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A MANUAL
OF
NAVAL AECHITECTUEE.
FOR THE USE OF
OFFICERS OF THE ROYAL NAVY,
OFFICERS OF THE MERCANTILE MARINE,
SHIRBUILDERS, SHIPOWNERS,
AND YACHTSMEN.
By W. H. white, F.R.S.,
ASSISTANT CONTHOLLEE AND DIRECTOR 0\? NAVAL CONSTRUCTION, ROYAL NA\Y ;
VICE-PRESIDENT OF THE INSTITUTION OF NAVAL ARCHITECTS;
MEMBER OF THE INSTITUTIONS OF CIVIL ENGINEERS AND MECHANICAL ENGINEERS ;
FELLOW OF THE ROYAL SCHOOL OF NAVAL ARCHITECTURE,
SECOND EDITION, REVISED AND ENLARGED.
TJic Lords Commissioners of the Admiralty have been pleased to authorise the
issue of this Book to the Ships of the Royal Navy.
LONDON:
JOHN MUREAY, ALBEMARLE STREET.
1889.
[The right of Translaticm is reserved.']
c
ENGINEERING LIBRARY
LONDON :
TRINTEU BY WILLIAM CLOWES AND SONS, LIMITLD,
STAMFORD STREET AND CHARING CROSS.
PREFACE TO SECOND EDITION.
In preparing this new edition it has been my endeavour to
leave the original plan of the work unchanged in its main features ;
but to bring the information given for all classes of ships up to
the date of publication, to correct faults, and to make additions
or extensions wherever they appeared desirable. To a large
extent the book has been rewritten, and a considerable amount
of new matter has been introduced, with the result of enlarging
the contents of the volume by about one-third as compared with
its predecessor.
The wide circulation which tlie first edition has attained both
in this country and abroad has been an incentive to me to spare
no pains in the revision now completed. So far as the scanty
leisure of a busy professional life has permitted, I have
endeavoured to add to the value and interest which the work
may have for all the classes of readers for whom it is designed.
If complete success has not been attained in this endeavour — as
indeed it is scarcely to be hoped for — an apology will hardly be
needed.
The exact and extensive information for various types of
merchant ships given in the following pages I owe to the
courtesy of many of the leading shipbuilding firms, whose practice
in recent years has been marked by rapid extensions of scientific
method. In this respect the present volume is distinguished from
the earlier edition perhaps more than in any other. The sources
of information are acknowledged in all cases ; but I would here
record the special obligations I am under to my friends Mr.
John Inglis, junior, and Mr. William Denny, for their ready and
836452
iv PREFACE TO SECOND EDITION.
repeated help iu my inquiries into questions relating to the
mercantile marine.
Another distinctive feature of this edition will be found in the
amplification of those portions of the work which are likely to be
of value to readers engaged in the design and construction of
ships. My most sanguine anticipations have been exceeded in
the welcome which the first edition received from shipbuilders,
naval architects and engineers; and I trust that they will find
the present volume much more valuable as a book of reference.
At the same time, I venture to hope that the naval officer, the
shipowner and the yachtsman will find the book no less suited to
their wants or less readable than before. It was iu the hope of
serving them chiefly that I first undertook the task, and my
desire to be of service is as strong as ever.
To Mr. W. E. Smith of the Controller of the Navy's Department
my thanks are due for valuable assistance rendered in the passage
of this edition through the press.
W. H. White.
London, 1882.
PREFACE TO FIRST EDITIOX.
This book has been uudertaken iu the hope that it may snp|)ly
a want in the literature of naval architecture. Existint?
treatises have baen written miinly for the use of those who
desired to obtain the knowledge of the subject required in the
practice of ship designing ; in all, or nearly all, these books
mathematical language is freely used, and without a considerable
knowledge of mathematics no one can follow the reasoning.
Mv work at the Royal Naval College has, however, shown me
that outside the profession of the naval architect there are to
be found very many persons, more or less intimately connected
with shipping, who desire to obtain acquaintance with the
principles of ship construction, but cannot obtain the information
from existing text-books. Ofiicei's of the Eoyal Navy have
repeatedly asked me to recommend a book which contained, in
popular laTiguage, a comprehensive summary of the theory of
naval architecture. Being unable to name such a book, and
feeling confident that the desire expressed by officers of the
Royal Navy will be shared by many officers of the mercantile
marine, as well as shipbuilders, shipowners, and others, I decided
to attempt the task now completed. I venture to hope that
the work may be found acceptable also as an introduction for
students to the more mathematical treatment of the subject
contained in other works, and that even naval architects them-
selves may find some valuable information herein.
Throughout the book, so far as seemed possible, popular
language is employed ; where mathematical language is used, it
is of the simplest character. Explanations are given of many
terms and mechanical principles, which need no explanation
to readers possessing a good knowledge of mathematics ; this
course having been followed in order to assist the general reader,
vi PREFACE TO FIRST EDITION.
and render it unnecessary for him to turn to other books. The
details of many important theoretical investigations are neces-
sarily omitted ; but the general modes of procedure are sketched,
and the practical deductions are fully explained. These deduc-
tions are clearly of the greatest value to the readers for whom
the book is mainly designed ; and it has been my endeavour to
make the survey of the theory of naval architecture, from this
point of view, as complete as possible. Practical shipbuilding is
not treated of ; but in the chapters on Strains, Structural
Strength, and Materials for Shipbuilding, will be found an out-
line of the principles which govern the work of the shipbuilder,
and an account of the principal features of the structures in
various types of ships. The principal deductions from theory
respecting the buoyancy, stability, behaviour, resistance, propul-
sion, and steering of ships, are set forth at length; practical
rules are given for regulating the draught and stowage of ships,
observing their behaviour at sea, and noting the dimensions of
ocean waves. In every case numerous illustrations of these
deductions are drawn from the particulars and performances
of representative ships, belonging to English or foreign navies,
and to the mercantile marine. Ships of war naturally receive
most attention, the information respecting them being more exact
and extensive than the corresponding facts for merchant ships ;
but the latter will also be found to receive considerable notice,
the latest types of clipper sailing ships and mail steamers being
described, and their performances discussed. The classes of war-
ships for which particulars are given range from the sailing
ships of half a century ago up to the circular ironclads and
central-citadel sbips of the present day.
Apart from the illustrative use made of these facts, it is hoped
that the mass of information thus brought together, some of which
has never before been published, will add to the value of the
book. Not only naval officers, but naval architects, may be glad
to have brought together in a compact form, and made easy of
reference, much information that either lies scattered or is in-
accessible elsewhere. To the notice of naval architects also I
would venture to recommend the chapters on Steam Propulsion
and Steering.
One great object which I have kept in view throughout has
been to endeavour to awaken in the minds of seamen an intelligent
interest in the observations of deep-sea waves and the behaviour
of ships. Upon such observations further progress in the theory
of naval architecture largely depends; and although much has
PREFACE TO FIRST EDITION. vii
been clone of late years, especially by officers of the Roval
Navy, still more remains to be done.
The success which has already attended my endeavours to
popularise a few out of the many problems of ship design, in
lectures delivered at the Eoyal Naval College to naval officers,
leads me to hope that a similar mode of treatment applied, as in
the present work, to the whole range of naval architecture may
be welcomed by a wider circle of readers. One incentive to
undertake the book was found in the requests made by many
officers who attended the lectures that they might be published ;
but it seemed preferable to enlarge their scope considerably
before publication, and although much of the material used
for the lectures has been embodied in this book, it considerably
amplifies and extends the treatment of the subjects included in
the four courses of lectures.
Much of the information contained in this book has necessarily
been drawn from the works of other Avriters ; in all such cases I
have endeavoured to acknowledge the sources of information. In
a few cases the substance of papers of my own, previously
published, has Leen used; these cases are also mentioned in the
text.
W. H. White.
London, 1877.
J
CONTENTS
CHAPTER I.
THE DISPLACEllEXT AND BUOYANCY OF SUIPS.
PAGE
Definitions of displacement and buoyancy ... ... ... ... ... 1
Useful displacement, or carrying power ... ... ... ... ... 2
Approximate rules for estimating displacement ... ... 3
Curves of displacement : their construction and uses ... ... ... G
Curves of tons per inch immersion : their construction and uses ... ... 7
Changes in draught of water produced by the passage of ships from the sea
to rivers or docks ... ... ... . • • • • • • • • • • • • • • 9
Eeserve of buoyancy for various types of ships ... ... ... •■• 10
Submarine vessels : fundamental principles of construction ... ... 12
FounderiDg of ships which are "swamped." Water-logged ships 1-4
Foundering of ships which have bottoms penetrated ... 15
Principles of watertight subdivision of ships : —
By transverse bulkheads ... ... ... ■•• ... .•• •■• 18
By longitudinal bulkheads ... ... ... ... ••• .•• 22
By decks or platforms ... ... ... ... ... ••• .■■ 23
Watertight subdivision in modern war-ships ... ... ... .. 25
Cellular double bottoms ... ... ... •• ••• ••• ••• 28
Examples of foundering caused by collision ... ... ... ... ... 30
Unsinkable ships ... ... ... ... ... ... ... ••• 32
Freeboard: rules for ... ... ... ... ... ... ... ••• 33
Load-draught: recent legislation respecting... ... ... ... ... 3-4
CHAPTER II.
THE TONNAGE OF SHIPS.
Early systems of tonnage measurements ... ... ... ... • • • 36
Builders' old measurement ... ... ... ... ... ... ... 38
Displacement tonnage : for war-ships ... ... ... ... ... 43
Financial tonnage (Xavy Estimates)... ... ... ... ... ... 43
New measurement (law of 1836) ... ... ... ... ... ... 4:4
Register tonnage (law of 1854) ... ... ... ... ... ... 4:6
Suez Canal and Danube rules ... ... ... ... ... ... ... 58
Tonnage laws of other maritime nations ... ... ... ... ... 59
Proposed revision of British tonnage law : —
Dead- weight tonnage ... ... ... ... ... ... .•• 61
Displacement tonnage ... ... ... ... ... .-. ••■ 64
Parallelopipedon tonnage... ... ... ... ... ■■• ••• GG
CONTENTS.
Freight tonnacje
Yacht measurements: for time allowances:^
Thames rule
Yacht Kacing Association
Other rules
PAGE
67
67
68
69
CHAPTER III.
THE STATICAL STABILITY OF SHIPS.
Condition of ships floatins; freely in still water
„ ,, inclined by mechanical couple
Stable, unstable, and indifferent equilibrium
Statical stability defined
Metacentre for transverse inclinations
Stiffness, cranlvness, and steadiness ... ...
Metacentric heights : for war-ships ...
yy „ for merchant steamers
„ „ for sailing sliips and yachts ...
Conditions governing the vertical position of the metacentre and centre of
buoyancy
Metacentric diagrams : construction and uses of
Stabihty of cigar-ships and submarine vessels
Inchning experiments : to determine vertical position of centres of gravity
of ships
Effect upon stability of vertical movements of weights
Heeling produced by transverse shift of weights
Effect upon stability of water in hold
„ „ of additions of removals of weiglits ...
Metacentre for longitudinal inclinations
Estimates for cliange of trim ...
Stability of ships partially waterborne ...
Atwood's formula for statical stability ...
Curves of stability : construction of ...
,, ,, causes influencing form and lan^e
,, ,, examples for war-ships ...
„ „ examples for merchant steamers
„ „ examples for sailing ships
73
74
75
76
77
77
79
80
84
88
91
97
99
102
102
104
108
109
112
115
118
119
120
123
126
128
CHAPTER IV.
THE OSCILLATIONS OF SHIPS IN' STILL WATER.
Comparison of ships with pendulums
Angular velocity, accelerating force, and moment of inertia
Instantaneous axis for unresisted rolling
Motion of metacentre during rolling ...
Formula for period of unresisted rolling
Changes in period produced by changes in distribution of weights
Dynamical stability : modes of estimating ...
132
134
137
139
140
141
144
CONTENTS. XI
PACK
Dipping oscillations ... ... .•• ••• ••• ••- ••• ••• 147
Effect of fluid resistance on rolling 149
Rolling experiments in still water ... ... ... •• 1^1
Still-water periods for typical war-ships 155
Curves of extinction and their analysis 157
Usefulness of bilge-keels I-GS
Effect of free-water in interior upon rolling 165
Effect of gusts or squalls of winds on rigged ships floating in still water ... 168
CHAPTER V.
DEEP-SEA WAVES.
Fundamental conditions of trochoidal theory ... ... ... ... 175
Construction of trochoidal profiles ... ... ... ... ... ... 177
Orbital motions of particles and advance of wave-form ... ... ... 178
Internal structure of wave ... ... ... ... ... ... -.• 180
Variations in direction and intensity of fluid pressure incidental to wave
motion ... ... ... ... ..• ••• ••• ••• ••• 183
Formula} for dimensions and speeds of waves ... ... ... ••• 187
Observations of waves : methods of conducting ... ... 190
„ „ summary of maximum dimensions recorded ... 19-i
Comparison of observation with theory ... ... ... ... ... 197
Conditions of a confused sea ... ... ... ... ... •■. .■• 200
The genesis of waves ... ... ... ... ... ••. ••• ••• 201
Relation of force of wind to dimensions of waves ... ... ... ... 20i
Prevalent waves in different regions ... ... ... ... ... ... 208
Utilisation of wave power ... ... ... ... 208
CHAPTER YI.
THE OSCILLATIONS OF SHIPS AMONG WAVES.
Early theories of rolling ... ... ... ... ... 210
Principal features of modern theory of rolling ... ... ... ... 211
The effective wave slope and virtual upriuht ... ... ... ... 213
Fundamental assumptions for mathematical investigation of unresisted rolling 218
Critical cases of rolling of ships : —
Amongst waves of synchronising periods ... ... ... ... 220
"Permanent" oscillations ... ... ... ... ... .•• 223
Phases of oscillation ... ... ... ... ... ... ... 225
Practical deductions from investigation of unresisted rolling, corai ared
with observations of the rolling of ships at sea ... ... ... ... 227
Influence of fluid resistance upon rolling ... ... ... ... ... 235
Graphic integration for resisted rolling : Mr. Fronde's method ... ... 237
M. Berlin's investigation for resisted rolling ... ... ... ... 239
Influence of bilge-keels in steadying ships ... ... ... ... ... 241
Usefulness of " water-chambers" in armoured ships ... ... ... 243
Rolling of ships with sail set ... ... ... ... ... ... ... 245
Effect of gusts and squalls of wind ... ... ... ... ... ... 249
Xll
CONTENTS.
Steail.ying effect of sails
Longitudinal oscillations : pitcliing and 'scending ...
Principal conditions affecting longitudinal oscillations
Influence of fluid resistance upon these motions
PAGE
251
252
253
258
CHAPTER VII.
METHODS OF OBSERVING THE ROLLING AND PITCHING MOTIONS OF SHIPS.
Necessity for such observations ... ... ... ... ... ... 261
Pendulum observations, and their errors ... ... ... ... ... 2G3
Spirit-levels and clinometers ... ... 267
Gyroscopic instruments and their drawbacks ... ... ... ... 268
M. Normand's instrument ... ... ... ... ... ... ... 271
Batten instruments : various arrangements of ... ... ... ... 272
Photographic apparatus ... ... ... ... ... ... ... 275
Automatic instruments ... ... ... ... ... ... ... 276
Description of Mr. Fronde's automatic instrument ... ... ... ... 277
Simultaneous observations of behaviour of ships and character of waves
much needed ... 280
CHAPTER YIII.
THE STRAINS EXPERIENCED BY SHIPS.
Necessity for careful study of subject... ... ... ... ... ... 282
Classification of principal strains ... ... ... ... ... ... 283
Longitudinal bending moments (hogging and sagging) : —
Due to unequal distribution of weight and buoyancy ... ... ... 284
Method of estimating bending moments ... ... ... ... 286
Curves of weight, buoyancy, loads and bending moments, construc-
tion and uses of, with examples for typical ships ... ... ... 287
Bending moments due to longitudinal fluid pressure ... ... ... 293
Extreme cases of support for ships among waves ... ... ... 294
Corresponding bending moments for typical ships ... ... ... 297
Influence of pitching and 'scending upon longitudinal strains ... 301
Bending moments of ships ashore ... ... ... ... ... 302
Transverse strains experienced by ships when —
Resting on the keel only in dock or ashore ... ... ... ... 304
Afloat in still water ... ... ... ... ... ... ... 306
Rolling among waves ... ... ... ... ... ... ... 307
Strains incidental to propulsion —
By sails 309
By screws or paddles ... ... ... ... ... ... ... 311
Local strains, produced by —
Concentrated load or support ... ... ... ... 312
Grounding: with special reference to iron ships ... ... ... 314
Loads on decks ... ... 316
Collision: with special reference to ramming ... ... ... ... 317
Propulsion... ... ... ... ... ... ... ... ... 321
CONTENTS. xiii
CHAPTER IX.
THE STRUCTCTBAL STRENGTH OF SHIPS.
PAGE
Gradual development of structural arrangements ... ... ... ... 325
Features common to structures of all ships ... ... ... ... ... 326
Ultimate effect of longitudinal bending strains ... ... ... ... 327
Construction of " equivalent girder " sections ... ... ... ... 328
Principles of the strength of beams and girders 331
Application of these principles to longitudinal strength of ships ... ... 335
Influence of form, proportions, and local requirements upon the scantlings
ofships 340
Longitudinal strength contributed by —
Upper decks of ships ... ... ... ... ... ■•• .-• 345
Bottoms below the bilges ... ... ... ... ... ... 347
Longitudinal framing and cellular construction ... ... ... 349
Skins and riders of ordinary wood ships ... ... ... ... 355
Skins of composite ships ... ... ... ... ... ... ... 357
Skins of diagonally built wood ships ... ... ... ... ... 358
Skins of iron and steel ships ... ... ... ... .•• ••• 359
Special axTangements of shallow-draught vessels ... ... ... 360
Maximum longitudinal strains of war ships ... ... ... ... ... 362
„ „ „ of merchant ships ... ... ... ... 364
Provision of transverse strength ... ... ... ... ... ... 367
Strength of transverse frames or ribs in wood and iron ships ... ... 368
Partial bulkheads of iron ships ... ... ... .•• .•• •■• 369
Transverse framing of ironclads and swift cruisers ... ... ... ... 370
Decks, beams and pillars as transverse strengtheners ... ... ... 372
Beam-knees and beam-end fastenings ... ... ... ... ... 374
Transverse bulkheads considered as strengtheners ... ... ... ... 376
CHAPTER X.
MATERIALS FOR SHIPBUILDIXG : WOOD, IRON, ASD STEEL.
Remarkable progress of iron shipbuilding ... 379
Great increase in sizes and speeds of ships of late years ... ... ... 381
Iron ships superior to wood in the combination of lightness with strength 383
Weights of hull and carrying power of ships 384
Resistance of single pieces of wood and iron to tensile and compressive
strains ... ... ... ... ••• ••• ••• ••• ■•■ 385
Moduli of elasticity of iron and timber ... ... ... ... ••• 391
Resistance of combinations of wood or iron to tensile and compressive
strains ... ... ... ... ••• ••• ••• ••• ••• 391
Modes of scarphing timbers and shifts of butts in wood ships 392
Butt and lap joints of iron plates or bars ... ... ... •• ••• 39o
Resistance to bending of wood and iron beams ... ... .•• ••• 397
Comparative durability of wood and iron ships ••• 400
Corrosion of iron ships : how caused and prevented ... ... ••• 406
Iron ships more easily built and repaired than wood ships 409
XIV
CONTENTS.
Cost of maintenance of wood and iron ships ...
Subdivision, a source of safety to iron ships ...
Fouling of bottoms of iron ships
Copper and other sheathings for ships' bottoms
Comparative wear of various metals in sea-water
Metal sheathing on wood ships
Copper sheathing on iron ships
Zinc sheathing for iron ships
Iron hulls in unarmoured war ships ...
Use of steel for shipbuilding : —
Rapid progress in recent years
Earlier examples ...
Qualities of mild steel
Economical advantages of
PAGR
412
413
415
417
419
420
420
422
4 1:4
426
427
427
429
CHAPTER X[.
THE RESISTANCE OF SHIPS.
Early theories of resistance
Resistance to direct and oblique motion of planes ...
Frictional resistance to motion of planes ... ...
Modern or stream-line theory : principle features of, for frictionless fl
Frictional resistance experienced by ships
Eddy-making resistance
Wave-making resistance : —
Mr. Scott Russell's theory
Professor Rankine's investigation
Mr. Fronde's experimental researches ...
Limiting speeds for economical propulsion
Economical propulsion frequently not the
design
Recent tendencies in merchant-ship design
Resistance at very high speeds : torpedo-boats, &c. ...
Mr. Fronde's system of model experiments : —
Its practical advantages ...
Mathematical basis for scale of comparison
Observations of change of draught and -trim for ships in motion
Resistance in a seaway
Air resistance ...
uids
condition in ship
433
435
437
440
446
449
451
454
455
459
461
464
466
469
471
475
477
477
CHAPTER XIL
PROPULSION BY SAILS.
Arrangement of sail-plans : work of naval architect ... ... ... 480
Summary of facts as to velocities and pressures of winds ... ... ... 481
Classification of winds ... ... ... ... ... ... ... ... 485
Actual and apparent direction and velocity of wind relatively to sails ... 486
CONTENTS.
XV
Case of ship ruuning before wind
Case of ship drifting dead to leeward ...
Case of shij) sailing on a wind
Ardency and slackness
Balance of sail ...
Plain sails for various rigs
Es.timates for sail areas
Comparative sail-spreads in various types
Longitudinal distribution of sail and position of centre of effort
Stations and rakes of masts ... ... ...
Vertical distribution of sail
i^ail-carryiug power
Forms and proportions of obsolete and receut sailing ship-s ...
Forms and proportions of yachts
PAGE
488
48S
490
492
493
49 i
495
497
501
505
508
509
512
514
CHAPTEU Xni.
bTEAM PEOPULSIOX.
Rapid development of steam navigation
Problem of steam-ship design ...
Measures of "horse-power" for marine engines
Principal types of marine engines : —
Weights and rates of coal consumptions
Advantages of economy in coal consumption
Use of " forced draught "...
Employment of the locomotive type of boiler
Fundamental principle of the action of propellers
Water-jet propeller and its applications
Paddle-wheels ...
Screw propellers : —
Theoretical investigations of their action
Experiments with models
Various arrangements of, in ships
Augment of resistance, produced by
Influence of "wake" upon efficiency of...
Comparative efficiency of single and twin-screws
Necessity for experimental trials of
Novel descriptions of
Efficiency as compared with paddles and jets
Estimates for power and speed of steam-ships : —
Efficiency of marine engines
'Efficiency of propellers
Admiralty coefficients of performance ...
Kankine's " augmented surface " method
Progressive steam trials and their uses ...
Estimates from model experiments
Steam-ship efficiency : —
No universal standard possible ...
Special conditions of armoured ships
515
516
518
523
525
527
528
530
532
533
544
548
549
550
653
555
557
560
561
562
564
566
570
571
578
580
581
xvi CONTENTS.
FAGB
Kassian circular ironclads ... ... ... ... ... ••• 58o
Russian yacht iu'arZja, and other typos ... ... 586
Influence of increase in size upon economical propulsion ... ... 588
Torpedo-boats and swift launches ... ... ... ... ... 593
Expenditure of power in various classes ... ... ... ... 595
CHAPTER XIV.
THE STEERING OF SHIPS.
Different modes of steering 597
Ordinary and balanced rudders 598
Fluid pressure on rudders : causes and measures of ... ... ... 600
Special features of screw-ship steerage 602
Force required at tiller-end : estimates of 607
Work to be done in putting a rudder over 610
Balanced rudders : advantages of 611
Steam and hydraulic steering apparatus 612
Turning effect of rudders 614
Conditions influencing readiness of ships to answer their helms 616
Initial motions of ships in turning 618
Motion in earlier stages of turning from a straight course 619
Modes of determining the path of a ship ... 620
Turning trials of T/iMwcZerer 621
Uniform turning motion 623
Drift-angles and their effects 624
Heeling in turning 627
Turning trials of war ships : deductions from recorded results of 630
Rules for forms and areas of rudders ... ... 637
Special rudders : —
Twisted surfaces 642
Gumpel's and Lumley's ... ... 643
Bow rudders 644
White's rudder 645
Steering-screws and water-jets 646
Mechanical steering paddles 647
Auxiliary rudders 648
Steering blades 649
Steering by propellers : —
In single-screw ships ... ... ... 650
Fowler's wheel ... ... ... ... ... ... ... ... 652
Twin-screws and other duplicate propellers ... 653
Manoeuvring in a seaway 657
Index ... ... 659
) \ J 1 J ,
NAVAL AECHITECTURE
CHAPTER I.
THE DISPLACEMENT AND BUOYANCY OF SHIPS.
A SHIP floating freely and at rest in still water must displace a
volume of water having a weight equal to her own weight. The
truth of this fundamental condition may be easily demonstrated.
Let Fig. 1 represent the ship (in proiile view and athwartship
section), WL being the surface of the water. If it is supposed
that the water surrounding the ship becomes solidified, and that
FIG 1.
Section athwurtshi i)s I'tnfUi _^_____ 7
^
K
the ship is then removed, there will remain a cavity representing
in form and volume the water displaced by the ship : this is
termed the "volume of displacement" (or, shortly, the "dis-
placement ") of the ship, being represented in the diagrams by
WKL. If the cavity is then filled up to the level of the
surface WL with water of the same density as that in which
the ship floated, and afterwards the surrounding water again
becomes liquid, there will obviously be no disturbance or
change of level in consequence of the substitution of the
water for the ship. Therefore the total weight of water poured
into the cavity — that is, the total weight of water displaced by
the ship — must equal her weight.
This fundamental law of hydrostatics applies to all floating
bodies, and is equally true of wholly submerged vessels floating
at any depth as of ships of ordinary form, having only a portion
of their volume immersed.
Ships which are of equal weight may differ greatlv in form
NAVAL ARCHITECTURE. chap. I.
and- dimensioDsi ^a'ad consequently the forms of their respective
dis.p.lncem^i3t.s will, differ; but when they are floating in water
of the same density, the volumes must be equal to one another,
because the weights of the ships are equal. On the other hand,
when a ship passes from water of one density to water of another
density, say from the open sea to a river where the water is com-
paratively i'resh, her volume of displacement must change, because
the weight of water displaced must be the same in both cases.
Under all circumstances the volume of displacement, multiplied
by the weight per unit of volume of the water in which the ship
floats, must equal the weight of the ship. It is usual to express
the volume in cubic feet, and for sf^a-water to take 64 lbs. as
the weight of a cubic foot: so that the weight of the ship
in tons multiplied by thirty-five gives the number of cubic
feet in the volume of displacement when she floats in sea- water.
At every point on the bottom of a ship afloat, the water
pressure acts perpendicularly to the bottom. This normal pressure
at any point depends upon the depth of the point below the
water surface; and it may be regarded as made up of three
component pressures. First, a vertical pressure ; second, a hori-
zontal pressure acting athwartships ; third, a horizontal pressure
acting longitudinally. Over the whole surface of the bottom a
similar decomposition of the normal fluid pressures may be
made ; but of the three sets of forces so obtained, only those
acting vertically are important in a ship at rest. The horizontal
components in each set must obviously be exactly balanced amongst
themselves, otherwise the ship would be set in motion either
. athwartships or lengthwise. The sum of the vertical components
must be balanced by the weight of the ship, which is the only
other vertical force; this sum is usually termed the "buoyancy;"
it equals the weight of water dis[ilaced, and the two terms
"buoyancy" and "displacement" are often usid interchangeably.
The total weight of a ship may be subdivided into the " weight
of the hull," or structure, and the " weight of lading." The latter
measures the "carrying power" of the ship, and is therefore
frequently termed the "useful displacement." Useful displace-
ment for a certain degree of immersion is simply the difference
between the total displacement and the weight of the hull : so that
any decrease in the Aveight of hull leads to an increase in the
carrying power. If the ship is a merchantman, savings on the
hidl enable the owner either to carry more cargo in a vessel of a
specified size or else to build a smaller vessel to carry a specified
cargo. If the ship is a man-of-war, such savings on the hull
CHAP. I.
THE BUOYANCY OF SHIPS.
render possible increase in the offensive or defensive powers, or
in tlie coal supply, engine power, or speed; or else enable certain
specified qualities to be obtained on smaller dimensions thm
woidd otherwise be practicable. Hence appears the necessity
for careful selection of the best materials and most perfect
structural arrangements, in order that the necessary strength
may be secured in association with the minimum of weight. It
is in this direction that all recent improvements in shipbuilding
have tended ; the use of iron hulls instead of wood has greatly
facilitated progress, and further advances are now being made
by the substitution of steel for iron. These improvements in
ship construction are described in Chapter X.
Having given the draught of water to which it is proposed
to immerse a ship, the volume of her immersed part determines
the corresponding displacement, and this displacement can be
calculated with exactitude from the drawings of the ship. This
is the method adopted by the naval architect ; but any details
of the method would be out of place here. At the same time
an approximate rule by which an estimate of the displacement
of the ship may be rapidly made may have some value. Assuming
that the length of the ship at the load-line is known (say L),
also the breadth extreme (B), and the mean draught (D), the
product of these three dimensions will give the volume of a
parallelopipedon. This may be written : —
Volume of parallelopipedon = V (cubic feet) = L X B x D.
The volume of displacement may then be expressed as a
'percentage of the volume (V) of the parallelopipedon ; and for
the undermentioned classes of ship^, the following rules hold : —
Classes of Ships
DisjilaceTnent equal
to Percentage of
Volume (V).
1. Fast steamships, such as her Majesty's yachts'!
or the Holyhead packets /
2. Swift steatii-crui-sers of R' lyal Isavj (Tnconsfant]
and TWa^re classes) ; corvettes and sloops ./
3. Gun-vessels of Royal Navy; merchant steamer?'^
(common forms) /
4. Old classes of nnarmoured steam line-of-battle\
ships and fiigates in Royal Navy . . .J
Early types of ironclads in Royal Xavy i
(Warrior and Minotaur classes)
Modern types of riggrd ironclads, with moderate
proportions of length to breadth
I\Iast less sea-going ironclads (ZJet'asfa;' ton class);"!
cargo-carrying steamers of moderate speed . j
o.
6
:}
43 to 46 per cent.
46 to 52 per cent
55 to 60 per cent.
50 to 55 per cent.
55 per cent.
60 to 62 per cent.
65 to 70 per cent.
]i -1
4 NA VAL ARCHITECTURE. chap. i.
To these approximate rules for steamers, a few corresponding
rules for sailing ships may be added. In the obsolete classes of
war-ships the displacements ranged from 40 per cent, of the
volume of the parallelopipedon, in brigs, to 45 per cent, in
frigates and 50 per cent, in line-of-battlo ships. It is to be
observed that these vessels had comparatively deep keels and
false-keels, especially the smaller classes ; which circumstance
tended to make tlieir "co-efficients of fineness" (or percentages)
appear smaller than they would otherwise have done. In modern
racing yachts, with very deep keels, the percentages vary from
22 to 33 ; in modern merchantmen the percentages frequently lie
between 55 and 60.
These approximate rules cannot be substituted for exact calcu-
lations of displacement ; tliey are of service only in enabliug a
fairly accurate estimate to be made when the principal dimensions
and character of a ship are known.
For example, take a wood-built corvette of the 'Encounter class
in the Royal Navy. Her dimensions are : — Length = L = 220
feet ; breadth = B = 37 feet ; mean draught = D = 15f feet.
Hence for parallelopipedon, volume is given by
V= L X B X D = 220 X 37 X 15f = 128,205 cubic feet.
By rule 2 in foregoing table, taking the upper limit, as these
vessels have only moderate speed —
Displacement (in cubic feet) = 52 per cent, of V
= ^^_ X 128,205 = m,m^ cubic feet.
There are 35 cubic feet of sea-water to the ton ; hence
Displacement (in tons) = 66,660 -^ 35 = 1904 tons.
The displacement of the class (see Navy List) is about 1930
tons. Being built of wood, the hull of such a vessel will weigh
about one-half the displacement ; the carrying power being con-
sequently about 950 tons. This is approximately the total
weight available, therefore, in a vessel of the Encounter class,
for engines, boilers, coals, stores, equipment, and armament ; and
the disposal of this available weight in the manner that will
secure the gieatest efficiency for the service intended is a
matter requiring careful consideration.
As another example, take the case of one of her Majesty's
armoured frigates, masted and rigged, such as the Alexandra, the
most powerful ship of that class yet completed. Her diuiensions
CHAP. I. THE BUOYANCY OF SHIPS. 5
are : — Length = L = 325 feet ; breadth = B = 63§- feet ; mean
draught = D = 26^ feet.
Hence
V = L X B X D = 325 X 63| X 26| = 543,156.
Also, by rule 6 in t1ie table —
Displacement \ = 60 to 62 per cent, of V = 61 (say)
(approximate) / = ^-^(^ x 5-13,15'j = 331,325 cubic feet.
And displacement in tons = 331,325 -i- 35 = 9465 tons.
The actual displacement is 9492 tons ; so that the approxima-
tion is fair.
In iron-built ships of the Alexandra type, about 40 per cent,
of the displacement is required for the hull ; so that 60 per
cent. — or about 5600 tons — would be a fair approximation to
the total carrying power, and this weight is what the designer
has in his power to distribute as he thinks best, over armour,
guns, machinery, coals, and all other parts of the equipment.
These examples will probably suffice to show the reader unfamiliar
with the exact processes for calculating the displacement of ^liips
how he may approximate to that displacement.
The percentages stated in the foregoing table are technically
known as "coefficients of fineness," expressing, as they do, the
extent to which the immersed part of the ship is " fined " or
reduced from the parallelopipedon. As measures of the com-
parative fineness of form of any two ships, it is, perhaps, more
satisfactory to take the coefficients expressing the ratios of the
respective volumes of displacement to the volumes of the right
cylinders described upon the greatest immersed athwartship
sections of the ships, and having lengths equal to the lengths of
the ships along the water-lines. But the determination of these
last-named coefficients involves the use of the drawings of the
ships in order to determine the areas of the immersed midship
sections ; an-l they are chiefly of use to the naval architect.
Ships vary in their draught of water and displacement as the
weio-hts on board varv, and in cargo-carrying merchant vessels
this variation is most considerable, their displacement without
cargo, coals, or stores, often being considerably less than one-
half of the load displacement. In ships of war the variation
in displacement is not usually so great, but even in them the
aggregate of consumable stores rt aches a large amount, and
when they are out of the ship, she may float 2 or 3 feet lighter
NA VAL ARCHITECTURE.
CHAP. I.
than when fully lacleu. Naval architects have devised a plan
by whicli, without performing a calculation for every Hue at
which a sliip
^^ may float, it is
possible to as-
certain the corre-
sponding disphice-
by a simple measure-
Fie:. 2 illustrates one
ment
ment.
of the "curves of displacement" drawn
for this purpose; it is constructed as
follows. The displacements up to several
water-lines are obtained by direct calculation
from the drawings of the ship, in the manner before
mentioned. Then a line AB is drawn, the point A
representing the under side of the keel, and the length
AB representing the "mean draught" of the ship when
fully laden ; this mean draught being half the sum of the draughts
of water forward and aft. Through B a line BC is drawn at
right angles to AB, the length BO being made to represent, to
Fcale, the total displacement of the ship when fully laden : an
inch in length along BC representing, say, 1000 tons of dis-
placement. Suppose the displacement to have been also calcu-
lated up to another water-line (represented by DE in the diagram)
parallel to and at a known distance below the load-line (BC).
Then on DE a length is set off representing this second dis-
placement on the same scale as was used for BC. Similarly the
lengths FG, HK, and so on, are determined, and finally the
curve CEGr ... A is drawn through the ends of the various
ordinates. When this curve is once drawn, it becomes available
to find the approximate displacement for any draught of water
at which the ship may float, supposing that she does not very
greatly depart in trim from that at which she floats when
fully laden.* For instance, suppose the mean draught for
which the displacement is required to be 4 feet lighter tlian
the load-draught. Set down Ba? re^jresentiug the 4 feet, on
the same scale on which AB represents the mean load-draught.
Through x draw xy perpendicular to AB to meet the curve,
and the length xy (on the proper scale) measures the displace-
* By "trim" the naval architect means the differehce in draught at the
bow of a ship from that at tlie stern.
CHAP. I.
THE BUOYANCY OF SHIPS.
ment at the light draughf. This brief explanation will doubt-
less render obvious the great practical usefulness of curves of
disphicement, which always form part of the calculations attached
to the designs of ships.
Another problem that frequently occurs is the determination
of the increased immersion which will result from putting a
certain weight on board a ship when floating at a known draught,
or the decreased immersion consequent on removing cenain
weights. Here again the naval architect resorts to a graphic
method in order to avoid numerous independent calculations.
The diagram, Fig. 3, represents a "curve of tuns per iiich
immersion;" the horizontal measurement from the base-line
AB representing (on a certain scale) the number of tons which
would immerse the ship one inch when she is floating at the
draught corresponding to the
ordinate
along
which
FIG 3.
the
measurement is made. The
construction of this curve is
very similar to that of the
curve of displacement in Fig.
2, the successive points on
the curve being found for the
equidistant water-lines, BC,
DF, FG, ka., by direct calcu-
lation from the drawings of
the ship ; and the length of
the ordinate mj determining
the number of tons required
to immerse the ship one inch
when floating at any mean
draught, Aaj. In this case also it is to be understood that at
the various mean draughts considered there are no considerable
departures in trim from that of the fully laden ship.
It will be observed in the diagram that the upper part of
the curve of tons per inch is very nearly parallel to the base-
line AB ; this arises from the well-known fact that, in the
neighbourhood of the deep load-line of ships of ordinary form,
the sides are nearly upright, and there is little or no cliange
in the area of the horizontal sections. For all practical put poses,
in most ships, no great error is involved in assuming that twelve
times the weight which would sink the ship one inch below
her load-line will sink her one foot, or that a similar lule holds
for the same extent of lightening from the load-draught. In
8 NAVAL ARCHITECTURE. chap. I.
fact, it is very common to find this rule holding fairly for 2 leet
on either side of the fully laden water-line. A rule which gives
a fair approximation to the tons per inch immersion at the load-
line, in te?-ms of the length and breadth of the ship, has therefore
considerable vahie. Using the same symbols as before, viz. : —
Length of the ship at the load-line = L (feet).
Breadth extreme „ „ = B „
we should have,
Area of eircumscribinor 1 t r> » / ^ x\
11, ='> = LxB = A (square leet).
parallelogram . . j ^
And then the following rules express, with a considerable amount
of accuracy, the number of tons required to immerse or emerse
the ship one inch when floating at her load draught : —
Tons per Inch.
1. For ships with fine ends = _1 x A.
2. For ships of ordinary form (including probably the'l _ j .
great majority of vessels) /~ 560 ^
3. For ships of great beam in proportion to length andl _ j^ •
ships with bluff ends /"SOO^"^'
One or two examples of these rules may prove useful. The
Invincible class of the Eoyal Navy are ships coming under rule 2,
being ships of ordinary form. Their dimensions are ; — Length
= L = 280 feet; breadth = B = 54 feet.
Area of circumscribing 1 a = 280 x 54 = 15,120 sq. ft.
parallelogram . . J .
.-. Tons per inch at load-line = .^-q- x 15,120 - 27 tons.
This is nearly exact for these vessels.
As a second example, take her Majesty's ship Bevastation,
a short, broad vessel, coming under rule 3. Her dimensions
are :— Length = L = 285 feet ; breadth = B = 62^ feet.
Area = A = 285 x Q^ = 17,740 square feet.
Tons per inch at load-line = ^ig x 17,740 = 35i tons (nearly).
The actual "tons per inch " for this ship is about 36.V tons.
The second rule in the foregoing table is that which should be
applied in most cases.
It is easy to see how the curves of tons per inch, and the
curves of displacement constructed for the case of ships float,
iiig in sea-water, may be made use of in order to determine
tlie change of draught produced by the passage of a ship into
CHAP. I. THE BUOYANCY OF SHIPS.
a river, or estuary, or dock, where the water is comparatively
fresh. For example, sea- water weighs 64 lbs. per cubic font,
whereas in one of the London docks the water weighs a1)0ut 63
lbs. per cubic foot — or ^-^ part less than sea-water. Since the
total weight of water displaced by the ship must remain constant,
it is only necessary to make the following corrections : —
Difference between weight of sea-water and river-water for the
volume immersed up to the draught at which the ship floats at sea
= glf X weight of ship = -^^ W.
Tons per inch immersion at this draught in river-water
= fl tons per inch for sea-water = f j T.
.•. Increase in draught of water when ship floats in river? water
= eV X W = M T = ,3^. (inches).
For any other density of water than that assumed above, the
correction would be made in a similar manner. As a numerical
example, take a ship having the following particulars: — Weight
= W = 6000 tons ; tons per inch at load-draught in sea-water =
T = 30.
Increased draught on entering London \ pnnA
docks, as compared with her draught! =— - — ^~~ '^\\ in.
attheNore ^ ) 6ixo0
The draufrht beino; observed when the vessel is about to leave
the sea, the curves of displacement and tons per inch will furnish
the corresponding values of W and T in the foregoing ex-
pressions.
The converse case, where a ship, on passing from a dock or
river to the sea, floats at a less draught, need not be discussed.
It is, however, of consideraUe importance to merchant ships,
exercising an appreciable effect upon their freeboard when
deeply laden.
The buoyancy of a ship has already been defined, and shown
to be measured by the displacement up to any assigned water-line.
'* Reserve of buoyancy " is a phrase now commonly employed to
express the volume, and corresponding buoyancy, of the part of
a ship not immersed, but which may be made watertight, and
which in most vessels would be inclosed by the upper deck,
although in many cases there are watertight inclosui-es above
that deck — such as poops, forecastles, breastwoiks, &e. The
under-water, or immersed, part of a ship contributes the buoyancy ;
the out-of-water part the reserve of buoyancy, and tlie ratio
lO
NAVAL ARCHITECTURE.
CHAP. I.
between the two has a most important influence upon the safety
of the ship against foundering at sea. The sum of the two, in
FIG 4.
=^^C
^J^i^W
nG 5.
^^w
L^
FIG 6.
Vf
FIG 7,
short, expresses the total
"floating power" of the
vessel, and the ratio of
the part which is utilised
to that in reserve is a
matter requiring the
most careful attention.
This fact has come into
prominence recently in
the discussion of ques-
tions of lading and free-
board, as affecting the
safety of merchant ships.
In Figs. 4-9 are given
illustrations of the very
various ratios which the
reserve of buoyancy bears
to the volume of dis-
placement in different
classes of ships. As this
is only a matter of ratio,
a box-shaped form has
been employed instead
of a ship-shaped, and in
all the cases the volume
of dis[dacement is the
same, so that the out-of-
water portions can be
compared with one
another as well as with
the displacement.
Fig. 4 represents the
condition of low-free-
board American moni-
tors, such as the Canoni-
cus or Passaic, which
were employed on the
Atlantic coast during the
Civil War. The upper decks of these vessels are said to have
been between 1 and 2 feet only above water ; their reserve of
buoyancy wao only about 10 per cent, of the displacement.
FIGS.
WW
FIG 9.
P^W/
CHAP. I. THE BUOYANCY OF SHIPS. II
Fio-. 5 represents the condition of the American monitor
Miantonomoli, with a reserve of buoyancy of about 20 per cent.
of the displacement ; this approxiraattdy shows her state when she
crossed the Atlantic in 1866, but all openings on her upper deck,
which was about 3 feet above water, were carefully closed or
caulked.
Fig. 6 represents the Cyclops class of breastwork monitors in the
Eoyal Navy. The upper decks of these vessels are only about
the same height above water as that of the Miantonomoli, but, by
means of an armoured breastwork standing upon the np[)er deck,
the reserve of buoyancy is increased to 30 per cent, of the dis-
placement.
Fig. 7 represents the Devastation class, in which tlie reserve of
buoyancy is 50 per cent, of the displacement.
Fig. 8 represents armoured frigates of high freeboard— such
as the Sultan or Hercules— oi the Ptoyal Navy, in which the
reserve of buoyancy reaches 80 or even 90 per cent, of the dis-
placement.
Fig. 9 represents ships of high freeboard and fine under-water
form typitied by her Majesty's ship Inconstant — in which the
reserve of buoyancy is equal to, or even greater than, the dis-
placement.
So much for vessels of war. As regards merchant ships, the
diversity of practice in loading renders it difficult to lay down
any rule; there seems, however, a concurrence of opinion in
fixing the minimum reserve of buoyancy at from 20 to 30 per
cent, of the displacement, varying it according to the season of
the year, the character of the cargo, extent of the voyage, &c.
But, perhaps, the greatest difficulty met with in attempting to
apply any such rule to merchant ships is found in the selection
of those parts of the ships which shall be regarded as contribut-
ing to the reserve of buoyancy. "Spar-decks," "deck-houses,"
" inclosed poops and forecastles," &c., are very commonly built
of comparatively slight scantlings, above the upper deck proper;
and the assignment of proper values to these erections in esti-
mating the reserve of buoyancy has given rise to much dis-
cussion, out of which no practical rule for guidance has come
which can command general acceptance.
Submarine vessels, such as have been built or proposed for
use in war, furnish examples .differing from ordinary ships.
They are intended at times to be wholly submerged, and then
have no "reserve of buoyancy," using that term in the same
sense as above. Such vessels, of course, require to be arranged
12 NAVAL ARCHITECTURE. chap. i.
so that the operators within them may control the vertif^al
motion?, either rising to the surface when necessary or sub-
merging the vessel to any desired depth. For all practical
purposes, water may be treated as if it were incompressible ; at
any depth in which submarine vessels would work, a cubic foot
of sea-water may be taken as weighing 64 lbs. The weight of
a vessel and all its contents may also be assumed to be
practically a constant quantity during the period of one sub-
mersion, and, as already explained, the displacement of the
vessel, when it floats at rest at any depth, must always equal
the weight. To produce vertical motions in such a vessel, it is
therefore necessary to give the operator the power of sliglitly
varying the displacement. If he can virtually decrease the
volume of displacement, below that corresponding to the total
weight, the vessel must sink; but if, when the desired depth is
reached, he can gradually restore the displacement to equality
w^ith the weight, no further sinking will take place, nor will
the vessel have any tendency to rise. Before she can rise, the
volume of water displaced must by some means be made to
exceed that corresponding to the weight; directly that condition
is fulfilled, the vessel begins to rise. A very simple arrangement
sufiices to give the operator the necessary control. For instance,
conceive that a small cavity is formed in the bcttom of the
vessel, and that, when this cavity is about half full of water, the
total displacement of the vessel, when entirely submerged, just
corresponds to the total weight. The other half of the cavity
may be then kept filled with compressed air, which is in com-
munication with an air chamber in the interior of the vessel.
The air in the air chamber would be compressed sufficiently to
have a considerable excess of pressure over that corresponding to
the maximum depth of immersion at which the vessel is to be
euiployed. When the compressed air is withdrawn from the
upper half of the cavity, by an apparatus worked A\ithin the
vessel, the water rises into the vacated space, the volume of
displacement becomes decreased by that space, and is therefore
less than will balance the weight; as a result, the vessel sinks.
The desired depth being reached, compressed air stored within
the vessel may be made use of to force the water once more
from the upper half of the cavity, thus restoring equality
between the weight and displacement ; the vessel then remains
at that depth. Lastly, when it is required to rise, by means of
compressed air the water is wholly expelled from the cavity ; the
displacement then exceeds th.e weight, and consequently the
CHAP. I. THE BUOYANCY OF SHIPS. \X
O
vessel rises. Other agencies may be employed to effect these
results; but the principle is the same for all — the operator
must have the power of virtually increasing or decreasing the
volume of displacement if the weight remains practically constant.
By means of detachable ballast the weight can be decreased ; and
the power of ascending rapidly to the surface in case of accident
can thus be secured. This is a very desirable feature in sub-
marine vessels, but does not take the place of the controlling
apparatus above described.
The foregoing remarks imply that the submarine vessel has no
onward motion, when she is made to move vertically; but, in
practice, this condition is not usually fulfilled, and the propelling
power itself has been made available for producing or controlling
the vertical motion, by means of a horizontal rudder worked by
the operator within the vessel. In the ^Yhitehead torpedo, a
similar rudder, governed automatically, is employed to keep the
torpedo at the desired depth below the surface. Another plan,
illustrated in a model to be seen in the Naval Museum at the
Louvre, consists in giving vertical motion to the submerged
vessel by means of a small screw-propeller, worked by a vertical
axis, and placed above the vessel. This screw is an auxiliary to
air chambers like those above described, and its chief purpose
appears to be the diminution of the vertical oscillations which the
other appliances may produce about the position which it is
desired to maintain. It will be obvious that if a vessel acquires
a considerable velocity while descending to any assigned depth,
as she may do if the operation is performed quickly, she will
probably be carried much beyond that depth, even though her
original displacement be restored by expelling water from the
balancing cavity. Conversely, if to make her rise again still
more water be expelled, there is a risk of too great a vertical
motion being produced ; and so oscillatory movements may take
place about the desired depth. A manoeuvring screw such as
the French vessel has, is one of the simplest and most effective
means conceivable for extinguishing these oscillations; and a
screw of similar character, if power were available, might be made
to give all necessary vertical motion to a vessel, although this
would be a less economical arrangement than the air chamber. It
will be evident that the risks incidental to service in these vessels
can only be minimised by the greatest care in management as
well as in design.
Ships founder when the entry of water into the interior causes
a serious and fatal loss of floating power. There are two cases
14 NAVAL ARCHITECTURE. chap. i.
requiring notice. The iirst, and less common, where the bottom
of the ship remains intact, but tlie sea breaks over and " swamps "
the vessel. The second, that in whicli the bottom is damaged
or fractured, and water can enter the interior, remaining in free
communication with the water outside. Damage to the under-
water portion of the skins of ships is by far the most fruitful
source of disaster; but many ships founder in consequence of
being swamped, seas breaking over them, and finding a passage
down through the hatchways into the hold.
The older sailing brigs of the Koyal Navy are believed by
many competent authorities to have been specially exposed
to this danger. Very many of them were lost at sea ; and their
loss was believed to have resulted from the lowness of their
freeboard, the height of their bulwarks, and the insufficiency
of the *' freeing scuttles" in tlie top-sides to clear rapidly the
large masses of water which lodged on the decks. In con-
sequence, water accumulated, passed into the interior, and
swamped the ships. The case of the steam-ship London furnishes
another illustration. She is said to have been lost in consequence
of a very heavy sea having swept away the covering of the engine
hatchway, and left open a large aperture, down through which
the water poured, putting out the fires, and leaving the ship a
lo"- on the water. Other seas washing over the unfortunate
vessel completed the disaster, and she gradually sank. The
United States monitor Weehatvhen also appears to have been lost
in this manner. While forming part of the blockading squadron,
and lying at anchor off Charleston with her hatchway forward
uncovered, the weather being comparatively fine, a sea broke
on the deck, poured down the open hatchway, and caused the
vessel to sink rapidly — it is said in three minutes — her extreme
lowness of freeboard and small reserve of buoyancy conducing
to this end. Still another, and slightly different, case in point
may be found amongst the vessels engaged in the timber trade.
It has been customary to load these ships very deeply, and often
to carry Jarge deck cargoes; thus interfering with the efficient
working of the ships. Meeting with heavy weather, and beiiig
only partially under control on account of the deck cargoes,
these vessels frequently ship large quantities of water, becoming
*' water-logged," and utterly unmanageable, even if they do not
sink.
The condition of a water-logged ship naturally leads to the
remark, that in any ship the maximum quantity of water that
can enter the interior may or may not suffice to sink her, ac-
CHAP. I.
THE BUOYANCY OF SHIPS.
15
corling as it is greater or less in weight than the reserve of
buoyancy which the ship possesses. The maxiinum quantity of
water that can enter the interior is determined by the unocouined
space : for to space which is already occupied by any substances
— cargo, coals, engines, &c. — the water can obviously find no
access. If the cargo be, like timber, very light, occupying a
very large portion of the internal space, then it may happen
that the total volume of the space unoccupied is less than that
of the reserve of buoyancy, and the ship remains afloat; but
this is not the common case, and if a vessel becomes swamped,
and the sea finds access into all parts of the interior through
the hatchways, she will most probably founder. Properly con-
structed and well-ladeu vessels are not, however, likely to founder
in this fashion. Their hatchways and openings in the decks are
carefully secured, and protected by high coamings and covers;
FIG 10.
Mc'i'n Df-rh n . r h
'^..
, i
L
/
LoiiH i-I>cck 'f
7 h---
\"' ' 1.
; <
- /
■\
while the interior is so subdivided into compartments, especially
in iron ship?', that, if a sea breaks on board, and finds its way
down a hatch, it does not gain free access from the space thus
entered to all other parts of the interior. Free water which
passes thus into a ship must considerably aifect her behaviour
in a seaway, althongh it may not jeopar.lise her safety : this
case is considered in Chapter VI.
Turning next to the case of the ship of which the skin is
penetrated below water, it is needless to cite exam23les of the
possibly serious nature of such an accident. Very many illus-
trations will at once occur to the mind of every reader; this
being a very common source of loss now that iron is the material
generally used in building merchant ships. The causes of the
under-water damage may be various — such as accidental collision,
local wear and tear, grounding, ramming, torpedo explosions, &c.
— but in all cases water can enter the ship, and this water
i6
NAVAL ARCHITECTURE.
CHAP. I.
remains in free communication with the water outside. So long
as that communication is maintained, water will continue to
pass into the ship until either it can find access to no further
space or has entered in such quantities as to exceed the reserve
of buoyancy, when the vessel sinks.
A simple illustration will render these statements clear. Take
a box-shaped vessel, such as in Figs. 10 and 11, and suppose a
hole to be broken through the skin under water. The water at
once passes into the interior in quantities dejDcnding upon the
area of the hole and the depth it is below the water-level.
A very simple rule approximately expresses the initial rate of
inflow.
FIG 11.
Main I>efjk a. c k
Wl
Jjowcr Deck
i/i
A
Let A = area of the hole (in square feet).
„ d = the depth below water in feet (taken about the centre
of the hole will be near enough for practical
purposes).
Then, if v = velocity of inflow of the water in feet per second,
v^ = 64 cZ (approximately); and v = '^\/d',
80 that, immediately after an accident, the volume of water
passing into the vessel in each second
= 8\/cZ X A (cubic feet).
Suppose, for example, the hole is 2 square feet in area, and.
has its centre 12 feet under water:
V = %/\J 12 = 27| feet per second.
Water flowing in per second = 27| X 2 = 55^ cubic feet.
If the vessel floats in sea-water.
Tons of water flowing in per second = 55J -=- 35 = 1-58.
Similarly, for any other depth or area of hole in the bottom
CHAP. I. THE BUOYANCY OF SHIPS. Ij
of a ship, this rule will enable the rate of inflow to be determined
very nearly.
Eeverting to Fig. 10, it is obvious that, if the water can find
free access to every part of the interior — which would be true if
there were no partitions forming watertight compartments — the
ship must sink: unless the power of her pumps is sufficient to
overcome the leak ; or some means is devised for checking the
inflow, by employing a sail, or a mat, or some other "leak-stopper ; "
or the total unoccupied space in the interior is less than the reserve
of buoyancy, a condition not commonly fulfilled. A considera-
tion of the preceding formula for the rate of inflow will show
that it is hopeless to look alone to the pumps to overcome
leaks that may be caused by collision, ram attacks, or torpedo
explosions; the area of the holes broken in the skin admitting
quantities of water far too large to be thus dealt with.* Hence
attention is directed to two other means of safety : the first,
minute watertight subdivision of the interior of the ship, to
limit the space to which water can find access ; the second, the
employment of leak-stoppers, which can be hauled over the
damaged part, and made to stop or greatly reduce the rate of
inflow. This latter is a very old remedy. Captain Cook having
used a sail as a leak-stopper during his voyages, and many ships
having been saved by similar means. It has acquired renewed
importance of late, and various inventors have proposed modifi-
cations of the original plan, but all these are based upon the old
principle of " stopping " the leak. Such devices are not embodied
in the structure or design of the ship, but form simply part of
her equipment; whereas watertight subdivision is a prominent
feature in the structure of a properly constructed modern iron
ship. It will be well, therefore, to sketch some of its leading
principles. In doing so, we shall, for the sake of simplicity, make
use of box-shaped vessels for purposes of illustration; but the
conclusions arrived at will, in principle, be equally applicable to
less simple forms, like those of ships.
There are three main systems of watertight subdivision: (1)
by vertical athwartship bulkheads ; (2) by longitudinal bulk-
heads ; (3) by horizontal decks or platforms. Besides these
there is the very important feature of construction known as
the " double bottom," the uses of which will be described further
* For a full discussion of this point the author to the Journal of the Royal
see a paper " On the Pumping Arrange- United Service Institution (1881).
menls of War Ships," contributed by
C
1 8 NAVAL ARCHITECTURE. chap. I.
on. In Figs. 10 and 11 the hole in the skin, admitting water
to the hold, is supposed to lie between two transverse bulkheads
(marked ah and ce) which cross the ship and form watertight
partitions rising to some height above the load-draught line
(WL) and terminating at a deck marked "Main Deck." The
great use of these bulkheads will be seen if attention is turned
to Fig. 11, which represents the condition of the box-shaped
vessel after her side has been broken through. The vessel has
sunk deeper in the water than when her side was intact ; and it
is easy to determine what the increase in draught has been when
one knows the volume {fgeh, in Fig. 10) of the damaged com-
partment, as well as the volume in that space which is occupied
by cargo, or machinery, or other substances. To simplify matters,
suppose this compartment to be empty ; and assume the length
ac to be one-seventh of the total length AA : then the volume
fgeb will be about one-seventh of the total displacement; and
when this compartment is bilged and filled with water up to the
height of the original water-line WL, one-seventh of the original
buoyancy will be lost. In fact, the compartment between the
bulkheads no longer displaces water ; in it the water-level will
stand at the height of the surface of the surrounding water ; and
since the weight of the ship remains constant, the lost buoyancy
must be supplied by the parts of the ship lying before and abaft
the damaged compartment. For this reason we must have —
f original water-line area x increase in draught
= j X displacement
= j X original water-line area X original draught.
Increase in draught = \ original draught.
This very simple example has been worked out in detail
because it illustrates the general case for ship-shape forms.
The steps in any case are : —
(1) The estimate of loss of buoyancy due to water entering a
compartment; this loss being equal to the part of the original
displacement which the damaged compartment contributed, less
the volume in the compartment occupied by cargo, &c.
(2) The estimate of the increased draught which would enable
the still buoyant portions of the vessel to restore the lost buoy-
ancy if the entry of water were confined to the damaged com-
partment.
And to these, in practice, must be added —
(3) The change of trim (if any) resulting from filling the
damaged compartment.
CHAP. I.
THE BUOYANCY OF SHIPS.
19
Keverting to Figs. 10 and 11, it will be obvious that, if the
transverse bulkheads ah and ce did not rise above the original
water-line WL, more than one-sixth of the original draught, they
would be useless as watertight partitions ; because, when the
compartment was bilged, their tops would be under water before
the increase of draught had suflSced to restore the lost buoyancy.
And when their tops are under water (unless the deck at which
the bulkheads end forms a watertight cover to the compartment),
the water is free to pass over the tops, or through hatchways
and openings in the deck, into the adjacent compartments, thus
depriving them also of buoyancy, and reducing the ship to a
condition but little better than if she had no watertight partitions
in the hold. Fig. 12 illustrates this serious defect. The main
deck at which the tranverse bulkheads ah and ce end is lower
than in Figs. 10 and 11, all other conditions remaining un-
FIQt2.
Warn jJeefi
/ - f^,-^S^3^
iW
Loivcf ifc-n '-"-^^^
4
^""W-
HI
changed ; and consequently, when the compartment is bilged,
the water can pour over the tops of the bulkheads into the
spaces before and abaft.
Hence this practical deduction. Watertight transverse bulk-
heads can only be efiScient safeguards against foundering when
care is taken to proportion the heights of their tops above the
normal load-line to the volumes of the compartments; or else
to make special provisions for preventing water from passing
into adjacent compartments by means of watertight plating on
the decks at which the bulkheads end, in association with water-
tight covers or casings to all hatchways and openings in the
decks.
A vessel would ordinarily be considered very well subdivided
if she would keep afloat with any two compartments filled
simultaneously. This was the recommendation of the council
c2
20 NAVAL ARCHITECTURE. chap. I.
of the Institution of Naval Architects in 1867 ; but in the
vessels of the Eoyal Navy it is not unusual to find the sub-
division so minute that from three to six of the largest compart-
ments may be simultaneously filled, without bringing the tops
of the bulkheads under water, or allowing water to pass into
compartments adjacent to those filled.
In iron or steel merchant ships efficient watertight subdivision
is commonly wanting : the consequent risk being accepted
rather than the interference with stowage of the hold which
might result, in some cases, from the multiplication of transverse
bulkheads. Sailing ships even of the largest size commonly have
but one bulkhead near the bow ; steamers are as a rule somewhat
better off, and in many of the largest passenger steamers the
subdivision is carried out thoroughly, transverse and longitudinal
bulkheads as well as decks being utilised as watertight partitions.
Efficient watertight subdivision is required by the Admiralty in
all merchant steamers placed upon the official list, the essential
condition being that the ships shall remain afloat in still water
with any one compartment thrown open to the sea. It is a
matter for congratulation that shipowners and shipbuilders are
uniting in this development of watertight subdivision in our
merchant ships, the Admiralty condition being much DDore than
satisfied in a large and increasing number of ships.
The midship compartments of a ship are usually the largest,
and claim most attention ; but those near the extremities are
also important, because, although their volume may be small,
when they are filled they cause a considerable change of trim.
Reverting once more to our box-shaped vessel in Fig. 10, instead
of supposing an empty midship compartment equal to one-seventh
of the length to be filled, and to cause a loss of one-seventh of
the buoyancy, let it be supposed that a compartment only half
as long and half as large at one end (shown by mkLK in the
diagram) is filled. The increase in the mean draught due to
this accident would be only one-thirteenth of the original draught,
but the trim would be altered very considerably (as shown in
Fig. 13); and the top of the bulkhead hhn, although as high
as those amidships, would be put under water by the change of
trim. Consequently, unless the main deck is made watertight as
far aft as the bulkhead hm, this very small compartment forward
might, from its influence on the trim, be large enough to sink
the ship; for when it is filled, if the deck does not form a
watertight top to it, the water will pass over (at h) into the
next compartment, the bow will gradually settle deeper and
CHAP. I,
THE BUOYANCY OF SHIPS.
2t
deeper, and at last the vessel will go down by tlie bead. It
Aviil be in the recollection of many readers that ships whicli
founder very eommonly settle down finally either by the head
or the stern, and the foregoicg simple illustration will furnish
an explanation of some such occurrences.
It should be added that the assumptions made in the box-
shaped vessel are fairly representative of actual ships. For
example, in her Majesty's ship Devastation, if one of the large
compartments amidships were filled, the ship would have an
increased drauoht of about 15 or 16 inches, and her trim woukl
be practically unaltered. If tlie aftermost compartments were
filled, so as to give the ship an increase of 7 or 8 inches in the
mean draught, the trim would be changed from 4^ to 5 feet, and
the tops of the bulkheads bounding these extreme compartments
FIG 13.
would be put under water. No evil would result, however, for
these bulkheads are ended at a watertight iron deck.
Passing from transverse to longitudinal bulkheads, the same
principles apply. The heights to which the bulkheads are
carried should be carefully proportioned to the sizes of the com-
paitments of which the bulkheads form boundaries; and water-
tight decks are no less useful as tops to such compartments when
the bulkheads cannot be carried high enough to secure the
restoration of the lost buoyancy. In this case, however, the
longitudinal partitions, supposing only one side of the ship to
be damaged, destroy the symmetry of the true " dis[)lacement,"
and the result is that the vessel heels over towards the damaged
side. Transverse inclination takes place without change of trim
if the damaged compartment is amidships; but if it be near
the bow or stern, both change of trim and transverse inclination
22
NAVAL ARCHITECTURE.
CHAP. I.
will result from tlie same accident. It is needless to do more
than deal with the latter, as the influence of change of trim
has already been described ; and in this case the box-shaped
vessel will once more furnish a simple illustration of what may
happen in ships.
In Fig. 14, suppose the large midship compartment bounded
by transverse bulkheads, ah and ce (in profile view), to be
subdivided by longitudinal bulkheads, fq^, rs (in section) ; in
the positions shown, these longitudinal bulkheads fairly represent
the coal-bunker bulkheads of an ironclad, being rather less than
one-fourth of the breadth of the ship within the side. The " wing
compartment " lying outside the bulkhead, marked rs in section,
FIG 1^.
Section
Profile
Main Deck
L
3^in Beck a c
__
r
W \
L
_.
iiotcei^ JJecTc "^
if
r--^
'
A
I 5 <
>
A
Section
after accident.
Flail.
and rr in plan, Fig. 14, may be supposed to contain three-
sixteenths of the total volume of the compartment between the
transverse bulkheads ab and ce; reckoning up to the load-line
WL, this will give,
Loss of buoyancy when wing"j
compartment is filled 1 = /g X f total displacement
with water )
= jf 2 total displacement.
Increase in mean draught = j^g original draught.
But this will be accompanied by a heel towards the damaged
side, as indicated in the lower section (Fig. 14), amounting, in
CHAP. I.
THE BUOYANCY OF SHIPS.
23
the example chosen, to the immersion of the damaged side to
about four times the extent of the increased mean draught due
to loss of buoyancy. Hence it is clear that, in arranging longi-
tudinal bulkheads, care must be taken either to carry them
high enough to provide against heeling or else to have water-
tight plating forming a top to the compartments.
Lastly, attention must be directed to the usefulness of
horizontal watertight decks or platforms in preventing loss of
FIG.15.
JSIairh Dech a c _ -
w
-J-' ''9 i
L
p|- If 1
J-
\ II ■ *
' 1 1 ' '
'r~ ■ 't e ■ " -" -^
buoyancy. It is unnecessary to repeat what has been said
especting decks lying above the normal load-draught line
and forming tops to spaces inclosed by longitudinal or trans-
verse bulkheads; consequently attention will be confined to
FIG 16.
Main Beck
W"
M
m
I —
the cases where a deck or platform lies below the load-line.
In such cases either one of two accidents may be assumed to
have happened : viz. the side has been broken through heloio
the platform, or else above it. Turning to Fig. 15, let it be
supposed that the large midship compartment bounded by
the transverse bulkheads ah and ce has a watertight platform
2)^ worked in it, at mid-draught. The volume of this compart-
24
NAVAL ARCHITECTURE.
CHAP. I.
ment up to the load-line \>(Aw% one-seventh of the displacement,
ihe buoyancy contributed by either of the parts into which it is
divided by the platform will be one-fourteenth the displace-
ment. If the side is broken through below the platform, the
whole of the water-line area WL contributes buoyancy when
the vessel is iniraersed more deeply ; therefore, if the whole
space is considered accessible to water (as shown in Fig. 10) —
Increase in mean draught dne to i ^ • • i i „ i <.
" ^ = -^^ original drangiit.
bilging compartment below pg- j ^"^
But if the side is broken through above the platform, only
-^- the water-line area contributes buoyancy ; therefore (as shown
in Fig. 17)—
Increase in mean draught due to 1 . • • ^ ^ i +
^ ^ ^ ^o original draught.
bilging compartment above jaq
FIG 17.
}-^
This contrast shows how important a thing it is to take
all possible measures to maintain the buoyancy of the ship at
the load-line; for any decrease of that buoyancy not merely
affects the draught of water, but also decreases the stability
of a ship, as will be shown hereafter. It may be added that,
in all cases where openings have to be made in a water-tight
deck or platform, either watertight covers must be fitted to
the openings or watertight trunks, carried to a sufficient height
above the load-line, must bo built around them.
All the methods of watertight subdivision illustrated above
are associated in well-built ships ; and the minuteness of sub-
division attained when care is taken is well exemplified in
Figs. 18-25, which represent the arrangements of the water-
tight partitions in a modern ironclad of the Royal Navy.
Such vessels have the great safeguard of a "double bottom,"
formed by a watertight inner skin fitted some di^stance within
CHAP. I. THE BUOYANCY OF SHIPS. 25
the outer skin. This inner skin extends from two-tliir.ls to
three-fourths of the total length of the ship; its terminations
are marked g g in the profile view (Fig. 18) and the '"plan
of double bottom " (Fig. 20). From the keel np to the turn
of the bilfre, the inner skin is worked about 3 or 4 feet within
the outer; as shown in the sections (Figs. 21-25), from the
points a downwards. At a there is a watertight longitudinal
partition (or frame), and the keel is also made watertight.
Above the turn of the bilge, the inner skin (iv, tv in the
sections) is usually worked vertically up to the height of the
main deck, thus inclosing "wing-spaces" in the region of the
water-line, or, as it is termed, " between wind and water."
The inner skin is here often 8 or 10 feet within the outer.
In addition to the longitudinal partitions at the bilges (a,
in sections) and at the keel, the doulde bottom is subdivided
by numerous watertight transverse partitions (shown by // in
Fig. 20), about 20 feet apart ; compartments, of very moderate
size, beini>: thus formed between the two skins.
Within the limits of the double bottom, the hold-space is
subdivided by means of transverse bulkheads (b h, Fig. 18),
and longitudinal bulkheads {I I, Fig. 19). Before and abaft the
duuble bottom there is only a single skin, and the subdivision
is effected by means of transverse bulkheads and horizontal
platforms (j) |:>, Fig. 18). Although there is no inner skin at
the extremities, the subdivision there is very minute, and the
compartments are small owing to the fineness of form of the
bow and stern. The "plan of hold" in Fig. 19, taken in con-
nection with the profile (Fig. 18), will give a very complete view
of the subdivision of the hold-space. Besides the main i)artitions
already alluded to, it will be observed that, in many cases, parti-
tions required primarily for purposes of stowage or convenience
are made watertiirht in order to make the subdivision more
minute. Examples will be found in the coal-bunker bulkheads,
the chain-lockers (immediately bii'fore the boiler-rooms), the
magazines and shell-rooms, and the shaft-passages. Slight
increase of cost and workmanship, with a very small increase
in weight, are thus made to contribute to much greater safety.
It need only be added that the principal bulkheads either run
up to the main deck, situated some 5 or 6 feet above water, or
are ended at a watertight platform.
The spaces occupied by the machinery almost necessarily
form large compartments amidships; but in recent ships the
stoke-holds have each been divided into two by means of a
26
NAVAL ARCHITECTURE.
CHAP. T.
middle-line bulkhead (I I, in Fig. 19) ; and in vessels propelled
by twin-screws, as is the case in our example, the engine-room
compartment is similarly halved. The great advantages result-
CHAP. I.
THE BUOYANCY OF SHIPS.
27
iug from this middle-line division are too obvious to need comment,
especially in ships which are mainly or wholly dependent upon
steam power for propulsion, and exposed to damage under water
by shot or shell, ramming and torpedo explosions.
The following table gives the number of compartments in
several of the most important ships of the Eoyal Navy : —
Ironclad Ships of Royal Navy.
Cla
Xames.
Largest
early types
Smaller
early types
Largest
recent
masted
types
Smaller {
masted typesl
Belted
ships
Mastless
or lightly
rigged
Eams
Monitors
Warrior
Achilles
Minotaur
Hector .
Eisistance
Monarch
Hercules
Sultan
Alexandra
Temeraire
Invincible
Triumph
Shannon
Nelson .
Devastation
Dreadnought
Inflexible .
Hotspur .
Bttpert
Oorgon
Glatton
W'atertight Compartments.
In Hold-
space.
In Double
Bottom and
Wincjs.
35
40
40
41
47
33
21
27
41
44
23
26
44
83
68
61
89
26
40
la
37
57
66
49
52
45
40
40
40
74
40
40
40
32
16
36
40
46
32
40
20
60
Total.
92
106
89
93
92
73
61
67
115
84
63
66
76
99
lot
101
135
58
80
97
The Devastation may be taken as a good example of a modern
war-ship, although she has no middle-line bulkhead in her engine
and boiler rooms. Her double bottom and wings are divided
into thirty-six compartments; the hold-space into sixty-eight
compartments. If the three largest compartments of the hold
(viz. the engine and boiler rooms) are filled, the vessel will only
be immersed about 0% feet. If she had a middle-line bulkhead,
like the later ships, each of these large compartments would be
halved, and it would be most improbable that both halves of
any compartment would be filled simultaneously. The total
28 NAVAL ARCHITECTURE. CHAr. i.
number of compartments in the hold wonld then be seventy-one,
and filling any six compartments a.midsliips would immerse the
vessel as befoie. The hxroest compartment in tlie donble bottom
holds only about 50 tons of water, corresponding to an increased
immersion of only \ \ inch ; and the whole double-bottom space
will carry 1000 tons of water ballast, the additional immersion
being 28 inches.
Similar watertight subdivision is carried out in the unarmonred
war-shiiis of the Koval Navv liaving iron or steel hulls ; and to
some extent it is applied also in composite ships. The Iris
despatch vessel is an illustration of recent practice : she is built in
sixty-one separate compartments. In foreign war-ships of recent
design the stime principles have been applied, and in some
instances carried even further than in English ships. For
instance, the lai'ge armoured frigate Admiral Buperre of the
French Navy is said to liave nearly two hundred separate com-
partments ; and it would appear that equally minute subdivision
has been secured in the large Italian ships Italia and Lepanto.
Nor are unarmoured ships exceptions to the prevalent foreign
practice.
The value of watertight subdivision is becoming increasingly
recognised in merchant ship construction. This fact has been
already mentioned, and in Chapter IX. details will be found of the
cellular system of construction now extensively employed in iron
and steel merchant ships, by means of which their watertight
subdivision of the hold-space is supplemented by the valuable
feature known as the " double bottom." In Figs. 18-25, the
double-bottom arrangements of war-ships have been illustrated,
and those recently adopted in merchant ships are shown in Fig.
I04a. Double bottoms are advantageous (1) as a means of
safety, (2) as a source of economy, when fitted to carry water-
ballast, (3) as an efficient arrangement of the thin materials
in the lower part of the structure, enabling them to resist
longitudinal strains. The last-mentioned feature is discussed
in Chapter IX. ; respecting the otlier two a few remarks may be
added.
The lower part of any ship is most liable to injury by touching
the ground, the thin bottoms of iron or steel ships being peculiarly
liable to serious damage. If there be an inner skin, however,
and the damage does not extend to it, fracture of the outer
skin may be very extensive, but no water will enter the hold.
Very many cases are on record, si) owing the great usefulness
of the inner skiu ; two only will Le mentione^d. The first is that
CHAP. I. THE BUOYANCY OF SHIPS. 29
of the Great Eastern, which has a coaiplete double bottom. Off
the American coast the vessel ran ashore, and tore a hole 80
feet long in her outer skin, but the inner skia remained intact,
and no water entered the hold. The second is that of her
Majesty's ship Agincourt, which ran on the Pearl Eock at
Gibraltar ; this ship has a partial double bottom, and fortunately
grounded at a part where the inner skin existed, so that no serious
consequences followed.
Considerations of safety and structural strength, chiefly influence
the adoption of double bottoms in war-ships : their use as
receptacles for water-ballast is unfrequent, although they are
generally arranged for such use when required. In merchant
ships, however, the chief inducements to use double bottoms have
been found in the commercial advantages of water-ballast. Instead
of having to incur delays and considerable expense in shipping
and discharging rubble-ballast, the commander of a ship fitted
for water-ballast can readily admit or discharge such ballast. In
some trades the consequent gains are greater than in others, but
it is now generally agreed that the balance of advantage, is in
favour of ships built with the improved form of double bottom,
illustrated in Fig. 104rt. The older forms of water-ballast tanks
used before the adoption of the cellular system were objection-
able in some respects, raising the cargoes high in the ships, and
decreasing the space available for stowage ; yet the experience
gained with these imperfect arrangements has largely influenced
subsequent practice.*
The parts of tlie inner bottom situated above the bilges (see
sections in Figs, 21-25) are often termed "wing-passage bulk-
heads," and are so far inside the outer skin that the chances of
their beins: broken through are much lessened. Similar bulk-
heads are not fitted in merchant ships ; but in many cases longi-
tudinal coal-bunkers are placed abreast the engines and boilers,
and a considerable increase of safety is obtained by making the
bunker-bulkheads watertight. In a war-ship it is at this part
that the greatest damage is likely to be done by ramming or
torpedo explosions ; and the best known remedy against either
is undoubtedly internal subdivision. To attempt to keep out
either a ram or a torpedo attack is hopeless ; the outer skin is
certain to be broken through, and possibly the inner also. But
whereas a grazing blow at low speed would suifice to tear a large
hole in the outer skin, only the direct blow of a ram moving at
* See a valuable paper " On Water- to Lloyd's Eegister) in Transactions of
Ballast," by Mr. Martell (chief surveyor Institution of Naval Architects for 1877.
30
NAVAL ARCHITECTURE.
CHAP. X.
good speed would be likely to penetrate the inner skiti of an
armoured ship.
An illustration of the usefulness of the wing-passage bulk-
head against ramming or collision was afforded in the accidental
collision of the Minotaur and Bellerophon ; the outer skin of
the BeUeroplion was broken, and the armour driven in, but the
ship remained on service for some time before the repairs were
FIG 26,
■Sy.V'-^ '^^'^'-'''-*'-^^^'''-^ k^'.«.^■k■.'.^^^,.^^k^'■,.^ ^^<^^k■^^■,.^^^^^v■^^^^■v.^^^^.<^^^^.^^^,^T^^?yg
k^\V^v»^V^V^.VVVV^V^^\v\V\N\VV^^^^
^vl,^^k^v^^^<,^^^vw^^vv^^^^■.'^^^<k<^':v<^.v^A^^k.vw.>.^^s^^.v^v^^^^^
^^^^^<~-^~-<■.-~^'■^^'-^-■vv'^^-■->-■■'■^^^'^■-"^^'^^^"^^^^■W^'''W■,S^^^^v^^^'^g
completed. Again, when the Hercules and Northumberland
came into collision, a very similar advantage resulted from the
existence of the wing-passage in the latter ship. In the case of
the Vanguard, although the vessel was lost, the existence of the
inner skin was an immense advantage to the ship, keeping her
afloat for seventy minutes after the collision, whereas, had there
been no inner skin, the vessel must have sunk in a very few
minutes. So much misapprehension has existed on this matter
CHAP. I. THE BUOYANCY OF SHIPS. 3 1
that it may be well to adduce a few facts in support of the
foregoing statement. Fig. 26 shows a cross-section of the
Vanguard, with the bow of the Iron Buhe in the position which
it probably occnpied at the time of the collision. It will be noted
that, althongh the armour was driven in, and the armour shelf (a)
damaged, the inner skin (s) was not pierced. This the divers
asserted after carefid examination, and there is conclusive
corroborative evidence that their report is correct. Evidence
given before the court-martial proves that at first the vessel sank
at the rate of only 8 inches in fifteen minutes, and at last at the
rate of one inch per minute ; this maximum rate of sinking
corresponds to a total inflow of only 27 tons of water per
minute, which would have been admitted by an aperture less
than one square foot in area. But the divers, after measurement,
reported that the hole in the outer skin was 10 feet in depth,
varying in breadth from 2 feet to 3^ feet. Assuming the area
to have been 20 square feet (which is probably less than the
truth), the initial rate of inflow of water per mioute, had there
been no inner skin, would probably have been at least 1000
tons, or nearly fortyfold what it actually was at the last. It
seems certain, therefore, that the damage to the armour shelf,
and other parts of the ship, admitted into the hold in the
aggregate no more water than a hole one square foot in area in
the skin of an ordinary ship with no double bottom would have
admitted, notwithstanding the fact that the Iron Duke struck
the Vanguard a blow much exceeding in force that delivered by
the projectile of a 35-ton gun at the muzzle. It is noteworthy
also (see Fig. 26, and the sections in Figs. 21-25) that in the
Vanguard the inner skin terminated about 4 feet under water,
whereas in most of her Majesty's ships it is carried to the main
deck, several feet above water — a preferable arrangement. Even
her loss supplies, therefore, a most striking example of the utility
of watertight subdivision, for she was kept afloat more than an
hour by this means, instead of foundering in a very few minutes,
as an ordinary iron ship similarly damaged in the outer skin
must have done. It would be out of place here to further dis-
cuss the circumstances attending the disaster, but it may be
observed that they illustrate the necessity for taking all possible
care in maintaining the integrity of bulkheads and other partitions
intended to be watertight, as well as for keeping in thorough
working order the doors or covers fitted to any apertures cut in
bulkheads or platforms for ventilation or for convenient access to
compartments in the hold.
The more recent case of the Grosser Kurfiirst has been treated,
32 NAVAL ARCHITECTURE. chap. I.
by some writers, as a proof of the small value attaching to water-
tight subdivision. This vessel sank in less than ten minutes
after her collision with the Konig Wilhehn, notwithstanding the
fact that she was extensively subdivided. The circumstances of
her loss are well known. She was proceeding in company with
her consorts, with watertight doors open in bulkheads and no pre-
cautions taken to provide for rapidly closing the doors, such as
would have been taken in action. In the endeavour to cross the
bows of the Konig Wilhehn, when a collision seemed imminent,
the Grosser Kurfilrst was driven at nearly full speed ; and this
rapid motion aggravated greatly the injury consequent upon the
entry of the spur of the Konig Wilhehn into her side, the skin-
plating being torn away for a considerable distance. The access
of water to the hold-space was thus made easy, and the ship sank
rapidly. Possibly the damage done might have caused her to
founder had all possible precautions been taken — doors closed and
all watertight partitions secured. But it is clearly unfair to
omit consideration of the exceptional circumstances above
mentioned, or to depreciate the value of watertight subdivision
because the Vanguard and Grosser Kurfilrst were sunk. On
the other side numerous cases can be mentioned in which ships,
which would otherwise have foundered, have been kept afloat
by their watertight bulkheads.
It cannot be claimed for the most minutely subdivided war-
ship that she is absolutely unsinkable. Comparatively large
spaces have to be provided for engines, boilers, and equipment ;
and this puts a practical limit on the minuteness of watertight
subdivision. Moreover, the damage inflicted by ramming or
torpedo attacks may be so extensive as to throw several compart-
ments open to the sea simultaneously. On the other hand, the
chances of escape are obviously increased, as the subdivision is
made more thorough. If the primary consideration in the design
of a ship were to make her as nearly as possible unsinkable, it
would clearly be desirable to associate extensive subdivision into
watertight compartments with the use of cork, or other packing
materials of small specific gravity. By this means, if there were
no limitations of size or cost, it might be possible to produce a
vessel which could sustain a very considerable amount of damage
before it ceased to be buoyant. The internal spaces to which
water could find access would, in the aggregate, bear a small pro-
portion to the reserve of buoyancy ; and when damaged the con-
dition of the vessel would resemble that of a water-logged timber-
laden ship. The drawbacks to this system are great ; size, cost,
and propulsive power would all require great increase, and it is
CHAP. I. THE BUOYAXCY OF SHIPS. y^y
scarcely probable that tlie plan will ever find favour, except on
;i limited scale. The system is applied, to some extent, in life-
boats; it is also adopted in special classes of armoured ships,
wherein the whole or a portion of tlio length is protected by an
under-water deck. For example, in the Indexible and other
" central-citadel " ships of the Eoyal Navy, cork-packing and ex-
tensive watertight subdivision are adopted before and abaft the
citadel and above the armour deck. Similar methods have been
used in certain special vessels designed for torpedo service in
foreign navies. In the Italian ships Italia and Le])a)ito, which are
protected below water by strong decks, extremely minute water-
tight subdivision of the water-line region above those decks
is trusted to preserve the buoyancy and stability. In the Vohj-
phemiis, of the Koyal Navy, a different system is applied ; the
hold-space is very minutely subdivided, and any loss of buoyancy
which may occur in action will be met, either wholly or partially,
by letting go iron ballast carried for that purpose. The reserve
of buoyancy in this vessel is small, if measured in the manner
described on page 10; but the detachable balhast represents a
further reserve of about ten per cent, of the displacement.
In the preceding pages considerable use has been made of the
" reserve of buoyancy " as a measure of the comparative safety
of ships ; and this measure very generally commends itself to
naval architects as a substitute for linear measurement in state-
ments of the " freeboard " of ships. Freeboard, in its common
use, means the height of the upper deck amidships (at the side)
above water, and is stated in feet and inches; but this must
necessarily be associated in some way with the size of the
ship. The old rule for freeboard, commonly known as "Lloyd's
rule," was based upon the " depth in hold " of ships, and may
therefore be taken as having roughly porportioned the relative
volumes of the in-water and out-of-water parts of a ship when
floating in still water. The rule was : —
Freeboard = from 2 to 3 inches per foot depth in hold.
In 1867 the council of the Institution of Naval Architects took
up this question, proposing to make the freeboard of ships mainly
dependent on the beam. Their rule was as follows : —
Freeboard (in feet) = one-eighth the beam, with the addition
of one-thirty-second part of the beam,
for every beam in the length of the ship,
above five beams.
D
34 NAVAL ARCHITECTURE. chap. i.
For example, a ship 160 feet long, and 82 feet beam, is jive
heams in length ; freeboard = J, x 32 = 4 feet. If she were
192 feet in length, or six beams (one beam in excess of the five) :
freeboard = I x S2 + ^.j X 22 = 5 feet. If slie were 224 feet
long, or seven beams : freeboard = J x 32 + ^2, x 32 = G feet.
And so on.
This rule obviously fails by the omission of any reference to
the dej^th of the ship ; deep, narrow ships, which would require
exceptional freeboard in consequence of their bad proportions,
would by this rule gain upon better-proportioned vessels,
and have a relatively low freeboard granted to them. More-
over, in the very long vessels now commonly employed, say with
a length ten times the beam, the allowance for the additional yi^;e
beams would be proportionately very great — in fact, the freeboard
required by the rule might be excessive. On tlie whole, therefore,
in spite of the authority on which the proposed rule rests, it
is not surprising that it has never come into general use.
In connection with the recent legislation for the safety of
merchant shipping, and the inquiry of the Royal Commission
of 1874, upon which that legislation has been based, the question
of freeboard, with its closely allied topic — load-draught — has
been much discussed. After taking the evidence of many pro-
fessional men, the commission came to the conclusion that no
general rule for freeboard and draught could, with advantage, be
laid down. Consequently the law now fixes no minimum of
freeboard, but requires the shipowner to mark upon the sides
of the ship the maximum draught which he proposes not to
exceed in loading her for any voyage. The decision as to ships
being overladen or not now rests with surveyors appointed by
the Board of Trade. These surveyors have the power of detaining
ships considered to be overladen ; and their decision is subject
to revision by local courts of survey.
The Committee of Lloyd's Eegister of Shipping have for some
years been in the habit of fixing the maximum load-line of
" awning-decked " ships (see page 55) classed with them ; and
this special practice is said to have given satisfactory results.
On the other hand, it is asserted by some authorities tliat the
existing law which leaves to the owner the responsibility of fixing
the load-line in each ship has tended to produce dangerously
deep loading in many instances. In order to remedy these evils,
and to supply the professional knowledge required in fixing a
reasonably safe load-line, it has been proposed to constitute a
central authority of a representative character, to which these
CHAP. I. THE BUOYANCY OF SHIPS. 35
difficult questions miglit be referred. In this authority it is
suggested that there should be included shipowners, shipbuilders,
seamen, underwriters — in short, members of all classes interested
in shipping ; and that they should have the assistance of com-
petent naval architects to make the calculations and investiga-
tions necessary for forming opinions on each case submitted. No
action has been taken in the matter up to the present time
(1882), but the general features of the scheme have been very
favourably received, and it may be adopted eventually. Many
persons who were formerly opposed to official interference with
the shipowner, have expressed their concurrence in this mode of
dealing with the load-line question for merchant ships.* The
difficulties surrounding the question would not be removed by
this action, but they might be better dealt with than under the
present system. The conditions of buoyancy and stability
belonging to the assigned load-line of each type of ship would
require careful investigation, in order that on the one side there
may be a reasonable amount of safety with the worst conditions
of lading likely to occur, and on the other that the owner might
be permitted to load deeply enough to provide for variations in
the character of the cargo carried on diffei'eut voyages.
In ships of war the freeboard is usually governed by con-
siderations of the height at which guns should be carried to be
fought efficiently, rather than by considerations of safety from
foundering. These considerations of fighting efficiency generally
involve the adoption of a height of freeboard much in excess
of what would be considered necessary in merchant ships. Even
ill the breastwork monitors, with their upper decks some 3 or
o\ feet above water, the reserve of buoyancy, augmented as it
is by the breastwork which stands upon the upper deck, is about
equal to that which good authorities fix for the average reserve in
merchant vessels fairly laden.
Hereafter it will be shown that the height of freeboard also
exercises an important influence in preventing ships from being
easily capsized by the action of the winds and waves.
* See the Evidence and Keports of the Royal Commission on Tonnage (1881).
d2
^6 NAVAL ARCHITECTURE. chap, ir.
CHAPTER II.
THE TONNAGE OF SHIPS.
x\t a very early period the necessity must have been felt for
some mode of measuring the sizes of ships, either for purposes
of comparison, or for estimating the cost of construction, or for
determining the carrying capacity, or for computing the various
dues and duties from time immemorial levied upon shipping.
In some ancient documents statements occur of the " tonnage,"'
or "portage," of ships; but it is not possible to settle how this
tonnage was calculated. Legal enactments respecting the ton-
nage measurements of merchant sliips are of comparatively
modern date, when contrasted with the period during which some
system of tonnage measurement is known to have been in
common use. Even the origin of the term " tonnage " is not
certainly known, although it is probable that it was based upon
some rough approximation to the number of butts, or tuns, of
wine which a vessel could carry. This kind of tonnage, there-
fore, must have depended upon the internal eafacitij of ships ;
and hence there would arise the desire to arrange some method
of calculation giving a fair approximation to the carrying power
of a ship, in terms of her principal dimensions — length, breadth,
and depth ; or in terms of the length and breadth only, jf the
depth maintained nearly a constant ratio to the breadth. When
such an empirical formula had been devised and well tested, it
would work satisfactorily so long as the types of ships, their
forms, proportions, and methods of construction remained un-
changed. Changes in any or all such features would, however,
make the empirical formula unsuitable ; and, resting upon no
scientific basis, it might be evaded by means of various devices
if it became the basis for the assessment of dues or taxes. So
lono- as the conditions remained unchanged these empirical rules
CHAP. ir. THE TONNAGE OF SHIPS. 2i1
answered another useful purpose, giving the means of approxi-
mately estimating the maximum dead weight of the cargo which
a ship could carry. This " dead-weight capability " may be
assumed to have been one of the fairest measures of the earnings
oi merchant ships in the earlier periods of navigation, when
passenger traffic was of very small importance. And for ships of
similar type, proportions and construction, the ratio of internal
-capacity to dead- weight capability was fairly constant. •
The earliest English tonnage law that can be traced was
passed in 1422 : it applied exclusively to one class of vessels,
the "keels" used in carrying coals at Newcastle, and is believed,
although this is not certain, to have reckoned tonnage by the
number of tons (dead weight) carried. In 16-18 and 169-4 the
same class was made the subject of special tonnage laws ; and in
the latter year it was provided that, in measuring keels, actual
weights of known amount should be put on board, the corresponding
draughts of water being noted and permanently marked on the
stem and stern. In 1775 this system was extended to all vessels
loading coals at all ports of Great Britain.'''
Another tonnage law, limited in its action to ships engaged
in carrying spirits, was passed in 1720, for the purpose of pre-
venting smuggling in small vessels of " thirty tons burthen and
under." This law prescribed internal measurements of length
of keel, and inside midship breadth : the continued product of
that length, breadth, and half-breadth being divided by ninety-
four, in order to determine the tonnage, xilthough these internal
measurements appear to make the rule express some fraction of
the internal capacity, yet, for the reasons given above, it also,
probably, gave an approximate expression for the maximum
dead weight, or '-burthen," in tons. Mr. Moorsom was of this
opinion, after a careful analysis of ships similar to those employed
in the spirit trade.
In passing it may be interesting to state that in France the
earliest tonnage laws were intended to express approximately the
internal capacity of ships, or some fraction thereof. By the
Ordonnance de la Marine of 1681, issued by Colbert, 1 ton of ton-
nage equalled 42 cubic feet of internal space, or about 1'44 cubic
metres. This was the space supposed to be required for the
stowage of four hariques, or wine-casks. In finding the internal
* For an excellent historical review the late Mr. Moorsom's book on TJte
of the earlier English legislation, see La v:s of Tonnage. London: 1852.
38 NAVAL ARCHITECTURE. CHAP. li.
volume three cross-sections were taken in the ships, the areas of
these sections were estimated roughly, and a mean area found^
which, multiplied by the length, and divided by forty-two, gave
the tonnage. The process was rough, but it appears that here
also, the final result gave a tonnage fairly approximating to the
dead-weight capability of the ships to which the rule applied
when it was framed. Bouguer, with his usual discrimination,
pointed out the weak points of this system ; and proposed
improved methods, anticipating by his suggestions (made in
1746) most of the proposals for tonnage measurements since
made. If internal capacity was to be the basis of tonnage, he
proposed to make the measurements in a strictly scientific
manner, much as is done under the Moorsom system now in use
(see page 46) ; and, if dead-weight capability was to be used, he
proposed to determine it by estimating the displacement between
the light and load-lines (see page 61). For port dues he
proposed to take the volume of the parallelopipedou circum-
scribing the ship, since that practically measured the space she
occupied.*
Reverting to English tonnage legislation, reference must next
be made to the law of 1773, which was the first legal tonnage
measurement applied to all classes of merchant ships. This
mode of estimation, known as " Builder's Old Measurement "
(B.O.M.), was based upon the long established practice of British
shipbuilders, but previously had no legal force, and was not
applied in an exactly uniform manner by different builders.
With these minor variations in practice, the use of B.O.Mi
tonnao-e can be traced back for centuries, and doubtless answered
its purpose well during the long period preceding the present
century, when naval architecture made little progress, types of
ships and methods of construction being almost stereotyped. It
was probably intended to express the dead-iveight capability of
ships, that being the basis of tonnage universally regarded as
the fairest when the law was passed. Up to that time, also,
there is reason to believe that the intention was fairly well
fulfilled ; but subsequently it was the object of shipbuilders and
shipowners to increase, as much as possible, the ratio of the
dead-weight capability to the legal tonnage, and the empirical
character of the rule made this an easy matter. The rule may be
briefly stated as follows : —
(rt) The length was taken on a straight line along the rabbet
* For details see the Traite du Navire.
CHAP. II. THE TONNAGE OF SHIPS. 39
of the keel of the ship from the back of the main sternpost to a
perpendicular line from the fore part of the main stem, under the
bowsprit. Fig. 27 shows this ; CA is the perpendicular line, and
AB is the length required. If the ship was afloat when the
measurements for tonnage were made, the length AB could not
be taken ; and to allow for the rake of the sternpost (BE), and
the consequent shortening of the keel, as compared with the
length along the deck or water-line, a deduction was permitted
of 3 inches for every foot of draught of water from the length
measured along the water-line from the perpendicular line AC to
FIG 27.
TJpppp Vcck _ / -
the back of the sternpost. Long after raking sternposts ceased
to be used in war- ships, a deduction continued to be made for the
" rake " of a post which was upright, in order to secure a small
diminution of the tonnage. By an additional act passed in 1819
the length of the engine-room was also deducted in ascertaining
the length for tonnage of merchant steamers ; but no similar
deduction was made in steamships of war.
(h) The breadth was taken from the outside of the outside plank
in the broadest part of the ship, exclusive of any additional
thickness of planking or doubling strakes that might be wrouglit
at that part. This reduction from the extreme breadth to obtain
the " breadth for tonnage " amounted to 10 or 11 inches in large
vessels, decreasing to 3 or 4 inches in small vessels ; it expressed
the excess in thickness of the " wales," worked in the neighbour-
hood of the water-line, over the ordinary bottom planking. In
iron ships the breadth extreme and breadth for tonnage are
usually identical, except in cases where the armour shelf " over-
hangs " the hull proper. The Devastation is a case in point.
Her breadth extreme (to outside of armour) is 62:^ feet; the
armour and backing (on both sides) project some 4;^ feet beyond
the hull beneath, and the breadth for tonnage was consequently
only 58 feet. In the American monitors, with overhanging
armour, similar deductions were made from the extreme breadth
in estimating the breadth for tonnage. For example, tlie Dictator
40 X AVAL ARCHITECTURE. chap. ii.
Lad a breadth extreme of 50 feet, and a breadth for tonnage
of -11 feet 8 inches.
(c) From the length obtained as described in (a) was deducted
three-fifths of the breadth for tonnage, the remainder being
termed the " length for tonnage." Tliis was multiplied by tlie
breadth, and their product by half the breadth, and dividing by
94, the quotient expressed the tonnage.
In algebraical language, if L = the measured length along the
rabbet of keel ; B = breadth for tonnagfe.
Length for tonnage = (L — 3 B) ;
(L - jJ B) X B X f
Tonnage B.O.M. = ^^
9-1
As an example take a ship for which L = 200 feet, B = 50 feet ;
rp P n -vr (200 - ^ x 50) x 50 x A)^
lonnage B.O.jL = =^ -^ —
170 X 50 X 25
= — 04 = 22601J2 tons.
The continued product in the numerator expresses capacity;
and it is probable, as remarked above, that the divisor 94 was
chosen with reference to the carrying power of the ships in tons
of dead weight. The following explanation has been suggested
as to the choice of the divisor. In the older classes of sailing
ships the length was commonly about four times the breadth ;
consequently the " length for tonnage " was about 3"4 times the
breadth. The mean draught was about one-half the breadth ;
and the coefficient of fineness for disj)lacement (see page 4j
was about one-lialf. Hence it followed that the displacement in
cubic feet, was not very different from the product
•5 X Length x Breadth x '5 Breadth ;
Introducing the value for the length for tonnage stated above,
this expression was supposed to resolve itself finally into the
approximate equation :
Displacement (in cubic feet) - {'^^^ X Length for tonnage
^ , , Breadth
X Breadth x ^
. • . Displacement in tons = 3550^ X Length for tonnage
^ , , Breadth
X Breadth x ^ — •
The hulls of these vessels are said to have weighed about 40 per
CHAP. II. THE TONNAGE OF SHIPS. 4 1
cent, of the displacemenf, 60 per cent, representing the carrying
power. Hence,
Approximate caiTving power 1 „ ,. , ^ ,, ^ ,
/• . 1 1 • 1 ^\ r = -; X ■\'i,^, X Length for tonnage
(in tons, dead weight) j ■' 'XH) '^ o h
T^ , , , Breadth
X lireadth x
2
= -i]^ X Length for tonnage
- , Breadth
x ]>readth X -
2 ,
which agrees with the B.O.M. rule. This investigation will be
seen to proceed upon certain fixed proportions of breadth to
length and draught, as well as of weight of hull to displacement.
Departures from these proportions rendered the rule useless as a
measure of carrying power; and it was evaded when its legal
enactment supplied a motive for so doing. In order to produce
vessels of small nominal tonnage but great carrying power, raking
sternposts and other small devices were employed ; but the adop-
tion of great depth, in association with very full forms under
water, was most influential. These deep heavy-laden " box-shaped "
vessels were, of course, far inferior to vessels of good proportions
as regards speed, safety and good behaviour at sea. The numerous
disasters which resulted, and the obvious inferiority of British to
foreign merchant ships, being distinctly traceable to the bad
influence of the tonnage law, led to an agitation for its repeal.
An Admiralty Commission investigated the subject in 1821, and
reported in favour of dead-weight capability, to be ascertained by
means of an approximate rule, based on a few internal measure-
ments. This rule also would have been easily evaded, and was
not adopted. A second Commission was appointed in 1833, and
rejDorted in favour of " internal capacity as the fairest standard
of measurement, including all those parts of a vessel which, being
under cover of permanent decks, are available for stowage." Great
opposition was raised to any change in the law ; but finally, in
1836, another tonnage law was enacted Icnown as the New
Measurement, in general accordance with the recommendations
of the Commission. To this New Measurement attention will
be drawn hereafter ; but it is first necessary to trace the continued
use of the B.O.M. rule, after it ceased to have any legal force,
and it will be convenient in this connection to describe the
tonnage measurements of war-ships.
Many private shipbuilders and shipowners, having been long
accustomed to tlie use of the earlier rule, and having their data
42
NAVAL ARCHITECTURE.
CHAP. II.
recorded in tliat form, preferred to resort to it in their business
trausactious, althougli it was not the legal measure ; and even
at the present time the use of the B.O.M. rule has not entirely
disappeared in the mercantile marine. For yachts a modification
of the same rule is still extensively employed in assessing time
allowances, as is explained on page 67. In yachts and war-
ships there was not so great a temptation to sacrifice good
qualities, in order to make the nominal tonnage small as
existed in merchant ships ; and the B.O.M. rule continued
to be employed in the Eoyal Navy and in some foreign navies
until comparatively recent periods. Until 1872 the B.O.M.
tonnage was the only one given in the Navy List for Her
Majesty's ships ; and still more recently a slight modification
of that rule was employed in the United States Navy. Even
now the B.O.M. tonnage is given for ships of the Eoyal Navy
built before 1872; but is supplemented in these cases by the
displacement tonnage, and does not appear for ships of more
recent date. The study of our naval history leads to the conclu-
sion that every marked change or improvement made during the
present century, while the old tonnage rule was employed for
war-ships, has been accompanied by a protest against, or disregard
of its limitations. By general consent displacement tonnage is
now taken as the fairest measure for war-ships, and a few examples
drawn from the Navy List will serve to show more clearly the
inconsistencies and errors involved in applying the old measure-
ment to modern ships.
Ships.
Displacement.
B.O.M.
(Warrior ....
{Devastation
{Minotaur ....
(Dreadnought .
(Hoice
[BeUerophon
(Glatton ....
{Boadicea ....
9,137
9,387
10,627
10,886
6,557
7,551
4,912
4,027
6,109
4,407
6,621
5,030
4,245
4,270
2,709
2,679
Taking these vessels in pairs, the first two illustrations show
how widely different may be the tonnages B.O.M., when the
displacements are very close to one another ; while the last two
illustiations show how, with nearly identical tonnages B.O.M.,
the displacements may differ considerably.
CHAP. II. THE TONNAGE OF SHIPS. 43
Bisi)laceme7it tonnage, as explained on page 2, expresses the
total weight of a ship (in tons) when immersed to her maximum
draught or "load-line." For war-ships this measurement is
especially suited, since they are designed to carry certain
maximum weights, and to float at certain load-lines, which are
fixed with reference to the character of the service. It has long
been the official tonnage for the war-ships of France and other
European countries, and now that it has been adopted for the
Royal Navy and the United States Navy may be said to be
universally employed. It will be obvious that a simple com-
parison of displacements affords no means of judging the relative
powers of two war-ships. A displacement of given amount may
be very differently distributed in different ships. For example, one
may be an armoured coast-defence vessel of low speed, small free-
board, heavily protected and armed, but carrying small weights of
coal or equipment. Another may be a sea-going armoured frigate
with high sides, good sail-power, large coal-supply and equipment,
higher speed, with lighter armour and armament. A third may be
an unarmoured cruiser of very high speed, intended to keep the
sea for long periods and to sail as well as steam, with large coal-
supply, good equipment and light armament. In each of these
cases and others which might be mentioned the distribution of the
constant displacement into the various percentages assigned to
hull, machinery, coals, armament, armour and equipment will
necessarily vary greatly. Consequently it is desirable when
using displacement tonnage as a means of comparison for war-
ships, and in order to estimate the skill displayed by the designers,
to restrict the comparison to ships of similar types, built for
similar service.
Displacement tonnage, it may be added, has no relation to the
dues occasionally levied on war-ships, as for example in passing
through the Suez Canal. For those purposes the register tonnage
or its modification for the canal dues is employed, the necessary
measurements for British ships being made by officials of the
Board of Trade (see page 59). Reference will be made here-
after to the proposals to use displacement tonnage for merchant
ships, instead of the present system.
Another kind of tonnage measurement, appearing in statistical
statements of shi})S building for the Royal Navy, may be mentioned
here. When a new ship is designed, an estimate is made of the
total weight of hull, armour (if any) and fittings, as well as an
estimate of the cost of the labour that will be expended on her
construction. This cost, when divided by the total weight of
44 NAVAL ARCHITECTURE. chap. ii.
liiill, ko,., gives the average expenditure on labour in building-
one ton weight, and lor statistical purposes that average expen-
diture per ton is reckoned as " a ton " in the shipbuilding pro-
grammes of the navy estimates. For example, if an armoured
ship has a total weight of hull, ko,., of 6,000 tons, and the total
expenditure on labour in lier construction is estimated at £150,000,
the average expenditure per ton weight of hull will V>e £25.
Then, as the work proceeds, it is assumed that for each £25 spent
on labour, a " ton " is added to the ship. It will be seen, there-
fore, that this kind of ton is really only an equivalent for money
spent on labour ; the expenditure on materials being stated sepa-
rately. Moreover, at difierent stages of the work the weight of
material actually worked into a ship for each unit-ton of expen-
diture must vary greatly, and the money-value of the unit-ton
will difter considerably in one class of ship from its value in
another class. The form of expression is, consequently, open to
misconception, and various proposals have been made to abolish
the term " tonnage " in statements of the kind now being con-
sidered, giving expenditure on labour simply. Such a change
would be advantageous in many ways, although it would be a
departure from long-established usage. Prior to 1874-5, the
amount of tonnage annually added to the Eoyal Navy was ex-
pressed in "Builder's Old Measurement," which was even less
satisfactory than the present^ form. It may be added that, on an
average, a "ton" in the shipbuilding programmes since 1874-5,
is about equal to 91 per cent, of a ton for armoured ships in pre-
ceding programmes, and to 144 per cent, of a ton of unarmoured
ships.
Kesuming our consideration of British tonnage laws, it now
becomes necessary to refer again to the new measurement which
was in force from 1836 to 1854. This law aimed at the determina-
tion of the internal capacity of ships, resembling in this respect
the French law of 1681. The rules laid down for the purpose
need not be reproduced here ; but it may be stated that they
involved the measurement of certain lengths, breadths, and
depths in a few specified positions, and were, consequently, open
to evasion. By means of various devices, shipbuilders were able
to secure a considerable excess in the true capacity over the
nominal capacity, amounting to as much as 15 per cent, in some
cases. Mr. Moorsom summed up his review of the operation of
this law as follows : — " Although it has suppressed the premium
hitherto given to the building of short, deep ships, and although
great improvements in our commercial navy have accrued under
CHAP. ir. THE TONNAGE OF SHIPS. 45
it, yet as it offers so many facilities for evasion, and is not, from
the very nature of its constitution, to be depended on generally
in its results, it cannot be expected to possess either the confidence
or approbation of the public." A third Commission on tonnage
was appointed in 1849, and it recommended that the " entire
cubic contents of all vessels externally " should be carefully
measured, and made the basis of dock, light, harbour, and other
dues. Poops, forecastles, and other covered-in spaces were also
to be measured and included in the tonnage. The total volume
in cubic feet Avas to be divided by o5, and 27 per cent, of the
quotient was to be the register tonnage of sailing vessels. In
steamers the tonnage due to the engine-room was to be deducted ;
this was to be done because corresponding deductions had been
made in preceding laws, but the Commission expressed a doubt
as to the propriety of making any such deduction. This proposal
was not adopted, and it is mentioned here chiefly because it has
been many times repeated since it was first made.
The principal objection urged to this system of external
measurement was, that the fairest measure of the earnings of a
ship was to be found in her interna} capaciiu, as affirmed by the
Commission of 1833. As this is a matter of considerable import-
ance in connection with the enactment of the tonnage law of
1854, which is still in force, it may be desirable to quote IMr.
IMoorsom's statement : " It is alleged," he writes, " that light
merchandise (meaning thereby such merchandise as fills the hull
of the vessel without wholly loading her to the load-draught of
water) forms the predominant cargoes of commerce, and consti-
tutes for the most part the profits of the ship ; and, therefore, it
is maintained that the internal capacity, on which the stowage of
this merchandise entirely depends, must be the fair and proper
basis for assessment. Besides, the poops, spar-decks, &c., which
are appropriated entirely to passenger traffic, frequently form a
large item in the profits of the ship." Again he says : " Having
assumed, as affirmed to be the case by the generality of ship-
owners . . . that the profits of a vessel are, for the most part,
directly dependent on the quantity of space for the stowage of
cargo and accommodation of passengers— having assumed this as
an incontrovertible condition of the question — all further investi-
gation of the subject has gone to prove the superior eligibility
and desirableness of internal measurement." These views were
embodied in the system of tonnage measurement which was in-
cluded in the Merchant Shipping Act of 1854, and which is
generally termed the "Moorsom system," because that gentleman
46 NAVAL ARCHITECTURE. CHAr. ii.
had most to do with its introduction. The register tonnage of all
British merchant ships has since been measured on this system,
and the regulations of 1854 are still in force (1882j with two
modilications, introduced respectively by Acts passed in 1867
and 1876. If the principle of measurement of internal capacity,
as the most equitable basis for tonnage, be accepted, the rules
devised by Mr. Moorsom are admirably adapted for correctly esti-
mating the tonnage. They rest upon scientific principles of
mensuration, are simple in their character, and involve only a
moderate amount of labour. Their excellence is illustrated by
the fact that, although they have been in operation nearly thirty
years, during which shipbuilding has sustained remarkable
developments, and the structure, sizes, lengths, and methods of
propulsion of ships have been greatly changed from the corre-
sponding features in the ships of the period when the rules were
framed, only small modifications in some points of detail are
needed to make them equally applicable to all classes of ships of
the present day. AVithout any modification the rules give results
fairly approaching to accuracy ; but if the principle of the exist-
ing law is maintained, certain simple modifications in the rules
would enable a still further approach to accuracy to be made.
A description of the existing rules for calculating tonnage
cannot be given here. For the hold-sjjaces below the tonnage-
deck, the process closely resembles that pursued by the naval
architect in calculating the volume of displacement for a ship.
Actual half-breadth measurements are taken by the surveyors
of the Board of Trade, in the interior of the ship, if that is
accessible. The longitudinal and the vertical intervals be-
tween these measurements are varied with the length and depth
of the ship, the intention being to space them sufficiently close
to indicate fairly the true shape of the interior, and to prevent
evasions of the law by any local thickening of the inside lining
or other devices. Having obtained these measurements, the first
step in the calculation is to find the areas of a series of equi-
distant vertical transverse sections of the hold-space below the
tonnage-deck ; and, secondly, to use these areas in estimating the
volume of the hold-space. If there is a deck above the tonnage-
deck, the volume of the space between the decks is separately
estimated. All closed-in spaces above the upper-deck — such as
poops, forecastles, deck-houses, &c. — erected for purposes of accom-
modation or stowage, also have their volumes separately estimated.
The sum of all these volumes in cubic feet, divided by 100,
expresses what is usually termed the "gross tonnage" of a
CHAP. II. THE TONNAGE OF SHIPS. 47
merchaut ship. By the Act of 1876 also, if, oii any voyage, a
ship carries cargo in any space upon the upper deck which has
not been measured into the tonnage under the Act of 1854, the
tonnage of the space occupied by the deck-cargo is to be measured
^ind added to the taxable tonnage. This later regulation was
understood to be aimed at the discouragement of deck-cargoes
on seagoing ships ; and it will be seen to have the effect of giving
ships a variation in tonnage from one voyage to another, although
in all cases the principle is maintained that space occupied by
cargo sball be reckoned into the tonnage. Dues are not paid,
however, upon the gross tonnage in most cases, but on the " nett "
or "register" tonnage obtained from the gross tonnage by
makino- certain deductions, to which attention will be directed
hereafter.*
In order to provide for the measurement of the gross tonnage
in laden ships, where the holds could not be cleared, the Act of
1854 contained an approximate rule (No, 2) based upon external
measurements. This was especially useful in dealing with foreign
ships entering British ports, and runs as follows : — The length is
taken at the upper deck from the fore point of the rabbet of
the stem to the afterpoint of the rabbet of the post. The
extreme breadth of the ship is also taken, and a chain is passed
under her at this place in order to determine the girth of the
ship as high up as the upper deck. Then the approximate gross
tonnage under the upper deck is estimated by the formulae :
(1) For wood and] 17 /Girth -j-BreadthY ^ Lg^o-th
composite ships . j " 10000 V 2 /
IS /Girth-|-Breadth\^^T- ,,
(2) For iron ships . = ^^^[^ \ ) X Length.
In the Act of 1854, larger co-efficients were given, namely,
loVoo for wood ships, and i.fu^io ^i' "'^^ '^v^^ ; but enlarged ex-
perience led, many years ago, to the substitution of the co-
efficients still in use. This approximate rule for the gross under-
deck tonnage is gradually falling into disuse, for two reasons —
First, all new British ships are measured by the more exact
method ; and secondly, so many foreign nations, including all the
* For full particulars of the Tonnage Appendix attached to the Minutes of
Laws now in force, the methods of Evidence taken before the recent Royal
measurement, processes of calculation, Commission on Tonnage. Parliamen-
&c., the reader may turn to the tary Paper, C 3074 (1881).
48 NAVAL ARCHITECTURE. chap. ii.
most important mercantile marines, have now adopted the
Moorsom system for gross tonnage, that their legal tonnage^
inscribed on the certificates of foreign ships, can be accepted.
Other approximate rules have been given for estimating gross
imder-deck tonnage. Mr. Moorsom proposed the following rules-
abont twenty-five years ago : If L be the inside length on upper
deck from plank at bow to plank at stern, B the inside main
breadth from ceiling to ceiling, D the inside midship depth
from upper deck to ceiling at limber-strake. Then the gross-
tonnage under deck may be approximately expressed by the
equation :
Tonnage = LxBxDxa decimal factor -f- 100, wherein the
decimal factor has the following values : —
Decimal
factor.
Sailing ships of usual form '7
, - -. (Two-decked . . . . -05
Steam vessels and clippers | Three-decked .... '68
r Above sixty tons "5
Y^^^t^ I Small vessels -45
These factors cannot be regarded as applying so well to ships
of the present day as to those of twenty-five years ago. It may
be interesting, therefore, to give another approximate rule for
gross under-deck tonnage in the form most useful iu making
rough estimates of the tonnage in new steamships, for which
the principal dimensions are known. Let L be the length, at
the load-line, from the front of the stem to the back of the stern-
IDOst; B the extreme breadth (moulded) to the outside of the
frames ; D the depth from the top of the upper-deck amidships
to the top of the keel : then, if ordinary methods of construction
are followed, the following rules hold fairly well for iron or steel
steamships of modern types : —
Gross tonnage under deck = L x B x D X decimal factor-^ 100.
Wherein the decimal factor has the following values : —
Decimal Factor.
Passenger steamers of high speed . , '65
Passenger and cargo steamers . . . '7 to '72
Cargo steamers -72 to '75
Special structural arrangements might sensibly modify the
value of these factors ; and it will be understood that they are
useful only in rough estimates, not as substitutes for exact calcula-
tions of tonnage.
CHAP. II. THE TONNAGE OF SHIPS. 49
Passing from gross to '•' iiett tonnage," it should be stated that
the nett or '•'register" tonnage is intended to express, in tons of
100 cubic feet, the volume of the spaces actually available in a
ship for remunerative service, such as the conveyance of passengers
or the stowage of cargo. Considerable discussion has taken place,
at various times, as to the determination of the spaces to be
included in this category in different classes of ships ; in other
words, as to what deductions shall be made from the gross tonnage
in estimating; the nett register tonnage. Before referring further
to these difficulties it may be well, however, to briefly summarise
the present practice.
In sailing ships the only deductions allowed are for the spaces
solely occupied by the crew, provided they do not fall below
72 cubic feet per man, and are properly ventilated. This
arrangement was authorised by the Act of 1867, and no limit is
assigned to the crew-spaces ; but if cargo is carried in them, the
deductions cease to be made. From the facts recorded as to
actual accommodation it appears to vary from nearly 10 per cent,
in small sailing ships down to o\ per cent, in vessels approaching
2000 tons gross tonnage ; the average may be taken at from
4 to 5 per cent. In other words, the nett register tonnage of
sailing ships may be assumed to be about 96 per cent, of their
gross tonnage. The Koyal Commission of 1881 recommended
that a further deduction should be allowed for the space occupied
by the sail rooms, the maximum allowance not exceeding 2J per
cent, of the gross tonnage. No legal force has yet been given to
this recommendation.
In steamers similar deductions are allowed for crew-space, and
the average percentage of gross tonnage assigned appears to be
nearly the same as that named for sailing ships. Much more
important deductions are allowed on account of the spaces
occupied by the machinery and coals, such spaces being regarded
as lost to the cargo-carrying capacity of the vessel, and therefore
not remunerative. The fundamental principle, that nett register
tonnage (upon which the dues are estimated for any ship) shall
only include spaces used for cargo-carrying or passenger accom-
modation is thus supposed to be maintained ; but the fairness of
making any such allowances to steamers, or, if any, how great
allowances, has been the subject of much discussion. The Act of
1854 is still in force, however, although confessedly imperfect,
and under it the deductions are made in one of two ways. The
space " solely occupied by and necessary for the proper working
of the boilers and machinery " is measured (shaft-passages, funnel-
E
:o NAVAL ARCHITECTURE. chap. ii.
casing!*, ventilation trunks, &c., being included herein). If this
space has a tonnage, in screw-steamers, above 13 per cent, of the
gross tonnage and under 20 per cent., the total deduction per-
mitted, for machinery and coal-space, is 32 per cent, of the gross
tonnage. In paddle-steamers, if the measured space has a
tonnage above 20 per cent, and under 30 per cent, of the gross
tonnage, the total deduction permitted is 37 per cent. This is
the first, or " percentage," method supposed to be applicable to
all ordinary steamers. The second method is applied where the
space occupied for the machinery falls below 13 per cent, or
above 20 per cent, of the gross tonnage ; the space may then be
measured (as before), and the total deduction from the gross
tonnage is to be 50 per cent, more than the measured space in
paddle-steamers, and 75 per cent, in screw-steamers. Tliese
additions to the measured space are considered to allow fairly for
the coal-stowage required for a voyage of average length.
Very soon after the law of 1854 came into operation the grave
defects of the rules for engine-room deductions became apparent,
and an attempt was made by the Board of Trade to introduce
amended rules. It was, however, decided that these amendments
could only be made by Act of Parliament, and hitherto no such
Act has been passed, although several have been introduced.
Under the existing law it is much to the advantage of the ship-
owner to arrange the machinery-space in the majority of ocean-
going screw-steamers, so as to bring it a little above 13 per cent,
of the gross tonnage, and to secure the 32 per cent, deduction.
Take, for example, two steamers, each of 3000 tons gross, and
suppose that in one the machinery space is 12f per cent, of the
gross tonnage, while in the other it is 13 J per cent. The deduc-
tions would be as follows : —
First steamer : Tons.
Actual machinery space . . . 380
Add 75 per cent, of ditto . . . 285
Total deduction 665
Second steamer : Tous.
Actual machinery space . . . 400
Deduction allowed (32 per cent, of ") q^q
gross tonnage) j
That is to say, the shipowner, by increasing the machinery-space
20 tons, secures an increase in the deduction of 295 tons. The
CHAP. II. THE TONNAGE OF SHIPS. 5 1
loss in space available for coals and cargo is therefore onlj-
20 tons, whereas he pays clues on a nominal tonnage 295 tons
less than would be charged on the ship with the slightly smaller
engine-room. This is but one illustration out of many that
might be given of the imperfection of the present percentage
system: but shipowners are naturally averse to a change which
would deprive tliem of this source of profit. A careful analysis
of many cases has shown that the actual space available for
stowage in ocean-going steamers coming under the percentage
rule exceeds the space corresponding to the nett tonnage by from
10 to 12 per cent. This is an obvious departure from the funda-
mental principle which was intended to be embodied in the Act
of 1854; and the owners of sailing ships as well as the proprietors
of docks have not failed to complain of the anomalies resulting
therefrom. As a result of the application of the percentage
method, and allowing for crew-space, the nett register tonnage of
the great majority of sea-going screw-steamers is about 64 per
cent, of the gross tonnage.
The second rule for engine-room deductions is also open to
serious objection as applied to certain classes of steamships. For
steamers making passages of 3000 to 4000 knots between coaling
stations, 75 per cent, of the measured machinery-space is said
to be a fair average allowance for the space actually occupied by
coals. It will be obvious that if this is true now, it could not
have been true when the law was framed, marine engineering
having been so greatly developed in the direction of economy in
coal consumption (see Chapter XIII) ; and it is also evident that
further improvements may sensibly affect the space required for
coals or fuel. Passing this difficulty by, however, and accepting
the foregoing statement, it will appear that for many steamers
employed on coasting or short sea- voyages, the coal-space actually
required falls much below 50 or 75 per cent, of the machinery-
space. In channel or river passenger steamers of high speed and
in tugs the anomaly is greatest : and recent cases have illus-
trated it most forcibly. By an interpretation of the Act of 1854
which has been upheld in the law courts, cases have occurred in
which, the nett tonnage of swift passenger steamers has been
reduced to little more than 22 per cent, of their gross tonnage,
and 30 to 40 per cent, is quite a common value. Tugs of
considerable gross tonnage, by the application of the same rules,
have actually had less than no register tonnage assigned to them,
entirely escaping the payment of many dues altliough enjoying
the privileges of harbours, rivers, &c., and earning large sums by
E 2
52 NAVAL ARCHITECTURE. chap. ii.
towing. Examples sucli as these indicate that some change in
tlie law is required.
As a matter of information it may be added that it is estimated
by competent authorities that in the sea-going screw-steamers,
Avhere the measured machinery-space falls below 13 per cent, of
the gross tonnage, the nett tonnage averages about 77 per cent,
of the gross. In the swifter vessels, having machinery space
exceeding 20 per cent, of the gross tonnage, the nett tonnage
averages about 57 per cent. Individual vessels may, of course,
depart considerably from these averages.
Various proposals have been made by the Board of Trade for
the purpose of removing these anomalies : and it is but right to
add that the officers of that Department have consistently en-
deavoured to improve the law of 1854, while maintaining its
fundamental principle, in the directions indicated by experience
of its working. In 18f3G the Department issued a circular
requesting consideration of a proposal to make the deduction for
engine-rooms as follows: — To measure the machinery-space,
exclusive of bunkers, and to allow 1^ times that space in all
paddle-steamers or If times in all screw-steamers, the total
deduction in any case not to exceed 50 per cent, of the gross
tonnage, except in tugs. This method was afterwards accepted by
the Commissioners for the Danube Navigation, and is usually
termed the " Danube Eule " ; it was embodied also in a Tonnage
Bill submitted to the House of Commons in 1874, but not
passed.
Again, in 1867, the Board of Trade submitted for consideration
a proposal to measure coal-bunkers as well as machinery-space,
and to make the total space thus occupied the allowance for
engine room, &c., it being provided that such allowance should
not exceed 50 per cent, of the gross tonnage, excepting tugs.
This proposal was embodied in the ]\Ierchaut Shipping Code of
1871, which was introduced into Parliament, but not proceeded
with. It was subsequently adopted in Germany, and is now
commonly termed the German Eule. This plan is specially
applicable to ships with permanent coal-bunkers ; but many
cargo-carrying steamers are constructed with shifting coal-bunker
bulkheads ; the space assigned to the coal varying with the
quantity required to be carried for the particular voyage, and
the space sometimes included in, and at others excluded from,
the bunkers being unavailable or available for cargo stowage.
Since the nett register tonnage cannot be allowed to vary with
the coal-space, some modification of the rule would be necessary
CHAP. II.
THE TOXNAGE OF SHIPS. 53
for such cases, and the C4erman Kule only provides for the
flediiction of fixed bunkers.
The majority of the Koyal Commission of 1881 reported in
favour of a combination of the Danube and Clerman Rules,
with certain modifications, as will appear from the following
extract :—" The deduction for propelling-space in steamers
should be the actual space set apart by the owner at his dis-
cretion for the engine and boiler-room and permanent bunkers,
provided that such space be enclosed, separated from the
hold of the ship by permanent bulkheads, and that the bunkers
be so constructed that no access can be obtained thereto other-
Avise than through the ordinary coal-shoots on deck or in the
ship's side, or from the openings in the engine-room or stoke-
hold ; but that to meet the varying requirements as to fuel
of steamers engaged in long voyages, and to encourage ample
ventilation to boiler and engine-rooms in hot climates, owners
of steamers should have the option to claim as deduction for
propelling-space the actual contents of engine and boiler-space,
plus 75 per cent, thereon in the case of screw-steamers and 50
per cent, in the case of paddle-steamers, without restriction as to
extent, construction, and use of bunkers, provided always that
the deduction for propelling-space shall not exceed 33 per cent,
of the gross tonnage of any screw-steamer, and shall not exceed
50 per cent, of the gross tonnage of any paddle-steamer," It will
be remarked that the limit of deduction for screw-steamers is
made considerably lower than in the C4erman or Danube Rules,
and that clauses are introduced with the intention of preventing
cargo from being carried in the permanent bunkers. We do not
propose to criticise these recommendations, but would remark
that, although they are evidently made with reference to the
existing regulations for the Suez Canal and Danube navigation,
where an international system of tonnage is in force (see page
58), they differ in the maximum percentage of deduction allowed.
Another proposal, favoured by JMr. Moorsom from the first, was
to make the gross tonnage of all ships the legal measurement on
w^hich dues should be assessed, allowing no deductions either for
crew-space or propelling-space. This method has received the
support of many eminent authorities, and has been adopted by
the United States. The Suez Canal Company also, at first,
attempted to make the gross tonnage the basis for dues, but were
over-ruled. Certain dock-charges are now assessed in this country
on gross tonnage, but register tonnage is more commonly employed.
It is impossible here to enter into a discussion of the justice or
rt NAVAL ARCHITECTURE. chap. 1 1.
J-r
policy of makiug deductions from the gross tonnage, especially
for the macliinery and coal-space of steamers, but it is to be
observed that the system is now universally established, except
in the United States, and that the weight of evidence taken before
the recent Royal Commission appears to favour the continuance
of that system, and its practically fair operation in association
with the existing methods of charging dock and harbour dues.
These methods of charging dues might be revised, of course, if
the tonnage law^s were altered, but the change would, in many
cases, involve a considerable amount of new legislation, and is,
therefore, not desired by dock-owners.
Apart from these objections to the use of gross tonnage, there
are others of perhaps a more serious character, since they relate
to the proper mode of estimating the gross tonnage and the
determination of the spaces which should be included therein.
The meaning of the Act of 1854 was clearly expressed in relation
to types of ships then existing ; but subsequent changes in ship-
construction, and particularly in the erections above the true
upper decks of ships, have given rise to new problems in tonnage
measurement, and caused many discussions between the Board of
Trade and shipowners.* According to the Act, " any permanent
olosed-in space on the upper deck available for cargo or for stores,
or for the berthing or accommodation of passengers or crew,"
should be measured and included in the gross tonnage. Any
slielter-place for deck passengers approved by the Board of Trade
was not to be included. In practice, however, the difficulty often
occurs that the builders or owners and the Board of Trade
officials take different views of the inclusion in, or exclusion from,
the gross tonnage of particular erections ; and there have been
instances where two surveyors of the Board of Trade have treated
sister ships differently as regards such erections. Without
imputing any improper motive, it may be said that shipowners
desire to obtain the greatest carrying capacity and comfort for
passengers on the smallest register tonnage. Hence ingenious
devices and modifications of previous methods are continually
being introduced in the upper works of ships, with the result
described above. On the one side it is alleged that the tonnage
law is made to operate against provisions for additional comfort
or safety ; on the other it is asserted that these provisions result
in larger earnings, and therefore should add to the tonnage. The
* For particulars of many of tliese of Evidence taken before the Eoyal
cases see the Appendix to the Minutes Commission of 1881.
CHAP. II. THE TONNAGE OF SHIPS. 55
majority of the Eoyal Commissiou of 1881 proposed to amend
the regulations of 1854 as follows: — "Gross tonnage should be
made to include all permanently covered and closed-iu spaces
above the uppermost deck; and erections, with openings either
on deck or coverings or partitions that can readily be closed in,
should also be included in the gross tonnage ; but the skylights
of saloons, booby hatches for the crew, light and air-spaces for
the boiler and engine-rooms when situated above the uppermost
deck, as well as erections for the purposes of shelter, such as
turtle-backs open at one end, and light decks supported on
pillars and uniuclosed, should not be measured for the purpose of
their contents forming part either of the gross or register
tonnage." These suggestions were evidently made in view of
the delinitions laid down by the International Commission on
Tonnage, which assembled at Constantinople in 1873 to discuss
the Suez Canal Kules, viz. :— " By permanently covered and
closed-in spaces on the upper deck are to be understood all those
which are separated off by decks, or coverings, or fixed partitions,
and therefore represent an increase of capacity, which might be
used for stowage of merchandise or for the berthing and accom-
modation of the passengers or the crew." It was also provided
in the iSuez Canal Eules that " spaces under awning-decks with-
out other connection with the body of the skip than the props
necessary for supporting them, and which are permanently
exposed to the weather and the sea will not be comprised in the
gross tonnage, although they may serve to shelter the ship's crew,
the deck passengers, and even merchandise known as deck-loads."
This last stipulation is not adopted l)y the majority of the Royal
Commission, who recommend that deck-loads should be dealt
witli in accordance with the Act of 1876 (see page 47).
Another class of objections to the present system of dealing
with light superstructures is represented by the cases of *' awn-
ing-decked" ships, in which a light covering-deck is built all
fore-and-aft, and carried by light bulwarks extending down to
tbe true upper deck. In such vessels it is customary to fix a
maximum load-line, and not to load them so deeply in relation
to their total depth as would be done if the full scantlings were
carried to the uppermost deck. It is asserted that this arrange-
ment is chiefly favoured because it prevents the lodgment of
water on the decks, gives a greater freeboard and increased
stability, thus adding to the safety as well as the comfort of ships.
Further, it is stated that the internal spaces between the awning
and upper decks in suck ships cannot be fully utilised even when
56 NAVAL ARCHITECTURE. chai-. ii.
the lio;htest camoes are carried. Oq these "rounds it is main-
tained. that the total internal space is not a measure of the
earnings in such ships, but unfairly raises their tonnage upon
\vhich dues are paid, as compared with the tonnage of ships in
which the erections above the upper deck are discontinuous —
such as poops, bridge -houses, forecastles, ka. On the other side
it is argued that increased comfort and safety ought to result in
larger earniugs, and that if the spaces are permanently enclosed
there can be no effectual guarantee that cargo or passengers will
not be carried above the upper deck. The Board of Trade, there-
fore, have resisted the endeavour to obtain some reduction of the
tonnage of the spaces between upper and awning-decks, and. the
majority of tl;o Eoyal Commission of 1881 support this action.
One more illustration must be given of the difliculties arising-
ill the application of the present tonnage laws to modern ships-
Water-ballast is now- very largely used in merchant sliips, and
there are various methods of carrying it. One of the plans most
approved at present is that illustrated by Fig. 104a Chapter IX.
In vessels built on this cellular system the double bottom is
nsually deeper than ordinary floors would be ; and the Board of
Trade surveyors, in measuring the tonnage of the Chill:a, built
by Messrs. Denny, at first followed the practice established for
ships previously built, in which the ballast-tanks were constructed
above ordinary floors. That is to say, the surveyors assumed a
depth of floor such as would have been used if the ship had been
built on the ordinary system, and estimated the under-deck
tonnage to this imaginary boundary. This method of procedure
was resisted by the builders, and eventually the Board of Trade
yielded, the surveyors having since measured all ships constructed
on the cellular system to the inside of the ceiling, excluding the
ballast-tanks from the tonnage. The diflerence in measurement
by the tw-o methods varies in some cases from 1^ to 2 per cent, of
the gross under-deck tonnage as finally measured ; a more con-
siderable difference has been produced by modifying the form of
the cross-sections, the inner bottom being built with a slight rise
towards the bilge, instead of being made level for a considerable
breadth athwartships. But while in most of the cellular-
bottomed ships the difference in tonnage may have been com-
paratively trifling, the principle involved is an important one.
The majority of the lioyal Commission of 1881 support the
original action of the Board of Trade in this respect, giving
various reasons why the cellular double-bottoms should not be
wholly excluded. These reasons need not be reproduced, but it
CHAP. II. THE TONNAGE OF SHIPS. 57
may be observed respecting the conclusion based upon them that
it seems a departure from the fundamental principle on which
the Act of 1854 was based, since cargo cannot be carried in
cellular double bottoms, except in very special cases— such as
those where oil is carried in the ballast-tanks— which might
be dealt with in a manner similar to that in which deck cargoes
are treated under the Act of 187G. Moreover, the use of an
imaii-inary floor-line for the inner boundary is objectionable,
in so far as it involves a virtual interference with structural
arrangements, tantamount to treating as a standard a particular
method of construction, wliich is certainly susceptible of improve-
ment, although at present it may be most commonly employed.
Summing up these remarks on the laws at present in force for
measuring the tonnage of British ships, it may be stated that
the rules laid down by Moorsom for calculating internal capacity
have answered their purpose well. They need amendment in
some matters of detail, in order that greater accuracy may be
secured in dealing with modern ships. It is questionable whether
these amendments need be made a matter for legislation, seeing
that, since the date when the rules were framed by Moorsom,
there has been a great advance in scientific knowledge on the
part of persons engaged in shipbuilding. Consequently, if the
principle is maintained of making internal capacity the basis of
tonnage, the mode of estimating that capacity need not be
rigidly prescribed. Moorsom's system would be maintained,
with variations in the mode of application to suit particular
cases. Correct mensuration of the various spaces having been
secured, the difliculties to be encountered include those enume-
rated above as to water-ballast, superstructures, awning-decks,
iVc, as well as those relating to deductions for crew-space and
propelling-space. The relative importance of those difftculties
will be differently appraised by different persons, and will vary
in different types of ships. But they represent conditions which
will continue to exist in connection with the basis of measure-
ment, although the form in which they appear may change with
developments in ship-construction. It appears on a review of
the last thirty years, that the operation of the Moorsom system
has been favourable, on the whole, to the progress of merchant
shipping ; and there can be no question but that it is immensely
superior to any preceding tonnage law. At the same time the
difficulties and anomalies incidental to its operation justify the
inquiry whether, having regard to the existing conditions of
trade and shipping, some better system cannot now be devised.
So NAVAL ARCHITECTURE. chap. ii.
To some of the suggestions made for alteration we shall refer
hereafter. Before doing so, however, we propose to glance briefly
at the use wliicli has been made of the Moorsom system for inter-
national purposes and in foreign mercantile marines.*
TJie first employment of the 31oorsom system for international
purposes was in connection with the Danube navigation. At first
the Euglisli law of 1854 was adopted, but subsequently modified
as to deductions for propelling and coal-space in the manner
described on page 52. The International Commission, which
met at Constantinople in 1873, also recommended the Moorsom
system for use on the Suez Canal, with certain modifications in
the deductions allowed for propelling-space, crew-space, &c. ;
'and certain stipulations as to enclosed spaces which have been
quoted on page 55. As the matter is iniportaut, the following
summary of the Suez Canal rules for tonnao-e is civen : —
The spaces measured for the gross tonnage in all ships are :
Space under the tonnage deck ; space or spaces between tonnage
deck and uppermost deck ; all covered or closed-in spaces, such
as poop, forecastle, officers' cabiu.s, galleys, cook-houses, deck-
houses, wheel-houses, and other inclosed or covered-in spaces
employed for working the ship. The deductions permitted in
all ships are : Berthing accommodation for the crew in fore-
castle and elsewhere — not including spaces for stewards and
passengers' servants; berthing accommodation for the officers,
except the captain ; galleys, cook-houses, itc, used exclusively
for the crew ; covered and closed-in spaces above the uppermost
deck employed for working the ship. In none of these spaces
]nust cargo be carried or passengers berthed, and the total deduc-
tion under all these heads must not exceed 5 per cent, of the
gross tonnage. In steamers with jix,ed coal-bunkers the German
Kule (see page 52) may be followed, or the owners may choose
to have their vessels measured by the Danube Kule. Vessels with
iiliiftiiKj bunkers would be measured by the Danube Eule. In no
case, except in tugs, must the deduction for the propelling power
exceed 50 per cent, of the gross tonnage ; so that the minimum
tonnage upon which a vessel can pay dues in passing through
the_ canal is 45 per cent, of her gross tonnage. The actual
* For much infovmatiou on this excellent summary of rules now in
subject we are indebted to the able force was also submitted by Mr. Gray,
Memoir prepared by ]MM. Kiaer and of the Board of Trade, to the Uoyal
Salvessen for the International Statis- <;(>mmissiou of 1881.
tical Congress (C'hristiania, 1876). An
CHAP. II. THE TON X AGE OF SHIPS. 59
average deduction from the gross tonnage of merchant steamers
iising^the canal is estimated at about 30 per cent. Owing to the
different methods of making the deductions, a British ship has
to pay Suez Canal dues upon a tonnage exceeding by about 10
to 12 per cent, that on which she is assessed in home ports. War-
ships, as well as merchantmen, use the canal, and have to pay
dues. For this purpose all the ships of the Koyal Navy are
measured by surveyors of the Board of Trade, and furnished with
special tonnage certificates. In them the deductions from the
gross tonnage vary from 30 to 50 per cent., according to the class
of ship. In 1876 the Danube Commission officially adopted the
Suez Canal Pailos, so that tlie same certificates are now available
for both navigations.
The jMoorsom system has now been adopted by all im-
portant maritime countries, although the modes of applying
it are not identical. In this list appear the United States,
Denmark, Austria, Cermany, France, Italy, Spain, Sweden,
the Netherlands, Norway, Greece, Finland, Ptussia, Japan
and Belgium. As regards gross tonnage there is practical
aojreement, the onlv difference being that a few countries in-
elude spaces (such as wheel-houses, &c.) necessary for the
working of the ships, as is done in the Suez Canal Rules,
while the majority do not. For sailing ships, also, the register
or nett tonnages closely agree, except for American ships, where
there is no deduction for crew-space. For steamers, however, the
deductions for machinery-space and coals are not made in the
same manner by different countries. In the United States, as
has already been stated, there is no deduction. The so-called
•'German Paile " has been adopted by Germany, Austria,
Italy, Norway, Bussia and Belgium; while the " Danube Rule"
is used by Denmark, Spain, Holland and Greece. The English
law is used by Sweden ; and in a slightly modified form by
France and Finland. M. Kiaer, who has given great attention
to the various systems of measurement, makes the following
statement as the result of a very extensive analysis.* If the
register ton in a steamer, according to the (lerman Rule, be called
100, an English register ton would be called 112, and an American
register ton 74. He is of opinion that for statistical purposes the
register tonnage of recent English, French, Danish, Swedish,
Finnish and .lapanese steamships may be considered to have
* See tlie Memoir mentioned on page 58, and also that on Lt8 Marines
Marchandes. Christiania: 1881.
6o NAVAL ARCHITECTURE. chap. il.
identical units : while a similar remark applies to another group
including- German, Norwegian, Austrian, Italian, Spanish, Ivussian,
Dutch and Belgian ships. These estimates may not be exact,
but they cannot fail to be of value in dealing with comparative
statistics of shipping.
Tiie principle of the tonnage law of 1854 having been sa
generally adopted by other maritime countries, by the Suez^
Canal Company and the Danubian Commission, and the remain-
ing diflerences being on points of detail, or possibly in the
conduct of some of the operations of measurement, it will be
evident that a close approach has been made to an international
tonnage. This, as the majority of the Eoyal Commission report,
is a weighty argument against any change in the principle on
Avhich the law of 1854 is based. The advanta2:es of an international
system of tonnage are obvious, and the approximation already
made is a great convenience. But, while this is true, it cannot
be admitted that there are insuperable difficulties in the way of
a change of system in consequence of the general adoption of the
existing English system. If an improved system of measurement
could be devised free from anomalies and difficulties such as are
associated with the Moorsom system, foreign nations would
doubtless avail themselves of it. Already very grave objections
have been raised by French writers of repute to the adoption of
the English laws ; and their abandonment has been suggested in
favour of other modes of measurement.
The inconveniences attaching^ to a chanoe of svstem are suf-
ficiently serious to make it necessary for the advocates of new
methods to advance strong arguments, and to defeat hostile
criticism of their schemes, before they can hope for success. It
is not enough to be able to show that the existing laws involve
difficulties, anomalies and inequalities, but the alternative pro-
posals must be shown to be free from similar faults. So far as
can be judged from a perusal of the evidence given before the
Koyal Commission of 1881, although certain amendments are
desired in the Act of 1854, particularly as regards the estimates
for the register tonnage of steamers, there is no general feeling in
favour of an entire change in the basis of measurement. Somo
authorities whose opinions are entitled to the most carei'ui con-
sideration were in favour of such a change, and we will briefly
summarise the principal alternative proposals.
The first is a proposal to return to a clead-iveigM basis of
measarement, the earliest mode of assessment (see page 37).
Mr. Waymouth, secretary to Lloyd's Registry, and a member of
CHAP. II. THE TONNAGE OF SHIPS. 6 1
the Eoyal Commissiou, advocates this system in a separate report
and his views were endorsed by several professional witnesses.
Mr. AVaymouth maintains that as the great majority of ships are
engaged in carrying cargo and not passengers, the tonnage laws
should be especially suitable to them. Freights, as a rule, are
now based upon the dead-weight capability of ships ; and when
light measurement goods are carried, the rates are raised propor-
tionately. In other words, it is asserted that the fundamental
principle laid down by Mr. Moorsoni (see page 45) no longer
holds good ; that internal ccqxieity in the present conditions of
the shipping trade is not the fair measure of the possible earnings
of ships under most circumstances, whereas dead-tveight capahUitif
is. This view of the matter is disputed, but the question cannot
be discussed here. It may be observed, however, that the special
mechanical appliances for packing in small compass many de-
scriptions of light goods, have produced remarkable reductions
in the space required for their stowage since the date when
Mr. Moorsom w-rote ; while the change from wood to iron and
steel, and the moditications introduced in modern types, have
tended to increase the internal capacity available for stowage.
Starting from this assumption, Mr. Waymoutli proposes to
ascertain the light-Une to which a ship would be immersed when
equipped for sea, but without cargo on board. For sailing-
vessels, no consumable stores are to be on board ; for steamers,
the engines are to be complete, and the water in the boilers, but
no coals are to be on board when the light-line is ascertained. A
maximum load-line is to be fixed by some central authority for
each ship. The dead-weight capabilit}" would then be easily and
accurately estimated, being the number of tons of sea water dis-
placed by the ship between her light and load - lines. For
passenger ships it is proposed to place the load-lines exactly as
if they were cargo ships, and at the maximum height above the
keel compatible with safety ; although it is admitted that these
vessels would never in their regular service load so deeply. The
reason given is '•' that no shipowner will carry light freight, pas-
sengers or cattle unless he earns at least as much as if he were
carrying a dead-weight cargo."
A '• register ton " according to this system would be 20 cwts.
avoirdupois, and it may be interesting to inquire how it would
be related to the register ton under the existing system. There
is, of course, no constant ratio between the two, the relative
accommodation assigned to cargo or passengers in different
classes of ships, the variations in the relative weights of ma-
62 NAVAL ARCHITECTURE. chap. ii.
chinery in various types of steamers, and other circumstances
affecting the ratio. In 1860 Mr. Moorsom gave the following
nile : — " To ascertain approximately the dead-weight cargo which
a ship can safely carry on an average length of voyage, deduct
the tonnage of the spaces appropriated to passenger accommoda-
tion from the nett register tonnage, and multiply the remainder
by the factor 1^." At present in iron sailing ships the correspond-
ing ratio usually lies between 1:^ and 1?,; in cargo steamers, \\
is a fair average, but 2 to 1\ is said to occur. For passenger
steamers the ratio of dead weight to nett tonnage varies greatly
with differences in the speed as well as in the proportionate im-
portance of cargo and passengers; and in some of the swiftest
seagoing vessels is less than unity.
Hence it will appear tliat difficulties would arise in changing
from the present basis to a dead-weight basis, if it were desired
for statistical purposes to leave unchanged the nominal aggregate
tonnaf^e of the British mercantile marine. This has been con-
sidered a matter of some importance in all revisions of the ton-
nage laws so far made ; and Mr. Moorsom chose the divisor 100
in the law of 1854, not merely because of its convenience, but
because it closely fulfilled the condition of keeping the aggregate
tonnage nearly the same as under preceding rules. Mr. Way-
mouth does not have regard to this consideration : his system
would make the aggregate tonnage considerably greater than at
present. It would be possible, no doubt, to keep the aggregate
register tonnage of the mercantile marine unchanged, if the labour
of determining the total dead-weight tonnage were incurred, and
a divisor found expressing the ratio of that total to the present
total register tonnage. But it would still remain true, for the
reasons given above, that the nominal tonnage of different classes
of ships would be very differently affected by the use of this
divisor in all cases, because the ratio of the dead-weight capa-
bility to the present register tonnage varies so greatly.
Tiie chief difficulties in connection with dead-weight measure-
ment are those relating to the fixing of a maximum load-line in
cargo vessels, and the assumptions which have to be made in ex-
tending the system to passenger steamers or vessels permanently
engaged in trades where light cargoes are the rule. The load-line
question has been discussed at page 34 ; but it is necessary to recall
attention to the proposals made by Mr. Wayraouth for equitably
assessing passenger steamers and vessels carrying light cargoes,
because these are the novel features in his scheme. Mr. Way-
mouth suggests, as has been stated above, giving to these vessels
CHAP II. THE TONNAGE OF SHIPS. (i\
3
a load-line deeper than they would ever be sailed at, expressly
for tiie sake of tonnage measurement ; and it must be admitted
that the suggestion is open to question, because it does not suf-
ficiently recognise the fact that for special services special types
of ships are built, some of which cannot be treated as cargo
carriers pure and simple, even in fixing a load-line. The majority
of the Commission dissent from this recommendation, and ob-
ject to the association of tonnage legislation with a decision of
the many vexed questions involved in fixing the load-line of any
class of ship. The latter objection does not seem well grounded,
since it is well known that in all recent inquiries into the loading
and seaworthiness of ships, the inUuence of the tonnage laws
upon the loading has been discussed ; while, on the other hand,
in the course of investigations into the working of the tonnage
laws, evidence has been freely given as to the load-line and free-
board of ships. Moreover, if it were clearly shown that a dead-
weight basis could be fairly ajDplied to all classes, the fixing of a
load-line either by the owner or by some central authority would
be an essential condition to the practical operation of the scheme ;
and, being so regarded, it would be done.
No one can fail to remark how the adoption of dead-weight
measurement would tend to remove most of the difficulties
inherent in measurement by internal capacity. Disputes would
no longer arise as to deductions for propelling-space, or water-
ballast tanks, or light erections above the upper deck. In all
these respects the builders and owners of ships would be left
perfectly free. On the other hand, with a dead-weight basis,
differences of opinion must be anticipated in fixing the load-line
of ships; and, as yet, no thoroughly satisfactory solution appears-
to have been found of the difficulty experienced in applying
that basis to classes of ships which are worked under entirely
different conditions.
It may be interesting to add that in the instances where a
dead-weight basis has actually been used — excluding coal-laden
English vessels (see page 37), the difiiculties involved in fixing
the load-line have been considerable. The tonnage law of Spain,
from 18.31 to 184-i was of this character ; but it was then changed
because of disputes as to the proper load-line. In Finland, until
1877, dead-weight tonnage was used, a certain ratio of freeboard
to depth in hold being fixed in estimating the load-line. Here,
also, the law has been altered, internal capacity having been
substituted for dead weight.
Another method of estimating tonnage by dead weight has
64 NAVAL ARCHITECTURE. chaj-. ii.
l>een proposed at difterent times, but never adojDted. The
tonnage on which dues were to be paid was to be governed by the
number of tons of cargo carried on each voyage; and to assist
in ascertaining the dead weight on board, an officially guaranteed
" curve of displacement " was to be carried by each vessel (see
paue 6). It will be seen, therefore, that the tonnage of a ship
would be a variable quantity. ^loreover, the attempt to assess
earnings by the dead weight cariied could not possibly succeed,
since it leaves almost untaxed the extremely valuable earnings
obtained from the carriage of passengers, and treats too favour-
ably the cases where light cargoes are carried. As regards
statistical uses this form of dead-weight tonnage would be more
objectionable than that described above.
The second proposal for a change in the tonnage law ' is
embodied in a separate report by Mr. Kothery (Wreck Com-
missioner} who was also a member of the Royal Commission of
1881. It may be shortly described as a proposal to make
" displacement tonnage " (see page 43) the basis of all dues.
This also is a revival of a proposal made years ago, and, like
dead-weight measurement, it requires the fixing of a load-line
for each ship, either by tlie shipowner or by some central
authority. We need not repeat what has been said respecting
the difticulties attending the fixing of a load-line ; but it should
be stated that Mr. Eothery contemplates the possibility of
leaving this to the discretion of the owner. It is further
suggested in liis report that, for tlie purpose of bringing tlie
register tonnage obtained on the new basis into approximate
agreement with the present register tonnage, the actual dis-
placement (in tons avoirdupois) should be divided by some
factor. Here, however, difficulties must arise, corresponding to
those mentioned in connection with the attempt to deal similarly
with dead-weight measurement and the present register tonnage.
The factor to be used would have very different values in differ-
ent classes of ships, with different structural arrangements, and
different reserves of buoyancy. Even in comparisons between
the gross tonnages and the displacements of ships considerable
variations occur, due to the wide divergencies in reserves of
buoyancy and methods of construction. In ocean-going steamers
the gross tonnage may vary from tv;o-thircls to one-half of the
displacement (in tons) ; in sailing ships between one-half and
five-elevenths of the displacement. When we pass from gross to
nett tonnage on the present system, these ratios of tonnage to
<lisp]acement are very little altered in sailing ships, but very con-
CHAP. II. THE TONNAGE OF SHIPS. 6^
siderably and unequally affected in different classes of steamers,
owing to the nature of the deductions for propelling-space. For
statistical purposes, therefore, the change to a displacement
basis would involve some difficulty in estimating the growth or
movements of shipping. This difficulty need not be a bar,
however, to a further consideration of the merits or defects of
the system.
Mr. Kothery advocates a displacement basis for tonnage, on
the grounds that, if the load-line is fixed, the tonnage can be
accurately estimated, without difficulties arising as to structural
arrangements, propelling-space, erections on deck, &c. ; and that
this tonnage is the fairest for assessing dock and harbour dues,
because it corresponds to the water-space actually occupied.
Eecognising the fact that in both the Moorsom system and in
dead-weight measurement, an endeavour is made to roughly
assess the earnings of ships, Mr. Eothery contends that the true
basis for canal, river, dock and harbour dues is to be found, not
in the earnings of ships, but in the service rendered to them.*
This service is supposed to be represented by the space occujned
by a ship, represented by her displacement, and by the time
during which it is occupied. Light dues are treated as of minor
importance when compared with dock and harbour dues.
Turning to the objections to this proposal, independently of
those connected with fixing the load-line, it must first be noticed
that the displacement is not a fair measure of the space required
by a ship. That space is more fairly measured by the parallolo-
pipedon of which the length equals the length of the ship
"over all," the breadth is her extreme breadth, and the depth
her mean draught, unless she trims excessively by the stern.
For it is evident that if these three leading dimensions are the
same, the possibility of berthing other ships in a dock or harbour
is not altered by variations in tlie " coefficient of fineness " for
displacement (see page 8). And we have seen that the co-
efficients of fineness may vary from 70 down to 40 in ships
of different classes, but with the same extreme dimensions.
Next, it is said that a displacement basis would furnish strong
inducements to the construction of excessively light hulls and
* Thereaderinterestedinthissubject Tonnage Bill of 1874, where this dis-
may turn with advantage to the tinction between the two systems of
evidence given by Mr. Farrer, Secre- taxation- is admirably stated and
tary to the Board of Trade, before the illustrated.
House of Commons Committee on the
66 NA VAL ARCHITECTURE. chap. ii.
engines, in order that on a given displacement the greatest
dead-weight carrying power might be secured. There is force
in this argument, but it aj^plies with practically equal force to
ships built to carry dead-weight cargoes under tlie present
tonnage law. And the tendency to undue lightness of con-
struction must always be kept in check by careful surveys, such
as are made on nearly all merchant ships by officers of the great
registration societies.
A third proposal put before the Royal Commission was to base
dock-dues, &c., upon either the area of the rec-tangle having the
length over all and breadth extreme of a ship, or upon the
volume obtained by multiplying that area by the mean draught.
This class of proposal will be seen to approximate to that made
by Bouguer in 1746 (see page 38). It is not favoured by the
majority of the Commission, chiefly because of the adverse
opinions of dock authorities. It has also been stated that such a
system might bring back box-shaped unseaworthy vessels,
resembling those built under the B.O.M. rule. Ou the other
hand it must be admitted that the circumscribing parallelo-
pipedon is the fairest measure of the space occupied ; and if the
dues of docks, harbours and canals were adjusted to include both
this space and the time it was occupied, the arrangement would
be fair on both sides. There may be objections to the adjustment
of dock and other dues, but the difficulties of the operation
cannot be so great as to prevent it from being undertaken if there
were a general feeling that a radical change was needed in the
tonnage svstem. Furthermore, it must be remarked that the
parallelopipedon system may be applied either to the actual mean
draught of a ship when she enters a dock, in which case the
tonnage for dues would be variable ; or to a maximum load-line,
fixed by the owner as at present, or fixed by some central
authority. Should the latter action be taken, as it may be, then
the fear as to the reproduction of box-shaped vessels is clearly
groundless, for the central authority would not fail to have
regard to the form in fixing the load-line. Apart from this
action, there is no good reason for believing that shipowners
would sacrifice speed, economy under steam, and good behaviour
at sea simply for the purpose of increasing the ratio of the dead
weight carried to the nominal tonnage and lessening the dock-dues.
On all these grounds it seems desirable that if any radical
change should be made in the tonnage laws, the parallelopipedon
system should receive further consideration. Its adoption would
introduce difficulties in connection with statistical statements of
CHAP. II. THE TONNAGE OF SHIPS. 67
tlie growth and movements of sbippiug, resembling those
described above for a dead-weight or displacement basis ; but in
neither case do these difficulties appear insuperable.
A few words will suffice respecting another kind of tonnage
measurement commonly employed in the mercantile marine.
Freight tonnage is simply a measure of cubical capacity.
Merchants and shipowners make considerable use of this measure-
ment, although it has no legal authority; it is also used in the
Admiralty service in connection with store-shi[)s and yard-craft.
A freight-ton, or " unit of measurement cargo," simply means 40
cubic feet of space available for cargo, and is therefore two-fifths
of a register ton. Mr. IMoorsom says that for an average length
of voyage the nett register tonnage, less the tonnage of the
passenger space, when multiplied by the factor 1^, will give a
fair approximation to the freight-tons for cargo stowage. This
rule has the same basis as that for dead-weight cargo given above.
In some cases the internal capacity of a ship available for freight
is expressed in tons of 50 cubic feet, this unit having especial
reference to import goods, and the preceding one to goods
exported. The freight-ton is, of course, a purely arbitrary
measure, but has a definite meaning, and is of service in the
stowage of ships.
The tonnage of yachts is measured by special rules, chiefly
for the purposes of regulating time-allowances in racing; and
so many persons are interested in the subject that it appears
desirable to devote some attention to it here. The Thames rule,
which has hitherto been most generally adopted in this country,
is as follows : —
(a) The length is measured on the deck from the fore part of
the stem to the after part of the sternpost (CD in Fig. 27,
page 39) ; let this be called L.
(h) The breadth is measured to the outside of the outside
plank at the broadest part wherever found ; let this be called B.
(c) From the length the breadth extreme is deducted, the
remainder being the "length for tonnage." This length for
tonnage is multiplied by the breadth, and their product by half
the breadth ; the result divided by 94 gives the tonnage. In
algebraical language,
B
(L - B) X B X 2"
Tonnage (Thames measurement) - — qt '
F 2
68 NA VAL ARCHITECTURE. chap, ii.
As an exami)le, take the case of a yacht for which the length
(L) is 1U2 feet; breadth extreme (B) 21 feet.
21
(102 - 21) X 21 X -2"
Tonnage (Thames measurement) = q^^
81 X 21 X 21
94 X 2
190 tons.
These modifications of the B.O.M. rule are not of any great
importance, except that the measurement of the length along the
deck, instead of along the keel, does away with any motive to
rake the sternpost excessively in order to decrease the nominal
tonnage. In other respects the objections urged above to the
B.O.M. rule apply here; bat there is one important exception.
Yachts are measured mainly for time-allowance in racing, and the
owner has not the same inducements to malform the vessel in
order to give her increased carrying power which the owner of
the cargo-carrying vessel had. The yachtsman seeks to secure
speed, and for that purpose favours good proportions and con-
siderable stability.
Prior to the present year (1882) the Yacht Racing Association
used a slight modification of the Thames rule. The length was
measured from out to out on the load-line, it being provided that
"if any part of the stern or sternpost or other part of the vessel
below the load water-line project beyond the length taken as
mentioned, such projection or projections shall, for the ^^urposes
of finding the tonnage, be added to the length taken as stated."
These rules put a severe penalty on beam as compared with
length ; and, since they took no account of depth, designers were
not slow to avail themselves of the possibility afforded them to
use large weights of ballast placed low down for the purpose of
securing large sail-carrying power on vessels of great length,
small beam and small nominal tonnage. It is admitted that this
deep, narrow type of vessel is practically uncapsizable and very
well-behaved at sea (see Chapter III.). It is also claimed for the
Thames Rule, and its modification, that it brought the type of
yacht built specially to sail under it into fair competition with
other types of yachts, such as the American, built to sail under
other tonnage rules. Furthermore it appears that the Thames
Rule approximately expressed the sail-carrying power of yachts
(see Chapter XII.). But notwithstanding all these considera-
tions, and the dislike of many yachtsmen to a change of rule, the
Yacht Racing Association have introduced a new system of
CHAP. II. THE TONNAGE OF SHIPS. 69
measurement, designed especially to check the tendency to
greater and ori-eater length, narrower beam and more ballast in
yachts of different classes.
The Yacht Kaciug Association rule of 1882 measures the
length and breadth as before, and expresses the tonnage by the
equation :
m (Leno-th + Breadth)^ X Breadth,
Tonnage = ^-^ ^^
A fraction counts as a ton. The divisor has been so chosen as
to keep the tonnage of existing yachts very nearly the same as
under the previous rule. It will be observed that no actual
measurement of depth appears in the amended rule, which is in
this respect no improvement upon its predecessors. Notwith-
standing its purely empirical character it may answer its intended
purpose fairly well, as it was devised by some of the most
eminent authorities on yacht sailing.
Besides these rules for yacht-tonnage there are many others
which have been proposed or employed to a limited extent.
None of these are free from objection, but a few of the principal
alternative rules may be described. In 1874 the Corinthian and
New Thames Yacht Clubs adopted the following rule for a short
time, but eventually abandoned it, in consequence of the
objectif>ns raised by yachtsmen:
rn Length X Breadth X Depth.
Tonnage = — ^00
In this rule the length and breadth for tonnage were measured as
in Thames measurement, the depth being the total depth up to
the top of the covering board. One obvious objection to the use
of the total depth is that owners desiring to decrease the nominal
tonnage would be tempted to decrease the height out of water to
an objectionable, although not to a dangerous, extent.
Displacement tonnage has been advocated for British yachts,
and was formerly in use for American yachts. It is urged in
favour of this mode of measurement that it would bring yachts
into the same category as other classes of ships, for which
economical propulsion is measured by the power required to drive
a given weight at a given speed. Also that the designer would
then have absolute freedom in choosing forms and proportions.
On the other hand it is argued that displacement tonnage favours
the construction of mere "racing machines," vessels broad in
relation to length, with shallow hulls, deep keels and small range
/O NAVAL ARCHITECTURE. chap. ti.
of stability, altlioiigli exceedingly stiff (see Chapter IIL). These
objections are emphasised by reference to the yachts actually built
in America to sail under displacement rules, which had very small
displacement in proportion to their extreme dimensions, great
" stiffness," large sail-areas, and high speed in smooth water, but
which proved inferior to the English type of yachts when sailing in
strong winds and heavy seas. This displacement rule has now
been abandoned in America, and there is no probability of its adop-
tion in this country. Minor objections to its use have been raised
on the grounds that variations in the amount of ballast carried at
different times would necessitate variations in time-allowance ;
also that many owners would object to having their yachts
measured accurately, fearing that their forms might be reproduced
or improved upon. Little weight attaches to these objections,
however, as compared with those stated above.
Another proposal which has found much favour, and has even
been temporarily adopted, is to base time-allowances upon the
sail-areas of yachts. One of the strongest advocates of this
method uses the following arguments : — " If, with smaller sails,
we outsail our rival, who can say that an improvement in the
form of the vessel is not the cause ? we have given the owner a
yacht of equal size and greater velocity." Further, it is asserted
as an observed fact that, when two well-designed yachts of dis-
similar forms are sufficiently near to equality of size to permit of
competitive sailing, their speeds will be about equal under most
conditions, if the sail-spreads are of equal area. A very common
practice has been to proportion the total sail-spread of yachts to
the area of the load water-plane, or to the product of the extiemo
length and breadth of that plane. The New York Yacht Club,
therefore, formerly based time-allowances upon the product of
these two extreme dimensions, instead of upon sail-area, which
vould have involved greater difficulties in measurement. It
will be observed, however, that the reasoning upon which the
proposal is based takes account of size or displacement as well as
sail-areas ; and that some definite regulation would be needed as
to the "classes" in which yachts should be ranged for com-
petitive sailing. Hence would arise considerable difficulty in
practically applying the proposal.
Some eminent authorities in yacht-construction have favoured
the determination of time-allowances on the basis of the " sail-
carrying powers." It is clearly of the greatest importance to the
speed of yachts that they should be capable of " standing-up "
under their canvas ; but before any rule of this kind could
CHAP. II. THE TONNAGE OF SHIPS. 7 1
be used much more care would have to be bestowed upon
the exact determiuation of the stability of yachts than is now
common.
Other methods for estimating yacht-tonnage for time-allow-
ances proceed on the assumption that the length, or some func-
tion of the length, should be the basis of measuiement. Enles
of this kind have been used in America, but in this country they
have been applied only to boats or small yachts. External bulk,
measured to the top of the upper deck planking, has also been
used in America and advocated here. Another proposal has been
to use the register (or fiscal) tonnage of yachts — a measure of
their internal capacity. This last suggestion is simple, as all
yachts are measured by surveyors of the Board of Trade for their
register tonnaoe. On the otlier hand, variations in the struc-
tures of yachts, affecting the thicknesses of their sides, would
make the " register tonnage " a very unfair comparison of their
external bulk ; and there would be a temptation to decrease the
freeboard, in order to lessen the tonnage, whether measured by
internal capacity or by accurate determination of the outside
shape. Besides these various rules there are many others in
force, for small boats, canoes and yachts. Space fails, however,
for the further discussion of this interesting subject; and it
must suffice to add that each rule tends to produce its special
type of vessel, adapted to derive the greatest advantage by
the combination of small nominal tonnage with large driving-
power.*
In concluding this chapter a short statement may be made
of the various kinds of tonnage measurements actually in use,
which have been described in the preceding pages : —
(1) Displacement tonnage.
(2) Financial tonnage (Navy Estimates).
(3) Builders Old Measurement, with its modifications in
Thames measurement for yachts.
(4) Register tonnage.
(5) Freight tonnage.
Besides these, descriptions have been given of other systems of
tounage, which are either applied to a limited extent (as in yacht
and boat sailing) or else not used. Some of these " tons " repre-
* The reader desirous of pursuing in estimating time-allowances in Mr.
the subject further will find a full Dixon Kemp's valuable Manual of
discussion of existing tonnage-rules used Yacht and Boat Sailing.
•&^
72 NAVAL ARCHITECTURE. chap. ii.
sent dead weight, others represent " capacity," and the B.O.M.
01" Thames Rules, are empirical measures, representing neither
weight nor ca[)acity in most cases. With such a variety of
measures and so many kinds of "tons," careful discrimination
is obviously needed to prevent mistakes when dealing with the
tonnage of ships.
CHAP. III. THE STA TICAL STABILITY OF SHIPS.
' '>
CHAPTER III.
THE STATICAL STABILITY OF SHIPS.
A SHIP floating freely and at rest in still water must fulfil two
conditions: first, she must displace a weight of water equal to
her own weight ; second, her centre of gravity must lie in the
same vertical line with the centre of gravity of the volume of
displacement, or " centre of buoyancy." In the opening chapter
the truth of the first condition was established, and it was shown
that the circumstances of the surrounding water were unchanged,
whether the cavity of the displacement was filled by the ship
or by the volume of water displaced by the ship. When the ship
occupies the cavity, the whole of her weight may be supposed
to be concentrated at her centre of gravity, and to act vertically
downwards. When the cavity is filled with water, its weight may
be supposed to be concentrated at the centre of gravity of the
volume occupied (i.e. at the centre of buoyancy), and to act
vertically downwards ; the downward pressure must necessarily
be balanced by the equal upward pressures, or "buoyancy," of
the surrounding water ; therefore these upward pressures must
have a resultant also passing through the centre of buoyancy.
In Fig. 28, a ship is represented (in profile and transverse section)
FIG 28
Sffftjon
oG
Profile
W
OB
' \ I
floating freely and at rest in still water. Her total weight may
be supposed to act vertically downwards through the centre of
gravity G ; the buoyancy acting vertically upwards through the
centre of buoyancy B. If (as in the diagram) the line joining
the centres G- and B is vertical, it obviously represents the
'4
jya val architecture.
CHAP. in.
common line of action of tlie weight and buoyancy, which are
oqnal and opposite vertical forces ; in that case the ship is
subject to no disturbing forces, and remains at rest, the hori-
zontal fluid pressures which act upon her being balanced amongst
themselves?. But if (as represented in Fig. 29) the centres
Ct and B are not in the same vertical line, the equal and opposite
forces of the weight and buoyancy do not balance each other,
but form a " mechanical couple," tending to disturb the ship,
either by heeling her or by producing change of trim or causing
both these changes. If D = total weight of the ship (in tons),
and GZ = perpendicular distance between the parallel lines of
action of the weight and buoyancy (in feet).
Moment of couple = D X GZ (foot- tons).
If the vessel is left free to move from this position, not
being subjected to the action of external forces other than the
fluid pressures, she will either heel or change trim, or both
heel and change trim until the consequent alteration in the form
of the displacement brings the centre of buoyancy into the same
vertical with the centre of gravity G. It is important to note
that, for any specified distribution of weights in a ship, supposing
no change of place in those weights to accompany her transverse
or longitudinal inclinations, the centre of gravity is a fixed
2)oint in the ship, the position of which may be correctly as-
certained by calculation. On the contrary, the centre of buoy-
ancy varies in position as the ship is inclined, because the form
of the displacement changes. Hence, in treating of the stability
of ships, it is usual to assume that the position of the centre
of gravity is known, and to determine the place of the centre of
buoyancy for the volume of displacement corresponding to any
assigned position of the ship. The value of the "arm " (GZ) of
the mechanical couple formed by the weight and buoyancy can
then be determined. If it is zero, the vessel floats freely and
at rest, in other words, occupies a " position of equilibrium ; " if
CHAP. III. STATICAL STABILITY OF SHIPS. 75
the arm (GZ) has a certain vahie, the moment of the couple
(D X GZ) measures the effort of the ship to change her position
in order to reach a position of equilibrium. In this latter case
the vessel can only be retained in the supposed position (see
Fig. 29) by means of the action of external forces ; and if her
volume of displacement is to remain the same as when she floats
freely, these external forces must also form a mechanical " couple "
the equal and opposite forces acting in parallel lines. For
example, suppose a ship to be sailing at a steady angle of heel,
and the resultant pressure of the wind on the sails to be repre-
sented by the pressure P in Fig. 29 (section) acting along a
horizontal line. When the vessel has attained a uniform rate
of drift to leeward, the resistance of the water will contribute
a pressure, P, equal and opposite to the wind-pressure ; and if d
be the vertical distance between the lines of action of these
pressures, we have
Moment of couple formed by | ^^xd (foot-tons) ;
horizontal forces . . . . '
which moment will be balanced by that of the couple formed by
the weight and buoyancy. Hence
D X GZ = P X fZ,
i"s an equation enabling one to ascertain the angle of steady heel
for a particular ship, with a given spread of sail, and a certam
force of wind. Its use is illustrated in Chapter XII.
Supposing a ship, when floating upright and at rest, to be
in a position of equilibrium, which is the common case: let
her be inclined through a very small angle from the initial
position by the action of a mechanical couple. If, when the
inclinino- forces are removed, she returns toward the initial
position, she is said to have been in stcibU equilibrium when
upright ; if, on the contrary, she moves further away from the
initial position, she is said to have been in unstable equilibrium
when upright; if, as may happen, she simply rests in the slightly
inclined position, neither tending to return to the upright nor
to move from it, she is said to be in neutral or indifferent equi-
librium. A well-designed ship floats in stable equilibrium when
upright; but many ships, when floating light, without cargo or
ballast, are in neutral or in unstable equilibrium when upright,
and consequently "loll over" to one side or the other when
acted upon by very small disturbing forces. Damage to the
skin of a ship which was in stable equilibrium when intact, and
the entry of water into the hold may also produce unstable or
76
NAVAL ARCHITECTURE.
