICAL HORSE-POTTERS.
Volts x Amperes
Formula :
746
= H.P., or 1 volt-ampere = .0013405 H.P.
Read amperes at top and volts at side, or vice versa.
'•
£ u.
35
1
10
20
30
40
50
60
70
80
90
100
110
120
1
.00134
.0134
.0268
.0402
.0536
.0570
.0804
.0938
.1072
.1206
.1341
.1475
.1609
2
,00268
.0268
.0536
.0804
.1072
.1341
.1609
.1877
.2145
.2413
.2681
.2949
.3217
3
.00402
.0402
.0804
.1206
.1609
.2011
.2413
.2815
.3217
.3619
.4022
.4424
.4826
jj
.00536
.0536
.1072
.1609
.2145
.2681
.3217
.3753
.4290
.4826
.5362
.5898
6434
5
.00670
.0670
.1341
.2011
.2681
.3351
.4022
.4692
.5362
.6032
.6703
.7373
.8043
|
.00804
.0804
.1609
.2413
.3217
.4022
.4826
.5630
.6434
.7239
.8043
.8847
.9652
.00938
.0938
.1877
.2815
.3A3
.4692
.5630
.6568
.7507
.8445
.9384
1.032
1.126
g .01072
.1072
.2145
.3217
.4290
.5362
.6434
.7507
.8579
.9652
1.072
1,180
1.287
9' .01206
.1206
.2413
.3619
.4826
.6032
.7239
.8445
.9652
1.086
1.206
1.327
1.448
10! .01341
.1341
.2681
.4022
.5362
.6703
.8043
.9383
1.072
1.206
1.341
1.475
1.609
111 .01475
.1475
.2949
.4424
.5898
.7373
.8847
1.032
1.180
1.327
1.475
1.622
1.769
12 .01609
.1609
.3217
.4826
.6434
.8043
.9652
1.126
1.287
1.448
1.609
1.769
1.930
13 .01743
.1743
.3485
.5228
.6970
.8713
1.046
1.220
1.394
1.568
1.743
1.917
2.091
U .01877
.1877
.3753
.5630
.7507
.9384
1.126
1.314
1.501
1.689
1.877
2.064
2.252
151 .02011
.2011
.4022
.6032
.8043
1.005
1.206
1.408
1.609
1.810
2.011
2.212
2.413
16 .02145
.2145
.4290
.6434
.8579
1.072
1.287
1.501
1.716
1.930
2.145
2.359
2.574
17
,02279
.2279
.4558
.6837
.9115 1.139
1.367
1.595
1.823
2.051
2.279
2.507
2.735
18
02413
.2413
.4826
.7239
.9653 1.206
1.448
1.689
1.930
2.172
2.413
2.654
2.895
19
J02547
.2547
.5094
.7641
1.019
1.273
1.528
1.783
2.037
2.292
2.547
2.801
3.056
20
.02681
.2681
.5362
.8043
1.072
1.340
1.609
1.877
2.145
2.413
2.681
2.949
3.217
21
.02815
.2816
.5630
.8445
1.126
1.408
1.689
1.971
2.252
2.533
2.815
3.097
3.378
22
.02949
.2949
.5898
.8847
1.180
1.475
1.769
2.064
2.359
2.654
2.949
3.244
3.539
23
.03083
.3083
.6166
.9249
1.233
1.542
1.850
2.158
2.467
2.775
3.083
3.391
8.700
24
.03217
.3217
.6434
.9652
1.287
1.609
1.930
2.252
2.574
2.895
8.217
3 539
3.861
25
.03351
.3351
.6703
1.005
1.341
1.676
2.011
2.346
2.681
3.016
3.351
3.686
4.022
26
03485
.3485
.6971
1.046
1.394
1.743
2.091
2.440
2.788
3.137
3.485
3.834
4.182
27
.03619
.3619
.7239
1.086
1.448
1.810
2.172
2.534
2.895
3.257
3.619
3.981
4.343
28
.0375
.3753
.7507
1.126
1.501
1.877
2.252
2.627
3.003
3.378
3.753
4.129
4.504
29
.0388
.3887
.7775
1.166
1.555
1.944
2.332
2.721
3.110
3.499
3.887
4.276
4.665
30
.0402
.4022
.8043
1.206
1.609
2.011
2.413
2.815
3.217
3.619
4.022
4.424
4.826
31
.04156
.4156
.8311
1.247
1.662
2.078
2.493
2.909
3.324
3.740
4.156
4.571
4.987
82
.0429
.4290
.8579
1.287
1.716
2.145
2.574
3.003
3432
3.861
4.290
4.719
5.148
33
.0442
.4424
.8847
1.327
1.769
2.212
2.654
3.097
3.539
3.986
4.424
4.866
5.308
34
.0455
.4558
.9115
1.367
1.823
2.279
2.735
3.190
3.646
4.102
4.558
5.013
5.469
M
.0469
.4692
.9384
1.408
1.877
2.346
2.815
3.284
3.753
4.223
4.692
5.161
5.630
40
.05362
.5362
1.072
1.609
2.145
2.681 3.217
3.753; 4.290
4.826
5.363
5.898
6.434
45
.06032
.603
1.206
1.810
2.413
3.016 3.619
4.223
4.826
5.439
6.032
6.635
7.239
50
.06703
.670
1.341
2.011
2.681
3.351 4.022
4.692
5.362
6.032
6.703
7.373
8.043
55
.07373
.737
1.476
2.212
2.949
3.6861 4.424
5.1611
5.898
6.635
7.378
8.110
8.841
60
08043
.8043
1.609
2.413
3.217
4.022 4.826
5.630 6.434
7.239
8.043
8.o47
9.659
65
08713
.871
1.743
2.614
3.485
4.357 5.228
6.099 6.970
7.842
8.713
9.584
10.46
70
09384
.938
1.877
2.815
3.753
4.692 5.630
6.568 7.507
8.445
9.384
10.32
11.26
75
.10054
1.005
2.011
3.016
4.021
5.027 6.032
7.037
8.043
9.048
10.05
11.06
12.06
80
.10724
1.072
2.145
3.217
4.290
5.3621 6.434
7.507
8.579
9.652
10.72
11.80
12.87
85
.11394
1.139
2.279
3.418
4.558
5.697| 6.836
7.976
9.115
10.26
11.39
12.53
13.67
90
.12065
1.206
2.413
3.619
4.826
6.032! 7.239
8.445
9.652
10.86
12.06
13.27
14.48
95
.12735
1.273
2.547
3.820
5.094
6.367
7.641
8.914
10.18
11.46
12.73
14.01
15.28
100
.13405
1.341
2.681
4.022
5.362
6.703
8.043
9.384
10.72
12.06
13.41
14.75
16.09
200
.26810
2.681
5.362
8.043
10.72
13.41
16.09
18.77
21.45
24.13
26.81
29.49
32.17
300
.40215
4.022
8.043
12.06
16.09
20.11
24.13
28.15 32.17
36.19
40.22
44.24
48.26
400
.53620
5.362
10.72
16.09
21.45
26.81
32.17
37.33 42.90
48.26
53.62
58.98
64.34
500
.67025
6.703
13.41
20.11
26.81
33.51
40.22
46.92 53.62
60.32
67.03
73.73
80.43
600
.80430
8.043
16.09
24.13
32.17
40.22
48.26
56.30
64.34
72.39
80.43
88.47
96.52
700
.93835
9.384
18.77
28.15
37.53
46.92
56.30
65.68
75.07
84.45
93.84
103.2
112.6
800
1.0724
10.72
21.45
32.17
42.90
53.62
64.34
75.07 85.79
96.52
107.2
118.0
128.7
900
1.2065
12.06
24.13 36.19
48.26
60.32
72.39
84.45; 96.52
108.6
120.6
132.7
144.8
1,000
1.3405
13.41
26.81
40.22
53.92
67.03
80.43
93.84, 107.2
120.6
134.1
147.5
160.9-
2,000
2.6810
26.81
53.62
80.43
107.2
134.1
160.9
187.7
214.5
241.3
268.1
294.9
321.7
3,000
4.0215
40.22
80.43120.6
160.9
201.1
241.3
281.5
321.7
361.9
402.2
442.4
482.6
4,000
5.3620
53.62
107.2
160.9
214.5
268.1
321.7
375.3
429.0
482.6
536.2
589.8
643.4
6,000
6.7025
67.03
134.1
201.1
268.1
335.1
402.2
469.2
536.2
603.2
670.3
737.3
804.3
6,000
8.0430
80.43
160.9 241.3
321.7
402.2
482.6
563.0
643.4
723.9
804.3
884.7
965.1
7,000
9.3835
93.84
187.7
281.5
375.3
469.2
563.0
656.8
760.7
844.5
938.4
1032
1126
8,000
10.724
107.2
214.5
321.7
429.0
536.2
643.4
750.7
857.9
965.2
1072
1180
1287
9.000
12.065
120.6
241.3 361.9
482.6
603.2
723.9
844.5
965.2
1086
1206
1327
1448
10,000
13.405
134.1
268.1 402.2
536.2
670.3
804.3
938.3 1072
1206
1341
1475
1609
1
1040
ELECTKICAL ENGINEERING.
Cost of Copper for Long-distance Transmission*
(Westinghouse El. & Mfg. Co.)
COST OF COPPER REQUIRED FOR THE DELIVERY OF ONE MECHANICAL HORSE-
POWER AT MOTOR SHAFT WITH 1000, 2000, 3000, 4000, 5000, and 10,000 VOLTS
AT MOTOR TERMINALS, OR AT TERMINALS OF LOWERING TRANSFORMERS.
Loss of energy in conductors (drop) equals 20%. Motor efficiency, 90%.
Length of conductor per mile of single distance, 11,000 ft., to allow for sag.
Cost of copper taken at 16 cents per pound.
Miles.
1000 v.
2000 v.
3000 v.
4000 v.
5000 v.
10,000 v.
1
$2.08
$0.52
$0.23
$0.13
$0.08
$0.02
2
8.33
2.08
0.93
0.52
0.33
0.08
3
18.70
4.68
2.08
1.17
0.75
0.19
4
33.30
8.32
3.70
2.08
1.33
0.33
5
52.05
13.00
5.78
3.25
2.08
0.52
6
74.90
18.70
8.32
4.68
3.00
0.75
7
102.00
25.50
11.30
6.37
4.08
1.02
8
133.25
33.30
14.80
8.32
5.33
1.33
9
168.60
42.20
18.70
10.50
6.74
1.69
10
208.19
52.05
23.14
13.01
8.33
2.08
11
251.90
63.00
28.00
15.75
10.08
2.52
12
299.80
75.00
33.30
18.70
12.00
3.00
13
352.00
88.00
39.00
22.00
14.08
3.52
14
408.00
102.00
45.30
25.50
16.32
4.08
15
468.00
117.00
52.00
29.25
18.72
4.68
16
533.00
133.00
59.00
33.30
21.32
5.33
17
600.00
150.00
67.00
37.60
24.00
6.00
18
675.00
169.00
75.00
42.20
27.00
6.75
19
750.00
188.00 '
83.50
47.00
30.00
7.50
20
833.00
208.00
92.60
52.00
33.32
8.33
COST OF COPPER REQUIRED TO DELIVER ONE MECHANICAL HORSE-POWER AT
MOTOR-SHAFT WITH VARYING PERCENTAGES OF Loss IN CONDUCTORS, UPON
THE ASSUMPTION THAT THE POTENTIAL AT MOTOR TERMINALS IS IN EACH
CASE 3000 VOLTS.
Motor efficiency, 90%. Cost of copper equals 16 cents per pound.
Length of conductor per mile of single distance, 11,000 ft., to allow for sag.
Miles.
10%
15%
20%
25%
30%
1
$0.52
$0.33
$0.23
$0.17
$0.13
2
2.08
1.31
0.93
0.69
0.54
3
4.68
2.95
2.08
1.55
1.21
4
8.32
5.25
3.70
2.77
2.15
5
13.00
8.20
5.78
4.33
3.37
6
18.70
11.75
8.32
6.23
4.85
7
25.50
16.00
11.30
8.45
6.60
8
33.30
21.00
14.80
11.00
8.60
9
42.20
26.60
18.75
14.00
10.90
10
52.05
32.78
23.14
17.31
13.50
11
63.00
39.75
28.00
21.00
16.30
12
75.00
47.20
33.30
24.90
19.40
13
88.00
55.30
39.00
29.20
22.80
14
102.00
64.20
45.30
33.90
26.40
15
117.00
73.75
52.00
38.90
30.30
16
133.00
83.80
59.00
44.30
34.50
17
150.00
94.75
67.00
50.00
39.00
18
169.00
106.00
75.00
56.20
43.80
19
188.00
118.00
83.50
62.50
48.70
20
208.00
131.00
92.60
69.25
54.00
ELECTRIC TRANSMISSION. 1041
Systems of Electrical Distribution In Common Use.
1. DIRECT CURRENT.
A. Constant Potential.
110 to 125 and 220 to 250]Volts.— Distances less than, say, 1500
feet.
For incandescent lamps.
For arc-lamps, usually 2 in series.
For motors of moderate sizes.
200 to 250 and 440 Volts, 3- wire. — Distances less than, say,
5000 feet.
For incandescent lamps.
For arc-lamps, usually 2 in series on each branch.
For motors 110 or 220 volts, usually 220 volts.
500 Volts. — Distances less than, say, 20,000 feet.
Incidentally for arc-lamps, usually 10 in series.
For motors, stationary and street-car.
B. Constant Current.
Usually 5, 6£, or 9£ amperes, the volts increasing to several
thousand, as demanded, for arc-lamps.
II. ALTERNATING CURRENT.
A. Constant Potential.
For incandescent lamps, arc-lamps, and motors.
Ployphase Systems.
For arc and incandescent lamps, motors, and rotary con-
verters for giving direct current.
Ployphase — 2- and 3-phase — high tension (25,000 volts and
over), for long-distance transmission; transformed by
step-up and step-down transformers.
B. Constant Current.
Usually 5 to 6.6 amperes. For arc-lamps.
References on Power Distribution. — Abbott, Electric Trans-
mission of Energy; Bell, Electric Power Transmission; Gushing, Standard
Wiring for Incandescent Light and Power; Crocker, Electric Lighting, 2
vols. ; Poole, Electric Wiring.
ELECTRIC RAILWAYS.
Space will not admit of a proper treatment of this subject in this work.
Consult Crosby and Bell, The Electric Railway in Theory and Practice ;
Fairchild, Street Railways ; Merrill, Reference Book of Tables and Formulas
for Street Railway Engineers ; Bell, Electric Transmission of Power ; Daw-
son, Engineering and Electric Traction Pocket-book.
ELECTRIC LIGHTING.
Arc Lights. — Direct-current open arcs usually require about 10 am-
peres at 45 volts, or 450 watts. The range of voltage is from 42 to 52 for
ordinary arcs. The most satisfactory light is given by 45 to 47 volts.
Search-light projectors use from 50 to 100 amperes at 48 to 53 volts.
The candle-power of an arc light varies according to the direction in which
the light is measured; thus we have, 1, mean horizontal candle-power;
2, maximum candle -power, which is usually found at an angle below the
horizontal; 3. mean spherical candle-power; 4, mean hemispherical candle-
power, below the horizontal.
The nominal candle-power of an arc lamp is an arbitrary figure. A 450-
watt arc is commonly called 2000 c.-p. and a 300-watt arc is 1200 c.-p.
These figures greatly exceed the true candle-power. Carhart found with
an arc of 10 amperes and 45 volts a maximum c.-p. of 450, but with the
same watts 8.4 amperes, and 54 volts he obtained 900 c.-p. Blondel.
however, found the c.-p. a maximum usually below 45 volts. Crocker
explains the discrepancy as probably due to a difference in size and quality
of the carbons.
Current for arc lighting is furnished either on the series, constant current,
or on the parallel constant potential system. In the latter the voltage
of the circuit is usually 110 and two lamps are connected in series. In
currents with higher voltages more lamps are used in series; for instance
10 with a 500-volt circuit.
1042
ELECTRICAL ENGINEERING.
Enclosed Arcs — Direct current enclosed arcs consume about 5 amperes
at 80 volts, or 400 watts. The chief advantages of the enclosed arcs, on
constant potential circuits are the long life of the carbons, 100 to 150
hours, as compared with 8 to 10 hours for open arcs; simplicity of con-
struction, absence of sparks, agreeable quality and better distribution of
Alternating-current enclosed arcs usually take a current of 6 amperes at
70 or 75 volts. With 70 volts and 6 amperes, in a 104-volt circuit, the
apparent watts at the lamp terminals are 625 and at the arc 420, the actual
watts being 445 and 390 respectively. The watts consumed in the inductive
resistance average 35 to 45.
incandescent Lamps. — Candle-power of nominal 16 c.p. 110-volt
lamp;
Mean horizontal 15.7 to 16.6
Mean spherical 12.7 to 13.8
Mean hemispherical 14.0 to 14.6
Mean within 30° from tip 7.9 to 10.9
Ordinary lamps take from 3 to 4 watts per candle-power. A 16 candle-
power lamp using 3.5 watts per candle-power or 56 watts at 110 volts takes
a current of 56 4- 110 = 0.51 ampere. For a given efficiency or watts per
candle-power the current and the power increase directly as the candle-
power. An ordinary lamp taking 56 watts, 13 lamps take 1 H.P. of elec-
trical energy, or 18 lamps 1.008 kilowatts.
Variation in Candle-Power, Efficiency, and Life. — The
following table shows the variation in candle-power, etc., of the General
Electric Co.'s standard 100 to 125 volts, 3,1 and 3,5 watt lamps, due to vari-
ation in voltage supplied to them. It will be seen that if a 3.1 watt lamp
is run at 10 per cent below its normal voltage, it may have over 9 times
as long a life, but it will give only 53 per cent of its normal lighting power,
and the light will cost 50 per cent more in energy per candle-power. If
it is run at 6 per cent above its normal voltage, it will give 37 per cent
more light, will take nearly 20 per cent less energy for equal light power,
but it will have less than one third of its normal life.
Per cent of
Normal
Voltage.
Per cent of
Normal Can-
dle-power.
Efficiency in
watts per
Candle, 3.1
watt Lamp.
Relative
Life. 3.1
watt Lamp.
Efficiency in
watts per
Candle.
3.5 watts.
Relative
Life.
3.5 watts.
90
53
4.65
9.41
5.36
91
57
4.44
7.16
5.09
92 '
61
4.24
5.55
4.85
93
65
4.10
4.35
4.63
94
69.5
3.90
3.45
4.44
3.94
95
74
3.75
2.75
4.26
3.10
96
79
3.60
2.20
4.09
2.47
97
84
3.45
1.79
3.93
1.95
98
89
3.34
1.46
3.78
1.53
99
94.5
3.22
1.21
3.64
1.26
100
100
3.10
1.00
3.50
1.00
101
106
2.99
.818
3.38
.84
102
112
2.90
.681
3.27
.68
103
118
2.80
.562
3.16
.58
104
124
2.70
.452
3.05
.47
105
130
2.62
.374
2.95
.39
106
137
2.54
.310
2.85
.31
The candle-power of a lamp falls off with its length of life, so that during
the latter half of its life it has only 60 per cent or 70 per cent of its rated
candle-power, and the watts per candle-power are increased 60 per cent < r
70 per cent. After a lamp has burned for 500 or 600 hours it ii more eco-
nomical to break it and supply a new one if the price of electrical energy
is that usually charged by central stations.
ELECTRIC WELDING.
1043
Specifications for Lamps. (Crocker.) — The initial candle-power
of any lamp at the rated voltage should not be more than 9 per cent above
or below the value called for. The average candle-power of a lot should
be within 6 per cent of the rated value. The standard efficiencies are 3.1.
3.5, and 4 watts per candle-power. Each lamp at rated voltage should
take within 6 per cent of the watts specified, and the average for the lot
should be within 4 per cent. The useful life of a lamp is the time it will
burn before falling to a certain candle-power, say 80 per cent of its initial
candle-power. For 3.1 watt lamps the useful life is about 400 to 450
hours, for 3.5 watt lamps about 800, and 4 watt lamps about 1600 hours.
Special Lamps. — The ordinary 16 c.-p. 110-volt is the standard
for interior lighting. Thousands of varieties of lamps for different voltages
and candle-power are made for special purposes, from the primary lamp,
supplied by primary batteries using three volts and about 1 ampere and
giving ^ c.-p., c,nd the % c.-p. bicycle lamp, 4 volts and 0.5 ampere, to lamps
of 100 c.p. at 220 volts. . Series lamps of 1 c.-p. are used in illuminating
signs, % ampere and 12.5 to 15 volts, eight lamps being used on a 110-volt
circuit. Standard sizes for different voltages, 50, 110, or 220, are 8, 16,
24, 32, 50, and 100 c.-p.
Nernst Lamp. — A form of incandescent lamp originated by Dr,
Walther Nernst, of Gottingen, is being developed in this country by the
Nernst Lamp Company, Pittsburg, Pa. It depends for its operation upon
the peculiar property of certain rare earths, such as yttrium, thorium, zir-
conium, etc., of becoming electrical conductors when heated to a certain
temperature; when cold, these oxides are non-conductors. The lamp com-
prises a "glower" composed of rare earths mixed with a binding material
and pressed into a small rod; a heater for bringing the glower up to the con-
ducting temperature; an automatic cut-out for disconnecting the heater
when the glower lights up, and a "ballast" consisting of a small resistance
coil of wire having a positive temperature-resistance coefficient. The bal-
last is connected in series with the glower; its presence is required to com-
pensate the negative temperature-resistance coefficient of the glower; with-
out the ballast, the resistance of the glower
would become lower and lower as its temper-
ature rose, until the flow of current through it
would destroy it. Fig. 171a shows the element-
ary circuits of a simple Nernst lamp. The
cut-out is an electromagnet connected in series
with the glower. When current begins to flow
through the glower, the magnet pulls up the
armature lying across the contacts of the cut-
out, thereby cutting out the heater. The
heater is a coil of fine wire either located very
near the glower or encircling it. The glower
is from'1/32 to 1/16 inch in diameter and about
1 inch long.
The material of the glower is an electrolyte,
so that this type of lamp is not well adapted
for operation on direct-current circuits be-
cause of the wasting away at the positive end
and the deposition of material at the nega-
tive end.
The lamps are made with one glower, or with two, three, or six glowers
connected in parallel, and for operation on 100 to 120 and 200 to 240 volt
circuits.
Cut-out
Coll
Glower
FIG. 171a.
ELECTRICAL ENGINEERING.
ELECTRIC WELDING.
The apparatus most generally used consists of an alternating-current
dynamo, feeding a comparatively high-potential current to the primary coil
01 an inductioa-coil or transformer, the secondary of which is made so
large in section and so short in length as to supply to the work currents
not exceeding two or three volts, and of very large volume or rate of flow.
The welding clamps are attached to the secondary terminals. Other forms
of apparatus, such as dynamos constructed to yield alternating currents
direct from the armature to the welding -clamps, are used to a limited
extent.
The conductivity for heat of the metal to be welded has a decided influ-
ence on the heating, and in welding iron its comparatively low heat conduc-
tion assists the work materially. (See papers by Sir F. Bramwell, Proc.
Inst. C. E., part iv., vol. cii. p. 1; and Elihu Thomson, Trans. A. I. M.E., xix.
877.)
Fred. P. Royce, Iron Age, Nov. 28, 1892, gives the following figures show-
ing the amount of power required to weld axles and tires:
AXLE -WELDING.
Seconds.
1-inch round axle requires 25 H.P. for 45
1-inch square axle requires 30 H.P. for 48
1^4-inch round axle requires 35 H.P. for 60
l}4-inch square axle requires 40 H.P. for 70
2-inch round axle requires 75 H.P. for 95
2-inch square axle requires 90 H.P. for 100
The slightly increased time and power required for welding the square
axle is not only due to the extra metal in it, but »a part to the care which it
is best to use to secure a, perfect alignment.
TIRE-WELDING.
Seconds.
1 X 3/16-inch tire requires 11 H.P. for 15
1J4 X %-inch tire requires 23 H.P. for 25
iy% X %-inch tire requires 20 H.P. for 30
1J4 X ^i-inch tire requires 23 H.P, for 40
2 X 34-inch tire requires 29 H.P. for 55
2 X %-inch tire requires 42 H.P. for 62
The time above given for welding is of course that required for the actual
application of the current only, and does not include that consumed by
placing the axles or tires in the machine, the removal of the upset and
other finishing processes. From the data thus submitted, the cost of welding;
can be readily figured for any locality where the price of fuel and cost of
labor are known.
In almost all cases the cost of the fuel used under the boilers for produc-
ing power for electric welding is practically the same as the cost of fuel
used in forges for the same amount of work, taking into consideration the
difference in price of fuel used in either case.
Prof. A. B. W. Kennedy found that 2J4-inch iron tubes *4 inch thick were
svelded in 61 seconds, the net horse-power required at this speed being 23.4
(say 33 indicated horse-power) per square inch of section. Brass tubing re/
quired 21 .2 net horse-power. About 60 total indicated horse-power would be
required for the welding of angle irons 3 X 3 X ^ inch in from two to three
minutes. Copper requires about 80 horse-power per square inch of section,
and an inch bar can be welded in 25 seconds. It takes about 90 seconds to
weld a steel bar 2 inches in diameter.
ELECTRIC HEATERS.
Wherever a comparatively small amount of heat is desired to be auto-
matically and uniformly maintained, and started or stopped on the instant
without waste, there is the province of the electric heater.
The elementary form of heater is some form of resistance, such as coila
of thin wire introduced into an electric circuit and surrounded with a sub-
stance, which will permit the conduction and radiation of heat, and at the
same time serve to electrically insulate the resistance.
This resistance should be proportional to the electro-motive force of the
current used and to the equation of Joule's law :
ELECTRICAL ACCUMULATORS OR STORAGE-BATTERIES.1045
H= 72
where 7 is the current in amperes; R, the resistance in ohms; t, the time in
seconds ; and 77, the heat in gram-centigrade units.
Since the resistance of metals increases as their temperature increases, a
thin wire heated by current passing through it will resist more, and grow
hotter and hotter until its rate of loss of heat by conduction and radiation
equals the rate at which heat is supplied by the current. In a short wire,
before heat enough can be dispelled for commercial purposes, fusion will
begin; and in electric heaters ft is necessary to use either long lengths of
thin wire, or carbon, which alone of all conductors resists fusion. In the
majority of heaters, coils of thin wire are used, separately embedded in
some substance of poor electrical but good thermal conductivity.
The Consolidated Car-heating Co.'s electric heater consists of a galvanized
iron wire wound in a spiral groove upon a porcelain insulator. Each heater
is 30% in. long, 8% in. high, and 6% in. wide. Upon it is wound 392 ft. of
wire. The weight of the whole is 23^ ibs.
Each heater is designed to absorb 1000 watts of a 500 -volt current. Six
heaters are the complement for an ordinary electric car. For ordinary
weather the heaters may be combined by the switch in different ways, so
that five different intensities of heating- surf ace are possible, besides the
position in which no heat is generated, the current being turned entirely off.
For heating an ordinary electric car the Consolidated Co. states that
from 2 to 12 amperes on a 500-volt circuit is sufficient. With the outside
temperature at 20° to 30°, about 6 amperes will suffice. With zero or lower
temperature, the full 12 amperes is required to heat a car effectively.
Compare these figures with the experience in steam-heating of railway-
cars, as follows :
1 B.T.U. = 0.29084 watt-hours.
6 amperes on a 500-volt circuit = 3000 watts.
A current consumption of 6 amperes will generate 3000 -*- 0.29084 = 10,315
B.T.U. per hour.
In steam-car heating, a passenger coach usually requires from 60 Ibs. of
eteam in freezing weather to 100 Ibs. in zero weather per hour. Supposing
the steam to enter the pipes at 20 Ibs. pressure, and to be discharged at 200°
F., each pound of steam will give up 983 B.T.U. to the car. Then the
equivalent of the thermal units delivered by the electrical-heating system in
pounds of steam, is 10,315 -f- 983 = 10^, nearly.
Thus the Consolidated Co.'s estimates for electric-heating provide the
equivalent of 10J^ Ibs. of steam per car per hour in freezing weather and 21
Ibs. in zero weather.
Suppose that by the use of good coal, careful firing, well designed boilers,
and triple-expansion engines we are able in daily practice to generate
1 H.P. delivered at the fly-wheel with an expenditure of 2>& Ibs. of coal per
hour.
We have then to convert this energy into electricity, transmit it by wire
to the heater, and convert it into heat by passing it through a resistance-coil.
We may set the combined efficiency of the dynamo and line circuit at 85#,
and will suppose that all the electricity is converted into heat in the resist-
ance-coils of the radiator. Then 1 brake H.P. at the engine = 0.85 electrical
H.P. at the resistance-coil = 1,683,000 ft.-lbs. energy per hour = 2180 beat-
units. But since it required 2*4 Ibs. of coal to develop 1 brake H.P., it fol-
lows that the heat given out at the radiator per pound of coal burned in the
boiler furnace will be 2180 •+- 2*4 = 872 H.U. An ordinary steam-heating
system utilizes 9652 H.U. per Ib. of coal for heating; hence the efficiency
of the electric system is to the efficiency of the steam-heating system as 872
to 9652, or about 1 to 11. (Eng'g Neivs, Aug. 9, '90; Mar. 3D, '92; May 15, '93.)
ELECTRICAL ACCUMULATORS OR STORAGE-
JBATTERIES.
The original, or PlantS, storage battery consisted of two plates of metallic
lead immersed in a vessel containing sulphuric acid. An electric current
being sent through the cell the surf ace of the positive plate was converted into
peroxide of lead, PbO2. This was called charging the cell. After being thus
charged the cell could be used as a source of electric current, or discharged,
Plante and other authorities consider that in charging, PbO2 is formed on
the positive plate and spongy metallic lead on the negative, both being con-
1046
ELECTRICAL ENGINEERING.
verted into lead oxide, PbO, by the discharge, but others hold that sulphate
of lead is made on both plates by discharging and that during the charging
PbO2 is formed on the positive plate and metallic Pb on the other, sulphuric
acid being set free.
The acid being continually abstracted from the electrolyte as the discharge
proceeds, the density of the solution becomes less. In the charging opera-
tion this action is reversed, the acid being reinstated in the liquid and
therefore causing an increase in its density.
The difference of potential developed by lead and lead peroxide immersed
in dilute H2SO4 is about two volts. A lead-peroxide plate gradually loses
its electrical energy by local action, the rate of such loss varying according
to the circumstances of its preparation and the condition of the cell.
In the Faure or pasted cells lead plates are coated with minium or
litharge made into a paste with acidulated water. When dry these plates
are placed in a bath of dilute H2SO4 and subjected to the action of the
current, by which the oxide on the positive plate is converted into peroxide
and that on the negative plate reduced to finely divided or porous lead.
The initial electro-motive force of the Faure cell averages 2.25 volts, but
after being allowed to rest some little time it is reduced to about 2.0 volts.
The "chloride" accumulator, made by the Electric Storage Battery Co.,
lead in which is afterwards by an electrolytic method converted into spongy
lead, while the zinc chloride is dissolved and washed away. Plates intended
for positive plates have the spongy lead converted into peroxide by immers-
ing them in sulphuric acid and passing a current through them in one
direction for about two weeks.
The following tables give the elements of several sizes of "chloride"
accumulators. Type G is furnished in cells containing 11-125 plates, and
type H from 21 plates to any greater number desired. The voltage of cells
of all sizes is slightly above two volts on open circuit, and during discharge
varies from that point at the beginning to 1.8 at the end.
Accumulators are largely used in central lighting and power stations, in
office buildings and other large isolated plants, for the purpose of absorbing
the energy of the generating plant during times of light load, and for giving
it out during times of heavy load or when the generating plant is idle. The
advantages of their use for such purposes are thus enumerated:
1. Reduction in coal consumption and general operating expenses, due to
the generating machinery being run at the point of greatest economy while
in service, and being shut down entirely during hours of light load, the bat-
tery supplying the whole of the current.
TYPE "B."
Size of Plates, 3 X 3 in.
TYPE "C."
Plates, 4MX 4 in.
TYPE "D."
Size of Plates, 6X6 in.
Number of plates
Discharge ( For 8 hours
in am- < - '
peres : ( '
Normal charge rate
Weight of each element, Ibs.. . .
Outside measurement I Width .
of rubber jar in -I Length.
inches: / Height.
Outside measurement ( Width..
of glass jar in •< Length.
inches : ( Height.
Weight of acid in glass jars in
Ibs
Weight of acid in rubber jars
in Ibs
Weight of cell complete, with
acid, in rubber jars in Ibs. . .
Height of cell over all in inches .
10
if*
4
10
15
oM
26
aS
N'>'e
13
8^ 10
50
ELECTRICAL ACCUMULATORS OR STORAGE-BATTERIES.104?
TYPE "E."
Size of Plates, 7% X 7% in.
TYPE " F."
Size of Plates,
10K X 10K in.
Number of plates
5
10
14
20
10
23
3
,!*
%
\\Y4
17
6^
31
14K
15
21
30
15
33
4
m
%
11J4
21
9
42
UK
9
20
28
40
20
43
JK
8
9^
Hfc
25
UK
54
1*K
11
25
35
50
•25
52
6%
8^
11
8%
• 9K
11J4
27
14^
66
14K
13
30
42
60
30
62
s4
11
11
9%
HH
35
17K
79
14K
15
35
49
70
35
71
m
3*
11
9%
1114
34
21
91
14K
9
40
56
80
40
86
9"
i*K
WK
53
18
11
50
70
100
50
106
I!
10%
i2K
15K
61
«•**
lefl
^ *
18
13
60
84
120
60
125
!S«
17%
10%
12K
15K
58
94
302
18
15
70
98
140
70
145
if*
if*
12%
15K
70
104
339
19
17
80
112
160
80
165
20
15
17%
19
90
126
180
90
184
21%
15
17%
Discharge ( For 8 hours
in am--<
peres: ( " 3 '
Normal charge rate.. . .
Weight each element.
Ibs
^ ( Width, in., ) rub-
,§£•< Length, " V ber
28 (Height, « j jar.
-5 8 I Width, " ) OQ .
0 1 i Length, » V § -3
S j Height, " I •a«
Weight of acid in glass
jars in Ibs
Weight of acid in rub-
ber jars in Ibs
114
376
19
124
415
19
Weight of cell com-
plete, with acid, in
rubber jar in Ibs. . ..
Height of cell over all,
in inches
TYPE " G."
Size of Plates, 15^ x 15t£ in.
TYPE " H."
Size of Plates,
15K X 32 in.
Number of plates
Discharge ( For 8 hrs.
in am- •< " 5 *'
peres: ( " 3 "
Normal charge rate.. . .
Weight of each ele-
ment, Ibs
Outside f Width,
measurement j T Anp.fh
of tank in 1 Len£th
inches. t Height
Weight of acid in
pounds
Weight of cell, com-
plete, with acid in
lead-lined tank in
pounds:
11
100
140
200
100
219
15K
19%
22%
160
482
26
13
120
168
240
120
260
16%
19%
22%
179
552
26
15
140
196
280
140
300
18%
19%
22%
197
621
26
17
160
224
320
160
341
20
19%
22%
216
689
26
25
240
336
480
240
503
27%
20%
22%
292
992
26
125
1240
1736
2480
1240
2538
11H
21K
24%
1242
4560
29
D*
10
14
20
10
20.4
%
9.5
36
21
400
560
800
400
790
25%
*!K
42%
515
1635
45
23
440
616
880
440
866
26%
81K
42%
552
1769
45
25
480
672
960
480
942
28%
aiK
42%
590
1904
45
125
2480
3472
4960
2480
4741
nu
aiK
43%
2512
8696
46
D*
20
28
40
20
38
%
19.2
68
Height of cell over all,
inches
* D = addition per plate from 25 to 125 plates; approximate as to dimen-
sions and weights.
2. The possibility of obtaining good regulation in pressure during fluctua-
tions in load, especially when the day load consists largely of elevators and
similar disturbing elements.
3. To meet sudden demands which arise unexpectedly, as in the case of
darkness caused by storm or thunder-showers; also in case of emergency
due to accident or stoppage of generating-plant.
4. Smaller generating-plant required where the battery takes the peak of
the load, which usually only lasts for a few hours, and yet where no battery
is used necessitates sufficient generators, etc., being installed to provide for
the maximum output, which in many cases is about double the normal
output,
1048 ELECTRICAL
The Working Current, or Energy Efficiency, of a storage-
cell is the ratio between the value of the current or energy expended in the
charging operation, and that obtained when the cell is discharged at any
specified rate.
In a lead storage-cell, if the surface and quantity of active material be
accurately proportioned, and if the discharge be commenced immediately
after the termination of the charge, then a current efficiency of as much as
98% may be obtained, provided the rate of discharge is low and well regu-
lated. In practice it is found that low rates of discharge are not economical,
and as the current efficiency always decreases as the discharge rate in-
creases, it is found that the normal current efficiency seldom exceeds 90%,
and averages about 85%.
As the normal discharging electro-motive force of a lead secondary cell
never exceeds 2 volts, and as an electro-motive force of from 2.4 to 2.5
volts is required at its poles to overcome both its opposing electro-motive
force and its internal resistance, there is an initial loss of 20% between the
energy required to charge it and that given out during its discharge.
As the normal discharging potential is continually being reduced as
the rate of discharge increases, it follows that an energy efficiency of 80%
can never be realized. As a matter of fact, a ma imum of 75% and a
mean of 60# is the usual energy efficiency of lead-sulphuric-acid storage-cells.
Important General Rules. — Storage cells should not be
allowed to stand idle when charged, and must not stand idle when uncharged
or after being discharged. If a battery is to be put out of commission
for any length of time, it should be fully charged, the electrolyte all drawn
off, the cells filled with pure water and then discharged slightly — say until
the E.M.F. is 1.95 volts. The cells should then be emptied, and the plates
dried in a warm atmosphere.
In mixing the electrolyte, the acid should always be poured into the
water.. The mixing must be very gradual in order to avoid excessive
heating. The acid solution must be cooled before the cells are filled with
it. The acid should be tested for impurities before mixing the electrolyte.
Tests for Impurities. — To test for copper and arsenic, add a small quantity
of dilute acid to an equal quantity of fresh sulphide of hydrogen (H2S).
The presence of copper will cause a black precipitate; that of arsenic, a
yellow precipitate.
To test for iron, add a few drops of nitric acid to a small quantity of
dilute acid and heat the mixture ; after cooling add a few drops- of potassium
sulphocyanide solution. The presence of iron will be indicated by a deep
red color.
Charging and Discharging. — Charging should be stopped when the voltage
is 26 volts per cell and gas is given off, except in the first charging, when
2.7 should be reached. Discharging should be stopped and the cells re-
charged when the voltage is down to 1.8 volts per cell when discharging at
normal rate.
ELECTROLYSIS.
The separation of a chemical compound into its constituents by means
of an electric current. Faraday gave the nomenclature relating to elec-
trolysis. The compound to be decomposed is the Electrolyte, and the
process Electrolysis. The plates or poles of the battery are Electrodes.
The plate where the greatest pressure exists is the Anode, and the other
pole is the Cathode. The products of decomposition are Ions.
Lord Rayleigh found that a current of one ampere will deposit 0.017253
grain, or 0.001118 gramme, of silver per second on one of the plates of a
silver voltameter, the liquid employed being a solution of silver nitrate
containing from 15% to 20% of the salt. The weight of hydrogen similarly
set free by a current of one ampere is .00001038 gramme per second.
Knowing the amount of hydrogen thus set free, and the chemical equiva-
lents of the constituents of other substances, we can calculate what weight
of their elements will be set free or deposited in a given time by a given
current. Thus, the current that liberates 1 gramme of hydrogen will liberate
8 grammes of oxygen, or 107.7 grammes of silver, the numbers 8 and 107.7
being the chemical equivalents for oxygen and silver respectively.
To find the weight of metal deposited by a given current in a given time,
find the weight of hydrogen liberated by the given current in the given
time, and multiply by the chemical equivalent of the metal.
ELECTRO-CHEMICAL EQUIVALENTS. 10-19
K1.KCTRO-CHEMIOAI* EQUIVALENTS,
•H
b»
*3
oJ'S &
££A
ri
Elements.
t>
3
£ § %£
& ®
PJ3
l>
•a
V^ a S
^S
<c 2
£j»
.2
o^-
o£ gjo
B.l
S *
®
§
sj
o o'hbo
° &
a u
if
e8
2
J3 *
^Hs o
§t>o
2«j
<!
0
H
0
o
ELECTRO-POSITIVE.
Hydrogen
H,
1.00
1.00
.010384
96293.00
0.03738
K.
39.04
39.04
.40539
2467.50
1.45950
Sodium
Na'
22.99
22.99
.23873
4188.90
0.85942
Alo
27.3
9.1
.09449
1058.30
0.34018
Magnesium
M ^
23.94
11.97
.12430
804.03
0.44747
Gold
An"
196.2
65.4
.67911
1473.50
2.44480
Silver
Ag,
107.66
107.66
1.11800
894.41
4.02500
Copper (cupric)
(cuprous)
Mercury (mercuric).. . .
" (mercurous)..
Tin (stannic) .
Cua
Cu,
Hg,
Hg,
Sn4
63.00
63.00
199 8
199.8
117.8
31.5
63.00
99.9
199.8
29.45
.32709
.65419
1.03740
2.07470
.30581
3058.60
1525.30
963.99
481.99
3270.00
1.17700
2.35500
3.73450
7.46900
1.10090
Sn,
117.8
58.9
.61162
1635.00
2.20180
Fe'
55.9
18.64$
.19356
5166.4
0.69681
*• (ferrous)
Fe*
55.9
27.95
.29035
3445.50
1.04480
Nickel
Ni2
58.6
29.3
.30425
3286.80
1.09530
Zinc....
64.9
32.45
.33696
2967.10
1.21330
Lead
Pba
206.4
103.2
1.07160
933.26
3.85780
ELECTRO -NEGATIVE.
On
15.96
7.98
.08286
Chlorine
r,\\
35.37
35.37
.36728
I.
126.53
126.53
1.31390
Bromine
Br,
79.75
79.75
.82812
Nitrogen
Ng
14.01
4.67
.04849
* Valency is the atom-fixing or atom-replacing power of an element com-
pared with hydrogen, whose valency is unity,
t Atomic weight is the weight of one atom of each element compared with
hydrogen, whose atomic weight is unity.
