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SCREW PROPELLERS
and ESTIMATION of POWER /or
PROPULSION 0/ SHIPS.
u4lso AIRSHIP PROPELLERS
BY
Rear Admiral CHARLES W. DYSON, U.S.N.
Vol. I.— text
Vol. II.— atlas
SECOND EDITION, REWRITTEN
NEW YORK
JOHN WILEY & SONS, Inc.
London: CHAPMAN & HALL, Lqhtbd
1918
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A^
Copyright, 1918
BY
CHARLES W. DYSON
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AUTHOR'S PREFACE
In 1901, while serving as an Assistant in the Bureau of
Steam Engineering, United States Navy Department, I was
requested by the EngineerinChief, the late RearAdmiral
George W. Melville, United States Navy, to prepare a paper on
the performances of the screw propellers of naval vessels.
During the preparation of this paper I became so interested
in the subject that I have continued my study of it up to the
present day.
From time to time, as points of interest have been developed
pointing to proper lines to follow in designing screws, papers
have been prepared and published in the Journal of the Ameri
can Society of Naval Engineers.
The work here submitted is a composite of these various
papers, eliminating from them all such statements and deduc
tions as later study has demonstrated to be erroneous.
In developing the theory of design set forth in this work, the
model tank trial curves of model hulls were supplied by Naval
Constructor David W. Taylor, United States Navy, and the
work is based upon these curves, Fronde's theory of the propeller
as developed by Mr. S. W. Bamaby in his work on " Screw
Propellers," and the data of trials of actual vessels as supplied
me by the Bureau of Steam Engineering, and I desire this work
to be to them an expression of my appreciation of the aid ren
dered me. My thanks are also due to Mr. Luther D. Lovekin,
who prepared the chapter on the geometry and draughting of
propellers.
It is hoped tluit the book may be found to be of such value
382795
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iv AUTHOR'S PREFACE
that the words of an eminent engineer, " Any man can design
a good propeller, but it takes an exceptionally fine engineer to
design a bad one," will be modified in that even the excep
tionally fine engineer will not be excluded.
Very sincerely,
C. W. Dyson.
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PREFACE TO SECOND EDITION
When the first edition of this work was presented to the
engineering world, it met with very generous criticism from all
soiurces but one, the tone being one of general approval. The
one dissenting critic, writing for the London ** Shipbuilding and
Shipping Record," made some caustic statements concerning the
work, and the opportunity is now grasped to inform him that
later experience has dembnstrated that every criticism made by
him was a just one.
In the first edition were two glaring faults, one being the
vagueness of the method for determining the thrust deduction
factor and the other, the method of applying it in determining
the characteristics of the propeller. These have both been
eliminated to a great degree by a more thorough study of the
effects of hull form and position of the propeller in relation to
the hull on the performance of the propeller. The approximate
method of computation called "the method of reduced diameter''
has been replaced by the more accurate method of " variation
in load."
The Charts of propulsive coefficients and Tip Speeds have
been replaced by the equations derived for the " law of varying
load " and the " law of varying power and speed."
The author's ideas concerning the phenomenon of cavitation
having become crystallized during the later years through more
thorough investigation, they are now presented in the chapter
devoted to that subject.
A chapter dealing with the design of the aeroplane propeller
has also been added, but this can not be regarded as of nearly
the same accuracy as that part of the work devoted to hydraulic
propellers as actual measurements of powers, revolutions and
thrusts occurring in actual flight are missing, and imtil such
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vi PREFACE TO SECOND EDITION
data are available, design curves and factors of absolute accuracy
can not be obtained.
The author having carried his work on propellers as far as
he feels able, will now lay it down, trusting that it will be picked
up by yoimger and more energetic hands, who, loving the sub
ject to the same extent, will carry the work along until " the
last word on propellers " has been said.
In making his final bow, the author desires to express his
thanks to:
EngineerinChief Robert S. Griffin, U. S. Navy, and Chief
Constructor David W. Taylor, U. S. Navy, for the practical
aid and encouragement they have given him throughout the
past many years. The large shipbuilding companies of the
United States for their generosity in providing him with data
of performances of vessels. The Marine Architects and Engi
neers of the United States for the praise and encouragement
in many forms that he has received from them.
Mr. Spencer Heath of the American Propeller and Manu
facturing Company of Baltimore, Md., to whom the author is
indebted for that part of the work devoted to materials for and
details of construction of aeroplane propellers.
Lieutenant Commander S. M. Robinson, U. S. Navy, who
has been of the greatest assistance in the prosecution of the
work.
The engineering press that has been extremely generous in
devoting its columns to encouraging notices of the author's
endeavors. The propeller expert of the London "Shipbuilding
and Shipping Record/' whose criticisms concerning the first edi
tion of the book spurred the author on to renewed investigations.
The publishers for their kindness in offering an opportunity
to present the subject matter in an enduring form.
And to the kind fate which led the author into a line of work
from which he has derived an enormous amoimt of pleasure for
seventeen years, and which located him in a position where this
line of work could be successfully carried out.
Very sincerely,
C. W. Dyson.
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CONTENTS OF CHAPTERS
INTRODUCTION
PAGB
A Short History of Screw Propeller Propulsion i
CHAPTER I
Block Coefficient, Thrust Deduction 7
Derivation of Block Coefficient to Use in Calculation of Propeller. . 7
Description Sheet for Correction of Block Coefficient 8
Use of Sheet for Correction of Block Coefficient 8
Exceptions from Rule 9
Thrust Deduction and Wake Gain 13
Control of the Value oi K 15
Mean Tip Clearance of Propeller, Estimate of 16
Estimate of K for Single Screw Ships 17
CHAPTER II
Estimation of Power, Indicated, Shaft, Thrust, Effective (Tow
rope) Horsepower 18
Indicated Horsepower 18
Shaft Horsepower 18
Thrust HorsQpower 19
Efficiency of the Propeller , 19
Effective (Towrope) Horsepower 19
Propulsive Efficiency 19
Estimate of Power 19
Admiralty Coefficient 19
Law of Comparison 20
Independent Estimate 21
Model Experiments 22
Values of C for Wetted Surface 23
Frpude's Surfacefriction Constants 24
Surfacefriction Constants for Painted Ships in Sea Water. ... 24
vii
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viii CONTENTS
PAGE
Estimate of Appendage Resistance 24
Surfacefriction Constants — ^Denny 25
Surfacefriction Constants — ^Tideman 24
Description of Sheet of Appendage Resistances 27
CHAPTER III
Early Investigations for Obtaining Data for the Design op
Screw Propellers. Empirical Formulas 31
Experiments in the Dwarf 31
Experiments in the Minx 31
Experiments in the Pelican 32
Empirical Formulas 32
CHAPTER IV
The Screw Propeller. Theoretical Treatment of 37
Taylor's — Motion of Elementary Plane 39
Rankine's Theory 40
W. Froude's Theory 41
GreenhilPs Theory 42
Resultant Equations from Theories 44
CHAPTER V
Practical Methods of Design. Design by Comparison. Taylor's
Method. Barnaby's Method 45
Method of Design by Comparison 46
Taylor's Method of Design 48
Bamaby's Method of Design 49
Corrections for Variations in Wake, Estimated Propulsive
Coefficient and in Blade Width Ratio. 51
Correction for Varying Values of Developed Area Ratio from
the Standard 52
CHAPTER VI
Third Method of Design: Design Based on Actual Trials of
Fullsized Propellers in Service over Carefully
Measured Courses 55
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CONTENTS ix
PAGB
The Dyson Method 55
Basic Condition for Design, Description 55
Definitions of Terms and Abbreviations 57
Table of Z Values 58
Values of Propulsive Coefficients at Reduced Loads 59
Indicated Thrust 61
Propulsive Thrust 61
Speed Thrust 61
Effective Thrust 61
Formulas for Diameter and Pitch of Propeller 61
Method of Changing from Basic Conditions to Other Condi
tions of Resistance 6^
Law of Efficiency 64
Power Corrective Factor Z, Derivation 65
Power Corrective Factor Z, Equation 67
Estimate of Revolutions for Other than Basic Conditions of
Resistance 68
Relation between Power and Revolutions when the Vessel
is Prevented from Advancing 70
To Find Apparent Slip or Approximate Power, Power and
Speed or Apparent Slip and Speed Known 71
Effect of Variations in Mechanical Effidency of Engine 72
Number of Blades and their Effect on Efficiency 73
R6sum6 of Design Sheets 75
Problems to be Encountered 76
CHAPTER Vn
Analysis op Pkopellers 77
Derivation of Basic Conditions of the Propeller and Expected
Performance at Other 77
Checking for Cavitation 70
Effect of Varying Number of Blades and Varying Projected Area
Ratio 81
Estimates of Performance 84
Conditions Affecting Performance 84
Correction of Basic Propeller for Variation from Standard
Form of Blade 85
Problems in Estimates of Performance, Three Blades 89
Problems in Estimates of Performance, Four Blades 99
Problems Showing Effect of Varying Conditions 103
Smooth Versus Fair Condition of Ship's Bottom 103
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CONTENTS
Wake Gain io6
Correction of EflFective Horsepower Curve for Expected Wake
Gain io8
Arrangement of Strut Arms and Influence on Wake 112
Problems in Wake Gain 114
Showing Effect of Change in Strut Arms 115
Propellers for Tunnel Boats 121
Propellers for Doubleended Ferry Boats 122
Problem in Estimating Power 124
Submarine Boats 126
CHAPTER Vin
Cavitation 130
Nature of Cavitation 130
Taylor's Statement of Causes 131
Net and Gross Effective Horsejx)wer 132
Gross Effective Thrust, Effect on Cavitation 132
Thrust Deduction, Effect on Cavitation. : 132
Problem Illustrating Effect of Projected Area Ratio 135
Z Affected by Cavitation 139
ilf , Power Corrector for Cavitation ; 139
Equation to the Tangent to Z Curve 139
Effect of Cavitation on Revolutions 140
Effect of Change of Load on Cavitation 140
Effect of Change of Projected Area on Cavitation 143
Effect of Change of Pitch on Cavitation 143
Effect of Reduction of Diameter on Cavitation 143
. Effect of Thrust Deduction on Cavitation 144
Effect of Wake Gain on Cavitation 144
Effect of Insufficient Tip Clearance on Cavitation 145
Effect of Blade Sections on Cavitation 145
CHAPTER IX
Design of the Propeller 146
Computations for Pitch, Diameter, Projected Area Ratio and
Propulsive Coefficient 146
Factors to be Considered 146
Problems, Classes of 146
Problems of Basic Condition (Full Diameter) 147
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CONTENTS XI
PAGE
Threebladed Propellers — Form for Computation 147
Modifications of Forms for Two and Four Blades 147
Problems of Sufficient Data — Reduced Load 148
Threebladed Propellers — Method of Design. 148
Variations for Two and Four Blades 153
Table of (P.A.^D.A.)XE.T.p 154
Table of I.T.D^(I S) 155
First Step in Computations 156
Second Step in Computations 157
Propellers where Insufficient Data for Accurate Design Exists. ... 158
First Step in Computations 158
Problems Illustrating the Above Methods 159
Fanshaped and Broadtipped Blades 178
Tugboat 181
Submarines 186
Doubleended Ferry Boat 188
Tunnel Boat 192
Fast Motor Boats 194
CHAPTER X
Design of Propellers by Comparison 196
Reduction to a Model Propeller 196
Design by Comparison — Similar Conditions of Resistance 197
' Comparative Speeds 198
CHAPTER XI
Effect on Performance of the Propeller Caused by Varying any
OF Its Elements 200
E£fect of Change of Blade Form on Performance 200
Some Points Governing Propulsive Efficiency 200
Excess Pitch 200
Variation of Blade Surface 200
Distribution of Power on Shafts 202
Four Shaft Arrangement. Effect of Position of Propellers .. . 204
Three Shaft Arrangement 204
Dead Wood Cut Away 204
Dead Wood Carried Well Aft 204
Propeller Working in Wake of Very Full Hull 204
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xii CONTENTS
CHAPTER XII
PAGB
Standaio) Forms of Projected Areas of Blades for Use with the
Charts of Design 207
Forms of Blades and Blade Sections 207
Variations from the Standard Form 212
Rake of Blades 214
Form of Blade Sections for Standard Blades 215
CHAPTER XIII
Thickness of the Blade at Root. Centrifugal Force. Fric
TiONAL Resistance of Propeller Blades 218
Thickness of Blade 218
Centrifugal Force — ^Increase of Stress 221
Frictional Resistance of Propeller Blades 223
CHAPTER XIV
Change of Pitch. The Hub. Location of Blade on Blade Pad.
Ddiensions of the Hub 228
Change of Pitch 228
The Hub 228
Location of Blade on Blade Pad 230
Dimensions of the Hub 231
CHAPTER XV
.Stopping, Baceing and Turning Ships , 234
Stopping 234
Backing 243
Turning 262
CHAPTER XVI
Materials for Construction of and General Requirements for
Screw Propellers 274
Material of Blades 274
Material of the Hub 275
General Requirements for Propellers 275
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CONTENTS xiu
CHAPTER XVn
PAGE
Geometry and Draughting of the Screw Propeller 277
Geometry of the Screw Propeller 277
Instructions for Sweeping Up 278
Geometry for Vertical Generatrix 280
Geometry for Inclined Generatrix 281
The Draughting of the Propeller 282
Standard Hubs 287
CHAPTER XVIII
Aeroplane Propellers. Design. Materials and Construction. 294
Design, Variables in 294
Description of Design Sheet 296
Problem in Design 298
Variations for Three and Four Blades 302
Case of Full Load and Full Diameter 302
Second Method of Design 303
Materials and Construction 307
CHAPTER XIX
Contents of Atlas 313
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SCREW PROPELLERS
INTRODUCTION
A SHORT mSTORY OF THE DEVELOPMENT OF
SCREWPROPELLER PROPULSION
John Bourne, in his "Treatise on the Screw Propeller/'
published in 1867, states that " the screw propeller is, in all
probability, a very ancient contrivance. In China it is said to
have been known for ages; but in European countries the idea
of a screw propeller appears to have been derived either from the
windmill or smokejack, or from the screw of Archimedes, an
instnmaent much used in some coimtries for raising water."