CHAP. 11.
neutral equilibrium in the upright portion. It will be shown
lioreafrer that there is a marked distinction between such in-
stability aud the conditions which lead to the capsizing of ships.
The statical stahilittj of a ship may be defined as the effort
which she makes when held steadily in an inclined position by
a mechanical couple to return towards her natural position of
equilibrium — the upright — in which she rests when floating
freely. This effort, as explained above, is measured by the
moment of the couple formed by the weight aud buoyancy.
Hence we may write, for any angle of inclination,
IMoment of statical stability = D x GZ.
But in doing so, it must be noted that in all ships, angles of
inclination may be attained for which the line of action of the
FIG. 30.
buoyancy, instead of falling to the right of GT (as in section,
Fig. 30), and so tending to restore the ship to the upright,
will fall to the left and tend to upset her or make her move
away from the upright position. This matter will be more fully
explained hereafter.
Starting from the upright, a ship may be inclined transversely,
or longitudinally, or in any " skew " direction lying between the
two. It is only necessary, however, to consider transverse and
longitudinal inclinations in connection with statical stability ;
the innumerable possible skew inclinations being easily dealt
with when the conditions of stability for the two principal
inclinations have been ascertained. The minimum stability of
a ship corresponds to transverse inclinations ; the maximum
stability, to longitudinal inclinations. It is, therefore, of the
greatest importance to thoroughly investigate the changes iu
CHAP. III. STATICAL STABILITY OF SHIPS. ^^
the statical stability of ships as they are heeled to greater and
greater transverse inclinations, especially for ships which have
masts and sails. Longitudinal stability is less important, but
claims some notice, especially as regards its influence on changes
of trim and pitching motions.
Taking first transverse inclinations, let them be supposed to ■
be small ; it is then easy to estimate the statical stability when
the position of the metacentre is known. For our present purpose
the metacentre may be defined, with sufficient exactitude, as the
intersection (M in the cross-section, Fig. 30) of the line of action
(BM) of the buoyancy when the ship is inclined through a very
small angle, with the line of action (B G3I) of the buoyancy when
the ship is upright and at rest. In vessels of ordinary forms,
no great error is introduced by supposing that, for angles of
inclination between the upright and 10 or 15 degrees, all the
lines of action of the buoyancy (such as BM) pass through the
same point (M) — the metacentre. For any angle of inclination
o within these limits the perpendicular distance (GrZ) of the line
of action of the buoyancy from the centre of gravity is deter-
mined by —
GZ = GM sin «.
Hence by what is usually termed the "metacentric method," it
follows that —
Moment of statical stability = D x G!M sin o.
As an example, take a ship weighing 6000 tons, for which the
distance GM = 3 feet, and suppose her to be steadily heeled
under canvas at an angle of 9 degrees. Then
Moment of statical stability = 6000 tons X 3 feet X sin 9°
= 18,000 X -loei = 2815 foot-tons.
For most ships the angles of steady heel under canvas lie within
the limits for which the metacentric method holds ; and conse-
quently this method may be used in estimating the "stiffness"
of a ship, i.e. her power to I'esist inclination from the upright by
the steady pressure of the wind on her sails. It must be noticed
that this term "stiffness" is used by the naval architect in a
sense distinct Irom "steadiness." A stiff ship is one which
opposes great resistance to inclinatirn from the upright, when
under sail or acted upon by some external forces ; a crank ship
is one very easily inclined ; the sea being supposed to be smooth
and still. A steady ship, on the contrary, is one which, when
exposed to the action of waves in a sea\Aay, keeps nearly upright,
her decks not departing far from the horizontal. Hereafter it
78 NA VAL ARCHITECTURE. chap. hi.
will be shown that frequently the stiffed ships are the least steady,
wliile crank ships are the steadiest in a seaway. At present we
are dealing only with still water, and must limit our remarks to
stiffness.
From the foregoing remarks it will be evident that, so far as
statical stability is concerned, and within the limits to which
the metacentric method applies, a ship may be compared to a
pendulum, having its point of suspension at the metacentre
(M, Fig. 30), and its weight concentrated in a " bob " at the
centre of gravity G. Fig. 31 shows such a pendulum, held
steadily at an angle a. The weight (D) acting downwards produces
a tendency to return to the upright, measured by tiie moment
D X GrM sin a, which is identical with the expression for the
righting moment of the ship at the same angle. But this com-
parison holds only while the ship and the pendulum are at rest ;
as soon as motion begins, the comparison ceases to be correct, and
the failure to distinguish between the two cases has led some
writers into serious error. If the centre of gravity of the ship
lies heloio the metacentre, she tends to return towards the upright
when inclined a little from it ; that is, her equilibrium is stahle.
If the centre of gravity of the ship lies ahove the metacentre, she
tends to move away from the upright when slightly inclined ;
that is, her equilibrium is unstable. If the centre of gravity
coincides with the metacentre, and the ship is inclined through
a small angle, she will have no tendency to move on either side
of the inclined position, and her equilibrium is indifferent. The
metacentre, therefore, measures the height to which the centre of
gravity may be raised, without rendering the vessel unstable when
upright ; and it was this property which led Bouguer, the great
French writer to whom we owe the first investigations on this
subject, to give the name, metacentre, to tiie point.
Changes in the height (GM) of the metacentre above the centre
of gravity produce corresponding changes in the stiffness of a
ship ; in fact, the stiffness may be considered to vary with this
height — usually termed the " metacentric height." If it is doubled,
the stiffness is doubled ; if halved, the stiffness is reduced by one-
half, and so on. Care has, therefore, to be taken by the naval
architect, in designing ships, to secure a metacentric height
which shall give sufficient stiffness, without sacrificing steadiness
in a seaway. In adjusting these conflicting claims, experience is
the best guide. The following tables contain particulars of the
metacentric heights of different classes of war-vessels, the vessels
being fully laden.
CHAP. III.
STATICAL STABILITY OF SHIPS.
It is to be noted that the first five groups in this table
include sailing ironclads. Experience has led to the selection of
metacentric heights of from 3 to 4 feet as the best suited for such
Ironclads.
1. Converted frigates (formerly two-deckers) ; Prince\
Consort class in Koyal Navy, and ear.iest French)
frigates {Gloire class) J
2. TFam'o7'andil/mci<aMr classes in Royal Navy ;i^toncZ/e^
class in French navy ./
3. Broadside ships with central batteries such as BeUeroA
pJion, Hercules, or Alexandra in Royal Navy . ./
4. Marengo class in French navy
5. Alma class of corvettes in French navy .
6. Devastation class of Royal Navy
7. Glatton (low freeboard monitor)
8. Garde-cotes {Belier class), French navy .
9. Inflexible (central citadel iron-clad) ....
LO. American type of monitor (Miantonomoh)
Metacentric
Height (Gil;.
Feet.
6 to 7
4 44
-2 " "2
11 01.
3
About 7
14
vessels, taking into account their ordinary spread of canvas. The
remaining groups comprehend maslless ships, in which the greater
metacentric heights are often unavoidable with the forms and
proportions rendered necessary by the special conditions of the
designs — such as moderate draught in association with thick
armour and heavy guns, or the necessity for providing against
possible losses of stability due to damage in action.
Unarmoureii Ships.
Metacentric
Height (GM).
Coast defence, and river service gunboats .
Screw line-of-battle ships (two deckers), of which a"!
few remain in the French and Royal navies ./
Screw frigates and corvettes of the old types .
Screw frigates of new type and very high speed, such i
as lacmstant class of Royal Navy, or Tourville\
of French navy J
Screw corvettes and sloops of recent design
Smaller clas^es of sea-going vessels ....
Tugs, torpedo-boats and small vessels, not sea-going
Feet. '
From 7 to 12
„ 4^ to 6i
2i„
2i„
3"
2
When the consumable stores of these vessels, armoured and
unarmoured, are removed, the metacentric heights are frequently
from six inches to one foot less than in the fully laden condition to
which the tables refer ; but there are many cases in which the
decrease in metacentric height due to such lightening is greater
than one foot, and there are others in which lightening is accum-
•
So NAVAL ARCHITECTURE. chap. iii.
panied by no loss or even by a gain of stiffness. This will be
explained hereafter.
Corresponding particulars of the metacentric heights of steam-
ships belonging to the mercantile marine are very scanty. Until
recently few attempts were made to obtain exact data on the
subject ; and for the fully-laden condition of any ship variations
in stowage necessarily produce variations in stiffness. The
designer obviously has no control over the stowage, w^hich is
chiefly in the hands of stevedores who regulate their procedure
by practical rules deduced from experience. In this respect,
therefore, the designs of war-ships and merchant ships differ
widely ; the naval architect assigns definite positions to all
the weights carried in the war-ship, and can aim at a definite
amount of stiffness ; whereas the stiffness of the merchant ship,
when laden, is practically governed by an ever-varying stowage
of cargo. So far as the facts on record enable a judgment to be
formed it appears that metacentric heights in fully laden
merchant steamers frequently lie between \\ and 3 feet: some-
times falling to 6 or 8 inches and at others exceeding 3 feet. A
large ocean-going steamer, for example, having a high reputation
for speed and good behaviour was found to liave a metacentric
height of \\ feet. Cargo-carrying steamers, laden with grain or
other homogeneous cargoes, have been found to have metacentric
heights of seven- tenths or eight-tenths of a foot ; whereas other
vessels have had metacentric heights of from 1^ to 2 feet under
similar conditions of lading.* Homogeneous cargoes are generally
regarded as those which least favour stiffness with a given dead
weight ; and there are many merchant steamers which could not
carry such cargoes without some ballast, although in actual
service with miscellaneous cargoes they are never ballasted.
Not a few instances occur where the amount of stiff'ness given
to merchant ships by improper stowage of heavy dead-weight
cargoes proves too great and leads to heavy rolling at sea.
Under the circumstances explained above it is not surprising
to find that private shipbuilders have hitherto paid but little
attention to exact investigations of the initial stability of
merchant ships except in special cases. A considerable amount
of attention has, however, been given to the subject recently,
and experiments have been made by many of the leading private
* For much valuable information as of the Institution of Naval Architects,
to the stability of cargo steamers, see a by Mr. IMartell (chief surveyor at
paper in vol. xxi. of the Transactions Lloyds).
CHAP. III. STATICAL STABILITY OF SHIPS. 8 1
firms to determine the metacentric heights of ships of various
classes, and there is reason to liope that the practice will become
general. From the designer's point of view interest chiefly
centres in the condition of ships when floating light with no
w^eights on board other than those belonging to hull, equipment
or machinery. Having ascertained the vertical position of the
centre of gravity for this condition, it is an easy matter to
approximate to the change in that position produced by putting
any weights on board, and thus to estimate the "metacentric
height " for a given stowage of dead weight. This will appear
more clearly from the explanations given hereafter (page 93).
Confining attention for the present to the light condition of
merchant steamers, the following table will be of some interest,
containing as it does results deduced from experiments made to
determine the actual stiffness of a number of vessels of various
classes.*
It will be remarked from tlie table that there are very consider-
able differences in the stiffness, as well as in the vertical position
of the centre of gravity (in relation to the total depth) of different
ships. Many of these vessels are sufficiently stiff, when floating-
light, to permit of their being shifted from berth to berth in port
without requiring ballast. Others are so stiff that they might, as
far as this quality is concerned, be safely trusted from port to
port with little or no ballast. Others, on the contrary, require to
be ballasted in order that they may stand upright without cargo ;
although when fully laden they may have sufficient metacentric
heights without ballast. Some of the steamers in this last cate-
gory are worked without ballast, coals being shipped as cargo is
discharged in order to preserve sufficient stiffness ; while others
use water-ballast as the most convenient method of meeting the
requirements of the case, and others of older type require rubble-
ballast, or pig-iron, to be put on board as cargo is discharged.
The explanatory notes attached to the table will enable the effect
of forecastles, poops and deck-houses upon the vertical position of
the centre of gravity to be traced, as well as the influence of
differences in the rig or structure of various ships. For purposes
* For many of the facts in tliis table J. Inglis, of Glasgow, Messrs. K. Naj ier
the author is indebted to gentlemen & Sons, of Glasgow. The remaiDing
connected with some of the leading examples are taken from the results
private shipbuilding firms — includiug of inclining experiments made on mer-
Messvs. Laird, of Birkenhead, Messrs. cantile steamers bought mto the Eoyal
Denny, of Dumbarton, Messrs. A. and Navy.
G
82
NAVAL ARCHITECTURE.
CHAP. III.
Tabular Statement of the Results of Inclining
3
^
Length
between
Perpen-
diculars.
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Feet ins.
440-0
350-0
390-0
340-0
320-0
320-0
313
285-0
290-0
290-0
264-0
253-0
234-0
Breadth,
extreme.
Depth
from
Upper
Side of
Keel to
Top of
Upper-
deck Beam
at side
amidships
(D).
Feet ins.
46-0
44-6
39-0
46-2
40-0
320-0 40-0
227-0
210-0
220-0
220-0
200-0
34-0
33-6
35-0
34-0
32-0
32-0
33-2
29-0
195-0 29-2
28-0
28-0
27-6
30-0
26-0
178^0 27^0
125-0 20-0
60-0 12-0
Feet.
36-25
34-5
30-8
34-0
28^5
22-7
26-5
25-5
26-5
25-8
16-6
23-
26-3
19-6
18-0
20-6
15-0
22-0
22-5
13-9
20-0
9^5
6-3
Expei'imental Data for Ships Floating Light,
with Water in Boilers, but no Cargo or
other Dead Weight ou Bnard.
Mean
Draught.
Displace-
ment.
Feet ins.
13-2
18-8
13-6
16-6
9-7
11-5
11-4
11-6
9.10
9^2
10-3
8-11
9-10
10-6
12-11
8-9
9-4
9-0
8-3
8-5L
9-6
4-9
3-11
Tons.
4570
4240
3200
3140
2110
1900
1880
1760
1610
1530
1410
1240
1130
1100
1040
860
780
780
750
630
600
180
32
Meta-
centric
Height
(G M).
Heicrht
of
Centre of
Gravity
• above
Top of
Keel (h).
Feet.
-1-0
1-2
- -7
2^3
2^9
5-2
-1^25
•2
2-1
1-5
2-4
1-5
2-
1^5
Ratio,
h: D.
•3
1-8
1^4
3-2
1-8
Feet.
22-5
20-5
17-9
20 •
18-
15-8
11^2
1-3 12-
-7 11.9
•83 11^5
12-8
12-7
10-4
11^5
7-4
4-3
•62
•594
•58
•588
•63
-696
17-
•64
15-4
•6
14^85
•56
14-9
12-7
14^5
14-1
•577
•765
•63
•536
'57
-67
•577
•77
•58
•565
•75
•575
•78
•68
CHAP. III. STATICAL STABILITY OF SHIPS.
83
Experiments made ok various Types of Merchaxt Steamships.
S
3
5c
oi
7
8
9
10
11
12
13
14
15
16
17
18
1!;
20
■-1
22
23
REMARKS.
f Trans-Atlantic mail steamer; new type ; cellular double bottom; large
I deck-houses ; light rig.
rMail steamer (old type) ; good speed ; good sail-spread ; forecastle, poop,
\ and deck-houses ; 180 tons of permanent ballast.
jCargo and passenger steamer ; good speed ; light rig ; deck-bouses and
\ turtle covers at ends.
Same type as (2); -with 75 tons of permanent ballast; deck-houses only.
fCargo and passenger steamer; good speed; light rig; poop and fore-
\ castle; continuous double bottom,
f Cargo and passenger steamer; good speed ; light rig; awning deck, and
I heavy deck-houses.
jCargo steamer ; moderate speed ; light rig ; turtle covers at ends, and
I I deck-houses ; water-ballast tank above ordinary floors.
Passenger and cargo steamer; high speed; light rig; deck-houses.
(Cargo steamer; moderate speed; light rig; forecastle and deck-houses;
1 continuous double bottom.
Ditto ditto ditto.
Passenger steamer (paddle-wheel) ; high speed ; light forecastle and full poo j ■.
Cargo steamer; low speed; light rig; flush deck.
Ditto ditto,
f Cargo and passenger steamer ; moderate speed ; light rig ; forecastle, poop,
\ and deck-house.
rArmed sloop ; composite built ; good speed ; full rig ; light armament ;
\ 150 tons of permanent ballast.
fCargo and passenger steamer ; moderate speed ; brig rig ; awning deck
\ and deck-houses above.
rCargo and jiassenger steamer; moderate speed; moderate rig; forecastle,
\ poop, and deck-houses.
Cargo steamer ; moderate speed; light rig; deck-houses.
Ditto ditto.
I Cargo and passenger (Channel service) ; good speed ; light rig ; poop, fore-
\ castle, and deck-house.
Cargo steamer; low speed; light rig; deck-houses; 80 tons of ballast.
Cargo boat ; low speed ; light rig; forecastle and raised quarter-deck.
Steam-launch.
(i 2
84
NAVAL ARCHITECTURE.
CHAP. III.
of guidauce in design fuller details would be required than are
here given ; in order that a new ship mii^ht have the position
of her centre of gravity determined approximately by comparison
with a completed ship of which the stiffness had been ascertained.
But, for our present purpose, the particulars given will suffice,
and the extension of the practice of incliniDg ships to determine
the position of the centre of gravity promises to become so
general that the facts given in the table will probably be supple-
mented ere long by much valuable data of the same kind.
Passing from steamers to sailing ships a brief summary may be
given of the recorded data, as to their metacentric heights, and
initial stability. Very few experiments were made on the older
class of sailing war-ships in the Eoyal Navy ; but from these ex-
periments, and from careful estimates made by naval architects
of the period, it appears that, when fully laden, these ships had
metacentric heights of from 4^ to 6^ feet ; and when light about
1^ to 2 feet less.* It must be remembered that these vessels
were heavily rigged ; and that their stiffness was, in many cases,
largely due to the presence of considerable weights of ballast and
water in their holds. From one- seventh to one-eis-hth of the dis-
placement was frequently assigned to water and ballast ; and in
some cases a larger proportionate weight was thus carried.
At the present time the most important classes of sailing
ships are those belonging to our mercantile marine and those
grouped as yachts. Considerable attention has been devoted
recently to the exact determination of the stability of both these
classes; and in the following table some of the principal results
are stated succinctly. A few facts as to various obsolete types of
war-ships, are also stated. For the merchant ships the light con-
dition only is represented as was done previously for merchant
steamers, and for similar reasons. For the yachts the load con-
dition appears ; as there is so little weight carried in them the
light condition needs no consideration. f For the war-ships the
* See the "Papers on Naval Archi-
tecture" (1827-33); and the "Reports"
of Messrs. Read, Chatfield and Creuze
(1842-46),
t For the facts respecting the sta-
bility of yachts, the author is almost
entirely indebted to the valuable inves-
tigations of Mr. Dixon Kemp (Trans-
actions of the Institution of Kaval
Architects for 1880). Theparticulars for
the Sunbeam are published with the
permission of Sir Thomas Brassey. For
those relating to merchant ships his
thanks are due to Mr. John Inglis,
junior, and Mr. Henry Laird. Much
valuable iuformation on the latter sub-
ject has also been obtained from the
excellent " Reports on Masting " made
to the Committee of Lloyd's Register
in 1877.
CHAP. III. STATICAL STABILITY OF SHIPS. 85
load and light conditions are both stated; in the light condition
all consumable stores and water are supposed to be removed from
the ships, but all spars, &c., are in place.
No accurate experiments appear to have been made to deter-
mine the metacentric heights of laden sailing merchantmen. It
is stated, however, on good authority tliat with ordinary .stowage
these vessels may obtain metacentric heights of 3 to 3 J feet. On
the other hand, it must be noted that the dead weight carried bv
such vessels frequently exceeds their weight (fully equipped) by
60 to 90 per cent. ; so that differences in stowage may produce
very considerable variations in stiffness. As a rule, a sailing
ship laden with a homogeneous cargo only would not possess a
metacentric height exceeding a foot or eighteen inches; and
would require to carry either ballast, or dead weight serving as
ballast, low down in the hold in order to obtain sufficient stiffness.
There are, however, exceptions to this rule, in which metacentric
heights of 2 to 3 feet can be secured with a homogeneous cargo,
and without ballast; in order to increase the stiffness even in
such vessels some dead weight or ballast would usually be
cariied, although less in propoition than in ships of ordinary
form. The opposite extreme to a homogeneous cargo is, of course,
that where the cargo consists of heavy materials, such as pig-iron,
rails, &c. ; and if care is not exercised in stowing such cargoes
excessive stiffness may be obtained, causing heavy rolling at sea.
The comparatively large metacejitric heights of the obsolete
classes of sailing war-ships doubtless tended to increase their
rolling ; but, as these vessels had to fight under sail, a considerable
degree of stiffness was essential, in order to prevent excessive heel-
ing and consequent inefficiency of the guns fought on the leeward
broadside (see Chapter XII.). In the yaclits it will be observed
that metacentric heights of from 3 to 4 feet are the rule; there
are, however, some classes of broad, shallow yachts in which
greater metacentric heights occur, rising in some extreme cases
to 8 or 10 feet.
In the foregoing remarks on the "metacentric heights" of
various classes of ships, attention has been confined to the relative
position of two points, namely, the metacentre and the centre of
gravity. It now becomes necessary to remark that the actual
vertical positions of these points are governed by entirely dif-
ferent considerations. For example, the vertical position of the
centre of gravity depends upon the distribution of the weights of
hull, equipment and cargo, or other weights to be carried. This
86
NAVAL ARCHITECTURE.
CHAP. III.
Tabular Statement of the Results of Inclining
S
3
o
a
M
1
2
3
4
5
11
12
13
U
15
16
17
18
19
Length
between
Perpen-
diculars.
Breadth,
extreme.
I Depth
from
Upper
' Deck at
Side amid
I ships.
(^See note.)
! (D)
War Ships : —
Feet.
113
100
100
141
131
Feet.
33
30
32
38
40
Feet.
19
15
17
27
27
Mean
Draught.
Feet ins.
15
13
13
12
16
15
17
16
•4
•8
■9
•9
•7
•0
•4
•0
Displace-
ment.
Merchant Ships (light condition) : —
25-4
24-6
24-6
22-7
22-3
15-
6
273
7
263
8
225
9
217
10
215
148
Yachts : —
86
100
90-5
85-75
81-25
79-5
103
154-75
43
1
38
3
37
5
35
"5
35
26
9
18-7
16-7
18-9
19-3
20-6
17-3
20-8
27-5
14-2
10-
13-2
9-
14-4
10-
13-2
10-
12-3
9-
13-7
10-
12-9
9-
17-3
13-
9
4
10
1
5
6
7
0
Meta-
centric
Height.
Height of
Centre of
Gravity
{See note)
(A)
Tons.
670
495
475
405
107r>
875
1055
890
Feet.
4
85
4
77
5
65
4
23
4
5
2
5
6
2
4
3
160
158
155
150
128
115
135
3
3
3
3-
4-
3-
Feet
15
12
12
13
18
19
17
19
•5
7-
•3
5-
•4
8-
•7
8-
-0
8-
8-
8-
45
12-
Ratio,
h: D.
9-7
1440
2-7
20-1
9-2
1100
-75
19-5
9-3
1010
-1-5
21-
8-7
8t,0
0
18-8
9-0
810
- -5
18-4
6-5
290
2-0
12-2
•8
■79
■7
•76
•65
•72
•64
-7
79
79
85
83
825
81
•528
-43
•57
•64
•72
■62
•64
* For the vessels i.amed in this table, except the yachts, the depth (D) is
The heiglit, h, of the centre of gravity is also estimated above the top of this
draught and the least freeboard; and the height of the centre of gravity is
to the mean draught. The lengths and breadths extreme for the yachts are
CHAP. III. STATICAL STABILITY OF SHIPS.
87
EXPEKIMENTS, ETC., MADE ON VAEIOTJS CLASSES OF SaILIIs'G ShIPS."
3
M
6
7
8
9
10
11
REMARKS.
18-gun corvette of 1832; load condition.
IB-gun sloop of 1830 ; load condition.
Brig; load condition.
Brig ; light condition.
Frigate; load condition.
Frigate; light condition.
Frigate; load condition.
Frigate ;
light condition.
12
13
14
15
16
17
18
19
Full ship rig ; estimate by Lloyds' surveyors ; registered length and breadth.
Ditto ditto ditto.
Poop,forecastle,and exceptionally heavy rig; resultofincliningexperiment.
Poop, forecastle, and full ship-rig ; ditto.
Forecastle, deck-house, and full ship-rig; ditto.
rrhree-masted schooner; estimate by Lloyds' surveyors; registered
\ length and breadth.
J/iVancZa, schooner ; 78 tonsof ballastN
Ji«??a?iar, yawl; 79 5 ,, „
Seahelle, schooner; 73 „ „
FJorinda, yawl ; 54 „ „
Bosevf Devon, \?i^\\ 57 „ „
Kriemhilda, cutter; 54 „ „
Eevenue cutter; 48 ,, „ .
(Sunbeam, three-masted schooner; 75 tons of ballast; Sir Tlicmas
i Brassey's yacht, with good steam-power.
The stability of these vessels
has 1 een fully inv(Stigated
by Mr. Dixon Kemjj.
reckoned to the top of the projection of keel, false-keel, &c., beyond the garb( ards.
projection. For the yachts, the Mai dfpth is taken ; i.e. the sum of the mean
measurtd from a line drawn parallel to the load-line, at a distance lelow it equal
taken at the load-line.
88 NAVAL ARCHITECTURE. chap. iil.
distribution is usually one of the given conditions of a war-ship
design, over which the naval architect has little control. In
merchant ships, as has been shown, the designer has even less
control over the vertical position of the centre of gravity for the
i'ully laden condition. But, while this is true, it is equally true
that the designer has considerable control over the vertical
position of the metacentre. That position depends only on the
form of a ship, especially near the load-line, and the extent to
which she is immersed ; and by means of changes in the form of
the immersed part of a ship, in the shape of the water-line
section, in the proportions of breadth to length, or breadth to
draught of water, the designer can obtain very various positions
of the metacentre in association with a constant total weight or
displacement. In making snch variations in form he has, of
course, to regard not merely the stability of the ship, but also the
resistance she will encounter in passing through the water.
It has been explained that the metacentre affords a ready
means of determining the line of action of the buoyancy for a
moderate inclination of a ship of ordinary form, and of avoiding
the necessity for determining the place of the corresponding
centre of buoyancy. But in practice the position of the meta-
centre is fixed with reference to the centre of buoyancy, corre-
sponding to the upright position of the ship. The distance
(B,M, Fig. 30) is given by the formula,*
-n Ttr _ Moment of inertia of water-line area
Volume of displacement
For transverse inclinations, such as we are now considerino-,
the moment of inertia would be calculated about the middle line
of the water-line section ; and this may be expressed in terms of
the length (L) and breadth extreme (B) of that section. It may
in fact be written,
IMoment of inertia = K x L x B^,
where K is a quantity ascertained by calculation for the par-
ticular ship. Since the cube of the breadth appears in the
expression for the moment of inertia, and only the first power of
the length, any increase in the breadth must be most influential
* The "moment of inertia" of an from tlie axis. The proof of the formula
area about any axis may be defined as given above involves mathematical
the sum of products of each clement of treatment which would be out of place
that area, by the square of its distance here.
CHAP. 111. STATICAL STABILITY OF SHIPS. 89
in adding to the value of the height (BiM) of the metacentre
above the centre of buoyancy.
The drawings of a ship furnish the naval architect with data
for exact calculations of the volume of displacement, the position
of the centre of buoyancy, and the moment of inertia of the
water-line area, corresponding to any assigned draught of water.
Details of the method of calculation would be out of place here ;
but it may be of interest to state certain approximate rules
derived from such calculations, by means of which rough
estimates may be made of the vertical positions of the centre of
buoyancy and transverse metacentre in ships of ordinary form.
I. For the approximate depth of the centre of buoyancy below
the water-line from two-fifths to nine-twentieths of the mean
draught may be taken. The larger coefficient should be used for
ships of full form. If tlie draught is increased by an unusually
deep keel or false keel the centre of buoyancy will lie higher
than in ships of ordinary form. In yachts, for example, it is
sometimes distant from the water-line only twenty-seven to thirty
per cent, of the mean draught.
n, II. For the coefficient K in the formula for the moment of
inertia of the water-line area, or plane of flotation, the following
approximate values may be taken :
Ships with extremely fine forms )
of load water-line . . j
Ships with moderately fine )
forms of ditto . • . j
Ships of full forms of ditto .
A rectangle .....
In applying these coefficients it must be noted that the length
and beam, in the formula for the height of the metacentre above
the centre of buoyancy, are to be measured at the load-line ; so
that these dimensions may differ from the extreme length and
breadth.
As an example, take her Majesty's ship Iron Duke, for wliich
length (L) is 280 feet, breadth extreme (B) 54 feet, mean draught
22 feet, displacement 6000 tons. Here K should about equal g'oV-
Hence
Moment of inertia of water-) ,, „^„ /-^.s^
T >= oVf,, X 280 X (o4r.
line area r 200 ^ \ /
Volume of displacement . . = 6000 X 35.
K
•04
05
to '
■055
06
to •
■065
08S
»
t
90 NA VAL ARCHITECTURE. chap. hi.
Height of metacentre above) 11 x 280 X (54)^ _ -i i.- ^
centre of buoyancy (B^M) J ""200 X 6000 X 35 "
Also (by Eule I.) approxi-\
mate depth of centre of „ nn s i. oo^i.
, ^ , , V = # X 22 feet = 8-8 feet,
buoyancy below water ^
surface >
Hence the metacentre shoukl be situated about 2'7 feet above
the water surface. Exact calculation showed it to be about 2.4 feet
above the water surface.
A t-till more rapid method of approximating to the height of
the metacentre above the centre of buoyancy is based upon a
combination of the preceding formula, with the rules for "co-
efBcients of fineness " given on page 3. Calling these coefficients
C, and using the same notation as before, we have
B,M KxLxB^
CxL X BxD
neglecting any small difference there may be between the length
between perpendiculars and breadth-extreme of the ship and
her greatest dimensions at the load-line. Reducing this expres-
sion, it appears that
which is an expression of the simplest character, and shows how
influential upon the height B^M is the ratio of breadth to mean
draught. The following are average values of the coefficient a,
determined from a considerable number of examples : —
Values of a.
Ships of ordinary forms . . . '09 to '1
Ships of full forms . . . . "08 to "09
The coefficient •! applies very fairly to nearly all classes of
unarmoured war-ships in the Eoyal Navy and to some merchant
ships ; tlie coefficient "09 applies fairly to the majority of
armoured ships and to many classes of merchant ships. For
vessels of exceptionally fine form or very deep keels, like yachts,
the coefficient rises to '15; and for vessels of very full form, the
coefficient falls to '08. From these statements it will be evident
that, while approximate rules may be useful in making rough
estimates, they cannot take the place of exact calculations, by
which the naval architect determines the actual positions of the
CHAP. III.
STATICAL STABILITY OF SHIPS.
91
metacentre and centre of buoyancy, corresponding to any assigned
draught of water in a ship of known form.
By means of a series of such calcuhxtions, it is possible to
construct a diagram — termed the "metacentric diagram " — show-
ing the vertical positions of the metacentre and the centre of
buoyancy for any mean draught of water between the deep load-
line at which the vessel floats when fully laden, and the light-
line at \Ahieh she floats when empty. Such diagrams are very
useful, especially for merchant ships subjected to great variations
of draught. The construction is very simple. Any horizontal
line WiLi (^ig- 30a) is taken to represent the load-line of the
ship. Through any point Wi on it a
vertical line B^Mi is drawn : the depth of
the centre of buoyancy corresponding to
the load-line is then set down below W^L^
on a certain scale, and this fixes the point
Bi. The length BilVr^ represents, on the
same scale, the corresponding height of "£-
the metacentre Mi, above the centre of -^^
buoyancy B. Through Wi the straight
line WjWaWa is also drawn, making an
angle of 45 degrees with WiLi. Then, for
some other water-line parallel to the load-
line WiLi (say WoL^, Fig. SOa), a corre-
sponding construction is performed. The
FIG 30 a
known distance between the two water-lines is set down from
WiLi, and W2L2 is drawn parallel to WjLj ; through the point
W2, where W2L0 cuts the line W1W2W3, a new vertical B^M, is
drawn. On this vertical are set off, to scale, the calculated depth
of the centre of buoyancy (B2) below the line WoLa, and the
height (B2M2) of the corresponding metacentre above the centre
of buoyancy. A similar process is ap[)lied to several other
parallel water-lines at still lighter draughts: and so finally a
series of points B^BoBg - are determined, through which a curve
is drawn, showing the locus of the centre of huoijancij for varia-
tions in mean draught from the extreme load condition to the
extreme light condition. In a similar manner a curve MiMoMg*-
is drawn, giving the corresponding locus of the metacentres.
Having obtained these curves, it is possible by means of simple
measurement to determine the vertical positions of the centre of
buoyancy and metacentre corresponding to any water-line parallel
to the load-line WjLi and inteimediate between it and the light-
line. For example, let WL (Fig. 30a) represent such a line
9.
NAVAL ARCHITECTURE.
CHAP. III.
at a given distance below WiLj. Where WL cuts W1W.W3
draw the vertical BWM ; the intersection of this vertical with
the metacentric curve gives the position M of the metacentre
corresponding to WL; and its intersection with the curve of
centres of bouyancy tixes the position B of the centre of buoy-
ancy. The metacentric locus is the more important, and the
other curve is chiefly valuable as the means of constructing that
locus. It should be remarked that the metacentric locus only
applies accurately to water-lines drawn parallel to WjLi. If, as
commonly happens, a ship changes trim considerably as she
lightens, then the vertical positions of both centre of buoyancy
and metacentre corresponding to the lighter line may not be
accurately represented by the points fixed on the metacentric
diogram by means of the 7nean draught, obtained by taking half
the sum of the draughts forward and aft.
From the preceding explanations, it will be obvious that in
different classes of ships the forms of meta-
centric curves (such as MiM^Ma, Fig. 30a)
may vary considerably. The only safe
course in practice is, therefore, to construct
tiie metacentric diao:ram for each class.
But it may be interesting to give a few
typical illustrations of such curves.* Fig.
30c shows a very common case for war-ships
of ordinary form ; the metacentric curve
gradually rises from the load towards the
light draught. On the same diagram are
indicated a convenient arrangement for the
most important data — displacement, and
tons per inch — at each draught. Another
form occurring less frequently in war-ships
makes the metacentric curve almost hori-
zontal between the extreme draughts. In vessels with "peg-
top " forms of cross-sections — such as the Symondite type of the
Royal Navy — the metacentre occupies its highest position in the
ship when she is at the load- draught, and falls gradually as the
draught lightens; see Fig. 30&. Another variety of metacentric
locus appears in Fig. 30a, where the metacentre first falls as the
draught lightens, then passes through a position of minimum
* For furtlier details on this subject
see a paper by the author on "The
Geometry of Metacentric Diagrams ; "
TrajhsaciiOTisof the Institution of Naval
Architects for 1878.
CHAP. III. STATICAL STABILITY OF SHIPS.
93
FIG 30 c
Disjiacement
tons
in |-
tons
35. S
SS4B
7S20
7661
}334
•hiugJit
as.n'
22'.Sf
Load
EKperimental
Light IS!
21.9i
c.a
height, and gradually rises again. This frequently occurs in
merchant ships of deep draught (in proportion to their beam)
when fully laden, and with approximately vertical sides in the
region between the load aud
light lines. The highest position
of the metacentre in these ships
usually corresponds to the light-
line : and the lowest to a draught
intermediate between the load
and light lines : very frequently
the heights at the load aud light
lines are nearly equal, and (as
indicated on Fig. 30a) the meta-
centric loL'us lies wholly below
the load-line. In war-ships, on
the contrary, that locus usually
lies wholly above the load-line,
the ratio of breadth to load-
draught being greater than the
corresponding ratio for merchant
ships. The range of draught from
the load to the light condition is
much less for war-ships than for
merchant ships.
Metacentric diagrams are chiefly useful as a means of rapidly
determining the stiffness of a ship when floating at a certain
water-Lne, and with the centre of gravity in a certain position,
which is fixed by an independent investigation. For a certain
mean drauglit and trim, the metacentre remains at a constant
height in the ship; and variations in the stowage of a given
amount of dead weight can only affect the stiffness by the chano-es
they produce in the vertical position of the centre of gravity.
^^ hen that position has been ascertained for any given condition
of stowage, it is usually shown on the metacentric diagram. For
instance, in Fig. 30a, when the ship floats at WL with M as the
metacentre, suppose the point G to represent the ascertained
position of the centre of gravity. Then GM represents (to scale)
the "metacentric height," which measures the stiffness of the
ship, as explained on page 78. For war-ships it is customary to
perform this construction for both the load and light conditions,
as well as for the condition of the ships when inclined (see page 98),
for the purpose of ascertaining the vertical position of the centre
of gravity. For merchant ships the light condition only can be
Note. — This diagram represents the
variations "in metacentric height
of H.M.S. Monarch. In the Light *
condition 430 tons of water-ballast
are supposed to be placed in the
double-bottom.
94
NAVAL ARCHITECTURE.
CHAP. III.
e 7 S 9 JO
19Ft
dealt with accurately in tlie same fashion ; since the stiffness in
the load condition varies with changes in stowage. In many cases,
however, the volumes and common centre of gravity of the total
volume of the spaces assigned to cargo are estimated ; the maxi-
mum load-line is fixed ; the corresponding dead weight is ascer-
tained, and thence the number of cubic feet of space available for
stowino; each ton of dead weight is ascertained. A homogeneous
cargo of this density is then supposed to be placed on board, with
its centre of gravity at the centre of gravity of the cargo-space.
The weight of the ship when floating light, as well as the posi-
tion of her centre of gravity in that condition, can be readily
ascertained by an inclining experiment. Hence, combining the
assumed cargo with these experimental data, a final result is
obtained for the vertical position of the common centre of gravity
of the fully-laden ship ; and her metacentric height is deter-
mined for the assumed
FIG.30<5? conditions of stowage,
which are about as little
favourable to stiffness
as any conditions likely
to occur in actual ser-
vice, and lie outside the
range of probability in
some classes of ships.
An interesting exten-
sion of this method is
shown on Fig. SOcZ.*
The metacentric locus
is drawn from light to
load lines in the usual
manner. In the light
i?e/emic6s.-l. Curve of metacentres ; 2. Curve condition M^ is the
of centre of gravity of homoG:eneoiis cargo ; metacentre, and G] the
3. Curve of centre of gravity of hull and homo- centre of gravity of the
geneous car2;o; 4. Curve of capacity for space ° •' .
occupied by cargo; 5. Scale of capacity (in ship lies above it, SO
units of 1000 cubic feet) ; 6. Scale for height of ||)at the vessel is in
of wate'r^°'' '''^'''" ' '^' ^''^' '^ '^'''' '^''''°^* unstable equilibrium.
It is found that a homo-
geneous cargo occupying about 58'5 cubic feet per ton of dead
weight would just fill the cargo-spaces and bring the ship to her
intended maximum load-line. If fully laden in this manner, the
* The author is indebted for this diagram to his friend Mr. John Inglis, juu.
CHAP. III.
STATICAL STABILITY OF SHIPS.
95
homogeneous cargo has its centre of gravity at C2, the common
centre of gravity of ship and cargo is at G-o, and the metacentre is
at M2, about 15 inches above the centre of gravity G2. As the ship
has taken in cargo, she has therefore acquired stiffness. So far the
diagram represents the common practice described above ; but it
furnishes lurther information of a valuable character. First,
there is a " curve of capacity "
giving the volume of the cargo-
space corresponding to various
heights of cargo in the hold ;
FIG30<?
second, there is a curve giving
the locus of the centre of gravity
of the cargo-space as the height
of the cargo is increased. The
curve of capacity resembles in its
construction the curve of dis-
placement described on page 6 ;
and the curve of centres of
gravity of cargo-spaces resembles
the locus of the centres of
buoyancy on metacentric dia-
grams. Having this data gra-
phically recorded, another step
may be taken. Suppose the ship
to be taking in cargo of the
assumed average specific gravity;
and while her lading is incom-
plete to be floating at a given
water-line intermediate between
the load and li2,"ht lines. Her
displacement at this given line is
known ; thence the dead weight
on board her is easily estimated, also the volume it occupies;
the height of its surface and that of its centre of gravity can
then be read off on the appropriate curves of capacity and centres
of gravity of homogenous cargo. Finally, the common centre of
gravity of hull and homogenous cargo can be found for the
given water-line. A curve passed through the points Gj G2, &c.,
gives the locus of this common centre of gravity of hull and
cargo throughout the period of loading; and the relation of this
curve to the metacentric curve shows how the stiffness varies,
under the assumed conditions, as the loadine: croes on.
Such a graphic record as that in Fig. 30fZ can scarcely fail to
References. — G-j. Centre of gravity of
ship without cargo ; Gj. Centre of
gravity of ship and cargo, snpp ising
the latter to be homogeneous, to fill
the holds, and to weigh 2250 tons ;
G-i. Centre of gravity of ship and
cargo, the dead weight being 1430
tons and other conditions as befjre ;
1. Curve of metacentres ; 2. Curve
of centre of gravity of ship and
cargo as the 2250 tons are dis-
charged ; 3. curve of centre of
gravity of ship and cargo as the
1430 tons are discharged ; 4. Scale
for mean draughts of water.
96
NAVAL ARCHITECTURE.
CHAP. III.
be of value ; although it does not strictly correspond to the con-
ditions of ordinary service, it enables any other conditions to be
readily estimated for. The greatest interest, of course, attaches
to the two extreme draughts ; and of these the fully-laden con-
dition is the more important, as previously indicated.
Fig. 30e contains another example of this method applied to
a cargo-steamer; but in this case the curves of capacity and
heights of centres of gravity of cargo are omitted. The reference
letters agree with those on Fig. ?>0d ; and it will be observed that
under the assumed conditions of stowage the vessel is in unstable
equilibrium both when light and when fully laden, whereas for a
considerable range of draught between these extremes she pos-
sesses a positive metacentric height, reaching a maximum value
of 1 foot about midway between load and light draught. This
vessel represents a class which is successfully employed in certain
trades, with the frequent use of water-ballast when homogenous
cargoes are carried.
Summing up the foregoing remarks on the metacentric method
of estimating stability, it may again be stated that the meta-
centre is simply a fixed point through wliich the buoyancy of a
ship may be supposed to act for all angles of inclination up to
10 degrees or 15 degrees in vessels of ordinary form. This is
tantamount to saying that the metacentre may be taken as a
hypothetical point of suspension for a ship in order to estimate
the righting moment when she is steadily heeled to any angle
within the limits named, as indicated on Fig. 30, page 76.
For vessels of unusual form — as, for example, the monitor type
w ith extremely low freeboard — the metacentric method cannot be
CHAP. III.
STATICAL STABILITY OF SHIPS.
97
trusted for such considerable inclination as in ordinary types.
On the other hand, there are certain forms for which the meta-
centric method applies to even greater inclinations, or even for
all possible inclinations. The well-known cigar-ships exemplify
the Jast-named condition. All transverse sections of these ships
are circles. Suppose Fig. 32 to represent the section containing
the centre of buoyancy B for the upright position, WL being
the water-line. Then obviously for any inclined position (such
as is shown in Fig. 33, where the original water-line is marked
WjLi, and the original centre of buoyancy Bi) the new centre
of buoyancy B determines the vertical line of action (BM) of
the buoyancy, which intersects the original vertical (BjlM) in the
centre (M) of the cross-section. Hence, if Gr be the centre of
gravity, we shall have for any angle of inclination a,
j\Ioment of statical stability = D x GIM sin a.
In other words, the cigar-ship may be regarded as a pendulum
turning about the point of suspension M throughout the whole
ranse of its transverse inclinations, instead of limiting that com-
parison to 15 degrees, as is done for ordinary ships.
The conditions of stability of a wholly submerged or submarine
vessel are as simple as those
of the cigar-ship. In Fig. 34
a cross-section of such a vessel
is given ; B is the centre of
buoyancy, and for a position
of equilibrium B and the
centre of gravity G must lie
in the same vertical line.
AVhen this condition is un-
fulfilled (as in the diagram),
the weight and the buoyancy
form a mechanical couple, just
as in the case of a ship having
FIG.34
^
i
fo >\-
/
I
/ ^^----
"""^' /I
4
z
i /
--•'' -
1 /
^^ —
. .
~l / ,-' —
.._
' / ^' V
/
^' !
a part of her volume above water. For the submarine vessel,
however, inclination produces no change in either the form of
the displacement or the position of the centre of buoyancy; for
all positions the buoyancy acts upwards through the same point
B, and the total weight downwards through the centre of gravity
G. Consequently stable equilibrium is onlv possible when the
centre of gravity lies (as in the diagram) below the centre of
buoyancy ; for obviou>ly, if G were placed vertically above B, and
the vessel were inclined ever so little, no position of rest could be
98 NAVAL ARCHITECTURE. chap. iii.
reaclie 1 until G was placed vertically below B. For wholly sub-
merged floating vessels, therefore, the centre of buoyancy takes
the place of the metacentre in vessels partially immersed, and for
all angles of inclination (such as a).
Moment of statical stability = D x GB sin a.
Attention will next be directed to some of the more important
practical applications of the metacentric method of estimating
stability. The first to be noticed will be the inclining experiment,
by means of which the vertical position of the centre of gravity
of a ship is ascertained after her completion. In designing a
new ship the naval architect makes an estimate for the position
of the centre of gravity ; and with care can secure a close ap-
proximation to accuracy. On the other hand, a lengthy and
laborious calculation is required in order to fix the position of the
centre of gravity accurately ; and it is now generally agreed that
for purposes of verifying estimates, as well as of obtaining trust-
worthy data for future designs, inclining experiments are desirable.
These experiments are simple as well as valuable, and it may be
of service to indicate the manner in which they are usually
conducted in ships of the Royal Navy.
The ship being practically complete — with spars on end, the
bilges dry, the boilers either empty or quite full, no water in the
interior free to shift, and all weights on board well secured so
that they may not fetch away when she is inclined — is allowed to
come to rest in still water. A calm clay is desirable, but if there
be any wind, the ship should be placed head or stern to it and
allowed to swing free, the warps being so led that they may
practically have no effect in resisting the inclination of the ship.
For the purpose of producing inclination, piles of ballast are
usually placed on the deck (see W, W, Fig. 35), being at first
equally distributed on either side, but in some cases the guns
of a ship have been traversed from side to side instead of using
ballast. Two or three long plumb-lines are hung in the hatch-
ways, and by means of these lines the inclinations from the
upright are noted. All being ready, and the ship at rest, the
positions of the plumb-lines are marked, and the draught of
water is taken. The position of the metacentre corresponding
to this draught can then be ascertained by calculation from
the drawings. Next a known weight of ballast (W, Fig, 35) is
moved across the deck through a known distance. The vessel
CHAP. III.
STATICAL STABILITY OF SHIPS.
99
becomes inclined, and after a short time rests almost steadily in
this new position ; in other words, is once more in equilibrium, as
shown in Fig. 36. Consequently, for this new position, the meta-
centre M must be vertically above the new centre of gravity (Grj) ;
for obviously the shift of ballast has moved the centre of gravity
of the whole ship through a certain distance GGi parallel to the
FIG.36.
deck, and it is this movement of the centre of gravity that pro-
duces the inclination. Suppose a to be the angle of inclination
noted on the plumb-lines when the ballast W has been moved
through the transverse distance d. Then (since GG^ is perpendi-
cular to GM) we have,
GGi = G]\r tan a ; or GM = GG^ cot a.
And if GGi can be determined, the distance of the centre of
gravity below the known position of the metacentre can be found,
and the true vertical position of the centre of gravity is ascer-
tained for the experimental condition of the ship. Any sub-
sequent corrections consequent on the removal of the ballast,
addition of water in the boilers, or other alterations in the
condition of the ship when
fully equipped, can be
easily made.
The value of GG^ can
be readily estimated by
means of a simple calcu-
lation, the character of
which may be better seen by means of an illustration. A uniform
lever (Fig. 37) is loaded with two weights, W, placed at equal
distances from the middle : it will tlien balance upon a support
placed at the middle (G) of the length. Now let one of the
h2
w
FIG 37.
w
Middle
r
nS 38
c.
lOO NAVAL ARCHITECTURE. chap. iii.
weights W be moved to the opposite end (as in Fig. 38)
through a distance d. Obviously the point about which the
lever will balance (that is, the centre of gravity of the lever and
tlie weights W) will no longer be at the middle, but at some
point (G-i, Fig. 88) to the right of the middle. If D be the total
weight of the lever and the weights it carries, by the simplest
mechanical principle it follows that
D X GGi = W . d ; whence GGi = — ^.
AVhat is true in this simple case is true also for the ship ; the line
GGj, in Fig. 36, joining the old and new positions of the centre
of gravity, must be parallel to the deck-line, across which the
weight W is moved, and the above expression for GGi holds.
Hence, since
W d
GM = GGi . cot a, while GGi = — j] — '
it follows that ^,-r ^^^ t
(jtM = -.— . a cot o,
an equation fully determining the position of the centre of
gravity G in relation to the known vertical position of the
metacentre ]\T, ascertained by calculation from the drawings.
As an example, suppose a ship for which tlie displacement
(D) is 40(J0 tons to have 60 tons of ballast placed upon her deck,
30 tons on each side. When the 30 tons (W) on the port side
is moved to starboard through a transverse distance of 40 feet
{d), the vessel is observed to rest at a steady heel of 7 degrees
from her original position of rest. Then, from the above expres-
sion—
GM = jz . dcoi a = tttttq X 40 X cot T
= ^ X 8-144 = 2-43 feet.
In practice it is usual to subdivide the ballast on each side into
two equal piles, and to make four observations of the inclinations
produced by —
(1) Moving one pile of ballast from port to starboard ;
(2) Moving second pile of ballast from port to starboard.
These two piles having been restored to their original places, the
plumb-lines should return to their first positions, unless some
CHAP. III. STATICAL STABILITY OF SmP:^.\ '.; ; '.' ■>. Jtpl
3 i
weights other than the baUast have shifted during the inclina-
tions. Then two other inclinations are produced and noted by—
(3) Moving one pile of ballast from starboard to port ;
(4) Moving second pile of ballast from starboard to port.
The results of observations (1) and (3), (2) and (4) should agree
respectively, if the four piles of ballast are of equal ^veight, and
if the distance d is the same for all ; the inclinations in (2) and
(4) should be about twice those iu (1) and (3). The values of
GM are deduced from each experiment, and the mean of the
values is taken as the true value of the metacentric height at
the time of the experiment. Thence it is easy to deduce the
metacentric height for the vessel in her fully equipped sea-
going condition, or in any other assigned condition.
The reason for great caution in preventing any motion of
weights on board, oth-n- than the ballast, during the inclining
experiment, will appear from the expression given above for the
motion (GGj) of the centre of gravity. Tiie moment due to the
motion of the ballast Wc7 is comparatively small ; in the above
example, which is a fair one,
W^ = 30 tons X 40 feet = 1200 foot-tons,
and
GG, = ^^ = 1% foot onlv.
' 4000 1^
Kow, if other weights, and particularly free water in the bilges
shift as the ship inclines, their aggregate moments may bear a
considerable proportion to W . d, and so the estimated value
of GGi may be less than the true one, if no account is taken of
the shift of water. For example, 5 tons of water free to shift 30
feet in a transverse direction would have a moment (5 X 30) of
150 foot-tons, or no less than one-eiglith that of tlie ballast, and
if its effect were unobserved through carelessness, the motion of
the ballast would be credited with producing an inclination
about one-eighth greater than it could produce if acting alone.
In the foregoing example, if such an error had been made, in-
stead of writing WcZ = 1200 foot-tons, it should have been 1200
4-150 = 1350 foot-tons; so that the metacentric height would
have been — •
GM = i?^ X cot 7° = 1^ X 8-14 = 2-75 feet.
In performing inclining experiments, too great care cannot,
therefore, be taken to ensure that no other weights shall shift
than those made use of to produce the inclinations.
I0.2 NAVAL ARCHITECTURE. chap. in.
A second useful application of the metacentric method is
found in a practical rule for estimating the angle of heel
produced by moving a weight athwa-rtships in a ship. Keferriug
to the formula
W
GM = -j^d cot a,
we may arrange it as follows,
*^^" = D7GM'
and for the case under consideration assume that all the quantities
on the right-hand side of the equation are known, the value of
tan a being thus determined. As an example, suppose a
weight (W) of 5 tons to be moved horizontally a distance (cl)
of 30 feet athwartships in a sliip of 1500 tons displacement (D),
having a metacentric height of 3 feet ; then,
4 5 ^ 30 1
tan a = — — X — = =^
1500 3 30
o = 2° (nearly).
This rule is of service in approximating to the heel produced
by transporting guns or heavy weights from side to side on
a deck or platform which is nearly horizontal athwartships.
When the vertical positions of weights already on board a ship
are changed, the result is simply a change in the position of
the centre of gravity of the ship ; for obviously the displacement
and position of the metacentre remain unaltered, since there is no
addition or removal of weights. The shift of the centre of gravity
can be readily estimated by the rule already given. Suppose the
total weight moved to be iv, and the distance through which
it has been rais*i or lowered to be h, then, if GGi be the rise or
lall in the centre of gravity,
GG, = ^-,
where D is the total displacement of the ship. If GM was the
original height of the metacentre above the centre of gravity,
for an angle a within the limits to which the metacentric method
applies,
Original moment of statical stability = D x Gj\[ x sin o
Altered moment of statical stability = D (GM + GGi) sin a.
The alteration is an increase when the weights are lowered ;
a decrease when the weights are raised. As an example, take
the case of a ship of 6000 tons displacement, having a metacentric
CHAP. III.
STATICAL STABILITY OF SHIPS.
TO3
height of 3^ feet ; and suppose spai-s, &c., iveighiug together 10
tons, to be lowered 70 feet. Then
GG. (fall of centre of gravity) = = — foot.
6U00
60
Ori";inal moment of statical 1 -, n rnn e + +^ , v^ „:„
"^ > = 19,500 toot-tons X sm a.
stabihty )
Altered moment of statical ) a(\r\r\ f<i-t 1 ^ \ •
1 ■,. r = oOOO \o\ -\-~-\ sin a.
stabditv i V •* 60/
20,200 foot-tons x sin a.
Another case where weights already on board a ship are
shifted, involves a motion of the centre of gravity of the weights
moved in both the horizontal and the vertical directions. For
example, when coal or grain cargoes are carried, and a vessel
FIG 30/
J^fer cargo iMj(s
'Before carrfo sliifh
is steadily heeled under sail to one side for a considerable period,
the cargo may shift to leeward. In such cases, if the inclining
forces were removed, the ship would obviously not return to the
upright, but would rest in an inclined position, which can be
very simply determined. Let Fig. 30/ illustrate this case.
WL is the load-line ; M is the raetacentre corresponding thereto.
Suppose, when the ship is upright in still water, the grain in the
hold has ab for its surface; and that after she has been steadily
heeled for a considerable time that surfa^-e changes to cd. Let
ah and cd intersect in e. Then, what has happened is this: a
wedge-shaped mass of grain originally at aec, of a known weight
W, and having its centre of gravity at g^, has been shifted into
the position led with its centre of gravity at g-,. Join g^g,.
Then, as explained above, if Gi be the centre of gravity of
the ship and cargo before any shift took place, its new position
I04 NAVAL ARCHITECTURE. chap. in.
G2 will be fouud on a line G1G2 drawn parallel to </ r/^ ; and we
must have
Now, if the inclining forces are supposed to be removed, the ship
Avill find her })osition of equilibrium, when the new position
G2 of the centre of gravity lies vertically below the metacentre M.
And since two sides of the triangle G1MG2 (GjM and Gi(t2) are
given, as well as the angle MGiGa, tliat triangle is fully known,
and the angle GiMG-a can be ascertained. This will be the
angle of heel required.
As an example take the case of a ship of 3200 tons displace-
ment, which when fully laden with a cargo of coals has a
metacentric height of 2^ feet. Suppose 80 tons to be shifted so
that its centre of gravity moves 20 feet transversely, and 4 feet
vertically. Then the corresponding transfers of the centre of
gravity of ship and cargo will be given by the equations.
Horizontal motion = -^Tin — - "^ ^^^t*
Vertical use = ^^^^ = -1 „
The angle of heel in this case would be given with quite
sufficient acL-uracy by the equation
, Horizontal transfer of centre of 2:ravity '5 1
tan a -^ — — ^= ^
Oiigmal metacentric heiglit 2*5 5
or a = 11 J° (nearly).
If the vertical rise in the centre of gravity had been greater,
the more accurate method of determining the heel would have
been applied. It need hardly be added that, in practice, all
possible precautions should be taken to prevent such shifts of
cargo, and that particular care is needed in grain-laden ships.
Ilie preceding illustration also serves to indicate how the
statical stability of a ship is affected by the presence of free
water in her hold. If the skin of the ship is intact, the water in
the hold may be treated as a load carried in her bilges, and its
motion towards the side to which the ship may be steadily heeled
will be equivalent to a shift of the centre of gravity in that
direction, and to a consequent change in the stability, resem-
bling that produced by a shifting cargo. Damage to the Lottom
of a ship may be so serious as to admit large quantities of water
into the hold, and to leave them in free communication with the
CHAP. III. STATICAL STABILITY OF SHIPS. 105
■water outside. This condition of things as a possible cause of
foundering has already been discussed at length ; * it is therefore
only necessary to refer to the effect upon the statical stability of
a ship having a bilged compartment. Except in the few cases
where watertight decks or platforms form tops to compartments,
it may be said that the bilged compartment ceases to contribute
any buoyant water-line area. In fact, taking the box-shaped
vessel in Fig. 11 (page 16) as an example, the effect of filling
the compartment is to reduce the original water-line area by the
area {fg) of the top of the compartment. Now it has been
explained above that the vertical position of the metacentre in
relation to the centre of buoyancy depends upon the form and
area of the buoyant water-line, or plane of flotation ; any decrease
therefore in area and moment of inertia must be accompanied by
a consequent decrease in the height of the metacentre above the
centre of buoyancy. But, on the other hand, the deeper immer-
sion of the ship, when the compirtment is bilged, leads to a rise
in the position of the centre of buoyancy in the ship. The differ-
ence between this fall of the metacentre and rise of the centre of
buoyancy measures the alteration in the metacentric height ; and,
for angles of heel up to 10 or 15 degrees in ships of ordinary
form, will give a fair measure of the change of stiffness produced
by filling the compartment. In some cases (and almost invariably
where a midship compartment is damaged) the stability is
decreased ; in others it is increased. Without an investigation
it is frequently not easy to determine the true character of the
chano^e. The difference between this case and that where water
in the hold is not in iree communication with the water outside
lies principally in the fact that with a damaged bottom, if there
be no horizontal watertight partition above the level of the hole,
the water in the bilged compartment always maintains the same
level as that of the water outside when the ship is held steadily
in any position. Having, therefore, determined by this condition
how much water will enter the damaged compartment, if we then
conceive the bottom to be made good, and the compartment to
contain that quantity of water, the statical stability of the ship
may be estimated at any angle of inclination to which the meta-
centric method applies in the same manner as was explained above
for a vessel having free water in the hold and the bottom intact.
The condition of a centra,l-citadel ironclad, when her uiiarmoured
ends above the shot-proof deck have been " riddled " by shot and
* iSee Chapter I. pages 15-24:.
106 NAVAL ARCHITECTURE. chap. in.
shell, furnishes an illustration of the foregoing remarks. In the
Inflexible, for example, the central armoured citadel is 110 feet
long ; before and abaft it the protection of the ship is secured by
a strongly-plated deck, about 6^ feet under water ; and the spaces
above this deck are minutely subdivided into watertight com-
partments, many of which are occupied by cork-packing, &c. Sup-
pose the ship, with her sides intact, to float at the mean draught
of 21 feet 7 inches, then her centre of buoyancy is about 13^ feet
above the keel-plates, and her transverse metacentre 17^ feet
above the centre of buoyancy. Supposing the unarmoured ends
above the plated deck to be completely riddled, every space being
thrown open to the sea, but the cork-packing to remain in place,
the ship would sink about 2 feet deeper in the water, her centre
of buoyancy would rise about 3 inches, and the metacentre would
only be 11 feet above the centre of buoyancy. In other words,
this serious damage to the ends would decrease the moment of
inertia of the buoyant water-line area about 37 per cent, from its
value in the intact condition. This fall in the metacentre reduces
its height above the centre of gravity from 8^ feet in the intact
condition to 2 feet in the riddled condition.
When other than statical conditions come into operation, as,
for instance, when a ship is rolling rapidly in a seaway, it is
important to distinguish between the cases of free water contained
within an undamaged skin and of water admitted to the interior
by fracture of the bottom. And, further, it is necessary to dis-
tinguish between the cases of serious and slight damage to the
bottom when dealing with the ship in motion, whereas no such
distinction is necessary in discussing the stability for a steady
heel. When held at a steady heel, free water in the hold will
adjust its surface horizontally, even if there be some obstruction
to the motion of the water towards this position of rest ; but if
the ship is in motion and changing her position rapidly, the
element of time has to be considered, and the free water con-
tained within an undamaged skin may not move rapidly enough
as compared with the motions of the ship to maintain the
horizontality of its surface. Similarly, when the ship is held at
a steady heel, it does not make any difference whether a hole
in the bottom of a bilged compartment is large or small ; the
final result will be that the compartment will be filled up to the
level of the water outside. But the time taken in filling the
compartment, or allowing any quantity of water to pass through
the hole, of course depends upon the size and situation of the
hole in the bottom ; and therefore, when a ship is in motion, and
CHAP. III. STATICAL STABILITY OF SHIPS. 107
the volume of any compartment up to the level of the water
outside may be constantly changing, there is a marked difference
between tbe stability in the cases of slight and serious damage.
It will be only necessary to refer once more to Figs. 15-17
(pages 23 and 24) in order to illustrate the beneficial effect upon
the statical stability of horizontal watertight platforms. When
the compartment above the flat jj^-iu Fig. 17 is filled, the stiffness
of the box-shaped vessel is less than before the damage occurred ;
owing to the loss in buoyant water-line area bringing down the
metacentre more than is compensated for by the rise in the centre
of buoyancy. When the compartment below the flat jiq^ in Fig.
16 is filled, there is no loss of buoyant water-line area, and con-
sequently no fall in the metacentre relatively to the centre of
buoyancy, while the latter point rises, owing to the deeper
immersion, the final result being an increase in stiffness as
compared with the undamaged vessel.
Longitudinal bulkheads, such as are shown in Fig. 14, page
22, are very valuable aids to the maintenance of transverse
stability when there is free water in the hold, by limiting the
transverse shift of that water as the vessel becomes inclined,
as well as by limiting the quantity of water admitted by damage
to the bottom. Longitudinal partitions, or "shifting boards,"
are similarly of great value, especially in grain-laden ships, in
preventing shift of cargo.
Double-bottom compartments (such as those described in Figs.
20-25, page 26) are commonly used for water ballast. The spaces
below the watertight longi-
PIQ 39^ tudinals (a. Figs. 21-25) at
the bilges are generally em-
ployed for this purpose, ar-
rangements being made for
readily filling or emptying
these spaces. It is most im-
portant that the compartments
used for water ballast should
be quite full ; otherwise, some
motion, and consequently a
decreased stability, will result as the ship becomes inclined.
When so filled, the weight of water ballast in the compartments
may be treated as if it were solid ballast, not capable of any
shift, in estimating the change in the stability produced by its
addition.
A ready rule for estimating the change in the metacentiic
■
w
w
A
1
L
""Hi
<--
L~~
\ 1
V
*^
loS NAVAL ARCHITECTURE. chap. in.
stability or stiffness of a ship produced by adding or removing
weights, of which the vertical positions are known, will be useful.
Suppose Fig. 39 to represent a case where weights amounting in
the aggregate to W tons have been put on board a ship, with
their centre of gravity h feet above the water-line (WiLj) at
which the ship floated before the weights were added. Let G be
the original position of tlie centre of gravity of the vessel, and
]\I the metacentre corresponding to the water-line WjLi ; then,
if D be her displacement to that line, her stability for any angle
o within the limits to which the metacentric method applies will
have been
Moment of statical stability = D X GM sin a.
The addition of the weights W will increase the immersion of the
ship by a certain amount, which can be estimated by the method
of "tons per inch" explained in Chapter I. It may be assumed,
however, that commonly the weights added are comparative ly
so small that their addition will only immerse the vessel a few
inches; the centre of gravity of those weights may be fixed
relatively to the original water-line WiL^.* Their moment about
WiLj will be = W X li foot-tons ; and then the expression for
tlie statical stability at the angle a will become altered by the
addition of the weights to
I. Moment of statical stability = (D x Gj\I — W x li) sin a.
Had the weights W been placed with their centre of gravity at a
distance A helow WjLi, tJie stability would have been increased
by the amount W/i sin a, and
II. Moment of statical stability = (D x GM 4- W x li) sin a.
Conversely, if weights are removed from above the water-line
WJji (say, W tons at a height li feet), the stability of a ship is
increased by the change, and for an angle a
III. Moment of statical stability = (D x GM + W x A) sin o.
Whereas, if the same weights are removed from an equal distance
helow WL, the stability is decreased; and
IV. Moment of statical stability = (D x GM — W x A) sin a.
As an example, suppose a ship of GOOO tons displacement, with
a metacentric height (GM) of o| feet, to have additional
* For the full mathematical treat- note) on the " Geometry of Metacentric
ment of this subject, see the Paper Diagrams."
previously mentioned (page 92, foot-
CHAP. III. STATICAL STABILITY OF SHIPS. IO9
guns, weighing 50 tons, placed on her upper deck, their common
centre of gravity being 18 feet above water. Eule I. applies, and
we have, for an angle a.
Original moment of statical ) ^aaa j. o 1 j^ a
'^ , .,. > = GOOO tons X 34 leet x sin a.
stability 1
— 19,500 (foot-tons) x sin a.
Moment of statical stability^
after the addition of the( = (19,500 - 50 X 18) sin a.
weisrhts
'O
= 18,600 (foot-tons) x sin a.
Suppose tlie same ship to have 100 tons of water ballast added,
instead of the guns, the centre of gravity of the ballast being
16 feet below the water-line. Then liule II. applies, and the
stability is increased, becoming for angle a
Altered moment of statical) ,,r> ^/^/^ in<^ ■^ r^\ •
^ , ...^ V = (19,500 + 100 X 16) sin a.
stability j
= 21,100 (foot-tons) X sin a.
It is unnecessary to give illustrations of the remaining rules for
the removal of weights.
When " metacentric diagrams," such as those given on page 93,
are available, the foregoing rules cease to be of much value ;
because the effect upon the vertical position of the centre of
gravity of the addition or removal of any weights, however large,
is easily estimated ; the corresponding change in draught can be
determined ; and the new position of the metacentre corresponding
to the altered draught is indicated on the metacentric diagram.
Where no metacentric diagrams are available, the approximate
rules giveu above will be of service to a commanding officer.
These various cases include the most important practical appli-
cations of the metacentric method to the stability of ships inclined
transversely. Attention must next be turned to longitudinal
inclinations, or changes of trim. The process by which the naval
architect estimates changes of trim produced by moving weights
already on board a ship is identical in principle with the inclining
experiment described on page 99 ; only in this case he makes use
of a metacentre for longitudinal inclinations (or, as it is usually
termed, the " longitudinal metacentre"), instead of the transverse
metacentre with which we have hitherto been concerned. The
definition of the metacentre already given for transverse inclina-
tions is, in fact, quite as applicable to inclinations in any other
direction, longitudinal or skew ; but it has already been explained
no NAVAL ARCHITECTURE. chap. iii.
that, as the transverse stability of a ship is her minimum, while
the longitudinal stability is her maximum, only these two need
be considered.
The general expression for the height of the longitudinal meta-
centre above tlie centre of buoyancy resembles in form that given
on page 88, for the transverse metacentre ; but for longitudinal
inclinations the moment of inertia of the plane of flotation has to
be taken about a transverse axis passing through the centre of
gravity of that plane. Hence, using the same notation as before,
we may write :
Moment of inertia of plane of flotation (for
estimates of height of longitudinal meta- [ = K^ x B x L''.
centre)
Height of longitudinal meta- \ ^ ^
. 1 + A K, X B X L^
centre above centre oi i -n
1 ( Volume of Displace
buoyancy j ^
meut.
Following out a process of reduction similar to that described for
the transverse metacentre, this last formula may be written
Height of longitudinal metacentre = r^ — ^ ^ r^ = &. tt.
^ ° UxLxBxl> D
The values of K and C vary considerably in different classes
of ships; and so does the ratio h; but the following averages
obtained for various types may be of some value, although no
approximations can be trusted to replace exact calculations from
ship-drawings : —
Values of 6.
TJnarmoured war-ships and merchant-)
, . . T ^ .■ > ... -07 to -08
ships of ordinary proportions . . . j
Armoured ship ; merchant ships of)
• 11^ ^ } . . . -OTo to -09
special classes j
The value '075 may be used as a rough approximation in most
cases ; but there are many exceptions to its use.
In ships of war the ratio of mean draught to length frequently
lies between 1 to 12, and 1 to 14 ; the average of these ratios 1 to
13 is, as nearly as possible, the average value of h stated above.
Hence, in such vessels, the height of the longitudinal metacentre
above the centre of buoyancy usually approximates to equality
with the length, in some classes exceeding it by 20 to 25 per
cent., and in others falling below it by 10 to 15 per cent. In sea-
going merchant ships the ratio of mean draught to length is
usually less than in war-ships ; and the height of the longitudinal
metacentre above the centre of buoyancy is sometimes 40 per
CHAP. II. STATICAL STABILITY OF SHIPS. Ill
cent, greater than the length. In vessels of extremely-
shallow draught, such as river steamers having small displace-
ments, but large moments of inertia of the planes of flotation,
the height of the longitudinal metacentre is exceptionally great
in proportion to the length. It need only be added that as ships
lighten, the heights of their longitudinal raetacentres usually
increase considerably, and for merchant ships where the variations
in draught are considerable, it is often found useful to construct
" metacentric diagrams," for the loci of longitudinal metacentres
resembling in character those described for transverse meta-
centres on page 91. Fur war-ships the changes from load to
light draught are less considerable, and it is not customary to
construct these longitudinal metacentric diagrams.
Damage to the skin of a ship, and the consequent admission of
water to the interior, usually affects the longitudinal as well as
the transverse stability ; and the general remarks made on page
105, may also be applied here. It is evident, moreover, that the
greatest loss of longitudinal stability must result from the flood-
ing of compartments near the bow and stern, unless the buoyancy
of the water-line area at the tops of these compartments is pre-
served by watertight flats or platforms, as explained on page 21.
The moment of inertia, it will be remembered, consists of the sum
of the products of each element of area of the plane of flotation
by the square of its distance from the transverse axis passing
through the centre of gravity of that plane ; hence the most
distant portions of the area contribute the largest part of the
moment of inertia, and if their contributions are withdrawn that
moment is considerably diminished. As an extreme example, the
Inflexible may be again mentioned. When the unarmoured ends
are intact, the longitudinal metaeentre of that ship is 292 feet
above the centre of buoyancy ; but when the ends are " riddled "
the corresponding height is reduced to rather less than 33 feet.
A comparison of the statements made respecting the heights of
the transverse and longitudinal metacentres, will show how much
greater is the longitudinal than the transverse stability of ships.
An example may enforce the contrast. The Warrior, has a
longitudinal metacentric height of about 475 feet against a
transverse metacentric height of 4*7 feet. To incline her 10
degrees longitudinally would require a moment one hundred
times as great as would produce an equal inclination transversely.
Or, to state the contrast difl"erently, the moment which would
hold the ship to a steady heel of 10 degrees would only incline
her longitudinally about -^^ degree, equivalent to a change of
trim of 6 or 8 inches on a length of 380 feet.
I 12
NAVAL ARCHITECTURE.
CHAP. III.
In Figs. 40, 41, are given illustiations of the change of trim
produced by moving weights already on board a ship ; but, before
proceeding further, it may be well to repeat the exphmation
given in an earlier chapter of the term "change of trim." The
difference of the draughts of water forward and alt (which commonly
takes the form of excess in the draught aft) is termed the trim
w
FIG 40.
1
d.
/
A
C
/
J
\c
(l
/i 1
t
.3
(
^''
of the ship. For instance, a ship drawing 23 feet forward and
26 feet aft is said to trim 3 feet by the stern. Suppose her
trim to be altered, so that she draws 24 feet forward and 25
feet aft, the " change of trim " would be 2 feet, because she would
then trim only one foot by the stern. In short, " change of
trim" expresses the sum of the increase in draught at one end
and decreasa in draught at the other ; so that, if the vessel be
inclined longitudinally through an angle a, and L be her length.
Change of trim = L x tan a.
Suppose the height of the longitudinal metacentre above the
centre of gravity to be GM, as in Fig. 41, then, when the weight
w is shifted longitudinally along the deck from A to C through
a distance d, we shall have, by similar reasoning to that given
in the case of the inclining experiment, the centre of gravity
moving parallel to the deck, and
Shift of centre of gravity (GGi) = — ^
d
CHAP. III. STATICAL STABILITY OF SHIPS. I 13
also
GGi = GM tau a = ~^-- \ wlience tan a =
U D X GM
and from the above expression,
Change of trim = L x tan a = ' x
Change of trim = — ^^^,_ — x -y^^ = '186 foot = 1\ inches.
D " GM-
Take the case of the Warrior, for which, at a draught of 25^
feet, length = L = 380 feet ; metacentric height = GM = 475
feet ; displacement = 8625 tons. Suppose a weight {w) of 20
tons to be shifted longitudinally 100 feet,
20 X 100 380
8625 ^ 475
It is usual to obtain for a ship the value of the "moment
to change the trim one inch," when floating at the load-
draught ; and then for changes of trim up to 2 or 3 feet no
great error is involved in assuming that for a change of trim
of any number of inches the moment required will equal that
number of times the moment which will change the trim one
inch. Substituting in the equation.
Change of trim = ^^^^— X ^^,
one inch as change of trim (i.e. ^ foot), we have,
1 w.d ^ L 1 , D , GM
r2= -D- ^ GFr ^^^^^^ ^'^^ 12^^^
Here wd = moment to change trim one inch. In war-ships of
ordinary proportions, as explained on page 110, the height, GM,
approaches to equality with the length, L, and the following-
rule holds with a fair degree of approximation : — " The moment
" to change the trim of a war-ship one inch — that is, the product
" of the weight moved by the longitudinal distance it is shifted
" — will very nearly equal (in foot-tons) one-twelfth of the
" ship's displacement (in tons)." In long fine vessels like the
Warrior, this rule will give results rather below the truth,
because GM is greater than L, whereas in short full ships its
results will be rather in excess, because GM is less than L.
In the Warrior, for example, where the metacentric height is
proportionately great, ji^ x D = 718 ; whereas the moment to
change trim one inch is S98 foot-tons. In the Hotspur, on the
contrary, ^^ X D = 331 ; \\ hereas the moment to change trim is
300 foot-tons, the metacentric height in this case being 211 feet,
and the length 235 feet. In sea-going merchant ships the
I
114
NAVAL ARCHITECTURE.
CHAP. III.
moment to change trim one inch would probably be 30 to 40
per cent, in excess of the approximate rule ; and clearly that rule
does not apply to shallow-draught vessels or special types.
The conditions are rather more complicated when weights are
to be added to a ship, being placed with their centre of gravity
in a certain known position, and it is required to determine
the resultant draughts of water at the bow and stern. A good
approximation may, however, be made as follows, supposing
that the weights added are small when compared with the total
weight of the ship — a supposition which will be fair in most
cases. First, suppose the weights to be placed on board directly
over the centre of gravity of the load-line section of the ship ;
then the vessel will sink bodily without change of trim, until she
reaches a draught giving an addition to the displacement equal
to the weights added. This can be estimated by the method of
tons per inch immersion previously explained. The centre of
gravity of the load-line section, or plane of flotation, usually
lies a few feet abaft the middle of the length of the ship at the
water-line, say, from one-thirtietli to one-fiftieth of the length
abaft the middle. Having supposed the weights concentrated
over this point, the next step is to distribute them, moving
each to its desired position ; each weight is multiplied by the
distance it would have to be moved either forward or aft, and
the respective sums of the products forward and aft being
obtained, their difference is ascertained, this difference consti-
tuting the "moment to change trim." The final step is to esti-
mate the resultant change of trim due to this moment by the
metacentric method previously explained. For example, take
the Warrior, and suppose the following weights to be placed on
board : —
Distance from
Weight.
Centre of Gravity
of Plane of Flotation.
Products.
Tons.
Feet.
Before.
Abaft.
10
140s
1400
, ,
30
20
120
40
Before .
8600
800
••
40
5
\ 200
GO
8
, ,
480
50
25
60
100
Abaft .
••
3000
2500
15
120J
^
1800
250
6000
7780
INIumen
6000
t to change
trim (by
the stern) .
. 1780
CHAP. III. STATICAL STABILITY OF SHIPS. II5
Moment to cbange trim one inch (say) = 890 foot-tons ;
1780
. • . Change of trim = ^^— - = 2 inches ;
Increase in mean ) Weights added __ 250 _ p • i
drauglit . . j Tons per inch 41
If the original draught of water was 25 feet forward, and 26
feet aft, mean 25^ feet, the altered mean draught will be 26
feet, and the corresponding drauglit forward will be about 25
feet 5 inches and aft 26 feet 7 inches.*
A vessel partially water-borne and partly aground loses sta-
bility as compared with her condition when aHoat. One of the
commonest illustrations of this fact is found in the case of boats
run bow-on to a shelving beach ; and instances are on record where
vessels in dock have fallen over on their sides in consequence of a
similar loss of stability,! when just taking or leaving the blocks, and
not supported by side-shores, while the water was being admitted
to or pumped out of the docks. For our present purpose it will
suffice to indicate in general terms the conditions influencing the
loss of stability. When afloat, the ship is wholly supported by
the buoyancy due to the water she displaces; when her keel
touches the blocks or ground, she is partly supported by the
upward pressure at that point, the remainder of her weight being
supported by the water then displaced, which is by supposition
less than the total displacement due to her weight. Having
given the height to which the water rises on the ship at any
instant, it is easy to estimate the corresponding buoyancy ; then
the difference between it and the weight of the ship measures the
pressure at the point of contact, and corresponds to the buoy-
ancy contributed by the volume of the ship lying between her
load-line when afloat and the actual water-line at the time she
is partly water-borne. What has really been done, therefore
*
To be exact, the alterations in the time by Mr. Barnes (now Surveyor
draught forward and aft should be of Dockyards at the Admiralty), and he
proportioned to the distances of the has since contributed an article on the
centreof gravity of the water-line plane same subject to the Annual of the
from bow and stern. Boyal School of Naval Architecture
t A well-known case is that of her (see page 85 of No. 4). To this
Majesty's troopship Perset^era?zce,which article, readers desirous of fully under-
fell over on her side when being un- standing the mathematical treatment
docked at Woolwich smie years ago. of the case may turn with advantage.
The matter was fully investigated at
Il6 NAVAL ARCHITECTURE. chap. iii.
is to transfer the buoyancy of this zone (acting through the
centre of gravity of the zom^) down to the point of contact of
the keel with the ground. And when the vessel is inclined
through a small angle from the upriglit, this pressure actually
tends to upset her, whereas the buoyancy it has replaced would
usually tend to right her. Hence the decreased stability.
It is possible to obtain a ready rule for estimating the loss.
Suppose —
P = pressure of end of keel on ground ;
li = height of centre of gravity of the aforesaid zone above the
point of contact of the keel and ground ;
W = total weight of ship.
Then a simple mathematical investigation shows that —
Loss of metacentric height (GM) due to partial "l _ P7i
grounding (approximately) J ~ W*
Take as an example the case of the Perseverance for which
P = 51 tons ; W = 1303 tons ; A = 13 feet,
51 X 13
* • . Loss of metacentric height = ,^ ^ = 6 inches (about).
^ 13u3 ^ ^
Vessels having a very considerable normal trim by the stern
are most liable to this kind of accident, and the upsetting
tendency due to the pressure reaches its maximum when the vessel
is about to take the ground along the whole length of the keel.
The practical method of guarding against such accidents of
course consists in carefully shoring, using mast-head tackles, or
otherwise supporting the vessel externally, in order to prevent
her from upsetting.
Up to this point attention has been directed exclusively to the
stability of ships inclined to angles lying within the limits to
which the metacentric method applies. For longitudinal in-
clinations, except in very special cases, nothing farther is
required ; but for transverse inclinations it is necessary to ascer-
tain the statical stability at greater angles, and to determine the
inclination at which the ship becomes unstable. The general
principles previously laid down for determining the moment of
the couple formed by the weight and buoyancy apply to all angles
of inclination ; and it is consequently only necessary to fix for
any angle the vertical line, passing through the centre of
buoyancy, along which the resultant upward pressure of the water
CHAP. III.
STATICAL STABILITY OF SHIPS.
117
acts. This is done by calculation from the drawings of a ship,
and involves considerable labour ; but the principle upon which
it is based may be simply explained. Fig. 42 shows the cross-
section of a ship which, when upright, floated at the water-line
WiLj, having the volume of displacement indicated by WiXLi,
and the centre of buoyancy B^. When inclined as in the diagram,
WL is the water-line, WXL the volume of displacement, and B
the corresponding centre of buoyancy. Since the displacement
remains constant, the volumes WXL and WiXLi are equal, and
they have the common part AYSLiXAY. Deducting this common
part, the remainder (AYiSW) of the volume "\YiXLi must
equal the remainder (LSLj) of the volume ^YXL ; or, as it is
FIG 42.
usually stated, the iveclge of immersion LSLi must equal the
loedge of emersion WiS\Y. In other words, the inclination of
the vessel has produced a change in the form of the displacement
equivalent to a transfer of the wedge WSWi to the equal, but
differently shaped, wedge LSLi. This is obviously a parallel
case to that of the lever explained on page 99. In Fig. 42, let
^1 be the centre of gravity of the wedge of emersion, g^ that of
the wedge of immersion, and v the volume of either wedge ; then
what has been done is equivalent to a transfer of this volume v to
the immer.*ed side, into the position having g., for its centre of
gravity. The moment due to this shift = v X g^g-^ ', and its con-
sequence is a motion of the centie of gravity of the total volume
ii8
NAVAL ARCHITECTURE.
CHAP. III.
of di^splacement V from the original position, B„ to the new one,
B, the line BjB being parallel to g/jo, and the length
BB, = I X g,g.,.
It thus becomes obvious that, when the positions of the centres
of gravity of the wedges {g^ and g.^ for any inclination are
known, the new position of the centre of buoyancy (B) can be
determined with reference to its known position (Bj) when the
ship is upright. And this is virtually the process adopted
in the calculation.* If B,K be drawn perpendicular to BM, Fig.
42, and gjh, g-^ro perpendicular to WL,then, by the same principle
as is used above, the length B^E = =y- X hJh'
Also, if the angle of inclination WSW^ be called a,
GZ = BiE - B,G sin a,
and, consequently,
Moment of statical stability = V x GZ = V(BiK - B^G sin a)
= V X lijio — V X B^G sin a.
This expression for the righting moment (in terms of the volume
of displacement) is known as " Atwood's formula," and is commonly
employed in constructing " curves of stability."
FIG. 43.
6&> 80° /00° IZO°
Angles of inclination.
X
Fig. 43 shows the method of construction for such a curve. On
the base-line OPX degrees of inclination are set off on a
certain scale, 0 corresponding to the upright ; the ordinate of the
curve drawn perpendicular to the base-line at any point measures,
on a certain scale, the " arm of the righting couple " (GZ) for
the corresponding angle of inclination. Thus, OP represents an
* For details of the method of calcu-
lalion, see aPaper contributed hyMr.W.
John and the Author to the Transac-
tions of the Institution of Naval Archi-
tects for 1871.
CHAP. III. STATICAL STABILITY OF SHIPS. I I9
inclination of 50 degrees, and the corresponding ordinate PN
represents the length of the arm of the couple formed by the
weiglit and buoyancy at that inclination. By calcalation, suc-
cessive values of GZ are found for inclinations differing by
an interval of 8 or 10 degrees ; and the curve is drawn through
the tops of the ordinates thus found. Measurement of the
ordinates renders any calculation unnecessary for inclinations
other than those made use of in drawing the curve. It will be
observed that, starting from the upright position the stability
gradually increases, reaches a maximum value, and then decreases,
finally reaching a zero value (where the curve crosses the base-
line) at the inclination where the ship becomes unstable. The
preceding explanation of the causes governing the position of
the centre of buoyancy will furnish the reason for this gradual
increase and after decrease in the stability. The length (OX)
measuring the inclination at which the ship becomes unstable
determines what is known as the range of stability for the ship,
and this is an important element of safety.
One of the simplest illustrations of a curve of stability is that
for the cigar-ship shown in section by Figs. 32, 33, page 96.
In such vessels, as previously explained, for any angle, o, GZ
= GM sin o, and the curve of stability is constructed by simply
setting up, at any point on the base-line, a length repre>enting
the sine of the angle of inclination corresponding to that point.
Fig. 43 shows this curve. The range is 180 degrees; the
maximum stability is reached at 90 degrees, and the curve is
symmetrical about its middle ordinate. Variations in the values
of the metacentric height (GM) aifect all the ordinates of the
curve in the same proportion.
Ship-shaped forms are less easy to deal with ; but a brief
explanation of the causes chiefly influencing the form and range
of curves of stability in ships will be of value. These causes may
be grouped under the following heads : — (1) Freeboard ; (2)
beam ; (3) the vertical position of the centre of gravity ; (4) the
vertical position of the centre of buoyancy when the ship floats
upright. Both freeboard and beam are of course relative
measures, and should be compared with the draught of water.
With freeboard, moreover, must be associated the idea of " reserve
of buoyancy " (see page 9). The vertical position of the centre of
gravity must be compared with the total depth <'f the ship (ex-
cluding projecting keel), and so must that of the centre of
buoyancy. It is also necessary to note the relation between the
mean draught and the depth of the centre of buoyancy below the
r 20
NAVAL ARCHITECTURE.
CHAP. III.
water-line, as that relation indicates roughly the fulness or fine-
ness of form in tlie under-water portion of the ship. Before
giving any illustrations of curves of stability for actual ships,
a few simple examples may be taken from bux-shaped vessels
in order to show the relative influence of the above-mentioned
features. The following cross-sections will serve the purpose : —
Dimensions.
No. 1.
No. 2.
No. 3.
Feet.
Feet.
Feet.
Beam ....
501
50i
57 „t
Draught .
.
21
21
21
Freeboard .
6i
13.1
6J
Metacentric height
(GM)
2-6
2-6
5
Taking No. 1 as a standard for comparison, its curve of stability
is shown by A in Fig. 44. The effect of adding 7 feet to the
freeboard — supposing the centre of gravity to be unchanged in
position — is seen by comparing the curve of stability B for No. 2
with the curve A.
FIG. 44.
20 30 40 50 60 70
Angles of Jnclijiation-
80
90
Similarly, the effect of adding 7 feet to the beam is seen
by comparing the curve of stability C for No. 3 with the other
two curves. Only a few further words of explanation will be
necessary.
At an inclination of 14^ degrees, the " deck-edge," or angle,
of No. 1 will be immersed; for No. 2 the corresponding inclination
is nearly doubly as great, viz. 27^ degrees. Fig. 45 shows No. 2
with its deck-edge " awash." Fig. 46 shows No. 1 at the same
inclination, with a considerable portion of its deck immersed.
Up to the inclination, wlien the deck-edge of either vessel is just
CHAP. III.
STATICAL STABILITY OF SHIPS.
121
immersed, the centre of buoyancy B moves steadily outward in
relation to the centre of gravity as the inclination increases, in
consequence of the gradual increase in the volume of the wedges
of immersion and emersion, and in the distance g^g^ between their
centres of gravity. But after the deck goes under water, this out-
ward motion of the centre of buoyancy relatively to the centre of
gravity becomes slower, or is replaced by a motion of return, in
consequence of the decrease in the distance g^g.^ between the
centres of gravity and the less rapid growth of the volumes of
FIG 45.
FIG 46.
the wedges. The increase in value of the term BiG sin a in the
formula,
V X GZ = f X A,7i, - V . BiG sin a,
also tends to diminish GZ as tl»e inclination increases. The
greater the angle of inclination corresponding to the immersion
of the deck-edge — in other words, the higher the ratio of free-
board to breadth — the greater will be the inclination at which
tlie statical stability reaches its maximum value. Up to 14^
degrees, the curves A and B in Fig. 44 are identical ; but then
B continues to rise rapidly, not reaching its maximum until
45 degrees, whereas A reaches its maximum at 20 degrees. The
low-freeboard box, moreover, has a range of less than 40 degrees,
whereas the high-freeboard box (No. 2) has a range of 84 degrees.
Turning to No. 3 section, and the curve of stability C, it will
be noticed that the increase of 7 feet in beam causes a consider-
able increase in the metacentric height (GM). For moderate
inclinations, GZ = GM sin a, and therefore this increase in GM
is accompanied by a corresponding increase in the steepness of
the earlier part of the curve of stability C, as compared with the
curves A and B in Fig. 44. The deck-edge becomes immersed,
however, at 13 degrees, the maximum stability is reached at 20
degrees, and the range of stability is less than 50 degrees as
122 NAVAL ARCHITECTURE. chap. iii.
against 84 degrees in curve B for the higher freeboard vessel,*
The comparison of these curves will show how much more in-
fluential increase of freeboard is than increase of beam in adding
to the amount and range of the statical stability of ships.
Lastly, to illustrate the effect of the vertical position of the
centre of gravity upon the forms of curves of stability, let it be
assumed that the high-freeboard vessel (No. 2 section) has its
centre of gravity raised one foot, leaving the value of the meta-
centric height (GM) 16 foot. This will be no unfair assump-
tion, seeing that the increase in freeboard, and consequently in
total depth, would in practice be associated with a rise in the
centre of gravity. The curve of stability D, Fig. 44, corresponrls
to this last case. For each inclination the decrease in the arm of
the righting coujjle, as comj)ared with curve B, is given by the
expression,
. Decrease in GZ = GGi x sin a,
There GG^ (rise in position of centre of gravity) is one foot.
Initially the curve D falls within A and B, the vessel beings
more crank. It has, however, its maximum ordinate at 45
degrees, and a range of 75 degrees, comparing very favourably
indeed with the curve C for the low-freeboard vessel with broad
beam (No. 3). The reader will have no difficulty in making a
more detailed comparison of the curves for these representative
vessels, should that be considered desirable.
Turning from these simple prismatic forms to actual ships, it
will be interesting to notice how the curves of stability for
different classes of ships illustrate the varying influence of beam,
freeboard, vertical position of the centre of gravity, &c. The
earliest curves of stability on record were constructed at the
Admiralty in 1867, prior to which date there appears to have
been no exact determination of the stability of ships at large
angles of inclination when their upper decks were partially under
water, or of their ranges of st-^bility. So long as ships of high
freeboard were employed exclusively this limitation of inquiry as
to variation in statical stability was natural enough ; but when
low-freeboard vessels came into use the necessity arose for more
extended calculations, in order to determine the angles of incli-
nation, at which the vessels became unstable. Since 1870 the
* A full discussion of this subject Barnaby, C.B., Director of Naval Con-
will be found in a Paper contributed to struction. Some of the preceding
vol. sii. of the Transactions of the illustrations are borrowed from this
Institution of Naval Architects by Mr. paper.
CHAP. III.
STATICAL STABILITY OF SHIPS.
123
practice of constructing curves of stability for each class of vessel
in the Royal Navy has been established ; and has been imitated
in foreio-n navies. IMore recently similar curves have been con-
structed for yachts and for various classes of merchant ships. A
large amount of valuable data has thus been accumulated already,
and important additions are continually being made thereto.
The first set of illustrations of curves of stability, contained in
Fig. 47, is limited to representative types of war-steamers, and to
FIC.4-7.
10
20
30 40 50 60 70
Angles of' IncLi-natioru
1. Juno.
2. Inconstant.
3. Endymion.
4. Serapis.
5. Invincible,
6. Achilles.
7. Miantonomoh.
8. Monarch.
9. Devastation.
10. Captain.
11. Glatton.
their fully-laden condition. In all cases the centres of gravity
have been ascertained by experiment ; and the distribution of
the weights is accurately known. Those weights are supposed to
be secured in such a manner that no shift takes place even at the
most extreme inclinations. This may be considered an improper
supposition, especially in cases where stability is maintained
beyond the inclination of 90 degrees from the upright ; but it is
to be observed that such extreme inclinations are not likely to
be reached, whereas for less inclinations the supposition affects
all classes similarly. Further, it is assumed in making the cal-
culations that througliout the inclinations no water enters the
interior through ports, scuttles, hawse-pipes and other openings
in the sides ; or througli hatchways, ladder-ways, and other
openings in the decks. This assumption is fair enough as regards
most of the openings, which are furnished with watertight covers,
plugs, &c. ; and as regards some of the hatchways which are
124
NAVAL ARCHITECTURE.
CHAP. III.
usually kept oi^en even in a seaway it is only necessary to re-
mark that they might be battened down on an emergency, while
their situation near the middle line of the deck prevents the
water from reac^hing them except at very large angles of incli-
nation. It is not usual to include erections above the upper
decks of war-ships in mnking calculations for curves of stability
unless they are thoroughly closed in and made watertight. For
example, deck-houses, open-ended forecastles and poops, &c., are
not included ; but closed batteries, breastworks, forecastles and
poops are reckoned in the contributories to stability. These par-
tially watertight erections no doubt aid the ships in recovering
from extreme lurches, &c., which put them under water only for
very short periods, so that their omission from the calculation is
on the side of safety. The following table gives the principal
dimensions, &c., of these representative war-steamshii^s : —
Height of
Upper
Name.
Class of Ship.
Length.
Breadth
Extreme.
Mean
Draught.
Deck
Amidships
Displace-
ment.
above
"\\'ater.
Unarmoured.
Feet.
Feet
Ins.
Feet
ins.
Feet ins.
Tons.
Endymion .
Old type steam frigate .
240
47
10
20
6
14 8
3300
Juno .
Covered- deck corvette .
200
40
0
17
4
14 6
2215
Inconstant
Swift cruising frigate
337
50
3§
23
lOi
15 31
5782
Serapis .
Indian trooi^ship
Armoured.
360
49
0
19
5
15 O"
5976
Glatton . .
Breastwork monitor .
245
54
0
18
9
3 0
4912
Miantonomoh
American monitor .
250
52
10
14
0
3 0
3842
Captain (late)
Low-freeboard , , (
High-freeboard ,^.'''^'^-
Mastless j ^^"P^- (
320
53
3
25
OJ
6 6
7790
Monarch .
330
57
6
24
U
14 0
8215
Devastation .
285
62
3
26
l|
11 3*
90«;i
Achilles .
Karly type ) broadside If
L^ter type / ships \
380
58
31
26
5
15 0
9484
Invincible
280
54
0
22
6
16 0
6060
* Only 4J feet aft.
In Fig. 47 the respective curves of stability for these
vessels appear with reference numbers, enabling them to be dis-
tinguished ; and they will repay a careful study, as illustrations
of the comjmrative stabilities of high- and low-sided vessels,
armoured and unarmoured. It will be remarked that the ordi-
nates of the curves have to be multiplied by the respective dis-
placements of the ships in order to obtain the righting moments.
As ships of war lighten by the consumption of coals, provisions,
stores, &c., their curves of stability usually lose in area and
range. This is due to the fact that the rise in the vertical posi-
tion of the centre of gravity as the ships lighten usually
CHAP. III.
STATICAL STABILITY OF SHIPS.
125
produces a greater effect in reducing the stability, than the
increase in freeboard produces in the contrary sense. Any sujh
decrease in stability can be prevented in ships fitted to carry
water ballast as all armoured ships are ; but as a rule there is no
necessity to use water ballast even in the extreme light condition.
There are, moreover, exceptions to the rule just stated: some
types having little, if any, less stability in the light condition
than they have when fully laden. As an example, reference may
be made to the two curves for the Lijlexihle in Fig. 47a. The
FIG 47a
Refere7ices.
1. Load condition, ends intact. 3. Load condition, ends riddled.
2. Light
4. Light
curve (1) shows the ship fully laden, and the curve (2) indicates
her condition when 1500 tons of coals and consumable stores
have been removed. This diagram also illustrates the influence
which damage to the shin of a ship and the consequent entry of
water into the hold may have upon the form and range of her
curve of stability. The curves 3 and 4 show the conditions of
statical stability of the Inflexible wlien the unarmoured ends are
completely riddled. Tiiis extensive damage would cause the ship
to sink more than 2 feet below her ordinary load-line, reducing
her freeboard by an equal amount, and lessening her stability
very greatly. The tabular statement on the following page will
supplement the information given in the diagram.*
This is an extreme illustration of the loss of stability due to
damage to the skin of a ship; but similar considerations hold
good in all ships, and the extent to which their stability may be
deci-eased by collision or other accident can be readily estimated
when the extent of the damage is known. Without any actual
damage to the skin of a ship water may find its way into the
* For a full discussion of the sta- Committee of 1878 {Parliamentary
bility of this ship see the Report of the Puiier).
126
NAVAL ARCHITECTURE.
CHAP. III.
interior through open ports or scuttles in the sides, or open
hatchways in the decks, the result being a more or less serious
decrease in stability. Such occurrences are clearly exceptional,
but they have happened in ships caught by squalls of wind in com-
a
IT.
N*
Condition of
Inflexible
(see Fig. 47a).
be
»
Sh
Q
s
a>
J
to
5
a .
Angle of
Maximum
Stability.
1^
'2. ^
Metacentr
Height (G
1. Fully laden, ends)
intact /
Feet. Ins.
24 7
Tons.
11,500
14°
31° -2
Feet.
3-28
74° -3
Feet.
8^25
2. Light condition,"!
ends intact j
21 10
10,000
18°
31 -7
3-98
71 -5
8-5
3. Fully laden, ends\
riddled /
26 8i
11,500
ir
13 -5
•57
30 -0
2^0
4. Light condition,!
ends riddled J
23 9
10,000
15°
20 -8
•79
36 •S
2^22
paratively smooth water. The Eurydice is an example. Fig. 47c,
page 128, sliows two curves of stability for that ill-fated vessel.
The first, marked 3, is the curve for her fully-laden condition with
all ports closed, and openings in sides and decks made watertight :
Curves of stability for merchant steamers.
Note. — The dimensions, &c., of these vessels appear in the Table on page 127
under the respective reference numbers marked on the curves.
the second, marked 4, is the curve corresponding to her condition
when she was capsized, the ports having been open, and the water
having entered through them. In curve 3, the freeboard (to the
upper deck) was betueeu 11 and 12 feet; whereas in curve 4 the
freeboard was viitually reduced to 4 feet. Having regard to the
CHAP. III.
STATICAL STABILITY OF SHIPS.
127
explanations given on page 120, as to the influence of freeboard on
range of stability, the reduction of range and area of the curve of
stability from 3 to 4 in Fig. 47c will be fully un lerstood.
Turning from war-ships to merchant ships, it is not possible to
give similarly full and exact information respecting their curves
of stability. The principal reasons for this difference have been
stated on page 80. In Fig. 47& there are given, however, the curves
for a considerable number of representative merchant steamships,
Particulars of the Vessels whose Curves of Stability are given in
Fig. \lh.
Height
9, A
of upper
a >
Ex-
Meta-
deck
Dis-
2S
■SO
Class of Ship.
Length.
/
treme
breadth.
Ifeaii
draught.
centric
height.
amid-
ships
place-
ment.
«^
above
water.
Ft. ins.
Ft. ins.
Ft. ins.
Feet.
Ft. ins.
Tons.
1
Long, swift steamer, miscella-\
neous cargo J
390-0
39-0
23-0
2-0
8-6
6400
2
(Steamer of moderate speed, mis-">
\ cellaneoiis cargo . . . . /
320-0
34-0
18-3
2-0
8-5
3560
3
(Steamer of moderate speed, ho-l
\ mogeneous cargo . . . ./
264-0
32-0
18-9*
11
5-2
3220
4
(Same vessel, but in light con-i
\ ditiou j
? J
' 1
8-11
1-5
15 -Oi
1240
5
f Steamer, large carrying power, 1
\ Lomogeneous cargo . . ./
320-0
40-0
23-6
0-4
6-li
6380
6
(Same vessel, 300 tons less cargo,1
\ and 300 tons water ballast ./, "
12
? 5
» 1
7
Same vessel, ligbt condition .
5 J
9 1
9-7
3-0
21-Oi
2110
8
(Passenger steamer, miscclla-)
\ neous cargo /
812-6
33-4
16-3
2-0
9-8
2870
9
(Same vessel, assumed initially'l
\ unstable /
9 )
^ 9
) )
-0-5
> 3
) )
10
Steamer, grain cargo
245-0
33-4
19-0
0-7
4-0
3G00
n
Steamer, cargo of iron .
285-0
35 4
18-0
3-5
6-6
3S00
12
Steamer, grain cargo
245-0
32-4
10-0
0-8
8-0
3100
13
Despatch vessel (Lv's) .
300-0
46-0
19-9
3-7
8-7:^
3735
laden to certain assumed load-lines, which are approximately those
at which the ships would be worked. The nature of the stowage
assumed in each case is explained in the tabular statement above,
and the principal dimensions, &c., of the vessels are also recorded
therein.*
* For a few of these examples of
curves of stability the author is in-
debted to Mr. Martell's Paper on
" Causes of Unseaworthiness " {Tram-
actions of the Institution of Naval
Architects for 1880). The remainder
have been obtained by direct calcula-
tions for ships bought into the Royal
Navy, and by calculations made by the
Author's pupils at the Royal Naval Col-
lege. For fuller details of certain of the
last mentioned calculations see a Paper
by thcAuthorinTransac^t'oHS of the In-
stitution of Naval Architects for 1881.
128
NAVAL ARCHITECTURE.
CHAP. III.
To the foregoing illustrations of curves of stability for steam-
ships may be added a few for sailing ships of various classes.
Fig. 47c contains these additional curves, and in the accompany-
ing tabular statement the principal dimensions, &c., of the vessels
appear. They include a few examples of the now obsolete sailing
ships of the Royal Navy, others of existing sailing ships of the
mercantile marine, and others of typical yachts.* In nearly all
3FP
FIG47<?
- J^ -
e
— — ^
^2 Ft /5
^/^^
*
^
\^
\
£;
^
^
^-^^
\
o
t=— 3-
r^^::N^
\
6^
•-3
"—IFh
^
><
^
^^
^
fe
^
ri
I*
^
id-
20
30°
40
SO
CO
SO
.90"
Curves of Stability for Sailing Vessels.
Note. — The dimensions, &c., of these vessels appear in the table on page 129,
under the respective reference numbers marked on the curves.
cases the fully-laden condition is taken. For the yachts and war-
shijDS the stowage is accurately known, so that the curves strictly
correspond to the actual condition of the vessels in their sea-going
trim. For the merchant ships a stowage has necessarily been
assumed, which is thought to be fairly representative of the ordinary
condition. It is probable, however, that in some cases these
merchant ships are stowed so that they have greater stability
than is indicated on the diagram, and in other cases less
stability. To illustrate these possible variations, the curves 6
and 7, or 8 and 9 may be taken. In curve 6 the centre of gravity
is supposed to be 1"7 feet lower than in curve 7 ; and in the
second example the centre of gravity for curve 8 is 1 foot lower
* For the facts as to sailing yachts
the author is indebted to the valu-
able researches of Mr. Dixon Kemp;
for those relating to the Sunbeam he
has to thank Sir Thomas Brassey :
most of those as to merchant sailing
ships are taken from the Reirort of the
Atalanta Committee, to whom they
were presented by Mr. W. John. The
curves 6 and 7 were calculated by the
Author's pupils at the Royal Naval
College for the ship built by Messrs.
A. & J. Inglis, of which the metacentric
diagram appears in Fig. 30t?.
CHAP. III.
STATICAL STABILITY OF SHIPS.
129
tlian for curve 9, The draught of water is the same iu curves 6
and 7, or in curves 8 and 9 ; and the differences in stability arise
entirely from variations in the vertical position of the centre of
gravity, as explained on page 122.
Particclaes of the Vessels whose Curves of Stability are given in
Fig. 47c.
Height
%t
of upper
s^
Ex-
Mean
draught.
Meta-
deck
Dis-
t. 3
Class of Ship.
Length.
treme
centric
amid-
place-
"-3
breadth.
Height.
ships
ment.
25 +*
above
water.
Ft. ins.
Ft. ins.
Ft. ins.
Feet.
Ft. ins.
Tons.
1
Sailing frigate, load condition .
i;si-o
40-7
17-4
6-2
10-9
1055
2
Sailing frigate, light condition.
9 »
; y
160
41
12-1
887
3
fSailing frigate, load condition,"!
\ ports shut j
141-0
38-8
16-7
4-5
10-6
1075
4
fSailing frigate, load condition,i
\ ports open j
? S
? ?
5 )
y i
5 5
9 9
5
Sailing brig, load condition
100-6
32-4
14-01
5-9
4-3i
483
6
Sailing merchantman .
222-0
35-4
16-9
30
5-3
2030
7
^Sailing merchantman, homo-'l
\ geneous cargo, and no ballast/
1-3
> 5
) 5
9 9
5 ?
9 9
8
Sailing merchantman .
273-0
43-1
19-10
3-5
5-8
3980
9
Sailing merchantman .
2-5
10
Small sailing merchantman
148*0
26-9
' >
3-5
3 9
9 9
787
11
Yacht
81-3
20-6
9-5
4-0
2-11
128
12
Yacht
85-9
19-3
101
3-7
31
150
13
Yacht
100-0
16-7
9-4
3-3
3-10
158
14
("Yacht (with auxiliary steam"!
\ power) Sunbeam . . . . /
154-9
27-1
13-0
3-45
4-4
576
In this connection it may be interesting to revert to the case of
a ship which is unstable when upright, but yet has a considerable
range of stability. Curve 9 in Fig. 475. will ilkistrate this case.
\Yhen the vessel is upright, the metacentre is '5 feet helow the
centre of gravity. Initially the curve of stability falls below the
base-line, and this is a graphic representation of instability. At
an inclination of 20 degrees the curve crosses the load-line, and
thence onward, the vessel has a positive righting moment until, at
80 degrees, she once more becomes unstable. The position (20
degrees) at which the curve crosses the base-line, is one of stable
equilibrium : the upright position and that where she is inclined
80 degrees cori-espond to unstable equilibrium. It is a general law
under the conditions assumed in calculating curves of stability
that positions of stable and unstable equilibrium occur alternately.
The position of 20 degrees is that to which the vessel would
" loll " over from the upright in still water ; and if moved slightly
from this position, either to greater or less angles of heel, she
K
1 30 NA VAL ARCHITECTURE. chap. hi.
■would return to it as her position of rest. This condition may
be reached either by altering the vertical distribution of weights
in a ship so as to bring the centre of gravity above the meta-
centre, or by affecting the metacentre so as to bring it below the
centre of gravity. The former case is more common, especially for
merchant ships when floating light : the latter case may occur
when ships are damaged by collision or in action, and water
enters the interior.
In concluding these remarks on curves of stability brief
reference may be made to a method of procedure that appears
well-suited for dealing with the changing stowage of merchant
ships. The designer commonly accepts a maximum load-draught
on which a certain dead weioht is to be carried. Although on
actual service this load-line may be departed from very frequeutl}^,
it may be used for purposes of calculation. Assuming the ship
to be floating at this line and to have her cargo-spaces filled with
homogeneous cargo, it is possible (as explained on page 95) to
approximate to the vertical position of the centre of gravity, and
to the value of the metacentric height. With these data a curve
of stability may be constructed, and it will represent a condition
of stowage less favourable to the vessel than any likely to occur
in practice ; while a very easy process enables one to pass from
this curve to that corresponding to any other stowage of the
same total dead weight. The case where both stowage and
draught vary can also be dealt with readily by the naval
architect. Yeiy frequently, as we have seen, merchant ships have
stability even on the beam-ends — 90 degrees of inclination to the
upright. Consequently, if it is desired to avoid the labour of
calculating a complete curve of stability for them, a simple
calculation may be made for this extreme position ; and if the
vessels then have righting moment or only a very small amount
of instability, no further inquiry need be made. A sufficient
amount of stiffness when upright, combined with such a range of
stability as would thus be indicated, cannot fail to be satisfactory.
The much greater range of stability frequently possessed by
merchant ships as compared with war-ships, and especially with
some classes of armoured ships, is chiefly due to the very
different vertical distribution of the weiohts. In the merchant
ships the great weights of cargo, &c., are carried low down in the
holds; and the centres of gravity consequently lie low in
proportion to the total depth. In war-ships, on the contrary,
although the weights of machinery, coals, ammunition, and
projectiles, are carried low down in the holds, heavy loads of
CHAP. III. STATICAL STABILITY OF SHIPS. 13 1
armour, armament, &c., have to be carried high np on the sides
or decks. As a consequence the centre of gravity lies higher (in
proportion to the total depth) in war-ships, and especially in
armoured ships, than it does in merchant shipfj, and this tends to
diminish the range of stability. Further the deep lading of
merchant ships brings the centre of buoyancy for the upright
position higlier in the ships than is usual in war-ships ; and this
diminishes the distance between the centre of buoyancy for the
upright position and centre of gravity, consequently tending to
lengthen the range of stability. In yachts tliese two features are
still further exaggerated, the distance between the centres of
gravity and centres of buoyancy being very small indeed, while
the centres of gravity are drawn low down by the heavy weights
of ballast fitted on the keels and floors.
K 2
i32 NAVAL ARCHITECTURE. chap. iv.
CHAPTER IV.
THE OSCILLATIONS OF SHIPS IN STILL WATER.
If a ship, floating in still water, has been inclined from a position
of stable equilibrium by the action of external forces, and is
afterwards allowed to move freely, she will perform a series of
oscillations, the range of which gradually decreases, on either
side of the position of equilibrium ; and will finally come to rest.
For all practical purposes attention may be limited to the case of
the transverse inclinations and oscillations of ships, reckoning
from the upright position where they are in stable equilibrium ;
and unless specially mentioned, it may be assumed that the
following remarks deal only with rolling motions in still water,
the other principal oscillations — viz. pitching— not taking place
to any sensible extent except in a seaway.
There is an obvious parallelism between the motion of a ship
set rolling in still water and that of a simple pendulum moving
in a resisting medium. Apart from the influence of resistance,
both ship and pendulum would continue to swing from the initial
angle of inclination on one side of the vertical to an equal
inclination on the other side; and the rate of extinction of the
oscillations in both depends upon the resistance, the magnitude
of which depends upon several causes to be mentioned hereafter.
In what follows, the term " oscillation " will be used to signify a
single swing of the ship from port to starboard, or vice versa*
The "arc of oscillation " will simply mean the sum of the angles
on either side of the vertical swept through in a single swing ;
for instance, a vessel rolling from 12 degrees inclination to port,
* In the usual matliematical sense in the text agrees with the practice of
an oscillation would mean a double the Royal Navy in recording rolling
swing, say from port to starboard and motions, and is therefore followed,
back again to port ; but the definition
CHAP. IV. OSCILLATION IN STILL WATER. 133
and reachino: 10 degrees inclination to starboard. Mould have
(10^ + 12') 22 degrees as the arc of oscillation. The i^eriod of
oscillation means the time occupied (in seconds, say) in perform-
ing a single swing.
No vessel can roll in still water without experiencing resist-
ance to her motion ; but considerable advantage results from
first considering the hypothetical case of unresisted rolling, and
afterwards adding the conditions of resistance. Eigorous mathe-
matical reasoning may be applied to the hypothetical case, but
this is not true of an investigation which takes account of the
total resistance experienced by a ship when rolling; and the
highest authorities are compelled to adopt a mixed method
when dealing with resisted rolling, superposing, as it were, data
obtained from experiments made to determine the effects of
resistance, upon the mathematical investigations of the hypo-
thetical case. No endeavour will here be made to follow out
either part of the inquiry, as such a course involves mathematical
treatment lying outside the province of this work ; but it is
possible in popular language to explain some of the chief results
obtained, and this we propose to do.
Supposing the rolling of a ship in still water to be unresisted
it may be asked. What is the length of the simple pendulum
with which her oscillations keep time, or synchronise ? It has
been sometimes assumed that the comparison made in the
previous chapter between a ship held in an inclined position
and a pendulum of which the length is equal to the distance
between the centre of gravity and the metacentre held at an
equal inclination, will remain good when the ship and the pen-
dulum are oscillating. In fact, it is supposed that the whole of
the weight may be concentrated at the centre of gravity (G, Figs.
30 and 31, page 76), while the metacentre is the point of suspension
for the ship in motion as well as for the ship at rest ; but this is
an error. If it were true, the stiffest ships, having the greatest
heights of metacentre above the centre of gravity, should be
the slowest-moving ships. All experience shows the direct
opposite to be true. For example, a converted ironclad of the
Prince Consort class, with a metacentric height exceeding 6 feet,
will make twelve or thirteen single rolls per minute, and an
American monitor, with a metacentric height of 14 feet, will
make more than twenty single rolls per minute, while vessels
like the Hercides or Sidtati, with metacentric heights under 3 feet,
will only make seven or eight rolls per minute. What is thus
shown to be true by experience had been proved nearly a century
134
NAVAL ARCHITECTURE.
CHAP. IV.
FIG 48.
and a half ago, by the great French writer Bouguer, iu his Traite
du Navire.
The necessity for carefully distinguishing
between the cases of rest and motion in
a ship may be simply illustrated by means
of a bar pendulum (such as AB, Fig. 48) of
uniform section, having its centre of gravity
at the middle point, G. To hold the pen-
dulum at any steady inclination to the
vertical must require a force exactly equal
to that required to hold at the same in-
clination a simple pendulum of length AG,
and of equal weight to the bar pendulum.
But if this simple pendulum were con-
structed, and set moving, it would be found
; to move much faster than the bar pendulum.
The simple pendulum keeping time with
the bar instead of having a length AG equal to one-half of
AB, will have a length AK equal to two-thirds of AB; and
it is important to notice the causes producing this result.*
Suppose the pendulum to have reached one extremity of its
swing, and to be on the point of returning : at that instant
it will be at rest. As it moves back towards the upright, its
velocity continually increases, reaching a maximum as the pen-
dulum passes through the upright position, and afterwards de-
creasing until at the other extremity of the swing it will once
more be instantaneously at rest. These changes of velocity,
accelerations or retardations, from instant to instant can only be
produced by the action of certain forces ; and according to the
first principles of dynamics, these changes of velocity really
measure the intensity of the forces. For instance, a body falling
freely from a position of rest acquires a velocity of rather more
than 32 feet in a second ; at the end of two seconds it has twice
as great a velocity ; and so on. This " rate of change of
velocity " — some 32 feet per second — is regarded as a measure
of the uniform accelerating force of gravity. For any other
accelerating force the corresponding measure is expressed by the
* A simple pendulum, as previously
explained, is one having all its weight
concentrated at one point (the " bob "),
and supposed to be hung from the
centre of suspension (A, Fig. 48) by a
weightless rod. The point K in Fig. 48
is termed the " centre of oscillation,"
and the bar pendulum will oscillate in
the same time, whether it is hung at
A or at K.
CHAP. IV. OSCILLATION IN STILL WATER. 1 35
ratio Avbieli the rate of change of velocity produced by gravity
bears to the change of velocity which would be produced by that
accelerating force, if its action continued uniform for one second.
For accelerating forces which are not uniform this mode of
measurement gives a varying rate of change from instant to
instant. In the case of the simple pendulum, the bob moves
in a circular arc, having a radius equal to the length of the
pendulum ; hence the linear velocity of the bob in feet per
second may be expressed in terms of the product of this radius
into the angular velocity.* Similarly, the changes in velocity,
measuring the accelerating forces, may be expressed in terms of
the product of the radius into the changes of angular velocity.
These accelerating forces at any instant act at right angles to
the corresponding position of the pendulum rod ; and so finally
we obtain for the simple pendulum : —
Moment of accelerating ^ = C X weight of the bob x (radius)"
forces about centre of [- x rate of change of angular
suspension . . .) velocity ;
where 0 is a constant quantity (viz. -^^, nearly— the reciprocal
of the velocity per second due to gravity). Hence follows this
important principle: for any heavy particle oscillating about a
fixed axis the moment of the accelerating forces at every instant
involves the product of the weight of the particle by the square
of its distance from the axis of rotation.
Turning from the simple pendulum to the bar pendulum
(Fig. 48), we may consider the latter as made up of a number of
heavy particles, and take each separately. For example, take a
particle of weight w at a distance x from the axis of rotation (A) ;
the moment of the accelerating force upon it, about the point A,
is given by the expression,
Moment = C X ty x a;^ X rate of change of angular velocity.
At any instant the change of angular velocity is the same for all
particles in the bar-pendulum, whatever may be their distance
from A ; whence it follows that for the whole of the particles
in the bar-pendulum —
Moment of accelerating ") = C x weight of bar x F x rate
forces at any instant • I of change of angular velocity.
* The angular velocity may be de- second if the rate of motion existing
fined as the angle swept through per at any instant were continued for a
second if the motion is uniform, or that second. These angles are usually stated
which would he swept through per in circular measure.
136 NAVAL ARCHITECTURE. chap. iv.
To determine F, we have only to sum up all such products as
w X 9r for every particle in the bar, and divide the sum by the
total weight of the bar. Or, using S as the sign of summation,
F =
S {u'x^)
Weiiiht of bar '
Turning to the case of a rigid body like a ship, oscillating about
a longitudinal axis which may be assumed to pass through the
centre of gravity, it is only necessary to proceed similarly. Take
the weight of each elementary part, multiply it by the square of
its distance from the axis of rotation, obtain the sum of the
products (which sum is termed the " moment of inertia "), and
divide it by the total weight of the ship ; the quotient {¥) will
be the square of the " radius of gyration " for the ship when
turning about the assumed axis. If the whole weight were con-
centrated at the distance Tc from the axis of rotation, the moment
of the accelerating forces and the moment of inertia would then
be the same as the aggregate moment of the accelerating forces
acting upon each particle of lading and structure in its proper
place.
It will be obvious from this attempt at a popuLir explanation
of established dynamical principles why we cannot assume that
a ship in motion resembles a simple pendulum suspended by the
metacentre, and having all the accelerating forces acting through
the centre of gravity. These accelerating forces developed
during motion constitute, in fact, a new feature in the problem,
not requiring consideration when there is no motion. For a
position of rest, it is only necessary to determine the sum of the
statical moments of the weight of each element about the centre
of suspension, and this sum equals the moment of the total
weight concentrated at the centre of gravity. But for motion,
there is the further necessity of considering the moment of
inertia, as well as the statical moment.
A ship rolling in still water does not oscillate about a fixed
axis, corresponding to the centre of suspension (A) of the
pendulum in Fig. 48 ; but still her motions are similar to those
of the pendulum. At the extremity of a roll, when her inclina-
tion to the upright is a maximum, the moment of statical
stability is also usually greater than that for any other angle
within the arc of oscillation, and this is an unbalanced force,
tending to restore the vessel to the upright. She therefore begins
to move back, and at each instant during her progress towards
the upright is subject to the action of a moment of statical
CHAP. IV.
OSCILLATION IN STILL WATER.
137
stability tending to make her move in the same direction, and
consequently quickening her speed. But the moment of stability
gradually decreases in amount, and at the upright is zero ; the
velocity reaching its maximum at that position. On the other
side of the upright the statical stability opposes further in-
clination, and at every instant grows in magnitude; the result
is a retardation of speed, and finally a termination of the motion
of the ship at the other end of the roll at an inclination to the
vertical equal to that from which she started. All this, be it
observed, is on the hypothesis of unresisted rolling. As a matter
of fact, with resistance in operation, it always acts as a retarding
force, tending to extinguish the oscillations.
The position of the
instantaneous axis about
which a ship is turning
at any moment, sup-
posing her motion to be
unresisted, and the dis-
placement to remain con-
stant during the motion,
may be determined by
means of a geometrical
construction due to the
late Canon Moseley. It
may be most simply ex-
plained by reference to a
cylindrical vessel with
circular cross-section such as is
F2FF3 be described concentric
touching the water surface at
FIG. 49.
shown in Fig. 49.
with the circular
If a circle
section, and
F, this circle will touch the
water-line corresponding to any other inclined position ; for all
the tangents to this circle cut off from the circular section a
segment equal in area to WVL. The circle F3F1F2 is termed
the "curve of flotation," and a right cylinder described upon
it as base Mould have this property: if the water surface is
supposed to become rigid and perfectly smooth, and the cylinder
of which F3F1F is a section, is supposed also to have a perfectly
smooth surface, and to project before and abaft the ship, carrying
her with it while the projecting ends roll upon the water surface,
the conditions for unresisted rolling will be fulfilled. To deter-
mine the instantaneous centre, it is then only necessary to consider
the simultaneous motions of the point of support, or " centre of
F, and the centre of gravity G. The point F has its
flotat
ion.
138
NAVAL ARCHITECTURE.
CHAP. IV.
instantaneous motion in a horizontal line ; consequently it must
be turning about some point in the vertical line FM. As to the
motion of the centre of gravity, it must be noticed that, resistance
being supposed non-existent, the only forces impressed upon the
floating body are the weight and buoyancy, both of which act
vertically; therefore the motion of translation of the centre of
gravity must be vertical, and instantaneously Gr must be turning
about some point in the horizontal line GZ. The point Z, where
the two lines GZ and FM intersect, will, therefore, be the instan-
taneous centre about which the vessel turns.
This simple form of vessel always has the centre of buoyancy
B, the centre of flotation F, and the metacentre M in the same
vertical line, for any position it can occupy. An ordinary ship
presents different conditions, as shown in Fig. 50 ; where the
FIQ.50.
•i^x
centre of flotation F does not lie on the vertical line BiZM^. Here,
however, the same principles apply : G moves about some centre
in the line GZO ; F about some centre in the vertical line FO ;
the point of intersection 0 of these two lines fixes the instanta-
neous axis for the whole ship.
In war-ships the centre of gravity G ordinarily lies near to the
water-line (WiLj, Fig. 50) for the upright position; while for
oscillations of 12 or 15 degrees on either side of the vertical, the
centre of flotation F does not move far away from the middle-
line A of the load-line section WiLi. In other words, the common
case for war vessels of ordinary form is that where the instantaneous
axis passes through or very near to the centre of gravity.
CHAP. IV.
OSCILLATION IN STILL WATER.
139
Although the position of the instantaneous axis changes from
instant to instant (as its name implies), it is not productive
of any serious error in most cases to regard the ship as rolling
about a fixed axis passing through the centre of gravity. In
theoretical investigations no such assumption is necessary, because
the principle known in dynamics as the "conservation of the
motions of translation and rotation " then becomes applicable.
The motion of translation of the centre of gravity is consi<!ered
separately from any motion of rotation ; this latter motion being
then supposed to take place about an axis passing through the
centre of gravity. By this means the " period " of an oscillation
in still water can be very closely approximated to, although there
is no fixed axis of rotation.
It may be interesting to show how the metacentre moves during
unresisted rolling, instead of being fixed in space, as is often
supposed. Taking once more the cylindrical vessel of circular
cross-section, we have a case where the metacentre is fixed in the
vessel, but moves in space as the vessel rolls. In Fig. 51 the
darker circle represents the vessel in her upright position ; the
lighter one shows her posi-
tion at the extremity of FIG. 51.
the roil. The centre of
gravity G- moves vertically,
as explained above, and
durinof the roll rises from
O
G to Gi, the corresponding
position of the metacentre
being Mi. As the ship
rolls therefore, the meta-
centre sways to and fro hori-
zontally; but in less sim-
ple forms it would neither
be fixed in the vessel nor
have so simple a motion.
Summing up the preceding remarks on unresisted rolling, it
appears that the active agent in producing the motion, after the
vessel has once been inclined and then set free, is the moment of
statical stability ; and that the moment of inertia about a longi-
tudinal axis passing through the centre of gravity is also of
great importance. Mathematical investigation leads to the follow-
ing expression for the period of oscillation of a ship : —
Let h = her radius of gyration (in feet),
m = metacentric height (GM) (in feet),
T = period in seconds for a single roll.
UO NAVAL ARCHITECTURE. chap. iv.
Then T = tt a/-^ = 3 • 1416 \/j^.
gni ^ gm
where g (measuring force of gravity) = 324 feet (nearly) per
second. This may be written,
T = -554a/^.
Ill
A fair approximation to the still-water, or "natural" period
of oscillation for a new ship can be made by means of this
equation. The metacentric height would be determined for a
war-ship as one of the particulars of the design ; and the distri-
bution of the weights would be known, so that the moment of
inertia could be calculated about the assumed axis of rotation
passing through the centre of gravity. This latter calculation
is very laborious, the weight of each part of the structure and
lading having to be multiplied by the square of its distance from
the axis; but with care it can be performed with a close approach
to accuracy. Calculations of this kind are rarely made, except
in connection with novel types of ships, for which thorough
investigations are needed in order to be assured of their safety
and seaworthiness. As examples of close estimates of natural
periods we may refer to the Devastation and a monitor of the
American type, which were under the consideration of the
Admiralty committee on designs for war-ships. It was estimated
that the Devastation would have a period of about 7 seconds;
the actual period obtained by experiment was 6| seconds. The
estimated period for the American monitor was 2^ seconds ; the
actual period, 2^^ seconds. The formula given for the period
supposes the rolling to be unresisted ; but the influence of resist-
ance is much more marked in the extinction of oscillations than
it is in afiecting the period of oscillation, and this accounts for
the close agreement of estimates made from the formula with the
results of experiments. This statement may be illustrated by
reference to experiments made both in this country and in
France. Mr. Froude discovered that the period of the Greyhound
remained practically the same after exceedingly deep bilge-keels
had been fitted, as it was without such keels. Similar results
were obtained with a model of the Devastation (see page 163).
MM. Eisbec and De Benaze, of the French Navy, ascertained
that the tug EJorn, which had a period of 2-18 seconds without
bilge-keels, had that period increased only to 225 seconds by
the addition of those keels. And yet in all these cases the
effect of the keels in extinguishing the oscillations was most
141
CHAP. IV. OSCILLA TION IN STILL WA TER.
marked. The Elorn was not merely set rolling in still water
but was also rolled (on specially contrived supports) in dry dock ;
when her natural period for unresisted rolling was found to be
2'03 seconds. This last experiment furthermore confirmed the
practical accuracy of the calculation that had been made before-
hand of the moment of inertia, and the natural period of this
vessel.*
The preceding formula for the still-water period enables one
to ascertain approximately the effect produced upon the period
by changes in the distribution of the weights on board a ship.
Such changes usually affect both the metacentric height and
the moment of inertia, and their effects may be summarised as
follows : — •
Period is increased by —
(1) Increase in the radius of gyration ;
(2) Decrease in the metacentric height.
Period is decreased by —
(1) Decrease in the radius of gyration ;
(2) Increase in the metacentric height.
" Winging " weights — that is, moving them out from the middle
liue towards the sides — increases the moment of inertia and tends
to lengthen the period. The converse is true when weights— such
as guns — are run back from the sides towards the middle line.
Eaising weights also tends to decrease the moment of inertia, if
the weights moved are kept below the centre of gravity ; whereas
if they are above that point, the corresponding change tends to
increase the moment of inertia. But all such vertical motions of
weights have an effect upon the position of the centre of gravity,
altering the metacentric height, and affecting the moment of
inertia by the change in the position of the axis about which it
is estimated. It is therefore necessary to consider both these
changes before deciding what may be their ultimate efiect upon
the period of rolling. The principles stated above will enable
the reader to follow out for himself the effect of any supposed
changes in the distribution of the weights, and it is not ne(;essary
to give more than one or two examples. A ship of 6000 tons
weight has a metacentric height of 3 feet and a period of
7 seconds ; a weight of 100 tons is raised from 15 feet below
the centre of gravity to 15 feet above. In consequence of the
*
For particulars of these valuable the Academy of Sciences in 1873 ; this
experiments see the Memoire presented is reprinted in Naval Science for 1874
by Messrs. Eisbec and De Benaze to and 1875.
142 NAVAL ARCHITECTURE. chap. IV.
transfer of the weight, the centre of gravity will be raised, and we
have
-n- c , e -i. 100 tons X 30 feet , . .
Kise 01 centre oi gravity = -— — = i loot.
^ •' bOUO tons ^
New value of GM = 3 - i = 2 l feet.
Originally, according to the formula for the period,
^ 3
7
h =
^^^3 = 22 (nearly).
The rise in the centre of gravity slightly alters the position of the
axis about w^hich the ship is considered to revolve, and this
produces a change in the moment of inertia ; but the change is
so small that it may be neglected.
Then, after the weights are moved, the period T will be given
by the equation,
T = -554 /F
^2i
.-. T = 7 X 1-1 =7-7 seconds (nearly).
The decrease of 6 inches in the metacentric height thus lengthens
the period about 10 per cent.
As a second case, suppose weights amounting in the aggregate
to 100 tons, placed at the height of the centre of gravity, to be
"winged" 15 feet from the middle line; their motion being
horizontal does not affect the position of the centre of gravity.*
Then we have,
Original moment of inertia = 6000 x ^^
Additional moment of inertia = 100 x loj' = 22500.
.'. New moment of inertia = 6000 x F + 22500.
,XT ;i- f +• vi 6000 X Z;2 + 22500
(iSew radius oi gyration)- = —-HI — .
^ ^^ ' 6000
4
* The expressions for changes in the it is only necessary to determine for
moment of inertia produced by wing- each position the actual distances of
ing weights not originally at the middle the weights from the axis passing
line, nor placed at the height of the through the centre of gravity,
centre of gravitj^, can be easily formed ;
CHAP. IV. OSCILLATION IN STILL WATER. 1 43
Originally, 7 seconds = '554 \/ — (1)
o
7.45
Now T = -554 \/ 3 (2)
Therefore T = 7\/l+i5.; also ¥ = 475
^ 4F
= 7-028 seconds.
This alteration in period is very slight, as compared with tliat
produced by the supposed transfer of weight in a vertical sense,
and furnishes an illustration of the much greater changes
rendered possible by alterations of metacentric heights than by
changes in the moments of inertia.
It is important to remark that in the mathematical investi-
gation upon which the formula for the period of oscillation
is based, it is assumed that there is no sensible difference
between the time occupied by the ship in swinging through
large or small arcs. Within a range of, say, 12 or 15 degrees on
either side of the vertical — for which range the metacentric
method of estimating the stability gives fairly accurate results —
this condition has been proved by direct experiment to be
fulfilled very nearly in vessels of ordinary form and high free-
board. For example, the Sultan was rolled in still water
until an extreme inclination of nearly 15 degrees on either
side of the upright was reached, and then allowed to come
to rest, the observations being continued until the extreme
inclination attained was only 2 degrees ; but the period of
rolling through the arc of 30 degrees was practically identical
with that for the very small arc of 4 degrees. This noteworthy
fact is usually expressed by the statement that the rolling of
ordinary ships is isochronous within the limits named above.
For larger angles of oscillation such ships would probably
have a somewhat longer period than for the small oscillations,
and it is possible to approximate to this increase.* But as yet
direct experiment has not been applied to determine the actual
periods when high-sided ships swing to 20 or 30 degrees on either
side of the vertical ; and the case is one which can be best dealt
* See a Paper contributed by Mr. W. John and the Author to the Transactions
of the Institution of Naval Architects for 1871 ; see also page 229.
T44 NAVAL ARCHITECTURE. chap. iv.
with by means of model experiments in the manner described on
page 153. Vessels of low freeboard or exceptional form may not
be isochronous through arcs of oscillation so large as those named
for ordinary vessels ; and the reasons for this difference will be
understood from the remarks made hereafter. For unresisted
rolling the theoretical condition for isochronism may be very
simply stated : — Within the limits of inclination to the vertical,
for which the statical righting moment varies directly as the
anirle of inclination, the rolliuo; of a vessel will be isochronous.
In other words, if the curve of stability is practically a straight
line for a certain distance out from the upright, the rolling will
be isochronous within the limits of inclination fixed by that
distance.
Before concluding these remarks on the hypothesis of unre-
sisted rolling, a brief exposition of the principles of dynamical
stalility must be attempted. On the assumption, that no account
shall be taken of the eifect of fluid resistance, dynamical sta-
bility may be defined as the " work " done in heeling the ship
from her upright position to any angle of inclination ; the
amount of work done, of course, varying with the inclination.
Work, it need hardly be said, is here used in its mechanical
sense of a pressure overcome through a distance ; for example, a
ton raised one foot may be taken as our unit of work, and then to
move 100 tons through a foot, or a ton through 100 feet, will
require 100 units of work, or " foot-tons." It has been shown how
to estimate the moment of the couple for statical stability at a
given angle ; and if the vessel is gradually inclined beyond
that angle, the forces inclining her must do work depending
upon the righting couples corresponding to the successive
PIQ 54 instantaneous inclinations, as well
as to the ultimate angle attained.
In short, it is easy to determine
the dynamical stability, when the
variations in statical stability are
known, and the curve of stability
has been constructed.
A simple illustration may make
this clearly understood. A man is
pushing at the end of a capstan bar (Z, in Fig. 51) with a force P,
the centre of the capstan (G) is distant I feet from Z. Then the
statical moment of the pressure P about G will equal P X Z, and
CHAP. IV. OSCILLATION IN STILL WATER. 1 45
this exactly corresponds to the expression fur the moment of
statical stability (D x GrZ) obtained in the previous chapter.
Now suppose the man to push the bar on through an angle A
(circukr measure) ; then —
Distance the man walks = Z X A ;
Work he does = pressure X distance through which it acts
= P X ? X A = statical moment x A.
Next suppose that, as the man pushes the bar round, he moves
inwards or outwards along it, varying the value of I from instant
to instant ; then we shall have a parallel case to that of the ship
where the arm of the righting couple varies from angle to angle
of inclination. The man walks for a very small distance from
the first position (GZ, Fig. 54), pushing as before ; then for
thnt very small angle a, GZ will have practically the constant
value /, and (as above)
Work = statical moment (for position GZ) x a.
By the time he has completed the angle A, he has moved in on
the bar to the position Zj: let GZj =■ Zp Then, as he pushes with
a constant force P, we must have for a very small angle a from
the position GZ^ —
Work = statical moment (for position GZ,) X a.
Similarly, for any other position, the work for a very small angle
beyond may be expressed in terms of the corresponding statical
moment. And what is thus true of the capstan is equally true
of a ship ; the work for any small inclination a from a given
position is given by —
Work = statical moment of stability for that position X a = dis-
placement X GZ (for that position) X a.
Turning next to any curve of stability (say, to Fig. 43, page 118),
we have a graphic delineation of the values of GZ for every
inclination until the vessel becomes unstable. Supposing OP
is taken to represent any assigned angle of inclination, and pm
drawn very close to PN (the distance Pj9 corresponding to the
very small angle a), the area of this little strip (PNwjp) will
graphically represent the product GZ x a. Consequently it
follows that on the curve of stability for a ship, reckoning from
the upright (0) to any angle of inclination (such as OP), the
dynamical stability corresponding to that inclination is repre-
sented by the area (OPN) cut off by the ordinate corresponding
to that inclination. The total area of the curve of stability
therefore represents the total work to be done (excluding fluid
resistance) in up.settiug a ship. l
146 NAVAL ARCHITECTURE. chap. iv.
Beaiiug tliis fact in mind, fresh force will be given to the
remarks made in the previous chapter as to the comparative in-
fluence of beam and freeboard upon the form and range of curves
of stability ; and the contrasts exhibited between the curves of
stability for various classes of ships given in that chapter, become
still greater when the consideration of their relative total areas is
added to that of their range. These, h.owever, are matters upon
which any one so desiring may proceed to independent investiga-
tion with the materials afforded ; and no more will here be said
respecting them. »
We owe the term, and the first investif^ation for dvnamical
stability, to the late Canon Moseley, and his formula differs
somewliat in appearance, though not in fact, from that given
above. It may be well, therefore, to briefly indicate the chief
steps in Canon Moseley's investigation. Starting from the
principle that, apart from resistance, the only external forces
impressed upon a ship rolling freely would be her weight and
buoyancy, he remarked that the work done upon her in producing
any inclination might be expressed in terms of the rise in space
of the centre of gravity, where the weight might be supposed
concentrated, and the fall of the centre of buoyancy, where the
buoyancy might be supposed to be centred. Turning to Fig. 42,
page 117, it will be seen that, when the ship is upright, B,G is
the vertical distance between these two centres, whereas in the
inclined position their vertical distance becomes equal to BZ.
In forming an estimate of the work done in producing an inclina-
tion, we are only concerned with the changes in the relative
vertical positions of these two points ; hence we may write, if
V = volume of displacement (in cubic feet).
Work done in producing an inclination a'[_V 7> n\
(dynamical stability in foot-tons) . . .j ~ 85 ^ ~ '^ '"
also,
BZ = RZ + BR = BiG cos a + BR ;
and by the principle of the motion of the centre of buoyancy
previously explained (see page 117),
BR = I {gA + cjJk).
Substituting these values in the foregoing expression —
Dynamical stability = ^{y (^i^^i+^2^^2) - B^G (1 -cos a);
= 35 { ^ igJh+gJh) - V . B,G vers a}-
This is Moseley's formula. But, since curves of stability have
CHAP. IV. OSCILLATION IN STILL WATER. 1 47
been commonly constructed for ships, instead of using this
formula, the dynamical stability has been much more easily
calculated by the method of areas explained above, and its
values for different inclinations are often represented by a curve.
Within the limits for which the rolling of a ship is isochronous,
the curve of stability is a straight line, as explained above.
Therefore for any angle a of inclination to the vertical within
these limits
GZ = GM . a
Statical Moment of Stability = Displacement X GZ
= Displacement x GM . a
And evidently the area of the portion of the curve of stability
cut off by the ordinate at the angle a will be given by the
expression,
Area of Triangle = i X base x height
= 1 X a X GM . a
= i GM X €?.
So that the amount of work done in heeling the ship from tlie
upright to the angle o, excluding fluid resistance, will be given
by the formula,
Dynamical Stability = Displacement X G]\[ x n-
= W X m X ,j.
This formula is a very convenient one, much used in practice,
and hoLling fairly well for ships of ordinary form up to angles of
10 or 15 degrees to the vertical.
Besides the motion ot' rotation about an axis passing through
the centre of gravity of a ship rolling in still water, there is a
motion of translation of the centre of gravity up and down a
vertical line ; and in the case of the cylindrical vessel (Fig. 51)
we have seen how the metacentre moves when the volume of
displacement is unchanged. But in few, if any, actual ships can
this condition of constancy of displacement be accurately fulfilled
at each instant ; and with certain forms of cross-section, such as
the Symondite type in Fig. 52, the departure from this condition
is very considerable, giving rise to what are called "dipping
oscillations" and "uneasy" rolling. Let it be assumed, fur
example, that the ship in Fig. 52 has rolled until WiLi, which
was her upright water-line, has come to the position shown, the
motion probably occupying only 2 or 3 seconds. Then it may,
and does, happen that the wedge immersed (LSLj) will be in-
l2
148 NAVAL ARCHITECTURE. chap. iv.
stantaneously greater than the wedge emerged (WSVVi) ; for, as
already explained, during such a motion, if the roll does not
exceed 15 degrees, the instantaneous centre will be nearly coin-
cident with the centre of gravity, and this in \\ar-ships of the
Symondite type was near the load water-line. Suppose W2L2 to
be the water-line at which the vessel would float if steadily held
at the assumed inclination ; for the instant, the buoyancy of the
layer WW2L2L constitutes an unbalanced lifting force, which
tends to set up a vertical motion in the ship. The ratio which
the buoyancy of this layer bears to the total displacement of
the ship determines whether this vertical motion will be con-
siderable or not ; and it is obviuus that with the " pegtop " form
of section in Fig. 52 the buoyancy of the layer may be great in
proportion to the total buoyancy. Moreover, after motion begins,
FIG 53.
as the water-line W2L2 is moved upwards towards WL, there
will still remain an unbalanced upward buoyancy, although one
decreasing in amount, up to the instant that A\'^2L2 reaches the
water surface; and consequently, instead of stopping, the ship
will be carried on beyond its position of rest, just as a pendulum
inclined on one side of the vertical swings over to the other, past
its position of rest in the vertical. Hence it follows that, if the
vessel were conceived to be kept at the inclination shown, by
forces that left her free to move vertically, she would " dip "
upwards and downwards about her statical position of rest until
the resistance of the water extinguished her oscillations.
Although ships rolling in still water are not thus held at a
definite inclination, they are at each inclination subjected to
CHAP. IV, OSCILLATION IN STILL WATER. 1 49
eonditions of a similar character, and they have a period for
their dipping oscillations which may be determined approxi-
mately, and the ratio of which to that of their rolling oscillations
exercises an important influence upon the extent to which
dipping proceeds. A single roll, even of a Symondite ship, may
not produce much vertical motion, but a succession of rolls may ;
and the explanation of this fact was thus given by Professor
Kankine : — *' Each roll sets going a fresh series of dipping
"oscillations, and should the periodic time of rolling happen to
"be double, quadruple, or any even multiple of the periodic time
"of dipping, so that each roll coincides with the rising part of
"the previously existing dipping motion, the extent of the
"dipping motion may go on continually increasing to an amount
" limited only by the resistance of the water." In short, when
these ratios of the periods of dipping and rolling obtain, the
ship is in a condition similar to that of a pendulum which
receives periodically a fresh impulse at the end of its swing; and
it is a matter of common observation how such an impulse,
although iu itself not of great magnitude, may by its repeated
applications in the manner described lead to considerable oscil-
lations. Dipping motions have not, however, the practical
importance of rolling motions, and therefore they will not be
further discussed. In vessels of ordinary form these motions are
not nearly so extensive as in vessels of the Symondite type, and
the reasons for the difference will be obvious.
Turning attention to the effect of fluid resistance upon the
rolling of a ship in still water, that resistance may be subdivided
into three parts: — (1) Frictional resistance due to the rubbing
of the water against the immersed portions of the ship, and
particularly experienced by the aniidship parts where the form
is more or less cylindrical. (2) Direct or head resistance, similar
to that experienced by a flat board pushed through the water,
and chiefly developed against the keel, bilge-keels, dead wood,
and flat or nearly flat surfaces lying near the extremities of
the ship.* (3) Surface disturbance, which involves the creation
of waves that move away from the ship, and have continually
to be replaced by ntw-made waves, each creation involving, of
course, a certain expenditure of energy, which must react upon
the vessel, and be equivalent to a check upon her motion. The
* See also Chapter XT.
150 NAVAL ARCHITECTURE. chap. iv.
aggregate effect of these three parts of the fluid resistance
disphiys itself in the gradual extinction of the oscillations
when the ship rolls freely under the action of no external forces
other than gravity and buoyancy ; and if obt-ervatious have been
made of tlie rate at which extinction proceeds in any ship, or in
a carefully constructed model of the ship (made on a reasonable
scale) it is possible to infer from thence the total resistance for
that ship, or for one identical with or very similar to her. But
to estimate by direct calculation the value of the resistance for
a ship of novel form, or for any ship independently of reference
to rolling trials for similar ships or models, is not, in the present
state of our knowledge, a trustworthy procedure. This difficulty
in theoretical investigation arises chiefly from the doubtfulness
surrounding any estimate of the " wave-making function " for
an untried type. It is possible to approxiamte to the first two
parts of the resistance, but the third, as yet, seems outside
calculation. For example, when the character of the bottom
of a ship is known — whether she is iron-bottomed, or copper-
sheathed, or zinc-sheathed, and whether clean or dirty — it is
possible to obtain the " coefficient of friction " for the known
conditions; then knowing the area of the suiface upon which
friction operates, and the approximate speed with which the
ship rolls, the total frictional resistance may be found within
narrow limits of accuracy. Similarly, when the " coefficient of
direct resistance " for the known speed has been determined by
experiments on a board or plane surface, it may be applied to
the total area of keel, bilge-keels, dead wood, &c., and so a good
approximation made to the total " keel " or " direct " resistance.
But the wave-making function cannot be similarly treated, and
so it becomes must important to make rolling experiments in still
water, in order that the true value of the resistance may be
deduced from the observations. The importance of the deductions
arises from the fact that fluid resistance has very much to do
with controlling the maximum range of oscillaticn of a ship
rolling in a seaway. This will be explained in Chapter VI. ;
for the present it is sufficient to remark that, if the rate of ex-
tinction of still-water oscillations is rapid, it may be assumed
that the range of rolling at sea will be greatly limited by the
action of the resistance ; whereas, if the rate of extinction is slow,
resistance will exercise comparatively little control over the
behaviour of the ship at sea.
Rolling experiments in still water were recommended strongly
by Bouguer in the Traite di^ Navire publi-hed in 1746, but their
CHAP. IV. OSCILLATION IN STILL WATER. 15 1
performance has only become common within the last few years
and they have been limited hitherto to war-ships. The late Mr.
W. Froude, conducted the greater number of those made on
ships of the Koyal Navy, and to him we owe our most valuable
information on the subject ; a few experiments have been made
by oiSeers in command. In the French navy such experiments
have been made systematically for some years, and many of the
results obtained have been collected and published. The objects
of these experiments are twofold: (1) to ascertain the period
of oscillation of the ship ; (2) to obtain the rate of extinction of
the oscillations, when the vessel is left free to move and gradually
comes to rest. Various means may be employed to produce the
desired inclination, from which the vessel is to have her rolling
motion observed. If she is small, she may be " hove-down," and,
after reaching the required inclination, suddenly set free. But
this is a process inapplicable to large ships, and the following is
the plan usually adopted : —
A number of men are made to run across the deck, from side
to side, their motions being regulated by some concerted signal,
so that they may run out from the middle line to the side and
back again, while the ship performs a half-oscillation. By this
simple means even the largest ships may be made to accumulate
motion verv quirklv, and to roll throuo;h considerable angles,
the running of the men being so timed as never to retard, but
always to accelerate, the rolling. For example, her Majesty's
ship Sultan was made to roll to an angle of 14^ degrees from
the upright by the motion of her own crew of about six hundred
men ; while the Devastation, weighing over 9000 tons, was made
to reach a heel exceeding 7 degre»?s by four hundred men running
eighteen times across her deck. If the motions of the men are
not well timed, similar results will not be obtained, and in some
trials large angles of oscillation have not been secured, on
account of non-compliance with this condition. AVhen a suffi-
ciently large range of oscillation has been obtained, the men are
made to stand still, and the observations are commenced.
In order to determine the period for a single roll, careful note
is taken of the times occupied by the ship in performing each
of several successive single rolls; and in this way the fact has
been established that vessels of ordinary form are practically
isochronous in their rolling motions. Hence, in fixing the period
for a ship, it is usual to observe how many oscillations {n,
suppose) are made in a certain interval of time (T seconds,
suppose) ; then the period = T -i- w.
152
NAVAL ARCHITECTURE.
CHAP. IV.
Careful observations are also made of the extreme angles of
heel reached at the end of each oscillation ; the difference between
the successive values marking the rate of extinction. A vessel
starting from an inclination of (say) 10 degrees to port only
reaches an extreme heel of 9 degrees to starboard, and then rolls
back to 8^ degrees to port, gradually coming to rest. These
observations are commonly continued until the arc of oscillation
has diminished to 2 or 3 degrees. Mr. Froude and M. Bertiu both
devised beautiful automatic apparatus for recording the rolling
motion of the ship in such a manner that the angle of inclination,
at each instant of her motion, as well as her extreme angles of
?3
00
Oil
FIG. 53.
\
\
s
\
\
\
\,
\
s.
\4,.
\
\
\
^
NO
\
\
V
^^
\
\
>
^"^.
'^
^
^^^
^
^
^
^-^
-^
^^
-N^
\
.^
"^^^-^
^-_
"^
Ii;;;;j;;2i^
1
t
1
i
iViim
her
ef
Osc
Tia
lion
s
13
id
24-
30
36
•12'
heel, can be traced, and the period also determined. But with the
aid of the simplest apparatus it is possible to make all the observa-
tions needed, and in Chapter VII. the common plan of making the
observations is described. The gradual degradation in the range
of oscillation is represented by means of, what are termed, " curves
of extinction " ; examples of these curves, obtained from Mr.
Fronde's experiments, are given in Fig. 53, for her Majesty's
ships Sultan, Inconstant, and Volage. A very brief explanation
of the construction of these curves will suffice. On the base-line
OX are set off equal spaces, each representing an oscillation ;
and since each oscillation is performed in the same period, each of
these spaces also represents for each ship a certain number of
CHAP. IV. OSCILLATION IN STILL WATER. 153
seconds. Any ordinate, drawn at right angles to OX, through
the points marking these equal spaces, shows the extreme angle
of heel reached at that particular oscillation ; and the difference
between any two ordinates so drawn shows the loss of range, or
extinction of the rolling, in the corresponding number of oscilla-
tions. For example, after making twelve oscillations from the
extreme angle (13| degrees) where the record of observations
began, the Sultan only reached an extreme angle of 8 degrees,
the loss of range in that number of rolls being 5f degrees. Here
the rate of extinction was slow, the vessel having a large moment
of inertia, no keel, and only shallow bilge-keels, to assist the
extremities in developing resistance to the motion. If there were
deeper bilge-keels, the rate of extinction would be much more
rapid.
Similar rolling experiments have been made with models ; and
a comparison of the curves of extinction obtained from models
with those obtained from the full-sized ships represented by the
models has proved that this simpler mode of procedure may be
adopted if proper precautions are taken. One of the earliest and
best experiments of this kind was made by the late Mr. Froude
on a model of the Devastation, and when the ship herself was
afterwards rolled it was tound that her curve of extinction was
practically identical with that obtained from the model. There
are many obvious advantages in such model experiments. They
can be made before the construction of a ship is begun ; by means
of them it is possible to test the influence of variations in form,
or changes in bilge-keels, &c., upon the curve of extinction ; and
any critical conditions affecting the safety of a ship when
damaged can be investioated. An excellent illustration of the
value of these model experiments is found in the case of the
Inflexible, to which reference will be made again.* In that case
the model had its lineal dimensions one twenty-fourth those of
the ship ; it weighed nearly a ton, was weighted so as to float at
the proper draught, had the centre of gravity in the estimated
position, and had its moment of inertia so adjusted that it oscil-
lated in still water in a period duly proportioned to the period
estimated for the ship. Similar conditions are essential to these
model experiments in all cases. The model for a new design
simply represents the form, displacement, stability, and period
* For details see the Report of the Committee (Parliamentary Paper, No. 1917
of 1878).
154 NAVAL ARCHITECTURE. chap. iv.
embodied in the design and calrulations ; and for a completed
ship represents tliose conditions as ascertained by observation
and calcuhxtiou. In all cases, moreover, the model must be made
to a reasonable scale; and great care must bs taken in recording
its behaviour when the rolling experiments are in progress,
minute differences for the model becoming exaggerated when the
results are increased in scale so as to apply to ships.
In most cases still-water rolling experiments are limited to
determinations of the period of oscillation and the curve of
extinction ; but in some cases they have been carried further,
with the intention of determining completely the motion of the
ship. The most thorough investigation of the kind with which
we are acquainted is that conducted by MM. Eisbec and De
Benaze, mentioned on page 140. By means of special apparatus
these gentlemen succeeded in obtaining an automatic record of
the vertical and horizontal motions of the centre of gravity of
the Elorn, as well as of her successive arcs of oscillation as
her rolling was extinguished by resistance. Their subsequent
analysis of these interesting records has advanced considerably
our knowledge of some matters, and more particularly of those
relating to the motion of the centre of gravity during rolling.
When resistance comes into operation, the considerations respect-
ii)g the instantaneous axis for unresisted rolling (stated on page
137) require considerable modification. The centre of gravity
of the Elorn, for example, was found to have motions of transla-
tion in the horizontal as well as in the vertical sense, and this is
doubtless true generally. Furthermore it appears that Avhile the
Elorn could not be said to perform her motions of rotation about any
fixed axis, there was a point — termed by the experimentalists the
point tranquille — \\ hich traversed the least path during the oscil-
latory motion of the ship. Their conclusions as to this point are
summarised as follows : — In the Elorn " the ijoint tranquille is
" always situated between the centre of gravity and the water-line.
" When there are no lateral keels and no ballast, it is near the
"water-line; when there are no bilge-keels, but the centre of
" gravity is lowered nearly a foot by ballast, it is very nearly
" midway between that point and the water-line ; lastly, when
" there is no ballast but immersed lateral keels it approaches very
"near to the centre of gravity, though still above that centre.
" The position of the point trmiquille may vary considerably in
" different ships ; more facts are needed in order to fix its ap-
" proximate position in any case. ... It is presumable that the
^' point tranquille rarely descends below the centre of gravity."
CHAP. IV. OSCILLATION IN STILL WATER. 1 55
These conclusions of the French experimentalists are in
general accordance with experiments made by the late Mr-
Froude in order to determine the " quiescent point," which was
found to lie very close to the centre of gravity in several ships
and models. A very simple procedure suffices to determiue
approximat(dy the vertical position of the "quiescent point"
wheu a ship is rolled in still water. Two or more pendulums, of
very short periods, are hung at different heights in the ship ; as
she reaches successive angles of extreme inclination to the
vertical the indications of these pendulums are noted, and the
true inclinations of the ship are simultaneously ascertained.
From this data, by means of the formula for the error of a pen-
dulum given in Chapter VII., the vertical position of the " quies-
cent point " may be ascertained with sufficiently close approach to
accuracy. Attempts have been made to frame mathematical expres-
sions fur the determination of the position of the instantaneous axis
of rotation at any period of the rolling motion ; but these investi-
gations have Httle practical importance ; and in estimates for the
natural periods of ships, it is usual, as previously remarked, to as-
sume that the axis of rotation passes through the centre of gravity.
Rolling experiments have now been made on most classes of
war-ships, and their natural or still-water periods have been
determined. It may be interesting to summarise the facts. For
gun-vessels, gun-boats and small craft, the period for a smgle
roll is from 2 to 3 seconds; these short periods being due to
the small radii of gyration consequent upon the small dimensions,
and to the necessity for securing a good "metacentric height."
For despatch-vessels, sloops, &c., below the size of cors^ettes,
periods of from 3 to \\ seconds are common ; and 4 seconds
is a good average. Unarmoured corvettes and frigates, pos-
sessing both sail and steam power, are found to occupy from
5 to 6 seconds in a single roll, but some of the modern types
of swift steamers have periods of 8 seconds, their metacentric
heights being less than those of earlier types. Turning to ar-
moured ships, the shortest periods yet observed are Ibund in
coast-defence vessels of shallow draught, great proportionate
beam, and large metacentric heights. An American monitor, for
example, was found to have a period of 2*7 seconds only, and
some of the French floating batteries have periods of 3 to 4
seconds. The French Gloire, the English converted ironclads
of the Caledonia class, and other types of second-class ships have
periods of 5 to 6 seconds. The Inflexible, notwithstanding her
large [^dimensions and considerable moment of inertia, has a
156 NAVAL ARCHITECTURE. chap. iv.
period of 5^ seconds only, due to her great metacentric height.
The Devastation of the Koyal Navy has a period of i5'^ seconds ; and
other first-class rigged ships have periods of 7 to 8|^ seconds. The
SuJtan is an example of small metacentric height and large radius
of gyration ; her period is 8*8 seconds. The Suffren of the French
Navy is less stiff than the Sultan and has a period rather exceeding
10 seconds. Tiiis is the longest period for a single roll of which
we have any knowledge ; and it is to be observed that, in man-
oeuvring in smooth water, tlie small initial stability of this class is
said to have caused some disadvantages, although in a seaway
the vessels are remarkably steady.
For merchant ships exact information respecting the still-water
periods seems entirely wanting. It will appear, moreover, from
the remarks made previously (page 80) that there may be con-
siderable variations in the period of any individual shij) on
different voyages, changes in the character and stowage of the
cargoes affecting both the metacentric height and the moment
of inertia. Still-water rolling experiments for merchant ships
have not found favour with owners hitherto, probably because of
the belief that their performance might involve" delays and
difficulties; but snch experiments might be very simply made,
and would furnish valuable information respecting the good or
bad stowage of the cargo carried on any voyage. Bouguer
suggested this method of inquiry into the character of the
stowage so long ago as 1746, and the counsel of the Institution
of Naval Architects endorsed the suggestion in 1867. To give
practical effect thereto the following course would be followed :
Careful note would be taken of the behaviour of a ship on various
voyages, and before starting a small series of rolling experiments
would be made to determine the still-water period of the ship
on each voyage. Hence would be discovered the mean period
corresponding to the voyages on which the ship was proved to be
well stowed by her good behaviour ; and the endeavour in stowing
the ship for further service would be to secure approximately the
same period as she possessed on the successful voyages. This
aim might not always be attained, nor would it always be possible
to secure the period desired. But in every case, from such rolling
exjjeriments, supplemented perhaps by an inclining experiment,
facts would be obtained enabling some idea to be formed of the
probable behaviour of the ship at sea. Apart from such experi-
ments there can be no check upon the character of the stowage ;
and in many cases where that character has been unsatisfactory
the discovery has been made under the trying circumstances of
CHAP. IV. OSCILLA TION IN STILL IVA TER. I 5 7
bad weather at sea when changes iu stowage were practically
impossible. That is a matter well deserving the consideration of
shipowners.
The determination of the period for a ship is a matter of
simple observation ; but the investigations by wdiich the value
of the resistance is deduced from curves of extinction, like those
in Fig. 53, are more difficult, involving mathematical processes
which cannot be reproduced here. The principle upon which the
investigations proceed may, however, be explained briefly. If a
ship started from a certain extreme angle of inclination to the
vertical, and her rolling was unresisted, she would attain an equal
inclination on the other side of the vertical before coming to rest;
but when she rolls under the action of resistance she comes to
resit when she reaches a smaller inclination on the other side of
the vertical. In other words the "loss of range" per oscillation
represents the amount of "mechanical work" done by the resist-
ance during that oscillation, which amount of work can be ascer-
tained by calculating the di/namioal stahilitij correspouding to the
loss of range. Suppose, for example, that a ship starts from an
inclination of Bi on one side of the vertical, and reaches an incli-
nation of 02 oil the other side of the vertical. Then, using the
approximate formula for the dynamical stability given on page
147, we have
B^
Dynamical Stability for inclination B^ = ^^' x '^^ X -;^ .
B?
d. = W xmx-^ .
Hence, Dynamical Stability corresponding | _ Ww (a%_ai\
to decrease of range . . . . j 2 ^ ^ ^ ^
^^ ' \b, + B.^ {B, - b:)
2
W . m
• Arc of oscillation x Loss of range.
2
This last expression measures, as explained above, the work done
by the fluid resistance during a single swing of the ship. More-
over it will be evident that when the curve of extinction for a
ship has been determined expeiimentally, if any value of Bi is
assumed, all the other quantities in the expression will be known.
The value of the work done by the resistance can thus be deter-
mined, and some data obtained from which to infer approximately
the laws which govern that resistance. In Chapter XI. the subject
of fluid resistance is dealt with at length; and a few general
remarks must suffice here. Fluid resistance to the motion of
158 NAVAL ARCHITECTURE. chap, iv,
a floating bo;ly, or of a body immersed in it, depends upon the
rate of motion. When a flat surface is pushed forwards, the
direct or head resistance, corresponding to the velocity, varies
with the area of the surface, and with some power of the velo-
city, and so would also the frictional resistance experienced by a
thin board drawn end-on through the water. The usual assump-
tions have been that for moderate speeds the resistance varied
as the square of the velocity, that for very low speeds it varied
nearly as the first power of the velocity, and for high speeds at a
greater power than the square. For such speeds as are common
in the rolling of ships, it is probable that the keel and frictional
resistances vary nearly as the square of the angular velocity ;
and this is the law which French investigators agree in applying
to the total effect of the resistance. Mr. Froude, however, whose
experience and labours in this subject, as well as his numerous
experiments, gave to his conclusions exceptional authority, was
of opinion that the total resistance consists of two parts, one
varying as the square of the angular velocity, the other as the
first power. The former comprehends keel and frictional resis-
tances ; the latter is mainly represented by surface disturbance.
It is only proper to add that by the analysis of curves of ex-
tinction published by French writers, as well as of curves obtained
from his own experiments, Mr. Froude gave good reason for
accepting his law of resistance.
Ships of ordinary form being isochronous for moderate angles
of inclination on either side of the vertical, all their oscillations
within limits, say, of 15 degrees on each side being performed
in practically the same time, it follows that, as the range of
oscillation increases, so will the mean angular velocity increase.
Or, as we may say, the mean angular velocity varies as the
arc of oscillation. Hence, it is possible to express the effect of
the resistance (measured by the loss of range) per roll in terms
of the arc of oscillation. For example, if 20 be written instead
oiO + 62, to express the arc of oscillation we may write.
Loss of range = aB -\- hO'^,
where a and & are constants determined from the still-water
rolling experiments. The values of the constants, of course,
vary with the character and form of the vessel, the depth of her
bil^e-keels, and the coefiicient of friction. The rate of extinc-
tion of the still-water oscillations of any ship decreases as she
approaches a state of rest. This is a matter of common obser-
vation and is fully borne out by the curves of extinction in
CHAP. IV.
OSCILLATION IN STILL WATER.
159
Fig. 53. From the foregoing remarks the explanation of this
fact is readily obtained; the greater the range of oscillation, the
quicker the motion, and the greater the resistance. Motion
and the existence of the retarding force due to resistance
cease simultaneously ; resistance has, therefore, sometimes been
termed a " passive " force, but it nevertheless exerts a very
important and beneficial effect upon the behaviour of ships at sea.
The following are a lew examples of the values of the constants
a and h, determined by the late Mr. Froude, for ships of the
Royal Navy : the angles 0 being measured in degrees :
Ships.
a.
b.
Sultan
Devastation
Inconstant . . . . ,
Narcissus
Volage
•0267
•072
•035
•037
•028
•0016
•015
•005L
•008
•0073
The first two ships in this table are armoured : the remainder
are unarmoured.
As an illustration of the use of the formula, suppose the Incon-
stant to be swinging through an arc of 16°. Here 9 = 8".
Loss of range = '035 X 8 + -0051 X 8^ = -61.
That is to say, the vessel would start from an inclination of
about 8°"3 on one side of the vertical, aud reach an inclination of
about 1°'7 on the other side.
According to the French authorities the loss of range would be
expressed very nearly by
Loss of range = N . 0^
for arcs of oscillation exceeding 6^ ; which correspond to values
of 0 exceeding 3°. The following values of N are given on the
Ships.
N.
Sultan (English ironclad)
Suffren (French ironclad)
Laqalissoniere (ditto)
0015
0083
0075
0123
0141
0170
015
016
0109
033
Inconstant (English frigate)
Volage (English corvette)
Annamite (French transport)
Hirondelle (despatch vessel)
Elorn (tug)
Navette (tug)
Crocodile (gun-vessel : bilge-keels)
i6o
NAVAL ARCHITECTURE.
CHAP. IV.
authority of M. Bertin, of the French Navy, whose hxbours iu this
department of naval science have been most extensive and
valnable.*
The preceding coefficients represent the rate of extinction of
the lolling in ships having no headway. M. Bertin has con-
ducted experiments for the purpose of ascertaining whether, when
a ship is moving ahead and simultaneously rolling, the coefficients
vary. The results for the Navette were as follows :
Speed of Ship.
Value of N.
Nil
4 knots.
8 kuots.
•0109
•0123
•015
The explanation suggested is as follows: — When the ship is
under-weigh she penetrates at each instant into water not yet
disturbed, of which the vhole inertia has to be overcome;
whereas, when she has no headway and is rolled, similar con-
ditions do not hold, and the inertia of the water is not so great.
It is interesting to add that Mr. Froude found in his analyses of
the rolling of the Devastation in a seaway that the actual resist-
ance was somewhat greater than that inferred from the still-water
experiments made under the usual conditions without headway.
The value or correctness of experimental data obtained by
rolling ships is in no way affected by the divergence of opinion
between English and French writers as to the mathematical
treatment of curves of extinction and the mode of expressing the
fluid resistance in terms of the angular velocity. After carefully
considering the statements on both sides, and the published
curves of extinction for French and Euglish ships, we are
strongly of opinion that the law proposed by the late IMr. Froude
most closely accords with experimental data. In other words,
the resistance appears to consist of two terms, one varying as
the first -power of the angular velocity, and the other varying
as the square. The discussion of this question led Mr. Froude
into a full investigation of the actual resistances of certain
typical ships. Not content with obtaining the aggregate value
of the resistances for these ships, he separated them into their
component parts, assigning values to frictional and keel resist-
* See various Papers on "Waves
and Eolling," contributed to Naval
Science, 1873-1874, and to the Bevue
Maritime, 1877-1880.
CHAP. IV.
OSCILLATION IN STILL WATER.
i6r
ances, as well as to surface disturbance. In doing so, he was led
to the conclusion that surface disturbance is by far the most
important part of resistance, as the following figures will show.
Ships.
Frictional.
Keel, Bilge-keel,
and Deadwood.
Total Re-
sistance.
Surface
Disturbance.
Sultan . . .
Inconstant .
Volage . . .
Greyhound . .
351
140
9G
120
5036
4060
2944
700
20,000
21,500
14,100
4,700
14,H10
17,300
11,060
3,880
The frictional and bilge-keel resistances in this table were ob-
tained by calculation from the drawings of the ship, making use
of data as to coefficients for friction and for head resistance which
had been previously obtained by independent experiments, and
which may therefore be regarded as leading to thoroughly trust-
worthy results. The total resistance in each case was deduced
from the curves of extinction obtained from still-water rolling
experiments ; and this also must be regarded as accurate. But
it will be noticed that in no case does the sum of the frictional
and keel resistances much exceed one-fourth of the total resist-
ance, while it is much less than one-fourth in other cases. The
consequence is that surface disturbance must be credited with
the contribution of three-fourths or thereabouts of the total
resistance. Waves are constantly being created as the vessel
rolls, and are constantly moving away, and the mechanical work
done in this way results in a reduction of the amplitude of succes-
sive oscillations. Yery low waves, so low as to be almost imper-
ceptible, owing to their great length in proportion to their height,
would suffice to account even for this large proportionate effect.
For example, Mv. Froude estimated that a wave 320 feet long
and only 1^ inch in height would fully account for all the work
credited to surface disturbance in the fourth case of the preceding
table. The lowness of these waves accounts for the fact that they
may have escaped notice at the time of an experiment, and
disposes of one argument that has been raised against the correct-
ness of the foregoing statements. Moreover it is worth notice
that the importance attributed by Mr. Froude to surface disturb-
ance derives considerable support from experiments made on
very special forms of ships. For example, in experimenting
upon the model of the Devastation, it was found that, when the
deck-edge amidships was considerably immer^ed before the
model was set free to roll, the deck appeared to act like a very
M
1 62 NAVAL ARCHITECTURE. chap. iv.
powerful bilge-piece, rapidly extinguishing oscillations. MM.
Eisbec and De Benaze, of the French navy, also found by
experiment that, when bilge-keels were moved high up the sides
of a vessel, so that, as she rolled, the bilge-keels emerged from
the water and entered it again abruptly, their effect became
much greater than when they were more deeply immersed ; as
one wouLl anticipate from the increased surface disturbance that
must exist when the bilge-keels are so high on the sides.
Experience with the low-freeboard American monitors furnishes
further support to this view; immersion of the deck and the
existence of projecting armour developing greatly increased re-
sistance— a circumstance which undoubtedly tells much in favour
of these vessels, and assists in preventing the accumulation of
great rolling motions.
The figures in this table also indicate the large proportionate
effect of " keel " resistance as compared with frictional resistance.
It has already been explained that this direct or keel resistance
is experienced by the comparatively flat surfaces of deadwoods,
keels, bilge-keels, &c. Now it will be obvious that the under-
water form of a ship has to be determined chiefly with reference
to considerations of propulsion and stability ; and that the naval
architect can only pay attention to the influence which that form
may have upon the resistance to rolling when he has satisfied
these primary requirements. But while the shape of the hull
proper is thus dealt with, the actual resistance to rolling may be
considerably influenced by fitting such appendages as keels,
bilo;e-keels, &c. The extent to Avhich the influence of these
appendages will be felt depends upon several conditions ; such,
for example, as their area, their position on the bottom, the
period of the ship, her form, and her moment of inertia. Bilge-
keels are the most important appendages in common use, and it
may be of interest to examine into their mode of operation.
The evidence in favour of the use of bilge-keels is now con-
sidered unquestionable ; but only a few years have elapsed since
many eminent naval architects regarded bilge-keels with sus-
picion. Direct experiment and careful observation have mainly
produced the change of opinion, showing that bilge-keels will
increase the rapidity of the extinction of still-water oscillations,
and limit the rolling of ships at sea. One very interesting series
of experiments was made by the late Mr. Fronde, for the informa-
tion of the Committee on Designs for Ships of War (1871). A
model of the Devastation was used for this purpose, and fitted
with bilge-keels which, on the full-sized ship, would represent
CHAP. IV.