$ Becquerel's extension of Faraday's law showed that the electro-chemical
equivalent of an element is proportional to its chemical equivalent. The
latter is equal to its combining weight, and not to atomic weight -i- valency,
as defined by Thompson, Hospitalier, and others who have copied their
tables. For example, the ferric salt is an exception to Thompson's rule, as
are sesqui-salts in general.
Thus: Weight of silver deposited in 10 seconds by a current of 10 amperes
= weight of hydrogen liberated per second X number seconds X currenl
strength X 107.7 = .00001038 X 10 X 10 X 107.7 = .11178 gramme.
Weight of copper deposited in 1 hour by a current of 10 amperes =
,00001038 X 3600 X 10 X 31.5 = 11. 77 grammes.
Since 1 ampere per second liberates .00001038 gramme of hydrogen,
strength of current in amperes
_ weight in grammes of H. liberated per second
.00001038
weight of element liberated per second
~~ .00001038 X chemical equivalent of element*
The above table (from " Practical Electrical Engineering ") is calculated
flpon Lord Rayleigh's determination of the electro-chemical equivalents and
Roscoe's atomic weights.
1050 ELECTHICAL EtfGIKEERIKG.
ELECTRO-MAGNETS.*
Units of Electro-magnetic Measurements.
Unit magnetic pole is a pole of such strength that when placed at a dis-
tance of one centimetre from a similar pole of equal strength it repels it
with a force of one dyne.
Gauss = unit of field strength, or density, symbol H, is that intensity of
field which acts on a unit pole with a force of one dyne, = one line of force
per square centimetre. A field of H units is one which acts with H dynes
on unit pole, or H lines per square centimetre. A unit magnetic pole has
4?r lines of force proceeding from it.
Maxwell = unit of magnetic flux, is the amount of magnetism passing
through every square centimetre of a field of unit density. Symbol, $.
Gilbert = unit of magneto-motive force, is the amount of M.M.F., that
would be produced by a coil of 10-^471 or 0.7958 ampere-turns. Symbol, F.
The M.M.F. of a coil is equal to 1.2566 times the ampere-turns.
If a solenoid is wound with 100 turns of insulated wire carrying a current
of 5 amperes, the M.M.F. exerted will be 500 ampere-turns X 1.2566 = 628.3
gilberts.
Oersted — unit of magnetic reluctance ; it is the reluctance of a cubic centi-
metre of an air-pump vacuum. Symbol, R.
Reluctance is that quantity in a magnetic circuit which limits the flux
under a given M.M.F. It corresponds to the resistance in the electric cir-
cuit.
The reluctivity of any medium is its specific reluctance, and in the C.G.S.
system is the reluctance offered by a cubic centimetre of the body between
opposed parallel faces. The reluctivity of nearly all substances, other than
the magnetic metals, is sensibly that of vacuum, is equal to unity, and is
independent of the flux density.
Permeability is the reciprocal of magnetic reluctivity. It is a number, and
the symbol is^ /*.
Permeance is the reciprocal of reluctance.
Lines and. Looj>s of Force. — In discussing magnetic and
electrical phenomena it is conventionally assumed that the attractions and
repulsions as shown by the action of a magnet or a conductor upon iron
filings are due to "lines of force" surrounding the magnet or conductor.
The "number of lines" indicates the magnitude of the forces acting. As
the iron filings arrange themselves in concentric circles, we may assume that
the forces may be represented by closed curves or "loops of force." The
following assumptions are made concerning the loops of force in a con-
ductive circuit:
1. That the lines or loops of force in the conductor are parallel to the
axis of the conductor.
2. That the loops of force external to the conductor are proportional in
number to the current in the conductor, that is, a definite current gener-
ates a definite number of loops of force. These may be stated as the
strength of field in proportion to the current.
3. That the radii of the loops of force are at right angles to the axis of
the conductor.
The magnetic force proceeding from a point is equal at all points on the
surface of an imaginary sphere described by a given radius ^ about that
point. A sphere of radius 1 cm. has a surface of 4?: square centimetres. If
<fr = total flux, expressed as the number of lines of force emanating from
a magnetic pole having a strength, M,
<£ = 47rJ/; M=<l>-*-4x.
Magnetic moment of a magnet = product of strength of pole M and its
length, or distance between its poles L. Magnetic moment = -—• •
* For a very full treatment of this subject see "The Electro-Magnet,"
published by the Varley Duplex Magnet Co., Phillipsdale, R. I.
ELECTRO-MAGKETS. 1051
If B = number of lines flowing through each square centimetre of cross-
section of a bar-magnet, or the "specific induction," and A = cross-section,
Magnetic Moment = LA B -r- 4 n.
axis of the bar, the north pole will be pulled forward, that is, in the direction
in which the lines flow, and the south pole will be pulled in the opposite
direction, the two forces producing a torsional moment or torque,
Torque = MLH — LA BH -J- 4^, in dyne-centimetres.
Magnetic attraction or repulsion emanating from a point varies inversely
as the square of the distance from that point. The law of inverse squares,
however, is not true when the magnetism proceeds from a surface of appre-
ciable extent, and the distances are small, as in dynamo-electric machines
and ordinary electromagnets.
Permeability. — Materials differ in regard to the resistance they offer
to the passage of lines of force ; thus iron is more permeable than air. The
permeability of a substance is expressed by a coefficient, n, which denotes
its relation to the permeability of air, which is taken as 1. If H = number
of magnetic lines per square centimetre which will pass through an air-
space between the poles of a magnet, and B the number of lines which will
pass through a certain piece of iron in that space, then /* = B -r- H . The
permeability varies with the quality of the iron and the degree of satura-
tion, reaching a practical limit for soft wrought iron when B = about 18,000
and for cast iron when B = about 10,000 C.G.S lines per square centimetre.
The permeability of a number of materials may be determined by mea1 *
of the table on the following page.
The magnetic Circuit. — In the electric circuit
E.M.F. . E
Current =-=r — — , or 1 = ^-
Resistance R
Similarly, in the magnetic circuit
Magnetomotive Force F
Magnetic I lux = — — , or 4>=-^--
Reluctance . R
Reluctance is the reciprocal of permeance, and permeance is equal to
permeability X path area -f- path length (metric measure); hence
One ampere-turn produces 1.257 gilberts of magnetomotive force and
one inch equals 2.54 centimetres; hence, in inch measure,
9-.l~^-^r- —j—
The ampere- turns required to produce a given magnetic flux in a given
path will be
A _ 0Z _ 0.3133#
'~~
Since magnetic flux •*• area of path = magnetic density, the ampere-turns
equired to i
of path, will
required to produce a density B, in lines of force per square inch of area
ivill be
This formula is used in practical work, as the magnetic density must
be predetermined in order to ascertain the permeability of the material
under itu working conditions. When a magnetic circuit includes several
1052
ELECTRICAL ENGINEERING.
cfualities of material, such as wrought iron, cast iron, and air, it is most
direct to work in terms of ampere-turns per unit length of path. The
ampere-turns for each material are determined separately, and the wind-
ing is designed to produce the sum of all the ampere-turns. The following
table gives the average results from a number of tests made by Dr. Samuel
Sheldon:
VALUES OF B AND H.
a
a
Cast Iron.
Cast Steel.
Wroughtlron
Sheet Metal.
3+2
S,d
CD
o>
'
cu
<3
11
"*f ^ rj
~*f O .4
V
X ft
CD
x ft •
CD
X ft
cu
JL ft
|ll
I'll
"4
|!l
• I
18
03^. g
"11
K
PQ
iS
c3 w fl
m
1
^
3
3
3
3
3
8
K
10
7.95
25.2
4.3
27.7
11.5
74.2
13.0
83.8
14.3
92.2
20
15.90
40.4
5.7
36.8
13.8
89.0
14.7
94.8
15.6
100.7
30
23.85
60.6
6.5
41.9
14.9
96.1
15.3
98.6
16.2
104.5
40
31.80
80.8
7.1
45.8
15.5
100.0
15.7
101.2
16.6
107.1
50
39.75
101.0
7.6
49.0
16.0
103.2
16.0
'03.2
16.9
109.0
60
47.70
121.2
8.0
51.6
16.5
106.5
16.3
105.2
17.3
111.6
70
55.65
141.4
8.4
59.2
16.9
109.0
16.5
106.5
17.5
112.9
80
63.65
161.6
8.7
56.1
17.2
111.0
16.7
107.8
17.7
114.1
90
71.60
181.8
9.0
58.0
17.4
112.2
16.9
109.0
18.0
116.1
100
79.50
202.0
9.4
60.6
17.7
114.1
17.2
110.9
18.2
117.3
150
119.25
303.0
10.6
68.3
18.5
119.2
18.0
116.1
19.0
122.7
200
159.0
404.0
11.7
75.5
19.2
123.9
18.7
120.8
19.6
126.5
250
198.8
505.0
12.4
•80.0
19.7
127.1
19.2
123.9
20.2
130.2
300
238.5
606.0
13.2
85.1
20.1
129.6
19.7
127.1
20.7
133.5
H = 1.257 ampere-turns per cm. =.495 ampere-turns per inch.
EXAMPLE. — A magnetic circuit consists of 12 inches of cast steel of
8 square inches cross-section; 4 inches of cast iron of 22 square inches
cross-section ; 3 inches of sheet iron of 8 square inches cross-section ; and
two air-gaps each Me mcn l°ng and of 12 square inches area. Required,
the ampere-turns to produce a flux of 768,000 maxwells, which is to be
uniform throughout the magnetic circuit.
The flux density in the steel is 768,000^-8 = 96,000 maxwells; the ampere-
turns per inch of length, according to Sheldon's table, are 60.6, so that the
12 inches of steel will require 727.2 ampere-turns.
The density in the cast iron is 768,000-^22 = 34,900; the ampere-turns
= 4X40=160.
The density in the sheet iron = 768,000 -f 8 = 96,000; ampere-turns per
inch = 30; total ampere-turns for sheet iron = 90.
The air-gap density is 768,000 -f- 12 = 64,000; ampere-turns per inch =
0.3133B; ampere-turns required for air-gap = 0.31 33 X 64,000^8 = 2506.4.
The entire circuit will require 727.2+160 + 90 + 2506.4 = 3483.6 ampere-
turns, assuming uniform flux throughout.
In practice there is considerable "leakage" of magnetic lines of force;
that is, many of the lines stray away from the useful path, there being no
material opaque to magnetism and therefore no means of restricting it to
a given path. The amount of leakage is proportional to the permeance
of the leakage paths available between two points in a magnetic circuit
which are at different magnetic potentials, such as opposite ends of a
magnet coil. It is seldom practicable to predetermine with any approach
to accuracy the magnetic leakage that will occur under given conditions
unless one has profuse data obtained experimentally under similar con-
ditions. In dynamo-electric machines the leakage coefficient varies from
1.3 to 2.
ELECTRO-MAGNETS,
1053
Tractive or Lifting Force of a Magnet,— The lifting power or
"pull" exerted by an electro-magnet upon an armature in actual contact
with its pole-faces is given by the formula
= Lbs.,
72,134,000
a being the area of contact in square inches and B the magnetic density
over this area. If the armature is very close to the pole-faces, this for-
mula also applies with sufficient accuracy for all practical purposes, but
a considerable air-gap renders it inapplicable. The accompanying table is
convenient for approximating the dimensions of cores and pole-faces for
tractive magnets.
Dimensions of Lifting Magnets.
Ampere-turns per
Ampere-turns per
Den-
inch of length.
Pull in
Den-
inch of length.
Pull in
sity
Ibs. per
sity
Ibs. per
B.
A IT*
Cast
Cast
sq. in.
B.
A J,,
Cast
Cast
sq. in.
Air.
Iron.
Steel.
Air.
Iron.
Steel.
10,000
3133
18
3.7
1.38
29,000
9,086
49
6.5
11.6
11,000
3447
19.2
3.81
1.65
30,000
9,400
52
6.7
12.4
12,000
3760
20.4
3.93
2
31,000
9,713
55
6.9
13.2
13,000
4073
21.6
4.05
2.3
32,000
10,026
58
7.1
14
14,000
4387
22.8
4.17
2.7
33,000
10,339
61
7.3
15
15,000
4700
24
4.3
3.1
34,000
10,652
64
7.5
16
10,000
5013
25.2
4.44
3.5
35,000
10,965
68
7.7
17
17,000
5326
26.5
4.58
4
36,000
11,278
72
7.9
18
18,000
5640
27.9
4.72
4.5
37,000
11,590
76
8.1
19
19.000
5953
29.3
4.86
5
38,000
11,904
80
8.3
20
20,000
6266
30.7
5
5.5
39,000
12,217
85
8.55
21
21,000
6580
32.2
5.16
6
40,000
12,532
90
8.8
22
21,500
6736
33.1
5.24
6.4
41,000
12,843
95
9.05
23
22,000
6893
34
5.32
67
42,000
13,159
100
9.3
24.25
22,500
7050
35
5.4
7
43,000
13,472
106
9.55
25.5
23,000
7206
36
5.48
7.3
44,000
13,785
112
9.8
26.75
23,500
7363
37
5.56
7.6
45,000
14.098
118
10.25
28
24,000
7520
38
5.64
7.9
46,000
14,412
125
10.5
29.3
25,000
7833
40
5.8
8.6
47,000
14,725
132
10.8
30.6
26,000
8146
42
5.97
9.3
48,000
15,038
140
11.15
31.9
27,000
8459
44
6.14
10
49,000
15,350
150
11.5
33.2
28,000
8773
46
6.32
10.8
50,000
15,665
160
11.9
34.6
Magnet Windings. — Knowing the ampere-turns required to pro-
duce the desired excitation of a magnetic circuit, the winding may be
approximately determined as follows:
For round cores under 1 inch in diameter make the depth or thickness
of winding, t, equal to the core diameter; over 1 inch, let £ = cube root of
core diameter. For slab-shaped cores let the coil thickness be equal to the
core thickness up to 1 inch, and to the square root of the core thickness
above that.
The ampere-turns produced by any coil will be
Vd*
At~ Ik '
in which V = volts at the coil terminals,
d!2 = area of the wire in circular mils,
Z = mean length in inches per turn of wire,
k = a, coefficient depending on the temperature of the coil.
1054 ELECTRICAL ENGINEERING.
The mean length per turn of wire is
g being the perimeter of the core. The size of wire required for a given
excitation will be
k Af
2 -
At 140° Fahr. fc = l. The table herewith gives the values of k at various
other practical temperatures.
Values of /»• in magnet-coil Formula.
Temp.
* !
Temp.
k
Temp.
k Temp.
k
100
o.923 ;
115
0.952
130
0.981
150
1.0195
105
0.933
. 120
0.902
135
0.99
155
1.029
110
0.942 !
125
0.971
145
1.01
160
1.0387
The rise above atmospheric temperature will be
V2
in which R= the resistance of the coil when hot, S= its radiating surface,
and kt is a variable coefficient (see p. 1032). The value of kt will be about
0.008 for electro-magnets of ordinary size not enclosed or shielded in any
way from the surrounding air.
For fuller treatment of the subject, see American Electrician, April and
May, 1901, and January, 1904.
Determining the Polarity of Electro-magnets. — If a wire
is wound around a magnet in a right-handed helix, the end at which the
current flows into the helix is the south pole. If a wire is wound around an
ordinary wood-screw, and the current flows around the helix in the direc-
tion from the head of the screw to the point, the head of the screw is the
south pole. If a magnet is held so that the south pole is opposite the eye of
the observer, the wire being wound as a right-handed helix around it, the
current flows in a right-handed direction, with the hands of a clock.
Determining the Direction of a Cnrrent. — Place a wire
carrying a current above and parallel to a pivoted magnetic needle. If
the current be flowing along the wire from N. to S., it will cause the N.-
seeking pole to turn to the eastward; if it be flowing from S. to N., the
pole will turn to the westward. If the wire be below the needle, these
motions will be reversed.
Maxwell's rule. The direction of the current and that of the resisting
magnetic force are related to each other as are the rotation and the for-
ward travel of an ordinary (right-handed) cork-screw.
DYKAMO-ELECTRIC MACHINES. 1055
DYNAMO-ELECTRIC MACHINES.
There are three classes of 4ynamo-electric machines, viz. :
1. Generators, for the conversion of mechanical into electrical energy.
2. Motors, for the conversion of electrical into mechanical energy.
Generators and motors are both subdivided into direct-current and alter-
nating-current machines.
3. Transformers, for the conversion of one character or voltage of current
into another, as direct into alternating or alternating into direct, or from
one voltage into a higher or lower voltage.
Kinds of Dynamo-electric Machines as regards Man-
ner of Winding.
1. Separately-excited Dynamo. — The field-magnet coils have no connec-
tion with the armature-coils, but receive their current from a separate
machine or source.
2. Series-wound Dynamo. — The field winding and the external circuit are
connected in series with the armature winding, so that the entire armature
current must pass through the field-coils.
Since in a semes-wound dynamo the armature-coils, the field, and the ex-
ternal circuit are in series, any increase in the resistance of the external
circuit will decrease the electro-motive force from the decrease in the mag-
netizing currents. A decrease in the resistance of the external circuit will,
in a like mariner, increase the electro-motive force from the increase in the
magnetizing current. The use of a regulator avoids these changes in the
electro-motive force.
3. Shunt-wound Dynamo. — The field -magnet coils are placed in a shunt
to the armature circuit, so that only a portion of the current generated
passes through the field-magnet coils, but all the difference of potential of
the armature acts at the terminals of the field-circuit.
In a shunt-wound dynamo an increase in the resistance of the external
circuit increases the electro-motive force, and a decrease in the resistance
of the external circuit decreases the electro-motive force. This is just the
reverse of the series-wound dynamo.
In a shunt-wound dynamo a continuous balancing of the current occurs,
the current dividing at the brushes between the field and the external cir-
cuit in the inverse proportion to the resistance of these circuits. If the
resistance of the external circuit becomes greater, a proportionately greater
current passes through the field-magnets, and so causes the electro-motive
force to become greater. If, on the contrary, the resistance of the external
circuit decreases, less current passes through the field, and the electro-
motive force is proportionately decreased.
4. Compound-wound Dynamo. — The field-magnets are wound with two
separate sets of coils, one of which is in series with the armature and the
external circuit, and the other in shunt with the armature, or the external
circuit.
Motors. — The above classification in regard to winding applies also to
motors.
Moving Force* of a Dynamo-electric Machine. — A wire
through which a current passes has, when placed in a magnetic field, a
tendency to move perpendicular to itself and at right angles to the lines
of the field. The force producing this tendency is P = IBI dynes, in which
Z=length of the wire, 7 = the current in C.G.S. units, and B = the induc-
tion, or flux density, in the field in lines per square centimetre.
If the current / is taken in amperes, P**IBI + 1Q~IB1 10 J.
If Pk is taken in kilogrammes,
Pk = IBI+ 9,8 10,000 = 10. 1937 IBI 10~8 kilogrammes.
EXAMPLE. — The mean strength of field, B, of a dynamo is 5000 C.G.S.
lines: a current of 100 amperes flows through a wire; the force acts upon
10 centimetres of the wire = 10. 1937 X 10 X 100X5000 X 10" 8 = . 5097 kilo-
grammes.
In the "English" or Kapp's system of measurement a total flow of 6000
1056 ELECTRICAL ENGINEERING
_____ per squ ________________ , — -
Ppin pounds, PP = 531/Z"Z?J?10-6 pounds.
Torque of an Armature. — The torque of an armature is the mo-
ment tending to turn it. In a generator it is the moment which must be
applied to the armature to turn it in order to produce current. In a motor
it is the turning moment which the armature gives to the pulley.
Let / = current in the armature in amperes, E— the electro-motive force
in volts, T = *he torque in pound-feet, <f> = the flux through the armature
in maxwells, N= the number of conductors around the armature, and n =
the number of revolutions per second. Then
Watts = IE = 2irnT X 1.356.*
In any machine if the flux be constant, E is directly proportional to the
speed and = <f>Nn -*- 108; whence
6NI
^J = 2nTX 1.356;
T
10* X 2. X 1.856" = 8.52 X 10- -«
Let I — length of armature in inches, d — diameter of armature in inches,
B = flux density in maxwells per square inch, and let m = the ratio of the
conductors under the influence of the pole-pieces to the whole number of
conductors on the armature. Then
These formulae apply to both generators and motors. They show that
torque is independent of the speed and varies directly with the current and
the flux. The total peripheral force is obtained by dividing the torque by
the radius (in feet) of the armature, and the drag on each conductor is
obtained by dividing the total peripheral force by the number of conductors
under the influence of the pole-pieces at one time.
EXAMPLE. — Given an armature of length I = 20 inches, diameter d=l2
inches, number of conductors N = 120, of which 80 are under the influence
of the pole-pieces at one time; let the flux density B — 30,000 maxwells
per sq. in. and the current 7 = 400 amperes.
, <t> = -^ X 20 X 30>000 X jfo" = 7,540,000.
7,540,000 X 120 X 400
8.52 X 100.000,000
" 424'8 V°™
Total peripheral force = 424.8 -*• .5 = 849.6 Ibs.
Drag per conductor = 849.6 -*• 120 = 7.08 Ibs.
The work done in one revolution = torque X circumference of a circle of
1 foot radius = 424.8 X 6.28 = 2670 foot-pounds.
Let the revolutions per minute equal 500, then the horse-power
_ 2670 X 500 _
33000
Electro-motive Force of the Armature Circuit. — From the
horse-power, calculated as above, together with the amperes, we can obtain
the E.M. F., for IE = H.P. X 746, whence E.M.F. or E = H.P. X 746 -*• /.
If H.P., as above, = 40.5, and / = 400, E = 4°-54^Q746 = 75.5 volts.
The E.M.F. may also be calculated by the following formulae:
/ •=« Total current through armature;
ed =« E.M.F. in armature in volts;
N «= Number of active conductors counted all around armature;
p = Number of pairs of poles (p — 1 in a two-pole machine);
n = Speed in revolutions per minute;
4> = Total flux in maxwells.
* 1 ft.-lb. per second = 1.356 watts.
DYKAMO-ELECTKIC MACHINES. 1057
* 10~~ *°r two"po^e machines.
Electro-motive •< p(}tNn for multipolar machines with
10" 60 series-wound armature.
Strength of the Magnetic Field. — The fundamental equation
for calculations relating to the magnetic circuit is
Magneto -motive Force
Flux =
Reluctance
Magneto-motive force is the magnetizing effect of an electric current.
It varies directly as the number of turns in a coil, and as the current. It
is numerically equal to 1.257 X amperes X turns.
Reluctance is the resistance any material offers to the setting up in itself
of magnetic lines. It varies directly as the length and inversely as the area
of the cross-section of the core, taken at right angles to the direction of the
magnetic lines, and inversely as the permeability of the material.
Let / = current in amperes, N = number of turns in the coil, A = area
of the cross-section of the core in square centimetres, I = length of core in
centimetres, fi the permeability of the core, and <p <= flux in maxwells.
Then
= 1 .257 NI
0 ~~ a 4- A^y
In a dynamo-electric machine the reluctance will be made up of three
separate quantities, viz.: the reluctance of the field magnet cores, the reluc-
tance of the air spaces between the field magnet pole-pieces and the arma-
ture, and the reluctance of the armature. The total reluctance is the
sum of the three. Let L\ , Lg, LS be the length of the path of magnetic
lines in the field magnet cores,* in the air-gaps, and in the armature respec-
tively; and let AI, A2, A3 be the areas of the cross-sections perpendicular
to the path of the magnetic lines in the field magnet cores, the air-gaps, and
the armature respectively. Let the permeability of the field magnet cores
be iii, and of the armature ju.3. The permeability of the air-gaps is taken
as unity. Then the total reluctance of the machine will be
A. +j^ u
Al t^i A2 ""
The formula for magnetic flux will now read
1.257 NI
(L, -f- Alfn) + (L2 -H A2) + (L3
The ampere turns necessary to create a given flux in a machine may be
found by the formula
Arr A K^i •«- 4i Mi) + (La -*• 42)
- ~
.
- - 1.257 ~ '
But the total flux generated by the field coils is not available to produce
current in the armature. There is a leakage between the field magnets,
and this must be allowed for in calculations. The leakage coefficient
varies from 1.3 to 2 in different machines. The meaning of the coefficient
is that if a flux of say 100 maxwells per square cm. are desired in the field
coils, it will be necessary to provide ampere turns for 1.3 X 100 = 130
maxwells, if the leakage coefficient be 1 .3.
Another method of calculating the ampere turns necessary to produce a
given flux is to calculate the magneto-motive force required in each portion
of the machine, separately, introducing the leakage coefficient in the calcu-
lation for the field magnets, and dividing the sum of the magnetive-moto
forces by 1.257. An example of this last method is appended.
EXAMPLE. — Given a two-pole generator with a single magnetic circuit
of the following dimensions, in centimetres and square centimetres: Z/i =»
150, L2 = each .5, L3 = 25; AI = 1200, A2 = 1400, A3 = 1000; leakage
* The length of the path in the field magnet cores LI includes that portion
of the path which lies in the piece joining the cores of the various field
magnets.
1058 ELECTRICAL
coefficient = A = 1.32; flux in armature = 10,000.000 maxwells. Re-
quired the ampere turns on field magnets. Let B = intensity of magnetic
induction, or flux density, and U = intensity of the magnetic field.
Armature: B = = 10'?°°n°00 = 10.000.
1000
From the permeability table, ^3 = 2000
Air-gaps:
M M P A LS 10,000,000 X 25 10_
M.M.F, - $ = 1Qoo X 2000 - 125'
10,000,000X2 X.5 _„
1400
Field Cores:
<f> X A ^ 10,000,000 X 1.32
At 1200
<ML, 10,000,000 X 1.32 X 150
MM'Fl = -AJZ = 1200 X 1692 - = 975-
Total M.M.F. = 125 + 7150 + 975 = 8250.
M.M.F. 8250
Ampere turns = — ^r==- = • = 6563.
1 .Zo i 1 .&oJ
In a machine having a double magnetic circuit, the calculation is slightly
varied. The total flux is created by the two separate sets of windings,
each set creating one half. The ampere turns are calculated for one set
of windings. The flux, <£, used in the calculation is taken as one half the
total flux created. The areas of the air-gaps A2 and of the armature A3
are also taken as one half the actual area. Except for these changes,
the calculation is made in the same manner as for the single magnetic cir-
cuit; the result is the ampere turns for one set of field windings.
In the ordinary type of multipolar machine there are as many magnetic
circuits as there are poles. Each winding energizes part of two circuits
The calculation is made in the same manner as for a single magnetic circuit.
Dynamo Design. — In the design of a motor or generator the follow-
ing data are usually given, being determined by local conditions Class,
viz., bipolar or multipolar. series, shunt or compound wound; size, in
kilowatts; voltage; and current. The following is an outline of the method
pursued in the complete design. (For complete method see Wiener's
Dynamo-electric Machines.)
Notation. — E = e.m.f. in external circuit in volts; W — total e.m.f. gener-
ated in armature in volts; e = e.m.f. necessary to overcome internal
resistances of machine; / = current in external circuit, in amperes; I = cur-
rent generated in armature in amperes; i = current in shunt field in am-
peres; HI = assumed flux density of field in maxwells per sq. inch; B —
actual flux density in armature, maxwells per square inch.; L = length of
armature in inches; D = diameter of armature in inches; I = length of
active conductor (i.e., that on pole-facing surface of armature) in feet; d =
diameter of armature conductor in mils; d2 = area of armature conductor,
circular mils; d' = diameter of insulated armature conductor in inches;
N = number of conductors on armature; p = number of pairs of poles in
field; C = number of bars on commutator; $ = magnetic flux in arma-
ture in maxwells; $' = total magnetic flux; A = leakage coefficient of
magnetic circuit; V = mean velocity of armature conductors in feet per
second; h = available depth of winding space on armature, inches (in a
slotted armature h is the depth of slot); r?i = number of wires stranded
in parallel to make one armature conductor; 772 = number of conductors
per layer on armature; n2 = number of layers of conductor on armature;
k,m,b = variables and factors explained in the text.
A value is first assumed for H\. This is governed by the size of the
machine, the style of armature, the number of poles, and the material of
the pole-pieces, magnet cores, and frame. For a smooth core armature
in a 1 kw. bipolar machine, with cast-iron pole-pieces, it^may be taken as
35,000 maxwells per sq. inch for cast-iron; for wrought iron or steel pole-
pieces it may be taken at 22,000 maxwells. For a 300 kw. bipolar machine
DYNAMO-ELECTRIC MACHINES. 1059
it may be assumed at 30,000 maxwells with cast-iron pole-pieces, and at
45,000 with wrought-iron pole-pieces. In multipolar machines, the figures
are from 5000 to 7000 higher in each case.
A formula for the length of active armature conductor is
The value of k is determined by multiplying 10~8 by a factor ranging from
50 to 72, depending on the percentage of polar arc, i.e. .the percentage ol
the armature subtended by the pole-pieces. If the percentage of polar arc
is 50 the factor is 50, if the percentage is 100 the factor is 72. V varies from
35 in a 1 kw. machine to 50 in a 200 or 300 kw. machine with a drum arma-
ture. With ring armatures, in high speed machines. V varies from 65 in a
1 kw. machine to 75 in a 25 kw.. 85 in a 300 kw, and 100 in a 5000 kw. ma-
chine. On low speed dynamos the figures are approximately one half
the above.
E' = (E + e). In series machines, under 1 kw., e is from 40 to 20 per
cent of E\ in machines of from 1 to 25 kw., from 20 to 10 per cent; in 25
to 500 kw. machines, from 10 to 4 per cent; and in machines of over 500
kw. from 4 to 2.5 per cent of E. In shunt-wound machines e has approxi-
mately one half the value used in series machines ; in compound-wound
machines approximately three quarters the value used in series machines.
The diameter of the armature core is found by means of the assumed
velocity and the given revolutions per minute, D = (12X60 V) -*- (r.pjn. X w).
The area of the conductors on the armature depends on the amount of
current to be carried, d2 = 300 7' -4- p.
In a series machine 7' = 7; in shunt and compound machines I' = I + i.
The current consumed in the shunt field varies with the size of the machine
approximately as follows
kw. = 1 5 10 20 50 100 500 2000
i = .087 .067 .057 .047 .037 .02757 .027 .0157
In large machines it is better, in order to diminish the eddy currents, to
make the armature conductors in the form of a cable, than to use single
wires. If the conductor on the armature is a single wire the thickness of
insulation varies from .012 to .020 inch, depending on the voltage. If the
conductor is a cable, each strand is insulated with a thickness of from .005
to .01 inch and the entire cable is covered with insulation of thickness
varying from .005 to .01 inch.
In a small machine with but a single layer of conductors on the arma-
ture L = / -r N. N = (1.885.000D X h) -i- d2.
For drum armatures N = 2 (n2 X w3) •*- n\',
for ring armatures N = (n2 X n3) -4- m.
A general formula given by Wiener for the length of armature is
r 12 X w, XI D X * h
L — - — - ; HZ = — j, — ; ^3 = -37.
n2 X n3 d' a'
The minimum number of bars on the commutator is Cmin = E'p -e- 6.
The value of b depends on the current as follows:
Amperes; over 100 100-50 50-20 20-10 10-5 5-2 2-1
b 10 10.5 11.5 12.5 15 20 20.
The number which may be used, provided it does not fall below Cmin is
C = (n2 X n3) -s- HI.
For drum armatures the number of conductors attached to each com-
mutator bar must be an even number. The quotient cf C, obtained as
above, by the largest even number which will give a result greater than
Cmin is the proper number of commutator bars for drum armatures. For
ring armatures it is the quotient of C by the largest number which will give
a result greater than Cmin. In each case the divisor is the number of
conductors which should be attached to each bar.
The flux through the armature is;
1060 ELECTRICAL ENGINEERING.
6 X p X Ef X 10»
N X r.p.m.
The flux density in the armature c-ore is
j;
B =
D X L X m'
where m is a factor depending on the percentage of polar arc. Assuming
100 per cent and 50 per cent as the limits of polar arc, the following are
the respective values of m at those limits In bipokir, smooth armature,
machines m = 1.00 and .70; in bipolar, toothed aimature machines
m = 1.00 and .55; in smooth armature multipolar machines m = 1 00
and .625, with from 1 to 12 poles: m = 1.00 and .60 with from 14 and 20
poles. "With toothed armatures the figures are slightly lower.
The area of the field magnet cores depends on the flux to be generated
<t>' = ^ X A.
A value for A is assumed, which will vary with the size and type of machine.
By means of this assumed value the principal dimensions of the magnetic
circuit are calculated. The true value of A is next calculated by means
of the formula
_ Joint permeance of useful and stray paths
Permeance of useful path
The permeance of a path is its magnetic conductance.
Permeance = (Permeability X Area) -*• Length.
The stray paths are those across the pole-pieces, across the magnet cores
and between the pole-pieces and the yoke joining the magnet cores.
With the new value of A, <£' is recalculated. If the true and assumed
values of A give a large difference in flux then the dimensions of the circuit
must be changed and A recalculated.
The areas of the various portions are found by dividing the total flux by
the allowable flux density. The allowable flux densities in maxwells per
square inch are as follows: Wrought iron, 90,000; cast steel. 85.000; cast
iron. 40,000.
The various areas being known, the winding of the magnets is calculated
as shown in the section on Strength of the Magnetic Field.
EXAMPLE. — Design a 200 K.W. bipolar, smooth drum armature, shunt
dynamo, with wrought-iron pole-pieces, and cast iron magnet cores and
yoke. Volts, 500; amperes, 400; R.P.M. , 450.
Assume HI = 40,000; V = 45; e = .Q3E; i = .0257; percentage of
polar arc = 85. Then E' =515; /' = 410 and k = 68 X 10~8.
Z = (515 XIX 100,000,000) -f- (68 X 45 X 40,000) = 420.7 feet.
D = (12 X 60 X 45) -J- (450 X 3.1416) = 22.91 inches.
^2 = 300 X 410 •*• 1 = 123,000. In this size of machine it is desirable
to use cables. Each conductor may be composed of three cables in paral-
lel, each composed of seven wires. A No. 12 B. & S. gauge wire has an area
of 6530 cir. mils, and 7 X 3 X 6530 = 137,130, which is near enough to d2.
To find d'" Number of strands on a diameter = 3. Insulation on each
strand = .005; insulation of cable = .008: diameter No. 12 wire = .080808;
d' = 3 X (.0808 + 2 X .005) + (2 X .008) = .2884 inch.
Assume h = .625; m = 3; n2 = 22.91 X 3.1416 + .2884 = 249; rj3 =
.625 -*- .2884 = 2 + . Then L = (12 X 3 X 420.7) -s- (2 X 249) = 30.41
inches.
Cmin = 515 X 1 -5- 10 = 51.5; C = (249 X 2 •* 3) -*- 4 = 41 (too small);
(249 X 2 -^ 3) -^ 2 = 83. .'. C = 83.
N = (2 X 249) X 2 -^ 3 = 332.
0 = 6 X 1 X 515 X 1,000,000,000 -^ 332 X 450 = 20,683,000.
Assume m = .94 ; B = 20,683,000 -^ (3.1416 X 22.91 X 30.41 X .94)
= 10777.
To calculate A would require more space than can be' spared here. As-
sume A = 1.34.
4>f - 1.34 X 20,683,000 = 27,715,220.
Area of magnet cores = 27 ,7 1:5,220 H- 40000 = 692 sq. inches.
Diameter of magnet cores = A/ 692 X - = 29.8 inches.
ALTERNATING CURRENTS. 10G1
ALTERNATING CURRENTS.*
The advantages of alternating over direct currents are: 1. Greater sim-
plicity of dynamos and motors, no commutators being required; 2. The
feasibility of obtaining high voltages, by means of static transformers, for
cheapening the cost of transmission; 3. The facility of transforming from
one voltage to another, either higher or lower, for different purposes.
A direct current is uniform in strength and direction, while an alternating
current rapidly rises from zero to a maximum, falls to zero, reverses its
direction, attains a maximum in the new direction, and again returns to
zero. This series of changes can best be represented by a curve the abscis-
sas of which represent time and the ordinates either current or electro-
motive force (e.m.f.). The curve usually chosen for this purpose is the
sine curve, Fig. 172; the best forms of alternators give a curve that is a very
close approximation to the sine curve, and all. calculations and deductions
of formula are based on it. The equation of the sine curve is y = sin x, in
which y is any ordinate, and x is the angle passed over by a moving radius
vector.
After the flow of a direct current has been once established, the only
opposition to the flow is the resistance offered by the conductor to the
passage of current through it. This resistance of the conductor, in treat-
ing of alternating currents, is sometimes spoken of as the ohmic resistance.
The word resistance, used alone, always means the ohmic resistance. In
alternating currents, in addition to the resistance, several other quantities,
which affect the flow of current, must be taken into consideration. These*
quantities are inductance, capacity, and skin effect. They are discussed
under separate headings.
The current and the e.m.f. may be in phase with each other, that is,
attain their maximum strength at the same instant, or they may not, de-
pending on the character of the circuit. In a circuit containing only resist-
ance, the current and e.m.f. are in phase; in a circuit containing induct-
ance the e.m.f. attains its maximum value before the current, or leads the
current. In a circuit containing capacity the current leads the e.m.f. If
both capacity and inductance are present in a circuit, they will tend to
neutralize each other.
Maximum, Average, and Effective Values. — The strength
and the e.m.f. of an alternating current being constantly varied, the maxi-
mum value of either is attained only for an instant in each period. The
maximum values are little used in calculations, except in deducing formulae
mean square," value. It is obtained by taking the square root of the mean
of the squares of the ordinates of the sine curve. The effective value is
the value shown on alternating-current measuring instruments. The prod-
uct of the square of the effective value of the current and the resistance of
circuit is the heat lost in the circuit.
The comparison of the maximum, average, and effective values is as
follows r
^Effec. = #Max. X 0 . 707 ; #Avei, = #Max. X 0 . 637 ; tf Max. - 1 . 41 X # Effec.
Frequency. — The time required for an alternating current to pass
through one complete cycle, as from one maximum point to the next (a
and b, Fig. 172) is termed the period. The number of periods in a second
is termed the frequency of the current. Since the current changes its direc-
tion twice in each period, the number of reversals or alternations is double
the frequency. A current of 120 alternations per second has a period of 1/60
* Only a very brief treatment of the subject of alternating currents can
be given in this book. The following works are recommended as valuable
for reference- Alternating Currents and Alternating Current Machinery, by
D. C. and J. P. Jackson; Standard Polyphase Apparatus and Systems, by
M. A. Oudin; Polyphase Electric Currents, by S. P. Thompson; Electric
Lighting, by F. B. Crocker, 2 vols.; Electric Power Transmission, by Louis
Bell; Alternating Currents, by Bedell and Crehore ; Alternating-current Phe-
nomena, by Chas. P. Steinmetz. The two last named are highly mathemat-
ical.
1062 ELECTRICAL ENGINEERING.
and a frequency of 60 The frequency of a current is equal to one half the
number of poles on the generator, multiplied by the number of revolutions
per second Frequency "is denoted by the letter f.
The frequencies most generally used in the United States are 25, 40, 60,
125, and "133 cycles per second The Standardization Report of the
A I.E.E recommends the adoption of three frequencies, viz. 25 60. and 120.
With the higher frequencies both transformers and conductors will be
less costly in a circuit of a given resistance, but the capacity and inductance
effects in each will be increased, and these tend to inciease the cost. With
high frequencies it also becomes difficult to operate alternators in parallel.
A low frequency current cannot be used on lighting circuits, as the lights
will flicker when the frequency drops below a certain figure. For arc lights
the frequency should not be less than 40. For incandescent lamps it should
not be less than 25. If the circuit is to supply both power and light a
frequency of 60 is usually desirable. For power transmission to long dis-
tances a low frequency, say 25, is considered desirable, in order to lessen
the capacity effects If the alternating current is to be converted into
direct current for lighting purpose, a low frequency may be used as the
frequency will then have no effect on the lights
Inductance.— A current flowing through a conductor produces a mag-
netic flux around the conductor. If the current be changed in strength or
direction, the flux is also changed, producing in the conductor an e.m.f.
whose direction is opposed to that of the
current in the conductor. This counter
e.m.f. is the counter e.m.f. of inductance
It is proportional to the rate of change
of current, provided that the permeabil-
ity of the medium around the conductor
remains constant. The unit of induct-
ance is the henry, symbol L. A circuit
has an inductance of one henry if a uni-
form variation of current at the rate of
FlQ. 172. one ampere per second produces a
counter e.m.f. of one volt.
The effect of inductance on the circuit is to cause the current to lag be-
hind the e.m.f. as shown in Fig. 172, in which abscissas represent time, and
ordinates represent e.m.f. and current strengths respectively.
Capacity. — Any insulated conductor has the power of holding a quan-
tity of static electricity. This power is termed the capacity of the body. The
capacity of a circuit is measured by the quantity of electricity in it when
at unit potential. It may be increased by means of a condenser. A con-
denser consists of two parallel conductors, insulated from each other by
a non-conductor. The conductors are usually in sheet form.
The unit of capacity is a farad, symbol C. A condenser has a capacity
of one farad when one coulomb of electricity contained in it produces a dif-
ference of potential of one volt: The farad is too large a unit to be conven-
iently used in practice, and the micro-farad is used instead.
The effect of capacity on a circuit is to cause the e.m.f. to lag behind the
current. Both inductance and capacity may be measured with a Wheat-
stone bridge by substituting for a standard resistance a standard of induct-
ance or a standard of capacity.
Power Factor. — In direct-current work the power, measured in watts,
is the product of the volts and amperes in the circuit. In alternating-cur-
rent work this is only true when the current and e.m.f. are in phase. If the
current either lags or leads, the values shown on the volt and ammeters
will not be truo simultaneous values. Referring to Fig. 172, it will be seen
that the product of the ordinates of current and e.m.f. at any particular
instant will not be equal to the product of the effective values which are
shown on the instruments. The power in the circuit at any instant is the
product of the simultaneous values of current and e.m.f., and the volts
and amperes shown on the recording instruments must be multiplied
together and their product multiplied by a power factor before the true
watts are obtained. This power factor, which is the ratio of the volt- amperes
to the watts, is also the cosine of the angle of lag or lead of the current.
Thus
P = IXEXpower factor = IXEXcos 0.
where 9 is the angle of lag or lead of the current.
ALTERHATIKG CURRENTS.
1063
A watt-meter, however, gives the true power in a circuit directly. The
method of obtaining the angle of lag is shown below, in the section on Im-
pedance Polygons.