Seaton, in his work on screw propellers, traces its develop
ment from the time when man first used his hands as paddles,
through the putting oar and the sculling oar, and the modified
application of the latter in the form of the screw propeller.
These suppositions and tracings of lineage are very interesting
to read and consider, but it hardly appears necessary to delve
so deeply in order to understand why this form of propulsion
exists and how it originated. To any people who were ac
quainted with the principle of the screw thread working in a nut,
and who were looking for a means of decreasing the labor neces
sary in propelling their marine craft, the screw propeller would
appear to be the rational application of the screw thread for this
purpose, as the oar, and, later, its rational successor, the paddle
wheel, were of the lever and fulcrum.
The idea of making a screw on the plan of a windmill to work
in water appears to have originated in England with Robert
Hooke, one of the most remarkable men that country has ever
produced.
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2 . . ; . •' SCREW PROPELLERS
He proposed the idea in 1681, in a work entitled " Philo
sophical Collections/' but it remained an idea only until 1731,
when a Monsieur Du Quet invented a contrivance for dragging
vessels up against a stream by means of a screw, or helical feather,
which is turned aroimd by the water.
Du Quet was followed in 1746 by Bougner, who proposed to
employ revolving arms, like the vanes of a windmill; but this
scheme, it is stated, had not been fotmd to possess suflSdent
force.
In 1768 Pancton, in 1776 Bushnell, an American, and in 1785
Bramah, all proposed various means of applying the screw pro
peller, the latter's proposal being notable from the fact that he
was the first who proposed to fix the screw at the stem " in or
about the place where the rudder is usually placed,'* to be worked
by a shaft proceeding direct from the engine.
The first application of the screw propeller to an actual vessel,
of which we have any record, was made by William L3rttleton in
1794.
The propeller consisted of three helical feathers wound on a
cylinder, and these cylinders were to be so fixed at the bow and
stem, or at the sides, as to be immersed in the water, and to
carry the vessel forward when put into rev9lution. Each cylin
der, or screw, was to be turned by an endless rope working in a
sheave.
Upon trial, the effect of the screw was much less than expected,
a speed of only two miles an hour being obtained. This inven
tion was said to have been brought from China.
In the years that followed, up until 1816, several inventions
were made and experiments tried, but with little success. In
1816, Robert Buchanan, in a work on steam propulsion of vessels,
in writing of the screw propeller, stated that " some mechanics,
however, still think favorably of it, and suppose that if a screw
of only one revolution were used, it would be better than where
a longer thread is employed." Experience has since amply
demonstrated that this proposed restriction of the length of the
screw was foimded upon just views.
Another period of years passed during which several inven
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INTRODUCTION 3
tions of screw propellers were made, but of which no trials oc
curred. In 1824 and 1825, Dollman, a Frenchman, and Perkins,
an Englishman, both proposed " two concentric axes turning in
opposite directions, and each bearing two blades, are placed at
the stem of the vessel, and by the revolution of the blades in
opposite directions the vessel is propelled."
We see this type of propeller in use today for torpedo pro
pulsion.
In this latter year, 1825, a company which had been formed
for carrying into operation a project of a gas vacuum engine
offered a reward for the best suggestion for propelling vessels
without paddlewheels. The reward was gained by Samuel
Brown, the inventor of the engine, who proposed to accomplish
the desired object by a screw placed in the bow of the vessel.
A vessel was built and fitted with a screw; and with this vessel
a speed of six or seven miles an hour is said to have been attained.
As the primary object of the experiment was to introduce the
gas vacuum engine, and this engine having failed, the propeller
was given practical credit for the failure, the company was broken
up, and the scheme abandoned.
In 1827, Tredgold indicated the desirability of making screws
with an expanding or increasing pitch. He stated, " if it (the
spiral) be continued, it should be made with a decreasing angle,"
because during the first revolution of the spiral the water would
have obtained all the velocity the spiral of the original angle
could commimicate.
In 1830, Josiah Sopley, an American, proposed a propeller of
eight or any other number of vanes, these vanes to form " seg
ments of spirals."
In 1836, John Ericsson patented an improved prc^eller appli
cable to steam navigation. This propeller consisted of two thin
broad hoops, or short cylinders, made to revolve in contrary
directions around a common center, each cylinder or hoop moving
with different velocity from the other;" such hoops or cylinders
being also situated entirely under the water at the stem of a
boat, and furnished each with a series of short spiral planes of
plates— the plates of each series standing at an angle the exact
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4 SCREW PROPELLERS
converse of the angle given to those of the other series, and kept
revolving by the power of a steam engine.
In some cases, Ericsson made use of two screws, one behind
the other; in others, of one screw on each quarter, but generally
he used a single screw of a number of threads placed before the
rudder in the stem. This propeller is stated to have been, very
successful and efficient.
In 1839, a Mr. Baddeley stated that many years before that
time a Mr. Weddell had fitted a vessel with a propeller with which
he had made a voyage to Africa. This is the first record we have
of the propeller being used for deepsea work and long voyages.
The conclusion arrived at after this trial was that paddlewheels
of large diameter and little dip had greater propelling efficiency
than a screw.
The first successful operation of the screw as a propeller,
however, may be considered to have occiured with that of
Ericsson in 1836, and with that of Smith in 1839, the latter
having fitted a screw consisting of a singlethreaded helix of one
complete convolution to a vessel of 237 tons burden named the
Archimedes. A double thread of half a convolution was after
wards tried, and found to be an improvement, but the best result
was obtained with two threads and onesixth of a convolution.
The first use made of the screw propeller by the British Navy
was in 1802, when a propeller invented by a man named Shorter
was tried on board H. M. S.'s Dragon and Superb and on the
transport Doncaster. This latter ship attained a speed of ij
miles per hour when deeply laden, with eight men only at the
capstan which worked the screw.
No further use of the screw propeller was made in the British
Navy until 1843, when H. M. S. Rattler was completed. This
vessel developed a speed of ten knots.
In 1845, ^^ fi^^ screw steamer, the Great Britain, crossed the
Atlantic.
The first vessel in our navy to be fitted with a screw pro
peller was the Waterwitch, in 1845 or 1846, followed by the Alle
gheny, in 1852. Both these vessels were originally fitted with
paddlewheels (horizontal submerged), the invention of Lieu
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INTRODUCTION 5
tenant Hunter, of the navy, and had proven failures. Their
engines being better adapted to driving screw propellers than
for paddlewheels, screw propellers were adopted in place of the
Hunter wheels.
Since the general adoption of the screw propeller for marine
propulsion, it has proven an exceedingly attractive field for the
inventor. The number of inventions and patents that have been
taken out covering every individual item of the instrument is
myriad, and one can hardly suggest anything concerning any
part of the propeller which he would not find had already been
suggested or patented by some one in the past.
For many years after its adoption for the propulsion of ships
the seeming vagaries in the performances of screw propellers in
actual service of propulsion cast a great mystery over it and over
the laws governing its action.
The greater part of this mystery is, however, not due to the
propeller, but can be directly attributed to the carelessness with
which trials of ships have been conducted and with which the
data of performances have been collected. The major part of
the remainder of the mystery is due entirely to the effect of
variations in hull form with the changing character of the flow
of water to the propeller accompanying these variations, and the
resultant effect on the propulsive eflBdency; and to incorrect
estimates of effective horsepowers required for given speeds,
these estimates of power having been based on frictional and
residual resistances of the bare hull of the vessel, the maUgn
influence of the appendages fitted to the hull not having been
appreciated and, therefore, having been entirely neglected.
The small residue of the mystery can be ascribed to the pro
peller itself, and is partly due to the myriad variations in blade
forms and sections which have been used, these apparently
depending upon the taste of the individual designer; and
finally, to the lack of a consistent basis of comparison by which
the performances of screw propellers could either be analyzed
or predicted with any degree, of certainty.
As the years rolled by they brought in their wake the model
tank by means of which a more nearly accurate value of the
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6 SCREW PROPELLERS
effective horsepower required for any desired speed of any given
hull can be obtained; more accurate instruments for the measure
ment of indicated and shaft horsepowers; better mechanical
construction of propelling engines by which mechanical effi
ciency has been greatly increased and brought to a more nearly
constant value; machining of propellers to designed diameter,
pitch and area, thus fixing more definitely the most important
characteristics, and reducing the frictional losses of the propeller;
more care in conducting trials over measured courses combined
with a better knowledge of the effects of shallow water and vary
ing currents on such courses.
All of these improvements have resulted in the production of
data of such accuracy that curves may be laid down, based on
these data, by means of which the performance of any given
propeller can be analyzed or predicted or by which a propeller
correctly proportioned for any given conditions can be designed.
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CHAPTER I
BLOCK COEFFICIENT, THRUST DEDUCTION
In erecting the column representing screw propeller design,
the stones that form the foundation are the stone of hull form
and the stone of eflFective horsepower to be delivered. The
other stones necessary to complete the colmnn are those of diam
eter, pitch, revolutions and projected area ratio. These form
the principal stones entering into the structure; in addition
there are also required the minor, less important ones called
blade form and blade section.
All of the above stones are so formed as to interlock and any
variation in one of them necessitates a change in every one of
the others in order to preserve the form and stability of the com
pleted colmnn.
The colmnn when completed may be called the " Colmnn of
Propulsive Efficiency," and in studying the different stones enter
ing into it, those forming the foimdation will be considered first.
Derivation of Block Coefficient to Use in Calculation
OF Propeller
Should there be , adopted for different classes of vessels
standard sets of bow and stem lines and standard shapes of mid
ship sections, there would be for all vessels of any class, no
matter what the ratio of Beam to Length on the Load Water
Line nor what might be the length of the middle body of the ship,
a constant condition of circumstances governing the flow of
water to the propellers.
It would also be found that the nominal block coeffi
cients{ =3SXDisplacementf(BeamXLength on Load Water
Line X Draught)}, would change, approximately, inversely with
7
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8 SCREW PROPELLERS
the ratio Beam 5 Length on Load Water Line, while the actual
hull conditions, so far as affecting the propeller performance,
would remain constant.
Bearing these facts in mind, and having adopted a standard
series of block coeflBdents and Beam ratios, it becomes necessary
to lay down a guide chart for the determination of the standard
block coeflBdent corresponding to any block coeflBdent, beam
ratio and midship section coeffident, also to correct the resultant
block for variations in positions of propellers from the standard
positions of the basic vessels.
Sheet 17. — For Correction of Block Coefficient
On this chart the abscissas are Block Coeffidents, while for
the Block Corrections the ordinates are values of Beam ^ Length
on L.W.L. For checking the Block by means of the Coeffident
of Immersed Midship Section, the ordinates are Coeffidents of
Immersed Midship Section. All vessels, whose Immersed Mid
ship Section coincides with the Standard Curve, will be of
standard fore and afterbody (abnormal designs of hull not
being considered). Those plotting below the Standard Curve
will be bluffer, forward and aft, and those plotting above the
curve will be finer than the Standard Hulls.
Use of Sheet 17 in Propeller Design
In the lower section of this Chart are shown three diagonal
lines, Xy F, and Z. Line X is for the Standard vessels from which
the Charts of propeller design were obtained. Such vessels have
coeffidents of Immersed Midship Section falling dose to the
curve of M.S. coeffident marked Standard, have propellers located
well dear of the hull so that loss, through interference of flow
of water to the screw by the hull, is a minimimi.
As the location of the screws draws closer in behind the hull,
and the influence of the wake has sensibly increased over that of
condition X, the line F takes the place of X. Where the pro
peller is located dose to and directly to the rear of the stem post,
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BLOCK COEFFICIENT, THRUST DEDUCTION 9
so that the full wake effect of the hull is encountered, line Z
replaces both X and F in the determination of the Block Coeffi
cient.
To apply this Chart, let us suppose we have three vessels,
i4, 5, and £, having the following characteristics:
ABE
Nominal Block Coefl5cient 78 .665 .61
Beam ^ Length on L.W.L 123 . 186 . 217
It is required to find the Block Coefficient to use in the
design of the propeller and also to estimate for the expected
appendage resistances.
Plot Ay Bj and £, on the chart with the nominal block coeffi
cients as abscissas and with the values of Beam^LX.W.L,
as ordinates. Through these plotted points and the unity ab
scissa point, pass a straight line, extending it until it cuts line X.