OSCILLATION IN STILL WATER.
163
the various depths given in the following table. The model was
one-thirty-sixth of the full size of the ship, and was weighted so
as to float at the proper water-line, to have its centre of gravity
in the same relative position as that of the ship, and to oscillate
in a period proportional to the period of the ship. In smooth
water it was heeled to an angle of 8J degrees, and was then set
free and allowed to oscillate until it came practically to rest,
the number of oscillations and their period being observed. The
foUowino: results were obtained : —
Model fitted with —
Number of Double
Rolls before Model
was practically
at rest.
Period
of
Double
Roll.
1. No bilge-pieces
2. A single 21-inch bilge-keel on each side
3. „ 36-inch „ „ „
4. Two 36-inch bilge-keels „ „
5. A single 72-inch bilge-keel „ „
01 1
o±d
12t
8
Seconds.
1-77
1-9
1-9
1-92
1-99
The great advantages resulting from the use of bilge-keels
are obvious from this table. It will be noted also that the
period of oscillation is changed but little as the resistance
becomes increased. Similar results have been obtained in other
cases. For example, in the Morn MM. Kishec and De Benaze
found the rate of extinction was nearly doubled by fitting bilge-
keels. M. Bertin found a yet larger increase in the rate of
extinction in certain barges upon which he experimented ; and
estimated that in some small vessels with deep bilge-keels their
effect represented more than 60 per cent, of the total resistance.
In all these cases the vessels were small, their periods of oscilla-
tion short, and their moments of inertia comparatively small, all
of which conditions tended to enhance the effect of the bilge-
keels. This will be better understood, perhaps, if the formula is
given by which an approximation can be made to the work done
by a bilge-keel during the swing of a ship. Assuming the resist-
ance to vary as the square of the angular velocity, and supposing
r to be the mean o-adius of the bilge-keel from the axis of rota-
tion (assumed to jjass through the centre of gravity), then a
mathematical investigation gives
"Work done in overcoming resist- \ ( Area of bilge-keel
ance of bilge-keel during ^^ r ~ "j '^J^ m p .
Single swing ^ V ol
M 2
X r
1 64 NA VAL ARCHITECTURE. chap. iv.
wIk^i'g T = period for a single swing, and 20 = arc of oscillation.
The constant C2 is determined by experiment. Mr. Froude
adopted I'G lbs. per square foot with the velocity of 1 foot per
second as a fair value for this coefficient Gj; and from his
published examples we may select an illustration of the use of
the i'ormula. For the Sultan,
Area of bilge-keels 420 square feet
Value of r 25 feet
6 (circular measure) '102
T (in seconds) 8-825
.-.Workof keels = 420 X (25)^ Xo-(-gT^|/x (-102)^ X I'^lb-^-
= 1890 (nearly).
From the general form of the expression for the work done by
bilge-keels, &c., it will he evident that their effect increases,
(1) With increase in area ;
(2) Witli decrease in the period (T) of the ship ;
(3) With increase in the arc of oscillation.
Also, having regard to the formula for the period given on page
140, it will appear that the effect of such keels increases as
the moment of inertia is diminished, or the metacentric height
increased, both of which variations shorten the period of oscilla-
tion for a ship. The influence which can be exercised upon the
period of a ship may be limited, for reasons previously stated ;
consequently the naval architect can work chiefly in the direction
of increasing the area and power of bilge-keels, knowing that
their influence cannot be otherwise than beneficial. Ships of the
Royal Navy recently constructed have been furnished with much
deeper bilge-keels than were formerly in use ; the limit of depth
in the larger vessels being fixed by the necessity for compliance
with certain extreme dimensions in order that the vessels may be
able to enter existing docks. The use of bilge-keels is also
becoming common in certain classes of merchant steamers, but
has not yet become general. One objection to their use has been
shown to be fallacious ; i\Ir. Froude having proved by towing
trials made with the Greyhound sloop-of-war that only a very
trifling increase in the resistance was caused by bilge-keels of
exceptional depth, even when the vessel was subjected to great
changes of trim.
The common practice is to fit one bilge-keel on each side, near
the turn of the bilge. In some cases two keels have been fitted
on each side ; but there are objections to the arrangement. Two
CHAP. IV. OSCILLATION IN STILL WATER. 1 65
shallow keels have much less power in extino^uishing oscillations
than a sinfjle deep keel of area equal to the combined areas of the
other two (see experiments with Bevasfation model, page 163) ; and
there is a difficulty, except in large ships, in placing two keels
on each side, sufficiently clear of one another without the risk of
emersiug the upper keel during rolling. The reason for the
comparative loss of power in two shallow keels is easily seen.
As a bilge-keel swings to and fro with the ship it moves at vary-
ino" velocities, and impresses accelerating motions on masses of
water with which it comes in contact, these accelerations being the
equivalents of the resistance. If there be two bilge-keels on
each side, the water encountered by one will probably have been
set in motion by the other keel, and consequently their combined
resistance is less than the sum of the resistances which they would
experience if acting singly. On the other hand, the addition of
a bi]ge-keel, instead of using a deeper single bilge-keel on each
side, may be the only possible means of increasing resistance in
some cases. As regards the emersion of bilge-keels it is only
necessary to remark that more or less violent blows or shocks are
received by such keels as they enter the water again ; and even
when no structural weakness results, the noise and tremor are
unpleasant. The power of side-keels placed near the water-line
is very great ; for example, in the Elorn the effect of such keels
was one third greater than that of ordinary bilge-keels. But for
the reasons given they are rarely used ; and in cases where an
overhanging armour-shelf a few feet below the water-line acted as
a side-keel, it has been found desirable to "fill-in" under the
shelf in order to diminish the shocks of the sea.
Another interesting case, having considerable practical import-
ance, is that where, from damage to the skin or from some other
canse, quantities of free-water enter the interior of a ship and
influence her rolling. In the preceding chapter (page 105) an
explanation has been given of the reduction in stiffness, or meta-
centric height, which may occur under these circumstances ; and it
will be obvious that this reduction must produce an increase in
the period of oscillation, as compared with the period of the ship
with sides intact. This change of period may be determined
approximately from the formula given on page 140, when the
metacentric heights for the two conditions are known; but a still
more important contrast between those conditions is that relating
to their curves of extinction, and these can be determined by
experiment alone. When water in the interior of a ship does not
completely fill the space containing it, but has a free surface and
1 66 ' NAVAL ARCHITECTURE. chap. iv.
can move from side to side as the ship rolls, it exercises a more
or less powerful extinguishing effect upon the oscillations. For
instance, if a ship containing free-water is heeled steadily to some
anirle, the surface of the contained water will be horizontal.
Supposing the ship to be let go, she will move back towards the
upright at a rate depending upon the initial inclination and her
natural period (allowing for the presence of the water). At any-
instant before she reaches the upright, the contained water will
be acted upon by the force of gravity and by the accelerations
due to the motion of the ship, and will tend to place its surface
normal to the resultant of these forces (see page 183). If gravity
alone acted, the water-surface would tend to become horizontal ;
but it might never actually become so during the motion, because
the rate at which the adjustment of the surface can proceed
depends upon the virtual head of the water contained within her,
whereas the motion of the ship proceeds at its own rate, and, as a
rule, faster than the motion of the water-surface. Consequently,
when the ship passes through the upright, the water-surface will
not have become horizontal, but be still inclined towards that
side of the ship which was initially lowest. In the other half of
the swing, as the ship increases her inclination on the other side
of the vertical, the action of gravity tends to reverse the motion
of the water-surface, and thus to retard the motion of the ship.
This is a very incomplete sketch of the actual behaviour of the
contained water ; and, in practice, its flow from side to side in a
ship would often be hampered by the presence of cargo, stores,
divisions, &c., in the hold, all of which considerations would tend
to complicate an exact statement of the problem. For our present
purpose it will suffice to state generally that the motions of the
contained water lag behind those of the ship, and therefore check
her oscillations. This view of the matter is confirmed by experi-
ence, and has been acted upon in the designs of special classes of
ships. In central-citadel ships, for example, having considerable
metacentric heights when intact, and comparatively short periods,
" water-chambers " have been formed above the armour decks ; into
which free-water can be introduced when desired, for the purpose
of increasing the resistance to rolling, and making the ships
steadier in a seaway. The Inflexible is the first vessel thus fitted
which has been completed, and the experience gained in her both
by still-water rolling and by her behaviour at sea has been con-
clusive as to the remarkable extinctive effect of the contained
water, even when its total weight did not much exceed one two-
hundredth part of her weiglit. In Chapter YI. some facts are given
CHAP. IV.
OSCILLATION IN STILL WATER.
167
respecting her rolling during the passage to the Mediterranean
in the aiSumn of 1881. The experimental inquiries of the In-
dexible Committee also furnished remarkable evidence of the
possible effects of free-water. From the results obtained with
the model of that ship, the Committee gave the following facts.
Wlien the ship is fully laden, with sides intact, her metacentric
height is 8^ feet, her period for a single swing they assumed to
be 4 to 4J seconds, and her curve of extinction is the upper curve
iu Fig. 54a. When the ends are riddled the metacentric height falls
FIG 54-a
to 2 feet, the period is increased to 10 seconds, and the curve of ex-
tinction is the steepest curve. Supposing the very extreme condi-
tion termed " riddled and gutted " to be reached, the metacentric
height is "24 foot, the period is 13 seconds, and the curve of ex-
tinction is the middle curve. Supposing the ship to be started with
a roll having a range of 10° in each of these conditions, then the
lo2$e8 of range will furnish a means of comparing the extinguish-
ine: effect of the resistance. These losses are given as follows : —
Condition of Inflexible.
Loss of Range.
Ship intact
„ ends riddled
„ ends riddled and gutted . .
1°
7.8
7-4
One other passage of the Eeport may be quoted before leaving
this subject: "It is obvious from the tabulated statement that
1 68 NAVAL ARCHITECTURE. chap. iv.
" extinctive power possessed by internal free-water is capable
"of being increased or diminished largely by comparatively
"small changes ia depth." Accepting this conclusion, it will be
evident that in any case where free-water is employed as a means
of increasing steadiness, experiments must be had recourse to in
order to decide upon the quantity of water to be admitted, and
its depth.
Before concluding this chapter it will be desirable to explain
briefly the practical use made of the theory of dynamical stability
(explained on page 144), in comparing the safety of ships under
the action of suddenly apijlied forces, such as gusts or squalls of
wind. These do not, it is true, commonly occur under the condi-
tion of smooth water that is assumed throughout the present
discussion ; but it is convenient to separately consider their
effect, and to deal with the action of the waves independently,
for which purpose it is necessary to suppose the water still, while
the wind acts on the ship.
lioughly speaking, it may be said that a force of wind which,
steadily and continuously applied, will heel a ship of ordinary
form to a certain angle will, if it strikes her suddenly when she is
upright and at rest, drive her over to about twice that inclination,
or in some cases further still. A parallel case is that of a spiral
spring; if a weight be suddenly brought to bear upon it, the ex-
tension will be about twice as great as that to which the same weio-ht
hanging steadily will stretch the spring. The explanation is
simple. When the whole weight is suddenly brought to bear upon
the spring, the resistance which the spring can offer at each instant,
up to the time when its extension supplies a force equal to the
weight, is always less than the weight ; and this unbalanced force
stores up work which carries the weight onwards, and about
doubles the extension of the spring corresponding to that weight
when at rest.
One point of difference, however, will become obvious between
the cases of the ship and the spring. It has been virtually
assumed that the vessel, with all sails set, has been becalmed, say
by some headland, but, suddenly passing out of this shelter, she
is struck by the wind, which heels her over and continues to
blow steadily for some time after its sudden application. Now
inclination of the ship at once reduces the moment of the wind-
pressure on the sails. Turning to the section, Fig. 29, page 74,
su])pose P to be the pressure of the wind, acting horizontally
CHAP. IV. OSCILLATION IN STILL WATER. 1 69
and athwartships, let h be the height of its line of action above
that of the equal and opposite fluid resistance P. Then initialhj
the inclining moment of the wind on the sails will be given by
tlie equation,
Moment of sail power = P x /i.
But the ship begins to heel as soon as the wind pressure begins
to act, and for an inclination « we should have approximately, if
the ship were at rest,
Moment of sail power = V x h cos^ a.
This law of decrease in the moment of the sails does not profess
to be accurate, and is known to be very invccurate for large
angles of inclination ; but it is generally accepted as sufficiently
near the truth for })ractical purposes. It must be noted, how-
ever, that in this method no account is taken of the reduction of
the effective pressure of the wind on the sails produced by their
motion to leeward, so that the results obtained therefrom can be
regarded only as very roughly approximate. This will be further
explained hereafter (see also Chapter XII.).
An illustration of the use of this curve of (cosines)^, or " wind
curve," is given in Fig. 55 ; it is marked WCDW. Two curves
of stability (1 and 2), for the Captain and Monarch respectively,
also appear in tliat diagram ; but the ordinates represent statical
moments of stability instead of simple GZ values, this arrange-
ment being made in order that the comparison between the two
ships may allow for their different displacements. It will be
assumed that they have equal sail spread and moments of sail,
so that one wind curve will serve for both ships. The force of
wind is supposed sufScient to hold the Captain at a steady heel
of nearly 10 degrees, and the Monarch at a slightly greater heel.
"No matter how far the vessels become inclinetl, if the wind con-
tinues to act upon them, the part of the areas of the curves
lying between the wind curve and the base-line will be absorbed
in counterbalancing the steady pressure of the wind. Hence
only the areas lying above the wind cnrve are available to resist
gusts or squalls ; and these areas are therefore termed the " reserve
dynamical stability." Supposing the r'.-serve to be large, the
ship is much safer than if it be small, and on reference to the
diagram (Fig. 55) it will be seen how very small was the reserve
in the Captain when compared with the Monarch. Lowness of
freeboard associated with a moderate metacentric height con-
tributed to give the ill-fated CapAain a curve of stability of quite
170
NAVAL ARCHITECTURE.
CHAP. IV.
a different character from that of any
masts and sails. Prior to her loss our
curves of stability for various chisses
but now that numerous and laboriou
made, the very exceptional character
clearly, as may be seen by reference
comparing her with the Monarch, as
other ship of war carrying
information respecting the
of ships was very meagre ;
s investigations have been
of the Captain stands out
to Figs. 47 and 47c. In
in Fig. 55, we have taken
Fia 55.
a rigged ironclad below the average as to the range of her
stability, but even then the contrast is most remarkable. This
will appear from the following statement, published, by authority,
soon after the loss of the Captain, when many persons expressed
fears, which were groundless, that a similar catastrophe might
happen to the Monarch : —
Monarch.
Captain.
Angle at which the edge of the deck is immersed
Amount of righting force in the above position "1
(in foot-tons of moment) J
Angle of maximum stability
Maximum righting force (in foot-tons of moment)
Angle at which the righting force becomes zerol
(range of stability) i
Reserve of dynamical stability at an angle of^
heel of 14 degrees (in foot-tons of work) . ./
28°
12,542
40°
15,615
69i°
6,500
14°
5,600
21°
7,100
54 J°
410
The last comparison is the most important as regards safety and
from it one sees how small was the margin of safety of the Captain
when sailing, as she is reported to have done on the day prior to
her loss, at an angle of heel of 14 degrees. Adding to the wind
pressure, the heave of the sea, and rolling oscillations, the reasons
of the disaster are obvious.
Fig. 55 also furnishes an illustration of the method by which
an approximation can be made to the maximum heel to which a
CHAP. IV.
OSCILLATION IN STILL WATER.
171
ship is driven by a squall of wind having a certain force if her
motion is unresisted. Let WW be the wind curve as before ; the
point C, where WW intersects the curve of stability (1) for the
Captain, determines the steady heel corresponding to the assumed
force of wind. The ship is iqyright and at rest when struck, and
between the upright and the angle of steady heel the moment of
sails continuously exceeds the statical righting moment ; hence
there is an unbalanced force throughout this part of the motion,
storing up work (represented by the area OWC) which is after-
wards expended in carrying on the ship until an inclination (EF)
is reached (about 20 degrees in this case) making the area (CEF)
above the wind curve equal to the area WOC. The Monarch
would be driven over to nearly an equal angle by the same squall ;
GH marks the inclination, the area GKH being equal to the area
WOK.
A still more critical case is that where the ship has just com-
pleted a roll to windward when the squall strikes her. Accumu-
lation of work then becomes far more serious ; the righting
moment and the moment of the sails act together as an unbalanced
moment all the time that the vessel is moving back to the upright,
the condition of things on the leeward side of the upright being
similar to that already described. Fio;. 56 illustrates this case
so X
V^K
for the Captain. The extreme angle of roll to windward, before
the squall strikes the ship, is indicated by the ordinate GHK (8
degrees); the ordinate LM marks the inclination (40 degrees)
she must reach to leeward before the reserve of dynamical stability
measured by the area CELMC can furnish the requisite amount
of work to destroy the motion due to the accumulated work of
roll and wind measured by the equal area GKOCWG.* This
* The wind curve is the same as in
Fig. 55, the corresponding angle of
steady heel being nearly 10 degrees ;
this curve will obviously be sym-
metrical about the upright position
indicated by OY. On the windward
172 NAVAL ARCHITECTURE. chap. iv.
case shows that even in a calm sea a rigged ship of low freeboard
or limited range of stability may run great risk of being capsized
if struck by a squall, and illustrates the great advantages
possessed by vessels having a large reserve of dynamical stability.
Ships of the mastless type are less affected by the action of these
suddenly applied squalls and gusts. Tlieir broadsides do not
offer sufficient surface to produce any sensible inclination in
storms of ordinary severity. For instance, in the Devastation
it is estimated that, with a storm of wind exerting a pressure
of 100 lbs. per square foot, an inclination of only 5 degrees
would be produced; but this pressure is about twice "as great
as that of a hurricane having a speed of 100 knots per hour.
Hence a far more moderate range and area of the curves of
stability is admissible for such vessels than is proper in rigged
ships, and the Admiralty committee on designs recommended a
range of 50 degrees as sufficient for such vessels, regarding them
as safe even with a less range of stability.
It is necessary to remark that in the preceding estimate for
the heeling effect of squalls no account has been taken of fluid
resistance, ^hich would assist in checking the motion, and bring
a ship up at a less inclination than has been indicated. When
the curve of extiuction for a ship is known, and her " coefficients
of resistance " have been deduced therefrom, it is possible to
make the necessary corrections in the estimates for heeling :
but this is not commonly done. The method to be followed will
be understood from the explanations given (on page 157) of the
manner in which the " work " done by the resistance during a
single swing can be measured from the curve of extinction.
Moreover, it must be noted that when a ship is struck by a
squall and moves away to leeward, her motion affects both the
relative velocity and pressure of the wind on her sails, as well
as the height of the centre of pressure. This matter has been
mentioned above, and was fully discussed by the Author in a paper
read before tlie Institution of Naval Architects in 1881 ; but
the treatment is of too mathematical a character to be reproduced
side (to the left) of OY it will be that it is convenient to indicate the
noticed that the curve of stability contrary tendency existing on the
is drawn lelow the base-line OX ; the windward side (i.e. a tendency to drive
reason for so doing is that on the the vessel back to leeward) by draw-
riglit-hand side (to leeward) ordinates ing the ordinates below the axis. No
measured above the axis tend to make other feature in the diagram appears
the vessel move back to windward, so to require further explanation.
CHAP. IV. OSCILLATION IN STILL WATER. 173
here. It may be interesting, however, to quote from that paper
a few figures illustrating the very great influence which the
action of fluid resistance, and the diminution in the moment
of wind pressure produced by the angular motion of the sails,
may have upon the angle to which a ship lurches when struck
by a squall. Taking the unarmoured frigate Endymion of the
Eoyal Navy, she is supposed to have reached an extreme incli-
nation of 20 degrees to the windward side of the vertical and
to be instantaneously at rest when a squall strikes her ; then, by
the method explained in Fig. 56, she would be driven over to 39
degrees on the leeward side of the vertical. All other conditions
remaining unaltered, except that the effect of the fluid resistance
is included, the extreme roll to leeward is found to be reduced
from 39 degrees to 31 degrees. And, taking one step further, if
allowance is made for the reductioa in the effective pressure of
the wind on the sails during the roll to leeward, the extreme
inclination reached is 22 degrees, or 2 degrees only beyond the
initial inclination to windward. The process of "graphic inte-
gration " by which these results are obtained is briefly explained
in Chapter VI., and it would enable the problem to be solved
completely, were it not for the fact that so little is known of the
laws governing the pressure of wind on sails. But enough has
been done to show how large is the margin of safety which is
provided by the method described in Fig. 5d,
Unfortunately, illustrations are not wanting of the possibility
of sailing vessels being capsized in smooth water by the action of
squalls. Two of the most recent are those of the American yacht
MohaicJc, and H.M.S. Enrydice* The Moliawh was at anchor off
Staten Island in 1876, with sail set, when the squall struck her.
Being unprepared for bad weatiier, the heavy furniture and
ballast shifted as the yacht heeled over ; and, soon after her deck
was immersed, the water poured into the cabin and cock-pit ; so
that all chance of righting was lost. It has been estimated that
if the curve of stability of the Mohaivk were calculated in the
usual manner, on the assumption that no weights shifted and no
water entered the hold, the angle of maximum stability would
have been reached at 30 degrees, and the range would have been
about 80 degrees. Under the circumstances described such
a curve obviously did not represent the actual conditions of
* See reports of evidence given Kemp's valuable work on Yacht and
before the Eurydice Court Martial ; Boat-sailing.
also, as to Mohaivk, see Mr. Dixon
I 74 NA VAL ARCHITECTURE. chap. iv.
stability of the vessel. In tlie case of the Eurydice also the
actual curve of stability at the time the vessel was struck by the
squall differed greatly from that made on the ordinary assump-
tions; and, as explained on page 126, the ports being open
virtually reduced the vessel to the condition of a low freeboard
rigged ship. The court martial recognised these facts in their
report ; and recorded their opinion that some of the lee-ports
being open "materially conduced to the catastrophe." In their
judgment also, these ports " having been open was justifiable and
" usual under the state of the wind and weather up to the time of
"the actual occurrence of the storm."
CHAP. V. DEEP-SEA WAVES. 1 75
CHAPTER V.
DEEP-SEA WAVES.
Many attempts have been made to construct a mathematical
theory of wave motion, and thence to deduce the probable
behaviour of ships at sea; and the diversity of these theories
affords ample evidence, if evidence were needed, of the difficulties
of the subject. To an ordinary observer perhaps no phenomena
appear less susceptible of matliematical treatment than the rapid
and constant changes witnessed in a seaway ; but it is now gene-
rally agreed that the modern or trochoidal theory of wave motion
fairly represents the phenomena, while preceding theories do not.
"Without attempting any account of the earlier theories, it is
proposed in the present chapter to endeavour, in a simple manner,
to explain the main features of tlie trochoidal theory for deep-
sea waves.
Let it be supposed that, after a storm has subsided, a voyager
in mid-ocean meets with a series of waves all of which are
approximately of the same form and dimensions; these would
constitute a single, or independent, series such as the trochoidal
theory contemplates. For all practical purposes, such waves may
be regarded as traversing an ocean of unlimited extent, where
the depth, in proportion to the wave dimensions, is so great as to
be virtually unlimited also; these are the conditions upon which
the theory is based. The bottom is supposed to be so deep down
that no disturbance produced by the passage of waves can reach
it; and the regular succession of the waves requires the absence
of boundaries to the space traversed. It is not supposed, however,
that an ordinary seaway consists of such a regular single series of
waves; on the contrary, more frequently than otherwise two or
more series of waves exist simultaneously, over-riding one another,
and causing a " confused sea," successive waves being of unequal
size and varying form. But sometimes the conditions assumed
176 NAVAL ARCHITECTURE. chap. V.
are fulfilled — a well-defined regular series of waves is met with ;
and from the investigation of their motions it is possible, as we
shall see hereafter, to pass to the case of a confused sea. Nor is
it supposed that only deep-sea waves are worthy of investigation ;
those occurring in shallower water also present notable features^,
but for our present purpose they are not nearly so important as
ocean waves, since these latter so largely influence the behaviour
of ships. It will be understood tlien that in what follows, unless
the contrary is stated, we are dealing with a single series of
regular deep-sea waves.
Any one observing such waves cannot fail to be struck witli
their apparently rapid advance, even when their dimensions are
moderate. A wave 200 feet in length, from hollow to hollow,
has a velocity of 19 knots per hour — faster than the fastest steam-
gljip — and such waves are of common occurrence. A wave 400
feet in length has a velocity of 27 knots per hour; and an
Atlantic storm wave, 600 feet long, such as Dr. Scoresby observed,
moves onward at the speed of 32 knots per hour. ]3ut it is most
important to note that in all wave motion it is the ivave form
which travels at these bigh speeds, and not the particles of water.
Tliis assertion is borne out by careful observation and common
experience. If a log of wood is dropped overboard from a ship
past which waves are racing at great speed, it is well known that
it is not swept away, as it must be if the particles of water ha-l a
rapid motion of advance, and as it would be on a tideway where
the particles of water move onwards ; but it simply sways back-
ward and forward as successive waves pass.
Before explaining this distinction between the motions of the
particles in the wave and the motion of the wave form, it will be
well to illustrate the mode in which, according to the modern
theory, the wave form or profile may be constructed. Fig. 57 will
serve tkis purpose. Suppose QR to be a straight line, under
which the large circle whose radius is OQ is made to roll. The
lenoth QU being made equal to the semi-ciicumferenee, the roll-
ingcircle will have completed half a revolution during its motion
from Q to E ; and if this length QR and the semi-circumference
QRi are each divided into the same number of equal parts (num-
bered correspondingly 1, 2, 3, &c., in the diagram), then obviously,
as the circle rolls, the points with corresponding numbers on the
straight line and circle will come into contact successively, each
with each. Next suppose a point P to be taken on the radius
ORi of the rolling circle ; this will be termed the " tracing point,"
and as the circle rolls, the point P will trace a curve (a trochoid,
CHAP. V.
DEEP-SEA WAVES.
^11
marked P, a.^^ l^, c^ 1h in the diagram) which is the theo-
retical wave profile from hollow to crest, P marking the hollow
and 7^2 the crest. The trochoid may, therefore, be popularly
described as the curve traced on a vertical wall by a marking-
point fixed in one of the spokes of a wheel, when the wheel is
made to run along a level piece of ground at the foot of the
wall ; but when thus described, it would be inverted from the
position shown in Fig. 57.
To determine a point on the trochoid is very simple. With
0 as centre and OP as radius describe the circle PcA. As the
rolling circle advances, a point on its circumference (say 3) comes
into contact with the corresponding point of the directrix-line
QR; tlie centre of the circles must at that instant be (S) verti-
cally below the point of contact (3), and the angle through which
the circular disc and the tracing arm OP have both turned is
given by Q03. The angle POc, on the original position of the
circles, equals Q03 ; through S draw Sc^ parallel to Oc, and make
Sc2 equal to Oc ; then c^ is a point on the trochoid. Or the same
result may be reached by drawing cc^ horizontal, finding its inter-
section (cg) with the vertical line S3, and then making CgCg equal
to cc^. In algebraical language, this may be simply expressed.
Take Q as the origin of co-ordinates, QR for axis of abscissa3 {x).
Let radius OQ = a,
„ OP = 5,
angle Q03 = %,
and X, y co-ordinates of point c^ on trochoid.
N
178
NAVAL ARCHITECTURE.
CHAP. V.
Then
X
CiCi
^1^3 ~*~ ^2 3
= a0 + 6 sin ^ ;
?/ = CiQ = OQ + Oci
= « + & cos Q.
The tracing arm (OP) may, for wave motion, have any value
not greater than the radius of the rolling circle (OQ). If OP
equals OQ, and the tracing point lies on the circumference of the
rolliuo- circle, the curve traced is termed a eijdoicl ; such a wave
is on the point of breaking. The curve EiTR, in Fig. 57, shows
a cycloid, and it will be noticed that the crest is a sharp ridge or
line (at E), while the hollow is a very flat curve.
A few definitions must now be given of terms that will be
frequently used hereafter. The length of a wave is its measure-
ment (in feet usually) from crest to crest, or hollow to hollow —
QR in Fig. 57 would be the half-length. The height of a wave
is reckoned (in feet usually) from hollow to crest ; thus in Fig. 57,
for the trochoidal wave, the height would be Vh ; or twice the
tracing arm. The i:ieriod of a wave is the time (usually in seconds)
its crest or hollow occupies in traversing a distance equal to its
own length ; and the velocity (in feet per second) will, of course,
be obtained by finding the quotient of the length divided by the
period, and Avould commonly be determined by noting the speed
of advance of the wave crest.
Accepting the condition, that the profile of an ocean wave is a
trochoid, the motion of the particles of water in the wave requires
FIG. 58.
Direction of Advance
to be noticed, and it is here the explanation is found of the rapid
advance of the wave form, while individual particles have little or
no advance. The trochoidal theory teaches that every particle
revolves with uniform speed in a circular orbit (situated in a
vertical plane which is perpendicular to the wave ridge), and
completes a revolution during the period in which the wave
advances through its own length. In Fig. 58, suppose P, P, P,
&c. to be particles on the upper surface, their orbits being the
CHAP. V.
DEEP-SEA WAVES. I 79
equal circles shown : then, for this position of the wave, the radii
of the orbits are indicated by OP, OP, &c. The arrow below the
wave profile indicates that it is advancing from right to left ; the
short arrows on the circular orbits show that at the wave crest the
particle is moving in the same direction as the wave is advancing
in, while at the hollow the particle is moving in the opposite
direction. It need hardly be stated again that for these surface
particles the diameter of the orbits equals the height of the wave.
Now suppose all the tracing arms OP, OP, &c. to turn through
the equal angles POj?, PO^, &e. : then the points _p, j9, _p, &c. must
be corresponding positions of particles on the surface formerly
situated at P, P, &c. The curve drawn through ^;, j?, 2?, &c. will
be a trochoid identical in form with P, P, P, &c., only it will have
its crest and hollow further to the left ; and this is a motion of
advance in the wave form produced by simple revolution of the
tracing arms and particles (P).* The motion of the particles in
the direction of advance is limited by the diameter of their orbits,
and they sway to and fro about the centres of the orbits. Hence
it becomes obvious why a log dropped overboard, as described
above, does not travel away on the wave upon which it falls, but
simply sways backward and forward. One other point respecting
the orbital motion of the particles is noteworthy. This motion
may be regarded at every instance as the resultant of two motions
— one vertical, the other horizontal — except in four positions, viz. :
(1) when the particle is on the wave crest ; (2) when it is in the
wave hollow ; (3) when it is at mid-height on one side of its orbit ;
(4) when it is at the corresponding position on the other side.
On the crest or hollow the particle instantaneously moves hori-
zontally, and has no vertical motion. At mid-height it moves
vertically, and has no horizontal motion. Its maximum hori-
zontal velocity will be at the crest or hollow; its maximum
vertical velocity at mid-height. Hence uniform motion along
the circular orbit is accompanied by accelerations and retarda-
tions of the component velocities in the horizontal and vertical
directions.
The particles which lie upon the trochoidal upper surface of the
wave are situated in the level surface of the water when at rest.
* It is possible to construct a very of advance ; and in lectures delivered
simple apparatus by which the simul- at the Royal Naval College such an
taneous revolution of a series of par- apparatus was used by the Author,
tides will produce the apparent motion
N 2
I So
NAVAL ARCHITECTURE.
CHAP. V.
The disturbance caused by the passage of the wave must extend
far below the surface, affecting a great mass of water. But at
some depth, supposing the depth of the sea to be very great, the
disturbance will have^ practically ceased: that is to say, still,
FIC.59.
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undisturbed water may be conceived as underlying the water
forming the wave ; and reckoning downwards from the surface,
the extent of disturbance must decrease according to some law.
The trochoidal theory expresses the law of decrease, and enables
the whole of the internal structure of a wave to be illustrated in
CHAP, V.
DEEP-SEA WAVES. l8l
the manner shown in Fig. 59.* On the right-hand side of the
line AD the horizontal lines marked 0, 1, 2, 3, &c. show the posi-
tions in still water of a series of particles which during the wave
transit assume the trochoidal forms numbered respectively 0, 1,
2, 3, &c. to the left of AD. For still water every unit of area in
the same horizontal plane has to sustain the same pressure : hence
a horizontal plane would be termed a surface 'or subsurface of
" equal pressure," when the water is at rest. As the wave passes,
the trochoidal surface corresponding to that horizontal plane will
continue to be a subsurface of equal pressure ; and the particles
lying between any two planes (say 6 and 7) in still water will, in
the wave, be found lying between the corresponding trochoidal
surfaces (6 and 7).
In Fig. 59, it will be noticed that the level of the still-water
surface (0) is supposed changed to a cycloidal wave (0), the con-
struction of which has already been explained ; this is the
limiting height the wave could reach without breaking. The
half-length of the wave xlB being called L, the radius (CD) of
the orbits of the surface particles will be given by the equation,
CD = R = ^ = 1 L (nearly).
All the trochoidal subsurfaces have the same length as the cyc-
loidal surface, and consequently they are generated by the motion
of a rolling circle of radius R ; but their tracing arms — measure-
ing half the heights from hollow to crest — rapidly decrease with
the depth (as shown by the dotted circles), the trochoids becoming-
flatter and flatter in consequence. The crests and hollows of all
the subsurfaces are vertically below the crest and hollow of the
upper wave profile. The heights of these subsurfaces diminish in
a geometrical progression, as the depth increases in arithmetical
progression ; and the following approximate rule is very nearly
correct. The orbits and velocities of the particles of water are
diminished by one-half fov each additional depth below the mid-
height of the surface wave equal to one-ninth of a wave length. f
For example —
Depths in fractions of a wave length below the^ n i 2 ■? 4 «
mid-height of the surface wave J 0' 9' 9» 9» 9> &c.
Proportionate velocities and diameters . . . 1, ^, ^, }, ^q, &c.
* This diagram we borrow from Mr. of the first constructed, and is therefore
Fronde's paper on "Wave Motion" in reproduced.
the Transactions of the Institution of f See'pa.gelOoi Shiphuildiuff, TJieo-
Naval Architects for 1862 ; it was one retical and Practical, edited by tlie
1 82 NAVAL ARCHITECTURE. chap. v.
Take an ocean storm wave 600 feet long and 40 feet high from
hollow to crest : at a deptli of 200 feet below the surface (| of
length), the subsurface trochoid would have a height of about
5 feet ; at a depth of 400 feet (f of length) the height of the
trochoid — measuring the diameter of the orbits of the particles
there — would be about 7 or 8 inches only ; and the curvature
would be practically insensible on the length of 600 feet. This
rule is sufficient for practical purposes, and we need not give
the exact exponential formula expressing the variation in the
radii of the orbits with the depths.
It will be noticed also in Fig. 59 that the centres of the
tracing circles corresponding to any trochoidal surface lie above
the still water-level of the corresponding horizontal plane. Take
the horizontal plane (1), for instance. The height of the centre
of the tracing circle for the corresponding trochoid (1) is marked
E, EF being the radius ; and the point E is some distance above
the level of the horizontal line (I). Suppose r to be the radius
of the orbits for the trochoid under consideration, and R the
radius of the rolling circle : then the centre (E) of the tracing
circle (i.e. the mid-height of the trochoid) will be above the level
line (1) by a distance equal to r" -^ 2 R. Now R is known when
the length of the wave is known : also r is given for any depth
by the above approximate rule. Consequently, the reader has
in his hands the means of drawing the series of trochoidal
subsurfaces for any wave that may be chosen.
Columns of particles which are vertical in still water become
curved during the wave passage ; in Fig. 59, a series of such
vertical lines is drawn (see the jine lines a, h, c, d, &e.) ; during
the wave transit these lines assume the positions shown by the
strong lines {a, h, e, d, &c.) curving towards the wave crest at their
upper ends, but still continuing to inclose between any two the
same particles as were inclosed by the two corresponding lines in
still water. The rectangular spaces inclosed by these vertical
lines (a, h, e, d, &c.) and the level lines (0, 1, 2, &c.) produced are
changed during the motion into rhomboidal-shaped figures, but
remain unchanged in area. Very often the motions of tliese
originally vertical columns of particles have been compared to
those occurring in a corn-field, where the stalks sway to and fro,
and a wave form travels across the top of the growing corn. But
while there are points of resemblance between the two cases, there
late Professor Eankine ; who, with the the trochoidal theory, originally pro-
late Mr. Froude, did much to develop pounded by Gerstner.
CHAP. V.
DEEP-SEA WA VES.
183
is also this important difference — the corn-stalks are of constant
length, whereas the originally vertical columns become elongated
in the neighbourhood of the wave crests, and shortened near the
wave hollows.
These are the chief features in the internal structure of a
trochoidal wave, and in the following chapter they will be again
referred to in order to explain the action of waves upon ships. It
is necessary, however, at once to draw attention to the fact that
the conditions and direction of fluid pressure in a wave must
differ greatly from those for still water. Each particle in the
wave, moving at uniform speed in a circular orbit, will be
subjected to the action of centrifugal force as well as the force of
gravity ; and the resultant of these two forces must be found in
order to determine the direction and magnitude of the pressure
on that particle. This may be simply done as
shown in Fig. 60 for a surface particle in a wave.
Let BED be the orbit of the particle; A its
centre ; and B the position of the particle in its
orbit at any time. Join the centre of the orbit
A with B ; then the centrifugal force acts along
the radius AB, and the length AB may be sup-
posed to represent it. Through A draw AC
vertically, and make it equal to the radius (R)
of the rolling circle ; then it is known that AC
will represent the force of gravity on the same
scale as AB represents centrifugal force. Join
BC, and it will represent in magnitude and direction the re-
sultant of the two forces acting on the particle. Now it is an
established property of a fluid that its free surface will place
itself at right angles to the resultant force impressed upon it.
For instance, take the simple case of a rectangular box (shown in
FIG 61.
Fig. 61) containing water, which is made to move along a smooth
horizontal plane by the continued application of a force F ; then
184 NAVAL ARCHITECTURE. chap. v.
we shall have uniformly accelerated motion, equal increments of
velocity being added in successive units of time.* In order to
compare this force with that of gravity, if/ is the velocity added
per second of time, and W is the weight of the box and water, we
should have,
F / /
"Now it is well known that under the assumed circumstances of
motion the surface of the water in tlie box will no longer remain
level, but will attain some definite slope such as AB in Fig. 61 ;
and it is easy to ascertain the angle of slope. Through any point G
draw GH vertical to represent the weight W, and GK horizontal
to represent the force F ; join HK, and it will represent the
resultant of the two forces, the water surface AB placing itself
perpendicular to the line, on the principle mentioned above.
The tangent of the angle w^hich the surface AB makes with the
horizon will equal the ratio of F to W.
Reverting to Fig. 60, the resultant pressure shown by BC must
be normal to that part of the trochoidal surface PQ where the
particle B is situated. Similarly, for the position Bj, CBi will
represent the resultant force ; PiQi drawn perpendicularly to CBj,
being a tangent to the trochoid at B^. Conversely, for any point
on any trochoidal surface in a wave, the direction of the fluid
pressure must lie along the normal to that surface. Hence it
follows that wave motion involves constant changes in the mas;-
nitude and direction of the fluid pressure for any trochoidal
surface ; these changes of direction partaking of the character of
a regular oscillation keeping time with the wave motion. At the
wave hollow the fluid pressure acts along a vertical line ; as its
point of application proceeds along the curve, its direction
becomes more and more inclined to the vertical, until it reaches a
maximum inclination at the point of inflexion of the trochoid ;
thence onwards towards the crest the inclination of the normal
pressure is constantly decreasing until at the crest it is once
more vertical. If a small raft floats on the wave (as shown in
Fig. 62), it will at every instant place its mast in the direction of
the resultant fluid pressure, and in the diagram several positions
of the raft are indicated to the left of the wave crest. These
motions of the direction of the normal to the trochoid may be
compared with those of a pendulum, performing an oscillation
See remarks on this subject at page 135 of Chapter IV.
CHAP. V.
DEEPS E A WAVES.
185
from an ano-le equal to the maximum inclination of the normal
on one side of the vertical to an equal angle on the other side,
and completing a single swing during a period equal to half the
wave period.
FIG. 62.
"'i^vr/ace ofSHIlWater
The maximum slope of the wave to the horizon occurs at a
point somewhat nearer the crest than the hollow, but no great
error is assumed in supposing it to be at mid-height in ocean
waves of common occurrence where the radius of the tracing arm
(or half-height of the wave) is about one-twentieth of the length.
For this maximum slope, we have
radius of tracing circle
Sine of ano;le =
radius of rolling circle
half-height of wave
length of wave-^6*2832
= 3-1416 X
height of wave
lenath of wave'
180^
heio-ht of wave
y. — ^ ^ •
lenath of wave
For waves of ordinary steepness all practical purpo.ses are served
by writing the circular measure of the angle instead of the sine ;
hence ordinarily we may say,
Approximate maximum wave slope I
(in degrees)
Take, as an example, a wave for which the dimensions were
actually determined in the Pacific, 180 feet long and 7 feet
high :
7
Maximum slope = 180° x -v^ = 7^ (nearly).
The variation in the direction of the normal was in this case
similar to an oscillation of a pendulum swinging 7 degrees on
either side of the vertical once in every half-period of the wave
1 86 NAVAL ARCHITECTURE. chap. v.
— some 3 seconds. These constant and rapid variations in the
direction of the fluid pressure in Avave water constitute the chief
distinction between it and still water, where the resultant pres-
sure on any floating body always acts in one direction, viz. the
vertical.
But it is also necessary to notice that in wave water the
intensity as well as the direction of the fluid pressure varies from
point to point, Keverting to Fig. 60, and remembering that
lines such as BC represent the pressure in magnitude as well as
direction, we can at once compare the extremes of the variation
in intensity. In the upper half of the orbit of a particle, centri-
fugal force acts against gravity, and reduces the weight of the
particle; this reduction reaches a maximum at the wave crest,
when the resultant is represented by CE = (R - r). In the lower
half of the orbit, gravity and centrifugal force act together, pro-
ducing a virtual increase in the weight of each particle ; the
maximum increase being at the wave hollow, where the resultant
is represented by CD = (R + r). If a little float accompanies the
wave motion, it may be treated as if it were a particle in the
wave, and its apparent weight will undergo similar variations. In
a ship, heaving up and down on waves very large as compared
with herself, the same kind of variations will occur, though per-
haps not to the same extent as in the little float. Actual obser-
vation shows this to be true. Captain Mottez, of the French
navy, reports that on long waves about 26 feet high the apparent
weights of a frigate at hollow and crest had the ratio of 12 to 8.
According to the preceding rules we must then have,
B-r_ 8
R-t-r 12'
2R_20
2r~ 4'
R = 5r = 5 X 13 = 65 feet.
Length of waves (by theory) =27rR = 6'28 x 65 = 408 feet.
This, in proportion to the height recorded, is not an unreasonable
length; but, unfortunately, Captain Mottez does not appear to
have completed the information required, by measuring the
actual length of the waves. The important fact he proved, how-
ever, is one that theory had predicted, viz. that the heaving
motion of the waves may produce a virtual variation in the weight
of a ship equivalent to an increase or decrease of one-fourth or
one-fifth, when the proportions of the height and length of the
waves are those common at sea.
CHAP. V,
DEEP-SEA WAVES. 1 87
Instead of the raft in Fig. 62, if the motions of a loaded pole
or plank on-end (such as SSi), be traced, it will be found that it
teads to follow the originally vertical lines, and to roll always
toward the crest as they do. Here again the motion partakes
of the nature of an oscillation of fixed range performed in
half the wave period, the pole being upright at the hollow and
crest.
A ship differs from both the raft and the pole ; for she has
both lateral and vertical extension' into the subsurfaces of the
wave, and cannot be considered to follow either the motion of the
surface particles like the raft or of an originally vertical line of
particles like the pole. This case will be discussed in the next
chapter.
The trochoidal theory connects the periods and speeds of waves
with their lengths alone, and fixes the limiting ratio of height
to length in a cycloidal wave. The principal formulae for lengths,
speeds, and periods for trochoidal waves are as follows : —
I. Length of wave (in feet) = 5-123 X square of period (in seconds)
= 5^ X square of period (nearly).
II. Speed of wave (in feet) ^.^23 x period = V 5-123 X length
per second) . . .j
= 2i \/length (nearly).
III. Speed of wave (in) 3^ .^^. gj^j^,^_
knots per hour) .j
IV. Period (in seconds) = \/ ^"^ = 5 \/ length (nearly).
V. Orbital velocity of) Jspeedof) 3"1416 X height of wave
particles on surface j ~ [ wave j length of wave
height of wave , , ,
= 71 X —j^=^==== (nearly).
\y length oi wave
To illustrate these formulae, we will take the case of a wave 400
feet long and 15 feet higii. For it we obtain,
4 -
Period = ^\/400 = 8| second.
9
Speed = T/\/400 = 45 feet per second.
= 3 ?f 8| = 26f knots per hour.
Orbital velocity of | ^ ^ 15 ^ ^^^^ ^^^^^^^^
surface particles j ^ 'X/^OO
1 88
NAVAL ARCHITECTURE.
CHAP. V.
It will be remarked that the orbital velocity of the particles is
very small when compared with the speed of advance ; and this
is always the case. In formula V, if we substitute, as an average
ratio for ocean waves of large size,
Height = ^Q X length,
the expression becomes —
g^o X length
Orbital velocity of surface particles = 7^ X \ . ^ ,=~
■' \/ length
= 0-355 V length.
Comparing this with Formula II. for speed of advance, it will be
seen that the latter will be between six and seven times the orbital
velocity.
The periods of waves are most easily observed, and the follow-
ing table will be useful as giving the lengths and speeds of
troc'hoidal waves for which the periods are known : —
Period.
Length.
Sp
Fp
per St
eetl of Advance.
Seconds.
Feet.
et
cond.
Knots
per Hour.
1
5-12
5
12
3-03
2
20-49
10
24
6-07
3
46-11
15
37
9-1
4
81-97
20
49
12-14
5
128-08
25
62
15-17
6
184-44
30
74
18-21
7
251-04
35
86
21-24
8
327-89
40
99
24-28
9
414-99
46
11
27-31
10
512-33
51
23
30-35
11
619-92
56
36
33-38
12
737-76
61
48
36-42
13
865-84
66
6
39-45
14
1004-17
71
73
42-49
15
1152-74
76
85
45-52
16
1311-56
81-97
48-56
As a mathematical theory, that for trochoidal waves is complete
and satisfactory, under the conditions upon which it is based ;
but sea-water is not a jperfeet fluid such as the theory contem-
plates; in it there exists a certain amount of viscosity, and the
particles must experience resistance in changing their relative
positions. There is every reason to believe that the theory
closely approximates to the phenomena of deep-sea waves, but it
is very desirable that extensive and accurate observations of the
dimensions and speeds of actual waves should be made, in order
to test the theory, and determine the closeness of its approxima-
CHAP. V.
DEEP-SEA WAVES. 1 89
tion to truth. The recorded observations ou waves are not so
complete or numerous as to furnish the test required; and, by-
adding to them during their service at sea, naval officers will
do much to advance one important branch of the science of naval
architecture.
Systematic observations of ocean waves scarcely appear to have
been attempted uutil within the last half-century. Amongst the
earliest workers in this field were Di-. Scoresby, Mr. Walker, and
Commodore Wilkes (United States navy) ; and of these the first
named is justly the best known.* In 1847, Dr. Scoresby made a
series of valuable observations on Atlantic storm-waves ; and in
1856 he made a still more extensive series of observations during
a voyage to Australia via the Cape of Good Hope, and a return
voyage to England via Cape Horn. The records of wave-pheno-
mena, published by Dr. Scoresby, constituted, until recently, the
most valuable information on the subject; but during the last
ten years very numerous and trustworthy observations have been
made by officers of the Royal Navy, and by officers of the French
navy. Of the French observers the most laborious and dis-
tinguished is Lieutenant Paris, who, during a voyage of more
than two years (1867-70), observed and recorded several times
each day the state of the sea and the force of the wind. He has
been followed by other officers, whose labours have resulted in
the accumulation of an unrivalled mass of facts respecting the
lengths, periods, speeds, and heights of ocean waves. Much of
this information has been published, and will repay careful
study.f No similar publication has appeared of the results of
observations of waves made by officers of the Royal Navy during
the period above-named ; but the regulations issued by the Lords
Commissioners of the Admiralty provide for the frequent conduct
of such observations, and an analysis of the records ought to
yield valuable information.
* For the data obtained by Dr. t Lieutenant Paris' very able Me-
Scoresby see the Be^ort of the British moir will be found in vol. xxxi. of
Association for 1850, and his Journal the Bevihe Maritime. The most com-
ofa Voyage to Australia. The results plete summary of the French observa-
of Mr. Walker's observations will be tions with which we are acquainted is
found in the Beport of the British As- M. Antoine's Des Lames de Haute Mer
sociation for 1842; these observations (Paris, 1879). Much interesting in-
were made at Plymouth. Commodore formation and valuable suggestion is to
Wilkes' " Narrative of the United be found in M. Bertin's essay on the
States Exploring Expedition" (1838- " Experimental Study of Waves," pub-
42) contains the details of his observa- lished in the Transactions of the In-
tions made to the south of Cape Horn. stitution of Naval Architects for 1873.
190
NAVAL ARCHITECTURE.
CHAP. V.
From a scientific point of view, and as a test of the trochoidal
theory, the observations made when a ship falls in with a single
series of approximately regular waves are most valuable. More
frequently observations have to be conducted in a confused sea,
successive waves differing from one another in lengths, heights,
and periods; and occasional waves occurring of exceptional size
as compared with their neighbours. Careful notation of such
phenomena would throw light upon the question of the super-
position of series of waves, and explain many apparent discre-
pancies met with in simultaneous observations of waves made by
ships sailing in company. It is, however, obviously essential to
the value of all these observations that they should be conducted
on correct methods, and be accompanied by full records of the
attendant circumstances.
THrectian at
FIG 62 a
i
-\t/r-
^
Beferences.
1, Initial position of ship. 2. Her position at time t from beginning of obser-
vations. 3. Her position at time t^ from ditto.
Supposing a single series of waves to be encountered, the
lengths and ijeriods of successive waves can be easily determined,
if the speed of the ship and her course relatively to the line of
advance of the waves are known. The method adopted by Dr.
Scoresby and other early observers is still in use, and may be
briefly described.*
Two observers (A and B Fig. 62a) are stationed as far apart as
* We here follow very closely the
Memorandum prepared by the late
Mr. Froude, and approved by the
Admiralty for use in the Royal Navy .
CHAP. V. DEEP-SEA WA VES.
191
possible, and at a known longitudinal distance from one another.
At each station a pair of battens is erected so as to define, when
used as sights, a pair of parallel lines at right angles to the ship's
keel. The observer at the foremost station notes the instant of
time when a wave crest crosses his line of sight; he also notes
how long an interval elapses before the next wave crest passes
that line. The second observer makes two similar notations for
the respective crests. Comparing their records, the observers
determine (1) the time (say t seconds) occupied by the wave
crest in passing over the length (L feet) between their stations ;
(2) the time (say t^ seconds) elapsing between the passage of the
first and second crests across either line of sight : this time is
termed the "apparent period" of the waves. Suppose the
ship to be advancing at a speed of V feet per second towards the
waves, her course making an angle of a degrees with that course
which would place her end-on to the waves. Then, expressing
the facts algebraically : —
Apparent speed of w^ave (feet per second) = ~
Real speed of wave „ „ = Vj = (^-7 - V) cos o.
Eeal length of wave (feet) = (Vi + V cos a) t^
T ^^
= L cos a . T •
-r, . , „ L COS a ^1 \j .ti
reriod 01 wave = ~
Vi t L- Yt
If the ship is supposed to be steaming aivay from the waves on
the same course at the same speed, all that is necessary is to
invert the sign of V in the foregoing equations.
As an example, take the following observations made by Dr.
Scoresby during his voyage to Australia, in 1856. The Boijal
Charter was scudding directly before wind and sea, at a speed of
12 knots. An interval of 18 seconds elapsed between the passage
of two successive wave crests across the observer's line of si^rht ;
and any single wave crest took 9 seconds to traverse a length of
320 feet. Here we have : —
a = 0 ; L = 320 feet ; ^1 = 18 seconds ; ^ = 9 seconds ;
V = 20*25 feet per second.
Substituting in the foregoing equations,
/320 \
Eeal speed of waves = Vi =\-V" + 20-25 j = 55*8 ft. per sec.
192 NAVAL ARCHITECTURE. chap. v.
18
Real length of waves = 320 X -^ = 640 feet.
Eeal period of waves = f^tr = 11^ seconds (nearly).
From the foregoing remarks it will be obvious that the simplest
method of observing the lengths and periods of waves can be
applied when a ship is placed end-on to the waves and is sta-
tionary. The true period and true speed of the waves can then
be obtained by direct observation, and the lengths estimated.
When ships are sailing in company a good estimate of the
lengtlis of waves may be made by comparing the length of a ship
with the distance from crest to crest of successive waves. Care
must be taken, of course, to note the angle which the keel of the
ship used as a measure of length makes with the line of advance
of the waves ; otherwise the apparent length of the wave may
considerably exceed the true length.
Another method of measuring wave lengths consists in towing
a log-line astern of a ship, and noting the length of line when a
buoy attached to the after end floats on the wave crest next abaft
that on which the stern of the ship momentarily floats. This was
the method used by Commodore Wilkes of the United States
navy in the observations of waves made by him south of Cape
Horn in 1839; it has also been used in the Royal Navy. For its
successful application a ship should be placed end-on to the waves,
or allowance must be made for the departure of the log-line from
that end-on position.
Wave heights are, in most cases, readily measured by the
following simple method. When the ship is in the trough of the
sea, and for an instant upright, the observer takes up a position
such that the successive average wave ridges, as viewed by him
from the trough, just reach the line of the horizon without
obscuring it. The height of his eye above the water-level cor-
rectly measures the height of the wave. In making such obser-
vations it is desirable to select a position nearly amidships, so
that the influence of pitching and 'scending may be diminished
as much as possible ; but if it becomes necessary to take stations
near the bow or stern allowance must be made, in estimating the
height of the eye above water, for the deeper immersion which
may be caused at the instant by pitching or 'scending. Due
allowance must also be made for changes of level occasioned by-
rolling or heeling, as well as for the fact that when a ship end-on
to the waves is in the middle of the trough the curvature of the
CHAP. V.
DEEP-SEA WAVES.
193
FIG 63.
wave liollow gives extra immersion to her ends, while the water
surface amidships is somewhat below her natural water-line.
This method of estimating wave heights was used by Scoresby,
and has been adopted by most of his successors. To measure
very high waves the observer may have to ascend the rigging ;
while for waves of less height a station on one of the decks may
suffice, or some temporary expedient devised for placing an ob-
server near the water-level.
Other methods of measuring wave heights have been proposed,
based upon the fact (mentioned at page 182) that at a considerable
depth below the surface of a disturbed sea, practically still water
may be found. Mr. Froude devised one of the best methods of
this kind ; the apparatus required being very simple and easily
managed. It consisted of a light tapered spar
of comparatively small diameter, graduated and
marked in such a manner as enabled an observer
to note with ease the rise and fall of the waves
upon it. When in use this pole was " anchored "
to the undisturbed water by means of a deep-sea
line, to the lower end of which a light frame (see
Pig. 63) was attached, this frame carrying a
certain amount of ballast. The pole thus
weighted stood upright, and performed extremely
small vertical oscillations as the waves passed ;
consequently an observer on board a ship near
the pole could note the heights and periods of
waves with a close approach to accuracy. This
method was applied by Mr, Froude in connec-
tion with his experiments with the model of the
Devastation at Spithead (see Chapter YI.). It is particularly appli-
cable to cases where waves of small height are to be measured,
and where horizon observations are not easily made. For general
use at sea it is scarcely likely to find favour ; nor was it expected
to do so by Mr. Froude. Any apparatus of this kind requires
that the ship using it must be practically " hove-to " during the
time occupied in putting the apparatus overboard, testing its
adjustments, making the observations, and afterwards recovering
it. On the other hand horizon observations, when practicable,
can be made without interference with the progress of the ship.
Similar objections apply to the automatic " wave-tracer " con-
structed in 1866 by Admiral Paris of the French navy, and tried
at Brest with considerable success. The design of this instrument
was very simple. A light pole was prepared (similar to that used
o
194 NAVAL ARCHITECTURE. chap. v.
by Mr. Fronde) upon which to measure the rise and fall of the
waves. This pule was of con.siderable length as compared with
the heights of the waves to be measured, its cross-section was of
small area ; and it was baUasted with sheet lead in order that it
mi;^ht float upright, with a considerable portion of its lengtli pro-
jecting above the surface of still water. No attempt was made to
" anchor " the pole to the subjacent undisturbed water ; and it
consequently performed sensible, but small, vertical oscillations
as the waves rose and fell upon it. Ou its upper end a float
w'as fitted, this float rising and falling with the waves and sliding
up and down the pole. By means of simple mechanism the
motions of the float were automatically recortled on a revolving
cylinder, and the wave profiles were thus traced.* Waves up to
10 feet in height were thus recorded, and Lieutenant Paris
claimed for the instrument a full realisation of the hopes of its
inventor. He frankly confessed, however, that " a ship not espe-
cially detached for the purpose could hardly be exp>:'cted to arrest
her progress several times a day " in order to make use of the
wave tracer. Furthermore, it is evident that in waves of consi-
derable height the instrument could not be used successfully,
unless anchored to the undisturbed water lying far below the
surface.
In this connection it may be proper to add that the automatic
instruments devised by Mr. Froude and M. Bertin for recording
the rolling of ships in a seaway, furnish also a means of obtain-
ing valuable information respecting the waves amongst which
the ships carrying such instruments may be situated. This will
appear from the description given in ChajDter VII.
Having briefly described the principal methods of conducting
observations on ocean waves, it may be well to summarise the
dimensions of the largest waves of which we have any trustworthy
accounts. The longest wave observed was measured by Captain
Mottez, of the French navy, in the North Atlantic, and had a
length of 2750 feet — half a mile — from crest to crest ; its period
was 23 seconds. Dr. Scoresby sj^eaks of waves he observed in
the Southern Indian Ocean spreading out to " a quarter if not
half a mile " in one undulation and crest. In the South Atlantic,
Sir James Ross observed a wave 1920 feet long. The largest
waves observed in European waters are said to have had a period
of 19| seconds, corresponding to a theoretical length of some 2000
* See the Revue Maritime, vol. xx,, and Transactions of the Institution of
Naval Architects for 1867.
CHAP. V. DEEP-SEA WAVES. 1 95
feet ; in the Bay of Biscay waves have been noted having a length
of 1320 feet. These monster waves are not, however, commonly
encountered, and waves having a length of 600 to 700 feet would
ordinarily be regarded as large waves. Dr. Scoresby's largest
Atlantic storm waves had lengths of about 500 to GOO feet, and
periods irom 10 to 11 seconds. According to the best authorities,
ocean waves of 24 seconds' period, and some 3000 feet in length,
may be taken as the extreme limit of size yet proved to exist ;
waves of 18 seconds' period, and about 1650 feet in length, con-
stitute the upper limit in all except extraordinary cases ; and
what may be called common large storm waves have periods
varying from 6 to 9 seconds, the corresponding lengths varying
from 200 to 400 feet.
Turning next to heights, we find reports of estimated heights
of 100 feet from hollow to crest, but no verified measurement
exists of a height half as great as this. The highest trustworthy
measurements are from 44 to 48 feet— in itself a very remarkable
height. Scoresby and others have measured heights of about
40 to 45 feet, and there are numerous records of heights exceed-
ing 30 feet, although waves having a greater height than 30 feet
are not commonly encountered. All these figures, be it under-
stood, refer to a single series of waves, and not to one or more
series superposed on one another, nor to any great local rise of
level due to the waves driving against a shore, or passing over an
isolate'! rock.*
An explanation of the cause of unintentional exaggeration in
the estimate of wave heights will at
once sugo-est itself when the variation , "■ '
in the direction of the normal to the
wave slope (previously explained) is
taken into account. To an observer "v-
standing on the deck of a ship which is rolling amongst waves,
nothing is more difficult than to determine the true vertical
direction, along which the height of the wave must be measured.
If he stands on the raft shown in Fig. 64, he will, like it, be
* Exception has been taken to the 48° N., longitude 40° W,, during a pas-
above statement of maximum wave sage from Queenstown to New York,
heights by Commander Kiddle, R.N'., From the account given of the method
in an article appearing in the Nautical of observing the wave heights, it ap-
Magazine for August, 1878. 'J hat pears that there were several possible
officer states that in January, 1875, sources of error, and of so serious a
waves 1180 feet loDg and 70 feet high character as to make the results of
were observed by him in latitude questionable value.
o 2
196 NAVAL ARCHITECTURE. chap. v.
affected by the wave motion ; and the apparent vertical at any
instant will be coincident with the masts of the raft and normal
to the wave slope. He will therefore suppose himself to be looking
horizontally when he is really looking along a line parallel to the
tangent to the wave slope at that point, which may be consider-
ably inclined to the horizon. Suppose TT, Fig. 64, to represent
this line for any position : then the apparent height of the waves
to an observer will be HT, which is much greater than the true
height. If the observer stands on the deck of a ship, the con-
ditions will be similar; the normal to what is termed the "effec-
tive wave slope" * determines the apparent vertical at any instant ;
and the only easy way of determining the true horizontal direc-
tion is by making an observation of the horizon as described
above. The extent of the possible error thus introduced will be
seen from an example. Take a wave 250 feet long and 13 feet
high ; its maximum slope to the horizontal is about 9 degrees.
Suppose a ship to be at the mid-height between hollow and crest,
and the observer to be watching the crest of the next wave;
standing about the water level, the wave height will seem to be
about 30 feet instead of 13 feet. The steeper the slope of the
waves, the greater liability is there to serious errors in estimates
of heights, unless proper means are taken to determine the true
horizontal and vertical directions. In some cases the apparent
height would be about three times the real height.
Next as to the ratio of the heights to the lengths observed in
deep-sea waves. All authorities agree that, as the lengths in-
crease, this ratio diminishes, and the wave slope becomes less
steep. The shortest waves are the steepest; and the greatest
recorded inclinations are for very short waves where the ratio of
height to length was about 1 to 6. For a cycloidal wave it will
be remembered that the ratio is about 1 to 3*14 ; so that in the
steepest deep-sea waves observed this ratio is only about one-half
that of the theoretical limiting case. For waves from 300 to 350
feet in length, the ratio of 1 to 8 has been observed, but these
were probably exceptionally steep waves ; for waves of 500 to 600
feet in length, it falls to about 1 to 20 ; and for the longest
waves, of uncommon occurrence, it is said to fall so low as 1 to
50. But it is obvious that all measurements of such gigantic
waves must be attended with great difficulties, so that the results,
even when the greatest care is taken, are only receivable as fair
approximations. It seems probable that, in waves of the largest
This jjlirase will be explained in the bucceediug chapter.
CHAP. V.
DEEP-SEA \VA VES.
197
size commonly met, the height does not exceed one-twentieth of
the length; and the higher limit of steepness in ocean waves,
which are large enough to considerably influence the behaviour
of ships, does not give a ratio of height to length exceeding 1 to
10. Long series of observations made in ships of the French
navy show that a common value of the height is about one-
twenty-fifth— from one-twentieth to one-thirtieth of the length.
Waves from 400 to 900 feet in length are sometimes encountered,
having heights of from 4 to 10 feet only, and tlie small ratio of
height to length of 1 to 50 has been repeatedly observed in waves
from 100 to 400 feet long.
Excluding these exceptionally low ratios of height to length, and
taking account of observations where the ratio did not fall below
1 to 40, the following approximate results have been obtained
from an analysis of the published French observations of waves,
made in all parts of the world.
Length of Waves.
Number
of Obser-
vations.
Length -i- Height.
Average.
Maximum.
30
40
40
40
40
40
Minimum.
5
9
10
17
15
17
100 feet and under
100 to 200 feet .
200 to 300 „ .
300 to 400 „ .
400 to 500 „ .
500 to 650 „ .
11
55
44
36
17
16
17
20
25
27
24
23
179
This table is worthy of study ; although the figures it contains
are not exact, and exception may reasonably be taken to the
method of averages as applied to these observations. But it
suggests much as to the comparative frequency with which waves
of certain lengths occur, and confirms the opinion that waves
become less steep as they increase in length.
The comparison of the relation between the periods and speeds
of ocean waves, with the relation which should hold in accordance
with the trochoidal theory (see page 187), has shown a very fair
ao-reement between theory and observation. In not a few cases
there are wide divergencies from such agreement; but it is
extremely probable that the observations showing these diver-
gencies were made under the conditions of a confused sea, not
embraced by the trochoidal formulae. It is to be observed that
in the cases where a single and approximately regular series of
198
NAVAL ARCHITECTURE.
CHAP. V.
waves has been encountered, observation nnd theory agree most
closely. For example, Conimodore Wilkes observed to the south
of Cape Horn waves having a length of 380 feet, and a period
of nearly 8-5 seconds ; according to the trochoidjil theory, the
period should have been about S'O seconds. Again, Dr. Scorcsby
observed Atlantic storm waves having lengths of 560 to 600 feet,
and periods of about 11| seconds : the period, according to the
trochoidal theory, for a wave 580 feet long, would be about 10"6
seconds. On his voyage to Australia, Scoresby noted waves
640 feet long and 11^ seconds period: the theoretical period for
waves of this length would be a little over 11 seconds. Lieu-
tenant Paris, also, in the Southern Indian Ocean measured waves
from 300 to 400 metres long, and having a speed of 19 metres per
second : their period, according to this data, must have been about
18 seconds, and, according to theory, it would have been about
15 seconds. On another occasion the same observer noted waves
180 metres long, and 10^ seconds period : according to theory the
period would have been about 10| seconds. As a last example,
reference may be made to a few observations of waves made in the
Pacific on board one of Her Majesty's ships where the periods
observed for waves from 180 to 320 feet long agreed almost
exactly with the theoretical periods.
Passing from these special test cases to the ordinary cases
where waves are less regular and uniform |^in character, it may be
well to give a few examples of the comparison between observed
and theoretical lengths of waves. The first table is based upon
the results of French observations, exceeding 200 in number, made
by different observers on various stations.
Lengths
OF Ocean Waves (in Metres).
Observed.
Calculated.
Observed.
Calculated.
Observed.
Calculated.
30
30
80
85
143
131
30
42
80
95
148
161
35
42
85
60
1.50
134
42
42
90
100
153
175
50
60
95
95
160
156
56
60
100
67
165
16L
60
52
100
lOS
170
171
60
67
105
116
170
144
65
52
114
124
172
175
65
73
120
112
180
108
70
67
120
120
180
147
70
74
130
164
180
185
75
60
135
131
190
200
79
80
140
IJ
Note. — A metre is 3-281 feet.
CHAP. V.
DEEP-SEA IV A VES.
199
The second table is based upon observations made on board
some of Her Majesty's ships.
Lengths of Ocean Waves (in
Feet).
Observed.
Calculated.
Observed.
Calculated.
Observed.
Calculated.
80
82
220
181
375
330
160
128
245
250
400
370
IHO
1S4
250
250
420
510
180
185
300
250
500
420
200
18i
300
323
530
440
200
250
350
328
630
520
On a review of all the observations witli which we are acquainted
it appears that usually the observed lengths are, on an average,
rather less than the theoretical lengths ; but it must be admitted
tliat here also the method of averages is not trustworthy, especially
when it is known that in some instances errors of considerable
proportionate magnitu'le exist in the individual observation^!.
These errors arise from various causes; one of the most common
being the failure to distinguish correctly the difference between
the real and the apparent speeds and dimensions of waves. In
addition there are the special diflSculties frequently eo countered
when the waves to be measured are the result of the superposition
of two or more series of waves, each moving at its own speed, and
all moving, possibly, in different directions. In such a confused
sea there is an entire want of regularity or uniformity in successive
waves which pass an observer on board a ship, and the best course
he can pursue is to note the particulars for a considerable number
of ^\aves in order that something like mean results may be
obtained. For example, in making a set of observations on board
one of Her Majesty's ships, when the sea was formed by two series
of waves running at different speeds in nearly the same direction,
the following results were noted. First, the intervals which ten
successive wave crests occupied in passing over a certain length
were respectively 6, 7, 4, 6, 6, 3, 6, 5, 7, and 6^ seconds ; the mean
being about 5'6 seconds. Second, the apparent lengths varied
from 250 to 420 feet. These apparent variations admit of easy
explanation, and for this purpose we will take the simple case
illustrated by Figs. G5-70. Fig. 65 shows a wave 400 feet long
and 20 feet high, having a speed of about 45 feet per second ;
Fig. 66 a wave 200 feet long aud 12 feet high, having a speed of
about 32 feet per second. The straight lines in both figures
indicate the level of still water. In Fiii. 67 the shorter wave is
20O
NAVAL ARCHITECTURE.
CHAP. V.
superposed upon the longer, the latter being shown by a dotted
line; the two crests coincide, and the resultant wave has a height
from hollow to crest of about 26 feet, while the length from hollow
to hollow is about 300 feet. The long wave form gains about
Fic.65.
Fic.ee
Fic67.
ric.69.
50 Fr-^,
Fic.70,
-100 Fl —
13 feet per second on the shorter wave. In 1\ seconds the profile
of the combined wave Avill have changed from the condition of
Fig. 67 to that of Fig. 68 ; the heights of successive crests being
about 30 feet and 5 feet, and the length between these crests being
CHAP. V. DEEP-SEA WAVES. 20I
about 200 feet. In less than 4 seconds the further change shown
in Fig. 69 will have occurred, and in less than 8 seconds the con-
dition shown in Fig. 70 will have been reached, a wave hollow
appearing where the crest of the 400-feet wave is placed. In
this last condition the height from this hollow to the adjacent
crests is only about 3 feet, and the crests are 160 feet apart. In
fact there occurs a long " smooth " in the series, but the next
wave series would have heights of about 25 feet. This simple
illustration shows how difficult the task of making observations
of waves may become in a confused seaway formed by the super-
position of several series of waves moving in different directions.
Here too we find a satisfactory explanation of the differences
sometimes noted in the simultaneous observations of waves by
ships sailing in company. In one instance, for example, one ship
reported the waves to be 450 feet long, whereas a second ship put
the length at 150 feet, and this is by no means an exceptional
case. The observer may, it is true, sometimes succeed in distin-
guishing the principal members of the waves in one or more of
the superposed series ; but this involves a long continuance of the
observations, and is rarely to be accomplished with certainty. It
is only necessary to add that in making such observations in a
confused sea the fullest particulars should be recorded, for with-
out a knowledge of the attendant circumstances no possible use
can be made of the results. For this reason also it is very desir-
able that any comparisons between the results of theory and
observation should be made by the observers at, or soon after, the
time the observations are in progress ; since no other person can
have an equally good knowledge of the particular circumstances
of each case.
No theory has yet been accepted which represents the genesis
of waves ; the trochoidal theory merely deals with waves already
created, and maintaining unaltered forms and velocities. There
can, of course, be no question but that waves result from the
action of the wind on the sea, and that there must be some
connection between the character and the force of the wind and
the dimensions and periods of the waves. But as yet we have
not sufficient knowledge to determine either the mode of action
of the w'ind or the law connecting its force with the dimensions
of waves. Here again is a field where careful and extensive
observations can alone be relied upon ; pure theory would be
useless.
202 NA VAL ARCHITECTURE. chap. v.
Ill the preceding pages it has been shown that, with care, the
lengtlis, heiglits, and periods of waves may be determined very
closely when the sea is not confused ; and it is also possible, with
care, to ascertain simultaneously the force or speed of tlie wind.
But it is to be noted that the rapidity with which waves travel,
and the fact that they maintain their lengths and speeds almost
unchanged even when the force of the wind decreases and the
wave height becomes less, make it necessary to exercise great
caution in associating any observed force of wind with the lengtlis
and periods of waves observed simultaneously. The importance
of this matter justifies further illustration.
If the wind is at first supposed to act on a smooth sea, and
then to continue to blow with steady force and in one direction,
it will create waves which finally will attain certain definite
dimensions. The phases of change from the smooth sea to the
fully formed waves cannot be distinctly traced. It is, however,
probable that changes of level, elevations and depressions, re-
sulting from the impact of the wind on the smooth surface of the
sea, and the f fictional resistance of the wind on the water, are the
chief causes of the growth of waves. An elevation and its corre-
sponding depression once formed offer direct resistance to the
action of the wind, and its unbalanced pressure producing motion
in the heaped-up water would ultimately lead to the creation of
larger and larger waves. This is }»robably the chief cause of
wave growth, frictional resistance playing a very subordinate
part as compared with it. So long as the speed of the wind
relatively to that of the wave water is capable of accelerating its
motion, so long may we expect the speed of the wave to increase ;
and with the speed the length, and also the height. Finally, the
waves reach such a speed that the wind force produces no further
acceleration, and only just maintains the form unchanged, then
we have the fully grown waves. If the wind were now suddenly
withdrawn, the waves would gradually decrease in magnitude and
finally die out. This degradation results from the resistance due
to the molecular forces in the wave— viscosity of the water, &c. —
and when the waves are fully grown, the wind must at every
instant balance the molecular forces. If the water were a perfect
fluid (the particles moving freely past one another), and if there
were no lesistance to motion on the part of the air, the waves
once formed would travel onwards without degradation. But in
sea-water the degradation takes place at a rate dependent upon
the ratio of the resistance of the molecular forces to the " energy "
CHAP. V. DEEP-SEA WAVES. 203
of the wave.* At each instant the resistance abstracts a certain
amount from the energy of the wave, and consequently the height
decreases. The period and length of the wave might remain
almost unchanged, and, it would seem from observation, really do
so, wliile the height decreases; just as it has been shown that in
a ship oscillating in still water the resistance developed gradual! v
diminishes the range of oscillation without decreasing the period
sensibly.
Between this condition of fully-grown waves and the case of
waves gradually dying out in a dead calm lies that which com-
monly occurs where the waves are gradually dying out, but the
wind still has a certain force and speed. Then an observer,
noting the dimensions of the waves and force of the wind simul-
taneously, might record lengths and periods corresponding, not
to the observed force of wind, but to the force which existed
when the waves were of their full size. On the other hand,
there would, in all probability, be a correspondence between the
observed force of wind and the observed heights, and an analysis
of the recorded observations made by officers of the French navy
confirms this view. Nothing but the closest attention on the
part of an observer can enable him to make his records a trust-
worthy basis for theory ; for it is in his power alone, having
regard to all the circumstances of the observations, to say
■whether, when observed, the waves are fully grown, and corre-
spond to the observed force of wind, or whether they are in
process of growth or of degradation. A series of observations
might settle this matter, if made in a careful and intelligent
mariner; the growth or degradation being indicated by the
alterations in heights of waves noted after certain intervals from
the first observations.
Perhaps the most favourable time for observations to be begun
would be that when on a nearlv calm sea a storm breaks, formino-
waves of which the dimensions gradually increase, but the oppor-
tunities are not likely to be numerous where the waves so formed
constitute an independent regular series. Usually the observer
would probably find himself in face of a very confused sea, when
the wave genesis is in its earlier stages ; bat if he could note tlie
* In wave motion the "energy" is the work done in raising the centre of
half "actual" and half "potential." gravity of its mass a certain distance
By "actual" energy is meant that due above the position which it would
to the motions of the pariiclcs in a occupy in still water. See remarks as
wave ; by " potential " energy is meant to this rise on page 182.
204 NAVAL ARCHITECTURE. chap. v.
times occupied by waves in attaining their full growth under the
action of winds of various speeds, he would do good, service.
Any pre-existing swell must be allowed for in making these
observations ; otherwise the assumption that the waves are formed
from smooth water would be departed from.
In concluding these remarks on wave genesis, we cannot do
better than quote from M. Bertin's essay on the subject, meu-
tioned above : — " The study of the time necessary for each swell
" to retain its fixed and permanent condition under the action of
" the wind which produces it is very interesting. If the time be
" so long as in general to exceed that during which the wind
" can remain pretty nearly constant, both in intensity and direc-
" tion, all interest in the connection between the wind and the
"swell would disappear. The length of waves and their in-
"clination for a given length would be just as irregular as
" meteorological variations. If, on the contrary, the waves soon
" reach their regular condition — a fact which seems to be pretty
" well established, inasmuch as those seas which are exposed to
" the action of constant winds present no extraordinary agitation
" — one is necessarily driven to adopt the law that for each length
" of waves there is a certain height that is most commonly met
" with, and that cannot be exceeded."
Passing from these general considerations it may be interesting
to refer to the attempts made by French investigators to formu-
late expressions connecting the dimensions of waves with the
force or speed of winds. Admiral Coupvent Desbois has laid
down a provisional theory, based upon ten thousand actual obser-
vations, that the cube of the height of the waves is proportional
to the square of the speed of the wind.* Lieutenant Paris sug-
gests, from an analysis of his own observations, that the speed of
waves is pi-oportional to the square root of the speed of the wind ;
but he is of opinion that much more extensive observations are
needed before any law can be accepted. Lieutenant Paris'
formula may be expressed as follows, reckoning speeds in metres
per second : —
Speed of wind = -073 (Speed of wave)\
Converting this into English measures, and reckoning speeds in
feet per second, we have —
Speed of wind = "022 (Speed of wave)-.
* Sc'e the Comptes-rendus de V Academic des Sciences of 186G.
CHAP. V.
DEEP-SEA WAVES.
20:
Whence making use of the formula connecting the speeds and
lengths of waves it follows that —
Speed of wind = '115 Length of wave.
When the sea was heavy Lieutenant Paris always found the
speed of the wind exceed that of the wave form ; but in moderate
seas having a speed of 36 feet per second, or less, he frequently
recorded speeds of wind which were less than the speeds of the
waves formed by the action of that force of wind. The following
table contains a few illustrations of this noteworthy feature in
these admirable records: —
Mean
Mean Speeds.*
Locality.
Heights
of Waves.
Wind.
Wave.
Metres.
Atlantic (region of trade winds) ,
1-9
4-8
11-2
South Atlantic
4-3
13-5
14
Indian Ocean (south of) ... .
5-3
17-4
15
Indian Ocean (region of trade winds)
2-8
6-5
12-6
Seas of China and Japan ....
3-2
14-6
11-4
West Pacific
3-1
8-5
12-4
* In metres per second ; a metre is 3'281 feet.
In the present state of our knowledge, we are not able to say
that there is anything impossible in the observation of waves
moving faster than the winds, which have a force corresponding
to their full growth, although this condition would scarcely be
anticipated. Eemembering what was said above as to the diffe-
rence between the rates of the actual orbital motions of particles
in their circular orbits and the apparent speed of advance of the
wave form, it will be clear that, even when tlie wave form
advances faster than the wind travels, the wind may be moving
much faster than the particles in the wave. Take, for example,
the waves of the Southern Indian Ocean. M. Paris gives them a
mean height of 5*3 metres, and a mean period of 7'6 seconds.
Diameter of orbits of surface particles . . = 5'3 metres.
Circumference of orbits of surface particles = 16 "6 metres.
16-6
Orbital velocity of particles -~rra = 2^ metres per second.
Velocity of wind observed = 17'4 metres per second.
Whether the relative velocity of the wind and the wave form
should be taken as the measure of the full effect of the wind, or
whether the relative velocity of the wind and the particles of
water in the wave does not also exercise considerable influence,
206
NAVAL ARCHITECTURE.
CHAP. V.
must for the present be considered at least a matter open to
debate. In the maintenance of the wave speed as the wind speed
shickens, we have a possible explanation of the apparent anomaly
in the above table ; and, further, it is difficult for an observer on
board a ship in motion to measure the speed of the wind accu-
rately. But actual observations, such as have been recommended
in this chapter, will settle this and many other doubtful points.
]\[. Autoine, of the French navy, has also endeavoured to frame
fonuula} connecting the dimensions and speeds of ocean waves
with the speeds of wind ; and for this purpose has made a very
len2,thy analysis of the returns furnished by French war-ships.*
Taking 130 observations made in vessels of the French navy,
M. Antoine classified them as follows in his Memoir of 1876 : —
Number of
Waves.
Mean
Lengths.
Mean
Heights.
Speed of
Wind.
Observations
per Series.
Calculated by
Calculated by
Observed.
Approximate
Formula.
Observed.
Appro.ximate
Formula,
Metres per
Second.
Metres.
Metres.
Metres.
Metres.
1-5
12
54-6
36
1-7
1
4
16
63-7
60
2-4
1-9
7
18
87-9
79-5
3-2
2-7
11
29
79-7
99-6
4
3-7
16
22
100
120
5-4
4-8
22
19
90
141
5-1
5-9
29
11
131
161
7-7
7-1
37
3
180
182
8-5
8-3
It will be observed that the calculated heights agree very
closely with the observed heights ; whereas there are very con-
siderable differences between the calculated and the observed
lengths. This is a suggestive contrast as will appear more
clearly in reference to the remarks made on page 203.
In obtaining the approximate formulas for lengths and heights
of waves, M. Antoine uses the following notation : —
LetV
V
2L
2T
2H
speed of waves (in metres per second),
wind „
length of waves (in metres)
period „ (in seconds)
height „ (in metres).
* See ISiotes comiilementaires sur Us Lames de haute mer, 1876 ; also Des
Lames de haute mer (Paris, 1879).
CHAP. V,
DEEP-SEA WAVES.
207
Then, assuming Admiral Coupvent Desbois' law to hold, the
following are considered to be good approximations : —
2H = 0-75 X ir^
1
2L = 30 v^
2T= 44 v^
V = 6-9 v+
• (1)
• C^)
• (3)
. (4)
The "constants" in equations (1) and (4), M. Antoine derives
from an analysis of numerous observations ; those in equations (2)
and (3) are derived from (4) by means of the theoretical formula
given on page 187.
In his most recent publicdtion, M. Antoine has somewhat varied
his procedure, and has attempted to investigate whether " in the
deformation of a wave the product of the length by the height
would not remain practically constant for waves created by the
action of a wind of a given forc^ : the value of this product is
termed the modulus of the wave" He retains the fundamental
formulae given above, and as the result of his analysis of over
200 observations forms tlie followino: table : —
Moduli of Waves
(Product
OF Height by Length).
Speed of Wind.
Moduli.
Metres per Second.
Calculated.
Observed.
0 to 2
0
to 51
80
3 to 5
78
to 148
170
6 to 8
184
to 255
362
9 to 13
297
to 443
379
14 to 18
493
to 648
595
19 to 25
685
to 960
650
26 to 32
1010
to 1283
1070
33 to 42
1332
to 1765
1516
M. Antoine adds, " According to the preceding formuhi?, the
modulus of a wave should be proportional to the expression —
(Speed of wind) ^| ;
I reserve to myself the investigation, when more numerous
observations have been made, of the problem whether one mio-ht
not suppose the modulus to be proportional simply to the speed
of the wind ; which would make the length of a regular wave
proportional to the square root of the height."
Attention has been drawn to the preceding attempts to connect
wave phenomena and wind forces with the hope that the subject
2o8 NA VAL ARCHITECTURE. CHAP. v.
will be treated also by English observers with the consideration
it undoubtedly deserves. The problem still awaits solution, for
the formula} given above are based upon reasoning to which grave
objections may be taken although they cannot be stated here.
Attempts have also been made by Lieutenant Paris to ascertain
what are the prevalent waves most likely to be encountered in
particular localities. The following table, prepared by him, gives
the result of observations extending over more than two years : it
stands alone, at present, as an effort to describe the mean condi-
tion of the sea. But it is well worthy of the attention of naval
ofiScers, who would render good service to science by endeavouring
to extend the investigation here begun : —
Localitv.
Atlantic (the Trades)
South Atlantic (region of the westerly winds) .
Indian Ocean, South (region of the easterly winds)
Indian Ocean (trade winds)
China Seas
West Pacific
Mean Period.
Seconds.
5
8
9
5
7
6
7
6
6
9
8
In concluding this chapter, brief reference must be made to
the attempts to obtain motive power for propulsion or other pur-
poses from the motions impressed upon a ship by the wave motion.
Mr. Spencer Deverell, of Victoria, was the first to draw attention
to the subject ; and his brother conducted a series of observations
in 1873 during a voyage from Melbourne to London, for the
purpose of proving that during an ocean voyage a ship will be
continually oscillating — rolling, pitching, and heaving — even
when there is a dead calm. Limits of space prevent any extracts
being given from the interesting records of these observations,
which will well repay perusal ; nor can any account be given of the
apparatus proposed for the purpose of obtaining motive power
from the wave motion.* The principle of all the proposals may
be simply explained. In a seaway the heaving and other motions
impressed upon a ship cause variations in her virtual weight (as
* See Papers on "Ocean Wave Power Institution of Naval Architects for
and its Utilisation," in the Transac- 1874, by Mr. Spencer Deverell; also a
tions of the Royal Society of Victoria Paper by Mr. Tower in the Transac-
for 1873; and "The Continuous Os- <iO)/s of the Institution of Naval Archi-
cillation of a Ship during an Ocean tects for 1875.
Yoyage," in the Transactions of the
CHAP. V. DEEP-SEA WAVES.
209
explained at pa,ii;e 186). If a weight inboard is snspended by a
spring-balance, the hitter will indicate less than the true weight
on the wave crest, and more than the true weight in the wave
hollow. The extensions of the spring will vary according to the
■virtual weight, being greatest at the wave hollow, and least at the
crest. By some appropriate mechanism these varying extensions
of the spring are made to produce rotary or other motions. Nume-
rous experiments have been made with models, but hitherto, we
believe, no practical use has been made of the principle.
2IO NAVAL ARCHITECTURE. chap. vi.
CHAPTER YI.
THE OSCILLATIONS OF SHIPS AMONG WAVES.
In the two preceding chapters we have discussed the condition
of a ship oscillating in still water, and the phenomena of wave
motion in the deep sea, subjects which have an interest iu them-
selves, but derive their greatest importance from their connection
with the subject now claiming attention. The motions of a ship
in a seaway are influenced by her stability, her inertia, by the
variations in direction and magnitude of the fluid pressure
incidental to wave motion and by tlie fluid resistance ; so that,
without clear and correct conceptions of each of these features in
the problem, it would be impossible to deal with their combined
effect.
All oscillations of a ship in a seaway, like those in still water,
may be considered as resolvable into two principal sets : the first,
the transverse oscillations of rolling ; the second, the longi-
tudinal oscillations of pitching and 'scending. It is, therefore,
only necessary to consider these two directions ; and of them,
the transverse, having by far the most important bearing upon
t!ie safety and good behaviour of ships, will receive the greatest
attention. Pitching and 'scending may become violent and
objectionable in some ships, but this is not commonly the case,
nor is it so difficult of correction as heavy rolling. Only a brief
discussion of these longitudinal oscillations will therefore be
necessary; and it will follow the remarks on rolling.
Very various causes have been assigned for the rolling motion
of a ship at sea. Some of the earlier writers, impressed by the
great speed of advance of waves, attributed rolling to the shocks
of waves against the sides of ships. Others considered motion as
originated by the slope of the wave surface ; observing that, if a
ship remained upright on the wave slope, her displacement
would change its form from that in still water, the centre of
CHAP. VI. OSCILLATIONS AMONG WAVES. 211
buoyancy moving out from below the centre of gravity towards
the wave crest, and the moment of stability thus produced
tending to make the vessel heel away from the wave crest. But
there were obvious objections to both these theories; it is a
matter of common experience that vessels often roll very heavily
in a long smooth swell, where the slope is so small that the
departure from the horizontal is scarcely perceptible, and where
no sensible shock is delivered against the sides of the ships.
The best of the earlier theories, put forward by Daniel Bernoulli
about a century ago, departed from the preceding theories, and
was content to speak of the oscillations of a ship as comparable
to those of a pendulum, subjected to the action of " impulses "
from the waves, no analysis being attempted of the character or
causes of these impulses. Some of the conclusions which Bernoulli
reached even now command respect ; but he, in common with
his contemporaries, failed to realise or to express the funda-
ment il condition wherein wave water differs from still water, viz.
that the direction and intensity of the fluid pressure are con-
tinually varying instead of being constant, as in still water.
For nearly a century the subject remained very nearly in the con-
dition in which Bernoulli, Euler, and other writers of that period
had left it ; and it was reserved for an Englishman, the late Mr.
W. Fronde, to have the honour of introducing the modern theory
of rolling. This theory rests upon the fundamental doctrine,
explained in the previous chapter, that in wave water the direction
of the pressure at any point is a normal to the trochoidal surface
of equal pressure passing through that point ; and in tliat
particular the modern theory differs from all that preceded it.
It is not ptit forward as a perfect theory, fully expressing all the
conditions of the problem ; but it far more completely represents
those conditions than any theory which preceded it, and has
exercised a great and beneficial effect upon ship designs during
the twenty years it has been before the world. Moreover^ in its
main features, it has secured the adhesion of the greatest autho-
rities on the science of naval architecture, both English and
foreign, some of whom have very considerably helped its exten-
sion. An attempt to describe in popular language the main
features of the theory cannot, therefore, be devoid of interest,
even though the avoidance of mathematical language may render
the description wliich follows incomplete.
At the outset it may be well to state that the modern theory
of rolling finds the governing conditions of the behaviour of a
ship among the waves to be twofold : —
p2
2 I 2 A'A VAL ARCHITECTURE. chap. vi.
(1) The ratio which the period of still-water oscillations of the
ship (or "natural period") bears to the period of the waves
anionji^st wliich she is rolliup'.
(2) The maunitude of the effect of fluid resistance.
Botli the natural period and the means of estimating the magni-
tude of the fluid resistance for any ship may be obtained from
experiments made in still water, as previously explained.
It will be convenient to deal separately with these conditions,
first illustrating the causes which make the ratio of the })erioils
80 important, and in doing so leaving resistance out of account ;
afterwards illustrating the effect of resistance in liiniiing the
range of oscillation. In })ractice the two conditions, of course,
act concurrently ; but the hypothetical separation here made will
probably enable each to be better understood.
Reverting to the case illustrated by Fig. 61, page 183, where a
small raft floats upon the inclined surface (AB) of the water in a
vessel wliich is moving horizontally, it will be noticed that the
raft is acted upon by the following fluid pressures : — P, acting
downwards on the upper side, an equal pressure, P, acting
upwards on the lower side, and the buoyancy h acting normally
to the surface AB through the centre of buoyancy of the raft.
If w be the weight of the raft (acting vertically downwards
through the centre of gravity) when the vessel containing the
water is in motion, this weight w must be combined with the
horizontal accelerating force due to the motion, in the manner
explained on page 181. Using the [same notation as before, v^q
have —
Resultant of weiojht and horizontal )
T . ,.^ > = w sec a,
accelerating torce J
This resultant will act perpendicularly to the inclined water
surface, just as the buoyancy h does ; and for equilibrium we
must have —
h = w sec a,
and the line of action of h must pass through the centre of
gravity of the raft. Hence it follows tliat the normal to the free
water surface indicates the direction towards which the raft will
tend to return if her mast is inclined from it ; just as in still
water the upright is her position of equilibrium. The normal to
the water surface may therefore be termed the " virtual upright "
for the raft when it and the water are subjected to horizontal
acceleration ; since the normal fixes the position of equilibrium.
CHAP. vr. OSCILLA TIONS AMONG IV A VES. 2 1 3
Next sui)pose this very^ small raft to float on the surface of a
wave, as in Fig. 62, page 185. Here reasoning similar to the
foreo-oing applies, if the raft be considered so small in relation to
the wave that it may be treated as if it replaced a particle, and
moved just as the particle would have done. In the preceding
chapter it has been shown that at any point in a trochoidal wave
the normal represents the direction of fluid pressure at that point,
and it has also been stated that this direction changes from point
to point along the wave surface, the variations in inclination
resembling the oscillation of a pendulum having a period for a
single swing equal to half the wave period. Tiie cases of Figs.
61 and 62, therefore differ in this : in the former, where the
water surface has a constant inclination, the "virtual upright"
also has a constant direction ; whereas on the wave the " virtual
upright," or position of equilibrium, in which the masts of the
raft will lie, varies in direction from instant to instant, the
variations bfing dependent upon the wave slope and wave
period. On the wave the raft is also subjected to vertical as
well as horizontal accelerations, affecting both the value of the
fluid pressure upon its bottom and its own apparent weight, but
affecting both equally, and therefore not changing the volume
of displacement of the raft from that in still water. The law
of this variation in the pressure and apparent weight has been
given in the preceding chapter, and illustrated by Fig. 60^
but for our present purpose the variation in the direction of the
pressure is of greater importance.
A ship differs from this hypothetical raft, having lateral and
vertical extension in the wave, as shown by ADC in Fig. 62.
Even though she may be small when compared with the wave,
it is obvious that she cannot be treated as a single particle re-
placing a particle in the wave. At any moment she displaces a
number of panicles which, were she absent, would be moving in
orbits of different ra^lii, and at different speeds. Her presence
must therefore introduce a disturbance of the internal motions
in the wave, and this disturbance must in some manner react
upon the ship and somewhat influence her bt-haviour. At present
our knowledge of the conditions governing the internal mole-
cular forces in the waves of the sea is not sufficient to enable
exact mathematical treatment to be applied in estimating the
effect of this disturbancp, and detern>ining at each instant the
position of the "virtual upright" for the ship. If the positions
of the virtual upright were known, each of them would be a
normal to a surface termed " the effective wave slope : " Con-
2 14 N.IV.IL ARCHITECTURE. chat-. \ i.
verst'ly, the effective wave slope may be defined as the suiface,
the iioriiifil to wliich at any point represents the instantaneous
position of equilibrium for the masts of tlic ship.
Although our knowledge of the subject does not enable the
form of the effective wave slope to be accurately determined,
certain considerations of a general character are known to
influence that form. For example, the size of the ship relatively
to the waves, the form of her immersed part, its lateral extension
along, and vertical extension into, the waves, as well as the
vertical position of her centre of gravity, are all known to affect
the effective wave slope. Moreover, that slope may differ con-
siderably from the upj er surface of the waves. Large ships, for
instance, when floating among very small waves, even with their
broadsides to the line of the wave advance, may be supported
simultaneously by the slopes of successive waves, and these
slopes being inclined in opposite directions, the effective slope
may be practically horizontal. Again, a ship of very great
breadth, such as the LivacUa, or the circular ironclads, when
floating broadside on to the waves, occupies so great an extent
of the slope of one of the largest ocean waves, that the effective
slope can only have a very moderate amount of steepness as
compared with the maximum slope of the wave surface. And, as
a final example, we may take the extreme case of a ship of
nnrrow beam but great draught of water, for which the effective
slope would have its steepness decreased in virtue of the fact
that trochoidal subsurfaces in a wave are flatter than the upper
surface, as explained on page 181.
All these illustrations serve to show that the determination of
the effective wave slope for a particular case can only be made
approximately. For the purpose of mathematical investigation
of the hypothetical case of unresisted rolling it is, however,
usual to assume that a ship falls in with waves so large relatively
to her own dimensions that she accompanies their motion.
Starting with this assumption of the relative smallness of a ship,
it has sometimes been assumed that the effective slope wiil
nearly coincide with the trochoidal subsurface passing through
the centre of buoyancy of the ship. In Fig. 62, let B represent
the centre of buoyancy of the ship shown in section by ACD ;
then TTi, the subsurface of equal pressure passing through B,
would be termed the effective wave slope, and the normal to it
NNi, would be taken as determining the instantaneous position
of equilibrium for the ship. In the diagram the ship is shown
purposely with htr middle line (GM) not coincident with the
CHAP. VI. OSCILLATIONS AMONG WAVES. 215
normal NNi ; j\[, the point of intersection of these lines, may be
reiTiU-ded as the metacentre for small transverse inclinations of
the ship from the virtual upright; the angle BMNi measures the
inclination of the ship from the instantaneous position of equi-
librium. Through the cmtre of gravity G, GZ is drawn perpen-
dicularly to NNj; then instantaneously the effort of stability, or
righting moment, with which the ship tends to move towards the
position NNj, is measured by the expression —
Kighting moment = apparent weight x GZ,
In estimating tlie apparent weight of the ship, which is prac-
tically equal to, and has a line of action paiallel to, the fluid
pressure acting along NNi, it is of coarse necessary to take
account of the radii of the particles situated in the subsurface
TTi. Very often the actual weight may be substituted for the
apparent weight without any great error; but this is a matter
easdy investigated, in accordance with the principles previously
explained.
This method of approximating to the effective slope, alth.ough
widely adopted, is not universally accepted, nor does it proiess
to be more than an average or approximation under the assump-
tion of the relative smallness of a siiip as compared with the
waves. In some cases the effective slope lies much nearer the
npper surface than TTj would be situated, and cases may occur
where the effective slope is steeper than the upper surface. But
amongst relatively large waves the effective slope is usually less
steep than the upper surface ; a iact which is confirmed by the
careful and extensive observations made by Mr. Froude on board
the Devastation. In practice, therefore, it is an error on the side
of safety to assume, as is not unfrequently done, that the
variations in inclination and m:ignitn.de of the fluid pressure and
the apparent weight of the ship may be determined from the
upper surfai-e of the wave. This was the plan adopted by Mr.
Froude in his earliest investigations, as well as that followed by
the x\dmiralty Committee on Designs for Ships of War in their
estimate of the probable limits of rolling of the Devastation class.
It will be seen that this substitution of the upper surface for the
less steep effective surface in no way affects the period occupied
by the wave normal in performing the set of motions from
upright at the hollow onward to upright at the crest of a wave.
The difference is solely one of the maximum in(dination to the
vertical reached by the wave normal, and taking the upper
2l6 NAVAL ARCHITECTURE. chap. vi.
surface usually somewhat increases this bej'ond the true maxi-
mum in the critical cases with which the mathematical theory
deals.
Suppose a ship lying broadside-on to the waves to be upright
and at rest when the first wave hollow reaches her ; at that
instant the noimal to the surface coincides with the vertical, and
there is no tendency to disturb the ship. But a moment later,
as the wave form passes on and brings the slope under the ship,
the virtual upright towards which she tends to move becomes
inclined to the vertical. This inclination at once develops a
righting moment tending to bring the masts of the ship into
coincidence with the instantaneous position of the normal to the
wave. Hence rolling motion begins, and the s-hip moves initially
at a rate de})endent upon her still- water period of oscillation.
Simultaneously with her motion, the wave normal is shifting its
direction at every instant, becoming more and more inclined to
the vertical, until near the mid-height of the wave it reaches its
maximum inclination, after which it gradually returns towards
the upright : the rate of tliis motion is dependent upon the periotl
of the wave. Whether the vessel will move quickly enough to
overtake the normal or not depends upon the ratio of her still-
water period to the interval occupied by the normal in reaching its
maximum inclination and returning to the upright again, which
it accomplishes at the wave crest; this interval equals one-half
the period of the wave. Hence it appears that the ratio of the
period of the ship (for a single roll) to the half-period of the
wave must influence her rolling very considerably, even during
the passage of a single wave, and still more is this true when a
long series of waves move past the ship, as will be shown here-
after.* It will also be obvious that the chief cause of tln^
rolling of ships amongst waves is to be found in the constant
changes in the direction of the fluid pressure accompanying wave
motion.
As simple illustrations of the foregoing remarks, two extreme
cases uiay be taken. The first is that of a little raft, like that in
Fig. 02, having a natural period indetiuitely small as compared
* It has already been explained that oscillation to a douhle roll, and the
■we follow the Admiralty method in terra period to the time occupied in
terming a single roll "an oscillation," performing the double roll. We again
and the time occupied in its perform- refer to the matter, as in many pub-
ance the "period of oscillation. Mathe- lished pnpers the mathematical terms
maticians commonly apply the term are employed.
CHAP. VI. OSCILLATIONS AMONG WAVES. 21 J
with the half-period of the wave. Her motions will consequently
be so quick as compared with those of the wave normal that she
will be able continuously to keep her mast almost coincident with
the normal and her deck parallel to the wave slope. Being
upright at the wave hollow, she will have attained one extreme of
roll about the mid-height of the wave, and be again upright at
the crest ; the period of this single roll will be half the wave
period. And as successive waves in the series pass under the
raft, she will acquire no greater motion, but continue oscillating
through a fixed arc and with unaltered period. The arc of
oscillation will be double the maximum angle of wave slope.
The other extreme case is that of a verv small vessel having a
natural period of oscillation, which is very long when compared
with the wave period. For instance, a small cylinder like that in
Fig. 49, page 137, may be so weighted that the centre of gravity
may approach closely to the height of the axis, but remain below
it; then, as explained previously, there will be stable equilibrium,
and a very long period of oscillation may be secured by disposing
the weights towards the circumference of the circular cross-sec-
tions. If such a vessel were upright and at rest in the wave
hollow, she would be subjected to rolling tendencies similar to
those of the raft, owing to the successive inclinations of the wave
normal — her instantaneous virtual upright. But her long period
would make her motion so slow as compared with that of the wave
normal that, instead of keeping pace with the latter, the ship
would be left iar behind. In fact, the half wave period during
which the normal completes an oscillation would be so short
relatively to the period of the ship that, before she could have
moved far, the wave normal w^ould have passed through the
maximum inclination it attains near the mid-heiaht of the wave,
and rather more than halfway between hollow and crest. From
that point onwards to the crest it would be moving back towards
the upright ; and the effort of the ship to move towards it, and
further away from the upright, would in consequence be diminished
continuously. At the crest the normal is upright, and the vessel
but little inclined — inclined, it will be observed, in such a sense
that the variations in direction of the normal, on the second or
back slope of the wave, will tend to restore her to the upright.
Hence it follows that the passage of a wave under such a ship
disturbs her but little, her deck remains nearly horizontal, and
she is a much steadier gun platform than the raft-like vessel.
No ship actually fulfils the conditions of either of these extreme
cases, nor can her rolling be unresisted as is here assumed. Expo-
2I(^ NAVAL ARCIII lECTURE. chap, v
rience proves, however, that vessels having very short periods of
oscilhitioD in still water (io tend to acquire a fixed .range of" oscilhi-
tion wlien they encounter hirge ocean waves, keeping their decks
approximately parallel to the effective wave slopes. Actual
observations also show that ve?sels having the longest periods of
oscillation in still water are, as a rule, the steadiest amongst
waves, keeping their decks approximately horizontal, and rolling
through small arcs. Hereafter, the details of some of these
observations of the behaviour of actual ships will be given; but
attention must be confined, at present, to the general hypothesis
of unresisted rolling among waves. Having cleared the way by
the foregoing illustrations, we shall now attempt a general sketch
of the method of investigation introduced by Mr. Froude.
The following as.'^nmptions are made in order to bring the
problem of the motion of a ship in a seaway within the scope of
exact mathematical treatment : —
(1) The ship is regarded as lying broadside-on to the waves
with no sail set, and without any motion of progression in the
direction of the wave advance : in otlier words, she is supposed to
be rolling passively in the trough of the sea.
(2) The waves to whi<-h she is exposed are supposed to form a
regular independent series, successive waves having the same
dimensions and periods.
(3) The waves are supposed to be large as compared with the
ship, so that at any instant she would rest in equilibrium with liei
masts coincident with the corresponding normal to the "effective
slope," which is commonly assumed to coincide with the uppej
surface of the wave.
(4) The righting moment of the ship at any instant is
assumed to be proportional to the angle of inclination of her
masts to the corresponding noimal to the effective wave slope
— the virtual ui)right.
(5) The variations of the apparent weight are supposed to be
so small, when compared with the actual weight, that they may
be safely neglected, except in very special cases.
(6) The effects of fluid resistance are considered separately,
and in the mathematical investigation the motion is supposed to
be unresisted and isochronous (see page 143).
Objections may be raised, with justice, against most of these
assumptions : and it was never intended that they should be
regarded as including all the varying circumstances which may
influence the rolling of a ship among waves. It is only proper
to add, however, that the results of experience and observation
CHAP. VI. OSCILLATIONS AMONG WAVES, 219
confirm the general accuracy of the deductions drawn from tlie
mathematical investigation based upon these assumptions ; and
this is one great recommendation in their favour. Another fact
worthy of notice is that no better and more complete assumptions
have been proposed on which to base a rigorous mathematical
investigation of the rolling of ships among waves. Many
attempts have been made in this direction, but the conclusion
reached up to the present time is that the problem lies beyon-l
the reach of purely mathematical treatment, and can only be
successfully attacked by the process of " graphic integration," to
be described hereafter.
Two possible objections to the foregoing assumptions may be
mentioned in passing. It may be thought that since ships
much more frequently encounter a "confused sea" than a
single regular series of waves, the latter condition should not
be supposed to exist. In reply it may be stated that extensive
observ^ations of the behaviour of ships seem to show that the
irregularities of a confused sea often tend to check the accumu-
lation of rolling, the heaviest rolling being produced by waves
which are approximately regular. No doubt there are exceptions
to this rule ; but, unfortunately, the attempt to express the con-
ditions of a confused sea in the mathematical investigation renders
the latter unmanageable. Another possible objection may be
taken to the assumption that the ships shall be regarded as small
in comparison with the waves. This is not always true; yet it
must be noted that — excluding the special case of synchronous
oscillations described on page 220 — the heaviest rolling is usually
produced by the largest waves, while the supposition of relative
smallness is favoured by the smallest dimension of the ship — her
bea'u — being presented to the length of the wave.
Upon the basis of the foregoing assumptions, dynamical equa-
tions are formed representing the unresisted rolling of the ships.
It is impossible, in the present work, to follow out the construc-
tion and Solution of these equations. The following are the
principal steps. Some fixed epoch is chosen wherefrom to reckon
the time at which the ship occupies a certain position on the wave
slope, and has an unknown inclination {%) to the vertical. The
inclination (0,) to the vertical of the wave normal for that position
can then be expressed in terms of the steepness of the wave and
the wave period ; both ascertainable quantities. Next the angle
(0 — ^1) between this normal and the masts can be deduced from
the preceding expressions ; and the righting moment correspond-
ing to that angle can be estimated. This moment constitutes
2 20 NAVAL ARCHITECTURE. c;r\r. vi.
the active iigency controlling the motion of the ship at that
instant, and it must be balanced by the moment of the accele-
rating forces, whioh can be expressed in terms of the inertia of
the yhip and the angular acceleration.* Finally, an equation is
obtained involving the following terms: — The angular accelera-
tion at that instant ; the inclination of the masts of the ship to
the vertical at that instant ; and the effort of stability at that
instant. The solution of this equation furnishes an expression
for the unknown angle of inclination (0) of the ship to the vertical
at any instant, in terms of her own natural period, the wave
period, the ratio of the height to the length of the wave, and
certain oth^r known quantitie-;. Assuming certain ratios of the
period of the ship to the wave period, it is possible from the
solution to deduce their comparative effect upon the rolling of
the ship; or, a^sumillg certain values for the steepness of the
waves, to deduce the consequent rolling as time elapses and a
continuous series of waves passes tlie ship. In fact, the general
solution gives the means of tracing out the uuresis^ted rollinu; of
a ship for an unlimited time, under chosen conditions of wave
form and period. A few of the more important cases may now be
briefly mentioned, it being understood that the investigation
deals with unresisted rolling only.
One critical case is that for which the natural period of the
ship for a single roll equals the half-period of the wave. This
had been foreseen by several of the earlier writers, including
Daniel Bernoulli, apart from mathematical investigation, from
the analogy between the motions of a ship and a pendulum. It
is a matter of common experience that, if a pendulum receive
successive impulses, keeping time with (or "synchronising" with)
its period, even if these impulses have individually a very small
effect, they will eventually impress a very considerable oscillation
upon the pendulum. A common swing receiving a push at the
end of each oscillation is a case in point. AYhen a similar syn-
chronism occurs between the wave impulse and the period of the
ship, the passage of each wave tends to add to the range of her
oscillation, and were it not for the deterrent action of the fluid
resistance, she would finally capsize. Such, in general terms,
was the oj)inion of the earlier writers, which recent and more
exact investigations have fully confirmed. Apart from the action
of resistance, it has been shown that the passage of a single wave
See tie explanations of these terms given at page 135.
CHAP. VI. OSCILLATIONS AMONG WAVES. 221
would increase the range of oscillation of tlie ship by an angle
equal to about three times the maximum slope of the wave. For
instance, in an Atlantic storm wave series, each wave being 250
feet long and 13 feet high, and having a maximum slope of some
9 degrees, the passage of each wave would, if there were no re-
sistance, add no less than 27 degrees to the oscillation of the ship ;
so that a very few waves passing her would overturn her. Here,
however, the fluid resistance comes in, and puts a practical limit
to the range of oscillation in a manner that will be explained
hereafter.
It may be well to examine a little more closely into the character
of the wave impulse which creates accumulated rolling in this
case. Suppose a vessel to be broadside-on in tlie wave hollow
when the extremity of her roll is reached, say to starboard, the
waves advancing from starboard to port. Then the natural ten-
dency of the ship, apart from any wave impulse, will be to return
to the upright in an interval equal to one-half her period, whic^i
by hypothesis will be equal to the time occupied by the passage
of one-fonrth the wave length. In other words, the ship would be
upright midway between hollow and crest of the wave near which
its maximum slope occurs. Now, at each instant of this return
roll towards the upright tlie inclination of the wave normal, fixing
the direction of the resultant fluid pressure, is such as to make
the angle of inclination of the masts to it greater than their in-
clination to the true vertical ; that is to say, the inclination of the
wave normal at each instant virtually causes an increase of the
righting moment. Consequently, when the vessel reaches the
upright position at the mid-height of the wave, she has by the
action of the wave acquired a greater velocity than she would
have had if oscillating from the same initial inclination in still
water. She therefore tends to reach a greater indhiation to port
than that from which she started to starboard; and tliis tendencv
is increased by the variation in direction of the wave normal
betvveen the mid-height and the crest — that part of the wave
which is passing the ship during the period occupied by the
second half of her roll. On reference to Fig. 62 — where the
directions of the wave normal are indicated by the masts of the
rafts — it will be seen that, when the ship during the second half
of the roll inclines he r masts away from the wave crest, the angle
between the masts and the wave normal is constantly less than the
angle they make with the vertical. The effect of this is to make
the righting moment less at every instant during the second half
of the roll on the wave than it would have been in still water. For
O 9 '>
NAVAL ARCHITECTURE.
CH^P VI.
unvesisterl rolling, it is the work done in overcoming the resistance
of tlie righting couple which extinguishes the motion away fiom
the vertical. On the wave, therefore, the vessel will go further
to the other side of the vertical from that on which she starts
tlian she would do in still water, for two reasons : (1) she will
acquire a greater velocity before she roaches the upright; (2) she
will experience a less ref-istacce from the righting couple after
passing the upright. From the above statements, it will be
evident that there must be a direct connection between the
maximum slope of the wave and the successive increments of her
oscillations.
More or less close approximation to this critical condition will
give rise to more or less heavy rolling ; but it is a noteworthy fact
that, even where the natural period of the ship for small oscil-
lations equals the half-period of the wave, and may thus induce
heavy rolling, the synchronism will almost always be disturbed
as the magnitude of the oscillations increases ; the period of the
ship will be somewhat lengthened, and thus the further incre-
ments of oscillation may be made to fall within certain limits,
lying within the range of stability of the ship. It will be
understood that this departure from isochronism in no way
invalidates what was said in Chapter IV. as to the isochronism
of ships of ordinary form when oscillating 10 or 15 degrees on
either side of the vertical. The character of the chansfe can best
be illustrated by reference to a common simple pendulum. Such
a pendulum swinging through very small angles on either side of
the vertical has, say, a period of one second ; if it swings through
larger angles, its period becomes somewhat lengthened, and the
following table expresses the change : — *
Ani^les of Swiucr.
Period.
Seconds.
Very small
1
30°
1-017
60°
1-073
90°
1-J83
120°
1-373
150°
1-762
For sliips the angles of swing are never so great as to make the
increase of period great proportionally, but yet, as above remarked,
* See Eeport of Committee ou De- cussion of the probable safety uf the
signs (1871), where Professor Rankiiic Devastation class,
applied similar reasoning to the dis-
CHAP. VI. OSCILLATIONS AMONG WAVES. 223
tlie increase may be sufficient to add sensibly to the safety of a
ship exposed to the action of waves having a period double of her
own period for small oscillations ; although it is by the action of
resistance that the overturning of a ship so circumstanced is
chiefly prevented.
A second interesting deduction from tlie solution of the
general equation for unresisted rolling is found in the " per-
manent oscillations of ships." If a vessel has been for a long
while exposed to the action of a single series of waves, she may
acquire a certain maximum range of oscillation, and perform
her oscillations, not in her own natural period, but in the possibly
different wave period. This case differs from the preceding one
in that the period of the ship for still-water oscillations does not
agree with the half-period of the wave; but, notwithstanding, the
oscillations among waves keep pace with the wave, their period
being " forced " into coincidence with the half-period of the wave.
At the wave hollow and crest a ship so circuQistanced is upright ;
she will reach her maximum inclination to the vertical when the
maximum slope of the wave is passing under her (about the mid-
height of the wave) ; and the passage of a long series of waves
will not increase the range of her oscillations, which are "perma-
nent" in botli range and period — hence their name. The
maximum inclination then attained depends, according to theory,
upon two conditions : (1) the maximum slope of the wave ;
(2) the ratio of the natural period of oscillation of the ship to one-
half the wave period.
Let a = maximum angle made with the horizon by the wave
profile ;
^ = maximum angle made with the vertical by the masts of
the ship ;
T = natural period of still- water oscillations of the ship ;
2Ti = period of wave.
If fluid resistance is neglected, and the conditions above stated
are fulfilled, mathematical investigation for this extreme case
leads to the following equation : —
fl- 1 « X T,^
1 ~ '|i 2
Three cases may be taken in order to illustrate the application of
this equation.
I. Suppose T = T,, then 0 becomes infinity', that is to say, we
2 24 NAVAL ARCHITECTURE. ch\p. vr.
have onoe more the critical case of synchronism previously dis-
cussed, respecting which nothing need be added.
rri2
II. Suppose T less than Tj, so that m^r is a proper fraction less
-•-1
than unity : thon % and a always have the same sign, which indi-
cates that the masts of the ship lean away from the wave crest, at
all positions, except when the vessel is upright at hollow and
crt St. The closer the approach to equality between Tj and T, the
greater the value of % \ which is equivalent to an enforcement of
the statement previously made, that approximate synchronism of
periods leads to heavy rolling. The smaller T becomes relatively
to Ti, the smaller does 0 become ; its minimum value being a when
T is indefinitely small relatively to Tj. This is the case of the
raft in Fig. 62, which keeps its masts parallel to the wave
normal.
III. Suppose T greater than T^: then 0 and a are always of
opposite signs, and, except at hollow and crest, the masts of the
ship always lean towards the wave crest. The nearer to unity is
the ratio of T to Ti, the greater is 0 ; illustrating as before he
accumulation of motion when there is approximate synchronism.
The greater T becomes relatively to Tj, the less does 0 become ;
in other words, as explained above, a ship of very long period
keeps virtually npright as the wave passes.
As an example of the use of the formula, take the following
figures drawn from the report on the behaviour of the Devastation
during her passage to the Mediterranean : —
a = maximum wave slope = li degrees ;
T = natural period of ship for single roll . . = ^•'^ seconds;
Ti = half (apparent, wave period. =6 „
If the conditions of permanent rulling had been fulfilled, the
formula would give —
Maximum inclination of ship, sup- ) , , ,,. ^
posing motion ««res/s^ef?, . •) ^ 1— (-tt-)
^ H ^ j^ _ 2-9,s = ^3 degrees (nearly).
The observed oscillation of the ship, from out to out, at this
time was about 7 degrees, and the less magnitude of this oscilla-
tion, as compared with that given by the formula, must be
accounted for chiefly by the want of absolute uniformity in a
sufficiently long series of waves to make the rolling permanent,
as well as by the steadying effect of the resistance. The example
CHAP. VI.
OSCILLATIONS AMONG WAVES.
225
has, however, been given merely as an illustration of the use of
the formula, not as a proof of its accuracy ; in practice all deduc-
tions from the tlieory of unresisted rolling, as to the extent of
oscillation, require to be modified to allow for the effect of fluid
resistance. It may be added that an inspection of the records of
rolling of a large number of ships, under various conditions of sea,
leads to the conclusion that the periods are rarely "forced" into
coincidence with the wave-period.
It is possible, by means of very simple experiments, to illus-
trate the influence which changes in the relative
periods of ships and waves may have upon the FIG 71.
rolling.* Let AB, Fig. 71, represent a pendulum
with a very heavy bob, having a period equal to
the half period of the wave. To its lower end,
let a second simple pendulum, EC, be suspended,
its weight being inconsiderable as compared with
the wave pendulum AB : then, if AB is set in
motion, its inertia will be so great that, not-
withstanding the suspension of BC, it will go on
oscillating very nearly at a constant range — say,
equal to the maximum slope of the wave — on
each side of the vertical. First suppose BC to
be equal in length and period to AB : then, if the
compound pendulum is set in motion, and AB moves throuo-h a
small range, it will be found that BC, by the property of syn-
chronising impulses, is made to oscillate, through very large
angles. Second, if BC is made very long, and of long period, as
compared with AB, it will be found that BC continues to ban"-
nearly vertical while AB swings, just as the ship of comparatively
long period remains upright, or nearly so, on the wave. Third, if
BC is made very short and of small period when AB is set moving,
BC vvill always form almost a continuation of AB, just as the
quick-moving ship keeps her masts almost parallel to the wave
normal. These illustrations appeal to many who cannot follow
the reasoning, but can apprehend the facts from the experiments.
A third notable deduction from the solution of the equation for
unresisted rolling is that, except when the conditions of synchro-
nism or permanent oscillation are obtained, the rolling of a ship
will pass through phases. At regular stated intervals equal
* Such experiments were made some
years ago by the late Professor Eankiue
and by the Author in connection witli
his lectures at the Eoyal Naval College.
Q
226
NAVAL ARCHITECTURE.
CHAP. VI,
inclinations to the vertical will recur, and the range of the oscil-
lations included in any series will gradually grow from the
miniunim to the maximum after attaining which it will once
more decrease. The time occupied in the completion of a phase
depends upon the ratio of the natural period of the ship to the
wave period. If T = ship's period for a single roll, Ti = half-
period of Mave, and the ratio of T to Ti be expressed in Llie form
-> where both numerator {p) and denominator [q) are the lowest
u-hoJe numbers that will express the ratio : then
Time occupied in the completion of a phase = 2 q . T seconds.
For example, let it be assumed that waves having a period of
9 seconds act on a ship having a period (for single roll) of
7 1 seconds.
ThenT.Ii=l'1.5=lZ -
T: U y 'S q
Time for completion of phase = 3 x 2 x 7| = 45 seconds.
Although the mathematical conditions for these "phases" of
oscillation are not fulfilled in practice, the causes actually operat-
ing on the ship — such as the differences in form of successive
waves, and the influence of fluid resistance — commonly produce
great differences in their successive arcs of oscillation. It is
important, therefore, in making observations of rolling to con-
tinue each set over a considerable j)eriod. In the Eoyal Navy
each set of observations extends over ten minutes, and the
minimum inclinations reached are always found to differ consi-
derably from the maximum inclination. The mean oscillation
for any set is frequently only a little more than half the maximum
inclination, and the following examples are fairly representative
in this respect.
Detached Squadron (1874).
Ships.
Mean Arcs of
Oscillation.
Maximum Arcs
of Oscillation.
Newcastle
Topaze
Immortalite
Narcissus
Doris
Degrees.
29-6
22-6
20
19-6
18-7
5-8
l;egrees.
58
50
39
36
48
15
llaleigh
CHAP. VI.
OSCILLATIONS AMONG WAVES.
227
Channel Squadron (1873).
Ships.
Mean Arcs of
Oscillation.
Maximum Arcs
of Oscillation.
BeUerophon
Minotaur
Agincourt
Hercules
Sultan
Degrees.
ltJ-9
22-3
16-4
8-1
6-6
Degrees.
25
46
37
14
12
111 comparing the rolling of ships, it is usual to take the mean
arcs of oscillation (i.e. the mean of the sums of successive incli-
uations on either side of the vertical), and on the whole this
appears the fairest course. But in analysing rolling returns, it is
always desirable to look further, and to note the maximum and
minimum oscillations, as well as the rate of growth of the range.
All these particulars are readily ascertainable from the forms upon
which the records of rolling are kept in the Royal Navy. For
considerations of safety, the maximum angle of inclination reached
is obviously of the greatest importance ; but usually it is taken
for granted that vessels will not roll so heavily as to be liable to
capsize, and, apart from this danger, the mean oscillations afford
the best means of comparing the behaviour of ships.
In concluding these remarks on the hypothetical case of
unresisted rolling among waves, it may be well to summarise the
conclusions which have the greatest practical interest, and to
compare them with the results of experience. It need scarcely
be remarked again that the actual behaviour of ships at sea is
influenced by fluid resistance ; and in a later portion of this
chapter we shall consider the character of that influence.
First: it appears that very heavy rolling is likely to result
from equality or approximate equality of the period of a ship and
the half-period of waves, even when the waves are very long in
proportion to their height. Many facts might be cited in support
of this statement, but a few must suffice. Admiral Sir Cooper
Key observed that the vessels of the Prince Consort class were
made to roll very heavily by an almost imperceptible swell, the
period of which was just double that of the ships. Admiral
R. Yesey Hamilton informed the Author that, on one occasion,
the Achilles, a vessel having a great reputation for steadiness,
rolled more heavily off Portland in an almost dead calm tlian she
did off the coast of Ireland in very heavy weather. Mr. Froude
Q 2
2 28 NAVAL ARCHITECTURE. chap. vi.
reports a very similar circumstance as having occurred during
trials with the Active. And, lastly, during the cruise of the
Combined Squadrons in 1871, when the Monarch far surjmssed
most of the ships present in steadiness in heavy weather, there
was one occassion when, through the action of approximately
synchronising periods, she rolled more heavily in a long swell
than did the notoriously heavy rollers of the Prince Consort
class.
The effects of approximate synchronism of periods may be
tested by changing the course of a ship relatively to the advance
of the waves; and this was done most satisfactorily during the
trials of the Devastation, the ship remaining in the same condi-
tion, and the waves, of course, remaining unchanged, while the
apparent period of the waves was altered by change of course and
speed.* Lying passively broadside-on to waves having a period
of about 11 seconds, the Devastation was observed to roll through
the maximum angles of 6^ degrees to windward, and 7^ degrees
to leeward, making the total arc 14 degrees. She was then put
under weigh, and steamed away from the waves at a speed of
7^ knots, having the wind and sea on her quarter, when her
maximum roll to windward became 13 degrees, and to leeward
14^ degrees, making the total arc 27^ degrees. The difference
between the two cases is easily explained, in view of the fore-
going considerations. When rolling passively in the trough of
the sea, the apparent period of the waves was their real period;
and this was less than the double period for the Devastation
(13J seconds). When she steamed away obliquely to the line of
advance of the waves, their apparent period became increased, and
the diagrams of the ship's performance then taken showed that
the speed and course of the ship had the effect of making the
apparent period of the waves just equal to the period of a double
roll for the Devastation — in fact, established that synchronism
of ship and wave which is most conducive to the accumulation
of motion.
This case also furnishes an example of what to every sailor is a
truism, viz. that the behaviour of a ship is greatly influenced by
her course and speed relatively to the waves. Theory, as we have
shown, takes account of the case which is probably the worst for
most vessels — the condition of a ship which has become unmanage-
able, and rolls passively in the trough of the sea. But so long as
* For an explanation of the term " apparent period," see page 191 of preceding
chapter.
CHAr. vr. OSCILLATIONS AMONG WAVES. 229
a ship is mauageable, the officer in command can largely influence
her behaviour by the selection of the course and speed, which
make the ratio of the periods of ship and wave most conducive to
good performance. In the case of the Devastation just cited, had
she steamed obliquely, as before, but head to sea, the apparent
period of the waves would have been decreased, and the rolling
would probably have been less than it was in either case recorded.
Of course, synchronism in some cases may be produced by steam-
ing towards, instead of from, the waves. For instance, if a ship
having a period of 4 to 5 seconds had been amongst the waves
which the Devastation encountered, when broadside-on, her period
would have been less than half that of the waves ; but if she had
steamed obliquely towards the waves, their apparent period might
have been lessened, and made about 8 to 10 seconds. However
obtained, such synchronism will probably lead to the heaviest
rolling the vessel is likely to perform ; and the steeper the waves
the heavier is the rolling likely to be.
Second: It follows from the investio;ation for unresisted rollinor
that the best possible means, apart from increase in the fluid re-
sistance, of securing steadiness in a seaway, is to give to a ship
the longest possible natural period for her still-water oscilla-
tions. This deduction it is which has been kept in view in the
design of many recent war-ships, both English and foreign, and
its correctness has been fully established by numerous observa-
tions.
It would be easy to multiply illustrations from the published
record of rolling of the ships of the Koyal Navy, as well as from
those of the French navy ; but space prevents us from doing this,
and we can only give a few, referring the reader to the original
documents for more.* During the cruise of the Combined
Squadron in 1871 some of the "converted" ironclads of
the Prince Consort class, and other of the earlier ironclads
having short periods were in company with armoured ships
of more recent design, having longer periods. The follow-
ing table of observations refers to a time when the weather
was reported to be exceptionally heavy, but unfortunately no
particulars were noted of the dimensions and periods of the
waves.
* See Parliamentary Papers, " IRe- on Designs for Ships of War; and
ports on Channel Squadrons," 1863-68; various reports on the behaviour of
the Report of the Admiralty Comnnittee ships in the French navy.
NAVAL ARCHITECTURE.
CHAP. VI.
Ships.
Lord Warden .
Caledonia . .
Prince Consort.
Defence .
Minotaur
Northumberland
Hercules .
Apjiroxiinate
Natural i'eriods.
Seconds.
5 to 5^
} 7 to 7^
8
Arcs of
Oscillation.
Degrees.
62
57
46
49
35
38
25
It may be interesting to note that the period of the Prince
Consort chiss, from 5 to 5^ seconds, would just synchronise with
the half-period of waves from 500 to 600 feet long. It has been
stated in the preceding chapter that these are almost identically
the dimensions which careful and extensive observalions have led
ns to accept as belonging to the very large Atlantic storm waves
Dr. Scoresby and others have encountered. Hence it is easy to
explain the relative bad behaviour of these converted ironclads
with their quick motion and short period. Another illustration
of the superior steadiness of ships of long period may be drawn
from the observed performances of the rejjresentative ships in the
Channel Squadron of 1873, as under : —
Ships.
Approximate
Natural Periods.
Mean Arcs of
Oscillation.
Bellerophon
Minotaur
Agihcourt
Hercules
Sultan ' . .
Seconds.
6i to 7
} 7 to 7J
8
8-9
Degrees.
16-9
/ 22-3
I 16-4
8-1
This, it should be understood, is a fairly representative case,
and by no means an exceptional one. In the French navy
similar results have been obtained. Almost at the outset of the
ironclad reconstruction, the returns from the French experimental
squadron of 1863 furnished evidence of the 8ame kind, as the
following table shows. The observations were made when the
vessels were running broadside-on to a heavy sea.
CHAP. VI.
OSCILLATIONS AMONG WAVES.
2^1
-, . Approximate
^•"'P^' Natural Periods.
Mean Arcs
of Oscillation.
Normandie
Invincible
Couronne
Magenta
Solferino . .
Seconds.
■ 5 to 5|
6
} 7 to 7J
Degrees.
/ 43-6
\ 41-4
37-7
/ 36
\ 35
The Magenta and Solferino were making only ten oscillations
per minute, whereas the other ships were making twelve.
A more recent and striking contrast is to be found in the be-
haviour of the French ironclad Ocean and other vessels of her
class, having periods of about 10 seconds for a single roll, as com-
pared with the behaviour of the armoured corvettes of the Alma
class having periods varying from 5^ to 5*7 seconds for a single
roll. It is recorded that in the first cruise of the Ocean she never
rolled more than 2 to 3 degrees on each side of the vertical, while
three of the corvettes were rolling 31, 35 and 36 degrees from the
vertical. The maximum inclination to the vertical reached by the
Ocean under any circumstances during this cruise never exceeded
7 degrees. It may be added that experience with the ships of the
Invincible (dass in the Royal Navy has given no less satisfactory
results. The commanding officer of one of these ships has stated
" that they may go through a commission and never heel or roll
more than one or two degrees."
Records of rolling have been mostly limited to the behaviour
of ironclad ships, the apprehensions entertained in some quarters
as to the unseaworthiness and bad behaviour of these vessels
having caused greater attention to be bestowed upon them than
upon unarmoured vessels. But now that rolling returns have
been ordered to be made in all her Majesty's ships, a large mass
of facts relating to unarmoured as well as armoured ships has
been collected, and is continually being increased. The Detached
Squadron has in this way enabled a good comparison to be made
between the behaviour of the early types of screw frigates, forming
the main strength of the squadron, and that of the swift cruisers
which have been in company — particularly the Inconstant and the
Raleigh, both ships of long period. The following table is taken
from the observations of rolling made in the heaviest weather
experienced by the squadron in the spring of 1875, and, like
the other examples given, is only a specimen of many similar
cases : — •
232
NAVAL ARCHITECTURE.
CHAP. VT.
Ships.
Approximate
Natural Periods.
Jlean Arcs of
Oscillation.
Newcastle
Topaze
Jmmortalite ... . •
Narcissus
Doris
Raleigh
Seconds.
1 • 1
8
Degrees.
29-6
22-6
20
19-6
18-7
5-8
In passing, it may be well to illustrate the importance of the
slower motion beiug associated with the smaller arc of oscillation
in ships rolling at sea. In the table on page 230, compare the
behaviour of the Lord Warden vi\i\i that of the Hercules; the
former rolling through an arc of 62 degrees about eleven or
twelve times each minute, while the latter rolled through 25
degrees only about seven or eight times each minute. A man
aloft, say, at a height of 100 feet, in the Lord Warden would be
swept through the air at a mean rate of some 1200 feet per
minute, having the direction of his motion reversed about every
5 seconds ; whereas a man placed as high in the Hercules would
only be moving at a mean rate of some 350 feet per minute, and
be subjected to a reversal of the direction only about once every
8 seconds. The maximum rates in passing through the vertical
would of course be greater than these n^ean rates. Hereafter it
will be shown how great are the strains brought upon the struc-
ture, masts, and rigging of ships which roll violently and rapidly;
but for the present purpose the foregoing figures must suffice.
The reader will have no difficulty in multiplying illustrations of
the fact, should he so desire.
The remarks on wave genesis made in the previous chapter will
assist the explacation of the undoubtedly greater average steadi-
ness of vessels of long natural periods. What njay be termed
ordinary storm winds may by their continued action produce
waves having lengths of 600 feet or under, with periods of 10 to
11 seconds or less ; and these waves would have half-periods
about equal to the still-water peiiods of the wooden screw frigates
of the older type and the converted ironclads. Extraordinary
conditions would, on the other hand, be required to produce waves
having periods double the still-water periods now commonly
given to the largest war-ships armoured and unarmoured; for
these waves would be from 1200 to 1500 feet in length — sizes
that have been noted, but are not often encountered. Before such
CHAP. VI. OSCILLATIONS AMONG WAVES. 233
waves could have reached these enormous dimensions, they would
probably have passed through a condition resembling that of the
ordinary storm wave ; and although, in becoming degraded, they
may lose in their lengths much more slowly than they do in their
lieights, yet they may once more, before dying out, approach the
lengths and periods of the ordinary storm wave, being less steep
than that wave w^hen fully grown. Summing up, therefore, it
appears probable that the ship of long period (say 7 to 9 seconds)
will much less frequently fall in with waves synchronising with
her own natural period than will the vessel of shorter period (say
4 to 6 seconds) ; and when these large waves are encountered,
their chimce of continuance is much less than that of smaller
waves ; so that on both sides the slower-moving ship gains, when
rolling passively in the trough of the sea.
Changes of course and speed of the ship relatively to the waves,
as before explained, affect the relation between the periods, and
may either destroy or produce the critical condition of syn-
chronism. But this is equally true of both classes of ship, and as
long as they remain under control, all ships may have their be-
haviour largely influenced by such changes, whether their period
be long or short. When synchronism is the result of obliquity of
course relatively to the waves, it implies the retention of control
over the vessel by her commander ; for when she becomes un-
manageable, a vessel falls off into the trough of the sea. Hence
such synchronism in the case of vessels of naturally long period
may be easily avoided by change of course ; for them rolling pas-
sively broadside-on to the longest waves of ordinary occurrence is
not the worst condition (see previous case of the Devastation). On
the contrary, the vessels of shorter period would occupy their
worst position relatively to such waves when rolling passively in
the trough of the sea. In short, synchronism of periods usually
results only from obliquity of course in the vessels of long period ;
it can only be avoided in storms of average severity by obliquity
of course in the quicker-moving ships. The coiitrast of conditions
speaks for itself.
One other important point of difference between very long
waves and ordinary large storm waves is the much less com-
parative steepness of the former. The fact was illustrated in
the previous chapter ; its bearing upon the behaviour of ships
will be obvious if the previous remarks on the influence of the
maximum wave slope are recalled to mind. It has been shown
that the upper limit attained during rolling motion is very
largely governed by that slope, as well as by the ratio of the
2 34 NAVAL ARCHITECTURE. chap. vi.
periods. Hence, for a certain fixed ratio of periods, that ship
will fare best which encounters the flattest and longest waves.
Probably i&\^ waves having tiie large periods of 13 to 16 seconds
luive slopes exceeding 4 or 5 degrees ; whereas waves having
periods of 8 or 10 seconds have been observed to slope 9 or 10
degrees to the horizon. Moreover, when the condition of synchro-
nism of periods results from the oblique motion of a ship rela-
tively to waves, that obliquity j)i'oduces a virtual reduction of the
wave sloj)e, and thus favours ships of long period w^hen rolling
among ordinary storm waves.
Third: It appears from the investigation of unresisted rolling
that vessels having very quick periods, say 3 seconds or less for a
single roll, fare better among ordinary large storm waves than
vessels having periods of 4 to 6 secon Is. The tendency in these
very quick-moving vessels is to acquire a fixed range of oscilla-
tion, keeping their decks approximately parallel to the effective
wave slope, as described for the little raft in page 185. As ex-
amples, the deep-sea fishing-boats used off the Dutch coast at
Scheveningen may be named ; and amongst war-ships, the
American monitor type. It is reported of the Miantonomoh, which
crossed the Atlantic about twenty-two years ago, with a height
of upper deck above water of only 3 feet, that she rolled but
moderately in heavy weather, and shipped very little water on
her low deck, even when broadside-on to large waves, the water
which did come on the deck on the weather side u.?ually passing
off again on tiie same side as that it broke over. This is very
good evidence that the motions of the monitor were so quick
relatively to the wave motion that her d"ck was kept approxi-
mately parallel to the surface ; otherwise, with the low freeboard,
much greater quantities of water would have been shipped. Ob-
viously such a vessel would not be a steady gun platform, as the
range of her oscillation might be considerable, being governed by
the wave slope. For instance, if the Miantonomoh were placed
broadside-on to Atlantic storm waves such as Dr. Scoresby ob-
.cerved, say, 600 feet long and 30 feet high, the maximum slope
of the wave would be about 9 degrees, and its period about 11
seconds. Once in every 5^ seconds (the half- wave period), there-
fore, if the ship kept pace with the wave, she would really suing
through a total arc of 18 degrees — 9 degrees on either side of the
vertical, although to an observer on board, owing to causes ex-
plained in the preceding chapter, she might seem to continue
nearly upright. The wave period is about twice the natural
period for a double roll of the monitor. In other words, while
CHAP. VI. OSCILLATIONS AMONG WAVES. 235
the wave normal or virtual upright iu 51. seconds completes a
sino-le set of motions between the hollow and crest, the monitor
can move twice as quickly, and may therefore keep her deck
nearly parallel to the surface.
When this quickness of motion is obtained by the adoption of
great beam a vessel has the further advantage (explained on
page 214) of a very flat effective wave-slope, so that her range
of oscillation may be very limited even among large waves.
The Kussian circular ironclads and the Livadia are examples of
tliis class. They are reported to be wonderfully steady; and in
exceedingly heavy weather in the Bay of Biscay the maximum
roll of the Livadia is stated to have been only 4 degrees.
Somewhat different couditions hold in the cases of small sea-
going vessels, for which the still-water periods are made short by
the smallaess of their momeut of inertia, and the necessity for
retaiuins: a sufficient amount of stiffness. For such vessels
the effective slope is very nearly the upper surface of the
waves, and their range of oscillation among large waves is
practically determined by the wave slope. Amongst smaller
waves, approaching the condition of synchronous periods, these
small vessels are much worse off than very broad vessels of identical
period, because the effective slope for the broad vessels is so much
flatter. In fact a small vessel of 3 seconds' period among waves
of about 180 feet in length, might accumulate motion and roll
heavily, much as larger vessels of from 4 to 6 seconds' period have
been shown to do among ordinary large Atlantic waves. The
Livadia, on the contrary, with her beam of 150 feet, might remain
almost free from rolling, even when her period was nearly identical
with that of the waves. On the other hand, it must be noted, and
will be more fully illusti'ated hereafter, that in these small vessels
the accumulation of rolling motion may be checked by the use
of bilge-keels to an extent not possible in larger vessels.
Oidy a passing notice has been bestowed hitherto upon the
very important effects of fluid resistance in modifying the rolling
of ships among waves. This branch of the subject is, however,
of great interest, and has attracted the attention of several able
investigators : although they are not agreed in all points, there are
many general considerations which command universal support ;
to some of these brief reference will now be made.
The deductions from the liypothetical case of unresisted rolling,
236 NAVAL ARCHITECTURE. chap. vi.
to which attention has been drawn, can be regarded only as of a
qualitative and not of a quantitative character. For example,
one of these deductions is that a ship rolling unresistedly among
waves having a period double her own natural period will accumu-
late great rolling motion, and infallibly upset. As a matter of
fact, we know that, while the assumed ratio of periods leads to
the production of heavy rolling, ships do not commonly, nor in
any but exceptional cases, upset under the condition of synchron-
ism ; in other words, the character of the motion is well described
by the deduction from the hypothetical case, but its extent is not
thus to be measured. Similarly, in other cases, the effect of
resistance must be considered when exact measures of the range of
oscillation are required, as they may be in discussing the safety
of ships. The problem, therefore, resolves itself into one of
correcting the deductions from the case of unresisted rolling, by
the consideration of resistance coming into play.
In accordance with the principles explained in Chapter IV., it
is possible by means of still-water rolling experiments to ascertain
the amount of resistance of a ship corresponding to any assigned
arc of oscillation. If the ship herself has not been rolled for that
purpose, but a model or a sister ship or similar vessel has been so
rolled, her coefficients of resistance may be estimated with close
approximation, and the retarding effects of resistance may be
determined. This is true within the limits of oscillation reached
by the still-water experiments, say, 10 or 15 degrees on each side
of the vertical, and in high-sided ships of ordinary form the limits
may probably be extended. In fact, it may be assumed that the
coefficients of resistance for most ships are or may be ascertained
by these rolling experiments for inclinations as great as are likely
to be reached by the same ships when rolling in a seaway, in all
but ex' eptional circumstances.
If a vessel rolls through a certain arc amongst waves, it appears
reasonable to suppose that the effect of resistance will be practically
the same as that experienced by the ship when rolling through an
equal arc in still water. The intrusion of the vessel into the wave,
as already remarked, must somewhat modify the internal molecular
forces, and she must sustain certain reactions, but for practical
purposes these may be disregarded, not being proportionally large.
Resistance is always a retarding force ; in still water it tends to
extinguish oscillation ; amongst waves it tends to limit tlie maxi-
mum range attained by the oscillating ship. This may be well
seen in the critical case of synchronism ; where a ship rolling
unresistedly would have a definite addition made to her oscillation
CHAP. VI. OSCILLATIONS AMONG WAVES. 237
by the passage of each wave. The wave impulse may be measured
by the added oscillation ; the dynamical stability corresponding to
the increased range exj^ressing the " energy " of the wave impulse.
At first the oscillations are of such moderate extent that the ano-ular
velocity is small, and the wave impulse more than overcomes the
effect of the resistance; the rolling becoming heavier. As it
becomes heavier, so does the angular velocity increase, and with
it the resistance ; at length, therefore the resistance will have
increased so much as to balance the increase of dynamical stability
corresponding to the wave impulse — then the growth of oscillation
ceases. As successive waves pass the ship after this result is
attained, they each deliver their impulse as before, but their action
is absorbed in counteracting the tendency of the resistance to retard
and degrade the oscillations.
When a ship is rolling "permanently" amongst waves, her
oscillations having a fixed range and period, a similar balance will
probably have been established between the wave impulse and
the resistance ; and here also the actual limit of range will fall
below the theoretical limit given by the formula for unresisted
permanent rolling on page 223. Eesistance may, in this case, be
viewed as equivalent to a reduction in the steejjness of the waves ;
this diminished slope taking the place of what has been termed
the "effective slope" for unresisted rolling.
Assuming that the coefficients of resistance for a ship have
been determined experimentally, and that the curve of stabilitv
has been constructed, it is possible to trace her behaviour amono-
waves of any selected form by means of the process of " graphic
integration," introduced by the late Mr. Froude. This process
may be regarded as the most valuable means yet suo-gested for
approximating to the maximum rolling to which a ship is likely
to be subjected in a seaway, and for pronouncing upon her safety
against or liability to capsizing. It has already been applied in
certain critical cases, and its accuracy has been confirmed by
comparisons of the results obtained by its use with the actual
behaviour of ships.* No detailed description of the process can
be given here, but it may be interesting to give an illustration of
its application. Fig. 71a contains the result of an investio-ation
made for H.M.S. Endymion when rolling, with no sail set, among
* For an example of these com- for a detailed account of the process of
parisons see the appendix to the Report graphic integration, see the Transac-
of the Inflexible Committee {Parlia- tions of the Institution of Naval Archi-
mentary Paper C-1917 of 1878) : and tects for 1875 and 1881.
238
NAVAL ARCHITECTURE.
CHAP. VI.
waves 512 feet long and 22 feet high. On the base-line AB,
abseissaj measurements correspond to time reckoned from some
selected epoch. Any ordinate of the curve of " wave slope " shows
the slope of the effective wave surface to the horizon at the instant
fixed by the corresponding abseissn. Similarly any ordinate of
the curve of "inclination of ship" shows the angle which her
masts make with the vertical at the corresponding time. Hence
it follows that the intercepts, or lengths of ordinate, between the
curves of inclination and wave slope show for each instant the
angle of inclination of the masts of the ship relatively to the
normal to the wave slope, which angle, as previously explained,
governs the virtual righting moment, and enables an opinion
to be formed as to the stability or instability of a ship.
FIG 71 «
^^p;^r^fT?ovt*^"
The '' curve of force " in Fig. 71a has ordinates represent-
ing successive values of the moment of the impressed forces
acting on the ship. For example, in the case under con-
sideration, the moment of the imj)ressed forces at any time
includes the instantaneous righting moment and the instan-
taneous moment of resistance. During certain parts of the
motion of the vessel the instantaneous rigliting moment tends to
add to her angular velocity, while the moment of resistance tends
to diminish it ; the corresponding ordinates of the force curve
then represent the differences between the moments. During
other parts of the motion the righting moment, as well as the
moment of resistance, tends to retard the angular velocity ; and
the corresponding ordinates of the force curve represent the sums
of the moments. In building up the force curve it is necessary to
know, therefore, instant by instant the inclination of the masts
of the ship to the wave-normal and her angular velocity, because
the instantaneous righting moment depends upon that incli-
nation, while the moment of resistance is governed by the
angular velocity. The piocess is really one of " trial and error,"
CHAP. VI. OSCILLATIONS AMONG WAVES. 239
but each step admits of a complete clieck and verification in
consequence of the inter-dependency of the curve of inclinati'^ns
and the force curve. In practice, the work of graphic iutegi atiou
can be rapidly peiformed, and after certain preliminaries have
been arranged in any particular case, the remaining steps are
very simple.
It will be understood that the process of graphic integration is
based on strict mathematical reasoning ; but it surpasses any
purely mathematical investigation in its inclusion of the effect
of fluid resistance, and in its scope of application. By means of
this process the rolling of a ship in the most confused seaway
can be approximated to, the appropriate curve of wave-slope
being supposed to be known. The behaviour of the same ship
under different conditions of sea can be compared ; the probable
effects of changes in bilge-keels, &c., can be investigated; and.
the probable rolling of different types under identical conditions
of sea can be contrasted. It is greatly to be desired that com-
parisons might be multiplied between the observed behaviour of
ships and their probable behaviour deduced by means of graphic
integration. Such comparisons would doubtless have the eifect
of still further establishing the great practical utility of the
process ; and they would probably throw much light upon certain
obscure questions, particularly upon those relating to the effective
wave slope.
Another method of investigation for the maximum rollino: of
ships among waves, including the effect of fluid resistance, has
been proposed by M. Bertin, and deserves mention, although it
does not compare, in our judgment, with the process of graphic
integration, either in completeness or in the scope of its applica-
tion. Starting from the fundamental conception that the heaviest
rolling will take place when a ship is exposed to the action of
waves whose period equals the still-water period of the shijj for a
double roll, M. Bertin considers that, apart from the action of
resistance, the passage of each half wave would add to the
amplitude of the oscillation of the ship an angle equal to the
maximum slope of the effective wave surface. This estimate, it
may be observed, differs somewhat from that of Mr. Froude,
mentioned on page 221 ; but the difference is unimportant. Even
when resistance is operating the wave form tends to add to the
amplitude of successive rolls, and will do so until a range of
oscillation is reached, for which the work done in overcoming the
moment of resistance balances the work (or dynamical stability)
corresponding to the increase of amplitude which the passage of
240 NAVAL ARCHITECTURE. chap. vi.
the wave tends to create. Using IM. JBertin's notation : —
B = the maximum slope of the effective wave surface ;
0 = the maximum amplitude of ndling ;
N = coefficient of resistance deduced from still-water
rolling experiments.
Then, as explained on page 159, M. Bertin would write
A(/) = loss of range due to resistance = N</)^ ;
and on the foregoing assumjDtions he would also write
A«^ = 9;
so that
N.^" = e.
" Supposing that the quantities neglected in the calculation
affect the values of ^ in very nearly the same manner for all
ships," M. Bertin finally proposes to introduce a constant into
this last equation, writing it
N.^2 = l\ e.
In his examples this constant is usually omitted. For instance,
La Galissoniere has a value of N = '0075, and when among svn-
chronising waves, for which G - 9°, her maximum roll is given
by the equation
The reciprocal of J^ M. Bertin terms the coefficient d'ecclisite.
In the examples given by him it varies from 8 or 9 in the smaller
classes of unarmoured war-ships, up to 11 to 15 in armoured
ships. Roughly speaking, if 9 degrees is a fair average slope for
ocean waves of large dimensions, the maximum roll obtained from
the above formula would be three times the coefficient cV ecclisite.
From this brief description it will be observed that M. Bertin
here confines attention to the critical case of synchronism, and
does not attempt the discussion of the limits of rolling likely to
be reached by a ship among waves of other periods. He is
careful to note the fact that this critical case is less likely to
occur as the still-water periods of ships are lengthened ; and that
for certain classes of war-ships the periods are so long that they
are never likely to encounter synchronising waves. In order to
meet such cases of departure from synchronism M. Bertin has
proposed an empirical formula, which need not be reproduced
here.*
* For full details of these iovestigations, see Les V agues et le Boulis.
Paris, 1877.
CHAP. VI. OSCILLATIONS AMONG WAVES. 241
The broad practical deduction from all these investigations is
that any increase in the fluid resistance to the rolling of a ship
tends to limit her maximum oscillations among waves. It has
already been explained (see Chapter IV.) that in the use of bilge-
keels is found one of the most convenient and effective methois
of influenc'ng the resistance to rolling, and that their employment
is most effective in small ships of short period. Formerly some
high authorities in the science of naval architecture opposed the
use of bilge-keels ; but extended experience has placed the
matter beyond doubt, and it may be well to quote a few facts in
support of this opinion. The Admiralty Committee on Designs
took evidence in 1871 as to the advantages or otherwise of bilge-
keels ; this evidence was not unanimouslv favourable to the
use of such keels, but its general tenour was so. Some of the
Indian troopships had been fitted with deep bilge-keels at that
time, and the reports of their effect on the behaviour of the
ships were most definite. The captain of the Serapis reported
that the bilge-keels, having been tried under all conditions of
wind and sea, had proved a perfect success, and added, " 1 can
confidently say her rolling has been lessened 10 degrees each
way." As regarded the Crocodile, no similarly severe tests had
at that time been made, but the opinion was confidently expressed
that "the rolling had been much checked by the bilge-pieces,"
the ship having often rolled heavily before they were fitted, and
being considered " remarkably steady " afterwards. Mr. Froude
also came forward with the reports of his experiments on models,
and strongly recommended the u«-e of deep bilge-keels — a
recommendation which was endorsed by the committee in their
report. These experiments were made at Spithead with the
same model of the Devastation as had previously been used
to determine the effects of different depths of bilge-keels upon
still-water oscillations.* At the time considerable doubt was
entertained in some quarters as to the safety of the Devastation ;
and it was intended to try the model amongst waves having
approximately the same period as its own for a double roll, in
order to obtain a verification of the theoretical investio-ations of
the probable behaviour of the ship when similarly circumstanced.
AVaves were found having the desired period, but they proved to
be proportionately much steeper than any waves would be that
would synchronise with the double period of the ship. Hence
the trials became simply a test of the relative merits of the
See the accounts of these experiments at page 163.
242 NAVAL ARCHITECTURE. chap. vi.
different bilge-keels, and in no sense a representation of the
probable behaviour of the ship. The results were found to be
as follows : —
Condition of Model.
Maximum Angle
attained.
With 6 feet bilge-keel on each side ....
„ 3 feet „ „ ....
„ no bilge-keels
5 degrees.
Model upset.
The deeper bilge-keels, therefore, proved very influential in
limiting the range of oscillation, the waves remaining of the
same character, and the variations in the depths of the keels
being the only changes made during the trials.
The most complete evidence of the usefulness of bilge-keels in
limiting the rolling of ships in a seaway is that afforded by the
experiments made off Plymouth in 1872. Two slooj)s, the
Greyhound and Perseus, had been placed by the Admiralty at
the disposal of Mr. Froude for this purpose; the Greyhound was
fitted with temporary bilge-keels about 3| feet deep, which were
not applied to the Perseus. So far as external form and dimen-
sions were concerned, the two vessels were very similar ; and by
means of ballast they were made to have practically the same
draught of water and still-water p-^^riod ; the latter being about
4 seconds for a single roll. With the one exception of the
bilge-keels, the conditions influencing the behaviour of the two
ships were thus made as nearly as possible identical ; and their
comparative rolling, when exposed to the same series of waves
simoltaneoasly, necessarily afforded a measure of the effect of
the bilge-keels. When the trials were mai'e, the waves were of
moderate length, and from 4 to 5 seconds' period ; the two
vessels were towed out and placed broadside-on to the waves,
in immediate neighbourhood, but not so close to one another
as to favour one by any shelter from the other. Their simul-
taneous rolling was then observed, and the Perseus was found to
reach a maximum roll about twice as great as that for the
Greyhound ; the proportions for the mean oscillations of the two
ships being much the same as those of the maximum. Thus,
taking twenty successive rolls, the mean for the Greyhound was
less than 6 degrees, whereas that for the Perseus was 11 degrees;
the maximum inclination of the Greyhound during this period
was about 7 degrees, that for the Perseus about 16 deo-rees.
Comment upon these facts is needless.
CHAP. VI. OSCILLATIONS AMONG WAVES. 243
The accidental loss of a portion of one of the temporary bilge-
keels attached to the Greijliound at the end of these trials
furnished an unlooked-for illustration of their beneficial effect.
Such a loss would not have occurred in a vessel with permanent
bilge-keels, but the deep bilge-keels in the Greyhound, beiiig
fitted for experimental purposes only, were not very strongly
secured to the hull, and a portion of one gave way. Its loss was
not known until afterwards, but it was noticed that the behaviour
of the ship had sustained a sudden change, the rolling being more
heavy than before ; and the cause could not be detected until the
detached portion of the bilge-keel was seen floating alongside.
This careful and conclusive series of experiments does not, of
course, fairly represent the ordinary conditions of bilge-keel
resistance, the depth of the keels fitted to the Greijhound being
proportionately very great indeed. But it exemplifies what may
be accomplished in this direction, and the facts obtained are very
valuable for the future guidance of naval architects. Circum-
stances may and do arise in the designing of war-ships which
make it difficult, if not impossible to associate requisite qualities
with the long still-water period which theory and observation
show to be favourable to steadiness. In all such cases the use
of bilge-keels must be advantageous, and in ships of small size
their effect may be most marked in limiting rolling. Merchant
ships with periods varying greatly according to the nature and
stowage of their cargoes may also derive benefit in all conditions
from bilge-keels. In the Royal Navy such keels have been
commonly fitted throughout the period of the ironclad reconstruc-
tion ; in the mercantile marine they are now very frequently
fitted. Care has to be exercised, of course, in fitting such keels,
in order that they may not interfere with the speed or steering
of the ships ; and it is customary to fit bilge-keels only over
about one-half of the length amidships, leaving the extremities
free from such appendages.
The extinctive effect of the "water-chamber" provided in the
Inflexible and other armoured ships of great stiifness, broad beam,
and moderate period, has been mentioned on page 166. It
niay be added here that on the passage of the Inflexible to the
Mediterranean she encountered very heavy weather in the Bay
of Biscay ; and notwithstanding her moderate period (5^ seconds)
she never rolled more than 10 or 11 degrees to the vertical, even
when exposed to the action of waves having apparent periods very
nearly synchronising with her own period and having heights
from 20 to 25 feet. This good behaviour may have been partly
K 2
244 NAVAL ARCHITECTURE. chap. vi.
due to tlie great beam (75 feet), but must have been largely
influenced by the free-water in the chamber aft.
It need hardly be added that, in making these lengthy
references to bilge-keel resistance and the extinctive effect of
contained water, it is not intended to pass by tlie fact that the
form of the immersed part of a ship and the condition of her
bottom very considerably affect the aggregate resistance. But
all these conditions are included in the determination of the
coefficients of resistance to rolling; and, moreover, the form of
a ship is determined by the naval architect mainly with reference
to its stability, carrying power and propulsion, not with reference
to the increase of the resistance to rolling. The latter is a sub-
ordinate feature of the design, and is best effected by leaving the
under- water form of the ship herself unaltered, and simply adding
bilge-keels. The depths of these keels should be made as great
as possible consistently with the conditions of service of the
ship, the sizes of the docks she has to enter, or other sj)ecial
circumstances.
Certain classes of ships present singular features considerably
affecting their behaviour at sea. Vessels with projecting armour,
like the American monitors, or the Glatton in the Koyal Navy,
or the Devastation class as they were originally designed, really
possess in these projections virtual side-keels of great efficiency
in adding to the resistance to rolling; and the records of the
behaviour of American monitors prove that the projections had
a steadying effect. There was, however, the drawback that the
alternate emersion and immersion of the armour shelf brought
considerable shocks or blows upon the under side of the pro-
jecting armour, tending to shake and distress the fastenings of
these singularly constructed vessels. Similar shocks were ex-
perienced in the Devastation when rolling in a seaway, although
the vastly different construction of the armoured side prevented
any injurious effects similar to those said to have been expe-
rienced in the American monitors. After several trials it was
decided to " fill-in " the projection of the armour shelf in the
Devastation in order to avoid the shocks ; the reduction of the
resistance being accepted when it liad been ascertained beyond
question that the vessel was singularly steady and well behaved.
Low freeboard also, as previously explained, develops deck
resistance by the immersion and emersion of the one or other
side that accompanies moderate angles of rolling ; and observa-
tions of the behaviour of monitors amongst waves have clearly
shown that conditions similar to those of still water obtain also
CHAP. vr. OSCILLATIONS AMONG WAVES. 245
for rolling amongst waves. In vessels of ordinary forms and
good freeboard nothing similar to this deck resistance exists ;
and therefore in monitors the use of bilge-keels is not so necessary
as it is in ordinary vessels.
Up to this point attention has been confined to the rolling of
sliips among waves when no sail is set ; it nov becomes necessary
to attempt an explanation of the still more difficult case where a
ship under sail is exposed to the action of the Avind and waves.
This explanation must necessarily be brief, and the avoidance of
mathematical language must make it even more imperfect than
it would otherwise have been. We would refer the reader
desirous of following out the subject to a discussion which is as
full as the present state of our knowledge seems to permit, and
which summarises both what is known and what yet requires to
be determined.*
When a ship with sail set is rolling amongst waves, the forces
operating upon her at each instaot include all those which would
be in operation if there were no sail set; and, in aldition, the
moment of the wind-pressure on the sails, as well as the moment
of the resistance of the air to the oscillatoiy motions of the sails.
Our knowledge of the laws which govern the pressure of the wind
on the sails is very imperfect ; a brief resume of that knowledge
will be found in Chapter XII. Exact estimates cannot be made,
therefore, for the moment of the wind-pressure at any instant,
even when the inclination of the masts to the vertical, the in-
stantaneous angular velocity of the sails, and the direction and
velocity of the wind are known. But, while this is true, certain
general principles may be establishiKl. For example, as a ship
rolls to windward the angular velocity of the sails increases the
relative velocity of the wind past the sails, and this increase is
greatest on the sail-area which is highest above water. Con-
sequently, during this roll to windward, the moment of the
pressure of the wind on the sails is increased, not merely by
the greater relative velocity of the wind on the sails, but by
the iiigher position of the centre of pressure. Conversely,
during the roll to leeward at any instant the inclining momeut
of the wind-pressure is decreased, and may be very largely
decreased, by the angular velocity of the sails. Any attempt at
* See the Paper on the " Rolling of Author to the Transactions of the In-
Sailing Ships" contributed by the stitution of Naval Architects for 1881.
246
NAVAL ARCHITECTURE.
CHAP. VI.
exact investigation must take account, therefore, of these varia-
tions in the moment of the wind-pressure.
Account must also be taken of the effect which the heaving
motion produces upon the instantaneous righting moment which
tlie sliip can oppose to the inch'ning moment of the wind-pressure.
It has been shown (on page 186) that a ship accompanying the
motion of the waves, and heaving up and down as they pass
under her, is subjected to accelerating forces which alternately
tend to increase and decrease her " virtual weight." Now the
" instantaneous righting moment " is equal to the product of that
virtual weight into the ordinate of the curve of stability corre-
sponding to the instantaneous inclination of the masts to the
normal to the effective wave slope. An illustration of this state-
ment is given in Fig. 72. NN^ shows the instantaneous direction
of the normal (that is
M the "virtual up-
right"). The masts
are inclined to the
normal at an angle
of 37 degrees. The
instantaneous right-
ing moment equals
the product of the
" virtual weight " (al-
lowing for heaving)
into the arm of the
righting lever mea-
sured on the curve of stability for 37 degrees inclination. When the
ship floats on the upper half of the waves her virtual weight is less
than the true weight, and may be as mucli as 20 per cent. less.
Consequently her instantaneous righting moment on the upper half
of the waves is correspondingly decreased. And since the force
of the wind is not similarly affected by the wave motion, it must
during this time have a greater inclining effect upon the vessel
than the same force of the wind would have in still water. It is
a matter of common observation, which the foregoing remarks
may help to explain, that boats and small craft are most fre-
quently Cfipsized when floating on wave crests. Of course, on the
lower half of the waves, from mid-height to hollow, the virtual
weights and instantaneous righting moments are greater than
the corresponding values in still water.
Fig. 72 also serves to illustrate another point of importance,
viz. that on the supposition that the wind acts horizontally, the
CHAP. VI. OSCILLATIONS AMONG WAVES. 247
moment of the wind pressure must be estimated in terms of the
inclination of the masts to the vertical at each instant. Whereas,
in consequence of the variations in the direction of fluid pressure,
the stability or instability of the ship must be estimated by
the inclination of the mast to the normal to the effective
wave slope. In Fig. 72 NV is the vertical ; the masts are
inclined 27 degrees to it, but the wave slope adds 10 degrees to
this inclination, and makes the angle by which safety or danger
of capsizing is to be reckoned 37 degrees. Remembering what
has been said in Chapter V. of the steepnesses of waves, it is
desirable, when considering the sufficiency of the range of the
curve of stability for any vessel, to regard it as abridged by 8 or
10 degrees in order to allow for the influence of wave slope upon
the virtual inclination to the position of instantaneous equilibrium.
A ship with sail power, besides having provision made for
resisting the heave of the sea, like a mastless ship, must be
capable of resisting the heeling action of a steady force of wind
continually applied, as well as the impulsive action of gusts and
squalls. For all tliese reasons a rigged ship requires a greater
range of stability than a vessel of the mastless type, and a glance
at the curves of the typical ships in Fig. 47 will show that in all
the types of rigged war-ships therein rej^resented, except the
ill-fated Captain, this condition was complied with. In her case,
however, the range of stability was very moderate : her initial
stability not great, and her sail spread large for an ironclad, all
of which causes contributed to her capsizing. ^Yithout discussing
the circumstances further, it may be interesting to make use of
the ship for purposes of illustration, since we have very full
published accounts of her qualities.
Suppose the Captain, with no sail set, to have floated on a
wave 400 feet long and 22 feet high, having a maximum surface
slope of about 10 degrees. The total range of stability for the
ship (see curve 10 in Fig. 47) being 54 degrees, if the allowance
of 10 degrees be made for wave slope, there will remain 44 degrees,
measuring the inclination to the vertical, which the ship would
have to reach before she became unstable. Under the assumed
conditions with sails furled, there would have been little or no
risk of her reaching such an inclination, the Captain having
proved herself to be a well-behaved ship in a seaway.
Next take the case where sail is set, and the ship is acted upon
by a steady pressure of wind which in still ivater would keep her at
a steady angle of heel, say, of 10 degrees ; this is within the truth,
as it appears from the official reports that, on the day before
248 NAVAL ARCHITECTURE. chap. vi.
she was lost, the Captain heeled from 10 to 14 degrees under
canvas. We have already discussed the case where the Captain
is sailing at a steady heel of 10 degrees in still water, and Fig. 55
page 170, illustrates it. CD is the " wind curve," indicating the
inclining effect of the wind on the sails for different angles of
heel ; and if by any means the vessel, which has been sailing at
a heel of 10 degrees, is carried over to a greater inclination, the
wind will follow, and always absorb that part of the area OCDPO
of the curve of stability lying between the line CD and the axis
of abscissae (or " base-line ") OP. It will be observed that the
wind curve cuts the curve of stability at an inclination of 47
degrees, marked by the ordinate DD, ; so that the same force
of wind that will steadily heel the ship 10 degrees will also hold
her at 47 degrees, where she will be on the verge of capsizing.
The effective range of the curve of stability, excluding the part
absorbed by the steady force of wind, is therefore about 37
degrees only, that being the limit of inclination to the vertical
which the ship can reacli without being blown over when
floating at mid-height on the wave. The decrease of 17 degrees
from the total range, thus shown to be requisite to provide for
the steady action of the wind is a very serious matter. Apart
from gusts and squalls, there would still be a good provision for
safety, taking into account the steadiness of the ship ; but even
shij3s reputed steady occasionally roll as much as this, and if the
Captain had reached a position 10 degrees beyond that indicated
in Fig. 72, she would have been on the point of capsizing.
With steeper waves having a greater slope, the capsizing point
would be sooner reached. In Mr. Childers' minute on the loss
of the Captain (pages 56 and 57) will be found similar illustra-
tions to the foregoing, only on waves of very exceptional steep-
ness, 200 feet long, 23 feet high, and having a maximum slope of
20 degrees ; then, supposing the Captain to be subjected to a
steady wind capable of inclining her 8 degrees in still water, it
is estimated that only 21 degrees inclination to tlie vertical
would suffice to bring her to the \er^e of capsizing. Eeverting
to Fig. 5."^, and taking the case of the Monarch exposed to a force
of wind equal to that assumed to act on the Captain, it will be
seen that, after providing for the steady action of the wind, there
remains an available range (EW) of over 55 degrees, instead of
37 degrees, as in the Captaiyi under identical circumstances.
From these two cases it will be evident that good range in the
curve of stability is of the highest importance in rigged ships.
The greatest danger of cap>izing results, not from the action
CHAP. VI. OSCILLATIONS AMONG WAVES. 249
of a steady force of wind, but from that of gusts and squalls
which may strike the sails of a ship, upon wliicli considerable
roUinp^ motion has been impressed previously by the action of
the wind or waves. At page 171 we have discussed the action
of such gusts of wind upon sailing ships rolling in still water;
similar but much more complicated conditions hold when a ship
rolling among waves is caught by a squall at the extreme of a
roll to windward. Various attempts have been made to deal with
this difficult problem, and to enable the naval architect to form
an opinion as to the ranges of stability sufficient in various
classes of rigged ships. None of these attempts can be regarded
as entirely successful, nor does the nature of the case permit of
its solution by exact scientific investigation. Before such an
investigation can be begun certain preliminary assumptions
must be made : as to the sail-spread that shall be associated with
a certain force of wind, the character of the waves amongst which
the ship is placed, the inclination of the masts and their angular
velocity at some instant, and the force of the sqnall as well as
the position of the ship when struck. In short, some combination
of circumstances has to be assumed as the worst likely to occur,
in order that an opinion may be formed as to the probability of the
ship capsizing or not. From this brief statement of the case,
and beaiing in mind what was said above as to the imperfect
knowledge we possess of the laws governing wind pressure, it will
be obvious that science has not yet enabled us to discuss with
certainty the behaviour of sailing ships when rolling in a sea-
way. The naval architect has, therefore, to resort to experience
in order to appreciate fairly the influence of seamanship and the
relative manageability of ships and sails of different sizes.
Having before him the curves of stability of sailing ships of
various classes, and the records of their performances at sea, the
designer can proceed with greater assurance in the determination
of the stability and sail-spread which shall be deemed sufficient
in a new ship. A good range and large area of the curve of
stability undoubtedly denote conditions which are very favourable
to the safety of a ship against capsizing. But, in practice, such
favourable conditions cannot always be secured in association
with other important qualities, and a comparatively moderate
rano-e and area of curves of stability have to be considered
when the question arises whether or not sufficient stability has
been provided. Under these circumstances experience, and the
analysis of the qualities of ships which have proved successful
and safe, are of the greatest value.
2^0
NAVAL ARCHITECTURE.
CHAP. VI.
Sailinji: ships of the mercantile marine and yachts usually have
jrreat range of stability when fully laden, for the reasons given in
Chapter III. Rigged war-ships, on the other hand, frequently
liave moderate range of stability. So far as experience enables
an opinion to be formed, it appears that in the smaller classes of
seagoing war-ships with steam as well as sail-power, a range of 60
to 70 degrees in the curve of stability suffices for safety ; in the
lai'ger classes, above corvettes, the corresponding range is about
70 to 80 degrees. It will be understood that these values are
based upon experience, and they probably provide a reasonable
margin of safety. The provision of a large range of stability
cannot be regarded, however, as- a guarantee against accident
apart from proper management and good seamanship. Examples
are not wanting of the truth of this statement, and one of the
most forcible is that of the merchant sailmg ship Stuart
Hahnemann. Her curve of stability is marked 8 in Fig. 47c page
128 ; the angle of maximum stability exceeded 40 degrees, and the
range exceeded 80 degrees. Tliis vessel was thrown on her
beam ends and sank: the Court of luquiry found that she was
Avell-bnilt and perfectly equipped, her loss being attributed to the
too long continued use of a heavy press of sail, so that when the
wind increased the sail could not be taken in.
Although it is impossible in the present state of our knowledge
to predict the worst possible combination of circumstances to
Avhich a sailing ship may be liable, it is possible to trace her
behaviour, with fair approximation to accuracy, when a certain
set of conditions has been selected. This can be done by
means of an adaptation of the process of graphic integration
to which reference was previously made. An example of
the results obtained in this manner is given in Fig. 71&.
The general construction re-
FIG 7\h.
fembles that described for
Fig. 71a. Measurements along
the base-line
Ordinates of
" wave slope "
slope of the
surf; ice to the
corresponding
instant from
represent time.
the curve of
represent the
effective wave
horizon at the
time. At the
which time is
counted, the ship is assumed to
have her masts inclined 20 de-
grees to the windward side of the vertical, to float at the mid-
CHAP. VI. OSCILLATIONS AMONG WAVES.
height of waves having a maximum slope of 9 degrees, and to have
no ano-ular motion. Her instantaneous inclination to the wave
normal is therefore 29 degrees. It is then supposed that she is
struck by a squall of wind, having such a force as wonld hold her at a
steady heel of 10 degrees in still water. This suddenly-applied wind
pressure follows her up as she rolls away to leeward, and at any
instant the process of graphic integration takes account of the
following forces as acting upon her :— (1) the moment of wind-
pressure on the sails, corrected for the angular velocity (as
described on page 245) ; (2) the moment of the resistance offered
by the water to the motion of the ship ; (3) the instantaneous
righting moment, corrected for heaving. The resultant of these
three moments at any instant appears as the ordinate of the
" curve of force " in Fig. 71& ; and the ordinate for the same
instant of the curve of inclination shows the inclination of the
masts to the vertical. Under tliese assumptions the vessel, which
started from 20 degrees to windward, is driven over by the squall
to 24 degrees to the leeward side of the vertical. If allowance
were not made for the reduction in moment of wind pressure due
to the motion of the sails away from the wind, then starting from
the same inclination to windward the squall would drive the
vessel over to 34 degrees to leeward. Further, were the effect of
the fluid resistance neglected, the angle reached to leeward of the
vertical would be 45 degrees. These figures are suggestive if not
strictly accurate. They show how impossible it is to pronounce
upon the maximum rolling of a ship without taking account of
all the circumstances which may influence that behaviour.