Reactance, Impedance, Admittance.— In addition to the
ohmic resistance of a circuit there are also resistances due to inductance,
capacity, and skin effect. The virtual resistance due to inductance and
capacity is termed the reactance of the circuit. If inductance only be
present in the circuit, the reactance will vary directly as the inductance.
If capacity only be present, the reactance will vary inversely as the capacity.
Inductive reactance =2nfL.
Condensive reactance = , ~ .
The total apparent resistance of the circuit, due to both the ohmic resistance
and the reactance, is termed the impedance, and is equal to the square root
of the sum of the squares of the resistance and the reactance.
Impedance = Z==v/722 + (2^/L)2 when inductance is present in the circuit.
/ x i T2
Impedance = Z = \ R2 + \y~fr<) wnen capacity is present m the circuit.
Admittance is the reciprocal of impedance, = l-f-Z.
If both inductance and capacity are present in the circuit, the reactance
of one tends to balance that of the other; the total reactance fe the alge-
braic sum of the two reactances; thus,
Total reactance =X=2xfL
- 1^ ; Z = V R2 +
In all cases the tangent of the angle of lag or lead is the reactance divided by
the resistance. In the last case
,
Skin Effect. — Alternating currents tend to have a greater density at
the surface than at the axis of a conductor. The effect of this is to make
the virtual resistance of a wire greater than its true ohmic resistance. With
low frequencies and small wires the skin effect is small, but it becomes quite
important with high frequencies and large wires.
The following table, condensed from one in Foster's "Electrical Engi-
neers' Pocket-book," shows the increase in resistance due to skin effect.
Skin-effect Factors for Conductors carrying Alternating
Currents.
Diameter
Frequencies
and
B. & S.
Gauge.
25
40
60
100
130
0
1.001
1 . 005
1.008
00
1.001
1.002
1.006
1.010
000
1 .002
1.005
1.010
1.017
0000
1.001
1.005
1.006
1.015
1.027
f
1.002
.007
.006
.016
1.008
1.040
1.022
1.100
1.039
1.156
1
.020
.052
• 1 111
1 263
1.397
if"
.053
.098
.118
.223
1.239
1.420
1.506
1.765
1 694
1.983
2"
.265
.531
1.826
2.290
2.560
For virtual resistance, multiply ohmic resistance by factor from this table.
1064
ELECTRICAL ENGINEERING.
Ohm's Law applied to Alternating-current Circuits. — To
apply Ohm's law to alternating-current circuits a slight change is neces-
sary in the expression of the law. Impedance is substituted for resistance.
The law should read
Impedance Polygons. — 1. Series Circuits. — The impedance of a cir-
cuit can be determined graphically as follows. Suppose a circuit to contain
a resistance R and an inductance L. and to carry a current / of frequency/.
In Fig. 173 draw the line ab proportional to R, and representing the direc-
tion of current. At b erect be perpendicular to ab and proportional to 2irfL.
Join a and c. The line ac represents the impedance of the circuit. The
angle 0 between ab and ac is the angle of lag of the current behind the e.m.f.,
and the power factor of the circuit is cosine 0. The e.m.f. of the circuit is
E-1Z.
R
FIG. 173. FIG. 174.
If the above circuit contained, instead of the inductance L, a capac ity C,
then would the polygon be drawn as in Fig. 174. The line be would be pro-
portional to 5 — j~ and would be drawn in a direction opposite to that of
ZTTJ(J
be in Fig. 173. The impedance would again be Z, the e.m.f. would be
ZXl, but the current would lead the e.m.f. by the angle 0.
Suppose the circuit to contain resistance, inductance, and capacity. The
lines of the impedance polygon would then be laid off as in Fig. 175. The
impedance of the circuit would be represented by ad, and the angle of lag
by 9. If the capacity of the circuit had been such that cd was less than be,
then would the e.m.f . have led the current.
27T/L
R b
27T/C
FIG. 175.
FIG. 176.
If between
amples the:
cluctances, or capacities in the circuit follow each other in all cases as do
the resistances, inductances, and capacities in the circuit, each line having
its appropriate direction and magnitude.
Ri=15 €,=.000100 R2
Li =.05
FIG. 177.
ALTERNATING CURRENTS.
1065
EXAMPLE. — A circuit (Fig. 177) contains a resistance, Rlt of 15 ohms a
capacity, C1( of 100 microfarads (.000100 farad), a resistance, R~ of 12
ohms, an inductance Llt of .05 henr.ys, and a resistance #3, of 20 'ohms
Find the impedance and electromotive force
when a current of 2 amperes is sent through
the circuit, and the current when an e.m.f.
of 120 volts is impressed on the circuit fre-
quency being taken as 60. Also find the
angle of lag. the power factor, and the power
in the circuit when 120 volts are impressed.
The resistance is represented in Fig. 178
by the horizontal line ab, 15 units long.
The capacity is represented by the line fee,
drawn downwards from 6. and whose
length is
= 26.55.
2X3. 1416X60X .0001 "
1 R2=12 '
FIG. 178.
From the point c a horizontal line cd, 12 units long, is drawn to represent
RZ. From the point d the line de is drawn vertically upwards to represent
the inductance LI. Its length is
27rfL1=2X3.1416X60X .05 = 18.85.
From the point e a horizontal line ef, 20 units long; is drawn to represent
72 3. The line joining a and / will represent the impedance of the circuit in
ohms. The angle 0, between ab and a/, is the angle of lag of the e.m.f. be-
hind the current. The impedance in this case is 47.5 ohms, and the angle
of lag is 9° 15'.
The e.m.f. when a current of 2 amperes is sent through is
IZ = E = 2 X 47 . 5 = 95 volts.
If an e.m.f. of 120 volts be impressed on the circuit, the current flowing
through will be
_ 120 120
7 = —~- «= = 2 . 53 amperes.
£ 47 . o
The power factor = cos 0 = cos 9° 15' = .987.
The power in the circuit at 120 volts is
7X#Xcos0 = 2.53X120X . 987 = 299 . 6 watts.
2. Parallel Circuits. — If two circuits be arranged in parallel, the current
flowing in each circuit will be inversely proportional to the impedance of
that circuit. The e.m.f. of each circuit is
R L tne e.m.f. across the terminals at either end
of the main circuit, where the various branches
separate. Consider a circuit, Fig. 179, con-
sisting of two branches. The first branch
L2 1 contains a resistance R} and an inductance Ll
in series with it. The second branch con-
tains a resistance R? in series with an induct-
FTP 17Q ance 7/2. The impedance of the circuit may
no. i/y. ke determined by treating each of the two
branches as a separate series circuit, and drawing the impedance polygon
for each branch on that assumption. Having found the impedance the
current flowing in either branch will be the reciprocal of the impedance
multiplied by the e.m.f. across the terminals. The current in the entire
circuit is the geometrical sum of the current in the two branches.
The admittance of the equivalent simple circuit may be obtained by
drawing a parallelogram, two of whose adjoining sides are made parallel to
the impedance lines of each branch and equal to the two admittances
respectively.
The diagonal of the parallelogram will represent the admittance of the
equivalent simple circuit. The admittance multiplied by the e.m.f. gives
the total current in the circuit.
EXAMPLE. — Given the circuit in Fig. 180, consisting of two branches.
Branch 1 consists of a resistance Rl = l2 ohms, an inductance Z/j = .05
henry, a resistance 7f2 = 4 ohms, and a capacity C\ =120 microfarads
(.00012 farad\ Branch 2 consists of an inductance 7/a = .015 henry, a
resistance 723 = 10 ohms, and an inductance 7,3 = .03 henry. An e.m f.
of 100 volts is impressed on the circuit at a frequency of 60. Find the ad-
10G6 ELECTRICAL ENGINEERING,
mittance of the entire circuit, the current, the power factoi, and the power
in the circuit. Construct the impedance polygons for the two branches
Ri=12 LI =.05 R2=4 Cj = OOQ12
-/=»
E.M.F.=IOO
L2=i.015
R3=10
FIG. 180.
L3=.0
separately as shown in Fig. 181. a and 6. The impedance in branch 1 is
16.4 ohms, and the current is r^-rX 100 = 6.19 amperes. The angle of
R2=4
STT/LI
=18.84
Ri=12
27T/C
=22.1
R3=10
27T/LS
11.3
27T/L2
-5.65
FIG. 181.
lead of the current is 12° 45'. The impedance in branch 2 is 19.5 ohms and
the current is rjr-r X 100 = 5. 13 amperes. The angle of lag of the current
19 . o
is 61°.
The current in the entire circuit is found by taking the admittances of
the two branches, and drawing them from the point o, in Fig. 181 c, parallel
to the impedance lines in their respective polygons. The diagonal from o
is the admittance of the entire circuit, and in this case is equal to 0.092.
The current in the circuit is .092X100 = 9.2 amperes. The power factor
is 0.944 and the power in the circuit is 100 X .944X9.2 = 868.48 watts.
Self-inductance of Lines and Circuits. — The following formulae
and table, taken from Crocker's " Electric Lighting/' give a method of cal-
culating the self-inductance of two parallel aerial wires forming part of the
same circuit and composed of copper, or other non-magnetic material.
ALTERNATING CURRENTS.
1067
I per foot = (l5 . 24 + 140 . 3 log M.) 10~*.
L per mile = (80. 5 + 740 log ~)lO-9,
in which L is the inductance in henrys of each wire, A is the interaxial dis-
tance between the two wires, and d is the diameter of each, both in inches.
If the circuit is of iron wire, the formulae become
L per foot = (2286 + 140 . 3 log ~ ) lO"',
L per mile = (l2070 + 740 log ^-) 10 ~6.
INDUCTANCE, IN MILLIHENRYS PER MILE, FOR EACH OF TWO PARALLEL
COPPER WIRES.
ll
American Wire Gauge Number
"fl
0000
000
00
0
1
2
3
4
6
8
10
12
3
6
0.907
1.130
0944
1 168
0.982
1.205
1.019
1.242
1.056
1.280
1.094
1 317
1 131
1.354
1.168
1.392
1.243
1.466
1.317
1.540
1.392
1.615
1.467
1.690
9
1 260
1.298
1.335
1 372
1 410
1.44711.485
1.522
1.596
1.671
1.746
1.820
12
1.353
1.391
1.428
1.465 1.502
1 540
1 577
1.614
1.689
1.764
1.838
1.913
18
1.484
1.521
1.558
1.596
1.633
1.671
1.708
1.744
1.820
1894
1.968
2.044
24
1.576
1.614
1 651
1 6881.725
1.764
1.800
1.838
1.912
1.986
2061
2.135
30
1.648
1686
1 723
1.760 1.797
1.835
1 871
1 910
1.984
2.058
2.134
2.208
36
1 707
1 745
1.784
1.818 1.856
1 893
1.931
1.968
2.043
2.117
2.192
2.266
48
1.799
1836
1.874
1.911 1.949
1.986
2023
2.061
2 135
2.209
2.285
2.359
60
1.871
1909
1.946
1.982 2.023
2.058
2.095
2 132
2.208
2.282
2.356
2.432
72
1.930
1968
2.005
2.042 2.079
2 116
2.154
2.192
2 266
2.340
2.415
2.489
84
1.971
2.016
2.053
2.092 2 128
2 166
2.203
2.240
2.312
2.389
2.464
2539
96
2023
2.059
2.097
2.134 2.172
2.210
2.246
2.283
2 358
2.433
2.507
2.582
Capacity of Conductors* — All conductors are included in three
classes, viz.- 1. Insulated conductors with metallic protection: 2. Single
aerial conductor with earth return; 3. Metallic circuit consisting of two
parallel aerial wires. The capacity of the lines may be calculated by means
of the following formulae taken from Crocker's "Electric Lighting ";
Class 1. Cperfoot =
\og(D+d)
C per mile =
38. 83k 10
log (D-r-d)
Class 2.
„ - , 7361X10-
C per foot =-r-— — -
Class 3.
log (4h-*-d)
C per foot of each wire
C per mile of each wire =
„ ., 38.83 X 10-
C per mile = —-
log (4h-*-d)
3681 X IP"1
log (2A •*• d) '
39.42 X 1Q-*
log (2A -f- d)
In which C is the capacity in farads, D the internal diameter of the metallic
covering, d the diameter of the conductor, ft the height of the conductor
above the ground, and A the interaxial distance between two parallel wires,
all in inches; fc is a dielectric constant which for air is equal to 1 and for
pure rubber is equal to 2.5. The formulae in cases 2 and 3 assume the wires
to be bare. If they are insulated, k must be introduced in the numerator
and given a value slightly greater than 1.
1068
ELECTRICAL
Single-phase and Polyphase Currents.— A single-phase cm-rent
is a simple alternating current carried on a single pair of wires, and is
generated on a machine having a single armature winding. It is represented
by a single sine curve.
Polyphase currents are known as two-phase, three-phase, six-phase, or
any other number, and are represented by a corresponding number of sine
curves. The most commonly used systems are the two-phase and three-
phase.
1. Two-phase Currents. — In a two-phase system there are two single-
phase alternating currents bearing a definite time relation to each other
and represented by two sine curves (Fig. 182). The two separate currents
may be generated by the same or by separate
machines. If by separate machines, the arma-
tures of the two should be positively coupled
together. Two-phase currents are usually gener-
ated by a machine with two armature windings,
each winding terminating in two collector rings.
The two windings are so related that the two
currents will be 90° apart. For this reason two-
phase currents are also called "quarter-phase"
FIG. 182.
currents.
Two-phase currents may be distributed on either three or four wires.
The three-wire system of distribution is shown in Fig. 183. One of the
return wires is dispensed with, connection being made across to the other
as shown. The common return wire should be made 1.41 times the area
of either of the other two wires, these two being equal in size.
Wi
FIG. 183.
FIG. 184.
The four-wire system of distribution is shown in Fig. 184. The two
phases are entirely independent, and for lighting purposes may be operated
a^ two single-phase circuits.
2. Three-phase Currents. — Three-phase currents consist of three alternat-
ing currents, differing in phase by 120°, and represented by three sine
curves, as in Fig. 185. They may be distributed by three or six wires. If
distributed by the six- wire system, it is analogous to the four- wire, two-
phase system, and is equivalent to three single-phase circuits. In the
three-wire system of distribution the circuits may be connected in two
different ways, known respectively as the Y or star connection, and the A
(delta) or mesh connection.
xxx:
FIG. 185.
FIG. 186.
ALTERNATING CURRENTS.
1069
The Y connection is shown in Fig. 186. The three circuits are joined
at the point o, known as the neutral point, and the three wires carrying the
current are connected at the points a, b, and c, respectively. If the three
circuits ao, bo, and co are composed of lights, they must be»equally loaded
or the lights will fluctuate. If the three circuits are perfectly balanced, the
lights will remain steady. In this form of connection each wire may be
considered as the return wire for the other
two. If the three circuits are unbalanced,
a return wire may be run from the neutral
point o to the neutral point of the arma-
ture winding on the generator. The
system will then be four-wire, and will
work properly with unbalanced circuits.
The A connection is shown in Fig. 187.
Each of the three circuits ab, ac, be, re-
ceives the current due to a separate coil
in the armature winding. This form of
connection will work properly even if the
circuits are unbalanced; and if the cir-
cuit contains lamps, they will not fluctuate
when the circuit changes from a balanced
to an unbalanced condition, or vice versa. .
Measurement of Power in Polyphase Circuits. — 1. Two-
phase Circuits. — The»power of two-phase currents distributed by four wires
may be measured by two wattmeters introduced into the circuit as shown in
Fig. 184. The sum of the readings of the two instruments is the total power.
If but one wattmeter is available, it should be introduced first in one circuit,
and then in the other. If the current or e.m.f. does not vary during the
operation, the result will be correct. If the circuits are perfectly balanced,
twice the reading of one wattmeter will be the total power.
The power of two-phase currents distributed by three wires may be
measured by two wattmeters as shown in Fig. 183. The sum of the two
readings is the total power. If but one wattmeter is available, the coarse-
wire coil should be connected in series with the wire ef and one extremity
of the pressure-coil should be connected to some point on ef. The other
end should be connected first to the wire a and then to the wire d, a reading
being taken in each position of the wire. The sum of the readings gives the
power in the circuits.
2. Three-phase Currents. — The power in a three-phase circuit may be
measured by three wattmeters, connected as in Fig. 188 if the system is
Y-connected, and as in Fig. 189 if the system is A-connected. The sum
FIG. 187.
FIG. 188.
FIG. 189.
of the wattmeter readings gives the power in the system. If the circuits
are perfectly balanced, three times the reading of one wattmeter is the
total power.
The power in a A-connected system may be measured by two wattmeters,
as shown in Fig. 190. If the power factor of the system is greater than
0.50, the arithmetical sum of the readings is the power in the circuit,
the power factor is less than 0.50, the arithmetical difference of the read-
ings is the power. Whether the power factor is greatei or less than 0.50
may be discovered by interchanging the wattmeters without disturbing the
1070
ELECTRICAL ENGINEERING.
relative connection of their coarse- and fine-wire coils. If the deflections of
the needles are reversed, the difference
of the readings is the power. If the needles
are deflected in the same direction as at
first, the sum of the readings is the
power.
Alternating-current Genera"
tors. — These differ little from direct-
current generators in many respects. Any
direct-current generator, if provided with
collector rings instead of a commutator,
could be used as a single-phase alternator,
The frequency would in most cases, how-
ever, be too low for any practical use.
The fields of _ alternators are always
separately excited; the machines are
sometimes compounded by shunting some
FIG. 190.
of their own current around the fields through a rectifying device which
changes the current to pulsating direct current. In all large machines
the armature is stationary and the field-magnets revclve.
TRANSFORMERS, CONVERTERS, ETC.
Transformers. — A transformer consists essentially of two coils of wire,
one coarse and one fine, wound upon an iron core. The function of a trans-
former is to convert electrical energy from one potential to ^another. If
the transformer causes a change from high to low voltage, it is known as a
"step-down" transformer; if from low to high voltage, it is known as a
"step-up" transformer.
The relation of the primary and secondary voltages depends on the num-
ber of turns in the two coils. Transformers may also be used to change
current of one phase to current of another
phase. The windings and the arrangement
of the transformers must be adapted to each
particular case. In Fig. 191 an arrange-
ment is shown whereby two-phase currents
may be converted into three-phase. Two
transformers are required, one having its
primary and secondary coils in the relation
of 100 to 100, and the other haying its pri-
mary and secondary in the relation of 100 to
86. The secondary of the 100-to-lOO trans-
former is tapped ^ at its middle point and
joined to one terminal of the other secondary.
Between any pair of the three remaining ter-
minals of the secondaries there will exist a
difference of potential of 50.
<100 Volfc*
100 Turns
o&TooWo
86 Turns
TJD o qTotfff
rns
100 Tun
JI--
•e-00 Volts— > *-50 Volts—*
FIG. 191.
There are two sources of loss in the transformer, viz., the copper loss and
the iron loss. The copper loss is proportional to the square of the current,
being the I2R loss due to heat. If /i, 72lf be the current and resistance
respectively of the primary, and 72, RZ, the current and resistance respect-
ively of the secondary, then the total copper loss is We — I\2R\ + /22#2 and
the percentage of copper loss is — — ^
— , where Wv is the energy delivered
p
to the primary. The iron loss is constant at all loads, and is due to hysteresis
and eddy currents.
Transformers are sometimes cooled by means of forced air or water cur-
rents or by immersing them in oil, which tends to equalize the temperature
in all parts of the transformer.
Efficiency of Transformers. — The efficiency of a transformer is the ratio
of the output in watts at the secondary terminals to the input at the primary
terminals. At full load the output is equal to the input less the iron and
copper losses. The full-load efficiency of transformers is usually very high,
being from 92 per cent, to 98 per cent. As the copper loss varies as the
square of the load, the efficiency of a transformer varies considerably at
different loads. Transformers on lighting circuits usually operate at full
MOTORS. 1071
load but a very small part of the day, though they use some current all the
time to supply the iron losses. For transformers operated only a part of the
time the "all-day" efficiency is more important than the full-load efficiency.
It is computed by comparing the watt-hours output to the watt-hours input.
The all-day efficiency of a 10-K.W. transformer, whose copper and iron
losses at full load are each 1.5 per cent, and which operates 3 hours at full
load, 2 hours at half load, and 19 hours at no load, is computed as follows:
Iron loss, all loads = 10 X .015= .15 K.W.
Copper loss, full load = 10 X .015= .15 K.W.
Copper loss, YQ load =. 15 X(i)2= .0375 K.W.
Iron loss K.W. hours =. 15X24 = 3.6.
Copper loss, full load, K.W. hours = .15X3= .45.
Copper loss, ^ load, K.W. hours = .0375X2= .075.
Output. K.W. hours=-( (10X3) + (5X2) }-=40.
Input. K.W. hours = 40 + 3. 6 +.45 +.075 = 44. 125.
All-day efficiency = 40 -s- 44 . 125 = .907.
The transformers heretofore discussed are constant-potential transformers
and operate at a constant voltage with a variable current. For the opera-
tion of lamps in series a constant-current transformer is required There
are a number of types of this transformer. That manufactured by the
(Jeneral Electric Co. operates by causing the primary and secondary coils to
approach or to separate on any change in the current.
Converters, etc. — In addition to static transformers, various machines
are used for the purpose of changing the voltage of direct currents or the
voltage, phase or frequency of alternating currents, and also for changing
alternating currents to direct or vice versa. These machines are all rotary
and are known as rotary converters, motor-dynamos, and dynamotors.
A rotary converter consists of a field excited by the machine itself, and
an armature which is provided with both collector rings and a commuta-
tor. It receives direct current and changes it to alternating, working as a
direct-current motor, or it changes alternating to direct current, working
as a synchronous motor.
A motor-dynamo consists of a motor and a dynamo mounted on the same
base and coupled together by a shaft.
A dynarnotor has one field and two armature windings on the same core.
One winding performs the functions of a motor armature, and the other those
of a dynamo armature.
A booster is a machine inserted in series in a direct-current circuit to
change its voltage. It may be driven either by an electric motor or other-
wise
ALTERNATING-CURRENT MOTORS.
Synchronous Motors. — Any alternator may be used as a motor,
provided it be brought into synchronism with the generator supplying the
current to it. The operation of the alternating-current motor and generator
is similar to the operation of two generators in parallel. It is necessary to
supply direct current to the field. The field circuit is left open until the
machine is in phase with the generator If the motor has the same number
of poles as the generator, it will run at the same speed ; if a different number
the speed will be that of the generator multiplied by the ratio of the number
of poles of the motor to that of the generator. Single-phase, synchronous
mot9rs are not self-starting. Polyphase motors may be made self-starting
but it is better to bring the machines to speed by independent means before
supplying the current. The machines may be started by a small induction
motor, the load on the synchronous motor being thrown off, or the field
may be excited by a small direct-current generator belted to the motor, and
this generator may be used as a motor to start the machine, current to run
it being taken from a storage battery. If the field of a synchronous motor
be properly regulated to the load, the motor will exercise no inductive effect
on the line, and the power factor will be 1. If the load varies the current
in the motor will either lead or lag behind the e.m.f. and will vary the
power factor. If the motor be overloaded so that there is a diminution of
speed the motor will fall out of step with the generator and stop.
Synchronous motors are often put on the same circuit with induction
motors. The synchronous motor in this case may, by increasing the field
excitation, be made to cause the current to lead, while the induction motoj
1072 ELECTRICAL ENGINEERING.
will cause it to lag. The two effects will thus tend to balance each other
and cause the power factor of the circuit to approach 1.
Synchronous motors are best used for large units of power at high voltages,
where the load is constant and the speed invariable. They are unsatis-
factory where the required speed is variable and the load changes. Two
great disadvantages of the synchronous motor are its inability to start
under load, and the necessity of direct-current excitation.
Induction motors. — The distinguishing feature of an induction motor
is the rotating magnetic field. It is thus explained: In Fig 192 let ab, cd
be two pairs of poles of a motor, a and b being wound from
/^\ r^N. one ^=> or Pa^r °f wires of a two-phase alternating circuit,
/\ a l^\\ and c and d from the other leg, the two phases being 90°
' ^ * apart. At the instant when a and 6 are receiving maxi-
mum current, so as to make a a north pole and 6 a south
pole, c and d are demagnetized, and a needle placed
between the poles would stand as shown in the cut. Dur-
_ ing the progress of the cycle of the current the magnetic
^ «S\ flux at a decreases and that at c increases causing the
FIG 192 point of resultant maximum intensity to shift, and the
needle to move clockwise toward c. A complete rotation
of the resultant point is performed during each cycle of the current.
An armature placed within the ring is caused to rotate simply by ths shift-
ing of the magnetic field without the use of a collector ring. The words
'rotating magnetic field*' refer to an area of magnetic intensity and must
be distinguished from the words "revolving field " which refer to the por-
tion of the machine constituting the field-magnet.
The] field or *' primary" of an Induction motor is that portion of the
machine to which current is supplied from the outside circuit.
The armature or "secondary'' is that portion of the machine in which
currents are induced by the rotating magnetic field. Either the primary or
the secondary may revolve. In the more modern machines the secondary
revolves. The revolving part is called the " rotor." the stationary part the
"stator." The rotor may be either of the ring or the drum type, the drum
type being more common. A common type of armature is the " squirrel-
cage.'' It consists of a number of copper bars placed on the armature core
and insulated from it. A copper ring at each end connects the bars. The
field windings are always so arranged that more than one pair of poles
are produced. This is necessary in order to bring the speed down to a
practical limit. If but one pair of poles were produced, with a frequency
of 60> the revolutions per minute would be 3600.
The revolving part of an induction motor does not rotate as fast as the
field, except at no load When loaded, a slip is necessary, in order that the
lines of force may cut the conductors in the rotor and induce currents
therein. The current required for starting an induction motor of the squir-
rel-cage type under full load is 7 or 8 times as great as the current for
running at full-load. A type of induction motor known as ' Form L,' built
by the General Electric Co., will start with the full load current, provided
the starting torque is not greater than the torque when running at full load
Induction motors should be run as near their normal primary e.m.f. as
possible, as the output and torque are directly proportional to the square
of the primary pressure A machine which will carry an overload of 50
per cent at normal e.m.f. will hardly carry its full load at 80 per cent of the
normal e.m.f.
An induction motor exercises its greatest torque when standing still, and
its least when running in synchronism with the rotating field. If it be over-
loaded it will slow down until the induced currents in the armature are
sufficient to carry the load.
ALTERNATING-CURRENT CIRCUITS.
Calculation of Alternating-current Circuits. — The follow-
ing formulae and tables are issued by the General Electric Co. They
afford a convenient method of calculating the sizes of conductors for, and
determining the losses in. alternating- current circuits. They apply to cir-
cuits in which the conductors are spaced 18 inches apart, but a slight in-
crease or decrease in this distance does not alter the figures appreciably. If
the conductors are less than 18 inches apart, the loss of voltage is decreased
and vice versa.
ALTERNATING-CURRENT CIRCUITS.
1073
Let W = total power delivered in watts;
D = distance of transmission (one way) in feet;
P* = per cent loss of delivered power (W)\
E = voltage between main conductors at consumer's end of circuit*
K = a constant; for continuous current = 2160;
T=a variable depending on the system and nature of the load; fcr
continuous current = 1 ;
M = a variable, depending on the size of wire and the frequency;
for continuous current = 1 ;
A = a factor ; for continuous current = 6 . 04.
D X W X K
Area of conductor, circular mils —
Current in main conductois =
PXE*
W XT
Volts lost in lines
Pounds copper =
P X E X M .
100
* X W X K X A
PUX E* X 1,000,000*
The following tables give values for the various constants*
Per cent of
Power Factor.
Value of K.
Value of T.
H
j£
300
95
85
80
100
95
85
80
System •
Single-phase
2160
1080
1080
2400
1200
120C
3000
1500
1500
3380
1690
1690
1.00
.50
.58
1.C5
.53
.61
1.17
.59
.68
1 25
62
.72
6.04
12 08
9.06
Two- phase 4-wire
Three-phase 3- wire
Values of M
25 Cycles.
60 Cycles.
325 Cycles.
y
10
*
s
*
«r-£
V*
>4
.g
§
1
I
0
Jjx
§
u.
S
5_
-goo
05
M) f-
00
M
1
H
&o
_o
0
.SP o
o
o
.s'S
|
o
rt
H- ' O
"55
«
I—} "y
* o
o
^
1
IS
1^
o ^
1^
|S
0 h
#5
1^
C fc«
1
C|-
0} |
£•1
2 1
O gj
si
si
ra |
si
JD
d
o?
&
1*
|£
II
•ftS
|£
Ifi
|g
Is
|£
fe
*J
s
*
P
^
§
0000
211,600
1.23
1.33
1.34
1.62
1.99
2.09
2 35
3.24
3.49
000
167 805
1.18
1.24
1 24
1.49
1.77
1.95
2.08
2.77
2 94
00
133X)79
1.14
1.16
1.16
1.34
1.60
1.66
1.86
2 40
2 57
0
105,592
1.10
1.10
1.09
1.31
1.46
1.49
1.71
2.33
2 25
1
83694
1.07
1.05
1.03
1.24
1.34
1.36
1.56
1.88
1.97
2
66,373
1.05
1.02
1.00
1.18
1.25
1.26
1.45
1.70
1.77
3
52,633
1.03
1.00
1.00
1.14
1.18
1.17
1.35
1.53
1.57
4
41,742
.02
1.00
1.00
1.11
1.11
1.10
1.27
1.40
1.43
5
33 102
.00
1.00
1.00
1.08
1.06
1.04
1.21
1.30
1.31
6
26,250
.00
1.00
1.00
1.05
1.02
1.00
3.16
1.21
1.21
7
20,816
.00
1.00
1.00
1.03
1.00
1.00
1.12
1.14
1.13
8
16,509
.00
1.00
1.00
1.02
1.00
1.00
1.C9
1.C9
1.07
* P should be expressed as a whole number not as a decimal; thus a d
per cent loss should be written 5 and not .05.
io ; 4
ELECTRICAL EKGINEERING.
Relative Weight of Copper Required In Different
Systems for Equal Effective Voltages.
Direct current, ordinary two-wire system 1 .000
three-wire system, all wires same size 375
neutral one-half size 313
Alternating current, single-phase two-wire, and two-phase four-wire 1.000
Two-phase three-wire, voltage between outer and middle wire same
as in single-phase two-wire 729
voltage between two outer wires same 1 . 457
Three-phase three-wire 750
four-wire 333
The weight of copper is inversely proportional to the squares of the
voltages, other things being equal. The maximum value of an alternating
e.m.f. is 1.41 times its effective rating. For derivation of the above figures,
see Crocker's Electric Lighting, vol. ii.
STANDARD SIZES OF ELECTRICAL MACHINES.
(Chiefly Selected from Bulletins of the General Electric Co.)
Direct-driven Direct-current Generators for Lighting
and Power.
125 or 250 Volts.
275 Volts.
$
fs
is
Dimensions.
in
V
fs
fj
Dimensions.
I
M
J£
r
A.
B.
C.
£
W
&^
£&
r
A.
B.
C.
6
25
305
3,500
40
48
21
10
300
150
40,000
116
129
40
6
35
300
4,600
42
52
23
10
400
150
55,000
132
145
41
6
50
280
6,250
46
53
26
10
400
120
62,000
135
147
42
6
75
270
8,800
55
66
26
14
550
100
82,000
152
180
42
6
100
270
11,200
58
71
28
18
800
100
95,000
173
206
44
8
160
230
15,000
67
85
30
18
1,000
100
115,000
178
212
46
8
160
150
21,000
79
96
35
24
1,600
100
175,000
264
258
54
8
200
200
22,000
79
96
35
8
200
150
30,000
85
112
37
Direct-connected Direct-current Railway Generators.
Form H. 575 Volts.
1
,-B
Is
Dimensions.
t>
f£
li
Dimensions.
&
M
l£
**
A.
B.
C.
I
*
M«
£
A.
B.
C.
6
100
275
15,OCO
81
95
28
10
500
100
96,000
160
178
48
6
150
200
29,000
99
114
35
10
500
90
110,000
161
180
50
6
200
200
39,000
116
133
37
10
500
80
118,000
162
180
51
a
200
150
50,000
119
136
41
12
650
90
117,000
173
188
48
6
200
120
58,000
121
140
48
12
800
120
113,000
173
188
48
8
300
150
55,000
125
141
41
14
800
100
118,000
186
200
46
8
300
120
65,000
129
145
45
14
800
80
135,000
187
201
48
8
300
100
75,000
130
146
48
16
1,000
80
150,000
187
209
50
8
400
150
68,000
J32
148
45
18
1,200
80
156,000
196
221
48
8
400
120
79,000
135
150
48
22
1,600
75
180,000
230
245
48
8
400
100
90,000
138
152
50
26
2.000
75
188.000
2S5
312
52
10
500
120
81,000
145
154
45
28
2,400
75
225,000
320
364
52
Dimensions in inches : A, height of frame above floor. B, diameter of
frame at base. C, width of frame base.
STANDARD SIZES OF ELECTRICAL MACHINES. 1075
Belted Generators. Compound- or Shunt- wound.
Type CE.
Dimensions, Inches.*
Poles.
Kw.
Speed.
Amp.
(a)
Amp.
(&)
Weight,
Lbs.
A.
B.
C.
D.
E.
2
2
IK
2H
1,350
2,100
12
18
6
9
[ 345
28
17
16
5
4
2
2
214
1,350
2,100
18
30
9
15
j- 455
31
20
20
5
4^
2
2
lu
1,350
1,875
30
44
15
22
j- 630
33
22
21
5
41/3
4
4
1,050
1,625
44
60
22
30
j- 870
38
26
24
m
6
4
4
lla
850
1,300
60
88
30
44
[ 1,240
41
32
27
m
7
4
4
11
15
850
1,300
88
120
44
60
j- 1,660
49
33
30
10
8K
(a) Full load, 125 volts; no load voltage, 120. (6) Full load, 250 volts; no
load voltage, 240.
Belted Generators. Slow Speed. Form H (Four Poles).
Amperes, full load.
Dimensions, Inches.*
Kw.
Speed.
Weight,t
Lbs.
125V.
250V.
500V.
A.
B.
C.
D.
E.
sy*
950
52
26
13
1,030
38
36
26
11
4J4
9
900
72
36
18
1,435
43
40
29
11^
6Vo
13tf
850
108
54
27
1,900
50
44
33
m*
8^
17
750
136
68
34
2,665
57
46
35
13^
8V6
20
700
160
80
40
3,350
61
53
39
15
10)4
30
675
240
120
60
4,935
68
59
46
20U
11
40
605
320
160
80
5,690
72
63
49
2234
15V£
50
600
400
200
100
7,140
79
66
52
23
18^fj
75
550
600
300
150
8,800
92
68
56
25
24^
IMrect-current Motors. Type CE.
H.P.
Speed (Shunt- wound) .
Weight,
LKo
Dimensions, Inches.*
110V.
115V.
125V.
500V.
A.
B.
C.
D.
E.
2
3
1,000
1,700
1,025
1,750
,075
,840
1,200
1,800
j- 335
28
17
20
5
4
3
5
1,000
1,680
1,025
1,725
,075
,820
1,200
1,800
j- 465
31
20
20
5
4^
5
W*
975
1,490
1,000
1,525
,050
1,600
1,250
1,650
540
33
22
21
5
4J4
&
795
1,220
815
1,250
860
1,310
1,000
1,500
808
38
26
24
7M
6
10
15
635
975
650
1,000
685
1,050
800
1,200
[ 1,150
41
32
27
m
7
15
20
665
1,000
690
1,040
750
1,125
750
1,125
!• 1,400
49
33
30
10
8JUS
s
Speeds for 220, 230, and 250 volts are the same as for 110, 115, and 125 volts.
* Dimensions in inches: A, length over all in direction of shaft, including
Sulley ; B, width or diameter at feet of frame ; C, height above floor ; D,
iameter of pulley; E, face of pulley,
f With rails ; includes pulley, but not wood base-frame,
1076
ELECTRICAL ENGINEERING.
STANDARD BELTED MOTORS AND GENERATORS.
(Crocker- Wheeler Electric Co., 1898.)
1
225
150
100
75
60
35
25
15
10
5*
3
2
1
1/6
Output.
Motor. Dynamo.
400 200
130
90
GO
45
31,
2-.',
13
10
7.
5
3
2
1
1000 83
1050 83
110082
1175 80
1200
1300
1600 67
1800 55
2200 55
Effi-
ciency.
450 88
45085
65088
90
70089
75088
825 86
I-
30000
11300
11000
6500
4500
3350
2400
1510
920
760
510
410
288
205
100
70
27
Outside Dimen-
sions in inches.
Net Over All.
46%
51%
Size of
Pulley.
45
45
45
3^45
3 45
45
Small Belted Dynamos and Motors (4»pole).
(Crocker-Wheeler Co.)
Size.
Output.
Motor
Speed.
Dynamo
Speed.
tlj
Dimensions, Inches.
(See foot-note on p. 1077.}
H.P.
Kvv.
230V.
500V.
125-
250 V.
550V.
A.
B.
D.
E,
« \
3
4
3U
975
1,300
1,100
1,375
1,200
1.600
1,400
1,750
[295
21
18
6
4^
5 1
5
5%
950
1,150
1,100
1,350
1,150
1,400
1,375
1,700
j-400
22
20
7
5
Mj
|
%
875
1,100
925
1,175
1,050
1,300
1,150
1,450
j-540
25
21
8
BM
Ri-polar Dynamos and Motors. (Crocker- Wheeler Co.)
Size.
Output.
Motor
Speed.
Dynamo
Speed.
Net
Weight,
Lbs.
Pulley.
H.P.
Kw.
115-
230V.
500V.
125-
250 V.
550 V.
Diam.
Face.
M
Lf
y4
1/6
1/12
2
f
1/25
2
975
1,500
1,000
1,450
1,200
1,400
1,600
1,800
,025
,500
,050
,550
,350
,600
1,600
1,300
1,300
1,600
1,800
2,200
1,450
1,450
1,750
1,950
288
205
100
70
27
19
5
4
3
3
1«
1*2
4
3^
3
SI
Grooved
1
Yz
y±
110 watts
STANDARD SIZES OF ELECTRICAL MACHINES. 1077
Direct-connected Alternators. (General Electric Co.)
25 CYCLES.
Poles. Kw. R.P.M.
12 72 250
12 108 250
14 160 214
16 240 187.5
2.) 210 150
20 360 150
Poles. Kw. RP M.
24 360 125
28 360 107
20 540 150
24 540 125
28 540 107
24 810 125
Poles. Kw. R.P.M.
28 810 107
32 810 94
24 1200 125
28 1200 107
32 1200 94
28 1800 107
Poles. Kw. R.P.M
32 1800 94
40 1800 75
32 2700 94
40 2700 75
40 4080 75
40 6000 75
From 360 to 810 kw. the machines are wound for 370 volts ; from 72 to
810 kw. for 480 volts; from 810 to 6000 kw. for 2300 volts; and from 360 to 6000
kw. for 6600 and 13,200 volts.
60 CYCLES.
Poles. Kw. R.P.M.
2(> 72 276
28 1 08 257
32 160 225
3<> 240 200
48 240 150
48 360 150
Poles. Kw. R.P.M
56 360 128.5
64 360 112.5
48 540 150
56 540 128.5
63 540 108
52 810 138.5
Poles. Kw. R.P.M
60 810 120 '
72 810 100
60 1200 120
72 1200 100
64 1800 112.5
72 1800 100
Poles. Kw. R.P.M.
80 1800 90
72 2700 100
84 2700 86
From 72 to 360 kw. the machines are wound for 240 volts ; from 72 to
1*200 kw. for 480 volts ; from 72 to 2700 kw. for 2300 volts; from 540 to 2700
kw. some machines are wound for 6600 volts.
The kw. ratings in the above table are based on the load that may be
carried without a rise in temperature of any part exceeding 40° C. above the
surrounding atmosphere when running continuously with non-inductive full
load. An overload of 25#, non-inductive, may he carried for two hours with-
out heating more than 55° C. When full non inductive load is thrown off,
with fixed normal excitation, the voltage will rise approximately 8#. When
full load with SQf, power factor is thrown off, with fixed excitation, the rise
will be approximately 2(Z%-
A rating one-sixth less is given all machines for a rise of temperature not
exceeding 35°C. above surrounding atmosphere.
Belt- driven Alternating-current Generators. 60 Cycles.
Size. Kw 80 50 75 100 150 200
No. of poles 6 6 8 8 12 12
Speed, r.p.m 1200 1200 900 900 600 600
Weight, with rails, Ibs 3000 3800 4750 5850 8100 9650
Floor- space with rails, ins. 51x56 58x56 68x67 74x67 80x79 87x79
Size of pulley, ins 16x7 16 x 10 21 x 13 21 x 15 32 x 19 32 x 23
Induction Motors. 60 Cycles.
FTP.,. .1 2 3 5 7.5 10 15 20 30 40 50 75 100 150 200
Poles 44466 668 8 8 10 10 12 12 14
Speed ' — 1800--' ' 1200 ' < 900 — ' ^-720-' 600 600 514
Weight 210 300 375 600 700 812 1062 1500 2380 3000 3490 5220 6800 9000 11000
Width, ins.* . 19 20 22 24 26 29 34 36 43 48 50 60 57 67 77
Length,"... 24 28 28 42 42 46 46 57 57 57 59 64 78 78 102
Pulley, diam. 4^ 4^41^ 88 8 8 13 13 13 16 16 26 28 36
" width. 2^ 2^ 2^ 4 5 6 7 7 9 11 13 17 17 21 23
* In direction of shaft, Form K motors. Forms L and M are 4 to 10 ins.
wider.
1078
ELECTRICAL ENGINEERING.
SYMBOLS USED IN ELECTRICAL DIAGRAMS.
-crrcn-SPST © ^~v W
-acbo-SPDT e "^
^g D: DPST
^ggglDPDT Galvanometer. Ammeter. Voltmeter. Wattmeter
Switches^ S^jsingle; -A/VVW. ~UTnnriPs— H^T!^»;
e' Non-inductive Inductive j Capacity
Resistance. Resistance. or Condenser.
Lamps.
Motor Shunt-wound Motor Series- wound
or Generator. or Generator. Motor or Generator.
Two-phase Three-phase Battery. Trans- Compound- Separately
Generator. Generator. former wound Motor excited Motor
or Generator, or Generator.
APPENDIX.
STRENGTH OF TIMBER.
Safe Loads in Tons, Uniformly Distributed, for "White-
oak Beams.
(In accordance with the Building Laws of Boston.)