In the cases taken, i4, B, and E are all on the same line passing
through the unity value of abscissas. Where this line crosses X,
at 5, project up to the Standard curve of midship section coeffi
cient. Should the M.S. coefficient of the vessel in question
plot near to the Standard curve of M.S. coefficient, the vessel's
ends may be considered standard, and the vessel's block coeffi
cient be taken as that given by the abscissa value of B. Should
it fall above this curve, that is, the M.S. be fuller than standard,
while the vessel plots at a value of JB^L.L.W.L. below X,
the ends will be finer; if below, fuller than standard, and the
block coefficients be modified accordingly, that is by multiplying
the standard B.C. by the inverse ratio of the midship section
coefficients, imless the vessel be one having a nominal blpck
coefficient of not less than .5 and the after body be very fine, in
which case the correction for variation of midship section should
not be made. Should the propellers be located in the condi
tions given by lines F or Z the fineness will be gauged, as before,
by the intersection of the line with X, but the actual block to
use for the propeller design will be that given by the abscissa
value of the point of intersection with Y or Z, except where
correction is made for variation from the Standard M.S. Coeffi
cient.
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10
SCREW PROPELLERS
The intersections of the cross line through D with the stand
ard lines X, F, Z, may be found mathematically as follows: ,
Fig. I.— Diagram fox Computing Slip Block Coefficient.
Vessel A  nominal block coefficient = i — a; = B.C^.
55L.L.W.L.=y.
B.C.« =
28(iB.C.„)+y'
.248(iB.C.n)+y'
B.C..=
164(1 B.c.n)+y
The above gives approximate block coefficients to use with
charts of design, but makes no allowance for variation of form of
immersed midship section from standard form.
It may be used when Sheet 17 is not available for graphic
correction of block coefficient.
While, in general, the slip block coefficients should be ob
tained as above described, there are cases, however, where the
method of estimating the slip block coefficient should depart from
this method. These cases are three in niunber, the first of which
has already been given but is here repeated:
I. The "vessel has a nominal block coefficient of not less than
.5, and a midship section coefficient much finer than standard
as given by Sheet 17; the propellers located in condition 3,
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BLOCK COEFFICIENT, THRUST DEDUCTION 11
Sheet 19. No correction should be made for variation of mid
ship section from standard.
2. Single screw ships of beam very broad as compared with
length and draft of vessel. In such vessels the immersed lines of
the vessel correspond to the lines below the turn of the bilge in
vessels of orthodox form. No correction should be made for
midship section variation. Such vessels are similar to shallow
draft ferry boats. In estimating the slip block coefficient of
single screw vessels, the condition of immersed hull body as to
nominal Block Coefficient existing when the tips of the upper
vertical blades are immersed to a depth of about 15 per cent
of the diameter of the screw should be used.
3. Single or twin screw timnel boats. These vessels have
the propellers so located that the only definite idea of the flow
of water to the propeller that can be obtained is that of its
direction and this may be considered as normal to the disc.
The only thrust deduction loss that occurs is that due to friction
in the tuniiel and amounts to Jir = 1.195 and this can be consid
ered as constant. Make no corrections in obtaining the slip
block coefficient, but use the nominal block coefficient for the
slip block coefficient.
The lines X, Y and Z may be called " orthodox " for usual
t)^s of hulls and location of propellers. There are, however,
many departures from these " orthodox '' conditions and each
of these departures produces a change in wake and, therefore,
a change in revolutions of propeller for given powers of engines
and speeds of vessel.
These departures may be classed imder four separate heads,
as follows:
I. Deep draft vessels fitted with propellers of diameters
bearing a ratio of less than .70 to the draft, the lower blades pass
ing close to or below the keel.
In such a case, with the vessel running at light draft with the
propeller diameter bearing a large ratio to the light draft, but
entirely submerged, the slip block coefficient will be the normal
from line Z corresponding to the L.L.W.L. or L.B.P., the beam
By and the displacement at the light draft. In estimating the
Digitized by LjOOQ IC
12 y SCREW PROPELLERS
apparent , slip, the value Log A^ must be taken from the curve
marked Xon Sheet 21. See Par. 2.
As the vessel is loaded and the draft increases, conditions
of wake change very slightly, and may be neglected, until after
passing a ratio of diameter to draft, D : H of .75. Shortly after
passing this ratio the wake rapidly reduces imtil D : H = about
.70, when the wake is that corresponding to the S.B.C. as taken
from line W^ Sheef 17, while the value of Log At must be taken
from the ciui^e^J^heet 21. The thrustdeduction factor {K, see
next section), will be that corresponding to the S.B.C. of the
light draft condition.
2. Shallow draft vessels, 14 ft. and less, of S.B.C.= approxi
mately .8 and greater. The S.B.C. will be that corresponding
to Line Z, but the value Log A^ must be taken from the curve F,
Sheet 21. This applies to single screw ships.
3. Submarines of the Lake type, by which term is meant all
submarines carrying their propellers beneath the hull, either
single screw or twin. Such vessels when working on the sur
face should have their S.B.C. taken off from the line J", when
trimmed by the stem and from V for even keel, while when sub
merged, the S.B.C. should be taken from the line V. The
nominal block coefficient to use with 54L.L.W.L, being that of
the surface condition. In both surface and submerged condi
tions, however, the value of Log A^ should be taken from Curve
F, Sheet 21.
4. Submarines of the Holland type, by which term is meant
all submarines carrying their propellers abaft and clear of the
hull. For both surface and submerged conditions the S.B.C.'s
should be taken from line Z7, the nominal B.C. being that cor
responding to the surface condition. The value log A^ for the
surface condition should be taken from Curve X, Sheet 21, and
for the submerged condition from Curve F of this same sheet.
5. Very fine vessels of high speed where heavy squatting
occurs, have the slip B.C. taken from Line X, Sheet 17, but
after reaching a certain amount of squat, the value log A^ grad
ually passes from Curve X, Sheet 21, to Curve F. In the case
of destroyers where the propellers are located abreast the stem
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blcx:k coefficient, thrust deduction 13
post, or where the propellers are several feet forward of the
stem post and the axes of foreandaft sections of the lower strut
arms are inclined downward from aft forward to bring them into
the stream lines, the departure from Curve X, Sheet 21, begins
at about vh VL.L.W.L. = 1.48 and reaches Y when
1^5 VL.L.W.L. = 2.13.
These five conditions are extremely important in their
bearing on revolutions and should be thoroughly borne in mind.
Thrust Deduction and Wake Gain — Sheet 18
When a propeller works at the stem of a vessel it operates
in a body of water which partakes, in a more or less degree, of
the forward motion of the vessel. When the propeller is so
located that the colimm of water entering the propeller enters
normal to the propeller disc and with very little disturbance, and
when, in addition, the propeller blade tips are well immersed and
pass the hull at a good distance from it, the wake, as the forward
motion of the water is called, will increase the effective thmst
of the propeller for any given indicated or shaft horsepower
which may be delivered by the propelling engine. This gain
is known as the wake gain.
Should the propeller be so located in relation to the hull that
the water entering the propeller, in place of entering normal to
the disc enters at a more or less obtuse angle to that plane,
or should the propeller blades be insuflSdently immersed so that
the propeller draws down considerable quantities of air into its
suction column, or should the propeller blades with certain forms
of ship's lines pass unduly dose to the hull, or should combina
tions of these conditions exist, the effective thrust per revolu
tion for any given indicated or shaft horsepower delivered by the
propelling engine will be reduced. This loss in propulsive
effidency is called the thrust deduction.
The action of the water leaving the propeller is illustrated
in Fig. lA. Should a piece of floss thread be taken and secured
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14
SCREW PROPELLERS
to the guard wires on the discharge side of a ventilating fan, it
would be seen that the particles of air instead of leaving the
fan normal to its disc, pass away in lines forming the generatrices
of concentric right hyperboloids of revolution, the maximum
belt diameter A being determined by the angle at which the tip
currents leave the fan, and this angle being, in turn, determined
by the entering angle of the currents entering the propeller or
fan at the tips.
The same state of flow undoubtedly exists in the case of
water flowing to a propeller, and the more nearly normal to the
disc of the propeller is the direction of entry flow, the greater will
Fig. iA. — ^Lines of Flow from Propeller.
be the belt area at A and the lower will be the thrust exerted at
the belt per unit of area, while at the same time its direction
will be more nearly in the direction of advance of the screw and
the greater will be the efficiency of propulsion.
Furthermore, the more the angularity of flow and turbulence
of flow occurring as the water enters the propeller, the greater will
be the change of direction of flow which must occur as the water
passes through the foreandaft length of the propeller blades.
Should this length be short, the water may leave the blades
before the change in direction has been accomplished and a
loss in efficiency in addition to the normal thrust deduction will
occiu:. This phenomenon occurs as the speed of advance of the
Digitized by LjOOQ IC
BLOCK COEFFICIENT, THRUST DEDUCTION 15
propeller for a given number of revolutions is reduced beyond a
certain amount, the phenomenon being referred to later in
this work as " dispersal of the thrust colimm." It is a com
rade of the phenomenon generally known as " Cavitation,'' and,
like its comrade, its arrival can be retarded by increasing the
projected area ratio of the propeller, which carries with it an
increase in the foreandaft length of the propeller and a greater
time allowance for the propeller to swing the currents of water
into the lines of efficient thrust; this retardation is, however, not
obtained without a price, which, is a reduction in the propulsive
efficiency at lower speeds where neither " cavitation '' nor '* dis
persal of the thrust column '' need be feared.
Li cases where the thrust deduction exceeds the wake gain,
and such cases are the usual ones where the standard block
coefficient (slip block coefficient) for the propeller position is .55
or greater, the result is a net loss in propulsive efficiency requir
ing an increase in revolutions with an accompan3dng increase
in engine power. Should the wake gain exceed the thrust
deduction, the opposite effect will be produced.
Calling the percentage increase of power required by the
thrust deduction loss, t, and the reduction in power caused by
the wake gain, w, the resulting factor to apply to the calculated
power to produce any given thrust can be represented by
K = {i+t—w) and where t=w, K = i.
Control of the Value of K
As the value of K is fixed by the character of the hull lines
and in certain cases by the position of the propeller relative to
these lines, there may exist a slight amount of freedom in fixing
the value of K for any given problem. By practical conditions
which are forced upon the designer, the propeller cannot be
removed farther aft from the fullness of the hull lines than a
certain distance, this distance being controlled by the necessity
for the shaft and propeller supports, and this maximum distance
fixes the minimum value of K for any hull.
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16 SCREW PROPELLERS
For some types of hull lines this value of K will increase as
the tip clearance between hull and propeller decreases below a
certain amount, this amount depending upon the slip block
coefficient of the vessel and upon the height of the horizontal line
of least tip clearance, usually the height of the hub center above
the base line of the vessel.
The amoimt of immersion of the upper tips of the blades
below the water surface appears to have some influence upon
the thrust deduction, but very slight as compared with hull tip
clearance, for vessels acting on the surface.
On Sheet 19 are shown four screw propellers illustrating posi
tions and resultant effect on thrust deduction for different types
of hulls. This same sheet also gives the variations of the thrust
deduction factor K for varying slip block coefficients and tip
clearances.
Where propellers are located as shown by position i, the
vertical through the hub center piercing the skin of the ship well
below the surface of the water, the thrust deduction factor K
increases as the relative tip clearance decreases and reaches the
hmit given by the lower bounding curve C1C2 where it has its
maximum value.
For vessels having the propellers located as shown by position
2, the vertical thrdugh the center of the propeller hub piercing
the skin of the vessel well above the water line, the midship
section of the vessel being standard or fuller than standard, K
appears to have the values given by the curve C1C2.
In cases where the propellers are located as shown by posi
tion 3, the vertical through the hub center passing entirely dear
of the vessel or piercing the hull well above the water, due to
fineness of midship section and of after body, the value of K
appears to be practically constant for all values of relative tip
clearance, the values for the different values of slip block coeffi
cient being given by the curve C3C2.
To obtain the relative tip clearance, a propeller having the
center of the hub 10 ft. above the base line of the vessel, and the
tip of an upper vertical blade 14 ft. above the base line are taken
as reference conditions, then calling:
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BLOCK COEFFICIENT, THRUST DEDUCTION 17
£P (Wing Screws) = (Actual horizontal tip clearance Xio)^
actual height of center of hub above base line.
H (Depth of Immersion of upper blade tip) = (Actual immersion
in feet X 14) s actual height of tip above base line.
Then
Relative Tip Clearance =
II
Where vessels are fitted with single screws, located directly
abaft the stem post, the amoimt of thrust deduction for any hull
appears to depend upon the slip block coefficient of the hull and
up©n the actual mean foreandaft clearance between the pro
peller blades and the skin of the ship, thus for ships of similar
blocks, the thrust deduction appears to be a fimction of the draft
of the vessel as the foreandaft blade clearances will vary with
the draft. The values of the thrust deduction factors for such
vessels apparently reach a minimum at about 20 ft. draft, and
are shown by the curve C3C2, while the maximum values are
reached at about 12 ft. draft and are given by the curve CC2.
Where with these shallow draft vessels, the propeller end of the
shaft line is gradually lowered as the block fulls, until at a .9 slip
block nearly the full length of the lower blade extends below
the keel, the thrust deduction factors follow the line CCC2.
These values of K hold, however, for effective thrusts equal
to or less than those corresponding to the line E,T. on Sheet 22.
When these critical thrusts are exceeded the value of K rapidly
increases. This increase in K is, however, treated as a loss in
propulsive efficiency and the percentages of the efficiency real
ized with thrusts JS.r., which can be realized with increased
thrusts are shown as curves on Sheet 22. The augmentation of
K produced by excess of effective thrusts over the values of the
critical thrusts, £.r., is expressed by Kxir^^jA , where
e.t. equals the actual effective thrust for any load condition
and E,T. equals the critical effective thrust for the same condi
tion.