Finally, on this part of the subject, reference must be made to
the steadying effect which sail exercises upon a ship. This effect
is a matter of common observation, and may be very simply
explained. If a ship with sail set were rolling in a calm, the air
would oppose great resistance to the oscillatory movement of the
sails, and the rolling would be rapidly extinguished ; this case is
parallel to that described for water resistance in Chapter IV.
When a ship is set rolling by the action of the sea, while the
wind blows uniformly, it is difficult to estimate separately the
effects of wind pressure and the air resistance to rolling. But
when squalls or gusts of wind act intermittently on a vessel the
influence of air resistance may become most important. Suppose,
for example, the wind to lull when a ship has reached her extreme
roll to leeward ; then, on the return roll to windward, both air
resistance and water resistance are tending to check the motion
and lessen the extreme an2;le of roll to windward. So that if the
252 NAVAL ARCHITECTURE. chap. vi.
squall strikes her a,2;ain in the most favourable position — the
extreme of the roll to windward — it finds the ship much less
inclined to the vertical than she would be if air resistance were
not operative. The following lurch to leeward would consequently
be much less heavy.
The longitudinal oscillations of pitching and 'scending expe-
rienced by ships among waves must be briefly considered before
concluding this chapter. In still water such longitudinal oscil-
lations do not occur under the conditions of actual service ; and
it is difficult, even for experimental purposes, to establish such
oscillations, because of the great longitudinal stability of ships.
On this account we have little definite information respectiBg
still-water periods for pitching, or the " coefficients of resistance "
for longitudinal oscillations. One or two small ships of shallow
draught and full form have been experimented with ; the period
of longitudinal oscillation having been found to have been about
three-fourths the period of transverse oscillation. Other observa-
tions made at sea appear to show that in many cases the period
of pitching oscillations lies between one-half and two-thirds the
l^eriod for rolling. In some cases it may fall as low as one-third
the period for rolling ; and in the Russian circular ships the two
periods must be nearly equal.
The formula for the period of unresisted pitching may be
expressed in the same form as that given on page 140 for the
period of unresisted rolling. Only the height m must be made
equal to the height of the longitudinal metacentre above the
centre of gravity ; and the radius of gyration h must be estimated
by multiplying each element of weight by the square of its
distance from the transverse axis passing through the centre of
gravity. It may be taken for granted that, as a rule, the effect
ujjon the period of the great height of the longitudinal meta-
centre above the centre of gravity of a ship more than counter-
balances the effect of the increased moment of inertia for longi-
tudinal oscillations ; whence it follows that the period for pitching
is usually considerably less than that for rolling. Calculations
for the period of unresisted pitching have been made in a few
instances ; but they have little practical importance.
The existence of waves supplies a disturbing force capable of
setting up the longitudinal oscillations ; this is a matter of fact,
and it is easily accounted for. Suppose a ship to be placed bow-
on to an advancing wave; its slope will at the outset rise upon
the foremost part of the ship above the water-level in still water;
CHAP. VI. OSCILLATIONS AMONG WAVES. 253
and perhaps simultaneously at the after pait of the ship the wave
profile may fall below the still-water level. The obvious tendency
of the bow will be to rise uuder the action of the surplus buoyancy
at that i^art, the stern falling relatively ; that is to say, a 'sceuding
motion will be established, and its initial rate will depend upon
the still-water period for longitudinal oscillations. After the
wave crest has passed the bow of the ship, supposing for the
instant that the wave is long as compared with the length of the
ship, there will probably be a reversal of the conditions. The
wave profile on the back slope of the wave would probably fa,ll
below the still-water load-line 'at the bow, and this excess of
weight over buoyancy would tend to check 'scending and cause
pitching to begin. The motion thus created by the passage of
the first wave would of course be modified by the passage of
succeeding waves in the series ; and in the end there would
probably be established a certain phase of pitching and 'scending
oscillations, corresponding in character to the phases of rolling
described above and largely influenced by the ratio of the apparent
wave period to the natural period for still-water longitudinal
oscillations.
This is the simplest case that can be chosen, and it by no
means represents all the conditions of the problem ; but it shows
how the existence of waves and their passage past a ship lead
to disturbances of the conditions of equilibrium existing in still
water, and to the creation of accelerating forces due to the excess
or defect of buoyancy. Ko account has here been taken of the
variations in the direction and magnitude of the fluid pressure at
differeut parts of the wave; although these variations would
undoubtedly produce some modification in the behaviour of the
ship, the modification would not be likely to change the character
of the motion, with which alone we are at present concerned.
This illustration also shows that the following are the chief
causes influencing the pitching and 'scending of ships: (1) the
relative length of the waves and the ships; (2) the relation
between the natural period (for longitudinal oscillations) of the
ship and the apparent period of the waves, this apparent period
being influenced by the course and speed of the ship in the
manner previously explained ; (3) the form of the wave profile,
i.e. its steepness ; (4) the form of the ship, especially near the bow
and stern, in the neighbourhood of the still-water load-line, this
form being influential in determining the amounts of the excesses
or defects of buoyancy corresponding to the departure of the
wave profile from coincidence with that line ; (5) the longitudinal
2 54 NAVAL ARCHITECTURE. chap. vi.
distribution of the weights, detevmining the moment of inertia. h\
addition, it need hardly be said that fluid resistance exercises a
most important influence in limiting the range of the oscillations ;
this resistance is governed by the form of the ship, and particu-
larly by that of the extremities, where parts lying above the
still-water load-line are immersed more or less as the ship pitches
and 'scends, and therefore contribute to the resistance.
This summary requires but few comments. It is obvious, that,
when the length of a ship is great as compared with the wave
length, there is no probability of extensive pitching motions being
produced. The Great Eastern, for example, with her length of
680 feet, could span from crest to crest even on the very large
Atlantic storm waves observed by Dr. Scoresby ; and on storm
waves of common occurrence she might be floated simultaneously
on three of them. Even less imposing structures, such as the
largest ships of the Eoyal Navy, with lengths of 300 to 400 feet,
are long as compared with ordinary storm waves, and therefore
are not likely, as a rule, to accumulate large angles of pitching —
a conclusion borne out by experience. Small vessels may, of
course, fall in with waves which are long relatively to their own
lengths ; but in such cases it is a common observation that the
vessels " float like ducks on the water " — that is to say, their
natural periods for longitudinal oscillations are so small as
compared with the wave period that they can very closely accom-
pany the motions of those parts of the wave slope upon which they
flotit. In fact, their condition furnishes a parallel to the case of
the little raft in Fig. 62, except that the raft follows the upper
surface of the wave, whereas the ship, stretching over a consider-
able length on the wave, and penetrating to some dej)th in it, does
not follow the upper surface, but, as it were, averages the slope of
a portion of a subsurface corresponding to her own length.
According to theory, the case of pitching is best dealt with in a
manner similar to that adopted for rolling motions. The ship is
supposed at every instant to have a tendency to move towards an
instantaneous position of equilibrium which is a normal to her
" effective wave slope " ; but in the determination of this effective
slope for longitudinal oscillations still greater difficulties are
encountered than in the similar problem for rolling. One thing,
however, is evident, even in the case where the length of the wave
is great as compared with that of the ship, viz. that the steepness
of the effective slope will be much less than the maximum slope
of the upper surface, both because of the length along the wave
which the ship occupies and of the depth to which she is immersed
CHAP. VI. OSCILLATIONS AMONG WAVES. 255
in it. Supposing her to be in the worst position, with the micklle
of her length at the steepest inclination of the wave, the slope of
the surface to the horizon, at the places occupied by the bow and
stern, will be much less than the maximum slope ; and, fun her, as
lemarked previously, all subsurface trochoids in the wave are less
steep than the upper surface. The effective slope has to be the
resultant of these varying conditions, and must therefore be much
less steep than the maximum surface slope. But even accepting
this conclusion, and assuming an effective slope, no practical
deductions of importance have yet been drawn from this method
of viewing the question, beyond those obtained from general con-
t^iderations, and stated in the preceding summary.
It has been asserted that in large ships extreme pitchino- is
not likely to occur; but it must be noted that even moderate
angles of pitching lead to very considerable linear motions at the
extremities of a long ship. For example, in the trials off
Berehaven with the Devastation, Agincourt, and Sultan, it is
reported that the Sultan on one occasion pitched so that the
bow appeared buried very deeply in the wave, and observers on
the deck of the Devastation could not determine whether the sea
broke over the forecastle, which is some 30 feet above water when
the ship is at rest in still water. Very similar remarks were made
on another occasion respecting the Agincourt. For each degree of
inclination from the upright, how^ever, a point on the bow of the
Agincourt would move vertically nearly 4 feet, and one on the
bow of the Sultan about 3 feet; so that very moderate angles
of inclination in still water would sufiice to bring the forecastle
deck close to the water-level. Amongst waves, with their varying
slopes into which the bow of a ship plunges, much more moderate
inclinations might produce the same apparent effect. For example,
the Devastation and Agincourt were tried steaming head-on to
waves from 400 to 650 feet long and from 20 to 26 feet high, the
speed of the ships being about 7 knots per hour. The periods of
these waves varied from 9 to 11 seconds ; their maximum slopes,
from 7^ to 9 degrees. Allowing for the speed of the ships, the
apparent periods of the waves varied from 7 to 9 seconds, givino-
apparent half-periods which probably approximated to equality
with the natural period (for a single oscillation longitudinally) of
the ships. It was a case, therefore, where the conditions were
conducive to heavy pitching, and the results of the observations
are interesting. The total arcs of oscillation for the Devastation
were, on an average, 8 degrees only, that is, about 4 degrees on
either side of the upright, or about one-half the maximum slope
256 NAVAL ARCHITECTURE. chap. vi.
of the surfafe of the waves ; the maxiinntn arc of oscillation was
rather less than 1"^ degrees, about 6 degrees on either side of the
upright, about three-fourths the maximum slope of the snrfiice.
The Agincourt pitched through rather smaller arcs than the
Devastation, but, supposing her motion to have reached the same
maximum, the bow would have been immersed in still water
about 20 feet below its normal draught ; yet we are assured that a
sea broke over the forecastle, which is some 10 feet higher above
still water, a circumstance which is attributable to the bow having
been plunged into an advancing wave slope. These facts are
mentioned in order to enforce the desirability of taking all
possible precautions in estimating the extent of pitching ; so
many of the attendant circumstances tending to exaggerate the
apparent motion, and to deceive the observer unless he has
recourse to actual measurement of the angular motion.
From the fore2:oing remarks it will be evident that further
progress in knowledge of the laws which govern pitching and
'scending must be largely dependent upon actual observations
made at sea in a trustworthy manner. The Admiralty instructions
provide for such observations when favourable opportunities pre-
sent themselves ; and this branch of the subject is one to which
naval officers might devote attention with great advantage. As
yet comparatively little information has been recorded ; and of
the published observations those made by M. Bertin are the most
valuable.* With the aid of an ingeniously-contrived instrument
(described in Chapter VII.) M. Bertin obtained simultaneous auto-
matic records of (1) the instantaneous inclination of the ship to the
vertical as she pitched ; and (2) the instantaneous position of the
normal to the effective wave slope. His conclusions from a careful
analysis of these observations may be briefly stated. With a ship
head to wind and sea, among waves of sufficient length relatively
to the ship to produce sensible pitching motion, and within
certain limits of the ratio of speed of ship to speed of wave, all
the ships for which observations were made followed the effective
wave-slope, just as the little raft in Fig. 62 follows the wave
motion. Under these circumstances, as the speed was increased,
but still fell within the assigned limit, the period for pitching was
decreased, because this increase in speed shortened the apparent
wave period ; but the angle of pitching remained nearly constant.
After this limit of speed had been surpassed the ships ceased to
* They are to be found in " Observa- avec Voscillographe doxible a hord de
tions de roulis et de tangage faites divers hatiments :" Qh-GYhowrg, ISIS.
CHAP. VI. OSCILLATIONS AMONG WAVES. 257
follow the effective wave slope, their pitching motions falling
behind instead of keeping pace with the effective slope. At
certain speeds the motion of the ship dropped one-fourth of the
period behind that of the effective slope ; and then the pitching
was found to have the same amplitude as in the case first described.
Further increase in speed and still further decrease in the appa-
rent wave period was found to produce much heavier pitching,
and at length led to the bows of the ships being buried so deeply
in the wave slopes that the experiments were stopped.
W hen the ships were running before the sea, and by their
motion lengthening the apparent period of the waves, the case
was fountl to be much simpler, the ships practically following
the effective wave slopes. Hence, from a review of the whole of
his observations, M. Bertin concludes that the best means of
reducing pitching, in the critical case where a ship is driven
head to sea, is to make her natural period of pitching as short as
possible, by concentrating weights amidships, and reducing the
moment of inertia. This conclusion, we need scarcely add,
agrees with the recommendations made by experienced seamen.
Nor need we dwell again upon the control ovei- the behaviour of
a ship which may be exercised by her commander by means of
variations in speed and course relatively to the waves. But it
may be proper to draw special attention to the fact that the
actual period observed for pitching motions will vary consider-
ably for the same ship under different circumstances, and usually
differ considerably from the still-water period for longitudinal
oscillations. Most commonly, so far as can be seen at present,
the observed periods of pitching closely agree \V\\\i. the apparent
periods of the waves which are large enough to produce consider-
able pitching motions.
The longitudinal distribution of the weights in a war-ship has
to be regulated by other considerations than those mentioned
above. It commonly happens that, to increase the offensive
powers, heavy weights of guns, or armoured batteries, have to be
carried near the extremities, thus adding to the moment of
inertia, slowing the period of pitching, and rendering it probable
that pitching oscillations will be more sustained, even if they are
not made more extensive. All that can be done, in most cases,
is to transport guns, anchors, or other relatively small weights
from the extremities to some position more nearly amidships,
when the vessel is making a voyage: these temporary changes
are, of course, the work of the commanding ofScer and not of the
designer. In merchant ships much more may be done towards
s
258 NAVAL ARCHITECTURE. chap. vi.
securing a longitudinal distribution of the cargo which favours
moderate pitching, if proper care is taken in its stowage. Heavy
weights, as a matter of common experience, should be kept out
of the extremities ; and where this simple rule is ignored
extensive pitching and unnecessarily severe longitudinal strain-
ing have to be expected.
Fluid resistance is known to play an important part, as
already stated, in limiting the range of pitching oscillations ;
but the naval architect has not the same control over this
feature as lie possesses in connection with rolling motions. It
would be difficult to fit any appendages equivalent to bilge-keels
in order to increase the resistance to longitudinal oscillations,
although something may be done in this direction ; and the
under- water forms of ships are settled mainly with reference
to their efficient propulsion, the effects of form on pitching
usually occupying a subordinate place. Attempts have been
made, however, to improve the forms of the bows of the ships in
order to lessen pitching ; and very diverse opinions have been
expressed as to tlie best form that can be adopted. Many
persons are in favour of V-shaped or " flaring " cross-sections ;
the out-of-water parts having a large volume as compared with
the immersed part lying beneath them. Others have strongly
objected to flaring bows, and have introduced U-shaped cross-
sections, with the view of reducing pitching, as well as of
reducing the excess of weight over buoyancy at the bow. The
advocates of the (J-shaped sections consider that "the bluff
" vertical sections encounter greater upward resistance than the
" V-shaped sections when the ship tends to plunge down through
"the water, and receive a greater lilting effect when the sea
" tends to rise up under the ship." * The adoption of pro-
nounced U-shaped sections for the bow has not become general,
nor does it appear likely to do so, other considerations leading
most naval architects to prefer finer under-water forms ; but the
use of flaring sections above water is now less common than it was
formerly, and naval architects agree that they are undesirable
except in special cases, as, for example, where room is required
at the bow to work a chase gun.
Vessels of low freeboard are subjected to deck resistance when
pitching among waves; and the Devastation furnishes an excel-
* Naval Science, yoI. iv., page 55. the Bows of the Helicon and Salamis,"
The reader may also consult on this in vol. vii. of the Transactions of the
subject a paper, by Dr. Woolley, " On Institution of Naval Architects.
CHAP. VI. OSCILLATIONS AMONG WAVES. 259
lent example of this action. When on trial off the Irish coast,
and steaming head to sea at moderate speeds, waves broke over
the fore part of the deck, as it was anticipated they would do
under these circumstances, the fittings on this deck having been
designed to exclude from the interior water lodging upon it.
An eye-witness, describing her motion, says: — "It invariably
"happened that the seas broke upon her during the upward
"journey of the bow ; and there is no doubt that to this fact her
" moderate pitching was mainly due, as the weight of water on
"the forecastle deck, during the short time it remained there,
"acted as a retarding force, preventing the bow from lifting as
"high as it otherwise would, and this, of course, limited the
"succeeding pitch, and so on." In American monitors, with
their exceptionally small freeboard, this kind of action would be
even more effective, were it not for the fact, that their natural
periods for pitching oscillations are probably so small as to make
them capable of accompanying very closely the motions of such
waves as wordd produce considerable pitching in the monitors.
Mr. Fox (assistant secretary of the United States navy), report-
ing on the behaviour of the Miantonomoh, head to sea in a heavy
Atlantic storm, said, " Siie takes over about 4 feet of solid water,
" which is broken up as it sweeps along the deck, and after
" reaching the turret is too much spent to prevent firing the
"guns directly ahead." This confirms the opinion that these
vessels move so quickly as to very nearly accompany the wave
slope ; their actual arcs of oscillation in pitching being consider-
able, and accurate practice with the guns in the line of keel
being impossible. But these are cases of comparatively un-
frequent occurrence, and are interesting chiefly as instances of
the effect of fluid resistance in limiting the pitching motions of
ships which immerse or emerge their decks. In ordinary ships
the decks are much higher, and the longitudinal oscillations
rarely acquire such a magnitude as to immerse the decks
considerably.
Various proposals have been made for the purpose of increasing
resistance to pitching. For instance, it has been suggested to
fit horizontal side-keels near the extremities, or to broaden out
the keel proper at those parts. At the bows of many recent
armoured ships external supports are fitted to the projecting
ram-bows ; and these supports act as side-keels, which give
increased resistance to pitching. The spur-bows themselves,
prolonged under water as they are, also tend to reduce pitching
by increasing resistance ; and in the French navy, where this
s 2
26o NAVAL ARCHITECTURE. chap. vi.
form of bow has been largely adopted for unarmoured as well as
for armoured ships, it is said that a sensible reduction in pitch-
ing has resulted. French naval architects, while favouring a
form of bow which reaches forward for a considerable distance
under water, prefer to make the stem fall aft considerably above
water; their intention in the latter particular being to reduce
the weight above water at the extremity at the same time that
they either increase the buoyancy by the spur-bow or ** fine " the
under water form to facilitate propulsion.
In ships of ordinary form the maximum amplitude of rolling
largely exceeds the corresponding maximum for pitching. M.
Bertin considers that a fair ratio for these maxima is one
(pitching) to six (rolling). We are not in possession of suffi-
cient data to verify this estimate; but of the fact just stated
there can be no doubt. Exceptions to this rule are to be found
in the Russian circular ironclads and the Livadia. As the
result of observations made on the latter in the Bay of Biscay,
it appears that when placed head to sea she pitched through
somewhat larger arcs than those she rolled through when broad-
side-on to the waves. This departure from ordinary conditions is
noteworthy.
CHAP. VII. OBSERVATIONS OF ROLLING. 26 1
CHAPTER VII.
METHODS OF OBSERVING THE ROLLING AND PITCHING MOTIONS
OF SHIPS.
Enough has been said in previous pages to show how variable, and
how liable to mislead an observer, are the conditions surrounding
the behaviour of a ship at sea. The ship, herself in motion,
is surrounded by water also in motion ; and it is extremely
difficult, by means of unaided personal observation, to determine
even so apparently simple a matter as the position of the true
vertical at any instant. To estimate correctly the angles
through which a ship may be rolling or pitching, it is therefore
necessary to bring apparatus of some kind into action ; and in
the use of such apparatus there are many sources of possible
error which must be prevented from coming into operation.
Upon the correctness of these observations we are greatly
dependent, since deductions from theory are thus checked, and
the extent to which they can be made a safe guide for the naval
architect in designing new ships is ascertained. Numerous
examples illustrating the substantial agreement of observation
with the chief deductions from theory have been given in the
previous chapter; but up to the present time the comparison
has been mainly of a qualitative character, and before more exact
results are obtained, it will be necessary to have compiled and
collated much more exact and extensive records than are at
present accessible.
The chief problem to be solved is this. What are the con-
ditions of wave motion that will produce the maximum oscillation
in a ship, of which the still-water period of oscillation as well as
the coefficients of resistance are known ; and what will be the
range of that maximum oscillation ? Or, it may be desirable to
ascertain generally what extent of motion will be impressed upon
262 NAVAL ARCHITECTURE. chap. vii.
a ship by a series of waves of certain assumed dimensions. Pure
tiieory will not be likely to supjdy correct answers to these
questions ; but there is reason to believe that they may be dealt
with satisfactorily by a combination of the experimental and
mathematical modes of investigation, such as the process of
" graphic integration " described at page 237. The development
of that process and its establishment in general use as a means
of predicting the behaviour of ships, demand an extensive com-
parison of the results obtained by its application with the
recorded observations of the behaviour of ships. Such a com-
parison can obviously be of use only when the individual obser-
vations are free from errors and accompanied by full particulars
of the conditions of wind and sea. Methods of observing correctly
the lengths, heights, and periods of waves have been described
in detail in Chapter V. ; and it is now proposed to sketch the
methods which have been adopted at various times for observini>-
the rolling and pitching oscillations of ships.
Of these methods, the following are the most important : —
(1) The use of pendulums, with various forms of clinometers;
these pendulums having periods of oscillation which are very
short as compared with the periods of the ships.
(2) The use of gyroscopic apparatus.
(3) The use of " batten " instruments, or alternatives.
(4) The use of automatic apparatus.
Taking these in the order they have been named, it may be
well to glance at their chief features, and to indicate the probable
correctness or otherwise of their records.
Pendulums, or clinometers, are the simplest instruments, but
they are not trustworthy indicators of the angles of inclination
attained by a ship when rolling in still water, and much less of
those moved through by a ship rolling or pitching at sea. When
a ship is held at a steady angle of heel (for example, as shown
by Fig. 30), a pendulum suspended in her will hang vertically,
no matter where its point of suspension may be placed,
and will indicate the angle of heel correctly. The only force
then acting upon the pendulum is its weight, i.e. the directive
force of gravity, the line of action being vertical. But when,
instead of being steadily inclined, the ship is made to oscillate
in still water, she will turn about an axis, passing through or
very near to the centre of gravity ; hence every point not lying
in the axis of rotation will be subjected to angular accelerations,
similar to those which were described at page 135 for a simple
CHAP. VII. OBSERVATIONS OF ROLLING. 263
pendulum. Supposing the point of suspension of the clinometer
to be either above or below the axis of rotation, it will be
subjected to these accelerating forces, as well as to the directive
force of gravity, and at each instant, instead of placing itself
vertically, the clinometer, or pendulum, will tend to assume a
position determined by the resultant of gravity and the accelerat-
ing force. If the period of the pendulum used is short as
compared with the period of the ship, the position towards which
it tends to move will probably be reached very nearly at each
instant. The case is, in fact, similar to that represented in
Fig. 71, page 225. If the length of the upper pendulum (AB) is
supposed to represent the distance from the axis of rotation of
the ship to the point of suspension of the pendulum which is
intended to denote her inclinations, the clinometer pendulum
may be represented by BC. As AB sways from side to side
the point B is subjected to angular accelerations, and these
must be compounded with gravity in order to determine the
position which BC will assume ; for obviously BC will no longer
hang vertically. The angular accelerating force reaches its
maximum when the extremity of an oscillation is reached, con-
sequently it is at that position that the clinometer will depart
furthest from the vertical position. In Fig. 71, suppose VAB to
mark the extreme angle of inclination reached by tlie ship, and
let AB be produced to D : then, to an observer on board, the angle
CBD will represent the exc ss of the apparent inclination of
the ship to the vertical above the true inclination.
It will be seen that the linear acceleration of the point of
suspension B depends upon its distance from the axis of rotation
A in Fig. 71. If B coincides with the axis of rotation, it is sub-
jected to no accelerating forces, and a quick-moving pendulum
hung very near to the height of the centre of gravity of a ship
rolling in still water will, therefore, hang vertically, or nearly so,
during the motion, indicating with very close approximation the
true angles of inclination. Hence this valuable practical rule :
when a ship is rolling in still water, if a pendulum is used to
note the angles of inclination, it should be hung at the height
of the centre of gravity of the ship; for if hung above that
position it will indicate greater angles, and if hung below will
indicate less angles, than are really rolled through ; the error of
the indications increasing with the distance of the point of
suspension from the axis of rotation and the rapidity of the
rolling motion of the ship.
The errors of the pendulum indications for still-water oscilla-
264 NAVAL ARCHITECTUTE. chap. vri.
tions may be approximately estimated from the following formula,
which was i)roposed by Mr. Froude : —
Let a = true angle of inclination reached by the ship ;
|3 = apparent angle of inclination indicated by the
pendulum ;
T = period of oscillation (in seconds) for the ship ;
li = the distance of the point of suspension of the pendulum
above the centre of gravity of the ship :
Then " = 3-27T^ + A^^^-
If, instead of 3'27, we write 3^, this takes the approximate
form, « = jy^^qigy^ X /3,
which will be sufficiently near for practical purposes. In the
case where the point of suspension is at a distance h below the
centre of gravity the corresponding approximate formula is
10 T2
a —
xjS.
lOT'-Sh
Take one or two simple illustrative examples. For the Prince
Consort T = 5^ seconds ; and h may be taken as 20 feet, if the
pendulum were placed on the bridge :
Th a_ 10 T^ _ 300 5
^° /3 10P + 3A 300 + 60" 6'
« = ^/3;
and the pendulum increases the true angle of heel by no less
than 20 per cent. In the Devastation a pendulum placed on
the flying deck may be taken as 25 feet above water ; also T
= 6f seconds.
Then
a
10 X mf 450 450 6
/3~10 X (6|)2+ 3 X 25 ""450+ 75 "525"" 7 '
Here the pendulum indications exaggerate the true angles of
inclination by about 16 per cent. ; notwithstanding the greater
height of the point of suspension above the centre of gravity,
the slower motion of the Devastation makes the error smaller than
in the Prince Consort.
So much for the simple case of still-water oscillations. When
we turn to the more complicated ease of a ship oscillating
CHAP. VII. OBSERVATIONS OF ROLLING. 265
amongst waves, there are good reasons for supposing that the
errurs of pendulum observations Avill be exaggerated. The
centre of gravity of the ship is then, as explained in the pre-
cedmg chapter, subjected to the action of horizontal and vertical
accelerating forces. If the pendulum were hung at the centre
of gravity (G) of the ship, shown on a wave in Fig. 62, page 185,
it would, therefore, no longer maintain a truly vertical position
during the oscillations, but would assume at each instant a
position determined by the resultant of the accelerating forces
impressed upon it and of gravity. The direction of this resul-
tant has been shown to coincide with that of the correspond-
ing normal to the effective wave slope. Hence follows another
useful practical rule. When a ship is rolling amongst waves, a
quick-moving pendulum suspended at the height of the centre of
gravity will place itself normal to the effective wave slope, and
its indications will mark the successive inclinations of the masts
of the ship to that normal, not their inclinations to the true
vertical. This distinction is a very important one. For example,
in an American monitor, supposing her to keep her deck very
nearly parallel to the wave slope as she might do, if a pendulum
were hung close to the height of the centre of gravity, it would
indicate little or no rolling motion; whereas the monitor would
really be reaching inclinations equal to the maximum wave
slope on each side of the vertical. On the other hand, if a
steady ship, such as the Inconstant, were amongst the same waves,
a pendulum hung at the centre of gravity would indicate
extreme angles of inclination i'ar in excess of the true roll-
ing ; for if the ship remained practically upright
during the passage of the waves, the pendulum ^'^ ^'*'
would indicate angles of inclination nearly equal i
to the effective wave slope.
When hung at any other height than at that
of the centre of gravity of a ship rolling amongst
waves, the indications of a pendulum are still
less to be trusted. Eeferring to Fig. 73, three
pendulums will be seen combined, viz. AB, to
which hangs BC, and from this is suspended a
third, CD. Supposing AB made to swing through
a fixed range, it will represent the wave oscillation ;
then the motion of BC will represent the oscillations of a ship
amongst the waves ; and finally CD will represent the clino-
meter pendulum suspended at some point other than at the
height of the centre of gravity of the ship. In view of what has
been said above, it will be obvious that the motions of the pendu-
266
NAVAL ARCHITECTURE
CHAP. VII.
lum BC will not be indicated correctly by the pendulum CD ;
yet this is a parallel case to that when a penduhiin or clino-
meter is trusted to indicate the angles of inclination to the
vertical of a ship rolling amongst waves.
For a ship rolling among waves there is clearly no fixed axis
of rotation, and the problem to be solved in discussing the
possible errors of indication in a quick-moving pendulum hung
at various heights in a ship is one of great difficulty. It would
be out of place to introduce this discussion here ; but reference
may be made to some interesting observations with pendulums
made by officers of the French navy. Admiral Bourgois made
simultaneous observations of the rolling of the ironclad ship
Magenta, in 1863, by correct batten observations of the horizon
(such as are described hereafter) and by quick-moving pendu-
lums hung in different vertical positions. In that ship he dis-
covered that a quick-moving pendulum hung nearly at the height
of the centre of buoyancy indicated practically correct angles of
inclination to the vertical when the ship reached her extreme roll.
Captain Mottez also made some similar experiments in the frigate
Syhille in 1865 when rolling heavily, and reached the following
conclusions : that no possible point of suspension could be found
where the indications of a pendulum were not influenced by the
acceleratino- forces resultinof from the rollinsr and heavins: of the
ship; but that the errors of indication were least when the pen-
dulum was hung at about mid-draught. These results may not
hold good in all cases, but they are of considerable practical
interest, and may lead other observers to make similar experi-
ments. It must always be an advantage to know where a pendu-
lum may be placed in a ship so as to indicate with approximate
correctness her angles of rolling, as circumstances may arise when
only pendulum observations are possible.
Pendulums are commonly hung above water in ships, and
under these circumstances their indications usually err in excess,
and in some cases the error is proportionately very great, as the
following examples will show. The figures are taken from
published returns of rolling for her Majesty's ships : —
Ships.
Pendulum
Indications.
Correct
Angles.
Lord Warden
Minotaur
»
BelUrophon
Degrees.
11-4
6-1
8-2
8-2
Degrees.
y-1
3-8
4-3
3
CHAP. VII. OBSERVATIONS OF ROLLING. 267
Many similar examples could be given, but they appear unne-
cessary ; the correct angles stated in the table were observed in
all cases with the accurate batten instruments which are now the
service fitting.
The misleading character of pendulum observations has been
for many years acknowledged ; and they are no longer made in
ships of the Royal Navy, except in special cases. When the hori-
zon is obscured, or usually at night, batten observations cannot
be made, while pendulum observations can ; and it is ordered that
under these circumstances the rolling indicated by the pendulums
shall be noted. To enable the results so obtained to be after-
wards corrected, simultaneous observations are made, when cir-
cumstances permit, of the indications of these same pendulums
hung in the same positions, and of the indications of batten
instruments.
In concluding these remarks on pendulum observations, it may
be proper to add that any other devices, such as spirit-levels,
mercurial clinometers, depending for their action on the direc-
tive force of gravity or statical conditions, are affected by the
motion of a ship much as the pendulum has been shown to be
affected. Suppose a spiritdevel to be placed in a ship, at the
height of the centre of gravity ; in accordance with the principles
previously explained, when its indications would lead an observer
to think it exactly horizontal, it would really be parallel to the
effective wave slope. Many persons who admit the faultiness of
the pendulum are disposed to cling to the use of the level ; but
on reflection it will be seen that both instruments are open to
similar objections. Moreover, the extreme sensitiveness and rapid
motions of the spirit-level make it ill adapted for any observations
in a seaway.
Several kinds of gijrosco^nc instruments have been devised for
the purpose of measuring rolling and pitching motions, all of
them being based upon the well-known principle — exemplified in
the toy gyroscope — that a delicately balanced heavy-rimmed
wheel spinning rapidly will maintain the plane of rotation in which
it is set spinning, until its speed of rotation is considerably
diminished. One of the earliest and best instruments of the
kind is illustrated by Fig. 74. It was devised and tried at sea
nearly twenty years ago by Professor Piazzi Smyth, Astronomer
Royal of Scotland, and can be used to measure " yawing " motions
as well as rolling and pitching.* It consists of a fly-wheel A,
See the description given by the inventor in vol. iv. of tlie Transactions of
the Institution of Naval Architects, from which the drawing is taken.
268
NAVAL ARCHITECTURE.
CHAP. VII.
the axis of which forms a diameter of the gymbal-ring B ; this
is carried by a second gymbal-ring, C, tlie pivots of which rest
on the frame F ; and the whole is mounted in an outer frame,
enabling it to be easily carried or placed in position. Suppose
the pivots of the ring C to be placed athwartships in a ship, the
instrument standing on the deck or on a table : then for trans-
verse oscillations the line-of-centres of the pivots will remain
parallel to the deck — that is to say, so far as rolling is concerned
FIC.74-.
the ring C must move with the ship. But it is free to oscillate
about its pivots as the ship pitches.
When the fly-wheel A is spinning rapidly and maintaining its
plane of rotation, it is practically uninfluenced by the motions
of the ship which so largely affect the pendulum ; and as its axis
is carried by the ring B, that ring also must maintain its position.
This maintenance of position by B further involves the non-
performance of any oscillations by C except in the transverse
sense. In other words, neither A nor B changes the direction
of its plane, while the ship rolls and pitches, so long as A spins
CHAP. VII. OBSERVATIONS OF ROLLING. 269
rapidly ; while C can accompany the rolling motion, but not the
pitching motion. Hence the graduated semicircle E, shown fixed
upon and across C, moves relatively to B as the ship rolls ; and
the pointer attached to the upper edge of B sweeps over an arc
on the semicircle equal to the arc through which the ship is
oscillating. On the left-hand side of the diagram there is shown
a graduated circle Gr, which has its centre coincident with one of
the pivots of C, and is Jixed to the frame F. As the ship pitches,
therefore, the frame F moves with her, and oscillates about the
ring C, which is prevented from accompanying the pitching in
the manner described. Pointers marked p are attached to the
under side of 0, and the arcs they sweep over upon the graduated
circle G indicate the arcs through which the ship pitches. By
this ingenious arrangement the simultaneous rolling and pitching
motions can be read off by observers with the greatest ease.
One point of disadvantage attaching to this as well as to all
other gyroscopic instruments should, however, be noted ; viz. that
there is no separate indication of the angles of inclination attained
on either side of the vertical. When the wheel A is set spiunino-,
if it were truly horizontal, then B would be vertical, and this
disadvantage would disappear. But a ship in a seaway changes its
position rapidly, and it is practically impossible to secure this
condition of initial horizontality ; hence the observer must be
content to note the total ares of oscillation. No doubt, in most
cases, the rolling of a ship not under sail approaches equal incli-
nations on either side of the vertical, the roll to leeward being
somewhat in excess of that to windward ; but in a ship under sail
the rolling takes place about an inclined position, and in any case
it is a great advantage to be able to ascertain the extreme incli-
nation on either side of the vertical.
Professor Smyth fully appreciated this defect of all gyroscopic
instruments, observing that they had " no power of determining
" absolute inclination, or angular position with reference to horizon
" or meridian ; " but he was unacquainted with any other instru-
ment which did not have its records affected by the accelerating
forces due to the motion of the ship, and so preferred the gyro-
scopic clinometer. Now we have other means of measurement free
from the objections belonging to pendulums or spirit-levels, and
can therefore afford to dispense with the gyroscope.
It has been mentioned that the maintenance of the plane of
rotation by a fly-wheel depends upon the maintenance of its
speed ; this is well illustrated in the common toy, which droops
as the speed decreases. The practical difficulties attending the
270 NAVAL ARCHITECTURE. chap. vii.
use of these instruments arise, therefore, from the extreme care
required in suspending the fly-wheels in order that friction or
other causes may have the least eifect in hindering free rotation,
and in the difficulty of maintaining continuous rotation. The
instrument shown in Fig. 74 is said to have been so well designed
that, when once carefully adjusted, it did not require readjustment
for some time ; but from the few records of its use that have been
published, it would appear that Professor Smyth limited any
single series of observations to a very brief period. When a con-
siderable time is occupied in making the observations, there is a
danger of the gyroscopic action being somewhat interfered with
by the loss of speed of rotation.*
On this point some interesting facts have been stated by
Admiral Paris, of the French navy, who produced a gyroscopic
clinometer some years ago, which automatically recorded the
rolling of a ship. The gyroscopic wheel in this instrument formed
the body of a top, the lower end of the axis about which it spun
being wrought to a sharp point, and resting on an agate bearing in
order to diminish friction. To spin this top, a string was wound
round the upper part of the axis, and drawn off gradually, giving
a gradually accelerated motion of rotation. It was found that
this top would revolve steadily on a support for about half an hour ;
but nine minutes sufficed to degrade its revolutions from 23 per
second to 12 per second ; and this lower speed sufficed to make
the top steady enough to be used for recording the motion of a
ship in a seaway; the observations Avere usually extended over
about ten minutes.
The automatic recording apparatus was extremely simple. As
the ship rolled, the gyroscopic top maintained its axis in the same
direction as that in which it was set spinning, and upon the upper
end of the axis a camel-hair pencil saturated with ink was fixed.
A sheet of paper was made, by means of clockwork, to travel
longitudinally over the pencil point, being curved in the trans-
verse sense, so that the point should just touch the paper as it
swayed to and fro. The paper, with the arrangements by which
it was made to travel, being attached to the ship, rolled with her,
while the axis of the top maintained its original direction ; hence
the pencil point traced out on the paper a curve showing the
* It may be interesting to add that, lying on its side instead of its bottom,
when the instrument illustrated in Fig. and the wheel B being horizontal. The
74 was used to measure "yawing," angles of "yawing" could then be read
it was placed with the pivots of the off on the graduated circle G.
ring C in a vertical line ; the frame
CHAP. VII. OBSERVATIONS OF ROLLING. 2 /I
inclinations of the ship at any instant on either side of the initial
position of the pencil. The rate at which the clockwork propelled
tlie sheet of paper being constant enabled the period of oscilla-
tion of the ship, as well as the arc of oscillation, to be read off
from the diagram traced. Admiral Paris appears to have en-
deavoured to set the axis of his top truly vertical before com-
mencing to record the motion, in order that the diagram might
show inclinations to the vertical as well as arcs of oscillation;
but in doins: this, he must have encountered considerable diffi-
culties, even if he was successful. ^Ye cannot further describe
his ingenious arrangements, but would refer readers to the full
details siven in vol. viii. of the Transactions of the Institution of
Naval Architects.
M. Normand has proposed an instrument for measuring rolling
differing from the gyroscope in principle, but intended to effect
a similar object, viz. the maintenance of an invariable plane, to
w^hich the motions of the ship could be referred. A spherical
vessel is entirely filled with petroleum, and hung on double
gymbal-rings like a compass. It contains a very light pendulum,
situated at the centre of the sphere, and formed as a flat disc,
carrying a pointer which stands at right angles to the disc. The
inventor supposes that the fluid in the central parts of the sphere
would have no angular motion set up in it by the recij)rocating
oscillations of the ship or the small oscillations of the sphere on
its gvmbal-rings, and that the pendulum would remain practically
horizontal while the vessel rolled, its indicator being vertical.
Much would obviously depend upon the position in the ship at
which this instrument was placed. Supposing it to be at the
centre of gravity, M. Normand's supposition might be nearly
fulfilled, and the sphere with its contents would act like a com-
mon pendulum, its motions being governed by those of the eflective
wave slope, and keeping time with the wave period. Under these
circumstances it is conceivable that the motions of the disc-
pendulum might be small, and the motions of the ship might be
fairly well indicated. But the use of any such instrument has
never, we believe, found general favour; for general service
simpler methods suffice, and for more scientific research it appears
preferable to have recourse to a different principle, hereafter to
be described, in order to secure the invariable vertical line of
reference which M. Normand aimed at securing.*
* Drawings and descriptions of this instrument will be found in vol. vii.
of the Transactions of the Institution of Naval Architects.
l"]! NAVAL ARCHITECTURE. CHAP. vil.
Batten instruments afford the simplest correct means of observ-
ing the oscillations of ships ; they can be employed whenever the
horizon can be sighted. The line of sight from the eye of an
observer standing on the deck of a ship to the distant horizon
Avill always remain practically horizontal during the motion of
the ship. Consequently, if a certain position be chosen at which
the eye of the observer will always be placed, and when the ship
is upright and at rest, the horizontal line passing through that
point is determined and marked in some way ; this horizontal
line can be used as a line of reference when the ship is rolling
or pitching, and the angle it makes at any instant with the
line of sight will indicate the inclination of her masts to the
vertical.
This principle may be apjjlied in different ways; one of the
most common, generally adopted in the ships of tlie Koyal Navy,
is illustrated in Fig. 75. The point E on the middle line of the
cross-section marks the position of the eye of the observer ; and
Line of SiVfht
St/rface of Sfi/.l Water
at equal distances athwartships, two battens CC and GG are fixed
perpendicularly to the deck, so that, when the ship is upright
and at rest, these battens are vertical, and at that time the line
FEF will be horizontal. This line may be termed the "zero-
line ; " and the points FF would be marked upon the battens,
being at a height above the deck, exceeding that of the point E
by an amount determined by the transverse curvature or "round"
of the deck. Suppose the diagram to represent the case of a
ship rolling among waves ; when she has reached the extreme
of an oscillation to starboard, EG marks the line of sight to the
horizon, and the angle GEF measures the angle of inclination of
the masts to the vertical. If the battens are placed longitudi-
nallv, instead of transversely, the angular extent of pitching may
be similarly measured. The angles are usually read off on that
side of the point of observation E towards which the vessel is
inclined; rolls to starboard being measured, for example, on the
starboard battens, rolls to port on the port batten^. Sometimes
the inclinations to both port and starboard are read off on one
CHAP. VII.
OBSERVATIONS OF ROLLING.
27,
batten, above aud below the zaro. It is a great practicdl cou-
venieuee to have the vertical battens graduated so that an
observer can at once read off and note down the angles of in-
clination in degrees. This graduation is very simply effected
when the positions of the battens reUitively to E have been fixed,
and the zero-line FEF determined. Once graduated, the battens
can, of course, be removed when the observations are not in pro-
gress, and replaced in the same positions when required.
The zero-line on the battens having been fixed in the manner
previously explained, the horizontal distance from the position
where the eye of the observer will be placed to the vertical batten
is measured; suppose this to be (I feet, it will be indicated by
EF in Figs. 75 and 76. Then, for any angle a, we have.
Vertical height (FG) to be set off above]
zero- line on batten j
>=<:?. tan a.
The value of tan a being taken from a table, the product d tan a
can be found. For instance, suppose cZ = 20 feet, and a = 15
degrees : tan o = 0*268,
and vertical distance (FGr)
to be set above zero-line
will be (20 X 0 268) =
5"36 feet.
Another form of the
batten instrument is shown
in Fig. 77. AB is a
straight-edged batten
pivoted at C, and carried by a frame having attached to it a
semicircular gra-
duatedarc. Suppose
that, when the ship
is upright and at
rest, the base of the
instrument is so
fixed that the
pivoted bar, occupy-
ing the position AB, 4
is horizontal. Then
the line ACB marks
the zero-line to whicli
angles of inclination may be referred. The instrument may, if
desired, be set transversely when rolling motions are being
observed; the observer looking along the edge of the pivoted
2 74 NAVAL ARCHITECTURE. chap. vii.
batten will always keep it pointed to the horizon, and its motions
can be observed on the graduated arc. For example, suppose the
position FE to have been reached, tlien the angle EOB (a little
over 20 degrees) will indii-ate the inclination of the masts of the
ship to the vertical at that instant.*
instead of looking lengthwise, and athwartships, along tlie
edge of the batten when the instrument is set transversely, the
observer may, if he prefers, stand before or abaft the instrument,
and move the pivoted bar so as to keep its edge always parallel
to the horizon ; the angular motion of the bar indicated on the
graduated arc will measure the inclination as before. To measure
pitching, the instrument should be set longitudinally in the ship,
the zerodine being adjusted as explained for rolling ; and the
observer will either look longitudinally along the edge of the
batten, in order to keep it pointed to the horizon, or will stand
and look athwartships, keeping the edge parallel to the horizon.
In either case the angles of [)itching may be read off from the
graduated arc.
It will at once occur to the reader that the angular motions of
such a pivoted bar miglit be readily made, by means of suitable
mechanism attached to some point on the bar, to furnish an
automatic record on a travelling sheet of paper moved at an
uniform speed by clockwork. This has actually been done in
some cases, a diagram being automatically traced, showing the
inclinations of the ship throughout the period of observation
Hereafter the character of such mechanism will be illustrated,
so that further description here is not required.
The proper conduct of observations with common batten
instruments requires at least two observers : one to note the
extreme angles of inclination attained by the ship, a second to
note the periods of successive rolls. In the Koyal Navy a single
series of observations would last ten minutes, and during that
time one observer would have to note the extreme inclinations for
from seventy to, perhaps, one hundred and fifty or two hundred
single rolls, according to the class of ship and character of the
waves.-f- The other observer would, meanwhile, note the times
of performing successive rolls, and the total number of rolls
during the ten minutes. To complete the materials required for
* It will be evident that this instru- t To facilitate the entry of the
mcnt could also be used at night, particulars, printed forms are issued to
when stars of known altitude were the ships of the Royal Navy,
visible.
CHAP. vii. OBSERVATIONS OF ROLLING. 275
a discussion of the behaviour of the ship, the dimensions and
periods of the waves ought to be observed simultaneously with
the rolling or pitching ; and this requires the attention of an
independent set of observers, whose work should be conducted
somewhat in the manner indicated in Chapter V. In large
war-vessels with numerous complements it is easy to carry
on such observations; in small vessels it is not always easy to
provide for the working of the ship and to detail officers for
observations of rolling and pitching. The most importmt
observations are, however, those made in large ships of new
types.
A very ingenious process for automatically makmg and re-
cording horizon observations of rolling, by means of photography,
has been devised by M. Huet of the French Navy, and successfully
applied in several vessels. The apparatus consists of a camera
fixed in the ship so that its axis is horizontal when the ship
is upright. The field of the object lens is narrowed to a vertical
slit, and a sheet of sensitive paper is made to travel parallel
to the lens, by means of clockwork, at a uniform rate. On this
sensitive paper a line is traced which would be in the same hori-
zontal plane with the axis of the camera when the ship was
upright, and this is taken as a line of reftrence. As the ship
rolls the sensitive paper receives at each instant an impression of
the sea and sky on the horizon ; the colours being quite distinct;
and their junction defining the instantaneous inclination of
the ship to the vertical. Let dj - the vertical distance of the
junction of sea and sky shown on the paper at any instant,
measured above or below the line of reference above named.
Then, if / is the horizontal distance from the lens of the camera
to the sensitive paper, and % the angle of inclination of the ship
to the vertical, ,
tan o = TT
is an equation determining the value of 0 at every instant. The
motion of the ship is, therefore, continuously recorded, and her
inclinations at any time as well as her extreme angles of ex-
cursion can be ascertained. As an economiser of labour on the
part of observers and an extension of the mftthod of batten
observations, this method is valuable. From specimens of the
diagrams obtained on the sensitive paper which M. Huet has
been good enough to furnish to the Author it also appears tliat
the photographic records obtained are precise and easily inter-
preted. Independent observations of the wave phenomena ac-
T 2
276 NAVAL ARCHITECTURE. chap. vii.
companyiiig rolling are necessary with this method, as well as
uith batten observations.
For all ordinary purposes batten observations of rolling and
pitching, such as are made in the Royal Navy, suffice ; but they
require the simultaneous attention of at least two observers, and
depend for their accuracy upon the care exercised by these
ofhcers. Moreover, they simply furnish the extreme inclina-
tions attained by the ship, and the period of her oscillation;
and although these may be associated with simultaneous observa-
tions of the waves, there is no continuous record of the ratio of
the angle of inclination of the ship to the angle of wave slope.
More complete information, such as is most valuable for scientific
purposes, can be best secured by means of automatic instruments,
the records of which may be made continuously during prolonged
periods. Such instruments require care both in their construction
and management ; but if they are based upon correct principles,
they can be, and have been, made capable of far surpassing the
results obtained by the most careful personal observation. Both
in France and in this country such instruments have been made
and used. M. Bertin, of Cherbourg, and the late Mr. W. Froude
independently constructed instruments for this purpose, based
upon very similar principles. That of Mr. Froude has been used
on board the Greyhound, Perseus, and Devastation witli great suc-
cess, and a description of its leading features will be welcomed
by all who take an interest in the subject of the behaviour of
ships at sea, and may not have had the opportunity of consulting
the descriptions which Mr. Froude published.*
Fig. 78 contains a general view of the instrument, mounted on
a rocking platform, AAA, the motions of which represent those
of the deck of a ship rolling in a seaway. The surface of the
rocking platform to which the instrument is secured is shown at
a considerable inclination, and the fixed frame upon which it
rocks will be readily distinguished.
Two fundamental principles, already explained, may be again
mentioned in order to facilitate explanation : (1) if a pendulum
of very short period is hung at the height of the centre of gravity
of a ship rolling among waves, it will at each instant stand
practically normal to the effective wave slope ; (2) if a pendulum
of very long period be hung in the ship, it will remain practically
* For these see vol. xiv. of Trans- particulars given in the text and the
actions of the Institution of Naval drawiuj; of the instrument are taken.
Architects ; from which most of the
-^o
CHAP. vir.
OBSERVATIONS OF ROLLING.
277
vertical while she rolls. In the instrument there are two such
peudulnms ; when the ship is upright and at rest, they both
occupy a vertical position which is marked on some J3art of the
apparatus that accompanies the motion of the sliip. When the
ship rolls, the oscillations of the quick-moviDg penduhim indicate
the angles of inclination, at every instant, of the masts of the
FIG 78.
ship to the normal to the effective wave slope; while tlie oscilla-
tions of the very slow-moving pendulum indicate the simul-
taneous inclination of the masts to the vertical. From these
two records the angles of wave slope at various times can be
deduced, being the algebraical difference of the pendulum incli-
nations; and the profile of the effective wave surface can be
constructed. In short, every important feature in the behaviour
278 NAVAL ARCHITECTURE. chap. vii.
of the ship is brought within the scope of analysis, by means
of the diagrams automatically traced by the instrument.
The quick-moving pendulum is shown in Fig. 78 by r (on
the right side of the drawing, and about mid-height on it). It
consists of a horizontal bra>s tube, filled with lead so as to form,
a heavy bar-pendulum ; this is suspended at each end on knife-
edges, situated near the upper part of the circumference of the
bar. The bar is only 2^ inches in diameter, and about 20
inches long ; so that the arrangement really produces a powerful
and sensitive pendulum, of less than 2 inches in length, and
consequently having a very short period.* It carries an arrange-
ment of light arms (^j), at the end of which is a pen, s; and as
the bar-pendulum swings to and fro, the pen s registers the
motion upon a sheet of paper carried by the cylinder h, which
is driven by clockwork. The pen s traces on the paper a con-
tinuous line, and as the cylinder li revolves, another piece of
clockwork I marks upon the paper a " scale of time ; " so that the
ditigram produced shows not merely the successive inclinations
of the ship to the effective surface, but also indicates the times
at which those inclinations are attained. The interval of tiuie
marked by this scale, between two consecutive extremes of
inclination, will sho^v the "period" of the coiresponding
oscillation.
Considerable practical difficulties had to be overcome in con-
structing the second pendulum, which has a very long period.
It consists of a heavy-rimmed wheel (a, in Fig. 78), 3 feet in
diameter, weighing 200 lbs. ; this is carried on an axis of steel,
1 inch in diameter, the centre of gravity of the whole being only
six-thousandths (0*006) of an inch away from the centre of the
axle. Here we see an arrangement identical in character with
a ship having very little initial stability, but great inertia ; the
two contributing to produce a very long period. The observtd
time for a single swing of this wheel-pendulum, as it may be
termed, has been found to be about 34 seconds ; the magnitude
of this period becomes evident when it is remembered that the
slowest-moving ships have periods for a single roll of about 10
seconds only, and that the half-period of the largest waves
commonly met with are still less. Friction rollers (c, c) support
the steel axle ; and the extreme delicacy of the suspension of
this heavy wheel is attested, says Mr. Froude, "by the fact,
* A pendulum having a length of 2 inches has a period for a single roll of
ahout two-tenths of a second only.
CHAP. VII. OBSERVATIONS OF ROLLING. 279
that, when at rest, a breath on the " circumference (of the wheel)
will move it perceptibly." This wheel-pendulum continues
almost unmoved as the ship rolls. The effects of any very
small motion which the wheel may acquire are easily eliminated,
and it practically indicates at every instant the true vertical
direction, as well as the inclination thereto of the masts. This
wheel is also made to record its motions on the revolving
cylinder Ic. A wooden semi-circle g is carried on the axis, and
by means of the light rods h, A— which are carefully counter-
balanced—the relative angular motions of the ship and the
steady wheel are made to move a pen, m, which draws a curve
on the paper stretched upon the cylinder 7v. The character of
this curve is similar to that traced by the pen s, moved by the
pendulum r; and both these curves are indicated by the curved
lines shown on the cylinder h, the rotary motion of the cylinder
and the motion of the pens parallel to its axis combining to
produce this result. The time scale is the same for both curves ;
and on that traced by the pen to the time interval between
any two consecutive extremes of inclination measures the cor-
responding period of oscillation of the ship. When the observa-
tions are over, the paper can be removed from the cylinder h,
and the diagrams drawn by the automatic apparatus can be
analysed. Into this part of the work, however, it is unneces-
sary now to enter, our purpose being to give only a general
sketch of the instrument. It furnishes the following informa-
tion : —
(1) The relative inclination of the ship and the effective wave
slope at any instant.
(2) The inclination of the ship to the vertical at any instant.
(3) The period of oscillation of the ship at any time— that
is, the number of seconds occupied in completing the roll from
port to starboard, or vice verm.
From 1 and 2 may also be deduced : —
(4) The angle of slope of the effective wave surface at any
instant.
(5) The period of this effective wave, which will agree with
the ai^j)arent period of the surface waves when the ship is floating
among relatively large waves.
If, therefore, careful observations are made, while the instru-
ment is at work, of the dimensions and periods of waves, the
comparison between the observed slope of the surface wave and
the deduced slope of the effective wave will furnish a test of
the correctness of the ordinary assumptions as to the effective
28o NAVAL ARCHITECTURE. chap. vii.
wave slope. It will also enable future estimates of the probable
rolling of ships to be made more precise than is now possible,
owing to the doubts surrounding this question of the effective
wave surftice*
In the instrument constructed by M. Bertin the heavy wheel-
pendulum has a period, for a single swing, of 40 seconds: and
the qnick-moving pendulum a corresponding period of '2 second.
Each pendulum automatically records its indications. M. Bertin
has made several series of observations with this instrument,
including pitching as well as rolling observations in his work,
and the results obtained, as well as their analysis, constitute
one of the most valuable additions made in recent years to
the experimental study of the oscillations of ships.-f-
It may be worth notice, in passing, that the wheel-pendulum
of either of these automatic instruments, stripped of its appliances
for recording its indications, would constitute a very trustworthy
substitute for the ordinary pendulums whose errors have been
described (on pnge 265). Some simpler instrument embodying
the same principles will probably yet come into general use
as a substitute for the pendulum.
Before concluding this chapter, it may be well to repeat that,
whatever method of observing the rolling or pitching may be
adopted, the observations made cannot have their full value
unless the attendant circumstances are fully recorded. For
example, the actual condition of tlie ship at the time should be
noted ; whether she is under sail or steam ; what portion of her
consumable stores remain on board ; whether the boilers are
full or empty ; whether there is anything unusual in her
stowage; whether there is any water in the bilges; and any
other features that would affect the still-Avater period of oscil-
lation. Her course and speed should also be stated, the former
being given relatively to the line of the wave advance, and the
angle between the two being stated in degrees where possible.
The dimensions and periods of the waves, both real and apparent,
should also be carefully determined, as explained in Chapter V.
* Independently of the iise of this Gnat care would be required to ensure
instrument, naval officers might do the simultaneity of the records of bat-
much to add to existing knowledge on tens and pendulums if this jDlan were
this point if they associated ordinary adopted.
batten observations with simultaneous f Observations de rouUs et de tan-
observations of the angles indicated by (jage faites avec Voscdlocfraplie doid)Ie,
short pendulums hung at the height of par M. Bertin. See page 256 as to
the centre of gravity of the ship. pitching.
CHAP. VII.
OBSERVATIOXS OF ROLLING. 28 I
jMoreover, no change should be made affecting the behaviour of
a ship for some time before the observations are comniencerl,
nor during their progress; a charge of course, an alteration
in the sail spread, a change of speed, or any other changes,
made immediately before the observations began, might seriously
influence the behaviour during the comparatively short time over
which a series of observations extends ; and it is needless to point
out the necessity for avoiding any changes during that short
time. The Admiralty instructions enforce these conditions,
providing that no change of course or speed, or spread of sail,
&c., shall be made for at least ten minutes before the observa-
tions are commenced.
One of the most perfect sets of observations of the behaviour
of a ship yet made were those conducted by the late Mr. Froude,
on behalf" of the Admiralty, on board the Devastation. But un-
fortunately for the scientific interest of the case, the weather
encountered during the passage of that ship to the Mediterranean
in 1875 was so moderate as neither to severely test her qualities
nor to afford good opportunities for showing the full capabilities
of the automatic instrument. Every naval officer proposing to
enter upon similar work may read with advantage the brief
report drawn up by Mr. Froude on the observations made during
the passage.*
Ordinarv observers have not similar advantages, but with the
aid of the appliances in common use much valuable information
has already been furnished, and it is to observations of a similar
character we must look chiefly for still further facts bearing on the
behaviour of ships at sea. An intelligent acquaintance with the
main deductions from modem theory, as well as with the moot
points of the subject, will enable the observer to supply much
more valuable information, seeing that he will be capable of
distinguishing the more important from the less important con-
ditions, and of giving a practical direction to his inquiries.
* Putlished as Parliamentary Paper No. 101 of 1876.
282 NAVAL ARCHITECTURE. chap. viii.
CHAPTER Ylir.
THE STRAINS EXPERIENCED BY SHIPS.
The structure of a ship floating at rest iu still water is usually
subjected to various straining forces tending to produce changes
of form ; and when she is rolling and j)itching in a seaway, or
propelled by sails or steam-power, her structure is still more
severely strained. In order to provide the necessary structural
strength to resist these straining forces, the naval architect has
to make choice of the materials best adapted for shipbuilding,
and further to distribute and combine these materials so as most
efficiently to resist changes of form or rupture of any part. By
these means he seeks to secure the association of lightness with
strength to the fullest possible extent, an object of which the
importance has already been illustrated.* Before it can be
accomplished satisfactorily, the designer of a ship must have an
intelligent appreciation of the causes and character of the strains
to be provided against ; otherwise materials may be concentrated
where strength is not chiefly required, or viee versa. The import-
ance of such knowledge has been recognised from the time when
the construction of ships began to receive scientific treatment, but
in this, as in most other branches of tlie subject, the greatest
progress has been made within comparatively recent times. We
now prcpose attempting a brief popular sketch of the chief
straining actions to which ships are subjected, and in a sub-
sequent chapter will discuss the principles of the structural
strength of shi[)S.
The chief strains to which ships are subjected maybe classified
as follows : —
(1) Strains tending to produce longitudinal bending — " hog-
ging " or "sagging" — in the structure considered as a whole.
See Chapter I. p. 3.
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 28^
o
(2) Strains tending to alter the transverse form of a ship ;
i.e. to change the form of athwartship sections.
(3) Strains incidental to propulsion by steam or sails.
(4) Strains affecting particular parts of a ship— " local strains"
— tending to produce local damage or change of form, inde-
pendently of changes in the structure considered as a whole.
Besides these there are other strains, of less practical im-
poitance, which are interesting from a scientific point of view, but
need nut now be discussed, as there is ample strength in the
structure of all ships to resist them, and there is no necessity in
arranging the various parts to make special provision against such
strains. Vertical shearing forces, for example, are in action in all
ships ; they tend to shear off the part of a ship lying before any
cross-section from that abaft it; but no such separatitn of parts
has been known to take place, nor is it likely to be accomplished
in ordinary ships.
The order indicated in this classification is that which will be
followed in our description, being the order of relative import-
ance of the straining actions. All of them require consideration,
but, while it is not difficult to provide against the last two classes,
it is important to bestow careful attention on the prevention of
changes of transverse form, and it is still more difficult to prevent
longitudinal bending.
In passing, it may be well to remark that a distinction must
be made between the tendency of any strain and its observed
effect upon the structure of a ship. No visible change of form
may result from the action of very severe strains, bt cause the
visible result of that action depends upon the strength and
rigidity of the structure relatively to the strains brought upon
it; nevertheless, the tendency of the straining forces is the same
as if actual change of form was produced. For instance, it is
very common to find wood ships " hogging " or " sagging " under
the action of longitudinal bending strains ; but iron ships, equally
strained, have strength and rigidity so much in a6cess of wooden
ships as to remain practically unchanged in form. Again, wood
ships frequently "work," altering form transversely, when rolling
in a seaway ; and forces of equal intensity acting upon a stronger
iron ship may give no external evidence of their existence. Yet
in both cases the tendency of the straining forces is the same.
This simple distinction is sometimes overlooked, and the absence
of straining forces inferred from, the maintecance of form.
Turning to the principal strains requiring consideration — those
tending to produce longitudinal bending — the case to be first
284
NAVAL ARCHITECTURE,
CHAP. VIII.
coDsidered is that of a ship floating at rest in still water. It has
already been sliown that there are two essential conditions of
equilibrium : the ship must displace a quantity of water having
a weight equal to her own weight, and her centre of gravity
must be in the same vertical line with the centre of buoyancy •
These two conditions may be fulfilled, however, and yet the
weight and buoyancy may be very unequalli/ distributed ; the
result being the production of longitudinal bending strains. As
a very simple illustration, take Fig. 79, representing a ship float-
ing at rest in still water. Supposing her to be divided by a
FIG 79.
tx
a
li i
•-ILL
a a
4\-
a
a
W,
/-^ — «*
V/^
w.
number of tiansverse vertical planes {cih, ah, &c.), let each piece
of the ship between two consecutive planes of division be con-
sidered separately. At the bow there will probably be one or
two portions for which the weight exceeds the buoyancy ; these
excesses of weight are indicated by Wi and Wj. Amidships the
fuller form of the ship gives greater buoyancy to those sub-
divisions, and it is very common to find the buoyancy exceed-
ing the weight, as indicated by B^, Bj, B3, in the diagram. At
the stern also the weight is likely to be in excess, as shown by
Wa and W4. The sum of these excesses of buoyancy will
evidently balance the sum of the excesses of weight at the
extrettjities ; and the second hydrostatical condition of equilibrium
requires that the resultant moment of these two sets of forces
about any point shall be zero
It will be seen that a ship
tlius circumstanced is in a con-
dition similar to that of the
beam in Fig. 80, which is
~:I1I^=^^^^^^ - ' supported at the middle, and
loaded at each end. Such a
beam tends to become curved, the ends dropping relatively to the
middle, and the ends of the ship tend to drop similarly, the
change of form being termed "hogging." Hogging strains are
very commonly experienced at every part of the length of ships
floating in still water.
»
MS
s
FIG 80. w
CHAP. VIII. STRALXS EXPERIENCED BY SHIPS.
285
If the conditions of Fig. 79 were reversed, the excesses of
buoyancy occurring at the extremities, and those of weight
amidships, the ship wouki resemble a beam supported at the
ends and loaded at the middle of the length. The middle
would then tend to drop relatively to the ends, a change of
form sometimes occurring in ships, and known as "sagging." It
is to be observed, however, that in all, or nearly all, ships, when
floatino- in still water, the fine form of the extremities under water
makes the buoyancy of those parts less than the corresponding
weights ; so that sagging strains are rarely experienced through-
out the whole length of a ship in still water. Among waves, as
Avill be seen hereafter, the conditions may be changed so as to
produce saggiog strains at every part of the length of a ship.
It is not uncommon to find the opinion expresssd that, when-
ever there is an excess of weight amidships in a ship, sagging
strains will be developed ; but this is not a necessity. Suppose,
for example, that Fig. 81 represents a vessel having an excess of
FIG 81.
a
"m
P vk'
ft
a
a
0
I
€f
f
r Y *
m
a
1
Wt
FIG 82.
a
W,
1
ueight (W2) amidships as well as at tlie extremities, and excesses
of buoyancy at the intermediate portions. This is the condition
of very many ships, such as paddle-steamers with their machinery
concentrated in a comparatively small length amidships, or in
ironclads with central armoured breastworks or batteries over-
lying the spaces occupied by the machinery. Such a vessel may
be compared to the beam in
Fig. 82, supported at two
points, and laden at the middle
and ends. According to the
view mentioned above, sagging
strains should then be pro-
duced under the middle-load ; r^.=^^^—
but it is easy to show that this may or may not be the case. For
this purpose a short explanation is needed of a few simple
principles, the application of which is general to ships as well as
to beams.
Suppose it is desired to obtain the '• bending moment " at any
2VI4
a
w,
286 NAVAL ARCHITECTURE. chap. viii.
section — say ah — of the beam in Fig. 82. Conceive the beam
to be rigidly held at that section, and reckoning from either end
of the beam up to ah, let an account be taken of every force
acting upon it, load and support, as well as of the distance of the
line of action of each force from the selected section db. JMultiply
each force by the corresponding distance, add up separately the
moments of the loads and supporting forces, and the differences
of the two sums will be the bending moment required. It is
immaterial whicli end is reckoned from in estimating the
bending moment. As a very simple case, suppose it to be
desired to find the bending moment of the forces acting upon
the middle section of the beam in Fig. 82. Let the weight of
the beam be neglected, and the supports be midvvay between the
middle of the length and either end. Suppose the following
values to be known : —
4 Z = length of beam; Wi = load on either end; 2 W2 = load in
middle.
Then each support will sustain a pressure (B) equal to Wj + Wo.
For the bending moment at the middle of the beam, we must
have,
Bending moment = W^ X 2 Z-(Wi + W^) 1= (Wi-W^) I.
Hence it will be seen that the following conditions hold : —
{a) If Wj is greater than W2, there will b3 a liogging
moment at the middle of the beam, and no section will be sub-
jected to sagging moment, notwithstanding that the middle load
2 W2 is carried.
(b) If Wi is less than W2, there will be a sagging moment at
the middle of the beam.
(c) Even in this second case the sections of the beam situated
between the ends and the supports will be subjected to hogging
moments, and so also will some part of the beam lying between
the supports and the middle.
The case of the ship is similar, but more complex, the estimate
of the bending moment experienced by the midship section
involving the consideration of many vertical forces, some acting
upwards and others downwards. But the foregoing is an illustra-
tion of the general mode of procedure; and tlie conditions of the
existence or non-existence of sagging strains amidships stated for
the beam are paralleled by somewhat similar conditions for the
ship. Reckoning from the bow or stern of a ship to the midsliip
section, or to any other cross-section, it is easy to estimate the
bending moment when the relative distribution of the weight and
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS.
287
buoyancy for that vessel has been determined. But in such a
determination lies the difficulty of practically applying the
principles just explained.
The longitudinal distribution of the buoyancy of a ship is
readily ascertainable from the calculations ordinarily made for
her displacement; but the corresponding distribution of the
weight can only be found by means of a laborious calculation.
Until quite recently very little exact information on this subject
Avas accessible ; but the work since done at the Admiralty and at
the Eoyal Naval College for various typical war-ships ; as well
as that done at Lloyd's Registry and by private shipbuilders for
various classes of merchant ships, has added much valuable
information, and enabled a more complete tlieory to be framed
as to the conditions of strain to which ships are subjected.*
It is usual to represent the distribution of the weight and
buoyancy of a ship by curves, similar to those shown in Fig. 83.
A base-line (AB) is taken to represent the length of the ship, and
at equidistant intervals ordinates are drawn to represent the
hypothetical planes of division above described. Midway between
any two ordinates a line is drawn perpendicular to the base-line,
and upon this is set off a length representing, on a certain scale,
the buoyancy of the length iu the ship lying between the
corresponding planes of division. A succession of points is thus
obtained, and through these the " curve of buoyancy " (BBB) is
drawn. The ordinary calculations for displacement afford a
ready means of constructing this curve accurately.
To construct the curve of weight (WWW) is a matter of much
greater difficulty. For each portion of the length in the ship
lying between two planes of division it is necessary to calculate
the weight of hull and lading in detail ; when this is found, it is
set oif on the line drawn midway between the ordinates corre-
sponding to the two planes of division, the scale for weight being
the same as that previously chosen for buoyancy. When a series
* These calculations for war-ships
■were commenced under the direction
of Sir Edward Reed, when Chief Con-
structor of the Navy, and have since
been extensively made. The principal
results of the earlier calculations, to-
gether with many generalisations there-
fiom, were published in part ii. of the
Philosophical Transncfionsofthe R()yal
Society for 1871. The Anthor had the
honour of assisting Sir Edward Rood in
the preparation of this memoir, and
the calculations upon which it was
based ; many of the facts stated in the
text are drawn from the memoir. As
to the strains of merchant ships, see
papers in the Transactions of the Insti-
tution of Naval Architects for 1874,
1877, and 1881.
288
NAVAL ARCHITECTURE.
CHAP. viir.
of points has been determined, and the curve of weight drawn, its
total area must equal that of the curve of buoyancy, and the
centres of gravity of the two areas must lie on the same ordinate ;
these conditions are only another form of statement for the two
essential conditions of equilibrium for the ship floating at rest.
Taking any ordinate (say PQ), the intercept (QR) between the
two curves represents the excess (or defect) of buoyancy at that
place. Where the curve of buoyancy lies outside the curve of
weight (reckoning from the base-line AB), buoyancy is in excess ;
where the curve of weight lies outside, the weight is in excess ;
at the sections where the curves cross, the weight and buoyancy
FIG 84.
are equal, and these are termed " water-borne" sections. A more
convenient mode of representing these excesses or defects of
buoyancy is furnished in Fig. 84. Here the base-line and the
dotted ordinates correspond to those in Fig. 83 ; and on any
ordinate of those curves the intercept (say QR) is* measured and
transferred to the corresponding ordinate QR in Fig. 84, being set
above the base-line AB when the buoyancy is in excess, and below
when the weight is in excess. The curve LLL drawn through the
points thus determined is termed the " curve of loads," and indi-
CHAP VIII. STRAINS EXPERIENCED BY SHIPS. 289
cates, at a glance, the unequal distribution of the weight and
buoyancy.
The diagrams in Figs. 83 and 84; represent the case of Her
Majesty's ship Minotaur (armour-plated frigate, 400 feet in
length). She is a vessel completely protected by. armour through-
out her length from the upper deck down to some 6 feet under
water ; the finely formed ends are thus burdened with an excess
of weight, the actual distribution of the weight and buoyancy
being as follows : —
First 80 feet from the bow . . Weight 420 tons in excess.
„ 70 „ „ stern . „ 450 „ „
250 feet amidships .... Buoyancy 870 „ „
This vessel in still water furnishes, therefore, an example of the
condition of the beam in Fig. 80. Hogging moments are ex-
perienced by all athwartship sections throughout the length, the
maximum moment, at the midship section, being equal to the
product of the total weight of the ship by 1^ of her length.
The curve j\DDI in Fig. 84 indicates the variation in the bend-
ing moments from end to end of the ship; the length of any
ordinate measuring the bending moment experienced by the
corresponding cross-section in the ship. This curve of moments
can be very easily constructed when the curve of loads has been
drawn.
This is a very common case of the distribution of weight and
buoyancy in ships ; including the older types of sailing ships and
many steam-ships. The excesses of weight at the extremities are,
however, proportionately greater in an armoured vessel like the
Minotaur than they are likely to be in unarmoured ships, and
this exaggerates the maximum bending moment experienced by
the midship section. It lies outside our present purpose to at-
tempt any exhaustive statement of the varying conditions of
weight and buoyancy either in ships of different classes or in the
same ship when the weights are differently distributed. Atten-
tion must, however, be drawn to the facts, obvious enough from
the preceding remarks, that the magnitude of bending strains in
still water does mA necessarily increase with deeper lading, and
that for a given water-line and total displacement differences of
stowage will greatly influence the strains. For example, if the
armour were taken off the bow and stern of the Minotaur and
stowed amidships, the excesses of weight at the extremities and
of buoyancy amidships would be greatly reduced, causing a great
reduction in the hogging moments at the midship section and
u
290 NAVAL ARCHITECTURE. chap. viii.
elsewhere. On the other hand, if the Minotaur floats light, with
engines, boilers, and all equipment removed as for a general repair,
the excesses of weiglit over buoyancy at the extremities and of
buoyancy over weight amidships become much greater than they
are iu the fully laden condition. Instead of an excess of weiglit
forwaid of 420 tons, there is, when light, an excess of 560 tons ;
wliile aft the excess increases from 450 to 500 tons; and amid-
ships, on a length of some 230 feet, when the ship floats liglit,
tiiere is an excess of buoyancy of 1060 tons, as against 870 tons
in the fully laden condition. The vessel is therefore subjected to
much severer hogging strains when floating light in still water
than she is when lully equipped. This is by no means an excep-
tional condition, and it explains the well-known fact that wood
vessels often hog most soon after they are launched, or when
lightened for thorough repairs. It was the practice formerly to
place ballast on board ships lying iu reserve in order to prevent
hogging.
FIG SS.
in the Devastation class of the Eoyal Na.vy, a far less simple
distribution of tlie weight and buoyancy is found than that
occurring in the Minotaur type. Figs. 85 and 86 illustrate this
case. The spur-bow and full form forward, as well as the absence
of high armoured ends in the Devastation, make the excess of
weight very small, as compared with the Minotaur — about 60 tons
excess only on the first 20 feet of length. Then follows about 57
feet of length, before the central breastwork, where buoyancy is in
excess by about 520 tens ; this is succeeded by a great excess of
weight — 550 tons on 32 feet of length — under the foremost turret.
Along the central part of the ship, where the armoured breastwork
is situated, and the machinery and boilers are placed, there is
very nearly a balance of weight and buoyancy, the difference not
amounting to more than 10 tons on a length of 75 ftet, although.
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 29 1
as showii by the diagrams, there are two small excesses of buoy-
ancy and one small excess of weight, the latter being due to the
pilot-tower. Under the after turret, another large excess of weight
occurs — 320 tons on 38 feet of length ; followed by a still hu-ger
excess of buoyancy— 570 tons on a length of 63 feet; thence to
the stern there is an excess of weight of 170 tons, owing to the
fineness of the form of the ship in the run. These variations are
indicated by the curves of weight (WWW) and buoyancy (BBB)
in Fig. 85 ; but are more clearly shown by the curve of loads
(LLL) in Fig. 86. The resultant bending moments are shown
by the curve MIMM, and offer a remarkable contrast to those for
the Minotaur (see MMxM, Fig. 84). For the first 50 feet from
the bow there is scarcely any bending moment to be resisted ill
the Devastation; whereas in the Minotaur the moment at the
corresponding part amounts to about 8U00 foot-tons. At the
after part also the hogging strains in the Devastation are very
small, the greatest hogging moment being less than one-seventh
as great as that in the Minotaur. But the most marked con-
trast is found amidships; the concentration of weight in the
turrets of the Devastation, the absence of great excesses of weight
at the ends, and the altered distribution of the excesses of
buoyancy, develop sagging moments, indicated in Fig. 86 by the
ordinates of the curve MMM being drawn helow the base-line AB.
The maximum bending strains are also made much more moderatCi
The maximum sagging strain in the Devastation is only a little over
one-third the maximum hogging moment in the Minotaur; the
exact figures are 15,800 foot-tons for the Devastation and 4'),000
foot-tons for the Minotaur. Part of this reduction in bending
moment is undoubtedly due to the less length of the Devastation ;
but expressing the maximum bending moment as a fraction of
the product of the length by the displacement — which is the
fairest method — it is about j}q for the Devastation against ^g for
the Minotaur.
When the excesses of weight and buovancv are differently
u 2
292 NAVAL ARCHITECTURE. chap. viii.
distiibuted in a ship having an excess of weight amidships, her
condition may be intermeliate between the two extremes already
iUnstrated. The Invincible is an example of this intermediate
class. When fully laden, there is an excess of weight of 115 tons
on the first 35 feet from the bow, then an excess of buoyancy of
220 tons on a length of 65 feet ; amidships, under the double-
storied central battery, there is an excess of weight of 275 tons
on a length of 80 feet ; next an excess of buoyancy of 380 tons
on a length of 70 feet, and on the last 30 feet of length to the
stern an excess of weight of 210 tons. The result of this distri-
bution of weight and bnoyancy is to develop maximum hogging
moments in the fore and after bodies, corresponding to those ex-
perienced by the Devastation ; but at the midship section, ins'ead
of a sagging moment, there is a minimum value of the hogging
moment, about one-third as great as the maximum bending
moment experienced by the after body.
The foregoing illustrations have been taken from calculations
made for war-ships, because the longitudinal distribution of the
weights in those vessels is arranged by the designer, and is
affected only by the consumption of coal, stores, &c. In merchant
ships and especially in cargo-carrying ships there is no similar
constancy in the longitudinal distribution of the weights ; and
the same ship may on different voyages be very differently laden,
as well as subjected to very different strains. The shipbuilder
has no control whatever over the stowage ; and cases frequently
occur where want of care and intelligfnce on the part of those
charged with the stowage of cargo produces unnecessarily severe
bending strains. As a basis for calculation and comparison of
ship with i^hip, the assumption may not unfairly be made that a
homogeneous cargo is carried which would fill the available spaces.
Some small adjustments may be required in order to preserve
the trim, but these are usually unimportant ; as there can be no
assurance that the strains resulting from this assumed stowage are
the greatest likely to be brought upon the structure.
Summing up these remarks on the longitudinal bending strains
produced by the unequal distribution of weight and buoyancy in
ships floating at rest in still water, it will be seen that very
considerable bending moments may be developed, the distribution
of the weights very greatly affecting the amounts and character of
the bending moments. Moreover, it is not always correct to say
that the midship section sustains the greatest strain, cases oc-
curring where there is a large excess of weight amidships, and yet
the contrary is tiue — very little strain being brought upon the
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 293
midship section, and the greatest strain being experienced by-
some section in the fore or after body. These still-water strains
are not nearly so severe as those experienced by a ship at sea ; but
they are, on the other hand, of constant occurrence, and may be
termed the " permanent " strains on the structure. Hence con-
siderable interest attaches to an investigation of their values, and
there is the further advantage that the investigation leads up to
the more important case of straining in a seaway.
Besides these vertical forces, a ship floating in still water
has to resist longitudinal fluid pressures, tending to compress the
lower part of the structure, and to produce longitudinal bending.
Euler, and some of the other early writers, on the subject, men-
tioned this fact, but they erred in their methods of estimating the
effect of these pressures. In Figs. 79 and 81, PP indicate the
pressures, which balance one another when the ship is at rest ;
their bending moment may be stated approximately as equal to
the product of P into the distance of the "centre of pressure " of
the immersed midsliip section below the middle of the depth
of that section, reckoning that depth from the upper deck to
the keel.* This moment is never absolutely great, but it some-
times assumes relative importance, especially in vessels with
concentrated weights amidships. For example, in the central-
battery ironclad Bellerophon, the vertical forces develop a very
small bending moment, whereas the longitudinal fluid pressures
produce a moment of over 3000 foot-tons — about one-fourth of the
maximum hogging moment experienced by any cross-section of the
ship when floating in still water. In the Invincible class, a nearly
identical ratio holds between the moment due to the horizontal
fluid pressures and the maximum hogging moment, which is
experienced by a section in the after body, in consequence of the
unequal distribution of weight and buoyancy previously parti-
cularised. This branch of the subject i>!, however, interesting
rather than practically important.
Passing from the longitudinal bending strains experienced by
ships in still water to those experienced when ships are at sea,
it is evident that the latter strains must be far more seveie and
distressing to the structure. This arises principally from three
causes. First, the existence of waves and the departures of the
wave profiles from the level of still water will produce exaggerations
* More exactly, the distance of the of gravity of the sectional area of the
centre of pressure should be reckoned parts on the midship section contribut-
from a point a little above the centre ing resistance to bending.
294 NAVAL ARCHITECTURE. chap. vili.
in the inequality of distribution of the weiglit and buoyancy.
Second, the rapid transit of waves past a sliip will produce con-
tinual variations in the distribution of the buoyancy, these being
necessarily accompanied by great and rapid changes in the
character and intensity of the bending moments brought upon
the structure. Third, the establishment of pitching and 'scending
movements in the ship, as well as of vertical heaving motions,
will lead to the development of accelerating forces tending to
increase the strain upon the structure. It will, of course, be
understood that we are still dealing with the longitudinal bending
of the ship considered as a whole, and not with local strains such
as may be produced by blows of the sea.
These general considerations are certain to command accept-
ance, but when an attempt is made to give them a more exact
apj^lication, in order to determine the probable maximum strain
which may be brought upon a ship exposed to the action of waves,
difficulties arise of a very serious character. In fact, the best
authorities agree in adopting a mode of treatment which has
w
much to recommend it, although it by no means comprehends all
the conditions of the problen), being rather a means of comparing
the strains of difft^rent ships than of estimating the absolute
maximum strain likely to be brought upon a jiarticular vessel
in a seaway. Two extreme cases are taken : one (illustrated by
Fig. 87) where the ship is supposed to be upright and to rest
instantaneously in statical equilibrium upon the crest of a wave
having a length equal to her own ; the other (see Fig. 88) where,
in instantaneous equilibrium, she lies across the hollow of the
FIG S3.
same wave, her bow and stern being at successive crests. The
waves are assumed to have the steepness likely to be associated
with their length ; the ship is supposed to displace as much water
on the waves as in still water ; her centre of gravity is supposed
CHAP. Mil. STRAINS EXPERIENCED BY SHIPS. 295
to be exactly over the centre of buoyancy corresponding to each
of the extreme positions ; and, instantaneously, she is treated just
as if the wave delivered its pressure upon her vertically, much
as still water does, the form of the displacement only being
changed. Objections may, of course, be urged to all these as-
sumptions; but, on the whole, they appear to embody the best
method at present available for comparing the longitudinal
bending strains of different classes of ships.
A glance at the dia2:rams shows how great a difference in the
distribution of the buoyancy is produced by the passage of the
wave; WL in each indicates the load water-line in still water.
On the crest (see Fig. 87) the buoyancy at the extremities of the
ship is decreased as compared with still water; the buoyancy
amidships being considerably increased. In the hollow (see Fig.
88) the conditions are reversed ; there is an increase of buoyancy
at the bow and stern which sink into the wave deeper than the
level of WL; while there is a decrease of buoyancy amid>hips.
Speaking generally, it may be said, therefore, that all classes of
ships supported on the crest of a wave of their own length
tend to hog tliyougliQut their length, the greatest hogging moment
being experienced either by the midship section or a section lying
near to it. This is true even for vessels with concentrated central
weights. On the other hand, in all except very few and unusual
cases, ships astride a wave hollow (as in Fig. 88) have excesses
of buoyancy at the ends and excesses of weight amidships ; conse-
quently they are subjected to sagging moments throughout the
length* the maximum bendiug moment being experienced at or
near the midship section, even by ships which in still water tend
to hog throughout the length.
A few facts for the Minotaur and Devastation will more clearly
illustrate the foregoing statement. When the Alinotaur floats on
the crest of a wave 400 feet long and 25 feet high, the excesses
of weight at the bow and stern become increased to 1275 and
1365 tons respectively — about three times as great as the corre-
* See the remarks made at page 285. feet ; and in the Devastation, similarly-
Special features may produce small circumstanced, the lowness of the free-
excesses of weight at the bow or stern board leads to the extremities of the
even when they are immersed in the deck being buried deep in the wave
adjacent wave slopes. For example, in slopes, causing excesses of weight of
the Minotaur, on the wave of her own about 25 and 65 tons resj ectively
length mentioned in the text, the forward and aft. But these may be
heavily armoured bow has a very safely neglected, since the resultant
small excess of weight, 10 tons on 10 hogging mcments are very small.
296 NAVAL ARCHITECTURE, chap. viii.
spouding excesses in still vva'er ; the excoss of buoyancy amid-
ships being 110 less than 26-10 tons. The maximum hogging
moment borne by the midship section is 1-10,000 foot-tons — more
than three times the maxiinuiu hogging moment experienced in
still water. These exaggerations of strain, however, leave the
character of the strain unaltered, every transverse section being
subjected to a hogging moment as in still water.
Astride the wave hollow, the ship is subjected to entirely
different conditions ; at both bow and stern there is an excess of
buoyancy of about 690 tons, and amidships an excess of weight
of 1380 tons. Tlirouirhout the length sao-ofine: strains have to be
resisted ; and the maximum sagging moment, borne by a trans-
verse section near the middle of the length, is about 71,800
foot-tons.
Ships of the Devastation type gain upon the Minotaur class
when placed upon the wave crest, because the added buoyancy
amidships is well situated in relation to the concentrated weights
there placed. Hogging moments are then experienced through-
out the length, but they are of moderate amount as compared
with those for the Minotaur type. When the Devastation floats
on a wave of her own length (300 feet by 20 feet high) — a
proportionately steeper wave than that assumed for the Minotaur
— the weight and buoyancy are distributed as follows. First
37 feet from the bow, weight 130 tons in excess ; next 34 feet,
buoyancy 90 tons in excess ; next 35 feet (under fore turret),
weight 580 tons in excess; next 84 feet (in wake of wave crest),
buoyancy 940 tons in excess ; next 22 feet, weight (under after
turret) 160 tons in excess; next 37 feet, buoyancy 260 tons in
excess; and thence to the stern, weight 420 tons in excess. This
case is more complicated than that of the Minotaur type, just as
it has been shown to be in still water. But the resultant bendino^
moments are far less severe ; the maximum hogging moment
amidships in the Devastation is only one-fourth (36,800 foot-tons)
that in the Minotaur.
The most critical case for the Devastation type is that when
the ship lies astride a wave hollow, as in Fig. 88. The substitution
of the wave profile for the horizontal surface of still water ex-
aggerates the excesses of weight amidships, while the immersion
of the extremities in the wave slopes decreases or does away with
any excess of weight existing there in still water. The lowness
of the freeboard in the Devastation helps the ship in this critical
position ; t!ie wave slopes cover the extremities of the upper
deck, the ship sinking bodily deeper into the wave than if she
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS.
297
had a lofty bow and stem like the Minotaur ; consequently there
are less excesses of buoyancy at the extremities, as well as less
sa-io-ino- moments amidships. The actual distribution of the
weight and. buoyancy in this position may be summarised,
ns follows. The first 80 feet of length from the bow, buoyancy,
920 tons in excess ; the first 95 feet of length from the stern
buoyancy 880 tons in excess ; on the midship length of about
135 feet, weight 1800 tons in excess. These are considerable
quantities, but compared with the corresponding figures for the
Minotaur on a wave crest, they appear moderate. The resultant
maximum sagging moments in the Devastation, experienced by a
section near the middle of the length, is 51,000 foot-tons ; about
(ico-thirds the corresponding sagging moment for the Minotaur,
and a little over one-third the maximum hogging moment for that
ship.
It has been previously remarked, that the fairest comparison
is that which expresses the bending moments as a fraction of the
product of the weight (W tons) into the length (L feet). As a
summary of the foregoing remarks the following table is given.
Maximum Bending Moment.
Minotaur.
Devastation.
On wave crest — hogging
In wave hollow — sagging
In still water
2^8 X W X L
513-XWXL
ffVxWxL
(Hogging)
^\ X ^^' X L
ihxWxL
J xWxL
( 0
(Sagging)
Allusion has been made to the great rapidity and magnitude
of the changes of strain to which ships are liable in a seaway,
and the statement may now be illustrated. From the time that
the Minotaur occupies the position shown in Fig. 87 to the instant
when she may lie across the hollow as in Fig. 88 will be an interval
of only 4^ seconds ; the straining actions at the commencement
of that brief interval tend to hog the ship with a moment of 140,000
foot-tons, while at its end their character has undergone a complete
change, and they produce a sagging moment of 74,800 foot-tons.
The sum of these quantities — say 215,000 foot-tons — may be
taken as a measure of the change of bending moment occurring
about once in every 4^ seconds. In the Devastation, owing to
her less length, the time interval between the two extreme posi-
tions will be less than 4 seconds ; the bending moment changing
Irom 37,000 foot-tons (hogging) to 51,000 foot-tons (sagging), the
298 NAVAL ARCHITECTURE. chap. viii.
sum of tlie two being about 88,000 foot-tons, or considerably
below one-half the corresponding sum in the Minotaur. As
between the two ships, the difference is very important; but it
Mill be understood that the present intention is rather to deal
with types and general principles than with particular ships.
These principles apply, moreover, with equal force to unarmoured.
vessels of war or to non-combatant vessels.
In the following table have been grouped the results of a
number of calculations for the bending moments of different
classes of ships. The \vaves assumed in each case have had
lengths equal to the lengths of the sliips; but it will be observed
that the ratio of heights to lengths of waves differ considerably
in the various examples, thus rendering an exact comparison im-
possible. Apart from such a comparison, however, the figures
will have an interest as illustrations of the singular differences
existing between the character and magnitude of the still-water
bending moments of various types of ships, and the contrast
between those still-water strains for a particular ship, and the
strains on a wave crest, or astride a wave hollow. So far as cal-
culations have yet been carried, the types represented by the
Minotaur and the Victoria and Albert lie at opposite extremes
amongst sea-going ships, the one having an exceptionally high
hogging moment on a wave crest, while the other sustains a very
large sagging moment when astride a wave hollow. Proportion-
ately higher bending moments are mentioned for the light-
draught merchant steamer in the table ; but that vessel was built
for river service, and was simply making a passage out to her
station when she failed under the strains recorded against her
name. For sea-going ships, so far as can be seen at present, the
maximum bending moment (in foot-tons) is likely to fall below
one-ttventieth of the product of the weight of the ship into her
length, if .the ratio of height to length assumed for the waves
does not exceed 1 to 15. Cases may be met with where the
maximum bending moment, estimated in the manner desciibed,
may exceed the limit named, because of some exceptionally
trying distribution of the load; and it is obviously very difficult
to assign the worst possible conditions of lading to any merchant
ship.
It will be evident that changes in the ratio of the height to the
length of the waves, upon which a given ship is supposed to float,
will produce corresponding changes in the bending moments.
Taking, for example, the position illustrated by Fig. 87, it will be
evident that an increase in the height and steepness of the waves
CHAP. VIII. ST/:.l/yS EXPERIENCED BY SHIPS.
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300 NAVAL ARCHITECTURE. chap. viii.
is likely to be accompanied by an increase in the hogging
moment. Tn comparing ships, therefore, it is important to treat
them simihirly as regards the character of the waves assumed in
making estimates for the bending moments. From the facts set
forth at page 19G as to the ratios of height to length in waves, it
appears that the following values of that ratio may be accepted
as fair averages in calculations of strains :
For ships below 300 feet in length . . 1 : 20.
For ships above 300 feet in length . . 1 : 25.
Greater ratios of height to length may occur, as before stated,
but they are of much less frequent occurrence than the average
ratios recommended for use.
All the forefroino; estimates of the relative distribution of the
weight and buoyancy have been made on the supposition that the
ship is upright ; but it commonly happens that, in a seaway,
a vessel rolls through large angles, while subjected to longitudinal
bending strains. Such inclinations from the upright necessarily
affect the distribution of the buoyancy along the length, and
without actual calculation it is not possible to ascertain how these
changes may affect the bending moments. It is, however, worthy
of note that the hypothetical cases in Figs. 87 and 88 represent
a ship bow-on to the waves ; the position in which she is likely
to roll comparatively little. On the other hand, if she is broad-
side-on, or nearly so, to the waves, and rolls considerably in con-
sequence, the wave form occupies a position relatively to her
length far less likely to cause such unequal distribution of the
weight and buoyancy as is assumed in Figs. 87 and 88. When
the ship lies obliquely to the waves, another kind of strain is
developed concurrently with longitudinal bending ; viz. the
twisting tendency, produced when the bow is lying on the slope
of one wave and the stern on that of the next wave, the fore
and after parts of the ship being subject to forces tending to heel
them in opposite directions. But all tliese are mutters which
should influence the structural arrangements in a degree
subordinate to that of the considerations which have received
most attention in this chapter ; and they are mentioned here
chiefly because in the following chapter some notice will be
taken of the manner in which the shipbuilder provides strength
to resist them.
Although in the accepted method for comparing the longitu-
dinal bending moments of ships no attempt is made to estimate
the effects of the accelerating forces incidental to the heaving and
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 301
pitching motions impressed upon ships by waves, the possible
importance of these effects is not overlooked. Matliematical
equations may be formed expressing the magnitude of the strains
proJuced at any instant by pitching; but they include so many
quantities which are unknown, or only partly known, that exact
estimates cannot be based upon them. Certain fundamental
principles may, however, be mentioned. The accelerating forces
attain their maximum value when a ship reaches the extreme of
a pitching oscillation, and is for the instant at rest. Their effect
may be simply expressed by the stitement that they tend to
make the extremities of the ship go on moving in the direction
in which tliey were moving before the motion ceased. For
example, the bow of a ship moves downwards when pitching, and
when the extreme of the pitch has been rea'-hed the accelerating-
forces tend to make the downward motion continue; that is to
say, having regard to the longitudinal distribution of the fluid
resistance which stops the downward motion, those forces usually
tend to produce hogging strains in the fore part of the ship.
The magnitude of the accelerating forces increases as the ampli-
tude of the oscillation increases, and as the period of oscillation
decreases. A quick-moving ship is likely to be more strained in
pitching than a slow-moving ship for a given amplitude of oscil-
lation; and it will be remembered that when the slow motion is
accompanied by increase in size, the amplitude of pitching is
likely to be decreased (see remarks on page 254). Nor does it
suffice to consider only the influence of the accelerating forces
upon the bending moments when a ship is pitching among waves.
The longitudinal oscillation gives rise to a variation in the dis-
tribution of the weight and buoyancy additional to that produced
by the passage of the wave profiles. At one instant the bow may
be buried deeply in the wave slope, and soon after it may be
almost out of water, the immersion and emersion depending upon
the relation between the wave motion and the longitudinal oscil-
lations of the ship. Furthermore at every instant except when
the extremes of an oscillation are reached, the fluid resistance to
pitching brings into play upon the ship reactions which must
sensibly affect the bending moment. And finally the heaving
motion which accompanies the pitching must cause variations in
the bending moment by causing variations in the " virtual
weight " (see page 186). This summary of the difficulties in the
way of an exact solution of the problem is not put forward as a
reason why further attempts should not be made at its solution ;
but simply as an indication of the reasons which have led to thj
302 NA VAL ARCHITECTURE. chap. vni.
adoption of a method of comparison based upon a statical hypo-
thesis and confessedly imperfect.
The best authorities at present agree in taking the exceptional
positions illustrated in Figs. 87 and 88 as affording fair compara-
tive measures of the maximum longitudinal bending strains
experienced by ships. Some writers, including tlie late Sir W.
Fairbairn, have, however, suggested the propriety of giving to
all ships strength sufficient to resist the far more severe bending
strains produced when vessels are aground and supported only at
the middle of the length, or at the ends. The advantage of
adopting such a standard may well be questioned, seeing that
the theoretical conditions of support — viz. Concentration of the
support at 'points along the length — are never likely to be
fulfilled, and rarely, if ever, approximated to. Many ships have
grounded, no doubt, and rested either at the middle part only
or else only at the ends; but a certain distribution of the
support has even then been secured^ and in nearly all such cases
the vessels have remained partially water-borne. Moreover,
accidents of this kind are of rare occurrence to any ship, and
are entirely escaped by the great majority of vessels; besides
which it must be remembered that failure or serious dama^-e ia
grounding, &c., is far more likely to result from excessive local
strains than from bending strains experienced by the ship as a
whole. The bottoms of ships crush up, or are much damaged,
very frequently before the structural strength against bending
strains is over-tasked. On the whole, therefore, the generally
accepted method which deals with ships afloat appears very much
snperior to the alternative proposal, based upon the condition of
ships ashore. There are a vast number of ships which have
been many years afloat on active service, and have displayed
no signs of weakness, which would utterly fail under the condi-
tions which Sir W. Fairbairn and others would have imposed; for
it appears that, in the extreme cases of support ashore, the
maximum bending strains reach from four to six times the
maximum strains incidental to the extreme cases of support
amongst waves. In some of these vessels, no doubt, the best
distribution of material has not been made, and mucli greater
longitudinal strength might be secured by improved arrange-
ments without increase in the total weights of hull ; but in most
cases it v\ould appear an unnecessary and uneconomical plan to
provide a large reserve of strength to meet a contingency that
may never be encountered, and which would necessitate heavier
hulls and decreased carrying power.
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 303
Only a few cases cau be given, from the many that might be
quoted, where vessels have grounded in a tideway and been l^ft
unsupported for considerable parts of their lengths, or have stopped
in launching and been suspended in exceptional positions. The
well-known case of the Northumherkond, which stopped on the
launchiug ways at Millwall ia 1866, and remained for a month
with one-eighth of her length unsupported, may be mentioned,
because it has been thoroughly investigated ; even this exceptional
position did not develop such severe bending strains as would
result from suspension on the wave crest. Had the ship been
supported only at the middle, the case would have been very
different ; as it was, the ship maintained her form unchanged. A
similar and more recent case is that of H.M.S. Neptune which
sto))ped on the launching ways ; her bottom crushed up, owing
to the concentration of the support near the middle of the length,
but the sheer was unbroken, and no serious damage done to the
structure. Very different from the condition of these iron ships
was that of the wood line-of-battle ship Gsesar, which stopped in
launching at Pembroke in 1853, and remained a fortnio^ht with
64 feet of the stern unsupported by the ways ; her stern dropping
no less than 2 feet in 90 feet. Lastly, as a converse case, we may
refer to the Prince of Wales, an iron steamer, which was left for
some time, owing to an accident, supported at the ends only, her
bow on the edge of a wharf, and her stern in the water ; she also
was uninjured. In none of these instances were the extreme con-
ditions of suspension at the ends or middle realised, nor are
they likely to be so.
In concluding this part of the subject, it is desirable to
glance once more at the conditions of strain in ships subjected
to longitudinal bending moments; for the character of such
strains is not affected by changes in the magnitude of the bend-
ing moment ; the intensity of the strains is alone affected. When
a ship hogs, the ends dropping relatively to the middle, the upper
parts of her structure tend to become stretched, i.e. they are
subjected to tensile strains, while the lower parts are subjected
to compressive strains ; and somewhere near the middle of the
depth there is a part of the structure subjected neither to tensile
nor compressive strains. Conversely, when a ship astride a wave
hollow is subjected to sagging moments throughout her length,
the lower parts are subjected to tensile strains, and the upper
parts to compressive strains, the parts near the mid-depth again
being free from strain. These two cases are practically of the
greatest importance, because the strains of all classes of ships,
304
NAVAL ARCHITECTURE.
CHAP. VIII.
\vheii floating amongst waves, may be grouped under them, no
matter what the still-water distribution of weight and buoyancy-
may be, and the wave-water strains are considerably greater than
the still-water strains. It is worthy of note, however, that, when
a ship is subjected ff)r a portion of lier length to hogging strains,
and for the remaining portion to sagging strains — a condition
exemplified by the Devastation in Fig. 86 — then the upper decks
and top sides of those parts subjected to hogging moments tend
to stretch, whereas they are subject to compressive strains at the
parts subjected to sagging moments. At those athwartship
sections of such a ship corresponding to the points cc in Fig.
'^'o, where the curve of moments MMM crosses the base-line AB,
no bending moments exist, and consequently there is no develop-
ment of either tensile or compressive strains. Tliese general
considerations must suffice for the present ; in the following
chapter we shall investigate more fully the character and
magnitude of the strains resulting from longitudinal bending
moments, as well as the manner in which these strains are
resisted by the structure of a ship.
Attention will next be turned to the causes and character of the
chief strains tending to produce changes in the transverse forms
of ships.
The most severe transverse bending likely to be experienced
by a ship at rest is that resulting from grounding or being docked.
Fig. 89 will illustrate this case. Suppose that, for an instant, the
vessel is wholly supported
FIG89
on her keel ; then the
blocks or the ground must
furnii-h an upward pressure
to balance the total weiglit
of ship and lading, and this
is indicated in the diagram
by 2 W acting vertically.
Considering each side of
the ship to bear an equal
load, the total of hull and
lading for one side of the
ship is W, a downward
pressure acting through g, the centre of gravity of the hull
and lading of that side. The transverse distance of g from the
longitudinal middle plane of the ship depends, of course, on the
distribution, in a transverse sense, of the weights carried. If these
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 305
weights are placed centrally, g will lie much nearer to the middle
plane than if the weights are ''' winged " — carried far away from
the middle. For instance, in an armoured ship several hundred
tons of armour may be carried on the broadside, and a great
weight of coal in the wings ; in which case g will lie far out. On
the other hand, a merchant ship may have her cargo — say of
rails or heavy materials — stowed almost at the centre, along over
the keel; in which case g will lie near the middle plane. When
the distribution of the weights is known, the position of g
can be determined ; the transverse bending moment will (under
the conditions assumed) equal the product of W into the distance
of g from the middle plane. This moment tends to make the
bilges drop relatively to the middle, and to break off the ribs of
the ship at the middle line, but before actual deformation takes
place the deck-beams and plating on the decks must be brought
into tension, and will effectually assist the lower parts of the
structure in resistino: change of form.
This is an extreme case, not often realised perliaps, but some-
times occurring. A ship left aground by the retreating tide is
either likely to remain partially water-borne or else, when left
high and dry, she will *' loll " over and rest on one of her bilges as
well as on the keel. A ship, when docked, is generally sup-
ported by shores as the water leaves her; so that the upward
pressure from the blocks is not equal to the total weight, nor
is the transverse bending moment nearly so severe when the
shores take part of the weight. It is, however, certain that ships
in dock, especially wood-built ironclad ships, require to be very
carefully supported by shores, in order to prevent changes of
transverse form ; and many cases are on record where such
changes have actually taken place. The converted ironclads of
the Eoyal Navy have, for example, been found to " break "
transversely when in dock, even when well shored; and it has
been suggested to use bilge-blocks in order to lessen the strains.
Such blocks have been used for this purpose, both in this country
and abroad, in vessels of unusual form. The American monitors
are said to be thus supported when in dock ; and the flat-bottomed
floating batteries built for the Royal Navy during the Crimean
War were docked on bilge as well as central blocks. The reduc-
tion of transverse bending strains by these special supports is
easily explained ; for instead of an upward pressure W at the
middle line and the downward force W forming a couple, the
resultant of the pressure on the keel-blocks and bilge-blocks will
necessarily lie some distance out from the middle and closer to
the line of action of the downward force W. x
3o6
NAVAL ARCHITECTURE.
CHAP. VIII.
Ships afloat and at rest in still water are not usually strained
80 severely as vessels supported on the keel only; for a reason
very similar to that just
FIG. 90. given. Fig. 90 illustrates
this case. Taking one half
the ship separately, its
weight W acts through </,
as before explained ; but
the support W is now
furnished by the buoyancy
of that half of the ship
acting upwards through
h, the centre of buoyancy
for that half. Probably
the case illustrated in the diagram is the most common, g lying
further from the middle than h ; but in some ships with great
weights of cargo stowed centrally over the keel, it is conceivable
that the relative positions of g and h may be reversed, g lying
nearer to the middle of the ship.
The horizontal fluid pressures also contribute towards producing
changes of transverse form. The pressures P, P in Fig. 90 are
equal and opposite when the ship is at rest, but, as she is not a
rigid body, or a solid, she tends to become compressed by the
equal and opposite pressures. This is a parallel case to that
given before for longitudinal bending strains ; only here the
pressures are much greater than for longitudinal strains. For
example, in the Minotmir the longitudinal pressures amount to
about 400 tons, whereas the transverse pressures would amount to
about 3500 tons. Tlie transverse pressures PP may be consi-
dered to act along lines at a depth below water equal to about
two-thirds of the mean draught when the ship is upright.
When she is inclined, similar, but possibly more severe compres-
sive strains will be caused by the fluid pressures, the tendency
being to force the bilges inwards, and thus to distort the trans-
verse form.
The most marked indications of these compressive strains are
usually to be found near the extremities, where the sides are flat
and nearly upright. Many instances have been noted where
" panting," as it is termed, has taken place in those parts of
badly constructed ships, the sides moving in and out under
varying conditions. Such changes of form are, however, very
easily prevented by simple structural arrangements, as will be
shown further on.
Kolling oscillations lead to a great increase in the strains
CHAP. viil. STRAINS EXPERIENCED BY SHIPS. 307
tending to alter the transverse forms of ships. This will be
obvious, from the remarks previously made respecting the ac-
celerating forces developed during rolling, and the changes in
magnitude and direction which these forces undergo during the
motion.* When the
period and range of the A
oscillation are known, /^""^^^^^^^^^^^^ii^-^
and the conditions of >^^^~^^^T^^^^^^^:^^=;^- 6
statical stability have /y^-^^^^^^^^^?!^;^^^ """^^^^^^''
been ascertained for the ~~~''«^^-^^^^^?5?ir-^ ^*^^^^^^^^^S^/
ship, it is possible to -'/7^^~^~~~---^^^^'/^^*^^^^
approximate to the rack- ^^^Sri:;':I^^?t^^^^^--,,~"^^^'"^^/^^=
ing strains produced J^VVV' J ~^^"'^^=^^yr~--~
by the accelerating '^^<S> / ^'W/
forces; but their general '^^'^*^^!!;2?'?^^^::ilIZii^'-^^
character can be under- ~ c
stood apart from cal-
culation. Keferring to Fig. 91, the cross-section of a ship will
be seen in an inclined position, representing the extreme angle
of heel attained when rolling. When the motion ceases, the
accelerating forces reach their maximum value, and their straining
effect is greatest. This straining action tends to distort the form
of the transverse section as indicated in a greatly exaggerated
form, by dotted lines, changing from ABCD (draivn lines) to ahcd
(dotted lines). At the angle B there is a tendency to make the
inclination of the deck to the side an acute angle; on the
opposite side, at A, there is a tendency to make the corre-
sponding angle obtuse. At the bilges corresponding changes are
indicated ; the general character of the change may be described
as resulting from the tendency of the parts to keep moving on in
the direction in which they were moving before the maximum
heel was reached. Experience fully confirms the theoretical
deduction, that rolling motion develops straining forces tending
to change the angles made by the decks with the sides. In
wood ships, working at the beam-arms is very common during
heavy rolling at sea. Beam-knee fastenings work loose, and
other indications of strain or working occur. At the bilges also
in wood-built steamships, working sometimes takes place during
rolling, and unless precautions are taken, pipes, &c., will be
broken at the joints, or disturbed by the change of form ; in fact,
the attention that has been bestowed by practical shipbuilders
See page 232.
X 2
308 NAVAL ARCHITECTURE. chap. viii.
upon beam-knees and other fastenings intended to secure rigidity
of transverse form can scarcely be paralleled from any other
part of the structure.
The racking strains produced by rolling have their effect
greatly enhanced by the changes in direction and intensity
occurring during each oscillation; and hence it is that the range
of oscillation as well as the period are such important elements in
a comparison of the transverse racking strains experienced by
two ships. Allusion lias already been made to this in discussing
the behaviour of ships at sea, but it is desirable to further
illustrate the matter, and for this purpose it is necessary to
make use of an approximate rule for the maximum value of
these racking strains. The late Professor Eankine, whose labours
in connection with naval architecture were worthy of his high
reputation in other branches of research, proposed such an ap-
proximate rule, which is as follows : — •
c Righting moment for
Moment ol racking JJ" '^ . ° i i .
° 1' = -j=r;5 VTT-^ \ maximum heel at-
forces . . . . J D--fB^ j ^^j^^^^^
where D = total depth of ship from upper deck to keel,
B = breadth of ship.
Applying this rule to two typical ships, one having a short
period like the Prince Consort class, and another having a long
period like the Hercules class, a remarkable contrast becomes
apparent. Actual observations show that the Hercules only rolled
15 degrees on each side of the upright when a converted ironclad
was rolling 30 degrees each way. Suppose these figures to be used.
For these two vessels, the respective values of B and D are
approximately equal, the ratio y,, i f)2 being about 1 to 3 for
each ship. Assuming this ratio to be used, it is found tliat the
moment of racking forces at the extreme of the heavy roll of the
Prince Consort would be about 7000 foot-tons, and the correspond-
ing moment at the extreme of the moderate heel of the Hercules
would be about one-third as great. The Prince Consort has a
j)eriod of about 5 seconds ; consequently, twelve times every
minute a racking moment of the amount stated will be acting
upon her structure, and at intervals of 5 seconds the distortion
will tend to take place in opposite directions. In the Hercules,
with a period of about 8 seconds, a racking moment less than one-
third the amount of that in the Prince Consort will be acting
only seven times every minute, and the tendency to distort will
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 309
chano-e its direction at intervals of about 8 seconds. The less
frequent change of strain and the diminished moment tell greatly
in favour of the slower-moving and steadier ship. What has here
been shown to hold good for particular ships holds good also for
ships in general. Lengthening the period of still-water oscilla-
tions not merely makes ships steadier in a seaway, but greatly
reduces the effect of strains tending to produce changes in the
transverse forms, or damage to the masts and rigging. Deep-
rolling ships are also the quickest in their motions, and require
the greatest strength in hull and equipment.
Hitherto investigations of the forces tending to produce changes
of transverse form in ships have been, for the most part, of a
qualitative character. Estimates of the magnitude of these forces
in different classes of ships are almost entirely wanting ; and no
data are availible for transverse strains, similar to the figures for
longitudinal bending moments given in the table on page 299.
Probably greater attention might, with advantage, be given to
the consideration of transverse strains, and it is to be hoped that
the subject will receive the consideration it deserves now that the
character and amount of longitudinal bending moments have been
so fully investigated.
Little need be said respecting the strains produced by the pro-
pelling apparatus upon the structure of a ship considered as a
whole, although this third class of strains is by no means unim-
portant. When a ship is propelled by sails, the effective wind
pressure may be resolved into two parts : one acting longitudi-
nally and constituting a " thrust " which propels the vessel on her
course; the other acting transversely, producing leeway and an
angle of steady heel. When the motion of the vessel is uniform,
the longitudinal thrust exactly balances the fluid resistance to
the motion ahead ; the thrust and resistance form a mechanical
couple ; and the " centre of effort " of the sails, where the
resultant thrust may be supposed to be delivered, will be at a
crreat heio-ht above the line of action of the fluid resistance.
This couple by its action naust produce two effects on the ship :
first, a change of trim — deeper immersion by the bow — corre-
sponding to its moment ; * second, a longitudinal racking action
upon the structure of the ship. The character of this racking
action may be simply illustrated by taking a rectangular frame
* For the principles upon which the calculation of this trim would be based,
see Chapter III. ; for a discussion of propulsion by sails see Chapter XII.
3IO
NAVAL ARCHITECTURE.
CHAP. VIII.
formed of four pieces of wood, joined to one another at the
angles, and supposing either pair of its parallel sides to be acted
upon by forces equal in magnitude, but opposite in direction.
Obviously, the rectangle would become distorted into a rhom-
boid, unless the connections were very strong ; but by means of
a diagonal tie, like that on an ordinary field-gate, this racking
or change of form may be very easily prevented. The corre-
sponding tendency in ships is also unimportant, because of the
large reserve of structural strength to resist such strains.
Similar considerations hold
good for the strains produced
by the transverse component
of the wind pressure. When
the drift to leeward has become
uniform the fluid resistance will
supply a lateral resistance (P
in Fig. 92) equal and opposite
to the transverse component of
the wind-pressure. Under the
action of this couple the vessel
will heel steadily to an angle
for which the righting moment
equals the moment of the in-
clining couj)le (see page 75).
At the same time a transverse
racking strain will be brought
into action on the structure of
the ship. The shrouds on the
windward side will be taut,
and have a tension (T Fig. 92)
brought upon them, which ten-
sion will be governed by the force
of the wind-pressure (P), the angle of heel of the ship, the over-
hanging weight of the masts, rigging and sails, the angle between
the shrouds and the mast, and the stiffness of the mast to resist
deflection under pressure. This tension also gives rise to a thrust
delivered by the mast upon its step (Q Fig. 92) ; and the united
action of these forces tends to produce an alteration in the trans-
verse form. Professor Rankine estimated the probable maximum
bending moment of these forces at one-half the moment of statical
stability corresponding to tlie angle of steady heel ; and if this
estimate be accepted, as it is reasonable to do, it will be seen that
the transverse racking moment for a steady pressure of wind is so
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 31 I
small in amount as to be practically unimportant in its effect upon
the ship considered as a whole. If the wind acts on the sails in
gusts or squalls the straining effect will be much increased ; and
when to this irregular action of the wind is added the influence of
the accelerating forces incidental to the rolling or lurching of
ships among waves, it is evident that great and variable strains
may be brought upon the structure of a sailing ship, of which the
amounts are not easily ascertainable. Experience proves, how-
ever, that when damage occurs under these circumstances it is
usually of a local character : as for example, a failure in the con-
nections of the shrouds to the ship at the channels and chain-
plates, or a disturbance of the deck near the wedging to the
masts. And with these local strains we are not at present
ccncerued.
With steam as the propelling agent, the case is simpler tlian
with sails. The thrust of the propeller will usually be delivered
in the direction of the course of the ship, and will therefore have
no transverse component ; moreover, the line of action of that
thrust will lie very much closer than it does with sail power to
the line of action of the fluid resistance. When the screw is
employed, the line of thrust for the propeller approximates to
coincidence with the line of action of the resistance ; and when
paddles, or jet propellers, are used, the thrust is delivered at a
comparatively small height above the line of action of the
resultant resistance. It is unnecessary, therefore, to add any
further remarks on this part of the subject, the ship considered
as a whole being but little strained by the propelling apparatus.
The last class of strains to be considered are those grouped
under the head of local strains in our classification. Of these,
there is such a great number and variety that an exhaustive
treatment of the subject will scarcely be found in works on ship-
building ; and all that can be done in the present sketch is to
select a few of the principal types, indicating the causes and
character of the strains. As a matter of convenience, we sliall
adjoin, in each case, a brief account of the arrangements by
which the strain is prevented from producing local damage or
faihire.
At the outset it may be well to note that the same circum-
stances which have already been mentioned as producing strains
upon a ship considered as a whole may and do produce severe
local strains. For example, a heavy load concentrated in a short
length, not merely contributes to the longitudinal bending
312 NA VAL ARCHITECTURE. chap, viii,
moment previously described, but also tends to push outwards
that part of the bottom upon which it rests. Similarly, the
thrust of a screw propeller not only tends to rack tlie ship as
a whole, but produces considerable local strain on that part of
tlie ship to which the " thrust-bearer " is attached. Again, the
downward thrust of a mast, besides tending to alter the transverse
form of the ship as a whole, produces a considerable local strain
on the step, and on the frame of the ship which carries the step.
And these are only a few illustrations of a general principle.
When the ship is treated as a whole, it is virtually assumed, that
these local strains have been provided against ; so that the
various parts of the structure can act together and lend mutual
assistance. As a matter of fact, however, it is not at all un-
common to find local failure supervening long before the limit of
the strength of a ship considered as a whole has been realised.
The case of the Neptune, previously quoted, well illustrates this ;
when she stopped in launching, her general structural strength
was ample even against the severe bending moments experienced ;
but while her longitudinal form remained almost unchanged, the
very exceptional local strains on a small portion of the bottom
forced it inwards, disturbing the decks, &c., above it. Many
similar examples might be added, but enough has been said to
show how important it is to provide carefully against local strains
in arranging the structure of a ship.
One of the chief causes of local straining has already been
mentioned ; viz. a great concentration of loads at certain parts
of a ship; and the converse case is also important — that where
there is a great excess of buoyancy on a short length. Examples
have been given of such concentration of loads ; one of the most
notable is that for the Devastation, in wake of the turrets (see
Fig. 85), where there is an excess of weight over buoyancy
550 tons on a length of about 30 feet. Still more concentrated
is the load of armour on a battery bulkhead, weighing perhaps
GO or 80 tons, and lying athwartships. Immediately in wake of
such concentrated loads the bottom tends to move outwards from
its true shape ; the local strain which is developed tending to
produce simultaneously both longitudinal and transverse change
of form. Many similar causes of straining will occur to the
reader ; it is only necessary to mention the cases of a vessel
with a heavy cargo, like railway iron, stowed compactly, or of
a vessel with heavy machinery carried on a short length of the
ship, or of the parts adjacent to the mast step of a sailing ship.
Surplus buoyancy on a ship afloat is not usually found so
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 313
much concentrated as surplus weight ; but in some instances the
excess of buoyancy produces a considerable local strain tending
to force the bottom upwards for a portion of the length. Lateral
pressures as well as vertical pressures require to be provided
against, especially near the extremities of ships.
To prevent local deformations of the bottom in wake of excesses
either of weight or buoyancy, the shipbuilder employs a very
simple and well-known device. The concentrated load or support
is virtually distributed over a considerable length by means of
strong longitudinal keelsons, bearers, &c. In not a few cases
these longitudinal pieces are additions to the main framing or
structure of the ship ; in other cases they form part of the main
structure, being effective against the principal strains as well as
against local strains. The latter plan is preferable, where it can
be adopted, favouring, as it does, lightness and simplicity of
construction. These longitudinal bearers and strengthenings can
only distribute loads or pressures when they are individually
possessed of considerable strength ; and to be efficient they must
be associated with structural arrangements which provide ample
transverse strength (such as complete or partial bulkheads, strong
frames, &c.), and form points of support to the longitudinals.
Frequently the longitudinals must be continued through a length
sufficient to connect and secure the mutual action of parts where
there is an excess of weight with others where there is an excess
of buoyancy. But in very many ships, and especially in iron
ships, there are cross-sections, like those at bulkheads, where
alteration of the form is scarcely possible. In such cases the
bearers distributing a concentrated load or pressure frequently
extend from one of the strong cross-sections to the next: just
as the girders of a bridge extend from pier to pier, and, if they
are made sufficiently strong, can transmit a concentrated load
placed midway between the piers to those supports without any
sensible change of form.
The Great Eastern furnishes a good example of the last-
mentioned arrangement. In the lower half of her structure there
is very little transverse framing. Xumerous and strong trans-
verse bulkheads supply the strength requisite to maintain the
transverse form unchanged. Strong girders, or frames, extend
longitudinally from bulkhead to bulkhead, and transmit the
strength of the bulkheads to the parts lying between them.
Arrangements of a similar, but not identical, character are also
made in the ironclad ships of the Royal Navy, and in merchant
ships built on the cellular system (see Chapter IX.). The engine
3r4 NAVAL ARCHITECTURE. chap. viii.
and boiler bearers in many iron steamers are also arranged on
this principle.
Vessels with few transverse bulkheads, or with none, have
strong keelsons, binding strakes, stringers, and other longitudinal
strengthenings on the Hat of the bottom below the bilges, these
pieces distributing loads and adding to the strnctural strength.
This is the common arrangement in wooden ships of all classes,
as well as in iron sailing ships. Kecentl}', however, in the wood-
built ships of the Royal Navy and the French navy iron bulk-
heads have been constructed, and, in some cases, iron bearers and
keelsons have been fitted. The wood-built American river
steamers furnish curious illustrations of the connection of parts
of a ship having surplus buoyancy with others having surplus
weight. Besides strong longitudinal keelsons, the builders have
recourse to the " mast-aud-guy " system. Poles or masts are
erected at parts of the structure having surplus buoyancy;
these masts are stepped upon strong timber keelsons. Chain
or rod-iron guys are then secured to the heads of the masts and
connected at their lower ends to parts of the vessel where con-
siderable weights are concentrated, thus hanging these parts on,
as it were, to the buoyant parts. In this fashion, the long fine
bows and sterns are prevented from dropping ; and, in wake of
the machinery, tendencies to alter transverse form are similarly
resisted. Such arrangements are, of course, only applicable to
vessels employed in smooth water, not subjected to tiie changes
of strain to which sea- going ships are liable. The guy-rods can
transmit tension, but not thrust; and the plan is said to have
answered admirably in these long fine vessels, having great
engine-power and high speed.
Grounding is another cause of more or less severe local strains,
the intensity depending upon the amount and distribution of
the supports. Very concentrated supports, as has already been
shown, may crush up the bottom ; distributed support such as a
ship obtains when docked or fairly beached produces strains
■which can be easily met. Every provision described above for
giving stiffness to the bottom of a ship is also efficient in help-
ing her when aground. In fact, to these provisions shipbuilders
mainly trust, making few special arrangements against local
strains due to grounding, and these almost wholly at the
extremities. Nor is this surprising, for it is impossible to
foresee all the conditions of strain, or to provide against them,
and such accidents to any individual ship are comparatively rare.
Penetration of the skin of a ship ashore often takes place with-
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 315
out any serious crushing up of the bottom ; and this danger is
of peculiar importance to iron and steel ships, having skin
plating never exceeding an inch in thickness, and in the great
majority of cases less than half that thickness. Sharp hard
substances, such as rocks, will penetrate the plating more readily
than they will penetrate the much thicker bottom of a wood
ship. This superiority of wood ships in sustaining rough usage
ashore without penetration of the bottom is well known ; and
some persons have attached such importance thereto as to
advocate the construction of ships with wooden floors and bottom
planking, but otherwise of iron. The plan has, however, obvious
disadvantaofes, and has not found much favour with ship-
builders, who prefer to accept this occasional disadvantage of irun,
rather than to sacrifice its superiority in other respects to wood.
It is sometimes assumed that iron bottoms are more inferior
to wood in their resistance to penetration than is really the case.
To the experiments of the late Sir W. Fairbairn, we owe more
exact knowledge on the subject than was previously accessible;
in these expeiiments, a few comparative tests were made of the
resistances of wood planks and iron plates to the punching action
of a very concentrated support.* Under the experimental con-
ditions an oak plank 3 inches thick was found equal in resistance
to an iron plate ^ inch thick ; and a 6-inch plank to a plate 1
inch thick. Planking appeared to offer a resistance proportional
to the square of the thickness ; whereas iron plating offered a
resistance proportional to the thickness only. The largest iron
ships have, therefore, bottom plating about equivalent to a 5-inch
or 6-inch oak plank. This would be quite as thick as, or thicker
than, the average bottom planking of large wood ships ; but
within this planking the wood ship probably would have solid
timbers and fillings, forming a compact mass, very difficult of
penetration, the iron ship having no similar backing to the thin
plating. It is therefore easy to see why wooden ships are, as
a rule, capable of standing more of the wear and tear incidental
to grounding than ordinary iron ships with a single bottom. To
attempt to increase the thickness of the bottom plating in order
to meet this comparative disadvantage would be wasteful and
unwise ; the preferable course is to fit an inner skin within the
frames, forming a double bottom. Then, if the outer plating is
broken through, and the inner still remains intact, no water
* See the account of the experiments given in Sir W. Fairbairn's work on
Iron Shipbuilding.
3l6 NAVAL ARCHITECTURE. chap. viii.
enters the hold, and no serious damage ensues, as explained at
length in the first chapter.
Such a cellular construction of the double bottom has a
farther advantage well deserving consideration. Tliin iron or
steel plating, stretching over the spaces between transverse
frames, not unfrequently shows signs of bending or " buckling "
between these supports when subjected to the upward or side-
ways pressure of the water; and this effect may be aggravated
by the strains due to hogging. By means of longitudinal
frames or keelsons running along upon the plating, and
attached to it, buckling may be prevented ; but wlien, in
addition, an inner bottom is worked buckling becomes almost
impossible. The experiments, made before the construction of
the tubular railway bridge across the Menai Straits was begun,
first demonstrated the great advantages obtained by the cel-
lular system applied to wrought-iron structure?, especially in
those parts subjected to compressive strains. Since then the
knowledge of this fact has been made generally useful, both in
ship and in bridge construction.
When a ship sags, the upper deck and top sides are subject
to compressive strains ; to meet these, as well as hogging strains,
more etficiently, a cellular construction of the deck has in some
few cases been adopted. The Great Eastern is a case in point,
to which reference will be made hereafter. Longitudinal sup-
ports are not commonly fitted to decks; the wood planks
usually assisting to prevent buckling in the iron or steel
plating, if any is fitted.
The local strains on the decks of ships constitute another
important group. Very heavy weights are placed upon certain
parts of the decks, resting only upon a certain number of the
deck-beams; and no little care is needed in connecting the
beams with the sides of the ship, arranging the pillars beneath
them, or taking other means to distribute the load. If the loads
to be carried were known, and the kind of pillaring determined,
it would be a comparatively easy matter to fix the dimensions of
the beams required to support the loads. In practice, however,
these conditions are not commonly fulfilled, and the breadth of
the ship amidships, or some other dimension, is had recourse to
in proportioning the sizes of the beams. Special cases occur
especially in war-ships, where the loads to be carried are exces-
sively great, and their positions can be fixed ; as, for example, the
turrets of a vessel like the Devastation, or the gnns in the battery
of a broadside ship. Beams of exceptional strength, or beams
CHAP. viil. STRAINS EXPERIENCED BY SHIPS. 31 7
spaced more closely than at other places, are often employed in
such cases ; but even then it is not sufficient to regard the beams
as girders supporting certain loads, with the assistance of the
pillars. Both beams and pillars, besides meeting these local
strains, have to assist in the maintenance of the transverse
form of the ship, as will be shown in the next chapter. Some-
times it happens, especially in wake of the machinery or boilers,
that it is difficult to fit pillars under some of the beams ; but
these beams are easily supported by longitudinal girders extend-
ing a sufficient distance fore and aft to have their ends upheld by
very strong pillars.
Another class of local strains, of special importance in a war-
ship, are those bronght upon the bows by collision with another
vessel. The importance of ram attacks is now so generally
recognised that the great majority of the ironclad ships of all
navies have been constructed with bows specially designed for
delivering an effective blow upon an enemy witliout receiving
serious damage themselves. Spur-bows, protruding forward under
water in such a fashion as to be able to strike the comparatively
weak bottom below the armour of the ironclad attacked, are those
which find most favour. Whatever may be the form of bow
adopted, it must be made exceptionally strong if it is to suc-
cessfully withstand the shocks and strains produced by ramming.
These strains may be arranged in three divisions : (1) direct
strains, tending to drive the stem and bow bodily backwards
into the ship ; (2) twisting strains, tending to wrench the bow
off when the blow is struck obliquely, or the vessel attacked
has motion across the bow of the ram-ship ; (3) strains tending
to perforate the skin of the ram-bow, resulting from the jagged
parts of the hull of the vessel which has been struck pressing
upon the ram, while the two vessels are locked together, and
while the wrenching just mentioned takes place. Similar
strains act upon the bow of any ship which comes into collision
with another; and unfortunately there are too numerous in-
stances of the truth of this statement in the records of ac-
cidental collisions between vessels of the mercantile marine, or
other ships not built for ramming. In fact, it is to these ordinary
vessels, and not to ships specially designed for ramming, that one
must look for the fullest evidences of the character of the strains
incidental to collision. The bows of many ships have actually
been crushed in ; or the skin has been penetrated ; or wrenching
strains — as in the ill-fated Amazon, of the Koyal Navy — have
been so serious in proportion to the strength of the bow as to
3l8 NAVAL ARCHITECTURE. chap viii.
twist the latter aucl cause the ship to founder. On the other
hand, we have ample evidence that the special arrangements of
ram-bows provide satisfactorily against strains which are fatal
to weaker bows.
At Lissa, the Austrian ram Ferdinand Max, a wood ship with
a strengthened ram-bow, struck and sank the Be d' Italia, besides
making other less successful attacks on other Italian ships ; yet
her bow sustained no serious damage, although it suffered more
than an iron-built ram would have done under similar circum-
stances. The improvised Confederate ram Merrimac sank the
Federal wooden frigate Cumberland at Hampton Roads, but
wrenched her own spur badly in consequence of its faulty
construction, and is said to have been consequently far less
efficient in her subsequent fight with the Monitor. The disas-
trous collision between the Vanguard and the Iroii i)M7i;e_ furnished
one of the severest tests yet put upon the strength of the ram-
bow in one of the modern types of iron-hulled ironclads. To
understand the severity of the test, it is necessary to note a few
facts given in evidence before the court-martial. At the time
of the collision the Iron Diike is said to have been going 1^
knots, her course being six points off that of the Vanguard ; the
direct force of the blow delivered was at least 12,000 foot-tons.
Fig. 26, page 30, illustrates the damage done to the Vanguard,
the armour being driven in bodily and the outer bottom pierced
by a huge hole some 20 or 30 square feet in area. Such a blow,
of course, reacted on the bow of the Iron Duke, tending to drive it
back into the ship ; and meanwhile the Vanguard had a speed
athwart the bow of the Iron DuJce of no less than 6 knots, tiie
motion producing a tendency to twist and wrench the bow, as
well as to perforate the skin. The simple and comparatively
light arrangements of the ram-bow answered admirably when
thus severely tested, subsequent examination proving it to be
so little damaged that the Lvn Duhe could, in action, have
ventured safely on a repetition of the blow, and yet have re-
mained efficient. Much greater damage was done to the ram-
bow of the German ironclad Konig Wilhehn when she came into
collision with the Grosser Kurfurd. A portion of the heavy iron
stem of the former was nearly wrenched out of place, and the
armour and bow-plating, &c., abutting on the stem were consider-
ably disturbed. Although in some respects the structure of tlie
bow of the German ship was inferior to that of the Iron Duke,
the differences in the injuries received are probably chiefly
due to the fact that at the time of collision the Grosser
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS.
319
Kurfurst was crossing the bows of the Konig Willielm at a high
rate of speed.
Figs. 93-95 have been drawn to illustrate the principal
features in the framing of a ram-bow in a ship having a water-
FIG93.
Profile
FIG 94.
Section at A.A.
line belt of armour extending to the bow; and only a few
explanatory remarks will be required. The stem is a solid iron
forging, weighing several tons.
Against direct strains tending:
Detail of ^I'easthook
(TlanatB.£.)
to force it backward, it is supported by the longitudinal
frames or breasthooks (I, I, in Fig. 93), as well as by the armour-
plating, backing, and skin-plating, all of which abut against the
stem. The breasthooks are very valuable supports, being very
320 NAVAL ARCHITECTURE. chap. viii.
strong yet light ; their construction is shown in Fig. 95 ; and the
foremost ends of the decks are converted into breasthooks in a
somewhat simihir manner. Wrenching or twisting strains are
well met by these breasthooks, stiffened as they are by numerous
vertical frames, the details of which appear in Fig. 94, while
their positions are indicated in Fig. 93. Perforation of the skin
is rendered difficult either by carrying the armour low down over
the bow as indicated by the dotted line in Fig. 93 or by doubling
the skin-plating forward below the armour. The former plan is pre-
ferable, being more efiicient against perforation, and also giving pro-
tection against raking fire when engaged bow-on to an enemy ; it
has been very generally adopted of late in the Eoyal Navy, and the
Frencb also favour this plan. Although the transverse framing of
the ram-bow is thus quite subordinated to the longitudinals (/, ?),
it plays an important part in binding the two sides together,
stiffening the breasthooks, and enabling a minute system of
watertight subdivision to be carried out. Even if the outer skin
should be broken througb in ramming, water would find access to
a very limited space, and consequently there would be little or no
danger, and no inconvenient change of trim. Such are the main
features of the ordinary ram-bow in a belted ship.
Recent ships of the central-citadel type are somewhat differ-
ently constructed for ramming. The armoured deck, situated
several feet under water, is the strongest part of the structure
which contributes the greatest support to the spur-bow. These
decks are usually curved downwards at the fore end, for the
purpose of gaining such a depth below water as will enable the
spur to pierce an enemy below the armour. The spur is attached
to the fore end of the deck; by which it is supported most
efficiently against direct and wrenching strains. Subsidiary
supports, breasthooks, &c., are also employed to a small extent ;
and in some cases arrangements have been made by which, if
the spur should become locked in the side of the vessel attacked,
it might actually be wrenched off without any serious damage to
the bow. Perforation of the skin below the armour deck is
provided against by doubling the plating.
Eam-bows in wood ships may be made fairly efficient, but not
so simply or satisfactorily as those of iron or steel ships, the differ-
ence being one inherent in the materials. To make the spur more
efficient, it is usually armed with a sheath of metal or iron.
Massive longitudinal and diagonal timbers are bolted inside the
frames, and associated with iron crutches or breasthooks, to prevent
the stem from being driven in or twisted when a ram attack is
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS. 32 1
made. But even wlien all possible care is taken in fitting and
fastening these strengthenings, the combination can scarcely be
considered satisfactory. Weakness, working, and decay must
affect it, as they do all other parts of a wooden structure.
Kepairs to such a bow must also prove difficult and expensive,
as compared with the corresponding work in an iron-built ram,
where all the parts are easy of access, and easily replaced. These
are, however, matters of detail requiring no further consideration
here, although they have great practical importance.
The superior strength of the bows of iron ships has been
illustrated frequently in the mercantile marine, as well as in war-
ships. Commonly, when collisions take place between two iron
ships, the vessel struck is seriously damaged, perhaps founders,
while the striking vessel escapes with little damage to her bows.
More than thirty years ago, when the Persia, one of the earliest iron-
built Transatlantic steamers, was on her first voyage, she closely
followed the Pacific, a wood steamer, and both are reported to
have fallen in with large ice-floes. The Pacific was lost with
all on board ; the Persia ran against a small iceberg at full speed
and shattered it, but sustained no serious damage.
The last class of local strains to be mentioned are those in-
cidental to propulsion. Some of these have already been alluded
to, viz. the strains connected with propulsion by sails, and those
resulting from the attachment of the thrust-bearer to the hull of
a screw-steamer. To these may be added the strains produced
by the moving parts of an engine, through the bearers to which
they are secured; vibration or working at the stern of screw-
steamers ; strains in wake of the shafts of paddle-steamers ; and
many others. The whole subject is, however, one of detail, re-
quiring to be dealt with during the construction of the vessel by
her builder and the maker of the engines. Here again the
general principle oi distribution 0/ s^ram underlies all the arrange-
ments made. The parts upon which the strains are primarily
impressed must be succoured by other parts of the structure, with
which they must be connected as rigidly as possible. Change
in the relative positions of the various parts cannot occur so long
as the connections are efficient, and without such changes working
cannot take place. Iron and steel are far better materials than
wood for making the connections, and they have been employed
very generally for the purpose, even in wood ships, with great suc-
cess. Vibration may, of course, occur without any absolute working
in the structure; for either the ship as a whole may vibrate to and
fro, or the observer may be deceived as to motion in the structure
Y
322
NAVAL ARCHITECTURE.
CHAP. VIII.
by movements in platforms, or minor fittings forming no part
of tlie structure -regarded as a whole, and incapable of resisting
strains or transmitting them. This distinction is especially im-
portant in vessels of great engine-power and high speed, wherein
vibration, either real or apparent, may be considerable, whereas
there is absolutely no working.
A single illustration of the usefulness of iron strengthenings in
resisting local strains due to propulsion must suffice. Figs. 96-98
contain the details of one of the best examples that could be
chosen ; representing the arrangements at the stern of one of the
wood-hulled ironclads of the Eoyal Navy. Similar strengthenings
have been extensively used in unarmoured wood ships. They
FIG. 96.
were introduced in consequence of the serious working and weak-
ness not unfrequently experienced at the sterns of the earlier
screw steam-ships with good engine-power ; and by their use these
objectionable results have been altogether prevented. Inside the
ship (see Fig. 96) the upper parts of the two stern-posts are cased
with iron plates; the heads of the posts are secured to iron
plating {cc) worked on the upper beams. Between the two posts
an iron knee (bh) is fitted, and strongly secured to the posts and
to the counter of the sliip. With a lifting screw, this knee could
not be fitted, but the screw-well might then be made an efficient
strengthener. Partial bulkheads of iron are built across the stern
at the fore side of the rudder-post and the aft side of the body-
post. The construction of these is shown in Figs. 97 and 98;
CHAP. VIII. STRAINS EXPERIENCED BY SHIPS.
2>^?>
their upper edges are secured to the deck-phiting (cc), while
their outer edges are bolted to the sides of the ship. Change of
form is thus rendered practically impossible at those two sections.
Change in the angle between the counter and the rudder-post
is rendered difficult by the external metal knee a, Fig. 90,
bolted to the post and the counter. Formerly these counter-knees
constituted the main strengthening at the sterns of wood sliips,
and they were very frequently broken in the " throat " by the
working of the post produced by the action of the propeller ; now
such accidents are scarcely known in the Koyal Navy. The
body-post is also strongly connected to the hull by the iron
plating {eld, Fig. 96) under the lower-deck beams, and the
brackets (ee). By these comparatively light and simple additions
of iron strengthenings, what had been previously found an almost
insoluble problem has been satisfactorily dealt with. This is but
one example from the many which any reader interested in the
subject will discover on investigating the details of construction
in various classes of ships.
The local strains incidental to propulsion by sails require to
be carefully guarded against. Masts must have considerable
strength in themselves to resist both the bending strains tending
to break them oif near the upper wedging-deck and the compres-
sive strains due to the thrust produced by the tension of the
shrouds. Strong shrouds, stays or other supports must be asso-
ciated with the masts ; these sliould have as good a "spread " as
possible (i.e. make as large an angle as possible with the masts) ;
and all such supports must be well secured to the hull proper
by chain-plates, channels, &c. Neglect of proper precautions,
Y 2
324 NAVAL ARCHITECTURE. CHAP. viil.
in making extensions of practice beyond the limits of precedent,
have led to accidents, and to the dismasting of many sailing
ships. During the period 1874-77 accidents of this kind were
so numerous amongst iron merchant ships of large size and great
sail-spread, fitted with iron masts, that the Committee of Lloyd's
Eegister of Shipping gave special attention to the matter. Their
professional officers drew up a report which contained a most able
and exhaustive discussion of the strains to which masts and
rigging are subjected, and of their strength to resist those strains.
In this report also appears a summary of the ordinary practice of
the mercantile marine in the equipment of sailing ships : and the
information there given is of no less value than the more
scientific portions of the work. When scientific analysis has
been carried to its limits in this matter, recourse must be had to
the particulars of the masts and rigging of ships which have
borne successfully the strain and stress of service when deciding
on the corresponding features in other ships. This method of
procedure has long been followed in the Eoyal Navy, where the
data as to masting, &c., obtained and tabulated long ago for the
now obsolete classes of sailing ships, have furnished rules for
practice up to the present time, and have made serious accidents,
such as dismasting, almost unknown. Considerable changes have
had to be made in consequence of alterations in the structures or
types of ships ; but where special causes have intervened, special
precautions have been taken. For example, in the Monarch,
where it was desirable to remove all possible obstructions to the
fire of the turret guns, the masts were made of exceptional size
and strength, in order that they might be capable of standing
with fewer shrouds than usual when the ship was cleared for
action. In other ships where the spread of the rigging has been
less than usual, the shrouds have been made exceptionally strong.
Eioid tripod supports to the masts have also been used in a
few rigged turret-ships, in order to secure an increased horizontal
range of fire for the guns. All these variations in practice
have been successfully carried out, by means of a careful
and intelligent adaptation of the experience gained in preceding
ships.
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 325
CHAPTER IX.
THE STRUCTURAL STRENGTH OF SHIPS.
The structural arrangements now adopted in various classes of
ships are the results of long continued development. Their
origin is lost in antiquity, and many of the succeeding steps can-
not be traced. During long periods, under the same conditions,
methods of construction have remained unchanged ; but altered
circumstances and fresh requirements have produced great and
rapid changes. From the canoe hollowed out of a single tree,
or the coracle with its light frame and flexible water-tight skin,
on to the enormous floating structures of the present time is a
very remarkable advance ; but the steps have been gradual, and
not unfrequently unintentional, the full value of a new feature
not being recognised until long after its introduction. The
history of this gradual change and improvement, culminat-
ing in the wonderful progress of the last half-century — into which
have been crowded the development of ocean steam navigation,
the introduction of iron and steel sea-going ships, and the use
of armoured war-ships — constitutes a most interesting field of
study ; but in the present work it cannot be touched. Nor can
the structural arrangements of existing types of ships receive any
detailed illustration, for which the reader must turn to strictly
technical treatises on shipbuilding. It will be our endeavour —
bearing in mind what has been already said respecting the causes
and character of the principal strains to which ships are
subjected — to make clear the general principles governing the
provision of their structural strength. In doing so, it will be
pos^sible to illustrate the distinctive features in the principal
classes of ships, to compare the relative efiiciencies of various
methods of construction, and to contrast the degrees of import-
ance attaching to difl'erent parts of the hull of any ship. All
that will be assumed is that the reader has a general acquaint-
326 NAVAL ARCHITECTURE. chap. ix.
ance with the names of the different parts ; and in most cases
even that extent of knowledge will scarcely be requisite in order
to follow the discus.'^ion.
All ships may be said to consist of two principal parts: (1)
the water-tight skin forming the covering of their bottoms, sides,
and decks, if they have decks ; (2) the framing or stiffening
fitted within the skin to enable it to maintain its form. There
are many ways of forming the skin in differrnt classes of ships ;
some of these will be described. Wood, iron, and steel are the
three materials at present used for the purpose in sea-going ships ;
brass skins have been fitted to some small vessels designed for
smooth-water services. A skin is an essential part of every ship ;
and much care and skill are required in its arrangements.
Vessels have been built with little or no framing ; but these are
not ordinary cases, and probably the greatest varieties of practice
are to be found in the arrangement of the framing, which con-
stitutes a very important element of the structural strength. In
constructing both skin and framing, and considering every detail
of the hull, the shipbuilder should seek most fully to combine
strength with lightness. To do this, he must possess an intelli-
gent acquaintance with the causes and character of the strains
to be resisted, their possible effects upon different parts of the
structure, and the principles of structural strength. He is then
able to choose from among the materials obtainable those best
adapted for his purpose ; he can duly proportion the strength
of the material to the strains on the various parts, massing it
where requisite, or lightly constructing parts subject to little
strain ; and so far as the requirements of convenience and
accommodation, or of fighting efficiency, permit, he can approxi-
mate to an ideally perfect structure, in which each part is
equally strong as compared with the strain it has to beUr. No
structure is stronger than its weakest part ; consequently a bad
distribution of the materials can only be made at the sacrifice
of strength, which might be secured if the material were dis-
tributed more in proportion to the straining forces.
Another important practical matter is that of the connections
and fastenings of the very numerous pieces making up the hull
of a ship. Unless great care is taken, the ultimate strength of
these pieces will never be developed, and the structure may fail
through lack of rigidity, even when it contains an amount of
materials which would be ample if they were properly combined.
The character of these connections must bear an intimate relation
to the qualities of the materials. With wood they are necessarily
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 327
different from what they would be with iron or steel. In fact,
the builder has to consider this feature iu makini^ the choice of
his material ; having regard not merely to the ultimate resistance
of a single 'piece to tensile or compressive strains, but also to the
possibility of making a comhination of two or more pieces efficient
against such strains. Having made his choice, he has to effect
the best possible connections and combinations, often at no small
cost, in order to secure the joint action of the various pieces, and
the rigidity of the structure considered as a whole.
In the present chapter it will be convenient to assume that
the best possible results have been secured by the builder in
each class of ship, and then to investigate their resistances to
the principal bending strains, tending to alter the longitudinal
and transverse form. Local strains have received in the preced-
ing chapter all the attention that can be given them; and in
the succeeding chapter we shall illustrate the capabilities of
wood, iron, and steel as materials for shipbuilding.
The severest strains to which ships are sabjected are those
tending to produce longitudinal bending ; and therefore the
greatest strength is requisite to prevent change of form in that
direction. If the ship were sabjected to excessive bending
moments, developing strains greater than her strength could
resist,- their ultimate effect would be to break her across at the
transverse section where the strains reach their maximum; and
this section would usually be situated near the middle of the
length. Unfortunately, cases are on record where this ultimate
effect has been produced, and vessels, when very severely
strained, have actually broken across ; * but ordinarily, instead
of actual fracture, we have only to consider a tendency to pro-
duce fracture at any cross-section of the ship, the structui'al
strength being ample in proportion to the strains. In either case
one thing is clear, viz. that resistance to longitudinal bending
or cross-breaking at any transverse section of a ship can only be
contributed by those pieces in the structure which cross the
probable line of fracture, i.e. the particular transverse vertical
* One of the most singular cases designed for the shallow waters of
on record is that of the Chusan iron China. Her length was 300 feet, beam
steamer, which broke in two outside 50 feet, and depth in hold only 11
Ardrossan, a few years ago, one part feet. Another case in point is that of
of the vessel floating into the harbour, the Mnry, which broke in two in the
■while the other sunk outside. It is Bay of Biscay ; she was also a shallow-
only proper to add that this ship was draught vessel of great length, in rela-
not built for sea-going service, being tion to her depth : see page 299.
328
NAVAL ARCHITECTURE.
CHAP. IX.
section of the sliip which is being considered. Pieces lying
longitudinally or diagonally in the ship may fulfil this condition,
and therefore contribute to the longitudinal strength ; but pieces
lying transversely, such as a transverse rib or frame or beam
adjacent to the line of fracture, do not cross it, and therefore do
not contribute to the longitudinal strength. By this simple rule
it is, therefore, easy to distinguish those parts of the hull which
are efficient against the principal bending moments. Chief
among these may be mentioned the skin planking or plating on
the outside of the ship ; the planking or plating on the decks ;
and the longitudinal frames, keelsons, shelf-pieces under beams,
water-ways, side-stringers, and diagonal iron riders. For any
transverse section of the ship, the enumeration of all these parts
and the estimate of their respective sectional areas are very
FIG. 99.
Midship Section
Equivalenl
Girder
simjde processes, upon which the calculation of the strength of
the ship at that section is based.
The greatest bending strains being experienced at or near the
midship section, let it be assumed for purposes of illustration
that the ship is upright, and that it is desired to ascertain the
strength of the midship section against cross-breaking strains*
In performing this calculation, it is usual to construct an
" equivalent girder " section, similar to that shown in Fig. 99.
On the left is drawn an outline of the midship section of an iron
ship with a double bottom, and with longitudinal frames between
the outer and inner skins, these latter being indicated by the
strong black lines. On the decks, the i3lanking, plating, and
stringers will also be distinguished from the transverse beams
upon which they are supported. The effective areas of all these
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 329
pieces which cross the midship section, and extend to some
distance before and abaft it, are represented in the " equivalent
girder" on the right. The deck planking, and plating on the
upper deck are concentrated iu the flange A ; those of the middle
deck in the flange B, and those of the lower deck in the flange
C. The inner and outer bottom plating, longitudinal frames,
&c., from the turn of the bilge downwards are concentrated in
the loNvest flange or bulb D; the vertical or nearly vertical
plating on the sides, together with the longitudinal stiffeners
worked upon it, form the vertical web EE, connecting the
flanges. It will be observed that the depths of the girder and
midship section are identical, and all the corresponding pieces in
both are situated at the same heights, the vertical distribution
of the pieces on the midship section being maintained in the
girder.
There are many important matters connected with the work
of constructing equivalent girders ; but one or two only of the
most important can be mentioned. First, it is necessary to
distinguish between the total sectional areas of the longitudinal
pieces on the midship section, and their effective areas which are
shown on the girder. A very simple illustration will show the
character of this distinction. In wood ships it is usual to arrange
the " butts " of the outside planking so that at least three planks
intervene between consecutive butts lying on the same transverse
section. Fig. 100 shows this arrangement ; l and I are two butts
placed on the same timber ; and the probable line of fracture of
the planking between these butts is indicated. Against tensile
strains tending to pull the butts open on any section such as 6Z,
the butted stiakes have little or no strength ; therefore, in order
to allow for this weakening of the midship section, one-fourth
of the total sectional area of the outer planking must be
deducted. Further, there must be bolts or wooden treenails
driven in the unbutted planks, to secure them to the ribs of the
ship ; and the holes cut for these fastenings at any cross-section
may be taken as equivalent to a further loss of about one-eigJith
of the total sectional area. Putting together the allowances for
butts and fastenings, it appears therefore that the effective sectional
area of planking thus arranged is about jive-eighths of the
total sectional area when resistance to tensile strains is being
considered. But when cominessive strains have to be resisted, the
conditions are different. If the butts are properly fitted and
caulked, the butted strakes are nearly, if not quite, as efficient
as the unbutted strakes ; and if the bolts and treenails properly
S30 NAVAL ARCHITECTURE. chap. ix.
fit their holes, no d(.^diictioii need be maile for these holes.
Hence, against compressive strains, the effective area practically
equals the total sectional area. Similarly, in iron ships, the
holes for the rivets securing the outer plating to the ribs cut
FIG 100.
^Wff^ff^lfmffWf^m
oio
o u
DoojODOTCOTODoaajoo^oaoGamamcd
away about one-seventh or one-eii;hth of the total sectional area,
and this deduction must be made from the total area in order to
find the area effective against tensile strains ; whereas against
compressive strains no such deduction is needed. In many
other instances similar allowances are required ; but the process
is an easy one when the details of the construction of a ship are
known.
Some shipbuilders prefer to dispense with this determination
of effective sectional areas, and use total sectional areas in con-
structing the equivalent girder ; which is therefore the same both
for hogging and for sagging strains. This procedure is not so
accurate as that described above, but it economises labour and
affords a fairly good means of comparison between ships of similar
type and structure. It is chiefly employed in calculations for
merchant ships where the severest strains experienced are usually
hogging strains bringing the decks and upper works into tension ;
and so long as the departure from accuracy is borne in mind the
process is unobjectionable. But in computing the strains corre-
sponding to a given bending moment, the employment of the
total instead of the effective sectional areas, leads to results which
fall below the truth ; so that larger " factors of safety " (see
Chapter X.) become necessary.
Another important matter is the determination of the relative
values of wood and iron, or wood and steel, when they act
together in resisting longitudinal bending. So long as the
strains put upon the materials do not surpass the limits of
elasticity of the wood — a condition which is fulfilled in nearly
all cases — it is a fact, ascertained by experiment, that the
wood will act with the metals and lend them valuable assist-
ance. This is very advantageous to the structural strength of
ships of all classes, in which iron stringers or ties are used on
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 33 1
the decks and elsewhere, with wood pknking over them. In
composite ships also, with a wood skin worked on iron ribs, or
in sheathed iron ships, wherein wood planks are worked outside
the iron platicg in order to receive zinc or copper sheathing,
this combined action of wood and iron is of great value. The
late Professor Eankine suggested some years ago that a fair
allowance, averaging the various strengths of the timbers used
in shipbuilding, would be to consider wood equivalent to one-
sixteenth of its sectional area of iron ; and this is the allowance
usually made in determining the effective sectional areas for
the portions of the deck-flanges (A, B, C, in Fig. 99), represent-
ing the wood planking, or for other parts where iron and wood
act together. In the following chapter this matter will be further
discussed.
When the equivalent girder has been drawn, the next step
is to estimate the strength of the midship section thereby
represented ; and this is done exactly in the same manner as if
the girder were the cross-section of a long beam, subjected to
the same bending strains as those to which the ship is subject.
The comparison of a ship tending to hog or sag to a beam is
a very old one, having been made by some of the earliest writers
on the theory of naval architecture. Like many other sugges-
tions, this was not made use of to any great extent until the
introduction of iron shipbuilding ; and the late Sir William
Fairbairn did much towards establishing the practice of treating
a ship as a hollow girder, so far as longitudinal bending is con-
cerned. Readers familiar with mathematical investigations of the
strength of beams will not require any further explanation
respecting the use made of the equivalent girder; but there
may be some not acquainted with these investigations, and to
assist such in understandin"- the conclusions stated farther on, a
brief explanation will be given of the principal steps by which the
strengtli of a beam may be calculated.
Fig. 101 shows the side view and section of a flanged beam,
which is bent by the action of the downw^ard pressures P, P and
the upward pressure Q. When it is thus bent, the convex upper
side AB must have become elongated, as compared with its
length when the beam was straight ; whereas the concave under
side CD must have been shortened. Hence at some intermediate
part — suppose at EF — there will be found a surface which is
neither stretched nor compressed, but maintains the same length
which it had when the beam was straight. The surface EF is
termed the "neutral surface"; all parts of the beam lying above
332
NAVAL ARCHITECTURE.
CHAP. IX.
it are subject to tensile strain, all parts below are subject to
compressive strain. In the sectional drawing of the beam, ef
corresponds to EF, and is termed the neutral axis of the cross-
section. On the neutral surface EF, let any two points ah be
taken. When the beam is bent, the corresponding length on the
upper surface is shown by cd, and that on the lower surface by
gli ; the fij;ure cglid therefore represents the shape into which the
bending of the beam distorts that part which was of the uniform
breadth ah throughout the depth of the beam, before it was bent.
For any layer in the beam the elongation or compression pro-
duced by the bending varies directly as the distance of that
layer from the neutral surface. Within the limits of elasticity
of the material, the elongation or compression also varies directly
as the strain applied ; that is to say, a bar of the material will
stretch twice as much with a given weight suspended to it as it
does with half that weight suspended ; and so on. Hence it will
Section
be seen that in a bent beam the stress on each unit of sectional
area in a cross-section^such as that in Fig. 101, or any other form
of section, varies directly with the distance of that unit from the
neutral axis ef. At the upper surface AB the stress will be twice
as severe as it is^^midway between] AB and] EF, and the tensile
strain at AB bears to the compressive strain at CD the same
ratio as the distance of AB from EF bears to the distance of
CD from that surface.
The question thus becomes important, What governs the
position of the neutral axis? The answer is very simple. It is
coincident with the centre of gravity of the cross-section of the
beam, supposing (as may fairly be done) that the external forces
P, P, Q act perpendicularly to the surface EF. This follows
directly from the consideration that the sum of all the tensile
forces developed on any cross-section of the beam must equal
the sum of the compressive forces. The neutral surface of the
beam contains the centres of gravity of all the cross-sections ;
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 333
and this condition holds for all forms of cross-section, and all
variations in form at different parts of the length ; the preceding
remarks containing no assumption that the beam is of uniform
cross-section throughout its length. When the form of the
cross-section of any beam is given, the above stated property-
enables the position of the neutral axis to be determined easily.
One further step remains to be explained. At any cross-
section of the beam in Fig. 101 (say, at the middle of the length)
the external forces (P and Q) give rise to a bending moment the
value of which is easily ascertained. The effect of this moment
is seen in the curvature of the beam ; but it may be asked by
what moment is the moment of the external forces balanced.
Obviously it must be balanced by the moment of the internal
forces {stresses, as they have been termed) developed by the elon-
gations and compressions; each of these stresses may be con-
sidered as a force acting perpendicularly to the plane of the
cross-section, and having for its fulcrum the neutral axis.
And in this resistance to the external forces the internal forces
all co-operate, from top to bottom of the beam. The total
moment of these internal forces, about the neutral axis for any
cross-section, is easily determined. It has been remarked that
the stress on each unit of sectional area varies directly as its
distance from the neutral axis. Let it be assumed, therefore,
that under the action of certain external forces, a stress of s lbs. is
experienced by a square inch of sectional area at one inch distance
from the neutral axis. Then the corresponding stress on a square
inch of sectional area at a distance y inches from the neutral axis
will be expressed by the equation
Stress = s .y lbs.
The moment of this stress about the neutral axis equals the pro-
duct of its amount by the distance y. That is
Moment of stress = s.if (inch-pounds).
This last expression holds good for each square inch of sectional
area. Hence for any cross-section of the beam
jMoment of resistance = Sum of moments of the
stresses on each unit
of sectional area :
= 2 {sy\ gA)
= s.S(2/\gA) = S.I.
where SA is an element of the sectional area at a distance y from
the neutral axis; and S is the sign of summation for all such
334 NAVAL ARCHITECTURE. chap. ix.
elements making up the total cross-sectional area A. The sum
of all these products (y-.SA) is termed the "moment of inertia"
(say I) of the cross-section, about the neutral axis ; and hence it
follows that the moment of resistance maybe succinctly expressed
as the product of the stress on a unit of sectional area at a unit of
distance from the neutral axis into the moment of inertia. This
moment of inertia depends upon the size and form of the cross-
section ; the stress (s) at distance unity from the neutral axis
depends, for a given cross-section, upon the magnitude of [^the
moment of the external forces producing bending in the beam.
Finally it should be noted that the foregoing equations hold good
only when the maximum stress experienced by the material in
the cross-section does not exceed the " elastic limit " (see page 386).
The upper and lower surfaces of any cross-section of the beam
are those which are subjected to the greatest stresses, being most
distant from the neutral axis. If li-^ and lu are the respective
distances of these surfaces from the neutral axis, and pi and ^2
the corresponding stresses per unit of area (say per square inch) ;
then from the foregoing expressions we have for any cross-section
2?i 'Pi Moment of Resistance
^ ~ hi~ hi ~ Moment of inertia (1) '
But this moment of resistance to bending must balance the
bending moment produced by the external forces, such as P and
Q in Fig. 101. Hence finally if M = bending moment of the
external forces, about any cross-section of a beam,
h^ ho I
are equations determining the maximuna stresses jh aiid j>,, when
the other quantities are known. The moment of inertia I is
proportional to the product of the area of the cross-section into
the square of the depth of the beam ; whereas the distances h^ and
A2 are proportional to the depth. Hence the ratio of the products
of the sectional areas by the depths of two beams of the same
material and similar cross-section, is a measure of their relative
strengths to resist bending moments.
From the foregoing general expressions a few important
deductions may be made. With a given sectional area, and a
certain material, changes in the forms of cross-sections of beams
may largely influence the moment of inertia, and therefore in-
fluence the resistance to bending. The flanged form of beam
shown in Fig. 101 is thus seen to liave great advantages, as
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 335
regards the association of strength with lightness; for the
material thrown into the flanges is at a considerable distance from
the neutral axis, and the moment of inertia is consequently-
increased. The vertical web must retain sufiicient strength to
keep the flanges at their proper distance apart and to efBciently
connect them. When this has been done, all the rest of the
available material should be thrown into flanges, and in lattice
girder beams and bridges the principle receives its fullest
development.
Kevertiug to the equivalent girder for a ship (Fig. 99), it is
possible to make use of the foregoing general principles in order
to compare the relative importance of different parts of the
structure, as measured by their resistance to longitudinal bend-
ing. The most important parts are the upper flange A and the
lower D ; the flange C, corresponding to the lower deck, lies so
close to the neutral axis imn) as to be of little assistance. The
flange B is of much more service, but cannot compare in impor-
tance with A. The web EE, formed by the side plating or
planking is mainly useful, when the vessel is upright, in forming
a rigid connection between the flanges and enabling them to act
together ; but on account of their distance from the neutral axis,
the parts of EE lying nearest to A and D ofler considerable
resistance to bending. When the vessel is inclined, the conditions
are somewhat changed ; she then resembles a hollow girder set
angle-wise. The parts contributing most to the longitudinal
strength will then be the upper deck, the sheer-strakes and side
plating adjacent to that deck, and the bottom in the region of the
bilges ; but the arrangements which are efficient when the vessel
is upright will also contribute greatly to the efficiency when
she is heeled over to the most considerable angles likely to be
reached in rolling. Vessels are sometimes thrown over on to
their beam ends, but this is a very exceptional position, and
need not have much influence upon the distribution of the
material. There is good reason to believe that a ship which is
strong enough to resist longitudinal bending moments when she
is upright will be sufficiently strong in every other position. By
general consent, therefore, the upright position is assumed in the
construction of the equivalent girder, and most care is bestowed
to meet the bending strains incidental to that position.
Hogging, it will be remembered, is the change of form pro-
duced by the ends of a ship dropping relatively to the middle,
the keel becoming arched upwards. The conditions of strain are
then similar to those in the beam, Fig. 101 ; the upper parts of
2>Z^
NAVAL ARCHITECTURE.
CHAP. IX.
the structure being subjected to tensile strains, the lower to
compressive strains, and the division between the two being
marked by a neutral surface. Sagging is the converse case where
the middle drops relatively to the ends ; the keel becoming
arched downwards, the upper parts of the structure being sub-
jected to compressive strains, and the lower to tensile strains,
the change of strain being marked by a neutral surface, not
agreeing in position with that for hogging. It will indeed be
evident, from what has already been said respecting the difference
between the total and effective sectional areas of parts of the
€hrder for Hot
PIG IOI«
"ff
Girder for Sagging
NoxUral
^
Saiteru Dech
Main Deck
KeutmJ, 4scis
Axis
§5"
m
£,nwer Deck.
s
"*
s
structure, that, strictly speaking, the equivalent girder for hogging
strains must be different from that for sagging strains ; although
in practice the two are sometimes treated as identical (see page
330). But while the sectional areas of the upper and lower
flanges A and D of the equivalent girder in Fig. 99 change
both their absolute and relative values, according as hogging or
sagging strains have to be resisted, it is still true, for both hog-
ging and sagging, that these are the two parts of the structure
which are of the greatest assistance in resisting change of form.
Their joint action is secured by means of the web formed by the
skin.
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 337
An example, taken from an actual ship may be of service both
as an ilhistration of the foregoing remarks respecting the relative
importance of the several parts of the structure, and as an indica-
tion of the simplie-ity of the calculations for the equivalent
CALCrLATIOX OF MOMENT OF InEETIA OF SECTION WHEN THE ShIP IS UNDER A
Hogging Strain.
Feet.
Total depth of orirder = 37-5
Neutral axis below top = ft, = 19-3
Neutral axis above bottom =h^ = \%-1
Distance
of Centre
Depths
Parts of Structure.
Effective
Sectional
Ajfas
= A.
of
Gravity
from
Neutral
Axis = ft.
Squares of
Distances
Products
Axft=.
of Webs
in
Girder
= (i.
Squares
of Depths
Products
^',xAxa^
Sq. ins.
Feet.
Feet.
Upper deck flange .
155-1
19-2
368-6
57,170
—
—
—
]Main deck flange
6.54: -1
10-6
112-4
73,521
—
—
—
Lower deck flange .
117-2
3-6
13-0
1,524
—
—
—
Wing passage bulk-'
Lead (part)
51-0
5-5
30-2
1,540
9-0
81
344
Coal bunkt-r bulk-'
head (part)
14.0
1-4
2-0
28
2-8
7-8
9
Shelf plate . . .
24-7
-85
•7
17
—
—
—
Skin plating .
C85-1
10-1
102-0
69,880
18-4
338-6
19,331
Bottom plating above "i
neutral axis . . /
19-0
•4
•2
4
•8
-6
1
Coal bunker bulk-'l
head (lower part), j
37-8
3-2
10-2
386
6-3
39-7
125
'Wing passage bulk-'l
head (lower part). J
63-4
4-6
21-2
1,344
9-3
86-5
457
Bottom plating above"!
bilge . . . ./
401-0
7-5
56-3
22,576
12-7
161-3
5 390
Bottom flange .
889-0
15-8
249-6
221,894
5-5
30-2
2,237
449.884
27.894
"When the ship is on
I = Mc
a wave c
ment of
rest —
inertia =
27,894
= 477,778
M = Bendiug
momen!
; at secti
F
oQ just (
oot-tons.
)ut8ide bat
Feet.
tery =
28,000 fo
ot-tons.
Maximum tensile strs
part of section .
lin on up
per ) _
28,000 ><
477,7
: 19-3_ J
78
-13 ton
3 per squ
are inch.
Maximum compressiv
lower part of sectio
e strain
1
oil ■! _
28,000 X
18-2 ,
07 tons
! pfer squ
are inch.
477,7
78
girders of ships. That selected is one of the investigations made
by the Author's pupils at the Eoyal Naval College for a broad-
side iron-clad frigate resembling the Invincible class in the Eoyal
Kavy. Fig. 101a represents the equivalent girders for this ship
z
338 NAVAL ARCHITECTURE. chap. ix.
Calculation of Moment of Inertia of Section when the Ship is undeu a
Sagging Stkain.
Feet.
Total depth of girder = 37-5
Neutral axis below top = /t, = 15'9
Neutral axis above bottom = /t, = 21-6
I'arls uf Structure.
Upper deck flange .
Main deck flange .
Lower deck flange .
Skin plating (part) .
Armour and backing
AVing passage bulk-'>
head . . . ./
Coal bunker bulk- 1
head . . • ./
Shelf plate .
Skin plating (part) .
Bottomplating above'l
bilge . . . ./
Bottom flange .
Effective
Sectional
Areas
= A.
Distance
of Centre
of
Gravity
from
Neutral
Axis = h.
Sq. ins.
202-9
777-8
148-6
681 -5
1657-5
43-8
65-0
46-3
24-7
92-4
360-1
767-2
Feet
15-8
7
6-6
5-2
2-6
1-3
11-0
19-2
Squares of
Distances
— h~.
249'
50'
62'
10'
10'
6
4
04
4
2
2
43-6
27-0
6-8
1-7
121
368-6
Products.
Ax/i2.
50,644
39,201
6
42,526
16,903
447
2,834
1,250
168
157
43,572
282,790
Depths !
of Web.-ij Squares
in of Depths
Girder
Feet.
15
6
6'
11-9
9-2
2-6
13-6
5-6
= d^.
249
42
42
141
84-6
6-8
185
31-4
Products
^.,xAxd^
14,175
5,843
154
767
326
52
5,552
2,007
480,501
28,876
Moment of inertia = 509,377
28,876
When the ship is ast^'ide the wave hollow —
M = Bending moment at section just outside battery = 47,120 foot- tons.
Foot-tons. Feet.
Maximum tensile strain on lower ■>_ 47,120 x 21-6
part of section / 509^77
Maximum compressive strain
upper part of section .
2 tons per square inch.
ou J ^ 47,120x15-9 ^ J . ^^,^^ ^ .,^^1^
• / 509,377 ^ ^
when subjected to hogging and sagging strains. The armour is
supposed to be efficient only against compressive strains, which is
an assumption on the side of safety. In estimating the effective
sectional areas of other parts of the structure the rules explained
on page 330 have been followed. Further explanations of the de-
tailed calculations appended will scarcely be required, beyond the
statement that the bending moments (M) for the extreme posi-
tions of support, on wave-crest and astride wave-hollow, were
estimated in the manner exi^lained in Chapter YIII., and are intro-
duced in the calculations for tlie purpose of determiniug the
corresponding maximum stress on the top and bottom respectively.
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 339
From the preceding explanations and illustrations it will be
obvious that the ratio of the de^tli of a ship to her lengili should
exercise great influence upon the provision of longitudinal
strength. The moment of resistance of an equivalent girder
section like that in Fig. 99 has been shown to be very largely
influenced by the depth; while the maximum longitudinal
bending moment for a ship is expressed in terms of the product
of her weight into the length. Broadly speaking, the shallower
a ship is in proportion to her length the greater should be the
amount of material contributing to the longitudinal strength;
and not unfrequently when the hull-proper is extremely shallow
recourse is had to some device for virtually increasing the depth
as is described by Figs. 105 and 106, page 361. War-ships of
rearly all classes are of much greater depth in relation to their
length than merchant ships ; and this fact, taken in connection
with their structural arrangements, explains the smaller strains
to which the material in war-ships is subjected. It must not be
supposed, however, that increase in depth j9er se necessarily leads
to a diminution in strains ; on the contrary, cases may occur where
an increase in depth obtained by building a light continuous
superstructure, upon a comparatively strong hull, actually leads
to an increase in the maximum strain brought upon the material
most distant from the neutral axis.* The reasons for this are
obvious enough;, on consideration of the fundamental equations
for the strength of beams, given on page 334 ; but the following
example may assist some readers. A belted ironclad having a
depth of 42 feet from the flat keel to the spar-deck amidships,
had a strongly-plated protective deck, 16 feet below the spar-
deck ; and calculations were made for the purpose of ascertaining
the maximum strains likely to be brought (1) upon the material
in the spar-deck when the sides were intact, and (2) upon the
material in the protective deck when the sides above that deck
were shot away in action, so that the protective deck became the
top of the girder. Under hogging strains the following w^ere the
results : —
I. With sides and spar-deck intact,
Total depth of girder = 42 feet
Neutral axis below top = 23 A „
* Readers desirous of following out adions of tlie Institution of Naviil
this subject may turn with advantage Architects for 1878.
to a Paper by Mr. Purvis in the Trans-
z 2
340 I^A VAL ARCHITECTURE. chap. ix.
Moment of inertia of )
• 1 - • 1 > = 376,000.
equivalent girder . j '
Using the same notation as before, for a given bending
moment (M).