W= safe load in pounds; P, extreme fibre-
4PBD* Stress = 1000 Ibs. per square iuch, for white
Formula : W = — — — oak ; B, breadth in inches; D, depth in inches;
Lt distance between supports in inches.
Size of
Timber.
Distance between Supports in feet.
6
8
10
11
12
14
15
16
17
18
19
21
23
25
26
Safe Load in Tons of 2000 Pounds.
2x6
0.67
0.5010.400.36
0.33J0.29
0.27
0.25
0.24
0.22
I 1
2x8
1.19
0.89
0.71
0.65
0.59
0.51
0.47
0.44
0.42
0.40
0.37
0.34
0.31
0.28
2x10
1.85
1.39
1.11
1.01
0.93
0.79
0.74
0.69
0.65
0.62
0.58
0.53
0.48
0.44
0.43
2x13
2.67
2.00
1.60
1.45
1.33
1.14
1.07
1.00
0.94
0.89
0.84
0.76
0.70
0.64
0.62
3x6
1.00
0.75
0.60
0.55
0.50
0.43
0.40
0.37
0.35
0.33
0.32
0.29
0.26
8x8
1.78
1.33
1.07
0.97
0.89
0.76
0.71
0.67
0.63
0.59
0.56
0.51
0.46
0.43
0.41
3x10
2.78
2.08
1.67
1.52
1.39
1.19
1.11
1.04
0.98
0.93
0.88
0.79
0.72
0.67
0.64
3x12
4.00
3.00
2.40
2.18
2.00
1.71
1.60
1.50
1.41
1.33
1.26
1.14
1.04
0.96
0.92
3x14
5.45
4.08
3.27
2.97
2.72
2.37
2.18
2.04
1.92
1.82
1.72
1.56
1.42
1.31
1.25
3x16
7.11
5.33
4.27
3.88
3.56
3.05
2.84
2 67
2.51
2.37
2.25
2.03
1.86
1.71
1.64
4x10
3.70
2.78
2.22
2.02
1.85
1.59
1.48
1.39
1.81
1.23
1.17
1.06
0.97
0.89
0.85
4x12
5.33
4.00
3.20
2.91
2.67
2.29
2.13
2.00
1.88
1.78
1.68
1.52
1.39
1.28
1.23
4x14
7.26
5.44
4.36
3.96
3.63
3.11
2.90
2 72
2.56
2.42
2.29
2.07
1.90
1.74
1.68
4x16
9.48
7.11
5.69
5.17
4.74
4.06
3.79
3^56
3.35
3.16
3.00
2.71
2.47
2.28
2.19
4x18
12.00
9.00
7.20
6.55
6.00
5.14
4.80
4.50
4.24
4.00
3.79
3.43
3.13
2.88
2.77
For other kinds of wood than white oak multiply the figures in the table
by a figure selected from those given below (which represent the safe stress
per square inch on beams of different kinds of wood according to the build-
ing laws of the cities named) and divide by 1000.
Hemlock.
Spruce.
White
pine.
Oak.
Yellow
Pine.
New York
800
900
750
900
750
1100
lOOOt
1100*
1250
Chicago
900
1080
1440
* Georgia pine.
f White oak.
1079
1080
APPENDIX.
MATHEMATICS.
Formula for Interpolation.
at = the first term of the series; n, number of the required term; an, the
required term; cZl5 cZ2, ^s« n'r.st terms of successive orders of differences
between alf a2, a3, a4, successive terms.
EXAMPLE.— Required the log of 40.7, logs of 40, 41, 42, 43 being given as
below.
Terms a,, rr.a, a3) a4: 1.6021 1.6128 1.6232 1.6335
1st differences: .0107 .0104 .0103
2d " - .0003 - .0001
3d • " 4- .0002
2; log 40.7 n = 1.7, n — 1 = 0.7, n — 2 = - 0.3.
- p.3)( - .0003)
- 0.3)( - 1.3)(.OOQ2)
For log. 40 n = 1 ; log 41 n
n - 3 = - .1.3.
an =1.6021 •}- 0.7(.0107) f
= 1.6021 4- .00749 4- .000031 -f .000009 = 1.6096 -f.
Maxima and Minima without the Calculus.— In the equation
y = a 4- bx 4- ex'2, in which a, 6, and c are constants, either positive or neg-
ative, if c be positive y is a minimum when x — — b -*- 2c; if c be negative y
is a maximum when x = - 6 -*- 2c. In the equation ?/ = a 4" &# + c/x, y is
a minimum when bx = c/#.
APPLICATION. — The cost of electrical transmission is made up (1) of fixed
charges, such as superintendence, repairs, cost of poles, etc., which may be
represented by a; (2) of interest on cost of the wire, which varies with the
sectional area, and may be represented by bx; and (3) of cost of the energy
wasted in transmission, which varies inversely with the area of the wire, or
c/x. The total cost, y = a -f bx 4- c/x, is a minimum when item 2 = item
3, or bx = c/x.
RIVETED JOINTS.
Pressure Required to Drive Hot Rivets.— R. D. Wood & Co.,
Philadelphia, give the following table (1897):
POWER TO DRIVE RIVETS HOT.
Size.
Girder-
work.
Tank-
work.
Boiler-
work.
Size.
Girder-
work.
Tank-
work.
Boiler-
work.
in.
tons.
tons.
tons.
in."
tons.
tons.
tons.
L£
9
15
20
1/^j
38
60
75
78
12
18
25
1/4
45
70
100
3/
15
22
33
l/^
60
85
125
TO
22
30
45
1M
75
100
150
1
30
45
60
The above is based on the rivet passing through only two thicknesses of
plate which together exceed the diameter of the rivet but little, if any.
As the plate thickness increases the power required increases approxi-
mately in proportion to the square root of the increase of thickness. Thus,
if the total thickness of plate is four times the diameter of the rivet, we
should require twice the power given above in order to thoroughly fill the
rivet-holes and do good work. Double the thickness of plate would increase
the necessary power about 40%.
It takes about four or five times as much power to drive rivets cold as to
drive them hot. Thus, a machine that will drive %-in. rivets hot will usually
drive j^-in. rivets cold (steel). Baldwin Locomotive Works drive ^j-in. soft-
iron rivets cold with 15 tons.
HEATING AND YENTILATIOK.
1081
HEATING AND VENTILATION.
Table of Capacities for Hot-blast or Plenum Heating
with Fans or Blowers.
(Computed by F. R. Still, American Blower Co., Detroit, Mich.)
J""1
> >,
10 wo'
tJ ®
£
is
.all
a
Q
Q W
3
02
y
2
Ss
CT^2
03 ^
fe *•*
D 55
&
^
1
LI
$2o
•5^^
-u .
>S
II
Ize of Blow(
housing.
1
o
a
05
evolutions
minute.
1
iff
u. Ft. of Ai
per hour.
.eat Units r
per hour
air from 0
elocity of 1
through C(
ft. per min
ree Area b(
Pipes in sq
eat Units g
per sq. ft.
per hour.
oj'3
w
S
«
W
o
O
W
>
h
n
CO
70
42
360
2^
6,900
415,200
1,021,000
90J
7.7
1760
580
80
48
320
3
8,500
510,000
1,255,000
"
9.45
714
90
54
280
4
10,500
630,000
1,550,000
"
11.66
880
100
60
250
5
12,500
750,000
1.845,000
"
13.9
1050
110
66
230
6
15,800
948,000
2,335,000
M
17.55
1325
120
72
210
8
19,800
1,118,000
2,900,000
"
22.
1650
140
84
180
10
26,200
1,572,000
3,870,000
"
29.1
2200
160
96
160
12
33,000
1,980,000
4,870,000
"
36.7
2770
180
108
140
15
41,600
2,496,000
6,130,000
44
46.3
3490
200
120
125
18
50,000
3,000,000
7,375,000
"
55.5
4140
ti
•s
o
mdensed
1
'3
1
3
||
rface in
. per
o
go £
•S-fe*
Iff
X .
o
a
WQ
as
d
"3
CO
trf
I*
gia
-la'S
l|3
£
£
*o £
* o
1
a
'8J§M
•So
i'J ®
S* 1
*§ *
-§ ^^
E
-u '5
tr "*"*
i
d
Q.1""1
'cS T~l
ta £g
t- _p
6-
® o 5
o
$ °*
$5
S
£2
O Q
cS
2
O II
ij .
O .
ro'S
§-2
3,0 o>'S
"3 2
rd'i3
-£
0>
W
._ Tt,
^J JD .
*a«W^W
§^a
s
'O <D -j'S
85<
G fe
s 9;
0)
D
53
.OPH
o a
PH
.2
.S
02
W
s1
CO
iS*0
^T'
g 03^ V
70
1,740
1055
3K
2
35
525
15
8,700
9.67
8,200
80
2,142
1295
4
2
43
645
18
10,700
13.05
10,000
90
2,640
1600
4Lj£ <>L£
53
795
23
13,200
14.72
12,500
100
3,150
1900
5
31^3
63
945
27
15,800
17.55
15,000
110
3,975
2410
5Vij
3
80
1200
34
19,900
22.20
18,900
120
4,950
2990
6
3
100
1500
43
25,000
27.80
23,800
140
6,600
3990
7
3L£
133
1995
57
33,100
36.80
31,400
160
8,310
5025
8
4
167
2505
72
41,700
46.30
39,600
180
10,470
6325
9
41^
211
3165
90
52,500
58.40
50,000
200
12,420
7560
10
5
252
3780
108
63,200
70.25
60,000
Temperature of fresh air, 0°; of air from coils, 120°; of steam, 227°. Pres-
sure of steam, 5 Ibs.
Peripheral velocity of fan-tips, 4000 ft.; number of pipes deep in coil, 24;
depth of coil, 60 inches; area of coils approximately twice free area.
WATER- WHEELS.
Water-power Plants Operating under High Pressures.—
The following notes are contributed by the Pelton Water Wheel Co.:
The Consolidated Virginia & Col. Mining Co., Virginia, Nev., has a 3-ft.
steel-disk Pelton wheel operating under 2100 ft. fall, equal to 911 Ibs. per sq. in.
It runs at a peripheral velocity of 10.804 ft. per minute and has a capacity
of over 100 H.P. The rigidity with which water under such a high pressure
as this leaves the nozzle is shown in the fact that it is impossible to cut the
1082
APPENDIX.
stream with an axe, however heavy the blow, as it will rebound just as it
would from a steel rod travelling at a high rate of speed.
The London Hydraulic Power Co. has a large number of Pelton wheels
from 12 to 18 in. diameter running under pressure of about 1000 Ibs. per. sq.
in. from a system of pressure-mains. The 18-in. wheels weighing 30 Ibs. have
a capacity of over 20 H.P. (See Elaine's " Hydraulic Machinery/')
Hydraulic Power-hoist of Milwaukee Mining Co., Idaho.— One cage travels
up as the other descends; the maximum load of 5500 Ibs. at a speed of 400
ft. per min. is carried by one of a pair of Pelton wheels (one for each cage).
Wheels are started and stopped by opening and closing a small hydraulic
valve at the engineer's stand, which operates the larger valves by hydraulic
pressure. An air-chamber takes up the shock that would otherwise occur
on the pipe line under the pressure due to 850 ft. fall.
The Mannesmann Cycle Tube Works, North Adams, Mass., are using four
Pelton wheels, having'a fly-wheel rim, under a pump pressure of 600 Ibs. per
sq. in. These wheels are direct-connected to the rolls through which the
ingots are passed for drawing out seamless tubing.
The Alaska Gold Mining Co., Douglass Island, Alaska, has a 22-ft. Pelton
wheel on the shaft of a Riedler duplex compressor. It is used as a fly-
wheel as well, weighing 25,000 Ibs.— and develops 500 H.P. at 75 revolutions.
A valve connected to the pressure-chamber starts and stops the wheel
automatically, thus maintaining the pressure in the air-receiver.
At Pachuca in Mexico five Pelton wheels having a capacity of 600 H.P.
each under 800 ft. head are driving an electric transmission plant. These
wheels weigh less than 500 Ibs. each, showing over a horse-power per pound
of metal.
Formulae for Calculating the Power of Jet Water-
wheels, such as the Pelton (F. K. Blue).— HP = horse-power delivered;
6 = 62.36 Ibs. per cu. ft.; E = efficiency of turbine; q = quantity of water,
cubic feet per minute; h = feet effective head; d = inches diameter of jet;
p = pounds per square inch effective head ; c = coefficient of discharge from
nozzle, which may be ordinarily taken at 0.9.
~ = .0174Ecd* VpS.
q = 529.2 -^ = 229^,— = 2.62cd* V~h = 3.99cd* Vp,
JLfl JLp
d,= m.e-?r= = VAJ¥=..
EC Vh3 EC Vp3
_
cVh
GAS FUEL.
Average Volumetric Composition. Energy, etc., of Vari-
ous Oases. (Contributed by R. D. Wood & Co., Philadelphia, 1898.)
Natural
Gas.
Coal-
gas.
Water-
gas.
Producer-gas.
Air.
Anthra.
Bituni.
CO ..
0.50
2.18
92.6
0.31
0.26
3.61
0.34
6.0
46.0
40.0
4.0
0.5
1.5
0.5
1.5
32.0
735,000
5
45.0
45.0
2.0
27.0
12.0
1.2
27.0
12.0
2.5
0.4
H ....
CH4
C.H,,
CO/"
4.0
2.0
0.5
1.5
45.6
322,000
25
2.5
57.0
0.3
2.5
55.3
0.3
trace
79
21
trace
76.1
N
O
"Vapor
Lbs. in 1000 cu. ft..
H. U. in 1000 cu. ft.
Cu.f t. from each Ib.
of coal approx. . .
45.6
1,100,000
65.6
137,455
85
65.9
156,917*
75
200t
* The real energy of bituminous producer-gas when used hot is far in
excess of that indicated by the above table, on account of the hydrocarbons,
which do not show, as they are condensed in the act of collecting the gas
for analysis. In actual practice there is found to be about 50# more effective
energy in bituminous gas than in anthracite gas when used hot enough t»
prevent condensation in the flues.
t Cubic feet of air required to burn 1 Ib. of coal with blast.
STEAM-BOILERS. 1083
STEAM-BOILERS.
Steam-boiler Construction. (Extract from the Rules and Sped-
ficatious of the Hartford Steam Boiler Inspection & Insurance Co., 1898.)
Cylindrical boiler shells of fire box steel, and tube-heads of best flange
steel. Limits of tensile strength between 55,000 and 62,000 Ibs. per sq. in.
Iron rivets in steel plates, 38,000 Ibs. shearing strength per sq. in. in
single shear, and 85$ more, or 70.300 Ibs., in double shear.
Each shell-plate must bear a test-coupon which shall be sheared off
and tested. Each coupon must fulfil the above requirements as to tensile
strength, but must have a contraction of area of not less than 56% and
an elongation of 25# in a length of 8 in. It must also stand bending 180*
when cold, when red hot, and after being heated red hot and quenched in
cold water, without fracture on outside of bent portion.
Crow-foot braces are required for boiler-heads without welds, and if of
iron limit the strain to 7500 Ibs. per sq. in., and stay-bolts must not be sub-
jected to a greater strain than 6000 Ibs. per sq. in.
The thickness of double butt-straps 8/10 the thickness of plates. In lap-
joints the distance between the rows of rivets is % the pitch. In double-
riveted lap-joints of plates up to \^ in. thick the efficiency is 70# and in
triple-riveted lap-joints 75# of the solid plate.
In triple-riveted double-strapped butt-seams for plates from *4 m- to V* m-
thick, the efficiency ranges from 8S# to 86$ of the solid plate.
In high-pressure boilers the holes are required to be drilled in place ; that
is, all holes may be punched y± in. less than full size, then the courses are
rolled up, tube-heads and joint-covering plates bolted to courses, with all
holes together perfectly fair. Then the rivet-holes are drilled to full size,
and when completed the plates are taken apart and the burr removed.
The rule for the bursting-pressure of cylindrical boiler-shells is the follow-
ing: Multiply the ultimate tensile strength of the weakest plate in the shell
by its thickness in inches and by the efficiency of the joint, and divide result
by the semi-diameter of shell ; the quotient is the bursting-pressure per
square inch. This pressure divided by the factor 5 gives the allowable
working pressure.
BOILER FEEDING.
GraTity Boiler-feeders.— If a closed tank be placed above the
level of the water in a boiler and the tank be filled or partly filled with
water, then on shutting off the supply to the tank, admitting steam from
the boiler to the upper part of the tank, so as to equalize the steam-pressure
in the boiler and in the tank, and opening a valve in a pipe leading from the
tank to the boiler the water will run into the boiler. An apparatus of this
kind may be made to work with practically perfect efficiency as a boiler-
feeder, as an injector does, when the feed-supply is at ordinary atmospheric
temperature, since after the tank is emptied of water and the valves in the
pipes connecting it with the boiler are closed the condensation of the steam
remaining in the tank will create a vacuum which will lift a fresh supply of
water into the tank. The only loss of energy in the cycle of operations is
the radiation from the tank and pipes, which may be made very small by
proper covering.
When the feed-water supply is hot, such as the return water from a heat-
ing system, the gravity apparatus may be made to work by having two
receivers, one at a low level, which receives the returns or other feed-supply,
and the other at a point above the boilers. A partial vacuum being created
in the upper tank, steam-pressure is applied above the water in the lower
tank by which it is elevated into the upper. The operation of such a
machine may be made automatic by suitable arrangement of valves. (See
circular of the Scott Boiler Feeder, made by the Q. & C. Co., Chicago.)
FEEJD- WATER HEATERS.
Capacity of Feed-water Heaters.— The following extract from
a letter by W. R. Billings, treasurer of the Tauntcta Locomotive Manufaetur-
ng Co., builders of the Wainwright feed-water heater, to Engineering Record,
February, 1898, is of interest in showing the relation of the heating surface
of a heater to the work done by it:
" Closed feed-water heaters are seldom provided with sufficient surface to
raise the feed temperature to more than 200°. Tfc« »ate of heat trans-
1084 APPENDIX.
mission may be measured by the number of British thermal units which
pass through a square foot of tubular surface in one hour for each degree
of difference in temperature between the water and the steam. The diffi-
culties which attend experiments in this direction can only be appreciated
by those who have attempted to make such experiments. Certain results
have been reached, however, which point to what appears to be a reasonable
. conclusion. One set of experiments made quite recently gave certain results
which may be set forth in the table herewith.
5°F 67 B.T.U. 1 Transmitted in one
Difference between
final tempera-
tures of water and
fcteam
79
...114
.. 129
...139
hour by each sq. ft.
of surface for each
degree of average
difference in temper-
atures.
" In other words, when the water was brought to within 5° of the temper-
ature of the heating medium, heat was transmitted through the tubes at the
rate of 67 B.T.U. per square foot for each degree of difference in temperature
in one hour. When the amount of water flowing through the heater was so
largely increased as to make it impossible to get the water any nearer than
within 18° of the temperature of the steam, the heat was transmitted at the
rate of 139 B.T.U. per sq. ft. of surface for each degree of difference in
temperature in one hour. Note here that even with the rate of transmission
as low as 67 B.T.U. the water was still 5° from the temperature of the
steam. At what rate would the heat have been transmitted if the water
could have been brought to within 2° of the temperature of the steam, or to
210° when the steam is at 212° ?
"For commercial purposes feed-water heaters are given a H. P. rating which
allows about one-third of a square foot of surface per H.P.— a boiler H.P.
being 30 Ibs. of water per hour. If the figures given in the table above are
accepted as substantially correct, a heater which is to raise 3000 Ibs. of water
per hour from 60° to 207°, using exhaust steam at 212° as a heating medium,
should have nearly 84 sq. ft. of heating surface— that is, a 100 H.P. feed- water
heater which is to maintain a constant temperature of not less than 207°,
with water flowing through it at the rate of 30CO Ibs. per hour, should have
nearly a square foot of surface per H.P. That feed-water heaters do not
carry this amount of heating surface is well known.'1
THK STEAM-ENGINE.
Current Practice in Engine Proportions, 1897 (Compare
pages 792 to 817.)— A paper with this title by Prof John H. Barr, in Trans.
A. 8. M. E., xviii. 737, gives the results of an examination of the proportions of
parts of a great number of single-cylinder engines made by different builders.
The engines classed as low speed (L. S.) are Corliss or other long-stroke
engines usually making not more than 100 or 125 revs, per min. Those
classed as high speed (H. S.) have a stroke generally of 1 to \y% diameters
and a speed of 200 to 300 revs, per min. The results are expressed in for-
mulas of rational form with empirical coefficients, and are here abridged as
follows :
Thickness of Shell, L. S. only.— t = CD-+-B; D = diam. of piston in in.;
B = 0.3 in. ; C varies from 0.04 to 0.06, mean = 0.05.
Flanges and Cylinder-heads.— I to 1.5 times thickness of shell, mean 1.2.
Cylinder-head Studs.— No studs less than % in. nor greater than \% in.
diam. Least number, 8, for 10 in diam. Average number = 0.7D. Average
diam. = D/40 -f J^in.
Ports and Pipes. — a = area of port (or pipe) in sq. in. ; A = area of piston,
sq. in.; V= mean piston-speed, ft. per miu.; a = AV/C, in which C '— mean
velocity of steam through the port or pipe in ft. per min.
Ports, H. S. (same ports for steam as for exhaust).— C= 45"0 to 6500, mean
5500. For ordinary piston-speed of 600 ft. per miu. a = KA ; K = .09 to .13,
mean .11.
Steam-ports, L. S.— C= 5000 to 9000, mean 6800; K= .08 to .10. mean .09.
Exhaust-ports, L. S.— C = 4000 to 7000, mean 5500; K = .10 to .125. mean .11.
Steam-pipes, H. S.— C = 5800 to 7000, mean 6500. If d = diam. of pipe and
D = diam. of piston, d = .29D to .32D. mean .30D.
Steam-pipes, L. S.— C = 5000 to 8000, mean 6000; d = .27 to .35D, mean .32P.
Exhaust-pipes, H. S.— C = 2500 to 5500, mean 4400; d = .33 to .50D, mean .377).
Exhaust-pipes, L. S.— C = 2800 to 4700, mean 3800; d = .35 to .45D, mean AOD.
LOCOMOTIVES. 1085
Face of Pistons.— F= face; D = diameter. F = CD. H. S.: C = .30 to .60
mean .46. L. S.: C= .25 to .45, mean .32.
Piston-rods. — d = diam. of rod; D = diam. of piston; L = stroke, in.;
d = CVDL. H. S.: C=. 12 to .175, mean .145. L. S.: C= .10 to .13, mean .11.
Connecting-rods.— H. S. (generally 6 cranks long, rectangular section):
b = breadth; h = height of section; L1 = length of connecting-rod; D = diam.
of piston; b = C V^L^ C= .043 to .07, mean .057; h = Kb ; K = 2.2 to 4, mean
2.7. L. S. (generally 5 cranks long, circular sections only): C = .082 to .105,
mean .092.
Cross-head Slides.— Maximum pressure in Ibs. per sq. in. of shoe, due to
the vertical component of the force on the connectiug-rod. H. S.: 10.5 to 38,
mean 27. L. S : 29 to 33, mean 40.
Cross-head Pins.— I = length; d = diam.; projected area = a = dl — CA;
A = area of piston; I = Kd. H. S.: C = .06 to .11, mean .08; K = 1 to 2,
mean 1.25. L. S.: C— .054 to .10, mean 07; K = 1 to 1.5, mean 1.3.
Crank-pin.— HP = horse-power of engine; L= length of stroke; I = length
of pin; I = C X HP/L + B\ d = diam. of pin; A = area of piston; dl = KA.
H. S.: C - .13 to .46, mean .30; B = 2.5 in.; K = .17 to .44, mean .24. L. S.:
C = .4 to .8, mean .6; B = 2 in.; K = .065 to .115, mean .09.
Crank-shaft Main Journal,— d = cHP -+- N; d = diam.; I = length; N =
revs, per min.; projected area = MA; A — area of piston. H.S.: C — 6.5 to
8.5, mean 7.3; K = 2 to 3, mean 2.2; M = .37 to .70, mean .46. L. S.: C = 6 to 8,
mean 6.8; K = 1.7 to 2.1, mean 1.9; M - .46 to .64, mean .56.
Piston-speed.— II. S.: 530 to 660, mean 600; L. S.: 500 to 850, mean 600.
Weight of Reciprocating Parts (piston, piston-rod, cross-head, and one-
half of connecting-rod).— W- CD* -f- LN*; D = diam. of piston ;L = length
of stroke, in. ; N = revs per min. H. S. only: C = 1,200,000 to 2,300,000, mean
1,860,000.
Belt-surface per I.H.P.— S = CHP+ B; S = product of width of belt in
feet by velocity of belt in ft. per min. H. S.: C = 21 to 40 mean 28; B = 1800.
L. S.: S = C X HP.; C = 30 to 42, mean = 35.
Fly-wheel (H. S. onl.y).— Weight of rim in Ibs.: W = C X HP + D^N*-^ =
diam. of wheel in in.; C = 65 X 1010 to 2 X ?012 mean = 12 X 10", or
1,200,000,000,000.
Weight of Engine per I.H.P. in Ibs., including fly-wheel.— W - C X H.P.
H. S.:'(7 = 100 to 135, mean 115. L. S.: C - 135 to 240, mean 175.
Work of Steam-turbines. (See p. 791.)— A300-H.P. De Laval steam-
turbine at the 12th Street station of the Edison Electric Illuminating Co. in
New York City in April, 1896, showed on a test a steam-consumption of
19.275 Ibs. of steam per electrical H.P. per hour, equivalent to 17.348 Ibs. per
brake H.P., assuming an efficiency of the dynamo of 90#. The steam-
pressure was 145 Ibs. gauge and the vacuum 26 in. It drove two 100-K.W.
dynamos. The turbine-disk was 29.5 in. diameter and its speed 9000 revs.
per min. The dynamos were geared doijn to 750 revs. The total equip-
ment, including turbine, gearing, and dynamos, occupied a space 13 ft. 3 in.
long, 6 ft. 5 in. wide, and 4 ft. 3 in. high.
The " Turbinia," a torpedo-boat 100 ft. long, 9 ft. beam, and 44}^ tons
displacement, was driven at 31 knots per hour by a Parsons steam-turbine
in 1897, developing a calculated I.H.P. of 1576 and a thrust H.P. of 916, the
steam-pressure at the engine being 130 Ibs. and at the boilers 200 Ibs. The
vacuum was 13J4 Ibs. The revolutions averaged 2100 per minute. The
calculated steam-consumption was 15.86 Ibs. per I.H.P. per hour. On
another trial the "Turbinia " developed a speed of 32^4 knots.
Relative Cost of Different Sizes of Steam-engines.
(From catalogue of the Buckeye Engine Co., Part III.)
Horse-power . .
Cost per H.P, $
50
20
75
17fc
100
16
1-25
15
150
14J4
200
13J6
250
13
300
12M
350
12.6
400
12.6
500
12.8
600
13H
700
14
800
15
1086'
APPENDIX.
GEARING.
Efficiency of Worm Gearing-. (See also page 898.)— Worm gear-
ing as a means of transmitting power, has until recently, generally been
looked upon with suspicion, its efficiency being considered necessarily low
and its life short. Recent experience, however, indicates that when prop-
erly proportioned it is both durable and reasonably efficient. Mr. F. A.
Halsey discusses the subject in Am. Machinist, Jan. 13 and 20, 1898. He
quotes two formulas for the efficiency of worm gearing due to Prof. John
H. Barr :
tan a (1 —/tan a)
approx
tana+/ tai
in which E — efficiency ; a = angle of thread, being angle between thread
and a line perpendicular to the axis of the worm ; / = coefficient of friction.
Eq. (1) applies to the worm thread only, while (2) applies to the worm and
step combined, on the assumption that the mean friction radius of the two
is equal. Eq. (1) gives a* maximum for E when tan a = 4/1 -f/2 _ / . . . (3)
and eq. (2) a maximum when tan a — 4/2 -f- 4/2 — 2 /. ... (4) Using a value
.05 for / gives a value for a in (3) of 43° 34' and in (4) a value of 52° 49'.
On plotting equations (1) and (2) the curves show the striking influence of
the pitch-angle upon the efficiency, and since the lost work is expended in
friction and wear, it is plain why worms of low angle should be short-lived
and those of high angle long-lived. The following table is taken from Mr.
Halsey's plotted curves :
RELATION BETWEEN THREAD-ANGLE SPEED AND EFFICIENCY OF WORM GEARS.
Velocity of
Pitch-line,
feet per
minute.
5
10
20
30
40
45
Efficiency.
3
5
10
20
40
100
200
35
40
47
52
60
70
76
52
56
62
67
74
82
85
66
69
74
78
83
88
91
73
76
79
83
87
91
92
76
79
82
85
88
91
9-2
77
80
82
86
88
91
92
The experiments of Mr. Wilfred Lewis on worms show a very satisfac-
tory correspondence with the theory. Mr. Halsey gives a collection of data
comprising 16 worms doing heavy duty and having pitch-angles ranging
between 4° 30' and 45°, which show that every worm having an angle above
12° 30' was successful in regard to durability, and every worm below 9°
was unsuccessful, the overlapping region being occupied by worms some of
which were successful and some unsuccessful. In several cases worms of
one pitch-angle had been replaced by worms of a different angle, an increase
in the angle leading in every case to better results and a decrease to poorer
results. He concludes with the following table from experiments by Mr.
James Christie, of the Pencoyd Iron Works, and gives data connecting the
load upon the teeth with the pitch-line velocity of the worm :
LIMITING SPEEDS AND PRESSURES OF WORM GEARING.
Double-
Double-
Single-thread
t
iread
thread
Worm 1" Pitch,
Worm 2"
Worm 2±"
2| Pitch Diam.
Pitch, 2£
Pitch, 4£
Pitch Diam.
Pitch Diam.
Revolutions per minute
128
06
201
150
272
905
425
390
128
96
201
150
272
905
201
9,35
272
31 P
425
498
Velocity at pitch-line in feet
per minute.... ....
Limiting pressure in pounds. . .
1700
1300
1100
700
1100
1100
1100
1100
TOO
400
APPROXIMATE HYDRAULIC FORMULA. 1087
APPROXIMATE HYDRAULIC FORMULJG.
(The Lombard Governor Co., Boston, Mass.)
Head (H) in feet. Pressure (P) in Ibs. per sq. in. Diameter (D) in feet.
Area (A) in sq. ft. Quantity (Q) in cubic ft. per second. Time (T) in seconds.
Spouting velocity = 8.02 +'H.
Time (T,) to acquire spouting velocity in a vertical pipe, or (Ta) in a pipe
on an angle (0) from horizontal:
Tl = 8.0-2 l/T/ -f- 32.17, Tj = 8.02 yS •*- 32.17 sin 0.
Head (H) or pressure (P) which will vent any quantity (0 through a
round orifice of any diameter (D) or area (A):
H = Q* + 14.1D4, H = £2 -*- 23.754':
P _ QS _j_ 34.1D*, P = £2 -*- 55.3.42.
Quantity (Q) discharged through a round orifice of any diameter (D) or
area (A) under any pressure (P) or under any head (H):
$ = VH x 23.75 x A*, Q = \/Hx 14.71 x D*.
Diameter (D) or area (A) of a round orifice to vent any quantity (Q) under
any head (H) or under any pressure (P):
D= 4/g -*- 3.84 l/fl, Z>= 4/$ -1-5.8 VP;
^ = Q -f- 4.89 VS, 4 = Q -f- 7.35 |/P.
Time (T) of emptying a vessel of any area (A) through an orifice of any
area (a) anywhere in its side:
T - .4164 VH + a.
Time (T) of lowering a water level from (£f) to (7t) in a tank through an
orifice of any area(n) in its side. Area of tank is (^4).
T = 0.4
Kinetic energy (K) or foot-pounds in water in a round pipe of any diameter
(D) when moving at velocity (F):
K = .76 x D2 x L x V.
Time-average-pressure (A. P.) in a pipe of any length (L) with water mov-
ing at any velocity ( V) •
A.P. = 0.1384LF-*- T.
Note.— This must not be confused with water-hammer pressure, which is
always many times greater than A.P. and for which no simple formula may
Area (a) of an orifice to empty a tank of any area (^4) in any time (70 from
any head (H):
a« T -i- 0.4094 \/H.
Area (a) of an orifice to lower water in a tank of area (A) from bead (H) to
(7i) in time CT):
a= r-*-0.409x4x(
1088
APPENDIX.
SPECIFICATIONS FOR TIN AND TERNE PI.ATTE.
(Penna. R. R. Co., 1902.)
Each sheet must (1) be cut as nearly exact to size ordered as possible,
(3) must be rectangular and flat and free from flaws, (3) must double-
seam successfully under all circumstances, (4) must show a smooth edge
with no sign of fracture when bent through an angle of 180° and flattened
down with a wooden mallet, (5) must be so nearly like every other sheet in
the shipment, in thickness, uniformity, and amount of coating, that no diffi-
culty will arise in the shops due to varying thickness of sheets, and (6) must
correspond for the different grades to the figures in the following table :
Kind of Coating.
Tin Plate.
Pure Tin.
No. 1
Terne Plate.
\i Tin, % Lead.
No. 2
Terne Plate.
^4 Tin, % Lead.
Amt. of coating per sq. ft. ...
Grade 1C . ... weight per sq. ft.
0.0185 Ib.
0.49
0.0364 Ib.
0.51
0.018'? Ib.
0.49
IX '• " "
0.62
0.64
0.62
" IXX .. " " "
0.71
6.73
0.71
" IXXX.. " " "
0.81
0.83
0.81
1 " IXXXX " " "
0.91
0.93
0.91
LIST OP AUTHORITIES QUOTED IN THIS BOOK.
When a name is quoted but once or a few times only, the page or pages
are given. The names of leading writers of text-books, who are quoted fre-
quently, have the word "various'11 affixed in place of the page-number.
The list is somewhat incomplete both as to names and page numbers.
Abel, F. A., 642
Abendroth & Root Mfg. Co., 197, 198
American Screw Co., 209
Achard, Arthur, 886, 919
Addy, George, 957
Addyston Pipe and Steel Co., 187, 188
Alden, G. I., 979
Alexander, J. S., 629
Allen, Kenneth, 295
Allen, Leicester, 582
Andrews, Thomas, 384
Ansonia Brass and Copper Co., 327
Arnold, Horace L., 959
Ashcroft Mfg. Co., 752, 775
Atkinson, J. J., 532
Babcock, G. H., 524, 933
Babcock & Wilcox Co., 538, 636
Baermann, P. H., 188
Bagshaw, Walter, 952
Bailey, W. H., 943
Baker, Sir Benjamin, 239, 247, 402
Balch, S. W., 898
Baldwin, Wm. J., 541
Ball, Frank H., 751
Barlow, W. H., 384
Barlow, Prof., 288
Barnaby, S. W., 1013
Barnes, D. L., 631, 861, 863
Barrus, Geo. H., 636
Bauer, Chas. A., 207
Bauschinger, Prof., 239
Bazin, M., 563, 587
Beardslee, L. A.. 238, 377
Beaumont, W. W., 979
Becuel, L. A., 644
Begtrup, J., 348
Bennett, P. D., 354
Bernard, M. & E., 830
Birkinbine, John, 605
Bjorling, P., 676
Blaine, R. G., 616, 1039
Blauvelt, W. H., 639, 649
Blechyaden, A., 1015
Bodmer, G. R., 753
Bolland, Simpson, 946
Booth, Wm. H., 926
Box, Thomas, 475
Briggs, Robert, 194, 478, 540, 672
British Board of Trade, 264, 266, 700
Brown, A. G., 723, 724
Brown, E. H.f 888
Brown & Sharpe Mfg. Co., 219, 890
Browne, Ross E., 597
Brush, Chas. B., 560
Buckle, W^5U
Buel, Richard H., 606, 834
Buffalo Forge Co., 519, 529
Builders' Iron Foundry, 874
Burr. Wm. A., 565
Burr, Wm. H., 247, 259, 290, 881
Calvert, F. Crace, 886
Calvert & Johnson, 469
Campbell, H. H., 398. 459, 650
Campredon, Louis, 403
Carnegie Steel Co., 177, 272, 277, 391
Carpenter, R. C., 454, 615, 718, etc.
Chad wick Lead Works, 201, 615
Chamberlain, P. M., 474
Chance, H. M., 631
Chandler, Chas. F.. 552
Chapman Valve Mig. Co., 198
Chauvenet, S. H., 370
Chase, Chas. P., 812
Chevandier, Eugene, 640
Christie, James, 394
Church, Irving P., 415
Church, Wm. Lee, 784, 1050
Clapp, Geo. H., 397, 403, 651
Clark, Daniel Kinnear, various
Clarke, Ed vf in, 740
Claudel,455
Clay, F. W., 291
Clerk, Dugald, 847
Cloud, John W., 351
Codman, J. E., 193 '
Coffey,B. H.,810
Coffin, Freeman C., 293
Coggswell, W. B., 554
Cole, Romaine C,, 329
Coleman, J. J., 470
Cooper, John HM 876, 900
Cooper, Theodore, 262, 263, 859
Cotterill and Slade, 432, 974
Cowles, Eugene H., 329, 831
Cox, A. J., 290
Cox, E. T., 629
Cox, William, 575
Coxe, Eckley B., 632
Craddock, Thomas, 478
Cramp, E. S., 405
Crimp, Santo, 564
Crocker, F. B., 1070
Cummins, Wm. Russell, W*
Daelen, R. M., 617
Dagger, John H. J., 829
Daniel, Wm., 492
D'Arcy, 563
Davenport, R. W., 690
1089
1090
LIST OF AUTHORITIES.
Deco3ur, P., 000
DeMeritens, A., 386
Denton, James E., 730, 761, 781, 932
Dinsmore, R. E., 963
Dix, Walter S., 208,
Dodge Manufacturing Co., 344
Donald, J. T., 235
Donkin, B., Jr., 491, 783
Dudley, Chas. BM 336, 383
Dudley, P. HM 401, 622
Dudley, W. D., 167
Dulong, M.,458, 476
Dunbar, J. H., 796
Durand, Prof., 56
Dwelshauvers-Dery, 663
E-gleston, Thomas, 235, 641
Emery, Chas. E., 603, 613, 820
Engelhardt, F. E., 463
Ellis and Howland, 577
English, Thos., 753
Ericsson, John, 286
Eytelwein, 564
Fairbairn, Sir Wm., 240, 264, 308, 354
Fairley, W., 531, 533
Palkenau, A.,509
Fanning,J.T.,564, 579
Favre and Silbermann, 621
Felton, C. E., 646
Fernow, B. E., 640
Field, C. J., 30, 937
Fitts, James H., 844
Flather, J. J., 961, 964
Flynn, P. JM 463, 559
Foley, Nelson, 700
Forbes, Prof., 1033
Forney, M. N., 855
Forsyth, Wm., 630
Foster, R. J., 651
Francis, J. B., 586, 739, 867
Frazer, Persifor, 624
Freeman, J. R., 581, 584
Frith, A. J., 874
Fulton, John, 637
Ganguillet & Kutter, 565
Gantt, H. L., 406
Garrison, F. L., 326, 831, 400
Garvin Machine Co., 956
Gause, F. T., 500
Gay, Paulin, 966
Gill, J. P., 657
Gilmore, E. ?., 241
G'aisher, 483
Glasgow, A. G., 654
Goodman, John, 934
Gordon, F. W., 689, 740
Gordon, 247
Goss, W. F. M., 863
Graff, Frederick, 385
Graham, W., 950
Grant, George B., 898
Grant, J. J., 960
Grashof, Dr., 284
Gray, J. McFarlane, 661
Gray, J. M., 958
Greene, D. It, 667
Greig and Eyth, 868
Grosseteste, W., 715
Gruner, L., 623
Hadfleld, R. A.,391,409
Halpin, Druitt, 789, 854
Halsey, Fred'k A., 490, 817
Harkness, Wm., 900
Harrison, W. H., 939
Hartig, J., 961
Hartman, John M., 364
Hartnell, Wilson, 348, 818, 838
Hasson, W. F. C., 1047
Hawksley, T., 485, 513, 564
Hazen, H. Allen, 494
Henderson, G. R., 347, 851
Henthorn, J. T., 965
Hering, Carl, 1045
Herschel, Clemens, 583
Hewitt, G. C., 630
Hewitt, Wm., 917
Hildenbrand, Wm., 913
Hill, John W., 17
Hiscox, G. D., 968
Hoadley, John C., 451, 688
Hobart, J. J., 962
Hodgkinson, 246
Holley. Alexander L., 377
Honey, F. R., 47, 52
Hoopes & Townsend, 210
Houston, Edwin J., 1061
Houston & Kennelly, 1058
Howard, James E., 242, 382, 385
Howden, James, 714
Howe, Henry M., 402, 407, 451, 51 fl
Howe, Malverd A., 170, 312
Howland, A. H., 292
Hudson, John G., 465
Hughes, D. E., 396
Hughes, H. W., 909
Hughes, Thos. E., 917
Humphreys, Alex. C., 652
Hunsicker, Millard, 397
Hunt, Alfred E., 235, 317, 392, 553
Hunt, Chas. V7., 340, 922
Huston, Charles, 383
Hutton, Dr., 64
Huyghens, 58
Ingersoll-Sergeant Drill Co., 503
Isherwood, Benj. F., 472
Jacobus, D. S., 511, 689, 726, 780
Johnson, J. B., 309, 314
Johnson, W. B., 475
Johnson, W. R., 290
Jones, Horace K., 887
Jones & Lamson Machine Co., 954
Jones & Laughlins, 867, 885
Keep, W. J., 365, 951
Kennedy, A. B. W., 355, 525, 764
Kernot, Prof. 494
Kerr, Walter C., 781
Kiersted, W., 292
Kimball, J. P., 498, 682, 637
KJnealy,J.H.,587
LIST OF AUTHORITIES.