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CHAPTER II
ESTIMATION OF POWER. INDICATED, SHAFT, THRUST,
EFFECTIVE (TOW ROI^E) HORSEPOWER
When speaking of the power required to drive any given vessel
at a certain speed, it is usually referred to as the Indicated
Horsepower where reciprocating engines are used for power
development, and as Shaft Horsepower where turbines or some
other form of rotary engine is used.
By Indicated Horsepower is meant the power developed in
the steam cylinders of the engine by the steam pressure on the
pistons acting through the distance travelled by them. It is
calculated by means of the following equation:
IHP _ PXLXAXN
33,000 '
where P = the mean effective pressure on the piston per stroke,
in pounds;
L= Length of piston stroke in feet;
iV= Number of strokes per minute;
A = Area of the piston in square inches.
There is a percentage of the Indicated Horsepower which is
lost in the engine itself and in the shaft bearings due to friction
of the moving parts. In this book this is taken as equal to
8 per cent. The remainder of the engine power is available for
tummg the propeller and is known as Shaft Horsepower —
where Shaft Horsepower = S.H.P. = .92 I.H.P.
This latter power being transmitted to the propeller, the
latter delivers a thrust in pushing the ship ahead, and the result
ing power, called Thrust Horsepower, is measured by multiplying
the actual thrust in poimds by the number of feet moved through
18
Digitized by LjOOQ IC
ESTIMATION OF POWER 19
by the ship per minute and dividing the product by 33,ocx>. The
equation is:
Thrust Ho^se■powe^=T.H.P. = ^^^^^^ =(^Xy)^326,
and the Efficiency of the Propeller =£=T.H.P.fS.H.P.
The power which would be actually necessary to tow a vessel
through the water at any given speed is usually referred to as the
Effective or Tow Rope Horsepower, and, calling the tension on
the towrope Tr, the equation for Effective Horsepower is:
Effective Horsepower=E.H.P. = ^^^^^^^=(rrXi^)^326
33)<:50oX6o
and the
Propulsive Efficiency =E.H.P. 4 I.H.P.
In the actual making of the estimate of I.H.P. or S.H.P.
necessary for the propulsion of any given vessel at any desired
speed, it is necessary, first of all, to obtain the proper value of
the E.H.P. required for this speed.
The methods of doing this are foiu: in number^ as follows:
1. The Admiralty Coefficient.
2. The Law of Comparison.
3. Independent Estimate.
4. Model Experiments.
Of these methods, 4 is to be preferred.
Admiralty Coefficient
The equation in which this coefficient occxurs is
I.H.P.=^,
in which
I.H.P. = Indicated horsepower of the engine;
Z?= Displacement, in tons;
. V = Speed, in knots per hour;
Ka = Admiralty Coefficient.
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20 SCREW PROPELLERS
Where the Shaft Horsepower is given instead of the Indi
cated Horsepower, the equation should read:
s.H.p.=^^^^
This coefficient, K^j must be derived from some ship for which
the displacement, power, and speed are known, and further, in
order that a dose agreement may be expected between the esti
mated speed and the actual trial speed of the ship, the coefficient
must be derived from a ship that is geometrically similar to the
ship imder design, and which has the corresponding speed. These
terms will be explained when the " Law of Comparison '' is
taken up. Furthermore, it is absolutely necessary that the con
ditions existing in the new ship are such as will permit the realiza
tion of an equal coefficient of propulsion with the compared
vessel. Where these conditions exist, we may write
D^XP.C.
E.H.P. = 
Ka
A moderate deviation in the first two requirements may not
seriously affect the value of the method, but such is not the case
with deviation from the third requirement.
Law of Comparison
1. Corresponding Speeds. The corresponding speeds for
similar ships are proportional to the square roots of their lengths.
2. Displacements. Similar ships have displacements pro
portional to the cubes of their lengths.
3. Corresponding Speeds. The corresponding speeds for
similar ships are proportional to the sixth roots of their dis
placements.
4. Horsepowers. The horsepowers of similar ships at cor
responding speeds are proportional to the sevensixths powers of
their displacements.
This rule (4) is not strictly correct, however, as the frictional
resistance does not follow the law of mechanical similitude.
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ESTIMATION OF POWER 21
5. Variation of Power wi'h Speed. Where the difference
between the two speeds compared is small, we may assume that
" The power for a ship is proportional to the cube of the speed,"
although this exponent may be widely departed from at high
speeds.
6. Variation of Power with Variation in Displacement
For small changes in draught, we may assume that " The powers
vary as the nth power of the Displacement," where n may vary
from f for large ships of moderate speed to i for ships and boats
of high speed.
In comparisons of hulls for similarity of form. Sheet 17
should always be employed on account of the great influence of
and coefficient of immersed midship section on fullness
L.L.W.L.
of lines*
Independent Estimate
The towrope resistance of a vessel is divided into three parts;
surface or frictional resistance, residual resistance, and appendage
resistance. The residual resistance is again divided into wave
making, eddymaking, and streamline resistance.
The equation used for the calculation of frictional resistance is
in which Rf is the force, in pounds, required to overcome the sur
face resistance, W is the wetted surface, in square feet, and v is the
speed, in knots per hour. / and n are quantities taken from
tables which can be obtained from any work on the " Resistance
of Ships," and which are included here.
The equation used for finding the residual resistance is given as
where Z?, v, and L are the displacement in tons, the speed in
knots per hour, and the length on the load water line, in feet.
6 is a numerical factor, having a value for long, fine ships of
about .35; moderately fine ships, .40; ships broad in propor
Digitized by LjOOQ IC
22 SCREW PROPELLERS
tion to length but with fine ends, .45; freighters, .5. The value
of b is also likely to be affected by speed, especially when the
speedlength ratio is high.
Total Bare Hull Resistance. As stated before, this is the
sum of the two resistances, frictional and residual, and the
equation for it is
Using this equation in the estimation of the E.H.P., the
equation for net E.H.P. takes the form
E.H.P.=o.0O3O7(m^ir+>+*^),
where the various letters have the same significance as before.
Wetted Surface. This is determined from the lines of the
ship and is a tedious operation. The surface is computed in
square feet. For a preluninary design, the wetted surface may
be computed by the equation W=Cy/DLf where D is the dis
placement, in tons, L the length on load water line, and C a
coefficient depending on the beam and draught.
Model Experiments
The fourth method for determining power is by aid of model
experiments in a towing basin. To illustrate the method, sup
pose that the towrope resistance for a paraffin model 20 ft. long
is 12.8 lb., when towed at the speed corresponding to 25 knots
for the fullsized vessel which has a length on load water line
of 700 ft., then
Vn^ : 2$ : : V20 : V700 .% »m=423 knots.
The wetted surface of the vessel is 67,540 sq. ft., therefore,
the wetted surface of the model:
Sfn : 67,540 : : 2o2 : 7002 .\ 5« = 55.i sq. ft.
The friction factor and the exponent taken from Froude's
tables are
7=0.00834 and » = 1.94;
Digitized by LjOOQ IC
ESTIMATION OF POWER 23
therefore the frictional resistance is
=/X5«XC=o.oo834XsSiX4.23^^ = 7S4lb.
The total frictional resistance of the fullsized vessel,
/=o.oo847 and n= 1.825, is 0.00847X67,540X25^*®^^ and the
E.H.P. (frictional).
0.00307 X0.00847 X67,54o X 25.^®^* = 15,600.
Taking the frictional resistance of the model from the total
towrope resistance of the model, gives for the residual resist
ance
12.87.54 = 5.2615.
The corresponding residual resistance for the ship is
Rw .* 5.26 : : 700^ : 20^. .*. i?,r= 225,500 lb.
At 25 knots the E.H.P. required to overcome this residual
resistance will be 0.00307X225,500X25 = 17,310.
The total E.H.P. will then be 15,600+17,310=32,910.
In all the above methods, the results obtained are those for
the bare hull only, and the appendage resistance increase called
for by Sheet 18 must be applied before we are in a position to
•compute correctly the propeller and the indicated and shaft
horsepowers.
(Credit must be given Peabody's work on "Propellers"
for the major part of the above sections on " Resistance of
Ships."— C. W. D.)
Table I
VALUES OF C FOR WETTED SURFACES
BtH
C
Bifl
1
C
BiH
C
2.0
1563
2.5
15.50
3.0
15.62
2.1
15.58
2.6
1551
31
15.66
2.2
15 54
2.7
15.53
3.2
15.71
2.3
15.51
2.8
15.55
Z'3
15.77
2.4
15 50
2.9
15.58
3.4
15.83
B = beam. H = draught.
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24 SCREW PROPELLERS
Table II
FROUDE'S SURFACEFRICTION CONSTANTS
Given by Taylor
Surfacefriction Constants for Paraffin Models in Fresh Water
Exponent ii«i.94
Length.
Feet.
Coefficient.
Length.
Feet.
Coefficient.
Length.
Feet.
Coefficient.
2.0
0.01176
10.
0.00937
14.0
0.00883
3.0
O.01123
10. s
0.00928
145
0.00877
4.0
0.01083
II.
0.00920
15.0
0.00873
SO
0.01050
II. S
0.00914
16.0
0.00864
6.0
0.01022
12.0
0.00908
17.0
0.00855
7.0
0.00997
12. s
0.00901
18.0
0.00847
8.0
0.00973
13.0
0.00895
19.0
0.00840
9.0
0.009S3
13. 5
0.00889
20.0
0.00834
Table III
SURFACEFRICTION CONSTANTS FOR PAINTED SHIPS IN SEA
WATER
Exponent » = 1.825
Length.
Feet.
Coefficient.
Length.
Feet.
Coefficient.
Leng h.
Feet.
Coefficient.
8
O.OI197
40
0.00981
180
0.00904
9
0.01177
45
0.00971
200
0.00904
10
0.01161
50
0.00963
250
0.00897
12
0.01131
60
0.00950
300
0.00892
14
0.01106
70
0.00940
350
0.00889
16
0.01086
80
0.00933
400
0.00886
18
0.01069
90
0.00928
450
0.00883
20
0.01055
100
0.00923
500
0.00880
25
0.01029
120
0.00916
550
0.00877
30
O.OIOIO
140
0.00911
600
0.00874
35
0.00993
160
0.00907
Estimate of Appendage Resistance: The resistance exerted
by the appendages attached to the underwater body of a ship,
that is, the resistances of the shaft struts, of the bilge and docking
keels, etc., is generaUy assumed, and in the writer's opinion cor
rectly so, to vary according to the Law of Comparison, and,
on this assumption, when reduced facsimiles of these appendages
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ESTIMATION OF POWER
25
Table VI
SURFACEFRICTION CONSTANTS. EXPONENT, 1.826
Given by Denny
Length.
Feet.
Coefficient.
Length,
Feet.
Coefficient.
Length,
Feet.
Coefficient.
40
0.00996
260
0.00870
SSO
0.00853
60
0.009S7
280
0.00868
600
0.00850
80
0.00933
300
0.00866
650
0.00848
100
0.00917
320
0.00864
700
0.00847
120
0.0090s
340
0.00863
7SO
0.00846
140
0.00896
360
0.00862
800'
0.00844
160
0.00889
380
0.00861
850
0.00842
180
0.00884
400
0.00860
900
0.00841
200
0.00879
420
0.00859
9SO
0.00840
220
0.00876
450
0.00858
1000
0.00839
240
0.00872
500
0.00855
Table V
TIDEMAN'S SURFACEFRICTION CONSTANTS
Derived from Froude's Experiments
Surfacefriction Constants for Ships in Salt Water of 1.026 Density
Iron Bottom Clean
Copper or Zinc Sheathed.
Length of
Ship in
Feet.
and Well Painted
Sheathing Smooth and in
Sheathii\g Rough and in
Bad Condition
/
n
/
n
/
n
10
O.OII24
1.8530
O.OIOOO
1.9175
0.01400
1.8700
20
0.01075
1.8490
0.00990
1.9000
0.01350
I. 8610
30
O.OIO18
1.8440
0.00903
1.8650
0.013 10
1.8530
40
0.00998
1.8397
0.00978
1.8400
0.01275
1.8470
50
0.00991
1.8357
0.00976
1.8300
0.01250
1.8430
100
0.00970
1.8290
0.00966
I . 8270
0.01200
1.8430
150
0. 00957
1.8290
0.00953
1.8270
0. 01 183
1.8430
200
0.00944
1.8290
0.00943
1.8270
0.01170
1.8430
250
0.00933
1.8290
0.00936
1.8270
O.OI160
1.8430
300
0.00923
1.8290
b. 00930
1.8270
O.OII52
1.8430
3SO
0.00916
1.8290
0.00927
1.8270
O.OM45
1.8430
400
0.00910
1.8290
0.00926
1.8270
0. 01 140
1.8430
4SO
0.00906
1.8290
C.00926
I . 8270
C.01137
1.8430
500
0.00904
1.8290
c. 00926
I . 8270
0.01136
1.8430
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26 SCREW PROPELLERS
are attached to the trial model of a vessel a curve of effective
horse powers for the hull and appendages is obtained.
Unfortimately such a curve is not always furnished the de
signer, and when only the effective horsepower curve for the
bare hull, or the estimate of the effective horsepower for the
bare hull fot^any desired speed is supplied to the engineer, it
becomes his task to correct this curve or estimate for the addi
tional effective horsepower required by the appendages.