Maximum strain on material ) ^^ _ Ih ht ., 23-^
!
= M X Z = M X
in spar-deck . . . f I 376,000
'5
II. ATith sides and spar-deck damaged,
Total depth of girder = 26 feet
Neutral axis below top =11 „
Moment of inertia of ) _ 91 n (\(\r\
equivalent girder . j
JMaximum strain on material ) iir H
in protective deck . . . j 210,000
Hence it is seen that the diminution in the depth produced by
breaking the continuity of the lightly constructed top sides, upper
deck and spar-deck, actually resulted in a diminution of tensile
strain in the ratio of 191 to 161. This diminution in tensile
strain was accompanied in this case by an increase in the com-
pressive strain on the bottom plating, the value of which may be
easily ascertained, if desired, from the foregoing data. Space
will not permit us to carry the investigation farther. It must
suffice to add that althouo-h our illustration has been taken from
war-ships, the point raised is chiefly important in merchant ship
construction, seeing that the adoption of continuous spar-decks or
awning-decks is now so common, and that the bottoms are usually
much stronger than the upper decks, under the principal hogging
strains which have to be resisted.
Furthermore it is necessary to remark that the ratio of length
to hreadth must be considered in adjusting the amount of longi-
tudinal strength to be given to a ship. For the upright position
the breadth influences the effective sectional areas of the decks,
bottom plating or planking, &c., included in the equivalent
girder. For the extreme " beam-ends " position the breadth
becomes the depth. For any intermediate or inclined positions
the breadth affects the depths and strengths of the corresponding
equivalent girder sections.
Equivalent-girder calculations are usually made for cross-
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 34 1
sections at or near the middle of the lengths of ships ; because
(as explained in the previous chapter) the severest hogging and
sao-o-ing moments, corresponding to exceptional positions of support
for ships afloat or ashore, are usually experienced by these cro?s-
spctions. Similar calculations may, however, be made for other
cross-sections lying towards the bow or stern, the moment of
resistance of the equivalent girder for any section being compared
with the bending moment experienced by that cross-section,
which bending moment is ascertained from the corresponding
ordinate of curves such as WsVsl in Fig. 86, page 291. Cases
occur where the presence of large hatchways or openings in the
deck, or peculiarities in the structural arrangements, — such as
the discontinuance of protective plating at some cross-section
in a central citadel or battery ship — lead to greater tensile and
compressive strains being brought upon the material at cross-
sections considerably distant from the middle of the length, than
are experienced by the material at the midship section. No
general law holds good in these matters, but each case must be
separately investigated. Broadly speaking, the diminution of
the bending moments from the middle of a ship towards her
ends, renders possible some diminution in the strength of other
cross-sections as compared with the strength of the midship
section. And although local strains and other considerations
interfere with the application of any general rule, the fullest
association of lightness with strength requires that the shipbuilder
shall bestow attention upon the longitudinal distribution of the
material in a ship.
In deciding upon what reductions of scantlings or thicknesses
are possible in the parts lying towards the ends of a ship, the
builder has to note two important facts. First, the giadual
narrowing of the ship towards the extremities is in itself a cause
of decrease in the strength of cross-sections ; it lessens the
sectional areas of the planking or plating on decks, sides, and
bottoms ; and not unfrequently, owing to the reduction in girths,
there are fewer longitudinal stiffeners at the ends than amidships.
Second, when a ship is very considerably inclined, the narrowing
of the decks produces a virtual decrease in the dej^th of the
equivalent girder sections ; tliis may be regarded as the source
of a still further loss of strength to the cross-sections lying
towards the extremities, which is not in operation when the
ship is upright. For the upright position the depth of the
equivalent girders then remains practically constant for all
cross-sections throughout the length.
342 NA VAL ARCHITECTURE. chap. ix.
These facts, taken in connection with local requirements, have
led shipbuilders to make only a small decrease in the thicknesses
of the planking, plating, &c., forward and aft as compared with
the thicknesses used amidships. In wood ships the thickest
outer planking, the wales, is reduced in thickness towards the
bow and stern. In iron ships of the mercantile marine it is
customary to maintain the midship thicknesses throughout one-
half the length, and at the extremities to reduce the thickness
of the outer skin by about ^ inch, besides either narrowing the
stringers on the decks or decreasing the thickness of stringers
and deck plating. Vessels framed on the longitudinal system
have, in addition, the depths of their longitudinal frames de-
creased towards the extremities, and as the girths of the sections
become less, the practice is to stop short one or more of the
longitudinals. These are the main changes that need now be
mentioned ; they do not effect any considerable difference in the
scantlings at the extremities as compared with those amidships
and although some writers have recommended much more marked
differences between the central part of a ship and her ends, the
general feeling and experience of shipbuilders have not gone in
this direction.
Local requirements, as remarked above, exercise a very great
influence on the longitudinal distribution of the material, often
in a direction exactly opposite to that in which the consideration
of the strength of the ship as a hollow girder would lead.
Many examples of this will occur to the reader who has an
acquaintance with the details of shipbuilding; only two or three
of the most important can now be mentioned. The plating
near the stern in a single screw steamer, from the girder aspect
of the case, might be made as thin as any plating on the ship,
but as a matter of fact it is as thick as any, the reason being
that the local strains due to screw propulsion require strong
plating to be fitted between the stern-post and the stuffing-box
bulkhead next before it. Passing to the other extremity of an
ironclad ship, another instance is found. In order to meet the
local strains produced by the chafing of the cables, and rubs or
blows of the anchors on the bows, it is usual in ships of the Royal
Navy to double the plating for some distance ; and this additional
thickn<ss, of course, adds much to the strength of a ram-bow;
but here again, reasoning from the girder, a minimum thickness
of plating should suffice.
Very similar remarks may be made respecting the vertical dis-
tribution of the material in the cross-sections of ships. Reasoning
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 343
exclusively from the analogy of the equivalent girder it will be
obvious that it would be advantageous to decrease the amount of
the material near the neutral axis ; whicli could be best done by
tliinking the skin-plating or planking at that part. Some
slight reductions in thickness have been made in many cases, but
there are other considerations which require to be taken into
account before proceeding far in this direction. Ships frequently
occupy inclined positions, and then side plating or planking
which is included in the " web " of the equivalent girder for the
upi'ight position, may be so placed as to be capable of yielding
the greatest assistance to the structure. On this account in iron
and steel ships the common practice is to keep the greater part
of the skin-plating of uniform thickness, fitting a few thicker
strakes on the bottom below the bilges where the severe local
strains due to grounding are principally felt, and thickening or
doubling the sheer-strakes. Wood ships usually have their
thickest planking in the neighbourhood of the middle of the
depth, where it can be least effective against longitudinal bending
strains when the ship is upright; but these wales are probably
the outgrowth of the rubbing strakes formerly fitted near the
main breadth, and they also form strong ties above and below
the lines of ports in many classes of wooden war-ships, thus re-
storing, to some extent, the loss of strength due to the want of
continuous longitudinal planking in wake of the ports. Moreover,
when vessels approach the "beam-end " position, the wales are of
considerable assistance in resisting longitudinal bending.
Modem war-ships have their structural arrangements very much
controlled by the necessity for protecting certain parts by armour.
The general considerations based upon the comparison of a ship
to a girder are therefore, to a large extent, overruled, material
being massed in flanges formed by decks near the middle of the
depth, or thrown into the centre of the web of the girder for the
upright position, instead of being added to the upper part or
to the upper deck. For instance, to increase the resisting j ower
of the target formed by the armoured side, the skin-plating behind
the armour is made about twice as thick as the bottom plating,
although its situation is frequently not very favourable to its
efScient contribution of longitudinal strength. Nor, to give one
other example, do the strongly-plated decks, fitted some 5 or 6 feet
above water (as in the belted shi| s) or an equal distance below
water (as in the central-citadel type), contribute to the longi-
tudinal strength at all to the same extent as the same weight of
iron differently distiibuted might do. The armour plating itself
344
NAVAL ARCHITECTURE.
CHAP IX.
also, even when arranged and fastened with the utmost care,
must be regarded rather as a load carried by the structure than
as adding much to the longitudinal strength.
From tile preceding rematks it will ajopear that although the
comparison of a ship to a girder in her resistance to longitudinal
bentliug is of great service to the shipbuilder, it only holds good
within certain limits. Keeping this in view we now propose to
pketch the character of the principal structural arrangements,
FIG 102.
Inside Yiew
which supply longitudinal strength to different classes of ships,
and to contrast the relative efficiency of those arrangements.
Wood ships, iron and steel ships, and composite ships will come
under review, as well as armoured ships ; but it must be under-
stood that no endeavour will be made to describe the structural
details of any class ; for these the reader must turn to works on
shipbuilding. To illustrate the contrast between these classes,
and to assist our explanations, Figs. 102, 103, 104, and 104a
have been prepared. The former shows, in cross-section and
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 345
inside elevation, the construction of a wooden ship according to
the former practice of the Royal Dockyards. Fig. 103, page
346, shows, in cross-section, the construction of an ordinary iron
merchant ship. Fig. 104, page 351, shows, in cross-section, the
construction of an ironclad ship of modern type. Fig. 104a, page
354, shows in cross-section, the construction of an iron or steel
merchant ship, with cellular double bottom. As we proceed,
repeated references will be made to these figures, and their prin-
cipal features will be noted in connection with the contribution of
individual parts to the general structural strength.
First, as to the upper flange in the equivalent girder for a wood
ship. The parts ordinarily included are as follows: the deck-
planking, allowing for its effective area in the manner explained
above; "and the thick "water-way" fitted upon the beam ends
(see Fig. 102). Such a flange is much less strong against the
tensile strains brought upon it by hogging than it is against the
compressive strains due to sagging; the effective area against
tensile strains being less than three-quarters of that against com-
pressive strains. It is a matter of common experience that,
under severe hogging straini=, signs of working and weakness
display themselves in the upper works of wood ships. In order
to add strength to the upper deck, iron stringers and plating were
worked under the wood planking in many of the later wood-built
ships of the Royal Navy. Examples of this addition will be
found in the converted ironclads of the Caledonia class, and in the
largest class of corvettes.
...
In iron, steel or composite ships the upper flange of the equi-
valent girder resembles that described for the later wood ships.
Fig. 103 shows the arrangement; the iron stringer plates on the
beam ends being drawn in strong black lines under the wood
planking. These stringers should always be strongly secured to
the uppermost strake of the side plating of an iron ship (termed
the " sheer-strake "), which is often made thicker or doubled, for
the purpose of increasing the longitudinal strength. Composite
ships also, although they have not an iron skin, are usually fitted
with a sheer-strake. At the outset of iron shipbuilding, the use
of deck-stringers was not general ; but as the sizes of ships in-
creased, the necessity for adding to the longitudinal strength of
the upper decks became apparent, and stringers were adopted.
The breadths of these stringers have been increased as still larger
vessels have been constructed ; and at the present time it is very
common to find the whole, or a great part, of the surface of the
upper and main decks in large iron or steel steam-ships covered
346
NAVAL ARCHITECTURE.
CHAP. IX.
witli plating. These complete or partial iron or steel decks, fitted
under the wood planking, are most valuable additions to the
structural strength, and have corrected weaknesses formerly too
common in the upper parts of iron ships. Complete iron and
steel upper decks have been fitted, from the first, in tlie iron-built
armoured ships of the Eoyal Navy, and have proved thoroughly
efficient. In the Great Eastern the exceptional strength required
FIG 103.
has been provided by a very unusual construction of the upper
dfck. This is a cellular structure formed by two strong iron
skins worked above and below deep girders running longitu-
dinally. Besides the unusually strong plating, the strength of the
girders in this ship therefore comes into play against hogging or
sagging strains ; whereas the transverse beams fitted almost
without exception in other ships can lend no assistance to the
decks against such strains. In the largest vessels afloat, except-
CHAP. rx. STRUCTURAL STRENGTH OF SHIPS. 347
iiig the Great Eastern, the simpler and lighter arrangement of
iron or steel decks, worked upon transverse beams, under the
planking is, however, found to answer every purpose.
Xext, as to the lower jianges in the equivalent girders of the
different classes of ships; this is a less simple case than the
preceding.
In wood ships the parts included in the lower flange vary-
considerably, according as hogging or sagging strains have to
be resisted. The bottom planking up to the bilge, the keel,
keelson, and binding strakes {h, Fig. 102) are all effective,
although not. equally effective, against both hogging and sagging
strains. It is a common practice to fill in the openings between
the ribs, from the keel up to some distance from the bilge ; and
this has a twofold advantage. In case of damage to the bottom
planking the fillings keep the water out of the hold; and, more-
over, when the vessel tends to hog, and her bottom is brought
under compression, the lower part of the frames is made into a
practically solid mass of timber, the fillings offering great resist-
ance to any change of form. When sagging takes place, and the
bottom is brought under tension, the fillings can lend no such
help to the pieces lying longitudinally, and the difference is
very considerable. It is, however, noteworthy that in ordinary
wood ships the severest longitudinal bending moments are those
tending to produce hogging, a fact which makes the use of fillings
of the greater value. To assist the bottom in resisting the tensile
strains due to sagging, iron stringers have been fitted in some
few cases in lieu of the ordinary thick binding strakes ; but
this arrangement is not so valuable as the use of iron
strengthenings to the upper deck.
In ordinary iron or steel ships the bottom flange of the girder
is made up of the keel, keelson, side keelsons (s, ^ig. 103), hold
st lingers (A), and the bottom plating. These are all effective
against botli hogging and sagging strains ; and, as already
explained, the difference in the sectional areas, effective against
tension and compression respectively, is not nearly so marked
as in the case of the corresponding part of a wood ship. The
transverse frames, or ribs, of the iron or steel ship are 20 inches or
2 feet apart, there being nothing corresponding to the fillings
of the wood ship. Fig. 103 by no means represents the universal
practice of shipbuilders as to the arrangement of the longitudinal
stiffeners to the bottom plating. There are very many varieties
of side keelsons, hold stringers, keelsons, keels, &c., some builders
preferring one arrangement, other builders preferring another
•->
48 NAVAL ARCHITECTURE. chap, ix.
arraugemeiit. But they have one feature in common. The main
frames lie transversely like those of a wood ship, and do not
contribute to the longitudinal strength, whereas the longitudinal
pieces are snp})lementary or subordinate to the transverse framing,
and are either fitted in between the ribs (like s), to secure a
direct connection with the bottom plating, or over-ride the ribs
(like h, Fig. 103).
For wood ships it is practically a necessity to place the ribs
transversely, and in the earliest iron ships the arrangements of
wood ships were naturally imitated to a considerable extent.
The moderate size of the earlier iron vessels rendered almost
nnnecessary any longitudinal strengthenings to the bottom other
than were furnished by the engine and boiler bearers, fitted
primarily as supports to the propelling apparatus. But as the
sizes of 8hips increased, the longitudinal strengthenings to the
bottom were multiplied, and in some cases the bottom was thus
strengthened, while the top flange of the girder was left almost
uncared for, the result being a great disproportion between the
strength of the top and bottom flanges. There are, of course,
many local strains to be borne by the bottom of a ship — such as
those due to grounding, the carriage of cargo, and possible
concentration of weights — which are not paralleled by any strains
that have to be borne by the decks; but to give greatly
di^projDortionate strength to either flange involves a bad distribu-
tion of the material. The recent use of iron and steel upper
decks and broader stringer plates has partially corrected an evil
formeily prevalent in merchant ships, but the upper flange is
still commonly made much weaker than the lower. If ships fail,
they usually yield to hogging strains; but cases have occurred
where the upper flange of the equivalent girder has yielded to
the compressive strains incidental to sao:";iug. The shallow-
draught steam-ship Mary, mentioned on page 327 is alleged to
have foundered in consequence of the upper deck crushing up
when she met with heavy weather in the Bay of Biscay on her
passage to the station for which she was designed.
There is no dispute but that the combination of strength with
lightness would be more efficiently secured if the main frames of
iron and steel ships were made longitudinal instead of transverse
at least for the parts below the bilges. The continued use of the
old system of framing is mainly due to the greater cheapness
of construction, rendered possible in consequence of the
familiarity of the workmen with this mode of building, and the
greater rapidity ^^i!h which the work can be carried on. More-
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 349
over, by fitting strong bottom plating, combined with numerous
intercostal side keelsons, hold-stringers, &c., sufficient longitu-
dinal strength can undoubtedly be given to the bottoms of even
the largest ocean steamers, and the additional weight involved is
not thought generally to be of so much importance as to render
it desirable to incur the greater cost of construction of the
longitudinal system of framing. Since 1887 there ha?, however,
been a remarkable extension of the " cellular " system of construc-
tion for iron and steel merchant ships, illustrated by Fig. 104a;
and the experience gained with these vessels has done much
towards removing the objections previously urged against longi-
tudinal framing for merchant ships.
Composite ships resemble ordinary iron ships in having the
main frames transverse ; and the bottom flanges of their equiva-
lent girders differ from those of the iron ships chiefly in that
they include wood keels and bottom planking. The latter
especially loses, as compared with iron plating, in its resistance
to the tensile strains due to sagging moments. No equally
intimate connection can be made between the intercostal side
keelsons of a composite vessel and the bottom planking, as are
possible between such keelsons and the bottom plating of an
iron ship. Nor can the composite ship have the help of fillings
between the frames like those of a wood ship. These are the only
points of difference that need be mentioned.
Although the transverse system of framing has been so
generally adopted in the mercantile marine, there are not a few
sliips in which longitudinal framing occupies the chief place.
The Great Eastern is the most notable example, and her structural
arrangements, due to the joint labours of the late Mr. I. K. Brunei
and Mr. Scott Russell, furnish good evidence of the superiority of
the longitudinal system.* Other and much smaller merchant
ships have been built on very similar principles; and in all the
iron-built ironclads of the Royal Navy great prominence is given
to longitudinal framing. Such framing is of the greatest
advantage in the lower parts of ships lying below the lower deck.
The comparatively flat surfaces of the bottom plating below
the bilge are best stiffened against buckling by longitudinal
* For mucli interesting information It is evident from the details therein
concerning the construction of this given that, at a very early period after
ship, and her predecessors, the Great the introduction of iron ships, Mr.
Western and Great Britain, see the life Brunei perceived the great advantages
of Mr. Brunei, published by his son. attaching to longitudinal framing.
350 NAVAL ARCHITECTURE. chap. ix.
fraDies, Mliieh form strong girders well secured to the bottom
plating, and contribute to the effective area of the lower
flange of the equivalent girder for tlie upright position. At the
bilge there is usually considerable transverse curvature in the
bottom plating, a fact which gives it great stiffness in itself
against buckling under compressive strains, due either to hogging
moments or to the concentration of surplus buoyancy ; hence
immediately at the bilge longitudinal frames are not so much
required for the purpose of preventing buckling. Very frequently
external bilge-keels are fitted just at this part of the bottom,
forming good stiffeners to the plating, besides adding their own
sectional areas to the lower flange of the girder. Above the
bilge, and below the lower deck, longitudinal frames are again of
great use, especially in adding to the longitudinal strength when
the ship occupies an inclined position, and is subject to hogging
or sagging moments. When we reacli the parts lying above the
lower deck, other considerations enter and make the longitudinals
of less importance ; in fact, the decks themselves with their
stringers, ko.., form most efficient longitudinal stiffeners, and
they are usually so close together as to render intermediate
longitudinals unnecessary. Sometimes, where a lower deck
does not extend throughout the whole length, but is broken
for some reason, its stringer plate is continued in order to form
a stiffener, as shown by Z, Fig. 103. It may, however, be regarded
as the rule that the decks need no aid from intermediate
longitudinal frames, the only framing required in the upper parts
of ships being vertical and transverse. Such framing stiffens
most efficiently the almost upright side plating, gives facilities
for attaching the beams to the side, and answers other purposes.
The extent to which it is adopted must of course depend upon
the special conditions of each class of ship. Widely spaced
vertical frames suffice in the upper parts of the Great Eastern;
whereas in armoured ships these frames are very closely spaced,
in order to assist in strengthening the target formed by the
armoured side. Fig. 104 illustrates the last mentioned case;
below the armour, the main frames are longitudinal, as shown
but behind the armour the principal frames are vertical, being
spaced only 2 feet apart (see the section at cd). The longitudinal
girders worked between the strakes of the wood backing are
not fitted primarily with a view to increase the longitudinal
strength of the stiucture, although they have this effect, but are
intended to increase the resistance of. the target formed by the
side of the ship against penetration or damage by projectiles.
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS.
351
Lookiuo- a little more closely into the arrangements illlustrated
in Fig. 104, it will be evident tbat the lower flange of its equiva-
lent girder includes the skin plating, both outer and inner, as well
as tbe numerous and strong longitudinal frames. These frames,
as already explained, are of great vaule in preventing buckling,
and resisting the tensile strains due to sagging, even when there
is only a single outer skin. But their efficiency in these respects
FIG 104.
■■is:-!--^ ,-\v,u-^c>k^f^JAi.^y! vi.iM ■^ftJr^Hi-;;»^^a|^:i.53y7Jg^.^-3>:b5^^
and the strength of the lower flange of the girder are both very
greatly increased by the adoption of the inner skin plating,
forming a double bottom. This celluUir construction is shown
by experiment to develop most efiiciently the strength of a
structure formed of wrought-iron plates and bars, any one of
which, taken singly, has little strength to resist bending. It is
unnecessary to repeat what has already been said respecting the
352 NAVAL ARCHITECTURE. chap. ix.
adaptability of double bottoms for water-ballast or the gain in
safety due to the use of double bottoms, this being so great
that, even if there were no gain in structural strength, the ship-
builder would be fully justified in adopting the arrangement.
Although the longitudinal frames play such an important part
in conuecting the two skins and stiffening the bottom, their
direct contribution to the moment of resistance of the equi-
valent girder section is not relatively great. This will appear
more clearly on reference to the exemplar calculations for an
ai-moured ship on pages 337-8. The inner and outer skins ai-e
the largest contributors to the moment of inertia of the lower
flange, and the longitudinals might be left out of the calculation
without seriously affecting the result. Their presence on the
structure is, however, of gieat impoitauce; for without them the
joint action of the two skins in resisting bending moments would
not be secured. Furthermore it must be noted that to give effi-
ciency to longitudinal framing, frequent "sections of support"
must, be provided by means of transverse bulkheads or " partial
bulkheads," as is further explained hereafter. Having made this
provision, the amount to which the main longitudinal frames
require to be reinforced by subordinate transverse frames, depends
upon the necessities of local strength in the bottom (see page 313).
In the armoured ships of the Royal Navy the " bracket-frames " are
4 feet apart, and this amount of stiffening to the bottoms is found
sufficient to meet all the ordinary strains to which the ships are
subjected during construction, launching, docking, or service
afloat. In cases of grounding also, although these are rare in
war-ships, this bracket-system of construction has stood the stress
of service exceedingly well. The Iro)% Duke, for example,
grounded twice on the China station, once on a soft bottom and
secondly on a rocky bottom. On this second occasion the outer
bottom was bulged in, the framing in the double bottom was bent
and broken over a considerable length, but the inner bottom
remained intact, and the ship was safely navigated to port after
she was got off.
Since 1877 a remarkable extension of the use of cellular
double bottoms has taken place in the mercantile marine. The
change must be mainly attributed to the enterprise of a few
leading shipbuilders, and to the support given to the movement
by the professional officers of the Registration Societies. One
great reason for this rapid progress is to be found, no doubt, in
the more general recognition of the commercial advantages
attending the use of water-ballast; the gain in safety has also
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 353
liad some weight, and is becoming increasingly evident to ship-
owners. It may fairly he supposed that the examples of the
Great Eastern and the armoured ships of the Navy, had some
influence upon the movement, as well as upon the character of
the structural arrangements of recent merchant ships built with
cellular double bottoms. Limits of space prevent us from
attempting to trace in detail the various methods of construction
adopted by different firms,* or to contrast these with the corre-
sponding methods of construction in war-ships. All that can be
done is to choose a good example of recent practice, such as is
ilhistrated in Fisr. 101a, and to sketch the main features.
Above the turn of the bilge the main frames are vertical and
have the usual spacing, about 2 feet. At the turn of the bilge
there is a continuous watertight longitudinal frame (AA, Fig.
104a), and upon this the vertical frames are stopped short, their
heels being connected to the longitudinal by bracket-plates (B).
The longitudinal A A has its outer edge connected by a con-
tinuous angle-bar to the bottom plating, while its inner edge is
similarly connected to the inner skin plating; in this way the
longitudinal forms a watertight side boundary to the ballast-
tank, or cellular bottom. Within the double bottom the main
frames are longitudinal as indicated on the section. The trans-
verse framing consists of " gusset " or '• bracket " plates, with
angle-bars on their edges and ends connecting them to the two
skins and the longitudinals ; these bracket-frames are spaced 4
feet apart, just as the corresponding frames in the armoured ships
are spaced (see Fig. 101). Intermediate between the bracket-
frames, simple angle-bar transverse frames are fitted (as shown on
lower section) to give additional support to the skin-plating, and
to provide for taking the ground as merchant ships frequently
have to do. Sometimes the bracket-frames are not fitted, plate-
frames lightened with holes being used instead, and this plan is
growing in favour. In certain parts of some large ships where
special strength is required, the plate or bracket frames have
been spaced only 2 feet apart; but this is not usually done.
Another feature deserving to be noted in Fig. 101a is the use of
deep transverse frames or partial bulkheads above the cellular
bottom, at intervals of about 12 feet ; and the combination there-
with of two intercostal side-keelsons. The outline of these
* For these see Papers by Mr. Mar- by Mr. J^hu in the Transactions for
tell in the Transactions of the Institu- 1880.
tion of Xaval Architects for 1877, and
2 A
154
NAVAL ARCHITECTURE.
CHAP. IX.
partial bulkheads is indicated by dotted Hues ou the section; and
tlieir value will be furtlier explained hereafter.
From this brief explanation it will be seen that the cellular
system now widely used for merchant ships, is very similar in
principle to, tiiough diiferent in details from, the longitudinal
FIG 104-a
system previously described for armoured ships. The greater
amount of support given to the bottom is a necessity in merchant
ships, which have to take the ground. Experience has shown
that a vessel can be built on this cellular system, and given all
the advantages of a water-ballast tank, as well as greater safety,
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 355
with no Greater weifrht of material than would be used in a
vessel of the same dimensions built on the ordinary transverse
system. The cost of workmanship in the cellular system is found
to be somewhat greater than in the ordinary system ; but this
excess in cost will undoubtedly be decreased as experience is
gained by the workmen. Ctllular double bottoms necessitate
the sacrifice of some of the hold-space as compared with the
ordinary transverse system of framing without any provision for
water-baHast. But as compared with other methods of forming
water-ballast tanks, the cellular system is more simple and
efficient, while it takes less away from the hold-space. One very
common arrangement for water-ballast consisted in building upon
the floors a series of longitudinal girders which carried an inner
skin, extending across the ship from bilge to bilge, and connected
in a watei tight manner to the outer bottom plating. These
ballast tanks, or partial double bottoms, answered fairly well, rtnd
the material used in their construction contributed somewhat to
the general structural strength; but not nearly to the same
extent as the material in the cellular bottoms. It is now not
uncommon to find the cellular system applied throughout the
whole length of the ship, in order to gain the greatest power of
controlling the trim by the admission of water-ballast into the
spaces near the extremities. In many cases, however, the double
bottoms of merchant ships only extend over poitions of the
length; and in war-ships as already explained (page 25) the
double bottom is usually stopped some distance short of the
extremities.
Continuing the investigation of the equivalent girders for
different classes of ships, attention must next be directed to the
webs or vertical portions, marked EE in Fig. 99.
In ordinary wood ships the outside and inside planking is
worked in one thickness, as shown in Fig.^. 100 and 102. The
individual planks or "strakes" are comparatively narrow, the
numerous butts and edge seams being caulked. This planking
with the shelf-pieces under the beams, and the diagonal strength-
eners, from the web of the girder. The ultimate strength of
these parts against cross-breaking strains is no doubt ample in
all or nearly all cases; and what has to be regarded is rather
their strength to resist the racking strains which always accom-
pany bending.
Reverting to the case of the beam in Fig. 101, it will be
seen that, although the total of the tensile forces experienced
by any cross-section equals the total of the compressive forces,
2 A 2
356 NAVAL ARCHITECTURE. chap, ix.
these two resultants act in opposite directions, and therefore
tend to rack or distort the beam, this racking strain reaching
its maximum at tlie neutral surface, and gradually decreasing
to nothing at the top and bottom of the beam. So long as the
beam is iu one piece, or so long as the pieces forming its web are
well connected together edgewise, there is no difficulty in meeting
this rackiuec strain. But if a beam were constructed of which
the web consisted of strakes or narrow planks placed edge on
edge, and having little connection edgewise, then obviously, as
the beam bent, these planks would be made to slide upon one
another by the racking strains.* And if these strakes were
crossed at right angles by ties, corresponding to the ribs or
timbers of a wood ship, these ties would add little to the strength
of the ^^eb against racking. For (to quote the well-known
illustration of Sir Robert Seppings), if a field-gate be made of
pieces, all lying parallel or at right angles to one another, its
resistance to distortion of form will be very small. On the
contrary, if the strakes forming the web are crossed by
diagonal ties — corresponding to the cross-bar of the gate — there
will be a great addition to the strength of the combination
against racking and distortion of form.
Such are the simple principles upon which the use of diagonal
" riders " or ties in wood ships is principally based. The side
planking above the bilge has in itself little strength to resist
racking strains; and in many cases these strains have been so
severe as to show marked evidence of their action. When the
line-of-battle ship Csesar stopped on the launching ways and broke
considerably, it was in the planking near the_ middle of her depth
that working was most apparent ; the diagonal riders also showed
signs of severe straining:. Moreover, it is a matter of common
observation that, when the caulking of the seams of planking in a
wood ship becomes slack and needs renewal, she is much more
liable to working in the longitudinal sense. This circumstance is
easily explainable, seeing that, when well caulked, there is a much
greater resistance to the relative motion of the planks which,
racking strains tend to produce. Diagonal riders furnish, how-
ever, the best corrective for this source of weakness, if a single
thickness of planking is worked.f
* For a well-known illustration of the edgewise through adjacent strakes of the
above statement, the reader may turn skin planking, in order to prevent rack-
to the springs of railway -carriages. ing. A similar plan of bolting is some-
t In some small vessels built by the times adopted in certain portions of the
late Mr. Ditchburn, bolts were drivtn bottom plankingof ordinary woodships.'
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 357
When first introduced into the Eoyal Navy by Sir Robert
Seppino-s, early in the present century, these riders consisted of
massive timbers, worked inside the transverse ribs of the ship.
But for many years past iron-plate riders have been substituted
for the timber riders, and with very great advantage. In Fig.
102 these riders are indicated in both the cross-section and the
inside view, being marked r, r. It will be observed that they are
worked inside the ribs, and inclined 45 degrees to the vertical.
Wood-built merchant ships are usually furnished with simiUir
iron riders, which are often worked outside the timbers ; and
that arrangement has some advantages in point of strength,
although it is not so convenient to execute during the construc-
tion of a ship. Whether fitted inside or outside, the riders
are usually incdined so that their upper ends slope towards the
midship section of the ship ; near the middle of the length (as
shown on the inside view (Fig. 102), the two systems of riders
belonging to the fore and after bodies respectively are made to
cross each other at right angles. In some cases where special
strength is desired, this duplicate arrangement of the riders is
carried right fore and aft, as in her Majesty's ship Caledonia ; but
the more common plan is to have one system only. It will be
observed that, as usually arranged, these iron riders are very
efficient aids against hogging strains, which are those most
injurious to wood ships. When hogging takes place, the ends
must drop relatively to the middle, a change of form which
would bring the iron riders under tensile strains, the kind of
strains which they are best fitted to resist. Against compressive
strains these thin narrow bands of iron cannot be nearly so effi-
cient as against tensile strains, so that, as commonly fittf^d,
riders are not of much service against sagging strains, except
amidships, where the two systems overlap one another. Of
course it is amidships that the severest strains are experienced,
so that the crossing of the riders there is a great advantage ; and
it has been suggested that, if the duplication of the systems were
carried through, say, one-third or one-half of the length amid-
ships, there would be a further gain in strength, owing to the
circumstance that the riders would then assist against sagging
as well as hogging.
Composite ships of the mercantile marine were usually built
with a single thickness of planking, and consequently needed
diagonal strengtheners. One common plan of fitting these was
to have rider plates riveted outside the iron frames, and inclined
43 degrees to the vertical. The upper ends of those riders were
')
58 NAVAL ARCHITECTURE. chap. ix.
attached to the sheer strake, and the lower to another detached
longitudinal tie, formed by a strake of plating worked at the
bilge.
The composite ships of the Royal Navy are built with their
outside planking in two thicknesses. The edge-seams of the
planks in the inner thickness are each covered by a plank of
the outer thickness ; the seams of the outer thickness being
similarly covered by the planks of the inner thickness. A
strong edgewise connection is thus made in the double skin,
and consequently diagonal rider plates are dispensed with. It
should be added that this plan of working the planking in two
layers is principally adopted because these vessels have their
bottoms covered with copper sheathing, and any injurious
galvanic action of the copper on the iron hull can thus be
avoided.
Other composite ships have been constructed with the skin
planking in two thicknesses, one or both of which had the planks
worked diagonally ; it was then unnecessary to fit diagonal rider
plates to assist the skin against racking strains.
Ihis diagonal system of planking has also been adopted in
some special classes of wood ships with great success. The
royal yachts are examples of this system of construction, and
Mr. White, of Cowes, has applied it in many vessels built at bis
yard. Three thicknesses of planking are employed, the two inside
being worked diagonally, and the outer one longitudinally. The
two diagonal layers are inclined in opposite directions, and the
skin thus formed possesses such superior strength to the skin of
an ordinary wood ship tbat there need be comparatively little
transverse framing above the bilges. Direct experiments with
models, and the experience gained with ships built on this
plan, have demonstrated its great superiority in the combina-
tion of strength with lightness. The royal yacht Victoria and
Albert, built on this plan, with her unusually powerful engines
and high speed, is subjected to excessively great sagging
moments,* but has continued on service for nearly thirty years
with complete exemption from signs of weakness. Like many
otber improved systems of construction, this is found rather more
expensive than the common jdan ; but if wood had not been
so largely superseded by iron and steel, probably much more
extensive use would have been made of the diagonal system.
See the facts stated at page 299.
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 7^Q
It may be mentioned that the large steam and sailing lannclies
employed in the Royal Navy are built on a somewhat similar
plan ; the skin planking is in two thicknesses worked diagonally,
with the two layers inclined in opposite directions. These, boats
answer admirably, and have frames only on the flat of the floor,
where the wear and tear of grounding have to be borne.
Iron and steel ships have outer skins fc^rmed by numerous
plates, each of which is strongly fastened at the edges, as well as
the butts, to the plates adjacent thereto. Such a combination is
very strong against longitudinal racking strains, and needs no
supplementary strengthening such as the diagonal riders of wood
or composite ships. Many proposals have been made, and several
plans have been patented for using diagonal strengthenings in
iron ships, the superiority of an iron skin, and its capability of
resisting and transmitting strains in all directions, not having
been apprehended. From the bilges upwards, the outside plating
forms the principal part of the web of the equivalent pirder
section in ordinary iron ships like that in Fig. 103 ; and when
properly stiffened, it acts this part most efficiently when the ship
is upright. When she is considerably inclined, some parts of the
same plating contribute strength to the flanges of the girder-
section for that position, as already explained. Vessels with
double bottoms extending far up the side, or with wing-passage
bulkheads like that in Fig. 104, gain much on vessels with
single bottoms, since the additional skin contributes to the
strength of the web of the girder for the upright position, and
to the strength of the flanges of the girders for inclined posi-
tions. Any other longitudinal bulkheads which extend over a
ctuisiderable length in the ship may also be regarded as contri-
buting to the longitudinal strength, and one of the most valuable
additions of this kind that can be made to a ship is a middle-line
bulkhead like that shown in Figs. 18-25 (page 26) for an ironclad
of recent type. The longitudinal bulkheads fitted in the Great
Eastern add greatly to her longitudinal strength. It need hardly
be said, however, that such bulkheads are fitted primarily with
a view to increase in safety or accommodation ; the increase in
structural strength being a secondary consideration.
Mention may also be made, in passing, of a plan upon which
a few iron ships have been built, intermediate in character
between ships with transverse frames and others with longitu-
dinal fiames. The main frames in these special vessels lie dia-
gonally, somewhat after the fashion of riders, and therefore cross
the probable- line of fracture of the plating in ordinary iron
360 NAVAL ARCHITECTURE. chap. ix.
ships, which line, it has been said, would lie in a transverse
plane. It is hoped, tliereby, either to divert the line of
fiacture from this transverse plane to some longer and stronger
dia2:onal line or else to make the diagonal frames add to the
strength of the transverse section which gives the smallest
effective sectional area to the bottom plating. The plan has
not found ftivour with shipbuilders, nor does it seem comparable
to the longitudinal system, either in cheapness and simplicity of
construction or the combination of lightness with strength.
Vessels designed for service in shallow waters often have their
hulls strengthened longitudinally by girders. It has been
shown that the dejytli of any cross-section of a vessel has a great
influence upon the amount of its resistance to bending strains ;
and in these special vessels the depths of the hulls are so small
as to render supplementary strengthenings essential. The
American river steamers before mentioned furnish good examples.
Their hulls are extremely shallow, and have to carry an enormous
superstructure of saloons, &c., although they have in themselves
little longitudinal strength. To supply this, what is termed a
" hog frame " is constructed. It consists of a strong side keelson
fitted along the flat floor of the vessel, at some distance out from
the keel. Upon this keelson are erected a series of timber
pillars, and along over the heads of the pillars a strong con-
tinuous timber beam or tie is carried, diagonal struts being
fitted between it and the keelson. A light but strong timber
girder of considerable depth is thus firmly combined with the
shallow hull, and made to help it efficiently against hogging.
In other light-draught vessels built for river or coast service, with
iron or steel hulls, arrangements have been adopted similar in
principle to the foregoing, iron or steel lattice girders having
been substituted for the more cumbrous and less efficient hog
frame. These vessels, being designed for smooth-water service,
are not subjected to longitudinal strains of so severe a character
as those exj)erienced by ships at sea, and, what is still more
important, their strains remain nearly constant in character as
well as intensity. Hence their case is much more easily dealt
with in the manner described, tlian is that of a sea-going ship
which has to bear rapid and extreme variations of longitudinal
bending strains while she rolls from side to side in a seaway. At
the same time, there is considerable range for the exercise of
ingenuity in securing the lightness of construction demanded by
the shallow draught. The conditions of the problem resemble
more closely those of bridge construction than those connected
CHAP. IX,
STRUCTURAL STRENGTH OF SHIPS.
;6i
with the construction of sea-going ships, with
which we are more especially concerned.
Fio-s. 105 and 106 furnish illustrations of
this class ; being respectively a side view
and cross-section of a tug-boat built for the
Godavery river from the designs of Mr. J. R.
Kapier, about fourteen years ago.* The
draught of water was not to exceed one foot ;
it was consequently necessary to make the
structure as light as possible, and steel was
used instead of iron. The hull proper is that
of a shallow open boat, about o\ feet deep ;
it is formed, as shown in Fig. lOG, of steel
plates \ inch thick, with each strake of
plating stiffened by a longitudinal angle-bar.
The transverse frames consist of angle-bars,
spaced 9 feet apirt, and therefore quite
subordinated to the longitudinal frames. The
hull proper, being so shallow and without a
deck, could not contribute the necessary
longitudinal strength ; but this is obtained
in a very ingenious manner. An awning was
necessary to furnish protection from a vertical
sun and tropical rains ; it is marked a, a in
the diao-rams, and is about 10 feet above the
bottom. To convert this into an efficient
upper flange, it is formed of steel plates
-jifj^ inch thick, each strake being stiffened by
a longitudinal angle-bar. Transverse angle-
bars are fitted, 9 feet apart, vertically over
the corresponding transverse frames of the
hull, and diagonal braces (c, c, Fig. 106)
connect the corresponding transverse stiff-
eners to hull and awning, preventing the
latter from being pulled or blown over.
Lattice girders (i, &, Fig. 106) formed by
diagonal and vertical bars, as shown in Fig.
105, are fitted on each side to strengthen the
connection between the awning and the hull,
I
* The drawings ami particulars are taken from vol.
viii. of tlie Transactions of tlie Institution of Naval
Architects.
M
;62
NAVAL ARCHITECTURE.
CHAP. IX.
and to enable them to act together in resisting longitudinal
bending. The diagrams explain further particulars. The vessels
are driven by paddles placed under the sloping stern ; the boiler
is placed at the bow, where there is also a steam capstan ; and
the tow-r(tpe is secured near
the middle of the length and
led along over the awning.
Before concluding this di-
vision of the subject it may be
desirable to glance at some of
tlie more important results of
calculations made to determine
the maximum tensile and com-
pressive strains, experienced by
the upper and lower parts of
tlie structures in various classes
of ships, when they are sub-
jected to longitudinal bending
moments. For these calcula-
tions it is commonly assumed
that a ship occupies one of the
extreme positions of support
illustrated by Figs. 87 and 88,
and the resulting bending
moments are estimated in the
manner explained on page 289.
Having constructed the equi-
valent girder for the weakest
section nearly amidship^=, its
moment of resistance to bend-
ing is calculated ; and, having
this data, the maximum tensile
and compressive strains on the
material can be found by
means of the formula on page
334. It has been fully ex-
plained that this method of procedure is chiefly useful for com-
parisons between ship and ship ; and must not be treated as a
determination of the actually severest strains to which a ship may
be subjected in a seaway.
Taking fir.st the various types of war-ships mentioned in
Chapter VIII., the following statements will form an interesting
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 36
j^o
supplement to the talDles on pages 297 and 299. Armoured
frigates of the Minotaur type are subjected to unusually severe
bending moments, tending to make them hog. From calculations
made at the Admiralty, it appears that the maximum tensile
strain on the material in the upper deck, estimated in accordance
with the assumptions explained above, is only about 5 tons per
square inch of sectional area. This is about one-fourth of the
ultimate strength of good iron plates such as were used in those
ships; and this satisfactory result is largely due to the great
depth of the ship, the use of strong iron deck- pi ding, and of a
partial double bottom with longitudinal frames. It should be
added that in this estimate the armour plating on the sides is
treated simply as a burden, contributing no resistance to tensile
strains.
The converse case to the Minotaur is presented by the central
citadel type, which experiences very great sagging strains when
astride wave-hollows. In the example of this type given in the
table on page 299 the maximum strain on the material, when tha
ship is astride a wave-hollow, was found by calculation to be 5^
tons per square inch. This ves-^el was built of mild steel, and tlie
maximum tensile strain on the bottom was, therefore, about one-
jifth of the ultimate tensile strength of the material. In this
calculation also the armour was treated only as a burden : but a
further calculation made on the assumption that the armour was
efft^ctive against compressive strains gave practically the same
result, the maximum tensile strain (on the bottom) being 5 tons.
The reason for this practical agreement may be given in passing.
AYhen the armour was excluded from the calculation, the neutral
axis of the equivalent girder was about seven-tenths of the total
depth above the bottom ; whereas with the armour included it
rose to three-fourths of the depth. Consequently the increased
moment of inertia of the girder section with armour included,
was nearly counterbalanced by the increased height of the neutral
axis above the bottom.
These two extreme cases represent unusually severe strains for
armoured war-ship^. For example, in the turret-ram (m-^ntioned
in table on page 299), the maximum strain on the material was
found to be only 2 tons ppr square inch of sectional area. In the
Devastation the maximum strain, under a sagging moment, was
only Ih ton per square inch. The corresponding maximum
strain for the "belted cruiser," under hogging moment, was 2J
tons per square inch. The central battery ship only sustains a
maximum strain of 2 tons to the square inch, as shown in specimen
364 NAVAL ARCHITECTURE. chap. ix.
-V-
calcnlations on page 338. These very moderate strains, it must
be remembered, are obtained in vessels which have very lightly-
constructed hulls, and in which the scantlings are limited by
considerations of local strength and durability. Were the
principal longitudinal bending moments exclusively considered,
much thinner bottom plating might be accepted : bat this
thinning would be objectionable, because it would reduce too far
the local strength and durability of the skin. In short, in these
vessels, as in many others, the scantlings are governed by con-
siderations of local strength, and when that is provided there is a
large margin of strength to resist principal strains. These
remarks do not apply to the plating on decks and other
strengtheners used to secure a due proportion betw(^en the upper
and lower flanges in the equivalent girder. Nor must it be over-
looked that frequently in war-ships the thickness of deck-plating
provided for protective purposes is far in excess of that required
for structural streno-th. Owinsc to these various influences the
position of the neutral axis varies greatly in relation to the total
depth of the equivalent girder in different classes of war-ships ;
but this variation has no practical importance, and all the strains
mentioned above are the maximum strains sustained by the
material most distant from the neutral axis.
To the foregoing facts for armoured war-ships one example
may be added for an unarmoured ship. In the Iris, when float-
ing on the crest of a wave 300 feet long, and 20 feet high, the
maximum tensile strain on the material in the upper deck is
5 tons per square inch. The neutral axis for hogging is 52-lOOths
of the depth, below the top of the girder, so that the maximum
compressive strain on the bottom is about 4'6 tons per square
inch. This vessel is built of mild steel, having a mean tensile
strength of abuut 28 tons per square inch.
Corresponding calculations for merchant ships have been made
by many authorities during tlie last ten years ; and the recorded
results are of great interest.* In most of these calculations it
has been assumed that the maximum bending moment likely to
be experienced, on a wave crest, may be taken as one thirty-fifth
of the product of the weight of a sliip into her length; but it
must be remembered that this value of the bending moment may
b.e exceeded under certain circumstances (see page 298), and that
* See various Tapers in tlie Tram- Also Papers in the rm??.sac/;"o??s of the
urUoiis of the Institution of Naval Institution of Engineers and Ship-
Architects for 1874, 1877, an.l 1878. builders in Scotland for 1878.
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS.
36'
iu some special classes of ships sagging strains may become most
important.
From tlie published calculations for the strength of merchant
steamers it appears that in the smaller classes the scantlings
found necessary to give sufficient local strength provided an ample
margin of longitudinal strength according to the equivalent
girder theory. In the larger classes the margin of longitudinal
strength is much less than iu the smaller; and, in some cases,
the maximum strains on the material, estimated in the manner
previously described, are much greater than the corresponding
maximum strains in war-ships of equal lengths. Mr. W. John,
whose labours iu this department have been most valuable and
extensive, published the following figures in 1874, for ships then
afloat, as illustrations of the increase in maximum strain accom-
panying increase in dimensions. All these ships were supposed
to be abuut eight beams in length, and eleven depths in length,
and their scantlings agreed with the then current practice for
first-class vessels.
Register Tonnage of
Maximum Tension ou
Vessel.
the Upper Works.
Tons per Square Inch.
100
1-67
500
3-95
1000
5-19
1500
5-34
2000
5-9
2500
7-1
3000
8-1
Other examples showed that if the proportions of length to
breadth and depth were increased the vessels were subjected to
greater strains ; and in one vessel over 400 feet long a maximum
strain of nearly 9 tons was found. Vessels having less proportions
of length to breadth and depth sustained smaller strains.
Later investigations have confirmed the generdl accuracy of
these conclusions, and shown that maximum strains of from 5 to
7 tons per square inch are brought upon well-built ships from
250 to 350 feet in length, and 8 to 10 beams, or 10 to 12 depths
in leno-th. The calculations for these maximum strains are based
upon the assumptions stated above.
One marked feature in many of these calculations for merchant
ships is the comparatively low position of the neutral axis of the
equivalent girders. The decks forming the upper flanges of the
366 NAVAL ARCHITECTURE. . chap. ix.
girders were so sliglitly strengthened in relation to the strength
of tlie bottom pUxting, &c., brlow the bilges, that the neutral axis
was situated only from SO to 40 per cent, of the depth above the
bottom. Hence it followed that the tensile strain on the upper
deck produced by hogging moments was frequently about twice
as great as the corresponding compressive strain on the bottom.
This relative weakness of the decks has been corrected to some
extent in recent ships by the use of strongly plated iron or steel
upper or main decks. In the very long and large ocean-going
steamers now building, great attention is being paid to the
strengthening of the principal decks, two or three decks being
completely plated.
The magnitude of the strains which calculation has shown to be
possible in many ships of extreme length and high ratios of length
to depth and breadth, has naturally led to a closer scrutiny of the
fundamental assumptions used in the calculation. It is a matter
of fact that many iron ships which, according to the equivalent
girder method, may be called upon to sustain strains of 6 to 7
tons per square inch, go on for years in active service without
displaying any signs of weakness. In fixed land structures of
wrought iron, such as girders or bridges, the maximum strain
which could be frequently applied would be not more than 4 to
5 tons per square inch ; so that the ship has not apparetitly so
great a " factor of safety " as the bridge. Nor is this the only
point of contrast between a ship and a girder.
The comparison of a ship to a girder in her resistance to
longitudinal bending, is based upon the assumption that the
various parts of the structure are so combined and supported as
to enable them to act together. Unless care be taken to provide
against local strains, failure by buckling, and other causes of
damage, the ultimate strength of the various parts of an iron or
steel ship cannot be developed, and the comparison to a well-
*eonstructed girder does not hold. Moreover in a ship at sea, the
simultaneous occurrence of longitudinal bending moments, trans-
verse and local strains still further complicates the problem ; for
many of the pieces in the structure have to assist in resisting all
these strains. In considering what ought to be the upper limit
of strain sustained by a ship when treated as a girder and
supposed to be instantaneously balanced on the crest or astride
the hollow of waves having a length equal to her own, it is,
therefore, absolutely necessary to proceed in accordance with
experience of ships that have been tested at sea, rather than by
analogy from wrought-iron structures, such as bridges. Here
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 367
again the calculatious made for Lloyd's Eegister give very
valuable information. Mr. John summarises the results as foUo^v^ :
In well-built iron ships, wherein local strains are properly m^t,
the maximum tension on the upper works may reach 6 to 7 tons
per square inch without any sign of weakness; when the tension
reaches 7 to 8 tons per square inch some signs of weakness are
occasionally met with : but when it reaches 8 to 9 tons per square
inch, the want of strengthening soon becomes apparent. In cases
where local strains or buckling of thin plating have not been
provided against, failure may take place even when the vessel, if
treated as a girder, is subjected to very small strains.
It may appear strange that a strain of, say 7 tons per square
inch, can be accepted for an iron ship under the assumed
conditions, whereas, in a fixed bridge, strains of 4 or 5 tons would
be considered a safe limit for the working load. The explana-
tion is very simple. The working load is frequently if not
continuously brought upon the bridge ; whereas the ship seldom
comes under the assumed conditions of extreme straining.* Loug
and large ships especially gain in this respect, seldom encouuter-
inir waves as Ions: as themselves : and this circumstance should
be borne in mind while comparing the maximum tensions shown
in the preceding table. Small, short ships may often encounter
waves as long as themselves, and although the resulting strains
may be very moderate their frequency and rapid alternations are
important features. Undoubtedly the smaller ships are relatively
less strained than the larger ships, the difference being mainly
due to the fact mentioned above that the scantlings of the
smaller ships are regulated by the requirements of local strength
and durability.
The principles which govern the provision of transverse strength
admit of being explained much more briefly than do those for
longitudinal strength. In nearly all classes, the transverse frames
or ribs, the deck-beams, and the planking or plating of the skin
and the decks, together witb the pillars under the beams, and the
beam-knees, &c., connecting the decks with the sides, contribute
to the transverse strength. Iron and steel ships have the further
advantage of the strength supplied by more or less numerous
transverse bulkheads ; and so have most composite ships, as well
♦ In the bridge also there are strains due to its vibration under the action of
wind or moving load, and those due to variations of temperature.
368 NAVAL ARCHITECTURE. chap. ix.
as many wood sliips of recent types. It will be convenient,
therefore, to arrange the discussion of this branch of the subject
under the following heads: — (1) The strength of the transverse
frames or ribs ; (2) the strength of deck planking or plating ; as
well as of deck-beams, and tlieir connections with the sides ; (3)
the strength obtained by pillars; (4) the usefulness of bulkheads
in relation to transverse strength.
With each transverse frame, or rib, a portion of the skin, both
inside and outside, may be considered to act in resisting changes
of transverse form. For example, suppose in Fig. 103 (page 346)
the ribs to be spaced 2 feet apart. If two imaginary planes of
division are drawn cutting the skin midway between the frame
chosen and the frames adjacent to it on either side, this strip of
skin may be regarded as forming an outer flange of a girder, the
web and inner flanoe of which are formed bv the frame. The
enlarged section, placed a little below the upper deck in Fig. 103,
shows the sectional form of this girder. Similarly each deck-
beam may be regarded as associated with a strip of the deck-
planking or plating ; and, taking the beams with the frames to
which they are attached, each of the combinations may be
regarded as a hoop-shaped girder having in itself considerable
strength to resist change of transverse form. Similarly in
wood ships each rib and beam may be regarded as associated
with the adjacent strips of inner and outer skins. It is un-
necessary to say anything further respecting the skins, as con-
siderable attention has already been given to their arrangements
in different classes; but it is desirable to note briefly some of the
chief differences in the construction of the transverse frames.
The ribs of wood ships are necessarily made up of several
lengths (or futtocks) which are either bolted and do^Yelled (as
shown in Fig. 102) or else connected to each other in some other
way, which leaves adjacent pieces comparatively free to bend in-
wards or outwards in relation to one anotlier. As a consequence
no single rib can be regarded as having much strength in itself
against strains tending to change its form : the butts of the
various futtocks are places of comparative weakness which can
scarcely be avoided. The shipbuilder, therefore, has recourse to
the plan of shift of butts, described on page 330 for planking, as
shown in the inside view. Fig. 102 ; and the effect is to succour
the ribs at the butts by the unbroken strength of adjacent ribs.
This object is effected satisfactorily ; but the framing must be
weaker than it would be if the individual ribs could offer con-
siderable resistance to changes of transverse form. Formerly it
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 369
was the practice to fit transverse timber riders within the ribs
in order to strengthen the latter, but the practice died out when
diagonal riders came into use.
The ribs of ordinary iron, steel and composite ships are much
stronger individually than those of wood ships. Fig. 103
explains their construction (see especially the enlarged sections),
and it will be noted that each frame is really a Z-shaped
girder, the flanged section giving it great strength to resist
alterations of form. The angle-bars and plates of which the
frame is made up are either obtained in one length or else
welded or butt-strapped into the necessary lengths : the whole
being so combined that there are no places of weakness corre-
sponding to the butts in the ribs of a wood ship. This superiority
shows itself markedly during the process of building a ship, the
frame of a wood ship usually being built up piece by piece,
whereas the frames and beams of iron and steel ships are very
frequently put together before being hoisted into place, and
sustain no sensible change of form during that operation. Below
the bilges floor-plates are fitted, gradually increasing in depth
towards the keel : these floors are of great value in resisting
transverse bending strains, as well as forming supports for
cargo, &c.
Vessels in which the main frames lie longitudinally usually
have their transverse frames spaced much more widely than in iron
sliips of the ordinary construction. In vessels of the mercantile
marine built on the system advocated by Mr. Scott Russell, the
only transverse frames — excluding the complete bulkheads — are
placed from 12 to 20 feet apart, and formed by plates fitted in
between the longitudinals, with stiffening angle-irons on the
edges of the plates. These plate-frames are termed " partial
bulkheads," resembling the outer rim of a transverse bulkhead of
which all the central parts have been cut away. Their principal
use is to furnish a series of sections having considerable transverse
strength and situated between the complete bulkheads ; also to
stiften the longitudinals, and keep them in their proper positions.
The Great 'Eastern has no other transverse frames than such
partial bulkheads ; but the existence of an inner skin adds greatly
to the transverse strength, this skin forming strong inner flanges
to the hoop-shaped girders, of which the outer bottom forms
the outer flanges, and the plate-frames the webs. It should be
added that in vessels so constructed the longitudinal frames are
commonly made very numerous, in order to stiffen the bottom ;
but even when these frames are spaced only 3 or 4 feet apart,
2 B
3/0 NAVAL ARCHITECTURE. chap. ix.
the spaces of bottom plating left without direct support have
areas of from 40 to 60 square feet, and hence results an amount
of flexibility in the bottom which may become objectionable.
To obviate this objection, and give greater support to the
bottom, as well as to increase the transverse strength, the ironclad
ships of the Royal Navy, built on tlie bracket-frame system illus-
trated by Fig. 104, have the transverse frames 4 feet apart.
Most of these frames, within the limits of the double bottom, are
formed as in the diagram, plate-brackets being fitted to connect
the inner and outer angle-irons with each other and with the two
skins ; as well as to secure the longitudinals to the skins, and
prevent any change of angle. This light and simple arrangement
gives considerable transverse strengtli, but it is reinforced at
intervals of about 20 feet by partial bulkheads similar to those
used by Mr. Russell, and forming watertight partitions in the
double-bottom space. Underneath the engine-room, where con-
siderable strength is required to meet the strains due to the
motions of the machinery, instead of bracket-frames, it is usual
to fit plate-frames filling the spaces between the longitudinals,
and to cut lightening-holes in them. Before and abaft the
double bottom also, where there is no inner skin to contribute
to the transverse strength, similar lightened plate-frames are
fitted.
The bracket-frame system of construction was introduced by
Sir Edward Reed when Chief Constructor of the Navy, and has
been generally adopted in the construction of foreign ironclads.
It differs from the system used in the Warrior and other early
ironclads mainly in the adoption of the complete double bottom
and the more complete subordination of the transverse to the
longitudinal framing. In the Warrior, for example, the transverse
frames were more numerous and heavier than in recent ships.
Their greatest spacing was about 44 inches ; and for a
considerable part of the girth intermediate frames were fitted,
reducing the spacing to 22 inches. All these were lightened
plate-frames, with strong, heavy, continuous transverse frames
on the inner edges. Moreover, about 30 or 40 feet of the length
at each end of the Warrior was framed transversely, the longi-
tudinals being stopped short ; and at these parts the transverse
frames were as closely spaced as those of ordinary merchant ships.
In the Minotaur class quite as great prominence was given to the
transverse frames, which were spaced 28 inches apart. The
changes effected in ships built on the bracket system have
enabled considerable savings to be made in the weight and cost
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 37 1
of hull, at the same time that the safety and general structural
strength have been increased. Examples of these savings appear
in the following chapter.
Allusion has already been made to the close spacing of the
transverse frames behind armour in all ironclads ; and it is
unnecessary to add to these remarks. If there were no armoured
side to be supported, a wider spacing of these frames would be
adopted; and, in fact, this is the arrangement made in the
unarmoured upper works of ships with central batteries, barbettes,
or citadels.
Iron and steel merchant ships, built on the cellular system
illustrated by Fig. lOia, are framed above the bilge much in
the same manner as other ships of the same classes ; while
within the double bottom they resemble the ironclads, but have
additional transverse stiffeners as explained on page 853. In
most of them, at intervals of 12 feet or thereabouts, deep plate-
frames or " partial bulkheads " are fitted, for the same purposes
as the corresponding strengthenings in ships built on Mr. Scott
llussell's system. To complete these partial bulkheads deep
plate beams are fitted across under the decks, and thus stations
of great transverse strength are secured at frequent intervals, at
which the longitudinals are supported.
The despatch vessels Iris and Mercury, built of steel in 1875,
before the movement in favour of cellular construction beirau to
have much influence in the mercantile marine, present some note-
worthy features. The transverse frames above the bilges are
formed in the ordinary manner of two angle-bars; but the frame
spacing is 4 feet. Below the bilges there is a cellular double
bottom ^\ ith bracket frames of the ironclad type. There are con-
tinuous longitudinal bulkheads about 6 feet within the side-
plating, rising from the top of the double bottom to the upper
deck. At intervals of 12 or 16 feet partial bulkheads are built
between these longitudinal bulkheads and the side-plating, and
thus a strong cellular construction is formed throughout the
depth of the ships. Longitudinal stiffeners and the upper and
lower deck plating assist to secure rigidity ; and the numerous
transverse bulkheads complete the work. The Iris has now been
in commission for a considerable time, and notwithstanding the
lightness of her hull-construction and her great engine power she
has shown no symptoms whatever of working or weakness.*
* For full particulars of the construction, see a Paper by the Author in the
Transactions of the Institution of Naval Architects for 1879.
2 B 2
Zl'2- NAVAL ARCHITECTURE. chap. ix.
The swift cruiser class of the Royal Navy have iron hulls
sheathed with wood plankhig, and consequently have no double
bottoms. The transverse frames are spaced 3^ feet apart, which
is about twice the frame-space of large iron merchant sliips ; and
this is found to answer admirably, notwithstanding the great
engine-power, fine forms, and heavy armaments carried on the
decks. Below the bilges strong longitudinal frames are intro-
duced to reinforce the transverse framing, and on alternate ribs
deep floor-plates are fitted intercostally to the longitudinals.
This framing is combined with good bulkhead arrangements, and,
apart from the sheathing, the construction presents but little
more difficulty than that of ordinary iron merchant ships, and it
is much more favourable to the association of strength with
lightness.
DecJc-heanis, 'planking, plating and pillars also assist in preserv-
ing the transverse forms of ships. The first duty of the beams
is to support the decks with their loads ; this was the purpose
for which beams were originally fitted. But the beams have
other uses. As the various transverse strains previously described
are brought to bear upon the structure, the tendency at one
time may be to increase the distance between opposite sides of
the ship, and at another instant to decrease it. In other words,
the beams have to act as ties and struts alternately between the
opposite sides. Similarly, the pillars were fir->t fitted as struts
or supports to the beams, to assist in supporting the decks ; but
as the vessel rolls in a seaway, the strains tending to produce
alteration of transverse form sometimes produce an increased
thrust upon the pillars, and at others produce a pull or tension,
if the pillars are well secured at both the heads and heels.
Should the pillars be only capable of acting as struts, and not as
ties, one important part of their possible usefulness is lacking,
because they are powerless to resist any increase in the heights of
the decks above the keel.
The beams of wood ships are ordinarily of wood, of rectangular
cross-section, and formed of different pieces, joined together by
more or less elaborate scarphs, some of which are illustrated in
Figs. 109-112, page 393. The beam-ends very frequently
rest upon a shelf-piece (see Fig. 102) which is bolted to the
inside of the frame timbers, and are so secured to it (by dowels,
&c.) as to be capable of withstanding a considerable force tend-
ing to pull the beam away from the side. Above the beam-end
another strong longitudinal timber, the " water-way," is securely
bolted to the timbers and strongly connected with the beam,
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 373
greatly increasing the strength of its connection with the side.
In all these ways the beam is made capable of acting as
a tie between the opposite sides. Its action as a strut is
secured by very accurately fitting its ends against the inside
of the timbers. Thus far the arrangement is satisfactory,
but it involves considerable skill and cost in scarphing the
pieces that form the beam, and connecting the beam with the
water-way, shelf-piece, &c. It will be noted, however, that the
rectangular form of cross-section is necessarily inferior to the
flano-ed form : and this is an unavoidable defect with wood
beams. These considerations have led to the extensive use of
iron beams in recent wood ships; similar care being taken to
make good the connection of the ends of these beams with the
side, in order that they may act as struts or ties. Wood pillars
also have fallen greatly into disuse even in wood ships, iron
pillars of less weiglit being readily made more efficient as ties
and no less efficient as struts under the beams.
Iron and steel ships have iron or steel beams, which can be
readily obtained of various sectional forms, all of which have
more or less of that flanged form which has been shown to be
so helpful to the association of strength with lightness (see
Fig. 116). Like the frames, these beams can be easily welded
or strapped, into what is practically one piece, capable of resisting
both tension and compression. Moreover, their ends are very
simply and strongly secured to the frames (see Figs. 103 and 104),
the stringer plates on the beam-ends greatly strengthening the
connection of the beams with the side. Iron tubular or flanged
pillars can be associated with the beams, and made to resist
either tension or compression. In every way, as regards strength
and simplicity, the iron or steel ship has the advantage of the
wood one in the character and connections of the beams and
pillars. The composite ship in these particulars resembles the
iron ship.
It has been explained above that deck-flats, whether formed by
wood planking or iron or steel plating, assist the deck-beams
greatly in the maintenance of transverse form. A completely
plated deck, for example, if well stiffened by strong beams and
bulkheads, is practically rigid when subjected to strains tending
to alter the transverse form. If a ship has a series of such decks,
the transverse frames or ribs really have little more to do than to
stiffen the sides between the strong decks, or between the lowest
of these decks and the bilges. In merchant ships of large size
two or three completely plated decks are now common, and they
^74 NAVAL ARCHITECTURE. chap. ix.
o
are of the greatest value in the maintenance of the transverse
form as well as in resisting longitudinal bending. This two-
fold usefulness has been previously mentioned, and it is as
applicable to the skins as to the decks of ships. In armoured
ships strongly plated "protective" decks are now the rule; and
these decks contribute greatly to the transverse strength, being
assisted by other plated decks which are built for structural
purposes only. Protective decks are also becoming common in
Avar-ships which have no side armour, and although fitted primarily
for protection to machinery, magazines, &c., they are valuable
additions to the transverse strength.
The lower decks of ships are often extended over only a
portion of the length, or else considerably weakened by having
large openings cut in them. Merchant ships, for example,
frequently have no lower decks in wake of the cargo holds, and
consequently there is not nearly the same strength of connection
between opposite sides at those parts as w'ould be secured by a
strong deck with its beams. To compensate in part for this loss
of strength, it is usual to fit a few strong beams — known as hold-
beams — in the cargo spaces ; the convenience of stowage is thus
little affected, ^^hile the strong beams form good ties and struts.
In very many cases where such precautions have not been taken,
serious working and change in transverse form have resulted.
Instead of hold beams, deep plate frames or partial bulkheads are
often fitted as previously explained.
Perhaps the greatest point of difference between the action of
the beams in wood and iron ships is to be found in their com-
parative resistances to change of the angles between the decks and
the sides of the ship. The strains tending to produce such
changes have been previously described ; and their effects on
wood ships have been so serious as to cause shipbuilders to
bestow great attention upon beam-knees and their connections.
A vast number of plans for beam-knees, have been proposed.
Formerly, before iron strengthenings became general, cumbrous
timber knees were fitted; and in countries where timber is
abundant such knees are even yet employed. Forged iron
knees are, however, now much more generally employed, and are
more efficient than timber knees, as well as less bulky. But even
with the best of these arrangements — such as the knees shown
under each beam-end in Fig. 102 — heavy rolling in a seaway
may produce sensible changes of angle. The usual indications
of these changes are loosening of the fastenings which secure the
iron knee to the side and to the beam-end; and in the larger
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 375
classes of wood frigates and line-of-battle ships in the Royal
Navy these indications were not at all uncommon, notwithstanding
the precautions taken in fitting and bolting the knees.
The reasons for the superior resistance of iron and steel ships to
any corresponding change will be obvious on comparing Fig. 102
with Figs. 103 and 104. The beam-ends of the iron and steel
ships are shaped into strong knees, far more capable, from their
form, of preventing change of angle. These stronger knees are
fitted against the sides of the frames, and strongly riveted to them :
the frames themselves are riveted to the skin, and in very many
cases the stringer plates on the beam-ends are also directly
connected with the skin, so that the beam-end cannot change
its position relatively to the side of the ship without shearing
off numerous rivets, or fracturing plates and angle-bars. Hence
it is obvious that, with properly proportioned knees and riveting,
change in the angle made by the decks of iron and steel ships
with the sides may be almost entirely prevented. Imperfect
fastenings in the beam-knees may permit, and in some cases
have permitted, working at the junction of the decks and sides
even in these ships ; especially when they have happened to be
associated with a considerable amount of flexibility in the frames
to which the beams are attached. Bat these cases can only be
regarded as examples of a defective application of principles
which, when properly applied, lead to satisfactory results.
Similar knees are formed on iron beams fitted to wood ships,
but then instead of attaching the beam-arm directly to an iron
frame, as can be done either in an iron or composite ship, it has
to be secured to the side by means of angle-irons riveted through
the beam, and bolted to the side planking and timbers. This
plan is more efficient in preventing change of angle than the
ordinary knees fitted to wood beams, but not so efficient as that
of iron and composite ships, the connection with the side not
being so perfect.
Sometimes deep plate-knees are fitted below a few of the beams
in iron ships, reaching from one deck to that next below it, for the
purpose of stiffening the side. The beams forming the boundaries
of large cargo-hatches or boiler-hatches in merchant ships are
often treated in this manner, and made deeper and stronger than
the other beams, for the purpose of compensating for the loss of
transverse strength produced by cutting off the beams to form
the openings in the deck. The growing use of partial bulkheads
in the holds of merchant ships has been mentioned above: at the
stations where they occur deeper beams are fitted, as shown (by
376 NAVAL ARCHITECTURE. chap. ix.
dotted lines) in Fig. 104a. In the iron and steel-built ships of
the Navy also, it is common to fit "partial bulkheads" at
intervals between the main and upper decks, in order to stiifen
the sides and to assist the beam-knees in preventing change of
angle. Each of these partial bulkheads is very simply formed
by a plate 3 or 4 feet wide, connected at its upper end to the
beams or stringer plate of the upper deck, at its lower end to
the stringer plate on the main deck, and also attached to the
side plating. They are commonly fitted above the deck at which
the main transverse bulkheads terminate ; below this deck the
main bulkheads give great assistance to the structure, and lessen
the strains brought upon the beam-arms.
Not unfrequently it is a convenience to be able to dispense
with knees to lower deck beams ; a case in point is illustrated by
Fig. 26, page 30. If the ship has a sufficient number of trans-
verse bulkheads, this disuse of beam-knees is no source of weak-
ness. Moreover, it will be remembered that the transverse
racking strains described in a previous chapter are likely to be
more severe on the upper and main decks than on the lower
decks. These racking strains chiefly cause the alterations of
angle between the decks and sides, as well as deformations at or
near the bilges ; but it is especially at the upper parts of the
structures of ships that their eiTects require to be provided
against by strong beam-knees and partial bulkheads.
Transverse bulkheads, ^vhen properly constructed, add greatly
to the transverse- strength of all ships, but are most valuable in
iron or steel ships having the main frames placed longitudinally
and the transverse frames widely spaced. The cross-sections at
which such bulkheads are placed may be regarded as practically
unchangeable in form, under the action of the severest transverse
strains experienced by a ship, provided the thin plating which
forms the partition be stiffened by angle-bars, T-bars, or Z-bars
riveted to its surface. The most perfect arrangement of the
stiflfeners is that which places one set vertical and the other
horizontal, the plating being thus prevented from buckling in
any direction. The decks which meet the bulkheads lend very
material help by stiffening them and thereby preventing change
of form. Having thus secured great local transverse strength,
it becomes necessary to provide the means of distributing it
over the spaces lying between any two bulkheads; this end is
best accomplished by means of strong longitudinal frames, which
are carried from bulkhead to bulkhead, and rest upon them just
as the girders of a btidge rest upon the piers. It thus appears
CHAP. IX. STRUCTURAL STRENGTH OF SHIPS. 2>17
that the efficiency of the transverse bulkheads as stiffeners to the
structure depends upon their strength and numbers, the distance
between consecutive bulkheads, and the capability of the longitu-
dinal framing to distribute the strengtli of the bulkheads. Ordi-
nary iron or steel ships, having comparatively few bulkheads, do
not gain so much from their help as sliips with bulkheads spaced
more closely. The desire to have large cargo-spaces in the hold,
free from break or interruption, overrides, in most cases, considera-
tions both of increased safety and greater strength. A compromise
is sometimes made by fitting, at intervals between complete trans-
verse bulkheads, "partial" bulkhead-!, formed by deep plate-
frames with angle-bars on both inner and outer edges, very
similar to those fitted in vessels built on the longitudinal system.
But there are considerable spaces in the length of ordinary
merchant ships for which the transverse frames have to furnish
the principal part of the transverse str(-ngth, and the fewness of
the bulkheads is one reason for retaining the close spacing of
these frames.
When a laro-e number of transverse bulkheads are fitted in an
iron or steel ship, the distribution of their strength over the
bottom mainly depends upon the longitudinal stiffeners — keel-
sons, hold stringers, &c. These include very various arrangements,
of very various degrees of efficiency ; but in none is the distribu-
tion so simply and efficiently made as in vessels where the main
frames are longitudinal (as in Fig. 104). Longitudinal bulkheads,
when they are fitted either at tlie middle line or towards the
sides (or wings), largely assist in the distribution of the strength
of transverse bulkheads. In short, all the pieces lying longitu-
dinally, which are efficient against longitudinal bending strains
as well as against some local strains, are also valuable distributors
of transverse strength.
Composite ships are often fitted with transverse irun bulkheads,
the vessels of that class belonging to the Royal Navy being ex-
ceptionally well subdivided. These bulkheads contribute much
transverse strength, which is distributed very similarly to that
for ordinary iron ships, except thut the longitudinal pieces are not
so well connected to the skin. Closely spaced transverse frames
are trusted, however, to supply the chief part of the transverse
strength.
Wood ships of recent types in the Royal Navy, and in some
foreign navies, have been furnished with transverse iron bulkheads,
and the results have been very satisfactory ; but there must be
greater difficulty in making the bulkheads succour parts lying
378 NAVAL ARCHITECTURE. chap. ix.
between tliem in wood ships than there is in iron ships ; and the
attachment of the bulkheads to the sides is not so efficient as it
is in either iron or composite ships.
The foregoing sketch of the arrangements made to secure
longitudinal and transverse strength in different classes of ships
has necessarily been hasty and im])erfect. It may, however,
serve as a guide to the reader whose interest in the subject
leads him to study it more in detail in works devoted to practical
shipbuilding. Keeping in mind the principles of structural
strength that have been illustrated, and the character of the
strains to be resisted, it will be possible to examine intelligently
the s)' stem of construction adopted in any ship ; otherwise such
an examination would be impossible.
CHAP. X. MATERIALS FOR SHIPBUILDING. 379
CHAPTER X.
MATERIALS FOR SHIPBUILDING: WOOD, IRON, AND STEEL.
Wood, iron, and steel are the three classes of materials from
which the shipbuilder of the present day can select. Wood ships
have been in use from time immemorial ; iron ships for sea-going
purposes have not yet completed the first half-century of their
construction ; steel ships are of a still more recent date. Already'
wood ships are superseded to a very large extent by iron, and it
is probable that before another half-century has passed iron will
have given place to steel. Hitherto the use of steel has not be-
come genera], for reasons which will be stated hereafter ; but
quite recently both in France and in this country considerable
progress has been made in the manufacture of mild steel well
adapted for shipbuilding, and it has been extensively employed
both in the Royal Navy and the mercantile marine.
In contrasting the merits of these materials, it will be con-
venient fiist to compare wood with iron ; afterwards briefly
comparing iron with steel. Before proceeding to this discussion,
it may, however, be interesting to give a few facts illustrating the
wonderful development of iron shipbuilding during the last thirty-
seven years.
In 1850, out of 133,700 tons of shipping added to the British
mercantile marine, only 12,800 tons, less than one-tenth, were iron
shijis ; in 1860, out of 212,000 tons added, 64,700 tons, nearly
one-third, were iron ships ; in 1868, out of 369,000 tons added, no
less than 208,000 tons were iron ships. In 1880, out of 401,000
tons of newly-built British ships, 384,000 tons, more than nine-
tenths, were iron ships.
If attention be limited to steamships, the results are still
more striking, wood having kept its place much better in
sailing ship.s, although even there it is yielding rapidly to iron.
In 1850, out of 275,000 tons of British mercantile steamers ou
380 NAVAL ARCHITECTURE. CHAP. x.
the Eegister, four-fifths (218,000 tons) were of wood. In 1860
the total had increased to 686,000 tons ; and nearly five-sixths
(536,000 tons) were of iron. In 1868 the grand total on tlie
Register had nearly doubled again, being 1,341,000 tons ; out of
this total, wood ships only represented 122,0U0 tons, steel ships
about 8800 tons, and the remainder (1,210,000 tons) were iron-
built. During 1880 a tonnage of 346,000 was added to British
steam-shipping, and more than 344,000 tons were iron or steel
built.
The Royal Navy presents a similar picture. In 1850 the
tonnage (B.O.M.) of wood ships had a total of 99,000 tons, against
19,500 tons for iron ships. In 1860 the proportion of wood to
iron was even greater than at the earlier date, 420,000 tons,
against 34,800 tons. But with the construction of armoured ships
iron hulls became general; and in 1870 the total tonnage of
wood ships had fallen to 386,000 tons, while that of iron ships
had nearly quadrupled since 1860, becoming 130,200 tons. At
the present time (1882) nearly all our effective ironclads, including
all the ships added to the Navy during the last fifteen years, have
iron or steel hulls ; and it is a significant fact that not a single
wood fighting ship is now being constructed for the Navy, nor
has one been laid down for nine years.
Iron shipbuilding originated in this country ; has liere received
its most important developments ; and has been the source of
very great national advantage. It has rendered us practically
independent of foreign supplies of shipbuilding materials ; which
were becoming more and more important in the later days of the
supremacy of wood shipbuilding, when the supplies of home-grown
timber were quite inadequate to home requirements. Such sup-
plies from abroad were liable to interruption in time of war ; and
during peace they placed English builders at a great disadvantage,
as compared with buihlers in countries where shipbuilding timbers
were abundant and cheap. The United States, Canada, France,
and Italy, all furnished ample supplies of suitable timber ; and
the shipbuilding trade — so peculiarly British — seemed about to
pass away into other hands, when the use of iron instead of wood
once more restored the balance, and enabled us to regain our
former national position.
But more than this : the use of iron ships has been the source
of world-wide advantage. Had wood remained in use, ocean steam
navigation could never have attained its present wonderful de-
velopment, and international communication must have remained
less regular and frequent. Without iron hulls, the ironclad re-
CHAP. X.
MATERIALS FOR SHIPBUILDING.
381
construction could never have been carried to its present position ;
nor could the swift cruisers have been built. Moreover, iron
shipbuilding has done very much to encourage progress in the
manufacture of wrought iron for all structural purposes, and
thus has indirectly benefited other departments of work. In
short, the experience of forty years fully confirms the wisdom of
the change from wood to iron, and proves that, although iron
has some drawbacks, it possesses a considerable balance of advan-
tage. Other nations, endowed with a wealth of shipbuilding
timber, have not failed to realise this : in France, Italy, and still
more noteworthy in the United States, iron is rapidly gaining
ground, and English models are being imitated or improved upon.
A better appreciation of the great increase in the sizes and
proportions of ships which has accompanied the use of iron hulls
in both the Koyal Navy and the mercantile marine will be
obtained from a few typical examples. Taking the Royal Navy
first, the following tabular statement will suffice : —
Date of
Dip-
Indicated
Class of Ship.
Con-
struction.
Name.
place-
ment.
Horse-
power.
Length.
Breadth.
Wood,, unarmoured.
Tons.
Feet.
Feet.
Largest sailing three-deckers
1815
St. Vincent .
4,700
—
205
53f
,, screw „
1859
Victoria . .
6,950
4,190
260
60
,, ,, two-deckers
1860
Duncan . .
5,700
2,820
252
58
,, ,, frigates .
185Y
Orlando . .
5,6U0
4,000
300
52
Wood, armoured.
Largest class
1863
Lord Warden
7,840
6,700
280
59
Iron, unarmoured.
Swift cruising frigate . .
1866
Inconstant .
5,780
7,360
337
50J
Iron, armoured.
Early broadside ships
]
1859
1861
Warrior . .
Minotaur
9,100
10,600
5,470
6,700
380
400
58
59^
Jlodern „
j
1865
Hercules . .
8,700
8,530
325
59
(
1873
Alexandra .
9,500
8,600
325
63§
1
1869
Devastation .
9,290
6,65 1
285
62i
Mastless type (sea-going)
1871
Dreadnought
10,89 )
8,000
320
631
(
1874
Inflexible
11,900
8,0L0
320
75
This increase in size has not merely been associated with the
special strains due to the use of armour, but with the adoption
of proportionately more powerful engines, and the attainment of
higher speeds. The best of the screw line-of-battle ships of the
old type attained from 12 to 13 knots at full speed ; this latter
speed was also the maximum of the finest wood frigates. But
now the armoured battle-ship has a speed of 14 to 16 knots ; and
the swift cruiser class have speeds of from 15 to 18 knots. Wood
hulls could scarcely be expected to meet satisfactorily these
greatly changed conditions ; but iron hulls have auswered the
382 NAVAL ARCHITECTURE. CHAP. x.
purpose, and there is no reason to think that the limits of the
capabilities of the material have been reached, even ia the largest
and swiftest ships afloat. Great engine-power in wood-built ships
is very trying and injurious to the structures; but no similar
wear and tear occurs with iron. The Orlando and her sister
frigate, the Merseij, were, when constructed, experiments in the
direction of applying large engine-power and great proportions
of length to breadth in wood ships ; but the results were any-
thing but satisfactory. These vessels required considerable repairs
during their brief period of service, and rapidly fell out of use.
Against this failure to sustain successfully the strains incidentnl
to screw propulsion, set tlie case of the iron-built Inconstant,
which is longer than the Orlando, of less beam, three knots faster,
with 80 per cent, greater engine-power, and yet, thanks to her
iron hull, displays no signs of working or weakness.
In the United States the attempt was made to build swift
cruisers, the famous Wanipanoag class, of wood. Without enter-
ing into any details of the controversy respecting this class, it
may be stated that, on all hands, it is now admitted that the
wood hulls were not well suited for the great engine-power put
into the ships. The fact that several of the class have been left
unfinished or unemployed after trial shows the estimation in which
the vessels are held hj the authorities of the American Navy.
Further, it is interesting to note that American shipbuilders are,
at length, devoting themselves energetically to the development
of iron ship construction. Several small iron vessels have been
recently added to their navy; and iron has been used for the
hulls of many large fast steamships for ocean navigation. French
designers have also acknowledged the superiority of iron to wood,
by building their swift cruisers on the model of the Inconstant,
and their ironclads on the bracket-frame system illustrated in
Fig. 104.
In the mercantile marine, as remarkable changes have been
made in the sizes and proportions of ocean steamers. Take,
for example, vessels on the Transatlantic service. About fifty
years ago, the wood-built Great Western was considered a re-
markably fine vessel; her dimensions were, length 210 feet,
breadth 35^ feet, tonnage (B.O.M.) 13-10 tons, load displacement
2300 tons. She was followed, in 1840, by the Great Britain,
built of iron, of which the dimensions were, length 290 feet,
breadth 51 feet, tonnage 3270 tons (register), original load dis-
placement 3000 tons. These dimensions were then considered
extravagant, if not unsafe ; but the ship was not long ago at work,
CHAP. X. MATERIALS FOR SHIPBUILDING. xZ\
O'-'v)
on the Australian line, although thirty-five years old. The
chanires made since her construction are still more remarkable.
The larirest Transatlantic steamers now at work are 500 to 550
feet long by 50 to 52 feet beam, their displacement, when fully
laden, being from 13,000 to 1-1,000 tons. No one can for a moment
suppose that such sizes and proportions could have been achieved
with wood as the material, in conjunction with very powerful
engines and extremely high speeds. Finally, as a crowning
example of what may be done with iron, take the Great Eastern,
680 feet long, 83 feet broad, of 22,500 tons (register), and load
displacement 27,400 tons, which after some twenty years afloat still
(1882) remains strong and efficient, having meanwhile performed
most arduous work in laying various submarine telegraph cables.
Iron sliips are proved to be superior to wood in the following
important particulars: — (1) Lightness combined, with strength;
(2) durability, when properly treated ; (3) ease and cheapness
of construction and repair ; (4) safety, when properly constructed
and subdivided. On the other hand, iron ships are inferior to
wood in — (1) easy penetrability of the bottom by rocks or other
hard pointed substances ; (2) fouling of the bottom, and conse-
quent loss of speed, after being afloat for some time. Compass
correction in iron ships is now so satisfactorily performed that
there is no need to refer to a matter which at the outset had
great practical importance. Taking these points in the order in
which they have been named, each of them will be illustrated
briefly ; and after concluding these remarks, a few will be added
on the subject of the use of iron hulls in unarmoured ships of war.
First, as to lightness combined with strength. In wood-built
ships of the Royal Navy it is found that about one-lialf the
total weight is required for the hull ; in similar ships of the
mercantile marine the hulls are somewhat lighter in proportion
to the displacement. In ordinary iron merchant ships the hull
frequently weighs only one-third of the total weight, high authori-
ties agreeing that the change from wood to iron effects a saving
of from 30 to 40 per cent, on the weight of the hull. The hulls
of iron ships of the Royal Navy are not, as a rule, so light as those
of iron merchant ships, the difference being due to differences of
form and proportions and the more elaborate fittings needed for the
special requirements of their service. In some of the earlier iron
vessels of the Navy, both armoured and unarmoured, the hulls
were as heavy as, or even heavier than, the hulls of wood ships, in
proportion to the displacements. But as the principles of iron ship
construction have become better understood, considerable savings
;84
NAVAL ARCHITECTURE.
CHAP. X.
in weight of hull have been effected simultaneously with an
increase in structural strength, and now it is not uncommon to
find the weight of hull only 30 to 40 per cent, of the total dis-
placement, in vessels carrying the thickest armour and heaviest
guns. This expression of the weight of hull as a fraction of the
displacement, or total weight, of the ship is by no means a com-
plete view of the comparison of wood and iron ships. It takes
no cognisance of the fact, to be hereafter illustrated, that forms,
sizes, and proportions are now commonly adopted that could never
have been used with wood as the material ; and it does not recog-
nise the variations which, for similar methods of construction,
have to be marie in the ratio of the weight of hull to the dis-
placement, in order to secure equal structural strength in vessels
of different sizes. It is, however, a sufficiently accurate mode of
comparison for our present purpose, and is very commonly used.
The following tabular statement will show at a glance the ad-
vantages in point of lightness possessed by iron ships of various
classes ; most of the figures are taken from actual ships, and may
therefore be accepted without question : —
Classes of Ships.
Wood merchant ships .
„ war-ships, unarmoured ,
„ „ ironclad. .
Iron merchant ships
passenger steamers
troopships, Eoyal Navy, early types
„ later types,
war-ships, unarmoured (swift cruisers)
ironclad, early types .
,, later types .
„ mastless type .
„ circular type (Russian)
»
11
■>■)
11
11
11
11
11
Percentage
of Displace-
ment.
Weight of
Weight
Hull
Carried.
35 to 45
55 to 65
50
50
48 to 50
50 to 52
30 to 35
65 to 70
40 to 45
55 to 60
50 to 52
48 to 50
48 to 50
50 to 52
50
50
52 to 58
42 to 48
40 to 45
55 to 60
30 to 35
65 to 70
20 to 22
78 to 80
Notes to Table.
The Orontes and Tamar are the representatives of the earlier troopships. The
Indian troopships represent the later types, and possess a double bottom, which
their predecessors did not possess, being safer as well as lighter.
In the weight of hull for the swift-cruiser class there is included a considerable
weight of wood sheathing, fixed outside the iron hull in order that the bottoms
might be coppered or zincked. This wood is unnecessary for structural strength ;
excluding it, the percentage for hull would sink to about 42 per cent, of the
CHAP. X.
MATERIALS FOR SHIPBUILDING.
\H
displacement, notwithstanding the great engine-power and high speed of the
ships.
The case of the ironclads is so important that the following additional illus-
trations may be interesting.
IroQclads of Royal Navy.
Early f Black Prince
types \ Defence .
Weight of
Hull.
' Bellerophon ....
Monarch
Invincible ....
, ^ , Devastation (mastless) .
•^ ^ I Temeraire (zinc sheathed)
! Alexandra ....
Recent
y Inflexible
Tons.
4970
3500
3650
3670
2740
2880
3600
3800
4350
Weight
carried.
Tons.
4280
2500
3800
4630
3200
6410
4940
5700
7550
The explanation given in Chapter IX. of the structural changes by which these
remarkable results have been accomplished need not be repeated. Perhaps the
saving in weight will be better appreciated when it is stated in another form.
In a large ironclad of 8000 to 9000 tons displacement the decrease in weight of
hull would amount to quite 800 or 1000 tons, and this being transferred to the
carrying power constitutes a most notable addition thereto. At the same time
a stronger, safer ship is obtained. The moderate freeboard of the mastless
type conduces to their greater lightness of hull.
Iron ships are, then, undoubtelly superior to wood ships in
their combination of lightness with strength ; and the chief causes
contributing to the difference may be briefly summarised.
Each piece in the structure of a ship may be regarded in a
twofold aspect : first, as an individual piece liable to be subjected
to tensile, compressive, bending, or torsional strains ; secondly,
as a piece combined with and fastened to adjacent pieces in order
that it may assist the general structural strength. Following
the method of the preceding chapters, this may be expressed by
saying that the various pieces making up the structure must
be arranged with reference to both the local and the general
requirements. JMoreover, the foregoing discussion will have
shown that tensile and compressive strains are of the first
importance: bending strains have to be borne by some pieces,
such as the deck-beams, the ribs, and longitudinals, but these
strains are less important; while torsional or twisting strains are
of rare occurrence, and scarcely require consideration.
Let the resistances of single 'pieces of wood and iron to tensile
or compressive strains be first considered. Take a simple tie-bar
2 c
386 NAVAL ARCHITECTURE. chap. x.
for example, and suppose a certain \veiglit suspended to one
end while the upper end is fixed. As the weight is gradually-
increased, the bar will begin to stretch : for a certain increment
of weight the elongations will be directly proportional to the
suspended weight, and when the latter is removed, the bar will
return to its original length : the limits within which this
condition holds are termed the "limits of elasticity," or some-
times the "elastic limits." As the suspended weights are still
further increased, and the limits of elasticity are passed, if the
weights are removed, the bar will be found not to return to its
original length, but to have a permanent elongation or " set."
Finally, as the weights are yet further increased, they will
become suflScient to break the bar ; and this determines the
ultimate strength of the bar. As a measure of precaution, the
strain brought upon this tie-bar, and likely to be frequently
repeated, ought not to exceed the limits of elasticity ; otherwise
the permanent set might, in the end, become dangerously
increased. And as a matter of fact, in structures exposed to
severe tensile strains, the maximum strain likely to be brought
frequently upon any piece is rarely allowed to exceed more than
one-half or one-third the strain which would just bring the piece
to its limit of elasticity. Within those limits, as was said, the
strains produce elongations proportioned to their magnitude.
Let the bar, for example, be L feet long, and let it be observed
to stretch -th part of its length, under a strain of P lbs. per
n
square inch of the sectional area of the bar : then for any other
strain Q we must have
^, • Q L
Elongation = p ^ —
If it were possible without passing the limits of elasticity to
double the length of the bar, and E were the strain which would
produce this elongation, we must have
L = =~ X - ; whence E = Fn.
P n
This is confessedly a hypothetical case, since no bar could be
stretched to double its length, and return to the original length
when the strain was removed; but the hypothesis can be
advantageously used in practice. The quantity E is termed the
modulus of elasticity, and its comparison for various substances
furnishes a ready means of estimating the relative efficiencies
CHAP. X. MATERIALS FOR SHIPBUILDING. 387
of the different materials ia resisting change of form.* This
is equally applicable to compression, within certain limits, as it
is to tension.
In a ship or any other structure it is desirable that no
permanent set shall take place in any piece ; in other words,
that no piece shall be strained beyond its elastic limits. In
different materials the elastic strength, as it may be termed, bears
various ratios to the ultimate strength. In wrought iron or
steel, for example, the limits of elasticity are not passed until
a strain is reached equal to about one-half to two-thirds the
breaking strain. In timber, on the contrary, the elastic strength
appears not to exceed one-third or one-fourth the ultimate
strength ; but the limits of elasticity have not been accurately
determined. For absolute resistance to fracture, the shipbuil ler
has to consider the ultimate strengths of the materials employed ;
for ordinary conditions of service he has to consider what shall
be the wo7-king strains which can be repeatedly brought upon the
various parts without producing permanent change of form.
The ratios which these working strains bear to the ultimate
strengths are termed " factors of safety." These explanatory
remarks will enable us to compare with more precision the
relative efBciencies of wood and iron.
Take, first, the ultimate resistances to tensile strains of these
two materials. Good iron plates, such as are used in the hulls
of her Majesty's ships, have a tensile strength of from 40,000 to
50,000 lbs. (18 to 22 tons) per square inch of sectional area, the
weight per cubic foot being 480 lbs. By means of careful tests
this strength is secured in all the iron used ; and it is a note-
worthy fact that iron can be procured of almost constant quality
and strength. Taking this as the standard, let us see how the
timbers chiefly used in shipbuilding compare with iron as to
their tensile strengths in proportion to their weights. One
feature in which all timbers differ from iron is in their want of
uniformity of quality and tensile strength. Even when the
utmost care has been taken to season timbers, considerable
variations are found to exist, not merely in different logs, but in
the strengths of different pieces cut from various parts of the
same tree. Such causes as the existence of knots, cross-grain, &c.,
* To illustrate the use of this for- under a strain of 1680 lbs. per square
mula, we will take an actual experi- inch. Hence E = 1152 x 1680 =
ment. A piece of English oak was 1,935,000 (nearly), the required
found to stretch yJj^ of its length modulus.
2 c 2
388
NAVAL ARCHITECTURE.
CHAP. X.
affect the strength ; and it is very different lengthwise of tlie
grain from what it is across the grain. Hence arises a difticulty
in ascertaining the average strengths of timber materials, and one
which is not easily surmountable ; with the greatest care in the
conduct of experiments, different investigators have reached very
diverse results. Taking the best of these experiments, the
following are the results for a few of the timbers most commonly
used : — *
Timbers.
Average Weight
per Cubic Foot.
Tensile Strength.
British oak
Dantzic oak
Dantzic fir
English elm
Pitch pine
Teak
African oak
Sabicu
Pounds.
54
52
36
35
40
48
62
57
Pounds per Square Inch.
7,600 to 10,000
4,200 to 12,8001
2,240 to 4,480
5,500 to 13,5001
4,600 to 7,800
3,300 to 15,0001
4,800 to 10,900
4,800 to 6,900
' Doubtful values ; Mr. Laslett gives 5700 lbs. as the upper limit for teak,
7400 lbs. for Dantzic oak, and 6700 lbs. for elm.
British oak may fairly be taken as the standard timber, and its
weight per cubic foot is about one-ninth that of iron, while its
ultimate tensile strength might be about one-fifth that of iron.
Here, then, the timber apparently gains upon the iron in its
ultimate strength compared with its weight ; but it is easy to see
that it does not really compare so favourably. First, the builder
would have no certainty that any piece of oak he might select
would reach the average of strength : it might fall so low as to
be only one-eighth the ultimate strength of iron, some specimens
tested having had that ultimate tensile strength. Second, to
guard against possible defects not discoverable on the surface,
and to meet the different range of elasticity, a larger factor of
safety would be employed with the timber than with iron — about
10 for timber, as against 4 or 5 for iron.
As a simple illustration, take the case of a tie-bar of oak, say
* These figures are based upon the experiments recorded in Tiniber and
experiments of Barlow, Tredgold,
Hodgkinson, and others, of which an
excellent summary is contained in the
late Professor Eankine's works, as well
as upon the more recent and valuable
Tiniber Treea, by Mr. Laslett, late
Admiralty Inspector of Timber. Sir
W. Fairbairn's tables have also been
examined in comparison with the
others.
CHAP. X. MATERIALS FOR SHIPBUILDING. 389
1 square foot in sectional area ; it would probably have an ulti-
mate tensile strength of about 570 tons, but would only be
trusted with a moving load of about 55 to 60 tons. An iron bar
of equal weight would have a sectional area of \ square foot, and
a tensile strength of 320 tons ; but, owing to its superior elasticity
and the confidence felt in its uniformity of strength, it would be
trusted with a load of from 65 to 80 tons. Or, to state the com-
parison somewhat differently, an iron bar capable of safely sus-
taining the same load as the oak bar need only have an ultimate
tensile strength of, say, 260 tons, which would be equivalent to a
sectional area of 13 square inches. The oak bar wo aid weigh 5i
lbs. per foot of length ; the equivalent bar of iron would weigh
about 45 lbs. per foot of length.
The same considerations apply to other timbers, oak being
superior to most, if not to all of them : and in these considera-
tions we find one of the explanations of the superiority of iron to
wood in the combination of lightness with strength. Professor
Kaukine proposed 5| tons per square inch as the average ultimate
tensile strength of shipbuilding timber; but, in view of the more
recent and extensive experiments which have been quoted, this
estimate appears too high, and 3 tons per square inch would be
sufficient allowance ; 48 lbs. per cubic foot is about the average
weight of these timbers.
Their ultimate resistances to compression also require consider-
ation, in comparison with the resistance of wrought iron to direct
compression.* Here authorities differ widely as to the strength
of wrought iron. Professor Kankine gives from 27,000 to 36,000
lbs. per square inch ; whereas Sir W. Fairbairn fixed it at 70,000
lbs., on the authority of Kondelet, the tensile strength being
45,000 to 50,000 lbs. per square inch. If the mean of the two
statements is taken, it will be found that the ultimate resistance
of iron to compressive strains is very nearly the same as its
resistance to tensile strains, and this is probably very near the
truth.
A fair average value of the compressive strengths of timbers
used in shipbuilding appears to be about 3^ tons per square
inch, which nearly agrees with Professor Eankine's estimate.
Against these strains, moreover, the use of so large a factor of
safety as against tensile strains scarcely appears necessary. Sup-
posing a factor of safety of 8 to be taken instea^l of 10, the safe
* The iron is not supposed to fail by " buckling." See remarks on this subject
at p. 396.
390
NAVAL ARCHITECTURE.
CHAP. X.
working load, on an average, for timber subject to compressive
strains would be about three-eighths of a ton per square inch:
for wrought iron the working load would be from 2J to 4 tons —
say, 3 tons as a safe average. As regards compressive strains
therefore timber in single pieces compares better with iron, in
strength relatively to weight, than it does in resistance to tensile
strains. All pieces in a ship, however, are liable to both classes
of strains, and consequently wood is inferior to iron, its inferiority
becoming more marked when one passes from single pieces to a
combination.
Taking the same timbers as in the list previously given, it
appears from experiment that their ultimate resistances to com-
pression are as follows : —
Timbers.
Compressive Strength.
British oak
Dantzic oak
Dautzic fir
English elm
Pitch pine
Teak
African oak
Sabicu
Pounds per Square Inch.
7,600 to 10,000
6,800 to 8,700
7,000 to 9,500
5,800 to 10,000
6,500 to 9,800
6,300 to 12,000
10,000 to 11,000
6,500 to 9,000
These factors of safety for both tensile and compressive strains
have been determined chiefly irom the practice of civil engineers
and are adapted to the conditions of fixed structures which have
to bear the working loads frequently. There is an important
difference between such structures and ships ; for the latter have
to resist the maximum strains (described in Chapter IX.) only on
rare occasions, and probably at long intervals, the strains ordi-
narily experienced being much less severe. It has been proved
experimentally that a severe strain only occasi(mally applied is
not so likely to produce serious damage as a less strain frequently
applied especially when the character and intensity of the latter
strain are continually and rapidly changing, provided that the
maximum strain does not surpass the limits of elasticity of the
materials. For these reasons, shipbuilders do not restrict them-
selves to the factors of saftty approved by civil engineers. At
present there are no recognised factors for the different classes
of ships, but the subject is receiving attention, and from the
analyses of the conditions of strain in numerous successful and
unsuccessful ships there will probably be deduced, ere long,
CHAP. X.
MATERIALS FOR SHIPBUILDING.
)9I
useful rules for practice correspoudiug to those of the civil
engineer
The moduli of elasticity of the two materials afford, perhaps,
the readiest means of comparing their relative resistances to
both tensile and compressive strains. Professor Eankiue gave the
following values : —
Materials. i Modulus of Elasticity.
Wrought iron .
28,000,000
English oak
1,450,000
Dantzic oak
1,190,000
Dantzic fir .
1,958,000
Erighsh ehn
. ' 700,000
Pitch pine .
1,226,000
Teak . .
. 1 2,400,000
More recent experiments made in the Eoyal Dockyards on
some of these timbers give somewhat different moduli of elasti-
city. English and Dantzic oak, for example, had moduli of
about 1,900,000 — greater than those assigned by Professor
Kankine ; whereas teak had a modulus of about 1,300,000,
or little more than one-half that in the above list. On the
w^hole, however, it seems not unreasonable to accept the average
modulus proposed by Professor Eaukine, viz. that timber shall
be considered to have about one- sixteenth the modulus of iron.
When iron and wood act together, therefore, this is the ratio
which should govern their equivalent sectional areas.* The ratio
of weights per cubic foot, it will be remembered, is about 1 for
wood to 10 for iron. No further remarks will be needed in
illustration of the superior combination of lightness with both
tensile and compressive strength, in single pieces of iron as
compared with single pieces even of the best timber.
The resistance offered by a combination of pieces of timber
to compressive strains does not compare less favourably with
that of iron than does tlie resistance of a single piece of timber
to that of a single piece of iron, provided only that there is good
workmanship in the fitting of the pieces together. This has
already been explained in connection with the effective resistance
to hogging strains offered by the lower parts of the wood ship
illustrated by Fig. 102, page 344. A plain " butt " (or flat end)
to two planks or timbers will effectively transmit a thrust, pro-
See the remarks on page 330.
392
NAVAL ARCHITECTURE.
CHAP. X.
vided only that the two ends are well fitted to one another,
and are prevented from changing their relative positions.
On the contrary, when several pieces of timber have to be com-
bined in order to resist tensile strains, their resistance compares
much less favourably with that of a combination of iron plates
or bars than does the ultimate tensile strength of a single
piece of timber with that of a single piece of iron. Against
tension a butt-joint is obviously quite ineffective: for in Fig.
102, if any two timbers abutting on one another in a rib or frame
were considered to act alone, and to be subjected to a strain
tending to separate the butts, they could oj)pose no resistance
except the friction of the dowel, which would be very trifling.
If a " strap " of wood or iron were fitted over the butts and bolted
to the timbers, it would resist the force tending to open the butts ;
and it has been shown that the weakness of the butts in any rib
FIG.107
is, so to speak, covered by the strength of the unbutted ribs
lying on either side. In many wood ships the timbers of con-
secutive ribs are bolted together, in pairs, to increase the strength
of the frame. In the case of the water-way fitted upon the beam-
ends of a wood ship (Fig. 102) the various pieces are plain-butted ;
but the butts are covered by strong carlings fitted underneath,
and to these the water-way pieces are do welled. This is an
exceptional arrangement, however, the almost universal plan
adopted where two pieces of timber have to be joined end-to-
end, in order to form a tie, being to "scarph" or overlap the
ends in some fashion more or less complicated and expensive.
Take the keel, for example, in a wood ship : the adjoining pieces
are secured by what is termed a "tabled scarph." Fig. 107 shows
the two parts of the scarph, thrown back to exhibit the projecting
" tabling " and the sunken recesses into which the tabling fits.
CHAP. X.
MATERIALS FOR SHIPBUILDING.
o
93
Fio-. 108 shows the two parts in place, with the fastening bolts
which assist the tabling in resisting tensile strains tending
to open the scarph. The plan is an excellent one, but necessi-
tates considerable skill and cost of workmanship in fashioning
the scarphs so that they may fit accurately. The same thing
is true in the beam-sc;irphs, illustrated in side view by Fig.
109, and plan in Fig. 110. This is termei a "hooked scarph,"
metal wedges or keys (7i-, h, Fig. 110) being driven to tighten
FIG. 109
1^®
® i/i
®
ipsi
FIG. no
i4-
J^
1 l[ ^^
ii
II i
■ '^'^^
up the scarph, and bolts and treenails being used to fasten it.
This hooked scarph is of comparatively recent introduction,
having replaced the simple but less compact and satisfactory
method illustrated in Figs. Ill (side view) and 112 (plan).
The fastenings in this case consist of dowels, treenails, and metal
bolts. Still another method of scarphing is illustrated in Fig.
113, and is known as a "plain scarph," being free from tabling
and hooks. It is not nearly so strong against tensile strains as
FIG.III
11
I
®
m ®
@
©
© ®
©
@
©
©
FIG. 112
in^
the preceding plans; but neither does it involve such care
and expense in fashioning. The keelsons, shelf-pieces, and some
other longitudinal ties, are frequently scarphed in this manner.
It will be noted that in the last plan, and the preceding one
(Figs. Ill, 112), the fastenings have to contribute the whole
resistance to separation of the scarph under tensile strains ; and
when these strains are acting, there is a tendency for the wood
to yield in wake of the comparatively small and hard metal bolts.
^I'he greater hardness and small size of the metal fastenings
in a wood ship is one fruitful source of weakness and working.
394 NAVAL ARCHITECTURE. chap. x.
Parts, at one instant under tension, tend to yield in wake of iron
or metal bolts ; soon after, under compressive strains, the tendency-
disappears, to be followed almost immediately by its reappear-
ance, if the ship is floating amongst waves. It will of course
be understood that we are here dealing with tendencies only,
and not with actual yielding ; the existence of a large reserve
of strength often preventing the tendency from passing into a
sensible change of form. When ships are weak, it is otherwise,
and then working takes place. It is worth notice, in passing,
that the use of timber treenails as fastenings in the outside
planking of a wood ship, or of coaks and dowels, also of hard
wood, is from this point of view a considerable advantage. Coaks
in particular, and treenails in some degree, have a larger " bear-
ing " surface on the wood planks, &c., than have metal bolts ;
besides which they are not so hard, both of which differences
tend to lessen the local yielding of the pieces fastened by them.
F1C.113
w
An assemblage of wood planks or timbers, such as is found in
the outside planking, or the flat of a deck, is not usually dealt
with by scarphing adjoining pieces together. Plain butt-joints
are then had recourse to (see Fig. 100, page 330), and the weakness
of the butted strakes on any transverse section is met by the
device, previously explained, of "shift of butts," This is, how-
ever, tantamount to a reduction of the total sectional area by
one-fourth, when resistance to tensile strains is being considered ;
and the holes for bolts and treenails necessitate a further
deduction.
Such are the best results obtained either in timber-ties (like
the keel, or beam, or shelf-piece) or in an assemblage of planking.
Either scarphing of an elaborate and expensive character must be
adopted, or shift of butts must be trusted. In all cases, moreover,
the greater hardness and small surface of the metal bolts tends
to produce yielding of the wood in wake of them when the parts
are under tension.
In every one of these particulars iron gains upon wood. The
rivets forming the fastenings of piece to piece are of the same
degree of hardness as the plates or bars ; so that yielding in
wake of them is not to be feared. What must be secured is
that the riveting is properly done, and the holes in the plates, (fee.
CHAP. X.
MATERIALS FOR SHIPBUILDING.
395
FIG 114-.
F!Gli5.
well filled by the rivets. Again, when two pieces of iron have
to be joined to form a tie, nothing can be simpler than the
connection. The pieces may either be lapped and riveted, as
in Fig. 114, or butted and strapped, as in Fig. 115. In either
case the shearing strength of the rivets may be made to fix tlie
ultimate resistance of the tie to tensile strains. With the lap
joints of Fig. 114 the resistance to compression is also measured
by the shearing strength of the rivets; whereas in- Fig. 115, if
the butts are carefully fitted, the rivets
in the straps need not sustain any
shearing strain under compression,
so long as the plates are prevented
from buckling. It is usual in iron
ships to have butts for the vertical
joints of the outside plating, the
transverse joints of the deck plating,
and other important parts ; but the
edge joints of the outside plating,
which are not subjected to great
teu!>ile and compressive strains, are
usually lapped, and the edges of the
deck plating are sometimes treated similarly.
The butts in a strake of plating are not necessarily such sources
of weakness, as are tlie butts in a strake of planking, because the
butt-strap gives great tensile strength to the butts, and may
be made to render the section of the plating in wake of a line
of butts quite as strong as its section in wake of the lines of
rivet-holes at adjacent transverse frames.* Shift of butts is had
recourse to also in assemblages of plating, but is of less importance
than in assemblages of wood planking. On the whole, in a well-
built vessel, the effective sectional area of an assemblage of plating
against tensile strains is probably not far from seven-eighths of the
total sectional area, as compared with jive-eighths for the skin of a
wood ship. It is unnecessary to repeat what was said in the
previous chapter respecting the further gain of the iron skin, on
account of the efficient edge connections of strake with strake,
although this is an important advantage.
Enough has been said to show that it is no exaggeration of the
merits of iron to say that whether in single pieces, or in simple
* See a Paper contributed by the
Author to the Transactions of the
Institution of Naval Architects fur
1873. The subject is too technical to
be discussed in these pages.
96
NAVAL ARCHITECTURE.
CHAP. X.
ties, or in assemblages of numerous plates, it stands far above
wood in its resistance to tensile strains. When exposed to com-
pressive strains there is an undoubted danger of thin iron plates
failing by buckling ; but this can only happen in an ill-designed
ship; the danger is easily guarded against, and when the plating
is stiffened by some simple frame or girder, it will compare most
favourably with wood in its resistance to compressive strains. A
remarkable illustration of failure in an iron ship, by the buckling
of her thin plating under compressive strains, is found in the
steamship Marij (mentioned at page 327). It appears that the
topside and deck plating were not sufficiently stiffened for the
voyage, and consequently buckled when the ship was astride
the wave hollows, their failure bringing upon the more rigid
parts of the u})per works an excessive strain, which caused the
ship to break nearly amidships.
Iiespecting the third class of strains, those due to bending
moments, it is only necessary to add a few words. When a bent
beam fails, fracture, as already explained, usually begins either at
the upper or lower surfaces. If one of these surfaces is stretched
the other is compressed, and wee versa: failure therefore results
from the excessive tensile or compressive strains brought upon
the bounding layers of material. And for our purpose it will be
sufficiently near the truth to assume that the resistance of these
layers in the bent beam is very nearly equal to the resistances to
dii-ect tension or compression previously stated. It is undoubtedly
a fact that in solid beams, like those of wood, of rectangular cross-
section, the intimate connection of the parts with one another does
somewhat affect the resistance of the bounding layers. For
example. Professor Raukine gives the following values :—
Timbers.
Strengths in Pounds per Square Inch.
Tensile.
Compressive.
Cross
Breaking.
Dantzic oak ....
Jamaica mahogany.
Pitch pine
12,780
7^800
7,720
8,800
8,740
16,600
9,800
Such considerable differences are, however, the exceptions rather
than the rule, and do not appear in the timbers most used.
With the flanged forms obtainable in wrought-iron beams,
similar variations are not likely to occur, and there is no sensible
error in assuming that the ultimate resistances of the flanges
CHAP. X.
MATERIALS FOR SHIPBUILDING.
397
correspond to the tensile and compressive strengths obtained
by direct pull or thrust.
A few examples of the great variety of forms in which iron
beams are made will be found in Fig. 116. It is unnecessary to
repeat what has already been said as to the increased strength
to resist bending obtained by using these flanged forms, instead
of the solid rectangular sections which are unavoidable with
wood.* But it may be proper to mention that this essential
difference between wood and iron affects the relative efficiencies
not merely of deck beams, but also of ribs, longitudinal frames
or strengtheners, pillars, and many other parts of the structure
of a ship.
FIG 116.
References.
a, T-iron.
h, angle-bulb.
c, Z-iron.
d, H-iron.
e, T-bulb.
/, bulb-plate with angle-
irons.
g, made-beam.
h, box-beam.
The simple angle-iron is sometimes used as a beam ; its form
may be seen from tlie sections /, g, h, in Fig. 116, and differs
from the T-iron in having a top flange on one side only of the
vertical web. Neither the angle nor the T form is well adapted
for resisting bending strains, because of the absence of a bottom
flange. The angle-bulb {h) is a great improvement in this re-
spect, and is used for light decks or platforms as well as under com-
pletely plated decks. Z-iron (c) is used for frames behind armour
in ironclads, for transverse framing, and for longitudinal stiffeners,
but not often for beams. H-iron {d) is expensive, and is not used
so much as the made-beam {g) of similar cross-section. Not unfre-
quently, instead of having double angle-irons on the upper edge of
the made beams, to a deck covered with iron or steel plating, only
single angle-irons are worked, a portion of the deck plating above
the beam then forming the upper flange. Sections e and / may be
regarded as interchangeable : the latter was formerly much in use,
* See page 373 as to beams ; also page 369 as to ribs.
398 NA VAL ARCHITECTURE. chap. x.
but since the iron manufacturers have made sucli advances as to
be able to produce the section e with ease, and at moderate cost,
the shipbuikler naturally prefers to obtain the finished form. The
boxbeam li is only used where exceptional strength is required,
to support some concentrated load, or to furnish a very strong tie.
Of the other sections sometimes used it is needless to speak ;
they all, or nearly all, exhibit the general characteristic of top
and bottom flanges, or bulbs connected by a thin vertical web.
Even for the largest ships, beams of these sections are now
procurable in one length, which is another great advantage as
compared with the two-piece or three-piece wood beams required
in large ships.
A practical rule, not pretending to exactness, for comparing
the strengths of beams may have some interest. For the flanged
iron beams such as are generally used in ships, the ultimate
breaking strength of any cross-section may be expressed approxi-
mately by the formula
Breaking strength = 20 tons x sectional area x — |— •
o
The sectional areas being expressed in square inches, and the
depths in inches, the breaking strength will represent a moment
in inch-tons. For example, take a beam of section d, Fig. 116,
suppose it to be 12 inches deep, and its top and bottom flanges to
be each 6 inches wide, the web and flanges being ^ inch thick.
Then, approximately,
Breaking strength = 20 tons x (12 + 6 + 6) ^ X :| X 12
= 960 inch-tons.
For a solid wood beam of rectangular cross-section the approxi-
mate rule for teak or oak would be,
Breaking strength = 3 tons x sectional area x — ^ —
The weight of the iron beam taken as our example would be
about 40 lbs. per foot of length, the sectional area of a teak beam
of equal weight would be about 120 square inches : suppose it to
be 12 inches deep by 10 inches broad. Then
Breaking strength (approximate) = 3 tons X 120 X ^
= 720 inch-tons.
As regards ultimate strength, the iron beam is therefore one-
third stronger than the wood beam of equal weight. But here
the necessity for taking account of worki]ig strengths as well as
CHAP. X. MATERIALS FOR SHIPBUILDING. 399
breaking strengths must be remembered. The comparatively-
large factors of safety required with timber increase the advan-
tages of iron, even when each beam is in a single piece. The
scarphs of the wood, beam further detract from its strength in
wake of them. And, moreover, it must not be overlooked that,
while the strength of tlie iron (20 tons per square inch) may be
safely looked for, the strength of the wood may vary over a very
extensive range.
Putting the working strengths instead of the breaking strengths,
the case stands approximately as follows :
Working strength of iron beam =
, depth
4 tons X sectional area X — q — •
Working strength of wood beam =
1 depth
-f^Q tons X sectional area x — T- — •
Weight of timber (per cubic foot) - (say) ^^^ weight of iron.
Sectional area of timber beam = 10 times sectional area of iron
beam of equal weight.
Hence, finally, for equal weights and eqiial deptlis.
Working strength of iron beam _ 4 x 1 X i^_ „.,
Working strength of wood beam ~ ^^q- x 10 x ^ ~ ^'
which represents a very considerable gain in favour of iron.
Besides being procurable in single pieces of a flanged form,
iron plates and bars can be combined readily to produce that
form ; on the other hand, wood must be used in rectangular or,
at least, solid timbers, and cannot readily have many pieces
combined into a flanged form. Examples of this difference have
already been given. Eefer, for instance, to the contrast between
the solid timber ribs spaced closely in the wood ship (see Fig. 102,
page 344) and the flanged transverse frames with the adjoining
segments of plating in the iron ship (Fig. 103, page 346). As
another contrast, compare the strong longitudinal frames or
girders, to which the adjacent parts of the inner and outer skins
form flanges in the ironclad ship (Fig. 104, page 351), with the
solid binding strakes or keelsons of a wood ship. Many other
illustrations of the facility with which iron can be thrown into
the form best adapted for resisting bending strains will present
themselves to the student interested in the detailed structural
arrangements : but we cannot now enlarge upon this important
feature. Nor need we do more than recall attention to the fact
400 NA VAL ARCHITECTURE. chap. x.
that when the ship, as a whole, is treated as a girder resisting
longitudinal bending moments, the component parts of the flanges
in tliat girder are mainly exposed to tensile and compressive
strains, in resisting which iron gains upon wood in the manner
explained above; the web of the girder is simultaneously sub-
jected to racking or distorting strains, against which the superior
edge connections in an iron ship make the skin greatly more
efficient than the skin of a wood ship.
From this brief sketch it will be understood why iron ships are
liohter in proportion to their strength than wood ships of the
same form and dimensions; as also why it is possible with iron to
construct ships of sizes, proportions, and speeds unattainable with
wood. It is, of course, possible by ill-considered structural ar-
i-angements to throw away much of the advantage that may be
gained by using iron hulls. Bad combinations, improper distri-
bution of the material, imperfect fastenings, and other faults may
lead to the production of weak, yet heavy, iron ships. In order
that a fair comparison may be made between the capabilities of
the two materials it is, however, necessary to assume that the best
use is made of both.
Next, as to the comparative diirahilittj of iron and wood ships.
For some years after the introduction of iron ships this was a
matter of dispute, but lengthened experience has settled it
definitively in favour of iron. Ships properly constructed of that
material, and properly treated during their service, suffer but
little deterioration during long periods. Wood ships, on the
contrary, even when constructed of well-selected and seasoned
timber, and carefully used, are, as a rule, subject to comparatively
rapid decay. Many examples may undoubtedly be found of
o-reater durability in wood ships, but these are exceptional cases ;
and, moreover, their occurrence has not put within the power of
shipbuilders any means by which similar durability can be
secured in other wood-built ships. For instance, the Sovereign of
the Seas, built at Woolwich in 1635, is said to have been pulled
to pieces forty-seven years later, the greater part of the materials
havino- been found in such good condition as to be used in re-
building her. Still more notable is the case of the Ro}/al William,
built about 1715, which remained on service for ninety-four years
with only three slight repairs. Both these vessels were built of
oak felled in the winter, and much importance was attached to
this circumstance ; but later experience in the HawJce sloop, built
in 1793, threw some doubt upon the previous conclusion, the
CHAP. X. MATERIALS FOR SHIPBUILDmC. 40I
vessel having fallen into such a state of decay in ten years that
she was taken to pieces.*
The very numerous schemes for preventing dry-rot and other
kinds of decay in timber, which were proposed and tried prior
to the introduction of iron ships, afford ample evidence that
these cases of long-continued service were not common. These pro-
cesses are now matters of history only, and will not be discussed ;
but there appears reason to believe that, on the whole, the best
results as to durability, were obtained with ships built of well-
selected materials, which were allowed to season naturally, prior
to being used in the ship, and after she was in frame.t This last-
named condition of course involved slow progress with the
construction of a ship, and was scarcely likely to have been
fulfilled in the mercantile marine at any period ; but in the Royal
iS'avy, in the earlier half of the present century, it was fiequently
fulfilled, and some of the ships then built proved very durable.
^yith such varying conditions — depeniing upon the selection
of the timber, the circumstances of its growth, the season when it
was felled, the processes of seasoning, preservation, &c. — it will
be readily understood that it is not an easy matter to assign the
average durability of wood ships. Probably experience with
ships of the Royal Navy prior to the general introduction of
steam propulsion or the use of iron furnishes the best data for
forming a just estimate ; for the subsequent changes in materiel,
from sailing to unarmoured steam ships, from these again to iron-
clads, and from wood hulls to iron, have all tended to introduce
other conditions than those of fair wear and tear into the cessation
of the service of wood-built ships. In 1811 Mr. Chatfield read a
paper before the British Association, at Plymouth, in which he
stated, as the result of careful examination, that thirteen years
was the average time during which wood-built war-ships remained
efficient when employed on active service, and receiving ordinary
repairs at intervals. Experience in the French navy points to a
very similar term of service for wood ships. Moreover, the Rules
for Wood Ships issued by the Committee of Lloyd's Register,
and guiding the construction of by far the greater number of
wood merchant ships, allow from twelve to fourteen years as the
* See the remarks of Mr. Ambrose f It may be interesting to mention
Bowden, quoted by Mr. Laslett at that Lloyd's rules for wood merchant
pages 68-70 of Timher and Timber ships strongly recommend the i^ract ice
Trees. of " salting" the timbers, beams, &c.
2 D
402 NAVAL ARCHITECTURE. chap. x.
average period of durability to be assigned to the best descriptions
of shipbuilding timber when properly seasoned and free from
defects. Less satisfactory materials, used in subordinate parts of
ships, or in vessels of inferior classes, have considerably shorter
periods assigned, ranging so low as from four to six years.
Under the most favourable conditions, therefore, the average
durability on active service of well-built wood ships, fairly used
and kept in good repair, may be taken at from twelve to
sixteen years. It has been shown that in some cases much
greater durability has been obtained ; ami, on the other hand,
many instances might be cited where vessels hastily constructed
of unseasoned or unsuitable timber have fallen into decay in
half, or less than half, the average time of service named. It is,
of course, understood that the period of service is considered to
expire when the cost of the repairs would be so heavy, if they
were thorough, as to make it more economical to replace the worn
ship by a new one. In the United States navy, for example,
many wood vessels, built with the greatest possible rapidity
during the Civil War, were condemned after only six or eight
years of service ; while others, on which work had been suspended,
actually rotted on the stocks. The hurried construction, and
use of any materials that could be procured, were undoubtedly
the chief cause of the rapid decay ; and on the other side of the
picture may be placed the durability of the earlier screw frigates
of the American navy, which remained efficient for periods
exceeding the average given above. Very similar results followed
the hurried construction of the gunboats built for the Koyal Navy
during the Crimean War ; they speedily fell out of service.
Recent experience with the wood ships of the Royal Navy may
be quoted in support of the views expressed.* Taking the un-
armoured wood ships, from frigates downwards, it appears that
after ten to fifteen years of service they have reached such a
condition as to render it impolitic to repair them. Special
requirements have kept a few such vessels on service for longer
periods; but no injustice is done to the class in fixing sixteen
years as the general upper limit of durability for sea-going wood
ships.
Ironclad wood-built ships are no longer-lived; in fact the
conditions in these ships are, on the whole, less favourable to
durability than they are in unarmoured ships. Nearly all the
* See Parliamentary Paper (No. 297) of 1876, of Vessels Launched, Broken
up, Sold, &c., from 1855.
CHAP. X. MATERIALS FOR SHIPBUILDING. 403
converted ironclads of the Royal Navy {Caledonia class) dating
from 1861, but not actually on service until two or three years
later, are now either on the Harbour Service List or else in such
a condition as to render their repair inexpedient. So also is the
Lord Clyde, which is about two years younger. In tlie French
navy, also, very similar steps have been taken, the earlier wood-
biiilt ironclads having been struck off the effective list. The
Italian navy furnishes still further example-', and so does the
Austrian ; but it is unnecessary to multiply illustrations of the
comparatively speedy decay of wood ships. Even when all
possible care has been taken in their construction, hidden sources
of decay may exist in the structure, and sooner or later produce
serious results. No certain length of service can be guaranteed
under these conditions to any wood ship; and not uufrequently it
happens that, in the examination of some apparently trifling
defect, the discovery is made of much more serious and unsuspected
decay, leading in some cases to the condemnation of the ship as
unfit for further service. With iron ships the conditions are
quite different, as we will now proceed to show.
Iron is not subject to those internal sources of decay to which
timber is liable : nor is it subject to the attacks of worms or
marine animals which can penetrate the comparatively soft
planking ; nor is it liable to rot in consequence of imperfect
ventilation or other causes. Moreover, in a well-built iron ship
there ought not to be any sensible working; whereas in wood
ships, however carefully constructed, the connections and fasten-
ings must, as we have shown, be less satisfactory ; the entire
prevention of working is practically impossible, and in such
working is found a fruitful source of weakness or decay. Corro-
sion or rusting of the surfaces is the special danger requiring to
be carefully guarded against in iron ships ; and it is by no means
insignificant in its character. Both outside and inside, an iron
ship is constantly exposed to conditions tending to promote
corrosive action. The above-water parts of the hull are the least
likely to suffer ; but even these, on the outside, have to resist the
effects of air, water, and weather, and in the inside are exposed to
changes of temperature, the condensation of vapour, and other
circumstances productive of rust, if left unchecked. The under-
water parts of the hull are much less favourably situated. Out-
side, the bottom plating is immersed in corrosive sea-water ; and
inside, the jdating, frames, &c. are to some extent exposed to
bilge-water, often very corrosive in its character, to the chemical
action of coal or other substances carried in the hold as cargo, and
2 D 2
404 NAVAL ARCHITECTURE. chap. x.
not unfrequently to galvanic action jn-oduced by metallic eonnec-
tion with pipes, &c., of copper, brass, or lead, immersed in the
same bilge-water as the iron. Moreover, in steamers there are
the great alternations of temperature in the parts adj;icent to the
boilers and engine-room, the condensation of steam upon the
surfaces of the iron, and the production of gases more or less
effective in aiding corrosion. Adding to these extraneous causes
the generally admitted facts that in iron, such as is used for ship-
building, the want of homogeneity in the various parts of the
same plate or bar may cause corrosion to begin, or accelerate its
progress ; and that when rust has once formed it tends to propa-
gate itself, eating deeper and deeper into the iron affected, it will
be evident that watchfulness and precaution are needed to ensure
the preservation of iron ships. Their durability, in short, is not
a result to be assumed as an intrinsic quality ; but they differ
from wood ships in this important feature :— with care and proper
treatment they can, at moderate expense, be maintained in a
sound and efiScient state for very many years ; whereas wood ships
cannot be so maintained without an unwise outlay. The causes
of decay in the iron ship lie upon the surface, and are to a great
degree preventable : those in the wood ship are deep-seated, diffi-
cult to discover, and practically incurable in the parts attacked.
A corroded plate or bar can be scraped free from rust, cleaned
and painted ; and if corrosion has not proceeded far before such
measures are taken, it is little or nothing the worse. On the con-
trary, a rotten timber or plank must be wholly or partially
removed, often with very considerable difficulty. Neglect of
preservative measures, of course, leads to the rapid decay of both
iron and wood ships; but when the best is done for both, iron
proves immensely more durable than wood.
General experience in mercantile and war fleets places this fact
beyond dispute ; but it does not yet enable one to fix an average
of durability for iron ships, properly treated, corresponding to the
average previously stated for wood ships. This is due, in part,
to the comparatively short time that iron ships have been in
general use : forty years or so, when contrasted with the lifetime
of some existing iron ships, being a period too short to give data
for fixing an average. Besides, it must be remembered that
experience was necessary in order to determine what measures
Mere best adapted to preserve iron ships, and what methods of
construction most favoured such preservation. Even at the
present time opinions on these matters are by no means
unanimous. But certain points are settled which, at the outset,
CHAP. X. MATERIALS FOR SHIPBUILDING. 405
were uncertain, and in all probability the durability of ships built
on these later methods — favourint^: the accessibility for inspection
of all parts of the bull, and the isolation of the outer skin from
many causes of corrosion by means of a double bottom — will prove
greater than the durability of ships of earlier types. Hence the
determination of the average durability of iron ships must be
postjioned to a later date.
Many of these early iron ship^, however, proved very durable.
Mr. Grantham records that the Aaron Manhij, the firet iron steam-
vessel, built in 1821, lasted thirty-four years; the Garry Owen
and Euphrates, river steamers, were in good order after twenty-
four years' service ; the Nemesis and Phlegefhon, the earliest iron
war-ships built for the East India Company in 1839, were still
at work twenty years after; and many other similar cases are
known.
Turning to existing iron ships, no less notable results may be
stated ; but only a few can be given. The Great Britain, mer-
chant steamer, was built in 1840, but is still afloat (1882). In the
Royal Navy the troopship Simoom is thirty years old, but is still
on active service. The Himalaya won golden opinions during the
Crimean War, has been almost continuously emj^loyed since, and
is quite as popular now as she was twenty-five years ago. The
Warrior and other iron-built ironclads, dating from 1859-61, are
yet strong and sound; whereas their wood-built contemporaries
in the French and British navies have fallen into decay. In the
navy of the United States very similar experience has been
obtained. The iron-hulled monitors which were on service during
the Civil War remain on the effective list; but the wood-built
monitors of later date have fallen into decay, and are being
replaced by iron. Curiously enough, in some of these iron vessels
wood beams were used, in consequence of the difficulty of pro-
curing iron beams ; and thus a very good illustration has been
given of the comparative durability of wood and iron. The wood
beams decayed after eight or ten years, and were then replaced,
at considerable cost, by iron beams; the iron hulls meanwhile,
although much neglected for a time, are said to have suifered no
serious loss of efficiency.
Durability, in the sense we have used the terra, is determined
by the period which elapses before repairs become too expensive
to be undertaken. Repairs to an iron ship are not nearly so
difficult or expensive as in a wood ship; and therefore the limit
of economical employment would not be so soon reached in the
iron ship as in the wood, apart from the less rapid decay. On
4o6 NAVAL ARCHITECrURE. chap. x.
the other hand, the oomparative thinness of the skin of an iron
ship makes even a small loss of tliickness important; and, what
is perhaps of greater importance, corrosion is not nniform nor
regular in its character over the whole surface of the bottom, but
often becomes localised, "pitting" the iron plates in places.
The rate of corrosion depends upon so many and such varying
conditions that no general law can be assigned. For example,
the same ship exposed to the action of differently constituted
sea-waters will be corroded at different rates. The existence of
galvanic action also rapidly accelerates and localises corrosion ;
and two phites or bars of iron apparently similar in quality are
often found to be very dilTerently affected by corrosion, as are
also different parts of the same plate or bar. It lies outside our
present purpose to attempt any discussion of this subject beyond
what has been done, but obviously the practical deduction to be
drawn from this want of regularity in the rate of corrosion of iron
ships is simply this : — to prevent serious corrosion, careful and
frequent inspections are necessary of all parts of the hull,
particularly of those situated below the water-line. Experience
confirms the view that where such inspections are made, and the
surfaces of the iron are kept protected by paint, varnish, or
cement, the rate of corrosion may be made very slow. This broad
general deduction is far more important than the deductions
made from laboratory experiments on the loss of iron by corrosion
under various conditions, although these experiments have a
certain value.*
The outer bottom plating of an iron ship, liable as it is to
cortosion on both surfaces, furnishes one of the best tests of the
possibility of lessening corrosion by the means just mentioned.
In the ships of the Eoyal Navy, when undergoing thorough
repair, it is usual, after tliey attain a certain age, to ascertain the
decrease in thickness of the })lating by careful drilling and
measurement. When thus treated a few years ago, it was found
that the Simoom, then over twenty years old, required only a
small number of new plates in her bottom, by far the larger
number of the plates having maintained sufficient thickness to be
safely trusted for further service. It is also worthy of mention
* An excellent summary of such 1872. Some of the conclusions from
experiments is contained in a Paper those experiments stated by Mr.
contributed by the late Mr. E. Mallet, Mallet appear, however, scarcely con-
F.E.S., to the TranFMctlons of the sonant with the results of experience
Institution of Naval Architects for with iron ships.
CHAP. X. MATERIALS FOR SHIPBUILDING. 407
that as yet (1882) not a single bottom plate in any of the iron-built
ironclads of the Navy has had to be renewed in consequence of
corrosion, although some of these vessels have been afloat twenty
years. Lloyd's Rules, the highest authority that can be quoted
for merchant ships, being based upon a very large range of
experience, fully recognise the slow progress of corrosion in iron
ships properly treated. Therein it is provided that, when an iron
vessel is twelve years old, she is to be thoroughly surveyed, and
all rust removed, the thickness of her plating being ascertained
by drilling : where the loss in thickness exceeds one-fourth of the
original thickness, new plates are to be fitted. Surveys made at
intermediate periods are trusted to discover any local wearing or
pitting, and it is not until another twelve years have elapsed that
another searching investigation is required. No absolute limit is
placed upon the period of service, the Rules providing that vessels
will be classed "so long as on careful annual and periodical
"special surveys they are found to be in a fit and efficient
" condition to carry dry and perishable cargoes to all parts of the
"world."
Laboratory experiments upon the loss of thickness in iron plates
subjected to the action of sea-water do not furnish trustworthy
data from which to compute the durability of the bottoms of iron
ships; and this for two reasons. The actual condition of service
in a ship cannot be represented, nor can all the variations in
quality of the iron be tried. To state the mean loss in thickness
for a certain period, as already remarked, is very misleading,
since local wear or "pitting" takes place, and may penetrate
deeply into a small portion of a plate of which the general
surface is but little worn. In iron vessels of considerable age
it is not uncommon to find local patches of corrosion, at which
the reduction from the original thickness of plates is twice or
thrice as great as the average reduction. Galvanic action
exaggerates local wearing : if a copper suction-pipe, for instance,
dips into the bilge-water which lies upon the inner surface of the
bottom plating, and this pipe and the plating are joined by ever
so circuitous a metallic connection, galvanic action will be set
up and the iron plate near the suction-pipe will waste. Cases
are on record where by this means holes have actually been worn
completely through the bottom of an iron ship, which in other
respects was satisfactory ; but this kind of action is wholly
preventible when proper precautions are taken. Pitting due to
other causes is not wholly preventible, but it may be much
lessened by careful selection of the iron plates used on the
4o8 AAVAL ARCHITECTURE. chap. x.
bottom, and by careful and frequent inspection, scraping, and
painting of the surfaces.
To show how limited is the use of laboratory experiments, one
example may be given. One careful experimenter (Mr. Malle )
estimated from his experiments that the mean loss in thickness
of iron'plates immersed in foul sea-water was ratlier over ^ inch
("UK)) ^^ '^ century: two other careful investigators (Dr. Calvert
and JMr. Johnson) reached the conclusion that the corresponding
loss would be about | inch (t^q)* '^^^^ mean result for all these
experiments would therefore be -f'-^-^ inch as the loss of thickness
in a century ; which would be less than the actual thickness of
the bottom plating of a large number of iron ships. As a matter
of fact, however, many cases are on record where, without pitting,
iron plates on the bottoms of ships have worn much more rapidly.
In the Megsera, for example, when fifteen years old, many plates
were found* to have become reduced \ inch from their original
thickness; and if this rate of wear had been maintained, the loss
in a ct-ntury would have been not much less than thrice as great
as that given by the laboratory experiments. It is, of course,
quite conceivable that under other conditions the wear in tlie
Megeera might have agreed with the laboratory experiments ; but
neither such experiments nor actual results on ships can furnish
any general law for the rate of corrosion.
The Eegnlations issued by the Admiralty for the preservation
of iron ships contain the best summary of the precautions neces-
sary for that purpose with which we are acquainted. As the
circulars on this subject are generally accessible, it will be suf-
ficient to summarise the main points. Galvanic action of copper,
brass, or lead upon the iron hull is to be prevented by making the
lower pieces of suction-pipes, &c., which are immersed in the
bilue-water, of iron or zinc or ziucked iron wherever that is pos-
sible. Where copper or brass pipes are unavoidable, they are to
be well painted or varnished and covered with canvas in order to
redufe their action on the iron. The gun-metal screw-propellers
are also to be painted for the same reason, and bands of zinc,
termed " protectors," are to be fitted near them, in order to con-
centrate the galvanic action of the propellers upon the protectors
and save the bottom plating : this plan has answered admirably.
In order to preserve the inner surfaces of the bottom plating below
the bilge from the injurious effects of the wash of corrosive
bilge-water from side to side as the ship rolls, cement is used,
and has proved of great advantage to both merchant and war
ships. Other surfaces of plates and bars in the interior are pro-
CHAP. X. MATERIALS FOR SHIPBUILDIXG. 409
tected by suitable paints or compositions. All partii of tiie hull
are ordered to be made as accessible as possible for inspection and
repairs. In cases where parts are necessarily inaccessible under
ordinary circumstances — such as under the boilers or engines, kc.
— careful records are to be kept of them ; and when opportunity
offers, as during a thorough repair at a dockyard, all such parts
are to be opened up and inspected. When a ship is in the reserve
or on service, all acce.^sible parts are to be inspected once a
quarter, cleaned and painted when necessary. Annually a more
thorough survey is to be made, by dockyard officers when pos-
sible; and then the only parts to be left unvisited are those
which cannot be reached without great difficulty — as, for in-
stance, spaces which can only be attained by lifting the boilers
or maciiinery. The use of double bottoms facilitates a thorough
examination; especially of the inner surface of the outer plating",
and all the parts of the inner plating underneath engines and
boilers. The outer surface of the bottom plating is to be sight"(l
at least once a year; it is protected by some anti-corrosive paint
or composition, and if the annual examination shows it to be
necessary, this protective material is renewed.
Such are the main points in the Admiralty Regulations. Con-
formity to them must prevent any serious corrosion taking place :
for rusting ought to be detected in its earlier stages, and the
surfaces, being frequently cleaned and coated, ought not to suffer
greatly. The system has now been in force for some years, and
has worked most satisfactorily. In a modified form it is applied
also to the preservation of the ironwork in the composite ships of
the Royal Navy.
Thirdly, iron ships gain upon wood in being more easily and
cheaply built and repaired. Upon this division of the subject
but few remarks will be necessary, although it has great prac-
tical importance.
Timber is only obtainable by the shipbuilder in pieces of which
the forms and dimensions are limited by causes beyond his
control ; and the greatest care has to be bestowed upon the
" conversion " of the logs, in order to get out of them the best
possible finished timbers. For some parts of a ship where the
curvature is considerable — as, for instance, the ribs — it is not
unfrequently a matter of difficulty to procure suitable timbei-.
Even when a good choice has been possible, considerable labour
and skill have to be expended on fashioning the pieces ; and we
have shown how difficult it often is to efi'ect a good combination
4 TO NAVAL ARCHITECTURE. chap. x.
of piece with piece. Manual labour is, moreover, almost a neces-
sity in the greater part of the work of building a wood sliip.
Iron, on the contrary, is obtainable by the builder from the
manufacturer almost of the sizes and forms required, the di-
•men>;ion8 of the pieces and their sectional forms being limited
only by the powers of the manufacturer, which continually in-
crease as the demand increases. The progress already made is
most remarkable, and there are yet no signs of the limit having
been reached. Less than twenty years ago an armour plate which
weighed 5 tons was considered heavy; now (1882) plates are com-
monly made weighing 20 or 30 tons, and plates of 40 or 50 tons
can be produced if desired. Another example is furnished by the
manufacture of wrought-iron beams. Formerly the sectional
form/ in Fig. 116, was largely used, and the section e was
made with difficulty by a special process: now e can be rolled
easily, even in the largest sizes. The section c also has replaced,
to a large extent, a girder formed by a plate with a single
angle-iron on each edge. But it is needless to further illustrate
a well-known fact : the progress of the iron manufacture tends
towards the production of finished sectional forms, and the avoid-
ance of cost and labour in combining plates and angles to produce
such forms.
In building an iron ship, less work is also required in fashioning
and combining the pieces than is the case with wood. Beams,
for instance, in the iron ship are given to the builder in one
length : costly scarphs like those in Figs. 109 and 110 are un-
necessary. Bending takes the place of the costly fashioning
required for the curved pieces of a wood ship. Welding, lapping,
and butt-strapping replace scarphing. And, what is no less
important, machinery can be, and is, extensively employed in the
preparation of the parts of an iron ship.
Any one who has witnessed the rapid progress" on the framing
of an ordinary iron ship, as compared with that on the erection
of the ribs of a wood ship, cannot fail to have noticed the much
greater simplicity of the operations required in the iron ship.
And although in a vessel built on the longitudinal system of
framing (see Fig. 104, page 351) the operations of construction are
less simple than those in an ordinary iron ship, yet even here all
that has been said above applies ; individual pieces are procured
of the forms and dimensions desired, they are combined simply,
and the work admits of being pushed on rapidly.
Iron ships are also much more easily repaired. All, or nearly
all, the surfaces of the skin-plating, as well as those of the trans-
CHAP. X. MATERIALS FOR SHIPBUILDING. \\ \
verse and longitudinal framing, in these ships may be, and should
be, made easily accessible for iuspection : for which purpose it is
highly desirable that the inside planking (or " ceiling ") should
be arranged in such a manner as to be readily removed. In
case of damage, therefore, the injured parts can usually be reached,
examined, and replaced without any great difficulty. Wood ships,
on the contrary, are not so readily examined or repaired. The
various parts are so closely associated, interlaced, overlapped, and
fastened, as to render a considerable disturbance unavoidable it
any considerable repair is needed. It is, for example, a task ot
some difficulty and expense to replace a rotten timber in the
framework by a sound one, and when a vessel has been aground
and had her bottom seriously damaged, the cost and difficulty of
the repair must be considerable.
From many notable examples of the ease with which the repairs
of iron ships may be effected, a few may be selected. The Great
Britain was for many months ashore in Dundrum Bay, and
although the bottom was battered by beating upon the rocks,
and the boilers were forced up about 15 inches, yet the damage
was almost confined to the lower part of the hull, her form re-
mained unaltered, and she was got off and repaired. The Tijne,
an iron steamer, ran ashore on the south coast, and remained
for several mouths in an exposed position; but she too was
ultimately floated and repaired, being made as strong and sound
as ever, although a large portion of her keel had been torn off
and her floor much injured.* The Great Eastern furnishes still
further proof of the ease with which an iron ship can be again
made efficient after serious damage to her bottom ; f and in the
Eoyal Navy one meets with similar cases. The Agincourt was
easily repaired after running on to the Pearl Kock ; and the
Bellero]jlion and Northumberland were again restored to efficiency
without large expenditure after being injured by collision. Still
more remarkable are the cases, of which several have been brought
to our knowledge, where iron ships which have grounded and
broken in two, have subsequently been floated, the separated
parts reunited, and the ships again employed successfully. We
regret that limited space prevents any details being given of these
occurrences.
* Mentioned by Mr. Grantham in Great Eastern will be found in the
his work on Iron Shiphuildiny. Much Life of Mr. I. K. Brunei,
interesting information respecting the f See the rernarks on page 29 as to
accidents to the Great Britain and the accident to that ship.
412 NAVAL ARCHITECTURE. CH \p. x.
Further, ii-on sliii»s, uuJer the ordinary conditions of service,
require much less expenditure on repairs tlian wood ships, in order
to meet wear and tear. This is a matter not admitting of question.
It is, of course, difficult to speak with certainty as to the com-
parative costs ; but probably it is within the truth to say that, on
an average, the deterioration in a wood ship is not far from twice
as great as that in an iron ship, in equal times, and under similar
conditions of service. The usual allowance for wood ships is that
in from twelve to fifteen years the casual repairs to meet ordiuaiy
wear and tear of the hull, apart from accidents, would about equal
the first cost ; for iron ships the corresponding term would prob-
ably be twice or thrice as great. The Parliamentary Returns for
the Royal Navy confirm this view, only the figures given represent
total outlay upon maintenance, repair, and alterations in the hull,
machinery, armament, (tc, and therefore tell against the iron
hull considered separately. This being understood, the following
figures will be interesting. During the eight years 1866-7-1 over
£124,000 in all was spent upon the miiintenance and repair of
the Warrior — a large sum, doubless, but corresponding to an
average annual outlay of about one twenty -fifth part only of the
first cost — although this period re[)resented what would have been
the latter half of the average life of a wood ship. The same
proportionate outlay occurred also in the Defence and Resistance,
which, like'the Warrior, date from 1859-60. Ship^ of less age,
of course, cost proportionately less. Tlie Bellerophon, for instance,
in these eight years, being new, only had spent upon her annually,
on an average, abuut one thirty- third part of her first cost, and
this included repairs after her collision with the Minotaur. In
their first five years of service the Invincible class cost annually
only about one-eightieth part of their first cost. While these
examides are not exactly to the point, they furnish a confirmation
of the views expressed above ; for the boilers and machinery are
subject to greater wear and tear than the hull, and the cost of
alterations in fitting or equipment is not fairly chargeable to
repairs.
The relative first cost of constructing wood and iron ships is a
matter upon which it is not easy to pronounce definitely. Some
authorities have estimated that in merchant ships the saving by
using iron instead of wood must amount to quite 10 per cent. :
others have asserted that, on the whole, in iron sailing-ships
merchandise can be carried at least 25 per cent, more cheaply
than in wood ships of equal size. But obviously the relation
between the first co.sts is not the sole, nor even the chief, condi-
CH\P. X. MATERIALS FOR SHIPBUILDING. 413
tion in the determination of the relative economies of the two
classes of ships ; and the changes in the prices of materials from
time to time must greatly influence that relation. For exam])le,
uhen iron was so dear a few years ago, wood sailing-ships of
moderate size were much in request because they were cheaper
than iron ships : but even under those unusual conditions no
attempts were made to reinstate wood in the construction of the
largest sailing ships, much less in that of steamers. In short, as
has been previously said, it is a question of the possibilities of the
two materials which lias determined the shipbuilder to abandon
wood : with iron he can achieve results not attainable with wood,
and he would be justified in incurring greater first cost in
building iron ships, even were that additional expense necessary.
In proportion to tiieir commercially remunerative powers, iron
ships are not dearer than wood; and in judgiug of these powers,
one has to consider, besides first cost, the durability of the
structure, probable expense of repair and maintenance, carrying-
power for cargo, &c. In war ships, instead of cargo, there have
to be carried weights of armour and equipment ; and it is quite
conceivable that, to gain a permanent superiority in this carry-
ing-power, it wouhl be really economical in the end to incur a
greater first cost. These considerations apply with greater force
to the comparison of steel and iron ships than they do to that of
iron and wood ships, as will appear farther on.
The last feature of superiority in iron ships to which reference
will be made is their greater safety when properly constructed.
Against all ordinary risks of foundering at sea iron ships may be
secured by efficient watertiglit subdivision, such as has been
described at length in Chapter I. It has there been remarked
that in very many cases other considerati(ms are allowed to
override those of safety; iron ships being built with so few
bulkheads as to be practically destitute of any provision against
foundering, other than the strength of the skin-plating and the
decks. But this failure to introduce bulkheads, in order to
obtain large cargo-holds, of course detracts in no measure
from the possible safety of iron ships. Much the same may be
said of the doorways and other openings cut in the bulkheads for
convenience of passage from one compartment to another : these
openings may be provided with watertight covers, but if they are
not closed when accidents happen, the efficiency of the system of
subdivision obviously ouglit not to be discredited in consequence.
Again it is possible, either by defects of workmanship or by wear
414 NAVAL ARCHITECTURE. chap. x.
and tear in service, for a partition .presumably watertight to be
really not so : such defects are, however, easily discovered by
testing, and are not difficult to remedy.
All that need l)e said, therefore, on this head is, that when the
internal space of an iron ship is subdivided into numerous com-
partments by longitudinal or transverse partitions rising to a
sufficient height, or by horizontal platforms, or an inner skin,
and all such partitions are really ivatertiglit, then that ship is
safer than any wood ship would be against foundering.
It is needless to quote instances of the insufficiency of the
subdivision practised in most iron merchant ships: they are, un-
fortuuiitely, of too common occurrence ; accidental, and perhaps
slight, collision leading to the rapid sinking of one or both of the
ships. The ill-fated troopship Birlcenhead is a case wherein the
oiiginal subdivision was satisfactory, but was marred by cutting
openings in the partitions, in order to make more easy the
passage from compartment to compartment in the hold. In the
Vanguard, according to the evidence given at the court-martial,
the doors in sjme of the bulkheads were open when the ship was
struck by the Iron Duke, as they naturally would be under the
circumstances ; although, had the ship been expecting a collision,
as in action, the doors would either have been closed or held
in readiness for closing. Some difficulty was experienced in
closing the doors in the Vanguard, and the results were very
serious, as the steam-pumps could never be brought into opera-
tion. Finally, as a case where the watertightness of a partition
proved of great importance, reference may be made to a case
which happened some years ago. On survey it was found that
the bulkheads of a steamer were not watertight; and they were
ordered to be made so. Almost immediately after, the vessel was
struck by another, and seriously damaged on the fore side of a
bulkhead, which had been caulked, the watertightness of which'
prevented any passage of water farther aft, and kept the vessel
afloat, bringing her passengers and freight safely into harbour.
Bulkheads in iron ships have also proved themselves of great
value against fire. The well-known case of the Sarah Sands
illustrates this. The nature of the material in their hulls gives
to iron ships a greater degree of safety from fire than wood
ships; although the existence of wood decks, inside planking,
fittings, &c., somewhat detracts from this superiority. In the
Sarah Sands, when employed as a troop-ship, and far away from
land, a serious fire in the alter part of the ship was kept from
spreading by tbe existence of a bulkhead, upon one side of which
CHAP X. MATERIALS FOR SHIPBUILDING. 415
cold water was thrown in large qaantities; and althoui^h the
yessel was much damaged, she was kept afloat and the lives of
those on board were saved, which could scarcely have been
hoped for had such a fire broken out in a wood ship.
Turning to the other side of the picture, brief reference tnust
next be made to the disadvantages attending the use of iron ships.
These are twofold: easy penetrability of the thin bottom by any
hard pointed substance, and fouling of the bottom. Respecting
the former, it is only necessary to refer to the remarks made iu a
previous chapter (page 315), and to add that the use of a double
bottom completely overcomes the difficulty, while it would be
unwise to attempt to meet it, as some persons liave suggested, by
greatly increasing the thickness of the outer bottom plating.
Folding is a much more serious drawback to the use of iron
ships. Wood ships with copper sheathing on their bottoms
can keep the sea for very long periods with a comparatively
small increase in resistance, and loss of speed, due to their
bottoms becoming dirty. Iron ships, on the contrary, even
when their bottoms are covered with the best anti-foulins: com-
positions yet devised, cannot usually remain afloat more than a
year without becoming so foul as to suffer a serious loss of speed ;
and very frequently a much shorter period suffices to produce
this condition. The prevention of fouling has naturally attracted
much attention; numberless proposals having been made with
the object of checking the attachment and growth of mariiie
plants and animals, which go on more or less rapidly on iron
ships in all waters, and especially in warm or tropical seas.
Various soaps, paints, and varnishes of a greasy nature have
been proposed for the purpose of rendering the attachment of
these marine growths difficult, and of securing a gradual washing
of the bottom when the ship is under weigh. Many others have
been suggested having for their common object the poisoning or
destruction of these lower forms of life. Sheets of glass, slabs of
pottery, coatings of cement, enamelling, and many other plans
for giving a smooth polished surface to the bottom, in order
to prevent the adhesion of plants and animals, have been re-
commended, and in several instances tried, but nut with much
success. In fact, it would be difficult to point to any other
subject which has been made the basis of so many schemes and
patents, with so little practical advantage. Between 1861 and
1866 over a hundred plans were patented for preventing fouling,
and in the subsequent period inventors have been quite as busy ;
4l6 . NAVAL ARCHITECTURE. chap. x.
but no cure for foulinj; has yet been devised, the best composi-
tions in use are only palliatives, and the question remains much
in the same position as it did fifteen or twenty years ago.
A distinction must be made between corrosion and fouling.
Tlie former, with frequent ins'jection, cleaning, and paintiug of
the outer bottom plating, can be made very slow ; and this course
is not merely advantageous in preserving the structure, but has
the effect of reducing the tendency to fouling. Neglect of pre-
cautions against corrosion has the effect of making fouling more
rapid. Some persons even go so far as to affirm that if all rusting
vere prevented on the bottoms ot iion ships, they would be free
fioni fouling ; and that if a smooth, clean surl'ace couhl be main-
tained, the plants and animals would not attach themselves.
Some serious objections to this view may be urged ; but it is
needless to dwell upon them, since the conditions laid down can
never be fulfilled in practice on the bottom of an iron ship, subject
to blows, abrasions, and all the wear and tear of service, besides
being almost constantly immersed in corrosive sea-water. All
iion ships with unsheathed bottoms become foul in a compara-
tively short time ; and cases are on record where a few months in
tropical waters have sufiSced to produce such an amount of fouling
as to reduce their speed very considerably. Under ordinary
conditions, if an iron ship can be docked and have her bottom
cleaned and re-coated once or twice a year, all goes well; but
lunger periods afloat induce an objectionable amount of fouling.
Hence it is that vessels intended for cruisers in the Royal
Navy, as well as special vessels in the mercantile marine,
intended to keep the sea for long periods and to maintain
their speed, have been either constructed on the composite
system, or else had their iron hulls sheathed over with wood
planking and covered with some metallic sheathing, such as
copper, jMuntz metal, or zinc. The clippers which were for-
merly employed in the China tea-trade, and whose annual races
home attracted so much notice, were built on tlie composite
system, resembling iron ships in all res[)ects except that they
had wood planking, keels, stems, and sternposts, and had their
bottoms copper-sheathed. These vess'ds could lie in the Chinese
ports unharmed, under cunditions which produced very objec-
tionable fouling in iron ships. In the Eoyal Navy at the
present time the con)posite system of construction is applied
to vessels up to the size of corvettes ; the outside planking being
worked in two thicknesses and the bottoms copper-sheathed.
For larger and swifter cruisers, such as the Volage and Inconstant
CHAP. X. MATERIALS FOR SHIPBUILDING. 417
classes, the use of an irou skiu becomes a necessity iu connection
with the provision of structural strength ; and in most of these
vessels copper sheathing has been adopted, two thicknesses of
wood planking being interposed between the sheathing and the
iron hull. Three of the ironclads of the Royal Navy, the
Siviftsure, Triumph, and Neptune, have also been built on a similar
plan. It has now (1882) been thoroughly tested during twelve
or thirteen years, and has proved satisfactory ; but it involves some
special dangers, and it is a very expensive method of construc-
tion, so that endeavours have been made to substitute zinc for
copper, and one thickness of wood for the two formerly employed.
•The ironclads Audacious and Temeraire have been thus sheathed,
and the earliest experiments proved sufficiently successful to
procure further trials of zinc sheathing in two or three other
vessels, some of which are now on service.
The anti-fouling properties of copper sheathing are due to the
fact that the action of sea-water upon its surface produces oxychlo-
rides and other salts which are readily soluble, and do not
adhere strongly to the uncorroded copper beneath. Hence the
salts, instead of forming incrustations, are continually being
washed off or dissolved away, leaving the sheathing with a
smooth, clean surface, and preventing the attachment of plants or
animals. Some chemists have attached importance also to the
poisonous character of the salts of copper in preventing fouling ;
but the foregoing is undoubtedly the more important feature,
and is commonly termed "exfoliation" of the copper. The rate
at which this wasting of the copper proceeds varies greatly under
different circumstances, and with different descriptions of copper ;
and formerly this subject received much attention, the aim being
to secure the minimum rate of wearing consistent with the
retention of anti-fouling properties. For this purpose Sir
Humphry Davy suggested to the Admiralty the use of "pro-
tectors," formed of iron, zinc, or some metal electro-positive to
copper. When these protectors were put into metallic connec-
tion with the copper sheathing and immersed, galvanic action
resulted, the protectors were worn away, and the rate of wearing
of the copper was decreased in proportion to the ratio of the
surface of the protectors to the surface of the sheathing. When
the protector had about y^ of the surface of the sheathing, there
was no wasting of the copper : with a smaller proportionate surface
of the protectors the copper wasted somewhat; but even when
the protectors had an area only j^^q part that of the sheathing,
there was proved to be a sensible diminution in the rate of wear-
2 E
41 8 NAVAL ARCHITECTURE. chap. x.
iiig. The limits of protection from fouling appeared to be reached
when the surface of the protectors equalled ^\^ part of the
surface of the sheathing. After experience on actual ships it
was found, however, that preservation of the copper by this
means led to rapid fouling, and the plan was abandoned. Nor
has any substitute been since found ; the practice being to
exercise great care in the manufacture of the copper, and to
regard its wasting as the price paid for preventing fouling.
Muntz metal — an alloy of copper and zinc in the proportions of
about 3 to 2 — has been used largely as a substitute for copper,
especially in the ships of the mercantile marine, and appears to
answer fairly well, being, of course, much cheaper than copper.
Such alloys are supposed by some persons to have the advantage
of not producing powerful galvanic action upon iron immersed
in sea-water and metallically connected with them; but this pro-
perty has not been definitely established. On the other hand, it
ap[)ears that, after being long immersed, the alloy tends to alter
in composition. Muntz metal sheets have been found to become
brittle after being some time in use ; and the explanation given
is that, the zinc being electro-positive to the copper, galvanic
action is established between the two metals in the alloy, and
part of the zinc removed. Muntz metal bolts have also been
found to perish through galvanic action, under certain circum-
stances, when immersed in sea-water. The introduction of a
third metal, such as tin, appears to prevent this objectionable
change, even when it is present in very small quantities.
In the Koyal Navy an alloy known as " Naval Brass " is now
used instead of Muntz metal for securities in gun-metal castings,
. or in connection with copper sheathing, under water. This alloy
consists of 62 per cent, of copper, 37 per cent, of zinc, and 1 per
cent, of tin. It answers admirably for bolts ; and trials have been
made with it rolled into sheets and plates of a thickness suitable
for the bottoms of ships. As regards strength and ductility the
trials were satisfactory ; but difficulties arose in connection with
the riveting and watertight work on the thicker plates. The
great expense of naval brass sheets, as compared with iron or
steel, would prevent their extensive use in ship-work apart from
other considerations ; but in certain special circumstances their
use might have been permissible had the trials proved wholly
satisfactory. In fact somewhat similar alloys have been used for
the construction of a few torpedo boats.
Zinc is another material largely used for sheathing the
bottoms of wood ships. When immersed in sea-water, the salts
CHAP. X.
MATERIALS FOR SHIPBUILDING.
419
formed on the surface of a zinc sheet are very much more
adherent to the uncorroded zinc than are the corresponding salts
of copper, and are comparatively insoluble — or perhaps, we
shoukl say, are slowly soluble — by ordinary sea- water. Hence it
appears that a coating of oxychloride of zinc, &c., is likely to
form on the sheathing, not being washed away or removed like
that on copper; and consequently zinc does not possess such
good anti-fouling properties as copper, nor present such a smooth
surface. It lasts for a considerable time under ordinary condi-
tions. In some waters, however, and those of the tropics especially,
zinc sheathing has been found to perish very quickly, owing
probably to ouch a composition of the water as favoured the rapid
solution of the salts formed on the surface, the exposure of the
uncorroded zinc, its rapid oxidation, and so on. Sir John Hay
records that, in the Trinculo, one commission on the African
coast sufficed to strip the bottom of zinc and leave the wood
exposed, fouling of course ensuing. Other cases are reported
where zinc sheets 1 inch thick have, under exceptional conditions,
been worn through in the course of twelve months.
Under ordinary conditions, zinc sheathing is much more
durable : in fact, to increase its anti-fouling qualities, it is often
put into communication with some metal, such as iron, which is
electro-negative to itself, in order that the galvanic action which
is produced may have the result of keeping the surface of the
zinc freer from incrustations to which marine plants and animals
can adhere. Apart from this, it may be interesting to give the
relative losses sustained by copper, zinc, Muntz metal, iron, and
steel, when suspended in the sea for purposes of experiment by
Dr. Calvert and Mr. Johnson.*
Metals.
Loss of Weight per Month on
each Square Foot of Surface.
In a Vessel of
Sea-water.
In the Sea.
Copper ....
Muntz metal
Zinc ....
Iron
Steel ....
lb.
0-0027
0-0015
0-0012
0-0056
O'OOGO
lb.
0-0061
0-0070
0-0204
0-0216
* See the Transactions of the
Literary and Philosophical Society of
Manchester for 1865, quoted at page
199 of Shipbuilding, Theoretical and
Practical.
2 E 2
420 NAVAL ARCHITECTURE. chap. x.
These results are open to some doul>t when applied as units in
estimating the probable loss occurring during long periods of
immersion in sea-water of various qualities ; but they are valuable
for purposes of comparison betvreen the metals, and between the
case of immersion in a vessel of sea-water and in the sea itself,
where there are many causes tending to remove the salts formed
on the surfaces. The greatly different rates of wearing in different
seas is a matter of common experience ; and the experiments made
by the late Mr. R. Mallet, F.R.S., furnish some valuable informa-
tion on this head.* Iron boiler plates which lost from 0'007 lb. to
0'009 lb. per square foot per month in dear sea-water, lost about
twice as much in foul sea-water. With steel, very similar results
were obtained.
Wood ships are protected from fouling by nailing the metal
sheathing directly upon the wood planking; iron ships cannot be
protected in quite so simple a way, the metal sheathing having
to be attached in a manner dependent upon its position in the
galvanic scale relatively to iron, and upon its anti fouling pro-
perties. Copper sheathing, for example, may produce serious
galvanic action upon the iron hull, or portions of the hull, if
there is intimate metallic connection between the sheatliing and
the iron; and even a very indirect metallic connection will
suffice to produce some action. Muntz metal, again, is electro-
negative to iron, and therefore requires to be insulated. Zinc, on
the contrary, being electro-positive to iron, need not be insulated
from it ; but since the rate of wasting required to prevent fouling
of the zinc is practically governed by the amount of galvanic
action set up on its surface by the iron, considerable care is
needed in adjusting the relative surfaces of the tw^o materials
subjected to galvanic action. A brief description will suffice to
show what has been done in practice to overcome these various
difficulties.
Ships of the Eoyal Navy built of iron, or on the composite
principle, and copper-sheathed, have two thicknesses of wood
planking interposed between the copper and the iron portions of
the hull. The inner thickness is bolted to the skin-plating or
to the iron frames with galvanised iron bolts ; the outer thickness
is bolted to the inner with malleable yellow metal bolts, the bolts
not being allowed to come into contact with the iron of the hull,
nor with the bolts of the inner thickness. Wood stems and stern-
* See reports of British Association, 1841-43 ; also vol. xiii. of the Trans-
actions of the Institution of Naval Architects.
CHAP. X. MATERIALS FOR SHIPBUILDING. 42 1
posts are fitted in many of the composite vessels; but in the
swift cruisers and ironclads brass stems and sternposts are
employed. The copper sheathing is not brought into contact
with the metal stems or sternposts, nor with the metal kingston-
valves, &Q., passing through the bottom; and by these means
it is endeavoured to insulate the copper from the iron hull.
Doubts have been expressed as to the sufficiency of these pre-
cautions, it being supposed that there must be some metallic
connection between the hull and the copper, resulting in corrosion
of the iron. It will suffice to say in reply that the precautions
taken at least prevent any powerful local action, such as might
otherwise take place in the neighbourhood of the fastenings. In
fact, after twelve years' experience with the sheathed ships of the
Inconstant and Volage classes, including service on very distant
stations and in tropical waters, no signs of serious galvanic action
or corrosion have been discovered upon careful examination.
Further, the copper sheathing has well maintained its anti-fouling
properties, which it could scarcely have done if it were causing
much galvanic action on the iron hull.
Ono special danger is necessarily incurred by such ships, and
ought not to be passed over. Any damage to the bottom
which stripped off the bottom planking and exposed a portion of
the iron skin, might place that portion of the skin within the
influence of powerful galvanic action : for it would be immersed
in the same sea-water as the copper sheathing, be almost certainly
in metallic connection therewith, and liave concentrated upon its
comparatively small area the action of the very large surface of
copper sheathing. The result might be very rapid corrosion of
the iron skin, and possibly its perforation by holes. Such an
accident, capable of stripping off w^ood planking 5 or 6 inches thick,
firmly attached to an iron hull, must of course be exceptional in
severity, aud of very rare occurrence. No such case has yet
occurred: but the Admiralty Regulations provide against the
contingency, the commanding officer being ordered to have his
ship examined and repaired with the least possible delay.
Allusion has already been made to the dangers attendant on
galvanic action of the kind described, where some metal valve
or pipe, connected with the iron skin and immersed in the same
sea or bilge water, has produced local corrosion of a very serious
and rapid character. The case of her Majesty's store-ship Supphj
illustrated this, and in the Megxra also there was reason to
believe that galvanic action had taken place.* To prevent such
* See the report of the Eoyal Commission on the loss of the Megcera.
42 2 NAVAL ARCHITECTURE. chap. x.
galvanic action on the iron skin, very stringent rules are, as
was shown above, laid down for the guidance of officers charged
with the construction or care of iron ships in the Eoyal Navy.
To illustrate the greatly increased rate of corrosion of iron,
incidental to galvanic action, a few examples may be taken from
the results of the experiments recorded by Mr. Mallet. An iron
plate immersed alone in clear sea-water was found to lose during a
certain period a quantity which we will denote by unity : it was
then immersed for an equal time in clear sea-water with an equal
surface of the following metals electro-negative to it, and the
corrosion increased as follows : —
Experiments.
Iron plate in contact with copper
„ brats
))
guu-metal
tin . .
lead . .
Relative Corrosion.
4-96
3-43
G-53
8-65
5-55
Other laboratory experiments, made on an extensive scale, have
given different results for the relative intensities of the action of
the various metals on the iron ; but they fully confirm the fact
that a greatly increased rate of corrosion results from galvanic
action. The first two materials, copper and brass, are those of
which the shipbuilder has need to take most heed in arranging
the sheathing or fittings of iron ships.
The increased cost of copper-sheathed iron ships is considerable,
and in composite ships of the merchant fieet the use of the two
thicknesses of planking was by no means common, doubtless
because of the additional outlay required. With a single thick-
ness of planking there is, of course, much greater risk of gal vanic
action, but in merchant ships Muntz-metal sheathing is commonly
used, and its action on iron is supposed to be comparatively
feeble. It has been asserted that no great difliculty would be
encountered in making sheathing of such an alloy of copper and
zinc as wouhl be electro-neutral to iron, and have no galvanic
action upon it when immersed in sea-water. We are unaware,
however, that any such sheathing has been tried, and nothing but
experience could show whether or not it would be effective against
fouling. Zinc sheathing has, however, been substituted for copper
in many recent ships of the Eoyal Navy, and if it had proved an
efficient anti-fouling material, it would have been much less costly
than copper, and could under no circumstances produce anything
but beneficial action on the iron hull.
CHAP. X. MATERIALS FOR SHIPBUILDING. 42 3
Yarious plans have been tried for attaching zinc sheathing
to iron bulls; tbat commonly used in the Koyal Navy is as
follows :— A single thiclmess of planks (3-inch to 4-inc]i) is bolted
outside the skin plating ; to this the zinc sheets are nailed : the
strakes of planking are not caulked, but the water which finds
its way under the sheathing can pass freely through the seams to
the iron skin. Iron stems and stern-posts are employed ; and by
various means a certain amount of metallic connection is made
between the zinc and the iron hull, such connection, as explained
previously, being desirable in order to keep the surface of the
zinc freer from incrustation. Hitherto the practical difficulty has
been to adjust the relative amount of the surfaces of iron and
zinc, contributing to galvanic action on the latter, in such a
manner as to prevent too rapid or too local wearing of the zinc,
without interfering with its anti-fouling properties. In fact, the
present condition of this question bears a considerable re-
semblance to that previously existing, when iron protectors were
under trial with copper sheathing. On wood ships, zinc usually
lasts for a considerable time, but is not very successful in pre-
venting fouling : there it has but little metallic contact to produce
galvanic action. On some merchant ships where the zinc has been
laid almost directly upon the iron skin, with felt or some similar
iraterial interposed, its rate of wear has been so quickened that a
single voyage has sufficed to destroy it. Between these two
conditions must lie the practically useful method of attachment,
and upon this expeiience with tictual ships can alone decide.
There is little hope that zinc can ever be made to equal copper
in its anti-fouling qualities and smoothnpss of surface. So far as
experience has gone it appears that a short period of immersion
of zinc in sea-water produces considerable roughness of surface ;
and that an unpainted zinc bottom is likely to be much rougher
soon after a ship is uudocked than a clean-painted iron bottom.
This feature in zinc sheathing exercises a sensible effect upon the
speed-trials of ships; and it is customary in the zinc-sheathed
ships of the Royal Navy to paint the bottoms, when the ships
are docked, with some anti-fouling composition. But, wliile this
comparative roughness tells against unpainted zinc sheithing in
the periods immediately succeeding undocking, the fouling which
succeeds is not nearly so serious at the end of a considerable time
afloat as it usually is in iron ships. The great extensions of
dock accommodations in all parts of the world make the use of
any kind of sheathing unnecessary on iron ships of the mercantile
marine; and the annual outlay on docking, cleaning and recoat-
424 NAVAL ARCHITECTURE. chap. x.
ing is very moderate, even in large ships. For ships of war,
M'hich frequently have to keep the sea for much longer periods
than merchant ships, zinc sheathing may be of service ; but,
althouofh it reduces the cost of construction and removes some
risks, it is not to be compared with copper-sheathing in its anti-
fouling qualities. The inferiority of zinc to copper has always
been recognised, and experience appears to show that for ships
having high speeds under steam, or designed for cruising under
sail, the disadvantages of zinc are sufficient to make it worth while
to incur the greatest first cost of copper, and the possible risks inci-
dental to grounding or collision.
IMany persons who admit the superiority of iron to wood hulls
in vessels of the mercantile marine question the desirability of
using iron hulls for war-ships, unless they are ironclads. Un-
armoured fighting ships, it is still urged, should be wood-built.
A few remarks on this matter will not, therefore, be out of place.