1091
Kirk, A. C., 706
Kirk, Dr., 1004
Kirkaldy, David, 296
Kopp, H. G. C., 472
Kuichling, E., 578
Kutter, 559
Landreth, O. H.,712
Langley, J. W., 409, 410, 412
Lanza, Gaetano, 310, 369, 864, 977
La Rue, Benj. F., 248
Leavitt, E. D., 788
LeChatelier, M.,452
Le Conte, J., 565
Ledoux. M., 981
Leonard, H. Ward, 1027
Leonard, S. H., 686
Lewis, Fred. H., 186, 189, 379
Lewis, I. N., 498
Lewis, Wilfred, 352, 362, 378, 890
Linde, G., 989
Lindenthal, Gustav, 385
Lloyd's Register, 264, 266, 700
Loss, H. V., 306
Love, E. G., 656
Lovett, T. D., 256
Lyne, Lewis F., 718
McBride, James, 974
MacCord, C. W., 898
Macdonald, W. R., 956
Macgovern, E. E., 545
Mackay, W. M., 542, 544
Mahler, M., 633
Main, Chas. T., 590, 780, 790
Mannesmann, L., 332
Manning, Chas. H., 675, 823
Marks, Win. D., 793, 811
Master Car Builders' Assoc., 878
Mattes, W. F., 399
Matthiessen, 1029
Mayer, Alfred M., 468
Mehrtens, G. G., 895, 405
Meier, E. D., 688
Meissner, C. A., 370
Melville. Geo. W., 674
Mendenhall, T.C.,23
Merriman, Mansfield, 241, 260, 282
Metcalf, William, »40, 412
Meyer, J. G. A., 795, 856
Meystre, F. J., 472
Miller, Metcalf & Parkin, 412
Miller, T. Spencer, 344, 927
Mitchell, A. E., 855, 856
Molesworth, Sir G. L., 562, 658
Molyneux and Wood, 736
Moore, Gideon E., 653
Morin, 435, 930, 933
Morison, Geo. S., 381, 393
Morrell, T. T., 407
Morris, Tasker & Co., 196, 196
Mumford, E. R., 1005
Murgue, Daniel, 521
Wagle, A. P., 292, 606, 878
Napier, 474, 669
Nason Mfg. Co., 478, 542
National Pipe Bending Co., 198
Nau, J. B., 367, 409
Newberry, J. S., 624
Newcomb, Simon, 432
New Jersey Steel & Iron Co., 253, 810
Newton, Sir Isaac, 475
Nichol, B. C., 473
Nichols, 285
Norris, R. Van A., 521
Norwalk Iron Works Co., 488, 504
Nystrom, John W., 265
Ordway, Prof., 470
Paret, T. Dunkin, 967
Parker, W., 354
Parsons, H. de B., 361
Passburg, Emil, 466
Pattinson, John, 629
Peclet, M., 471, 478, 731
Pelton Water Wheel Co., 191, 574, 583
Pence, W. D., 294
Pencoyd Iron Works, 179, 232, 868
Pennell, Arthur, 555
Pennsylvania R. R. Co., 307, 375, 899
Philadelphia Engineering Works. 526
Philbrick, P. H., 446
Phillips, W. B., 629
Phoenix Bridge Co., 263
Phoenix Iron Co., 181, 257
Pierce, C. S., 424
Pierce, H. M., 641
Pittsburg Testing Laboratory, 248
Platt, John, 617
Pocock, F. A., 505
Porter, Chas. T., 662, 787, 820
Potter, E. C., 646
Pottsville Iron & Steel Co., 250
Pouillet, 455
Pourcel, Alexandre, 404
Poupardin, M., 687
Powell, A. M., 975
Pratt & Whitney Co., 892, 908
Price, C. S., 638
Prony. 564
Pryibil, P., 977
Quereau, 0. H., 853, 862
Ramsey, Erskine, 638
Rand Drill Co., 490, 505
Randolph & Clowes, 198
Rankine, W. J. M., various
Ransome, Ernest L., 241
Raymond, R. W., 631, 650
Reese, Jacob, 966
Regnault, M., various
Reichhelm, E. P., 651
Rennie, John, 928
Reuleaux, various
Richards, Frank, 488, 491, 499
Richards, John, 965, 976
Richards, Windsor, 404
Riedler, Prof., 507
Rites, F. M., 783, 818
Roberts-Austen, Prof.* 451
Robinson, S. W., 583
Rockwood, G. L, 781
John A. Roebling's Sons' Co., 214, 921
1092
LIST OF AUTHORITIES.
Roelker, C. R., 265
Roney, W. R., 711
Roots, P. H. & F. M.,526
Rose, Joshua, 414, 869, 970
Rothwell, R. P., 637
Rowland, Prof., 456
Royce, Fred. P., 1043
Rudiger, E. A., 671
Russell, S. Bent, 567
Rust and Coolidge, 290
Sabin, A. H., 387
Sadler, S. P.. 639
Saint Yenant, 282
Salom, P. G., 406, 1056
Sandberg, C. P., 384
Saundera, J. L., 544
Saunders, W. L., 505
Scheffler, I. A., 681
Schroter, Prof., 788
Schutte, L.,&Co., 527
Seaton, various
Sellers, Coleman, 890, 953. 975
Sellers, Wm., 204
Sharpless, S. P., 311, 639
Shelton, F. H., 653
Shock, W. H., 307
Simpson, 56
Sinclair, Angus, 863
Sloane, T. O'Connor, 1027
Smeaton, Wm., 493
Smith, Chas. A., 537, 874
Smith, C. Shaler, 256, 865
Smith, Hamilton, Jr., 556
Smith, Jesse M., 1050
Smith, J. Bucknall, 225, 303
Smith, Oberlin, 865, 973
Smith, R. H., 962
Smith, Scott A., 874
Snell, Henry L, 514
Stahl, Albert W., 599
Stanwood, J. B,, 802, 809, 813, 818
Stead, J. E., 409
Stearns, Albert, 465
Stein and Schwarz, 410
Stephens, B. F., 292
Stillman, Thos. BM 944
Stockalper, E., 490
Stromeyer,C. E., 395
Struthers, Joseph, 451
Sturtevant, B. F., Co., 487, 578
Stut, J. C. H., 844
Styffe, Knut, 383
Suplee, H. H., 769, 772
Suter, Geo. A., 524
Sweet, John E., 826
Tabor, Harris, 751
Tatham & Bros., 201
Taylor, Fred. W., 880
Taylor, W. J., 646
Theiss, Emil, 818
Thomas, J. W., 369
Thompson, Silvanus P., 1064, 1066
Thomson, Elihu, 1052
Thomson, Sir Wm., 461, 1039
Thurston, R. H., various
Tilghman, B. F., 966
Tompkins,C.R.,388
Torrance, H. C., 401
Torrey, Joseph, 582, 820
Tower, Beauchamp, 931, 934
Towne, Henry R., 876, 907, 911
Townsend, David, 973
Trautwine, J. C., 59, 118, 311, 482
Trautwine, J. C., Jr., 255
Trenton Iron Co., 216, 223, 230, 915
Tribe, James, 765
Trotz, E , 453
Trowbridge, John, 467
Trowbridge, W. P., 478, 513, 733
Tuit, J. E., 616
Tweddell, R. H., 619
Tyler, A. H., 940
Uchatius, Gen'l, 321
Unwin, W. Cawthorne, various
Urquhart, Thos., 645
U.S. Testing Board, 308
Vacuum Oil Co., 943
Vair, G. O., 950
Violette, M , 640, 642
Vladomiroff, L., 316
Wade, Major, 321, 374
Wailes, J. W., 404
Walker Mfg. Co., 905
Wallis, Philip, 858
Warren Foundry & Mach. Co., 18P
Weaver, W. D., 1043
Webber, Samuel, 591, 963
Webber, W. O., 608
Webster, W. R., 389
Weidemann & Franz, 469
Weightman, W. H., 762
Weisbach, Dr. Julius, various
Wellington, A. M., 290, 928, 935
West, Chas. D., 916
West, Thomas D., 328
Westinghouse & Galton, 928
Westinghouse El. & Mfg. Co., 1048
Weston, Edward, 1029
Whitham, Jay M., 472, 769, 792, 84t
Whitney, A. J., 389
Willett, J. R., 538, 540
Williamson, Prof., 58
Wilson, Robert, 284
Wheeler, H. A., 908
White, Chas. F., 714
White, Maunsel, 408
Wohler, 238, 240
Wolcott, F. P., 949
Wolff, Alfred R , 494, 517, 528, 5X
Wood, De Volson, various.
Wood, H. A., 9
Wood, M. P., 386, 389
Woodbury, C. J. H., 537, 931
Wootten, J. E., 855
Wright, C. R. Alder, 331
Wright, A.W.,289
Yarrow, A. F., 710
Yarrow & Co., 307
Yates, J. A., 287
Zahner, Robert, 498
Zeuner,827
INDEX.
abb-alt
Abbreviations, 1
Abscissas, 69
Abrasion of manganese steel, 407
Abrasive processes, 965-967
Absolute temperature, 461
zero, 461
Absorption of gases, 480
of water by brick, 312
refrige rating-machines, 984
Accelerated motion, 427
Acceleration, definition of, 423
force of, 427
work of, 430
Accumulators, electric, 1045-1048
Adiabatic compression of air, 499
curve, 742
expansion of air, 501
expansion in compressed air-
engines, 501a
expansion of steam, 742
Adiabatically compressed air, mean
effective pressures, table, 50 Ib
Admiralty metal, composition of,
325
Admittance of alternating cur-
rents, 1063
Aiken intensifier, 619
Air, 481-527
and vapor mixture, weight of,
,484.
binds in pipes, 579
carbonic acid allowable in, 529
'•> compressed, 498-511 (see Com-
pressed air)
compressors, effect of intake
temperatures, 506
compressors, high altitude, table
of, 503
compressors, tables, 503-505
cooling of, 531
density and pressure, 481, 482
flow of, in pipes, 485, 489
flow of, in ventilating ducts, 530
flow of through orifices, 484, 518
friction of, in underground pas-
sages, 531
head of, due to temperature dif-
ferences, 533
heating of, by compression, 498
horse-power required to com-
press, 501
loss of pressure of in pipes, 487 ;
tables, 488-490
manometer, 481
properties of, 481
pump for condenser, 841
Air, specific heat of, 458, 484
lift pump, 614
pyrometer, 453
thermometer, 454
velocity of, in pipes, by anemom-
eter, 491
volumes, densities, and pressures
(table), 481
volume transmitted in pipes, 864
weight of, 165, 481; table, 484
Alcohol, compressibility of, 164
Alden absorption dynamometer,
979
Algebra, 33-36
Algebraic symbols, 1
Alligation, 10
Alloys, 319-338
aluminum, 328
aluminum, tests of, 330
aluminum-antimony, 331
aluminum -copper, 329
aluminum -copper-tin, 330
aluminum -silicon-iron, 330
aluminum -tin, 330
aluminum -tungsten, 330
aluminum -zinc, 330
antimony, 336
bearing metal, 333
bismuth, 332
caution as to strength of, 329
composition of, in brass foundries,
325
composition by mixture and by
analysis, 323
copper-manganese, 331
copper-tin, 319, 320 N
copper-tin-lead, 326
copper-tin-zinc, 322, 325
copper-zinc, 321
copper-zine-iron, 326
fusible, 333
Japanese, 326
liquation of metals in, 323
nickel, 332
variation in strength of, 323
white metal, 3,36
"Alloy" steels, 407-410
Alternating currents, 1061-1078
admittance, 1063
average, maximum, and effective,
values, 1061 m
calculation of circuits, 1072
capacity, 1062
capacity of conductors, 1067
converters, 1071
delta connection, 1069
1093
1094
alt-bai
INDEX.
Alternating currents, frequency,
1061
generators for, 1070
impedance, 1063
impedance polygons, 1064-1066
inductance, 1062
induction motor, 1072, 1077
measurement of power in poly-
phase circuits, 1069
Ohm's law applied to, 1064
power factor, 1062
reactance, 1063
single and polyphase, 1068
skin effect, 1063
synchronous motors, 1071, 1076
transformers, 1070
Y connection, 1069
Altitude by barometer, 483
Aluminum, 167, 317
alloys, 319, 328 (see Alloys)
alloys, tests of, 330
brass, 329
bronze, 328
bronze wire, 225
electrical conductivity of 1028
solder. 319
steel, 409
strength of. 318
wire, 225
American base-box system, 182
Ammonia-absorption refrigerating-
machine, 984, 987 ; test of, 997
Ammonia-compression refrigerat ing-
machines, 983, 986; test of,
999
Ammonia gas. properties of, 992
Ammonia liquid, density of, 992
specific heat of, 992
Ampere, 1024
Analyses, asbestos, 235
of boiler scale, 552
of boiler water, 553, 554
of cast iron, 371-374
of coals, 624-632
of coal, sampling for, 632
crucible steel, 411
fire-clay, 234
gas, 651
gases of combustion, 622
magnesite, 235
Analytical geometry. 69-71
Anchor forgings, strength of, 297
Anemometer, 491
Angle, economical, of framed struc-
tures. 447
of repose of building material.
929
Angles, Carnegie bulb, properties
of, table, 278
Carnegie steel, properties of,
table. 27 9a
Pencoyd steel, weights and sizes,
.179
trigonometrical properties of, 66
plotting without protractor, 52
problems in, 37, 38
Angular velocity, 425
Animal power 433-435
Annealing, effect on conductivity,
1029
effect on steel, 392, 412
influence of on magnetic capac-
ity of steel, 396
non-oxidizing process of, 389
of steel, 394, 413
of steel forgings, 396
of structural steel, 394
Annuities, 15-17
Annular gearing, 898
Anthracite, classification of, 624
composition of, 624
sizes of, 632
space occupied by, 625
Anthracite-gas, 647
Anti-friction curve, 50, 939
metals, 932
Antimony, properties of, 167
in alloys, 331, 336
Apothecaries' measure and weight,
18, 19
Arc, circular, 57
circular, Huyghen's approxima-
tion of length of, 58; table, 114
circular, relations of. 58
Arc-lights, electric, 1041
Arches, corrugated 181
flooring, 281
tie-rods for, 281
Area of circles 1-1000, table, 103-
107
of circles A-lOO, table advanc-
ing by i. 108-112
of geometrical solids, 61-63
of geometrical plane figures,
54-60
of irregular figures, 55, 56
of sphere, 61
of sphere, table, 118
Arithmetic, 2-32
Arithmetical progression, 11
Armature-circuit, e.m.f. of, 1056
Armature torque of, 1056
Asbestos, 235
Asphalt um coating for iron, 387
Asses, work of, 435
Asymptotes of hyperbola, 71
Atmosphere, equivalent pressures
of, 27
pressure of , 481 . 482
moisture in 483
Atomic weights (table) 163
Authorities, list of, 1089
Avogadro's law of gases, 479
Avoirdupois weight, 19
Axles, railroad, effect of cold 384
steel, specifications for, 397
steel, strength of, 299
Automatic cut-off engines 753
Babbitt metal. 336, 337
Babcock & Wilcox boilers, testa
with various coals, 636
Bagasse as fuel, 643
Balances, to weigh on incorrect, 19,
Ball-bearings 940
Balls, hollow copper, 289
IHDEX.
baii-boi
1095
Bands and belts, theory of , 876
for carrying grain, 912d
Bars, eye, tests of, 304
iron, flat, commercial sizes of,
table, 170
iron, various shapes, commer-
cial sizes of, 171
Lowmoor iron, strength of, 297
steel, effect of nicking, 402
twisted iron, tensile strength of,
241
twisted , Cilmore's experiments on ,
242
various, weights of, 169
wrought iron, compression tests
of, 304
wrought iron, weight of, table, 171
Barometer, leveling with, 482
to find altitude by, 483
Barometric readings for various
altitudes, 482
Barrels, to find volume of, 64
number of, in tanks, 126
Basic Bessemer steel, strength of,
390
Batteries, storage, 1045-1048
Baume's hydrometer, 165
Bazin's experiments on weirs, 587
formulae, flow of water, 563
Beams, deck, properties of Carne-
gie, table, 278
formulae for flexure of, 267
formulae for transverse strength
of, 268
special, coefficients for loads on,
270
steel, formulae for safe loads on,
269
variously loaded, 271
yellow pine, safe loads on, 1023,
1079
Beardslee's tests on elevation of
elastic limit, 238
Bearings, allowable pressure on,
935-937
ball, 940
cast-iron, 933
for steam turbines, 941
high speed, 941
oil pressure in, 937
overheating of, 938
pivot, 939
roller, 940
steam-engine, 811-813
Bearing-metal alloys, 333
Bearing-metals, anti-friction, 932
composition of, 326
Bearing pressure on rivets, 355
Bed-plates of steam-engines, 817
Bell -metal, composition of, 325
Belt conveyors, 912d
dressings. 887
Belts, arrangement of, 885
care of, 886
cement for leather or cloth, 887
centrifugal tension of, 876
endless, 886
evil of tight , 885
Belts, lacing of, 883
length of, 884
open and crossed, 874, 884
quarter twist, 883
sag of, 885
Belting, 876-887
formulae, 877
friction of, 876
horse-power of, 877-880
notes on , 882
practice, 877
rubber, 887
strength of, 302, 886
tables, 877,878
Taylor's rules, 880-882
theory of, 876
width for given H.P., 879
Bending curvature of wire rope,
921
Bends, effects of on flow of water
in pipes, 578
in pipes, 488, 672; table, 199
Bent lever, 436
Bessemer converter, temperature
determinations in, 452
steel (see Steel, Bessemer)
Bessemerized cast iron, 375
Bevel wheels, 898
Billets, steel, specifications for, 401
Bins, coal-storage, 912a
Binomial, any power of, 33
theorem, 36
Birmingham gauge, 28
Bismuth, properties of, 167
alloys, 332
Bituminous coal (see Coals)
Blast-furnaces, consumption of
charcoal in, 641
steam-boilers for, 689
temperature determinations in,
452
Blocks or pulleys, 438
efficiency of, table, 907
strength of, 906
Blooms, steel, weight of, table,
176
Blow, force of, 430
Blowers, 511-526
and fans, comparative efficiency,
516
blast -pipe diameters for, 520
capacity of, 517, 1081
experiments with, 514
for cupolas, 519, 950
pressure, 950
rotary, table of, 526
steam -jet, 527
velocity due to pressure, 514
Blowing-engines, dimensions of,
526
Blue heat, effect oA steel, 395
Board measure, 20
Bodies, falling, laws of, 424
Boiler compounds, 717
explosions, 720
feed-pumps, 605, 726
furnaces, height of, 711
furnaces, use of steam in, 650
1096
boi-cal
INDEX.
Boiler heads, 706
heads, strength of, 284, 286
heads, wrought-iron, 285
heating-surface for steam heat-
ing, 538
scale, analyses of, 552
tubes, area of, table, 197
tubes, dimensions of, table, 196
tubes, expanded, holding power
of, 307
Boilers, horse-power, 677
for steam heating, 538
incrustation of, 550
locornotive, 855
marine, 1015
plate, strength of, at high tem-
peratures, 383
steam, 677-731 (see Steam-boiler)
Boiling, resistance to, 463
Boiling-point of water, 550
Boiling-points of substances, 455
Bolts and nuts, 209, 211
.-•effect of initial strain in, 292
holding power of in white pine,
290, 291
square-head, table of weights of,
210
strength of, table, 292
taper, 972
track, weight of, 210
variation in size of iron for, 206
Bomb calorimeter, 634
Braces, diagonal, with tie, stresses
in, 442
Brackets, cast-iron, strength of,
252
Brake, Prony, 978
Brass, composition of rolled, 203
alloys, 325
plates and bars, weight of, table,
202, 203
tube, seamless, table, 198-200
wire, weight of, table, 202
Brazing of aluminum bronze, 328
metal, composition of. 325
solder, composition of, 325
Brick, absorption of water by,
312
for floors. 281
kiln, temperatures in, 452
specific gravity of, 165
strength of, 302, 312
weight of, 165, 312
Bricks, fire, number required for
various circles, table, 234
fire, sizes and shapes of, 233
Bricks magnesia, 235
Brickwork, measure of, 169
weight of, 169
Bridge iron, durability of, 385
links, steel, strength of, 298
members, strains in, 262-264
Memphis, proportions of mate-
rial. 381
Memphis, tests of steel in. 393
trusses, 442
Brine, boiling of, 463
properties of, 464, 994
Briquettes, coal, 632
British thermal unit (B.T.U.), 455,
660
Britannia metal, composition of,
336
Bronze, aluminum, strength of
328
ancient, composition of, 323
deoxidized, composition of, 327
Gurley's, composition of, 325
manganese. 331
phosphor, 327
strength of, 300, 319, 321
Tobin, 325, 326
Buck-shot, sizes and weights of
204
Buildings, construction of, 1019-
1023
fire-proof. 1020
heating and ventilation of. 534
transmission of heat through
walls of, 478
walls of, 1019
Building-laws, New York City,
1019-1021
on columns, New York, 252.
1019
on columns, Boston, 252
on columns, Chicago 252, 255
on structural materials, Chicago,
. 3?1
Building-materials, angle of repose
of, 929
coefficients of friction of, 929
sizes and weights. 169, 184
Bulb angles, properties of Carne-
gie steel, table, 278
Bulkheads, plating and framing for,
table, 287
Buoyancy, 550
Burr truss, stresses in, 443
Bushel of coal, 638
of coke, 638
Bush-metal, composition of, 325
Butt-joints, riveted, 358
Cables, chain, wrought-iron, 308,
340
flexible steel wire, 223
sizes, weight, and strength, 230
338
lead-incased power, sizes and
weights, 222
suspension -bridge. 230
Cable-ways, suspension. 915
Cadmium, properties of, 167
Calculus, 72-79
Calcium chloride in refrigerating-
machines. 994
Caloric engines, 851
Calorie, definition of, 455
Calorimeter for coal, Mahler bomb,
634
steam, 7 28-7 31
steam, coil, 729
steam, separating, 730
steam, throttling 729
Calorimewic tests of coal, 636
INDEX.
cam-chi
1097
Cam, 438
Canals, irrigation, 564
speed of vessels on, 1008
Candle-power of electric lights, 1042
of gas lights, 654
Canvas, strength of, 302
Cap-screws, table of standard, 208
Capacity, electrical, 1062
electrical, of conductors, 1067
Car-heating by steam , 538
Car-journals, friction of, 937
Cars, steel plate for, 401
Car-wheels, cast iron for, 375
Carbon, burning out of steel, 402
effect of, on strength of steel, 389
gas, 646
Carbonic acid allowable in air, 529
Carnegie steel sections, properties
of, 272T280
steel sections, weights and sizes,
177, 178 t
Carriages, resistance of, on roads,
435
Carriers, bucket, 912a
Casks, volume of, 64
Cast copper, strength of, 300, 319
Cast iron, 365-376
analyses of, 371-374
bad, 375
bearings, 933
Bessemerized, 375
chemistry of, 370-374
columns, eccentric loading of, 254
columns, strength of, 250-253
columns, tests of, 250, 251
columns, weight of, table, 185
compressive strength of, 245
corrosion of, 386
durability of, 385
influence of phosphorus, sulphur,
etc., 365-368, 370
malleable, 375
mixture of, with steel, 375
pipe, 185-190 (see Pipe, cast-
iron)
pipe-fittings, sizes and weights, 187
relation of chemical composition
to fracture, 370
shrinkage of, 368
specific gravity of, 374
specifications for, 374
strength of, 296, 370-374
strength in relation to silicon
and cross-section, 369
tests of, 369
variation of density and tenac-
ity, 374
Castings, iron, analyses of, 373
iron, strength of, 297
malleable, rules for use of, 376
shrinkage of , 951
steel, 405
steel, specifications for, 397, 406
steel, strength of, 299
weight of, from pattern, 952
Catenary, to plot, 51, 52
Cement as a preservative coating,
387
Cement for leather belts, 887
mortar, strength of, 313
Portland, strength of, 302
specific gravity of, 166
weight of, 166, 170
Center of gravity, 418
of gravity of regular figures, 419 ]
of gyration, 420
of oscillation, 421
of percussion, 422
Centigrade thermometer scale, 448
-Fahrenheit conversion table, 449
Centrifugal discharge elevators, 912a
fans (see Fans, centrifugal)
force, 423
force hi fly-wheels, 820
pumps, 607-609 (see Pumps,
centrifugal)
tension of belts, 876
C.G.S. system of measurement, 1024
Chains, crane, sizes, weights, and
properties, 232
link-belting, 9126
monobar, 9126
pin,912c
roller, 912c
specifications for, 307
strength of, table, 307, 339
tests of, table, 307
Chain-blocks, efficiency of, 907
Chain-cables, proving tests of, 308
weight and strength of, 340
Chalk, strength of , 312
Change gears for lathes, 955, 956
Channels, Carnegie steel, properties
of, table, 277
open, velocity of water in, 564
strength of, 297
weights and sizes, 178-180
Charcoal, 640-642
absorption of gases and water by,
641
bushel of, 170
composition of, 642
consumption of, in blast-fur-
naces, 641
pig iron, 365, 374
results of different methods of
making, 641
weight per cubic foot, 170
Chemical elements, table, 163
symbols, 163
Chemistry of foundry irons, 370-374
Chezy's formula for flow of water, 558
Chimneys, 731-741
draught, power of, 733
draught, theory, 731
effect of flues on draught, 734,
for ventilating, 533
height of , 734
height of water column due to
unbalanced pressure in, 732
lightning protection of, 736
rate of combustion due to, 732
sheet -iron, 741
size of , 734
size of, table, 735
stability of , 738
1098
chi-col
IXDEX.
Chimneys, steel, 740
steel, foundations for, 741
tall brick, 737
velocity of air in, 733
weak, 739
Chord of circle, 58
Chords of trusses, strains in, 445
Chrome steel, 409
Circle, 57-59
area of, 57
area of, 1-1000, table, 103-107
area of, ^-100, advancing by £,
table, 108-112
equations of, 70
length of arc of, 57
length of arc of, Huyghen's ap-
proximation, 58
length of chord of, 58
problems, 39, 40
properties of, 57
relations of arc, chord, etc., of, 58
relations of, to equal, inscribed,
and circumscribed square, 59
sectors and segments of, 59
Circuits, electric, e.m.f. in, 1030
electric, polyphase, 1068 (see
Alternating currents)
electric, power of, 1031
Circuit, magnetic, 1051
Circular arcs, lengths of, 57
arcs, lengths of, tables, 114, 115
functions, calculus, 78
inch, 18
measure, 20
mil, 18
mil wire gauge, 30
mil wire gauge, table, 29
pitch, 888
ring, 59
segments, table of areas of, 116
Circumferences of circles, 1-1000,
table, 103-107
of circles, ^-100, table, advanc-
ing by i, 108-112
of circles, 1 inch to 33 feet, table,
113
Cisterns, capacities of, 121, 126
Classification of iron and steel, 364
Clay, cubic feet per ton, 170
fire, analysis of Mt. Savage, 233
Clearance in steam-engines, 751,792
Coal, analyses of, 624-632
anthracite, sizes of, 632
bituminous, classification of, 623
calorimeteric tests of, 636
classification of, 623-624
conveyors, 912a
cost of, for steam power, 789
DuLong's formula for heating,
value of, 633
evaporative power of, 636
foreign, analysis of , 631
furnaces for different, 635
heating value of, 633, 634
handling machinery, 912-912d
hoisting by rope, 343
products of distillation of, 639, 651
relative value of, 633-637
Coal, sampling of, for analysis, 632
semi-bituminous, composition of,
625, 626
space occupied by anthracite, 625
storage bins, 912a
vs. oil as fuel, 646
washing, 638
weathering ol, 637
weight of, 170, 638
"Welsh, analysis of, 632
Coal-gas, composition of, 652
manufacture of, 651
Coatings, preservative, 387-389
rustless, for iron and steel, 388
Coefficients of expansion, 460
of expansion of iron and steel, 385
Coefficient of elasticity, 237, 314
of fineness, 1002
of friction, definition, 928
of friction, tables, 929, 930
of friction of journals, 930, 932
of friction, rolling, 929
of performance of ships, 1003
of propellers, 1011
of transverse strength, 267
of water lines, 1002
for loads on special beams, 270
Coils, electric, heating of, 1032
Coil pipe, table, 199
Coke, analyses of, 637
making of hard, 638
ovens, generation of steam from
waste heat of, 638
by-products of manufacture, 638-
639
weight of. 170, 638
Coking, experiments in, 637
Cold -chisels, form of, 955
Cold, effect of, on railroad axles, 384
effect of, on strength of iron and
steel, 383
drawing, effect of, on steel, 305
drawn steel, tests of, 305
rolled steel, tests of, 305
rolling, effect of, on steel, 393
saw, 966
Collapse of corrugated furnaces, 266
resistance of hollow cylinders to,
264-266
Color determination of tempera-
ture, 454
scale for steel tempering, 414
Columns, built, 256
cast-iron, strength of, 250
cast-iron, tests of, 250, 251
cast-iron, weight of, table, 185
eccentric, loading of, 254
Gordon's formula for, 247
Hodgkinson's formula for, 246
maximum permissible stress in,
255
Merriman's formulae for, 260
mill, 1022
Phoenix, dimensions of, 257-259
steel, Merriman's tables for, 261
strength of, 246, 247
strength of, by New York build-
ing laws, 1019
IKDEX.
col-con
1099
Columns, wrought -iron, built, 257
wrought -iron, Merriman's table
of, 260
wrought -iron, tests of, 305
wrought -iron, ultimate strength
of, table, 255
Combination, 10
Combined stresses, 282, 283
Combustion, analyses of gases of, 622
heat of, 456, 621
of fuels, 621
of gases, rise of temperature in, 623
rate of, due to chimneys, 732
theory of, 620
Composition of forces, 415
Compound engines, 761-768 (see
Steam-engines, compound)
interest, 14
locomotives, 862, 863
numbers, 5
proportion, 6
shapes, steel, 248
units of weights and measures, 27
Compressed-air, 488, 498-511
adiabatic and isothermal com-
pression, 499
adiabatic expansion and com-
pression, tables, 502
compound compression, 5016
cranes, 912
diagrams, 5016
drills driven by, 506
engines, adiabatic expansion in,
501a
engines, efficiency, 506
for motors, effect of heating, 507
flow of, in pipes, 489
formula?, 501
heating of, 498
hoisting engines, 5056
horse-power required to compress
air, 500
losses due to heating, 500
loss of energy in, 498
machines, air required to run,
505a
mean effective pressures of
adiabatically compressed air,
table, 5016
mean effective pressures, com-
pound compression, table,
5016
mean effective pressures, tables,
502, 503
mine pumps, 511
motors, 507
Popp system, 507
practical applications of, 5056
pumping with, 505a
reheating of, 506
shop operation by, 509
tramways, 510. 511
transmission , 488
transmission, efficiencies of, 508
volumes, mean pressures per
stroke, etc., table, 499
work of adiabatic compression,
601
Compressed steel, 410
Compression, adiabatic, formulae
for, 501
adiabatic, tables, 502
and flexure combined, 282
and shear combined , 282
and torsion combined, 283
in steam-engines, 751
members in structures, unit
strains in, 380
Compressive strength, 244-246
strengths of woods, 311
strength of iron bars, 304
tests, specimens for, 245
Compressors, air, 503-505
air, effect of intake temperature,
506
Condensers, 839-846
air-pump for, 841
circulating pump for, 843
continuous use of cooling water
in, 844
cooling towers for, 844
cooling water required, 841
ejector, 840
evaporative surface, 844
increase of power due to, 846
jet, 839
surface, 840
tubes and tube plates of, 840.
841
tubes, heat transmission in, 472
Conduction of heat, 468
of heat, external, 469
of heat, internal, 468
Conductivity, electric, of steel, 403
electrical, of metals, 1028
Conductors, electrical, heating of,
1031
electrical, in series or parallel,
resistance of, 1030
Conduit, water, efficiency of, 589
Cone, measures of, 61
pulleys, 874
Conic sections, 71
Connecting-rods, steam -engine, 799,
800
tapered, 801
Conoid, parabolic, 63
Conservation of energy, 432
Construction of buildings, 1019-
1023
Convection, loss of heat due to, 476
of heat, 469
of heat, Dulong's law of, table
of factors for, 477
Conversion table, Centigrade-Fah-
renheit, 449
tables, metric, 23-26
Converter, Bessemer, temperature
determinations in, 452
Converters, electric, 1071
Conveying of coal in mines, 913, 914
Conveyors, belt, 912d
cable-hoist, 915
coal, 912a
horse -power required for, 912c
screw,
1100
coo-cyl
INDEX.
Cooling of air for ventilation, 531
towers for condensers, 844
Co-ordinate axes, 69
Copper, 167
ball pyrometer, 451
cast, strength of, 300, 319
drawn, strength of, 300
balls, hollow, 289
manganese alloys, 331
nickel alloy, 332
plates, strength of, 300
plates, weight pf, table, 202
round bolt, weight of, table, 203
strength of, at high temperatures,
309
tin alloys, 320
tin alloys, properties and compo-
sition of, 319
tin-aluminum alloys, 330
tin-zinc alloys, properties and
composition, 322, 323
tubing, weight of, table, 200
weight required in different sys-
tems of transmission, 1075
wire, table of dimensions, weight,
and resistance of 202, 218-
.220, 1034
wire, cost of, for long-distance
transmission, 1036, 1040
zinc alloys, strength of, 323
zinc alloys, table of composition
f and properties, 321
zinc-iron alloys, 326
Cordage, technical terms relating
to, 341
weight of, table, 906
Cork, properties of, 316
Corn, weight of, 170
Corrosion of iron, 386
of steam-boilers, 386, 552, 716-
721
Corrosive agents in atmosphere 386
Corrugated arches, 181
furnaces, 266, 702, 709
iron, sizes and weights, 181
plates, properties of Carnegie
steel, table, 274
Cosecant of an angle, 65; table, 159-
162
Cosine of an angle, 65; table, 159-
162
Cost of coal for steam-power, 789
of steam-power, 790
Cotangent of an angle, 65; table,
159-162
Cotton ropes, strength of, 301
Couloumb, 1024
Counterbalancing of hoisting-en-
gines, 909
of locomotives, 864
of steam-engines, 788
Counterpoise ~ system of hoisting,
910
Couples, 418
Coverings for steam-pipe, tests of,
470, 471
Coversine of angles, table, 159-
162
Cox's formula for loss of head
575
Crane chains, 232
Cranes, 911
classification of, 911
compressed air, 912
electric, 912
jib, 912
stresses in, 440
travelling, 912
guyed, stresses in, 441
simple, stresses in, 440
Cranks, steam-engine, 805
Crank angles, steam-engine, table,
830
pins, steam-engine, 801-804
pins, steel, specifications for, 401
shafts, steam-engine, 813-815
shaft, steam-engine, torsion and
flexure of, 814
Cross-head guides, 798
pin, 804
Crucible steel, 410-414 (see Steel,
crucible)
Crushing strength of masonry mate-
rials, 312
Cubature, 75
Cubes of numbers, table, 86-101
of decimals, table, 101
Cube root, 8
roots, table of. 86-101
Cubic feet per gallon, table, 122
measure, 18
Cupola practice, 946-950
result of increased driving, 949
Cupolas, blast-pipes in, 520
blast-pressure in, 948
blowers for, 519, 950
charges for, 946-947
charges in stove foundries, 949
dimensions of, 947
loss in melting iron in, 950
slag in, 948
Currents, electric (see Electric cur-
rents)
Current motors, 589
Cutting speeds of machine tools,
953; table, 954
stone with wire, 966
Cycloid, construction of, 49
differential equations of, 79
differential measure of, 60
integration of , 79
Cycloidal gear-teeth, 892
Cylinder condensation in steam-
engines, 752, 753
Cylinder, measures of , 61
Cylinders, hollow, limit of thickness,
288
hollow, resistance of, to collapse,
264-266
hollow, under tension, 287, 289
hydraulic, thickness of, 617
hydraulic press, thickness of,
288
locomotive, 854
steam-engine (see Steam-engines)
table of capacities of, 120
INDEX.
cyl-ela
1101
Cylindrical ring, 62
Cylindrical tanks, capacities of, table,
121
Dalton's law of gaseous pressures,
480
Dam, stability of, 417
D'Arcy's formula, flow of water,
563
formula, table from, of flow of
water in pipes, 569-572
Decimals, 3
squares and cubes of, 101
Decimal equivalents of fractions, 3
equivalents of feet and inches,
112
gauge, 32
Deck -beams, weights and sizes,
177
properties of Carnegie steel, 278
Delta connection for alternating
currents, 1069
metal, 225, 326
Denoniinate numbers, 5
Deoxidized bronze, 327
Derrick, stresses in, 441
Diagonals, formulae for strains in,
444
Diametral pitch, 888
Differential gearing, 898
calculus, 72-79
of algebraic function, 72
of exponential function, 77
partial, 73
coefficient, 73 ; sign of , 76
second, third, etc., 75
pulley, 439
screw, 439; efficiency of, 974
windlass, 439
Differentiation, formulae for, 73
Discount, 13
Disk fans (see Fans, disk)
Displacement of ships, 1001, 1008
Distillation of coal, 639
Distiller for marine work, 847
Domes on steam-boilers, 711
Draught power of chimneys, 732
theory of chimneys, 731
Drawing-press, blanks for, 973
Dredge, centrifugal pump as a,
609
Dressings, belt, 887
Drift bolts, resistance of, in timber,
290
Drill gauge, table, 29
press, horse-power required by,
963
Drills, rock, air required for, 505a
rock, requirements of air-driven,
506
twist, speed of, 957
tap, 970, 971 ; sizes of, 208
Prilling holes, speed of, 956
machines, electric, 956
Drop in electric circuits, 1029-1031
press, pressures attainable by,
973
Drums for hoisting-ropes, 917
Dry measure, 18
Drying and evaporation, 462-467
in a vacuum, 466
Ducts, cold-air, for steam -heating,
539
Ductility of metals, table, 169
Dulong's formula for heating value
of coal, 633
law of convection, table of factors
for, 477
law of radiation, table of factors
for, 476
Durability of iron, 385, 386
Durand's rule for areas, 56
Dust explosions, 642
fuel, 642
Duty, measure of, 27
of pumping-engine, 610
trials of pumping-engines, 609-
612
Dynamo-electric machines, 1055-
1060
machines, classification of, 1055
machines, design of, 1058-
1060
machines, e.m.f. of armature cir-
cuit, 1056
machines, moving force of,
1055
machines, strength of field,
1057
machines, torque of armature,
1056
machines, types of, 1055
machines, tables of, 1074-1077
Dynamometers, 978-980
Alden absorption, 979
Prony brake, 978
traction, 978
transmission, 980
Dyne, definition of, 415
Earth, cubic feet per ton, 170
Economical angle of framed struc-
tures, 447
Eccentrics, steam-engine, 816
Economizers, fuel, 715
Edison wire gauge, 30; table, 29
Efficiency of a machine, 432
of compressed-air engines, 506
of compressed-air transmission,
508
of electric transmission, 1038
of fans, 516, 520, 525, 526
of fans and chimneys for ventila-
tion, 533
of injector, 726
of pumps, 604, 608
of riveted joints, 359, 362
of screws, 974
of steam-boilers, 683, 689
of steam-engines, 749, 775
Effort, definition of, 429
Ejector condensers, 840
Elastic -limit, 236-239
apparent, 237
Bauschinger's definition of, 239
elevation of, 238
1102
ela-exh
INDEX.
Elastic-limit of wire rope, 917
relation of to endurance, 238
Wqhler's experiments on, 238
Elastic resilience, 270
resistance to torsion, 282
Elasticity, coefficient of, 237
modulus of, 237
moduli of, of various materials,
314
Electrical conductivity of steel,
403
Electrical engineering, 1024-1077
alternating currents, 1061-1077
direct currents, 1024-1060
Electrical horse-power, 1031; table,
1039
machines, tables of, 1074-1077
resistance, 1027-1032
symbols, 1078
Electricity, standards of measure-
ment, 1024
systems of distribution, 1041
units used in, 1024
Electric circuits (see Circuits, elec-
tric)
currents, alternating, 1061-1078
(see Alternating currents)
currents, direct, 1024-1060
current, direction of, 1054
currents, heating due to, 1031
current required to fuse wires,
1032
currents, short xurcuiting of,
1036
heaters, 546, 1044
light, stations, economy of en-
gines in, 785
lighting, !
lighting, 1041-1043
motors, alternating current, 1071,
1077
motors, direct current, 1055, 1074
r!076
railways, 1041
storage-batteries, 1045-1048
transmission, 1033-1041 (see
Transmission, electric)
wires (see Wires, electric)
welding, 1046
Electro-chemical equivalents, 1049
Electro-magnets, 1050-1054
polarity of, 1054
strength of, 1053
winding for, 1053
Electro-magnetic measurements,
1050
Electrolysis, 1048
Elements, chemical, table, 163
of machines, 435-440
Elevators, coal, 912a
Ellipse, construction of, 46, 47
equations of , 70
measures of, 59, 60
Ellipsoid, 63
Elongation, measurement of, 243
E.M.F. of electric circuits, 1030
of armature circuit, 1056
Emery, grades of, 968
wheels, speed and selection of, 967
Emery-wheels strains in, 969
Endless rope system of haulage,
914
screw 440
Endurance 9f materials, relation of
to elastic limit. 238
Energy, conservation of. 432
definition of, 429
measure of. 429
of reov il of guns, 431
sources of, 432
Engines, blowing, 526
compressed air, efficiency of,
506
fire, capacities of, 580
gas, 847-850 (see Gas-engines)
gasoline, 850
hoisting, 908
hot-air, 850
hydraulic, 619
marine, 1017-1019
marine, steam and exhaust open-
ings, sizes of, 674
marine, steam-pipes for, 674,
1016
naphtha, 850
petroleum, 850
petroleum, tests of, 851
pumping, 609-612 (see Pumping-
engines)
steam, 742-847 (see Steam-en-
gines)
winding, 909
Engine-plane, wire-rope haulage,
913
Epicycloid, 50
Equation of payments, 14
of pipes, 491
Equations, algebraic, 34, 35
of circle, 70
of ellipse, 70
of hyperbola, 71
of parabola, 70
quadratic, 35
referred to co-ordinate axes, 69
Equilibrium of forces, 418
Equivalent orifice, mine ventilation,
533
Equivalents, electro-chemical, 1049
Erosion of soils, 565
Ether, compressibility of, 164
Evaporation, 462-467
by exhaust steam, 465
by multiple system, 463
factors of, 6956-699
in salt manufacture, 463
of sugar solutions, 465
of water from reservoirs and
channels, 463
latent heat of, 462
total heat of, 462
unit of, 677
Evaporator, for marine work, 847,
1016
Evolution, 7
Exhaust -steam, evaporation byt
465
for heating, 780
IHDEX.
exh-flo
1103
Exhauster, steam -jet, 527
Expansion, adiabatic, formulae for,
501 ; tables, 502
by heat, 459
coefficients of, 460
of iron and steel, 385
of liquids, 461
of solids by heat, 460
of steam, 742
of steam, actual ratios of, 750
of timber, 311
of water, 547
Explosions, dust, 642
Explosive energy of steam-boilers,
720
Exponents, theory of, 36
Exponential function, differential
of, 77
Eye bars, tests of, 304
Factors of evaporation, 6956-699
Factor of safety, 314
in steam-boilers, 700
Fahrenheit -Centigrade conversion
table, 449
Failures of stand-pipes, 294
of steel, 403
Fairbairn's experiments on riveted
joints, 354
Falling bodies, graphic representa-
tion, 425
bodies, laws of, 424
Fans and blowers, 511-526
capacity of, 517, 1083
comparative efficiencies, 516
Fans, best proportions of, 512
centrifugal, 511, 518-523
disk, 524-526
efficiency of, 520, 533
experiments on, 515, 516, 522
for cupolas and forges, 519
influence of speed of, 523
influence of spiral casings on,
523
pressure due to velocity of, 513
quantity of air delivered by,
514
Farad, definition and value of,
1024
Feed-pump (see Pumps)
Feed water, cold, strains caused by,
727
water heaters, 727, 1083
water heaters, marine practice,
1016
water, saving due to heating,
727
water, purification of, 554
Feed-wire, stranded, table of sizes
and weights, 222
Fibre-graphite lubricant, 945
Fifth roots and powers of numbers,
102
Fineness, coefficient of, 1002
Finishing temperature, effect of in
steel rolling, 392
Fink roof -truss, 446
Fire, temperature of, 622
Fire-brick arches in locomotives,
857
Fire-brick, number required for
various circles, table, 234
sizes and shapes of, 233
weight of, 233
Fire-cay, analysis of Mt. Savage,
234
pyrometer, 453
Fire-engines, capacities of, 580
Fire-proof buildings, 1020
Fire-streams, 579-581
discharge from nozzles at differ-
ent pressures, 579
effect of increased hose-length,
.581
friction loss in hose, 580
pressure required for given length
of, table, 581
Fireless k>comotive, 866
Fits, forcing and shrinkage, 973
Fittings, cast-iron pipe, sizes and
weights, table, 187
Flagging, strength of , 313
Flanges for cast-iron pipe, table,
193
pipe, standard, table, 192
pipe, extra heavy, table, 193
Flat plates in steam-boilers, 701,
709
plates, strength of, 283
rolled iron, weight of, table, 172,
173
Flexure of beams, formulae for, 267
and compression combined, 282
and tension combined, 282
and torsion combined, 283
Fliegner's equation for flow of air,
485
Flight conveyors, 912a
Flights, sizes and weights of, 912c
Floors, loads on, 281
maximum load on, 1021
strength of, 1019, 1021
Flooring material, 281
Flow of air in pipes, 485
of air through orifices, 484, 518
of compressed air, 489
of gases, 480
of gas in pipes, 657-659
of gas in pipes, tables, 658
of metals, 973
of steam, capacities of pipes,
672
of steam, in pipes, 669-671
of steam, loss of pressure due te
friction, 671
of steam, loss of pressure due to
radiation, 671
of steam, Napier's rule, 669
of steam, resistance of bends
valves, etc., 672
of steam, tables of, 668, 669
of steam, through a nozzle, 668
of water, 555-588
of water, Bazin's formulae, 563
of water, Chezy's formula, 558
of water, D'Arcy's formula, 563
1104
flo-fue
IKDEX.