These appendages usually consist of the following, the vari
ous items being given in the order in which they most frequently
occiu::
1. Rudder and Stem Post.
2. Bilge Keels.
3. Struts, Bosses, and Shafting.
4. Docking Keels.
5. Small Scoops over openings in hull.
6. Large Scoops over openings in hull.
All other appendages that may be fitted are regarded as
extraordinary and must be allowed for by the designer.
No. I is encountered in all vessels, either single or multiple
screw.
No. 2 is met with in most vessels of any considerable size.
No. 3 exists only in vessels having two or more propellers,
although in some cases of singlescrew vessels, the dead wood
may be cut away and the propeller shaft supported by a strut.
In some cases of twinscrew ships, the form of stem known as
the " Lundborg " stem may be used and there will be no stmts.
In such a case the appendage resistance will be less than when
stmts are fitted.
No. 4 is only met with in large, heavy vessels where such keels
are required to better distribute the weight of the hull when
docking.
No. 5 is foimd in all torpedo boats and destroyers built at
the present date.
No. 6 is foimd in those torpedo boats and destroyers built
from ten to twelve years ago.
The resistances due to the bilge and docking keels and shafts
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ESTIMATION OF POWER 27
are probably those due to their wetted surfaces only, and can be
calculated as such. The other appendages enter into the total
residual resistance (wave ajid eddy making), and are estimated
as var3dng according to Froude's Law of Comparison.
Sheet i8. In preparing the curves of appendage resistance
as given on Sheet i8, advantage has been taken of trials made in
the Washington Model Tank by Naval Constructor (now Chief
Constructor) D. W. Taylor, U. S. N., on models of battleships
and destroyers, where, the model having been run through
a series of speeds while fitted with appendages, these appendages
were removed, one by one and other series were run after each
removal, until the bare hull condition was reached when a final
series of trials was made.
The reductions in resistances caused by refining the append
ages were obtained from model tank trials of similar vessels but
ones in which more care had been taken in placing appendages
and in locating them so that their axes would more nearly coin
cide with the lines of flow of the water in proximity to the hull.
The curves as shown are cumulative and are erected on values
of speed of ship (v) divided by the square root of the length on
the load water line (VlX.W.L.), as abscissas, the ordinates
being percentages of the bare hull resistances of the vessel at
these same abscissa values.
In Taylor's work on " The Speed and Power of Ships " is
shown the following figure:
This figure shows the relations between speed of ship in knots,
Vy length of ship in feet, L, and values of vtVl. The shaded
areas indicate humps in the bare hull resistance curves while the
dear areas between the shaded areas indicate hollows.
Returning to Sheet i8, and comparing it with Fig. 2, it is
seen that the first hump in the bare hull curve extends from
about z;5VZ = .75 to ^;^VZ = .83, and that a corresponding
hump in the appendage resistance curve attains its maximum
value 2itvT Vl = .75. Fig. 2 shows another hump at vr Vl = 1.0
to 1.09 but the appendage curve shows no corresponding rise.
Turning again to Fig. 2, a wide hump extending from vtVl
= 1.25 to ^;^VZ=I.6s is found and on Sheet 18 is found a cor
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28
SCREW PROPELLERS
responding hump in the curves of appendage resistance. It will
be noted that no matter which class of appendages is shown, the
himips are in evidence. Evidently the causes producing the
cf? 1^ o va ^, 09 M
'^. ^ ^ B
humps in the resistance curve of the bare hull produce an aug
ment of resistance to an even greater degree in the cases of the
appendages.
Sheet i8 is built up as follows: The base of zero appendage
resistance taken as the bare hull and rudder. The bilge keels
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ESTIMATION OF POWER 29
are then adde d and the appendage resistances for the various
values of z;5 Vl.L.W.L. rise to the values given by curved line
marked i. /
Two propeller shafts with struts well aft, and with the strut
section axes in the direction of motion of the vessel are then
added, and the resistances rise to the curve nimibered 2. This
curve is a combination of two curves, one from z'tVl.L.W.L. =0
to = .95 being taken from the model tank results for a large, heavy
vessel while the portion from .95 to the end was obtained from the
corresponding curves of a light, fast ship.
Again applying more appendages, docking keels were added
in one case, and in the other the large shafts and struts of the two
shaft arrangement were replaced by the four much smaller
shafts and struts required to transmit the same total power as
was transmitted by the two shafts. In the case of the light, fast
vessel, while the two shaft arrangement was retained, injection
scoops were added. The new percentage resistance curve is
marked 3.
Now, returning to the two shaft arrangement, an additional
strut was placed on each shaft, located well forward and with the
axes of its sections made parallel to the stream lines of the water
close to the hull. The appendage percentage resistance in this
case rises from 3 to 4.
Removing these forward struts and fitting in their place
others having their section axes parallel to the direction of
motion of the vessel caused the appendage percentage resistances
to rise from curve 3 to curve 5. All of the se curves except two
have been extended from z>jVl.L.W.L. = .9S to the extreme
right hand of the sheet by maintaining approximately the same
ratio between them and curve 2 as existed at z;ryL.L.W.L. = .73.
In actual service where the vessel is propelled by its own
propellers, the resistances indicated by the hmnps are not in
evidence. The humps are caused by abnormal increases in
wake and these abnormal wakes deliver a large " wake gain "
to the propellers, increasing the nominal propulsive efficiency of
the hull and propeller by a considerable amount, in some cases
to what may be regarded as almost unbelievable.
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30 SCREW PROPELLERS
Finally it must be borne in mind that the appendage percentage
resistance for any given vessel varies with the displacement of
the vessel and that the only satisfactory manner of estimating
this percentage is to tow the model at the displacement corre
sponding to the proposed trial displacement of the actual ship.
There is an additional curve, No. 6, shown on this same sheet
which is the appendage resistance curve for a vessel of the mer
chant type, fantail stem, twin screw; the appendages are two
struts^ one per shaft, small bilge keels, rudder post and rudder.
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CHAPTER in
EARLY INVESTIGATIONS FOR OBTAINING DATA FOR THE
DESIGN OF SCREW PROPELLERS. EMPIRICAL FOR
MULAS
Numerous experiments were carried out during the period
from 1843 to 1848, in the British naval vessels Ratiler, DwarJ
and Minx, and in the French naval vessel Pelican^ to ascertain
the effect produced by varying the characteristics of propellers.
The experiments in the Rattler commenced in 1843, and their
main purpose was to ascertain the best length of propeller (fore
and aft) to obtain a maximima speed of ship. The original pro
peller had a foreandaft length of 5 ft. 6 in., and this was suc
cessively reduced to 4 ft. 3 in., 3 ft., i ft. 6 in., and i ft, 3 in. An
advantage was found to result from diminishing the length.
Various kinds of propellers were tried including some with flat
bands set at an angle with the axis, but it was found that the
ordinary twobladed screw with a uniform pitch was as efficient
as any propeller of the different varieties tested.
The main purposes of the experiment which were made in the
DwarJ in 1845, were to determine the proper pitch and length of
the propeller relatively with its diameter. It was found that the
speed of the vessel increased somewhat as the length of the pro
peller was diminished, but that relatively with the power con
simaed, the result obtained with the shortest propeller was worse
than with the longest of them.
In 1847 and 1848, experiments in the Minx were made to
determine the relative efficiencies of propellers with uniform and
with variable pitches. Of the latter, propellers with axially
increasing pitch, with radially expanding pitch increasing from
the hub towards the circmnference, and propellers in which the
pitch increased both radially and axially were tried. The con
clusion reached from these last series of experiments was that the
31
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32 SCREW PROPELLERS
benefit obtained by departure from the form produced by a
uniform pitch was found to be very inconsiderable, if any.
In all of the preceding cases the actual thrust of the propellers
was measured by means of dynamometers fitted on the pro
peller shafts. In the series of tests which were made on the
Pelican, while more elaborate and which appear to have been
conducted with greater scientific accuracy than the British tests,
no dynamometer was fitted.
The experiments conducted in the Pelican in 1847 and 1848
were repeated in 1849 on board the same vessel, using propellers
of larger diameter than the original, and the results obtained in
the earlier experiments were corroborated.
The object aimed at in the Pelican tests was the determina
tion of the specific efficiency of all kinds of screw propellers in
vessels of every size, proceeding at every speed, and under all
circiunstances of wind and sea, to the end that the particular
species of propeller most proper for a given vessel might be
readily specified. Another object in view was the determina
tion of the value of the revolving force that it was necessary to
bring to act upon the propeller shaft to obtain any definite
number of revolutions in a given time, supposing, of course,
that the form of the vessel was known as well as the dimensions of
the propeller. It is readily seen that the problem thus proposed
for solution is the general problem of screw propulsion whose
correct answer has been sought by many since the early days of
the Pelican tests.
The conclusions arrived at by these tests may be briefly sum
marized, as follows: " Not only does the efficiency of a screw
increase with its diameter, or rather with the relative resistance,
but the proper ratio of the pitch to the diameter, and the corre
sponding fractions of the pitch, vary with the relative resist
ance, the ratio of the pitch to the diameter diminishing when
the fraction of the pitch increases, while the fraction of the
pitch varies with an inverse progression."
Bourne, " Treatise on Screw Propellers," states that these
tests enable us, with any given diameter, to specify the best
pitch and the best length of screw that can be employed, whether
Digitized by LjOOQ IC
f EARLY INVESTIGATIONS 33
the screw is formed with two, four, or six blades. For taking K
as the resistance per square metre of immersed midship section
(equal 6 kilogranmies or 13.23 lb. per square metre at a speed of
I metre per second), B^ the area of immersed midship section
in square metres, D the diameter of the screw in metres, and P
the pitch of the screw in metres, then
and Z> multiplied by the ratio of pitch to diameter, given in an
empirical table obtained by the experiments, will give P.
T.. ,1 PX fraction of Pitch (tabulated) ^ ^. .
Fmally, . ■^, , ^= Length of screw.
number of Blades
For years after these experiments had been completed there
was apparently no systematic attack made upon the propeller
problem, engineers being apparently perfectly well satisfied with
the results obtained by the use of such formulas as the following:
d is the diameter of the L.P. cylinder of the engine in feet;
Z is the stroke in feet;
Pc is the block coefficient of vessel;
Z is a multiplier = (2.4— P^) for twin screws;
and = (2.7 —Pc) for single screws;
22= revolutions per minute.
Ride I. D= diam. of screw in feet = Z X ^dxL,
Ride II. D = diam. of screw in feet =xXPe yj ' ' ' ■,
in which for single screw, nc = 7 . 25
for twin screw, nc = 6 . 55
for quadruple screw, nc = 6 . 25
for ttubinedriven center screw, x=6.$$
for turbinedriven wing screw, it = 5 . 75
for ocean express steamer, nc = 7 . 61
for ocean express steamer, nc = 6 . 88
for ocean express steamer, nc = 6 . 5 1
for ocean express steamer, a; = 6 . 88
for ocean express steamer, nc = 6 . 04
In no case must P^ have a less value than .55.
Digitized by LjOOQ IC
34 SCREW PROPELLERS
Rule ni. A =irZ)2^4, where Z? = diameter of propeller.
The thrust of the propeller in pounds =2AxV{V—v).
The work done per minute = 2^4 XV(V—v)X6ov ft. lbs.
V^PXR, and t^= speed of ship in feet per minute.
^ ^, ^ , 2AxV(Vv)X6oD AxV(Vv)Xv
The thrust horsepower = ^^ = ^^ — .
33,000 27s
K E is the eflRdency of propeller and engine,
27s £
Let (F— »)^F=5=slip in per cent, then
Vv^sV
andt^=F— 57, or F(i— 5).
Substituting these values in the equation for I.H.P., there
results:
. ' ^^ 27s £ 350 £
But V==PXR; therefore
IHP ^X(^X^)'(^"^)
350 E
In actual practice there are disturbing causes which increase
the value of the factor above 350, as with very large hubs the
column of water flowing through the propeller is hollow, and the
equivalent diameter is then less than D. Also the apparent slip
s is less than the real slip. To know how large a real propeller
should be for actual practice another factor is necessary, hence
Ride TV. For good work and high efficiency:
D= /LH.R ,,/ C "V_ /LH.P. ^/ C \3
where x=.2Pc—s, where P^ is the block coefficient of the vessel
and s the apparent slip.
For singlescrew ships and for center propellers of triple
screw ships:
x.i?>Pc+Sy and C=4So.
Digitized by LjOOQ IC
EARLY INVESTIGATIONS 35
To determine the pitch of the propeller, using the same nota
tion as in the rules for diameter, calling the area of the propeller
disc Ay the diameter D, and the pitch P,
RideV. i4 =.78542)2.
Thrust=2^XF(Ft^)lb. = i.S7Z>2xF(F»).
Taking V{V—v) =sVy where 5 = the apparent slip,
Thrust=i.S7Z)2x:i:F2 1b.
Assuming that for any given speed and size of ship, the thrust
remains constant, then
sD^V^ = constant, that is
DXV varies inversely as y/s.
Let V be the speed of the ship in knots, V the speed of the
propeller = z; ^ (i — 5) , then
PXR _ V . p^ 101.33 p
101.33 15 " R(isy
In all of these rules the only controlling influences that are
considered are the power of the engine driving the propeller, the
desired revolutions, and the actual block coefficient of the vessel.
No attention is paid to the variation in block coefficient that is
produced by varying the length of the middle body of the vessel,
the fore and the after bodies remaining constant; nor is any
attention paid to the variations of the speed of wake of the vessel
at different positions in it, these variations modifying the per
centage apparent slip that should be used with any particular
set of after body lines.