More than forty years ago two iron steamers, the Nemesis and
Fldegetlion, were built for the East India Company, and success-
fully employed in the Chinese war of 1842. A few years later
several iron frigates were ordered to be built for the Koyal Navy ;
but these were ultimately converted into troopships, the Simoom
and Megsera amongst the number. This change was made after
a series of experiments had been conducted with targets repre-
senting the sides of the Simoom and other vessels. These vessels
had strong transverse frames spaced only 1 foot apart ; and it was
found that a very serious amount of splintering took place from
the side of the ship first struck, while the opposite side was
considerably damaged. On the whole, it was considered that the
damage done by solid and hollow spherical shot to these iron
ships was likely to prove of a more destructive character to the
crews than the corresponding damage in a wood ship. But it was
remarked that iron plating above ^ inch in thickness sufficed to
break up the shell and hollow shot from the heaviest guns then
mounted in ships. This feature was undoubtedly a very great
advantage of the iron sides, as compared with wood ; and the
destruction of the Turkish fleet at Sinope, as well as the experience
with our own ships during the Crimean War, proved how gieat
was the danger of wood hulls exposed to the fire of shell guns.
On the whole, however, the decision arrived at from the trials in
the Simoom target still holds good ; and from that time to this
no fighting ship of the Koyal Navy has been built with uncovered
iron sides, and closely spaced frames, in Avake of the gun decks.
CHAP. X. MATERIALS FOR S'HIPBUILDING. 425
Iron hulls were confined to armoured ships until the construction
of the swift cruiser class, of which the Inconstant was the earliest
example. In order to secure the requisite structural strength, an
iron hull was then considered necessary ; but tlie transverse frames
were widely spaced, and the shattering effect of projectiles was
still further reduced by covering the thin iron plating with wood
planking. The Simoom target experiments had shown that wood
so applied reduced splintering and damage : subsequent experi-
ments at Shoeburyness, with targets representing respectively the
sides of a wood frigate and those of a swift cruiser, have confirmed
the soundness of this view, even when the vessels are exposed to
the fire of heavier guns than those in use over thirty years ago.
There are a few classes of unarmoured war-ships in w hich guns
are fought behind thin uncovered iron Or steel plating ; but these
guns are mounted for the most part on the upper deck " in the
open." As examples, reference may be made to despatch vessels
su.-h as the Iris, or to cruisers such as the Leander class in the
Eoyal Navy : the coast-defence gunboats of the Comet class also
come under tliis category. Before and abaft the central batteries
or citadels of ironclad ships, there are frequently considerable
portions of the top sides formed by tliin uncovered iron plating ;
but in action these unprotected spaces would not be occupied by
men, and Sf)linteriug would not be productive of serious conse-
quences. There are, however, a few cases where guns are fought
under cover of a deck, and behind thin plating unprotected by
wood planking, as for example in the belted ships of the Nelson
class in the lioyal Navy ; very special arrangements being made
to prevent splintering. The plating is of steel, about twice the
thickness of an ordinary iron side : there are no numerous vertical
frames behind it to be shattered ; and any damage that may be
done is restricted to a limited space by means of " traverse bulk-
heads" which are splinter-proof. On the whole, therefore, it may
be safely asserted that the unarmoured or partially protected iron
fighting-ships of the Royal Navy are not open to the objections
which were fairly urged against the Simoom and her consorts more
than thirty years ago, and which apply with considerable force to
iron-built merchant ships of the present day, unless they carry
guns, only on the upper deck, and are fortified by " coal -protection."
Having reviewed the relative advantages of wood and iron as
materials for shipbuilding, we propose, before concluding this
chapter, to glance at the advantages to be gained by the substitu-
tion of steel for iron.
426 NAVAL ARCHITECTURE. chap. x.
Prior to 1870 steel was used to a very limited extent, and
chiefly in cases where extreme lightness of hull or shallowness of
draught was essential. Taking the twenty years from 1850 to
1870 it appears that over 3,(300,000 tons of iron ships were built
for the British mercantile marine, while only 27,000 tons of steel
sliips were constructed ; and from 18GG to 1875 only three small
ships were built of steel in the United Kingdom. In the lioyal
Navy steel was used continuously from 1864 to 1875 for certain
portions of the internal framing of iron ships and armoured
vessels ; but always under special precautions. Early in 1873,
however, the French began to use the so-called " mild steel " or
"ingot-iron" in the construction of war-ships; the Admiralty
followed this example in 1875, ordering two despatch vessels to
be constructed wholly of steel ; and in 1877 the use of the same
material in the mercantile marine, received the sanction of
Lloyd's Register. Since 1875 the progress made in the use of
mild steel has been extremely rapid. In the lioyal Navy it has
almost superseded iron, which is used for minor portions of the
structure simply on account of its cheapness. In the mercantile
marine great advances have been made, as the following iigures
will show. In 1878, 4500 tons of steel shipping were classed at
Lloyd's ; in 1879, 16,000 tons ; in 1880, 35,400 tons ; and in 1881,
41,400 tons. At the end of 1880, thirty-six steel vessels were
under construction, having an aggregate tonnage of 114,000 tons.
During the year 1881, 71,500 tons of steel ships were built and
registered in the United Kingdom ; and at the close of that year
188,600 tons of steel ships were under construction.* Some
of the great steamship companies have already decided to use
steel exclusively, an 1 the example thus get will probably be
followed extensively.
This rapid progress in steel shipbuilding must be attributed
mainly to the introduction of " mild steel " ; a material which is
in no respect inferior to iron, which can equally well withstand
all the operations of the shipyard, is very ductile and malleable,
about 25 to 30 per cent, stronger, under tensile strain, than
the best iron ship-plates, and only 2 to 2^ per cent, heavier for
equal volumes. Most of the varieties of steel used in shipbuilding
before 1873 had the serious disadvantage of lacking uniformity
in strength, ductility and malleability. If these serious faults
were avoided by exceptional care in manufacture, the price of
* For many of these figures the Author is indebted to Mr. Waymouth, Secretary
to Lloyd's Register.
CHAP. X. MATERIALS FOR SHIPBUILDING. 427
the material became so high as to be practically prohibitive
except in very special cases. Not unfrequently steel plates made
under similar conditions, and presumably of the same quality,
disjDlayed, when tested, singular differences in their qualities.
Consequently the shipbuilder and shipowner had not the same
assurance of safety with steel as was possible with iron. Moreover,
it was found with these earlier descriptions of steel that much
greater care was required in the manipulation during the various
processes of building — such as punching, bending, forging and
riveting — than was needed in the corresponding operations on iron.
These steels were much stronger than iron, having tensile
strengths from 30 to 50 tons per square inch, as against 17 to 22
tons for good iron. And on account of their greater strength
these varieties of steel were used in exceptional cases notwith-
standing their known faults and greater cost. Vessels for river
service like that illustrated in Figs. 105 and 106, pages 3(il-2,
steamers for the Channel service, blockade-runners, and other
classes in which lightness of hull was the most important condi-
tion to be fulfilled, were all built of steel. It is but proper to add
of these early steel ships that most of them performed their work
well, and some of them have displayed remarkable durability
under very trying conditions of service. The failures and diffi-
culties to which allusion has been made were chiefly experienced
in the shipyard.
Mild steel is free from most of the defects mentioned above.
It can be produced in large quantities, of uniform quality, and at
a cost which does not compare unfavourably with that of good
wrought iron. The tensile strength of the material now in
common use is not so high as that of earlier varieties of steel,
but the ductility is much greater. From 26 to 32 tons per
square inch represent the limits of tensile strength not commonly
exceeded ; the elongation of a sample before fracture under tensile
strain frequently reaches 25 to 30 per cent, in a length of 8
inches. But there is reason to believe that still higher tensile
strength, up to 35 or 40 tons per square inch, may be obtained,
if desirefl, in association with excellent working qualities, and
without that degree of hardness which would make the steel
take a "temper" when heated to a low cherry-red and plunged
into water having a temperature of 82" Fahrenheit.
Another property of mild steel deserving notice is the practical
equality of the strength and ductility of samples cut lengthwise
or breadthwise from plates. With iron, as is well known, the
samples cut lengthwise would have about one-fifth or one-sixth
greater tensile strength and much [more ductiliiy than the erofs-
428 NAVAL ARCHITECTURE. chap. x.
M'ise samples from the same plate ; and care has to be taken iu
many parts of iron ships to adjust the plates and butt-straps in the
manner most favourable to this inequality of strength. Closely
connected with this uniformity of strength and great ductility is
the capacity of mild steel to bear rough usage. Under percus-
sive strains — produced by the blows of steam-hammers, falling
weights, the explosion of gun-cotton, &e. — mild steel has been
proved greatly superior to the best wrought iron. In cases of
collision, grounding, &c., ships built of mild steel have had their
plating bulged and bent without cracking under circumstances
which would have broken through less ductile iron plates. And in
the shipyard much work can be done on steel cold, which could
only be done on iron after heating. One most important feature
in the working qualities of mild steel should be mentioned. It
should not be subjected to percussive strains or shocks when at a
" blue-heat "—say fiom 430° to 580' Fahr., at which heat its
ductility is at a miuimum. Very little care is needed, however, to
avoid this dangerous temperature.
The "elastic limit" for mild steel (see the remarks in page
386) has been found to vary from about 55 to nearly 80 per cent,
of the ultimate strength ; and 60 per cent, is probably a fair
average value. For superior qualities of iron about the same
percentage of the ultimate strength probably represents the
elastic limit. Hence it follows that, notwithstanding its greater
ductility, mild steel can bear " w^orking strains " having as great
a ratio to the ultimate strength, as superior wrought iron can
bear. This is an important matter : mild steel may be trusted
with working loads from 25 to 30 per cent, greater than superior
iron.
Since steel loses nothing as compared with iron in the variety
of the forms in which it is produced, the efficiency of its connec-
tions, and its adaptability to the combinations required in the
structures of ships, its greater strength makes it possible to use
thinner and lighter plates and bars than would be needed with
iron, in order to secure a certain strength. The reductions made
in thickness are influenced by various considerations: such, for
example, as the tensile strength of the steel used, the character
of the flaming which supports the plating and assists it against
buckling, the requirements of local strength, or considerations of
durability. In order that the full advantages of the greater
tensile strength of the steel may be realised, it is obviously
necessary to take proper precautions against local failure of the
reduced thicknesses of plates and bars. If, on the contrary, the
system of framing u>ual with iron is perpetuated with steel, it
CHAP. X. MATERIALS FOR SHIPBUILDING. 429
may be necessary to limit the reduction in thickness in order to
secure sufficient rigidity between the supports. In the majority
of the earlier steel ships the frames were transverse, and spaced
much as they would have been in iron ship?. The reductions in
scantlings varied with the character of the steel used : in some
cases these reductions were about one-fourth of the scantlings
used in iron, in others one-third, and in a few cases as much as
one-half. These reductions were accompanied, of course, by pro-
portionate savings in weights of the hull and additions to the
carrying power.
With mild steel such as is now used the reductions in scantlings
vary from 15 to 20 per cent, of the scantlings usual in iron.
Lloyd's Kules permit a reduction of 20 per cent, on the plates
and frames of a ship built of mild steel having a tensile strength
varying from 27 to 31 tons per square inch. This tensile strength
is at least 35 to -10 per cent, greater than that of good iron, but
the limit of reduction appears to have been fixed with reference
to the rigidity of steel and iron plates, when supported at intervals
corresponding to the ordinary frame-spaces in ships built on the
transverse system. The saving in weight of hull does not amount
to 20 per cent., however ; because in that weight are included a
considerable weight of forgings, woodwork and fittings, not
affected by the reduction in scantlings. Moreover, as iron is
cheaper than mild steel, it is still commonly used for minor
portions in the internal works in steel ships — such as divisional
bulkheads, platforms, &c., contributing very little to the general
structural strength. Making allowance for these restrictions, it
is stated by the best authorities that in ships classed at Lloyd's,
the use of steel effects a saving from 13 to 15 per cent, on the
weight of iron which would be used in a ship of the same dimen-
sions. This reduction in the weight of the hull, and consequent
increase in the carrying power, is always of value in a mercliant
ship ; although its relative importance may vary considerably in
ships of different types, engaged in different trades, and perform-
ing voyages of different lengths and at various speeds. It is not
possible here to discuss the economical advantages of steel ships
at any length, nor to compare their first costs and subsequent
earnings with those of iron ships. But an illustration or two
mav be of interest.* As the first, take a cargo and passenger
* On this subject see a valuable of the facts given above. See also a
Taper by Mr. "W. Denny in the Pro- Paper by Mr. Price in the Proceedings
ceedings of the Iron and Steel Institute of the Institution of Mechanical
for 1881, from which we borrow some Engineers for 1881.
430
NAVAL ARCHITECTURE.
CHAP. X.
steamer for the Eastern trade, 310 feet long, 39 feet broad, and
27-5 feet deep. If built of iron or of steel, the weights would
compare somewhat as follows :
Iron Ship.
Steel Ship.
Iron or steel in the hull
Other weights of hull
Tons.
1360
600
Tons.
1170
600
Total weight of hull
Weight of macliinery
1060
260
1770
260
Carrying power (coals and cargo)
2220
3360
2030
3550
Displacement
5580
5580
This transfer of 190 tons from the hull to the carrying power
might be of very considerable importance on a long voyage where
a large coal-stowage was necessary; and on any voyage the
additional freight must be of value. To the subject of relative
first cost we shall refer hereafter.
As a second example we may compare two fast passenger steamers
of about 8500 tons displacement when fully laden. Their weights
may be distributed somewhat as follows if they are supposed to
be employed on the Australian line via the Cape of Good Hope : —
Iron Ship. Steel Ship.
Iron or steel in the hull
Other weights of hull
Total weight of hull
Weight of machinery
„ coal (maximum)
,, cargo (about)
Displacement
Tons.
2600
1100
Tons.
2250
1100
3700
1100
2500
1200
3350
1100
2500
1550
8500
8500
That is to say the use of steel would increase the cargo
capacity by about 30 per cent. It will be understood, of course,
that these figures must be treated as approximate only.
The use of steel in war-ships has been productive of similar
advantage to the carrying power. Previously to the general use
of steel, very superior qualities of iron were used, and the
scantlings were reduced as much as possible, consistently with
CHAP. X. MATERIALS FOR SHIPBUILDING. 43 1
strength, in order to diminish the weight of hulls. Many of the
internal portions of the structure had been made as thin in iron
as was consistent with durability, and here no reductions were
possible when steel was used. Moreover in war-ships a large
portion of the weight of hull goes into elaborate iittings, which
are indispensable and unaffected by the change from iron to steel.
Notwithstanding these limitations, very substantial gains have
been obtained i'rom the use of steel. One example must suffice.
It has been estimated that in one of the first steel-built ships of
the Koyal Navy the use of steel lightened the hull by 175 tons —
12 per cent, on the total weight of the hull, including the fittino-g
— and increased tiie weight of coal carried by nearly one-third,
as compared with what it would have been in an iron-built ship
of the same dimensions and speed.
Turning to the relative cost of iron and mild steel a few facts
may be stated : — In 1877 steel was about twice as costly as the iron
in common use ; but it is important to notice that the sources of
supply were then comparatively few. Moreover the iron used \\\
mercantile shipbuilding has never been subjected to thorough and
severe testing such as is universally applied to steel, which fact
necessarily tends to increase the price of steel. For ships of the
Koyal Navy equally searching tests have been applied to both
materials ; and under these conditions a very short time elapsed
before mild steel could be procured at a lower price than superior
ifon. The same thing holds good in the French navy. And in
the mercantile marine as the sources of supply for mild steel have
been multiplied, and the manufacture has been more thoroughly
understood, its price has steadily fallen relatively to iron. In
1880 steel seems to have been about 50 per cent, dearer than iron;
and at the time of writing (the close of 1881) a still closer
approach to equality in price has been made. Some persons
consider that steel will ultimately be as cheap as iron of ordinary
ship quality ; but this seems doubtful at present, and every one
agrees that to maintain the high standard of excellence which
has been reached with steel, a continuance of the established
system of testing is necessary. Apart from these facts, however,
it may be assumed that even as prices have stood during the last
four or five years, steel ships have proved themselves economically
superior to iron ships in many trades ; for, if this were not true,
the shipowners who have had experience with steel ships would
not continue to add to their number.
Reduced thicknesses of plates and bars in steel ships necessitate
great care to prevent corrosion. Experience with steel ships is
432 NAVAL ARCHITECTURE. chap. X,
at present so limited tliat it is not possible to form a definite
opinion respecting the relative rates of corrosion of iron and steel
when immersed in sea-water. So far as experience has gone it
appears that with proper precautions in cleaning and coating,
steel does not corrode more rapidly than iron under the ordinary-
conditions of service. Many of the early steel ships with very
thin plating have continued at work for twenty years ; and
although they are not constructed of mild steel their great
durability is noteworthy. In one particular there is reason to
suppose that mild steel requires special care under certain cir-
cumstances. The manufacturer's '* scale " adiieres much more
strongly to steel plates than to iron, and from experiments made
for the Admiralty, as well as from experience on actual ships, it
seems that if this scale is not thoroughly removed it may set up
galvanic action on adjacent parts of the surface which are free
from scale when the plates are immersed in sea-water. Merchant
ships are usually built in the open air, and in them the scaling
is often performed without much difficulty. Steel ships of the
Eoyal Navy are usually built under cover, and after many experi-
ments it has been found preferable to remove the scale by
immersing the plates in a bath of dilute hydrochloric acid, and
subsequently washing them with water, before they are worked
into the ship. In this manner at small expense clean surfaces
can be obtained, and pitting or rapid local corrosion from the
action of the scale may be prevented.
As to fouling, steel ships appear to be no better off than iron
ships, requiring to be docked and coated just as frequently.
On a review of the facts which have been stated above, it can
scarcely be doubted that the rapid development of steel ship-
building in recent years is but the prelude to the general substi-
tution of steel for iron. That substitution has been made in the
Koyal Navy, and very nearly completed in the French navy ;
similar changes will doubtless be made also in merchant ships,
and will be hastened if improved metallurgical processes enable
manufacturers to reduce the price of steel. It may well happen
also that mild steel may ultimately be displaced by a stronger
material having equally good qualities as regards ductility and
workability. If manufacturers can succeed in producing such steel
at moderate cost, shipbuilders will avail themselves of the oppor-
tunity to advance still further the combination of strength with
lightness.
CHAP. XI. THE RESISTANCE OF SHIPS. 433
CHAPTER XL
THE RESISTANCE OF SHIPS.
Xo branch of the theory of naval architecture has a richer litera-
ture than that which forms the subject of this chapter. It would
be a formidable task merely to enumerate the names of eminent
mathematicians and experimentalists who have endeavoured to
discover the laws of the resistance which water offers to the
progress of ships ; and still more formidable would be any
attempt to describe the very various theories that have been
devised. Again and again has the discovery been announced of
the "form of least resistance," but none of these has largely
influenced the practical work of designing ships, nor can any be
regarded as resting on a thoroughly scientific basis. In fact, a
century and a half of almost continuous inquiry has firmly
established the conviction that the problem is one which pure
theory can never be expected to solve.
Although earlier theories of resistance are now discarded, and
the present state of knowledge on the subject is confessedly
imperfect, great advances have been made within the last half-
century, and most valuable experimental data have been collected.
The modern or "stream-line" theory of resistance may now
be regarded as firmly established. Many eminent English
mathematicians have been concerned in the introduction and
development of this theory, as well as in the conduct of the
experiments by which it has been put to the test. Of these,
however, two only need be named. The late Professor Rankine
did much to practically apply the theory to calculations for the
resistances and speeds of ships ; and the broad generalisations
which we owe to him have served ever since as guides to later
investigators.* The late Mr. W. Froude is the second worker in
* See div. i. chap. v. of Shi^plnilding, TJieoretical and Practical, edited by
Professor Eankine.
2 F
NAVAL ARCHITECTURE. chap. xi.
434
this field of inquiry, whose labours deserve especial mention.
The experiments ^hich for some years he conducted for the
Admiralty are beyond all comparison with any that have gone
before them ; the greatest value attaches to the small portions of
his results which have yet been published; and should the in-
quiry be completed on the lines laid down by him, and the
results fully discussed, naval architects will be in possession of a
mass of facts which cannot but prove highly advantageous to the
designs of future ships. These experiments of Mr. Froude have
been carried on upon the basis of the stream-line theory of
resistance, and have fully confirmed its soundness. In addition,
however, to this service, Mr. Froude did much to elucidate and
popularise the theory. His clear and masterly sketches of its
main features are well worthy of careful study;* and they have
the advantage of being almost entirely free from mathematics, so
that the general reader can readily follow the reasoning and the
experiments by which it is supported. In attempting, as we now
propose to do, a brief outline of this modern theory, we gladly
acknowledge our indebtedness to both Professor ilankine and
Mr. Froude.
A few prefatory remarks are necessary in explanation of teruas
that will be frequently employed. Water is not, what is termed,
a 'perfect fluid ; its particles do not move past one another with
absolute freedom, but exercise a certain amount of rubbing or
friction upon one another, and upon any solid body past which
they move. Suppose a thin board with a plane surface to be
immersed in water and moved end-on, or edgewise, it will experi-
ence what is termed fridional resistance from the water with
which its surface comes into contact. The amount of this fric-
tional resistance will depend upon the area and the length of
the plane, as well as the degree of roughness of its surface and
the speed of its motion. If this plane is moved in a direction at
right angles to its surHice, it encounters quite a different kind
of resistance, termed direct or sometimes head resistance; this
depends upon the area of the plane and the speed of its motion.
Sliould the plane be moved obliquely, instead of at right angles
to its surface, the resistance may be regarded as a compound
of direct and frictional resistance. Supjiosing either direct or
oblique motion to take place, the plane would leave an eddying
"wake" behind it, as indicated somewhat rougldy in Fig. 117,
* See British Association Reports for 1875, and vols. xv. to sxi. of the
Transactions o\ the Institution of Naval Architects.
CHAP. XI.
THE RESISTANCE OF SHIPS.
435
FIG. 117
and tlie motion thus created amongst the particles constitutes a
very important element in their
resistance to the pas^nge of the plane.
If the plane is not wholly immersed, or
if its Tipper edge is near the surface,
and it is moved directly or ohliquely,
it will heap up water in front as it
advances, and create waves which will
move away into the surrounding water
as they are formed, and will be suc-
ceeded by others. Such wave-making
requires the expenditure of power, and constitutes a virtual in-
crease to the resistance. If the plane were immersed very deeply,
it would create little or no surface disturbance, and, therefore,
require less force to propel it at a certain speed than would a
plane of equal immersed area moving at the surface with a portion
situated above that surface. If there were no surface disturb-
ance, the resistance would be practically independent of the
depth of immersion. This statement is directly opposed to the
opinion frequently entertained ; which confuses the greater
liydrostatical pressure on the plane, due to its deeper immersion,
with the dynamical conditions incidental to motion. It may,
therefore, be desirable to add a brief explanation.
Supposing a deeply immersed plane to be at rest, then the
pressures on its front and back surfaces would clearly balance
one another at any depth. When this plane is moved ahead at a
uniform speed, it has at each instant to impart a certain amount
of motion to the water disturbed by its passage ; but the
momentum thus produced is not influenced by the hydrostatical
pressures on the phine, corresponding to the depth of its im-
mersion. Water is practically incompressible; apart from surface
disturbance, the quantity of water, and therefore the weight, set
in motion by the plane, will be nearly constant for all depths, at
any assigned speed. In other words, if there be no surface
disturbance, the resistance at any speed is independent of the
depth. This is equally true of direct, oblique and frictional re-
sistance, and has been established experimentally. For example.
Colonel Beaufov ascertained the resistances of a plane moving
normally to itself, when submerged to depths of 3, 6 and 9 feet
below the surface, and found them practically identical at all the
depths. These experiments also served to establish the following
very useful rule : The resistance per square foot of area sustained
by a whollv submerged plane moving normally to itself through
2 F 2
436
NAVAL ARCHITECTURE.
CHAP. XI.
sea-w,iter at aimiforin speed of 10 feet per second is 112 lbs. ; and
for other speeds the resistances vary as the squares of the speeds.
Beanfoy also endeavoured to determine the laws governing
the resistance of a wholly submerged plane set at various angles
to its line of motion. Prior to the test of experiment it had been
assumed that such oblique resistance varied with the square of
the sine of the angle made by the plane with its line of motion ;
so that for a given speed of advance, and an angle of obliquity a,
Oblique resistance = Direct resistance X sin^ a.
Beaufoy's experiments proved this assumption to be incorrect,
and, as the records are not now generally accessible, it may be well
to summarise the results.
Beaufoy's Experiments on Eesistances of Submerged Plaxe-surfaces.
Angles (if Plane
with Hue of
90°
80°
70°
60°
50°
10°
30°
20°
10°
motion .
Sines of Angles .
1
•985
•910
•866
•766
•643
•5
•342
•174
(Sines)2 of Angles
1
•97
•88
•75
•587
•413
•25
•117
•03
Resistances .
1-00
•915
•845
•828
•722
•579
•321
•272
From this table it appears that up to angles of 50 to 60 degrees
the resistance varies with a fair approach to agreement with varia-
tions in the sine of the angle multiplied by the direct resistance ;
and this is an approximate rule which is of considerable value in
practice. The theoretically correct law connecting the direct and
oblique resistances on the front of a plane surface has been de-
termined by Lord Rayleigh, and is as follows : — Let P = the
" direct resistance " experienced by the front surface of a plane
when moving normally to itself at a certain speed ; and Pi the
corresponding resistance when it is inclined at an angle o to the
line of motion. Then
Pi
_2 7rsina
4 + 77 sin a
P =
sma
•037 + -5 sin a
.P
This formula takes no account of the negative pressure on the
back surface of the plane.
M. Joessel of the French Navy has conducted a series of
valuable experiments on the same subject and has deduced
therefrom a formula similar in form but not identical with Lord
Bayleigh's. It is as follows : —
Pi=-
sin a
39 + "61 sin o
P,
CHAP. XI. THE RESISTANCE OF SHIPS. 437
but Pi and P here stand for the total pressures on the front and
back surfaces of the plane.
There is no necessity for making any comparison between the
results obtainable from these two furmulse and Beaufoy's experi-
ments, as the reader will have the means of makino- it : in
practice the simpler rule above stated is generally followed.
Numerous experiments have been made to determine the
frictional resistances of planes moved through water; the most
recent as well as most valauble being those conducted by the late
Mr. Froude for the Admiralty. Frictional resistance is measured
by the momentum imparted to the water in a unit of time; this
momentum being imparted, at each instant, to a current or
"skin" of water which is then adjacent to the surface. This skin
of water has a motion given to it in the direction of advance of
the plane ; while the particles within it move in frictional eddies.
The extent to which the frictional resistance causes disturbance
— that is to say the "thickness of the skin" — varies with the
velocity and other circumstances of the motion. From instant to
instant the frictional current thus created is left behind bv the
moving surface, and a "frictional wake" is formed which follows
the surface. The forward motion of this wake is gradually com-
municated to larger masses of water, its velocity is consequently
decreased, and finally it ceases to be perceptible. It need scarcely
be repeated that the momentum imparted to the water in a unit
of time by a plane moving at a given speed is independent of the
depth of immersion and the corresponding hydrostatical pressure
on the plane ; it being understood that we may neglect any small
variations in the density of the water produced by changes in
that depth. The governing conditions of the frictional resistance
are the area and length of the plane, its degree of roughness, and
the speed of advance.
Passing from these general considerations to the results of
experiments on actual plane surfaces, attention must be limited
to those obtained by Mr. Froude, and summarised by him in the
following tabular statement and prefatory remarks.
Mr. Feoude's Experiments on Surface- friction.
This table represents the resistances per square foot due to various lengths of
surface, of various qualities, when moving with a standard speed of 600 feet per
minute, accompanied by figures denoting the power of the speed to which the
resistances, if calculated for other speeds, must be taken as approximately
proportional.
Under the tigure denoting the length of surface in each case, are three columns,
A, B, C, which are referenced as follows : —
438
NAVAL ARCHITECTURE.
CHAP. XI.
A. Power of speed to which resistance is approximately proportional.
B. Resistance in pounds per square foot of a surface the length of which
is that specified in the heading — taken as the mean resistance for
the whole length.
C. Resistance per square foot on unit of surface, at the distance sternward
from the cutwater specified in the heading.
Nature
of
Surface.
Length of surface, or distance from cutwater, in feet.
2 feet.
8 feet.
20 feet.
50 feet.
A.
B.
C.
A.
B.
C.
A.
B.
C.
A.
B.
C.
•226
•232
•423
•337
•456
Varnish .
ParafBne
Tinfoil . .
Calico .
Fine sand .
Medium sand
Coarse sand .
2^oo
I "95
2-i6
1*93
2^00
2^00
2-00
•41
•3^
•30
•87
•81
•90
1-10
•390
•370
•295
•725
•690
•730
•880
1-85
1-94
1-99
1-92
2-00
2^00
2"00
•325
•314
•278
•626
•583
•625
•714
•264
•260
•263
•504
•450
•488
•520
i-8s
1-93
1 •go
r89
2^00
2^00
2 00
•278
•271
•262
•531
•480
•534
•588
•240
•237
•244
•447
•384
•465
•490
1-83
I- 83
1-87
2^o6
2'00
•250
•246
•474
•405
•488
Note. — Beaufoy's experiments made in the Greenland Docks (1794-98) gave values of
A between 1-7 and 1-8, closely agreeing in this respect with the later experiments of
Mr. Froude,
From these experiments the following deductions have been
made. First: that the law formerly assumed to hold is very-
near] y conformed to, the frictional resistance varying approxi-
mately as the square of the velocitij, when the area, length and
condition of the surface remain unchanged. Second : that the
length of the surface sensibly affects the mean resistance per
square foot of whetted surface; and especially when very short
planes are compared with planes of 50 feet or upwards. For
greater lengths than 50 feet it appears that the mean resistance
per square foot of area remains nearly the same as for the plane
50 feet long. Mr. Froude explains this important experimental
fact as follows : — " The portion of surface that goes first in the
"line of motion, in experienciug resistance from the water, must
"in turn communicate motion to the water in the direction in
" which it is itself travelling ; consequently the portion of the
" surface which succeeds the first will be rubbing, not against
"stationary water, but against water partially moving in its own
"direction; and cannot, therefore, experience as much resistance
" from it."
A third important deduction is the great increase in frictional
resistance which results from a very slight difference in the
apparent roughness of the surface. For instance, the frictional
resistance of a surface of unbleached calico — not a very rough
surface — was shown to be about double that of a varnished surface.
CHAP. XI. THE RESISTANCE OF SHIPS. 439
This varnished surface, it is interesting to note, ,<;ave results just
equal to a surface coated with smooth paint, tallow, or composi-
tions such as are commonly used on the bottoms of iron ships.
The frictional resistance of such a surface moving at a sp( ei] of
600 feet per minute would be about \ lb. per square foot ; which
would give a frictional resistance of about 1 lb. per square foot of
immersed surface for the clean bottoms of iron ships when moving
at a speed of about 12-8 knots. This unit is worth noting.
The foregoing remarks on the resistance experienced by plane
surfaces moving through water will assist the reader in following
the discussion of the more difficult problems connected with the
resistances of ship-shaped solid bodies. In many of the earlier
theories of resistance the immersed surface of a ship was assumed
to be subdivided into a great number of pieces, each of very-
small area, and approximately plane. The angle of obliquity of
each of these elementary planes with the line of advance < f the
ship — her keel-line — was ascertained ; and its resistance was
calculated exactly as if it were a detached plane moving alone
at the assumed speed. For quantitative purposes, experiments
were to be made with small planes of known area moved at
known speeds, and set at different angles of obliquity ; the
resistances being observed. But obviously there was a radical
error in applying unit-forces of resistance, obtained from the
movements of detached planes, to the case of a ship where all the
hypothetical elementary planes were associated in the formation
of a fair curved surface, and none of them could have that eddying
wake (like that in Fig. 117) which necessarily accompanied each
experimental plane and formed so important an element of its
resistance. This objection does not apply to the experiments
made under the auspices of the French Academy of Sciences,
during the last century, by Bossut, Condorcet, D'Alembert,
Eomme, and others ; these experiments having been directed to
the discovery of the resistances experienced by solid bodies of
various forms moved at different depths. Very few of the
models tried, however, had any pretension to ship-shaped forms ;
and this is also true of the subsequent experiments, made in
this country, by Beaufuy.
Satisfactory experiments on the resistances of ships can alone
be made with sliip-shaped models of reasonable dimensions. This
is the principle upon which i\Ir. Froude proceeded in his ex-
perimejits, and although many doubts were expressed at first
respecting the correctness of the results deduced from models
when applied to full-sized ships, there are now good reasons for
440
NAVAL ARCHITECTURE.
CHAP. XI.
trusting that method, some of which reasons will be stated
further on.
The modern theory of resistance does not make any hypo-
thetical subdivision of the immersed surface of a sliip, but regards
it as a whole. AVhen such a surface, with its fair and com-
paratively gentle curves (like those in Fig. 118), is submerged
and drawn through water, the particles are diverted laterally,
and can glide over or past the ship without sudden or abrupt
changes of motion, corresponding to those which occur when
particles escape over the edge of the plane in Fig. 117. The
paths of the particles are indicated roughly in Fig. 118 by the
curved lines, the ship-shaped body being shown in black. After
passing the broadest part of the vessel, the particles close in over
the after part, and, gliding over the continuous surface, form a
wake astern.
In the modern theory, the total resistance is considered to be
made up of three principal parts: (1) frictional resistance due to
FIG. 113.
the gliding of particles over the rough bottom of the ship; (2)
" eddy-making " resistance, at the stern ; (3) surface disturbance,
or wave-making resistance. The second of these divisions only
acquires importance in exceptional cases ; it is known to be
very small in well-formed ships. It will, therefore, be necessary
to bestow most attention upon frictional and wave-making re-
sistance, to examine the conditions governing each, and to
contrast their relative importance. It will be assumed throughout
that the ship is either dragged or driven ahead at uniform speed
by some external force which does not affect the flow of the water
relatively to her sides. This is the condition always assumed
when the resistance of a ship is being treated. It is advantageous
to separate propulsion from resistance, since the latter depends in
all ships Ujion the form, proportions, and condition of the'
bottom ; whereas there are many means of propelling ships.
Suppose the ship to be moving ahead at uniform speed
through an ocean unlimited in extent, and motionless except for
CHAP. XI. THE RESISTANCE OF SHIPS. 441
the disturbance produced by the passage of the ship. Under
the conditions assumed, there will obviously be no change in
the relative motions of the ship and the water if she is supposed
to remain fixed, while the oce;m flows past her at a sj)eed equal
to her own, but in the opposite direction to that in which the ship
really moves. Making this alternative supposition has the
advantage of enabling one to trace more simply the character of
the disturbances produced by introducing the solid hull of the
ship at a certain speed into water which was previously undis-
turbed. First, let the water be assumed to be frictiouless, and
the bottom of the ship to be perfectly smooth. These are only
hypothetical conditions, but it is possible at a later stage of the
inquiry to introduce the corrections necessary to represent the
actual conditions of practice. Take any set of particles situated
a long distance before the ship, and moving in a line parallel
to her keel. If the ship were not immersed in the ocean current,
these particles would continue to move on in the same straight
line, which would be horizontal. When the ship is immersed
her influence upon the motion of the particles may extend
to a very long distance ahead, but there will be some limit
beyond which the influence practically does not extend ; and
outside this, the particles whose motion is being traced will be
moving at a steady speed in a horizontal line parallel to the
keel. As they approach the ship, however, their path must be
diverted in order that they may pass her ; and this diversion
will be accompanied by a change in their, speed. Supsposing for
the sake of simplicity that the particles maintain the horizontality
of their motion and are only diverted laterally : then, as they
approach the bow of the ship, they will move out sideways from
the keel-line, and lose in their speed of advance. Many con-
siderations must govern the extent of this lateral diversion and
loss of speed ; such as the form of the bow, the extreme breadth
of the sliip, and the athwartship distance from the line of the
keel of the original line of flow of the particles. At the broadest
part of the ship amidships the velocity of the particles of water
must be greatest, because the breadths of the "streams" (see page
443) in which they flow, are there less than at the bow, and the
same quantity of water has to pass the two places. After the
midship part of the ship has been passed, and her breadth begins
to decrease, the path of the particles will converge towards the
keel-line ; and their speed will again receive a check. Finally,
after flowing past the ship, and attaining such a distance astern
as places them beyond the disturbing influence of the ship, the
442 NAVAL ARCHITECTURE. chaf. xi.
])articles will regain tlieir original direction and speed of flow,
provided that there is no surface disturhance. This last-mentioned
condition could only be fulfilled in the case of a vessel wholly
immersed, at a great depth, below tlie surface of an ocean limit-
less in depth ; in the case of the ships which are only partly
immersed, the retardations and accelerations described must cause
the formation of bow and stem waves, and these we shall
consider further on.
Although we have assumed, for the sake of simplicity, in the
foregoing remarks that the particles maintain their horizontality
of flow, it should be luiderstood that the assumption is not
supposed to represent the aciual motion of the water in passing a
ship. Diversion from the original line of flow is almost certain
to have a vertical as well as a lateral component ; but as to the
paths actually traversed by the particles, we have little exact know-
ledge. Mr. Scott Eussell is of opinion that at the foremost part
of a ship the particles move in layers which are almost horizontal ;
while at the stern the particles have a considerable vertical com-
ponent in tlieir motion, besides converging laterally. Professor
Kankine asserts that " the actual paths of the particles of water
"in gliding over the bottom of a vessel are neither horizontal
" water-lines nor vertical buttock-lines, but are intermediate in
" position between those lines, and approximate in well-shaped
" vessels to the lines of shortest distance, such as are followed by
"an originally straight strake of plank, when bent to fit the
" shape of the vessel." But, whatever paths may be followed,
if at a considerable distance astern of a shij), wholly submerged
in a frictionless fluid, the particles have regained their original
direction and speed of flow, which they had at a considerable
distance ahead of the ship, then their flow past the ship will
impress no end-wise motion upon her. To this point we shall
recur.
Professor Eankine has laid down geometrical rules for con-
structing the paths, or "stream-lines," along which the particles
of a frictionless fluid would flow in passing a body very deeply
submerged, supposing the particles to move in plane layers of
uniform thickness. Fig. IIU was constructed by Mr. Froude
in accordance with these rules.* The form of the immersed body
with its comparatively blunt bow and stern is indicated in black ;
*
See the address to the Mechanical described at pages 106, 107 of Ship-
Section of the British Association in building. Theoretical and Practical.
1875. Professor Rankihe's method is
CHAP. XI.
THE RESISTANCE OF SHIPS.
44.
the curved lines indicate the paths of particles. Between any two
of these stream-lines, the same particles would be found through-
out the motion, and these would form a " stream " of which the
stream-lines mark the boundaries. It will be noted that, as the
streams approach the bow, they broadeu, their speed being
checked, and the particles diverte I laterally ; the amount of this
diversion decreases as the athwartship distance of the stream from
the keel-line increases, and at some distance athwartship the
departure of the stream-lines from parallelism with the keel, even
when passing the ship, would be very slight indeed. As the
streams move aft from the bow, they become narrowed, having
their minimum breadth amidships, where the speed of flow is a
maximum. Thence, on to the stirn, the streams converge,
broaden, lose in speed, and fiually at soine distance astern resume
their initial direction and speed. Since there is no friction, there
can be no eddying wake.
So much for a vessel wholly submerged; a ship only partly
immersed would be differently situated, because even in a fric-
tionless fluid she would produce surface disturbance. At the
bow, where the streams broaden and move more slowly, a wave
crest will be formed, of the character shown in Fig. 120 ; amid-
ships, where the conditions are reversed, some depression below
the normal water-line will probably occur; and at the stern,
where the conditions resemble those forward, another wave crest
will be formed. Between the bow and stern waves a train of
waves may also exint, under certain circumstances. The existence
of such waves, when actual ships are driven through the water,
is a well-known fact; every one readily sees why, at the bow,
water should be heaped up, and a wave formed, but the existence
of the stern wave is more difficult to understand. As remarked
above, there is but one reason for both phenomena. A check to
the motion of the particles is accompanied by an increase of
pressure; the pressure of the atmosphere above the water is
})ractically constant, and hence the increase of pressure in the
444
NAVAL ARCHITECTURE.
CHAP. XI.
water must produce an elevation above the normal level, that is
to say, a wave crest. Conversely, amidships, accelerated motion
is accompanied by a diminution of pressure, and there is a fall
of the water surface below the still- water level, unless the inter-
mediate train of waves should somewhat modify the conditions of
the stream-line motion.
These waves require the expenditure of force for their creation,
and, when formed, they may travel away into the surrounding
nG.I20
fluid, new waves in the series being created. In the case, therefore,
of a ship moving at the surface of frictionless water, the only
resistance to be overcome will be that due to surface disturbance.
For the wholly submerged body which creates no waves there
will be no resistance, when once the motion has been made
uniform ; the stream-lines once established in a frictionless fluid
will maintain their motion without further expenditure of power.
This remarkable result follows directly from a general principle,
which is thus stated by Professor Rankine : — " "When a stream of
" water has its motion modified in passing a solid body, and re-
" turns exactly to its original velocity and direction of motion
" before ceasing to act on the solid body, it exerts on the whole
" no resultant force on the solid body because there is no per-
' manent change of its momentum." In every stream surround-
ing the submerged body in Fig. 119, this has been shown to hold;
each stream regains its initial direction and velocity astern of the
body. The partially immersed ship in the frictionless water
differs from the submerged ship in producing surface disturbance.
Perhaps the general principle will be better understood if we
borrow one of Mr. Froude's many simple and beautiful illustra-
tions. Taking a perfectly smooth bent pipe (Fig. 121), he supposes
it to be shaped symmetrically, and divides it into four equal and
CHAP. XI. THE RESISTANCE OF SHIPS. 445
similar lengths, AB, BC, CD, DE. The ends of the pipe at A and
E are in the same straight line ; a stream of frictionless fluid flows
through it, and has uniform speed throughout. From A to B
maybe supposed to correspond to the forward part of the entrance
of a ship, where the particles have to be diverted laterally, and
react upon the inner surface of the pipe, as indicated by the small
arrows/,/,/, the resultant of these normal forces being G. At
the other end of the pipe, from D to E may be taken to represent
the "run" of a ship, where the stream-lines are converging and
tending to resume their original directions ; on DE there will be
a resultant force J equal to G. Similarly, the resultant forces on
the other two parts BC and CD are equal. The final result is that
the four forces exactly neutralise one another, and there is no
tendency to force the pipe on in the direction of the straight line
joining A to E, altliough at first sight it would appear otherwise.
The same thing will be true if, instead of being uniform in section,
the pipe is of varying size ; and if instead of being symmetrical
in form, it is not so : provided only that at the end E the fluid
resumes the velocity it had at A and flows out in tlie same
direction. The forces required to produce any intervening changes
in velocity and direction must have mutually balanced or neutra-
lised one another, as in the preceding example, before the stream
could have returned to its original velocity and direction of
motion.
Applying these principles to the stream-lines surrounding a
ship, it will be possible to remove one or two difficulties which
have given rise to erroneous conceptions. It has been supposed,
for example, that a ship in motion had to exert considerable
force in order to draw^ in the water behind her as she advanced.
As a matter of fact, however, the after part of a ship has not to
exercise " suction " at the expense of an increased resistance, but
sustains a considerable forward pressure from the fluid in the
streams closing in around the stern. Any cause which prevents
this natural motion of the streams, and reduces their forward
pressure on the stern — such as the action of a screw-propeller —
causes a considerable increase in the resistance, because the
backward pressures on the bow are not then so nearly balanced
by the forward pressures on the stern. Again, it will be evident
that — apart from its influence on surface disturbance — the extent
of the lateral diversion of the streams, in order that they may
pass the midship part of the ship, does not affect the resistance
so much as might be supposed ; since the work done on the
foremost part of the ship in producing these divergences is, so
446 .NAVAL ARCHITECTURE. chap. xi.
to speak, given back again on the after part where the streams
converge. Very considerable importance attaches, however, to
the lengths at the bow and stern over which the retardations of
the particles extend ; since these lengths exercise considerable
influence npon the lengths of the bow and stern waves created by
the motion of the ship. And, further, the ratios of these lengths
of entrance and run to the extreme breadth of the ship must be
important, as well as the curvilinear forms of the bow and stern,
since the extent to which the particles are retarded in gliding
past the ship must be largely influenced by these features ; and,
as we have seen, the heiglits of the waves will depend upon the
maximum values of the retardations. In otlier words, with the
same lengths of entrance and run, differences in the " fineness " of
form at the bow and stern may cause great differences in the
heights of the waves created, as well as in the energy required to
create and maintain such waves.
Such are the principal features of the stream-line theory of
resistance for frictionless fluids and smooth-bottomed ships. The
sketch has been necessarily brief and imperfect, but it will serve
as an introduction to the more important practical case of the
motions of actual ships through water. Between the hypothetical
and actual cases there are certain important differences. First,
and by far the most important, is the frictional resistance of the
particles of water which glide over the bottom ; secondly, friction
of the particles on one another in association with certain forms,
especially at the sterns of ships, may produce considerable eddy-
making resistance, although this is not a common case ; thirdly,
friction mav so modifv the stream-line motions as to alter the
forms of the waves created by the motion of the shiji, and
somewhat increase the resistance.
First, as io frictional resistance. Its magnitude depends upon
the area of the immersed surface of the ship, upon the degree of
roughness of that surface, or its " coefficient of friction," upon
the length of the surface, and upon the velocity with which the
particles glide over the surface. From what has been said above,
it will appear that this velocity of gliding varies at different
parts of the bottom of a ship, being slower at the bow and stern
than it is amidships. Professor Kankine endeavoured to estab-
lish a simple formula for computing the resistances of ships when
moving at speeds for which their proportions and figures are well
adapted. Under these circumstances he considered that " the
whole of the ajpreciable resistance" would result from the for-
CHAP. XI. THE RESISTANCE OF SHIPS. 447
mation of frictional eddies : in other words, that the wave-making
factor in the resistance might be neglected. It is now known that
this assumption was not a true one except for moderate speeds ;
whereas it was applied by Raukiue to considerable speeds. On
the other hand, his method of approximating to the frictional
resistance and attempt to allow for variations in the velocities of
gliding of the particles over the surface may still be studied with
advantage. Rankine supposed that the wetted surface of a ship
could be fairly compared with the surface of a trochoidal riband
having the following properties : — (1) the same coefficient of
friction as the bottom of the ship ; (2) the same length as the
ship ; (3) a uniform breadth equal to the mean girth of transverse
sections of the wetted surface : (4) an inflexional tangent, making
an angle with the base of the trochoid, of which the value was to
be deduced from a process of averages applied to the squares and
fourth powers of the sines of the angles of greatest obliquity of the
several water-lines in the fore body. For any trochoidal riband
in which the angle made by the inflexional tangent with the base
was 0, Rankine had previously obtained the following expression
for the resistance due to frictional eddies.
Resistance = Length X Breadth X Coefficient of Friction
X (Speed)^ X (1 + 4 sin^ 0 + sin* (f).
The last term was styled the "coefficient of augmentation."
Hence
Resistance = Coefficient of Friction x (Speed)^
X " Augmented Surface."
And his supposition was that for ships of good forms a similar
expression would hold, within the limits of speed usually attained.
For clean-painted iron ships the formula was very simply stated: —
Resistance = Length X Mean Girth of Wetted Surface x Coeffi-
cient of Augmentation X (Speed in knots)'^ -r- 100
_ Augmented Surface X (Speed in knots)'-^
" loo
This method of estimating the probable resistances of ships
has been extensively employed by some shipbuilders, and is un-
doubtedly of use when the speeds to be attained are comparatively
moderate. As the speeds increase, and the wave-making resistance
assumes importance, the method necessarily fails; the total
resistance then varies with a higher power of speed.
Mr. Froude investigated the frictional resistances of ship-shaped
models, and as the result of a series of experiments came to a
448 NAVAL ARCHITECTURE. chap. xi.
conclusion which greatly simplifies the calculation of this impor-
tant factor: viz. that no sensible error is involved in calculating
the frictional resistance "upon the hypothesis that the immersed
"skin is equivalent to that of a rectangular surface of equal
"area, and of length (in the line of motion) equal to that of the
" model, moving at the same speed." Hence, it is only necessary
to experiment with such a plane surface as will enable the proper
coefficient of friction to be found, then to measure the immersed
surface of the ship, and to apply the coefficient, neglecting the
variations in speed of the particles at different parts of the surface.
This method of estimating the frictional resistance on the
immersed surface of a ship obviously takes no account whatever
of \\\e forms and proj)ortio7is of ships. Two ships of very different
forms, but of equal area of bottom and equal length, will have the
same frictional resistance for the same speed ; but they are likely
to have different total resistances. The influence of form and
proportion is greatest at high speeds, and it is chiefly felt in the
direction of surface disturbance or wave-making ; eddy-making
or wake formation also depends upon form, especially at the
stern.
The remarks made (on page 437) respecting the general
character of frictional resistances to the motion of planes, apply
also to the case of the curved wetted surfaces of ships ; and, from
an inspection of the coefficients of friction previously given, it is
ea^y to see why foulness of bottom often causes a considerable
reduction in the speed of ships. Furthermore it is most impor-
tant in Comparing the frictional resistances of a small model and
a full-sized ship to make the necessary corrections in the co-
efficients of friction on account of differences in length. Such
corrections must always appear in the records of model experi-
ments. (See page 472.)
Frictional resistance is the most important element of the total
resistances of most ships ; and in well-formed ships moving at
moderate speeds it constitutes nearly the whole of the resistance.
This fact has been established experimentally, but was predicted
on theoretical grounds. The experiments made by Mr. Froude
on her Majesty's ship Greylioimd, and those made by him on
numerous models, show that for speeds of from 6 to 8 knots — or
about the half-speed of ordinary ships — the frictional resistance
with clean bottoms is 80 or 90 per cent, of the total resistance,
and at the full speeds, even of the swiftest ships, the frictional
resistance equals 50 or 60 per cent, of the total resistance.
When the bottoms become foul, and the coefficients of friction
CHAP. XI. THE RESISTANCE OF SHIPS. 449
are doubled or trebled in consequence, frictional resistance, of
course, assumes a still more important place ; the practical eifect
of which is, as already remarked, a great loss of speed, or a con-
siderably greater expenditure of power in reaching a certain speed.
Second, as to eddy-maldng resistance. It is generally agreed
that in well-formed ships with easy curves at the entrance and
run (more particularly the latter) this factor in the resistance is
comparatively unimportant. Experiments indif^ate that eddy-
making ordinarily bears a fairly definite proportion to frictional
resistance ; and Mr, Fronde estimated eight per cent, of the fric-
tional resistance as a fair allowance for eddy-making in a well-
formed ship, when (to revert to our old illustration) the stream-
lines would converge easily towards the stern, and have regained
very nearly their original velocities and directions before they
leave the ship. With a full stern, and abrupt instead of gently
curved terminations to the water-lines of a ship, the particles of
water cease to act upon her at a period when they still retain a
considerable forward velocity ; and the momentum thus created,
and not given back in forward pressure on the stern, is a virtual
increase to the resistance. Behind the stern of such a vessel will
lie a mass of so-called "dead-water," an eddying wake like that
behind the plane in Fig. 117. Such a form of stern is objection-
able, and is never adopted unless its use is unavoidable in order
to fulfil other and more important conditions than those affecting
the resistance. The floating batteries built during the Crimean
War were constructed with very full sterns, and great displace-
ment in proportion to their extreme dimensions ; their perform-
ances under steam were very indifferent as compared with those
of better-formed ships. But they were designed for very special
services, to float heavy guns and armour, and economical propul-
sion was not made a feature in their designs.
In order to diminish eddy-making resistance as much as
possible, careful attention must be given to the forms of the
various adjuncts to a ship, as well as to the shape of the ship
herself. Outlying pieces — such as stern-posts, rudders, struts to
shaft-tubes in twin-screw ships, supports to sponsons in joaddle-
steamers, &c. — may occasion a sensible increase to the total
resistance, if improperly shaped. No general rule can be laid
down in this matter ; but IMr. Froude pithily expressed an impor-
tant fiict when he said, " It is blunt tails rather than blunt noses
that cause eddies," In other words, the after terminations of out-
lying parts should be made as fine as possible consistently with
other requirements.
2 G
450 NA VAL ARCHITECTURE. CHAP. xi.
Next as to wave-making resistance. The general character of
the causes which create waves at the bows and sterns of ships
moving in a frictionless fluid have already been sketched
on page 443. Similar causes operate when the motion takes
place in water, although the friction of the particles against each
other and against the surface of the ship affect both the
dimensions and positions of the waves. At the bow and stern, the
motion of the particles of water relative to the ship has its
minimum, and there are wave crests; amidships the relative
motion has its maximum speed, and there may be a wave hollow.
In other words, considering the ship as in motion and the water
as motionless except for the motion she impresses upon it, the
particles of water at the bow and stern will have motion in the
same direction as the ship ; those amidships will have motion in
the opposite direction. Besides these two principal wave crests
at the bow and stern, there may be other minor waves created ;
the great principle being that a crest will be formed wherever
the particles attain a maximum speed in the direction of the
advance of the ship ; and a hollow will be formed where the
particles have a maximum speed in the opposite direction.
The principal waves at the bow and stern will each be followed
by a train of waves, successive waves in the series having
diminished heights.
It will, of course, be remembered that throughout this dis-
cussion no proj)eller is supposed to be in action, which could
modify the relative motions of the water and the ship. But it
is worth notice that the action of propellers may create additional
wave crests, or modify considerably those formed by the ship.
Paddle-wheels, for example, placed nearly amidships accelerate
the steruward motion of particles, and produce an additional
wave. Screw-propellers, on the contrar}^, being placed aft, give
sternward motion to the particles, and tend to degrade the stern
wave, as well as to cause considerably greater resistance by
partially destroying the forward pressure of the water upon the
stern ; but they also create a local upheaval of the water, and
confuse the phenomena of the waves.
The laws which govern the wave-making resistance of ships
are not yet fully understood, systematic investigation of the
subject having been begun within the last half-century. Mr.
Scott Russell was one of the earliest workers in this field, and
made a large number of experiments, chiefly upon canal boats
and small vessels, before putting forward his well-known " wave-
line " theory of constructing ships. The theory is not in complete
CHAP. XI. THE RESISTANCE OF SHIPS. 451
accordance with more recent investigations, but it has the great
merit of having enforced the importance which might attach to
the wave-making factor in the resistance, unless the lengths of
"entrance" and "run" in a ship were suitably proportioned to
her intended maximum speed. By the " entrance " is meant that
part of a ship bounded by the stem and by the foremost ath wart-
ship section which has the full dimensions of the midship section :
the "run" is the corresponding length at the stern; and the
" middle-body," or " straight of breadth," is that part of a ship
amidships where the cross-sections maintain the form of the
midship section. The entrance and run have also been termed
the " wave-making features," because the waves which accompany
a ship are produced, as we have seen, by the accelerations and
retardations of the particles of water resultiug from the motion of
the entrance and run relatively to those particles. It is obvious
on reflection that the lengths as well as \h.Q forms of entrance and
run must greatly influence both the bow and the stern waves.
During each interval occupied by a ship in advancing through a
distance equal to the length of her entrance the sets of particles
then contiguous thereto undergo accelerations which lead to the
production of the bow-wave ; and this interval of time depends
upon the ratio of the length of entrance to the speed of the ship.
Similarly, importance must attach to the ratio of the length of
the run to the speed. If a ship be formed so that these ratios
are suitably adjusted for the maximum speed she is destined to
attain, and the curves of the bow and stern are easy and fair, it
may be hoped that the wave-making resistance will not assume
undue importance. When such a ship has reached her uniform
speed and the waves have been fully formed, the maintenance of
those waves will require but a comparatively small expenditure
of force. In fact, the case is parallel to that of the deep-sea waves
(described at page 202), which will travel over immense distances
without any great loss of speed; but with this important
difference that, whereas the ocean-waves gradually become
degraded, the waves accompanying ships, under the favourable
conditions described, are kept to their full heights at the expense
of a virtual increase in the resistance.
If the lengths of entrance and run are not suitably adjusted to
the maximum speed of the ship, the waves which are formed, or
a certain portion of them, diverge from her path, carrying off into
still water the energy impressed upon them. The ship has, there-
fore, to be continually creating new waves, and the expenditure
of force involved in this creation may form a very serious feature
2g2
452 NAVAL ARCHITECTURE. chap. XI,
of the total resistance. IMoreover, when the speed of a ship ex-
ceeds that of the waves which her entrance and run naturally
tend to form, other series of waves make their appearance, even
more important than the diverging waves, and requiring a very
large expenditure of power for their maintenance. These waves
have a length proportioned to the speed of the ship, and actually
kt^ep pace with her; although the wave-making features of the
ship are not adapted to their formation on account of the inade-
quate lengths of entrance and run.
It is now universally admitted that for every vessel there is a
certain limit beyond w^hich increased speed cau only be secured
at the expense of a very rapid growth in resistance. This limit
is "somewhat less than that appropriate to the length of the
wave which the ship tends to form," which length obviously bears
a close relation to the leng^th of entrance and run.* This g-eneral
endorsement of a principle first enunciated by Mr. Scott Eussell
naturally leads to a closer consideration of his wave-line theory.
According to this theory the water displaced by the bow of a
ship forms a "solitary" wave, wholly situated above the level of
still-water, and travelling as a heap of water. This bow-wave is
sometimes styled the " wave of displacement," and its companion
stern-wave is named the " wave of replacement." The latter wave
Mr. Eussell supposed to be the leading wave in a trochoidal series
resembling the deep-sea waves described in Chapter V. In order
to prevent undue wave-making, the theory prescribed that the
length of entrance given to a ship should be at least equal to the
length of the solitary wave having a natural speed equal to
the maximum speed proposed for the ship; and the length
of run should be two-thirds the length of the entrance. Eules
were also laid down for guidance in designing the forms
of the entrance and run, so that the resistance might be
minimised, but these need not be reproduced liere.j For deep
water and for the small heights which waves attain when travel-
ling with ships, no error of practical importance is involved in
estimating the period and speed of solitary waves of translation
by the rules previously given for trochoidal waves. In shallow
water there would be a necessity for considering the waves of
translation separately, and also for altering the rules given for the
* The apparent exceptions to the f Particulars will be found in Mr.
foregoing statement furnished by tor- Russell's work on Naval Architecture,
pedo-boats and swift launches are dis- also in vols. i. and ii. of the Tra^isac^toHS
cussed on pa^e 466. of the Institution of Naval Architects.
CHAP. xr. THE RESISTANCE OF SHIPS. 453
trochoidal deep-sea waves; but into these special circumstances it
is not necessary to enter, since they are important only in vessels
designed for river or shallow-water service, and scarcely affect sea-
going ships. Treating the wave of translation as a trochoidal
wave in the relation of its length and velocity, the rules of Mr.
Scott Russell may be stated in the following simple form : — Let V
be the maximum speed of the ship (in knots per hour) ; Li be
the length of entrance appropriate to the speed V, and L2 the
length of run (both lengths being expressed in feet) : then
L, = 0-562 X V2,
L2 = 0-375 X V2 = f Li.
For example, let V = 15 knots, then, to avoid undue wave-making
the theory prescribes : —
Length of entrance = 0'56-2 x 15' = 126 feet;
Length of run = 0-375 x 15^ = 8-1 leet.
With these dimensions Mr. Scott Eussell considered there mi^ht
be associated any required length of middle body, the additional
resistance for the assigned speed being chiefly due to friction on
the enlaroed immersed surface.*
Of these two rules, that relating to the length of run is
thought to have the greatest practical importance, many success-
ful vessels having had a less length of entrance than that pre-
scribed by the formula ; whereas vessels with shorter runs than
the formula prescribes have done badly. As a matter of fact,
however, sea-going vessels usually have greater lengths both of
entrance and run, in proportion to their maximum speeds, than
are required by these rules ; and instead of having the run only
two-thirds as long as the entrance, the lengths of entrance and
run are commonly equal, or nearly so.
It will be observed from the preceding formula that
L, + L2= 0-937 V-;
whence
Y^ = 1-067 (Li X L2) ; and V = 1-03 V^i + L, (nearly).
So far as can be seen at present, this last equation enables a fair
approximation to be made to the speed (V) at which a small in-
crea-e in speed causes an increase in resistance altogether dis-
proportionate to that which would accompany an equal increase
in speed when the vessel was moving more slowly. Putting the
* See further on tliis subject the experiments of Mr. Froude mentioned at
page 457.
454 ^^ V^^ ARCHITECTURE. chap. xi.
equation in this form allows for any variations which may be
desirable in practice in the ratio of the length of entrance to that
of run ; although neither of these can become very short in
proportion to the speed without producing increased resistance.
Suppose, for instance, that the common practice is adhered to, and
the lengths of entrance and run made equal to one another : it
may be desired to know what are the lengths appropriate to a
speed of 16 knots. Here
Li + L2 = 0-937 X (IG)- = 240 feet (nearly).
Professor Rankine, in 1868, suggested another mode of deter-
mining the limit of speed at which wave-making resistance begins
to grow at a very disproportionate rate.* Taking the quotient
of the volume of displacement divided by the area of the load-
water section of a ship, he termed it the mean depth of immer-
sion (A'). The velocity of the waves which are formed by a ship
he considered to be equal to that acquired by a heavy body in
falling freely through a distance equal to half the mean depth of
immersion ; this velocity might therefore be expressed approxi-
mately by the formula
Velocity (feet per second) = 4^/2^.
If the actual speed of the ship exceeds this natural velocity
of the waves formed by her advance, those waves will become
divergent, and the wave-making factor of the resistance will
increase. In other words the limiting speed for economical pro-
pulsion is that expressed in the above formula. This theory was
tested by observations made during the steam-trials of actual
ships, and was fairly confirmed ; but the observations w-ere not
sufficiently numerous to justify the general adoption of the
method.
The experimental researches of the late Mr. Froude and of his
son, Mr. R. E. Froude, have considerably advanced our know-
ledge of the general character of the waves which accompany
ships. Those experiments have mostly been made on models ;
but the wave-phenomena thus observed have been repeatedly
compared with similar observations made during the steam-trials
of ships belonging to the Royal Navy. According to these ob-
servations the weaves produced by the motion of ships in deep
water previously undisturbed may be classified as follows: — (1)
* See Transactions of the Institution of Naval Architects for 1868. The
experiments made to test this theory were conducted by Mr. John Inglis, jun.
CHAP. XI. THE RESISTANCE OF SHIPS. 455
waves produced by the advance of the bow ; (2) waves produced
by the stream-line motions near the stern. Of these, the bow
waves are more important. Each of these sets of waves may be
divided into two distinct series : — (1) diverging waves, the crest-
lines of which trail aft ; (2) transverse ivaves, of which the crest-
lines are nearly perpendicular to the keel-line of the ship. Mr.
Fronde did not a2;ree with Mr. Scott Kussell as rpo^ards the bow
producing a solitary wave of translation ; but considered that all
the waves produced in deep water are gregarious (like deep-sea
waves described in Chapter V.), successive crests following one
another at regular intervals ; those intervals, as well as the heights
of the waves, varying with changes in the speed of the ship.
Taking the bow-waves, for example, the highest crests appear
near the bow of a ship, and against her sides. The lengths of
the waves, measured outwards from the ship along the crest-lines,
are only moderate, and they gradually die away to the level of
still water towards the outer ends. The leading wave in each
series is followed by a number of other waves, of which the
heights gradually diminish as their distance from the bow in-
creases, but the actual termination of the series of waves cannot
be distinguished. Similar remarks apply to the two classes of
stern-waves. At low speeds neither the diverging nor the trans-
verse waves attain such dimensions as to practically affect the
resistance. At moderate speeds the diverging waves become
apparent, and their crest-lines are commonly inclined aft at an
angle of 40 to 50 degrees to the keel-line. It appears that only
the leadino; wave in the diver^ino; series at the bow touches the
side of the ship in most cases, the highest points in the following
waves in that series being at some distance from the ship. In
other words, as the wedge-shaped entrance is driven forward it
" throws off on each side a local oblique wave of greater or less size,
" according to the speed and the obtuseness of the wedge, and
" these waves form themselves into a series of diverging crests
". ; . . which after becoming fully formed at the bow pass clear
"away into the distant water and produce no further effect on the
" resistance." The " length," measured normally to the crest-lines
of these diverging waves, appears to agree, or nearly so, with that
of deep-water waves travelling at the speed which the ship's speed
w^ould give if resolved normally to the crest-lines. As the speed
increases so do these diverging waves increase in magnitude, and
represent a larger amount of resistance ; and the wave phenomena
are complicated still further by the appearance and rapid growth
of the transverse series of waves as that limit of speed is ap-
45 6 NAVAL ARCHITECTURE. chap. xi.
proached where the wave-making resistance begins to grow
ra[)iclly in importance. When that limit is passed the transverse
series of waves becomes even more important, affecting the total
resistance very largely and sometimes very singularly.
In Fig. 121a is reproduced a drawing prepared by Mr. Froude
to represent tlie result of careful observations of the wave pheno-
mena attending the motion at relatively high speed of a model
having a long middle-body.* The drawing indicates the positions
of the diverging waves, while the profile of the waves in the
traLsverse series is defined against the side of the model. This
profile was drawn from exact measurements, but the vertical scale
is exaggerated for the sake of clearness, so that the waves appear
FIG \Z\a
about twice as high as they really were relatively to the model.
Unlike the diverging waves, those in the transverse series appear
directly behind one another, successive wave-crests and hollows
reaching the sides of the ship. In the diagram the distance from
crest to crest is about 115 feet, the speed of the model correspond-
ing to about 14| knots per hour for a full-sized ship. It will be
observed that (in accordance with the formula on page 187) an
ocean wave having this speed would be about 120 feet in length,
so that there is a very fair agreement between the observed waves
and trochoidal waves of equal speed. Hence it appears that as the
speed of a ship is increased, so the lengths from wave-crest to wave-
crest will increase in the ratio of the squares of the speeds ; and the
See the Transactions of the lustilutiou of Naval Architects for 1877.
CHAP. XI. THE RESISTANCE OF SHIPS. 457
positions of wave-crests and hollows must vary, relatively to the
ship, as her speed is varied. These variations in the relative
positions of the waves and the after body of the ship were found,
on analysing the results of numerous experiments, to sensibly
affect the resistance of models having identically the same
entrance and run, with Fig. 121a, but varying lengths of middle-
body.
The earlier investigations of the late Mr. Froude on this
important feature of wave-making resistance were made with a
series of models having the same lengths and forms of entrance
and run (160 feet), but varying lengths of middle-body— ranging
from 310 feet down to nothing. The maximum speed appropriate
to this length of entrance and run, according to the formula on
page 454, would be rather less than thirteen knots; and so long
as this speed was not exceeded, the wave-making resistance
remained nearly of constant amount for all the models. At
higher speeds considerable differences in the wave-making resist-
ance were produced by variations in the total lengths of the
models. When the length and speed of a model were such that a
wave-crest of the transverse series was placed at or near the
middle of the length of the run, the wave-making resistance was
decreased. On the contrary, if the length and speed were so
related that a wave-hollow of the transverse series occupied the
position named, an increase in the wave-making resistance took
place. Hence Mr. Froude argued that the absolute length of a
ship, as well as her length of entrance and run, must affect her
resistance when moving at relatively high speeds ; and that
variations in speed must influence the resistance by altering the
relative positions of the hollows and crests of the transverse series
of waves situated near the stern of a ship.
These conclusions have been confirmed generally, and our
knowledge of the subject much extended by the investigations of
Mr. E. E. Froude.* It is impossible here even to summarise the
valuable experimental results, and the provisional theory based
upon the experimental investigations, which constitute the most
recent addition to this branch of the science of naval architecture.
By means of elaborate observations of the wave-phenomena
accompanying the motion of models through water, the general
characteristics of the bow and stern series of waves, classified
above, have been determined. Moreover, it has been shown that
* See the Paper " On the Leading Phenomena of the Wave-making Resistance
of Ships." — Tranmctions of tlie Institution of Naval Architects for 1881.
458 NAVAL ARCHITECTURE. chap. xi.
tliG variations in wave-making resistance accompanying varialions
in speed, after a certain limit of speed has been passed in a given
ship, may probably be explained by the " interference " of waves
belonging to the transverse bow series, with the leading wave in
the transverse series originated at the stern. That is to say —
" the height of the waves made, and the amount of the resistance
" caused, will be at the maximum or minimum according as the
" crests of the bow-wave series coincide with the crests or troughs
"of the natural stern-wave series. ... In either of these two
" cases the crest of the resultant wave coincides with the crest of
" the larger of the two components, while, if the crests of one
"series fall on the slopes of the other, the resultant crest position
" will be a compromise between the crest positions of the com-
" ponents, though nearer to the larger of the two."
The increase or diminution in resistance produced by variations
in the relative positions of the wave-crests or hollows near the stern
of a ship, is governed by various considerations. For example, the
height of the leading transverse wave in the bow series is affected
by the form of the entrance of a ship and the speed at which she
is driven. A sain the heio-ht of the crest in that wave of the
transverse bow series which lies on or near the stern, as compared
with the height of the leading bow wave, will depend upon the
number of intervening waves, which number will depend upon the
length and speed of the ship. The form of the stern and speed
of the ship also influence the magnitude of the waves originating
there, and so of the waves composed of the bow and stern series.
These general considerations do not, however, enable an exact
estimate to be formed of the magnitude of wave-making resistance
in a ship of given form moving at a given speed, and for this
purpose model experiments are essential.
The following passage in the remarks of Mr. R E. Fronde
deserves quotation here, although it relates to a different aspect of
wave-making resistance. He says : — " It is a reasonable inference
". . . . that the wave-making features of a ship will operate more
" effectively to make short waves if their displacement is disposed
"broadwise rather than deepwise; and more efiectively to make
" lung waves if it be disposed deepwise rather than broadwise.
" Now the diverging waves being necessarily much shorter than
" the transverse waves, we see that flaring-out the end sections of
" a ship, or increasing the ratio of breadth to depth will cseterls
"■imribus tend to increase the resistance due to diverging waves
"and diminish that due to transverse waves: while giving V-
" sections or increasing ratio of depth to breadth will have the
CHAP. XI,
THE RESISTANCE OF SHIPS.
459
" opposite effects. These inferences are visibly corroborate 1 by
" the appearance of the wave systems caused in the cases referred
" to. Again it is worth noticing that the experiments at Torquay
"have sliown that, as a rule, moderately U-shaped sections are
'• good for the fore-body, and comparatively V-shaped sections for
" the after-body. This would seem to show that in the wave-
" making tendency of the after-body the diverging wave element
" is less formidable than in that of the fore-body, and this infer-
" ence corresponds with the fact that the stern diverging wave
" series is visibly less marked than that of the bow."
Another important deduction from these model experiments
may be mentioned, before concluding our remarks on wave-
making resistance. Supposing that the lengths of entrance and
run provided in the design for a new ship to be ample in propor-
tion to her intended full speed, a diminution in the total resistance
may be usually secured by adopting still greater lengths of entrance
and run, \Nith finer lines at the extremities and a greater extreme
breadth, the displacement remaining unchanged. This is con-
trary to the opinion formerly entertained as to the influence on
resistance of an increase in the area of the immersed midship
section ; but there is ample evidence of the truth of the principle.
An excellent illustration is found in the experiments made with a
model of the merchant steamer Merkara, and models of alternative
forms but identical displacement.*
The dimensions of two of these vessels (in feet) were as under : —
Models.
Length.
Extreme
Breadth.
Mean
Draught.
Entrance.
Middle-Body.
Run.
Total.
Merkara . .
Model B . .
144
179-5
72
Nil
144
179-5
360
359
37-2
45-88
16-25
18
The MerJcara had an area of immersed surface of 18,660 square
feet; model B an area of 19,130 square feet; the displacement
in each caf^e was 3980 tons. So far as surface friction went^
therefore, the Merhara had a small advantage; as to eddy-
making, the two ships must have been practically equal, and the
difference between the two would arise from differences in the
wave-making resistance. On trial it was found that about 18
knots marked the limit of speed for the Merhara, where a slight
* See the details given by Mr. Froude in vol. xvii. of the Transactions of the
Institution of Naval Architects. The Merhara was built by Messrs. Denny.
46o NA VAL ARCHITECTURE. chap. xi.
increase in speed led to a disproportionately large increase in the
wave-making resistance. At a speed of 19 knots the wave-
making resistance of the model of the Mer'kara was found to
be fully 60 per cent, of the whole resistsmce, whereas at the
actual maximum speed of the ship — 13 knots — wave-making
resistance was only 17 per cent, of the whole. No limit of
speed corresponding to 18 knots in the Merhara was found for
model B up to speeds of 19 or 20 knots; and this Avant of any
disproportionate increa'^e in the wave-making made tlie resistance
of B at a speed of 18 knots only 75 per cent, that of the Mer'kara,
whereas at 13 knots the difference in the resistances was very
trifling.
Applying the formulae of the wave-line theory to these two
vessels, we have —
ForMerZ;«ra V LTTl; = V^88 = 17 (nearly).
Limiting speed V = 17 x 1*03 = 17| knots (nearly).
For model B V Li + L. = V 3o9 = 19 (nearly).
Limiting speed V = 19 X 1*03 =19*57 knots (nearly).
There is consequently a close agreement between theory and
experiment as to the limit of speed beyond which the growth of
resistance becomes disproportionately great.
Summing up the foregoing remarks, it appears : —
(1) That frictional resistance, depending upon the area of the
immersed surface of a ship, its degree of roughness, its length,
and (about) the square of the speed, is not sensibly affected by
the forms and proportions of ships: unless there be some un-
wonted singularity of form, or want of fairness. For moderate
speeds, this element of resistance is by far the most important :
for high speeds, it also occupies an important position — from 50
to 60 per cent, of the whole resistance, probably, in a very large
number of classes, when the bottoms are clean; and a larger
percentage when the bottoms become foul. '
(2) That edchj-mahing resistance is usually small, except in
special cases, and amounts to some 8 or 10 per cent, of the fric-
tional resistance. A defective form of stern causes largely in-
creased eddy-making.
(3) That wave-making resistance is the element of the total
resistance which is most influenced by the forms and proportions
of ships. Its ratio to the frictional resistance, as well as its
absolute magnitude, depend upt n many circumstances ; the most
important being the forms and lengths of the entrance and run.
CHAP. XI. THE RESISTANCE OF SHIPS. 46 1
in relation to the iutended full speed of the ship. For every ship
there is a limit of speed beyond which each small increase in
speed is attended by a disproportionate increase in resistance ;
and this limit is fixed by tlie lengths of the entrance and run
— the " wave-making features " of a ship.
The sum of these three elements constitutes the total resist-
ance offered by the water to the motion of a ship towed through
it, or propelled by sails ; in a steamship there is in addition an
*' augment " of resistance due to the action of the propellers, as
will be explained hereafter (see Chapter XIII.).
In preparing designs for ships the naval architect commonly
has to choose forms and proportions that will enable certain con-
ditions to be fulfilled, and to make considerations of diminished
resistance subordinate to those conditions. This is particularly
true in war-ship design. For example, handiness is held to be aa
essential quality in most classes of war-ships, and handiness can
only be secured in association with moderate lengths, rarely
exceeding 300 to 350 feet in the largest modern armoured vessels,
and only reaching 400 feet in a few vessels. In merchant ships,
on the contrary, the power of turning rapidly is less valued, and
lengths of 500 to 550 feet are by no means uncommon. Again,
in war-ships the vertical distribution of the weights is fixed with
especial reference to their powers of offence and defence ; heavy
weights of guns, armour, &c., are carried high up, and conse-
quently the ratios of length and draught to beam, as well as the
under-water forms, have to be largely influenced by the necessity
for providing sufficient stability. Merchant ships, on the other
hand, carry their heavy weights of cargo comparatively low down
in the holds, and can be made sufficiently stable for all practical
purposes with ratios of length and draught to beam which are
scarcely possible in war-sliips. Ships of the central citadel type
afford still more striking instances of the difference now under
consideration. In them the beam is made proportionately greater
than in ships with armoured belts throughout the length in tlie
region of the water-line, so that the ships may retain sufficient
stability when the unarmoured ends are riddled. The provision
of good sail power as well as steam power also affects the forms of
many classes of war-ships, moderate lengtli and considerable beam
being necessary to secure stiffness and handiness when under sail.
Even in merchant sailing ships, with their radically different
vertical distribution of weights, greater ratios of length and
draught to beam can be accepted than are adapted to the condi-
tions of war-ships with steam and sail ; and in merchant steamers
462
NAVAL ARCHITECTURE.
CHAP. XI.
wherein sail is quite subordinated to steam the difference is
still greater.
Her Miijesty's ship Greyliound, of which the name has become
well known in connection with Mr. Fronde's experiments, is in all
respects a contrast to the merchant steamer Merhara, and a com-
parison of the resistances experienced by the two vessels when
moving at the same speeds will serve to point the preceding
general statement. The following are the particulars of the
Greijliound: — Length (from stem to body-post) 160; breadth ex-
treme, 33^ feet; mean draught, 13f feet; displacement, 1160
tons; area of immersed surface, 7540 square feet. In order to
ascertain the resistance the GreyJiound was towed by the Active at
varying speeds, the maximum being about 13 knots. When she
moved through the water, the vessel necessarily communicated
motions to the water in her neighbourhood ; the general character
of these motions having been indicated in the preceding sketch
of the stream-line theory. Changes in her own speed must have
been accompanied by corresponding changes in these motions;
and thus, in addition to the ship herself, a certain weight of
water, which may be regarded as associated with her, must have
undergone changes of speed corresponding to those impressed on
the ship. Mr. Froude obtained data from which to estimate this
weight of water, making special experiments for the purpose, and
found it to be about one-fifth or one-sixth the w^eight of the ship.
The virtual weight of the Greyliound, when towed, was, therefore,
about 1400 tons. The tow-rope strain, or resistance, correspond-
ing to various speeds was found to be as under. For purposes
of comparison, the corresponding approximate results for the
Merhara are also given ; her actual weight being 3980 tons, and
her virtual weight perhaps 4600 or 4700 tons.
Speed of Ships.
Resistance (in Tons).
Greijhound.
Merhara.
4 knots
6 „
8 „
10 „
12 „
0-6
1-4
2-5
4-7
9
1
2-3
3-9
6
9
The full speed of the Greyhound when driven by her own
steam power was 10 knots ; at that speed the resistance was only
2.1^,0 part of her actual weight; 13 knots is the full speed of the
CHAP. XI. THE RESISTANCE OF SHIPS. 463
Merhara ; the corresponding resistance (11-5 ioTi^) is only I-^q
part of the actual weight. It will be remarked that for speeds,
below 8 knots, where frictional resistance constitutes almost the
whole resistance, the greater surface of the bottom of the Mc7'hara
makes her resistance greater than that of the Greyhound; but
at the higher speeds the greater wave-making resistance of the
shorter and smaller ship makes her resistance gradually approxi-
mate to that of the Merkara.
So long as frictional resistance forms the larger part of the
total resistance, the law which was formerly received as general
holds fairly well, the resistance varying nearly as the square of
the speed. In the Merlcara, for example, the law holds very
closely up to the speed of 13 knots, at which the frictional resist-
ance formed about 80 per cent, of the total. In the Gi^ej/hound,
the same law holds very fairly up to about 8 knots only, the
frictional resistance at that speed being about 70 per cent, of the
total ; but beyond that speed the gradual growth in importance
of the wave-making factor makes the total resistance vary with
a higher power than the square of the speed. At 10 knots it
varies nearly as the cube of the speed ; and at 12 knots, nearly
as the fourth power, the frictional resistance then being only
35 per cent, of the total. This contrast illustrates the principle
previously laid down that considerable lengths of entrance and
run and iiue forms are advantageous, not merely in adapting
vessels for high speeds, but in keeping down the law of increase
in terms of the velocity for more moderate speeds. If economical
performance under steam had been the sole or principal condition
to be fulfilled in the Greyhound, it would undoubtedly have been
preferable to adopt greater proportions of length to breadth, and
finer forms at the extremities ; then, with the same lengths of
entrance and run, associated perhaps with a certain length of
middle body, there would probably be somewhat greater frictional
resistance than in the actual ship, but a very considerable decrease
in the wave-making resistance, and on the whole a less resistance
would have to be overcome in obtaining the designed speed.
Such latitude of choice in forms and proportions was not, however,
possible in the design of the Greyhound. She was intended to be
efScient under sail, as well as to have moderate speed under
steam ; hence, moderate proportions of length to breadth became
necessary, in order to secure sufficient " stiffness," and handiness.
It may be interesting to add that the lengths of entrance and
run in the Greyhound were each 75 feet ; so that, according to the
formulae on page 453, no abrupt and inordinate growth of wave-
464 NAVAL ARCHITECTURE. chap. xi.
making should have occurred during the experiments. Nor did
any such sudden change take [dace; although the bluff form of
the ship made the wave-making factor in the resistance of such
considerable amount.
The tendency in the merchant service has been, for many years
past, towards an increase in the proportion of length to breadth in
steamers; and in Chapter X. several examples of the change
have been given. The common plan is that illustrated in the
Merhara, a certain length of parallel middle body being introduced
between lengths of entrance and run, sufficient to prevent any
undue growth of the wave-making resistance within the intended
limits of speed. Continuance of this policy of construction, and
the gradual advances made by the same owners on the lengths of
ships, may be regarded as good evidence of its advantages from
a commercial point of view. But having regard to the experi-
ments above mentioned, and to the probability that higher speeds
will be required in future ships, shipowners and shipbuilders
may well consider whether the ratio of beam to length might not
be increased advantageously, instead of adding largely to the
length. Mr. Froude has demonstrated two most important facts.
First, that within the ordinary limits of speed for merchant
steamers (say, 13 knots) it would be possible to obtain as good
results with a slightly greater draught and much more moderate
proportions of length to breadth than are now commonly em-
ployed ; and with a less area of immersed skin. The a'lvantages
of the more moderate proportions are greater handiuess and
stiffness, the requirement of less structural strength and weight
of hull, and the less serious loss of speed resulting from foulness
of bottom; the gain in all these respects is not unimportant.
Secondly, that if very high speeds have to be attained — say,
speeds of 18 to 20 knots — it is preferable to decrease the length
of the middle body, or to have none ; increasing the lengths to
entrance and run at the expense of the middle body, and making
the extreme breadth greater.
Mr. Froude summed up his investigation as follows : — *
" In view of the importance of large carrying power combined
" with limited draught — a limitation which the Suez Canal has
" done much to emphasise — and I may add, in view of the prac-
" tical sufhciency of what may be called moderate speed, the
" prevailing tendency to great length, including a long parallel
* See page 184 of the Transactions of the Institution of Naval Architects
for 1876.
CHAP. XI. THE RESISTANCE OF SHIPS. 465
" middle body, is a fair result of ' natural selection.' This form,
" if rationally treated, is perhaps^ under tlie conditions indicated,
"the best adapted for commercial success; though where deep
"draught is unobjectionable, a shortened form with no parallel
" middle would be, as I have shown, unquestionably superior ; or
" were it an object to obtain very high speed, without notable
"increase of resistance, parallelism of middle body would even
" with the longer form be inadmissible. The logic of the circum-
" stances shapes itself thus : — Large displacement means large
"dimensions, somehow or somewhere; but the limitation of
" draught forbids enlargement of dimension except in the direc-
" tion of length, since increased ratio of breadth to depth would
"involve an objectionably raised metacentre, and objectionable
" increase of skin ; greatly extended length has, therefore, for
" mercantile purposes become essential to large carrying power.
" Now with, a very long ship, if the ends are so far fined as in
" effect to limit the resistance to surface friction, the parallelism
" of the remainder clearly assigns a valuably increased carrying
" power to the ship as a whole ; or, what comes to the same
" thing, secures a given carrying power with less total skin and
" therefore less resistance at moderate speed."
The principles of construction here set forth have since been
applied to practice by several eminent private shipbuilders with
the most satisfactory results ; and it seems probable that, without
sacrificing the undoubted advantages of great length, greater pro-
portionate beam will be adopted in future merchant ships.
Although economical propulsion requires the provision of appro-
priate lengths and fineness of entrance and run, it is possible to drive
vessels at speeds far exceeding those for which their dimensions
would appear well adapted if judged by the ordinary rules. The
fast torpedo-boats recently introduced are remarkable illustrations
of this statement. Vessels from 50 to 100 feet in length have been
driven at speeds of 16 to 22 knots an hour ; for which speeds,
according to the wave-line theory, the appropriate lengths of
entrance and run would be from 250 to 500 feet. In these
extreme cases, however, the expenditure of power in relation to
the weights driven is abnormally great ; and at the higher speeds
there is a wide departure from the laws which usually hold good
for the relation between the resistance and the speed of ships.
It has been shown in the comparison between the Merlcara and
the Greyliound that for low speeds the resistance varied nearly as
the square of the sj eed ; and that as the speed increased the
resistance varied at a higher power than the square of the speed.
2 H
466 NAVAL ARCHITECTURE. chap. xi.
This is the common case for ships of ordinary form moving at
speeds for which their lengths of entrance and run would be
considered fairly appropriate ; it holds good also for the torpedo-
boats so long as their speeds do not rise beyond the economical
limit appropriate to their lengths. But as that limit is surpassed,
so the power of the speed according to which the resistance varies
first increases beyond the square, reaches a maximum, and finally
at the abnormal maximum speed actually falls below the square :
that is to say the resistance at the maximum speed varies at a
less power of the speed, than it does at the low speeds of 6 to 8
knots, where frictional resistance is almost the sole obstacle to
progress. This remarkable departure from ordinary rules was
first remarked in the steam-trials of some of the earliest fast
boats ; it has since been confirmed by numerous steam-trials of
similar vessels, and by model experiments conducted by Mr.
Froude. The following is an example. The resistance of a boat
about 80 feet long was found to vary nearly as the sq_uare of the
speed up to 10 knots per hour ; beyond this speed the power of
the speed according to which the resistance varied gradually
increased until at 13 knots it exceeded the ciibe ; but when the
speed had reached 17 to 18 knots the resistance varied at a less
power than the square. Comparing this with the performance of
Her Majesty's ship Iris, the behaviour of the torpedo-boat appears
most remarkable. The Iris is 300 feet long and has attained a
measured mile speed of 18^ knots per hour. Up to 13 knots per
hour the resistance varied nearly as the square of the speed ; and
the law of growth gradually increased with the speed until at 18
knots the resistance varied at a somewhat less rate than the cube
of the speed. If it were possible to push the Iris to much higher
speeds, there can be no question but that a change in the law
connecting the resistance with the speed would occur similar to
that which actually takes place in the torpedo-boat ; only in the
ship this change would not be reached until the speed of 30 to 40
knots per hour was attained. These are suggestive facts ; of
which a complete explanation has yet to be given. The wave-
making phenomena accompanying the motion of ships at rela-
tively high speeds have been very carefully observed by Mr.
R. E. Froude, and the principal results are recorded in the Paper
quoted on page 458. Extensive observations have also been made
of the behaviour of torpedo-boats driven by their own engines.
Hence it appears that, when at full speed, the torpedo-boats are
carried on the back slope of a wave having a length corresponding
very closely to the speed of the vessels. Great alterations of trim
CHAP. XI. THE RESISTANCE OF SHIPS. 467
also take place at these high speeds from the still-water condition,
the bow rising and the stern falling. Mr. Yarrow has made a series
of experiments on the changes of trim, accompanying changes
in the speed of some of the torpedo-bjats built by him ; noting
at the same time the profile of the wave water along the sides of
the boat. From the results which he has communicated to the
author one example has been taken, and illustrated by Fig. 121&.
It is the case of a boat about 80 feet long steaming at a speed
of 18|- knots an hour. By dotted lines is shown the still-water
condition of the boat, floating on an even keel : by drawn lines is
shown her condition under steam, and the outline of the water at
her side. She was found to alter trim about | inch to the foot
when under-way ; which on her length would make a rise of 40
inches of the bow relatively to the stern. On the other hand,
the bow rose relatively to the water surface rather more than a
foot, while the stern sank less than six inches. In short, as was
FiG \Z\h
:SS
s^
Fig. l21h.—Note. The dotted lines show the outline of bocat and water-surface,
when she is at rest in still water. The drawn lines show the corresponding
particulars for full speed.
above remarked, the-boat at this high speed was carried on the
back slope of a wave which she had created, and which was
travelling at about the same speed as herself.
The very great expenditure of power necessary to drive these
small vessels at the higher speeds has already been mentioned ; a
few figures may serve to illustrate the statement. When the Iris
is moving at the speed of eighteen knot^^, her resistance is less
than the one-hundredth pai-t of her weight ; at the same speed in
a torpedo-boat the resistance would be about one-sixteenth of the
weight. When the Shah moves at a speed of 16 to 17 knots, less
than one-two-hundredth part of her weight measures the resist-
ance; for the torpedo-boat the corresponding resistance would be
one-twentieth of her weight. At twelve knots the resistance of the
Merliara is less than one-four-hundredth part of her weight ; for
the torpedo-boat the corresponding resistance would be about one-
fortieth of her weight. Such comparisons as these are obviously
incomplete, and throughout them the torpedo-boat is placed at a
disadvantage because of her relatively small size (see the remarks
on page 474), but they indicate the penalty which has to be paid
when small vessels are driven at very high speeds.
2h2
468 NAVAL ARCHITECTURE. chap. XI.
Ill this connection it is natural that allusion should be made to
the greatly increased speeds now (1882) realised by ocean steamers
as compared with those attained ten years ago ; and to the pro-
bability that yet higher speeds will be reached in future
ships. Instead of averaging 10 to 12 knots, the fastest ocean
steamers now average 14 to 16 knots, and other vessels are
approaching completion which are expected to possess higher
speeds. Without attempting to predict the extent to which
progress may be made, it is evident that even with existing types
of marine engines the limit of speed has not been reached, and
will be fixed rather by commercial considerations than by any
other. Increase in the sizes of ships and the power of engines
may possibly go much farther ; but higher speeds will be costly
and will entail additional risks. There have been many proposals
for modifying the forms of ships in such a manner as would
enable them to attain extraordinarily high speeds on moderate
dimensions ; but none of these plans has yet found acceptance
with naval architects, and it is certain that no moditication of
form can enable a vessel moving at high velocity through water
to escape from a great resistance, involving a large proportionate
expenditure of engine power. In the course of his experiments
Mr. Froude has determined the resistances of models moving at
speeds corresponding to from 50 to 130 knots per hour for full-
sized ships. The results are most interesting and instructive, but
they do not encourage the hope that, in practice, any such speeds
will be realised.*
In the preceding pages it has been shown that the problem to
be solved by the naval architect is not to determine any exact
geometrical form of least resistance of which he can make use in
all cases, but in the design of each ship to select the forms and
proportions which are compatible with the special conditions to
be fulfilled, and which will make the resistance as small as
possible. Even when thus narrowed, the problem is one of con-
siderable difficulty ; mainly because of our ignorance of the laws
which govern the wave-making resistance. At present only a
few of the more important conditions influencing wave-making
have been determined, and these rather in a qualitative than a
quantitative fashion. The determination of the resistances of
ships is, therefore, necessarily a matter of experiment in the
present state of our knowledge ; and apart from experiments great
uncertainty must always attend estimates of the resistances of
* See Return No. 313 of 1873 to order of the House of Commons.
CHAP. XI. THE RESISTANCE OF SHIPS. 469
new types of steamships, as well as of the engine power required
to attain certain speeds. This is especially true of types in which
novel forms or proportions are introduced, or in which the speeds
to be attained lie quite outside the range of previous experience.
The case of vessels similar in form and not very different in speed
from others which have been completed and tried can be dealt
with, as will be explained in Chapter XIII. ; but radical changes
can only be made with any certainty on the basis of careful
experiments, and such experiments are best conducted on models
according to the system introduced by the late Mr. Froude. lu
1868, a committee was a})pointed by the British Association to
report " on the state of existing knowledge on the stability, pro-
pul>ion and sea-going qualities of ships," and in their Report,
presented in the following year, they recommended a series of
experiments to be made in order to determine the resistances of
full-sized ships, model experiments being regarded as of doubtful
value. From this Report, Mr. Froude dissented, contending
"that experiments on the resistances of models of rational size,
" when rationally dealt with, by no means deserve the mistrust
" which they are usually dealt with ; but on the contrary
"can be relied on as truly representing the resistances of the
" ships of which they are the models." His views were supported
by numerous experiments ; and the value of the process by which,
from a comparatively inexpensive series of experiments on models,
a close approximation can be made to the resistances of ships
being recognii^ed by the professional ofScers of the Admiralty.
Mr. Froude received assistance in the establishment of experi-
mental works, which have continued in useful operation for the
last ten years. During the greater part of that period Mr. Froude
personally superintended the work, and his labours have been of
the greatest value to the Royal Navy, at a time when changing
conditions rendered the adoption of novel types and higher speeds
imperative. Since his lamented death, the work has been con-
tinued, on behalf of the Admiralty, by his son, Mr. R. E. Froude.
Similar experimental works have been established in Holland,
and attempts in the same direction have been made in France
and Italy. The establishment at Amsterdam is conducted with
marked ability by Dr. Tideman, Chief Naval Constructor, who
has published an interesting account of a long series of experi-
ments made on models of different types of ships. At this place
were made the experiments upon which the design of the yacht
Livadia (built on the Clyde for the Emperor of Russia) was based.
This remarkable vessel is 230 feet long, 150 feet broad, and of 8
470 NAVAL ARCHITECTURE. chap. xi.
to 9 feet draught, her form and proportions departing so consider-
ably from those of any preceding vessel that it is difficult to con-
ceive how any estimate of the engine-power could have been
made independently of such experiments. It may reasonably be
anticipated that this experimental method of comparing the
merits of various forms will be extended hereafter so as to em-
brace the mercantile marine as well as the Koyal Navy, and steps
are already being taken to create an experimental establishment
by one of the leading Clyde firms. Such an extension will un-
doubtedly be productive of large economies in steam-power and
coal consumption in future merchant steamers; for similar savings
have already been effected in war-ships. The following is an
example : —
In designing the Medina chiss of river-service gunboats for
the Koyal Navy, the draught of water was limited to less than 6
feet, and the full speed was fixed at 9 knots. The question arose
which of two forms would be preferable : a vessel having a length
of 110 feet and an extreme breadth of 26 feet, or a vessel of
equal length, but 34 feet broad, and having greater fineness and
length of entrance and run. Having experimented with models
of the two forms, Mr. Froude reported that the broader vessel
with a displacement of 370 tons, would have only two-thirds as
great resistance as the narrower vessel with a displacement of
350 tons. The results since obtained, on the measured-mile
trials, with vessels built on the broader form, have fully confirmed
the experiments made with the models. Without experiments
the result could scarcely have been predicted; and it is a re-
markable illustration of the fallacy of the opinion, formerly enter-
tained very generally, that a greater area of midship section
involved an increased resistance. The smaller actual resistance
of the vessels with the larger midship sections was undoubtedly
mainly due to the decrease in wave-making resistance produced
by the longer and finer entrance and run. Whatever the ex-
planation, there can be no question of the fact that this change
of form was productive of a very advantageous diminution of
resistance : saving one-third the engine-power required to attain
the desired speed, and reducing the first cost of the machinery,
as well as the cost of maintenance and repair during all the
subsequent service of the numerous vessels in this class.
As such importance attaches to these experiments, it is desirable
that, before concluding this chapter, a brief account should be
given of the process by which the resistance of a full-sized ship
is obtained from the ascertained resistance of the model. For
CHAP. XI.
THE RESISTANCE OF SHIPS.
471
this purpose, Mr. Froude made use of a " scale of comparison,"
based upon the stream-line theory, and stated it as follows : —
" If the sliip be D times the dimension of the model, and if at
" the speeds Vi, V2, V3 the measured resistances of the
" model are Rj, R25 R3 > then for speeds ViVl^, "^2v'JL)j
" V3 VL> of the ship, the resistances will be D^Ri, D^R2>
*' D^Rg To the speeds of the model and ship thns
" related it is convenient to apply the term corresponding speeds."
This general statement will, perhaps, be better understood by an
example ; for this purpose we cannot choose a better example than
that published by Mr. Froude for the Greijlioimd, and illustrated
by Fig. 122.
The curve AA in the diagram is termed a "curve of resist-
ance ; " measurements along the b.ise-line XY representing speeds
W 25.000
FIQJ22
aSq'..—\ -I \ r"" 80,6 I a
VIOO 120 140 160 ISO 200 220 2
ri
"(t
IS
00
ISO 200 220 240 260 280
Speed, in Feet per minute
Jo.
-25.000
-^ 20.000
§ 10.000
^
300 320 K Resistance
qfS/up in lbs
(in feet per minute), and the lengths of the ordinates drawn
perpendicular to XY representing the resistances of a ship or
model (in pounds) at the various speeds. To construct the
curve, the model is towed at a certain speed — say, 240 feet per
minute — and its resistance recorded by means of suitable dyna-
mometrieal apparatus ; a length (ad, in Fig. 122) representing
this resistance 'is then set off along the ordinate drawn perpen-
dicularly to XY at the point {d) corresponding to the speed.
This process having been repeated for a considerable number of
speeds, a series of points (such as a) is determined, and through
these the curve A A is drawn. By simple measurement of an
ordinate of this curve the resistance can be ascertained at any
speed within the limits over which the experiments extend.
Having measured the immersed surface of the model, and ascer-
tained by experiment its proper coefficient of friction, the
472 NAVAL ARCHITECTURE. chap. xi.
frictioual resistance can be easily calculated for each of the
experimental speeds. The value of the frictioual resistance at
each speed is then set off from the base-line XY, on the same
scale as was chosen for the total resistance curve AA, the length
dh representing the frictioual resistance at the speed of 240 feet.
A curve of frictioual resistance (BB) is thus obtained for the
model ; and this operation completes all that need be done for
the model ; furnishing the data from which the resistance of the
full-sized ship can be estimated.
In the case of the Greyhound the model was one-sixteenth of the
full size of the ship : hence for the scale of comparison mentioned
above, D = 16 ; \/D = 4; and the "corresponding speeds" of the
ship will be four times those of the model. In Fig. 122 the
speeds in feet per minute marked heJoiv the line XY are speeds
for the model; those marked above the line are speeds for the
ship. For resistances at the corresponding speeds, the law stated
above becomes —
Kesistance of ship = (16)^ x resistance of model
= 4096 X resistance of model.
This change, therefore, simply amounts to an alteration in the
scale of measurement of the ordinates of the curve AA ; whatever
length represents 1 lb. for the model must represent 4096 lbs. for
the ship. The appropriate correction is made in Fig. 122 by the
scale of "resistance of ship" drawn at the right-hand side of the
dicigram. It will be remarked that this scale provides for resist-
ance in fresh water, as well as in sea-water, the salt-water resist-
ance exceeding that for fresh water in the ratio in which the
density is greater than that of fresh water; but this is not an
important feature of the experiments, having been introduced
only because fresh water is used in the experimental tank.
Havino: corrected the vertical scale of resistance in the manner
described, it would be possible to measure the resistance of the
ship fur any speed from the ordinates of the curve AA, were not
a correction needed in the frictioual resistance on account of
the length of the ship exceeding that of the model so greatly.*
This difSculty Mr. Froude meets by a simple device. The
frictioual resistance of the ship is calculated for the various
speeds, making use of her actual coefficient of friction (allowing
for her greater length), and these values are set off (on the proper
scale, and on ordinates representing the corresponding speeds)
* See the remarks on page 448.
CHAP. XI. THE RESISTANCE OF SHIPS. 473
downwards from the curve BB, which represents the frietional
resistance of the model; through the points thus determined
the curve CCC is drawn. Then, to determine the resistance
of the ship at any speed, instead of measuring from the base-
line XY, it is necessary to measure from the line CC.
Take, once more, the speed of 240 feet per minute for the
model; this represents a speed of 960 feet for the ship (or about
9^ knots per hour). The length ae on the ordinate, corresponding
to this speed, re^sresents the total resistance of the ship, on the
proper scale ; and the length &c represents on the same scale the
frietional resistance of the ship, while cd represents the diminu-
tion of the frietional resistance of the ship as compared with the
model, and will be seen to be of considerable amount.
In the conduct of these experiments the greatest care is needed
to secure uniform motion of the models at any assigned speed, as
well as the correct measurement of the strain on the towing
apparatus, and the avoidance of any c mditions which would
render the behaviour of the model dissimilar from that of the
ship represented when she is moving in smooth water of great
depth and extent. It will be obvious that any errors made in
the model experiments will be greatly magnified in passing from
the model to the ship ; but the possibility of such errors occurring
has been minimised by the beautiful apparatus contrived by Mr.
Froude, this apparatus being to a large extent automatic in its
action and giving a continuous record of the results for each run
of a model at a certain speed.* Supposing the data for the
model to have been accurately determined, it is, however, obvious
that its practical usefulness depends upon two conditions: (1)
the accuracy of the law of "corresponding speeds;" (2) upon the
possibility of making an approximation to the correction in frie-
tional resistance required in passing from the model to the ship.
Upon the second condition nothing need be added ; but a few
remarks in explanation of Mr. Fronde's "scale of comparison"
may be of service. Previous w riters had remarked upon the im-
propriety of comparing the resistance of a ship with that of a
model moving at the same speed ; and M. Reech had pointed out
that when the resistance varied as the square of the speed, if
models of different sizes were moved at velocities varying as the
square roots of their lineal dimensions, their resistances would
vary as the cube of the lineal dimensions. This rule of M. Reech
* For details of this apparatus see vol. xv, of the Transictions of the
Institution of Naval Architects.
474 NAVAL ARCHITECTURE. chap. xi.
is identical with Mr. Fioude's scale of comparison, but rests upon
a less general hypothesis ; it can be easily demonstnited. Suppose
a wholly submerged body to have Si square feet of wetted
surface, then, for a speed of Vi feet per second, we should have
Eesistance = Ri = K.SiVi2 (1),
where K is a coefiScient determined by experiment. For another
body of similar form, having the wetted surface Sg and moving at
the speed V2,
Resistance = R2 = K.S2V22 (2);
whence it follows that
5i = /IlVSi
R2 IV^/'S^
(3).
If the first body have lineal dimensions D times those of the
second, then
!=»' W'
and further, if the velocities Vi and Vg are related to one another
as the square roots of the lineal dimensions,
^ = VD=(f;) =D (5).
Substituting from (4) and (5) in (3) we have at these "corre-
sponding speeds "
K2
so that, under this limited assumption as to the law of resistance,
the " scale of comparison " holds good. Mr. Fronde first showed
that it held good generally for wave-making resistance, whatever
might be the law of resistance; provided that the frictional
resistance was separately considered. His reasoning may be
briefly summarised.* According to the stream-line theory of
resistance, the "displacements," which the motion of a wholly
submerged body imposes on the surrounding volumes of fluid,
" are for a given body identical in configuration at all velocities,
" and this configuration is similar for all similar bodies." This
law of similarity would also hold good for a partially submerged
body, if the surface of the fluid were supposed to be uninfluenced
See Beports of British Association for 1868.
CHAP. XI. THE RESISTANCE OF SHIPS. 475
by gravity, and consequently the wave phenomena — the " upward
disturbances of the surface " — would be identical for the same body
at all speeds, and be similar for similar bodies. As a matter of
fact the elevations and depressions of the surface are the results
of the joint action of gravity and the stream-line accelerations ;
and hence it follows that the surface disturbances in two similar
bodies " will retain their similarity wherever, and in the manner
" which, the operation of gravity permits ; and this will be when
" the similar bodies are moved with velocities proportioned to
" the square roots of their respective dimensions." When the
two similar bodies move at those " corresponding speeds," and the
configurations of the waves are similar, the energy expended on
wave-making will vary with the cube of the dimensions ; because
the mass elevated is as the square of the dimension, and the
elevation is as the square of the speed, that is to say as the
dimension.
The correctness of this reasoning has been verified by very
many observations made on models of similar forms but different
sizes, and by a comparison of the wave-phenomena of models with
those of ships. It has already been remarked that careful
observations of the waves accompanying models are usually made
in association with the res stance experiments ; and in several
cases, notably those of the Greyhoimd, the Shah and the Iris, the
waves raised by the ships themselves were carefully noted and
found to be similar to those raised by the respective models.
Having thus established the similarity for ships and models it
is a great practical advantage to be able to study the wave-
phenomena on the moderate scale in which they occur in model
experiments, instead of having to deal with the large dimensions
incidental to the motion of full-sized ships; 3Ir. Froude fully
realised the possibilities thus opened to him, and one of the
principal aims of his experiments was "to deduce general laws
by which the influence of variation of form upon wave-making
resistance might be predicted." Unfortunately the task so ably
undertaken was left incomplete ; but, from the investigations
already made by Mr. R. E. Froude (see page 458), it may be
hoped that his intentions will yet be realised.
These model experiments have added greatly to our knowledge
of many minor but interesting matters relating to the motions of
ships through still water. For example, the recording apparatus
devised by Mr. Froude enables a record to be kept of the vertical
motions which the centre of gravity of the model performs as the
speed is varied, as well as of the changes in trim. It has thus
47^ NAVAL ARCHITECTURE. chap. xi.
been ascertained that ships moving at ordinary speeds usually
sink bodily below tlieir still-water drauglit, and that at such
speeds the bow usually sinks more than the stern. There will be
DO diiBculty in accounting for these changes of level when the
character of the stream-line motions, and the variations in the
resultant pressures of the water upon the different parts of the
length of a ship are considered (see page 443) ; nor will it be a
matter for surprise that when the cross-sections of the bow of a
ship are V-shaped the subsidence is less than when those sections
are U-shaped. Although the foregoing statement is fairly repre-
sentative for ordinary conditions, it does not apply when ships
are moved at velocities very high relatively to their dimensions.
In torpedo-boats, for example, the ordinary laws hold good only
for the lower speeds. Mr. Thornycroft has made some valu-
able experiments on this matter, and a brief summary of the
results may be of interest.* A boat 67 feet long was driven at
various speeds, the maximum being about 19 knots; observations
were made from which the vertical position of the centre of
gravity, and the trim of the boat could be determined at each
speed. It was found that as the speed increased so the vessel
sank more deeply up to about 12 knots ; after which the boat
rose as the speed increased. At 12 knots the bodily subsidence
was about 5 inches, at 19 knots the bodily rise was 3 inches, these
measurements being taken in relation to the still-water draught.
In this case the boat trimmed by the stern, as compared with her
still-water trim, throughout the trials ; but it must be remembered
that she was driven by her own propeller and not towed.
Experiments with models, made by Mr. Froude, have shown
very similar results as regards mean draught and trim at very
high speeds.-f- For example, a model about 10 feet long was
towed at various speeds, the maximum being about 850 feet per
minute — or 8^ knots per hour. At first the trim altered very
little from the still-water condition, but as the speed increased
the bow gradually rose, while the stern fell. Ultimately at the
maximum speed the bow had risen 2^ inches, while the stern had
sunk to an equal amount with reference to their still-water levels.
This model represented a full-sized ship of 360 feet in length, and
the maximum experimental speed represented a speed of more
than 50 knots for the ship. The vertical displacements of the
* See the British Association Be- the proposals of the Eev. C. Kamus,
ports for 1875. published as Parliamentary Paper
t See the very admirable Report on (No. 313) of 1873.
CHAP. XI. THE RESISTANCE OF SHIPS. 477
bow aud stem of the ship if moved at this enormous speed would
have been about 1\ feet.
In conclusion, it should be mentioned that in the actual pro-
pulsion of a ship the air exercises an appreciable resistance,
especially if she is a rigged ship ; and that the resistance of the
water in a seaway must be different from that of smooth water,
which alone has been considered in this chapter. Respecting
the last-mentioned feature, it will suffice to say that the state of
the sea and the motions of pitching and rolling vary so greatly
at different times that any attempt to express the increase in
resistance by an exact method would be hopeless, even if there
were a complete theory for resistance in smooth water. Experi-
ence, however, confirms the accuracy of an opinion which would
be formed on the most superficial investigation, viz. that great
length, size, and weight in ships give them a greater power of
maintaining their speed in a seaway. The regularity of the
passages made by the large Transatlantic steamers, under very
various conditions of wind and weather, supply the best possible
illustration of this general statement, w'hich has, however, to do
with propulsion rather than with resistance.
As to air resistance, there have been very few trustworthy ex-
periments. Mr. Froude, in his experiments with the Greyhound,
which was not rigged at the time, found that, when the speed
of the wind past the ship was 15 knots per hour, it produced an
effect on the hull measured by a force of 330 lbs. For other
speeds of wind past the ship, it was assumed that the effect
varied as the square of the speed ; and it need hardly be added
that in the case where a ship is steaming head to wind air resist-
ance must be greatest, since the speed of the wind past the ship
then equals the sum of her own speed and that of the wind.
The absolute force of the air resistance in the Greyliound was
thus found to be small ; but if the vessel had been masted and
rigged, the resistance would have been greater. JMr. Froude did
not expressly state, in his report on this experiment, what scale
of allowance he employed in estimating the additional resistance
due to the passage of the masts and rigging through the air ;
but from the particulars which he subsequently furnished to the
Author, it appears that the total resistance of the masts and rig-
ging was taken about equal to that of the hull. At a speed of 10
knots through still air, this would give a total air resistance of
about 300 lbs., the corresponding total of water resistance being
about 10,200 lbs. ; making the air resistance about .}^ part of
478 NAVAL ARCHITECTURE. chap. xi.
the water resistance. If the ship steamed head to wind at a
speed of 8 knots, the actual speed of tlie wind being 7 knots, it
would pass the ship with a relative speed of 15 knots ; the air
resistance would then probably have a total of about 650 lbs.,
whereas (if the water were smooth) the total water resistance
would be about 5300 lbs., the air resistance risiug to about ^ of
the water resistance. These results may not be exactly correct,
but they are sufficiently so for illustrative purposes ; they exphiin
the considerable decrease in speed in ships — especially rigged
ships — steaming head-to-wind ; and they are so considerably in
excess of what would have been predicted on purely theoretical
grounds as to indicate the desirability of further experiments
on the air resistance to rigged ships. Up to the present time,
we have little information of an exact or trustworthy character
on this important subject.
The experiments required are very simple. All that is necessary
is to allow a ship to drift before the wind, to note the uniform
speed which she will ultimately attain through the water, and to
measure the velocity of the wind past the ship; her condition
aloft must also be recorded, as to spars on-end, running rigging
rove, &c. The water should be approximately smooth, and the
ship should owe her drift simply to the air pressure, not to tides
or currents. The resistance of the water at the uniform speed
of driit must then exactly equal the total air resistance ; and this
water resistance could be ascertained by other experiments made
either with the ship or with models. Accuracy would be in-
creased and more valuable information obtained if the same ship
were made the subject of several experiments, including two
sets : one made with the same condition as to spars and rigging
aloft, but with different forces of wind ; the second set made
with different conditions of rig, while the actual speed of the
wind remained constant. This is a matter which will be likely
to commend itself to the attention of naval men when they learn
the imperfect condition of our present knowledge of the subject.
Other modes of making the required experiments might be
suggested did space permit ; but it must suffice to add that, with
the aid of suitable dynamometric apparatus and good anemo-
meters, the air resistance corresponding to a certain speed of wind
might be obtained with the ship moored instead of drifting.
As to the air resistance on the hull only, there appears good
reason for adopting the rule which Mr. Froude has suggested,
viz. that, if the above-water portions of the hull are projected back
upon the midship section of a ship, and the total area (A) in-
CHAP. XI. THE RESISTANCE OF SHIPS. 479
closing these projections is determined, then the air resistance on
that area (A) will approximately equal the air resistance on the
hull for any assumed speed. In the Greylwund the area A was
somewhat less than 400 square feet ; Mr. Froude has ascertained
by experiment that at a speed of 1 foot per second the air resist-
ance per square foot on a plane area is about equal to loVoo ^''^•
A speed of 15 knots per hour equals about 25^ feet per second ;
and since the air resistance varies as the square of tlie speed, the
speed of 15 knots should correspond to a pressure of about 1-09 lb.
per square foot of area. Hence the total air resistance on the
Greijhound for a speed of 15 knots past the ship should be about
436 lbs. by this law ; and by experiment it was determined to be
330 lbs. This approximate rule may be found useful for purposes
of comparison between different types of ships ; and in mastless
ships it will give a fair estimate of the total air resistance at any
assigned speed of wind past the ships. Eigged ships present a more
difficult problem, which can be best dealt with experimentally.
480 NAVAL ARCHITECTURE. chap. xii.
CHAPTER XII.
PROPULSION BY SAILS.
The efficient management of a ship under sail furnishes one of
the most notable instances of skilful seamanship. In different
hands the same ship may perform very differently. Changes in
stowage and trim also affect the perlbrmance ; but such changes
as an officer in command can make are necessarily limited in
their scope and character ; and some ships can never be made
to sail well, having some radical fault in their designs. Without
intruding upon the domain of seamanship, the naval architect
requires, therefore, to study very carefully the conditions of sail-
power, and the distribution of sails in a new design, if the com-
pleted ship is to be fairly successful. His success or failure
greatly depends upon the possession of information respecting
the performances and sail-spread of ships of similar type and rig ;
having such inforuiation, the process by which the total sail-
spread and the distribution of the sail are determined in the new
ship is by no means difficult or complex. Taking the exemplar
ships, and the reports on their sailing qualities, an analysis is
made of the sail areas, the distribution of the sail longitudinally
and vertically, the transverse stability, and some other par-
ticulars. Furnished with these data, and having regard to the
known qualities of the completed ships, it is possible to secure
similar, or perhaps imjjroved, performance in the new design.
Apart from such experience, however, the naval architect would
be unable to be equally certain of obtaining good results ; and
in cases where great strides are taken in a new design, away
from the sizes and proportions or sail plans of existing ships, the
arrangement of the sail-power cannot but be, to a large extent,
experimental. Illustrations of this are to be found ia the earlier
ironclads of the Eoyal Navy, such as the Achilles and Minotaur
classes, in which the sizes, lengths, and proportions of length to
CHAP XII PROPULSION BY SAILS. 48 1
breadth were all much greater than in preceding ships. When
first fitted with four masts, the Achilles did not p rform well
under sail ; but as now arranged with three masts, she stands
high among the ironclads. The Warrior, on the other hand, a
ship of the same class as the Achilles, proved successful under
sail from the first ; having only three masts. In fact, although
the general principles of propulsion by sails were long ago
formulated, and although many emineut mathematicians and
naval officers have endeavoured to assist the naval architect by
constructing general rules for guidance, there is even now no
accepted theory fully representing the conditions of practice. In
this chapter attention will be confined to a few of the fundamental
principles of propulsion by sails, and to the simple rules which
are commonly observed by naval architects in arranging the sails
of a ship.
It will be evident that accurate investigation of the behaviour
of sailing ships must depend greatly upon correct knowledge as
to the laws which govern the pressure of wind on the sails. Most
of the data available are due to the labours of French experi-
mentalists. Colonel Beaufoy made a few experiments on air
resistance, and the late IMr. Froude gave some attention to the
subject, but was prevented from pursuing it by the pressure of
other work.* Of late years, special attention has been drawn to
the laws of wind pressure on railway structures in consequence of
the Tay Bridge disaster, and a mass of information has been
collected.
In the following table a summary is given of the results of
experiments made with thin jjlates, placed normal to the line of
motion of the air relatively to their plane surfaces. If
A = area in square feet of plane surface of plate,
V = the relative velocity of the wind and the plate, in feet, per
second,
R = pressure on plate (or air resistance), in pounds,
then it is found from experiments with small plates that
where A; is a constant coefficient.
* An excellent summary of the periments will be found in vol. xxxi.
French experiments is given in Spon's of the Revue Maritime et Coloniale.
Dictionai^y of Engineering. Beaut'oy's For the details of recent observations
experiments are mentioned in the on wind pressures, see Parliamentary
Papers on Kaval Architecture, vol. i. Paper (C 3000) of 1881.
The details of Lieutenant Paris's ex-
2 I
482
NAVAL ARCHITECTURE.
CHAP. XII.
Of all the experiments on thin plates those of Mr. Froude
were made under the conditions most favourable to exactness,
practically uniform motion having been secured. The experi-
ments of Morin and Didion were made with delicate chronometric
apparatus, and nearly agree with Mr. Fronde's result. The
observations of Lieutenant Paris were carefully conducted, but
having been made on board ship were necessarily subjected to
many disturbing causes, besides which, any accurate determina-
tion of the relative velocity of the wind and the plate could
scarcely be hoped for under the circumstances. On the whole,
therefore, the value of Z; given by Mr. Froude is to be preferred,
and if it is accepted, a pressure of one pound per square foot
corresponds to a relative velocity of about 14|- knots per hour —
24^ feet per second.
Experimentalist.
Date.
Value of ^.
Mode of Experiment,
Borda . . •
Thibault . .
Morin \
1763
1832
(1835
•00184]
•0020G[
•00L9 J
Plates moved through still air on a re-
volving fan-wheel.
and > . .
Didion J
\ to
(1837
•0016
Plate falling vertically.
Kouse . . .
•00229
Hutton, . .
Paris . . .
Froude, , .
1872
1876
•00188
•00239
■0017
Plate exposed to actual wind on board ship.
Plate moved through still air.
It is necessary to add that the experiments above-mentioned
were made on small plates, not exceeding three or four square feet
in area ; and that there is no evidence to show that the same co-
efficients connecting pressure (per unit of area) and velocity, hold
for large plane areas as have been found to hold good for small
areas.
The report of the committee appointed by the Board of Trade
to consider the wind pressure on railway structures gives the
results of a great number of observations made with anemometers,
and proposes a formula for connecting velocity and pressure based
upon these observations. This formula is
P = -01 V^.
Where P = the maximum pressure, in pounds on the square foot,
occurring during the storm to which V refers,
V = the maximum run (in miles) of the wind in any one
hour.
CHAP. XII.
PROPULSION BY SAILS.
483
Tliis formula would give a value P of 1 lb. per square foot, for a
velocity of only teu miles per hour, or 14f feet per second, which
will be seen to differ widely from the results given above for
experiments made on small plates. But it will also be remarked
that the results are not strictly comparable ; because, in the first-
named experiments, the pressure is expressed in terms of a
uniform velocity, whereas in the anemometric observations the
velocity is the " maximum hourly run," and the pressure is the
"maximum pressure" likely to be experienced during the hour.
In other words, the wind has a varying velocity, alternating above
and below the average for the hour, and tiie proposed formula
allows for this variation. If it be assumed that the two sets of
observations are practically correct, then it follows that the
maximum velocity of the wind during an hour's run is likely
to exceed the average velocity by about 65 per cent. All these
anemometric observations were made on comparatively small
pressure plates ; and there is no evidence to show that the
formula recommended for use is strictly applicable to large areas
of varied forms.
Passing from the simplest case of normal impact to that where
the wind impinges obliquely on a plane surface, we find a still
more uncertain state of knowledge. The most elaborate experi-
ments on oblique impact were made by Thibault ; and in
Fig. 122a the results are graphically recorded. Abscissae
A
^^^~^~^^^^'"'------..
-
FIG \ZZa
\^ '■■-if •-..
1.
1 [ 1 r
I 1
. 1 1,1 1 1 1
1 1 r-^
^-^. ■■ 1
50°
SO"
70°
GO"
50°
40°
30°
20° 15° 10°
measurements correspond to values of the angle of incidence of
the wind on a plane ; ordinate measurements indicate the values
of the normal pressures. The curve ABC shows Thibault's
experimental data : the curve ADC shows what the normal
pressure would be if it varied directly as the sine of the angle
of incidence : the curve AEC shows what it w^ould be if it varied
2 I 2
484 NAVAL ARCHITECTURE. chap. xii.
as the square of the sine of that angle. Up to angles of incidence
of 50 to 60 degrees the curves ABC and ADO are very close
to one another : this range corresponds to the case of rolling dis-
cussed on pages 169 and 245. For angles of incidence below 30
degrees such as occur in ships sailing "close-hauled " (see page 486),
the experimental curve is intermediate between the other two.
These experiments of Tiiibault were also made on small planes.
Wlien we pass from plane surfaces to sails, we are in still more
doubt as to the laws of wind pressure. The only experiment we
have been able to trace was made by Tiiibault about half a century
ago. He attached small sails (about I* 2 square foot in area) to
the arms of a fan- wheel, and noted the resistances when the sails
were tightly stretched as planes, and when they bellied out under
the action of the air. His conclusion from these small-scale
experiments was very interesting, although it can scarcely be
regarded as certainly applicable to the enormously greater areas
of the sails in a large ship. It was that the normal pressure on
the curved sail was equal to tliat on a plane sail of equal area ;
the effect of the curvature counterbalancing the reduction of the
area when projected on a plane normal to the wind. But expe-
rience appears to show that the more nearly plane the surface of
a sail can be kept, the greater will be the propelling force derived
from the wind pressure upon it. " All slack canvas," says
Mr. Fincham, "whether sailing by the wind or large, lessens the
" effect of the sail ; and even before the wind, when the slack
"reef is out the power which acts on the sail will be reduced
" very considerably on the curved surface ; less even than the
" base of the same curve, or than if the sail were set taut-up, but
" reduced to the same hoist or distance between the yards as
" when slack." Up to the present time, therefore, accurate
knowledge is almost entirely wanting respecting the laws which
govern wind pressures on large sails. We cannot certainly express
the pressure per unit of area on large sails corresponding to a
given velocity of wind and to a certain angle of incidence ; and
need further experiments on a larger scale, accompanied with
more accurate observations than are now common, respecting the
velocity and pressure (on small planes) of the wind. Such
experiments would be by no means difficult to arrange, and they
could be best conducted on board small sailing vessels, such as
yachts, of which the stability had been ascertained by experiment
and calculation. It would be necessary to place the vessel beam-
on to the wind, to hoist certain sails, and to note the correspond-
ing angles of steady heel. By means of anemometers the velocity
CHAP. XII. PROPULSION BY SAILS.' 485
and pressure (on small areas) could be measured simultaneously ;
and the total pressure per unit of area on the sail set could be
deduced from the righting moment due to the observed angle of
heel. The areas and forms of the sails set could be varied, and
thus much valuable information could be obtained.
Before leaving this subject a brief statement may be added
respecting the ordinary classification of winds. Authorities
agree in assigning a speed of from 60 to 100 knots per hour to a
hurricane (Force 12). Accepting the coefficient deduced from
small thin plates the pressure corresponding to these velocities
would be from 18 to 50 lbs. per square foot. The " storm- wind "
(Force 11) would have a speed of 45 to 50 knots, and a pressure
of from 11 to 13 lbs.; the "heavy gale" (Force 10) would have
a speed of about 40 knots, and a pressure of 8 to 9 lbs. ; the
" strong gale " (Force 9) a speed of about 34 knots, and a pressure
of 6 lbs. ; the " fresh gale " (Force 8) a speed of about 28 knots,
and a pressure of about 4 lbs. ; the " moderate gale " (Force 7) a
speed of about 23 knots, and a j)i'essure of 2f lbs. ; the " strong
breeze " (Force 6) a speed from 15 to 20 knots, with a pressure
from 1 lb. to 2 lbs. ; and the " fresh breeze " (Force 5) the upper
limit of 1 lb. pressure, corresponding to a speed of 14 knots as
above. All these pressures are supposed to act on a plane area
of one square foot placed at right angles to the direction of the
wind.
If the speeds of wind given above are taken to mean " hourly
runs," and the approximate formula of the Board of Trade
Committee is used for estimating maximum pressure, then the
" hurricane " would correspond to maximum pressures of 48 to
130 lbs. per square foot, and all the other pressures just named
would be proportionately increased (about 2f times). From the
report of this Committee it appears that, under exceptional cir-
cumstances, pressures of 80 to 90 lbs. per square foot have been
noted in this country ; but from 50 to 60 lbs. are unusually high
pressures, and the Committee recommended that 56 lbs, per
square foot should be taken as a maximum wind pressure in
calculations for railway bridges and viaducts.
Sails attached to ships are not fixed in position like the planes
and sails considered above, but necessarily move with the ship.
Hence, in dealing with the propulsive effect of a wind of which
the absolute direction and force are known, it is necessary to
take account also of the motion of the ship ; or, as it is usually
expressed, it is necessary to determine the apiMvent direction
and velocity of the wind. This cau be done easily in any case
486 NAVAL ARCHITECTURE. chap. xii.
for which the course and speed of the ship, as well as the true
direction and velocity of the wind, are known ; the simple
general principle being that the apparent motion of the wind is
the resultant of the actual motion of the wind, and a motion
equal and opposite to that of the ship. A vane at the mast-head
would indicate the apparent direction of the wind, and not its
true direction ; an anemometer on board would measure the
apparent velocity of the wind.
Take the simplest case : a vessel with a single square sail
running " dead before " the wind. If the speed of the wind is
V feet per second, and that of the ship v, as the direction of both
motions is identical, the resultant of the actual speed of the wind
and the reversed motion of the wind will be V — v feet; and this
apparent motion will govern the propulsive effect. For example,
let the speed of the wind be 15 feet per second ; that of the ship
5 feet per second ; the apparent speed of the wind will be 10 feet
(15 — 5); and, accepting the coefficient given above for normal
impact on small planes, the pressure per square foot of area of
sail will be given by the equation : —
The pressure of this wind on ajixed sail would be about 2^ times
as great. From this simple illustration it will be seen that it is
most important to determine accurately the apparent motion of
the wind.
As a second illustration, take the case of a vessel sailing on a
wind close-hauled, with the wind hefore the beam. To simplify
matters, let a single square sail be considered set on the yard
marked XY in Fig. 123.
^ AB represents the middle
FIG. 123 iiT line of the ship, the out-
/ w line of the " plan " being
c ^ ^ 7^"*^^^ indicated. The line WWx
Z?f '^dn— J^^ represents the actual
^ .^1^7 ~^ direction of the wind ; let
^ y/ MWi represent (on a cer-
/' / tain scale of feet) its vel-
^ "Wj ocity. The line CC shows
the course of the ship ;
and on WiD (which is drawn parallel to CC) a length WiD is
set off to represent a motion equal and opposite to that
of the ship, the same scale being used for WjD as was
CHAP. XII.
PROPULSION BY SAILS.
487
employed for the length MWi. Join MD ; then MD represents
in maguitucle and direction the apparent velocity of the wind.
MD is greater tlian the actual velocity MWi; but its direction
makes a more acute angle with the sail on XY than does the
actual direction WW^.
The case of a ship sailing with the wind abaft the beam is
illustrated in Fig. 12-1; the reference letters being similar to those
in Fig. 123, no description is needed. Here the resultant MD is
less than the actual velocity MWj ; but, as in the previous case,
it makes a more acute angle with the sail on XY.
"With these two examples before him, the reader will have no
difficulty in readily de-
termining the apparent
velocity and direction of
the wind, corresponding
to observed actual speeds
and directions of the wind,
and observed speeds of a
ship on a certain course.
But this is by no means
a complete solution of the
question which presents
itself in practice, and
takes the form : — Given a
c -
v.,
D
X
M'/
FIG. 125
certain actual direction and speed of wind, and the sail area
and angle of bracing for the yards, what will be the course
of the ship, and her speed of advance ? To answer the question
fully and correctly requires data beyond those at present
possessed ; but an approximate solution is possible.
Keverting to the case of a ship sailing on a wind (Fig. 123),
suppose the apparent direction and speed of the wind to have
been determined ; and fur-
ther suppose the normal
pressure on the sail corre-
sponding to this apparent
wind to be known. In
Fig. 125, let EM repre-
sent iu magnitude the
pressure which the ap-
parent wind would have upon the sail if placed normally to it,
the line EM corresponding to MD produced in Fig. 123. The
pressure acting along EM may be regarded as the resultant of
two components: one (EF) acting parallel to the sail XY, and
488 NAVAL ARCHITECTURE. chap, xii,
not sensibly affecting it; the second (FM) acting normally to
tlie sail. This normal pressure, again, may be regarded as made
lip of three pressures : one of tliese (shown by GM) acts longitudi-
nally ; the other (FG) acts athwartships, and the third acts verti-
cally, at right angles to the other two, which act horizontally. For
moderate angles of steady heel under sail, such as are common
in ships, the vertical component of the normal pressure is not of
much importance, and it is usually neglected. In all cases, how-
ever, it tends to increase the immersion of a ship ; and in some
cases, when the angle of heel is considerable, this effect may be
noteworthy. Let it be assumed for the present that only the
horizontal components FG and GM require to be considered.
When the motion of the vessel has become uniform under the
action of a wind of constant force and unchanging direction, it
will take place along some line, such as CO, lying obliquely to
her middle line AB. This motion may be resolved into two
parts : one, a direct advance, in the line AB, the other a drift to
leeward perpendicularly to AB. The angle made by the line CO
with the keel-line AB, is called the " angle of leeway." Its
magnitude depends upon the ratio of the velocity of advance, or
headway, along AB to the velocity of drift or leeway, and these
velocities are governed by varying conditions.
If a ship were running before the wind there would be no lee-
way, and her motion would closely resemble that described in the
previous chapter, the effective wind pressure taking the place of
the tow-rope, but being applied at a considerable height. Hence,
Avhen the motion has become uniform, the wind pressure will be
opposed by an equal and opposite fluid resistance, and these forces
will form a mechanical couple tending to change the trim, as was
previously explained. The actual change of trim would, however,
be small in most cases. For instance, in the Greylwund running
dead before the wind at a speed of 6 knots, the resistance would
be about 1^ tons, the moment of the couple less than 100 foot-
tons, and the change of trim less than one inch.
As a second extreme case, suppose a ship to have her sails
braced fore-and-aft, with wind abeam, and to drift bodily to
leeward, moving parallel to her original position, and making no
headway. When uniform speed of drift had been obtained, a
lateral resistance would be developed equal and opposite to
the effective wind pressure, and forming with it a mechanical
couple causing the ship to heel. This lateral resistance, for
a given speed of drift, is obviously much greater than the re-
sistance to headway at the same speed. The ratio of the two
CHAP. XII. PROPULSION BY SAILS. 489
resistances may vary greatly in different classes of ships ; on ac-
count of differences in form or draught, or in tlie areas of keels,
deadwoods, and other approximately flat surfaces immersed. Such
surfaces experience a lateral resistance resembling that offered to
plane surfaces moving parallel to themselves, and are, therefore,
very effective in checking leeway. The curved and approxi-
mately cylindrical portions of the bottom of a ship permit the
particles of water to glide past them with less abrupt changes of
motion, and therefore contribute less to the lateral resistance.
Exact measures of that resistance have not been determined,
similar to the measures for head-resistance described in the pre-
ceding chapter. Speaking generally, it is necessary for efficiency
under sail, and weatherliness, that there should be considerable
lateral resistance ; and in some classes of ships various devices
are employed in order to increase the lateral resistance, and to
diminish leeway. In shallow-draught or flat-bottomed vessels,
" lee-boards " are often fitted ; these boards can be dropped at the
sides of the vessels, and made to project beyond the bottom.
Sliding keels, or " centre-boards," are sometimes fitted so as to be
housed in recesses formed within the vessels, or to be lowered
below the bottom. Very deep keels and great rise of floor are also
commonly adopted in yachts designed for racing, for the same
purpose,
A rough approximation is sometimes used for comparing the
lateral resistances of ships of similar form ; by assuming that
those resistances are proportional to the resistances which would
be experienced by the immersed parts of their longitudinal
middle-line planes, if they were moved to leeward at certain
speeds. It need hardly be stated that this method of procedure
can only be applied within the limits named : because two ships
having the same area of middle-line plane might differ greatly in
fineness of form, areas of keel, &c., and so have very different
lateral resistances. A more trustworthy method of estimation
consists in finding the aggregate areas of the keels, deadwoods
and other approximately flat surfaces, and calculating their re-
sistances by Beaufoy's formula, given on page 436 ; while the
remaining portions of the wetted surface would have their
resistances estimated according to the formula for frictional re-
sistance on page 438. But even this mode of estimating lateral
resistance cau be treated only as fairly approximate, not as
exact.
The conditions of actual practice in sailing ships lie between
the two hypothetical cases, above described, of no leeway and no
490 NAVAL ARCHITECTURE. chap. xii.
headway. A "sailing sliip proceeding at uniform speed under
certain conditions of wind and sail-spread, usually follows a course
making an angle of leeway with her keel-line, and in doing so
both heels and changes trim. From what has been said above
it will be seen that a jyriori estimates of the angle of leeway for
a given ship and a certain set of conditions cannot be made with
certainty. Experience shows that in successful ships the angle
of leeway is seldom much more than 6 degrees and rarely exceeds
12 degrees; in less successful ships, or shallow-draught vessels
with no drop-keels, the angle of leeway may be much greater.
The tangent of the angle of leeway (AMC, in Fig. 125) equals
the ratio of the speed of drift to the speed ahead. These speeds
depend upon various conditions, some of which have been men-
tioned. It will be evident for example, that variations in the
angle (A^IX) to which the yards are braced will affect both
the absolute and the relative values of the transverse and longi-
tudinal components of t!ie wind pressure. If the normal pressure
(FM) were known, we should have —
Transverse pressure ^ ^G ^^^ ^^^^
Longitudinal pressure LtM
Suppose AMX = 30 degrees: then
Transverse pressure = longitudinal pressure \'3.
The speeds ahead and to leeward clearly do not depend simply
upon this ratio of the longitudinal to the transverse wind
pressures ; they are governed far more by the relative resist-
ances of the water to the motion of the ship ahead and to
leeward. Even if the two pressures were exactly equal, the
resistance to leeway would be much greater than the resistance
to headway, and the speed of advance would much exceed the
speed of drift. Moreover it must be noted that the magnitude
and direction of the fluid resistance are affected by the action
of the wind upon the sails. Heeling destroys that symmetry
of form in the immersed part of the ship which exists when she
is uprij^ht ; and thus the character of the stream-line motions is
changed from that considered in the preceding chapter. Change
of trim may also affect the resistance somewhat, but probably not
to so serious an extent as heeling. Leeway, again, causes the
vessel to move obliquely through the water, instead of along her
line of keel ; and this oblique motion not merely involves
additional resistance, but leads to an unequal distribution of
the d\namical pressures on the leeward side. The most intense
pressures are experienced on the lee bow, and this effect is
CHAP. XII. PROPULSION BY SAILS. 49 1
enhanced by the heeling; so that the tendency is to make the
bow " fly up into the wind." From this brief statement it will
appear, therefore, that any exact determination of the speed and
course as well as magnitude and direction of the fluid res'stance
experienced by a sailing ship is scarcely to be hoped for ; even
when the force and direction of the wind, the spread of sail and
bracing of the yards, are assumed to be given. But it will also
be obvious that in every case when uniform motion has been
attained on a certain course the lono-itudinal and transverse
components of the fluid resistance will balance respectively the
corresponding components of the effective wind pressure.
Confining attention for the moment to the longitudinal compo-
nents, it will be evident that if the component of the effective wind
pressure exceeds the corresponding component of the resistance,
the velocity of headway will be accelerated. Reverting to Figs.
123 and 125 it will be seen that the increase in speed must affect
both the direction and velocity of the apparent wind, and so
influence the value of the longitudinal component of the effective
wind pressure. But so long as GjM, Fig. 125, exceeds the longi-
tudinal component of the resistance so long will the speed be
increased. If the resistance is small even at very high speeds,
then it is theoretically possible for a vessel sailing on a wind to
attain a speed exceeding that of the wind. In ice boats this
condition is realised. There is practically no leeway, and the
frictional resistance of the sledge or " runner " on which the
boats run is exceedingly small even at high speed. With the
wind varying from a point before the beam to an equal amount
abaft the beam speeds are said to have been reached about equal
to twice the real velocity of the wind.
When a ship, sailing at a uniform speed, under the action of a
wind of which the force and direction are constant, maintains an
unchanged course without the use of the rudder, it is clear that
the resultant pressure of the wind on the sails and the resultant
resistance of the water cannot form a couple tending to turn the
vessel. Under these circumstances, therefore, these equal and
opposite forces must act in the same vertical plane. If it were
possible to determine the line of action of the resultant resistance
for any assumed speed, on a certain course in relation to the
direction of the wind, then it would follow that the sails should
be so trimmed as to bring the line of action of the resultant wind
pressure into the same vertical plane with the resultant resistance,
if the course is to be maintained without the use of the rudder.
The less the rudder is used in maintaining the course, the less
492 NAVAL ARCHITECTURE. chap. xii.
will the speed of the ship be checked thereby. In practice, how-
ever, the theoretical conditions cannot be fulfilled, because the
line of action of the resultant resistance cannot be determined in
the present state of our knowledge, even under given conditions
of speed and course ; because that line of action changes its
position with changes in the speed, the angle of leeway, and the
transverse inclination of the ship, not to mention the changes
consequent on the alterations in the force and direction of the
wind ; and because it is not possible to determine accurately the
line of action of the resultant wind pressure on the sails, when set
in any given position. The problem which thus baffles theory is,
however, solved more or less completely in practice ; the skilful
seaman varies the spread and adjustment of his sails in order to
meet the chans'es in the line of action of the resistance. In a
well-designed vessel, the distribution of the sail is such that the
commanding officer has sufficient control over her movements under
all circumstances. Some vessels, however, are not so well arranged
for sailing purposes, and in them " ardency " or " slackness "
when sailing on a wind may be practically incurable.
" Ardency " is the term applied when a vessel tends to bring
her head up to the wind, and she can only be kept on her course
by keeping the helm a-weather ; the resultant resistance must
then act before the resultant wind pressure. The contrary condi-
tion, where the resultant resistance acts abaft the resultant wind
pressure, and makes the head of the ship fall off from the wind,
is termed "slackness," and can only be counteracted by keeping
the helm a-lee. Of the two faults, slackness appears the more
serious ; for a vessel thus affected seldom proves weatherly. To
avoid excess in either direction, the naval architect distributes
the sails of a new ship, in the longitudinal sense, by comparison
with the arrangements in tried and successful vessels, conforming
to some simple rules whicli will be stated hereafter.
From the foregoing explanations it will appear that the greatest
care must be taken in determining the angle to which the yards
shall be braced, or the sails set, in order to secure the greatest
speed when sailing on a wind. This is pre-eminently a question
of seamanship ; but it has engaged the attention of many eminent
mathematicians, whose investigations still remain on record. All
tliese investigations were based upon certain assumptions, as to
the effective pressure of a wind acting obliquely upon the sails,
the apparent direction and velocity of that wind being known.
In Fig. 125, for example, if EM represents in direction and
magnitude the " pressure due to the apparent velocity " of the
CHAP. XII. PROPULSION BY SAILS. 493
wind — that is, the pressure it would deliver upon a plane area,
say, of one square foot placed at right angles to EM — the effective
pressure (FM) would, according to the law formerly received,
have been expressed by EM sin^ EMX. It has been shown that
this law cannot be accepted ; and therefore the elaborate deduc-
tions which have been made from investigations based upon it
have now little interest. Even if the true law were determined,
mathematical inquiries could never be trusted to replace the
judgment of the sailor in determining the most efficient angle
for bracing the yards or trimming the sails. So many varying
circumstances have to be encountered in the navigation of a
sailing vessel that theory can never be expected to take complete
cognisance of them all. The decision as to the best mode of
handling a sailing ship must always rest, where it has always
rested, in the hands of her commander. One thing, however, is
obvious from the preceding remarks, viz., that it is a very great
advantage to a ship in sailing close-hauled to be able to brace
her yards up very sharply, in order to secure the most advan-
tageous angle of incidence (EMX, Fig. 125) of the wind upon
the sails, and thereby render the propelling force as great as
possible under the circumstances. In this respect, square-rigged
vessels compare unfavourably with fore-and-aft-rigged vessels,
the shrouds, stays, &c., imposing serious limitations upon the
bracing of the yards. After bringing together and digesting a
great mass of facts respecting sailing ships, Mr. Fincham summed
up this matter as follows : — " When close-hauled, experience has
" shown that the yards in square-rigged vessels can seldom be
" braced sufficiently sharp to obtain the most advantageous
" position for plying to windward." He also gave from 13 to 17
degrees with the keel as the angles which the " feet " of the sails
of a fore-and-aft-rigged vessel seldom exceed on a wind, such
angles being less than can be reached in all, or nearly all, square-
rigged vessels. In yachts the corresponding angles are said to
seldom exceed 10 degrees. It must be observed, however, that in
all fore-and-aft-rigged vessels there is a sensible difference in
the angle at the head and foot of a sail. For all the sails except
those set on a stay, such as foresail or jib, the angle at the foot is
less thciu that at the head : for sails set on a stay the converse
may hold good.
Passing from these general considerations respecting pro-
pulsion by sails to the practical problems which the naval
architect has to solve in determining the sail-spread appropriate
494 NAVAL ARCHITECTURE. chap. xii.
to any new desigu, it becomes necessary to note an important
distinction. In all his calculations the naval architect is
accustomed to deal only with plain sail or ivorMyig sail, and not
to include all the sails with which a ship may be furnished.
Plaia sail may be defined as that which would be commonly set
in a fresh breeze (Force 5 to 6), which is usually assumed to
correspond to a pressure of about 1 lb. per square foot of canvas.
The following tabular statement shows concisely what sails
would generally be included in the plain sail of various classes
of shii3s ; and although the sails not included are of value,
especially in light winds, yet it will be obvious that those named
in the table are very much more important.
Style of Rig.
Ship
Barque .
Brig . .
Schooner
Cutter .
Plain Sail.
Jib, fore and main courses, driver, three topsails, and
three top-gallant sails.
As ship, except gaff-topsail on mizen-mast.
As ship, exclusive of mizen-mast.
Jib, ibre stay-sail, fore-sail, and main-sail.
Jib, foresail, and main-sail.
Notes to Table.
In brigs, one half the main course and the driver are sometimes taken instead
of the whole of the main course.
In schooners, the fore-topsail is sometimes included.
In yawls, besides the sails named for cutters, the gaff-sail on the mizen is
included.
It will be understood in what follows that, except in any cases
specially mentioned, we are dealing only with plain sail, and not
with total sail area.
In arranging the plan of sails for a new ship, the naval
architect has to consider three things : (1) the determination of
the total sail-spread ; (2) the proper distribution of this sail in
the longitudinal sense, including the adjustment of the stations
for the masts ; (3) the proper distribution of the sail in the
vertical sense, in order that the vessel may have sufficient stiff-
ness. On each of these points we now propose to make a few
remarks, taking them in the order they have been named.
First : as to the determination of the total area of plain sail in
new design.
Other things being equal, the propelling effect of the sails of a
ship depends upon their aggregate area. Wind pressure and the
management of ships are necessarily varying quantities. Hence
CHAP. XII. PROPULSION BY SAILS. 495
for equal speeds the area of plain sail iu two ships should be
made proportioual to their respective resistances at those speeds.
For speeds such as are ordinarily attained uader sail it appears
not unreasonable to assume that frictional resistance furnislies by-
far the larger portion of the total resistance ; and when the
bottoms of two ships are equally rough — having the same co-
efficient of friction — the frictional resistances will be proportional
to the immersed or " wetted " surfaces of the bottoms. Farther,
if the two ships are similar in form, but of different dimensions,
the wetted surfaces will be proportional to the two-thirds power
of their displacements ; for these surfaces will be proportional to
the squares of any leading dimension — say the length — while the
displacements will be proportional to the cubes of the same
dimensions. Put in algebraical language, if Wi be the dis-
placement of one ship, S^ the wetted surface, and Aj the area of
plain sail; while Wo, So, and A2 are the corresponding quantities
for another similarly formed ship : then for equal speeds under
sail we must have,
S,_A,_/WAf
Suppose, for example that, Wi = 8 W2 ; then
Although the attainment of a given speed under certain
conditions does not form part of the design of a sailing ship, as it
does in a steamship, yet it may be interesting to notice iu
passing a roughly approximate method for determining the sail-
spread of a new ship when it is desired to give her greater speed
than that of the typical ship or ships used as examples. Let it
be assumed, as may be fairly done, that the resistance of these
ships varies as the square of the speeds, within the limits of
speed considered. Further let it be assumed that the effective
pressure (per square foot) of the wind on the sails is the same for
both ships.* Then, if Vi and V2 be the maximum speeds, and
the other notation remains as before, we have,
* This latter assumption is not of the wind. The character of the
strictly correct ; since the difference correction required will be understood
in speed must produce some difference from the remarks previously made
in the apparent direction and velocity (page 486).
496 NAVAL ARCHITECTURE. chap. xii.
where yfc is a constant, and the same for both ships. Hence
t<Tj<
is an equation from which the new sail-spread (A2) may be deter-
mined approximately ; but for the reasons given above it has
little practical value.
Keeping to tlie ordinary assumption that equality of speed is
aimed at in the new and old sailing ships compared, it would no
doubt be preferable when arranging the sail-spread of a new ship
differing considerably in form from the exemplar ship to de-
termine the resistances by model experiments, and then to
proportion the sail-areas to those resistances. But this has
never yet been done, and it is never likely to be done with a
view to influencing practice, seeing that steam propulsion is gain-
ing so much on propulsion by sails. On the whole, the equation
on the previous page, although obtained under the limitations
stated, is found a sufficient guide in most cases, when comparing
Ihe sail-power of ships not similar in form, provided the dis-
similarity is not very great. For some years past it has been
usual in the Koyal Navy to compare the " driving powers " of
the sails in different ships by the ratio —
Sail-spread : (Displacement) 3.
But it is fully recognized that if there is considerable difierence
in form, it would be preferable to use the ratio —
Sail- spread : Wetted Surface.
It may happen that when the equation on page 495 is used to
determine the sail-spread for a new ship, it gives results which
are inadmissible. For example, a ship may not have sufficient
stability to carry the sail-area which the formula would assign to
her: or it may be impossible to find room for the efficient
working of the theoretical sail-spread. This statement is tanta-
mount to another, which is fully borne out by experience,
viz. that in ships of different types and sizes, different " driving
powers " of sail have to be accepted, and the hypothetical con-
dition of equal speeds is abandoned.
Formerly it was the practice to proportion the area of plain
CHAP. XII. PROPULSION BY SAILS. 497
sail to the area of the ivater-line section of ships ; and this would
agree with the foregoing rule so long as the condition of
similarity of form was strictly fulfilled. But, when the vessels
compared are somewhat dissimilar in form and proportions, it
becomes preferable to express the sail-area as a multiple of
(displacement) ^ rather than as a multiple of the area of the
water-line section. Very similar remarks apply to another
method once commonly used, in which the area of plain sail was
proportioned to the area of the immersed midship section ; a plan
which was applicable only wheu the vessels compared were
similarly formed. Still another method of stating the sail-spread
is to express it as a multiple of the displacement (in tons). A
ship of 3500 tons displacement with 24,500 square feet of plain
sail would be described as having 7 square feet of cativas
per ton of displacement. It will be obvious from the explana-
tions given above that, if anything like a constant ratio of
sail-area to displacement is maintained, the large ships would
have been much superior to the smaller in di'iving power and
speed. Hence it was the practice, in former times, to increase
the ratio greatly as ships diminished in size ; so that the smaller
classes might be as fast as, or faster than, the larger. This
practice still holds good, in yachts and vessels designed to
perform well under sail ; as size is diminished the sail-spread is
made proportionately greater, and the consequent risks are
accepted, because it is recognised that the smallness of individual
sails make them easily handled.
A full statement of the sail-spread considered desirable in
different classes of ships would occupy space far exceeding
the limits at our disposal.* The treatise on Masting Ships
published some i. years ago by Mr. Fincham contains detailed
information on the subject that can still be studied with
advantage, embracing, as it does, not merely the particulars
of sailing ships of all classes, but also those of the classes
of unarmoured steamships of the Royal Navy designed before
the ironclad reconstruction began. In this work the area
* For the facts as to mercliant ships on Masting" made by Lloyd's sur-
given hereafter, the Author has chiefly veyors, he has also obtained valuable
to thank Mr. John Ferguson (of data. For the facts as to yachts, he
Messrs. Barclay, Curie & Co.) and is almost entirely indebted to the
Mr. Bernard Waymouth (Secretary of works of Mr. Dixon Kemp.
Lloyd's Eegister). From the " lleport
2 K
498 NAVAL ARCHITECTURE. chap. xil.
of plain Sciil is expressed as a multiple of the area of the
water-line section, and the following figures may be interest-
ing. For ship-rigged vessels the area of plain sail is said
to have been from 3 to 4 times the water-line area ; for brigs
and schooners from o^ to 3f times, and for cutters from 3
to 3J times. These ratios were for sailing vessels ; in their
unarmoured successors, possessing both steam and sail power,
the ratio is not so high, and in a great many ship-rigged
vessels falls to 2 or 3. In yachts of the present day the
ratio varies from 3^ to 5^, 4^ being a common value in vessels
having a great reputation for speed. In the armoured ships
of the Royal Navy the corresponding ratio is in some cases
a little above and in others a little below 2. In sailing ships
of the mercantile marine the corresponding ratio has been
found to vary from 2\ to 3 in a large number of examples,
2^ being a good average; but this mode of measuring the
sail-spread is not commonly employed by private shipbuilders.
Taking the ratio of sail-spread to area of immersed midsliip
section, it appears that in the obsolete classes of sailing war-
ships this ratio varies from 25 to 30 in line-of-battle ships,
up to 30 to 45 in frigates, and 40 to 50 in brigs and small
craft. This is the mode of measurement still commonly used
in the French navy, and M. Benin thus summarises their
practice. In the obsolete sailing line-of-battle ships the ratio
was from 30 to 35, in frigates 35 to 40, for smaller classes
sometimes as high as 50. In the unarmoured ships, with
steam and sail, the French practice has given ratios of sail-
spread to midship section, varying from 28 in line-of-battle
ships to 40 in frigates and cruisers. lu the French iron-
clads the ratio has not exceeded 20. For English ironclads,
equipped for sailing, the ratio varies from 18 to 25 ; for un-
armoured frigates of the older classes it is about 32, and
for the swift cruisers 26. For corvettes and sloops the corre-
sponding ratios are 23 to 33. For sailing ships of the mercan-
tile marine the ratio vaiies from 22 to 35 in a great number of
ships examined, about 28 being a good average value. For
racing yachts the ratio varies greatly — from 50 to 70 in English
yachts, and exceeding 80 in American yachts of the broad
shallow type.
The ratio of sail-spread to displacement is not commonly
used for war-ships or yachts, but is frequently employed for
merchant ships. It is unnecessary to repeat the remarks
made above as to the limitations within which this mode of
CHAP. XII. PROPULSION BY SAILS. 499
measurement can be usefully employed. In a considerable
number of sailing merchantmen of modern design this ratio
has been found to vary from 4^ to 8, the largest ratio occurring
in the ships of least displacement. For ships below 2000
tons displacement ,6^ is a good average value ; for larger
ships up to 4000 tons displacement 5J to 6 is a fair value.
Simply as a matter of comparison it may be stated that in
the obsolete classes of sailing men-of-war the ratio of sail-
spread to displacement varied from about 6 in the largest
classes (4000 to 5000 tons displacement) up to 12 or 15 in
frigates (of 1200 to 2000 tons displacement), and 20 to 30
in the brigs and small craft. For racing yachts the corre-
sponding ratio varies from 30 in a yacht of 300 tons displacement
up to 60 in one of 30 tons. For the unarmoured ships of
the Koyal Navy, having steam as well as sail power, the
ratio is about 5 to 7 for frigates, 5 to 6 for corvettes, and
9 to 12 for sloops. For the unarmoured ships it commonly
varies between 3 and 4, rising to 6 in a few of the smallest
vessels.
Another mode of comparing sail-spreads occasionally used in
the mercantile marine is to express the ratio of the sail-spread to
the under-deck tonnage. For ships of similar class (as explained
in Chapter II.) this tonnage bears a fairly constant ratio to the dis-
placement at the deep load-line. Hence the practice now being
described is open to the same objections as were urged against
the preceding method. From 12 to 16 are common ranges in the
ratio of sail-spread to under-deck tonnage, and 13 is a good
average in ships of moderate size.
Comparing these various classes by the ratio which the sail-
spread bears to the two-thirds power of the displacement, the
following results may be interesting. The numbers represent,
for some typical ships of war, the quotient : —
Sail-spread -r- (displacement) ^.
Sailing : —
Line-of-battle ships . . 100 to 120
Frigates ....
Corvettes . . . \ 120 to 160
Brigs ....
Steam : —
Ironclad ships . . . . 60 to 80
Unaruioured :
Frigates .... "1
Corvettes . . . . i 80 to 120
Sloops .... J
It will be remarked that the proportionate sail-power of the
steam unarmoured frigates, &c., is, on the whole, less than that of
the sailing vessels, and that the armoured ships stand still lower
in the scale. But it must be noticed that some of the steamships
2 K 2
500 NAVAL ARCHITECTURE. chap. xii.
have finer forms and proportions than the sailing ships, so that
their resistances may be proportionately less. Further, it is
important to note that the great increase in displacement which
has accompanied the construction of ironclads renders it
practically impossible to give to these heavy vessels a spread of
sail comparable in propelling effect to that of the sailing line-of-
battle ships, even if other and more important qualities were
sacrificed. Take, for example, the 80-gun sailing line-of-battle
ship Vanguard, with a displacement of 3760 tons and sail-spread
of 28,100 square feet. Here the quotient sail-spread -f (dis-
2
placement) ^ is not much below 120 ; in the best of the completed
ironclads built for distant services — the Invincible class — the
corresponding quotient is about 75, and in most of the heavier
ironclads it is still less. If the Hercules, of over 8800 tons dis-
placement, were furnished with a sail-power proportioned to that
of the 80-gun ship, her total area of plain sail would have to be
made nearly 50,000 square feet, the actual area being less than
29,000 square feet. After careful investigation, Mr. Barnaby
reported as follows : — " It is impossible to obtain so much sail by
any multiplication of the number of masts without making them
much loftier, unless they were placed so close together as to allow
the yards, when braced round, to overlap each other considerably.
In this latter case the canvas could scarcely be considered as
efficient as in the old ships, and this would involve a further
increase upon the area given above." * Without attempting any
discussion of the actual sailing qualities of the ironclad fleet, we
may therefore conclude that the great size of nearly all the rigged
ships renders it unreasonable to expect that they could be made
as efficient under sail as were the vessels which depended on sail
alone for propulsion. Nor does the progress of the ironclad
reconstruction at home and abroad tend in this direction ; on the
contrary, lighter rigs and less sail-power have been given to the
most recent masted types, and some of the most powerful vessels
have had no sail-power.
2
In the mercantile marine the ratio sail-spread to (displacement) ^
is seldom used. An examination of a great number of cases
shows this ratio to range from 70 to 110 in vessels of various
sizes and types by different builders. Probably 80 to 85 may
* See page 342 of the Appendix to the Eeport of the Committee on Designs
for Ships of War.
CHAP. XII. PROPULSION BY SAILS. 50T
be taken as a fair averai^e for ships of moderate size; but
the facts stated show that there is 110 approach to uniformity of
practice.
For racing yachts the ratio of sail-spread to the two-thirds
power of the displacement has been found to vary from 180 to
200 ; yachts not designed for racing have ratios from 130 to 180.
In the American yacht Sapplio, of small displacement and great
beam, with an enormous sail-spread, the ratio reaches 275. This
extreme case leads us naturally to a repetition of the remarks
made on page 496 as to the limitations to the use of the ratio as a
measure of the driving power. Tlie form of the Sapplio is very
unlike that of the English yachts ; hence, instead of using the
ordinary formula, it is preferable to actually measure the wetted
surfaces and to compare the sail-spreads therewith. If this is
done the ratio of sail-spread is found to be about 2.7 for the
Sapplio, nearly the same in several English yachts of large size,
and about 2 in other yachts. What is shown to be the fairest
comparison here would also be so as between many of the other
classes mentioned above, and for exact comparisons between
those classes wetted surface should be used.
Secondly : it is important to secure a proper longiiudinal dis-
. trihution of the sails, in order that neither excessive ardency nor
excessive slackness may result, and that sufficient handiness or
manoeuvring power under sail may be secured. It has already
been shown that the difficulties attending any attempt at a
general solution of this problem are insuperable ; and we are now
concerned only with the methods adopted in practice.
The line of action of the resultant wind pressure changes its
position greatly under different conditions : the naval architect
therefore starts with certain assumed conditions which are seldom
or never realised in service, in order to determine the " centre of
effort" of the wind on the sails. All the plain sails are supposed
to be braced round into the fore-and-aft position, or plane of the
masts, and to be perfectly flat-surfaced. The wind is then
assumed to blow perpendicularly to the sails, or broadside-on to
the ship, and its resultant pressure is supposed to act perpendicu-
larly to the sails, through the common centre of gravity of their
areas. This common centre of gravity is determined by its ver-
tical and longitudinal distance from some lines of reference, those
usually chosen being the load water-line, and a line drawn per-
pendicular to it through the middle point of the length of the
load-line, measured from the front of the stem to the back of the
502
NAVAL ARCHITECTURE.
CHAI'. XTI.
sternpost. Fig. 126 shows a full-rii^ged vessel with her sails
placed as described ; the centre of gravity of the area of plain
sail or " centre of effort " being marked C. A specimen calcula-
tion, illustrating the simple process by which the point C is
determined, is appended.
Calculation for the Centre of Effort of the Sails of a Ship.
Sails.
Areas
Distances of Centres
of Gr.ivity from
Middle of Load-line.
Longitudinal
Moment of Sails.
Heights
of Centres
of Gravity
above
Load-line.
Vertical
IMoments
of Sails.
Before.
Abaft.
Before.
Abaft.
Sq. ft.
Feet.
Feet.
.Tib
1000
145
, ,
145,000
, ,
48
48,000
Fore course . . .
2300
85
, ,
195,500
, ,
36
82,800
„ topsail .
2500
83
, ,
207,500
, ,
74
185,000
,, top-gallant sail .
1100
82
, ,
90,200
108
118,800
Main course . , .
3000
20
60,000
35
105,000
,, topsail . . .
2500
23
57,500
76
190,1 00
,, top-gallant sail
1100
25
27,500
110
121,000
Driver
1600
120
, ,
192,000
40
64,0 '0
Jlizen topsail . . .
1300
100
, ,
130,000
66
85,800
,, top-gallant sail
Total area of plain sail
600
17,000
103
••
61,800
92
17,000
-e of effort
3 load-line
55,200
638,200
528,800
) 1,055,600
17,000
528,800
Centi
abov
■ 62-1 feet.
) 109,400
Centre of effort before
middle
of load-line . . .
6-43 feet.
Centre of lateral resis
Centre of effort before
tance a
centre
baft ditto . . . .
of lateral resistance .
6-0 „
12-43 feet
When the centre of efibrt of the sail-area has been determined
relatively to the middle of the load-line, it is usual also to deter-
mine the longitudinal position of another point, commonly styled
the " centre of lateral resistance." This is marked L in Ficf.
126, and is simply the centre of gravity of the immersed portion
of the plane of the masts — the same plane area which was referred
to in an earlier part of the chapter as considerably influencing
the leeway of a ship sailing on a wind. It will, of course, be
understood that the point L is no more supposed to determine the
true line of action of the resultant resistance than the point C
is supposed to determine the line of action of the resultant wind
pressure. But, on the other hand, experience proves that the
longitudinal distance between the centre of effort C and the
centre of lateral resistance L should lie within the limits of
certain fractional parts of the length of the load-line.
From the drawings of a ship the position of the centre of
lateral resistance may be determined by a very simple calcula-
tion ; and the particulars required for an approximate calculation
are easily obtainable from a ship herself, being the length at the
CHAP. XII.
PROPULSION BY SAILS.
503
load-line, draught of water forward and aft, area of rudder, and
area of aperture in stern for screw, if the vessel be so con-
structed.
The distance of the centre of effort before the centre of lateral
resistance varies according to the style of rig ; and in determin-
ing it, regard must be had also to the under-water form of a ship.
A full-bowed ship, for example, should have a greater propor-
tionate distance between the two centres than a ship of the same
extreme dimensions and draught, but with a finer entrance. In
ships trimming considerably by the stern, and with a clean run,
tlie distance between the centres should be made proportionately
less. In ship-rigged vessels and barques it appears that the centre
of effort is from one-fourteenth to one-thirtieth of the length
before the centre of lateral resistance ; one-twentieth being a
common value. The greater distance (one-fourteenth) occurred
in the old sailing ships of the Royal Navy, with full bows and
clean runs ; this has been almost equalled in some of the later
masted ironclads, where the centre of effort has been placed one-
sixteenth of the length before the centre of lateral resistance.
The smaller distance occurs in screw frigates of high speed and
fine form, such as the Inconstant; in the unarmoured screw frigates
which preceded them, the distance was from one-twentieth to one-
twenty-fourth of the length. In brigs, one-twentieth of the length
is a fair average for the distance between the two centres. In
schooners and cutters, the two centres are always very close
together, their relative positions changing in different examples,
and the centre of lateral resistance sometimes lying before the
504 NAVAL ARCHITECTURE. chap. xii.
centre of effort. Mr. Dixon Kemp considers that for racing
yachts the centre of effort of the sails should be placed about
one-fiftieth of the length before the centre of lateral resistance ;
and for cruising yachts recommends that they should lie in the
same vertical line. For yawls the centre of effort should be a
little further aft than in cutters or schooners. It is to be noted,
however, that in a vessel with square sails the longitudinal posi-
tion of the centre of effort will vary but very slightly, however
wide may be the differences between the angles to which the
yards are braced. On the contrary, in a schooner or cutter the
centre of gravity of the jtlain sail must move forward with any
angle of departure from the hypothetical position in the plane of
the masts.
In the designs of sailing men-of-war, it was formerly the prac-
tice to express the longitudinal position of the centre of effort in
terms of its distance from the centre of buoyancy ; and it was
generally agreed that the centre of effort should lie further
forward thtm the centre of buoyancy. Chapman, the famous
Swedish naval architect, laid down the rule that the distance
between these two centres should be between one-fiftieth and one-
hundredth of the length ; but considerable departures were made
from this rule in practice. Cases occurred where the distance
was as great as one-thirtieth of the length.
A similar practice still prevails in the designing of merchant
sailing ships; and even greater variations occur in the relative
positions of the two centres. Cases have occurred where the
centre of effort has been as much as one-twentieth of the length
before the centre of buoyancy ; and others where it has been one-
fiftieth of the length abaft. Such variations clearly indicate an
absence of conformity to any fixed rules, other considerations —
such as convenience of stowage or accommodation — largely in-
fluencing the longitudinal distribution of the sail.
Having decided upon the proper distance between the centre
of effort and centre of lateral resistance for a new design, it is
next necessary to station the masts and distribute the sail in such
a manner that the required position of the centre of effort may
be secured, in association wdth sufficient manoeuvring power and
a proper balance of sail. In the following table the results of
experience with various classes of ships are summarised, all
the vessels being supposed capable of proceeding under sail
alone.
The length of a ship at the load-line, from the front of the
CHAP. XII.
PROPULSION BY SAILS.
505
stem to the back of the sternpost, being called 100, the other
lengths and distances named will be represented by the following
numbers : —
Distance from Front of Stem.
Rig and Class of Vessel.
Base of Sail.
Foremast.
Mainmast.
Mizenmast.
Ship or Barque Rig : —
• •
. .
• •
125 to 160
Obsolete classes of sailing-"*
ships of war . . . ./
12 to 15
55 to 58
80 to 90
• •
Unarmoured war - ships,"*
steam and sail . . ./
13 to 18
56 to 59
84 to 86
■ •
Sailing merchantmen ' .
20 to 22
53 to 55
80 to 88
• «
( 64 to 66 •^
Ditto (four masts)
14
38 to 40
■ Jiggermast.^
86 to 87 J
• »
Brig
17 to 19
64 to 65
. .
160 to 165
Schooner*
16 to 22
55 to 61
• •
160 to 170
Cutter
36 to 42
variable j
170 to 190
Yawl
38
, ,
\ abaft >
sternpost )
, .
Ketch ......
39
• «
90
■ •
This table requires only a few words of explanation. The
four-masted merchantmen named therein are vessels of large size
(260 to 280 feet in length, and 3500 to 4500 tons load displace-
ment) ; they require very large spreads of canvas, and the
employment of the fourth or "jigger" mast enables the designer
to keep the centre of effort lower than it could be kept, with an
equal sail-spread, on three masts. Four masts were originally
fitted in the ironclad Achilles, but the rig did not prove success-
ful. Similar remarks apply to the five-masted rig of the
Minotaur class. In the merchant steamships, 400 to 550 feet
long, four or five masts are sometimes employed ; but in them
efficient performance under sail is not looked for. This is also
true of the Great Eastern which, with her six masts, carries a
sail-spread altogether disproportionate to her size.
The "rake" given to the masts in ditferent classes of ships
requires a few words of explanation. In nearly all cases it is
an inclination aft from the vertical line drawn through the heel
of the mast ; but in vessels with " lateen " rig the foremast
commonly rakes forward considerably. The following are com-
* These are Fincham's rules : in placed much closer together, in order
modern schooner-yachts no fixed rule to increase the size of mainsail,
ajjpears to be followed, the masts being
506 NAVAL ARCHITECTURE. chap. xii.
moil values for the rake aft. In cutters, from /^ *o \ of the
length; in schooners, for foremast, from ^q to \, and for main-
mast, from \ to ^; in brigs, for foremast, from 0 to g^, for main-
mast, from 1^ to j^; in ships, for foremast, from 0 to ^, for
main and mizen masts, from 0 to ^.2. It is customary to have
the greatest rake '\\\ the aftermost mast, and the least in the fore-
mast. Graceful appearance, greater ease and efficiency in
supporting the masts by shrouds and rigging, and the possibility
of bracing the yards sharper when the masts are raked aft and
the rigging led in the usual way, are probably the chief reasons
for the common practice. The "steeve" given to the bowsprit
is also in great measure a matter of appearance ; but it is
useful, especially in small vessels, in giving a greater height
above water for working the head-sails in a sea-way. In some
large war-ships intended to act as rams, the bowsprits are fitted
to run-in when required, and the steeve is very small ; but the
height above water is considerable.
It will be observed that the table also gives a length for the
"base of sail," in terms of the length of the ship, and this
exercises an important influence on the manoeuvring power of a
vessel. In Fig. 126 it would be measured from the foremost
corner (or "tack") of the jib to the aftermost corner (or "clew")
of the driver ; in other classes it would be measured between
extreme points corresponding to those named. The base of sail
was usually proportionally greater in vessels wholly dependent
on sail-power than it is in vessels with steam- and sail-power, the
foremast being placed further forward and the mizenmast
further aft than is now common. Special circumstances may,
however, limit the length of the base of sail ; and one of the
most notable cases in point is to be found in her Majesty's ship
Temeraire, a hrig-rigged vessel of over 8400 tons displacement,
where the departure from ship rig has been made in order to
facilitate the arrangements for the heavy chase guns at the bow
and stern.
Experience has also led to the formation of certain rules for
determining the proportionate areas of the sails carried by the
different masts, with various styles of rig. According to Mr.
Fincham and other authorities, in ship-rigged sailing vessels of
the earlier classes, if the area of the plain sail on the mainmast
was called 100, that on the foremast varied from 70 to 77, and on
the mizenmast from 46 to 54. It is now usual in the ships of
the Royal Navy to make the corresponding sails on the fore and
main masts alike, except the courses; and calling the sail-area
CHAP. XII. PROPULSION BY SAILS. 5^7
on the mainmast 100, that oii the foremast would commonly be
from 90 to 95, that on the mizen 45 to 55, and the jib from
15 to 20, the latter agreeing fairly with the practice in sailing
vessels. In barque-rigged vessels the sail-area on the mizen is
often about one-third only of that on the main; the sail-area on
the foremast having about the same proportion as in ships. In
brigs the sail on the foremast varies from 70 to 90 per ^cent.
of that on the main; in schooners it is often about 95 per
cent.
In sailing merchantmen the distribution of sail varies con-
siderably. The following appear to be good average values.
Calling the sail-area on the mainmast 100 in ship-rigged
vessels, that on the foremast varies from 90 to 95, and on the
mizen from hh to 60; the jib varies from 10 to 12. In barque-
rio-o-ed vessels the corresponding numbers are : mainmast 100,
foremast 90 to 95, mizen 25 to 30, jib 10 to 15. In four-masted
ships the main and mizen carry about equal sail-areas; callmg
this 100, the jib is about 8 to 10, the foremast 85 to 95, and the
jigger 55 to 60 in some good examples ; in a four-masted barque
the jigger has been found as little as 20 to 25.
Another feature somewhat affecting the handiness of a ship
under sail, particularly in the earlier movements of any manoeuvre,
is the distance of the centre of gravity of the ship from the
centre of effort. This consideration was formerly treated as of
great importance, but it now has little influence in the actual
arrangement of sail plans. The longitudinal position of the
centre of gravity for the load-drauglit is usually fixed by other
and more important conditions; and its position changes con-
siderably as the amount and stowage of weights on board are
varied. It will suffice to say, therefore, that, when the ship is
turning, her motion of rotation may be regarded as taking place
about a vertical axis passing through the centre of gravity ; which
point simultaneously undergoes a motion of translation. Hence it
follows that the turning effect of any forces will vary with the
distance from the centre of gravity of their line of action.*
Suppose a ship to have all plain sail set, and balanced so that
her course can be kept without using the rudder, the line of
action of the resistance will then lie in the same vertical plane
with the resultant wind pressure, which may be supposed to
pass through the centre of effort. Then, in tacking, the resist-
* See further, Chapter XIV.