Flow of water, experiments on, 566-
573
of water, fall per mile and slope,
table, 558
of water, Flynn's formula, 562
of water, formulae for, 557-564,
1089
of water in pipes, 557
of water in pipes at uniform
velocity, table, 572
of water in cast-iron pipe, 566
of water in house-service pipes,
table, 578
of water in 20" pipe, 566
of water in pipes, table from
D'Arcy's formula, 569-572
of water in pipes, tables from
Kutter's formula, 568, 569
of water, Kutter's formula, 559
of water, Moleswbrth's formula,
562
of water, old formula for, 564
of water over weirs, 555, 586
of water, Vr for pipes and con-
duits, table, 559
of water through orifices, 555,
584
Flowing water, horse-power of, 589
water, measurement of, 582
Flues, collapsing pressure of, 265
corrugated, British rules, 266, 702
corrugated, U. S. rules, 709
(see also Tubes and Boilers)
Flywheels, steam-engine, 817-824
(see Steam-engines)
Foaming or priming of steam-
boilers, 552, 718
Foot and inches, decimal equiva-
lents of, table, 112
Foot-pound, unit of work, 428
Force, centrifugal, 423
definitions of, 415
expression of, 429
graphic representation of, 415
moment of, 416
of acceleration, 427
of a blow, 430
of wind, 492
units of, 415
Forces, composition of, 415
equilibrium of, 418
parallel, 417
parallelogram of ,.416
parallelopipedon of, 416
polygon of, 416
resolution of , 415
Forced draught in steam-boilers,
714
draught, marine practice, 1015
Forcing and shrinking fits, 973
Forges, fans for, 519
Forging, heating of steel for, 413
hydraulic, 618, 620
of tool steel, 413
Forgings, strength of, 297
steel, annealing of, 396
Foundry iron, analyses of, 371-374
irons, chemistry of, 370
Foundry irons, grades of, 372
ladles, dimensions of, 953
practice, 946-953
practice, moulding-sand, 952
practice, shrinkage of castings,
practice, use of softeners, 950
Fractions, 2
product of, in decimals, 4
Frames, steam-engine, 817
Framed structures, stresses in, 440-
447
Framing, for bulkheads, table, 287
for tanks, 287
Francis's formulae for weirs, 586
Freezing-point of water, 550
French measures and weights, 21-26
thermal unit, 455
Frequency of alternating currents,
1061
Friction and lubrication, 928-945
brakes, capacity of, 980
coefficient of, definition, 928
coefficient of, tables, 929, 930
fluid, laws of, 929
gearing, 905
laws of, of lubricated journals,
934
moment of, 938
Morin's laws of, 933
of air in mine passages, 531
of car-journals, 937
of lubricated journals, 931
of metals under steam pressure,
933
of motion, 929
of pivot bearings, 939
of rest, 928
of solids, 928
of steam-engines, 941
of steel tires on rails, 928
rolling, 928, 929
unlubricated, law of, 928
work of, 938
rollers, 940
Frictional heads, flow of water, 577
Frustum, of pyramid, 61
of cone, 61
of parabolic conoid, 64
of spheroid , 63
of spindle, 63
Fuel, 620-651
bagasse, 643
charcoal, 640-642 (see Charcoal)
coke, 637-639 (see Coke)
combustion of, 620
dust, 642
economizers, 715
for cupolas, 948
gas, 646, 1082 (see Gas)
gas for small furnaces, 651
heat of combustion of, 621
peat, 643
petroleum, 645
pressed, 632
sawdust, 643
straw, 643
solid, classification of, 623
INDEX.
fue-geo
1105
Fuel, wet tan-bark, 643
theory of combustion of, 620
turf, 643
weight of, 170
wood, 639. 640
Functions, trigonometrical, of half
an angle, 67
of sum and difference of angles,
66
of twice an angle, 67
tables of, 159-162
Furnaces, blast, temperature deter-
minations in, 452
corrugated, 266,709
down draught, 635, 712
for different coals, 635
gas-fuel for, 651
industrial, temperatures in, 451
open-hearth, temperature deter-
minations in, 452
steam-boiler, formulae for, 702
steam-boiler (see Boiler-furnaces) "
Fusible alloys, 333
plugs in boilers, 710
Fusibility of metals, 167
Fusing-disk, 966
Fusing temperatures of substances,
455
Fusion, latent heat of, 461
of electric wires, 1032
g, value of, 424
Gallons per cubic foot, table, 122
Galvanic acti9n, corrosion by, 386
Galvanized wire rope, 228
Gas, ammonia, 992, 993
analyses by volume and weight,
651
anthracite, 647
bituminous, 647
carbon, 646
coal, 651
fired steam-boilers, 714
flow of in pipes, 657-659 (see
Flow of gas)
fuel, 646-651, 1082
fuel, cost of, 651
fuel for small furnaces, 651
illuminating, 651-659 (eee Illu-
minating-gas)
natural, 649
producer, 649
producer, combustion of, 650
producer, from ton of coal, 649
sulphur-dioxide, 992
water, 648, 652-657 (see Water-
gas)
and vapor mixtures, laws of,
480
Gas-engines, 847-850
combustion of gas in Otto, 849
efficiency of, 848
pressures developed in, 849
temperatures developed in, 849
tests of, 848
use of carburetted air in, 849
Gas-pipe, cast-iron, weight of, table,
188
Gas-producers, use of steam in, 650
Gases, absorption of, 480
Avogadro's law of, 479
combustion of, rise of tempera-
ture in, 623
densities of , 479
expansion of, 479
expansion of by heat, table, 459
flow of, 480
heat of combustion of, 456
law of Charles, 479
Mariotte's law of , 479
of combustion, analyses of, 622
physical properties of, 479
specific heats of, 458
weight and specific gravity of,
table, 165
waste, use of, under boilers, 689,
690
Gasoline-engines, 850
Gauges, limit, for screw threads, 205
limit, for screw threads, table, 206
Gauge, wire, 28-30
sheet metal, 28, 30-32
Stub's wire, 29
decimal, 32
Gauss, definition and value of, 1052
Gear, reversing, 816
worm, 440
wheels, calculation of speed of,
891
wheels, formulae for dimensions
of, 890
wheels, milling cutters for, 892
wheels, proportions of, 891
Gearing, annular, 898
bevel, 898
chordal pitch, 889
comparison of formulae, 902, 903
cycloidal teeth, 892
differential, 899
efficiency of, 899
forms of teeth, 892-899
formulae for dimensions of, 890
friction, 905
involute teeth, 894
pitch, pitch-circle, etc., 887 1
pitch diameters for 1-inch circular
pitch, 889
proportions of teeth, 889-891
racks, 895
relation of diametral and circular
pitch, 888
speed of, 905
spiral, 897
strength of, 900-905
stepped, 897
toothed-wheel, 439, 887-906
twisted, 897
worm, 897, 1086
Gears, lathe, for screw-cutting, 955
Generators, electric, 1055-1060,
1074-1077
alternating current, 1070, 1077
(see Dynamo electric machines)
Geometrical progression, 11
problems, 37-52
propositions, 53
1106
ger-hea
INDEX.
German silver, 300, 332
silver, conductivity of, 1028
Gilbert, definition and value of, 1050
Girders, allowed stresses in plate
and lattice, 264
building, New York building
laws, 1020
iron-plate, strength of, 297
steam-boiler, rules for, 703
Warren, stresses in, 445
Glass, skylight, sizes and weights,
184
strength of, 308
properties of, 167
Gold-melting, temperature deter-
minations, 452
Gold-ore, cubic feet per ton, 170
Gordon's formula for columns, 247
Governors, steam-engine, 836-839
Grade line, hydraulic, 578
Grain elevators, 912d
weight of, 170
Granite, strength of, 302, 312
Graphite, lubricant, 945
paint, 387
Grate surface in locomotives, 856
surface of a steam-boiler, 680
Gravel, cubic feet per ton, 170
Gravity, acceleration due to, 424
center of, 418
discharge elevators, 912a
specific, 163-165 (see Specific
gravity)
Greatest common measure or divi-
sor, 2
Greek letters, 1
Green's fuel economizer, 715 t
Greenhouses, hot-water, heating of,
542
steam-heating of, 541
Grinder, horse-power required to
run, 963
Grindstones, speed of, 968, 969
strains in, 968
varieties of, 970
Gurley's bronze, composition of, 325
Gun-bronze, variation in strength
of, 321
Guns, energy of recoil of, 431
formula for thickness of, 288
Gun-metal (bronze), composition of,
325
Guy-ropes for stand-pipes, 293
Guy-wires, table of sizes, weights,
and strength of, 223
Gyration, center of, 420
table of radii of, 421
radius of, 247, 249
Hammering, effect of, on steel, 412
Hardening of steel, 393, 414
Hardness of copper-tin alloys, 320
of water, 553
Haulage, wire-rope, 912d-916
wire-rope, endless rope system,
914
wire-rope, engine-plane, 913
wire-rope, inclined plane, 913
Haulage, wire-rope. tail-rope system,
913
wire-rope, tramway, 914
Hauling capacity of locomotives,
853
Hawley down-draught furnace, 712
Hawsers, flexible steel wire, 223
Hawser, hemp, weight of, 223
manila, weight of, 223
steel, weight of, 223
steel, table of sizes and proper-
ties, 229
table of comparative strength of
steel, hemp, manila, and chain,
230
Head, frictional, in cast-iron pipe,
table, 577
loss of, 573-579 (see Loss of head)
of air, due to temperature differ-
ences, 533
of water, 557
of water, cpmparison of, with
various units, 548
of water, value in pounds per
square inch, table, 189, 190
Heads of boilers, 706
of> boilers, unbraced wrought -
iron, strength of, 285
Heat, 448-480
conducting power of metals, 469
conduction of, 468
convection of, 469
effect of, on grain of steel, 412
expansion due to, 45 9 ^
generated by electric current,
1031
latent, 461 (see Latent heat)
loss by convection, 476
mechanical equivalent of, 456
of combustion, 456
of combustion of fuels, 621
quantitative measurement of, 455
radiating power of substances,
468
radiation of, 467
radiation of various substances,
475
reflecting power of substances,
468
resistance of metals , 468
specific, 457-459 (see Specific
heat)
steam, storing of, 789
transmission of, from steam to
water, 472, 473
transmission of, in condenser
tubes, 473
transmission of, through building
walls, etc., 478,534
transmission of, through plates,
471-475
transmission power of various
substances, 478
treatment of crucible steel, 411
unit of, 455, 660
units per pound of water, 548
Heaters, electric, 1044
feed-water, 727, 1083
INDEX.
hea-hyd
1107
Heating and Ventilation, 528-546
blower system, 545, 1081
boiler-heating surface, 538
computation of radiating surface,
536
heating value of radiators, 534
heating surface, indirect, 537
hot-water -heating, 542-544 (see
Hot-water heating)
overhead steam -pipes, 537
534-541
(see
steam -heating,
Steam-heating)
transmission of heat through
building walls, 534
Heating a building to 70°, 545
by electricity, 546, 1044
by exhaust steam, 780
of electrical conductors, 1031
of greenhouses, 541, 542
of large buildings, 534
of steel for forging, 413
of tool steel, 412
surf ace of steam-boiler, 678 ; meas-
urement of , 679
value of coals, 634, 635
value of wood, 639
Height, table of, corresponding to
a given velocity, 425
Heine boiler, test of, with different
coals, 688
Helical springs, capacity of, 349,
350
springs for locomotives, 353
steel springs, 347
Helix, 60
Hemp ropes, strength of, 301
rope, table of strength and
weight of, 340
rope, table of strength of, 338
rope, flat, table of strength of,
339
Henry, definition and value of, 1024
Hobson's hot-blast pyrometer, 453
Hodgkinson's formula for columns,
246
Hoisting, 906-916
by hydraulic pressure, 617
coal, 343
counterpoise system 910
cranes, 911 (see Cranes)
effect of slack rope, 908
endless rope system, 910
engines, 908
engines, compressed-air, 5056
engines, counterbalancing of, 909
horse-power required for, 907
Koepe system, 910
limit of depth for, 908
loaded wagon system, 910
pneumatic, 909
rope, 340
rope, iron, or steel, dimensions,
strength and properties, table,
226
ropes, stresses in, on inclined
planes, 915
rope, sizes and strength of, 343,
906
Hoisting rope, tension required to
prevent slipping, 916
suspension cable ways, 915
tapering ropes, 910, 916
Holding power of bolts ha white
pine, 291
power of expanded boiler-tubes,
307
power of lag-screws, 290
power of nails in woods, 291
power of spikes, 289
power of wood screws, 290
Hollow cylinders, resistance of, to
collapse, 264-266
shafts, torsional strength of, 282
Hooks, proportions of, 907
Horse-gin, 434
Horse, work of, 434
Horse-power constants of steam-
engines, 757
cost 9f , 590
definition of, 27, 429
electrical, 1031
electrical, table of, 1039
hours, definition of, 429
nominal, definition of, 756
of fans, 516
of flowing water, 589
of locomotive boilers, 679
of marine boilers, 679
of a steam-boiler, 677
of a steam-boiler, builders' rating,
679
of steam-engines, 755-761
of windmills, 497
required to compress air, 500
Hose, fire, friction losses in, 580
Hot-air engines, 850
Hot-blast pyrometer, Hpbson's,
453
Hot boxes, 938
water heating, 542-544
water heating, arrangement of
mains, 544
water heating, computation of
radiating surface, 543
water heating, indirect, 544
water heating of greenhouses,
542
water heating, rules for, 544
water heating, sizes of pipes for,
543
water heating, velocity of flow,
542
House-service pipes, flow of water
in, table, 578
Howe truss, stresses in, 445
Humidity, relative, table of, 483
Hydraulics, 555-588 (see Flow of
water)
Hydraulic apparatus, efficiency of,
616
cylinders, thickness of, 617
engine, 619
forging, 618, 620
formulae, 557-564, 1087
grade-line, 578
machinery, friction of, 616
1108
hycl-iro
INDEX.
Hydraulic pipe, 191
power in London, 617
press, thickness of cylinders for,
288
presses in iron works, 617
pressure, hoisting by, 617
pressure transmission, 616-620
pressure transmission, energy of,
616
pressure transmission, speed of
water through pipes and valves,
617
ram, 614, 615
riveting machines, 618
Hydrometer, 165
Hygrometer, dry and wet bulb,
483
Hyperbola, asymptotes of, 71
construction of, 49
equations of, 71
curve on indicator diagrams, 759
Hyperbolic logarithms, tables of,
156-158
Hypocycloid, 50
I beams (see Beams)
Ice, properties of, 550
making machines, 981-1001 (see
Refrigerating machines)
manufacture, 999
melting effect, 983
Illuminating-gas, 651-659
calorific equivalents of constitu-
ents, 654
coal-gas, 651
fuel value of, 656
space required for plants, 656
water-gas, 652
Impact, 431
Impedailce, 1063
polyi^ns, 1064-1066
Impurities of water, 551
Incandescent lamp, 1042
Inches and fractions as decimals of
afoot, table, 112
Inclined-plane, 437
motion on, 428
stresses in hoisting-ropes on, 915
plane, wire-rope haulage, 913
Incrustation and scale, 551,716
India-rubber, vulcanized, tests of,
316
Indicated horse-power, 755
Indicators, steam-engine, 754-761
(see Steam-engines)
Indicator tests of locomotives, 863
Indirect heating surface, 537
Inductance, 1062
of lines and circuits, 1066
Induction motors, 1072
Inertia, definition of, 415
moment of, 247, 419
Ingots, steel, segregation in, 404
Injector, efficiency of, 726
equation of , 725
Inoxidizable surfaces, production of,
388
Inspection of steam-boilers, 720
Insulation, Underwriters', 1033
. Insulators, electrical value of, 1028
Integrals, 73
table of, 78, 79
Integration, 74
Intensifier, hydraulic, 619
Interest, 13
compound, 14
Interpolation, formula for, 1080
Involute, 52
gear-teeth, 894
gear-teeth, approximation of, 896
Involution, 6
Iridium, properties of, 167
Iron and steel, 167, 364-389
and steel boiler-plate, 382
and steel, classification of, 364
and steel, effect of cold on
strength of, 383
and steel in structures, formulae
for unit strains in, 379
and steel, inoxidizable surface
for, 388
and steel, latent heat of fusion of,
459
and steel, manganese plating of,
389
and steel, Pennsylvania Rail-
road specifications for, 378
and steel, preservative coatings
for, 387
and steel, rustless coatings for,
387
and steel, specific heat of, 459
and steel, tensile strength at high
temperatures, 382
bars (see Bars)
bridges, durability of, 385
cast, 365-376 (see Cast iron)
coefficients of expansion of, 385
color of, at various tempera-
tures, 455
copper-zinc alloys, 326
corrosion of, 386
corrugated, sizes and weights, 181
durability of, 385, 386
flat-rolled, weight of, 172, 173
for stay-bolts, 379
for U. S. ^tandard bolts, varia-
tion in size of, 206
foundry, analyses of, 371-374
foundry, chemistry of, 370-374
malleable, 375, 376 (see Malleable
iron)
pig (see Pig Iron)
plates, approximating weight of
403
plate, weight of, table, 174, 175
rivet, shearing resistance of, 363
rope, table of strength of, 338
rope, flat, table of strength of
339
shearing strength of, 306
sheets, weight of, 32, 174
silicon -aluminum alloys, 330
tubes, collapsing pressure of, 26£
wrought, 377-379 (see Wroughl
iron)
IKDEX.
MT-loC
1109
Irregular figure, area of, 55, 56
solid, volume of, 64
Irrigation canals, 564
Isothermal compression of air, 499
expansion of steam, 742
Japanese alloys, composition of, 326
Jet-condensers, 839
Jet propulsion of ships, 1014
Jet, reaction of, 1015
Jets, water, 579
Joints, riveted, 354-363 (see Riv-
eted joints)
Joists, contents of, 21
Joule, definition and value of, 1024
Joule's equivalent, 456
Journal-bearings, 930-939
cast-iron, 933
of engines, 810-815
Journals, coefficients of friction of,
930
lubricated, friction of, 931, 932,
934, 935, 937
Kelvin's rule for electric transmis-
sion, 1036
Kerosene for scale in boilers, 718
Keys, dimensions of, 977
for machine tools, 976
for shafting, sizes of, 976
holding power of , 978
sizes of, for mill-gearing, 975
Kinetic energy, 429
King-post truss, stresses in, 442
Kirkaldy's tests on strength of
materials, 296-303
Knots, 344
Knot or nautical mile, 17
Koepe system of hoisting, 910
Krupp steel tires and axles, 298, 299
Kutter's formula, flow of water, 559
formula, table from, of flow of
water in pipes, 568, 569
Ladles, foundry, dimensions of, 953
Lag-screws, holding power of, 290
Lacing of belts, 883
Lamps, arc, 1041
Lamps, incandescent electric, 1042
life of, 1042
specifications for, 1043
Lamps, Nernst, 1043
Lap-joints, riveted, 358
Land measure, 17
"Lang Lay" rope, 229
Lap and lead in slide valves, 824-835
Latent heat of ammonia, 992
heat of evaporation, 462
heat of fusion of iron and steel,
459
heats of fusion of various sub-
stances, 461
Lathe, change-gears for, 956
cutting speed of, 953
horse-power to run, 961-963
rules for screw-cutting gears, 955
setting taper in, 956
tools, forms of, 955
Lattice girders, allowed stresses in,
264
Law of Charles, 479
Laws of falling bodies, 424
of motion, 415
Lead, properties of, 167
pipe, weights and sizes of , table,
200
pipe, tin -lined, sizes and weights,
table, 201
sheet, weight of, 200
and tin tubing, 200
waste-pipe, weights and sizes of
200
Leakage of steam in engines, 761
Least common multiple, 2
Leather, strength of, 302
Le Chatelier's pyrometer, 451
Levelling by barometer, 482
by boiling water, 482
Lever, 435
bent, 436
Lighting, electric, 1041-1043
Lightning protection of chimneys,
736
Lignites, analysis of, 631
Lime, weight of, 170
and cement mortar, strength of,
313
Limestone, strength of, 312, 313
Limit, elastic, 236-239
gauges for screw-threads, 206
Lines of force, 1050
Links, steam-engine, size of, 815
steel bridge, strength of, 298
Link-belting, sizes and weights, 9126
Link-motions, steam -engine, 834-
836
Lintels in buildings, 1020
Liquation of metals in alloys, 323
Liquid measure, 18
Liquids, expansion of, 461
specific gravity of, 164
specific heats of, 457, 458
Locomotives, 851-866 .
boiler pressure, 859
boilers, size of, 855
compounding of, 863
counterbalancing of, 864
cylinders, 854
dimensions of, 8596-862
drivers, sizes of, 859
effect of speed on cylinder pres-
sure, 859
efficiency of, 854
exhaust -nozzles, 856
fire-brick arches in, 857
fireless, 866
forgings, strength of, 297
formula for curves, 859a
free-steaming, 855
fuel waste of, 863
grate surface of, 856
hauling capacity of, 853
horse-power of, 855
indicator tests of, 863
light, 865
link motion,. 859a
1110
loc-mea
IHDEX.
Locomotives, narrow-gauge, 865
oil consumption of, 943
performance of high-speed, 859a
petroleum -burning, 865
safe load on tires, 865
smoke-stacks, 856
speed of, 859a
steam distribution of, 858
steam -ports, size of, 859
testing apparatus, 863
tractive power of, 853, 857
types of, 858
valve travel, 859
water consumption of, 862
weight of, 857
Wo9tten, 855
Logarithms, 77
hyperbolic, tables of, 156-158
tables of, 129-156
use of, 127-129
Logarithmic curve, 71
shies, etc., 162
Logs, area of water required to
store, 232
weight of, 232
Long measure, 17
measure, French, 21
Loops of force, 1050
Loop, steam, 676
Loss of head, 573-579
of head, Cox's formula, 575
of head, in cast-iron pipe, tables,
574, 575 m
of head in riveted steel pipes, 574
Low strength of steel, 392
Lowmoor iron bars, strength of, 297
Lubrication, 942-945
Lubricants, examination of oil, 943
measurement of durability, 942
oil, specifications for, 944
qualifications of good, 942
relative value of, 942
soda mixture, 945
solid, 945
specifications for petroleum, 943
Lumber, weight of, 232
Machines, dynamo-electric, 1055-
1060 (see Dynamo-electrio
machines)
Machines, efficiency of, 432
elements of, 435-440
Machine screws, table of propor-
tions of, 209
screws, taps for, 970
shop, 953-978
shops, horse-power required in,
965
tools, keys for, 976
tools, power required for, 960-965
tools, proportioning of, 975
tools, soda mixture for, 945
Machinery, coal -handling, 912-912d
horse-power required to run, 964
Maclaurin's theorem, 76
Magnesia bricks, 235
Magnesium, properties of, 168
"Magnetic balance, 396
Magnetic capacity of iron, effect of
annealing, 396
circuit, 1051; units of, 1050
field, strength of, 1057
Magneto -motive force, 1050, 1051
Magnets, electro-, 1050-1054
Magnolia metal, composition of,
334
Mahler's calorimeter, 634
Main-rods, steel, specifications for,
401
Malleable castings, rules for use of.
376
iron, 375
iron, strength of, 376
Malleability of metals, table, 169
Man-wheel, 434
Man, work of, tables, 433
Mandrels, standard, 972
Manganese, properties of, 168
bronze, 331
copper alloys, 331
effect of on steel, 389
effect of on cast iron, 367
plating of iron, 389
steel, 407
Manila rope, 340; weight and
strength of, 304, 344
Mannesmann tubes, strength of,
296
Manometer, air, 481
Marble, strength of, 302
Marine Engineering, 1001-1019 (see
Ships and Steam-engines)
Marine boilers, 1015
engines, comparison of old and
modern, 1017
engines, three-stage, triple-ex-
pansion, 1017-1019
Marriotte's law of gases, 479, 742
Masonry, crushing strength of, 312
materials, weight and specific
gravity of, 166
Mass, definition of, 427
expression of, 429
Materials, 163-235
strength of, 236-346
strength of, Kirkaldy's tests,
296-303
structural, stresses permissible in,
381
various, weights of, 169; table, 166
Maxima and minima, 76
without calculus, 1080
Maxwell, definition and value of,
1^)50
Mean effective pressures of adia-
batically compressed air, 5Qlb
effective pressure of compressed
air, table, 502, 503
Measurements, miner's inch, 585
Measurement of air velocity, 491
of elongation. 243
of flowing water, 582-588
of vessels, 1001
weir-dam, 586
Measures, apothecaries, 18, 19
board, 20
IKDEX.
mea-nic
1111
Measures, circular, 20
dry, 18
liquid, 18
long^ 17
nautical, 17
of work, power, and duty, 27
old land, 17
shipping, 19
solid or cubic, 18
square, 18
surface, 18
time, 20
timber, 20
Measures and weights, metric sys-
tem, 21-26
Mechanics, 415-447
Mechanical equivalent of heat, 456
powers, 435
stokers, 711
Mekarski compressed-air tramway,
510
Melting-points of substances, 455
Members, bridge, strains allowed in,
262-264
Memphis bridge, tests of steel in, 393
bridge, proportions of materials
in, 381
Mensuration, 54-64
Mercurial thermometer 448
Mercury-bath pivot, 940
Mercury, compressibility of, 164
properties of, 168
Merriman's formula for columns, 260
Mesure and Nouel's pyrometric tele-
scope, 453
Metacentre, definition of, 550
Metaline lubricant, 945
Metals, anti-friction, 932
coefficients of expansion of, 460
coefficients of friction of. 930
electrical conductivity of, 1028
flow of, 973
heat-conducting power of, 469
life of under shocks, 240
properties of, 167-169
resistance overcome in cutting of,
960
specific heats of, 453
specific gravity of, 164
weight of, 164
table of ductility, inf visibility,
malleability, and tenacity, 169
tenacity of, at various tempera-
tures, 382-384
1 Meter, Venturi, 583
; Meters, water delivered through, 579
| Metric conversion, tables, 23-26
measures and weights, 21, 22
screw-threads, cutting of, 956
-Mil, circular, 18, 29 30
i Mile-ohm, weight of wire per, 217
Mill columns, 1022
power, value of, 589
Milling cutters for gear-wheels, 892
cutters inserted teeth, 960
cutters, number of teeth in, 958
cutters, pitch of teeth, 957
cutters, spiral, 960
Milling cutters, steel for, 957
machines, cutting speed of, 958-
960
machines, feed of, 959, 960
machines, high results with, 959
machine vs. planer, 960
Miner's inch, 18
inch measurements, 585
Mines, centrifugal fans for, 521
Mine fans, experiments on, 522
ventilation 531
ventilation, equivalent orifice, 533
Modulus of elasticity, 237
of elasticity of various materials,
314
of resistance, 247
of rupture 267
Moisture in atmosphere, 483
in steam, determination of, 728-
731
Molesworth's formula, flow of water,
562
Moments, method of, for determin-
ing stresses, 445
Moment of a couple, 418
of a force, 416
of friction, 938
of inertia, 247,419
of inertia of structural shapes,
248, 249
statical, 417
Momentum, 428
Monobar, 9126
Morin's laws of friction, 933
Mortar, strength of, 313
Motion, accelerated, formulaa for,
427
friction of, 929
Newton's laws of, 415
on inclined planes, 428
perpetual, 432
retarded, 424
Motors, alternating-current, 1071,
1077
compressed-air, 507
electric, direct-current, 1055,
1074-1076
water-current, 589
Moulding-sand, 952
Moving strut, 436
Mule, work of, 435
Multiphase electric currents, 1068
Muntz metal composition of, 325
Multiple system of evaporation 463
Mushet steel, 409
Nails, cut vs. wire, 290
cut, table of sizes and weights, 213
wire, table of, sizes and weights,
214, 215
Nail-holding power of wood, 291
Naphtha engines, 850
Napier's rule for flow of steam, 669
Natural gas, 649
Nautical measure, 17
mile, 17
Newton's laws of motion, 415
Njckel-copper alloys, 332
1112
nic-pip
IKDEX.
Nickel, properties of, 168
steel, 407
steel, tests of, 408
Nozzles for measuring discharge of
pump ing-engines, 584
Oats, weight of, 170
Ocean waves, power of, 599
Oersted, definition and value of,
1050
Ohm, definition and value of, 1024
Ohm's law, 1029
law, applied to alternating cur-
rents, 1064
law, applied to parallel circuits,
1030 •
law, applied to series circuits,
1029
Oil, amount needed for engines,
943
as fuel, 6.46
fire-test of, 944
lubricating, 942-945 (see Lubri-
cants)
paraffine, 944
well, 944
pressure in bearings, 937
tempering of steel forgings, 396
vs. coal as fuel, 646
Open-hearth furnace, temperature
determinations in, 452
steel (see Steel, open-hearth)
Ordinates and abscissas, 69
Ores, weight of, 170
Orifice, equivalent, in mine ventila-
tion, 533
flow of air through, 484, 518
flow of water through, 555
rectangular, flow of water
through, table, 584
Oscillation, center of, 421
radius of , 421
Overhead steam -pipe radiators, 537
Ox, work of, 435
Oxygen, effect of, on strength of
steel, 391
TT, value and relations of, 57
Packing-rings of engines, 796
Paddle-wheels, 1013, 1014
Paint, 387
qualities of, 388
quantity of, for a given surface,
388
Parabola, area of, by calculus, 74
construction of, 48
equations of , 70
Parabolic, conoid, 63
spindle, 64
Parallel rods, steel, specifications
for, 401
forces, 417
Parallelogram, area of, 54
definition of, 54
of forces, 416
of velocities, 426
Parallelopipedon of forces, 416
Parentheses in algebra, 34
Partial differential coefficient, 73
payments, 15
Payments, equation of, 14
Peat, 643
Pelton water-wheel, 597, 1081
tables of, 598, 599
Pencoyd shapes, weights and sizes
177, 178
Pendulum, 422
conical, 423
Percussion, center of, 422
Perfect discharge elevators, 912a
Perforated plates, excess of strength
of, 359
plates, strength of, 354
Permeability, magnetic, 1051
table, 1052
Permutation, 10
Perpetual motion, 432
Petroleum as a metallurgical fuel
646
burning locomotives, 865
cost of, as fuel, 646
engines, 850
Lima, 645
products of distillation of, 645
products, specifications for, 944
value of, as fuel, 645
Pewter, composition of, 336
Phoenix columns, dimensions of,
257-259
Phosphorus, influence of, on cast
iron, 366
influence of, on steel, 389
Phosphor-bronze, composition of,
325, 334
specifications for, 327
springs, 352
strength of, 327
Fictet fluid, 982
ice-machine, 985
Piezometer, 582^
Pig-iron, analysis of, 371
chemistry of , 370
charcoal, strength of, 374
distribution of silicon in, 369
grading of, 365
influence of silicon, etc., on, 365
tests of, 369
Pillars, strength of, 246
Pins, taper, 972
Pine, strength of, 309
Pipes, air-bound, 579
bent, table of, 199
block-tin, weights and sizes of.
table, 200
capacity of , 573
cast-iron, 185-190
cast-iron, gas, weight of, 188
cast-iron, safe pressures for, ta-
bles, 189, 190
cast-iron, thickness of, for various
heads, 188, 189
cast - iron water, transverse
strength of, 251
cast-iron, weight of, 185, 188
cast-iron, weight of 12-foot
lengths, 186
IXDEX.
pip-pou
1113
Pipes, coiled, table of, 199
effects of bends in, 488, 578, 672
equation of, 491
fittings, cast-iron, sizes and
weights, 187
fittings, spiral -riveted, table, 198
flanges, for cast-iron pipe, table,
193
flanges, extra heavy, table, 193
flanges, table of standard, 192
flow of air in, 485, 489
flow of gas in, 657
flow of steam in, 669-673
flow of water in, 557, 566-572
for steam-heating, 540
house-service, flow of water in,
table, 578
lead, safe heads for, 201
lead, tin-lined, sizes and weights,
table, 201
lead, weights arid sizes of, table,
200
loss of air-pressure in, 487; tables,
488, 489, 490
loss of head in, 573-579 (see Loss
of head)
quantity of water discharged by,
573
riveted hydraulic, weights and
safe heads, table, 191
riveted-iron, dimensions of, table,
. 197
riveted, safe pressures in, 707
riveted-steel water, 295
spiral riveted, table of, 198
steam (see Steam-pipes)
table of capacities of, 120
threads on, 195
wrought -iron, standard, table of
dimensions, 194
volume of air transmitted in,
table, 486 /
water, relation of diameter to
capacity, 566
Pipe-coverings, radiation through,
671
Pistons, steam-engine, 795
Piston-rings, steam-engine, 796
Piston-rods, steam-engine, 796-798
Piston-valves, steam-engine, 834,
1016
Pitch, diametral, 888
of gearing, 887
of rivets, 357-359
of screw propellers, 1012
Pitot tube gauge, 583
Pivot -bearings, 939
Pivot -bearing, mercury bath, 940
Plane, inclined, 437 (see Inclined
plane)
surfaces, mensuration of, 54
Planers, cutting speed of, 953
Planer, heavy work on, 960
horse -power required to run, 963
tools, forms of, 955
vs. milling-machine, 960
Plates, acid-pickled, heat transmis-
sion through, 474
Plates, areas of, in square feet, table,
123
boiler, strength of, at high tem-
peratures, 383
brass, weight of, table, 202
corrugated-steel, properties of,
table, 274
Carnegie trough, properties of,
table, 274
circular, strength of, 283
copper, weight of, table, 202
copper, strength of, 300
flat, cast-iron, strength of, 286
flat, for steam-boilers, rules for,
701,706,709
iron, approximating weight of,
403
iron, weight of, table, 175
of different materials, table for
calculating weights of, 169
stayed, strength of, 286
for stand-pipes, 293
perforated, strength of, 353, 360
punched, loss of strength in, 354
steel boiler, specifications for, 399
steel, corrections for size of, in
tests, 380
steel, for cars, specifications for,
401
steel, specifications for, 400, 401
steel, tests of, 297, 390
strength of flat, 283-286
strength of flat unstayed, 284
transmission of heat through, 471
transmission of heat through, air
to water, 474
transmission of heat through
steam to air, 475
Plate-girders, allowed stresses in,
264
girder, strength of, 297
Plating for bulkheads, table, 287
steel, stresses in, due to water-
pressure, 287
for tanks, table, 287
Platinum, properties of, 168
wire, 225
Plugs, fusible, in steam-boilers, 710
Pneumatic hoisting, 909
Polarity of electro-magnets, 1054
Polyedron, 62
Polygon, area of, 55
construction of, 42, 43
definition of, 55
table of, 44, 55
Polygons, impedance, 1064-1066
of forces, 416
Polyphase circuits, 1068
Popp system of compressed air,
507
Population of the United States, 12
Port opening in steam-engines, 828
Portland cement strength of, 302
Postal transmission, pneumatic, 509
Potential energy, 429
Pound-calorie, definition of, 455
Pound per square inch, equivalents
of, 27
11U
pow-rad
INDEX.
Powell's screw-thread. 975
Power, animal, 433
definition of, 429
factor of alternating currents,
1062
hydraulic, in London. 617
measure of, 27
of electric circuits. 1031
of a waterfall, 588
of ocean waves, 599
unit of 429
Powers of numbers tables, 7, 86-
102
of numbers, algebraic, 33
Pratt truss, stresses in, 443
Preservative coatings, 387-389
Press, hydraulic, thickness of cylin-
ders for, 288
Pressed fuel, 632
Presses, hydraulic, in iron works
617
punches, etc., 972
Pressure, collapsing of flues, 265
collapsing, of hollow cylinders, 264
Priming, or foaming, of steam-
boilers, 552, 718
Prism, 60
Prismoid, 61
rectangular, 61
Prismoidal formula, 62
Problems, geometrical, 37-52
in circles, 39, 40
in lines and angles, 37 , 38
in polygons, 42
in triangles, 41
Producers, gas, use of steam in, 650
Producer-gas, 646-651 (see Gas)
Progression, arithmetical and geo-
metrical, 11
Prony brake, 978
Propeller, screw, 1010-1013 (see
Screw-propeller)
shafts, strength of, 299
Proportion, 5
compound, 6
PuUeys, 873-875
arrangement of , 874 •
arms of, 820
cone, 874
convexity of , 874
differential, 439
for rope-driving, 925
or blocks, 438
proportions of, 873
speed of, 884, 891
Pulsometer, 612
tests of , 613
Pumps and pumping-engines, 601-
614
air, for condensers, 841
air-lift, 614
boiler- feed, 605
boiler-feed, efficiency of, 726
centrifugal, 606-609
centrifugal, as suction-dredge, 609
centrifugal, efficiency of, 608
centrifugal, relation of height of
lift to velocity, 606
Pumps, centrifugal, sizes of. 607
centrifugal tests of" 609
circulating for condensers 843
compressed air mine, 511
depth of suction of. 602
direct-acting, efficiency of, 604
direct-acting, proportions of steam
cylinder. 602
duplex steam, sizes of, 604
feed for marine engines, 843
horse-power of, 601
jet, 614
leakage test of, 611
lift, water raised by 602
piston speed of, 605
single steam, sizes of, 603
speed of water in passages of 602 ,
605
suction of, with hot water 602
theoretical capacity of, 601
vacuum, 612
Pump-valves, 606
Pumping by compressed air. 505a
Pumping-engines duty trials of,
609
economy of, 782
table of data and results of duty
trials of , 611
triple-expansion, 782
use of nozzles to measure dis-
charge of, 584
Punches, clearance of , 972
spiral, 972
Punched plates, strength of, 354
Punching, effect of, on structural
steel, 394
and drilling of steel, 395
Purification of water, 554
Pyramid, 60
frustum of , 61
Pyrometer, air, Wiborg's, 453
copper-ball, 451
fire-clay, Seger's, 453
Hobson's hot-blast, 453
Le Chatelier's, 451
principles of, 448
thermo-electric, 451
Uehling-Steinbart , 453
Pyrometric telescope, 453
Pyrometry, 448-455
Quadratic equations, 35
Quadrature of plane figures, 74
of surfaces of revolution, 75
Quadrilateral, definition of, 54'
area of, 54
area of, inscribed in circle, 54
Quadruple -expansion engines 772
Quantitative measurement of heat,
455
Quarter-twist belt, 883
Quartz, cubic feet per ton, 170
Queen-post truss, stresses in, 442
inverted, stresses in, 443
Rack, gearing, 895
Radiating power of substances, 468
INDEX.
rad-riv
1115
Radiating surface, computation of,
for hot-water heating, 543
surface, computation of, ior
steam heat, 536
Radiation of heat, 467
of various substances, 475
table of factors for Dulong's laws
of, 476
Radiators, experiments with, 545
heating value of, 477 , 534
overhead steam -pipe, 537
Radius of curvature of wire rope, 922
of gyration, 247,420
of gyration, graphical method for
finding, 248
of gyration of structural shapes,
249
of oscillation, 421
Rails, size of bolts for splicing 210
size of spikes for, 212
steel, maximum safe load on, 865
steel, specifications for, 398
steel, strength of, 298
Railroad axles, 384
trains, resistance of, 851
trains, speed of, 859
Railways, electric, 1041
narrow-gauge, 865
Railway, street, compressed-air,
510, 511
Ram, hydraulic, 614
Ratio 5
Reactance of alternating currents,
1063
Reamers, taper, 972
Reaumer thermometer-scale, 448
Recalescence of steel, 402
Receiver- space in engines, 766
Reciprocals of numbers, tables of,
80-85
use of, 85
Rectangle definition of, 54
v.alue of diagonal of, 54
Red lead as a preservative, 387
Reduction, ascending and descend-
ing, 5
Rectangular prismoid, 61
Reese's fusing disk, 966
Reflecting power of substances, 468
Refrigerating - machines . a i r - m a -
chines, 983
ammonia-absorption, 984, 987
ammonia-compression, 983, 986
cylinder-heating, 997
ether-machines, 983
heat-balance, 990
ice-melting effect, 983
liquids for, pressures and boiling-
points, 982
operati9ns of, 981
pipe-coils ior, 985
performances of, 994-997
properties of brine, 994
properties of vapor, 993
relative efficiency of, 988
relative performance of ammonia-
compression and absorption
machines, 983
Ref rigerating-machines , sulphur-di^
oxide machine, 985
temperature range, 991
tests of, 990-992
using water vapor, 988
Refrigeration, 981-1001
means of applying the cold, 999
Registers for steam -heat ing, 539
Regnault's experiments on steam,
661
Reluctance, magnetic, 1050, 1051
Reservoirs, evaporation of water
in, 463
Resilience, 238
elastic, 270
Resistance, elastic, to torsion, 282
electrical, 1027-1032
electrical, effect of annealing,
1029
electrical, effect of temperature,
1029
electrical, in circuits, 1029-1031
electrical, internal, 1031
electrical, standard of, 1029
electrical, of copper wire, 1029,
1034
electrical, of steel, 403
elevation of ultimate, 238
of metals to repeated shocks,
238 .
modulus of, 247
of ships, 1002
of trains, 851
work of , of a material, 238
Resolution of forces, 415
Reversing-gear for steam-engines,
dimensions of, 815
Retarded motion, 424
Rhomboid, definition and area of,
54
Rhombus, definition and area of,
54
Rivet -iron and -steel, shearing re-
sistance of, 363
Rivets, bearing pressure on, 356
cone-head, for boilers, weight of,
211
diameters of, table, 360
in steam-boilers, rules for, 700
pitch of, 359
pressure required to drive, 1080
rules for strength of , 360
steel, specifications for, 401
Riveting, efficiency of different
methods, 355
hand, strength of, 355
hydraulic, strength of, 355
machines, hydraulic, 618
of structural steel, 394
pressure required for, 362
Riveted iron pipe, dimensions of,
table, 197
joints, 299, 354-363
ioints, drilled vs. punched holes,
355
joints, efficiencies of, 359, 361
joints, notes on, 356
joints, proportions of, 35,8, 359
1116
riv-sel
IHDEX.