The empirical rules for determining the developed area of the
propeller are equally as crude as those for obtaining pitch and
diameter, as the following will show:
JT XT p
Rule VI. Area of developed surface in square ieet^K^J— — —
where jK^=P,Xilf and
for foiubladed single screws, JIf =20; for twin, 15;
for threebladed single screws, M = ig; for twin, 14.3;
for twobladed single screws, JIf =17.5; for twin, 13.1.
Rule VII. Calling the developed surface, 4,; Pr the pitch
ratio =P^Z?; D the diameter, in feet; V the velocity of the
Digitized by LjOOQ IC
36 SCREW PROPELLERS
propeller in feet per second = (PXl2)56o; and G a coefficient
which varies in value from .42 for long narrow blades to .5 for
broad and short turbine propeller blades^ then
r=thrust m pounds = (DxVA]xV^XG)^Pr.
From this formula for thrust, the following formula for
developed siuiace is obtained:
(TXP \^
dxv^xgI
Taking the apparent, slip as a percentage of F, so that it is
represented by sV, then
Speed oiship=v=V—sV=V(i—s).
The efficiency of the engine and propeller being represented
by Ey then
r=(LH.P.X33,oooX£)56ot;=(LH.P.XSSoX£)^F(i5).
Substituting this value of T in the first equation for A„ there
results,
. _ [ LH.RX550XE Pr P_f LH.P.X55oX£xP. 1^
• 1 F(i5) ^DXV^XG] 1 DxV^{is)xG J'
The values usually assimied for 550 E are given as follows:
For ordinary merchant cargo steamers, 550 £ = 330
For express and naval reciprocators, 550 E = 360
For turbinedriven ships, 550 £ = 38
Having now shown some of the purely empirical formulas
formerly generally and at present, occasionally used in the deter
mination of propeller dimensions, it is time to turn to the other
extreme and examine the work of the pure theorists, and this will
be taken up in the following chapter,
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CHAPTER IV
THEORETICAL TREATMENT OF SCREW PROPELLER
The Screw Propeller
Theories of Design
The three most important theories of design, given in the
order of their importance; are: i. Froude's; 2 Rankine's, and
3. Greenhill's. The assumptions for each of these being as fol
lows:
Froude. Assmnes the element as a small plane moving
through the water along a line which makes a small angle with
the direction of the plane. He then takes the normal pressure
upon the elementary area, which gives propulsive effect to vary
as the area, as the square of its speed and as the sine of the slip
angle.
Rankine. The fimdamental assiunption is that as the pro
peller advances with a certain slip, all the water in an elementary
ring of radius r is given a certain velocity in a direction perpen
dicular to the face of the blade at that radius. Then, from the
principle of momentum, the thrust from the elementary ring is
proportional to the quantity of water acted upon in one second,
and to the stemward velocity communicated to it.
Greenhill. Approaches the problem from a direction entirely
different from that of either of the two preceding theorists. He
assmnes that the propeller is working in a fixed tube with closed
end. The result is that the motion transmitted to the water is
wholly transverse. The blade is assumed perfectly smooth, so
that the pressure produced by the reaction of the water is normal
to the blade and has a foreandaft component which produces
thrust.
In all the above theories, the loss by friction is taken as that
37
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88
SCREW PROPELLERS
due to the friction of the propelling plane moving edgewise,
or nearly so, through the water.
In all the theories in connection with which mathematical
methods are to be used, it is practically necessary to regard
the blade as having no thickness. This is a serious defect in the
theories, as they all use a true slip based upon true pitch and
consider the designed pitch of the driving surface of the blade as
this true pitch. The fact of the matter is that the face pitch
of a blade with thickness, or its nominal pitch as it may be called,
is very different from the true or actual pitch, and this fact
causes complications in using the mathematical formulas.
It would be necessary, in case these theoretical formulas were
adhered to, to compare each formula with experimental results
and select that one which
seemed to agree more closely.
Then, using this as a semi
empirical formula, with coeffi
cients and constants deduced
from experiments or experi
ence, problems could be satis
factorily dealt with. When
the vast niunber of various
conditions for which we may
be called upon to design a
propeller are considered, it is
readily seen how impossible
it would be to tabulate the
correctors which would be
required to cover all, or even
a large number of these con
ditions.
In order to give a thorough
understanding of the study
that has been put on the
subject of the propeller, it
Fig. 3.
will be well to present these in their mathematical form for
the determination of thrust and torque, and in doing this
Digitized by LjOOQ IC
THEORETICAL TREATMENT 39
nothing better can be done than to give Naval Constructor
Taylor's presentation of the theories, as set forth in '^ his work
on " The Speed and Power of Ships."
Fig. 3 indicates the motion of a small elementary plane blade
area of radius r, breadth dr in a radial direction, and circum
ferential length dl. This element is seen with its center at O.
If w is the angular velocity of rotation of the shaft, the cir
cular velocity of the element is wr. AOB is the pitch angle ^,
BC the slip and BOC the slip angle 0. Now, tan ^=P^2irf.
Considering Fig. 3 as a diagram of instantaneous velocities, the
line OA or wr represents the circular velocity of the element.
If there were no slip, the actual velocity along the helical path
would be OB and AB would represent the axial velocity or the
velocity of advance, and
AB=OA tan e=wr tan e^wr^^—.
2irf 2ir
When there is slip the circular velocity of the element is
imchanged, but the velocity of advance becomes AC^ the speed
of the screw is the same as the speed of advance when the slip is
zero.
, Denote the percentage slip by 5, then
S^BC^AB = {ABAC)^ABJ'^V^^'^=^VJ^.
\2x / 2ir Wp
From which the speed of advance
V,=^'^{is)^dBC^s'^.
2X 2X
If w is taken as the angular velocity per second and r is taken
in feet, then OA, or the circular velocity, is in feet per second and
therefore all other velocities will be in the same units.
Finally, taking the components, we have:
Velocity of element in direction perpendicular to its plane
^CD=BC cos e=s^ cos e.
2X
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40 SCREW PROPELLERS
Axial or rearward component of this velocity
CECD cos e=^s^ cos2 e.
Transverse component of the same velocity
^DE^CD sin ^=5^ sin ^ cos ^.
2ir
Rankine^s Theory. Referring to Fig. 3, and considering the
annular ring of mean radius r.
Annular area = 2irrdr.
Volimie of water acted on per second
= 2irrdrXAE = 2irrdrX^(is ^^ e).
00
Stemward velocity communicated
^EC^s^cosH=Mcos^e.
2X 60
Therefore elementary thrust = mass of water per second X stem
ward velocity imparted = dT =  27rrdr ^(i—s sin^ 6) Xs^cos^ $
g 60 60
= ^ — 5(1 —5 sin^ e) cos^ d 27rrdr.
g 3600
Lety = cot^= — , then2irrdf = — dq; sin2^= ;
p 2t 1+3^
C0S2(?=^.
Whence
_w f^ f\, qdq (qdq qdq \\
At the axis ^'=0. Neglecting the hub, if q denote now the
cotangent of the pitch angle of the blade tips, on integrating the
expression for dT, is obtained.
Digitized by LjOOQ IC
THEORETICAL .TREATMENT 41
^jw f^ t^[^ loge(i+g^) / loge(i+g^) 1 f \\
g 3600 2ir L2 2 \ 2 i+q^/1
"g 3600 4x L t ^ <f i+Wj
Now, pq=2Trr\ f(f^/^T^f^\ ti.^^=.'^ if d is extreme
4x 4
diameter. Whence
^3600 4 L 2^ \ 5^ 1+5^/ J'
and finally,
r=
/<^^4'=^('^^r^)]'
I44OOJ
and the torque,
2t
IF. Froude's Theory. 11 I is the total foreandaft blade
length of all blades at radius r, then the total elementary plane
area at this radius is Idr. This area advances at the angle
(Fig. 3), with velocity OCy and from Froude's experiments if a
is a thrust coefficient, the resultant pressure normal to the blade is
=Wr a OCT sin 0.
The elementary thrust is equal to this pressure X cos 6. Then
(fr=Wr a OC^ sin cos ^.
Now
wp ^
s^ COS e
. ^ CD 2ir ^ /»
sm 0=— =— = , == COS e.
27r
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42 SCREW PROPELLERS
Also
i+f
Whence
36CX) J J 1+52 ^ ^ ^ 2T
Whence, deducting the hub.
The quantity under the integral sign is dependent only on shape
and proportions of the propeller and independent of its dimen
sions. Let it be denoted by the symbol X. Then
T=^^IPdsX, and
3600^
GreenkUTs Theory. Referring again to Fig. 3,
Elementary area = 2wrdr.
Velocity of feed of the water =ilC=—(i —5) =^(i —5).
2t 60
Circular velocity =^— cot 6=swr=S'rr^.
2T 60
Circular momentum per second.
= —Twrdr^ (i  5)5— r.
g 60 60
? 3600
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THEORETICAL TREATMENT 43
Torque = drcukr momentum Xr.
Whence de=^V^^(i^)4^r^dr.
P g 3600
Integrating from r=o to r =, there results
2
^3600 288oog
And g=^.
2ir
The equations for thrust and torque are further modified, in
all the theories, by corrections for frictional and head resistances,
the thrust being decreased and the torque increased.
The decrease from thrust for friction
where F= J^^^g£/g.
The addition to the torque for friction
=^ffdF?Z, where Z= fJ^VT+fdp.
In both equations / denotes the coefficient of friction and is
taken sufficiently large to cover all edgewise resistance, both
skin and head resistance together.
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44 SCREW PROPELLERS
Final Formulas for the Three Theories
The resulting equations for thrust and torque for the three
foregoing theories may be expressed thus:
Rankine: T=p^d^R%asps^) JdfR^Y.
Q=^[fd^R2{ys 8s^)+fdfR^Z\.
Froude: T^fdB?{as^^)fdfB?Y.
GreenkiU: T=d*F?{as^s^)JdfF?y.
Q=Md*R^iys b^)+{dfB?Z\.
2t
These equations simply show the form of the expressions, and
do not imply that the values of a, /5, y and 8 are the same in all
the theories, but simply imply that in each case the values of
these factors will be constant for a given propeller. The actual
values of these factors will vary with the theory used.
Having obtained the values of T and of Q, the efficiency can
be obtained as follows: Denoting the pitch by />, as before, the
revolutions per minute by iJ, and the slip by 5, the speed of ad
vance of the propeller is p{i—s)Rj and the useful work done per
minute is Tp{i—s)R, while the gross work delivered to the pro
peller is QX2tR.
:. Efficiency = (Useful Work) ^ (Gross Work) =
Tp(is)R^2QirR=^^^^^=e.
Q 2t
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CHAPTER V
PRACTICAL METHODS OF DESIGN. DESIGN BY COMPARI
SON. TAYLOR'S METHOD. BARNABY'S METHOD
The practical methods of design can be divided into
1. By " Direct Comparison," when all the conditions for a
satisfactory vessel of a similar form to the one under consid
eration are known.
2. By methods based on trials of model propellers in model
tanks. This may also be classed under the head of " direct
comparison," as the Laws of Comparison are assmned to cover
propellers as well as hulls.
3. By methods based on actual trials of fullsized propellers
in service over carefully measured courses.
The first method practically insures a propeller of equal
propulsive efficiency with that of the propeller on the compared
vessel, but gives no opportimity for improvement in performance.
The second method is open to the decided objection that the
conditions under which the model screw is tried in the tank are
radically different from those under which the fullsized screw
operates. In fact, propellers whose models have shown high
tank efficiencies have failed most signally in service, while other
propellers whose models gave poor efficiency have delivered a
high propulsive coefficient. This latter has been ascribed to a
high hull efficiency but this explanation does not exactly satisfy
when the fact is considered that where two or more propellers
for the same vessel have been tested, that propeller whose model
gave the highest efficiency has failed, while the propeller with the
lower tank efficiency has succeeded.
The writer is inclined to the belief that the true cause of
these discrepancies exists in the use of an incorrect method of
45
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46 SCREW PROPELLERS
derivation of the model screw dimensions from those of the
fulll^ize propeller.
Method of " Design by Comparison "
The following orthodox method is taken from Peabody's
" Naval Architecture," and is that which is generally used:
Z)i = Diameter of original propeller;
Z)2 = Diameter of 2d propeller or of model propeller;
Li = Length of compared vessel;
£2= Length of new Vessel or model hull behind which model
screw should operate if fitted to a hull (which is not
usually done);
Pi = Pitch of original propeller;
P2 = Pitch of 2d or model propeller;
i?i = Revolutions of original propeller;
i?2 = Revolutions of 2d or model propeller;
z>i = Speed of compared vessel;
V2 = Corresponding speed of new or model hull.
Then Z)2=Z>iX^=Z)ir;
(L2Y «
p
P2PP1 =rPi where same ratio of — is retained for the model
as that of the original propeller.
Apparent slipi
fiXi?! 101.33^1
Apparent slip2,
^' " PiXRi
S2
i^^lXTT— 101.33 Z^lf^ T^ «
PP.X^ ^^^^^^
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PRACTICAL METHODS OF DESIGN 47
which, when pr becomes — p '^^ ^ or the apparent
slip of the model, is equal to the apparent slip of the original
propeller.
Tipspeedi=iJiX7rZ)i;
Tipspeed2=i?2X7rZ)2 = ^XxZ)ir=i?i7rZ)ir^; and
T.S.2 < T.S.i, depending upon the value of r.