5oS NAVAL ARCHITECTURE. ' chap. xrr.
ance tends to throw the head of the ship up into the wind
and to assist the helm, but it tends to resist the helm in wearing.
The further forward of the centre of gravity the centre of effort
is placed, the greater will be the initial turning effect of the
resistance wlien a manoeuvre begins. But as soon as changes
are made in the sails which "draw" in order to assist the
manoeuvre, and as soon as the action of the rudder is felt, the
speed and course of the ship alter, and the initial conditions no
longer hold, the line of action of the resistance changing its
position from instant to instant.
Lastly : in arranging the sails of a sliip, it is necessary to con-
sider their vertical distribution, which governs the height of the
centre of effort, and the "moment of sail" tending to produce
transverse inclination.
The specimen calculation on page 502 shows the ordinary
method of estimating the vertical position of the centre of effort
when the plain sail is braced fore-and-aft; and no explanation
will be needed of this simple calculation. In previous chapters,
explanations have been given of the action of the wind on the
sails, and of the resulting strains on the rigging and topsides.*
It will su£6ce, therefore, to state that, if the line of action of the
wind is assumed to be horizontal, the steady speed of drift to
leeward will supply a resistance equal and opposite to the wind
pressure, and having a line of action approximately at mid-
draught. This couple will incline the ship transversely until an
angle of heel is reached for which the moment of stability equals
the moment of the inclining couple. Let A = area of plain sail,
in square feet; h = the height (in feet) of the centre of effort
above the mid-draught, when the ship is upright; m = the meta-
centric height (GM) in feet of the ship ; D = the displacement
(in pounds) ; p = the pressure, in pounds per square foot, which
the assigned velocity of the wind would produce upon a plaue
placed at right angles to it; and a = the angle of steady heel.
Then, within the limits of the angles of steady heel reached
in practice, the following equations may be considered ta
hold:—
Moment of sail, to heel ship = A x h x p cos^ a ;
Moment of statical stability = D X w X sin a ;
See pages 310, 323.
CHAP. XII. PROPULSION BY SAILS. 509
whence is obtained the following equation for the angle a,
« + XjoI S"i a - 1 = 0.
Since a is usually an angle of less than 6 or 8 degrees, this equa-
tion may, without any serious error, be written,
D . m . T . K.p.li
-T ^ sm a = 1 : or sin a = -r^ —
K . p . Ii L> .m
Suppose, for example, that |J = 1, and that, in the case of Fig,
126, D = 6,800,000 ; m = ^ feet ; A = 15,600 ; and the mean
draught 20 feet. Then A = 62 + 10 = 72 feet ;
_ 15,600 X 72 _ 468^ _ 1_
^^° " ~ 6,800,000 X 3 ~ 8500 ~ 18 y'^^^^^yh
a = 3j degrees .(nearly).
It has already been remarked that, for the force of wind when all
plain sail would be set, the normal pressure per square foot is
usually assumed to be about 1 lb, ; and it is very common, in
comparing the stiffness of ships, to assume that the pressure p has
the value unity.
Looking back to the formula for the angle of steady heel, it
will be seen that, if the ratio of D . m to A . h be the same for
any two vessels, an equal force of wind p per square foot of area
of sail will produce equal angles of heel in both ships. Hence it
has become the practice in the Royal Navy to use this ratio as a
measure of the " power of a ship to carry sail." The smaller the
ratio, the less is the stiffness of the ship under canvas; the
greater the ratio, the stiffer is the ship. Very considerable varia-
tions occur in this ratio in different classes. In the Inconstant, a
vessel designed for high speed under steam as well as for sailing,
the number expressing the power to carry sail is as low as 15 ; in
the converted ironclads of the Prince Consort class, with meta-
centric heights twice as great as that of the Inconstant, and with
a much smaller proportionate spread of canvas, the corresponding
number is 51. In some of the earlier ironclads, such as the
Warrior and Minotaur classes, the sail-carrying power is repre-
sented by 30 to 35; in the recent ironclads it has been repre-
sented by 17 to 25. In the various classes of unarmoured ships
very different values occur : from 20 to 25 probably represents
the sail-carrying power of the screw frigates of the older type,
from 15 to 20 that of the corvettes, and from 10 to 15 that of the
smaller classes. Exact information is wanting as to the meta-
SIO NAVAL ARCHITECTURE. chap, xii
cenlric heights of the older classes of sailing ships of the Koyal
Navy, so tliat no exact estimates can be made of their sail-
carrying'powers. It appears probable that in the smaller classes
the numbers varied between 10 and 15; for the frigates, from
15 to 20 ; for the line-of-battle ships, from 20 to 30.
The diminution of the mefacentric heights in some recent types,
in order to secure longer periods of oscillation, which favour
greater steadiness, has led to a decreased stiffness as compared
with preceding types ; this latter feature being indicated by the
smaller numbc-rs of the sail-carrying power. In other words,
greater angles of steady heel under canvas are now common than
were formerly customary. It was important when ships had to
ficrht under sail that the angle of heel should not be excessive, and
5 or 6 degrees was the limit named by writers on the subject ; in
steamships there is no equally powerful reason for securing equal
stiffness, steadiness being the chief desideratum, and angles of
heel under plain sail of 8 or 10 degrees sometimes occur.
Respecting the actual sail-carrying powers of merchant ships,
there is no recorded information, and (from the remarks on page
85) it will be obvious that on different voyages, with varying
character and stowage of cargoes, there must be great variations
in the metacentric height, carrying with them considerable
changes in the sail-carrying power. Assuming that the ships are
so stowed that they have metacentric heights of 3 to 3^ feet, the
sail-carrying powers in a great number of cases we have investi-
gated lie between 14 and 18. Mr. W. John gives 12 to 20 as
corresponding values with 3^ feet metacentric height. It may
be desirable again to state that sailing merchantmen have forms
and proportions such that, if they are stowed so as to secure the
amount of stiffness assumed, they must have a large range of
stability. But they are liable to be much less favourably situated,
both as regards stiffness and stability, if improperly stowed.
The spread of sail carried by yachts has been shown to be
enormous in proportion to their displacement, and their meta-
centric heights being moderate, their sail-carrying powers are
small. In some very successful English yachts the sail-carrying
power lies between 4 and 8. For cruising vessels it has been
found to lie between 6 and 8. In the Sunheam, with auxiliary
steam-power, it is 84. In match sailing, steady angles of heel
of 20 to 30 degrees are said to be not uncommon ; but there is
little risk of such vessels being capsized, as the ballast brings the
centre of gravity very low, and they have extremely great range
of stability (see curves on Fig. 47c, page 128).
CHAP. XII. PROPULSION BY SAILS. 5II
Useful as the formula ou page 509 is for purposes of com-
parison, it does not enable one to estimate, with certainty, the
actual angle of steady heel corresponding to a certain velocity
and direction of the wind, as well as a given sail-spread and
bracing of the yards. The reason is twofold. First : there are
the difficulties arising from our comparative ignorance of the
laws governing the pressure of wind on sails (see page 484) ;
second, there is the uncertainty as to the distribution of the wind
pressure over the large aggregate area of the sails, extending as
that area does to a very considerable height. It is quite con-
ceivable that sensible differences in the velocity of the wind may
occur within the limits of height included in the sail-spread ; and,
if so, the moment of the wind pressure on the sails will be affected
thereby. Further, it is probable that, with a given velocity of
wind, the average pressure per unit of area on a sail is influenced by
the size and form of the sail. And finally it is not possible to
say how adjai^ent sails affect one another, nor how the wind
pressure is influenced by obliquity of impact.
From a careful comparison of a large number of recorded
angles of steady heel " under all plain sail," it appears that those
angles considerably exceed the values which would be given by
calculations based on the ordinary hypothesis that "plain sail"
corresponds to an average wind pressure of 1 lb. per square foot
of canvas. The grounds for this assumption do not appear to
have been thoroughly investigated hitherto, although from the
time of Chapman onwards the opinion has been generally enter-
tained by seamen. And further investigations, with anemometric
apparatus, are much required. In fact, the common system of
estimating the "force of wind " by personal judgment appears to
be open to serious question; and it is to be hoped that anemo-
meters may be more generally used on board ship than they
have been hitherto for the purpose of measuring both the
velocity and the pressure of the winds which produce certain
observed inclinations. When such exact data are available,
trustworthy estimates may become possibilities; at present
they are not so.
The heights of the masts and the depths of the sails were
formerly proportioned to the extreme breadths of ships. Hence
it became the practice to express the height of the centre of
effort above the load-line in terms of the breadth. For ship-
rigged vessels and barques the ratio of this height to the breadth
usually lies between 1^ and 2; for brigs and schooners between
1^ and If ; and for the other rigs mentioned in the table ou
512 NAVAL ARCHITECTURE. chap. xii.
page 505 it has nearly the same vahie. These approximate
estimates are not to be put in place of exact calculations for
the position of the centre of effort, but they are useful never-
theless. In order that the moment of sail may be estimated,
the half-draught must be added to the height of the centre of
effort above the load-liue.
Generally, if there be no similar vessels to compare with a new
design, the problem of the vertical distribution of the sail takes
the form of a determination of the height h of the centre of effort
above the centre of lateral resistance. In that case the whole of
the quantities in the formula given above, except the height h,
may be supposed known, the maximum angle of steady heel a
being assigned for a pressure of 1 lb. per square foot of canvas.
Hence
h = — J-- sin a,
very nearly, when a does not exceed the usual limits.
There are also practical rules by which the ratios of the areas
of the different sails, the lengths of the masts and yards, and
other features of a plan of sails are governed ; but for these we
are unable to find space, and they can be consulted by those
readers desiring information, in the standard works mentioned
above.
In conclusion, brief reference must be made to the changes
introduced of late years into the proportions of length to breadth
in sailing ships. It was formerly assumed that the length of a
successful sailing ship should not exceed four times the beam ;
in many vessels having a high reputation for performance and
speed, the length was not much more than three times the beam.
The great increase in the proportionate lengths of steamships
and the consequent improvement in their performance appears
to have affected the construction of sailing ships ; the clippers
of the mercantile marine frequently have lengths from five to
six times the beam. There can, of course, now be no question
as to the diminution of the resistance by the increase in
the length, and greater fineness of form. In these clippers the
requisite stiffness appears to have been secured with the use of
very little ballast, by associating appropriate fineness of the
under-water form with the greater length.
The passages made by some of these clipper ships are notable
even in the days when steam navigation is being successfully
CHAP. XII.
PROPULSION BY SAILS.
513
introduced for the longest voyages.* On the China trade, until
the Suez Canal was opened, the clippers competed successfully
with steamers, occupying from 90 to 100 days as against 75 to 80
days for the steamers. On the Australian service also the clippers
have done equally well. The ThermopylaB, for example, made the
passage from London to Melbourne in 60 days, a time only one-
half longer than that taken by some of the best steamers now
employed on that service.
We liave been favoured by the designer of this remarkably
successful vessel, Mr. Way mouth, Secretary to Lloyd's Register,
with the following particulars of her design ; which will enable a
comparison to be made between the modern sailing ship and one
of the most successful sailing frigates of the Royal Navy, her
Majesty's ship Pique.
Particulars.
Thermopylae.
Pique,
Length
Breadth
Displacement
Area of plain sail
Area of plain sail -=- (displace- 1
ment)^ 1
210 feet
36 „
1,970 tons
17,520 sq. ft.
110
1G2 feet
48i„
1,912 tons
19,086 sq. ft.
124
The sail-spreail of the Thermopylse is, therefore, less proportion-
ally than that of the Pique; but her greater length and fineness
of form probably cause a considerable diminution in resistance,
and give to the Thermopylse greater speed in making passages
than the sailing frigate possessed.
Another clipper, also designed by Mr. Waymouth, has made
no less remarkable passages, viz. the Melbourne, owned by
Messrs. Green, and employed on the Australian service. In 1876
this vessel made the passage from England to Melbourne
in 74 days; experiencing far from favourable conditions during
part of the voyage. Prom the Cape, however, fine fair winds
were obtained, and for seventeen consecutive days 300 miles a
day were averaged. The three longest runs in this time were
374, 365, and 352 miles per day. This vessel is about 3500 tons
displacement, and her area of plain sail is rather less than 21,000
square feet ; the ratio of sail-spread to the two-thirds power of the
* For a mass of ioteresting information on the subject, see the article un
" Clipper Ships" in Naval Science for 1873.
2 L
514 NAVAL ARCHITECTURE. chap. xii.
displacement being about 90 to 1, or about the same as in the
wooden screw frigates of the Royal Navy.
Another example of high speed under sail being obtained in
vessels which have good proportions of length to beam and fine
form is found in the Inconstant, of the Royal Navy, which lias
made runs at speeds of from 13^ to 14^ knots per hour under sail
alone.
The smaller proportions of lengtli to breadth adopted in the
old sailing ships of war were probably chosen because these
vessels were required to be pre-eminently handy under sail, in
order to be efficient in action. In this respect the modern
merchantman could scarcely compare with the earlier class ; the
performance of their voyages does not necessitate the possession
of similar quickness in manoeuvring. Moreover, the sailing ships
of war had to be loftier than the merchantman, to carry consider-
able weights of armament, &c., on the decks, instead of cargo in
the hold, and yet to be stiff under canvas, so that no great heel
should be produced when going into action. In short, as with
steamships of the present day, so with the sailing ships of the
past : vessels of war had to be designed to fulfil conditions which
permitted far less latitude in the choice of forms and proportions
than is possible in the designs of merchant ships. The large
number of sailing ships still employed in the mercantile marine
of this and other countries makes it desirable, however, to notice
any change which promotes their efficiency; and undoubtedly
one such change is to be found in the increased lengths and
fineness of form adopted in recent ships.
It is interesting to note that, in yachts designed for racing,
the proportions of length to beam are commonly between 4 to 1
and 6 to 1, the upper limit being reached in comparatively few
cases. The general selection of these proportions is good evidence
that they are well adapted for the class ; in which handiness and
weatherliness are no less important than speed with the wind
abaft the beam. There are, however, several cases on record in
which these vessels have attained speeds of 13 or 14 knots per
hour ; and the American yacht Sappho is said to have made 16
knots per hour, for several consecutive hours, during her passage
across the Atlantic.
CHAP. XIII. STEAM PROPULSION. 515
CHAPTER XIII.
STEAM PROPULSION. '
FoPiTY-FiVE years ago the employment of steamships in ocean
navigation was a matter of warm debate. Steamers had been
successfully employed on rivers, lakes, and inland waters, as
well as on coastwise services and short sea .passages. But it
was urged that long voyages must still be performed by sailing
ships, either because steamers could not carry coal sufficient to
propel themselves over long distances or because the expendi-
ture on the propelling power would be so great as to render
remunerative service impossible. The Transatlantic service, with
its voyage of 3000 miles, was more especially kept in view in
these discu.-sions ; and when the Great Western and Sirius made
successful passages from England to New York in 1838, the
arguments against the capabilities of steamships for sea-going
services, in competition with sailing ships, were practically
destroved. From that time onwards steam navioration has been
continuously and rapidly developed. The sizes and speeds of
individual ships have been gradually increased, and their capa-
cities for performing long voyages made greater. For many
years sailing ships remained in sole possession of the China and
Australian trade; but the opening of the Suez Canal, and the
consequent saving on the length of voyage from England to
China, have led to the extensive use of steamers on that route;
while the progress made in steamship construction has enabled
the longest ocean voyage that requires to be performed, from
England to Australia, to be successfully accomplished by
steamers.
In the construction of steamships of war, similar progress has
been made ; but the period over which it has extended is less by
ten or twelve years than the corresponding period in the
mercantile marine. So late as 1846 experimental squadrons
of sailing ships belonging to the Eoval Navy were attracting
2 L 2
5l6 NAVAL ARCHITECTURE. chap, xili
the greatest attention of all persons interested in naval affairs ;
and the steam reconstruction of the Navy was not fairly begun
until several years after. Into the causes of this delay it is now
unnecessary to enter ; but it is important to note the great
advances which have been made during the last twenty years.
The earliest screw line-of- battle ships had speeds of about 9 or
10 knots ; the latest and fastest vessels of that class did not
exceed 13 knots. The armoured battle-ships now afloat have
speeds of 14 or 15 knot?, and are twice or thrice as heavy as
their predecessors. The earlier types of unarmoured frigates and
corvettes attained speeds of 10 to 13 knots ; existing types of
frigates and corvettes have speeds ranging from 13 to 18 knots.
Hereafter it will be shown how great is the proportionate ex-
penditure of power required to attain these higher speeds, but
the mere statement of the facts v\ill sufSce to illustrate the
contrast between the steaming capabilities of war-ships of the
present day and those of twenty years ago.
It would be beside our present purpose to attempt even a
sketch of the history of steam navigation, either for the mer-
cantile marine or the Eoyal Navy ; although the interest and
importance of the subject cannot well be exaggerated. In this
chapter we propose simply to treat of steam propulsion as it
affects the work of the naval architect; and although referem^es
will necessarily be made to the work of the marine engineer, no
descriptions will be given of the various types of engines and
boilers in common use, nor of the many ingenious devices by
which it is sought to obtain increased power and efficiency with
a certain weight of propelling apparatus. Even when thus
restricted, the field of inquiry that remains open is very large,
and deserving of the most careful study. It includes a con-
sideration of all the circumstances which the designer of a
steamer has to take into account when determining the form,
dimensions, and engine-power required to attain a certain
assigned speed. An exhaustive discussion of these subjects is
impossible without recourse to mathematical investigations such
as cannot be introduced into this work; but it will be possible
to indicate in general terms the principal deductions from such
investigations, and to illustrate the principles by which the
development of steam propulsion has been guided.
The problem of steamship design is not one admitting of any
general solution ; because the conditions to be fulfilled, in asso-
ciation with the attainment of certain speeds, vary greatly in
different classes of ships. These conditions commonly include a
CHAP. XIII. STEAM PROPULSION. 5 T 7
certain minimum carrying power; limitations in the draught of
water, dependent upon the service in which the vessel is to be
employed ; limits of length, or in the ratio of length to breadth
and depth ; and the capability of steaming certain distances
without requiring to take more coal on board ; besides others
that need not be mentioned. In order to fulfil all these require-
ments and to secure the assigned speed, joint action is necessary
on the part of the naval architect and marine engineer. Upon
the latter devolve the actual design and construction of the
propelling apparatus; and his skill is displayed in providing
machinery which shall be compact, durable, strong, as light as
possible in proportion to the power developed, and economical in
the consumption of fuel. The requirements of the engineer also
exercise considerable influence upon the internal arrangements,
particularly in the a[)propriation of the spaces for the machinery,
the efficient ventilation of those spaces, and the structural
arrangements necessary to resist the local strains incidental to
propulsion. Furnished with the opinion of the engineer on all
these matters, and with data as to the ratio which the weight of the
machinery will bear to its power, the naval architect proceeds to ap-
proximate to the form and dimensions most suitable for the new ship.
This approximation is necessaiily made tentatively. In the
earlier stages, the engine-power must be expressed in terras of
the assigned speed, and of a displacement which is itself un-
known. Upon the power of the engines must depend their
weight, and the weight of coal to be carried for a voyage of
given length. And, further, the weight of hull, as well as the
weights of certain parts of the equipment, must vary with the
total weight of the ship, her extreme dimensions, type and
structural arrangements. Apart from experience, a problem
involving so many unknown quantities could scarcely be solved ;
but, guided by the results obtained in actual ships, the designer
can proceed with a considerable degree of confidence. For
example, he may express the weight of hull, &c., as a fraction of
the displacement ; and if the new ship is not very dissimilar
from existing types, of which the performances under steam have
been recorded, it is also possible to determine, in terms of the
displacement, the power and weight of the machinery, as well as
the appropriate coal supply. The remaining part of the dis-
placement will consist of the weights to be carried ; these are
given quantities, and hence an equation may be formed from
which the displacement may be estimated with a close approach
to accuracy.
5l8 NAVAL ARCHITECTURE. chap. xiii.
The case is more diflicnlt wlien the new design is to be of
novel form or unprecedented speed ; and apart from model
experiments such as were described in Chapter XI., page 471,
considerable doubt may surround the approximation to the
dimensions and displacemeut. With such experiments, how-
ever, it is possible to compare the resistances of alternative
forms; to select that which best fulfils the essential conditions,
in association with the least proportionate resistance ; and after-
wards to express with a fair approach to accuracy the engine-
power required to propel the sliip at the desired speed, in terms
t-f the product of that speed into the corresponding resistance.
Measures of Horse-Fower : Effective, Nominal and Indicated.
The "useful work" performed by the engines of a steamer
moving at a certaia speed, is measured by the product of the
resistance corresponding to that speed into the distance through
which that resistcince is overcome in a unit of time.* It will be
remembered that the term resistance has been applied to the
strain which would be brought upon a tow-rope if the ship were
drawn along by some external force which did not interfere with
the free flow of water past her hull. Suppose the resistance (1\)
to be expressed in pounds, and the speed (S) in feet per second ;
then the
Useful work (per second) = E . S (units of work).
One "horse-power" represents 33,000 units of work per
minute, or 550 units per second; hence for the horse-jaower
corresponding to the useful work, or " effective horse-power," as
it is termed, we have
Effective horse-power (E.H.P.) = ^^.
, 550
For example, in the Greylwwid experiments it was found that
the resistance at a speed of 16-95 feet per second, equalled
10,770 lbs.
Effective horse-power = 12!™xl6;95 ^ g^^.
550
This effective horse-power differs considerably from the actual
* See the remarks on " Work " at page 144.
CHAP. XIII. STEAM PROPULSION. 519
horse-power developed by the engines ; but before endeavouring
to explain the causes which influence the ratio wliich the useful
work bears to the total work of the engines, it may be well to
describe how the latter is usually expressed, in order to assist
readers unfamiliar with the subject.
The power of marine engines is expressed either in " nominal "
or " indicated " horse-power. Indicated horse-pow er measures
the work done by the steam in the cylinders during a unit of
time. If the eflective mean pressure of the steam upon the
pistons is f lbs. per square inch of the total piston area (A
square inches) ; if I be the length of the " stroke " of the pistons
(in feet), and n the number of strokes made per minute : then
the total mean pressure on the pistons will be ^jA lbs., and the
distance through wliich it acts (or speed of piston) will be nl
ftet per minute. The work performed per minute is therefore
given by the expression —
Work = p . A X w Z (units),
and this is equivalent to
Indicated horse-power (I.H.P.) = ^ ' ' „^/^ .
^ ^ ' 33,000
The effective mean pressure of the steam is ascertained from
diagrams, drawn by means of the useful little instrument known
as the " indicator ; " and hence the term " indicated horse-power "
is derived.* It will thus be seen to have a definite meaning,
although it is by no means a complete representation of the
efficiency of the propelling apparatus. It takes no account of
the efficiency of the boilf^rs as steam generators, or of the rate of
coal consumption, or of other important matters ; but notwith-
standing these omissions, the naval arcliitect most fairly expresses
the power required to drive a ship by the indicated power of her
eno^ines. The same measure will be emploved in the estimates
which appear in the subsequent parts of this chapter, except
where the contrary is expressly stated.
" Nominal " horse-power was formerly the sole measure which
appeared in the Xavy List for her Majesty's ships ; it is still the
only measure appearing in the Mercantile Navy List, and is still
* For details of this instrumeut and information respecting the very various
its mode of application, the reader pressures of steam, and speeds of
must refer to works on the steam- piston, used in different types of
engine, wherein will also be found engines.
520
NAVAL ARCHITECTURE.
CHAP. XIII.
used in the French and American navies. Simultaneously with
the introduction of displacement tonnage, instead of the B.03r.
for the ships of the Royal Navy, indicated horse-power was
introduced into the Navy List ; it alone appears for ships of
recent design, but for vessels of earlier date both the nominal and
indicated powers appear. Tlie following examples will show how
greatly different in different ships might be the ratio of
the nomint»l power to the actual or indicated power of the
engines.
Horse-power.
Ratio of
I.H.P.
to N.H.P.
Indicated.
Nominal.
Albacore
Spiteful .
Supply .
Sintoovi .
Hector .
Jgincourt
Seller oplwn
Monarch
Penelope
109
796
265
1576
3256
6867
6521
7812
4703
60
280
80
400
8C0
1350
1000
1100
600
1-82
2-85
3-31
3-94
4-07
5-08
6-52
7-13
7-84
The cause of these differences is to be found in the rules by
which the nominal horse-power was calculated. For all ships,
instead of the true mean pressure of the steam on the pistons, a
fictitious pressure of 7 lbs. per square inch was assumed. In
screw steamers, the intended piston speed (say in feet per minute)
was taken as the true speed, and
lbs.
Nominal ) _ 7 X area of pistons x intended speed of piston
horse-power j 33,000
In paddle steamers not even the intended piston speed was re-
garded, but a fictitious speed was assumed, according to a law
which has been thus stated —
Assumed
per minute)
and for these vessels
speed of piston (feet | ^ ^29-7 (length of stroke)^
mte) j ^ == ^
lbs.
„ . , , 7 X area of pistons x assumed speed
Nominal horse-power = ^ — . „ £ .
The manufacturer of the engines was usually under no obligation
CHAP. XIII. STEAM PROPULSION. 521
to conform to the assumed speeds of piston, and often exceeded
them ; while the assumed mean pressure was much below the
effective mean pressure ; two facts which explain the very
different ratios of nominal to indicated horse-power which existed
in different vessels. The change from nominal to indicated
horse-power for the ships of the Eoyal Navy has so generally
commended itself that further remarks are needless.
In the French navy the nominal horse-power is one-fourth of
the power which it is expected the engines will develop ; and in
a large number of cases the actual indicated power is found to lie
between 4 and 4^ times the nominal power. A French " horse-
power" (cheval vapeur) is rather less than the English, being
32,549 foot-pounds per minute, instead of 83,000. To convert
French into English measures, the former must be multiplied by
0-9863.
Nominal horse-power for the British mercantile marine is not
defined by law. Formerly the rule established by the practice of
Messrs. Boulton and Watt was generally employed ; it was very
similar to the old Admiralty Rule for paddle steamers, the same
effective pressure of 7 lbs. per square inch of piston area being
assumed ; but the
Assumed speed of piston = 128 'V Length of stroke.
This rule has not fallen into disuse, but is sometimes stated as
follows : — Let D^ = sum of squares of diameters of cylinders (in
inches) ; then —
Nominal 1
1 > = T^ X D^ X 'V length of stroke,
horse-power J 4/ ^ °
The commercial nominal horse-power is, however, very frequently
represented by the following expression: —
1 nominal horse-power = 30 circular in-hes of piston area.
A " circular inch " being a circle of 1 inch diameter, the total
nominal horse-power of a set of engines would be obtained by
finding the number of circular inches in all the piston areas, and
dividing by 30. This rule corresponds with that of Messrs.
Boulton and Watt, when the piston speed is assumed to be 200
feet per minute.
Various proposals have been made with a view to improving the
commercial method of measuring horse-power, but none of them
522 NAVAL ARCHITECTURE. chap. xiii.
has founri general favour. In 1872, the council of the Institu-
tion of Naval xVrchitects, having been consulted on the subject
by the Board of Trade, replied as follows : — " The term nominal
"horse-power, as at present ordinarily used for commercial
"puiposes, conveys no definite meaning." .... "The majority
"of the committee were of opinion that no formula depending
"upon the dimensions of any parts of the engines, boilers, or
" furnaces could be relied upon as giving a satisfactory measure
" of the power of an engine ; and that even if the varieties of
" engines and boilers now in use could be comprised under one
" general expression for the power, the progress of invention
" would soon vitiate any such expression or formula." The com-
mittee could not agree to any alternative mode of measuring
engine-power, but the plan which met with least objection was to
take either the indicated power on a trial trip as the nominal
power, or some submultiple, such as one-fourth of the indicated
power; the latter would be very nearly the same as the French
rule. So far as we are informed, no action has yet been taken to
give effect to the recommendations, and to assign a uniform or
definite meaning to a nominal horse-power in the mercantile
marine.
Principal Types of Marine Engines : Relative Weights and Bates
of Coal Consumption.
In selecting the type of engine to be employed in a new ship
in consultation with the marine engineer, the designer has to
consider the ratio of the weight of the various types to their
indicated horse-power, and their relative coal consumption. It is
usual to express the weight of machinery in "hundredweights
per indicated horse-power" and the coal consumed in "pounds
per indicated horse-power per hour." Both these quantities may
be affected by the special conditions to be fulfilled in various
ships, especially in war-ships, even for any single type of engine ;
but the following brief statement may be of service, representing,
as it does, the average results of good practice. Four types of
machinery — including in that term both engines and boilers —
are now extensively used in the Eoyal Navy and the mercantile
marine. First, the earlier type with low-pressure steam (25 to
30 lbs.), simple-expansion and jet condensers, such as is fitted in
the Warrior and other earlier ironclads. Second, the type
largely used in the Eoyal Navy in vessels built in 1863-71, with
low-pressure steam (30 lbs.), simple-expansion and surface con-
CHAP. XIII.
STEAM PROPULSION.
523
(leiisers. Tliird, the compound type, with high-pressure steam
(60 to 120 lbs.), that has been almost universally adopted in the
mercantile marine, and largely used in ships of the Royal Navy
during the last ten years. Fourth, what may be termed the
"torpedo-boat" type, with locomotive boilers worked at 110 to
140 lbs. pressure, under forced draught, and with lightly-con-
structed but beautifully-finished compound engines. Besides
these types there are others in use, but nothing need be said
r. specting them here.*
For the four selected types the average weights and rates of
coal consumption at full speed are approximately as follows : —
Rate of Coal
Weight per
Consumption
Type of Jlachineiy.
indicated
per indicated
Horse Power.
Horse Power
per hour.
cwts.
lbs.
1.
Simple expansion : jet condenser
3^
4 to 6
2.
do. do. surface condenser
3
3 to 4
3.
Compound : Royal Navy ....
3 to 3J
2 to 2S
„ mercantile ....
3J to 5
\l to 2*
4.
Torpedo-boat : small scale
J to f
3J to 4
Torpedo-ships : large scale .
1^ to IS
Zl to 4
It may be proper 10 explain further that the weights and coal
consumptions for the first three types correspond to the trials
made with natural draught ; whereas in the fourth group the
stokeholds are closed, and air is forced into them under pressure
by the action of powerful fans. The large consumption of fuel is
due, therefore, to the action of the forced draught, the boilers
being relatively overworked; and it has yet to be discovered by-
experience how long a vessel fitted with such boilers could
continue to run at full speed. Hitherto this type of machinery
has been used only in vessels where the maintenance of high
* While these sheets were passing
through the press, the Author was
furnished by Mr. Kirk (of Messrs.
Napier & Sous) with the results of the
earliest trials made with the triple
eximnsion (three cylinder) engines,
designed by Mr. Kirk for the s.s.
Aberdeen. These results appear to
promise a very notable advance in
economy of coal-consumption — amount-
ing to 20 to 25 per cent, as com-
pared with good compound engines, on
an ocean voyage. Further experience
with the new type will determine its
relative value more precisely ; but if
the promise of the first trials is ful-
filled the system must have a remark-
able influence on the economical per-
formance of long voyages.
524 NAVAL ARCHITECTURE. chap. xiii.
speeds for comparatively short times meets the conditions of
service ; and fresh water has been used in the boilers.
Other types of high-pressure boilers have been tried on a small
scale, and some of these are said to combine lightness equal to
that of the locomotive boiler (water included), with greater
economy in coal consumption. Of these special "coil" boilers
that devised by Messrs. Herreshoff appears to be one of the most
promising. It has been fitted in a large number of launches,
yachts, and torpedo-boats, a few of which have been purchased
for the Eoyal Navy. Exhaustive trials have been made by
engineer officers of the United States navy on this type of boiler,
and in some of the most recent trials it has been stated that the
expenditure of anthracite coal was only 2^ lbs. per indicated
horse-power per hour when steaming full speed. This boiler
requires fresh water for its most eflScient action ; and when this
condition is fulfilled it appears to be capable of being steamed
continuously over long periods. It has the further advantages of
enabling steam to be raised quickly, and of practically removing
risk of serious damage by explosion. On the other hand, it has
some disadvantages, requiring very careful treatment to keep
steam ; but intelligent management and special training are also
needed with the locomotive type of boiler. So far as we are
informed, experience with the Herreshoff boiler has been limited,
up to the present time (1881), to small vessels having only one
boiler. The difficulties of successfully working a group of such
boilers may be greater than those incidental to dealing with a
siogle boiler ; but they will probably be overcome. There are other
forms of coil boilers in use, some of which have given satisfactory
results, and in this direction further progress may be expected.
If this expectation is realised, and economical rates of coal con-
sumption can be associated with extreme lightness in the boilers,
the effect upon steamship construction will be marked.
Another means of economising the weight of machinery re-
quired for a given horse-power is found in the application of
" forced draught " to ordinary high-pressure boilers. There are
various methods of doing this. One of the most common hitherto
has been the use of steam-jets in the funnel : this gives a greatly
increased rate of combustion, but is wasteful of steam. It is
stated on good authority that, whereas the rate of combustion has
been increased from 40 to 50 per cent., the gain in indicated
horse-powtr has only been 15 per cent, above that obtained with
the natural draught. In other words, the rate of coal consump-
tion per indicated horse-power per hour has been increased about
CHAP. XIII. STEAM PROPULSION. 525
one-third by the use of the steam Wast ; and on this, as well as on
other grounds, this form of forced draught can only be considered
applicable for comparatively short periods. Another plan of
forced draught consists of blowing air into the funnel, but this
did not succeed in the experiments made in this country. Still,
another proposed by M. Bertin, and tried in France, consists in
compressing air by suitable machinery, and delivering jets into
the base of the funnel ; * this is said to have been successful,
giving an increase of 40 per cent, on the indicated horse-power
with about 20 per cent, increase on the coal burnt per indicated
horse-power per hour. Still, another plan consists in blowing air
into the ash-pits, but this was not found successful. General
opinion now favours the method of drawing air down by fans and
putting the whole stokehold under pressure. This has been
done largely in recent French war-ships, and in some vessels
built in this country. Further experiments are also in progress
in ships of the Koyal Navy. It is stated that in this manner an
increase of from 30 to 50 per cent, may be obtained as compared
with the indicated horse-power obtained with natural draught.
This advantage of course involves less economy in coal consump-
tion, but not so great a reduction as with the steam blast.
Probably with ordinary high-pressure boilers 20 to 25 per cent,
increase in the rate of coal burnt per indicated horse-power per
hour would not be far from the result attained with forced draught,
although we cannot give a decided statement on the point from
the facts on record.
A few simple examples may be of service as illustrations of
the influence which the type of machinery selected may have
upon the size or the efficiency of a ship.
First, let attention be directed to the advantages which may
result from the use of a type of machinery which economises
fuel. Her Majesty's ship Devastation has engines of the low-
pressure surface-condensing type, which indicated on trial more
than 6600 horse-power, and drove the ship 13-8 knots per hour.
These engines weigh 1000 tons, and the total coal supply carried at
the normal draught is 1350 tons. The Nelson, an armoured ship of
later date, has compound engines, which on trial developed as
nearly as possible the same power, and weigh only about 30 to 40
tons more than the engines in the Devastation, although they
* See a Memoire in the Proceedings of La Societe d' Encouragement pour
rindustrie NationaJe, 1877.
526 NAVAL ARCHITECTURE. chap. xiii.
consume only two-thirds as much coal per hour. Hence it follows
that, if the engines of the Nelson were fitted in the Devastation,
900 tons of coal would have sufficed to drive the latter ship as
far as the 1350 tons she carries can drive her; so that, if the
steaming distance were kept unaltered, the use of compound
engines in the Devastation would enable no less than 400 tons to
be added to the weight of armour, armament and equipment :
or, if it should be preferred to increase the steaming distance,
keeping the coal supply at 1300 tons, would permit the ship with
compound engines to travel nearly half as far again as she can
with her present machinery.
In ocean-going mercantile steamers, economy in coal consump-
tion is no less important than in war-ships, because their commer-
cial success depends so largely upon their power of carrying
caro-o. For instance, a laro-e Transatlantic steamer with com-
pound engines burns, say, 800 tons of coal on the voyage ; if she
had simple engines of the jet-condenser type she would burn
1800 to 2000 tons, and with the surface-condenser type about
1200 to 1400 tons. Hence it will be seen how considerable would
be both the saving on coal and the gain in carrying-power result-
ing from the adoption of an economical type of machinery.
The longer the voyage and the larger the proportionate coal
supply, the greater are the gains of the modern type. For
example, a steamer which now has to carry a weight of coal
equalling three-tenths of her total displacement, in order to per-
form the voyage to Australia, might have nearly one-fourth of the
displacement available for cargo. But if she had engines of the
early type, consuming coal twice as rapidly, she would require to
carry coals amounting to three-fifths of her total weight, and could
carry no cargo. If she had engines of the surface-condensing
type, the coal supply would have to be increased to nearly one-
half the displacement ; and after allowing for the small saving
on the weight of engines, as compared with the compound type,
the weight of cargo that could be carried would be very small —
not one-half that which the modern ship would carry. These
are not mere estimates, but simple statements of fact based upon
the particulars of ships now employed upon the service. And it
is to the improvements ia marine engines, which have brought
about such great economy in consumption of fuel, that the
moderate size of these successful ships is due. When the design
of the Great Eastern was in contemplation, no such results had
been attained, and it appeared necessary to build a ship of
extraordinary dimensions, for a service which is now success-
CHAP. XIII. STEAM PROPULSION. 527
fully accomplished by ships of less than one-fourth her dis-
placement.
Next, we will ilhistrate the influence which the use of forced
draught may have upon the maximum speed attainable with a
given weiglit of machinery in a ship fitted with ordinary boilers.
Take, for example, the despatch vessel Irh of the Koyal Navy.
At her load-draught she attained a speed of 18 knots per hour,
with an indicated horse-power of about 7300; and at 16 knots
she required about 5000 horse-power. Suppose a new vessel to
be built of identical form, with compound engines which, with
natural draught, sliould develope 5000 horse-power, the weight of
the machinery would be, say, 800 tons, and the coal consumption
about 2 lbs. per indicated horse-power per hour. Next, suppose
that the forced-draught system is applied to this vessel, and that
the French experience is repeated, the same machinery, with 20
or 30 tons of special appliances, will develope 6500 horse-power,
and increase the speed to something like 17;^ knots. Of course
this increased development of power and more rapid combustion
in proportion to fire-grate area does not favour ecjnomy in coal
consumption. Probably the coal burnt per hour, as compared
with the natural draught and 16 knots speed, would be in-
creased from about 5 tons to about 8 tons. This forced-
draught condition is not designed, however, to be continued for
long periods ; and it will be observed that if the 6500 horse-
power were put into the ship on the ordinary compound principle,
there would be at least 200 tons greater weight of machinery
than with the forced-draught arrangement, besides a considerably
greater first cost. Hence, it will be seen that for war-ships, which
only rarely and for comparatively short intervals need to be
driven at full speed, this forced-draught system promises to be
most useful. Experience in vessels now under construction will
soon place the matter beyond the experimental stage. JFor
merchant ships steaming over long distances, and mostly at
speeds approaching their full speeds, the forced-draught system
does not appear to be suitable ; but for special vessels steaming
short distances it may be worth consideration.
For short distance steaming at high speeds, the locomotive
type of boiler, and engines running at high piston speeds, similar
to those fitted in torpedo-boats, also deserve consideration. It
is true that as yet experience on a large scale with this type of
machinery is comparatively limited. Nearly all its applications
have been in vessels having moderate engine-power fitted with a
single boiler ; but in the torpedo-ram Polyphemus, of the Eoyal
528 NAVAL ARCHITECTURE. CHAP. xiii.
Navy, and in some foreign vessels of war, the experiment is now
being tried on a larger scale. As tlius applied, the extremely
small ratio of weight of machinery to indicated horse-power
attained in the torpedo-boats is not reached, for reasons which will
be obvious. Proposals have been made, it is true, to fit very quick-
running engines in order to save weight, and to " gear down " from
their speed to the appropriate speed of the screws in large ships ;
but nothing of the kind has yet been done. But supposing that
the extreme lightness of the torpedo-boat machinery could not
be attained, quite an appreciable saving might be effected in
special vessels, such as the Channel passenger steamers, where
shallowness of draught and high speeds are of the first import-
ance. To illustrate this, take the case of the fast steamers built
by Messrs. Samuda, which required 2800 horse-power to drive
them 18^ knots on the measured mile. They have simple engines
with low-pressure steam — type (1) in the table on page 523, and
the total weight of the machinery is 320 tons. If it were possible
to fit machinery as light in proportion to its power as that in the
Pohjphemus, then about 220 tons would suffice for the same power.
The coal consumption would reach one-third more, perhaps, with
the locomotive type of boiler ; but on this short run this difference
is unimportant. This is, of course, an incomplete comparison,
because the change suggested involves the substitution of screws
for paddle wheels, and might also necessitate changes in form.
Enough has been said, however, to justify the statement made
above, that for short distances the use of the torpedo-boat type
of machinery may be worth consideration.
For ocean steaming at high speeds over long distances, the
locomotive type of boiler does not appear suitable, in the form
which has been used in torpedo-boats ; because of its incapacity
for being worked continuously for long periods at high power,
its need of fresh water, and its relatively high rate of coal con-
sumption. There is no doubt but that the first two difficulties
might be overcome by special arrangements ; such as the use
of spare boilers which would permit individual boilers to be
shut off and cleaned at fiequent intervals, or the fitting of
special condensing boilers to furnish fresh water to the loco-
motive boilers. Such arrangements would involve some ad-
ditional weight and work in management, but they are
practicable. A more serious matter is the high rate of coal
consumption, which has not yet been reduced much below about
double the rate of a good compound engine. To illustrate this
statement take again the case of a first-class Transatlantic
CHAP. XIII. STEAM PROPULSION. 529
steamer, developing about 5500 horse-power, and burning 850
tons on the voyage. Suppose her machinery in full working
order to weigh 1250 tons and to be capable of developing 6500
horse-power on the measured mile ; also, suppose that 1000 tons
of coal are carried — tlie total weight of machinery and coal will
be 2250 tons. Next, suppose that the torpedo-boat type of
machinery is to be fitted, with spare locomotive boilers, con-
densing boiler, &c., and that the weight of machinery complete
is 450 tons — or about 14 cwts. per horse-power indicated on a
measured mile run — the coal consumption on the voyage,
including that for condensing, may be put at something like
1800 tons: so that 2000 tons of coal would require to be
carried and, with the machinery, a total weight of 2450 tons
would be reached. These figures are not put forward as accurate,
but simply as indicative of the condition that, under present
circumstances, fur long distance steaming the economy of weight
in machinery possible with locomotive boilers is counterbalanced
or more than counterbalanced, by increased coal consumption.
For longer distances than the Transatlantic passage, the com-
parison would, of course, be more favourable to the compound
type. At the same time it is far from improbable that improve-
ments may be introduced into marine boilers, resembling the
locomotive type, by which their rate of coal consumption may be
reduced, their weights being kept below that of ordinary high-
pressure boilers such as are now in general use. Or it may
happen that other types of boilers suitable for raising high-
pressure steam, economical in coal consumption, and light in
proportion to their power will come into use. From the remarks
made above as to the Herreshoff boiler, it will appear that there
is already some prospect of such a change; but further ex-
perience is needed. Meanwhile in some large war-ships of great
speed and power, there is being carried out a combination of the
ordinary high-pressure and the locomotive boiler. About one
half the maximum power is being put into the one kind of
boiler, and one-half into the other. There are separate sets of
engines connected with each description of boiler ; and arrange-
ments are made to throw the engines using the higher-pressure
steam in or out of gear wath the screw shafting. Under
ordinary circumstances of cruising the economical boilers would
be worked and the engines connected with them. When
full speed is to be reached the whole machinery is put into
operation. Besides the reduction in weight of machinery thus
rendered possible there is a reduction in the waste-work of the
2 M
530 NAVAL ARCHITECTURE. chap. xiii.
engines when the sliips are steaming at moderate speeds (see
page 564).
From this brief sketch of the present condition and probable
developments of marine engines and boilers it will be seen that
for every new design the selection of the most appropriate type
of machinery is a matter of great importance. This selection is
the joint work of the naval architect and the marine engineer,
upon whose united action and cordial agreement the ultimate
success of the new ship must largely depend.
General considerations relating to Propellers.
The selection of the type of engine for a new steamship is
closely associated with the choice of a suitable propeller; in fact,
the character of the service for which a ship is designed may
virtually decide the choice of a propeller, and make the selection
of the engine depend upon that choice. For general service,
three kinds of propellers are available, the screw, the paddle and
the water-jet : no other propellers have claims to serious con-
sideration. The paddle has been in use from the earliest days of
steam propulsion, the screw for about forty years, and the water-
jet was first employed so long ago as 1813. The last-mentioned
propeller can scarcely be regarded as having passed beyond the
stage of experiment, having been adopted in several small
vessels and floating fire-engines, but only in one ship of moderate
size, her Majesty's ship Waterwitch. It has, however, attracted
so much attention, and been so strongly recommended, that it
cannot be left unnoticed. The paddle-wheel was the first pro-
peller employed, and although it has now given place to the
screw for ocean navigation, it still remains in common use for
river and shallow-water steamers. The screw is now by far the
most important propelling instrument, and there seems no present
probability of any other propeller replacing it ; so that it claims
most attention. It is proposed to glance at the distinctive
features of the other two propellers before passing to the con-
sideration of the screw ; and in order to compare their relative
efficiency, it may be well to state briefly the fnndamental principle
of the action of all propellers.
The action of the propeller drives stern wards a stream of water,
and the reaction of that stream drives the ship ahead. This
reaction is measured by the sternward momentum communicated
to the stream in a unit of time, and may be expressed as follows : —
Let C = the cubic feet of water acted upon by the propeller per
CHAP. XIII. STEAM PROPULSION. 53 1
second : for sea-water weighing 64 lbs. per cubic foot, the weight
of water acted upon per second must be 640 lbs. Let v = the
sternward velocity (in feet per second) impressed upon the stream :
then the magnitude of the force of reaction R is measured by the
added velocity (as explained on page 135), and we must have—
Reaction (R) - ^ = -JL •
Weight of water acted upon g 32-2'
R = — ^ X weight of water acted upon
X 640 lbs. = 20v lbs. (nearly).
32-2
This reaction measures the propelling force, or thrust of the
propeller. When the ship is in uniform motion, there must be
an exact balance bet^veen this thrust and the total resistance then
opposing the motion of the ship. When the thrust exceeds the
resistance, the motion of the ship will be accelerated ; when the
converse happens, the motion will be retarderl. It is, however,
important to note the fact mentioned above, viz. that, when a
propeller acts upon the streams of water flowing past a ship, their
natural flow (described in Ohapter XI.) is interfered with more or
less; the result being an increase in the resistance experienced
by the ship. This point will be further elucidated.
From the foregoing general expression it appears that the
thrust of a propeller depends upon the quantity of water acted
upon per second and the stermvard velocity impressed. So long
as the product Gv is unaltered, so long does the thrust remain
constant, no matter how 0 and v may be individually varied. It
may be noted, however, that it is usually preferable to make
the value of the velocity v as small as possible, in order
to reduce the waste- work perf »rmed in giving motion to the race,
and to lessen the speed at which the propeller has to be driven ;
so that, theoretically, it is advantageous to adopt a form of pro-
peller which will operate upon the largest possible quantities
of water. In practice this conclusion requires modification, be-
cause it may happen that in dealing with larger quantities of
water, and giving the " race " a smaller sternward velocity, the
increase on the " waste-work " of machinery and propellers (as
explained hereafter) may more than counterbalance the gain re-
sulting from the reduced velocity of the race. Moreover, all
conditions which affect the flow of water to the propeller must
exercise a sensible effect upon its efficiency. And, lastly, the
2 M 2
532
NA VAL ARCHITECTURE.
CHAP. XI II.
position in relation to the sliip in which a propeller is placed may
greatly afl'ect its efficiency, more especially throngh its influence
upon the stream-line motions, and the effect of those motions
upon the supply of water to the propeller.*
The Water-jet Propeller.
The water-jet is the simplest of the three propellers. In her
Majesty's ship Watei -witch it is applied in the following manner.
Openings are made in the bottom of the ship to permit the pas-
sage of water into the interior. The water which enters necessarily
has the forward motion of the ship impressed upon it, then passes
into a turbine driven by the main engines, and is expelled, with
considerable velocity, through passages leading to an outlet or
nozzle placed on each side, at the level of the load-line. These
nozzles direct the issuing streams sternward when the ship is to
be moved ahead, and in the opposite direction when she is to go
astern ; arrangements being made by which the direction of out-
flow can be easily reversed. The sternward velocity with which
the issuing streams are impressed is, of course, the difference
between their actual velocity of outflow (V) through the nozzles
and the speed of advance (v) of the ship. If A = the joint area of
the outlets in square feet, we have —
Cubic feet of water acted upon per second = AN ;
Weight of sea-water acted upon per second = 64 AV lbs.
Sternward velocity (in relation to still water) =\ — v;
Thrust: or momentum created per I = A. V (V — v)
second in sea- water i ^ , ^^ ,^^ . ,,
= 2AV(V-v) lbs. (nearly).
It is important to note that the propelling effect due to the
reaction of the streams issuing from the nozzles is as great when
the outlets are placed above water as when they are under water,
if the velocity of outflow and the speed of the ship are the same.
* Eeaders desirous of following out
the mathematical treatment of this
subject may consult with advantage
the Paper "On the Mechanical Prin-
ciples of the Action of Propellers," con-
tributed to vol. vi. of the Transactions
of the Institution of Naval Architects,
by the late Professor Eankine ; the re-
marks of the late Mr. Fronde on that
Paper, and his Paj^er on the " Screw Pro-
l^eller" in vol. xix. of the Transactions
should be read ; also the Paper by Pro-
fessor Cotterill in vol. xx. of the
Transactions, and his Papers published
in Nos. 2 and 3 of the Annual of the
Koyal School of Naval Architecture.
CHAP. XIII. STEAM PROPULSION. 533
If the nozzles are placed above water, the turbine has to do some
small amount of additional work, in raising the water-jets to the
height of the nozzles before expelling them. If the nozzles are
placed under water, their projection beyond the sides of the ship
will cause additional resistance, especially if they are of large
sectional area. In the Waterivifch, as stated above, the nozzles
are placed at the level of the load-line.
The following points require careful consideration in making
use of the water-jet propeller, if its efficiency is to be made as
great as possible : — First : the arrangement of the inlets in the
bottom ; otherwise waste-work may be done in giving motion to
masses of water which do not enter the ship. Second : the
arrangement of the pipes and channels by which the jets are
conducted from the inlets to the outlets; otherwise the frictional
and other resistances of the water in passing through these chan-
nels may become unnecessarily great. Third : the determination
of the sectional areas of the outlets, their positions, and the forms
of their casings ; otherwise the sectional areas of the jets may be
too small to secure economical propulsion, or the passage of the
casings through the water may give rise to serious resistance.
Besides these matters, there are the equally important questions
relatinor to the design of the engines which drive the turbine, and
of the turbine itself; but these concern the marine engineer.
Usually, the inlets and outlets of a vessel propelled in this
manner are placed amidships, where the streams produced by the
passage of the ship in the surrounding water have their maximum
sternward motion relatively to her. This fact may somewhat
reduce the efficiency of the propeller, as compared with what its
action would be if the water were undisturbed by the passage of
the ship. If it be assumed that there is no such disturbance,
and if the waste-work done in forcing the water through the
passages be left out of account, then the following equations hold
good : —
Useful work of propeller 1 ^ ^y^^.j^ ^^^^ -^ propelling ship
(in unit of time) J
= Thrust X velocity of ship
= 2AY (V -v) . V.
Total work of propeller = Useful work -f waste-work in i-ace
= 2AV (V -v)v-{- AV(V - vf
= AV(V^ - v~).
„„ . Useful work 2v
534 NAVAL ARCHITECTURE. chap. xiii.
Hence it follows that the more nearly V approaches v, the nearer
will the efficiency approach unity. Again it will be evident that
as the efficiency increases and the value of V — v diminishes, the
area A must be increased to maintain a constant thrust, the speed
of the ship being assumed to remain unchanged ; or, to state the
same thing rather differently, as the efficiency increases and V — v
diminishes, AV the quantity of M'ater acted upon must be in-
creased : hence it is advantageous, under the assumed conditions,
to deal with large quantities of water.
In practice, however, these conclusions need some qualification.
There are, for example, various limitations to increase in the area
of outlets, and the apparatus required to give the desired
velocity of outflow to large quantities of water may be of a
character which involves considerable losses of efficiencv, while
further losses of a serious character may result from the resistances
to be overcome in driving such masses of water through the pas-
sages in the interior of the ship. In fact it may happen that,
taking into account the efficiency of the whole propelling appa-
ratus, a less quantity of water and a higher velocity of ejection
may be preferable to the conditions which the hypothetical case
discussed above would indicate as most favourable to efficiencv.
In the trials made with jet-propelled vessels, this feature of the
subject has not received very careful consideration, so that a
definite opinion cannot be formed. It seems probable, however,
that the velocities of ejection have been too high in relation to
the speed of the ship to favour efficiency ; the quantities of water
operated upon being too small. In the trials made the results
have been dealt with in the aggregate, and mostly in the way of
a rough comparison with results of speed-trials made with vessels
of similar form and size driven by screw propellers. Hitherto, so
far as we are a\^are, there has been no exhaustive scientific
analysis, including the tow-rope resistance and " effective horse-
power" (see page 518) of a jet-propelled vessel, which Avould
enable the ratio of the effective horse-power to the indicated
horse-power to be ascertained, and compared with corresponding
ratios for vessels driven by screws or paddles. Until such an
analysis is made, the true relative efficiency of jet-propellers
cannot be determined.
Meanwhile, using the best information available, there is good
reason for considering the jet-propeller distinctly inferior in
efficiency to screws. The Waterwiicli, for example, was tried
against two twin-screw vessels, the Yi;per and Vixen, of equal
length and beam with her, of similar form in the forebody,
CHAP. XIII. STEAM PROPULSION. 535
but not nearly so 'nell shaped aft, the twin-screws being carried
br double deadwoods and thus involvino^ increased skin friction,
as well as eddy resistance, as compared with the Waterivitch.
The Vixen was a composite vessel: the other two were iron-
hulled. Comparing the Fipe?* and Waterivitch the following
results were obtaiuefi on the measured mile. For the Viper,
with displacement of 1180 tons, and 696 indicated horse-power, a
speed of 96 knots : for the Waterivitch with displacement of 1160
tons, and 760 horse-power, a speed of 9'3 knots. This inferior
performance of the jet-propeller must be attributed partly to
the waste work in forcing water through the passages, and
partly to the comparatively small quantity of water acted upon.
The joint sectional areas of the nozzles in the Waterivitch scmovLnie^
to 5 J square feet ; and at full speed about 150 cubic feet of
water was delivered per second. The twin-screws of the Viper,
on the other hand, operated on more than 2000 cubic feet of
w'ater per second.
Experiments have been made with the Waterivitch to test
the effect of reducing the sectional areas of the nozzles, and
the results obtained indicate some decrease of efficiency as
compared with the performances with full-sized nozzles, just
as might be expected from the general considerations stated
above. No experiments have been made with nozzles enlarged
beyond the sectional area of 5J square feet, which has been
shown to be proportionately very small. Considerable changes
would have been required in the ship before this enlargement
of the nozzles couLl be effected ; but there is every reason to
believe that in any future jet-propelled ship fitted with turbines
it would be found advantageous to adopt nozzles of greater size,
and to reduce the velocity of outflow of the jets.
Another very interesting comparative trial has been made
in Sweden on two torpedo-boats of about 23 tons displacement
and of identical form, with boilers of the same size and type.
One of the boats was driven by twin-screws, and the other by
uater-jets to which motion was given by centrifugal pumps.
The twin-screw boat attained 9^ knots with 80 indicated horse-
power : while her jet-propelled rival attained 8 knots with
rather more indicated hi jrse- power. It is probably no exaggera-
tion to say that to increase the speed of such a boat from 8
to 9^ knots would require from 60 to 70 per cent, increase in
power. Hence it will be seen that the screws in this trial
showed an enormous superiority over water-jets.
A jet-propelled vessel, with turbine, has also been built for
53^ NAVAL ARCHITECTURE. chap. xili.
the German uavy. She is said to be about 170 tons displace-
ment, and to have attained a speed of 7 knots with 292 indicated
horse-power. In this case we are unable to give a comparison
with a screw sliip of similar form and power.
The latest and most novel experiment in jet-propulsion has
been made recently in Germany by Dr. Fleischer, in a vessel
named the Hijdromotor, 110 feet lonp^, 17 feet beam, and with a
mean draught of 6| feet, her displacement being 105 tons.*
It is claimed for this vessel that with 100 indicated horse-power
she attained a speed of 9 knots ; but we are not furnished with
particulars of the conditions under which the speed-trials were
made, and these conditions may have differed from those usual
in English measured mile trials, where all possible care is taken
to determine accurately the true mean speed and to eliminate
the influence of wind and tide. Apart from the reported
performance there are, however, many features of great in-
terest in this vessel. There ^is no centrifugal pump, but the
steam acts directly upon the water in two reservoir cylinders
placed above two large pipes leading to the nozzles, which
are situated nearly amidships on either side of the keel. In
each cylinder there is a "float" or piston of nearly the same
diameter as the cylinder, and with a closed spherical top.
When the cylinder is full of water this float is at the upper
part of the cylinder ; when steam is admitted into the top
of the cylinder it presses the float down and expels the water
at a high mean velocity. After a certain portion of the stroke
has been made the admission of steam is shut off automatically,
and the rest of the stroke is performed by the expansion of
the steam, the velocity of ejection decreasing as the float
approaches the bottom of the cylinder. The exhaust valve
to the condenser is then opened, and as the steam rushes out
from above the float a vacuum is formed, and the water enters
the cylinder partly through the ejecting nozzle and partly
from a separate valve communicating with the water-space of
the surface condenser. The float is thus raised again to the
top of the cylinder, after which the operations described are
repeated. In the Sydromotor there are two cylinders working
alternately : Dr. Fleischer proposes in larger or swifter vessels to
* For particulars see the two pam- Fleischer. Kiel 1881. See also En-
phlets entitled Der Hijdromotor and gineeriny of September 9, 1881.
Die Pliysih des Eydromotors hj Dr.
CHAP. XIII. STEAM PROPULSION. 537
use a large number of similar cylinders in order to obtain the
necessary thrust. The cylinders are placed as high as convenient
in the vessel, so that the vacuum produced by the exhaustion of
the steam may be utilised in raising a volume of water above
the sea-level, and thus adding an effective " head " of water
to the steam pressure during the down stroke. In the Sydromotor
the mean speed of outflow is said to have been 66 feet per
second, rather less than 12 cubic feet of water being expelled
per second.
This general sketch of the principal features of the new
system must suffice. It will be seen to be very simple, to avoid
the waste-work of the engines used to drive centrifugal pumps,
and to lessen very much the resistances incurred in driving the
water from the pumps to the nozzles. On the other hand, there
must be losses from condensation of steam in the cylinders ; but
these are wood-lined, and it is asserted that the losses are not
serious. The velocity of ejection is high, reckoned as a mean,
and it is variable during the stroke ; while the quantity of water
operated upon is small ; neither of which conditions favours
eih'ciency. We are not in possession of sufficient trustworthy
information to enable an analysis to be made of the performances
of this vessel as compared with other jet-propelled ships or with
screw steamers. Dr. Fleischer claims for her a ratio of useful
to total work of 34 per cent, at full speed. This is below the
efficiency usually obtained in screw steamers at full speed, and
much below that in many such steamers (see page 571)). But it
should be noted that there are no records of dynamometric
towing experiments with the Hijdromotor, so that the efficiency
claimed for her is probably an estimate. Without pronouncing
any opinion on the merits of this novel and ingenious system of
propulsion we must now pass on ; but the particulars here given
may be of value, and the furtlier trials with the system will
be carefully watched by all persons interested in steam navi-
gation.
It has been urged by the advocates of jet-propellers that even
though they should prove less efficient than screws or paddles,
they should be adopted for vessels of war, because they have the
following advantages : — First, that they cannot be so easily
damaged in action or fouled by wreckage as the other propellers ;
secondly, that they give greater control to the commanding
officer in managing the machinery; thirdly, that they give
increased manoeuvring power ; fourth, that they can be used as
pumps to clear a ship rapidly of large masses of water in cases of
538 NAVAL ARCHITECTURE. chap. xiii.
accident or damage. The first and second claims may be
admitted, respecting the third, reference may be made to
Chapter XIV. As to the fourth, it is only necessary to remark
that the efficient realisation of this idea in minutely subdivided
war-ships would practically jeopardise that subdivision, the
maintenance of which is of far greater importance to the safety
of a ship than any possible increase in pumping power.* Jet-
propellers are undoubtedly well adapted for special vessels, such
as floating fire-engines, where pumping power has to be pro-
vided, as this power can also be made available for propulsion.
Saddle- Wheels.
Paddle-wheeL«, like jet-propellers, give direct sternward
momentum to streams of water, the reaction of which constitutes
the thrust or propelling force. These streams form what is
termed the "paddle-race: " and their cross-sectional areas depend
upon the area and immersion of paddle-floats. *' Feathering "
paddle-floats are now generally employed ; the common paddle-
floats being fixed radially upon the wheels. The s'peed of the
floats depends upon their radial distance from the centre of the
wheel and the number of revolutions of the wheel in a unit of
time. Suppose the centre of the floats to be 16 feet from the
centre of the wheel, and the wheel to make 16 revolutions per
minute, then speed of floats in feet per second (V) would be
given by
„ 2 X 3-1416 X 16 X 16 ^. ^ . , . , ,
V = Ycs ^ ^^'° ^^^^ (nearly).
If the speed of the ship is called v, the difference (V — v) between
that speed and the speed of the paddle-floats is termed the
s?*p of the paddles, and is usually expressed as a fraction of
V, or
V- v
Slip (per cent.) = y X 100.
Suppose in the example chosen — which is taken from an actual
* See a Paper " On the Pumping Journal of the Royal United Service
arrangements of Modern War-sliips," Institution for 1881.
contributed by the Author to the
CHAP. XIII. STEAM PROPULSION. 539
ship that the speed v is 224 feet per second (about 13 knots
per hour) :
Slip (per cent.) = ^^^M^ "^ ""^^ ^ ^^^ (nearly).
From 20 to 30 per cent, appears to be a fair average for the slip
of paddle-wheels \vhen working under favourable conditions : in
some cases even a greater slip occurs. Being usually placed
amidships, they operate on water which has its maximum stem-
ward velocity relatively to the ship, and this fact somewhat
reduces the efficiency. With a certain speed of revolution it
lessens the sternward momentum which the floats can impress
upon the paddle-race. With a certain indicated power, the
speed of the paddle-wheels may be increased in consequence of
working in the disturbed water, but the waste-work on the
engine, friction, " churning " of the water, (Src, will be also in-
creased ; so that there must be less efficient action than- if the
paddle worked in still water. If the motion of the water be
disregarded, and the paddles assumed to operate on water which
is undisturbed by the passage of the ship, it is possible to
express the thrust of the propeller in a simple form. Let
A = cross-sectional area of the paddle-race on both sides ; then,
if V and v have the same values as in the preceding equations for
slip of paddle-wheels.
Cubic feet of water acted upon per second = A . V ;
Thrust: or momentum created per") _ 2^y (V — v) lbs. nearly;
second in sea- water 3
the exact determination of A is not an easy matter. With the
common or radial float it is generally supposed to equal the
product of the length (or transverse measurement) of the floats
into their maximum depth of immersion ; whereas with feather-
ing floats it is assumed equal to the area of the float. Certain
rules have been established by experience for fixing the size of
the paddle-wheels, "the length of the floats, their breadth, and
maximum immersion. Mr. Scott liussell summarises these rules
as follows : *— The size of the paddle-wheel should be determined
by considering the intended speed of the ship, the average slip
of the paddles in similar vessels, and the number of revolutions
* See his work on Naval Architecture.
540 NAVAL ARCHITECTURE. chap. xiii.
])er minute considered most suitable for the engines.* The
height of the paddle-shaft and of the engines in the ship should
also be noted, in order to determine their effect on the stability.
In the fully laden condition of the ship the wheel should not
be buried in the water more than one-third to one-half its radius ;
in the light condition the upper edges of the paddle-floats should
be at least six inches under water when they are vertical. The
length (or transverse measurement) of the floats should not
exceed one-third or one-half the breadth of the shijD except in
special cases. In a radial or common paddle-wheel the number
of the floats should about equal the number of feet in the
diameter ; and the breadth of the floats should be about f inch
or 1 inch for each foot in the diameter. In a feathering paddle
the floats should be about one-half as numerous and twice as
large as the floats in a common paddle-wheel. These are only
approximate rules for deep-water steamers ; for shallow-draught
vessels these rules would not be followed, but the special
conditions on which a vessel was to be employed would be
considered.
The chief practical difficulty with paddle-wheels applied in
large sea-going steamers was connected with the variations in
their performance produced by changes in the draught of water
and the immersion of the floats. In performing a long voyage,
the consumption of coals and stores might produce a change of
draught amounting to several feet; and the paddle-floats which
were too deeply immersed to be -most efficient when the voyage
began, might not be sufficiently immersed when it ended. When
variations in draught are not considerable, the voyages being
short, and the changes in the weights small, paddle-wlieels can
be employed with the greatest success. Eolling motions, of
course, greatly affect the action of paddles in ships at sea, and
not merely influence their propelling effect, but give rise to
serious straining actions upon the propelling apparatus. A
paddle-wheel at one instant submerged far below its normal
depth, and having its revolutions retarded by the change, might
a few seconds after, on the roll of the ship in the opposite direc-
tion, be lifted almost clear of the water and " race " violently
* From tlie comparison of a great 40 to 45 revolutions were made, and
number of higli-speed paddle steamers, iu others as many as 70 revolutions.
we find that from 20 to 30 revolutions In fact, no rule can be laid down for
per minute were common, iu some cases the res'olutions.
CHAP. XIII. STEAM PROPULSION. 54 1
beyond the normal speed. In smooth water no similar disturb-
ances of the regular action of paddles occur; and they are
there applied with the greatest advantage.
Paddle-wheels, notwithstanding their direct sternward action
on the water, do a considerable amount of waste-work, besides that
which is effective in propelling a ship. This waste-work consists
in overcoming the resistance offered by the water to the entry and
exit of the floats, and in " churning " the water — driving it in
other than the sternward direction, delivering blows, &c. Various
devices have been proposed for lessening this waste-work, feather-
ing paddles being the most common. Mathematical investi-
gation shows that, with the best paddle-wheels, the waste-work
at least equals the work done in giving sternward motion to the
paddle-race.
The action of the paddle-floats must exercise some influence
upon the stream-line motions of the water past the ship, and con-
sequently afi'ect the resistance. The water in the paddle-race
would, if the ship were towed, close in around the stern, and
probably have some small motion in the direction of her advance,
forming a " wake " ; but by the action of the paddles it is driven
astern with a considerable velocity, and this change must be
equivalent to an increase in the resistance experienced by the ship
when self-propelled, as compared with the resistance measured by
a tow-rope strain. It is, however, to be noted that the paddles
would rarely, if ever, be immersed to more than one-third or one-
half of the draught of water, so that the disturbance of the stream-
line motions may not extend to the greater portion of the water
surrounding the ship and at any instant atfected by her motion.
The "augment of resistance" due to the action of paddle-
wheels has been made the subject of experiment at Amsterdam
by Ur. Tideman.* His experiments were conducted on models,
both of ships and paddle-wheels, and the results are interesting ;
but the trials were not sufBciently numerous or exhaustive to be
conclusive. These trials indicate considerable variations in the
ratio which the augment of resistance bears to the tow-rope
resistance ; both for a particular model moving at different speeds,
and for different models moving at an identical speed. In the
case of one model, paddles, a single screw and twin-screws were
tried ; and the paddles caused a greater augment of resistance
* See the Keport in tlie Memorial van de Marine Q)" Aflevering): Atn-
sterJam, 1878,
542 NAVAL ARCHITECTURE. CHAP. xiii.
than the screw?. It must not be supposed, however, that this
always holds good ; and further experimeuts in this direction can
{iloue enable a correct judgment to be formed. Except as a
matter of scientific interest, such experiments are not likely to
be made : since paddles are only used, at present, in special
classes of ships, where the screw cannot be conveniently
employed.
Comparing paddle-wheels with water-jets, delivered by centri-
fugal pumps as in the Waterivitch and other vessels, it appears
that the waste-work of jDaddles is probably not greater than, if so
great as, that of jets, when allowance is made for the frictional
resistances experienced by the water in passing from the inlets
to the nozzles. Paddle-floats, moreover, can be made much
larger than can the sectional areas of nozzles without serious
practical inconveniences. Hence, on the whole, paddles are
commonly preferred to jets, and they are equally applicable even
in the shallowest waters, except, perhaps, in cases where very
narrow channels have to be navigated ; but even under these
special circumstances the paddle is commonly used, being placed
astern instead of amidships. When paddles are fitted so that
they can be disconnected, and the wheels on opposite sides of a
ship worked in opposite directions, they give as great manoeuvr-
ing power under steam as water-jets ; besides being more efficient
propellers. On the other hand, paddles are more liable to injury
than the nozzles for water-jets : and this difference is of special
importance in war-ships.
As compared with the screw-propeller, paddle-wheels are dis-
tinctly inferior for general sea service for the reasons given on
page 540. In smooth water trials the paddle does not compare so
badly with the screw, and is thought by some authorities to be
about equal to the screw in efficiency, although this opinion is
open to question. For shallow-draught vessels of high speed
the paddle-wheel is usually better adapted than the screw.
Paddle steamers have also attained some of the highest speeds
yet reached on the measured mile. Her Majesty's yacht Victoria
and Albert steamed at a speed of 17 knots ; the Holyhead packets
attained 17f to 18 knots ; the Channel steamers recently built
attained 18^ knots, and so did the Mahrousse, a paddle yacht
built in this country for the Viceroy of Egypt. All these speeds
are very high, even when compared with the measured mile
speeds of most of the finest screw steamers in existence. They
are only exceeded by the speeds of special vessels like the Iris
and Mercury of the Roj'al Navy, and those of the torpedo-boats.
CHAP. XIII. STEAM PROPULSION. 543
The Screw-Propeller.
Before proceeding with the discussion of the special features
of screw-propellers, it will be desirable to explaiu a few of the
terms that will be frequently employed. The diameter of a screw
is measured fi'om the circle swept by the tips of its blades during
their revolution ; the area of this circle measures the screw-disG.
The pitch of a screw is the length of a complete turn measured
parallel to the axis ; in other words, it is the distance which the
screw would advance in one revolution if it worked in a solid nut.
The speed of a screw is the distance it would advance in a unit of
time if it worked in such a nut, and is clearly equal to the
product of the number of its revolutions, in that unit of time, by
the pitch. The difference between the speed of the screw (say,
V feet per second) and the speed of the ship (y feet per second)
is usually termed the slip of the screw, and expressed as a per-
centage of the speed of the screw. For example, a screw of
which the pitch is 14 feet makes 72 revolutions per minute, and
drives a ship 8*2 knots per hour : required the slip.
Speed of screw = V = — ^ — = 16-8 feet per second.
Speed of ship =v = 82 x 1-688= 138 „ „
Slip (per cent.) = -^ X 100 = -^ X 100 = 17-85.
This slip (V — v), if the screw worked in water undisturbed by the
passage of the ship, would clearly be the sternward velocity
relatively to still water of the particles in the propeller race. In
practice, however, the screw works in water which has been
disturbed by the passage of the ship ; and hence, strictly speaking,
the slip (Y — v) should be termed the apparent slip. The real slip
may be defined as the total change in the velocity of particles in
the race produced by the action of the propeller. The passage
of the ship produces a forward motion of the surrounding-
particles, and forms a wake (as explained in Chapter XL), in
which the screw works ; it then has to destroy this forward motion
before it can impress a sternward motion, relatively to still water,
upon the race ; but the apparent slip takes account only of that
sternward motion, and hence may differ considerably from the
real slip. In some cases the curious phenomenon of apparent
544 NAVAL ARCHITECTURE. chap. xiii.
" negative slip " is observed, the speed of tlie screw being less
tliau that of the ship ; but more commonly the apparent slip is
positive, and varies from 10 to 30 per cent., 20 per cent, being
the average in very many cases.
The theoretical investigation of the action of a screw-propeller
involves many serious difficulties. The curved helicoidal surfaces
of the blades are set obliquely to the line of motion, and conse-
quently communicate rotary as well as stern ward motion to the
water in the screw-race. The thrust of a screw-propeller is
measuied, of course, like that of a paddle or jet, by the sternwarcl
momentum generated in the race during a unit of time ; but
while this principle is accepted, its application to the estimate of
the actual thrust of a particular screw necessitates certain assump-
tions and the use of data obtained experimentally. Moreover,
the determination of the efficiency of a screw-propeller requires,
as was shown in the case of a jet, a determination of the ratio of
the useful work done by the propeller to .the total work; and
here again difficulties arise. As a screw revolves and communi-
cates motion to the race, its surfaces experience frictional
resistances from the surrounding water, which frictional resistances
lessen the effective thrust, and increase the work which has to be
done in turning the screw. Besides this, the rotary motion given
to the water must be accompanied by some centrifugal action and
by a diminution in the pressure of the screw upon the water,
resulting in a decrease of thrust. Nor can the question of the
supply of water to the screw, as affected by its position and the
form of the stern of a ship be overlooked, while the " augment
of resistance," due to the action of the screw, is a matter of the
utmost importance. All the foregoing difficulties exist even when
the form, size, area, and number of blades, and other particulars
are assumed to be known for a screw-propeller; but in
practice these features also require to be determined, and
upon that determination the efficiency of the screw will largely
depend.
This enumeration of the difficulties surrounding an investiga-
tion of the efficiency of screw-propellers has not been put forward
as a justification of the view which has been sometimes expressed
that any such theoretical investigation must be of little value,
but rather as an explanation of the fact that no general theory
has yet found acceptance, notwithstanding the labours of many
eminent writers on propulsion. Amongst these writers the late
Professor Eankiue and the late Mr. Froude stand pre-eminent ; a
CHAP. XIII. STEAM PROPULSION. 545
brief sketch of their methods of procedure may therefore be of
interest.*
Professor Kiiukine assumed as the basis of his investigation
that the number and surface of the blades in a screw would be
adjusted by rules derived from practical experience, so that the
whole cylinder of water in which the screw revolved should form
a stream flowing aft; that is to say, the race was assumed to
consist of a cylindrical column of water having the screw disc,
less the sectional area of the boss, for its athwartship section, the
flow of water to the screw being supposed to be ample. The
motion of the particles of water in this race was supposed to be of
a spiral character, and the particles at a given radial distance
from the axis of the screw were assumed to have identical
motions impressed upon them by the action of those portions of
the screw blades which would be cut off by the cylinder having
the same distance as its radius and a very small thickness.
Hence it followed that the race could be imagined to be made up
of a series of concentric hollow cylinders, " each having a rotatory
motion and a sternward motion : these motions would be, in
general, different for each cylinder, so that they would slide
throuo^h each other and rotate within each other." On these
assumptions it was possible to approximate (1) to the quantity of
water acted upon by the screw in a unit of time ; (2) to the
sternward momentum generated in a unit of time, which
measured the thrust, if friction were neglected ; (3) to the loss of
thrust and increase of waste-work due to the friction of the
screws; (4) to the effect upon the efficiency of the screw produced
by its action in water which had been disturbed by the passage
of a ship. All this Kankine did in a manner worthy of his high
reputation, and his investigation will always maintain its value as
the first attempt in a new direction. Further, he gave examples of
the application of his formulae to the numerical calculations for
the screws of actual ships. In accordance with his fundamental
assumptions he deteiTuined approximately the disc area, or
diameter, for the screw appropriate to any ship, but did not
* See Professor Rankine's Paper of the Transactions. For an excellent
" On the Mechanical Principles of the summary and extension of Rankine's
Action of Propellers," in vol. vi. of the method see also a Paper "On Screw-
Transadions of the Institution of Propellers," by Professor Cotterill in
Naval Architects; and Papers by Mr. No. 3 of the Annual of the Royal
Froude in vols, vi., viii., and xix. School of Naval Architecture.
2n
546 NAVAL ARCHITECTURE. chap. xiii.
attempt to fix the areas or numbers of the blades, leaving them
to be determined by dediictiou from experience. It will be
obvious, however, that in this determination of the forms and
numbers of the blades necessary to give motion to a complete
<'ylindrical column of water lies a great practical difficulty, and
hence it followed that this masterly investigation had little
influence on practice.
The investigation of the efficiency of screw-propellers made by
the late Mr. Froude proceeded on entirely different lines from
those followed by Professor Eankine. ]\Ir. Froude began by a
consideration of the frictional and normal resistances experienced
by a plate moved obliquely through water (see page 436), making
use of the results of experiments conducted by Colonel Beaufoy
and himself, as well as of the mathematical investigations of Lord
Eayleigh. He then traced out the analogy between the motion
of such a plate and a small portion or element of the area of a
screw surface, which is set obliquely to the plane of rotation and
made to revolve around the axis of the screw. For such an
element (or unit of area) of the screw surface, the normal pressure
and frictional resistance were estimated, as if it alone were acting
on the water, allowance being made for the angle of obliquity,
the speed of rotation, the speed of the ship, and the true slip.
In this manner the propulsive force or longitudinal thrust for
each element of area, and the transverse component of the forces
operating on it, were ascertained. The effective work done is, as
before explained, that expended in overcoming the ship's
resistance through the distance she advances in a unit of time ;
the total work done is that expended in overcoming the transverse
component of friction and normal pressure through the distance
the element of area travels in its circular path in the same unit
of time. lu his published paper Mr. Froude confined his mathe-
matical formula) to one such unit of the screw surface, and did
not attempt to integrate the expressions so as to represent the
varying radial distances and obliquities of the elements making
up the whole screw surface. This fact must be borne in mind in
considering the conclusions stated below, for it is obvious that the
aggregate effect of the total surface of a screw-propeller must
differ from the summation of the effects of each unit of area
estimated on the hypothesis that it alone is acting. That
hypothesis assumes that the momentum generated per unit of
time is due to the action of the unit of area upon water which
would be undisturbed but for its action, whereas most of the
corresponding units of area in a screw surface must come into
CHAP. XI II. STE'AM PROPULSION. 547
operation upon water which has been disturbed by the action
of adjacent portions of the area. Moreover, it is clear that in a
propeller with two or more blades there may be interference of
the action of one blade with another, as well as the interference
just mentioned of adjacent portions of the same blade. This
disturbing element in the problem can only be dealt with at
present experimentally.
Eeverting to Mr. Froude's investigation, it may be added that
he virtually assumed in his mathematical formulae the whole
screw surface to be converted into an equivalent plane area with
a constant angle of obliquity. For the main purpose he had in
view this assumption was permissible, although not strictly
accurate. He chiefly desired to show that increase in the
diameter and surface of sm-ew-propellers, although it enabled a
larger quantity of water to be operated upon, might be accompanied
by such an increase in the waste-work of frictional and edgeways
resistance as w^ould make it preferable, on the whole, to use screws
of less diameter and surface, but greater pitch. And it must be
admitted that this lesson was much needed at the time. Another
point which should be noted with reference to Mr, Froude's
investigation is the omission of any attempt to express the
influence which the stream-line motions and frictional wake
may have upon the performance of a screw placed at the stern
of a ship. In other papers ^Ir. Froude had most ably outlined
the great features of that influence ; but in this paper he only
alluded to its importance, and to the complex nature of the
phenomena.
It now remains to add a brief summary of the [rincipal deduc-
tions made by Mr. Froude from his mathematical investigation :
they are as follow :— First, for maximum efficiency the mean
effective angle of the screw-blade measured from an athwartship
plane, or '•' pitch-angle," should be -15 degrees ; which is obtained
when the pitch is about twice the extreme diameter. Second, for
maximum efficiency the slip-angle must vary directly as the square
root of the coefficient of friction, and inversely as the square
root of the coefiicient of normal pressure, which gives a slip of
about 12JL per cent., with the values of the coefficients adopted
in the investigation. This is the veal slip; the apparent slip
will usually be less, and will vary according to the amount and
character of the disturbance of the water in which the screw
Avorks. Third, that for maximum efficiency the area of
the screw-blades may be expressed approximately by the
formula.
2x2
548 NAVAL ARCHITECTURE. chap. xiii.
Area (in square feet) = 89 x —^ 5
where K = the resistance of the vessel (in pounds) at her maxi-
mum speed.
V = her maximum speed (in feet per second).
Fourth, that -since at moderate speeds the resistance of a ship
varies as the square of her speed, the same propeller should,
within those limits of speed, drive a ship with the same per-
centage of slip; but that outside those limits of speed the
percentage of slip should increase. Filth, that for moderate
speeds, if the blade-areas of the screws of two similar ships have
the ratio of the squares of the respective dimensions, the per-
centage of slip should be the same. Sixth, that, if two ships
have the same resistance at different speeds, the area of screw-
blades which will overcome the resistance while maintaining
a given slip, will be less, in the ratio of the squares of the speeds,
for the ship which has the higher speed. The last three deduc-
tions are obtained from the formula for blade-area given above.
Seventh, tliat the maximum efficiency which can be realised
under the most favourable conditions is about 77 per cent. ; but
that the percentage of slip might be increased considerably
(even as high as 30 per cent, with the screw working in undis-
turbed water) without any serious decrease of efficiency in screws
of ordinary proportion.
Limits of space prevent us from making any comparison
between the results of steamship trials and these deductions.
It cannot be doubted, however, that this new departure, and the
numerous trials with model screws made bv the late Mr. Froude,
and since his death by Mr. E. E. Froude, will result in very
considerable extensions of our knowledge of the action of screw-
propellers. Experimental investigations of this nature, made
Avith the ingenious apparatus devised by Mr. Froude, by which
the greatest accuracy of observation is secured, and supplemented
by mathematical analysis, will probably do much more to advance
our knowledge than any theoretical investigation. But, to make
such model experiments of the fullest value, the results must
be carefully compared with the performances of similar full-scale
screws in actual ships.
In concluding these remarks on the theory of the screw-
propeller, allusion must be made to the valuable labours of
Professor Cotterill, who has shown how the two methods of
Eankine and Froude are related to one another, and under what
CHAP. XIII. STEAM PROPULSION. 549
circumstances they will yield identical results. His Memoir
on this subject, mentioned on page 532, will well repay the perusal
of all who are engaged in steamship design.
Passing from tliis branch of the subject it may be well to
glance at some important features of screw-propulsion, which
have been certainly ascertained and have great practical interest.
In the majority of screw steamers there is a single-screw, placed
in an aperture between the body of the ship and the sternpost to
which the rudder is hung. In a few cases the single-screw has
been placed abaft the rudder, no aperture being requisite.
Twin-screws, one under each counter, have been largely em-
ployed in war-ships during the last ten or twelve years ; in
merchant ships their use has hitherto been rare, except in cases
of shallow draught, but several ocean-going steamers have been
constructed lecently with twin-screws. A singular arrangement
of twin-screws has been adopted in some river steamers. For the
purpose of bringing the shafts closer together, the screws have
been placed with a short longitudinal interval between them,
and the circles swept by their inner tips have overlapped. This
can scarcely have favoured efficiency. Another method of using
two screws, adopted in the cigar-ships and in certain tug- vessels,
has been to run the shaft throughout the length, and to have a
screw at the bow as well as at the stern ; tlie primary object in
this arrangement may be supposed to be the power of rapidly
reversing the course witliout turning. In some ferry-steamers a
similar arrangement has been made with two continuous shafts,
each with a bow and stern screw. A few instances occur where
an annular shaft rotates round a solid shaft, the two working in
opposite directions, and each carrying its own screw-propeller.
This is the arrangement adopted in submarine locomotive
torpedoes. Multiple screws have also been used in special cases.
Some of the shallow-draught vessels built for service on the
I^Iississippi during the American Civil War had four screws; the
Russian circular ironclads were fitted with six screws, and the
imperial yacht Livadia has three screws. Of all these varied
arrangements of screw-propellers we propose only to consider
two, viz., the single and the twin-screw systems.
One condition essential to the efficiency of all arrangements of
screws is that they shall have a good supply of water, in order that
the race may have its full sectional area. Amongst tlie more
important circumstances influencing the supply of water to the
screw may be mentioned the form of the stern of the ship, the dis-
550 NAVAL ARCHITECTURE. chai'. xiii.
tance of the screw abaft the stern, and the immersion of the upper
blades when they are passing through the vertical position. If
the screw is not sufficiently immersed, it will create considerable
surface disturbance, have a less compact and well-defined race,
and do more waste-work. If the stern is bluff or very fall, the
efficiency of a single-screw will be decreased because the water
cannot flow freely to certain parts of the screw-disc, which are
masked by the sternpost and body of the ship. If the screw is
close under the stem, as it usually is in single-screw ships, it has
to act at some disadvantage as compared with what it would have
to do if placed further astern. Fineness in the " run " of single-
screw steamships is now recognised as a desirable and necessary
feature. In the earlier periods of steam-propulsion, this was not
so well understood, and in many of the blnff-sterned vessels of
the Eoyal Navy, converted from sailing into steamships, the
prejudicial effect of their forms on the action of the screw was
most marked. One case alone can be cited out of the many on
record. The screw-frigate Dauntless, built in 1848, was first
tried with a full stern, and her performance being unsatisfactory,
she was lengthened aft about 10 feet, and made of much finer
form in the run. In her earlier trials, when the displacement
was 2300 tons, she was driven at a speed of 7'3 knots with 836
horse-power (indicated). After the alteration, with the same
screw and nearly the same displacement, the ship attained a
speed of 10 knots with 1388 horse-power; but had the form
remained unaltered the engine-power for that speed would have
been at least 1900 horse-power. The alteration of the stern and
consequent decrease in resistance, as well as the better supply of
water to the screw may be assumed therefore to have effected a
saving of no less than 30 per cent, in the power.
From the remarks made above it will have been seen that
screw-propellers placed near the stern of a ship most cause a
more or less considerable " augment " of the resistance which that
ship would experience if towed. Under the latter circumstances
the stream-lines (as explained on page 445) close in around the
stern and produce a forward pressure, which counterbalances to a
large extent the stern ward pressure of the streams upon the bow.
But when rapidly-revolving screws are placed close to the stern^
and made to give sternward momentum to large quantities of
water, there is a lessened forward pressure on the stern, and a
consequent increase in the resistance. The proportionate amount
of the augment is governed by various considerations, and
therefore has widely different values in different ships. IMost of
CHAP. XIII. STEAM PROPULSION. 55 1
our exact iuformation 011 this subject is due to the experimeutal
researches of the late Mr. Fronde ; Dr. Tidemau iu Holland and
Chief-Engineer Isherwood in America having- added some useful
data. In single-screw ships with the screws before the rudder-
post, the augment is said to have varied from 20 to 45 per cent, of
the tow-rope resistance ; the highest values occurring in wood or
composite ships with thick rudder-posts and rudders. These
rudder posts, &c., are found to represent about 10 per cent, of the
tow-rope resistance iu some cases. If the single-screw is carried
abaft the rudder the augment is considerably reduced. In fact
i\tr. Fronde stated, as the result of direct experiment that, with a
single-screw placed one-third or one-fourth of the extreme
breadth of a ship clear of the stern, the increase of resistance
produced by its action was only one-fifth of that produced by the
screw iu its ordinary position. No screw has been placed so far
aft as this in an actual ship, nor is it likely to be so placed on
account of the risks involved ; there can be no question, however,
that for efficiency as a propeller the position abaft the rudder is
usually to be preferred. Trials made in torpedo-boats confirm this
statement, although the difference in efficiency is not very great,
and for the sake of greater haudiness it is preferred to place
the rudder abaft the screw.
Dr. Tideman's results are contained in the publication men-
tioned on page 541 ; they are numerous and interesting, showing
considerable variations in the augment with ships of different
form. This broad conclusion is confirmatory of the experiments
made by Mr. Fronde, wherein it appeared that different degrees
of fulness in the "run" or after part of a ship immediately
before the screw very sensibly influenced the augment of re-
sistance. It would appear that Dr. Tideman did not use rudder-
posts, &c., in his trials with single-screws ; and this would
necessarily affect the values given by him as compared with those
above stated for single-screws.
The trials made by Chief-Engineer Isherwood, U.S.N., were
conducted on a steam-launch about 54 feet long, and are ex-
cellent examples of what might be done, on a larger scale, in
the record and analysis of steamship performance.* In order to
determine the resistance of the launch it was towed, at various
speeds, with no screw attached, the tow-rope strain being
measured by a dynamometer. Other trials were made with
screws of different sizes and shapes, the thrusts corresponding to
* Sec the Report of the Secretary of the United States navy for 1874.
552 NAVAL ARCHITECTURE. chap. xiii.
various speeds being measured by a dynamometer mounted on
the shaft. The materials were thus obtained for a comparison of
the tow-rope strain with the thrust of the screw-propeller at
different speeds ; and although the experiments are not exactly
correspondent to those of Mr. Froude and Dr. Tideman, owing to
the screw being attached to the vessel, the difference is not
important. The tow-rope strain for a speed of 7*5 knots was
found to be about 725 lbs. ; the corresponding thrust being
867 lbs. or about 20 per cent, greater than the tow-rope strain.
At lower speeds the thrust was not nearly so great in proportion
to the tow-rope strain.
For twin-screws fitted in the usual manner under each counter,
there are a-yriori reasons tor anticipating that the augment of
resistance will be less in ships of good draught, than with single-
screws fitted in the ordinary manner. These screws are carried
some distance clear of the body of the ship ; and there is nothing
to prevent the free flow of water to them unless the supports to
the outboard portions of the shafts are badly arranged. In deep-
draught sliips the screws are well immersed, and their sweep
leaves untouched a considerable part of the streams flowing past
the ship near the region of the water-line, where the form is
fuller than below. In vessels of very shallow draught these
conditions may not hold good; but then single-screws are
frequently not applicable, and the choice lies between twin-
screws and paddles. These general conclusions are borne out by
the few experiments made by the late Mr. Froude on models of
twin-screws, which show that they cause a less augment of
resistance than single-screws placed in tlie ordinary manner. In
the case of the Iris, for example, the augment was about 10^ per
cent, of the tow-rope strain. It is probable, moreover, that with
increased fulness of form in the run the advantage of the twiu-
screws in this respect Avould be increased ; but further experi-
ments are needed to settle this matter.
Dr. Tideman has also made experiments on the augments of
resistance produced by single and twin-screws carried behind the
same model. These experiments show a marked inferiority in
the augment caused by the single-screw; and therefore do not
agree with the experiments made at the Admiralty Experimental
Works. We are not in possession of all the facts as to the
Amsterdam experiments ; but it would appear that the single-
screws were tried without any rudder-post or rudder behind
them, which has been shown to be a great advantage, and that
the Dutch method of supporting the outboard portions of the
CHAP. XIII. STEAM PROPULSION. 553
shafts in twin-screw ships is less favourable to the action of the
screws than the corresponding method in the English ships.
Without in the least desiring to express any doubt of the accuracy
of the results obtained by Dr. Tideman, we therefore attach the
greater value to those obtained by Mr. Fronde, as representative
of English practice. And this opinion is supported by the com-
parative performances of single and twin-screw steamers to which
reference will be made hereafter. In the Imperial Eussiaii yacht
Livaclia, the augment of resistance produced by the action of her
three screws is said to have been 22 per cent, of the tuw-rope
resistance.
In order that the best results may be obtained with twiu-
screws, great care must be bestowed upon the arrangement and
shaping of the sti-uts, tubes, &c., supporting the outboard portion
of the screw-shaft-!. Otherwise very considerable eddy-making
resistance may be caused ; and the nett resistance of the hull
proper — stripped of these excrescences —may be increased by a
large percentage, which would balance, or perhaps exceed, the
diminished aui^ment due to the action of the screws. With care,
however, this adventitious resistance may be avoided for the
most part ; and the simple rules to be followed have already been
stated on page -±19. It may be added that as the sizes and nett
resistances of ships increase, the relative importance of the
resistances of struts, &c., diminishes; but this is no reason for
treating them as unimportant even in the largest ships.
Any comparison of single and twin screw-propellers would be
incomplete which did not take account of their relative advan-
tages of position as regards the " Irictional wake " of a ship.
Mr. Froude first drew attention to the influence upon economical
propulsion which might result from the utilisation of some of the
vis viva of this wake by the screw ; and other writers have since
amplified his treatment of the subject.* This frictioual wake
must be distinguished from the forward motion of the stream-lines
at the stern described on page 445 for a frictionless fluid. The
actual wake of a ship, of course, combines the stream-line motions
with those due to the frictional drag of the skin upon the water ;
but attention is now devoted exclusively to the frictioual wake.
* See Papers by Mr. Froude in the also desires to aclcuowledge liis ubliga-
I^rawsacijons of the Institution of Naval tions to Mr. R. E. Froude for more
Architects for 1865 and 1867: and a recent experimental data on this
Paper by Professor Osborne Reynolds in subject,
the Transactions hx I'd' Q. The Author
554 NAVAL ARCHITECTURE. chap. xiii.
The momentum of that wake has already l^een reckoned in the
resistance of the ship ; and were there no propeller at work — as
is the case in a sailing ship — the water in the wake would continue
to move forward after the passage of the sliip, until by its dispersion
over larger quantities of water and its degradation by resistance
from adjacent masses of water, the motion gradually disappeared
at some distance abaft the ship. Hence it will ba evident that
a single-screw revolving close to the stern of a ship, and pervading
in its motion a considerable portion of the sectional area of this
frictional wake, may utilise some of its vis viva, and gain in
effective thrusi. Twin-screws, on the other hand, being carried
clear of the body of the ship, do not have a similar opportunity
of gaining in effective thrust; and this tells against their
relative efficiency. To what extent this advantage of single-
screws compensates for their greater augmentation we arc not
yet in a position to decide.
Still another feature affecting the relative efficiency of single
and twin-screws is the unequal forward motion of the wake at
different depths. Speaking generally, it may be said that the
greatest forward motion occurs near the surface, and the least
near the depth of the keel ; the actual variations in speed at
different depths must be very different in different ships. Pro-
fessor Reynolds, remarking on this circumstance, pointed out the
fact that the upper blades of a single-screw must do the larger
share of the propulsion, and that it was possible for the lower
blades to be doing little work, or even hindering the action of
the upper blades. Shocks and vibration may also result from
the rapid, revolution of the blades through layers of the wake
having such unequal forward motions. Accepting these con-
clusions as fairly indicative of existing conditions, it will be
obvious that single-screws are less favourably situated than
twin-screws, not being so well immersed, nor so clear of the body
of the ship, while they are of greater diameter and consequently
sweep through layers of the wake, for which the inequality of
forward motion is greater. The question of the deeper immersion
of the screws deserves separate consideration ; as it constitutes
a marked advantage for twin-screws in smooth water steaming,
and still more at sea. All that can be said, hort'ever, is that the
effective thrust of a screw has been shown experimentally to
be greatly reduced when it is near the surface.* Common
* See Proressor EejnioUs' experi- the Institution of Naval Architects for
ments recorded in the Transactions of IST-i.
CHAP. XIII. STEAM PROPULSION. 555
experience confirms these experiments and shows that a partial
emersion of a screw results in serious diminution of thrust,
frequently accompanied by racing of the engines unless they
are fitted with "governors."
Tliese remarks on the comparative efficiency of single and
twin screws have been carried to some length, because of their
important bearing upon the future of steam navigation. The
constant additions which are being made to the sizes and speeds
of ships make it necessary to use greater and greater powers;
and the question arises whether it is desirable to put all ^ this
power upon a single shaft and a single screw, or to duplicate
the machinery and the propellers. The risks run tlirough
accidents to the shafts or propellers of single-screw steamers
receive too frequent illustration in practice to need comment
here ; and the proportionate decrease in sail-power, now generally
accepted in the larger steamships, makes the consequences of
disablement of the propelling apparatus more serious than they
were formerly. Even if it could be shown that twin-screws were
less efficient' propellers than single-screws, their advantages in
other respects would recommend them for adoption at least in
the larger classes of ocean-going merchant steamers. There is
far less risk of total disablement of the propelling apparatus, and
with eitlier screw at work a twin-screw ship is not merely under
control, but able to make good headway. Twin-screws give
greater handiness to a ship, and enable her to be manceuvred
in case of serious damage to the rudder or steering gear. The
duplication of engines and propellers also enables the water-
tight subdivision of the engine-rooms to be increased, as
explained on page 26. Against these undoubted advantages
are to be set the following considerations: — That twin-screws
would be more liable to damage than single-screws when ships
are going into or out of docks, coming alongside wharves, or
taking the ground. That more space might be required for the
machinery and shaft-passages, and a larger engine-rooni staff
found necessary because of the duplication of the machinery;
while the weight and- cost of the twin-screw engines might be
greater than those for single-screw engines. Of these considera-
tions the only one which seems to have much weight is that
relating to possible damage to the propellers in harbour; but
this risk may be lessened by the use of some kind of " guard "
fitted over the screws, and will scarcely be thought to outweigh
the undoubted advantages of twin-screws. Already a number of
556 NAVAL ARCHITECTURE. C^ap. xiii.
twin-screw merchant steamers have been built, and it is probable
that their employment will be extended, as many shipowners,
shipbuilders, and engineers have expressed their approval of this
system of propulsion. In the Eoyal Navy all recent ships of
large size or high speed have been fitted with twin-screws: and
this practice has been imitated in all the principal foreign navies.
Tile gains in raanosuvring power, watertight subdivision, and
security against disablement have been the primary motives for
the adoption of twin-screws in war-ships : but experience with
those vessels has shown that in addition to these advantages
twin-screws compare favourably with single-screws in their
efficiency as propellers.
The details in support of this statement cannot be given here,
but they are already published,* and include a careful comparison
of the trials of a considerable number of single and twin-screw
ships. As a rough indication of the results, although not an
accurate comparison of efficiency, it may be stated that the ratio
of indicated horse-power to wetted surface, was found to be 11 per
cent, in favour of one group of twin-screw ships as compared
with a group of single-screw ships of approximately similar form
and equal size. For two other groups the advantage of the twin-
screw ships rose to 18 per cent. ; the sizes and speeds of the ships
being greater. It cannot be asserted as yet that equal advantages
would certainly be obtained in merchant steamers, which have
greater lengths and fineness of form, and consequently experience
less resistance than war-ships of equal displacements at high
speeds. But the very satisfactory results attained in war-ships
may encourage private shipowners to make trials of twin-screws,
with the hope that, at least, no loss of efficiency will be involved
as compared with single-screws. ,
From the brief sketch which has been given of the present
slate of the theory of the screw-propeller it will be evident
that we are yet largely dependent upon experiment and ex-
perience for the selection of suitable forms and proportions
of screw-propellers. There have been numberless patents,
proposals, and trials of screws during the last forty-five years,
* See a Paper contributed by the performances of the earlier twin-screw
Author to vol. xix. of the Transactions vessels, built by Messrs. Dudgeon, will
of Institution of Naval Architects. An be found in vol. vi. of the Transactions,
interesting summary of facts as to the
CHAP. Xlll.
STEAM PROPULSION.
557
and no settlement has yet been reached. Not a tew of these
proposals have been chimerical ; and many of the experimental
trials have been made under conditions which prevent any
satisfactory analysis of the results. On the other hand, some
of the trials have furnished valuable information which has
subsequently been applied in practice.* Still it remains true
that in any case lying outside the region of precedent and
experience the selection of the most suitable propeller —
including in that determination the diameter, pitch, form,
and area of blades, &c., of the screw or screws — is a matter
for experiment. And it is also true that the choice of the
FIG.I26 a
4-- f
t-i/
^ 5000
i~ 3000
-^ 2000 |-
---!-—+
-/^/\ j ■ — + 4-OOQ
3000
i\caU of. Speed of Sliifi in. Knots per Sout
propeller exercises frequently a very marked effect upon the
expenditure of power required to attain a given speed. Many
illustrations might be given of these statements, but only one
or two can be selected.
The case of H.M.S. Iris is one of the most recent and
remarkable. When first tried on the measured mile she had
four-bladed screws of 18 feet 6^ inches diameter, with a mean
pitch of 18 feet 2 inches, and a blade-area of 194 square
feet. The powers corresponding to various speeds were deter-
mined, and this information was used for the construction of
the curve of indicated horse-power AAA in Fig. 126rt. In that
diagram, abscisste measurements represent speeds in knots, and
* For an excellent summary of facts bearing on this subject, see Mr. Bourne's
Treatise on the Screw Propeller-
558 NAVAL ARCHITECTURE. chap, xi 11.
ordinates represent the indiccited horse-powers corresponding to
the several speeds. The results of this series of trials were very
disappointing, and it was decided to remove two of the four
blades from each screw, leaving all other conditions unchanged.
With this reduction in blade-area the curve of indicated horse-
power, determined from another series of trials, fell to BBB,
Fig. 126a. The highest power developed was 4369 horse-
power, and the corresponding speed vras 15f knots, whereas
in the lirst series of trials 6200 horse-power was required for
15f knots, and 4369 horse-power corresponded to only 14?;
knots. These remarkable results led to fresh trials. The
third series of trials was made with four-bladed screws, 16
feet 3^ inches in diameter, 19 feet 11^ inches pitch, with a
blade- area of 144 square feet ; and the results are graphically
recorded by the curve CCC in Fig. 126a. The performance
will be seen to agree very closely with that of the preceding-
series of trials. Lastly the vessel was iEitted with two-bladed
screws, 18 feet li inches in diameter, 21 feet 3:^- inches pitch,
and having a blade-area of 112 square feet. The trials made
with these propellers are recorded in the curve DDD, and
the performance will be seen to be rather better than that
of either the second or the third series. Considerable vibration
took place, however, with these screws at certain speeds, although
there Avas no troublesome vibration at the full speed of 18*6
knots ; and it was decided to accept the four-bladed screws
of the third series as the working propellers. A most thorough
analysis of these trials has been made by Mr. Wright, Engineer-
in-Chief to the Eoyal Navy; but there are many matters in
the comparative performances of these screws ^vhich have, as
yet, not received satisfactory explanation.* The broad fact
remains, however, that with nearly the same indicated horse-
power, and with practically the same number of revolutions
of the engines per minute, a change in the screws enabled
the speed to be increased from 16i knots to 18^ knots per
hour. Or, to state the case somewhat differently, whereas on
the first trial a speed of 16^ knots required 7500 horse-power
and 91 revolutions, on the third series of trials an equal speed
was attained with 5100 horse-power and 85 revolutions.
Another illustration of the influence which the choice of
* For a full account of these trials, Paper in the TraJJSfflcito/is of the Insti-
andananalysis thereof, see Mr. "Wright's tution of Naval Architects for 1879.
CHAP. XIII.
STEAM PROPULSION.
559
a suitable propeller may have upon the performance of a
steamer, may be taken from iuformatiou placed at the dispo.sal
of the Author by Mr. Yarrow. It was desired to determine
the best form of propeller for a torpedo-boat of high speed,
and a long series of trials was undertaken, no less than twenty-
live different screws being tried progressively, so that curves
of indicated horse-power could be drawn for each. From
these trials Ave have selected two extreme cases, and recorded
the results in Fig. 126&. The curve AAA in that diagram
records the ascertained performance of a two-bladed screw of
5 feet 6 inches diameter, 4 feet 0 inches pitch, having a blade-
area of 496 square inches — with 560 horse-power indicated this
nai?et.
/J 20 21 22 23 24
SOO—^c-
/
' ■ i
1 i
w/ ^x
i ;
1 /\
/ i 4
V \
y 1 i
1 '1
: r i
; ._ _ J \ 1
1
' 1
t
550
y^
500
. ^J .
450
i
4-00
350
yio
250
1 ■
1
ZOO
ISO
j
100
T^^H
rfcaZc of Sveed ofJBoatinSnotsjicr Hour
screw drove the boat 20^ knots per hour. The curve BBB
belonirs to a two-bladed screw 4 feet 4 inches diameter, 5 feet
pitch, and 540 square inches of blade-area — with 520 horse-
power indicated this screw drove the boat at the remarkable
speed of 23 knots per hour, 20^ knots being attained with
430 horse-power. Some donbt attaches to the accuracy of
the determination of the indicated horse-power in torpedo-
boats, but the comparative expenditure of power with these
two screws is not likely to be affected by any such inaccuracy,
and the influence of the propeller is even more marked than
in the case of the Iris.
560 NAVAL ARCHITECTURE. chap. xiii.
In order that trials of the kind now under consideration
may be made to yield the fullest possible information they
must embrace a determination of the tow-rope resistances of
the vessel at various speeds, the corresponding thrusts of the
propellers, the work done in overcoming the friction of the
engines, shafting, and propellers, the slip of the screw, &c.
Such an investigation requires the greatest care in observation,
and involves a very large amount of labour, even when applied
as it was by Mr. Isherwood to the steam-launch mentioned
on page 651. For large ships, driven by engines of considerable
power, the difficulty and laboriousuess of the task would neces-
sarily be much increased, and, as a matter of fact, we are not
aware of any such investigation having been made. But by
a judicious use of models, both for screws and ships, it may
be found possible hereaft<^r to avoid much of this labour, and
to select the most suitable screws without the trouble and
expense of experiments on a large scale. Much valuable
information affecting the performances of large ships may also
be obtained from observations made on the propulsion of small
vessels or steam-boats; and in this respect the performances
of the fast torpedo-boats recently constructed furnish a great
field for study. It is impossible to dwell upon this subject
here, but one very interesting experiment recently made by
Mr. Thorny croft must be mentioned. The torpedo-boat
Lightning of the Koyal Navy was originally fitted with a
screw-propeller 5 feet 6 inches in diameter; this was removed
and a novel arrangement devised by Mr. Thornycroft was
substituted. The screw-propeller is formed with a very large
boss, and is of very small diameter. It is placed within a
tube only 3 feet in diameter, and abaft it is fixed an arrange-
ment of "guide-blades" into which the water from the screw
is delivered. These blades are so shaped that the fluid pressure
on them has a forward component, constituting a thrust which
assists that on the propeller in propelling the vessel. Mr.
Thornycroft states as the result of experiments that the effect
of the guide-blades was about one-fifth of the whole propelling
effect; and it is understood that the aggregate performance
of the vessel with the new propeller was equal, if not superior,
to that with the original propeller of nearly twice the diameter.
It need scarcely be remarked that, if similar apparatus can
be applied on a laige scale, enormous engine-powers may be
efficiently utilised on draughts of water not exceeding those
CHAP. XIII. STEAM PROPULSION. 56 1
at present accepted for the larger classes of ships.* In this
way one of the difficulties incidental to the attainment of
much higher speeds than have yet been reached may be over-
come.
Notwithstanding the drawbacks to its efficiency which have
been mentioned above, and the want of accurate knowledge re-
specting many features of its performance, the screw has quite
superseded the paddle for ocean navigation and deep-water
service ; has been proved equal, if not superior, to the paddle on
smooth water trials of speed, and has surpassed the jet on the
only occasions when fair comparative trials have been made.
Provided that the draught of water of a ship is great enough to
permit the use of a screw or twan-screws of sufficiently large
diameter, they are generally preferable to paddles. When the
draught is too limited even for twin-screws, paddles are usually
preferred to multiple-screws, the latter being used only in special
cases as explained on page 549. It has been questioned whether
in smooth water the screw is so effective as the paddle ; but the
early trials made between the 'Rattler and Alecto, as well as those
between the Niger and Basilisk, indicated a decided superiority
in the screw, and this opinion has been confirmed by a careful
comparison of the measured mile performances of paddle and
screw steamers of similar types. The chief cause of the greater
efficiency of the screw, as ordinarily applied, must be found in
the relatively large quantities of water upon which it operates in
a unit of time, as compared with the quantities dealt with by
paddles or jets. This advantage compensates, or more than com-
pensates, for the disadvantage attending the obliquity of action,
frictional resistance and considerable augment of resistance which
accompany screw propulsion.
Smooth- water performances are not the true test of efficiency ;
in a seaway the screw is far more superior to the paddle than it
is on the measured mile. Eolling motions, which would seriously
affect the paddle, leave the screw almost uninfluenced. Pitching
oscillations of course affect the screw more than the paddle ; but
if the screw is well immersed, or, still better, if twin screws are
employed, the loss of efficiency on account of pitching does not
appear to be at all serious in large ships. Considerable varia-
* Mr. Thornycroft-'s iavention will be found described in the speci6cation of
his Patent.
2 o
562 NAVAL ARCHITECTURE. chap. xiii.
tions in the draught of water may also take place, yet leave the
screw efficient ; whereas it has been shown that this is not equally
true of the paddle. The screw lends itself much more readily
than the paddle to the association of steam with sail power ; the
absence of projecting paddle-boxes is a great advantage in steam-
ing head to wind and in general service ; and, finally, in war-
ships the screw is much less exposed to damage in action. The
most convincing argument in favour of the superiority of the
screw under all conditions of service is, however, to be found in
the fact that it has almost entirely replaced the paddle in sea-
going ships of the mercantile marine, wherein economical propul-
sion is of the highest importance.
Estimates for the Horse-Fower and Speed of Steamships.
Attention will next be directed to the methods by which, in
designing a new steamship, an approximation is made to the
indicated horse-power required to propel her at a given speed.
A few preliminary explanations will be necessary, in addition to
those given on page 519, as to the meaning of the term " indicated
horse-power."
When an engine is in motion under its load, a considerable
part of the indicated horse-power must be expended in overcom-
ing frictional and other resistances, working the air-pumps, &c.,
and only the remaining part of the power is available to give
motion to the propeller. The frictional resistance may be di-
vided into two parts, viz. the initial or constant friction — due to the
dead weight of the moving parts, the tightness of piston-packings,
shaft-bearings, &c. — which is probably the same for all speeds ;
and, second, the friction due to the " working load " on the
engines, which varies with the speed and thrust. General
experience appears to indicate that the ratio of the available
power to the total indicated power, when well-designed marine
engines are working at full speed, varies from 70 to 80 per cent. ;
and this ratio expresses the efficiency of the mechanism. Hitherto
the determination of this ratio, by direct experiment, has been
made in very few cases. The late Mr. Fronde devised a method
by which the "constant friction" of the engines might be in-
ferred from the results of a series of trials made at different
speeds ; and this method has since been extensively used, but
the results are not of so certain a character as to command com-
CHAP. XIII. STEAM PROPULSION. 563
plete confidence.* So far as his investigations extended, Mr.
Froude estimated that in the engines of screw steamers working
at full speed, the constant friction amounted to one-eighth or
one-sixth of the gross load on the engine ; one-seventh being a
fair average value. In the Iris the corresponding value for the
constant friction was found to be about one-twelfth ; and of this
about 70 per cent, was proved by direct experiment to belong to
the resistance of the engines, the remainder being due to the
friction of the shaft-bearings. The results obtained from the
progressive trials of a large number of merchant ships, have
shown the constant friction, by Mr. Fronde's method, to
vary from 5 to 15 per cent, of the gross load at full power,
in some cases being even lower. Mr. Isherwood, in the trials
of the steam launch above mentioned, found, by experiment,
that the constant friction of the engines was rather under
3 per cent, of the gross load at full power. Although it is
an undoubted fact that the proportion of the constant friction
to the gross load may vary considerably in different types of
engines, yet the great variations in its relative value instanced
above, for engines of very similar type, show that the analysis
from progressive trials cannot be implicitly trusted. The expla-
nation is probably to be found in the great difficulty of obtaining
exactly accurate results at extremely low speeds on these trials.
Hence it is the opinion of all authorities on the subject that some
dynamometric apparatus should be used to determine the power
actually delivered to the screw-propeller by marine engines when
working at different speeds. One of the last pieces of work
performed by the late Mr. Froude for the Admiralty consisted of
the construction of such a dynamometer, entirely novel in its
character, and probably well adapted for its purpose.f The
instrument was not completed until after his death, and the
trials made with it up to the present time have been only pre-
liminary. But these trials are to be continued, and from them
much useful information may be hoped for, not merely as to the
values of initial friction, but the " friction of the load." As to
* For Mr. Froude's method see from the analyses of progressive trials.
Transactions of the Institution of j For a description of the Dynamo-
Naval Architects for 1876. The Author meter see the Proceedings of the Insti-
ls indebted to Mr. W. Denny and Mr. tution of Mechanical Engineers for
John Inglis, junior, for much valuable 1877.
data as to constant friction deduced
2 O 2
564 NAVAL ARCHITECTURE. CHAP. xiii.
the latter there is little exact information available for marine
engines. For laud engines the friction of the load is usually
assumed to be about 14^ per cent, of the useful load ; Mr. Froude
adopted nearly the same figure as a fair value for marine engines ;
]Mr. Islierwood gives 7^ per cent, for the engines of the steam
launch.
In passing, it may be desirable to draw attention to the very
important influence which the "constant friction" may have
upon the expenditure of power, at speeds which are moderate or
low in proportion to the speed at full power. This is a matter of
the greatest interest in war-ships which usually cruise at very
moderate speeds, although their engines are adapted for possible
propulsion at much higher speeds. As an illustration we will take
the case of the Iris, which has engines capable of developing about
7500 horse-power, and driving her 18 knots per hour, but which
can be driven at 9 knots with about 800 horse-power. It was stated
above that at full speed the horse-power expended in overcoming
constant friction was only 8 per cent, of the gross indicated horse-
power. At 9 knots, however, the constant friction would be absorb-
ing no less than 30 per cent, of the gross indicated horse-power ;
and at 6 knots about 50 per cent., if both sets of engines were
kept at work. Hence it will be obvious that at these moderate
speeds it would be economical to stop one set of engines entirely,
and keep the ship straight by using a little helm — a conclusion
which is quite borne out by experience with the ship. The
possibility of effecting this economy is another advantage of the
duplication of engines in the twin-screw system. Moreover, it
will be clear that in war-ships of large size and very high speeds,
the still further subdivision of the machinery, say into four sets
of engines instead of two, must be advantageous so far as economy
of power under the ordinary conditions of service are concerned.
Passing from the engines to the propellers of steamships, still
further " waste " of the gross indicated horse-power occurs. In
jet-propellers there is the friction of the water in the passages
through which it is delivered ; with paddles there is the friction
and " churning " of water by the floats ; with screws there is the
frictional and edgeways resistance of the blades. The greatest
interest naturally attaches to the last-mentioned source of waste ;
and we are fortunate to have some trustworthy experimental data.
In the towing experiments made with the Greyhound (see page
462) it was found that when the two-bladed screw revolved freely,
as the ship moved ahead at 10 knots, the additional resistance
amounted to about 11 per cent, of the nett resistance without the
CHAP. XIII. STEAM PROPULSION. 565
screw. Ill similar experiments made by Mr. Isherwood with a
steam launch, the corresponding increase in resistance produced
by the free revolution of different screws varied from 8^ to 21
per cent, of the nett resistance of the vessel, the higher values
occurring in the screws with the larger number of blades and
larger blade-area. In both these cases the rate of revolution of
the screws was considerably less than that at which they would
have been driven if they had propelled the vessels at the speeds
at which the towing experiments were made ; so that the waste-
work on the screws in propelling would have exceeded that
indicated by the experiments. For the Iru detailed calculations
were made, with the best data available for the probable screw
friction, and the following were the results for full speed. With
the 'original four-bladed screws at 91 revolutions, the nett horse-
power on screw resistance was 1120 horse-power ; with the work-
ing four-bladed screws now on the ship at 97 revolutions 420
horse-power; with the two-bladed experimental screws of the
last series of trials 330 horse-power. (See page 558 for descrip-
tion of the screws.) It is difficult to convert this nett horse-
power into indicated horse-power; but probably an increase
of one-third will be within the truth. Assuming this ratio to
hold, the waste-work of the first screws absorbed 20 per
cent, of the maximum I.H.P. on the first trials ; that of the
working screws absorbed about 8 per cent, of the maximum
horse-power on their trials; and that of the experimental
two-bladed screws absorbed about 6 per cent. These figures,
although approximations only, afford good evidence of the im-
portance attaching to all possible reductions in the resistance of
screws by using the least blade-area consistent with efficiency at
sea as well as in smooth water ; disposing that area in the form
which will enable the necessary propelling effect to be produced
with the least friction; keeping the surface of propellers clean
and smooth, and so shaping the edges as to diminish edgeways
or eddy-making resistance. It may be interesting to add here,
although only indirectly connected with the foregoing remarks,
that in high-speed torpedo-boats the use of thin screw-blades of
great strength and elasticity has been found to favour improved
performance.
Summing up these general considerations it appears that the
ratio which the indicated horse-power bears to the "effective
horse-power " of a steamship (defined on page 518) depends upon
(1) the efficiency of the mechanism of the engines; (2) the
efficiency of the propeller ; (3) the augment of the nett resistance
566 NAVAL ARCHITECTURE. chap. xiii.
of the hull produced by the action of the propeller (see page 550).
It appears further that the present state of our information does
not enable us to deal witli each of these efficiencies separately ;
and so, to arrive at the exact value of the indicated horse-power
required to drive a given ship at any assigned speed. Hence it
happens that in estimates for the engine-power of a new ship it is
customary to include all the above-named factors in one approxi-
mate solution ; although the approximation may be made in any
one of several methods.
The oldest method of approximation, and that still most
generally employed, is to proceed by the comparison of a new
ship with existing ships, making use of " coefficients of perform-
ance " based upon their trials. The ordinary forms of these
coefficients are known as the " Admiralty coefficients," it having
been the practice from a very early period in the construction of
steamships for the Royal Navy to make careful trials of speed
and to tabulate the information thus obtained for guidance in
future practice. The Admiralty formulae may be expressed very
simply.* Let D = displacement of ship (in tons) at the draught
of water on the trial ; A = the corresponding area (in square feet)
of the immersed midship section ; V = speed (in knots) per hour;
and P = indicated horse-power, then
A X V^
Oj (midship-section coefficient) = — p ;
C2 (displacement coefficient) = ^ — .
In these expressions it is assumed — (1) that the resistance of
the ship will vary as the square of the velocity, and the work to
be done in propelling her as the cube; (2) that the useful or
propelling efi'ect of the engines, after allowing for the waste-work
to be done in overcoming frictional resistances, &c., of the
machinery, and the waste-work of the propeller, will vary as the
indicated horse-power ; (3) that for similar ships the resistances
corresponding to any assigned speed will vary as the area of the
immersed midship section, or the two-thirds power of the displace-
ment. The character of the first and last assumptions, and the
limits within which they may be applied, have already been made
* It may be interesting to state that the midship-section coefficient in their
Prencli naval architects generally use estimates for speed and power.
CHAP. XIII. STEAM PROPULSION. 567
the subject of comment in the preceding chapter. It has been
shown that, so long as the speeds attained do not exceed the
limits where wave-making resistance becomes important in pro-
portion to frictional resistance, the law of the total resistance
varying as the square of the speed holds fairly. Beyond that
limit the law of variation involves a higher power of the speed.
The second assumption also appears to hold fairly well with
engines of similar and good design, and with any selected
propeller of good proportions. It cannot, however, be applied
without correction when the propellers of the two ships com-
pared are of dissimilar character — one, say, a paddle, and the
other a screw ; nor can it be applied to all types of engines, the
waste-work being greater in some than in others. The greater
the similarity in ship, engines, and propellers, the greater will be
the degree of accuracy possible with this method of estimation.
With the foregoing limitations, the coefficients of performance
furnish a good means of comparing the economy of propelling
power in ships of similar form and proportions, and not very
different sizes, as well as of estimating the probable power for a
new ship. Of the two coefficients, that for the displacement is,
on the whole, the more trustworthy, giving a fairer measure of
the resistance than the midship-section coefficient, especially
when dealing with ships which are not of exactly similar form.
As an example of the use of these coefficients, take the case of
her Majesty's ship BelleropJwn. On the measured mile, with a
displacement of 7369 tons, a midship-sectional area of 1207
square feet, and an indicated power of 6312 horse-power, she
attained a speed of 14"053 knots per hour.
^ 1207 X (14-053)3 .01
^' = 63T2 = ^^^ '
^ _ (7369)^^ X (14-053-^) _ ™
' 6312
The ship is 300 feet long, 56 feet broad, and had a mean draught
of water, on trial, of 24| feet ; hence her
Coefficient of fineness* =^^,, ' -^ — stt = O'^^.
300 X 56 X 24^
When her Majesty's ship Hercules was designed, if the perform-
ances of the Belleroplion had been known, the engine-power
* See page 4.
568 NAVAL ARCHITECTURE. chap. xiil.
required might have been approximated to in the following
maimer — her length being 325 feet, breadth 59 feet, and mean
draught 24§ feet, her displacement was 8680 tons, and the area
of midship section 131 4 square feet. For these dimensions —
Coefficient of fineness = -^^-^ — r -;— - = 0'64,
32o X 59 X 24|
or nearly the same as the fineness of the Belleroplwn. It might
have been assumed therefore that the Hercules would have co-
efficients of performance very nearly equal to those stated above.
On trial the vessel attained 14*69 knots per hour; let this be
taken as the designed speed, and let the corresponding horse-
power be required. Using the midship-section coefficient 531,
Probable I.H.P. = ^^li^i^^^' = 7845 (nearly).
Ool
Using the displacement coefficient 166,
Probable I.H.P. = (8680)' X (11-69)3 ^ ^^^
166 ^ "^
The actual indicated po^^er required to drive the Hercules at the
speed of 14*69 knots was rather more than 8520 horse-power, or
about 6 per cent, above the approximation from the displacement
coefficient, and about 9 per cent, above that from the midship-
section coefficient. These results bear out what was said above
as to the displacement coefficient being on the whole the more
trustworthy ; and they are sufficiently close to the truth for
practical purposes. It may be explained, however, that the
variation of the resistance at these high speeds for ships of this
type depends upon some higher power of the speed than the
square ; and the naval architect would allow for this in his
estimate, increasing the power somewhat above that given by the
foregoing apjH'oximate method. In making this increase, he
would be guided by the recorded performances of the exemplar-
ship at some less speed than the full speed ; nearly all the vessels
of the Eojal Navy having been tried at reduced-boiler power
as well as full power. For example, the BelleropJion, steaming at
a speed of 1215 knots, had a midship-section coefficient of 543
and a displacement coefficient of 171, as against 531 and 166 for
a speed of 14*05 knots, indicating that the power required to
drive the ship varied with a higher power than the cube of the
speed. It really varied between those speeds as V^ ^ ; and if this
CHAP. XIII. STEAM PROPULSION. 569
correction is made for the Hercules in the preceding calculation,
the probable indicated horse-power will rise to 8300, or within 1\
per cent, of the power actually developed. To ensure the attain-
ment of the speed, desired, the naval architect would almost
certainly provide some margin of indicated horse-power above
that to which the approximate method conducts.
The difficult part of the work in practice lies in the selection
from available data of exemplar-ships most nearly resembling
the new design, in order that the appropriate coefficients may be
obtained. In making this selection, it is necessary to compare
carefully the fineness of form, the dimensions, the lengths of
entrance and run in proportion to the maximum speeds, and some
other particulars of the new ship and the completed ships ; and to
make allowances for greater or less fineness of form, differences
in the frictional resistance, or any other matter affecting the
speed under steam. In the Eoyal Navy, for the greater number
of classes, little difficulty is experienced in discovering suitable
examples; but when entirely new conditions are introduced, it is
not possible to proceed with equal certainty, and then it becomes
necessary, in proceeding by this comparative method, to allow a
considerable margin of power and speed.
Take, for example, the Devastation, a vessel of very full form,
moderate proportions of length to beam, and one of the earliest
deep-draught twin-screw ships. It was estimated in designing
this ship that with 5600 horse-power and a displacement of 9060
tons, a speed of at least 12^ knots would be obtained ; this would
give a displacement coefficient
_(9060fxil2ir_,,,
^2 - 5600 ~
On the measured mile, with a displacement of 9190 tons, the
ship steamed 11-91 knots with 3400 horse-power, the displace-
ment coefficient being 218 ; and at full speed she realised 13'84:
knots with 6650 horse-power, the corresi^onding coefficient being
175. Had only the estimated power — 5600 horse-power — been
realised, the vessel would have steamed about 13 knots, that is,
about I knot faster than the estimated speed. Or, had she
steamed 12^ knots, the indicated horse-power required would
have been only 4000 horse-power, instead of 5600 horse-power,
as estimated.
When the Devastation had been tried, and her coefficients
determined, it was an easy matter to determine the appropriate
570 NAVAL ARCHITECTURE. CHAP. xili.
engine-power for the succeeding deep-draught ships with twin-
screws ; and the superior performances of twin as compared with
single-screws rendered it possible to economise engine-power.
This was done ; and in the Alexandra, Temeraire, and other
vessels, tlie engines were made less powerful and weighty than
they would have been with single-screws. Subsequent trials
have fully justified this procedure. Take, for example, the
Alexandra. It was estimated that 8000 horse-power would suffice
to drive the ship about 14 or 14J knots, when fully laden and
weighing 9500 tons. On the measured mile the speed of 15
knots was attained, and the engines exerted 8600 horse-power,
600 horse-power more than the guaranteed power. When allow-
ance is made for this excess of power, it appears from calculation
that the fully-laden ship would have exceeded the upper limit of
her intended speed with 8000 horse-power. Had she been fitted
with a single-screw, instead of twin-screws, in all probability at
least 500 or 600 horse-power additional would have been required
to attain the same speed.
Another method of approximation which has been largely used
consists in the determination of the ratio of the indicated horse-
power to the wetted surface in the exemplar-ship or ships at the
trial speeds ; and the estimate from this ratio of the probable
value of the corresponding ratio for the new ship at her designed
speed. This method of procedure will be seen to correspond to
that described for sailing ships on page 495, It can be safely
used when the speeds considered are moderate in proportion to
the dimensions ; for which speeds the resistance of the new ship,
as well as those of the exemplar-ships, vary nearly as the square
of the speeds. From the remarks made on the surface friction of
ship-shaped forms on page 448, it will appear that larger differ-
ences of form, wathin the stated limits of speed, can probably be
dealt with by this method, than by the use of the "Admiralty
coefficients," and more particularly than by the use of the
midship-section coefficient. Beyond the limits of speed where
wave-making resistance assumes relative importance, neither the
wetted surface ratio nor the Admiralty coefficients can be applied
without correction of the kind indicated above.
The late Professor Rankine proposed a method for computing
the probable speed and power of steamships closely resembling
that just described. Assuming that the speeds were kept within
the limits for which the resistance varied sensibly as the square
of the speed, Bankine approximated to the resistance by means
CHAP. xiir. STEAM PROPULSION. 57 1
of the " augmented surface " described on page 447. The nett
resistance of the hull in well-formed ships with clean bottoms he
thought might be expressed in the form —
Nett resistance (in pounds) = Augmented surface (in square feet)
X Speed of ship (in knots) —- 100.
The ratio of the "Effective Horse-Power" (estimated from the
nett resistance) to the Indicated Horse-Power, he assumed to be
1 : 1*63 ; and thence obtained as a final approximate rule for
practice : —
-p I ki T TT P Augmented surface x (speed in knots)^
Probable l.M.r. _ ^^qO
This divisor was termed the " coefficient of propulsion," and its
value might vary considerably in different ships with differences
in the roughness of the bottom, the efficiency of the engines and
propellers, or defects of form. In some cases it was found to be
as low as 16,000. The remarks made above as to the use of the
wetted surface apply here also. Either method, depending as it
does upon the assumption that the resistance varies as the square
of the speed, fails to include a very large number of the cases
occurring in practice ; and Kankine's coefficient of propulsion,
like the Admiralty coefficients, rarely has a constant value for a
large range of speed in the same ship. Moreover, on the basis
of the experiments made by Mr. Froude, it may be questioned
whether the computation of the augmented surface is to be
preferred to that of the wetted surface, even for estimates of
surface friction. As a provisional theory, this of Eankine's was
valuable; but subsequent experiments with ships and models
have practically superseded it.
Attention must next be directed to the very valuable assistance
in speed-calculations derivable from 'progressive steam-trials ; that
is to say, the trial of the same ship at several different speeds,
and the determination of the horse-power, and other particulars
for each speed. Trials of this kind have been made occasionally
with ships of the Royal Navy for a long time past, but the system
has not been generally adopted. Formerly the measured mile
trials were made with full and half boiler-power; the regula-
tions now in force provide for trials at full, two-thirds, and one-
third boiler-power. In subsequent service the expenditure of
power and coal at still lower speeds are ascertained in deciding
on the most economical rate of steaming. As early examples of
572
NAVAL ARCHITECTURE.
CHAP. XIII.
more extended trials, made for special purposes, we may refer to
the trials made with the Flying Fish in 1856, to test different
kinds of propellers and forms of bow ; those made on Her
Majesty's yacht Victoria and Albert in 1855-56 ; and those made
on the Warrior in 1861. In the case of the Victoria and Albert,
the trials were very exhaustive, and the curve of horse-power
corresponding to various speeds (see Fig. 126tZ, page 586) was con-
structed similarly to those previously given for the Iris. Out-
side the Royal Navy also such trials were occasionally made.
]Mr. Isherwood, in 1869, tried the steam launch, to which so many
references have been made, j)rogressively ; and determined the
FIG.I26C
"^^8 9JL' 10 -U
Speedin hurts -per lionr
js M IS 16 n
Eeferences.
AAA — Curve of indicated horse-power.
B B B — „ „ „ thrust.
C C C — „ „ revolutions of screw.
E E E — „ „ slip of screw (apparent).
F F F — „ „ slip of screw, expressed as percentage of
its speed.
G G G — „ „ coefficients of performance.
power, revolutions and slip of screw, mean-pressure, &c., for a
large number of speeds, in order that he might construct curves
for all these features of the performance. Mr. Thornycroft did
very similar work for some of the small swift vessels built by
liim.* All these progressive trials were, however, exceptional,
and it is only within the last ten years that their conduct has
become frequent in the mercantile marine, although their value
is now widely recognised. This change of practice and develop-
ment of progressive trials is chiefly to be attributed to the action
of Mr. W. Denny (of Dumbarton), whose firm took the lead in
* See Transactions of the Institution of Naval Architects for 1869 and 1872.
CHAP. XIII. STEAM PROPULSION. 57
'>
this movement, and greatly assisted its progress by the publica-
tion of a large amount of valuable information obtained on the
trials of ships built by them.* At the present time progressive
trials are commonly made with new ships by the principal ship-
builders on the Clyde, and are growing in favour with ship-
builders generally. An example of the ordinary method of
recording these trials is given in Fig. 126c, and represents the
"performance of a very successful steamer built by Messrs. K. &
J. Inglis, of Glasgow. Abscissae measurements on the base-line
represent speeds in knots per hour. The curve AAA represents,
by its ordinate measurements, the variation of the indicated
horse-power with tlie speed ; it was drawn through points
determined by trials made at a series of four or five speeds
between 8 knots and 15^ knots. The curve B B B represents, by
its ordinates, the variation of the " indicated thrust " with varia-
tions of the speed. This curve is obtained frum the curve AAA
taken in connection with the curve C C C, which represents, by its
ordinates, the variation of the revolutions of the screw with the
speed, these revolutions being counted for each trial speed, and
the curve C C C being drawn through the points thus obtained.
Since the indicated thrust equals the fraction
33,000 X I.H.P.
Pitch of screw x revolutions per minute'
while the indicated horse-power is expressed by the product
(see page 519),
Mean piston pressure X stroke X revolutions,
it is obvious that the curve BBB, by its ordinates, represents
" mean piston pressure " for any speed as well as " indicated thrust,"
the scales being different in the two cases. At the zero of speed
there is an ordinate value for tlie curve BBB; this represents the
" constant friction " (see page 562). The curve E E E represents
the apparent slip of the screw in knots, and F F F the percentage
of slip ; these are obtained from the curve C C C, the pitch of the
screw being given. Another curve GGG also appears, its
ordinates being proportional to the quotient of the cube of the
speed by the indicated horse-power ; it is derived from curve
* See Papers by Mr. W. Denny con- builders in Scotland for 1875 ; aud to
tributed to the Proceedings of the the British Association for the same
Institution of Eugineers and Ship- year.
574 NAVAL ARCHITECTURE. chap. xiii.
AAA. This curve GGG is termed the "curve of coefificients,"
and its ordinatos can obviously be made to represent, by suitable
scales, both the Admiralty coeflScients and Eankiue's coefficient
of propulsion. Were these coefficients really " constants," the
curve of coefficients would become a straight line parallel to the
base-line.
With these graphic records of progressive trials before him, the
designer of new ships of similar form and type can proceed with
greater assurance of success than is attainable with less extensive
information. If a ship of practically identical form and size, but
less speed, is to be built, his task is simply one of measurement
from the curves, with some slight correction for difference in
constant friction. If the speed of such a ship is to be greater
than that of her predecessor, it is also possible to make a close
approximation — provided that the excess in speed is not very
considerable — from an inspection of the curves of indicated horse-
power and coefficients. When the sizes and speeds of ships are
both varied, but approximately similar forms are maintained, the
problem is more complicated, but still it can be dealt with
approximately, by an application of Mr. Froude's law of " corre-
sponding speeds " explained on page 471.*
Supposing that in the graphic record of the results obtained
on a progressive trial, the constant friction of the engines be
determined, and then eliminated from the indicated thrust by
drawing a line parallel to the base-line through the point where
the original curve of indicated thrust (B B B, Fig. 126c) cuts the
ordinate of the zero speed. The line so drawn forms a new base-
line, giving the indicated thrusts and mean piston pressures,
excluding constant friction ; and the corresponding corrected
indicated horse-power curve can be constructed. In what follows
•we shall speak of these corrected curves, and of the derived curve
of coefficients.
Next let it be assumed, although not strictly nor necessarily
true, that the corrected indicated thrust bears a constant ratio to
* Mr. Froude indicated this applica- gave an illustration of the method,
tion in a Paper on " Useful Displace- Mr. John Inglis, junior, was led to
ment " contributed to the Transactions the same practice by a study of Mr.
of the Institution of Naval Architects Froude's writings, and contributed a
in 1874. The Author had also applied valuable Paper on the subject to the
it commonly in his professional work Transactions of the Institution of
for some time before the publication of Naval Architects in 1877.
the first edition of this book, and therein
CHAP. XIII. STEAM PROPULSION. 575
the nett resistance at any speed. For any speed Vj of a ship that
has been tried, let T^ = the corrected thrust (or mean pressure)
and Pj = the corresponding horse-power. Then, with the fore-
going assumptions, if we increased tlie lineal dimensions of the
ship D times, and towed the larger ship at a speed of V^ '\/D,
her resistance at that speed (or indicated thrust) would be expres-
sible in the form
T2 = Ti . D^
and the corresponding horse-power would be
P2 = T2 X Vj /\/D X a constant,
while Pi = Ti X Vi X the same constant.
Hence
JP2 T2 ,_ 7
This is an expression from which the horse-power for the larger
ship can be found for a speed VjA/D, when that for the exemplar-
ship has been ascertained from the progressive trials at speed Vi.
To the value of P2, thus determined, must be added the assigned
percentage for constant friction, of which particulars are given
on page 563, in order to find the indicated horse-power required
for the speed (ViA/i)). In this manner not merely the power for
full speed can be estimated approximately, but that for any other
speed, and so a new curve of indicated horse-power can be drawn
for the new ship. This could not be done, it will be seen, unless
curves such as those in Pig. 126c were available; and they are
therefore of great value. If the difference in size is considerable
between the two ships, it may be necessary to deal with the
frictional resistance separately, and to apply the foregoing rules
to the wave-making resistance only; but this kind of correction
is not usually made.
Using the same notation as before, another deduction may
be made from the foregoing investigation. Suppose the coeffi-
cient of performance curve for the exemplar- vessel to be drawn
from the equation
Coefficient — ^P^Q*^^^ X Area of midship section
Indicated Horse-power
Let Ai = area of midship section in smaller vessel ; A2 = corre-
sponding area in larger vessel ; then obviously A2 = \y~ . A^.
576 NAVAL ARCHITECTURE. chap. xiii.
Also, the following values will hold good : —
V^ X A
Ci = Coeflicieut for smaller vessel at speed V = — p — ^ ;
2.
C, = Coefficient for larger vessel at speed VV D = p 5
. Cx_A, V, 1 _ A, ^ Pi.D|_i
• •C.-A/Pi'Di-D^Ai'' Px.Df
That is to say, with the preceding assumptions, the coefficients
of performance for two similar vessels steaming at "corresponding
speeds" are identical. This statement holds good for both the
Admiralty coefficients as well as for Kankine's coefficient of
propulsion. In practice it may be modified by some departure
from the assumptions; but the broad deduction is useful for
practical purposes in comparing efficiencies of vessels similar in
form and method of propulsion, but unequal in size.
From this investigation it follows that for two ships of unequal
size, but similar form and similarly propelled, driven at the same
speed, the larger will have the higher coefficient of performance ;
the indicated horse-powers usually increasing at a more rapid rate
than the cube of the speed.
In applying the results of progressive trials to speed calcula-
tions care is required, of course, to secure, if possible, similar
conditions in the exemplar-ship and the new design as regards
not merely form, but type of engine and propeller, and equal
smoothness of bottom. Differences in the coefficient of friction,
arising either from different degrees of roughness or greatly
different lengths of ships (see page 436), must be allowed for ;
and this can be done without difficulty, if desired, in comparing
small ships with large. In fact, to secure the closest approxima-
tion to the horse-power in a new ship, every part of the work
requires to be done with scrupulous care and intelligence. For
rough estimates, on the other hand, some of the foregoing correc-
tions may be omitted; and more especially the correction for
constant friction of engines when approximating to the indicated
horse-power for full speeds.
One example only can be given of the approximate formulas
based on corresponding speeds. We will choose Her Majesty's
ships Hercules and Greyhound, which are very similar in form, but
different in size, speed, and character of bottom.
CHAP. XIII.
STEAM PROPULSION.
S77
The similarity of the forms will appear from comparing the
ratios of the lengths, breadths, draughts, and cube-roots of the
displacements given in the Table below. Using the letter D to
express this ratio, we have,
3/8676
D
y5on3_
V 1157 ~-^^'^^'
10'5 knots (nearly).
VD - Vl'y57 = 1-4 (nearly).
On trial, the Hercules attained a speed of 14*69 knots.
Corresponding speed ] _ 14'fi9 _ 14*69
for Greyhound . j VD 1'4
On trial, the Greyhound attained a maximum speed of 1004
knots with 786 indicated horse-power ; at that speed her resist-
ance was varying about as the cuhe of the velocity, and therefore
the horse-power would vary as the fourth power. Hence
Indicated horse-power for ] _ -^^ / lOS y „ -p,
speed of 10-5 knots . j" " ^^^ ^ [jMl) = ^^^ ^.P.
Ships.
Length.
Breadth.
Mean Draught.
Displacement
ou Trial.
Hercules .
Greyhound .
Feet.
325
1721
Feet.
59
331
Feet.
24-6
13-7
Tons.
8676
1157
The thrust of the propeller in the Greyhound at 10-5 knots
might therefore be considered proportional to the quotient
940 ^ 10-5 ; if for the Hercules at 14*69 knots a corresponding
assumption is made, and the thrust considered to be proportional
to the quotient of the requii-ed indicated horse-power (P, say)
-^ 14-69. In both ships the engines would be working at full
speed ; and for our present purpose it may be assumed that the
thrusts would be proportioned to the resistances of the two ships.
Using the law of comparison propo.sed by Mr. Froude,
for Gi'ey-
Jwund at 10'5 knots
Resistance for Hercules^
at 14-69 knots .
/T. nr-TXT (resistance
(1-957)' X \
= 7-5
X
resistance for Grey-
hound at 10"5 knots.
Hence, approximately,
I.H.P. for Hercules at 14-69 knots
7-5 X 940
14-69 10-5 '
I.H.P. for Hercules at 14-69 knots = 9870 horse-power.
2 p
578 NAVAL ARCHITECTURE. chap, xiii.
This power is largely in excess of that actually developed in the
Hercules, when she attained a speed of 1469 knots : but it must
be remembered that in the calculation tlie same coefficient of
friction has been assumed for the Hercules as for the Grei/hound ;
whereas the Hercules was tried with a cleanly coated iron bottom^
and the Greyhound with a copper bottom somewhat deteriorated
by age. A correction is therefore necessary, and it may be simply
made.
It has been estimated that for a speed of 600 feet per minute
the coefficient of friction for the bottom of the Greyliound was
about 0'325 lb. per square foot of surface, as against 0*25 lb. for
a cleanly painted iron bottom ; and this difference would involve
an increase of between one-seventh and one-eighth in the total
resistance, and indicated horse-power for the speed of 10"5 knots.
In other words, if the Greijhound, instead of being tried with her
worn copper, had been tried with a cleanly coated iron bottom,
like that of the Hercules, the speed of 10"5 knots would probably
have been attained with about 830 horse-power, instead of 940
horse-power. Making this correction in the foregoing equation,
we have, approximately,
7-5 X 14-69 X 830
I.H.P. for Hercules at 14-69 knots =
10-5
8715 horse-power.
This is a close approximation to the actual power (8529 horse-
power) which was developed on the measured-mile trial of the
Hercules; but the same degree of accuracy may not always be
secured in estimates made in this manner.
"When unprecedented speeds have to be attained, or novel
types of ships constructed, the only available method of making
a trustworthy estimate of the engine-power required is found in
recourse to model experiments. By means of such experiments,
as explained in Chapter XL, the resistance and effective horse-
power for any assigned speed can be determined ; but when this
has been done there still remains the determination of the ratio
of the effective to the indicated horse-power. Experiments with
model propellers may assist in the solution, enabling an estimate
to be made of the augment of resistance, and possibly of the
waste-work done by the propeller itself. And, as to the waste-
work of the machinery, fticts are already recorded which may be
of service (see page 562). In this way, step by step, the approxi-
mation can be carried forward with greater certainty than would
CHAP. XIII. STEAM PROPULSION. 579
otherwise be possible. This power of dealiDg with novel questions
in propulsion, shipbuilders owe entirely to the genius and energy
of the late Mr. Fronde ; and examples of its advantages are beiug
rapidly multiplied. Amongst the more recent may be mentioned
the cases of the Infiexihle in the lioyal Navy, and the Imperial
Russian yacht LivacUa. The Injlexible was of entirely novel
form and proportions, but the estimates of the engine-power
required for lier intended full speed have been closely verified
by the measured-mile trials. The Livadia was a still greater
departure from previous practice, and in her case, too, the method
of model experiments proved successful. Dr. Tideman's trials on the
tow-rope resistances of a model were supplemented by an interesting
series of trials on a large-scale model propelled by its own screws ;
and sueh a supplement cannot fail to be of value in extreme cases.
Ordinarily, having ascertained the effective horse-power for a
new ship from the model experiments, it is possible to approxi-
mate to the indicated horse-power from experience with other
ships. Information as to this ratio is still of moderate amount,
and needs extension ; for it is clear that it may have a very wide
range in different types of ships and various forms of propellers.
For screw steamers the ratio has been determined in many cases
by a comparison of model experiments with measured-mile trials.
Writing in 1876, after a careful analysis of the experiments
available, Mr. Fronde fixed from 37 to 40 per cent, of the indi-
cated horse-power as a fair value for the effective horse-power in
single-screw ships when steaming at full speed. Subsequent trials
have given much higher percentages, reaching to 50 or even 60
per cent, in some single-screw ships of fine forms and unusually
good performance. In some of the comparatively full-formed
twin-screw ships of the Eoyal Navy the corresponding percentage
has reached 45 to 50, and for the finer forms it has attained about
the same values as for some of the most successful single-screw
ships. In torpedo-boats and vessels driven at extraordinarily
high speeds a still higher ratio of effective to indicated horse-
power has been attained, according to the comparison of the
inodel experiments with measured-mile trials; but in these
extreme cases two difficulties present themselves. First: the
calculation of the indicated horse-power is open to some question,
no matter what care may have been taken ; and second, in passing
from the model to the full-sized boat the skin-friction correction
cannot be made with certainty. Further experiments are needed
therefore, and will probably be made, as the results will have a
wide interest and range of application.
2r2
580 NAVAL ARCHITECTURE. chap. xiii.
Limits of space prevent any further consideration of this
important branch of sliip construction, altliough we have by no
means exhausted the subject, or even mentioned some interesting
proposals relating to speed calculations ; for these we can only
refer readers to the original papers.*
Steamship EJiciencj/.
The subject of steamship efficiency has occupied much atten-
tion, and several standards of comparison have been proposed.
None of these standards can be employed universally, however,
in the com]3arison of different types of ships ; because (as was
remarked on page 461), in many types, and more especially in
ships of war, the choice of forms and proportions is largely
influenced by other considerations than those relating to economical
jn-ojndsion. It is unnecessary to repeat the remarks already made
on this point, although their importance is frequently overlooked ;
no distinction being made between the ideal conditions of forms
of least resistance, propellers of maximum efficiency, and engines
of perfect construction, and the conditions of practice with all
their limitations or restrictions. Bearing this distinction in mind,
we now proceed to summarise the circumstances which chiefly
influence economy of steam-power.
First, and most influential, is the adoption of forms and pro-
portions wliich lead to diminished resistance. Examples of the
remarkable effects produced by increasing the length, and the
fineness of form, were given in Chapter XI. To these may now
be added a few others, as the subject possesses considerable in-
terest. Some of the first-class Transatlantic mail steamers are
about equal in weight and load-draught to the largest ironclad
frigates of the Eoyal Navy; and the measured-mile speeds of the
two classes are not very different, being from 14 to 15 knots.
In the mail steamers the length is from 9 to 11 times the beam ;
in the earlier ironclad frigates, such as the Warrior and Minotaur,
it is from 6^ to 6f time ; in the later ironclad frigates, such as
the Hercides and Alexandra, from 5 to 5^ times. For our present
purpose it will be sufficient to compare the indicated horse-power
* See Mr. Kirk's Paper in the ceecZmgrs of the Institution of Engineers
Transactions of the Institution of and Shipbuilders in Scotland ; the Ee-
Naval Architects for 1880: various ports of the British Association Com-
Papers by Mr. K. Mansell in the Pro- mittee on Steamship Performance, &c.
CHAP. XIII. STEAM PROPULSION. 58 1
with the total weights driven ; if this mode be followed, the
vessels compare as under : —
H.R
Transatlantic steamer . 0"5 per ton of displacement ;
Earlier ironclad frigates . 0'6 to 0'7 „ „ „
Later „ „ . 0-9 to 1 „ „ „
These are average values for the different classes ; and they illus-
trate the considerably increased expenditure of power rendered
necessary in the recent ironclads by reason of their moderate
length and proportions.
To compare only the performances under steam of these various
classes, and not to have regard to their contrasts in other respects,
would be very misleading. The merchant steamer is built for re-
munerative service in carrying car^o and passengers ; handiness,
or quick turning, is of minor importance. In a modern war-ship,
on the contrary, the provision of a necessary amount of stability
and protection limits the choice of proportions (see page 461) ;
while handiness is of the utmost importance, and to secure this
quality, moderate length is needed. Adopting the moderate length,
and being limited in draught, the displacement required has been
obtained by greater beam and fulness of form, which cause
greater resistance. But the price paid for increased manoeuvring
power under steam might not be too high, even if it were wholly
additional to the cost of the long ship. In ironclad ships, how-
ever, this is not the case ; but reckoning the total cost of hull
and engines, the shorter type of ship can be made smaller and
cheaper than a ship of the longer type fulfilling the same condi-
tions as to speed, armour, armament, and coal endurance.
This question was very exhaustively discussed by Sir Edward
Eeed when Chief Constructor of the Navy, in order to justify his
policy in passing from the Warrior and Minotaur types to the
moderate proportions of the Belleroplion and Hercules* From
many illustrative cases, we will select one which seems to have
peculiar interest. Taking the ironclad frigate Hercules, of which
all the particulars and performances were known, an estimate was
made of the dimensions and cost of a vessel which should have
the same battery and guns, the same armour protection on the
water-line belt, the same speed and coal supply, and wliich
should be constructed on the same system as the Hercules ; the
* See a Paper contributed to the Transactions of the Royal Society in 1868,
and chap. ix. of Our Ironclad Ships.
582
NAVAL ARCHITECTURE.
CHAP. XIII.
jiroportion of length to breadth and the coefficients of per-
t'ormance under steam were, however, to bo identical with those
for the Minotaur. The following tabular statement shows the
result of careful calculations : —
Pfirticulavs.
Length (in feet)
Breadth (in feet)
Displacement (tons) ....
Wei:j;ht (in tons) of —
Hull
Armour and backing on belt
„ „ ,, on batteries
Engines, boilers, and coals .
Equipment and armament .
Indicated horse-power for speed of 14
knots
First cost of —
Hull . 1 at average pi ices for ironclads
Xew Ship
(as estimated).
69
Engines
:)
built prior to 1869.
385
571
S088
4574
1518
398
1460
1138
6585
£
326,500
55,500
Hercules.
59
8676
4022
1292
398
1826
1138
8529
£
287,400
72,000
After crediting the long ship with less powerful and costly
engines, it appears, therefore, that the total cost of the Hercules
for hull and engines would be about £22,000 less. The more
powerful engines of the Hercules would undoubtedly be more
expensive to keep at work, owing to their greater consumption of
fuel ; but " the interest at a low rate on the difference of prime
cost would quite make up for the additional cost of fuel in the
Hercules, supposing her to be in commission and on general
service." The longer and larger ship, moreover, would be more
costly to man and maintain in repair ; but her most serious
drawback would be her slow rate of turning as compared with
the Hercules. On her trials at the measured mile the Hercules
turned a complete circle in 4 minutes, the diameter being about
560 yards, or rather more than five times her ow-n length. What
the corresponding figures for the new ship -svould be with equal
rudder-power, it is not easy to decide apart from trial. The con-
trast needs no further comment ; it is generally admitted that very
great advantages are obtained by adopting moderate lengths in
war-ships and accepting the greater expenditure of steam-power.
As speeds are increased so the limit of length must be raised
which would give the best combination of qualities ; and if
higher speeds than 15 or 16 knots per hour are desired, greater
lengths than 300 to 325 feet must be accepted.
c HAP. XI 1 1 . 5 TEA M PR OP ULSION. 583
From the tabular statement given above, it will appear that
one important item in which the Hercules gains upon her rival is
in the weight of belt armour, the length of water-line to be pro-
tected being less. This matter — the area requiring to be pro-
tected— must exercise great influence upon the selection of the
forms and proportions most appropriate in ironclads. In the design
of central-citadel ironclads another consideration has weight,
viz. the selection of proportions which shall secure sufficient
stability for the ships when their uuarmoured ends are riddled.
The Inflexible, for example, has a less ratio of length to breadth
(4J to 1) than any ironclad of equal speed yet designed ; but by
fining the extremities and making other modifications in form
her performance compares favourably with that of other vessels
of recent design with equal length, greater draught, and ratios of
length to breadth of 5 or 5^ to 1. The " displacement co-
efficient "' of the Inflexible at 14 knots is nearly 190 : that for
tlie Alexanch'a, of equal length, nearly 11^ feet less beam, and
nearly 2 feet greater draught, with 2000 tons less displacement,
is 175 for 15 knots, and at 14 knots would probably be about
equal to the coefficient of the Inflexible.
In the ironclad reconstruction, as armour has been thickened,
tlie ratio of length to breadth has been reduced; and so far as
the Eoyal Navy is concerned, there is no reason to suppose that
anything but advantage has resulted from the change. It is
possible, however, tliat tlie resistance at the high speeds of 14 or
15 knots, considered necessary in battle-ships, would become so
great in vessels having extremely large ratios of breadth to
length as to make it impolitic to adopt such proportions. The
extreme case of the Russian circular ironclads will enable fuller
explanations to be given on this point ; and the extraordinary
character of these vessels will appear from the following brief
statement.
The vessels were originally designed for coast-defence services
in the shallow waters of the Black Sea ; it was desired that they
should carry thick armour and heavy guns ; and the circular
form was chosen because it gave the least surface and the greatest
carrying power in proportion to the displacement. It may be
admitted that, if these vessels had been stationary floating forts,
this view of the matter would have been correct ; in the com-
pleted ships the hull is said to weigh only about oneflfth of the
displacement, whereas in vessels like the Devastation about 30 or
35 per cent, of the displacement is expended on the hull. But
when from mere stationary flotation we pass to the case of loco-
584 NAVAL ARCHITECTURE. chap. xiii.
motion even at moderate speeds, the conditions are far less
favourable to the circular form. It is admitted as the result of
careful experiments made by Mr. Froude, and confirmed by the
performances of the Novgorod, that a circular ship experiences
about jive times as great resistance as a ship like the Injiexihle or
Devastation moving at equal speed. Let it be supposed that a
circular ship is required to be built to steam as fast and as far as
the Devastation, and to carry the same dead veeight of armour,
guns, &c., exclusive of engine and coals. The same type of
engine is to be used in both cases, and the rate of coal consump-
tion is to be identical in both. Taking the Parliamentary Keturn
for the Devastation, it appears that the following is the distribu-
tion of weights : —
Engines (developing 6600 horse-power)
Coals
Hull
Dead weight carried ....
Total displacement
The engines of the Devastation are of the surface-condener
type, which preceded the compound principle now generally
adopted ; and they consume about 3 J lbs. of coal per indicated
horse-power per hour. Had they been of the latest compound type,
about 900 tons of coal would have sufficed to carry the ship as far
as she can steam with her present engines, and the engines might
have been only a little heavier (see page 526). Suppose that the
total weight of engines and coals remams as in the actual ship,
and that the coals carried amount to 1200 tons, we shall have con-
verted i\\e: Devastation into a ship with modern engines, and assumed
a coal supply less than she could actually carry. What would be the
dimensions of the corresponding circular ship ? is the question to
be solved. Using the data furnished by Captain Goulaeff, of the
Russian navy,* who argued strongly in favour of the novel type,
it appears that the displacement of a circular vessel carrying
4070 tons dead weight, exclusive of engines and coals, and
steaming as fast and as far as the Devastation, would be at least
20,000 tons. The weights would be distributed somewhat as
follows: —
. 1000 tons,
. 1350 „
. 2880 „
. 4070 „
. 9300 tons,
* In a Paper published in the Transactions o!" the lastitutionof Naval Archi-
tects of 187G.
CHAP. XIII.
STEAM PROPULSION. 585
Engines (developing about 34,000 horse-power) . 6,000 tons.
Coals (to steam 7^ days at full speed) . . . 0,100 „
Hull (20 per cent, of disp'acement) .... 4,000 „
Dead weight (as in Devastation) .... 4,070 „
Total displacement . . 20,170 tons.
If the proportions of the existing ships were followed, this
vessel would be about 230 feet in diameter, and 19^ feet draught.
The circumference at the water-line would be about 720 feet;
whereas the total length of the water-line requiring to be
armoured in the Devastation would not exceed 640 feet; and
consequently an armour belt of equal depth and thickness on the
two ships would weigh about one-eighth more for the circular
ship than for the Devastation. The deck area of the circular
ship would be about 41,000 square feet; the corresponding area
in the Devastation would not exceed one-third that for the circular
ship ; and here, for equal protection, the Devastation would be at
a great advantage. On the upper and breastwork decks of the
Devastation, the mean thickness of the [dating may be taken at
2^ inches ; the total weight is about 500 tons. On the circular
ship, 2^-inch plating over the whole area of the deck would
weigh about 1600 tons.
It is needless to pursue this investigation further, for no
one is likely to contemplate the construction of a vessel nearly
twice as heavy as the heaviest existing ships, when it can be
shown that the circular form compares so disadvantageously
with other existing types. Moreover, it has yet to be proved
that vessels of the circular form can be driven at such speeds
as 14 knots, without serious departures from the normal trim
and draught. Mr. Froude stated, as the result of experiments
with circular models, that, as the speed is increased, the vessels
"dive" below their normal draught; and this circumstance
deserves careful consideration in discussion of the merits of such
ships. The existing ships are reported to have made very low
speeds, from 7 to 10 knots, although they have a very large
amount of engine-power in proportion to their displacement. The
Novgorod, for example, had engines of 480 nominal horse-power,
said to develop about 2200 horse-power (indicated) ; her displace-
ment is 2490 tons ; and the speed about 7^ knots. Contrasting
this with the performance of the monitor Ahjssinia, which, with
a displacement of 2800 tons, was driven 7^- knots by 560 indicated
horse-power, the reader will obtain another proof of the extrava-
586
NAVAL ARCHITECTURE.
CHAP. XIII.
gant expenditure of power required in the circular ships. For
their special purpose they may be exceedingly well adapted, but
they cannot be regarded as models for general service. At the
same time, the information derived from their performances is
most valuable and instructive.
The same remark applies to the performances of the Imperial
Russian yacht Livadia. She is 235 feet long, 153 feet broad,
and on the measured-mile trial had a displacement of about 4400
FIG 126
Curves of Indicated Horse-Power.
AAA — Livadia,
B B B — Iris.
C C C — MerJcara.
D D D — Victoria and Albert.
E E E — Charles Quint.
12 000
II 000
3 G 7 8 9 10 II 12
Scale nf speed in Jaiois per liour.
13 14-
/5
le
tons, on a draught of about 7 to 8 feet. With 12,350 indicated
horse-power she is said to have attained a speed of 15725 knots
per hour; with 10,200 horse-power, a speed of 14-83 knots; with
about 4800 horse-power 13 knots, and with 3000 horse-power 11
knots. In Fig. 12Qd, the curve AAA shows the curve of indi-
cated horse-power based on these iigures, the construction being-
similar to that explained for Fig. 126a, page 557. For purposes
of comparison there also appear the corresponding curve BBB
for Her Majesty's ship Iris, the curve C C C for the Merhara cargo
and passenger steamer built by Messrs. Denny (mentioned on
page 459) ; the curve D D D for Royal Yacht Victoria and Albert ;
and the curve EEE for tlie fast passenger steamer Charles
Quint, built by Messrs. Inglis. The Table on opposite page gives
the principal particulars of the vessels thus compared : —
CHAP. XIII.
STEAM PROPULSION.
187
It is unnecessary to comment on the great proportionate ex-
penditure of power in the Livadia as compared with the other
vessels, but it should be noted that her displacement bein^^
greater than that of the other ships somewliat favours her
in the comparison of the ratios of horse-power to displace-
ment. When compared with short bluff- formed armoured
ships designed to steam only at low speeds, the Livadia does
not show so badly. For example, the Hotsjmr ironclad ram of
the Royal Navy is 235 long, 50 feet beam, and on trial drew 20^
feet, with a displacement of 4180 tons. Her speed of 1 1 "3 knots was
attained with 1980 indicated horse-power. The Livadia is said to
have required 3000 horse-power for 11 knots speed, and the greater
constant friction of her engines would necessarily tell against her
at this low speed. But allowing for this the expenditure of
Ships.
Length.
Breadth
extreme.
Measured Mile.
Mean
Di-aught.
Displace-
ment.
Livadia
Iris
Merhara
Victoria and Albert .
Charles Quint .
feet
235
300
370
300
315
feet
153
46
40i
33A
feet
7^
18
17
14
14^-
tons
4400
3290
3980
2000
2480
power — measured by its ratio of horse-power to weight driven —
must have been about 40 per cent, greater in the Livadia than
in the Hotsimr. Other comparisons have been made somewhat
more favourable to the Livadia* but it is unnecessary to repro-
duce them here. It must suffice to say that her trials have
demonstrated one very interesting fact, viz., that if the necessity
arises, in vessels of moderate speed and a given length and dis-
placement, it is possible to exchange the ordinary form of
midship section (where the draught of water is about half the
extreme breadth) for a very broad shallow section of equal area ;
and by making suitable changes in the other cross sections so as
to favour a considerable amount of fineness in the longitudinal
sections (buttock and bow-lines) to obtain the given speed with
from 30 to 50 per cent, more power than would be required in
the ship of ordinary form.
* See Captain Goulaeff's Paper in the Transactions of the Institution of
Naval Architects for 1881.
588
NAVAL ARCHITECTURE.
CHAP. XIII.
As compared with the circular form, the Livadia will be seen
to have a distinct advantage. This arises from two causes. When
towed at speeds varying from 7 to 13 knots, the Livadia model
is said to have experienced only about 60 per cent, of the
resistance experienced by a model of one of the circular ships
having equal displacement. Moreover, her three screws are
much better placed than the multiple screws of the circular
ships, being far more clear of the hull, having a better supply of
water, and causing less augment of resistance. Notwithstanding
this improvement in performance, it cannot be admitted that the
Livadia form is well adapted for use in protected war-ships; and
for the ordinary purposes of navigation it does not seem likely to
be accepted. As regards the former statement, it may be explained
that the Livadia form, besides beiug more expensive in propel-
ling-power and coal-consumption, has such an enormous area of
the plane of flotation that a very great weight of horizontal or
oblique armour would be required. For example, in a compari-
son which we have made between Her Majesty's ship Alexandra
and an enlarged Livadia, the figures stand approximately as
follow : —
Alexandra.
Enlarged Livadia.
Length
Breadth
Draught (mean).
Displacement (tons).
Indicated horse-power .
Speed
325 feet
63 feet 10 inches
26 feet 6 inches
9500
8600
15 knots
300 feet
200 feet
11 to 12 feet
9500
12,500 to 13,000
15 knots
This increase in engine-power would necessitate a proportionate
increase to weight of machinery and coals ; there would be
practically the same length of water-line to protect, and the area
of deck requiring horizontal armour would be about double that
of the Alexandra. Hence it follows that on the Livadia form the
association of speed, coal-endurance, armour and armament actu-
ally existing in the Alexandra could not be repeated. It might
be possible, of course, to adopt the Livadia form in connection
with some entirely new disposition of the armament or the pro-
tective material, but we cannot pursue the subject further here.
For any selected type economical propulsion is favoured by
increase in size. This is true generally, and has been mentioned
in previous chapters. If the particular case is taken where the
CHAP. XIII.
STEAM PROPULSION.
589
resistance varies with the wetted surface, and as the square of the
speed, this relative economy is easily illustrated. Suppose two
similar ships to be comparerl, the weight of one being Wi and
that of the other W2. Let D be the ratio which the length or any
other dimension in the larger ship bears to the corresponding
dimension in the other. Then it must follow that
Wi = D\ Wo,
the weight increasing with the cxihe of the ratio of corresponding
dimensions. On the other hand (as explained at page 495), the
resistances will bear to one another the ratio of the two-thirds
.oower of the displacement; and if Ej, E2 represent the resist-
ances,
E,
K2
the resistance increasing only with the square of the ratio of
corresponding dimensions. For instance, a ship twice as long,
twice as broad, and hvice as deep as another will have eight times
as great displacement, but, when moving at the same speed, will
experience oxi\j four times the resistance, and require o\\\j four
times the engine-power. No doubt the longer ship would re-
quire to have greater structural strength than the smaller ; and
consequently the hull might have to be made somewhat heavier
in proportion to the displacement, although in actual practice
this is often not done. But even supposing this additional weight
of hull were allowed, the larger ship would be far more economical
of steam-power in proportion to the dead weights carried.
As an illustration, take the following comparison between two
merchant steamers whose performances on the measured mile
were recorded, their forms being similar : —
Particulars.
Displacement .
Indicated horse-power
Speed
Indicated borse-power\
(Displacement)'^
Steamer A,
1830 tons
1620 II.P.
12-y knots
10^
Steamer B.
3600 tons
2430 H. P.
12-95 knots
101
The last line in this comparison shows that the assumed law
holds very closely in these sliijis. If these vessels were fitted
with compound engines, and employed on a service where they
590
NAVAL ARCHITECTURE.
CHAP. XIII.
would have to steam 3000 knots at full power, their weights
would be distributed somewhat as follows : —
Distribution of Weights.
Steamer A.
Steamer B.
Weight of engines, &c.
,, ,, coals ....
„ » li"ll
„ „ cargo and equipment
Displacement
Tons.
320
360
550
Tons.
480
540
1240
1230
600
2260
1400
1830
3600
The expenditure of 360 tons of coal in the smaller vessel
■would carry only 600 tons of cargo and equipment over the
distance named ; adding 50 per cent, to this expenditure, the
larger ship can carry more than twice as much cargo and equip-
ment. This comparison, of course, tlikes no account of the
relative first cost of the two vessels.
Irrespective of any assumed law of resistance, it is possible in
general terms to indicate the economy of propulsion obtained by
increase in size. Using the same notation as before, let the two
ships compared be supposed moving at the speed V, their resist-
ances, excluding the frictional resistances on the bottoms, being
Ri and Ra- Let R be the resistance of the smaller vessel when
moving at the speed V -^V-O ; and let it be supposed that between
this speed and the speed V the resistance varies with some un-
known power (2w) of the speed. Then
2n
R2 \s/Vi
^^ , whence R = :r^
Also, by the law of comparison which Mr. Froude has established,
Ri (for large ship) = D^ X R = W"'. Ro,
Ro
= rt = D
,3-)l
and, as before.
W,
Wi (for larj>-e ship) = D^. Wo; whence ^^ =& = D^
so that finally, for equal speeds of two similar ships,
1 W, _ R. _ a 1
D' Wo Ro
a
or -
b
1)"
CHAP. XI 11. STEAM PROPULSION. 59 1
The greater tlie value of n for a certain value of D, the less ^Yill
be the ratio a : h measuring the ratio of the increased resistance,
involved in enlarging the ship, to the corresponding increase in
disj^laceraent and carrying-power. If the resistance between the
speeds V and V -r VD varies as tlie square of the speed, n - 1,
and the final equation assumes the form
1 Wi Ri
D ■ Wo ~ Ro'
agreeing with that previously obtained for the law of variation.
But if the resistance between the speeds Y and V -4- VD varied as
the/oM/-;7i power of the speed, then n = 2, and we have
1^ Wi Ri
If the resistance of the smaller vessel between the speeds Y and
Y -4- \'D varies as the sixth power of the speed, then u = 3,
L Wx _ -, _ Ri
D^*w;~ ~ R/
that is to say, the small ship would experience as great a resist-
ance at the speed Y as the larger ship of similar form if the
foregoing assumptions held good. As a matter of fact, however,
whatever may be the hiw of variation in the wave-making
resistance in terms of the speed, the frictional resistance does not
vary more rapidly than the square of the speed, and this would
make the resistance of the smaller vessel less than that of the
larger." It is easy to make the necessary correction for friction
in the manner explained on page 472.
The comparison of the Merhara and Greyhouncl type will
furnish a good illustration of the foregoing equations. At
12 knots, for the Merhara, n may be taken as unity, and for the
Greylwund as 2 nearly ; in both ships R2 = 20,000 lbs. Suppose
both vessels to have their lengths and other dimensions increased
by one-third; then D = 1^. The Merhara has a displacement
of 3980 tons ; the Greylwund one of 1160 tons ; the enlarged
Merhara would weigh 9-130 tons, the enlarged Greyhound about
2750 tons.
* For some interesting graphic illus- of the Institution of Xaval Architects
trations of the above equations, see a for 1881.
Paper by Mr. Biles in the Transactions
592 NAVAL ARCHITECTURE. chap. xin.
For enlarged MerUra, E^ = 20,000 x (3)'= 35,555 lbs.
For enlarged Greylioimcl, R^ = 20,000 x i = 26,666 lbs.
o
The Oreylwund type, therefore, gains more in economy of pro-
pulsion by enlargement than does the Merhara ; although the
latter type benefits considerably by the same process, and would
have much greater carrying-power in proportion to the expen-
diture of fuel as the size increased.
To the foregoing considerations, which have had regard only
to smooth-water performances, it is necessary to add one remark.
In ocean steaming, the longer, larger, heavier ship is far more
likely to maintain her speed under varying circumstances of
wind and sea than is the smaller vessel. These two sources of
gain in larger ships fully explain the general adoption of the
policy which has resulted in very large increase of the sizes of
ocean steamers.
Increase in size and variation in proportions may, as explained
in Chapter X., affect the ratio which the weight of hull bears to
the displacement. No general law can be stated for this ratio ;
but it is obvious that, whereas in small ships of moderate length
and proportions, the scantlings which give sufficient local strength
also give an ample margin of strength against the principal
strains, the reverse may hold good, at least for certain portions of
the structures, in ships of extreme lengths and proportions. The
longer, larger vessel might, therefore, have a relatively heavier
hull, and this increase in weight of hull must be set against the
proportionate saving on propelling apparatus and coal. There is
reason to believe, however, that the balance of advantage in a
commercial sense on long voyages must always remain with the
larger ship when the difference in size is considerable. As an
example take the Merhara and the enlarged Merhara mentioned
above. If 1600 horse-power was required to drive the Merhara
12 knots, 2800 horse-power would suffice for the latter. For
voyages of equal length at that speed the weights of coal burnt
would bear to one another the same ratio as the horse-powers.
Take 400 tons for the weight of engines, &c., for the smaller ship ;
then 700 tons will be about the corresponding weight for the larger
ship ; if the Merhara be credited with a coal supply of 500 tons,
the larger ship should carry about 880 tons. Suppose further
that in the Merhara the hull weighs 33 per cent, of the displace-
ment, as is common in iron cargo-ships; whereas in the larger
CHAP. XIII. STEAM PROPULSION. 59
-7
ship it is increased to 40 per cent. : then in the Merhira there
will remain 1800 tons available for cargo and equipment, which
can be propelled over a certain distance by an expenditure of
500 tons of coal, as against 4100 tons in the large ship, which
requires an expenditure of less than 900 tons of coal for an equal
distance.