Riveted joints, single-riveted lap,
357
joints, calculated strength of
double-riveted, 361
joints, tests of double-riveted
lap and butt, 360
joints, tests of, table, 303
pipe, flow of water in, 574
pipe, weight of iron for, 197
Roads, resistance of carriages on,
435
Rock-drills, air required for, 505a
requirements of air-driven, 506
Rods of different materials, table
for calculating weights of,
169
Roof -truss, stresses in, 446
Roofs, safe loads on, 184, 281
strength of, 1019
Roofing materials, 181-184
materials, weight of various,
184
Roller-bearings, 940
Rolling of steel effect of finishing
temperature, 392
Ropes and cables, 338-346
cable-traction, 226
charcoal-wire, 228
cotton and hemp, strength of,
301
for coal-hoisting, 343
hemp and wire, table of, working
loads for, 339
hemp, table of, strength and
weight of, 340
hoisting (see Hoisting-rope)
"Lang Lay," 229
locked-wire, 231
manila, 340
manila, weight and strength of,
344
splicing of , 341
steel flat, table of sizes, weight,
and strength, 229
steel-wire hawsers, 229
stevedore, 340
table of, strength of iron, steel,
and hemp, 338
table of strength of flat iron,
steel, and hemp, 339
technical terms relating to, 341
transmission, 340
wire (see Wire-rope)
Rope-driving, 922-927
English practice, 926
horse-power of, 924
pulleys for, 925
sag of rope, 925
tension of rope, 925
various speeds of, 924
weight of rope, 928
Rotary blowers, 526
steam-engines, 791
Rotation, accelerated, work of,
430
Rubber belting, 887
vulcanized, tests of, 316
Rule of three, 6
50
Rupture, modulus of, 267
Rustless coatings for iron, 388
Safety, factor of, 314
valves for steam-boilers, 721-
724
Salt brine, properties of, 464
manufacture, evaporation in, 463
solubility of, 464
solution, specific heat of, 458
weight of, 170
Sand-blast, 966
Sand, cubic feet per ton, 170
moulding, 952
Sandstone, strength of, 312
Saturation point of vapors, 480
Sawdust as fuel, 643
Sawing metal, 966
Scale, boiler, 716
boiler, analyses of, 552
Scales, thermometer, comparison
of, 448; table, 449
Scantling, table of contents of, 21
Schiele's anti-friction curve, 5(
939
Screw, 60
bolts, efficiency of, 974
conveyors, 912rf
differential, 439
differential, efficiency of, 974
efficiency of, 974
(element of machine), 437
propeller, 1010-1013
propeller, coefficients of, 1011
propeller, efficiency of, 1012
propeller, slip of, 1012
Screws, cap, table of standard,
208
lag, holding power of, 290
machine, proportions of, 209
machine, taps for, 970
set, table of standard, 208
threads, 204-207
threads, English standard, 205
threads, limit gauges for, 206
'^threads, metric, cutting of, 956
thread, Powell's, 975
threads, Sellers, 204
threads, standard for taps, 207
threads, U. S. standard, 204
threads, U. S. standard, table of
pitches. 204
threads, U. S. standard, table of
proportions of, 205
threads, Whit worth, table, 205
wood, holding power of, 290
Sea- water, freezing-point of, 550
Secant of an angle, 65
table of, 159-162
Sector of circle, 59
Sediment in steam-boilers, 717
Seger's fire-clay pyrometer, 453
Segment of circle, 59
Segments, circular, table of areas of,
116
Segregation in steel ingots, 404
Self-inductance of lines and cir-
cuits, 1066
INDEX.
sep-sol
1117
Separators, steam, 728
Set-screws, holding power of, 977
standard, table of, 208
Sewers, grade of, 566
Shaft-bearings, 810
Shaft -governors, 838
Shafts, hollow, 871
hollow, torsional strength of, 282,
806
steam-engine, 806-813
steel propeller, strength of, 299,
815
Shafting, 867-872
deflection of, 868
formulae for, 867
horse-power transmitted by, 869-
871
horse-power to drive, 963
laying out, 871, 872
keys for, 975
Shaku-do, Japanese alloy, 326
Shapes of test specimens, 243
structural, properties of, 272-280
Shear and compression combined,
282
and tension combined, 282
poles, stresses in, 442
Shearing, effect of, on structural
steel, 394
resistance of rivets, 363
unit strains of, 379
strength of iron and steel, 306
strength of woods, table, 312
Sheaves, wire-rope, 917, 919
Shells of steam-boilers, material
for, 700
spherical, strength of, 286
Shell-plate formulae for steam-boil-
ers, 701
Sheet brass, weight of, 203
copper, weight of, 202
metal, strength of, 300
metal, weight of, by decimal
gauge, 32
Sheets, iron and steel, weight of,
174
Shibu-ichi, Japanese alloy, 326
Shingles, weights and areas of, 183
Skips, coefficient of fineness of, 1002
coefficient of performance, 1003
coefficient of water-lines, 1002
displacement of, 1001, 1009
horse-power of, 1009
horse -power for given speeds,
1006
horse-power of, from wetted sur-
face, 1005
jet propulsion of, 1014
resistance of, 1002
resistance of, per horse-power
1006
rules for measuring, 1001
rules for tonnage, 1001
speed in canals, 1008
trials of, 1007, 1008
twin-screw, 1017
wetted surface of, 1005
Shipping measure, 19, 1001
Shocks, resistance of metals to re-
peated, 240
stresses produced by. 241
Shop operation by compressed air,
509
Short circuits, electric, 1036
Shot, American standard, sizes of,
204
Shrinkage fits, 973
of cast iron, 368
of castings, 951
Signs, arithmetical, 1
Sign of differential coefficients, 76
of trigonometrical functions, 66
Silicon-aluminum -iron alloys, 330
Silicon-bronze, 328
Silicon-bronze wire, 225, 327
Silicon, distribution of, in pig iron,
369
influence of, on cast iron, 365, 370
influence of, on steel, 389
relation of, to strength of cast
iron, 369, 370
Silver-melting, temperature deter-
minations, 452
Silver, properties of, 168
ore, cubic feet per ton, 170
Simplex gas-engine, test of, 848
Smokestack guys, 223
Simpson's rule, 56
Sine of an angle, 65
tables of, 159-162
Single-phase circuits, 1068
Sinking-funds, 17
Siphon, 581,582
Skin effect of alternating currents,
1065
Skylight glass, sizes and weights, 184
Slag in cupolas, 948
in wrought iron, 377
Slate roofing, dimensions and areas,
183
roofing, weight of, 183
Slide-valves, steam-engine, 824-835
(see Steam-engines)
Slope, table of, and fall in feet per
mile, 558
Smoke prevention, 712-714
Smoke-stacks, locomotive, 856
sheet -iron, 741
Snow, weight of, 184, 281, 550
Soapstone lubricant, 945
strength of, 312
Soda mixture for machine tools,
945
Softeners in foundry practice, 950
Softening of water, 554
Soils, resistance of, to erosion, 565
Solder, brazing, composition of, 325
for aluminum, 319
Solders, composition of various,
338
Soldering aluminum bronze, 329
Solid bodies, mensuration of, 60-64
measure, 18
of revolution, 62
Solubility of common salt, 463
of sulphate of lime, 463
1118
sou-sta
INDEX.
Sources of energy, 432
, 163-K
gravity and Baume's hydrom-
Specific gravity, 163-165
;ravity and Baume's hyd
eter compared, table, 165
gravity of brine, 464, 994
gravity of cast iron, 374
gravity of copper-tin alloys, 320
gravity of copper-tin-zinc alloys,
323
gravity of gases, 166
gravity of ice, 550
gravity of metals, table, 164
gravity of liquids, table, 164
gravity of steel, 403
gravity of stones, brick, etc., 166
Specific heat, 457-459
heat, determination of, 457
heat of air, 484
heat of ammonia, 992
heats of gases, 458
heat of ice, 550
heat of iron and steel, 459
heat of liquids, 457
heats of metals, 458
heat of saturated steam, 660
heat of superheated steam, 661
heat of water, 550
heats of solids, 457, 458
heat of woods, 458
Specifications for boiler-plate, 399
for car-wheel iron, 375
for cast iron, 374
for chains, 307
for elliptical steel springs, 352
for helical steel springs, 353
for incandescent lamps, 1043
for oils, 945
for petroleum lubricants, 943
for phosphor-bronze, 327
for spring steel, 401
for steel axles, 397
for steel billets, 401
for steel castings, 397, 406
for steel crank-pins, 401
for steel forgings, 397
for steel main-rods, 401
for steel parallel rods, 401
for steel rails, 398
for steel rivets, 399, 401
for steel splice -bars, 398
for steel tires, 398
for steel in Memphis bridge, 382
for structural steel, 400
for structural steel for bridges,
399
for structural steel for buildings,
398
for structural steel for ships, 399
for tin and terne -plate, 1088
for wrought iron, 378, 379
Speed of cutting-tools, 953, 954
of vessels, 1006-1009
Sphere, measures of, 61
Spheres of different materials, table
for calculating weight of, 169
table of volumes and areas, 118
Spherical segment, area and vol-
ume of, 2
Spherical polygon area of 61
triangle area and volume of, 61
zone, aiea and volume of 62
shells, strength of, 286
shell, thickness of, to resist a
given pressure, 286
Spheroid, 63
Spikes, boat, sizes and weights of,
212
holding power of, 289
street -rail way, 212
track, 212
wire 213
wrought. 213
Spindle, surface and volume of, 63
Spiral. 50, 60
conical, 60
construction of, 50
plane, 60
gears, 897
Spiral-riveted pipe, table of, 198
riveted pipe-fittings, table, 198
Splice-bars, steel, specifications for,
. ?98
Splicing of ropes, 341
of wire rope, 346
Spring steel, strength of, 299
Springs, 347-353
elliptical, 347
elliptical, sizes of, 352
elliptical, specifications for, 352
for engine-governors, 838
helical, 347
helical, formulae for deflection and
strength, 348
helical, specifications for, 353
helical, steel, table of capacity
and deflection, 347, 353
laminated steel, 347
locomotive, specifications for, 400
phosphor-bronze, 352
semi-elliptical, 347
to resist torsion. 352
Spruce, strength of, 310
Spur gears, machine-cut, 905
Square, definition of, 54
measure, 18
root, 8
roots, tables of, 86-101
value of diagonal of, 54
Squares of numbers, table, 86-101
of decimals, table, 101
St. Gothard tunnel, loss of pressure
in air-pipe mains in, 490
Stability, 417
'of a dam, 417
Stand-pipes, 292-295
failures of, 294
guy-ropes for, 293
heights of, to resist wind-pres-
sure, 293
heights of, for various diameters
and plates, table, 294
thickness of bottom plates, 295
thickness of plates in, 293
wind strain on, 293
Stand-pipe at Yonkers, N. Y., 295
Statical mpment, 416, 417
IKDEX.
sta-ste
1119
Stay-bolt iron, 379
Stayed surfaces, strength of, 286
Stays, steam-boiler, loads on, 703
steam-boiler, material for, 703
Stay-bolts in steam-boilers, 710
Steam, 6597676
determining moisture in, 728-
731
dry, definition, 659
dry, identification of , 730
expansion of, 742, 743
flow of, 668-674 (see Flow, of
steam)
gaseous, 661
generation of, from waste heat of
coke-ovens, 638
heat required to generate 1 pound
of, 660
latent heat of, 659
loss of pressure in pipes, 671
mean pressure of expanded, 743
moisture in, 728
properties of, as applied to steam-
heating, 540
Regnault's experiments on, 661
relative volume of, 660
saturated, definition, 659
saturated, density, volume, and
latent heat of, 660
saturated, properties of, table,
663-668
saturated, specific heat of, 600
saturated, temperature and pres-
sure of, 659
saturated, total heat of, 659
superheated, definition, 659
superheated, economy of steam-
engines with, 783
superheated, properties of, 661
superheated, specific heat of, 661
temperature of, 659
weight of, per cubic foot, table,
662
wet, definition, 659
work of, in single cylinder, 746-
753
Steam-boiler, 677-731
Steam-boilers, bumped heads, rules
for, 706
conditions to secure economy of,
682
construction of, 700-711, 1085
construction of, United States
merchant- vessel rules, 705-708
corrosion of, 386,716-721
dangerous, 720
domes on, 711
down-draught furnace for, 712
effect of heating air for furnaces
of, 687
efficiency of, 683
explosive energy of, 720
factors of evaporation, 696-699
factors of safety of , 700
feed-pumps for, efficiency of, 726
feed-water heaters for, 727
feed-water, saving due to heat-
ing of, 727
Steam-boilers, flat plates in rules for,
701,706,709
flues and gas-passages, propor-
tions of, 680
foaming or priming of, 552, 718
for blast-furnaces, 689
forced combustion in, 714
fuel economizers, 715
furnace formula?, 702
furnaces, height of, 711
fusible plugs in, 710
gas-fired, 714
girders, rules for, 703
grate-surface, 678, 680
grate -surf ace, relation to heating
surface, 682
gravity feeders, 1083
heat losses in, 684
heating-surface in, 678
heating-surface, relation of, to
grate-surface, 682
height of chimney for, 735
high rates of evaporation, 687
horse-power of, 677
incrustation of, 716-721
injectors on, 725, 726 (see Inject-
ors)
inspection of, Philadelphia rules,
708
marine, corrosion of, 719
maximum efficiency with Cum-
berland coal, 689
measure of duty of, 678
mechanical stokers for, 711
performance of, 681-685
plates, ductility of , 705
plates, tensile strength of, 705
pressure allowable in, 706-708
proportions of, 678-681
proportions of grate-spacing, 681
proportions of grate-surface, 680
proportions of heating-surface,
678
proportions of grate- and heating-
surface for given horse-power,
678
proportions of, leating-surf ace per
horse-power, 679
safe working-pressure, 707
riveting, rules for, 700
safety-valves for, 721-724
safety-valves, discharge of steam
through, 724
safety-valves, formulae for, 721
safety-valves, spring-loaded, 724
scale in, 716
scale compounds, 716
sediment in, 717
shells, material for, 700
shell-plate formulae, 701
smoke prevention, 712-714
stays, loads on, 703
stays, material for, 703
stay-bolts in, 710
strains caused by cold feed-water,
727
strength of, 700-711
strength of rivets, 700
1120
ste
INDEX.
Steam-boilers, tannate of soda com-
pound in, 7 18
tests of, 685-699
tests of, at Centennial Exhibition,
685
tests of, hydraulic, 700
tests, rules for, 690-6956
tubes, holding power of, 704
tubes, iron vs. steel, 704
tubes, material for, 704, 709
tube plates, rules for, 704
use of kerosene in, 718
use of zinc in, 720
using waste gases, 689, 690
Steam-calorimeters, 728-731
Steam -domes on boilers, 711
Steam-engines, 742-847
advantages of compounding, 762
at Columbian Exposition, 774
bearings, size of, 810-813
bed-plates, dimensions of, 817
capacity of, 748
clearance in, 751
compound, 761-768
compound, best cylinder ratios,
768
compound, calculation of cylin-
ders of, 768
compound, combined indicator
diagrams, 764
compound, condensing, 788
compound , cylinder proportions
in, 765
compound, economy of, 780
compound, efficiency of, 784
compound, expansions in two-
cylinder, 765
compound, formulae for expan-
sion and work in, 767
compound, high-speed, perfor-
mances of, 778,779
compound, high-speed, sizes of,
778,779
compound marine, approximate
horse-power of, 766
compound marine, cylinder ra-
tios of , 766
compound, non-condensing, effi-
ciency of, 784
compound, pressures in two
cylinders, 765
compound, receiver type, 762
compound, receiver, ideal dia-
gram, 7 63
compound, receiver space in,
766
compound, steam-jacketed, per-
formances of, 778
compound, steam- jacketed, test
of, 788
compound, Sulzer, water con-
sumption of, 783
compound, two vs. three cylin-
ders, 781
compound, velocity of steam in
passages of, 772
compound, water consumption
of, 777
Steam-engines, compound, Wolff
type, 762
compound, Wolff, ideal diagram,
763
compression, best periods of, 752
compression, effect of, 751
condensers, 839-847 (see Con-
densers)
connecting-rods, dimensions of,
799
connecting-rod ends, 800
Corliss, 773, 780
cost of, 1085
counterbalancing of, 788
cranks, dimensions of, 805
crank -pins, dimensions of, 801-
804
crank-pins, pressure on, 804
crank-pins, strength of, 803
crank-shafts, dimensions of, 813
crank-shafts for torsion and flex-
ure, 814
crank-shafts for triple-expansion,
815
crank-shafts, three-throw, 815
crosshead and crank, relative
motion of, 831
crosshead-pin, dimensions of, 804
cut-off, most economical point
of, 777
cylinder condensation, experi-
ments on, 753
cylinder condensation, loss by,
752
cylinders, dimensions of, 792
cylinder-heads, dimensions of , 794
cylinder-head bolts, size of , 795
dimensions of parts of, 792-817
eccentrics, dimensions of, 816
eccentric-rods, dimensions of, 816
economic performance of, 775-791
economy at various speeds, 780
economy, effect on, of wet- steam.
781
economy of compound vs. triple-
expansion, 781
economy of, in central stations,
785
economy of, simple and com-
pound compared, 780
economy under variable loads,
784
economy with superheated steam,
783
effect of moisture in steam, 781
estimating I.H.P. of compound,
755
estimating I.H.P. of single-cylin-
der, 755
efficiency in thermal units per
minute, 749
exhaust steam used for heating,
780 f
expansions in, table, 750
expansive working of steam in , ta-
ble, 747
flywheels, 817-824
flywheels, arms of, 820
IKDEX.
ste
1121
Steam-engine, flywheels, centrifugal
force in, 820
flywheels, diameters of, 821
flywheels, formulae for, 817
flywheels, thickness of rim of, 823
flywheels, speed variation in, 817
flywheels, strains in, 822
flywheels, weight of, 818, 819
flywheels, wire- wound, 824
flywheels, wooden rim, 823
foundations embedded in air, 789
frames, dimensions of , 817
friction of, 941
governors, fly-ball, 836
governors, flywheel, 838
governors, shaft, 838
governors, springs for, 838
guides, size of, 798
high piston speed in, 787
high-speed Corliss, 787
high-speed, performances of, 777-
780
high-speed, sizes of, 777-780
horse-power constants, 756-758
indicated horse-power (I.H.P.)
of single-cylinder, 755-761
indicator diagrams, 754
indicator diagrams, to draw
clearance line on, 759
indicator diagrams, to draw ex-
pansion curve, 759
indicators, effect of leakage, 761
indicators, errors of, 756
indicator rigs, 759
limitation of speed of, 787
links, size of , 815
link motions, 834-836
mean and terminal pressures, 743
marine, 1015-1019
mean effective pressure, calcula-
tion of , 744
measures of duty of, 748
non-condensing, 776, 778, 779
oil required for, 943
pipes for, 673
pistons, clearance of , 792
pistons, dimensions of , 795
piston-rings, size of, 796
piston-rods, fit of , 796
piston-rods, size of, 797
piston-rod guides, size of , 798
piston-valves, 834
prevention of vibration in, 789
progress in, 773
proportions of, 792-817, 1086
quadruple expansion, 772, 773
ratio of expansion of steam, 745
reversing gear, dimensions of,
816
rotary, 791, 792
shafts, bearings for, 810-813
shafts, bending resistance of, 808
shafts, dimensions of, 806-813
shafts, equivalent twisting mo-
ment of, 808
shafts, flywheel, 809
shafts, twisting resistance of, 806
single -cylinder, economy of, 775
Steam-engines, single-cylinder, water
consumption of, 776
single-cylinder, high-speed, sizes
and performances of, 778
slide-valves, crank-angles, table,
830
slide-valves, cut-off for various
lap and travel, table, 831,
.832
slide-valve, definitions, 824
slide-valve diagrams, Sweet's,
826
slide-valve diagrams, Zeuner's,
.827
slide-valve, diagram of port open-
ing, cut-off, and travel, 833
slide-valve, effect of changing lap,
lead, etc., 829
slide-valve, effect of lap and lead
825
slide-valve, lead, 829
slide-valve, port opening, 828
slide-valve, ratio of lap to travel,
.829, 831
slide-valves, relative motion of
crosshead and crank, 831
slide-valve, setting of, 834
small, coal consumption of, 786
small, water consumption of,
786
steam consumption per horse-
power-hour, 750
steam-jackets, influence of, 787
superheated steam in, 783
three-cylinder, 815
to change speed of, 837
to put on center, 834
triple-expansion, 769-772, 1017-
1019
triple -expansion and compound,
relative economy, 781
triple-expansion, crank-shafts for,
815
triple-expansion, cylinder pro-
portions, 769
triple-expansion, cylinder pro-
portion formulae, 769-771
triple-expansion, cylinder diame-
ters, 773
triple-expansion, cylinder ratios,
771
triple-expansion, high-speed, sizes
and performances of, 779,
780
triple.-expansion , non-condensing,
779
triple-expansion , sequence of
cranks in ,77 2
triple-expansion, steam -jacketed,
performances of, 779, 780
• triple-expansion, Sulzer, water
consumption of, 783
triple -expansion, theoretical mean
effective pressures, 770
triple-expansion, types of , 771
triple-expansion, water consump-
tion of, 777
valve-rods, dimensions of, 815
1122
ste
ItfDEX.
Steam-engines, water consumption
of, 753, 776, 777, 783, 785, 786
water consumption from indica-
tor-cards, 760
work of one pound of steam, 749
work of steam in single-cylinder,
746-753
wrist-pin, dimensions of, 804
Steam heat, storage of, 789
heating, 534-541
heating, diameter of supply mains,
539
heating, indirect, 537
heating, indirect, size of registers
and ducts, 539
heating of greenhouses, 541
heating, pipes for, 540
heating, properties of steam and
condensed water, 540
jackets on engines, 787
jet blower, 527
jet exhauster, 527
jet ventilator, 527
loop, 676
-metal, composition of, 325
pipes, 674-676
pipes, copper, strength of, 675
pipes, copper, tests of, 674
pipes, failures of, 676
pipes for engines, 673
pipes for marine engines, 674,
1016
pipes, riveted-steel, 675
pipes, uncovered, loss from, 676
pipes, valves in, 675
pipes, wire- wound, 675
pipe coverings, tests of, 471
power, cost of, 790
power, cost of coal for, 789
separators, 728
turbines, 790
vessels (see Ships)
Steel, 389-414
aluminum, 409
analyses and properties of, 389
and iron, classification of, 364
annealing of, 412, 413
axles, specifications for, 397
axles, strength of. 299
bars, effect of nicking, 402
beams, safe load on, 269
Bessemer basic, ultimate strength
of, 390
Bessemer, range of strength of,
.391, 392
billets, specifications for, 401
blooms, weight of, table, 176
bridge-links, strength of, 297
burning carbon out of, 402
castings, 405
castings, specifications for, 397,
406
castings, strength of, 299
chrome, 409
old-drawn, tests of, 305
cold-rolled, tests of, 305
color-scale for tempering, 414
columns, 256-261
Steel columns, Merriman's tables of
261
crank-pins, specifications for, 401
crucible, 410-414
crucible, analyses of. 411
crucible, effect of heat treatment,
411
crucible, selection of grades of,
410
crucible, specific gravities of, 411
effect of annealing on grain of, 392
effect of annealing on magnetic
capacity, 396
effect of cold on strength of, 383
effect of finishing temperature in
rolling, 392
effect of heat on grain, 412
effect of oxygen on strength of,
391
electrical conductivity of, 403
eye-bars, test of, 304
failures of, 403
fluid-compressed, 410
for car-axles, specifications, 401
for rails, specifications, 401
for milling cutters, 957
forgings, annealing of, 396
forgings, oil-tempering of, 396
forgings, specifications for, 397
hardening of, 393
heating of, for forging, 413
in Memphis bridge, tests of, 393
ingots, segregation in, 404
kinds of, for different uses, 397
life of, under shock, 240
low strength of, 392
main-rods, specifications for, 401
manganese, 407
manganese, abrasion of, 407
mixture of, with cast iron, 375
Mushet, 409
nickel, 407
nickel, tests of, 408
open-hearth, range of strength
of, 391, 392
open-hearth structural, strength
of, 391
parallel-rods, specifications, 401
plates (see Plates, steel)
rails, specifications for, 398
rails, strength of, 298
range of strength in, 391, 392
recalescence of, 402
relation between chemical com-
position and physical charac-
. ter of, 389
rivet, shearing resistance of, 363
rivet, specifications for, 399
rivets, specifications for, 401
rope, table of strength of, 338
rope, flat, table of strength of
339
shearing strength of, 306
sheets, weight of, 174
specific gravity of, 403, 411
specifications for, 397-402
splice-bars, specifications for,
398
INDEX.
ste-str
1123
Steel, spring, strength of, 299
springs (see Springs, steel)
strength of, 297r303
strength of, variation in, 398
structural, annealing of, 394, 395
structural, drilling of, 395
structural, earliest uses of, 405
structural, effect of punching
and shearing, 394
structural, for bridges, specifica-
tions of, 399
structural, for buildings, specifi-
cations of, 398
structural, for ships, specifications
of, 399
structural, properties of, 272-280
structural, punching of, 395
structural, riveting of, 394 •
structural, specifications for, 400
structural, size and weights, 177-
180
structural, treatment of, 394-396
structural, upsetting of, 394
structural, welding of, 394
struts, 259
tempering of, 414
tensile strength of, at high tem-
peratures, 382
tensile strength of pure, 392
tires, specifications for, 398
tires, strength of, 298
tool, heating of, 412
tungsten, 409
water-pipe, 295
welding of, 396
wire gauge, tables, 29
working of, at blue heat, 395
working stresses in bridge mem-
bers, 262
Stevedore rope, 340
Stokers, mechanical for steam-
boilers, 711
under-feed, 712
Stone-cutting with wire, 966
Stone, specific gravity of. table,
166
weight of, table, 166
strength of, 302, 312
Storage-batteries, 1045-1048
efficiency of, 1048
Storage of steam heat, 789
Storms, pressure of wind in, 494
Stoves, compressed-air heating, effi-
ciency of, 507
Stove foundries, cupola charges in,
949
Strain, 236
Strains, formulae for unit, in iron
and steel in structures, 379
Straw as fuel, 643
Stream, open, measurement of
flow, 584-588
Streams, fire, 579-581 (see Fire-
streams)
running, horse-power of, 589
Strength, compressive, 244-246
compressive, of woods, 311
loss of, in punched plates, 353
Strength, range of, in steel, 391, 392
shearing, of iron and steel, 306
shearing, of woods, table, 312
tensile, 242
tensile, of iron and steel at high
temperatures, 382
torsional, 281
transverse, 266-271
of aluminum, 318
of aluminum-copper alloys, 328,
329
of anchor-forgings, 297
of basic Bessemer steel, 390
of belting, 302
of blocks, 906
of boiler-heads, 285
of boiler-plate at high tempera-
tures, 383
of bolts, 292
of brick, 302, 312
of bridge-links, 298
of bronze, 300, 319-332
of canvas, 302
of cast iron, 370, 374
of cast iron, relation of, to sili-
con, 369
of cast-iron columns, 250-254
of cast-iron water-pipe, 251
of chains, table, 307
of chain cables, table, 340
of castings, 297
of cement mortar, 313
of chalk, 312
of columns, 246, 250-261
of columns. New York building
laws, 1019
of copper at high temperatures,
309
of copper plates, 300
of copper-tin alloys, 320
of copper-tin-zinc alloys, graphic
representation, 323
of copper-zinc alloys, 323
of cordage, table, 906
of crank-pins, 803
of double-riveted seams, calcu-
lated, 361
of electro-magnet, 1053
of flagging, 313
of flat plates, 283-286
of floors, 1019, 1021
of German silver, 300
of glass, 308
of granite, 302, 312
of gun-bronze, 321
of hand and hydraulic riveted
joints, 355
of iron and steel, effect of cold on,
383
of lime-cement mortar, 313
of limestone, 312, 313
of locomotive forgings, 297
of Lowmoor iron bars, 297
of malleable iron, 367
of Mannesman tubes, 296
of marble, 302
of masonry, 312
of materials, 236-346
1124
str-ten
IKDEX.
Strength of materials, Kirkaldy's
tests, 296-303
of perforated plates, 353
of phosphor-bronze, 327
of Portland cement, 302
of riveted joints, 299, 354-362
of roofs, 446, 1019
of rope, 301, 338, 339
of sandstone, 312
of sheet metal, 300
of silicon -bronze wire, 327
of soap stone, 312
of spring steel, 299
of spruce timber, 310
of stayed surfaces, 286
of steam-boilers, 700-711
of steel axles, 299
of steel castings, 299
of steel, open-hearth structural,
391
of steel propeller-shafts, 299
of steel rails, 298
of steel tires, 298
of stone, 312
of structural shapes, 272-280
of timber, 309-312, 1079
of twisted iron, 241
of unstayed surfaces, 284
of yellow pine, 309
of welds, 300, 308
of wire, 301, 303
of wire and hemp rope, 301, 340
of wrought -iron columns, 255
tensile, of pure steel, 392
Stress and strain, 236
Stress due to temperature, 283
Stresses allowed in bridge members,
262-264
combined, 282
effect of, 236
in framed structures, 440-447
in steel plating due to water
pressure, 287
permissible in structural mate-
rials, 381
produced by shocks, 241
Structural shapes, elements of,
248
shapes, moment of inertia of, 248,
273-280
shapes, properties of, 272-280
shapes, radius of gyration of,
248
shapes, sizes and weights, 177-180
steel (see Steel, structural)
Structures, formulne for unit strains
in iron and steel in, 379
Strut, moving, 436
Struts, steel, formulae for, 259
strength of, 246
wrought-iron , formulae for, 259
Sugar manufacture, 643
solutions, concentration of, 465
Sulphate of lime, solubility of, 464
Sulphur dioxide and ammonia-gas,
t properties of, 992
dioxide refrigerating-machine , 985
influence of, on cast iron, 367, 370
Sulphur, influence of, on steel, 389
Sum and difference of angles, func-
tions of, 66
Superheated steam, economy of
stearn-engines with, 783
Surface condensers, 840-844
Surfaces, unstayed flat, 284
Suspension cableways, 915
Sweet's slide-valve diagram, 826
Symbols, chemical, 163
•electrical, 1078
Synchronous motor, 1071
T shapes, properties of Carnegie
steel, table, 279
Tail-rope system of haulage, 913
Tanbark as fuel, 643
Tangent of an angle, 65
table of 159-162
Tanks, plating and framing for,
287 m
capacities of, tables, 121, 125,
126 s
Tannato of soda boiler compound,
718
Taps for machine screws, 970
formulae and table for screw-
threads of, 207
Tap-drills, sizes of, 208
table of, 970, 971
Taper, to set in a lathe, 956
pins, 972
Tapered wire rope, 916
Taylor's rules for belting, 880-882
theorem, 76
Tees, Pencoyd steel, weights and
sizes, 179
Teeth of gears, forms of, 892
of gears, proportions of, 889, 890
Telegraph-wire, copper, table of
size, weight and resistance of , 221
joints in, 217
tests of, table, 217
Telescope, Mesuro and Nouel's
pyrometric, 453
Temperature, absolute, 461
determination by color. 454
determinations of melting-points,
452
of fire, 622
rise of, in combustion of gases,
623
stress due to, 283
effect of, on strength, 309, 382
Tempering, effect of, on steel, 412
of steel, 414
oil, of steel forgings. 396
Tenacity of metals, 169
of metals at various tempera-
tures, 309 382-384
Tensile strength, 242-244
strength, increase of, by twist-
ing, 241
strength of iron and steel at high
temperatures, 382
strength of pure steel, 392
tests, shapes of specimens for,
243
IKDEX.
ten-tra
1125
Tension and flexure, combined, 282
and shear, combined, 282
Terne-plate, 182
specifications for, 1088
Terra-cotta, weight of, 181
Test-pieces, comparison of large and
small, 393
Tests of aluminum alloys, 330
of aluminum brass, 329
of cast iron, 369
calorimetric , of coal, 636
compressive, of wrought - iron
bars, 304
compressive, specimens for, 245
tensile, precautions in, 243
tensile, specimens for, 243
tensile, table of, 242
of brick, 312
of cast-iron columns, 250-254
of centrifugal pumps, 609
of chains, table, 307
of chain cables, 308
of cold-drawn steel, 305
of cold-rolled steel, 305
of fans, 514, 522, 524
of gas-engines, 849
of petroleum-engines, 851
of hydraulic ram, 615
of lap and butt riveted joints, 360
of materials, Kirkaldy's, 296-
303
of nickeUsteel, 408
of pine timber, 309
of pulsometers, 613
of pumping-engines, 611
of riveted joints, table, 303
of steam-boilers, 685-699
of steam-boilers, rules for, 690-
6956
of steel eye-bars, 304
of steel plate, 390
of steel in Memphis bridge, 393
of turbine wheels, 596
of woods, 306
of wrought-iron columns, 305
of vulcanized rubber, 316
Theory of exponents, 36
Thermal capacity, definition of, 457
units, 455, 660
units, comparison of British and
French, 455
Thermodynamics, 478
Thermometers, 448
Thermometer, air, 454
scales, comparison of, 448
scales, comparison of, table, 449
Threads, pipe, 195
Three-phase circuits, 1068
Toothed- wheel gearing, 439, 887-
906 (see Gearing)
Tidal-power, utilization of, 600
Tie-rods for brick arches, 281
Tiles, weight of, 181
Timber beams, safe loads, 1023
expansion of, 311
measure, 20
properties of, table, 310
resistance of drift-bolts in, 290
Timber beams strength of, 309-312,
1079
table of contents in feet, 21
weight of, table, 310
Time, measure of, 20
Tin, properties of, 168
-aluminum alloys, 330
-copper alloys, 319, 320
-copper-aluminum alloys, 330
-copper-zinc alloys, 322, 323
lined pipe, sizes and weights,
table, 201
pipe, weights and sizes of, 200
plate, 182
plate, specifications for, 1088
plate, American packages of
182
plate, comparison of gauges and
weights, table, 182
Tires, steel, friction of, on rails, 928
steel, specifications for, 398
steel, strength of, 298
Tobin bronze, analyses and proper-
ties of, 325, 326
Toggle-joint, 436
Tons per mile, equivalent of, 27
Tonnage of vessels, 19, 1001
Tools, machine, speed of, 953
metal -cutting, forms of, 955
Tool-steel, heating of, 412
Torque of an armature, 1056
Torsion and compression com-
bined, 283
and flexure combined, 283
elastic resistance to, 282
of shafts, 806
Torsional strength, 281
Total heat of evaporation, 462
Track bolts, 210
spikes, sizes and weights of, 212
Tractive power of locomotives, 853,
857
Tractrix, 50
Trains, railroad, resistance of, 851
railroad, resistance due to friction,
939
railroad, speed of, 859
Trammels, to describe an ellipse
with, 46
Tramway, compressed-air, 510
Tramways, wire-rope, 914
Transformers, electric, 1070
Transmission, compressed-air, 488
compressed air, efficiency of, 508
electric, 1033-1041
electric area of wires, 1033
electric, cost of copper, 1040
electric, economy of, 1036
electric, efficiency of, 1038
electric, systems of, 1041
electric, weight of copper for
1033, 1076
electric, wire table for, 1037
hydraulic -pressure, 616-620 (see
Hydraulic - pressure transmis-
sion)
of heat (see Heat)
pneumatic postal, 509
1126
tra-ven
INDEX,
Transmission, rope, 922-927 (see
Rope-driving)
wire-rope, 917-922 (see Wire
rope)
Transmission-rope, 340
Transporting power of water, 565
Triple -expansion engine, 769-772
(see Steam-engines)
Transverse strength, 266-271
strength of beams, formulae for,
268
strength, coefficient of, 267
Trapezium , 54
Trapezoid, 54
Trapezoidal rule, 56
Triangle, mensuration of, 54
problems in, 41
spherical, 61
trigonometrical solution of, 68
Trigonometry, 65-68
Trigonometrical formulae, 66
functions, relations of, 65
functions, signs of, 66
functions, table of natural, 159-
161
functions, table of logarithmic,
162
Triple-effect evaporator, 463
Trough plates, properties of steel,
table, 274
Troy weight, 20
Trusses, Burr, 443
Fink roof, 446
Howe, 445
King-post, 442
Pratt, 443
Queen-post, 442
roof, 446
Warren girder, 445
Whipple, 443
Tubes, boiler, table, 196
boiler, table of areas of, 197
condenser, 840
horse -power of water flowing in,
589
of different materials, table for
calculating weights of, 169
expanded boiler, holding power
of, 307
iron, collapsing pressure of, 265
Mannesmann, strength of, 296
seamless brass, table, 198
steam-boiler, holding power of,
704
steam-boiler, iron vs. steel, 704
steam-boiler, material for, 704,
709
strength of small, 266
welded solid-drawn steel, 199
wrought-iron, extra-strong, 196
Tube plates, steam-boiler, rules for,
704
Tubing, brass, weight of, table, 200
copper, weight of, table, 200
lead and tin, 200
zinc, weight of, table, 200
Tungsten-aluminum alloys, 330
Tungsten steel, 409
Turbines, steam, 790, 1085
steam, bearings for, 941
Turbine wheels, 591-599
wheels, dimensions of, 597
wheels, efficiency of, 594
wheels, Pelton, 597
wheels, proportions of, 591
wheels, table, 595
wheels, tests of, 596
Turf as fuel, 643
Turnbuckles, 211
Turret lathes, cutting-speed of, 954
Tuyeres for cupolas, 948
Twin-screw vessels, 1017
Twist-drill gauge, tables, 29
Twist-drills, sizes and speeds, 957
Twisted iron bars, 241
Two-phase currents, 1068
Type metal, 336
Uehling-Steinbart pyrometer, 453
Unequal arms on balances, 19
Units, electrical, 1024
equivalent value of electrical and
mechanical, 1026
of the magnetic circuit, 1050
Unit of evaporation, 677
of force, 415
of power, 429
of heat, 455, 660
of work, 428
Unstayed surfaces, strength of, 284
Upsetting of structural steel, 394
United States, population of, 12
standard gauge, sheet-metal, 30
standard gauge, sheet -metal, ta-
ble, 31
Vacuum, drying in, 466
pumps, 612
Valve-gears, steam-engine, 824-836
Valve-rods, steam-engine, 815
(see Steam-engines)
Valves, marine-engine, 1016
pump, 606
in steam -pipes, 675
Vapors, saturation-point of, 480
Vapor water, weight of, 484
and gas mixtures, laws of, 480
for refrigerat ing-machines, 982
Varnish, 387
Velocity, angular, 425
definition of. 423
expression of, 429
linear, of a turning body, 425
measure of, 27
of air in pipes by anemometer,
491
parallelogram of, 426
table of height corresponding to a
given acquired 425
of water in cast-iron pipe, 567
of water in open channels, 564
Ventilating fans, 517-525
ducts, flow of air in, 530
Ventilation, 528-546
air-cooling for, 531
blower system , 545
IHDEX.
veil-win
1127
Ventilation, efficiency of fans and
chimneys, 533
head of air, 533
of large buildings, 534
of mines, 531
Ventilators, centrifugal, for mines,
521
Ventilator, steam -jet, 527
Venturi meter, 583
Versed sine of an angle, 65
sine, relations of, in circle, 58
Verticals, formula for strains in,
444
Vertical high-speed engines, 777
Vessels (see Ships)
Vibration of steam-engines, 789
Vis- viva, 428
Volt, 1024
Vulcanized rubber, tests of, 316
Walls of buildings, 1019
Warehouse floors, 1019
Warren girders, stresses in, 445
Washers, sizes and weights of, 212
Washing of coal, 638
Water, 547-555
abrading power of, 565
analyses of, 553, 554
boiling-point of, 550
boiling-point at various baro-
metric pressures, 483
comparison of head, in feet, with
various units, 548
compressibility of, 164, 551
consumption of locomotives, 862
consumption of steam-engines,
753,776,777,783,785
erosion by flowing, 565
evaporation of, in reservoirs and
channels. 463
expansion of, 547
fall, efficiency of. 588
fall, power of, 588
flow of, 555-588 (see Flow of
water)
flowing in tube, horse-power of,
589
flowing measurement of, 582-
588
freezing-point of, 550
hardness of, 553
head of, 557
head of, equivalent to pounds per
square inch table. 549
heat-units per pound, 548
horse-power required to raise, 601
impurities of 551
jets, 579
meters 579
power 588-620
power plants, high-pressure, 1081
power, value of. 590
pressure due to weight of, 549
pressure of one inch. 27 549
pressure of one foot 27, 549
price of 579
pumping by compressed air, 505a
purification of 554
Water, quantity discharged from
pipes, 573
•elation of
diameter of pipe to
capacity, 566
softening of, 554
specific heat of, 550
transporting power of, 565
velocity of, in cast-iron pipe,
567
velocity of, hi open channels,
564
weight of, 27,547,548
gas, 648
gas, analyses of, 653
gas, manufacture of, 652
gas plant, efficiency of, 654
gas plant, space required for,
656
lines, coefficient of, 1002
pipes, riveted-steel, 295
pipe, cast-iron, transverse
strength of , 251
pipe, cast-iron, weight of, 188
tower (see Stand-pipe)
vapor and air mixture, weight
of, 484
vapor, weight of, table, 484
wheel, 591-599
wheel, Pelton, 597, 1081
wheels, power of, 1082
Watt, definition and value of, 1024
Waves, ocean, power of, 599
Weathering of coal, 637
Wedge, 437
volume of , 61
Weighing on incorrect balance, 19
Weights and measures, 17-27
and measures, Metric, 22-26
Weight and pressure per unit area,
Metric equivalents of, 27
of materials, 164-166 (see also
material in question)
Weir-dam measurement, 586
Weirs, flow of water over, 555, 586
Bazin's experiments, 587
Weir formulae, Francis's, 586
table, 587,588
Welding, electric 1044
of steel, 394, 396
Welds, strength of, 300, 308
Wetted surface of ships, 1005
Wheat, weight of, 170
Wheel and axle, 439
Wheels, emery, 967-970 (see Emery
wheels)
polishing, speed of, 968
turbine. 591-599 (see Turbine
wheels)
Whipple truss, stresses in, 443
White-metal alloys. 336
composition of, 335
Whitworth process of fluid com-
pressed steel, 410
Wiborg's air-pyrometer, 453
Wind, 492-494
force of, 492
pressure of, in storms, 494
strain on stand-pipes, 293
1128
win-wro
IKBEX.