Again,
I.H.P.2=I.H.P.i//»;
Disc area2 = J^Z^i V;
Disc areai = i^Z)i2;
I.T. per square inch disc area2
_ I.H.P.1 X//' X33,ooo _ I.H.P.1 X i32,oooXr >.
r^ 4
I.T. per square inch disc areai
_ I.H.P.iX33.ooo _ IH.P.i Xi32,ooo
p.xi?ix^z>x^ PiX/exX^A^ '
4
I.T.2 r^ u ^ IT.2
.•.j^=, or where ^=r,j;;j^=r.
In other words, with dififerent percentage losses from blade
friction due to change in tip speeds, the model screw is supposed
to deliver an equal percentage of the power driving it as effective
thrust, with the original propeller, and its apparent slip is sup
posed to be equal to that of the original propeller, although the
thrusts per square inch of disc area have been changed in the
ratio r, the two screws working xmder approximately the same
conditions of resistance.
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48 SCREW PROPELLERS
Taylor's Method of Design
This method of design is based entirely upon the trials of
model propellers in the Model Tank, and from the results ob
tained were derived practical coefllcients and constants for full
sized propellers.
The factors dealt with in this method of design are efficiency,
diameter, pitch ratio, mean width ratio of the blade and blade
thickness fraction.
In this method there is a primary variable, p fixed by the
conditions of the problem. Its value is expressed by
p /S»H.P.
where S.H.P. is the shaft horsepower absorbed by a propeller of
D feet diameter at R revolutions per minutt when advancing at
a speed of V^ knots.
Another factor b is expressed by the following equation:
Diagrams of pb, efficiency and real slip for various pitch
ratios, mean blade width ratios, blade thickness fractions and
.speed of wake for elliptical threebladed propellers are prepared
from model tank trials of model propellers, and from these the
necessary factors for use are obtained.
In the above equations F^ is not the speed of the ship through
the water but is the speed of advance of the propeller through the
disturbed water in which it works.
For determining the thickness of the blades, Taylor has ob
tained the following expressions:
The compressive stress in pounds per square inch for blades
of the usual ogival section
where C is a coefficient depending on radius and pitch ratio, Pi
is the shaft horsepower absorbed by the blade, iJ = the revolu
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PRACTICAL METHODS OF DESIGN 49
tions per minute of the propeller and / and t are the width and
thickness of the blade in inches. In determining Sc the values
of C, / and t at about .2 the radius of the propeller should be used,
this fraction of the radius being the approximate radius of the
hub for threebladed propellers of the builtup type, and also
being approximately the point of maximum stress.
Put /= 12 chdy where d is diameter of propeller in feet, h is the
mean width ratio of a blade and c is a coefficient depending upon
the shape of the blade.
For the thickness t, calling the axial thickness of the blade
Tdf and the thickness at the tip kTd, then at .2 radius
tri2Tdlk+.S{lk)] = l2Td(.S + .2k).
In practice k is seldom less than .1 or greater than .2. When
*=o, t=9.6Td; * = .!, t=g.84Td; k = .2, t=io.QSTd] hence it
is a sufficient approximation to assume t=ioTd.
Substituting these in the stress formula,
LetCi=^, then
1200
'LeX%^='X,chT=y, then
y
Values of Sc are given as curves plotted on values of x and y.
Barnaby's Method
Mr. Sydney W. Bamaby has recast the results obtained by
Mr. R. E. Froude from trials of model propellers into the follow
ing form for use in the designing of propellers:
He has chosen a standard wake value of 10 per cent, a coef
ficient of propulsion of .5, the resistance of the bare hull only
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60 SCREW PROPELLERS
being omsidered, and a blade having an elliptical fonn of devel
oped area, the major axis being the radius of the propeller and
the minor axis being .4 that radius. The total developed area of
the blade being the area of this ellipse less the area included
within the radius of the propeller hub.
Bamaby's factors are tabulated, and as so tabulated are for
fourbladed propellers, but can be used for three or twobladed
propellers by taking account of Froude's determinations of the
relative efficiencies of these numbers of blades.
The size and revolutions of the propeller are given by the
following expressions:
i4«DiscArea=C^X^^,
y
R * Revolutions = Ca X jr,
where D « diameter of propeller in feet =
■s
F> Speed of ship in knots perhour.
As the values of Ca and Ca vary with the pitch ratio, call
this ratio
where P"> the pitch of the propeller in feet
Then
A'Ca^, ...... (i)
•• ^'' I.H.P.'
R'C^l (2)
•• ^B y,
. I.H.P.XJg« ,.
*=* xn (3)
ys
Digitized byCjOOQlC
PRACTICAL METHODS OF DESIGN 51
Equation (3) is used as an aid in proportioning propellers
which must have a given speed of revolutions.
For threebladed propellers the formula for Ca becomes
^^~ LH.P. '
while for twobladed propellers it becomes
^^""lIlp:
Corrections for Variation in Wake, Estimated Propulsive
Coefficient and in Blade Width Ratio
" The standard wake has been taken as 10 per cent of the
speed of the vessel. In a very full ship it might be as much as
30 per cent. Therefore the speed of the ship, F, should be
reduced when using the constants, by about 20 per cent for a
very full ship, and by amounts varying from 20 per cent to noth
ing, as the fullness of form varies from " very full " down to what
may be considered a " fairly fine " vessel when no correction may
be made.''
E H P
" The standard value of the propulsive coefl5cient= ''' ,
I.H.P.
has been taken as .5. A correction can be made for any ex
pected deviation from this assumed value. If the propulsive
coefficient is estimated at 55 per cent, then the LH.P. must be
multiplied by — .
SO
To correct for varying width ratios of blades, Professor C. E.
Peabodj^ suggests that the method proposed by Naval Construc
tor Taylor, be used, namely, to make the thrust proportional to
the width of the blade.
Suppose the blade is .6 as wide as the radius of the propeller,
then
AC vtLILP: . c 3^YL
D' ^ V
Digitized by LjOOQ IC
.g2AV^
S.H.P.
^ RD
62 SCREW PROPELLERS
CORBECnON FOR VARYING VALUES OF DEVELOPED ArEA RaTIO
From the Standard
By assuming that the total thrust that can be delivered by
any propeller of fixed pitch, diameter and revolutions will vary
directly as the develop)ed area ratio, a series of curves can be
laid down as shown on Sheet i6, by which the values of
and
can be obtained for any desired value of developed area, H.A.,
divided by disc area, D.A.
The values of Ca are shown as ordinates on the left of the
sheet, the abscissa values being increasing values of H.A.TD.A.
P
On the right are curves of pitch ratio, — , inclined close to
the vertical, while the curves approximating more closely to the
horizontal are those of propeller efficiency, not propulsive effi
ciency. These curves oi P^D and of efficiency are both erected
on values of C/2 = ^^ as abscissas.
In this equation, however, V does not equal the speed of the
ship as in the Bamaby formula but equals the speed of the ship
Xa coefficient M, whose values change with the wake, and which
must be obtained from the analysis, by means of these curves, of
the trials of numerous vessels.
To obtain the correct value of M from the actual trial results
of vessels, a value of M = i is first assumed, and with the I.H.P.;
the .F = speed of ship and the revolutions obtained on trial for
this I.H.P. and F, together with the actual diameter, D, and
measured pitch, P, and disc area in square feet of the propeller
s=:' — , the values
4
i.H.p;
Digitized by LjOOQ IC
PRACTICAL METHODS OF DESIGN 63
^ RD
are obtained. Taking this value of C^ as the value of the
ordinate at the abscissa value H.A.rD.A. of the actual pro
peller, and projecting across to the ordinate erected at the abscissa
whose value is that of the Cr so obtained, a point is plotted.
Through this point draw a line parallel to the line AB, Sheet i6.
This line will be the locus of all values of C^ and C^ for any
value of M. Where this locus crosses the value oi PiD oi the
actual propeller will be the approximate location of the pro
peller on the chart.
Now, in the formula
^ _ RXD
the values Cr, J?, /?, and 5= speed of ship are known, and from
these known values the value of M can be obtained as
«* =t; ^»
CbXS
Where curves of I.H.P. — Speed, Revolutions — Speed are avail
able through a range of speeds, a corresponding curve of M can
be laid down. If M continues at a nearly constant value through
a long range of speeds and then suddenly rises and continues to
rise rapidly as higher speeds are reached, it is an indication that
the propeller is breaking down and that an improvement at
the higher speeds can be expected should the acting surface
of the propeller be increased.
From the results of trials of vessels similar to that for which
it may be desired to design a propeller, the approximate best
value of M to use may be determined. Taking the estimated
I.H.P. , 5(speed of ship) XM, and varying disc areas of propellers
up to as high a diameter as may be fitted, find the value of Ca
for each of these assumed disc area values and find the corre
sponding values of Cr for the desired revolutions and the values
of D corresponding to the different values of disc area.
Assuming a value for H.A.^D.A. of any value, say, .34, take
Digitized by LjOOQ IC
54 SCREW PROPELLERS
the values of Ca and Cr corresponding to any one diameter value
and plot it on the chart and through the point thus obtained draw
a line parallel to the line of constant helicoidal area ratio, CD.
The line so obtained will contain all the diameters for H.A. ^D.A.
= .34, but Cx and Cr varying. Where this line crosses the line of
maximum efficiency will be the position of the desired propeller
xmless the resultant diameter is too great, when a larger value of
H.A.^D.A. should be tried.
From the location of the obtained propeller on the chart, can
be obtained:
Diameter. Deduced from value of Cr.
PhD. Given on Chart.
H.A.^D.A. Assumed in computation.
Efficiency of propeller but not propulsive coefficient.
P
The pitch will be = Diameter Xy^.
The projected area of the propeller will equal
Helicoidal Area  ,,. , . , , 1 j
for eUiptical blades.
V'+g
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CHAPTER VI
THIRD METHOD OF DESIGN: DESIGN BASED ON ACTUAL
TRIALS OF FULLSIZED PROPELLERS IN SERVICE
OVER CAREFULLY MEASURED COURSES. THE DYSON
METHOD
In November, 1915, Sir Archibald Denny in reading a paper
on " Model Tank Experiments on Naval Propellers," rather
emphatically stated that in the future the rules for the correct
designing of propellers should he derived from data carefully taken
from the trials of smooth bottom vessels carefully run over accu
rately measured deep water courses.
This statement by such a noted authority is in line with the
views of the author of this book and outlines exactly the plan
which he has been following since 1901 when he first took up the
study of propellers seriously. The results obtained from these
years of study will now be given as clearly as it is in his power to
present them.
All screw propellers when working under similar conditions
of resistance arrange themselves in one great family in which
the position of any particular propeller is fixed by its diameter,
its pitch and its projected area ratio, the latter fixing the dimen
sions of the thrusts and the resultant tip speeds, and most im
portant of all, the efficiency; the propulsive coefiicient being
this efficiency as modified by the existing hull conditions.
Let this condition of equal resistance be called the Basic
Condition, as it applies equally to all propellers.
Sheet 20, Basic Condition
On Sheet 20, are shown the curves of Indicated Thrust per
square inch of disc area of the propeller, I.T.£>; the curve of
Tip Speeds in feet per minute corresponding to these values of
55
Digitized by LjOOQ IC
66 SCREW PROPELLERS
I.T.D, marked T.S.; the curves of i minus the apparent slip as
modified by the dififerent values of slip block coefficient from unity
to the phantom ship of zero block, marked i— 5; and finally
the values of the propulsive coefficients wliich can be obtained
at this condition of standard resistance, the hulls having the
minimum losses possible due to thrust deduction; the propulsive
coefficient curve is marked P.C., and the condition of Basic
hull efficiency or Basic thrust deduction corresponds to the
value Jf =1.
These curves are laid down on values of projected area ratio,
P.A.5D.A., as abscissas.
The Basic Curve is that of I.T.^,, and is represented by the
equation
:T.. = .8.S4(^Y',
where I.T.x> = Indicated thrust per square inch of disc area of the
propeller = (33 ,000 X I.H.P.) ^ (Pitch X Revolu
tionsXX Diameter of Propeller in feet X144.
T.S.=The tipspeeds of the propellers in feet per minute
= Revolutions XttX Diameter in feet, corre
sponding to these values of I.T.2> and of P.A.
5D.A. are also shown as a curve.* It should be
thoroughly borne in mind that these tip speeds
and the corresponding values of I.T.2> are
coincident only xmder the conditions of resist
ance for the Chart. Should the resistance
change the tip speed may change and the cor
responding value of I.T.z> will also change
for a constant value of I.H.P. , but the value of
LT.x)XT.S. or I.T.^jX Revolutions, will remain
constant.
I— 15=1 — apparent slip imder Basic condition of resist
ance =P.T.p^E.T.p= Propulsive thrust divided
by effective thrust. These curves are shown foi
different values of slip block coefficient varying
Digitized by LjOOQ IC
THIRD METHOD OF DESIGN 57
from unity to the zero value of the phantom
ship.
P.C. = Propulsive coefficient of the propeller = Basic
E.H.P.^Basic LH.P.=Basic E.H.P.5(Basic
S.H.P.h.92), the ratio between I.H.P. and
S.H.P. for welldesigned, welladjusted and
welllubricated reciprocating engines without
attached pumps being taken as S.H.P..92
I.H.P.
The curve of P.C. is seen to rise rapidly from zero value of
P.A.^D.A., at which point the propeller would be of infinite
diameter and pitch but of zero tip speed, to a maximum value
where P.A.^D.A. = .2. It then falls gradually to P.A.^D.A.