Side by side with the development of the sizes and speeds of
ocean steamers, there has recently been progressing the construc-
tion of a class of very small vessels, possessing remarkably high
speeds — the so-called " swift steam-launches " and torpedo-boats.
Vessels of from 50 to 100 feet in leno-th have been driven at
speeds of from 16 to 23 knots per hour in smooth water, con-
siderably exceeding the measured-mile speeds of the fastest sea-
going ships. The earliest exam[»les of these swift boats were
designed and built by j\Ir. Thornycroft about 1862, and the type
has since received some of its most important developments in
the successive vessels built by his firm.* Mv. Yarrow also has
built a large number of very fast boats for torpedo and other
services. Allusions have been made to the remarkable perfor-
mances of these small vessels in previous pages. The extraor-
dinary features in their curves of resistance, the wave-phenomena
attending their motion at high speeds, and their behaviour in
relation to the surrounding water have been discussed on page
466. The principal characteristics of their machinery have been
described on page 523. But it is impossible to consider the
results attained in these vessels without beins; led to the con-
sideration of the possibility of applying similar methods of
construction on a larger scale to ships employed on distant
voyages. It may well happen, as before remarked, that from the
study of this problem further progress may result ; and in stating
some of the dijSiculties to be overcome, we do not desire to
express a contrary opinion.
First of all, then, it must be noted as a direct consequence of
the law of "corresponding speeds," that the very advantageous
conditions of resistance attained by these torpedo-boats at speeds
of 16 to 22 knots per hour could not be reached in larger ships
until extraordinary sj^eeds had been attained. That law, it will
* For an excellent summary of in- 1881 : and Papers by Mr. Donaldson,
formation, see the Paper by Mr. in the Journal of the Royal United
Thornycroft in the Froceedinys of Service Institution, for 1877 and 1881.
the Institution of Civil Engineers, for
2 Q
594 NAVAL ARCHITECTURE. CHAP. xiir.
be remembered, states that corresponding speeds bear to one
another tlie ratio of the sixth roots of the displacements. A large
torpedo-boat is, say, 30 tons in displacement, and a despatch
vessel, like the Iris, of 3700 tons displacement; the corres-
ponding speeds are then related to one another in the ratio
1 : 2-2. Hence to speeds ranging from 16 to 22 knots in the
torpedo-boats will correspond speeds of 35 to 50 knots in the
ship. Up to 13 knots in torpedo-boats the resistance varies as
the square or cube of the speed : similar laws of variation must
hold for the despatch vessel up to 30 knots per hour. And
if still larger ships are considered, the speeds corresponding
to those where resistance grows slowly in the torpedo-boat are,
of course, still higher. For a Transatlantic steamer of 10,000
tons displacement, for example, 13 knots in the torpedo-boat
would be represented by 34 knots in the ship, and 22 knots
in the torpedo-boat by nearly 60 knots in the ship. The highest
speeds yet attained by first-class seagoing steamships of 9000 to
10,000 tons displacement are from 16 to 18 knots. Suppose
speeds of 25 knots to be aimed at, then the corresponding
speed of the torpedo-boat would be about 10 knots, at which
the resistance is known to vary at a rather higher rate than
the square of the speed.
It may be urged, of course, that if these high speeds were
aimed at, forms would be selected differing greatly irom those
of the torpedo-boats, and making less proportionate resistance.
This is quite possible, although the inquiry involved in this
selection must be laborious, and could only be conducted by
means of model experiments. Supposing it to be successful
it must still remain true that at such high speeds very great
resistances must be encountered in proportion to the displace-
ments driven ; and to overcome these resistances very great
engine-powers will be needed. Hence it follows that the
en<>-ineerinfr problem to be solved in such cases will be not
O or
dissimilar to that so admirably dealt with in the torpedo-boats,
viz. : how to minimise the ratio of the weight of the propelling
apparatus to its power. From the remarks made on page 528,
as to the unsuitability of the locomotive boiler for long-distance
steaming, on account of its need of frequent cleaning and high
rate of coal consumption, it will appear that a solution of the
larger problem stated above has not yet been reached. But it
may be ; and by further improvements in engines and boilers,
while maintaining the lightness which is essential, the equally
essential economical ratio of coal consumption may also be secured.
CHAP. XIII.
STEAM PROPULSION.
595
The following table exhibits in a succinct form the expeuditure
of power required to attain certain measured-mile speeds in
screw-steamers of different classes and sizes. For ships of the
Koyal Navy, speed trials are always made and recorded ; for
merchant ships corresponding trials are often omitted, or are
made when the vessels are light. It will be understood therefore
that, although the figures given for merchant ships are taken
from good examples, they cannot be guaranteed to the same
extent as those for war-ships.
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596 NAVAL ARCHITECTURE. chap. xiir.
Although the table is confined to comparatively few classes, it
represents the conditions of a very large number of ships, and
may be of service in roughly approximating to the engine- power
required in a new ship belonging to any of these classes. It also
furnishes many illustrations of the effect of changes in the sizes
and forms of ships upon economy of propulsion.
CHAP. XIV. THE STEERING OF SHIPS. 597
CHAPTER XIV.
THE STEERING OF SHIPS.
Ships are ordinarily manoeuvred by means of rudders, sails, or
propellers driven by steam-power. Steering by sail-power alone
may be accomplished by the skilful seaman, if his ship has been
well designed. Steering by the action of the propellers alone is
also a possibility in certain classes of steamships, and this may
be a great advantage under certain circumstances. Rudders are
fitted, however, in all classes of ships, and form the most important
means of controlling their movements under all ordinary conditions
of service ; so that in this chapter attention will be chiefly
directed to the principles upon which the action of rudders
depends. A brief notice will suffice respecting manoeuvring by
the use of propellers ; but nothing will be said respecting man-
oeuvring under sails alone, as that is peculiarly a matter of sea-
manship. The principal facts which concern the naval architect
in arranging and distributing the sail-spread of a ship have been
already discussed in Chapter XIL
The rudder is almost always placed at the stern of a ship, which
is the most advantageous jDosition for controlling her movements
when she has headway. In what follows it will be understood
therefore, that, unless the contrary should be stated, v^e are deal-
ing with stern rudders. After discussing their action, a few
remarks will be made respecting the use of bow rudders, auxiliary
rudders, and other supplementary methods of increasing the turn-
ing power of ships.
Two kinds of rudders require to be noticed. First, the ordinary
rudder, which rotates about an axis near its foremost edge, and is
hung to the sternpost of the ship. Fig. 127 shows the common
arrangement in a single-screw ship. AA is the axis of the
rudder, the line passing through the centre of the pintles by which
the rudder is hung to the after sternpost, or rudder-post. In the
598
NAVAL ARCHITECTURE.
CHAP. XIV.
FIG. 127
Ei'ofile
plan, AB represents tlie rudder put over to port, the helm being
a-starboard. In sailing ships, paddle-steamers, jet-propelled ves-
sels, and twin-screw ships, the
ordinary rudder is hung to the
after end of the ship, there being
only one stern post in such vessels.
Fig. 128 shows the commou
arrangement in twin-screw ships ;
and, apart from the propellers, the
drawing will also serve for the
other classes named. A few ships
have had the rudders placed before
the single-screw propellers, but
this is not a common plan ; when
it is adopted, the rudder is gene-
rally of the ordinary kind, and is
placed in the after deadwood below
the screw-shaft.
The second form to be noticed is the haJaneed rudder, which
differs from the ordinary form in having a part of its area —
usually about one-third — before the axis about which it rotates.
This kind of rudder has been used in many steamships of the
mercantile marine and the Eoyal Navy. Fig. 129 illustrates a
common arrangement : AA is
the axis. It will be observed
that there is no rudder-post, the
Aveight of the rudder being
taken inboard, and the lower
bearing at the after end of the
^ keel being made use of simply
to steady the rudder. In some
cases balanced rudders have
been fitted without the lower
bearing, the rudder-head being
made exceptionally strong ; but
this plan has considerable dis-
advantages, especially as regards
liability to derangement by
shocks or blows of the sea. Usually the balanced rudder is
made in one piece, and, when put over, occupies a position
similar to that indicated (in plan) by Fig. 130, the part AC
before the axis A being rigidly attached to the part AB abaft it.
When the rudder is thus made in one piece, it is termed a
FIG. 128
JPj^ofile
CHAP. XIV.
THE STEERING OF SHIPS.
599
FIG. 129
"simple" balanced rudder. Experience has shown, however,
that, while it is advantageous when a vessel is under steam, to
use the large area of the balanced
rudder, it may be preferable, when
she is under sail alone, to use a less
area. To enable both these objects
to be attained, the so-called " com-
pound" balanced rudder has been
devised ; it is fitted in Her Majesty's
ships Hercules and Sultan, and has
proved very satisfactory. The part
before the axis is attached to a
hollow annular head ; up through
which passes the rudder-head wliich
carries the after part of the rudder ;
and the two parts are hiuged to
one another along the axis. When
the ships are under steam, the two
parts can be locked together and
made to act as a simple balanced
rudder ; when the ships are under
sail, the fore part of the rudder can
be locked fast in the line of the keel (as shown by AC, Fig, 131),
occupying a position resembling that of the rudder-post in
ordinary screw-steamers, and the after part alone (AB) is used
to steer the ship.
Both ordinary and balanced rudders may be regarded simply as
plane surfaces which, by means of suitable mechanism, can be
placed at an angle with the keel-line. It is customary to speak
of the "angle of helm" rather than the rudder angle. "Helm
a-starboard " means that the rudder has been put over to port, and
that the head of the ship moves to port. " Helm a-port " means
that the rudder has been put over to starboard, and that the
head of the ship moves to starboard. A sailing ship has
" weather-helm " when the rudder has been put over to the
leeward side, in order to make the head of the ship fall off from
the wind. When the helm is " a-lee," the rudder has been put
over to the windward side, in order to bring the head of the ship
up to the wind.
In discussing the action of the rudder, it will be convenient to
consider separately the following features : —
(1) The causes which produce, and govern the amount of, the
pressure on the rudder, making it effective in turning a ship.
600 NAVAL ARCHITECTURE. chap. xiv.
(2) The relation which exists between the pressure on the rudder
and the force required at the tiller-end to hold the helm at
any angle desired ; as well as the work to be done in putting
the helm over.
(3) The turning effect on a ship produced by the pressure ou
the rudder.
The first and second of these subdivisions are very closely con-
nected ; in discussing the third, it will be necessary to distinguish
between, what may be termed, the initial motion of a ship when
her helm is put over, and her subsequent motion when the speed
of rotation has become approximately uniform.
When a rudder is placed obliquely to the keel-line of a ship,
and streams of water impinge upon its surface in consequence of
the motion of the ship, or the action of her propeller, the
motions of these streams must be more or less checked or diverted^
and a change of momentum is produced (see page 435), which
reacts upon the rudder and causes a normal pressure upon its
surface. If all these streams were moving with uniform velocity
and in parallel lines before they impinged on the rudder, the
normal pressure upon it could be estimated approximately by the
rules stated for thin plates on page 436 ; and since rudders are
commonly not wholly submerged, these rules would probably give
somewhat less than the true pressure. In practice the streams
impinging upon a rudder do not move in parallel lines or with
uniform velocity ; and to estimate strictly the normal pressure
on a rudder it would be necessary to take account of the velocity
and direction of motion of the water in each elementary stream,
in order to determine the change of momentum. Approximate
estimates suffice, however, for all practical purposes, and in
making such estimates it is customary to express the speed of
approach of the streams to the rudder either in terms of the
speed of the ship or that of her propeller ; assuming the same speed
for all the streams. If the vessel is moving ahead in a straight
course and her helm is put over, it is usual to assume that the
streams are flowing parallel to the keel, and that the angle of
obliquity to be used in estimating the effective pressure on the
rudder is the angle which it makes with the keel. As soon as
the turning effect of the rudder begins to be felt by a ship, and
she acquires angular motion as well as translatory motion, the
conditions are altered, and the effective angle of obliquity of the
rudder is usually made less than its angle with the keel. This
has been proved experimentally and will be made the subject of
further remark (on page 62G), when considering the phenomena
CHAP. XIV. THE STEERING OF SHIPS. 6oi
attending the turning of ships. It may be added that for the
purposes for which approximate estimates of the rudder pressure
are made, it is safer to take the helm-angle with the keel as the
effective angle of obliquity.
Although these assumptions are commonly made in calcula-
tions for the sizes and strengths of rudders and steering gear, no
one supposes them to strictly represent the facts, even in the
simplest case, such as that of a sailing ship running dead before
the wind. From the explanations given on page 441, as to the
stream-line motions at the stern of a sailing ship thus circum-
stanced, it will appear that the speeds and directions with which
the streams impinge upon the rudder will vary with the headway,
the form of the stern, the roughness of the bottom, and the helm
angle. When a ship is not running before the wind, she has
leeway as well as headway, and is inclined to the upright, all of
which circumstances affect the stream-line motions, and the
normal pressure on the rudder; but their influence cannot be
exactly estimated, and is of little practical importance.
In any case, however, the rudder pressure which is effective
for turning a ship has no connection with the hydrostatical
pressure which would be acting upon the suiface, if the rudder
were put over to any angle when the ship was at rest in still
water. This distinction is mentioned because some persons have
confused hydrostatical pressure, with the pressure or reaction
due to the relative motion of the streams and the rudders, and
have proposed to shape the rudder according to laws based upon
this wrong assumption. The mistake made is similar to that
referred to at page 435, as to the relative resistances of a plane
surface wholly or ptirtly submerged ; but there can be no
question that without motion of the ship, or of the water past the
ship, the rudder can have no steering power.
Paddle-wheel steamers and jet-propelled vessels differ somewhat
from sailing ships in their steerage-power. The latter require to
be in motion if the water is still— to have "steerage-way" —
before the rudder can act ; but the former may acquire steerHge-
power with little or no headway by means of the action of their
propellers. If the wheels of a paddle steamer are started, for
example, when she is at rest in still water, a paddle-race is driven
astern at considerable speed on each side ; and it is a matter of
common experience that this motion of the race rehitively to the
rudder will develope an effective pressure and bring the ship
under control by her rudder, before she has gathered much head-
way. It is probable th;it similar conditions hold good in jet-
6o2 NAVAL ARCHITECTURE. chap. xiv.
propelled vessels, althougli experience with them is limited, lu
both those classes of vessels, however, when their sjjeed has been in-
creased by the continued action of the propellers, and approximately-
uniform motion has been attained, the influence of the propeller-
race becomes far less, and the steering-power of the rudder is
governed mainly by the speed of the vessel, the fineness of the
run, and other conditious closely agreeing with those described
for sailing ships.
The steerage of screw steamers presents certain special features
deserving carei'ul consideration. In single-screw ships as ordinarily
constructerl, the propeller is situated immediately before the
rudder ; when a vessel is moving ahead the race is driven aft
more or less directly upon the fore side of the rudder, and when
she is moving astern the action of the propeller induces a forward
pressure on the after side of the rudder. The particles of water
in the propeller-race have rotary as well as sternward motion
communicated to them (see page 544) and, moving in more or
less spiral paths, impinge upon the rudder in directions which
may depart wiilely from parallelism with the keel-line. Experi-
ments have been made to determine the " position of zero-
pressure " for rudders placed behind single-screws, and they indi-
cate clearly the obliquity of the motion of the streams in the
race. Herr Schlick, for example, divided an ordinary rudder into
two equal parts, in the steamer Vinodol ; the line of section being
horizontal. When the screw was at work the lower half found its
position of rest at an inclination of rather less than 10 degrees on
one side of the keel-line, while the upper half rested at nearly an
equal inclination on the other side of the keel-line. In other
cases the helm has been left free while the screw was at work, and
the rudder has been found to rest at a sensible angle to the keel-
line, the effective pressure of the streams delivered by the lower
blades being predominant over that of the streams delivered by
the upper blades. This position of rest or zero-pressure is clearly
that from which the effective rudder-angle should be reckoned,
and not from the keel-line, in estimating the initial pressure on a
rudder put over when a screw-ship is proceeding on a straight
course. Further it will be noted that to obtain equal pressures
on opposite sides of the keel the helm must be brought to a
greater angle with the keel-line on one side than on the other.
This has been considered disadvantageous, and various proposals
have been made to remedy the supposed loss of eflfieiency (see
page 642) ; but they have not found i'avour in practice.
The influence of the propeller upon the steerage of single-screw
CHAP. XIV. THE STEERING OF SHIPS. 603
ships is illustrated by the well-known practice of " slewing " ships
completely round in a very limited space. Suppose a vessel to
be at rest in still water, and that her screw is started ahead ; it
delivers a race having considerable sternward velocity and thus
gives good steerage- power before the vessel has gathered head-
way.. The head of the ship begins to turn, say to starboard, the
helm being a-port ; and when headway is becoming sensible the
engines are reversed, the helm put a-starboard, and by the action
of the screw a pressure is developed on the aft si<le of the rudder
tending to augment the previous motion of the head of the ship
to starboard. In this manner, by suitable manipulation of engines
and rudder, the ship can be turned completely round in a very
small space, if that manoeuvre should be thought necessary.
The time occupied in turning would, of course, be considerable as
compared with that needed for turning under- way.
Twin-scre\\s, placed in the manner indicated in Fig. 128,
are not so favourably situated as single-screws for influencing the
effective rudder-pressure by the motion of \\iq race. But the
same kind of influence is exerted to some extent ; and to give it
marked effect, rudders of large longitudinal dimensions have been
fitted in many recent twin-screw war-ships. These broad rud'lers
sweep out to a considerable distance from the keel-line, even for
moderate helm-angles, and their after parts, at least, come fully
under the influence of the screw-race. Experience shows this
simple expedient to be very effective, one of the most recent
examples being found in the InflexiUe, where an addition fitted to
the after part of the rudder caused a sensible improvement in
the steering. No serious difficulty is encountered in the steering
of twin-screw ships when proper care is bestowed upon the rudder
and steering gear, and it will be seen that the facts as to the
turning trials of twin-screw ships given at the end of this chapter
confirm this statement.
So far as the action of the rudder is concerned, therefore, the
form of the after part of either single or twin-screw steamers is
not so important as it is in sailing, paddle, or jet-propelled
vessels; but it has been shown (on page 55U) how necessary to
the efficiency of screws as propellers is fineness of form in the
after body.
Broadly speaking, it may be said that, when a screw steamer
is moving ahead, the velocity with which the streams impinge
upon her rudder, if placed abaft the screw, equals the speed of the
screw, and therefore equals the sum of the speed of the ship and
slip of the screw. When the slip is considerable, as it may be
6o4 NA VAL ARCHITECTURE. CHAP. xiv.
in some cases, the increase in rudder-pressure and steering effect
above that due to the headway of the ship may be a most
valuable element in her handiness. Similar reasoning applies
to the case where the propeller is driving a ship astern at a
steady speed. But the most important case of screw-ship
steerage is that when, to avoid a collision or any other danger,
the engines of a screw steamer are suddenly reversed, say, from
full speed ahead to full speed astern. The vessel will then
maintain headway for a short time, but the effect of the propeller
race upon the rudder may more than counterbalance the effect of
headway, and the vessel may steer as if she were moving astern,
the resultant pressure being delivered upon the after surface of
the rudder.
This feature of screw-ship steerage has long been known. An
experiment was made with the Great Britain in 1845; and it was
found that, when the vessel was going astern at the rate of 9 or
10 knots, if the engines were rapidly reversed, she steered im-
mediately as if she were going ahead. Similar experience ap-
pears to have been gained with the Archimedes and other early
screw steamers. Further experiments of a more detailed character
have been made recently by a Committee of the British Associa-
tion, appointed in consequence of action taken by Professor
Osborne Keynolds. The main purpose of the inquiry was to
discover the best rules for the guidance of ships' captains in
endeavouring to avoid collisions ; and the following extracts from
the final Report summarise the principal conclusions reached after
making numerous experiments. There are some parts of this
summary to which further reference will be made ; and the
second paragraph is that which is most closely related to the
matter now under discussion.
" It appears, both from the experiments made by the Committee,
*' and from other evidence, that the distance required by a screw
" steamer to bring herself to rest from full speed by the reversal
"of her screw, is independent, or nearly so, of the power of her
" engines, but depends upon the size and build of the ship, and
" generally lies between four and six times the ship's length. It
"is to be borne in mind that it is to the behaviour of the ship
" during this interval, that the following remarks apply.
"The main poiut the Committee have had in view has been to
"ascertain how far the reversing of the screw in order to stop a
"ship did, or did not, interfere with the action of the rudder
" during the interval of stopping ; and it is as regards this point
" that the most important light has been thrown on the question
CHAP. XIV. THE STEERING OF SHIPS. 605
" of handling ships. It is found an invariable rule that, during
" the interval in which a ship is stopping herself by the reversal
" of her screw, the rudder produces none of its usual effects to
" turn the ship ; but that under these circumstances the effect of
"the rudder, such as it is, is to turn the ship in the opposite
" direction from that in which she would turn if the screw were
" going ahead. The magnitude of tliis reverse effect of the rudder
" is always feeble, and is different for different ships, and even for
" the same ship under different conditions of lading.
"It also appears from the trials that, owing to tlie feeble
"influence of the rudder over the ship during the interval in
" which she is stopping, she is then at the mercy of any other
"influences that may act upon her. Thus the wind, which
" always exerts an influence to turn the stem (or forward end) of
"the ship into the wind, but which influence is usually well
" under control of the rudder, may, when the screw is reversed,
" become paramount, and cause the ship to turn in a direction
" the very opposite of that which is desired. Also the reversed
"screw will exercise an influence which increases as the ship's
" way is diminished to turn the ship to starboard or port, accord-
" ing as it is right or left lianded : this being particularly the case
" when the ships are in light draught."
" These several influences, the reversed effect of the rudder, the
" effect of the wind, and the action of the screw, will determine
" the course the ship takes during the interval of stopping. They
" may balance, in which case the ship will go straight on : or any
" one of three may predominate and determine the course of the
" ship. The utmost effect of these influences when they all act
"in conjunction — as when the screw is right banded, the helm
"starboarded, and the wind on the starboard side— is small as
" compared with the influence of the rudder as it acts when the
" ship is steaming ahead. In no instance has a ship tried by the
" Committee been able to turn with the screw reversed on a circle
"of less than double the radius of that on which she would turn
"when steaming ahead. So" that even if those in charge could
" govern the direction in which the ship will turn while stopping
" she turns but slowly, whereas in point of fact those in charge
" have little or no control over this direction, and unless they are
"exceptionally well acquainted with their ship, they will be un-
" able even to predict the direction."
Summing up these remarks on the causes which govern the
pressure on the rudders of different classes of ships, it may be
said generally that without motion of a ship through the water,
6o6 NA VAL ARCHITECTURE. CHAP. xiv.
or of the water past tlie rudder, it can have no steering power. A
ship or boat anchored in a tidal current or river may be turned
to some extent from the line of flow by the action of her rudder,
because the water has motion relatively to the rudder. A ship
almost destitute of headway may be under command, if her pro-
peller is at work and delivering a race which flows past the
rudder. But for a ship at rest in still and undisturbed water the
rudder is powerless. The hydrostatical pressure sustained by the
sides of the rudder, if held at any angle, balance one another, and
are obviously quite distinct from the reaction due to change of
momentum in streams having motion relatively to the rudder.
In all cases of relative motion of water and rudder the normal
pressure depends upon the area of the immersed part of the
rudder ; the angle of its obliquity to the position of zero-pressure,
or, roughly speaking, to the keel-line ; and the spseds and direc-
tions with which the streams impinge upon the rudder-surface.
In sailing ships the motions of the streams depend principally
upon the motions of the ships, and the forms of the after body.
In paddle steamers and jet-propelled vessels similar considerations
are most influential, although the action of the propellers may
influence the steerage of ships starting from rest, or reversing
their course. In screw steamers the action of the propellers is
most important, especially when the slip is considerable, and the
velocity of the race is high.
It must be added that, when ordinary rudders are employed,
and hung either to a broad rudder-post abaft the screw, as in
Fig. 127, or to the body of the ship, as in Fig, 128, the check
put upon the motion of the streams by the rudder must produce
a reaction and pressure not merely upon the rudder itself, but
upon the portion of the stern-post or deadwood adjacent to the
rudder. This additional pressure will be delivered on the side
towards which the rudder is put over, and there is good reason
for believing that it considerably assists the rudder pressure in
steering a ship, being most valuable in cases where the rudder
is hung to the body of the ship. With simple balanced rudders
placed as in Fig. 130, there is no corresponding pressure on the
deadwood, but instead of it a normal pressure on the additional
rudder-area placed before the axis. Compound balanced rudders,
with the forward part locked fast (as in Fig. 131), of course,
resemble the case illustrated in Fig. 127 for an ordinary rudder.
Besides these normal pressures on the rudder, sternpost, and
deadwood, there will be a certain amount of /^^■c^^■o?^aZ resistance
on the rudder surface when placed obliquely; but this is of little
CHAP. XIV. THE STEERING OF SHIPS. 607
importance, as compared with the normal pressures, except for
very small angles of helm : and, so far as it produces any effect
on the steering, it will act against the normal pressures.
Next : reference must be made to the force required at the
tiller-end to hold the rudder at any angle. This will, of course,
depend upon the length of the tiller and the mode of applying
the force ; but it may be assumed that both these conditions are
given. In Fig. 132 au ordinary rudder is shown. The resultant
pressure upon it is P, acting through the centre of effort C of
the immersed rudder-area. AT represents the tiller, Q the force
required at its end, if applied normally to the tiller, in order to
FIG. 132
hold the rudder over. Apart from friction of the pintles, rudder
bearings, collar, &c., we should have,
P X AC = Q X AT.
These frictional resistances vary considerably in different vessels,
but may be made comparatively small by means of careful
arrangements; in most cases they probably act with the force
Q in resisting the motion of the rudder back towards the keel-
line. Neglecting friction, and supposing the other conditions
fixed, the force Q at the tiller-end will vary with the distance
AC of the centre of effort from the axis of the rudder. On the
same assumption the force Q may be determined approximately
for any helm-angle, if the distance AC is known, since the normal
pressure P can be estimated roughly in the manner desciibed on
page 436. In practice the maximum helm-angle varies from
oO to 45 degrees ; so that inquiries as to the variation in the value of
AC need not be carried beyond 45 degrees except it be done for
scientific purposes. Formerly it was assumed that the centre of
effort coincided with the centre of gravity of the immersed area of
the rudder, and that the pressure due to the reaction of the streams
6o8 NAVAL ARCHITECTURE. CHAP. xiv.
was uniformly distributed over that area. Experience and in-
vestigation have proved this view to be incorrect for a thin phite
set obliquely to the line of motion, and for actual rudders. In
the case of balanced rudders, for example, it has been ascertained
that, when the area before tlie axis was about one-half as jxreat as
the area abaft the axis, a dynamometer attached to the tiller-end
when at 40 degrees indicated little or no strain, showing that the
centre of effort was then practically coincident with the axis. With
ordinary rudders a similar excess of pressure probably exists on
the forward part; although it is conceivable that in twin-screw
ships the more direct action of the race on the after part of the
rudder may tend to modify the position of the centre of effort.
If the rudder be treated as a rectangular plate advancing obliquely,
its leading edge (corresponding to the fore edge of a rudder) may
be regarded as continually entering water which was comparatively
little disturbed by the previous motion, and which, therefore,
reacts more powerfully on that part of the area than does the
water which impinges upon the after part, and which had been
previously disturbed by the motion of the plane. This matter
has been dealt with mathematically by Lord Eayleigh and
experimentally by M. Joessel, the late Mr. Froude and others.
For a rectangular plane of breadth &, the distance d, of the centre
of pressure from the forward edge has been expressed by the
following formulae ; a being the angle made by the plane with its
line of motion :
Lord Eayleigh . . d = - — -b
2 4 * 4 -j- TT sin o *
M. Joessel . . . r? = -195 & -|- '305 J.sin o.
Herr Hagen, after numerous experiments on comparatively
small planes, proposed the following approximate formula : *
For angles below 10 degrees there must obviously be con-
siderable difficulty in determining experimentally the value of d ;
but from 10 degrees up to 45 degrees there is greater certainty.
The results obtained independently by Mr. Froude and M. Joessel
agree closely with one another, and confirm the general accuracy
of Lord Eayleigh's formula. At 10 degrees the centre of effort is
about one-fourth the breadth from the leading edge ; at 20 degrees
* See the abstract of his original Paper published in vol. 56 of the Proceed-
incjs of the Institution of Civil Engineers.
CHAP. XIV. THE STEERING OF SHIPS. 609
about three-tenths of tlie breadth ; at 30 degrees three-eighths of
the breadth ; at 40 degrees four-tenths of the breadth. These
values may not apply exactly to rudders, owing to the variations
in the directions and velocities of the streams impinging upon
the surface ; but they may be treated as approximately correct.
M. Joessel was led from his experiments to a very simple law,
which confirms previous practice : viz., that for a rectangular
plane hinged at its fore edge, and inclined at an angle a to the
line of motion, the moment of the normal pressure about the axis,
divided by sine a is a constant. Using the notation of Fig. 132,
this law is as follows —
P X AC = constant X sin a.
The constant in this expression is simply the moment of the
normal pressure when the plane advances at right angles to itself,
which moment can be found by the rules already given. If this
law be accepted, the estimate for the force required at the tiller-
end at any angle a can be very readily made. In a balanced
rudder of the usual proportions about one-third of the total area
is placed before the axis ; as it is desired to give the rudder the
power of " righting " itself rapidly when the strain on the steering
ropes is relieved. But the distance of the centre of pressure
abaft the axis is small, even at the larger angles, and for angles
below 10 or 15 degrees the centre of pressure is probably a little
before the axis. Hence it liappens that with such a rudder, properly
balanced, a small force applied at the tiller-end suffices to hold
the rudder steady; whereas, in an ordinary rudder having an
equal area and held at an equal angle, the force at the tiller-end
has to balance the very considerable moment of the pressure
about the axis.
M. Joessel some years ago proposed a special form of balanced
rudder designed to still further diminish the force required at the
tiller-end when dealing with large areas and considerable helm-
angles. Instead of being formed in one solid blade, it consists of
two or three blades set parallel to one another and turning about
one axis. The distance between the blades is made considerable
in relation to their fore and aft measurement, so that the streams
of water can pass freely between them and operate upon the
surface of each blade. Very extensive experiments have been
made with these rudders in the French navy and a few trials
have been made in the Royal Navy. They are reported to have
fulfilled the expectations of M. Joessel, and to have enabled very
large effective rudder-pressures to be obtained with moderate power
2 R
6lO NAVAL ARCHITECTURE. chap. xiV.
at the steering wheel. From the particulars which M. Joessel has
himself furnished to the Author and from official reports of the
trials of French ships, it is evident that with these two or three-
bladed rudders and a given power at the wheels, French war-ships
have been turned much more quickly and in less space than with
ordinary rudders. In one example with 35 degrees of helm, a vessel
fitted with an ordinary rudder turned in a circle of 340 metres
diameter, occupying 6| minutes in the manoeuvre ; whereas with
equal helm and the same number of revolutions of the screw, a
two-bladed rudder enabled her to complete a circle of 270 metres
diameter in 5| minutes. It does not appear, however, that the
double or triple-bladed rudders are greatly superior in steering
effect to single-bladed balanced rudders. For instance, in two
French armoured corvettes of the same class, one had the usual
form of balanced rudder, the other a triple Joessel rudder of
about 75 per cent, greater area. Under nearly identical condi-
tions of speed and helm-angle the first turned in a circle of which
the diameter was about 5*7 times her length, and the other, with
the triple rudder, turned in a circle of which the diameter was
about five times the length. In some English ships with simple
balanced rudders the corresponding ratios have been quite as
low as any obtained with the Jcessel rudder. The advantage in
point of steering of the Joessel rudder is obtained at the expense
of a greater weight ; but this is not important. It is also stated
that there is a sensible loss of speed, especially in high-speed
ships when multiple-bladed rudders are used ; and in recent
French ships, supplied with steam steering gear, this form of
rudder does not appear to have been fitted. Larger rudders
can of course be worked with these appliances, and economy
of power at the steering wheel becomes less important ; so
that the Joessel principle loses much of its value. Its ingenuity
remains.
The ii:orh to be done in putting a rudder over to any angle in-
cludes that required to overcome the moment of the pressure about
the axis, and that needed to overcome the frictional and other
resistances of pintles, bearings and steering gear proper. There
may, of course, be a considerable amount of waste-work between
the steering wheels and the tiller-end, through friction of wheels,
rods, chains, blocks, &c. ; but with these we are not now con-
cerned. The useful work done in putting the rudder over is that
spent in overcoming the moment of the effective pressure on the
rudder at each instant as it moves from amidships to the extreme
angle (see the parallel case on page 144). For a balanced rudder
CHAP. XIV. THE STEERING OF SHIPS. 6ll
this useful work is very trifling. For an ordinary rudder it may
be represented approximately by the expression —
Useful work = Constant x vers. a.
where a is the extreme angle reached, and the " constant "
equals the product of the pressure on the rudder when moved
normally to itself at the given speed by half the mean breadth
of the rudder. As an example, suppose it was desired to put over
an ordinary rudder, having an area of 180 square feet, and a mean
breadth of 7 feet, to an angle of 45 degrees, the ship having a
single screw, for which the speed is 25 feet per second (about 15
knots) ; neglecting the obliquity and varying speeds of the streams
in the screw-race, and supposing them all to flow fore and aft at
a speed of 25 feet per second, the following expressions hold : —
lbs. sq. ft. lbs.
Normal pressure on rudder = 1-12 x 180 X (25)2 = 126,000;
Useful work = Normal pressure x Half mean breadth x vers. 45^
= 126,000 lbs. X 3| feet x (1-*n/2)
= 129,000 foot-pounds (nearly).
If steam steering gear were applied, and 12 seconds were named
as the time for putting the helm hard over, the nett horse-power
of the steering engine would be given by the expression :
AT .. 1 129,000 „., , , 1 ,
Nett horse-power = -^-^ ^ = 20 (roughly).
The actual indicated horse-power of the engine would, of course,
be much greater in order to allow for its own waste-work, friction
of steering gear, rudder, &c.
When manual power alone is available for steering, balanced
rudders have the great advantage of enabling large areas to be
put over rapidly to considerable angles ; and it was this supe-
riority over ordinary rudders which led to their general use in
the larger ships of the Koyal Navy between 1863 and 1868.
The balanced type of rudder has been long known. Earl
Stanhope proposed it in 1790; it svas fitted to a ship by Captain
Shuldham about thirty years later, and adopted in the Great
Britain about 1845. It Mas not introduced into the Eoyal Navy
until 1863, when the steering gear in use, worked by manual
power, had failed to give satisfaction in the long swift ships of
the Warrior class, and in many other screw-steamers of less size.
The extreme angles of helm that could be reached did not
2 R 2
6l2 NAVAL ARCHITECTURE. chap. xiv.
exceed 18 to 25 degrees ; and to secure even these results there
was such a multiplication of tackles between the steering wheels
and tillers as made the loss of power in friction veiy considerable,
and tlie time of putting the helm over very long. On one occasion,
lor example, the Blach Prince was turned in a circle with her
rudder 30 degrees from the keel-line ; to put the helm over
occupied 1^ minute, to complete the circle Si minutes were taken,
and forty men were engaged at the steering wheels and relieving
tackles. On another trial, the Minotaur, with eighteen men
at the wheels and sixty at the relieving tackles, turned a
circle in about 7f minutes, 1^ minute being occupied in putting
the helm over to the very moderate angle of 23 degrees. Balanced
rudders enabled both these faults to be corrected, the helm being
put up to angles of 35 degrees or 40 degrees very quickly, by the
application of a very moderate force at the steering wheels.
The Belleroplion was the first ship fitted on this principle; and
on trial her rudder, which had an area about 25 per cent,
greater than that of the Minotaur, was put over to an angle of
37 degrees in about 20 seconds by eight men, when the ship was
steaming nearly at the same speed as the Minotaur had attained.
The Hercules also, steaming at a higher speed than the Minotaur,
had her larger rudder put over to 40 degrees in 32 seconds by
sixteen men at the steering wheels, and completed a circle in
4 minutes. Further examples of the economy of power and
lapidity of motion rendered possible by the balanced rudder will
be found in the records of trials of her Majesty's ships.*
Various proposals were made about the same time as balanced
rudders came into use, to reduce the work necessary to put
ordinary rudders hard over. Mr. liuthven, known chiefly for
his advocacy of the jet-propeller, devised a very clever system
of counterbalancing ordinary rudders by means of weights fitted
within the ship; but we are not aware that the plan has ever
been adopted. There are obvious objections to the additional
weights and complication involved in such an arrangement ;
especially if applied to rudders of as large area as can be con-
veniently dealt with on the balanced system.
The introduction of steam and hydraulic steering apparatus
has, however, restored the use of ordinary rudders in the largest
screw-steamers of the Eoyal Navy. In vessels possessing sail-
power as well as steam-power, it has been found tliat the balanced
* See a valuable Paper by Mr. Barnaby in the Transactions of tbe Institution
of Naval Architects for 1863.
CHAP. XIV. THE STEERING OF SHIPS. 613
rudder, \Yith its large area and facility of movement, might,
unless carefully managed, cause ships to miss stays, or to tail in
manoeuvring under sail alone. The compound balanced rudder
was devised to remove this objection, and has answered its intended
purpose ; but it is costly. Moreover, in all ships it is admitted
that the ordinary rudder is less liable to serious damage, by
striking the ground or other accidents, than the balanced rudder.
When efficient apparatus had been devised by which the rudders
of the largest vessels could be brought under the control of
one man, and put over rapidly to any angle desired, there was
every reason, therefore, to resume the use of ordinary rudders.
And with twin-screw propellers these rudders possessed further
advantages over the balanced type, in enabling the power of the
screw-race on either side to be utilised more efficiently. One
example will suffice of the great advantages gained by using steam
steering engines in large ships. The Minotaur is now fitted on
this principle, and on trial it was found that the rudder could be
put over to 35 degrees in about 16 seconds by two men ; the circle
was turned in about 5^ minutes, and its diameter was less than
two-thirds as great as that on the former trial. Placing these
figures beside those stated above, when manual power alone was
used at the steering wheels, it will be seen how great has been
the improvement made in this ship, of which the rudder remains
unaltered ; and comparing the helm-angle and time for putting
the rudder over with the figures given for ships with balanced
rudders, it will be seen that the ordinary rudder with steam
steering is at no disadvantage.
In ships of war, steam steering gear has the further advantage
of placing the control of the largest ships in the hands of one or
two men, possibly in those of the commanding officer himself. To
secure this advantage, such gear has been fitted in ships ^^itll
balanced rudders, where the gain in manoeuvring power has been
comparatively small. Large merchant steamers are similarly
fitted, the Great 'Eastern having been one of the first vessels
furnished with a steering engine. A small auxiliary engine is
now usually employed for the purpose, steam having been
generally preferred to hydraulic power after numerous trials,
although some arrangements on the hydraulic principle have
given great satisfaction. Plans have been devised for taking
power off the main screw-shafts in order to steer ships, but tliey
have not found much favour ; and the arrangements now in use
having proved thoroughly satisfactory, it is unlikely that the
power of the main engines will Le utilised for steering. The
6i4
NAVAL ARCHITECTURE.
CHAP. XIV
great majority of ships are still steered by manual power, and
are likely to continue in that condition, their moderate sizes and
speeds enabling ordinary appliances to put their helms over
quickly to sufficiently large angles.
Thirdly : as to the effect of the rudder in tunnng a ship. This
is the purpose for which the rudder is fitted, but the preceding
remarks have been necessary in order to clear the way for the
description that will now be attempted.
Suppose a ship to be advancing on a straight course and with uni-
form speed, the stream-line motions on either side being perfectly
symmetrical ; then it is known, as the result of model experiments,
that the least disturbing cause will produce a departure from
this balance of the stream-line motions, and cause the vessel to
swerve from her original course. Immediately after the helm
begins to move over, such a disturbing cause is developed in
FIG. 133
the pressure on the rudder, the magnitude of which increases
as the helm-angle becomes larger. Fig. 133 shows the plan of
a ship, with the rudder (AB) put over to the angle BAD ; the
arrow indicates the line of action of the resultant pressure P.
Let G indicate a vertical axis passing through the centre of
gravity of the ship ; through Gr draw the line HL parallel to the
line of action FC of the resultant pressure on the rudder, and
along HL suppose two equal and opposite forces P, P to be applied.
These forces will balance one another, and therefore will not
produce any change in the conditions to which the ship is
subjected independently of them. By this means the single force
P on the rudder is replaced by a single force P acting along HG,
and a couple formed by the pressure P on the rudder and an
equal force acting along LG; the arm of this couple is GF, and
it evidently tends to turn the vessel in the direction indicated
by the arrows at the bow and stern. The single force P acting
along HG tends to produce a simultaneous motion of translation
CHAP. XIV. THE STEERING OF SHIPS. 615
of the vessel along its line of action. This force P may be
resolved into two componenls : if GH represents P, HK will be
its component acting parallel to tlie keel, and KG the component
acting perpendicularly to tlie keel. The transverse component
is usually larger than the longitudinal ; but it is not so important
because at each instant it has opposed to it the great force of
lateral resistance* and therefore can cause but a very small
speed of drift. The longitudinal component, on the contrary,
may exercise a sensible effect in checking the speed of a ship
while she is turning. As the rudder is put over, the value as
well as the direction of P change, and the absolute and relative
values of these component forces will change ; but at each instant
conditions similar to those described will be in operation. It
becomes important, therefore, to trace the consequent motion of
the ship; and for the sake of simplicity it will be assumed that
she is a steamer, the propelling force being delivered parallel to
the keel-line.
Ultimately, when the rudder has been held at a steady angle
for some time, the ship will be found to be turning in a path
■which would be very nearly a circle, and is usually treated
as if it were a circde. Her speed will be less than it would
be if she were steaming on a straight course with the same
engine-power, and her ends will be turning about the vertical
axis passing through the centre of gravity, with a nearly uniform
motion, or angular velocity. Before this condition could have
been reached, however, there must have been a period during
which the angular velocity was gradually accelerated up to its
uniform value, while the headway was being checked, and before
the drift to leeward had supplied a resistance balancing the
component of the rudder pressure and the centrifugal force. It
will be well, therefore, to glance at this period of change before
considering the case of uniform motion.
As soon as the rudder is put over, an unbalanced couple will
be brought into operation, and the ship will begin to acquire
angular velocity. At first this velocity will be very small; and
as the resistance offered by the water to rotation varies very nearly
as the square of the angular velocity,-|- that resistance is of little
importance in the earliest stages of the motion. The initial
* See page 488. of the angular velocity almost identical
t The analyses which we have made with that deduced from the experi-
from numerous turning trials of the mcnts made by Mr. Froudconfiictional
Warrior enables us to state that in her resistance.
case the resistance varies with a power
6l6 NAVAL ARCHITECTURE. chap. xiv.
values of the angular acceleration M'ill therefore chiefly depend
upon the ratio which the moment of the couple bears to the
moment of inertia of the ship about a vertical axis passing
tluough the centre of gravity (Gr, in Fig. 133). That moment
of inertia is determined by multiplying the weight of every part
of the ship by the square of its distance from the axis of rotation ;
and the moment of inertia would evidently be much increased
if heavy weights were carried near the extremities instead of
being concentrated amidships. Hence, with a certain rudder area
put over to the same angle in the same time, in two ships similar
to another in outside form and immersion, but differing in their
moments of inertia, the ship having the less moment of inertia
will acquire angular velocity more quickly than her rival. More-
over, it will be evident that a ship of which the rudder can be
put over quickly to its extreme angle will acquire angular
velocity more rapidly than she would with the same rudder
put over slowly. As the angular velocity is accelerated, the
moment of the resistance increases, exercising an appreciable
effect upon the acceleration ; and finally a rate of motion is
reached for which the moment of the resistance balances the
moment of the couple due to the corresponding pressure on
the rudder, the angular velocity then becoming constant.* It
will, of course, be understood that, simultaneously with this
acquisition of angular velocity, a retardation of headway will
have taken place, and carried with it some change in the pressure
on the rudder, which will also be affected by the considerations
mentioned on page 626 ; the balance between the lateral resistance
and the other forces named above will also have been established.
Four features, therefore, chiefly affect the readiness of a ship
to answer her helm: (1) the time occupied in putting the helm
hard over ; (2) the rudder pressure corresponding to that position ;
(3) the moment of inertia of the ship about the vertical axis
passing through the centre of gravity; (4) the moment of the
resistance to rotation. Only the first and second of these can be
much influenced by the naval architect ; their importance has
already been illustrated from the turning trials of the Minotaur.
The moment of inertia is principally governed by the longitudinal
distribution of the weights in the ship ; in arranging these
weights, considerations of trim, convenience, and accommodation
are paramount. The moment of resistance depends upon the
* See the similar case iireviously illustrated for the effect of resistaace to the
oscillations of ships among waves ; page 237.
CHAP. XIV. THE STEERING OF SHIPS. 6 I 7
form and size of the immersed part of the hull ; and is especially
influenced by the fine parts of the extremities. In some ships
the deadwood forward and aft has been cut away considerably,
in order to increase the handiness; but this practice is not
common, and for sea-going and sailing ships it is open to the
objection that it diminishes the lateral resistance and the resist-
ance to rolling. Hence it rarely happens that a designer
endeavours to exercise much control over the resistance to rota-
tion ; but in torpedo vessels, yachts and small craft the attempt
is sometimes made.
Closely associated with this readiness to answer the helm, or to
acquire angular velocity, are the conditions which control the
decrease of that velocity when a vessel has had her head brought
round to a new course upon which it is desired to keep her.
The greater the ratio of the moment of resistance to the moment
of inertia, the more rapid will be the rate of extinction of the
rotation ; and, conversely, the greater the ratio of the moment of
inertia to the moment of resistance, the slower will be the rate
of extinction. Both moment of inertia and moment of resistance
must be considered; and possibly the helm would be brought
into action to assist in keeping the ship on her new course.
Deep draught, considerable length, fine entrance and run, deep
keels and other features which lead to an increased resistance to
rotation, are not, therefore, altogether disadvantageous. They
make a vessel slower in acquiring angular velocity, but they enable
her to be kept well under control. Shallow-draught vessels are
not unfrequeutly less manageable by the helm than deep-draught
vessels ; they quickly acquire angular velocity, and turn rapidly,
but have comparatively small resistance in proportion to the
moment of inertia, and are not easily kept on a new course,
" steering wildly " in some cases, as a sailor would say. In such
cases the addition of a deep keel and consequent increase of
resistance to rotation and drift often greatly improves the
steerage. Vessels of the circular form possess great moment of
inertia, whereas nearly the whole resistance to rotation must be
due to skin friction, and can be but of moderate amount. It
might, therefore, be expected that these vessels would be difficult
to check and keep on any desired course if they had been tui-ned
through a considerable angle and acquired a good angular
velocity. It has, in fact, been asserted that the vessels are
" ungovernable " under the action of their rudders ; and their
designer, Admiral Popoff, in rcplyiug to these criticisms, dwelt
upon the manoeuvring power obtained by the unusual number of
6l8 NAVAL ARCHITECTURE. chap. xiv.
their propellers, not claiming for tliem great bandiness under
the action of the rudders alone.*
Experienced seamen declare that, when a steamer has headway,
and the helm is put over, " the head appears to turn " compara-
tively slowly while the stern swerves suddenly to "the right or
the left."f This is quite in accordance with theoretical con-
siderations. Professor Eankiue many years ago published an
investigation for the instantaneous axis about which a ship
should begin to turn when the rudder was first put over, on the
supposition that the first action of the rudder might be regarded
as an impulse. His construction for this instantaneous axis is
shown in Fig. 133. The length GL represents the "radius of
gyration " of the ship about the vertical axis passing through the
centre of gravity G ; and is measured on the line HL drawn per-
pendicular to the arm FG of the couple.j Join FL, and produce
FG to M; draw ML perpendicular to FL, meeting FM in the
point M ; that point will be the " instantaneous axis " about which
the first movement of the ship takes place, and M may lie con-
siderably before the centre of gravity. To determine the instan-
taneons motion of any point in the ship, it is only necessary to
join that point with M, and to describe a small circular arc with
M as centre. It M'ill be understood that this construction only
applies to the motion of the ship at the first moment after the
rudder is put over.
Purely theoretical investigation does not enable one to lay
down the path traversed by the centre of gravity of a ship in
turning from a straight course under the action of her rudder.
The equations of motion can be framed in general terms ; but our
knowledge respecting the resistance offered by the water to the
motion of the ship is not sufficient to enable all the quantities to
be expressed, and a complete solution reached. Hence it
becomes necessary that the problem should be attacked by actual
experiment, and that careful observations should be made of
successive positions occupied by a ship so that the path traversed
might be subsequently plotted. In such determinations of the
path of a ship it is convenient (1) to take the original straight
course as the Ime of reference, from which to measure the angles
turned through by the keel-line of the ship in specified times ;
* See a lecture delivered at Kicolaieff Sternway," by Captain Allen, E-ISr.,
in 1875, of which a translation appeared in Naval Science for 1875.
in Naval Science. % See page 136 for an explanation of
t See an interesting article, " On the term " radius of gyration."
CHAP. XIV. THE STEERING OF SHIPS. 619
(2) to take as an origin of co-ordinates the position of the centre
of gravity of the ship on her straight course at the instant when
the helm begins to move over ; (3) to note the path of the centre
of gravity while the ship turns. This centre in most ships is
situated very near the middle of the length ; so that the path of
the latter poiat will serve for all practical purposes, as the path
of the centre of gravity. With these means of reference, if the
place of the centre of gravity is fixed at frequent intervals of
time, a curve can be drawn through the points thus obtained, and
Mill be the path required. If simultaneous observations are made
of the angles through which the head of the ship has turned from
her original course, the instantaneous positions of the keel-line
are known for a series of positions, and its instantaneous inclina-
tion to the corresponding tangents to the path of the centre of
gravity can be ascertained.
Until questions of steam tactics for war-ships became impor-
tant, and the employment of ships as rams occupied attention,
no attempts appear to have been made to determine accurately
the path traversed. In recent years, however, many such obser-
vations have been made both in the Royal Navy and in foreign
navies ; their great practical value is now generally recognised,
and additions are rapidly being made to our knowledge.
The French experimental squadrons of 3864-66 were subjected
to very exhaustive turning trials, and the observations made
would have sufficed to determine the complete motions of the
ships from their straight course ; but this was not done, attention
being chiefly devoted to the determination of tiie circular paths
in which each ship turned after her motion had become uniform.*
Since then it has been recognised that for tactical purposes it
was more important to know what was the nature of the path
traversed immediately after the helm was put over, and where
the ship would be placed when she had turned through the first
90 degrees, as well as her position when she had turned through
180 degrees and reversed her course.
One of the earliest proposals for determining accurately the
motion of a ship in turning was made by M. Risbec of the
French navy, and applied by him to a small vessel, the Elorn, at
Brest, in November, 1875.* This method is, we believe, still
generally used in the French navy, and is exceedingly well
adapted for its purpose.f In its main features it resembles
* See Mitliodes de Navigation, &c., -f See vol. xlix. of the lievue Mari-
by Admiral Bourgois. Paris : Arthur time for further particulars.
Bertrand.
620
NAVAL ARCHITECTURE.
CHAP. XIV.
methods of observation previously known, and occasionally
applied, and a brief account of it may be of interest. Two
observers are stationed at a considerable distance apart on a line
parallel to the keel-line of the ship, as indicated by the points
A and B, Fig. 133a. They are each furnished with a simple
sighting instrument (or azimuth instrument), and at frequent
intervals of time, at a given signal, observe simultaneously, and
record the angles a and /3 made with the line AB by their
respective lines of sight to a floating object, 0, placed within the
path traversed by the vessel. This object may be anchored if
there is no tide or current, but otherwise may be a simple buoy
or boat with a flag-staff. A large number of observations being
made, a series of triangles, such as AOB, can be constructed, the
length AB being constant, and the errors of observation can be
eliminated by a careful
FIG 133a. 11-
comparison and analysis
of the results. To com-
plete the plotting of the
path of the ship, it is
necessary to fix the posi-
tion of any such triangle
as AOB ; this is done by
a third observer, C, who
notes and records the
bearings of a tixed and
distant object, with refer-
ence to the keel-line,
each time that the signal
is given fur the first two observers to note the "bearing of O from
tlieir stations. The angle LCD is that which he has to determine
in each case, and this may be done in other ways than that named
above.
Another very excellent series of trials was made on the
Thunderer at Portland in 1877. The details of the observations
and their principal results will be found in the Appendix to the
Beport of the Inflexible Committee. In some respects these trials
were more exhaustive than any previously made, and the utmost
care was taken to check the several observations and eliminate
errors. They well deserve the study of all who are interested in
the turning trials of ships. Fig. looh shows the path of the .'■hip
when turning from a straight course on which her speed was
nearly 1 0^ knots, and it may be well to lock a little more closely
into the facts ascertained for the Thunderer, as they are doubtless
CHAP. XIV.
THE STEERING OF SHIPS.
621
fairly representative for war-ships of her class, and indicate what
must happen in all ships when turning.
The path of the ship when she begins to turn away from her
straight course will be seen to be spiral, and not circular ; conse-
quently when she has turned through oGO degrees she is found
(at E) somewhat within the line AC of her original course. As she
acquires angular velocity, so her bow turns inwards from the
FIG 1336
, li in s
---,c/
References.
AC, original straight course of ship.
A, her position when helm begins to move over,
she has turned
^»
B,
?J
J)
180°.
E,
>>
5J
360^
F,
>>
J»
540°.
G,
)>
)^
720°.
tangent to the path of her centre of gravity, and the angle
between this tangent and the keel-line, or "drift-angle," {ayigle
cle derive) as it is termed, gradually increases. Owing to the ex-
istence of this drift-angle the thrust of the propellers, when a ship
622
NAVAL ARCHITECTURE.
CHAP. XIV.
is tuniinor, is delivered at each instant athwart her course ; and to
this must be mainly attributed the loss of speed which takes
place, and which is commonly attributed to the "drag" of the
rudder. Her angular velocity meanwhile undergoes rapid accele-
ration, and as she turns centrifugal force comes into operation,
and the sliip heels from the upright. By degrees these transitory
conditions give place to uniform conditions, if the helm is kept at
a constant angle and the engines at a nearly constant speed ; and
ultimately the ship moves in a practically circular path, with a
constant drift-angle, and a steady angle of heel. The time occu-
pied in attaining this state of uniform motion varies in different
ships; the time occupied in putting the helm hard over must
largely influence the time occupied in acquiring uniform augular
velocity, and other considerations must affect the periods occupied
by different ships in passing through the various changes sketched
above. In the following table appears a summary of facts for the
earlier portions of the turning of the Thunderer which will render
further explanation unnecessary : —
Turning Tkials of Thunderer.
At end of time.
Time.
Speed of
ship.
Angular
velocity
per second.
To put helm over 3l°
To turn ship's head 45°
90
135 ...... .
180
360
Seconds.
19
56
89
123
159
320
Knots.
10-4
9-25
8-3
7-75
7-5
7-14
0^ 20'
1 18
1 18
1 15
1 12
1 G|
At 360 degrees the turning motion had become practically
uuifcrm. It appears that with steam steering gear similar condi-
tions of uniform motion are usually reached as soon as, or sooner
than, they were reached in the Thunderer. With manual power only
similar conditions are sometimes not reached until a vessel has
made two or more circuits. When a ship has turned through 90
degrees her motion will not be uniform and her path is s-till spiral.
Hence it is desirable that a commanding officer of a war-ship should
determine by actual observation, at different speeds and with
different helm-angles, how the ship would be placed, in relation
to her course and i^osition at the instant when the helm was j^ut
CHAP. XIV.
THE STEERING OF SHIPS.
62
down, after she has turned through 90 degrees. We shall revert
to this subject hereafter.
We must now pass to the consideration of the motion of a ship
in still water, after it has become uniform. The centre of gravity
of the ship will then be moving in a circular path, and all other
points in her will be moving in concentric paths. The fore end
of keel-line of the ship will be turned within the tangent to the
path of the centre of gravity, making a drift-angle with it of
greater or less amount. In Fig. 133c, 0 represents the centre of
the circle ; G^GGo the path of the centre of gravity ; G the instan-
taneous position of that point, and TGTi the tangent at G ;
AB is the keel-line; BGTj is the drift-angle for G. From 0
a perpendicular OP is let fall on AB. Then the tangent to the
FIGI33f.
circular path describel by the point P coincirles with the keel-
line ; consequently there is no drift-angle at P, and it is some-
times termed the " pivoting point," because, to an observer on
board, the ship seems to be turning about it (see also remarks on
page 618). It will be understood, of course, that 0 is the true
centre of motion for the ship in turning. In the Thunderer the
pivoting point P varied from 67 to 103 feet before the centre of
gravity, or from 80 to 40 feet abaft the bow. As the speed and
drift-angle increased, the point P moved forward. Cases may
occur where the drift-angle at the centre of gravity is so consider-
able that the pivoting point lies before the bow, and is found on
the keel-line produced. By means of a construction similar to
that shown for the centre of gravity G the drift-angle can be
determined for any other point on the keel-line. Take, for
624 NAVAL ARCHITECTURE. chap. xiv.
example, the extreme after-end B: join OB, draw QB per-
pendicular to OB, and the angle DBQ is the drift-angle at B.
The angle DBQ is greater than tlie drift-angle BGrT, for the
centre of gravity ; and it will be obvious that, for all points lying
between B and the pivoting point P, the drift-angle will remain
of the same sign, but decrease ia value as the distance of the
point under consideration from P diminishes. At P the drift-
angle has a zero value, in passing through which it changes sign,
and for all points lying before P the drift-angles have negative
values, as compared with the angle BGTi. That is to say, if a
point such as A is taken, lying on the fore side of P, and OA. is
joined, the line drawn through A perpendicularly to OA, repre-
senting the tangent to the circular path of the point A, will lie
on the other side of the keel-line AB, from that on which the
tangent GT^ is situated.
The value of the drift-angle measured at the centre of
gravity, varies in different vessels, and also varies in the
same vessel under different conditions of speed and helm-
angle. In the Thunderer experiments with a constant helm-
angle, and practically a constant time for putting the helm hard
over, the drift-angle varied from 5| degrees at 8 knots to 9^
degrees at 11 knots. In the Iris, under similar conditions, the
variation in drift-angle was only from 6^ degrees at 9 knots to
7 degrees at 16^ knots. In some of the experiments made with
French ships, drift-angles from 16 degrees to 18 degrees have been
reached. Further experiments are needed in order to determine
the law of variation, but so far as can be seen at present, the drift-
angle becomes greater a^ the area of rudder and the angle of helm
(up to 45 degrees) are increased, speed being constant; and alfO
sometimes increases with increase in speed, other things remaining
the same.
As a consequence of the drift-angle, the bow and stern of a
ship revolve in circles of different diameters when the motion
has become uniform. In the Thunderer this difference varied
from 60 to 100 feet on a mean diameter of 1300 feet, the stern,
of course, moving in the larger circle. In the French ironclad
Solferino, the diameter of the circle swept by the stern exceeded
that swept by the bow as much as 40 metres on 900 metres. The
larger the drift-angle the greater is this difference.
Another consequence of the drift-angle, to which allusion has
already been made, is the reduction in speed sustained by a ship
in turning. In several cases where the loss of speed has been
accurately measured, it has been found to reach tuv-tenths to
CHAP. XIV. THE STEERING OF SHIPS. 625
three-tenths of the speed on the straight course before the helm
was put over. In experimental trials with small vessels, fitted
with rudders of very large proportionate area, the loss of speed
has been much greater, amounting it is said to 40 or 50 per cent,
of the speed on the straight. Id the Delight gunboat, Admiral
Sir Cooper Key ascertained that when the balanced rudder was
very large and it was put over to 40 or 45 degrees, the first quadrant
was turned through in about 31 seconds, and the diameter of the
circle was 205 feet, or only twice the length of the ves?el ; but
the loss of speed was so considerable, due to the large drift-angle
and the drag of the large rudder, that the whole circle took two
minutes forty-six seconds to perform. With an ordinary rudder
of small area put over to equal angles, and about the same speed
on a straight course, the first quadrant took 33J seconds. The
diameter of the circle was 225 feet, and yet the loss of speed was
so much less in turning that the whole of the larger circle was
completed in two minutes thirty-eight seconds. This example
illustrates a well-known fact in screw-ship steerage ; viz., that a
very lar^'O rudder-area will increase the drift-angle, and diminish
the time during which the angular velocity is becoming uniform,
as well as the space required for turning, but may lengthen the
time. The case somewhat resembles in character that described
for twin-screws on page 654.
On consideration of the facts above stated it will be seen that
the motion of a ship in turning resembles that of a ship sailing
on a wind, except that in the latter case the path of the centre of
gravity is straight instead of being curved. At each instant the
vessel moves obliquely to her keel-lino.
To the "angle of leeway" in the sailing ships (see page 488)
the " drift-angle " of the ship which is turning may be considered
to correspond : but whereas in the first case all points in the
ship are moving in parallel lines, and the angle of leeway has a
constant value ; in the second case (as explained above) the drift-
angles for different points have different values, or possibly
different signs. This variation in the drift-angle complicates the
problem, rendering difficult any general statement of the con-
ditions which govern the flow of water relatively to different
parts of the immersed surface of a ship which is turning, or the
distribution of the fluid pressures. There can, of course, be no
question but that, on the side of the sliip most distant from the
centre of her path, there will be an excess of pressure, usually
styled the force of lateral resistance (see page 615). Nor can it
be doubted that cases occur, wherein the pivoting point P lies
2s
626 NAVAL ARCHITECTURE. chap. xiv.
before tlie bow, and there is a considerable accumulation of
pressure on the outer or lee-bow, which pressure not merely
checks the speed, but assists the rudder in turning the ship. If
the pivot point P lies (as in Fig. 133c) between the bow and the
middle of the length — as it very frequently does — the case is less
simple. For points on tlie keel-line abaft P, there are positive
drift-angles ; and if small " drop-rudders," hinged at their fore
ends, were let down below the keel and left free, they would
probably find their positions of rest at some angle of inclination
to the starboard side of the keel-line AB. BQ in Fig. 133c may
be taken as an indication of the position of rest for one such rudder.
For points on the keel before P the positions are reversed : similar
drop-rudders placed at any of these points would find their position
of rest at some inclination to the port side of AB. These rudder-
indications simply show that, in the case of which Fig. 133c
is an illustration, the flow of water for points abaft P is in-
wards, and that there is an excess of pressure on the outer side ;
whereas for points before P tlie flow is outwards, and the excess
of pressure is on the inner side of the bow. The last-mentioned
excess clearly acts against the rudder ; whereas the excess on the
outer side probably assists the rudder, and in many cases may be
supposed to more than counterbalance the pressure on the inner
bow. It will be seen therefore that an increase in the drift-angle, and
consequent movement of the pivot point towards the bow, is likely
to be accompanied by an increase in the turning power of a ship.
It must be noticed here also that the same circumstances
sensibly affect the flow of the Mater at the stern, even of screw
steamei's, and reduce the effective helm-angle (see remarks on
page 600). Turning to Fig. 133c, let BR represent the rudder, and
BD the middle line of the ship produced. Then RED represents
the angle made by the rudder with the keel, and for motion on
a straight course this would be taken as the effective helm-angle.
For a ship turning rapidly, however, the angular motion of the
stern causes the flow of water to take place very differently ; and,
if for an instant the helm were left free, while the angular motion
of the ship continued, it would find its position of rest (or zero-
pressure) at some line, such as BQ, Fig. 133c, inclined more or less
to the keel-line. The ordinary assumption is that, if OB is joined
and BQ drawn perpendicular to it, BQ will be approximately the
position of rest ; and it has been shown that the angle DBQ is the
drift-angle for B. On this assumption, therefore, the eifective
helm-angle is the difference between the angle made with the
keel-line by the rudder and the drift-angle at the stern. This
CHAP. XIV. THE STEERING OF SHIPS, 627
reduction may be very considerable, amounting to one-half of the
apparent helna-angle. French experimentalists have endeavoured
to determine the reduction exactly in some cases, and assert that
it commonly reaches one-half of the apparent helm-angle ; there-
fore practically reducing the turning effect of the rudder by
nearly one-half, as compared with what the same angle of rudder
with the keel would give at the first instant the helm is hard
over, and before a ship has acquired much angular velocity.
Further observations are needed, however, in order to decide this
matter ; but it is evident that, in ships where the greatest angle
of helm with the keel-line cannot be made to exceed 30 deo-rees a
reduction of 10 or 15 degrees involves a very serious loss of efficiency.
Supposing the effective helm-angle and the corresponding-
normal pressure on the rudder to have been determined, then,
when the turning motion of a steamship has become uniform, the
forces acting upon her would be as follows : (1) the pro^Delling
force delivered parallel to the line of keel; (2) the pressure de-
livered perpendicularly to the surface of the rudder; (3) the
centrifugal force acting at each instant along the radius of the
circular path traversed by the centre of gravity ; (4) the re-
sistance of the water to the motion of the ship. Of these the
first and third, acting through the vertical axis passing through
the centre of gravity of the ship, do not tend to produce rotation
about that axis. The pressure on the rudder and the lateral
resistance, each exercise a powerful turning moment, and the sum of
these moments must be balanced by the moment of the resistance to
rotation. But while these general considerations may be stated, it
is not possible, at present, to express definitely the values of either
the moments of the lateral resistance or the resistance to rotation.
In concluding these remarks on uniform angular motion, it
may be well to refer to the heeling which accompanies turning.
The forces which tend to produce heeling are as follow : — ■
1. The centrifugal force acting outwards through the centre of
gravity of the ship, and tending to make her heel away from the
centre of the circde.
2. The lateral component of the rudder-pressure, acting through
the centre of pressure of the rudder and usually at some depth
below the centre of gravity of the ship, tending to make her
heel inwards towards the centre of the circle.
3. The lateral component of the fluid resistance on the outer
side of the ship, which equals in magnitude the resultant of the
centrifugal force and the rudder-pressure, and acts through the
centre of lateral resistance.
2s2
628
NAVAL ARCHITECTURE.
CHAP. XIV.
Fig. \oM shows the distribution of these forces in the Thun-
derer, determined from the turning trials made at Porthand.
Here again it is common to find the rudder-pressiire credited with
FIGI33rf.
Side most distuni
from centre o£ circle.
the heeling effect ; whereas it may, in most cases, be neglected
in comparison with the centrifugal force. A fair approximation
to the angle of heel for a ship in taming is given by the follow-
ing equation : —
sin d
1 ^d v"
61 m R
where 0 = angle of heel,
v = speed of ship in feet per second,
E = radius of circle turned (in feet),
w = " metacentric height ; " the height of trans-
verse metacentre above centre of gravity,
d = distance of centre of gravity above centre of
lateral resistance.
This expression for sin 9 should strictly be multiplied by
cos 0, where (p is the drift-angle for the centre of gravity; but
this correction may be neglected if <p falls below 10 degrees, as it
frequently does.
In the Thunderer, the centre of lateral resistance was found to
be from -43 to '49 of the mean draught below the water-line;
probably a fair approximation for war-ships of ordinary form
would be from -45 to '5 of the mean draught. From the foregoing
equation it will be seen that —
The angle of heel varies (1) Directly as the square of the speed
of ship ;
(2) Inversely with the metacentrie
height ;
(3) Inversely with the radius of the
circle.
CHAP. XIV.
THE STEERING OF SHIPS.
629
Hence it is obvious that ships of high speed, fitted with steam
steering gear, capable of turning in circles of comparatively small
diameter, are those in which heeling may be expected to be
greatest. Moderate values of the metacentric height further tend
to increase the heeling. If the speed be doubled, the angle of
heel will be about quadrujyied, if the radius of the circle turned
and the metacentric heights remain constant. In order to main-
tain a certain angle of heel under these altered conditions of
speed, the metacentric height would also have to be quadrupled ;
but such an increase in stiffness is clearly undesirable even if it
were practicable. The following figures may be interesting : —
Speed on
straight.
Diameter
of circle.
Draught.
Metacen-
tric height.
Angle of
heel.
Thmiderer . ; . . . .
Tourville (French) . . .
Victoiieuse (French) . .
Knots.
8-2
9-4
10-4
15
10
Feet.
1,340
1,250
1,240
2,030
1,290
Feet. ins.
26 3
26 1
26 1
Feet.
3-12
0 1
0 52
1 11
1 14
3 30
2 0
It is important to notice that in taking observations of the
angle of heel for a ship in turning, allowance must be made for
the effect of the centrifugal force upon the indications of
pendulums or clinometers. The error of indication is usually iu
excess, and the correction is very easily made when the diameter
of the circle and time of turning have been ascertained.
Although it is the rule in large ships to heel outwards in
turning, after a sensible angular velocity has been attained, the
first effect of putting a large rudder over quickly may be to cause
the ship to heel inwards under the influence of the rudder-pressure,
and this heel may be the greater because of the com[iaiatively
sudden application of the force (see page 168). This condition
was actually illustrated in the Thunderer, the initial heeling took
place imvards ; it was of small magnitude and was quickly
succeeded by a considerable heel outwards as the ship acquired
angular velocity. Cases are also conceivable, and have occurred,
where the heeling has taken place inwards throughout the motion.
If the circle turned has a very large diameter, if the distance d is
small (as in light-draught vessels such as torpedo-boats) the
inclining moment of the centrifugal force will be small, and the
inclination may take place as supposed, especially if the rudder
is placed low down. It is also possible, though not likely to
6.^0 NAVAL ARCHITECTURE. chap. xiv.
occur in ordinary forms of ships, that the centre of gravity may
fall so low down |as to be below the centre of lateral resistance ;
in which case, of course, the inclination would be inwards. If
bow-rudders are fitted, their tendency is clearly to make a vessel
heel outwards from the centre of the circle.
Besides heeling transversely a ship will also cliange trim
when turning under the action of her rudder. The longitudinal
inclinations are, however, so small as to have no practical impor-
tance, and frequently they are scarcely appreciable.
For many years past turning trials have been commonly made
with new ships of war, both in the Koyal Navy and in foreign
navies. The primary intention in these preliminary or constructors'
trials has been to thoroughly test the efficiency of the rudder and
steering gear, a rough idea of the relative handiness of the ships
also being obtained. For ships of the Eoyal Navy these pre-
liminary turning trials are made in smooth water and light winds,
with the helm hard over to port or to starboard, the ship running
with engines at full or half power. The observations made
include — (1) a record of the time occupied in putting the helm
over ; (2) a record of the times occupied in turning the half circle
and full circle respectively ; (3) a measurement of the diameters
of the " circles " in which the ship turns. In some cases the
turning trials are extended to other speeds than those corre-
sponding to full or half power ; or to angles of helm varying
from " hard over " down to small angles with the keel-line ; but
these extensions are not common. Additional trials are also
made in tnin-screw ships, or ships with other kinds of duplicate
propellers, to determine their behaviour when one jDropeller is
working ahead and the other astern, or when one propeller only
is at work. It need hardly be added, however, that even the
fullest constructors' trials do not furnish all, or nearly all, the
information respecting the steering qualities of ships which com-
manding officers require. Continued experience in management,
and the further trials which can be made during the service of a
ship at sea, enable commanding oflScers to acquire an intimate
knowledge of the turning powers of their ships under various
conditions of wind, sea, speed, and helm-angle. The experience
thus gained is of the greatest value, not merely as regards the
management of individual ships, but in the aggregate it should
form the basis of any system of naval tactics. In the Royal Navy
the regulations provide for the conduct of such turning trials in
ail new ships, and for the record of the results in the " Ship's
CHAP. XIV. THE STEERING OF SHIPS. 63 1
Boots," for the information of officers who may succeed to the
command : and in recent years these regulations have been the
means of putting on record some of the most detailed and
trustworthy data rehiting to screw-ship steerage. The interest
whicli is now taken in tlie subject by naval officers also affords
a guarantee of further additions to our knowledge of this im-
portant subject. In tlie French navy great attention is also
being bestowed upon the subject, and there, as well as in the
Royal Navy, officers are anxious to determine all the phenomena
attending the turning of ships, as well as to trace the paths
traversed. Limits of space prevent any description here of the
methods of observation proposed or adopted in connection with
turning trials ; for these reference must be made to other
publications.* But it may be of service to deduce from the
results of these trials a few of the more valuable principles and
facts, which they have established :
(1) Tlie path trdver.-;ed by the centre of gravity of a ship
whi'e she turns from a straight course through 180 deofrees — that
is, reverses her course — is usually more or less spiral, and not a
circular arc as Admiral Boutakoff assumed in his Tactiques
Navales. Allusion has already been made (see page 618) to the
principal circumstances which influence the form of this part of
the path. For tactical purposes two points on it are of the
greatest importance : viz., the position of the ship when she has
turned through 90 degrees, and her position when she has reversed
her course. The perpendicular distance between this reversed
course and the original course is termed the " tactical diameter "
{diametre d'evolution). But its determination does not fix the space
required for turning; because it leaves unknown the distance
which the ship advances parallel to her original course from the
instant when her helm is put over to that when her head has
swung through 90 degrees. In Fig. loSb, for instance, let A be the
position of the ship when the helm began to move ; B her position
when 90 degrees have been turned through. Draw AC as a prolon-
gation of the original straight course, and BO perpendicular to AC ;
then AC is the distance required, or as it has been termed the
" advance " of the ship. This may become very considerable
under some circumstances, in proportion to the tactical diameter,
* See various Papers in the Revue Service Institution for 1879 " On the
Maritime from 1877 to 1881. See Turning Powers of Ships," from wliich
also a Paper contributed by the Author Paper many of the facts and illustra-
te the Journal of the Pioyal United tions given in the text are reproduced.
6^2 NAVAL ARCHITECTURE. chap. xiv.
'a
or to the simultaneous movement, sometimes termed the " trans-
fer," in a direction at right angles to the original course.* For
example in the Thunderer the tactical diameter was 1320 feet, the
"advance" to the 90 degrees position was 1000 feet, and she was then
at 700 feet perpendicular distance from her original course. In the
Iris, at 10 knots the tactical diameter was 2300 feet, the advance for
90 degrees was about 1470 feet, and she was then 1010 feet distant
from her original course. It will be noted that when the head of
a ship has swung through 90 degrees, the tangent to the path of the
centre of gravity will have only turned through 90 degrees less the
drift-angle at that instant, which will have different values in differ-
ent ships, and under varying circumstances in the same ship. The
ratio of the advance to the transfer at the 90 degrees position will
also vary greatly in different ships. In shallow-draught vessels, and
more especially in those of high speed, such as torpedo-boats, the
momentum in the direction of the original course, which the
vessels have at the instant when the helms are put down, is not
quickly destroyed by the lateral resistance, and they "sheer off"
in turning, the advance having a considerable relative value.
(2) After the turning motion of a ship has become uniform the
path of her centre of gravity is practically a circle having a
diameter somewhat smaller tlian the tactical diameter. The
French use the term diametre de giration, for this circle ; final
diameter has been proposed as the English equivalent. In the
Thunderer trials, the mean ratio of the final to the tactical diameter
was about 100 : 105. In trials with the Iris, at speeds from 9 to
14 knots, nearly the same mean ratio held good. In trials with
the French armoured corvette Victorieuse, the ratio was about
100 : 117.
(3) Most of the turning trials hitherto made on new ships —
the constructors' trials, as they have been termed above — may be
supposed to give approximations to the tactical diameters of the
ships. For war-ships, the following results have been obtained.f
With manual power and ordinary rudders the diameter of the
circle for large ships has been found to vary between six and
* These terms — advance and trans- f For details see Admiral Bouta-
fer — were suggested by Captain Co- koff's Tadiques Navales, M. Dislere's
lomt), E.N. They express the mean- Marine Cuirassee, Admiral Bourgois'
ing very simply of measurements Etudes Siir les Manoeuvres dts Combats
which in mathematical langunge would sur Mer, M. Lewal's Principes des
be styled the "co-ordinates" of the Evolutions N^avaJes, and the Author's
centre of gravity at any time, referred Paper " On the Turning Powers of
to the axes described on page 618. Ships," mentioned on page G31.
CHAP. XIV. THE STEERING OF SHIPS. 633
eight times the length of the ships. For small ships, wherein
manual power suffices to put the helm over rapidly and the speed
is low, the diameter falls to three or five times the length. For
swift torpedo-boats, with manual power only at the helm and very
small angles of helm, the diameter of the circle for full speed has
reached about twelve times the length, and for half speed about
four or six times the length. With manual power and halcmced
rudders, the diameter for large ships has been reduced to four or
five times the length, and nearly equal results have been ob-
tained with ordinary rudders worked by steam or hydraulic
steering gear. About three times the length is the miuimum
diameter attained in large war-ships turning under the action of
their rudders. In the despatch-vessel Iris, with steam steering
gear, the diameter of the circle was from eight to nine times the
length, which is to be explained by her relatively small rudder, and
extremely fine form. In the Shah swift frigate with steam steering
and a larger rudder-aiea, the diameter of the circle varied from
five to six times the length. Corresponding facts as to merchant
ships are not numerous ; but it would appear that diameters from
seven to eight times the length are not uncommon with steam
steering gear and good helm-angles. In these ships great handiness
is not sought for, moderate rudder-areas are common, and it is
chiefly desired to have the vessels well under control. At the
same time it may be suggested that larger rudder-areas might be
advantageously adopted now that steam steering gear is so
extensively used.
(4) It will be understood that in all cases the propellers of
the ships were working at full speed when the preceding results
were obtained. But it also appears that differences of speed do
not greatly affect the diameters of the circles, although they
affect the time of turning, so long as the helm-angle remains
constant, and about the same time is occupied in putting the
helm over. With steam steering or with balanced rudders these
conditions may be fulfilled, and the diameter remains nearly
constant in smooth w^ater and light winds. In the Thunderer, for
example, at speeds from 8 to 10 knots, the diameter only varied
from 1400 to 1320 feet. In the Iris, for speeds varying from 9 to
14 knots, the diameter varied only from 2300 to 2400 feet ; at the
still higher speed of 16^ knots it was nearly 2700 feet, but this
was a single trial. In the Bellerophon, with balanced rudder and
manual power, the diameter of the circle at 14 knots was 1680
feet, and at 12 knots 1G50 feet. In large ships, with manual
power only available at the steering wheels, a shorter time sulfices
^34 NAVAL ARCHITECTURE. chap. xiv.
to put the helm over, or larger angles can be reached, at lower
speeds, and then the diameters of the circles are decreased. In
the Warrior, for example, while the diameter of the circle at 14
knots was 2340 feet, at 12 knots it was 1580 feet only.
(5) 1'ho time occupied in putting the helm hard over exercises
a considerable influence on both the time occupied in turning
the circle and upon its diameter; but more particularly affects
the latter. The case of the Minotaur, mentioned on page 613, is
a good illustration of this, and as another the trials of the sister
ships Hercules and Sultan may be cited. The latter has steam-
power applied to her balanced rudder, which can be put over in
about half the time occupied by the manual power in the Hercules.
The diameter of the circle in the Hercules was nearly twice as
great as that for the Sultan; the time of turning for the Sultan
was rather less than that for the Hercules, although the speed
was half a knot less. It will be evident that the distance
traversed by a ship in turning will depend upon the rapidity
with which her uniform angular velocity is acquired, the rate of
that velocity, and the check to her headway, all of which will
be affected by the time occupied in putting the helm up. By
means of balanced rudders or steam steering, the mean angular
velocity, or speed with which the ends of a ship turn relatively
to the middle, has in some cases been almost doubled as com-
pared with the results obtained with ordinary rudders and manual
power.
(6) Other things remaining unchanged, an increase in the
rudder-area is most influential in diminishing the space traversed
in turning ; and this diminution may be of the greatest value to
a war-ship intended to act as a ram. This point has been illus-
trated by the performances of the Sultan and Hercules with their
rudders acting as simple balanced rudders, and with the after
parts of the rudder alone at work. Further, it appears that
increased rudder area and helm-angle may, in some cases, check
the headway so much as to produce no greater turning effect than,
if so great as, would be produced by smaller rudders and less
helm-angles. In his experiments on the gunboat Delight, with
balanced rudders of different sizes, mentioned on page 625,
Admiral Sir Cooper Key found that the largest rudders diminished
the space traversed in turning, made the time of turning the first
quadrant less (that is, enabled the full angular velocity to be
more quickly attained), but somewhat increased the time of
completing the circle, in consequence of the greater check to
the headway.
CHAP. XIV.
THE STEERING OF SHIPS.
635
(7) For the same ship, with the same angle of helm and about
the same time occupied in putting the helm over, the time
occupied in turning the circle appears to vary nearly inversely
as the speed. Take, for example, the following published results
for the Warrior and Hercules: —
Warrior.
Hercules.
Times
Products
Times
Products
Speeds.
of Turning
of Speeds
Speeds.
of Turning
of Speeds
Circle.
by Times,
Circle.
by Times.
Knots.
Jlin. Sec.
Knots.
Min. Sec.
3
28 46
86-3
0
9 32
57-2
6
15 30
93
8
7 21
58-8
9
10 40
96
10
6 22
63-6
12
8 45
105
12i
4 28
54-2
14^
7 21
104-1
14-7
4 0
58-8
The following results for the Thunderer are also interesting:
they relate to the second circle turned when the motion had
become uniform : —
Times
Products
Speeds.
of Turning
of Speeds by
Circles.
Times.
Knots.
iJin. sec.
5-83
7 6
41-4
6-87
5 38
38-7
7-14
5 24
38-5
7-24
5 16
38-1
This approximate rule will be seen to rest upon the facts that
the diameters of the circles at different speeds are practically
equal under the assumed conditions, and that the loss of speed in
turning bears a fairly constant ratio to the speed on a straight
course. It may be of some service in estimating the time that
will be occupied in turning at any selected speed, when the
performance of a ship at some other speed is known ; but it
clearly cannot be used with safety except the fundamental
assumptions are fulfilled.
(8) Up to helm-angles of 40 degrees, the turning power of the
rudder has been found to increase with increase in the helm-
angle. Theoretically, if the streams impinged upon the rudder
parallel to the keel-line, and the effective pres.*ure on the rudder
636
NAVAL ARCHITECTURE.
CHAP. XIV,
varied with the sine of the angle of inclination, 45 degrees would
be the angle of maximum turning effect. This may be seen very
easily. Using the notation of page 607, the moment of the
pressure (P) on the rudder will vary very nearly as the product
P X GA cos o (Fig. 133) ; the distance AC from the axis to the
centre of effort of the rudder being very small as compared
with AG. Hence, approximately,
Moment of pressure on
rudder about G . .
= P X GA cos a
= Pi sin a X GA cos a
= iPi sin 2a GA.
This will have its maximum value when sin 2a = 1 and a =
45 degrees. Balanced rudders are usually arranged so that
they can be put over to 40 degrees ; ordinary rudders are
seldom put over beyond 35 degrees, and with manual power
only, the angle seldom exceeds 25 degrees iu large screw
steamers.
Experience fully confirms these conclusions, as will be seen
from the following examples: — Admiral Sir Cooper Key found
that the Delight gunboat behaved as under, when the helm-angle
alone was varied : —
Helm-angle.
Time of Turning
Full Circle.
Diameter of
Circle.
degs.
10
20
30
40
min. sec.
3 52
3 18
2 57
2 47
Feet.
615
405
275
205
Admiral Halsted, in the trials conducted with the floating
battery Terror obtained the following results : — -
Helm-angle.
Time of Turning
Full Circle.
degs.
10
20
30
40
min. sec.
6 19
5 28
5 1
4 42
Lieutenant Coumes, of the French navy, gives the following
CHAP. XIV.
THE STEERING OF SHIPS.
^11
results for the ironclad corvette Victoi'ieuse for an initial speed of
about 12^ knots : —
Helrn-anfrle.
degs.
7
14
21
27
32*
Time of Turning
Full Circle.
mln
sec.
9
48
6
50
5
50
5
20
5
20
Diameter of
Circle.
Metres.
1,060
933
750
572
465
In practice, as has been shown above, it may happen that, with
large rudder-areas, the least time in turning through the complete
circle does not occur with the largest angle of helm, althouo-h
the least diameter of circle does then occur (see page 625). But
for tactical purposes the first quadrant or first half circle is more
important usually than the complete circle, and within these
limits large rudders at large angles economise both space and
time. Moreover, in such a case the commanding officer can use
his large rudder at a somewhat less angle if he wishes to turn
completely round in the least time, or at the full angle, if
economy of space is more important.
Attention will next be directed to some matters of practical
interest relating to the determination of the areas and forms of
rudders, and the helm-angle to be adopted in new ships. It will
be convenient if the last-named problem is taken first. From the
remarks made above it will be evident that, so far as the steerino-
effect is concerned, a possible helm-angle of 40 to 45 degrees would
be advantageous, or even a greater angle, if regard is to be had to
the reduction of the effective helm-angle which takes place in
turning (see page 626). Other considerations come in, however, and
affect the decision. It may be very difficult with certain forms
of stern to secure a large angle of helm, even when all care is
taken and recourse had to various mechanical devices. Moreover,
when manual power only is used, as in the great majority of
ships, it becomes important, with ordinary rudders, to decide
between the relative advantages of the area and helm-anfle
which are possible with a certain power available at the tiller-
end. Mr. Barnes drew attention to this matter some years ago,
basing his investigation on the old law, that the effective pressure
on the rudder varied as the square of the sine of the angle
638 NAVAL ARCHITECTURE. chap. xiv.
of inclination.* Adopting the law of the sine, it may be
interesting to make a similar comparison between a narrow
rndder held at a certain angle by a given force at the tiller-end»
and a broader rudder of equal depth held at a smaller angle by
the same force. Let it be supposed that the rudders are of
similar form, so that their areas and the distances of their
centres of effort (C, Fig. 132) from the axis will be proportional
to the extreme breadths, Bi and B2 ; then for the narrow rudder
we may write,
Area of rudder = Sj = depth of rudder X Bj x / =/• d . B,,
where / is some fraction of the breadth applicable to both
rudders. Using the notation previously adopted, oi being the
helm-angle,
Pressure on rudder = Pi . S, . Y^ sin aj
= Pi ./(? . Y^ , Bi sin a, = Ci . B, sin n^.
Tir ^. ( 1 +■» r pressure X AC
Moment ci pressure about ) /-. n • -r>
. p J 1 V = <^ = Ci . Bi sm o, X r . B,
axis 01 rudder . . .( r-. t-. o -
J I = r . Ci X Bi^ sm a^.
If S2 be the area of the broad rudder, 02 its angle, B2 its breadth,
similar expressions will hold for it, the constants Ci and r being
identical. Hence, in order that the moments of pressure about
the axes of the rudders may be equal, we must have.
whence.
Cj r . Bi^ sin a, = Cj r . B^^ sin 02
sin ai Ba^
sm 02 Bi^'
The last equation succinctly expresses the relation which must
hold when the force applied at the tiller-end is the same in
both cases.
For the turning effect of either rudder, we may take
Turning effect = pressure x AG x cos of helm-angle;
and, since AG is the same for both rudders,
Turning effect of narrow rudder _Bi sin a^ cos a, B2 cos «i
Turning effect of broad rudder ~ B2 sin 02 cos 03 ~ Bi co^ a '
* See his Paper in the Transactions of the Institution of Naval Architects for
1864.
CHAP. XIV. THE STEERING OF SHIPS. 639
Suppose, as an example, the narrow rudder put over to 40 degrees
and the broad to 20 degrees by the same force on the tiller-end :
^ ^ ^ / sin 40° ^ ^ / 0-643 ,07 -p
Turning efiect of narrow rudder_ ^ _^^ cos 40°
Turning effect of broad rudder cos 20°
^ __ 0"766 T , . , X
= 1-37 X -^:^= 11 (nearly).
The broad rudder, with an area 37 per cent, greater than the
narrow one, has therefore less turning effect by about 11 per
cent. If the ship had sail-power as well as steam, the smaller
area of the narrow rudder would have the further advantage
of cheeking the headway less when the ship was manoeuvring
under sail alone.
It will be seen on reference to page 609, that in his multiple-
bladed rudders, M. Joessel endeavoured to associate large effective
rudder-area with comparatively small longitudinal dimensions in
order to reduce the force required at the tiller-end, and he based
his procedure on reasoning similar to that above.
Various rules have been used for determining the area of the
rudder for a new ship. For sailing ships of former types, having
lengths about 3^ to 4 times the beam, the extreme breadth of
the rudder was commonly made one-thirtieth of the length, or one-
eighth of the breadth of the ship. The mean breadth of a rudder
commonly varied between seven-tenths and nine-tenths of the
extreme breadth. For steamships a similar rule is used, the ex-
treme breadth of the rudder being made from one-fortieth to one-
sixtieth of the length. Mr. Scott Kussell has proposed to make
a slight modification of this rule, the extreme breadth of the
rudder being one-fiftieth of the length ^jZms 1 foot. Another mode,
commonly used for English and foreign ships of war, is that by
^^hich the area of the immersed part of the rudder is propor-
tioned to the «rea of that part of the longitudinal middle-line
section of the ship situated below the load-line ; the same area
which is made use of in determining the "centre of lateral
resistance" for sailing ships (see page 488). As the area of this
section depends upon the product of the length of the ship into
the mean draught, while the rudder-area depends upon the pro-
duct of its breadth into the draught of water aft, it will be seen
that this rule agrees in principle with the old rule. In sading
ships, the rudder-area was often about one-thirtieth or one-fortieth
640 NAVAL ARCHITECTURE. chap. xiv.
of the area of the iniddlo line plane; in the screw line-of-battle
ships and frigates, similar values were common ; from one-fortieth
to one- fiftieth are common values in ironclad ships of moderate
length with ordinary rudders. In the long ironclads of the
Warrior and Minotaur classes, the rudder-area varies between
one-fiftieth and one-sixtieth of the area of the middle-line plane ;
whereas in the ironclads fitted with bahmced rudders it rises to
one-thirtieth, and in some recent types in the French navy and
in the Russian circular ironclads has been made one-tiventieth. One-
fortieth would probably be a fair average for steamships of war.
In merchant ships much smaller rudders are used, and values as
low as one-hundredth have been met with.
None of these rules can be regarded as entirely satisfactory ;
because they take no cognisance of the law of variation of
the resistance to rotation. When the angular velocity has become
constant, that resistance varies nearly as the square of the angular
velocity ; and the moment of the pressure on the rudder should
be proportioned thereto. In fact, it appears on investigation that
the pressure on the rudder, which — other things being equal —
depends upon the rudder-area, should in similar ships vary, not
with the area of the middle-line plane, but with the product of
that area into the square of the length, if the speed of turning is
to be equal, after the motion has become uniform. In this state-
ment it is assumed, of course, that the ships compared are of
similar form ; the limitations, explained on page 489, for lateral
resistance in sailing ships, being similar to those which will hold
here. If regard is had to the initial motions of the ships under
the action of their rudders, the moments of the pressure on the
rudder should be made proportional to the moments of inertia of
the ships. In other words, the products of the rudder-areas into
the lengths of similar ships should be proportional to the moments
of inertia, which will involve the product of the displacements
into the squares of the lengths. The displacements will vary
as the cubes of the lengths ; tiie moments of inertia will therefore
vary as the fifth powers; the area of the middle-line plane will
vary as the square ; and therefore, under this mode of viewing the
question, the rudder-areas should be proportional to the products
of the areas of the middle-line planes into the squares of the
lengths. Expressed algebraically, if Aj and A2 are the areas of
the middle-line planes of two similar ships ; a^ and a^ the rudder
areas; li and I2 the lengths: the rule would be,
a, ^ A, AY
CHAP. XIV.
THE STEERING OF SHIPS.
641
This would give a much larger area to the rudders of long ships
than is commonly adopted; and as a matter of fact, long ships
usually turn more slowly than short ships in consequence of their
proportionately small rudders.
Great differences of opinion have been expressed respecting the
best form for rudders. In Fig. 13 i a few of the commoner
forms are illustrated. The
balanced rudder a has been
previously described ; & is a
form much in vogue for the
older classes of sailing ships
and unarm oured screw-ships
of the Koyal Navy, the
broader part being near the
heel of tlie rudder, and the
narrower part near the water-
line ; c is a form now com-
monly used in the steamships of the Koyal Navy ; d is the oppo-
site extreme to h, the broadest part of the rudder being placed
near the water-line : this form is much favoured in the mercantile
marine, especially for sailing ships, and is recommended on the
ground that the lower part of a rudder is less useful than the
upper part ; but this is a misconception of the real facts of the
case. From the remarks made on page 554 as to the unequal
motion of the currents in the wake of a ship, it appears that the
fineness of the run near the keel should make the lower part of
the rudder the most effective ; and this has been verified ex-
perimentally.* Hence it seems probable that, with the form of
rudder d, the narrower, lower part does quite as much work in
steering as the broader, upper part : whereas, by tapering the
rudder, the power required to put the helm over is made con-
siderably less than it would be if the breadth were uniform. These
considerations would not have equal force in screw steamers where
the rudder is placed abaft the screws ; and then the form c is to
be preferred, as the broadest part of the rudder is much less
likely to be emerged by pitching than with the form d. In war-
* See the account of an experiment
made by Mr. Fronde, cited by Dr.
Woolley, in a Paper " On Steering
Ships," read at the British Association
in 1875. A model was fitted with a
rudder of uniform breadth, divided into
two equal parts at the middle of the
dei^th, and the lower half, when fixed
at 10 degrees only, balanced the upper
half fixed at 20 degrees when the
model was towed ahead.
2t
642 NAVAL ARCHITECTURE. chap. xiv.
ships having under-water protective decks at the extremities, the
rudder-head and steering gear are phxced under those decks, six
or seven feet below water. It then becomes necessary to use very
broad rudders in order to gain sufficient area, and this form \^
advantageous also, because it enables the rudder to sweep out
into the race of the twin-screws. With steam steering gear these
broad rudders can be easily manipulated. In some vessels, to
obtain greater command over their movements, the keel has been
deepened aft, and the rudder thus made to extend below the
body of the ship into less disturbed water. The case of the
Chinese junks previously mentioned also bears out the advantages
obtained by placing rudders in water which has a maximum
stern ward velocity relatively to a ship. In the floating batteries
built during the Russian war, " drop-pieces " were fitted at
tiie bottom of the rudder, and hinged to the heel, so that, when
the rudder was put over, they might drop down below the keel
and increase the steerage. The results in this case were not
entirely satisfactory, but the circumstances of these vessels were
peculiar.
A few special forms of rudders may be mentioned before
passing on.
One proposed by Professor Rankine some years ago for screw-
steamers was to be on the balanced principle, but to have curved
sides, in order that the propeller-race in passing might com-
municate a pressure which should have a forward component and
help the ship ahead to a small extent.
Herr Schlick has proposed a very similar rudder, the surface
of which is to be twisted, so that the currents driven oldiquely
from the screw-propeller may move freely past the rudder when
it is amidships, and not impinge upon its surface as they do
upon that of an ordinary rudder. By this change it is supposed
that two advantages will be gained: (1) there will be little or
no check to the headway of a ship when the helm is amidships :
(2) steering power will be obtained from all parts of the
rudder surface immediately the helm is put over to either
side, whereas with plane-surfaced rudders, placed behind screw-
propellers, this is not the case. Experiments made at Fiume
with small vessels are said to have demonstrated the great
superiority of the new rudder in both these particulars. The
following particulars have been furnished to the Author by
Herr Schlick, The Vinodol is 140 feet long, 19 feet broad, and
8h feet mean draught. She was first fitted with an ordinary
rudder of 26 sc^uare feet area (immersed). With 89 to 90 revo-
CHAP. XIV. THE STEERING OF SHIPS. 64.-?
liitious of the screw per minute she traversed a distance of 2^
knots in 14f minutes, and turned a circle of about 1000 feet
diameter in 4f minutes. Subsequently a twisted rudder, having
an immersed area of 17^ square feet, was fitted. With the same
steam-pressure and cut-ofi' as before, 91 revolutions were made
per minute, and the measured distance was run in 14 minut^^s
6 seconds, showing a gain in speed of about 4 per cent. ; the
circle turned had a diameter of 900 feet and was completed
in 4 minutes 55 seconds. The vibration at the stein was also
reduced.
Another special rudder is that patented by Mr. Gumpel. It
is a balanced rudder as to suspension, but it is carried on crank-
arms ; and the fore edge has attached to it a vertical pintle,
wliich works freely in a fore-and-aft slot cut in the counter of
the ship. When the helm is put over, therefore, the fore edge of
the rudder is constrained to remain at the middle line, the rudder
being moved bodily over to one side of the keel by means of its
crank-arms. This movement would be especially useful in the
case of a twin-screw ship, pince it would bring the rudder more
into the race. It is asserted that the force required at the tiller-
end to hold the rudder at any angle is less than that for an
ordinary rudder ; and the crank-arms can be so proportioned that,
when the rudder is hard over, little or no force is required at
the tiller to hold it there. Mr. Grumpel has tried the rudder in a
small steam yacht with great success ; but it has not been tested
on a large scale. The plan is an ingenious one, but now that
balanced rudders are giving way to ordinary rudders moved by
steam-power, there is not much probability that further trials will
be made on a larger scale ; and there are obviously greater risks
of damage and derangement with this rudder than with simple
balanced rudders.
Mr. Lumley proposed to make ordinary rudders in two parts,
hinging the after part to the fore jaart, which was attached
in the usual way, to the sternpost. \^'hen the helm was put
over to any angle, it moved the fore part of the rudder through
an equal angle ; but the after part was made to move over to a
greater angle by means of a simple arrangement of chains or
rods, and thus a greater pressure on the rudder was obtained.
Several ships were fitted on this plan, and it was favourably
reported upon in some cases, but has now fallen into disuse, at
least in the Royal Navy, the principal reason probably being
that the apparatus for working the after part of the rudder was
liable to derangement.
2x2
644 NAVAL ARCHITECTURE. CHAP. xiv.
Of the auxiliary aijpliances fitted to increase the steering power
of ships, the most important are how-rudders. These rudders are
rarely fitted except in vessels which are required to steam with
either end foremost; either to avoid the necessity for turning,
or to be capable of service iu rivers or narrow waters where there
is little room for turning, or to meet some other special require-
ment. In nearly all cases, moreover, arrangements are made by
which such rudders can be locked fast in their amidship position
when the ship is steaming ahead. Few ships of the Eoyal Navy
are thus fitted. The jet-propelled Water-witch, intended to steam
indifferently with either end foremost, had rudders at both ends.
Many coast-defence and river-service gunboats have rudders
hinged to their upright stems for use when steaming astern in
narrow waters. The cable ship Faraday had a bow-rudder for
use when steaming astern ; when steaming ahead it was locked
fast amidships, and similar arrangements are not uncommon in
< ouble-bowed river or ferry steamers which do not turn when
reversing their course. Ordinarily, bow-rudders have been hinged
at their after edge either to the stem or to an axis situated a little
abaft the stem, a recess being formed to shelter the rudder when
locked amidships. Several obvious objections arise to this mode
of fitting, especially in war-ships, and for use when steaming
ahead. Eudders so placed are very liable to damage or derange-
ment from collision or blows of the sea. If put over to a good
angle they must cause a considerable increase of resistance and
disturbance of the flow of water relatively to the ship. Moreover,
if hinged at their after edges to the body of a ship, these bow-
rudders have a further disadvantage, if used when going ahead,
because the accumulation of pressure which then takes place on
the fine part of the bow abaft the rudder, on the side to which
the rudder is put over, acts against the rudder-pressure and
diminishes its turning effect.* This additional pressure re-
sembles that described on page 606 as acting on the deadwood or
sternpost before an ordinary stern-rudder when a ship is going
ahead ; only in that case it increases the turning effect of the
rudder. Hence it appears that, if bow-rudders have to be used as
auxiliaries to stern-rudders when a ship is moving ahead, they
should be so placed that the streams flowing past them should
not subsequently impinge directly upon the hull and reduce the
speed of turning. This can be done either by using balanced
* This effect may often be observed in the slow motion of a Thames passenger
steamer when turning astern with helm hard over to swing clear of a pier.
CHAP. XIV. THE STEERING OF SHIPS. 645
rudders placed in large recesses in the bow, or by placing the
rudders under the bow in clear water, somewhat as has been
described for the drop-rudders of Chinese junks. A rudder
was placed under the bottom of a torpedo-boat built by Messrs.
Herreshoff and purchased for the Royal Navy, and it was found
on trial that the boat steered perfectly both going ahead and
going astern. Tlie propeller, as well as the rudder, was placed
under the boat in this case ; and besides steering well the boat
could be stopped very quickly. Drop bow-rudders have been
fitted to other torpedo boats in association with rudders at the
stern. On trial they have been found to diminish sensibly both
the time and spice required for turning when going ah3ad, and
to improve the steering when going astern. Bit the heeling
effect was very marked in some of the smaller boats, especially if
the helm was put over very quickly, and on this account their
use has not become general (see page 630 as to heeling). In the
Polyphemus a balanced two-bladed drop-rudder is fitted under
the bow, at a part where the keel curves up considerably ;
and it is so arranged that, when desired, it can be drawn up
into recesses in the ship. At the time of writing no extensive
turning-trials have been made with this novel ship, but there is
every reason to anticipate that the bow-rudder will be a vahiable
auxiliary to the stern-rudder when going ahead, will be of the
greatest service when going astern, and will materially assist in
stopping her headway rapidly. Similar rudders are being tried
in one or two corvettes of the Royal Navy.
Mr. J. S. White of Cowes has recently patented a plan for
increasing the manoeuvring powers of boats and vessels, which
has proved exceedingly successful in the boats to which it has
been ajtplied. The deadwood is cut away aft for a considerable
distance, the screw-shaft being carried externally and supported
at the after end from the body of the boat. A rudder is placed
in the usual position abaft the screw, and before it, beneath the
curved keel, a balanced auxiliary rudder is also fitted. By
cutting away the deadwood the resistance to rotation is much
decreased ; and the two rudders working together enable the
boat to be turned in a small space, both when going ahead and
going astern. The speed astern is also greater than in boats of
the same general form, having the ordinary arrangement of screw
and rudder aft. Hitherto no trial of the plan has been made on
a large scale. It will be obvious that, to gain the increased
manoeuvring power, certain risks have to be accepted, the propeHer
and rudders bting unusually exposed.
646 NAVAL ARCHITECTURE. chap. xiv.
Steering screws have also been suggested as a means of
considerably increasing tlie speed of turning, or of enabling a
single-screw steamship to turn without headway. The principle
of most of these proposals is to fit a screw of moderate size
in the deadwood either forward or aft, in such a manner that,
when set in motion by suitable mechanism, its thrust shall be
delivered at right angles to the keel-line. Small manoeuvring
screws, driven by manual power, had been previously proposed
and tried in sailing sliips ; but Mr. Barnaby, we believe, first
suggested the use of similar and larger screws, driven by steam-
power, for the Warrior and Minotaur classes of the Royal Navy :
proposing to fit the steering screws at the bows of these ships,
in apertures cut in the deadwood for the purpose.* Subsequently
the late Astronomer Royal, Sir George Airy, proposed a similar
screw, but suggested that it should be placed in the after deadwood
below the main propeller-shaft. Other proposals of a similar
character have also been made ; but we are unaware of any trials
having been made on actual ships. There cau be no doubt as to
the manoeuvring power that might thus be obtained ; but con-
siderable practical difficulties would have to be overcome in
carrying the plan into practice and communicating driving power
to the steering screws.
The use of water-jets expelled athwartships from orifices near
the bow and stern has also been repeatedly suggested ; not merely
for jet-propelled vessels but for screw steamers. Trials were made
of this principle on a gunboat belonging to the Royal Navy in
1863, but they were not so successful as to lead to an adoption
of the plan. Nor can it be doubted, after an impartial investiga-
tion of the subject, that for a given amount of engine-power much
better results might be hoped for from the employment of a
steering screw, such as is described above, than from the use of
water-jets.
A special form of steering screw proposed by Herr Lut-
schaunig deserves to be mentioned.f It consists of a small screw
carried by the rudder, and put over by the helm to the same
angle as the rudder. By means of a simple train of mechanism
the steering screw is made to revolve by the motion of the
main propeller-shaft; and its thrust is always delivered at an
angle with the keel when the rudder is put over. A very
similar arrangement has since been patented, and fitted to several
* Bee the Transactions of the Institution of Naval Architects for 1863 and
1864. t See the Transactions for 1874.
CHAP. XIV. THE STEERING OF SHIPS. 647
boats and small vessels by Mr. Kundstadter. Trials made with
these vessels are said to have given satisfactory results both as
regards speed and turning power. Prior to the actual trial of
this principle it was anticipated that considerable steering power
might thus be obtained if the steering screw was suitably
arranged for working in the race of the main propeller. The
real test of the plan must be found in its capacity for with-
standing the rough usage incidental to service afloat ; and as
yet experience with the vessels so fitted has not been sufficiently
extensive to enable a decision to be reached. It is clear, however,
that the mechanism of the steering screw is of a character and
occupies a position which renders it liable to derangement, while
damage to it might interfere seriously with the efficiency of the
main screw propeller.
The difficulties experienced in the steerage of high-speed
torpedo-boats have given rise to various devices for increasing
the manoeuvring power. To some of these attention has been
directed on page 645, and another is mentioned on page 652.
One of the most ingenious mechnnical arrangements made for
this purpose is the " steering paddle " patented by Mr. Thorny-
croft. It consists of a broad-bladed paddle placed near the stern
of the boat, and operated by steam-power somewhat in the manner
in which a " scull " over the stern is operated by hand. In the
small boat to which it was fitted it answered perfectly, and
enabled her to be " slewed " without headwav. On a larger scale
it would also be practicable, no doubt ; but it would require a
comparatively large engine-power in a ship of large size to
produce results at all comparable with those obtained in the
experimental boat.
Professor Rankine mentions the case of a twin passenger
steamer, the Alliance, designed by Mr. George Mills, in which
manoeuvring paddle-wheels were fitted at the bow and stern, the
axes of the wheels lying fore and aft, and their thrust being
delivered athwartships. No reports of the performances of this
vessel are recorded, but we are informed that the plan was adopted
chiefly to enable the vessel to " cant off " from the piers on the
Clyde.
Auxiliary rudders of various kinds have been tried, but none
have proved so successful as to pass beyond the experimental
stage, or to be used apart from the special circumstances for
which they were devised. In some of the floating batteries built
during the Crimean War, in which the shallow draught and
peculiar form made steering very difficult, auxiliary rudders were
64S NAVAL ARCHITECTURE. chap. xiv.
fitted on each side at some distance before the stern, and arranged
so that they could be put over to an angle of about 60 degrees.
No sensible improvement in the steering appears to have resulted
from these additions. Another form of auxiliary rudder was
proposed by Mr. Mulley, and tried at Plymouth in 1863. It
consisted of a rudder fitted on each side of the after deadwood, at
a short distance before the screw aperture ; it was hinged at the
fore edge, and, when not in use, could be hauled up close against
the side, but, when required, could be put over to 38 degrees
from the keel-line. When applied to a paddle-wheel tug, it
answered admirably, steering her by its sole action, and making
her turn more rapidly when acting in conjunction with the main
rudder. It completely failed, however, when tried on her
]\[ajesty's screw-ship Cordelia, and produced a distinct turning
effect on the ship in the direction opposite to tiiat in wliich it
was expected to act. The explanation of the failure suggested by
the inventor is probably correct : the action of the screw-pro-
peller may have produced a negative pressure on the side of the
deadwood abaft the auxiliary rudder when it was put over; and
the turning effect of the negative pressure more than counter-
bahmced the effect of the auxiliary rudder. Possibly, if the latter
had been placed further before the screw, it might have suc-
ceeded, as it did in the p-iddle-wheel vessel.
Another kind of auxiliary rudder was tried in her Majesty's ship
Sultan. She was fitted with sliding rudders, one on each side,
arranged so as to counterbalance one another ; when one was allowed
to project under the counter, the other was drawn up into a casing
within the ship, and both could be " housed " when desired.
The area of each of these auxiliaries, when fully immersed, was
about one-sixth of the area of the main balanced rudder, and
it was set about 50 degrees from the keel-line. On trial it was
found that the small area and the position of the auxiliary rudder
rendered its steering effect so small as to be practically un-
important.
The most recent trials of auxiliary rudders. in the Royal Navy
were made in the corvettes of the Comus class. It was desired
to give these unarmoured vessels the advantage of a submerged
rudder in addition to the ordinary rudder, for use in case of
damage to the latter in action. For this purpose a recess was
formed in the deadwood under the shaft, and before the single
screw propeller. The auxiliary rudder was pla'-ed in this recess,
hinged at the fore end, and when housed amidships it nearly
made good the recess in the deadwood, completing the shape of
CHAP. XIV. THE STEERING OF SHIPS. 649
the ship. It could be put over to nearly 30 degrees, but as manual
power only was available, the time occupied in putting the helm
over was very long. On trial it appeared that, although the
area of the auxiliary rudder approached equality to that of the
ordinary rudder, it possessed little steering power. It was theu
decided to fit side-blades on the Joessel principle as a further
experiment, and when this was done the auxiliary rudder proved
capable of turning the ship in about three times the period which
suflSced for a complete circle witli the ordinary rudder, the
diameter of the ciicle being increased about four times. This
result was not satisfactory, and, as it involved a sensible loss of
speed, wdien the auxiliary rudder was locked amidships, it was
finally decided to remove the side-blades, and to leave the single-
bladed rudders as first fitted, simply as a reserve in case of
damage. In subsequent vessels of the class similar rud<lers have
not been fitted. These experiments incidentally furnished re-
markable evidence of the gain in steering effect, for the ordinary
case of headway, obtained by placing the rudder abaft the screw.
For sternway it is probable that such auxiliary rudders may be
found useful.
Steering blades or boards somew^hat similar in principle to
those tried in the Sultan have been used successfully in vessels
designed for shallow-water service. These blades were set at an
angle of about 45 degrees from the keel-line on either side, and
could be pushed out from the stern or dropped down into the
water on the side towards which the head of the ship was to be
turned. The idea is an old one, and has been made use of on
some occasions to steer sea-going ships which have lost their
main rudders.
Of the very numerous plans of "jury rudders" which have
been proposed, we can say nothing in the space at our disposal.
They are all based upon the principles explained above for the
ordinary rudder, and are more or less satisfactory expedients
for taking the place of the rudder properly belonging to any
ship.
In conclusion, allusion must be made to various methods of
steering steamships by means of their propellers alone, indepen-
dently of the action of the rudder.
Single-screw ships, as ordinarily fitted, do not possess this
power. As explained on page 603 they can be slewed without
headway by using the rudder and the screw. It is also a matter
of common experience that, with the helm amidships and screw in
650 NAVAL ARCHITECTURE. chap. xiv.
motion, a single-screw sliip can be turned completely round ; but
this cannot be called steering, since the commanding officer has no
control over the direction in wliich the ship turns (see the results
of trials stated on page 605). In most cases the turning under
these circumstances will be performed slowly and in circles of
large diameter. This steering effect of the screw results chiefly
from the unequal thrust delivered on the blades during their
motion in consequence of the unequal forward motion of layers at
different depths in the wake; as explained on page 554.* In
well-immersed screws the upper blades experience the greatest
thrust ; and the excess in the transverse component of this
thrust over the corresponding component of the thrust on the
lower blades gives a steering effect, which tends to turn the bow
of the ship towards the side on which the screw descends. If the
screw be right-handed the head of the ship will usually turn to
starboard, if it be left-handed she will turn to port, under the
action of a well-immersed screw, and when proceeding at uniform
speed ahf ad. Under these conditions also, if the helm is left free,
the rudder M'ill rest in a position inclined to the keel-line, on that
side towards which the particles of water in the race are driven
by the lower blades of the propeller. Should circumstances
occur to cause a relief of thrust on the upper blades, and to make
the thrust on the lower blades the greater of the two, the steering
effect will, of course, be d iff* rent. This may happen, if the screw
is not well immersed, or in starting from rest, or in suddenly
reversing the engines when the ship is at speed on a given
course. Many interesting facts bearing on this subject will be
found in the Reports of the British Association Committee,
mentioned on page 604, but they cannot be reproduced here.
It must be added, however, that when the rudder is in use the
screw also exercises a steering effect of the kind described, and
makes it possible to turn a ship more quickly in one direction
than in another, when she is moving ahead. The difference in
the times of turning is more considerable in some cases than in
others. For example, in the Belleroplion turning to starboard the
circle was completed in 4 minutes ; but turning to port, a circle
of the same diameter occupied 4 minutes 20 seconds. In the
floating battery Terror, where the peculiar shape of the stern
gave a great excess of thrust to the upper blades, the circle with
starboard helm occupied 5 minutes 12 seconds, and that with
* See also Professor Osborne Reynolds' Paper in the Transactions of the
Institution of Naval Architects for 1873.
CHAP. XIV. THE STEERING OF SHIPS. -651
port helm 6 minutes 18 seconds. With the helm left free she
turned to port and completed a circle in 5 minutes 52 seconds, or
less time than she turned to starboard (with port helm) under the
action of her rudder hard over. On consideration it will be seen
that, when the rudder is used in a ship with her screw well
immersed, the streams delivered by the lower blades impinge
more directly upon the lower part of the rudder when it is put
over to the side on which the blades descend when the ship is
going ahead, than they do when the rudder is put over to the other
side. This circumstance further assists the steering to one side as
compared with the other. No general rule cm be stated including
all these varying conditions, but commanders soon become familiar
with the gen^^ral tendency in a particular ship. And pilots
always allow for the steering effect of the screw in entering rivers,
harbours, or docks.
Various proposals have been made for the purpose of gaining
steeling- power from the direct thrust of single-screws. One of
the earliest plans was that proposed by Mr. Curtis, in which the
screw was attached to the shaft by means of a suitable joint, and
■was carried by a frame hinged like a rudder to the stern. The
frame, carrying the propeller, could be put over with the helm
to any angle desired; and the thrust of the screw, driven by
the main engines, was then delivered at an angle with the keel-
line, exercising a powerful turning effect on the ship. On trial it
was found that this turning effect was very powerful indeed, and
the motions of the small vessel so fitted were very rapid; but
there was far less control over the motion than with the rudder,
and this fact, together with the difficulties and risk of derange-
ment to the propelling apparatus which would attend the adoption
of the plan on a large scale, has prevented its use.
Kecently a most ingenious plan for effecting the same object
has been patented by an American, Colonel Mai lory, who has
devised a method for rotating the screw through a complete circle,
and meanwhile keeping the main engines running continuously
in one direction. A boat fitted with the Mallory propeller can
be turned almost on her centre, stopped very rapidly, and kept
thoroughly under control by the action of the screw alone, no
rudder being fitted. The American torpedo vessel Alarm (of 140
feet length and 750 tons displacement) has also been fitted with
this propeller, and the Report of the Board of Naval Engineers
who conducted the trials is very favourable. It is asserted that,
without any loss in efficiency as a propeller when compared with
single or twin- screws, there is an enormous gain in mauceuvring
652 NAVAL ARCHITECTURE. chap. xiv.
po\>er. The only drawbacks are considered to be "increased cost
and complexity of mechanism and necessarily decreased reliability
and durability," but for torpedo-boats, small rams and gun-boats,
the Board consider the advantages of the Mallory system to far
outweigh its disadvantages. Further experience with the Alarm
will give valuable information as to possible extensions of the
system to special classes of ships in which handiness is of supreme
importance.
Another very ingenious and promising method of increasing
the manoeuvring power in single-screw ships has been fitted by
Mr. Thornycroft to a large torpedo-boat, in connection with the
novel form of propeller described on page 560. The " guide-blades "
behind the screw are enclosed by a casing, and abaft this casing
is another easing carried by the rudder. When the helm is put
over, the water from the screw is therefore delivered into the
after casing which is set obliquely to the keel-line, and the
manoeuvring power thus obtained has proved to be most remark-
able on trial, the boat which previously traversed a large circle
in turning could be slewed almost without headway, the bow
remaining nearly at rest.
A clever manoeuvring propeller was invented some years ago
by Mr. Moody and applied to a few barges on the Clyde. It was
subsequently proposed by Mr. Fowler, who does not appear to
have been aware of the other invention, and fitted to the American
torpedo-vessel Alarm as well as to a few small vessels. This
propeller consists of a feathering paddle-wheel placed at the stern,
the axis of the wheel being vertical. By means of suitable
mechanism the paddle-floats can be made to " feather " at any
point in their revolution ; and in this way the maximum thrust
can be delivered in different directions, and made either to propel
the vessel ahead or astern, or to steer her on any desired course.
The apparatus is said to have answered well in the Alarm, as
regards handiness, but not to have been favourable to speed. It
has since been removed, and a Mallory propeller substituted,
with a considerable gain in speed and even greater handiness.
Another American iuventioo of a. very similar kind consists of
two feathering wheels placed on opposite sides of the stern-post
and made to revolve in opposite directions when the ship is
turning. All such propellers are obviously more liable to
derangement, damage and fouling than screws, nor can they be
so efficient as propellers.
Vessels fitted with duplicate propellers, such as disconnecting
paddle-wheels, water-jets, or twin-screws, cau be manoeuvred more
CHAP. XIV. THE STEERING OF SHIPS. 653
or less successfully by the propellers alone. By making one
propeller deliver its thrust ahead and. the other astern, a ship
can be made to turn uearlv on her centre without headwav ; if
only one propeller is used, she will describe a circle of more
or less considerable diameter ; and if the rudder is used in asso-
ciation with either of these conditions it is possible to increase
the speed of turning or lessen the space traversed. The principle
is the same for all three propellers, but the distance between
the lines of thrust of twin-screws is commonly less than one-half
the extreme breadth of a ship, whereas, with disconnecting
paddles, the corresponding distance would commonly be four-
tliirds the extreme breadth ; and with water-jets the distance
somewhat exceeds the breadth. Notwithstanding this advantage,
twin-screws compared favourably with water-jets on the only
occasion on which we know their turning powers to have been
tried in competition. No similar competitive trials appear to
have been made with twin-screws and disconnecting pa^ldles ;
but the restricted use of paddle-wheels makes it unnecessary to
inquire into their relative merits.
Turninsf trials with twin-screw vessels have established the
following conclusions : —
(1) That with ordincoy rudders of suitable forms and areas such
vessels can be steered as efficiently as single- screw ships, when both
screws are working full speed ahead. Balanced rudders applied to
twin-screw ships have not always been so successful as in single-
screw ships ; but this partial failure probably arose from the fore-
and-aft position of the twin-screws, as in other cases better perform-
ances have been obtained with twin-screw ships fitted with balanced
rudders than with sister ships fitted with ordinary rudders.
For example, the Iron Duke, with twin-screws and an ordinary
rudder, occupied about 4 minutes 38 seconds in turning a
circle 505 yards in diameter; her sister ships, the Audacious
and Invincible, with balanced rudders, occupied about 41 minutes,
and turned in circles having diameters of about 400 and 325
yards respectively. Compare with these the performances of
the Resistance, a single screw-ship of the same length and dis-
placement, with an ordinary rudder; she occupied 6^ minutes in
turning a circle 600 yards in diameter, and although her lower
speed would account for some part of the slowness of turning, her
performance, on the whole, was distinctly inferior to that of the
twin-screw ships.
(2) That with helm amidships, one screw working ahead and
the other astern, such vessels can be turned nearly upon their own
654 NAVAL ARCHITECTURE. chap. xiv.
centres, but the time of turning is considerably greater than when
both screws are working ahead and the rudder is used. It will be
remarked that, when the screws are thus worked, that wliich is
turning ahead delivers its race aft, and tends to diminish the
pressure on that side of the deadwood to which it is adjacent ;
whereas that which is turning astern delivers its race forward and
tends to increase the pressure on its side of the deadwood. Tlie
head of the ship turns towards that side where the screw is
working astern, and consequently the excess of pressure on the
same side of the deadwood aft helps the thrusts of the pro-
pellers in turning the ship. This fact tells sensibly in favour of
the manceuvring power of twin-screws. Another circumstance
worth noting is the difference which exists between the effective
thrusts of the two screws ; that which is working ahead has the
greater thrust, and the excess in thrust constitutes a force tending
to propel the vessel ahead, increasing the space she requires in
turning. If the ship is of tine form and easily moved at moderate
speeds, she may therefore traverse a considerable space in turning
under the assumed conditions ; if she is of large size and full
form the difference in the thrusts may only suffice to give her a
small speed when she will occupy little space. To illustrate this
statement we may take the cases of Her Majesty's ships Iris and
the ill-fated Captain, which have nearly equal lengths. With
one screw ahead and one astern, the Iris traversed a circle of
about 500 yards diameter, say 5 times her length ; whereas the
CaiAain traversed a circle of 150 yards mean diameter, or about
1^ times her length. By suitably adjusting the revolutions of
the engines, a twin-screw ship might, of course, be turned upon
her centre.
(3) That when the screws are woiking in opposite directions,
as in the preceding case, if the helm is put over, the time of
turning is usually greater than when both screws are working
ahead and the rudder is used ; but the vessels turn nearly upon
their centres. For example, the Captain took 5 minutes 24
seconds to complete a circle of 750 yards diameter with both
screws full speed ahead and helm hard over ; as against 6
minutes 52 seconds in the other condition, when she turned
nearly on her centre. The explanation of the difference is to
be found in the diminished efficiency of the rudder produced by
the absence of headway, as well as by the action of the screw
which is working full speed astern on the side towards which
the rudder is put over. It is worthy of remark, however, that the
rudder does some work under these circumstances; for the time
CHAP. XIV. THE STEERING OF SHIPS. 6^
o:)
of turnincj has been fouud to be less than when the same vessel
was turned by the action of the screws alone. Mr. Barnaby gives
a case where the times for the two conditions were respectively 4^
minutes and 6 minutes 55 seconds. A possible explanation of
this circumstance may be found in the turning effect of the
accumulated pressure that will act on the side of the dead-
wood before the rudder, and will assist the screws in turning the
ship.
(4) That when one screw is stopped and the other worked full
speed ahead, with the rudder hard over, vessels can be turned
somewhat more slowly than when both screws are working ahead.
As to the relative diameters of the circles described under these
two conditions, there is less agreement. Mr. Barnaby gives a case
where a twin-screw ship completed the circle in 3 minutes 48
seconds with both screws working ahead ; and in 3 minutes 58
seconds with one screw stopped ; the diameter of the circle in
the latter case being one-third less than in the foraier. In the
Captain, the corresponding results were 5 minutes 24 seconds to
complete a circle 750 yards in diameter, when bjth screws were
worked ahead, and 7 minutes 50 seconds to complete a circle 874
yards in diameter, when one screw was stopped. In the Iris the
corresponding results were 8 minutes 14 seconds to complete a
circle of 767 yards diameter at a speed of 10 knots with both
screws, and 10 minutes to complete a circle of 613 yards diameter
with one screw stopped.
(5) That with one screw only at work and the helm amidships,
the ship can be turned completely round ; but the time of turning
is considerable, and the diameter of the circle large as compared
with the other modes of turning. In the Captain, abjut 9|
minutes were occupied in turning a circle nearly 1100 yards in
diameter. Even this turning power might be of service, however,
to a vessel of which the rudder and one screw had been damaged.
(6) That with one screw at work ahead the other being stopped,
or allowed to revolve freely, the ship can be kept on a straight
course by the use of the helm. The angle of helm required varies
in different ships, and possibly at different speeds in a given
ship. In the Iris at speeds of 7 to 8 knots about 8 degrees to
10 degrees of helm sufficed. In the Nelson at 10 knots, 16 degrees
of helm were required. Other cases have come under notice
where the helm hard over did not keep a ship straight ; but the
fact simply proved that either the maximum helm-angle available
was too small or that a form and area of rudder had been adopted
which were not suited to the ships. For eff^'ctiveness under these
656 NAVAL ARCHITECTURE. chap. xiv.
conditious tlie rudder should cdearly be made broad ia order to
sweep out into the race of the screw at work.
It is usual in twiu-screw ships to place the sliafts parallel to
one another and to the keel ; but more than once it has been
suggested that advantage in steering might result from making
shafts diverge from one another, in order to increase the leverage
of the thrust of either propeller about the centre of gravity.
This plan has been applied in the Faradmj, a ship built for
the special purpose of laying submarine telegraph cables, and
therefore requiring great handiness under all conditions of wind
and sea. It is said to have proved very successful; and with
the rudder locked amidships, some of the most delicate operations
connected with laying and splicing cables were performed in a
rough sea and strong wind, the ship being manoeuvred by the
screws alone. The shafts in this vessel diverge from parallelism
with the keel-line by being at a greater distance from it at their
fore ends than at the after ends ; abreast of the centre of gravity
the distance between the shaft-lines is about 40 leet, near the
propellers the distance is about half as great. Another inter-
esting fact in the management of this exceptional vessel is that,
in order to maintain her position with wind or sea on the beam,
the two propellers were frequently worked at different speeds and
sometimes in opposite directions. She furnishes, in fact, one
of the most remarkable illustrations of the manoeuvring power
obtainable by the use of twin-screws.*
Jet-propelled vessels, when moving ahead at full speed, derive
their steering power from the reaction of the water in the wake
upon the rudder; and as previously explained, this is likely to be
less than that on a rudder placed in the race of a screw. In the
trials made with the twiu-screw ship Viper and the jet-propelled
Watericitch, there was practical identity of length and draught,
as well as approximate equality of displacement and speed ; but
the Viper was constructed with two deadwoods, and had a rudder
on each, while the Watericitch had only one rudder at work, the
rudder at the fore end being locked. Hence any exact comparison
between the manoeuvring powers of the two systems of propulsion
can scarcely be made from the trials of these ships; but the
following facts may be interesting. When steaming full speed
ahead, the Viper turned a circle in 3 minutes 17 seconds, as
compared with 4 minutes 10 seconds for the W ater witch ; a saving
* See an account of the vessel, field, F.R.S., to the Institution of
communicated by Mr. C. W. Merri- Xaval Architects in 1876.
CHAP. XIV.
THE STEERING OF SHIPS.
657
of time in the twin-screw ship of about 20 per cent. With one
screw reversed, the other full speed ahead, and the rudders hard
over, the F^per turned on her centre in rather less time than
with both screws working full speed ahead (3 minutes 6^ seconds,
mean of trials in opposite directions).* The Waterwitcli, under
similar conditions, with one nozzle reversed, also turned on her
centre, but occupied more than twice the time of the Yii^er (6^
minutes), and half as long again as she took when steaming full
speed ahead. Making allowance for the additional rudder of the
Vi'peT, and the additional resistance to turning which her peculiar
form of stern involves, it appears that the twin-screws possess
some advantages over the jets in manoeuvring ; but further trials
would be required to settle this point conclusively. It is, how-
ever, certain that ample manoeuvring power can be secured with
twin-screws in association with greater propelling efficiency than
has yet been obtained, or is likely to be secured with water-jets.
In conclusion it may be remarked that, throughout the pre-
ceding discussion, it has been assumed that the manoeuvres of ships
are performed in smooth water, in order that the principles of
the action of the rudder, or of auxiliary appliances for steering,
might be more simply explained. When ships are manoeuvred
in rivers, currents, or a seaway, their performances necessarily
differ from those in still water; but all the varying conditions
of practice can scarcely be brought within the scope of exact
investigation ; and the foregoing statement of principles will
probably enable the conditions of any selected case to be
intelligently treated.
* It will be observed tliat this is an
exception to the deduction marked
No. 3 on p. 654 ; but the explanation
of the difference is simple. As the
Vi'per has two rudders, that placed
behind the screw, which was driving
the ship ahead, always remained
thoroughly efficient in assisting to turn
the ship, although the other rudder,
placed behind the screw, which was
driving the ship astern, was less
efllcient.
2 u
( 659 )
INDEX
Admikalty : —
Eegulatious for preservation of iron and
steel shipSj 408
Coefficients for steamship performance,
566
Air resistance to motion of ships, 477, 479
American :—
Tonnage law for war-ships, 43
River steamers : special construction of,
314, 360
AVood-built ships, rapid decay of, 382
Angidar velocity of ships : —
When rolling, 135, 158
When turning, 615, 616
Ardency of sailing ships, 492
Armour : —
Contribution of, to structural strength of
ship.«, 343, 344
Progress in manufacture of, 410
Atwood's formula for statical stability,
118
Augment of resistance due to screw-pro-
peller, 544, 551
Augmented surface, 447
Automatic instruments for measuring and
recording rolling, 274, 275
Axis of rotation of a ship : — •
When rolling, 137
When turning, 618
Balanced rudders : their advantages and
disadvantages, 598, 599, 609, 611, 613
Barques : —
Plain sail of, 494
Position of centre of effort of sail, 503
Stations of masts and base of sail, 505
Batten instruments for observing rollino;
and pitching, 272
Beam of ships : —
Effect upon metacentric stability, 90
„ range of stability, 120
„ the resistance and projjulsion,
458, 459, 470, 583
Eatio to length in sailing vessels, 512, 514
„ „ unarmoured war-ships, 461
„ „ ironclads, 461, 580
Beams : —
Calculations of bending moments due to
loads on, 286
Principles of strength, 333, 344
To decks : as transverse strengtheners of
ships, 305, 317, 372
Methods of scarphing wood, 393, 394
Sectional forms in iron or steel, 397
Approximate rules for strength, 398
Knees of, 375
Bearers, longitudinal, contribute to local and
general strength of ships, 313
Behaviour of ships at sea (see Eolliug and
Pitching).
Bending moments : —
Methods of estimating, for beams, 286
Longitudinal, for ships, 283,297,299,365
Transverse, for ships, 304, 305, 310
Eesistance of beams and girders, 334
„ ships to longitudinal, 335
„ ships to transverse, 367
Bilge-keels : —
Means of increasing fluid resistance to
rolling, 161, 163, 165
Means of increasing steadiness in a sea-
way, 241
Boilers : —
Locomotive, 523, 527, 528
Herreshoff, 524
Forced draught in, 524
2 u2
66o
INDEX.
Bottom, double (see Double Bottom) : —
Of iron ships, special dangers of, 315,
40G
Of wood ships, strong against grounding,
315
Bow rudders, 64i, 645
Bows of ships : —
Influence of form upon pitching, 258
„ „ upon resistance, 459
Construction of, for ramming, 319
Bowsprits, steeve of, 506
Bracket frame : system of construction for
iron ships, 351, 354, 370
Brass skins, 326
Brigs : —
Loss of older classes by swamping, 14
Plain sail, and position of centre of effort,
494, 503
Stations of masts, and base of sail, 505
Buckling, special danger of, in iron or steel
ships, 316, 349, 396, 428
Builders' old measurement tonnage : —
Antiquity of rule, 38
Examples of calculation, 40
Eationale of rule, 40
Objections to, and abolition of, 41, 42
Bulkheads, as watertight subdivisions : —
Arrangement of transverse, 17, 26
„ oflongitudinal, 21,26,28, 29
Necessity for care of, and doors to, 413
Protection against fire, 414
Means of maintaining stability, 105, 106
Use of transverse, 314, 367, 377
„ partial, 353
„ longitudinal, 359
Buoyancy : —
Definition of, 2
Eeserve of, in different classes of ships, 11
Loss of, causes ships to founder, 13, 14
Centre of, 73, 89
Strains due to unequal distribution of
weight and, 284, 288, 290, 299
Butt joints : —
In wood ships, 329, 391, 394
In iron ships, 395
Captaiit, Her Majesty's ship (late) :—
Curve of stability and principal dimen-
sions, 123, 124
Safety under sail in still water, 170
Upsetting angle, amongst waves, 248
Cargoes ; —
Dangers of shifting, 103
Stowage of, checked by rolling experi-
ments, 156
Cellular construction for iron ships, 316,
340, 351
Central-citadel ironclads : —
Ram-bows of, 320
Forms and proportions of, 461, 583
Centre boards of sailing vessels, 489
Centre of buoyancy : —
Defined, 73
Approximate rules for position of, 89
Motion of, as ship heels, 117, 121
Centre of eifort of sails : —
Method of estimating position, 502
Longitudinal position of, 503, 507
Vertical position of, 508, 511
Centre of flotation, 137
Centre of gravity : —
AVeight may be supposed concentrated
at, in ship at rest, 73
Height of metacentre above, in various
classes of ships, 79, 82, 86, 129
Inclini ng experiment to determine vertical
position of, 98
Motion of, when weights are shifted, 99,
103
Effect of vertical position of, upon range
of stabihty, 122
Effect of position of, relatively to centre
of effort of sails, 507
Centre of lateral resistance, 502
Centre of pressure on rudder, 608
Chinese junks, steering of, 642, 645
Cigar-ships : —
Conditions of stability for, 97
Curve of stability, 119
Still-water oscillations of, 137, 139
Circular ironclads, Russian : —
Behaviour at sea, 235
Weights of hull for, 384
Rolling in a seaway, 214
Steaming capabilities of, 583, 588
Rudder arrangements and steerage, 617,
640
Clipper ships, proportions and performances,
513
Coal consumption, rates of, for various types
of engines, 523
Coal protection, 425
INDEX.
66r
CoelBcients of: —
Augmentation (Rankine's), 4-17
Fineness, for displacement, 3
Moment of inertia of plane of flotation,
89, 90
Friction (skin), -iSS
Steamship performance, 566, 576
Collision : —
Examples of accidental, 30, 31, 318
Local strains produced by, 317, 318, 319
Construction of ram-bows to withstand,
319, 320
Compartments, watertight : — ■
Methods of forming, 17, 18
Of ironclad ships, 27
Composite ships : —
Arrangements of decks, 345
„ framing, 349
„ skins, 357, 358
„ beam-end connections, 373
Freedom from fouling of the bottom, 416
Compound engines : —
Economy of fuel with, 523
Weights of, 523
Compressive strengths of wood and iron,
388, 390
Copper sheathing : —
Anti-fouling properties of, 417
For iron ships, 417, 420
Protected by zinc bands, 418
Insulation of, in Inconstant class, 421
Corinthian Yacht Club, rule for tonnage, 69
Corrosion of iron ships : —
Causes of, 403, 406
Experiments on rate of, 419, 422
Means of preventing, 408
Curves of : —
Displacement, 6
Extinction for rolling in still water, 152,
167
Flotation, 137
Loads and bending moment, 288, 291
Metacentres and centres of buoyancy, 91,
96
Progressive speed trials, 572
Resistance for models andfull-sized ships,
471
Rolling motion of a ship under sail, 250
Stability, 120, 123, 125, 128
Tons per inch of immersion, 7
Turning for steamers, 618, G21
Cutters : —
Plain sail for, 494
Position of centre of effort, 503
Station of mast and base of sail, 505
Danube rule for tonnage, 52, 58
Dead-weight tonnage for merchant ships,
37, 60, 61, 64
Decks : —
Contributories to longitudinal strength,
345
Local strains on, 316
Require strengthening in many iron ships,
366
Resistance of, to rolling and pitching,
with low freeboard, 167, 258
Utilised as watertight partitions, 19, 23
Devastation ;—
Inclination under wind pressure, 172
Mr. Froude's rolling experiments with
model, 163, 241
Performances at sea, 224, 228, 255
Compared with circular ironclads, 585
Diagonal riders : —
For ordinary wood ships, 344, 356
Not necessary for iron ships, 359
For composite ships, 358
Framing for iron ships, 359
Planking for wood and composite shi2)s,358
Dipping oscillations of ships, 148
Disc area of screw propellers, 543
Dismasting of merchant sailing ships, 324
Displacement : —
Api^roximate rules for, 3
Compared with B.O.M. tonnage, 42
,, „ gross register tonnage, 64
Curves of, 6
Definition of term, 1
Most suitable tonnage for war-ships, 43
Tonnage recommended for yachts, 69
Double bottoms : —
Cellular construction of, 316, 354, 359
Effect upon stability of water ballast in,
107
Facilitate preservation of skins, 409
Uses of, in iron ships, 25, 27
Draught of water : —
Changes in, by altered density of water, 9
„ „ addition or removal of
weight, 7
Displacement for any, 6
662
INDEX.
Draught of water {continued) : —
Effect upon, of entry of water into bold, 18
With changes of trim, 113
Durability of wood and iron ships compared,
403
Dynamical stability (see Stability).
EcoNOJiicAL propulsion of steamships : —
Favoured by suitable forms and propor-
tions, 463, 580
Favoured by increase in size, 588, 591
„ certain types of machinery, 525
„ suitable propellers, 557
Not of paramount importance in all cases,
461, 581
Eddy-making resistance of ships, 434, 449,
460
Effective horse-j)ower, 518, 579
Efficiency of marine engines, 523
„ iDiopellers, 533, 547
„ steamships, 580
Elastic limit, 386
Engines, marine; —
Measures of power, 518
Of swift steam-launches and tori^edo-
boats, 523, 528, 593
Types in common use, 522
Weights per indicated horse-power and
rate of coal consumption, 523
Entrance of ships : connection between speed
and length of, 452
Ec|uilibriiun of ships : —
When floating in still Avater, 1, 73
Stable, unstable, and indifferent, 75, 78
Instantaneous position of, among waves,
212, 218
Experiments : —
Against targets representing sides of un-
armoured ships, 424
On air resistance, 477, 479
On deck resistance to rolling, 167
On rate of corrosion of iron, 419, 422
On resistance of ships, 435, 471, 477, 479
,, „ wood and iron to pene-
tration, 315
On screw propulsion, 550, 557, 559, 561
On screws and paddle-wheels, 561
„ „ water-jets, 535
On steerage of siugle-screAV ships, 604, 650
,, „ twin-screw ships, 653
,! „ jet-propelled ships, 657
Experiments (continued) : —
On still-water rolling, 151
On strengths of iron and steel, 387, 391,
426
On strengths of timber, 388, 390
On the effect of bilge-keels, 161, 165, 241
On waste of metals in sea water, 419
To determine vertical position of centre
of gravity of ships, 98, 99
To determine "quiescent point" ox point
tranquille of ships, 154
Factoes of safety for wood and iron, 388,
390
Fastenings in ships : —
Importance of proper, 326
Metal bolts in wood ships, 393
Filings, between frames of wood ships, very
useful, 315, 347
Flanged forms of beams and girders very
advantageous, 344, 399
Formulge : —
Admiralty, for steamship performance,
566
Atwood's, for statical stability, llS
Centre of pressure on rudder, 608
Expressing relative economy of steam-
power in large and small steamers, 589
For augmented surface of a ship, 447
Heeling force when steering, 628
Maximum angle of heel in unresisted
rolling among waves, 223
Moseley's, for dynamical stability, 146
Normal pressure on a plane advancing
obliquely, 436
Period of unresisted rolling in still water,
140
Sail-carrying power, 509
Trochoidal waves, 187
Fouling of bottom : —
Especial disadvantage of iron ships, 415
Effect on resistance of ships, 416, 448
Proposals for preventing, 417, 424
Foundering of ships, causes of, 13
Framing of ships : —
Diagonal, for iron ships, 359
Longitudinal, for iron ships, 351, 352
Subordinate to skins, 326
Transverse, in iron and composite ships,
348, 368
Transverse, in wood ships, 348, 368
INDEX.
663
Freeboard : —
Various rules forj 33, 34:
Effect of, upon the stability, 120
Freight-tounage, 67
French :—
Experiments on still- water oscillations,
154, 159
Observations of deep-sea waves, 198, 205,
207
Eule for nominal horse-power, 521
Frictioual resistance : —
To rolling of ships, 157, 159, 235
To motion of ships, 436, 438
Constant, of engines, 563
Importance of, 448, 460
Froude, the late Mr, W., F.R.S. :—
Investigations on resistance to oscillation
of ships, 151, 241
^Modern theory for rolling among waves,
211
Report on behaviour of Devastation, 228
Experiments : —
On usefulness of bilge-keels, 163, 241
On resistances of ships and models,
433, 444, 456, 471
On relative efficiencies of upper and
lower parts of rudders, 641
On frictional resistance, 438
On wave-making resistance, 455, 457
On air resistance, 482
On ratio of effective to indicated horse-
power, 579
On screw propulsion, 548
On circular ships, 584, 585
On planes and rudders, 608, 641
Galvanic action : —
Accelerates corrosion of iron skins, 421
Assists in preventing fouling of zinc
sheathing, 419
Means of preventing, 422
Special danger in iron ships copper-
sheathed, 421
Girders : —
Equivalent, for longitudinal strength of
ships, 331, 336
Comparison of ribs and adjacent parts
of skin to, 368
Lattice, used as strengtheners to shallow
ships, 361
Trinciples of strength, 334
Graphic integration, 250
Greyhound, Her Majesty's Ship : —
Rolling experiments in still water, 16 1
„ „ in a seaway, 242
Model experiments on resistance, 471
Used as basis for calculations of perform-
ance under steam of large ships, 577
Grounding, local strains produced by,
314
Gunboats, iinarmoured : —
Use of iron hulls for, 425
Engine-power and speeds, 595
Selection of forms and proportions for, 470
Head resistance, to motion of bodies through
water, 434
Headway, advantage of, to ships in turning,
601
Heaving of ships among waves, 186, 247
Heeling produced by : —
Entry of water into hold, 22
Action of wind on sails, 75, 169, 310,
488, 508
Shifting weights athwartshij^s, 102
Turning, 627
Helm:-
Angle of greatest efficiency, 637
Importance of quick motion, 612, 616
Power to put it over, 609
Starboard and port : weather and lee,
599
Hog frame in shallow-draft vessels, 360
Hogging :—
Causes of, in still water, 284
,, on wave crest, 294
Conditions of strain incidental to, 299,
365
Holyhead packets, steaming capabilities of,
5i2
Horse-power of marine engines : —
Effective, 518
Indicated, 518
Nominal, 519
Hulls of ships : —
Advantages of iron as compared with
wood, 383
Recent use of steel, 426
Should combine lightness with strength, 2
Suitability of iron for imarmoured war-
ships, 425
Weights of for various classes, 384
664
IXDEX.
Iron, as a material for sbipbuikliiig : —
Compared with wood, 382
Modulus of elasticity, 391
Progress in manufacture of, 410
Eesistance to bending strain, 398
„ perforation, 315
Simple combinations possible with, 395
Tensile and compressive strength of, 387,
391
(6'ee also Corrosion Fouling and Wood.)
Ironclads : —
Behaviour at sea, 227, 230
Cost of maintenance and repairs, 412
Expenditure of eugine-power, 595
Local requirements in structures, 364
Long and short types compared, 582
Longitudinal strains of, 363
Eapid decay of wood-built, 402
Eudder areas of, 640
Sailing capabilities of, 500, 509
Speeds under steam, 516, 581
Structural arrangements of, 351, 370
Watertight subdivision of, 27
Weights of hull for, 384
Iron ships : —
Beam-end connections, 373
Causes of corrosion, 403, 406
Compared with steel ships, 426
Construction of decks, 345
„ ram-bows, 319, 320
Copper and zinc sheathing for, 416
Features of superiority to wood ships,
321, 383, 409, 413
Fouling of bottoms, 415
Foundering of, due to bulkheads being
insufScient, 414
Great durability of, 405, 407
. Iron sides with close frames in front of
guns, 425
Methods of framing, ordinary and special,
348, 359
Penetrability of bottom, 315, 415
Progress in construction and sizes, 380
Skins of, 359
Strains of, compared with those on a
bridge, 367
Isochronism of oscillations of ships in still
water, 143, 151
Jet-propelled vessels :—
Steaming capabilities of, 532, 538
Steerage of, 601, 656
Joessel rudders, 609
Junks, Chinese, steerage of, 642
Jury rudders, 649
Keels : —
Method of scarphing in wood ships, 392
Bilge (see Bilge-keels).
Sliding, to diminish leeway, 489
Keelsons :^
Longitudinal strengtheners, 313, 347
Method of scarphing, 392
Knees, to beams : methods of fitting, 375
Lap-joints for iron plates and bars, 395
Lateral resistance (see Eesistance).
Launches : —
Of Eoyal Navy, diagonal planking of, 359
Swift-steam : engines of, 523, 595
„ position of screws in, 551
,, remarkable speeds of, 593
Launching : severe strains due to accidents
in, 303, 312
Leaks, rate of inflow of water through, 16
„ usefulness of stoppers, 17
Leeboards, use of, in shallow-draught
vessels, 489
Lee-helm, 599
Leeway : —
Angle of, 488
Causes of, in ships sailing on a wind, 487
Lloj'd's Eegister, investigations on masting,
324
Lloyd's rule for freeboard, 33
Local strains (see Strains).
Longitudinal : —
Bending moments (also, see Bending), 299
Bulkheads (also, see Bulkheads), 22
Framing well adapted for iron ships, 313,
316, 348
Oscillations (also, see Pitching), 252
Strength (see Strength).
Liu-ching : strains consequent upon, 307
Mast and guy system, 314
Masts : — •
Heights of, 511
Number of, 505
Proportion of sail carried bj' each of the,
506
Eake of, 505
Stations of, in sailing vessels, 505
Supported by tripods in turret-ships, 324
INDEX.
665
Materials for shipbuilding (see Wood, Iron,
Steel).
Megcera, Her Majesty's Ship : rate of corro-
sion of skin, and loss of, 408, 421
Merchant ships : —
Cellular construction of, 354
Check upon stowage of cargoes, 151, 156
Dead-weight tonnage for, 37, 60, 61, 64
Longitudinal bending moments experi-
enced by, 299
Longitudinal strains on, 365
Nominal horse-power for engines of, 519
521
Parallelopipedou tonnage for, 65
Ratios of length to breadth, 464, 512,
580
Register tonnage for British, 46
Reserve of buoyancy, 11
Rules for freeboard, 33, 34
Rudder areas for, 633
Sailing capabilities of, 513
Stability under different conditions, 83,
85, 87
Steaming capabilities of, 515, 581, 595
Suez Canal tonnage for, 55, 58
Waterlogged vessels, 14
Weights of hull and carrying power, 385
Metacentre for transverse inclinations :
Approximate rules for estimating position
of, 89, 90
Change of position due to entry of water
into the interior, 105
Effect of metacentric height upon period
of still-water oscillations, 141
Explanation of term, 77
Graphic representation of heights of, for
different draughts, 91
Height above centre of gravity, 79, 83, 87
Motion during rolling, 129
Metacentre for longitudinal inclinations : —
Height above centre of gravity in various
classes, 110
Use of, in estimating change of trim, 112
Metals, rates of waste in sea-water, 419
„ galvanic action on iron, 422
Model experiments : —
On efficiency of bilge-keels, 161, 165,241
On resistances of ships, 47 1
Moduli of elasticity : —
Method for estimating, 386
Values for iron and timbers, 391
Moment : —
Righting, for transverse inclinations, 74,
118
Longitudinal bending, 284, 293, 299
Of inertia : explanation of term, 88, 136
„ its effect on rolling, 141
„ its effect on turning, 616
Of resistance of girders and ships to
bending, 334, 338
To change trim, 112
Transverse bending, 304
Motion of particles in screw-race, 545, 554
Muntz metal for sheathing ships, 416, 418,
422
Naval, brass, 418
Neutral axis and neutral surface of beams,
331, 332
Observatioks : —
Of dimensions and periods of waves, 190,
194
Of rolling and pitching by :—
Automatic instruments, 275, 277
Batten instruments, 272
Photography, 275
Gyroscopic instruments, 267, 271
Pendulums, 262
Spirit-levels, 267, 271
Wheel-pendulums, 280
Oscillations of ships (see Rolling, Pitching,
and Dipping).
Paddle-wheels : —
Principles of propulsion by, 538
Practical rules for, 540
Compared with screws, 561
„ water-jet propellers, 542
Disadvantages of, in sea-going steamers,
540
For manoeuvring, 652
High speed obtained in ships driven by,
542
Panting, produced by transversecompression
on ends of ships, 306
Pendulums : —
Comparison of oscillations with those of
ships, 132
Departure from isochronlsm with large
angles of swing, 222
Discussion of motion of simple, and bar,
135
666
INDEX.
Pendulums (continued) : —
Errors of, when used to measure rolling
motion of ships, 264
Use of, for measuring rolling and pitch-
ing, 262
Use of, to illustrate behaviour of ships
at sea, 225
Wheel, 277, 280
Periods of ocean waves ; —
Formula3 for, 188
Facts respecting, 199, 205, 207
Methods of observing, 190
Periods of pitching for ships, 252
Rolling for ships in still water, 1-iO
Experiments to determine ditto, 151
Pillars,contribution of to structural strength,
372
Pitch of screw-propellers, 543
Pitching and 'scending of ships : —
Causes of, 253
Governing conditions, 254
Influence of form of bow and stern, and
longitudinal distribution of weights,
257, 258
Of low-ended ships, 259
Periods for, 252
Planking of wood ships (see Skins).
Platforms : —
As watertight partitions, 24
Effect on maintenance of stability, 107
Plating of iron ships (see Skins).
Portage of ships (see Tonnage).
Propellers : —
Fundamental principles of, 530
Mallory, 651, 652
Paddle-wheels, 539
Screws, 543
' Water-jet, 532
Use of, for manoeuvring, 652
Propulsion : —
By sails, 480
By steam-power, 515
Strains incidental to, 321, 323
Racking strains on ships : —
Incidental to propulsion, 309, 312
Mode of resisting, 356, 359
Produced by rolling, 307
liadius of gyration : —
Defined, 136
Effect upon period of pitching, 252
Piadius of gyration (continued) : —
Effect upon period of rolling, 141
„ turning, C16
Rake of masts, 505
„ sternposts in yachts and ship?, 39
Ram attacks : —
Best met by watertight subdivision, 29
Construction of bows to meet strains of,
319
Register tonnage : —
Law of 1854 and approximate rules, 45,
47, 48
Allowances to steamships, 49, 50
Compared with displacement, 64
(Also see Tonnage.)
Repairs : relative cost in iron and wood
ships, 412
Reserve of buoyancy for various types of
ships, 11
Reserve of dynamical stability, 169
Resistance of water (to advance of ships): —
Augment of resistance due to screw-
propeller, 544
Early theories of, 433, 439
Frictioual, direct, and eddy-making, 435,
437, 438, 446, 460
Largely independent of area of midship
section, 470
Model experiments on, 469
Steam-line theory of, 440, 443
Summary of results, 460
Values of, for certain ships, 462
Resistance, wave-making, 450, 455, 459
To rolling of ships, 157, 159, 235
To pitching and 'scending, 258
To planes moving obliquely, 436
Resistance, lateral : —
To ships sailing on a wind, 489
To turning of ships, 615
Resistance of air to motion of ships, 477,
479
Ribs (see Framing, Transverse).
Riders, diagonal, for wood and composite
ships, 357
Rigging :—
Air resistance to, 477, 479
Spread of, 323
River steamers, shallow-draught ; special
features of, 314, 360
Rolling of ships in still water : —
Coefficients of extinction, 159, 160
INDEX.
667
Rolling of ships in still water {contd.) :—
Dipping oscillations whicli accompany,
147, 149
Effect of changes in stiffness and distribu-
tion of weights, 141, 143
Effectof moment of inertia upon, 135, 141
„ resistance upon, 149, 151
Extinction of rolling, 153
Hypothetical case of unresisted rolling,
133
Instantaneous axis of rotation, 137, 138,
154
Isochronous rolling, 143
Oscillations resemble those of pendulums,
132
Periods of, 140
Eesistance due to keels and bilge-keels,
surface friction and surface disturbance,
158, 161, 163
Resistance due to internal free-water, 165,
167
Resistance in a seaway compared with
resistance in still, water, 160
Still-water experiments, 151, 155
Rolling of ships among waves : —
Behaviour of quick- moving ships, 217
„ slow-moving ships, 217
Dangers of synchronism of periods of
ships and waves, 220, 227, 240
Early theories of, 211
Effects of changes in speed and course of
ships, 228, 233
Governing conditions of, 211
Importance of ratio of wave period to
period of ships, 216, 229, 231, 233
In a seaway with sail set, 246, 252
Methods of measmiug angles of (see
Observations of Rolling).
Motion of a small raft, 213, 217
Pendulum illustrations of, 225
Permanent rolling, 223
Phases of oscillation, 226
Records of, 225, 229
Safety due to increased period as angle of
swing increases, 222
Safety or danger in a seaway, 240
Sketch of modern theory, 211, 218
Small rolling of vessels having very short
periods, 234, 235
Steadiness secured by bilge-keels, 240,
241, 242
Rolling of ships among waves (contd.) : —
Steadying effect of sails, 251
„ „ a "confused sea," 219
Strains on structure due to, 307
Rudders : —
Ordinary and balanced, 597, 606, 610
Auxiliary, 644, 647
Bow, 644
Centre of pressure of, 608
Considerations respecting areas of, 634,
637
Effective pressures on, 436, 608
Force required on tiller-end, 607
Gumpel's and Joessel's, 609, 643
Lumley's, 643
Mallory, 651, 652
Rankine's and Schlick's, 642
Ruthven's counterbalancing weight ap-
plied to, 612
Run of ships : —
Connection between speed of ships and
length of, 453
Effect of form upon rudder pressure, 601,
603
Sagging : —
Causes of, in still water, 285
Astride wave hollows, 294
Conditions of strain incidental to, 303,
336
Sailing vessels : —
Arrangement of sail, 480, 499
Areas and forms of rudders, 639, 641
Area of sail in terms of wetted surface
and displacement, 497
Area of sail in terms of underdeck
tonnage, 499
Balance of sail, 492
Base of sail, 505
Centre of effort, position of, in, 502, 507
Determination of aggregate sail area, 494,
499, 506
Forms and proportions of, 513
Heel of, under canvas, 75, 169, 310, 488,
509, 511
High speeds of modern, 514
Longitudinal distribution of sail, 501
Plain sail for various styles of rig, 494, 499
Propelling effect of wind on sails, 486
Range of stability necessary for safety, 250
Register tonnage of, 49
668
INDEX.
Sailing vessels {continued') : —
Steadying action of sails, 251
Steerage of, 601
Stiffness, or sail-carrying power, 509
Strains due to propulsion, 321, 323
Under action of squalls of wind, 169
Vertical distribution of sail, 508
With more than three masts, 505
Scarphs of various pieces in wood ships, 393
'Scending (see Pitching).
Schooners : —
Plain sail of, •494, 499
Centre of effort of, 504
Stations of masts, and base of sail, 505
Screw-propellers : —
Compared with paddle-wheels and water-
jets, 535, 561
Conditions for maximum efficiency, 547
Diameter, pitch, disc-area and slip, 543
Experiments to determine best propellers
for Iris, 557
for torpedo boats, 559
Effect of propeller race upon steerage,
605, 650
Large diameters not always advantageous,
547
Mallory, 651, 652
Manoeuvring powers of single and twin,
653
Motion of iDarticles in race, 545, 554
Necessity for free flow of water to, 550
Principles of action, 544
Upper blade does most work, 554
Use of twin and multiple, 549
Virtual increase of resistance produced
by, 544
Screws, steering : modes of fitting, 651
Shallow-draught vessels : —
Special structural arrangements, 314, 360
Difficulty of steering, 616
Shearing strains on ships, unimportant, 283
Sheer strakes, useful as longitudinal
strengtheners, 345
Shift of butts for planking and ribs of wood
ships, 330, 368
Ship-rig : —
Plain sail of, 494
Stations of masts, 505
Position of centre of effort, 503
Base of sail, 505
Simoom target, experiments on, 425
Skins of ships : —
Arrangements in comjjosite ships, 358
„ iron ships, 359
„ wood ships, 330, 355
Essential features of all classes, 320
Ecsistance to penetration of wood and
iron, 315
Slackness of sailing ships, 492
Slip of paddle-wheels, 538
„ screw-propellers, 543
Speeds : —
Of merchant steamers, 515, 581, 595
Of sailing ships, 513
Of unarmoured war-ships and ironclads,
516, 595
Lengths of entrance and run appropriate
to, 453
Spirit-levels, not trustworthy instruments
for measuring rolling, 267, 271
Stability, statical : —
At wood's formula for, 118
Amongst waves, reckoned from normal
to effective slope, 212
Affected by shifting cargoes and free-
water in hold, 102, 105
Construction and use of curves of, 118
Definition of, 76
Effect of adding or removing weights, 108
„ heaving motion upon, 186, 247
„ raising or lowering weights, 102
Less for mastless than for rigged ships,
172
Metacentric method of estimating, 77, 96
Of cigar and cylindrical forms, 97
Of ships partially -waterborne, 115
Of submarine vessels, 97
Eange of, required for safety, 250
Stability, dynamical : —
Definition of, 144
Efi'ect of suddenly applied forces with
reference to, 168
Mode of estimating, 147
Moseley's formula for, 146
Eeserve of, 169
Steadiness : —
Assisted by deep bilge-keels, 241
„ sails, 251
Definition of, 77
Increased by lengthening still-water
period of shijDS, 141, 218
Lessens transverse straining, 307
INDEX.
669
Steamships : —
Economical propulsion of, 463, 580
Engine-power and speeds of various
classes, 595
Estimates of speed and engine-power, 562,
580
Measm-es of engine-power, 518, 521
Ordinary conditions of design, 517
Progress in construction of, 515
Register tonnage of, ■45, 48
Steerage of, 601
Steam steering gear : advantages of, 613
Steel, as a material for shipbuilding : —
Features in which it is superior to iron,
426, 427
Mild steel used in the Eoyal Navy, 429
Objections to use of, 427
Precautions against buckling and corro-
sion, 432
Savings due to use of, 430
Steerage of sailing and steamships, 601
Steering-blades, use of, 649
Steering-gear : —
Manual, Gil, 633
Steam and hydraulic, 612
Steering-screws, proposed use of, 651
Steering trials : —
Axis of rotation, 615, 618, 623
Deductions from trials of steamers, 631,
653
Drift angle, 621
Initial motions of ships, 615, 618
Preliminary or constructors' trials, 630
Path described by the ship, 620
" Pivoting point," 623
" Tactical diameter " and " advance "
of a ship, 631
Steeve of bowsprits, 506
Stern : —
Strengthenings of, in wood screw-
steamers, 322
Effect of length and form upon resist-
ance, 446, 449, 453, 459, 465
Sternway, steerage of ships having, 605, 607
Stiffness : —
Definition of, 77
Effect of form and stowage of ships upon,
81,88
Effect of variations in, upon periods of
oscillation, 141
Measured by metacentric height, 78
Measiire of power to carry sail, 509
Stowage of weights or cargo : —
Effect upon stability, 80, 102, 108
„ longitudinal bending moments,
285, 289
Proposal to check by rolling experiments,
156
Strains experienced by ships : —
Classification of principal, 283
Incidental to propulsion by sails, 309
„ „ steam, 311
Strains : —
Local, due to concentrated loads and
supports, 312
Due to collision, 317
„ grounding, 314
„ propulsion, 321
On decks, 316
Longitudinal bending : —
In still water, 284
„ when light, 290
Among waves, 294, 301
"When vessel is heeled over, 300
Measures of longitudinal, in mercantile
and ironclad ships, 362, 365
Racking or sheering, 308
Transverse : —
Ship aground, 304
„ afloat, 306
„ rolling in a seaway, 307
Values (numerical), of bending, 299
Stream-line theory of resistance, 440, 443
Strength of shipbuilding materials (see
Wood, Iron, and Steel).
Strength of ships : —
As influenced by proportions of length,
breadth and depth, 339, 340
Against local strains, 312, 342
„ longitudinal bending, 327, 335
„ transverse strains, 367
Compared with that of a bridge, 367
Considerations governing vertical and
longitudinal distribution of thematerial,
341, 342
General remarks on, 325
Sometimes reduced by increasing the
depth, 339
Stringers : —
On decks, valuable strengthenings, 345,
351, 373
In hold, uses of, 314, 347, 373
Subdivision, watertight (see Watertight
Subdivision).
6/0
INDEX.
Submarine ships : —
Priuciples of construction, 11
Stability of, 97
Eesistance of, 435, 441
Suez Canal : tonnage for dues, 55, 58
Tables : —
Angles of heel as measured correctly and
as given by pendulum clinometers, 26G
Behaviour of ships at sea : observations
of, 226, 227, 230, 231, 232, 242
Beaufoy's experiments on oblique resist-
ances, 43G
Calculation for centre of effort of sail, 502
„ of change of trim, 112, 115
Coal consumption, weights, &c., of marine
engines of different types, 523
Coefficient : —
Of extinction, 159, 160
Of fineness, for displacement, 3
For tons per inch, 8
Formomentof inertiaofwater-plane,89
Comparative weights of iron and steel
ships, 430
Corrosion and waste of metals in sea-
water, 419
Displacement and B.O.M. tonnage, 42
Equivalent girder, calculation of, 337
Experimental determination of pressure
of wind, 482
Froude's experiments on surface friction,
438
Galvanic action of metals on iron, 422
Illustrating economy of propulsion in
large steamers, 589, 590
Illustrating increase of I.H.P. aiid sizes
of ships, 381
Influence of bilge-keels on range and
period of rolling, 163, 242
Influence of freeboard and beam on range
of stability, 120
Influence of helm-angle in circle-turning,
636, 637
Lengths, speeds, periods, heights, &:c., of
ocean waves, 187, 188, 198, 199, 205,207
Livadia compared with Devastation , Alex-
andra, and other ships, 585, 587, 588
Longitudinal bending moments in ships,
297, 299, 365
Metacentric heights of war-ships, 79
Modulus of elasticity of iron and timber,
391
Tables (continued) : —
Nominal and indicated horse-power, 520
Particulars : —
Of stability for Captain and Monarchy
170
Of Hercules and long type of ironclad,
582
Of I.H.P. and M.M. speeds for various
vessels, 595
Period of rolling as effected by arc of
rolling, 222
Principal dimensions, &c. : —
Of war-ships, 124
Of merchant steamers, and results of
inclining experiments, 82, 83, 127
Of sailing vessels and yachts, 86, 87,
129
Eeduction of speed on circle, 629
Eesistances : —
Of Oreylwnnd and Merhara, 462
Of keels, bilge-keels, skin and wave-
making, 161, 438
Sail, plain, with various styles of rig, 494,
499
Stability of ships at various angles (curves
of stability), 120, 123, 125, 128
Stability of Inflexible, 126
Stations of masts, base of sail, &c., 505
Steadying action of water on armour
deck of Inflexible, 167
Strengths and weights of iron and ship
budding timbers, 388, 390, 396
Tonnage, register, of merchant steamers,
48
Turning trials of Thunderer, 622
„ ,, Warrior and Her cides,G3o
Watertight compartments of ironclads, 27
Weigtits of hull and carrying power, 384,
385
Tensile strengths of wood and iron, 388, 390
Thames rule tor yacht tonnage, 67
Thrust, indicated, 573
Timbers, shipbuilding : —
Compressive strengths, 390
Moduli of elasticity, 391
Tensile strengths and weights, 388, 390
(See also Wood.)
Tonnage of ships : —
A. i mi . alty Commissions of, 1821, 1833, 41
Awning-decked ships, 55
Builders' old measurement, 38
Breadth for tonnage, 39
INDEX.
671
Tonnage of sliips {continued) : —
Cellular-bottomedships,howmeasured,56
Commission of 1849, 45
„ 1881, 49, 53, 55, 60, 63, 66
„ Danube, of 1876, 59, 60
„ International, at Constantinople
in 1873, 55
Countries using Moorsom system, 59
Danube rule, 52, 58
Dead-weigbt tonnage, 37, 60, 61, 64
„ cargo a ship can carry, 62
Deck spaces, allowances for closed in, 54
Displacement tonnage, 42, 43, 64, 65
Earliest English law relating to "keels"
or coal barges, 37
Early laws, 37
Freight tonnage, 07
German rule, 52, 58
Length of keel for tonnage, 39
Merchant-shipping act of 1854, 45
Moorsom system, 45
New measurement of 1836, 41
Origin of B.O.M. rule, 40
Parallelopipedon tonnage, 65
Parliamentary " tons weight of hull," 43
Register tonnage, 46
Approximate rules for, 47, 48
Gross, 46
Nett, 47
Of sailing ships, 49
Of tugs, 51
Suez Canal rules, 55, 58
{See also Builders' old measurement, dis-
placement, &c.)
Tons per inch immersion, 7
Torpedo attacks : watertight subdivision a
precaution against, 27
Torpedo boats (see swift-steam launches).
Transverse : —
Bulkheads {see Bulkheads).
Oscillations (see Rolling).
Strains on ships afloat in still water, 306
,, „ aground, 304
„ ,, in a seaway, 307
„ „ under sail, 310
Strength, 367
Trim of ships : —
Affected by entry of water into hold, 21
Change of, in ships under sail, 309, 488
„ when ships are turning, 630
Estimates for change of, 112, 115
How measured, G
Tripod supports to masts, 324
Trochoidal theory for waves (see Waves).
Twin screws : —
First used in shallow-draught vessels, 549
Good performances of, in deep-draught
ships, 552
Steering power of, 652
{See also Propellers and Screw-propellers.)
UxARMOUKED war-ships : —
Structural arrangements of, 344, 368, 371
Speeds and dimensions of, 381, 51G
Sailing capabilities of, 499, 509
Steaming capabilities of, 595
Use of iron hulls for, 425
Weights of hull for, 384, 385
Useful displacement, 2, 384
„ work of marine engines, 518
Utilisation of ocean-wave power, 208
Volage class of Royal Navy, 372
Wampanoag class, United States navy :
failure of, 382
War-ships (see Ironclads and Unarmoured
Ships).
Water-chamber of Inflexible, 166, 243
Water :—
Weights per cubic foot of sea and river, 2,9
Draught of {see Draught).
Not a perfect fluid, 434
Velocity of inflow into damaged ship, 16
Water ballast : —
Methods of carrying, 29
Effect upon stability, 107
Water-jet propellers (see Jet Propellers).
Waterlogged ships, 14
Watertight subdivision : —
Principles of, 17
By decks and j^latforms, 24
By longitudinal bulkheads, 22
By transverse bulkheads, 19
Imperfection of, in many merchant ships,
413
Maintenance of stability b}', 104
Of ironclads, 27
Wave-line theory of resistance, 450
Wave-making resistance of water : — •
To advance of ships :^
Defined, 435
Expenditure of force on, 444
Governing conditions of, 450, 454, 459
Importance of, at certain speeds, 460
To rolling of ships, 149, 163
72
INDEX.
Waves, deep-sea : —
Advance of form, and motion of particles,
176, 178
Construction of profiles, 177
Dimensions corresponding to given forces
of wind, 207
Effective slope of, 213, 214, 279
Exaggeration of heights, 195
Fluid pressures in, 183
Heaving motion produced by, 186, 217
Internal structure, 180, 183
Influence of ratio of wave period to still-
water period of ship, 212, 216, 217,
229
Maximum slopes, 185
Methods of observing dimensions, 190,
194
Ratios of heights to lengths, 196, 234
Speed of wave compared with speed of
wind, 205, 206, 208
Simimary of observed dimensions, 194,
1 207
Superposition of series, 200
Theoretical formulae for, 187
Utilisation of power, 208
Viscosity of, 188
Longitudinal strains of ships amongst,
294, 299
Oscillations of ships amongst (see
Pitching and Eolliug).
Transverse strains of ships amongst, 307
Weights, per cubic foot : —
Of iron, 387
Of principal shipbuilding timbers, 388
Of sea and river water, 2, 9
Weights of hulls in various classes of ships,
384, 385
Weights per indicated horse-power for
various types of marine engines, 523
•Winds : —
Apparent direction of, 486
Condition of ships sailing on a, 486
Connection between force of wind and
size of wave, 205, 207
Normal j)ressures, forces,and speeds of,482
Normal pressure affected by size and
height of sail, 511
Oblique action on sails, 483
Outstripped by ice yachts, 491
Wing-passages of ironclads, 27
Wood, as a material for shipbuilding : —
Causes of decay in, 403
Compared with iron, 383
Moduli of elasticity, 391
Eesistance of combinations to tensile and
compressive strains, 391, 392
Resistance to bending strains, 396
Resistance to perforation, 315
Tensile and compressive strengths of,
388, 390
Wood ships : —
Average durability of, 401
Construction of ram-bows, 318
Decks of, 345, 372
Features in which inferior to iron or steel,
373, 383
Methods of framing, 348, 368
Metal sheathing on bottoms, 420
Rapid decay of many, 402
Skin planking of, 331, 332, 355
Stern strengthenings of screw-steamers,
322
Strength of bottoms, 315
Work, mechanical :—
Definition of, 144
Done in inclining ships, 146
„ putting rudder over, 609, 611
Useful, of marine engines, 518
Yachts : —
Displacement tonnage, 69
Forms and proportions of racing, 514
Her Majesty's, special construction of, 358
„ speed of, 542, 572
Ice, speed of, 491
Power to carry sail, 510
Sail-spread of, 494, 498
Time allowance on racing by New York
rule, 70
Tonnage measurement : —
By Thames rule, 67
By Corinthian rule, 69
By sail-spread, 70
Yards : bracing of, when sailing on a
wind, 492
Yawing : mode of measuring, 270
Yawls : plain sail of, 494, 498
Zinc sheathing for bottoms of wood and iron
, ships, 417, 419, 423
Zinc protectors to copper sheathing, 417
LONDON : PRINTED BT WILLIAM CLOWES AND SONS, LIMITED, STAJIFOBD STREET
AND CHAniKG CROSS.
UNIVERSITY OF CALIFORNIA LIBRARY
BERKELEY
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