Windlass, differential, 439
Windmills, 494-498
capacity of 496
cost of, 498
economy of, 497
efficiency of, 494
horse-power of, 497
Winding-engines, 909
Wire, aluminum, properties of, 225
aluminum bronze, properties of,
225
brass, properties of, 225
brass, weight of, table, 202
copper, properties of, 225
delta-metal, properties of, 225
copper, rules for resistance of, 222
copper, specifications for, 225
copper telegraph, size, weight,
and resistance of table, 221
copper, weight of, table, 202
electric , carrying capacity of, 1033
electric, fusion of, 1032
electric, heating of, 1032
electric, insulation of, 1033
electric, table, 1034-1035
galvanized iron, specifications for,
224 >
galvanized iron, for telegraph and
telephone lines, 217
galvanized steel strand, 223
gauges, tables, 29
insulated copper, 221
iron, 216
nails, 214, 215
phosphor-bronze, strength of, 327
piano, size and strength of, 224
plough-steel, 224
phosphor-bronze, properties of,
225
platinum, properties of, 225
silicon bronze, properties of, 225
silicon bronze, strength of, 327
stranded feed, table of sizes and
weights, 222
strength of, 216, 301, 303
telegraph, joints in, 217
telegraph, tests of, table, 217
telegraph, weight per mile-ohm,
217
wound flywheels, 824
ropes, 226-231
rope, bending curvature, 921
rope, bending stress of, 918
rope, care of, 231
rope, elastic limit of, table, 917
rope for guys and rigging, 228
rope for transmission, dimensions,
strength, and properties, 227
rope, galvanized steel, dimen-
sions, strength, and proper-
ties, 229
rope, locked, 231
rope, plough-steel, 227, 228
rope, radius of curvature of, 922
rope, sheaves for, 917, 919
rope, splicing of, 346
rope, strength and weight of, 301,
340
Wire rope haulage, 912-916 (see
Haulage)
ropes, tapered, 916
rope tramways, 914
rope transmission, 917-921
rope transmission, deflection of
rope, 920
rope transmission, horse-power
transmitted, 919
rope transmission, inclined, 921
rope transmission, limits of span,
920
rope transmission, long-distance,
921
rope, use of , 231
table , copper , 2 1 8-220 , 1034 , 1035-
1037
Wiring-tables, 1037
Wohler's experiments, on strength
of materials, 238
Wood as a fuel, 639, 640
composition of, 640
compressive strengths of, 311
expansion of, 311
heat required to expel water
from, 640
heating value of, 639
holding power of bolts in, 291
nail-holding power of, 291
screws, holding power of, 290
specific gravity of, table, 165
weight of, table, 165
strength of, 302, 309-312, 1079
tests of, 306
weight of, per cord, 232
Woods, shearing strength of various
table, 312
specific heats of, 458
weight of various, table, 310
Wooden flywheels, 823, 824
Woodstone, properties of, 316
Woolf compound engines, 762
Wootten's locomotive, 855
Work, definition of, 27, 428
expression of, 429
measure of, 27
of acceleration, 430
of accelerated rotation , 430
of adiafcatic compression, 501
of friction, 938
of a horse, 434
of a man, 433
rate of, 27
unit of, 27, 428
World's Fair buildings, specifica-
tions of wrought iron for, 379
Worm-gear. 440
Worm-gearing, 897, 1086
Wrist-pins, steam-engine, 804
Wrought iron, 377-379
iron bars, compression tests of, 304
iron built columns, 257
iron columns, tests of, 305
iron chain cables, 308
iron columns, Merriman's table
for,. 260
iron, influence of chemical com-
position on properties of, 377
ItfDEX.
1129
Wrought iron , influence of rolling on,
377
iron pipe, standard, table of
dimensions, 194
iron, slag in, 377
iron, specifications for, 378
iron, strength of, 245, 297, 300,
304, 378
iron, strength of, at high temper-
atures, 383
iron tubes, extra-strong, table,
196
Xylolith, properties of, 316
Y connection for alternating cur-
rents, 1068
Yield-point, 237
determination of, 237
Z bars, Carnegie steel, properties of,
table, 280
weights and sizes, 178
Zero, absolute, 461
Zeuner's slide-valve diagram, 827
Zinc, properties of, 168
aluminum alloys, 330
-copper alloys, strength of, 323
-copper alloys, table of composi-
tion and properties, 321
-copper-iron alloys, 326
-copper-tin alloys, specific gravi-
ties of, 323
-copper- tin alloys, table of proper-
ties and composition, 322
-copper-tin alloys , variation in
strength of, graphic representa-
tion, 323
-copper-tin alloys, variation in
strength of, 324
tubing, weight of, table, 200
use of, in boilers, 720
Zone, spherical, 62
of spheroid, 63
of spindle, 63
ALPHABETICAL INDEX TO ADYERTISEIEHTS.
PAGE
ALLIS-CHALMERS COMPANY
ALPHONS CUSTODIS CHIMNEY CONSTRUCTION CO.. . , ,22
AMERICAN ENGINE COMPANY 6
AMERICAN MANUFACTURING COMPANY, THE 13
AMERICAN SHEET & TIN PLATE COMPANY , 28
ANSONIA BRASS & COPPER COMPANY .12
ATLANTIC, GULF, & PACIFIC COMPANY , 26
ATLAS PORTLAND CEMENT COMPANY 24
BALDWIN LOCOMOTIVE WORKS 2
BONNOT COMPANY, THE 18
BOSTON BELTING COMPANY 15
BOSTON BLOWER COMPANY 20
BRIDGEPORT CHAIN COMPANY, THE 21
CARPENTER & COMPANY, GEO. B 14
CHAPMAN VALVE MANUFACTURING COMPANY 17
CRESSON & COMPANY, GEO. V 14
EPPING-CARPENTER COMPANY 5
GARVIN MACHINE COMPANY, THE. . 18
GENERAL ELECTRIC COMPANY, THE.. . 2
GOUBERT MANUFACTURING COMPANY, THE 9
GREEN FUEL-ECONOMIZER COMPANY, THE 8
HANCOCK INSPIRATOR COMPANY, THE 3
HARRISBURG FOUNDRY AND MACHINE WORKS 6
HARTFORD STEAM BOILER INSPECTION AND INSURANCE CO 16
HENDEY MACHINE COMPANY, THE 19
INGERSOLL-RAND COMPANY 4
JEWELL BELTING COMPANY. ... 15
KENNICOTT WATER SOFTENER COMPANY ; 10
KEUFFEL & ESSER COMPANY 27
LAMBERT HOISTING ENGINE COMPANY 11
LIDGERWOOD MANUFACTURING COMPANY 11
LODGE & SHIPLEY MACHINE TOOL COMPANY, THE 20
MAURER & SON, HENRY ' 22
MORSE TWIST DRILL AND MACHINE COMPANY 17
NATIONAL METER COMPANY 25
NATIONAL TUBE COMPANY 3
NEW YORK INSULATED WIRE COMPANY - 21
NORTON EMERY WHEEL COMPANY ' 16
NORWALK IRON WORKS COMPANY, THE 5
~UEEN & COMPANY, INCORPORATED 27
.ANDOLPH-CLOWES COMPANY 23
RIDER-ERICSSON ENGINE COMPANY 10
ROEBLING'S SONS COMPANY, JOHN A. ..»...: 12
SELLERS & COMPANY, WILLIAM, INCORPORATED 19
SIMMONS COMPANY, JOHN 25
SKINNER CHUCK COMPANY, THE 20
SNIDER-HUGHES COMPANY, THE 20
STIRLING COMPANY, THE 8
UNIVERSAL DRAFTING MACHINE COMPANY. 21
WALWORTH MANUFACTURING COMPANY 28
WARREN FOUNDRY & MACHINE COMPANY 23
WILEY, JOHN & SONS 24-26
YALE & TOWNE MANUFACTURING COMPANY, THE 1
CLASSIFIED INDEX TO ADVERTISEMENTS.
BELTING AND HOSE. ' PAGE
Boston Belting Co 15
Jewel] Belting Co 15
BLOWERS. Boston Blower Co 20
BOILER INSPECTION AND INSURANCE.
Hartford Steam Boiler Inspection and Insurance Co 16
BOILER TUBES. National Tube Co 3
BOILER TUBES (BRASS). Randolph-Clowes Co 23
BOILER WATER, SOFTENING AND PURIFICATION.
Kennicott Water Softener Co 10
BOILERS, STEAM.
Stirling Co., The 8
BOOKS. John Wiley & Sons 24-26
BRASS RODS, SHEETS, TUBES, WIRE, ETC.
Ansonia Brass & Copper Co 12
Randolph-Clowes Co 23
CASTINGS. Warren Foundry & Machine Co 23
CEMENT, AMERICAN PORTLAND. Atlas Portland Cement Co 24
CEMENT MACHINERY — ROTARY KILNS, BALL AND TUBE MILLS, MIXERS,
ETC.
Bonnot Co., The 18
CHAIN. Bridgeport Chain Co 21
CHAIN HOISTS. Yale & Towne Mfg. Co., The 1
CHIMNEYS. Alphons Custodis Chimney Construction Co 22
CHUCKS, MILLING CUTTERS, REAMERS, SPRING CUTTERS, TAPS, ETC.
Morse Twist Drill and Machine Co 17
Skinner Chuck Co., The 20
COMPRESSORS — AIR, GAS, ETC.
Ingersoll-Rand Co 4
Norwalk Iron Works Co., The 5
CONDENSERS, WATER-TUBE HEATERS, ETC.
Snider-Hughes Co., The 20
COPPER WIRES, CABLES, BARS, SHEETS, TUBES, ETC.
Ansonia Brass & Copper Co 12
!RUSHERS — ORE, ROCK, STONE.
Geo. V. Cresson Co 14
DRAFTING MACHINES. Universal Drafting Machine Co 21
DREDGING ENGINEERS AND CONTRACTORS.
Atlantic, Gulf & Pacific Co 26
DRILLS, POWER AND HAND.
Ingersoll-Rand Co 4
Norwalk Iron Works Co., The 5
DRILLS, TWIST. Morse Twist Drill and Machine Co 17
DRYER CYLINDERS. Warren Foundry & Machine Co 23
ELECTRICAL GENERATORS, MOTORS, ARC AND INCANDESCENT LAMPS,
ETC.
General Electric Co., The 2
EMERY AND CORUNDUM WHEELS. Norton Emery Wheel Co t . . 16
ENGINEERS AND CONTRACTORS.
Allis-Chalmers Co 7
ENGINES.
Allis-Chalmers Co 7
American Engine Co 6
Harrisburg Foundry and Machine Works
Rider-Ericsson Engine Co 10
ENGINES, BLOWING.
Lambert Hoisting Engine Co H
Lidgerwood Mfg. Co . . . . 11
FEED-WATER HEATERS, SEPARATORS, TRAPS, EXHAUST HEADS, ETC. -
Goubert Manufacturing Co 9
FIRE BRICK, TILES, SLABS, CUPOLA LININGS, CLAY RETORTS, ETC.
Maurer & Son, Henry. , • 23
CLASSIFIED INDEX TO ADVERTISEMENTS.
PUBI/-ECONOMIZERS AND FURNACES.
Green Fuel-Economizer Co., The 8
HOISTING MACHINERY — ELEVATORS, CONVEYORS, ETC.
Lambert Hoisting Engine Co 11
Lidgerwood Mfg. Co. 11
HYDRANTS. Chapman Valve Mfg. Co 17
INSULATED WIRES AND CABLES.
Ansonia Brass & Copper Co 12
New York Insulated Wire Co 21
LOCOMOTIVES. Baldwin Locomotive Works 2
METERS. National Meter Co 25
MILLING MACHINES, SHAPERS, PLANERS, PUNCHES, ROLLS, SHEARS,
LATHES, MACHINE TOOLS, BOLTS, ETC.
Garvin Machine Co 18
Hendey Machine Co 19
Lodge & Shipley Machine Tool Co., The 20
Sellers & Co., William (Incorporated) 19
MINING ANI? QUARRYING MACHINERY.
Allis-Chalmers Co 7
Ingers oil Rand Co 4
Norwalk Iron Works 5
PACKING — PISTON, VALVE, JOINT. Boston Belting Co 15
PIPE, WATER AND GAS.
National Tube Co 3
Simmons Co. , John 25
Walworth Mfg. Co 28
Warren Foundry & Machine Co 23
PNEUMATIC TOOLS. Ingersoll-Rand Co 4
PUMPING MACHINERY.
Allis-Chalmers Co 7
Epping-Carpenter Co 5
National Meter Co 25
Rider-Ericsson Engine Co 10
Snider-Hughes Co., The 20
RUBBER GOODS. Boston Belting Co
SCALE-PREVENTION. Kennicott Water Softener Co 10
SHEET STEEL, TIN PLATE, GALVANIZED IRON, ETC.
American Sheet & Tin Plate Co 28
STEAM SPECIALTIES AND ENGINEERING APPLIANCES.
Goubert Manufacturing Co 9
Hancock Inspirator Co
Walworth Mfg. Co 28
SURVEYING INSTRUMENTS.
Keuffel & Esser Co 27
Queen & Co., Incorporated ^7
TOOL GRINDERS. Norton Emery Wheel Co !°
TRANSMISSION ROPE. n
American Manufacturing Co • j^
Geo. B. Carpenter & Co {4
VALVES— GAS, WATER, AND STEAM. Chapman Valve Mfg. Co. ...... 17
Hancock Inspirator Co -^
WATER-SUPPLY. Rider-Ericsson Engine Co 1U
WIRE ROPE AND TELEGRAPH, TELEPHONE, AND TROLLEY WIRE.
Ansonia Brass & Copper Co 12
Koebling's Sons Co., John A. 12
Triplex Blocks
are available for almost
every contracting and
engineering work. They
are the most efficient
hand hoists made, and
effect pronounced savings
in time, labor and repair
bills.
Tale <y Towne Chain Blocks
are constructed upon the
most approved mechan-
ical principles, and each
part is carefully made and
inspected. This makes
each block absolutely safe
and promotes ease of operation and
long life.
TRIPLEX. — For greatest ease and quick-
ness. 14 sizes. YL to 20 tons.
DUPLEX. — For ease and handiness. 10
sizes. Yi to 10 tons.
DIFFERENTIAL. — The Cheapest reliable
chain block. 7 sizes. ^ to 3 tons.
ELECTRIC HOIST. — Best where conditions
justify it. 4 sizes, i to 6 tons.
Catalogues and other information sent on request.
The Yale & Towne Mfg. Co.
9-15 Murray Street, New York
Local Offices: Chicago, Boston, Philadelphia, San Francisco
BALDWIN LOCOMOTIVE WORKS.
Burnham, Williams & Co.,
Philadelphia, U. S. A.
LOCOMOTIVES
of all descriptions.
Mine and Furnace Locomotives operated by
• Steam, Compressed Air, and Electricity.
The General Electric Company's
Type M Control
(Sprague-General Electric System)
FOR ELECTRIC TRAINS HAS BEEN ADOPTED EXCLU-
SIVELY BY THE NEW YORK UNDERGROUND RAILWAY.
(Interborough Rapid Transit Company)
ALL ELECTRIC TRAINS ON MANHATTAN ISLAND ARE
EQUIPPED WITH THE SPRAGUE-GENERAL
ELECTRIC SYSTEM OF CONTROL.
General Office: SCHENECTADY, N. Y.
New York Office : 44 Broad Street, Sales Offices in all large cities
THE HANCOCK VALVES
Made in one gr^de ONLY
FOR. ALL KINDS OF SERVICE
OUR GUARANTEE
"We guarantee that each and every
Hancock Globe, Angle, 60° and Cross
Valve, with our monogram on it, has
been tested with 1000 pounds water
pressure and found tight before
leaving the works. ' '
Write for our book of
•• VaJves"
The Hancock Inspirator Co,
85-87-89 Liberty St. 22-24-26 So. Canal St.
NEW YORK CHICAGO
NATIONAL TUBE COMPANY,
MANUFACTURERS OF
LAP- AND BUTT-WELDED WROUGHT PIPE
0/8 INCH TO 30 INCHES DIAMETER.)
Charcoal-Iron and Mild-Steel Boiler-Tubes
FOR
Marine, Locomotive, and Stationary Boilers,
SEAMLESS TUBES.
TROLLEY POLES, OIL- AND WATER-WELL TUBULAR GOODS.
LOCAL SALES OFFICES:
BOSTON, NEW YORK, PHILADELPHIA, PITTSBURG, CHICAGO.
SAN FRANCISCO,
FOREIGN SALES-OFFICE: LONDON, ENGLAND
3
AIR POWER
APPLIANCES
For thirty-five years the standards of
progress in engineering work
AIR AND GAS COMPRESSORS
ROCK DRILLS
COAL-MINING MACHINERY
STONE CHANNELERS
PNEUMATIC PUMPING SYSTEMS
PNEUMATIC TOOLS
Complete Pneumatic Power Equipments
Descriptive literature sent on request
INGERSOLL-RAND
CO.
II BROADWAY, NEW YORK
OFFICES IN ALL THE PRINCIPAL CITIES OF THE WORLD
[HE NORWALK AIR COMPRESSOR
OF STANDARD PATTERN
is built with Tandem
Compound Air Cylind-
ers. Corliss Air valves
on the intake cylinders
insure small clearance
spaces. The Intercooler
between the cylinders
saves power by remov-
ing the heat of compres-
sion before the work is
done, not after, and
the compressing is all
done by a straight pull
and push on a continu-
ous piston rod. The
Compressor is self-con-
tained ; the repair bills
are reduced to a minimum, and the machine is economical and efficient.
Special machines for high pressures and for liquefying gases. Compound and
Triple Steam Ends.
4 catalog, explaining its many points of superiority, is sent free to
bus/ness men and engineers who apply to
THE NORWALK IRON WORKS CO.,
SOUTH NORWALK, CONN.
EPPING-CARPENTER COMPANY,
PITTSBURG, PA.
IMPROVED PUMPING MACHINERY
FOR EVERY SERVICE.
Also Surface Condensers, with Air and Circulating Pumps,
both Single and Duplex.
New York Office,
141 Broadway.
Cleveland Office,
New England Building.
Harrisburg
Engines
8 TO 3.0OO HORSE POWER
HIQH SPEED. MEDIUM SPEED
AND CORLISS
Harrisburg ^""A™ Works
HARRISBURG, PA.
AMERICAN-BALL DUPLEX
COMPOUND ENGINE
AND
DIRECT-CONNECTED
GENERATOR.
The latest develop-
ment in practical
steam-engineering.
The highest econ-
omy of steam with
the simplest possi-
ble construction.
Complete electric and steam equipments fur-
nished of our own manufacture.
AMERICAN ENGINE CO.,
New York Qffice-95 Liberty St. Bound Brook, N- J.
e
ALLIS=CHALMERS CO.,
GENERAL OFFICE:
CHICAGO, U. S. A.
New York Life Building.
SOLE: BUILDERS OF
REYNOLDS CORLISS ENGINES
FOR ALL POWER PURPOSES.
Reynolds Horizontal Cross-Compovind Engine.
HIGH DUTY,
TRIPLE EXPANSION
AND COMPOUND IUIIIIII1U LIIUIIlLUl
Sewerage and Drainage Pumps.
Blowing and Hoisting Engines.
RIEDLER PUMPS AND AIR COMPRESSORS.
BRANCH OFFICES:
NEW YORK, 7J Broadway*
BOSTON. PITTSBURG* CHARLOTTE. ATLANTA.
NEW ORLEANS. DENVER. SPOKANE.
SALT LAKE CITY. SEATTLE. SAN FRANCISCO.
7
THE
Stirling Consolidated Boiler Co.
Successors to the plants and water-tube boiler
business of the Stirling Company, Barberton,
Ohio, and the Aultman & Taylor Machinery
Company, Mansfield, Ohio.
MANUFACTURERS OF
Stirling, A. & T. Horizontal, and Cahall
Vertical Water=tube Boilers, Chain
Grate Stokers, and Superheaters.
Works General Offices
BARBERTON, OHIO TRINITY BUILDING
MANSFIELD, OHIO ill BROADWAY, NEW YORK
GREEN'S FUEL ECONOMIZER
FOR STEAM BOJLERS.
AD VANTAGES. -Heats the feed water to a High Temperature, thui
•ffeetlnff a GREAT SAVING- IN COAL. Can be applied to any type of bullet
without stoppage of works. A large volume of water always in reserve at the
•raporatlve point ready for immediate delivery to the boilers.
SOLE MAKERS IN THE UNITED STATES.
THE GREEN FUEL ECONOMIZER CO. of Matteawan, I. I
I
The Stratton
Steam Separator
INSURES
Dry Steam
Its construction is familiar to
engineers in every part of
the world, and the plan on
which it operates has never
been improved upon. The
unrestricted flow of steam
contrasts strongly with the
baffle-plate type.
We also manufacture
THE GOUBERT
FEED=WATER HEATER
Which is used in most of the largest
street-railway and electric plants
in the country. It has straight
tubes, free exhaust, curved tube-
plates, and is made in sizes from
50 to 6,000 horse-power.
Send for our new Catalogs.
The Goubert
Mfg. Comp'y
85 Liberty St., N. Y., U. S. A.
9
DOMESTIC WA1ER=SUPPLY
Without Depending on the W«nd.
THE IMPROVED RIDdR
AND IMPROVED ERICSSON
HOT-AIR PUMPING-
ENGINES
In use for twenty-five years.
More than 20,000 sold.
Specified by the Leading Engi-
neers of this country.
Catalogue on application to neaf
est store.
RIDER=ERICSSON ENGINE CO.,
35 "Warren Street, New York.
239 Franklin Street, Boston.
692 Craig Street, Montreal, P. Q.
40 Dearborn Street, Chicago.
40 Worth 7th Street, Philadelphia.
Teniente-Bey 71, Havana, Cuba.
SOFT WATER
FOR ALL
INDUSTRIAL
PURPOSES.
KENNICOTT
WATER
SOFTENER CO.,
3580 Butler St.,
Chicago.
10
HOISTING ENGINES
of the LIDGERWOOD make
are built to gauge on the Duplicate
Part System. Quick delivery assured.
STAN DARD 1or3Xf)S£3,.
Over 24,000 in use.
STEAM AND ELECTRIC HOISTS.
CABLEWAYS,
HOISTING AND
CONVEYING DEVICES,
For
Mining, Quarrying, Logging,
Dam Construction, etc.
LIDGERWOOD MFG. CO,,
Send for Latest Catalogue. 96 LIBERTY ST., NEW YORK.
HOISTING ENGINES
ELECTRIC HOISTS
are strictly up to date and built for
business, and are built to gauges and
templates adapted for General Con"
trading, Pile*driving, Quarrying, Min-
ing, and all Hoisting and Conveying
Purposes.
LOGGING ENGINES
CABLEWAYS
Send for Catalogue D.D.
LAMBERT HOISTING ENGINE CO.,
MAIN OFFICE AND WORKS :
115=121 Poinier Street, Newark, N. J., U. S. A.
New York Office, - = 85 Liberty Street.
Boston. Philadelphia, Allegheny, Toledo, St. Louis, San Francisco.
THE
ANSORIA BRASS & COPPER CO.
MANUFACTURERS OF
COPPER WIRE AND CABLES
For Trolley Roads, Electric Lighting Companies,
Power Transmission Plants, Etc.
DRAWN COPPER BARS
For Switchboards, Commutators, Armatures, Etc.
SOLE MANUFACTURERS
"TOBIN BRONZE"
Rods for Yacht Shafting, Bolts, Pump Pistons; also Sheets, Tubes, Etc.
99 JOHN ST., NEW YORK CITY
MADE Af,
TRENTON.'^. %)«
o^ Dozen Reasons <u?/Cy
i&re is more e/lMEI^ICtfN p^o'Sp°iL
used man. all omer brands combined >
1 7/i5 sel/- luhncattny-
2 Sirelcfced injjrocess of manufacture-
3 Outer yarns edged io retard external a)ear~
4 Kirenamla tlemp ihroughou i-no spongy core-
P j j. ' j.i 1C r ^ j
5 l\.ope cut io exact lengths required"
e Coils to.ooo/t wny a)tmouJ a spnce-
7 Larft stock m all sizes insures prompt sMpmenis-
8 Our expert splicers sent anyalnere-
r? JT It. . -/ .
9 Lxperi consultation jrirtn upon reouesr*
10 Dnris designed &> dradinjfsfirnmecTjfrahS'
11 flo order wo small or toolaraefor us-
12 li is i fie finest example of tne
rope makers* art.
•AMERICAN MFG CO.
65 WALL ./TI^EET NEW
'* The Blue Book of Rope Transmission " free upon requesi.
"OLD COLONY"
Transmission Rope
Our Old Colony selected long fibre Manila Transmission Rope
embodies every point of high quality and efficiency that long experience
and scientific experiment have contributed to the art of rope making.
It is the one rope on the market sold absolutely on its merits, its price
being always based on the market value of the best marks of Cebu
Manila hemp, of which it is made.
In the manufacture of Old Colony Rope the question of price is
not considered, the purpose at all times being to better its quality, if
possible, rather than to decrease its cost. In equipping your plant
with Old Colony Rope you are getting absolutely the best that money
can buy.
GEO. B. CARPENTER ®L CO.
200, 202. 204. 206, 208 S. Water St., Chicago
Our 900-page general catalogue of mill supplies, etc., is wort*
owning. Send 25c. in stamps.
GECXV.CRESSONCCX,
MaJn Office autid Works,
Allegheny Ave* west of Seventeenth St., Philadelphia, Pa.
New York Office: J4J Liberty St*
Engineers, Founders, and Machinists.
Manufacturers of
POWER TRANSMITTING MACHINERY,
CRUSHING ROLLS and JAW CRUSHERS.
•%•
Builders of
SPECIAL MACHINERY TO ORDER.
14
i ESTABLISHED 1828 ^
RUBBER. GOODS \
The Trade Mark
of Excellence.
FOR
RAILWAYS, STEAMSHIPS, MILLS,
MINES, SMELTERS, & ALL
MECHANICAL PURPOSES.
Belting', Hose, Packings,
Rubber Covered Rollers,
etc., of Superior Quality
Manufactured by
James Bennett Forsyth, Gen. Mgr.
Original Mfrs. Boston, New York, Buffalo, Chicago,
Vulcanized 256-260 100-102 90 109*
Rubber Goods, Devonshire St, Reade St. Pearl St, Madison St,
JEWELL BELTING COMPANY
EXCLUSIVE MANUFACTURERS OP
VICI BELTING
OFFICE AND FACTORY
HARTFORD, CONN.
BRANCHES:
New York
Memphis
Chicago
Philadelphia
Cincinnati
San Francisco]
CLUNG AGENTS IN PRINCIPAL CITIES.
16
ORGANIZED, I860.
•r-^CONH-^
^4NDg|
THOROUGH INSPECTIONS
AND
ftuurance against Loss or Damage to Property and Loss of
Life and Injury to Persons caused by
STEAM BOILER EXPLOSIONS
L. B. BRAINERD, President and Treasurer.
F. B. ALLEN, Vice-President.
J. B. PIERCE, Secretary.
L. F. MIDDLEBROOK, Asst. Secretary.
UNIFORM QUALITY, QUICK-CUTTING,
WONDERFUL DURABILITY, WATERPROOF,
NO DUST, NO ODOR.
NORTON
EMERY
WHEELS
ILLUSTRATED CATALOGUE FREE.
WALKER UNIVERSAL TOOL AND GUTTER GRINDER.
NORTON EMERY WHEEL CO.,
WORCESTER, MASS,
16
Morse Twist Drill and Machine Co,,
NEW BEDFORD, MASS,, U, S, A.,'
MANUFACTURERS OF
Arbors. Beach, Stetson, and Center Drill Chucks.
Counterbores and Countersinks. Increase Twist and
Constant Angle Drills. Drills with Oil Holes. Drills
with Grooved Shanks. Dies. Gauges. Mandrels.
Metal-slitting Saws. Milling Cutters. End Mills.
thell End Mills. Taper Pins. Adjustable and Ex
ansion Reamers. Reamers with Oil Holes. Screw
lates with Dies. Sockets. Sleeves. Taps and
Tap Wrenches.
We also make Special Tools and Machines
and solicit your correspondence.
A copy of our latest Catalogue sent free to any address.
CHAPMA¥VALVE MFG. co.,
WORKS AND MAIN OFFICE:
INDIAN ORCHARD, MASS,
BRANCH OFFICES:
BOSTON, NEW YORK, PHILADELPHIA, BALTIMORE,
ALLENTOWN, PA.; CHICAGO, ST. LOUIS, SAN FRAN-
CISCO, LONDON, ENGLAND; PARIS, FRANCE; AND
JOHANNESBURG, SOUTH AFRICA.
VALVES
MADE IN ALL SIZES AND
FOR ALL PURPOSES AND
PRESSURES.
CORRESPONDENCE SOLICITED.
17
MODERN
CEMENT MACHINERY
FOR EITHER WET OR DRY PROCESS
ROTARY KILNS
BALL MILLS
TUBE MILLS
DRYERS, MIXERS, ETC.
THE BONNOT COMPANY
CANTON, OHIO
U.S.A.
THE GARVIN MACHINE CO.
Main Offices and Works : •
Spring and Varick Streets, New York
Manufacturers of
Milling Machines
Universal, Plain, Ver-
tical, Profile, Hand,
Lincoln and Du-
plex Styles
Screw Machines
Monitor Lathes
Forming Machines
Tapping Machines
Drill Presses
Cutter Grinders
Hand Lathes
SPECIAL MACHINERY
Send for new Catalog.
No. 2 Garvin Universal Milling Machine
IS
The Hendey Machine Company,
TORRINGTON, CONN.,
MANUFACTURERS OF
MACHINE TOOLS,
SPECIALTIES:
Hendey-Norton Milling Machines,
Hendey-Norton Lathes,
AND
Hendey Pillar Shapers*
19
FAN AND PRESSURE BLOWERS,
EXHAUST FANS FOR ALL USES.
Hot Blast Heating Apparatus, Dry
IKiln Outfits, Steam Fans, Forges,
[High and Low Pressure Engines.
SEND FOR CIRCULARS.
BOSTON BLOWER CO,,
HYDE PARK, MASS.
THE SNIDER-HUGHES CO.
SHERIDAN STREET, CLEVELAND, OHIO.
MANUFACTURERS OF
STEAM-PUMPS FOR EVERY SERVICE.
JET AND SURFACE CONDENSERS.
Estimates furnished on request.
YOUR CORRESPONDENCE IS SOLICITED.
SKINNER
LATHE, DRILL, PLANER CHUCKS-
A 6"X9"
ILLUSTRATED
CATALOG
SENT ON
APPLICATION.
'THE SKINNER CHUCK co,
NEW BRITAIN, CONN.
LATHES
Engine Lathes and Turret Lathes
14-inch to 48-inch Swing
High Speed Lathes for straight turning
Axle Lathes for railroads.
EFFICIENT, ACCURATE, DURABLE.
THE LODGE & SHIPLEY MACHINE TOOL GO,
CINCINNATI, O., U. S. A.
20
EFFICIENT tn ,i f -TW--1HI HI DURABLE
THE UNIVERSAL DRAFTING MACHINE saves the
waste of time and distraction of mind caused by
the continual changing of tools.
This results in rapid work and better work, as the
mind is left free for concentration upon the design.
Send for complete information.
UNIVERSAL DRAFTING MACHINE CO.
220-226 Seneca Street
CLEVELAND, O. ^ U. S. A.
ALL OUR WIRES
NAT'L BOARD OF FIRE UNDERWRITERS
STANDARD.
NEW YORK INSULATED WIRE CO*
MAIN OFFICE: 114 LIBERTY STREET, N. Y.
Branches: CHICAGO, 192 Desplaines St.; BOSTON, 7 Otis St.; SAN FRANCISCO, 33 Second St.
WELDLESS STEEL WIRE CHAIN.
TWICE THE STRENGTH OF WELDED.
TRIUMPH PATTERN. 14 sizes.
Send for results of voluntary tests made by the
British Scientific Society.
THE BRIDGEPORT CHAIN CO., Bridgeport, Conn.
WE MAKE OVER TEN MILES PER DAY.
A LPHONS CUSTODJS
CHIMNEY CONSTRUCTION COMPANY
• NEW YORK •' .,-^TV""V! •." . T--. BENKETT BLDG. ;/ /•"
GIII1EI8.
Over 4,500 Chimneys
built during the past
20 years.
Chimneys straightened, pointed, banded, without inconveniencing or delaying
the plant. Estimates cheerfully furnished on application. Write for catalogue and
references. AMERICAN BRANCHES:
New York, 517-520 Bennett Bldg. Philadelphia, 720 Arcade Bldg.
Chicago, 822-4 Marquette Bldg. Boston, 725 Exchange Bldg.
OTHEK BRANCHES IN ALL PRINCIPAL CITIES OF EUROPE.
ESTABLISHED 1856.
HENRY MAURER & SON,
MANUFACTURERS OF
FIREBRICK.TILES,8lllB5,C«POLIlLIil8,
Clay Retorts for Gas Works.
Office, 420 East 23d Street,
Works, Maurer, N. J.
,P. O., Telegraph, and R. R. Station.)
23
NEW YORK.
170 BROADWAY, NEW YORK CITY
Warren Foundry and
Machine Co.
MANUFACTURERS OF
ALSO ALL KINDS OF
Flange Pipe, Condenser Tubes,
DRYER CYLINDERS
AND
SPECIAL CASTINGS
RANDOLPH-CLOWES Co.
WATERBURY, CONN.
BRASS AND COPPER ROLLING MILLS
AND
TUBE WORKS.
SEAMLESS BRASS and COPPER
TUBES and SHELLS
Up to 36 Inches Diameter.
28
ATLAS
PORTLAND
CEMENT
Is the Standard American Brand.
Used by all the leading Engineers and
Contractors throughout the United States,
and preferred by the U. S. Government.
ATLAS PORTLAND CEMENT CO.,
30 BROAD STREET, NEW YORK.
Machine=shop Tools and Methods.
By W. S. LEONARD,
Instructor in Machine-shop Practice and in Practical Machine Design,
Michigan Agricultural College.
THIRD EDITION, REVISED AND ENLARGED.
8vo, vii -f- 554 pages, 689 figures. Cloth, $4.00.
CONTENTS.— The Measuring System of the Machine-shop; Standards of
Length. The Hammer and its Use. Chisels: their Forms and Uses. Files and
Filing. The Surface-plate and Scraper. The Vise and Some Vise Accessories.
Drilling machines. Drills and Drilling. Drill-sockets, Drill-chucks, and Acces-
sories. Construction and Use of Reamers and Bits. Lathes. Turret-machines
and Turret-machine Work. Lathe- and Planer-tools. Lathe-centers, Work-
centers, etc. Methods of Driving Work in the Lathe; Dogs and Chucks. Lathe-
arbors, or Mandrels, and Arbor-presses. Some Examples of Engine-lathe Work;
Thread-cutting in the Engine-lathe. Screw-threads, Taps, and Dies. Bolt- and
Nut-threading Machines. The Boring-bar and its Use. Horizontal Boring-
and Drilling-machines and Work; Crank-boring Machine. Vertical Boring- and
Turning-mills, Tools and Work. Planers and Shapers and Planer and bhaper
Work. Slotting-machines and the Work to which they are Adapted. Key-
seating Machines and Keys. Milling-machines and Milling-machine Work,
Special Gear-machines. Grinding-machines and Methods. Polishing- and
Buffing-wheels. The Interchangeable System of Manufacturing. Miscellaneous
Machine-shop Methods. Tables, Recipes, etc. Appendix : Questions on the
Text; Index.
PUBLISHED BY
JOHN WILEY & SONS.
THE GREATEST
WATER METER
RECORD EVER MADE.
450,000
Crown, Empire, Nash, Gem
METERS IN USE.
National Meter Company,
NEW YORK, CHICAGO, BOSTON, LONDON.
OFFICE & SALESROOM
wj 106-110 CENTRES!^
"MRISB5} NEW YORK
iCAO 38» SOUTH sr.f »«*»» » ******
TKe Gas-
A Treatise on the inter-
nal-Combustion Engine
using Gas, Gasoline,
Kerosene, or
other Hydrocarbon as
Source of Energy. By
F. R. HUTTON, Professor
of Mechanical Engineer-
ing in Columbia Uni-"
versity. 8vo, xviii +
481 pages, 243 figures.
Cloth, $5.00. : : :
NEW YORK.
PYROMETERS
FOR AL.L. TECHNICAL PURPOSES.
The Queen Mercurial Pyrometer, for stack Temper-
atures, reading to 1000° F.
The Queen Metallic Pyrometer, for oven Temper-
atures, reading to 1500° F.
The Queen-Chatelier Pyrometer, for Furnace
peratures, with direct reading scale to 3000° F.
For a complete list and descriptions of the Pyrometers
manufactured by us send for our Pyrometer Catalogue.
QUEEN & CO., Inc.
59 Fifth Avenue, 1010 Chestnut Street,
NEW YORK, PHILADELPHIA.
KEUFFEL & ESSER CO.,
127 PULTON ST., NEW YORK.
BRANCHES:
111 Madison St., Chicago; 813 Locust St., St. Louis; (
421-3 Montgomery St., San Francisco.
Manufacturers and Importers of
DRAWING MATERIALS.
SURVEYING INSTRUMENTS.
MEASURING TAPES.
Paragon, Key, and other Brands of Drawing Instruments.
Paragon, Anvii, Universal. Normal, Duplex, and other Drawing Papers.
Standard Profile and Cross-section Papers, Cloths, and Books.
Helios, Columbia, and Parchmine Blue Print Papers.
Nigrosine and Umbra Positive Black Process Paper.
Maduro Brown Print Paper.
K.& E. Co.'s Patent Adjustable and Duplex Slide Rules.
Thacher's Calculating Instrument.
Paragon Scales, with White Edges. Patent Triangular Scales,
Triangles, T Squares, Drawing Boards and Tables.
Columbia and Kallos Indelible Drawing Ink.
TOJIA/O/TO i cue i o D I SUPERIORCONSTRUCTION; ACCU-
IHANbl/b, LEVELS, &C. I RACY AND WEAR GUARANTEED.
Architects' Convertible Levels, Surveying and Prismatic
Compasses. Aneroid Barometers, etc.
Surveyors' Chains, Rods, Poles, etc.
We Warrant all our Goods!
K. & E. Steel and Metallic Tapes.
Catalogue 500 Pages sent free on Application. Write for our Pamphlet
on "Photo. Printing from Tracings."
: Grand Prize, St. Louis, 1904; Gold Medal, Portland, Ore., 1905.
27
WALWORTH M'FG CO.
Installation of High=pressure Power
Plants a Specialty.
Extra Heavy
Bronze Seat Gate Valves.
Bent Pipes
Gun-iron Flanged Fittings
and Drums
FOR HIGH-PRESSURE STEAM PLANTS
NEW YORK OFFICE
PARK ROW BUILDING
GENERAL OFFICES
128-136 FEDERAL 5T.
BOSTON, MASS.
CABLE ADDRESS
WALMANCO.
Write for Draughtsman's Book o! Dimensions
Trade Mark
" The Best is the Cheapest"
The BEST ROOF is made of
MF Roofing Tin
It has held during the last sixty years
the Host Favored and leading place in
the race for superiority in Roofing Materials
The BEST METAL CORNICES
?est Bloom
Galvanized Sheets
The trade mark signifies the highest standard of reliability. The
easy working qualities of the Metal make it the favorite of the Metal
Worker. When in need of galvanized sheets for construction work,
don't be satisfied with substitutes, insist ^>n the genuine.
Our Products are for sale by all Metal Houses
American Sheet & Tin n Plate Company
PITTSBURGH, PA.
C- H
Consulting Engineer
OVERDUE.
SEP 5
14
MAR 20 1934
,-EB M 193'
A937
5 1
YA 02257
288901
I
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