= .25, after which its rate of fall increases until P.A. 5D.A. = .54,
where it rapidly decreases until at P.A.hD.A. = .S5, the value
of P.C. has reached its minimum, and this minimum value it
retains up to the limit of design which is taken as P.A.hD.A.
= .650. For hydraulic propellers the ordinary range of design
extends from approximately P.A.^D.A. = .2 to P.A.5D.A.=
.650, the propulsive efficiency decreasing as the thrusts, tip
speeds and projected area ratios increase. When air ship
propellers are considered, however, they Sire found to lie to the
left of the vertex of the propulsive efficiency cm^e, and the action
is the direct opposite, that is as the thrusts, tip speeds and pro
jected area ratios increase, the propulsive efficiencies increase
with them.
Before going further into the subject of design it will be
well to give the
Definitions of Terms and Abbreviations used in the Work
I.H.P.p= Indicated Horsepower of Propelling Engine on one
propeller, without thrust deduction.
S.H.P.,=B.H.P.p = .92 I.H.P.p = Shaft or Brake Horsepower
applied to the line shafting and measured by torsion
of shaft abaft the thrust bearing, without thrust
deduction.
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58
SCREW PROPELLERS
e.h.p.=Net eflfective or towrope horsepower required to tow
the hull at any given speed, the hull being fitted with
all appendages, e.h.p. ^ number of propellers equals
the effective horsepower that must be delivered by
one propeller.
I.H.P. = Indicated Horsepower which can be delivered by the
propeller under Basic conditions.
S.H.P. = B.H.P. = .92 I.H.P; = Shaft or Brake Horsepower ab
sorbed by the propeller under Basic conditions.
E.H.P. = Effective (towrope) Horsepower which can be deliv
ered by the propeller under Basic conditions.
i?= Thrust deduction factor due to form of hull and location
of propeller when net effective thrusts do not exceed
critical thrusts shown on Sheet 22. Sheet 19.
z;= Actual speed of vessel corresponding to e.h.p.
F = Basic speed corresponding to E.H.P.
e.h.p. ^ E.H.P. = Net load factor under which the propeller is
operating.
^;^F = Speed factor under which the propeller is operating.
Z= Value of exponent in 10^ in equation for "power at
other than Basic condition." It has the following
values:
Table VI
VALUES OF Z TO BE ADDED OR SUBTRACTED FROM LOG I.H.P.
c. h. p.
Z
e. h. p.
E.H.P.
Z
e. h. p.
E.H.P.
Z
E.H.P.'
Empir.
Calc.
Empir.
Ca]c.
Empir.
Gale.
.01
.015
.02
.025
.03
.04
.05
.06
.07
.075
.08
.09
1.603
1359
1.165
2.0828
1.8994
1.7693
1.6684
I 58594
145582
1.3549
1.27244
I. 20271
II715
I . 1423
I. 0891
.1
.2
.3
.4
.5
.6
.7
.8
.9
I.O
105
I.I
1.0268
.728
.5493
.4238
.3267
.2432
.1690
.1065
.05402
.0225
.0450
I. 0414
.7279
•5445
.4144
.3135
.2310
.1613
.1009
.0477
.0221
.0431
1. 15
1.2
125
13
1.35
1.4
1.45
15
155
1.6
1.65
1.7
1.75
.065
.084
.102
•1195
.1361
.1518
.1676
.1823
.197
.21
.225
.239
.250
.0632
.0825
.1009
.1x86
.1357
.1521
.1681
.1834
.1932
.2126
.2265
.2400
2531
Digitized by LjOOQ IC
TfflRD METHOD OF DESIGN
59
eAp. = Gross eflfective horsepower which would be delivered
by the 'propeller with a total power LHP.^ if no
thrust deduction existed,
e.t. = Net effective thrust.
e,L = Gross effective thrust.
E.T. = Critical effective thrust.
Z? = Diameter of propeller in feet.
P = Pitch of propeller in feet.
T.S.= Tipspeed of Propeller in feet per minute under Basic
conditions.
P.A.5D.A. = Projected Area ratio of 3bladed propeller.
i(P.A. ^D.A.) = Projected Area ratio of 4bladed propeller,
f (P.A. ^ D. A.) = Projected Area ratio of 2bladed propeller.
P.C. = Basic propulsive coefficient for total projected area ratio
no matter what the number of blades of the propeller,
p.c. = Actual propulsive coefficient delivered by the propeller.
The value of p.c. depends upon the value of P.C, of K, and
of the load factor e.h.p.^E.H.P., and of v^V.
Where z^r F is not less than the values corresponding
to the curve marked " Critical Thrusts " on Sheet 22,
the value of p.c. depends upon the first three factors,
only.
The relative values of p.c. and P.C. for varying values of
e.h.p.^E.H.P., where the values of v^V sue equal to or greater
than those corresponding to the critical thrust, E.T., disregard
ing the value of Ky are given in the following table; the actual
values of propulsive coefficient would be reduced, however,
inversely as the value of K:
Table VII
VALUES OF p.c^P.C. FOR VARYING VALUES OF e.h.p.5E.H.P.
e. h. p.
p. c.
P.C
e. h. p.
p. c.
p.c
e. h. p.
U
e. h. p.
^•
e. h. p.
p. c.
E.H.P.
E.H.P.'
EH.P.
E.H.P.
E.H.P.'
P.C
.025
1.002
.4
1. 061
I.O
1.0
13
.9873
1.6
•9843
.OS
1. 143
•5
1. 061
1.05
.997
135
.9868
1.6s
.9838
.075
1.097
.6
1.05
1. 10
.9917
1.4
.9863
1.7
.9833
.1
,1.064
.7
1.033
115
.9901
145
.9858
I.7S
.9828
.2
!i.o69
.8
1.022
1.2
.989
15
.9853
1.8
.9823
.3
1.063
.9
1. 019
125
.9884
155
.9848
1.8s
.9818
Digitized by LjOOQ IC
60 SCREW PROPELLERS
These values of p.c.^P.C. are obtained from the values of Z
and of e.h.p.7E.H.P. by means of the following equation:
Log p.c. =log P.C.+log ( ^ '^ j +Z where Z is additive for
values of e.h.p.rE.H.P., less than unity, and subtractive for
those greater than unity. The empirical values of Z have been
used but the calculated are better.
Above the critical thrusts (Sheet 22), these values of p.c.^
P.C. and the corresponding values of Z only hold up to a point
where the value v^V is slightly less than e.h.p.^E.H.P., this
limiting point being taken as
^^F=e.h.p.^(I.ISE.H.P.),
or, in other words, an increase of 15 per cent in the effective thrust
over the effective thrusts for the basic condition of the propeller.
After passing this point the value of Z changes very rapidly,
due to cavitation of the suction coliunn, causing a rapid increase
in power and a corresponding decrease in the value of the pro
pulsive coefficient. Where thrust deduction exists, the final
ratio of actual to basic propulsive coefficient for any projected
area ratio of propeller becomes at thrusts equal to or less than
those corresponding to the Curve Critical Thrusts, £.r., (Sheet
22), and at positions above that curve,
p.c^K.P.C.
where the effective thrusts are greater than the critical thrusts,
£.r., the final value of p.c. becomes log p.c.=log P.C.+log
{^)^^^{mh'
s = Apparent slip of propeller at speed v.
5= Apparent slip of propeller at basic speed V under basic
conditions of power and resistance.
I.T.= Total indicated thrust exerted by the propeller xmder
basic conditions,
_ LH.P.X33^ooQ _ S»H.P.X33>ooo
PXR .92XPXR
Digitized by LjOOQ IC
TfflRD METHOD OF DESIGN 61
R = T.S. i^vD = Basic revolutions.
I.T.D = I.T. ^ ( 144 XD^ ] = Indicated thrust per square inch of
disc area imder basic conditions.
P.T.= Total propulsive thrust of the propeller under basic con
ditions,
^ E.H.P.X33,°°o ,IT.XP.C.
There is often a different expression for indicated thrust
given than the one above, so in order to avoid confusion, the
writer has adopted the term " Speed Thrust," to differentiate
between the two. V.T. = Speed thrust imder basic conditions^
^ LH.P.X33,ooo _ S.H.P.X33,ooo ^
7X101.33 .92 XFX 101.33*
E.T.= Effective thrust under basic conditions,
_ E.H.P.X33,ooo
FX 101.33
The ratio between the indicated and speed thrusts and be
tween the propulsive and effective thrusts is
^ c_LT._ P.T. _ FXioi.33
V.T. E.T. PXR *
Derivation of Formulas under Basic CoNDinoNS
Formula for Pitch:
Speed of ship in feet per minute ~ 101.33 ^ ^
Digitized by VjOOQ IC
62 SCREW PROPELLERS
Apparent slip of propeller in feet per minute under Basic
conditions
rJJ
. p^ .PX.RXyZ? _ ioi.33XFXyX£>
T.S. T.S.X(i5) ■
Derivation of Equation for D:
I.T. = (I.H.P. X33,ooo) ^ (PXR).
TT TT • /tiiV*'7?2\ IH.P.X33.000
, ^ I.H.P.X33.000 _ 29i.8Xl.H.P
36yXl.T.z)XPXie LT.dXPXR'
. ^^ / 29i.8Xl.H.P. _ / 29i.8Xl.H.P.X(i5)
\I.T.„XPXie V I.T.z>xrx (101.33)
^:
2.88 XI.H.P.X (15)
I.T.cXF
This formula applies to threebladed propellers only, and re
quires modifications, as follows, for four and for twobladed ones:
Fourbladed
jy^ /252.4iXl.H.P _ /25 2.4iXl.H.P .X(i.S')
\ LT.dXPXR V I.T.cX7>
■4
:^x 101.33
2.491 Xl.H.P.X(i.^
I.T.dXK
Twobladed
/ 389XI.H.P. ' _ /389Xl.H.P.X(i5)
\ LT.i>XPXie > I.T.x>XF.X 101.33
X 101.33
/3.84Xl.H.P.xTI^
I.T.z>XF
4'
This may be expressed by the following general equation:
„^ / ^XI.H.P. _ /BxLH.P.xCi"^
yi.T.„XPXR y LT.dXV
Digitized by CjOOQIC
TfflRD METHOD OF DESIGN 63
also
5XtXLILP.
^^^" LT.z>XT.S. '
whence for any value of Z?,
^XttXLH.P.
P=,
Z>Xl.T.i>XT.S.
and
7rXJ?Xioi.33
Method of Changing i:rom Basic Conditions to Other
Conditions of Resistance
It has been explained how for Basic conditions of resistance
of any vessel, and without thrust deduction, and with a given
propeller, the vessel will run at a speed V with an indicated
horsepower, I.H.P., shaft horsepower S.H.P., with which power
an effective (towrope) horsepower E.H.P., will be delivered.
The revolutions under these conditions will be R and the tip
speed T.S.
Should the speed be reduced by reducing the power of the
engines, by increasing the displacement, by fouling of bottom,
by condition of wind or sea, etc., or should the opposite exist and
the speed be increased, the conditions of resistance will differ
from the Basic conditions and the following changes will occur
in the propeller performance from those which existed under the
Basic condition:
I. Basic condition of resistance for F, but
I.H.P.j, = Engine power Reduced
Increased
e.h.p. = Effective H.P. delivered Reduced
Increased
Rj, = Revolutions Reduced
Increased
t.s. = Tipspeed Reduced
Increased
«; = Speed Reduced
Increased
Where thrust deduction exists, the new engine power will be
I.H.P.,=ii:xI.H.P.p.
Digitized by LjOOQ IC
64 SCREW PROPELLERS
The effect on the thrusts will be variable, depending upon the
values of the speed and load factors, v^V and e.h.p.^E.H.P.
2. Basic condition of Paiver constant but
z; = Speed for E.H.P.
Reduced
Increased
I.H.P. = Power
Constant
Constant
E.H.P. = Effective Horsepower
Constant
Constant
i?tf= Revolutions for E.H.P.
Reduced
Increased
t.s.= Tipspeed
Reduced
Increased
Thrusts
Increased
Reduced
Where iT is greater than unity, I.H.P. becomes iTXl.H.P.
In these changes of condition, so long as the Basic I.H.P.
remains constant the corresponding E.H.P. also remains constant
no matter what the speeds of ship, provided, however, that
the speed of ship is not so low as to produce serious augmentation of
thrusts. When such thrusts are attained the apparent slips will
increase rapidly^ while delivering the same E.H.P., and this in
crease of slip will be accompanied by a decrease in propulsive
efficiency.
The above paragraph is justified by the comparison of very
accurate trial results of several vessels which were of sufficiently
fine after body and where the propellers were so well located as
to practically insure a value of unity for K. In these cases
the agreement between the actual indicated, shaft and effective
(towrope) horsepowers and those of the basic conditions of the
propellers were so close as to lead to the following conclusion:
Law of Efficiency. Shoyld a screw propeller working in
the wake of a vessel deliver a certain effective {towrope) horsepower
with a certain indicated or shaft horsepower under any given con
dition of resistance^ it will deliver' the same effective with the same
indicated or shaft horsepower under any other condition of resistance
so long as it is operating in the wake of the same hull, and so long
as the effective thrusts are well below the " Critical effective thrusts J^
The law of propulsive efficiency just given, renders it possible,
where a vessel has been tried up to and beyond the speed for
which the effective (towrope) horsepower is equal to the Basic
E.H.P. of the propeller used, to obtain the value of K at once,
as, —
Digitized by LjOOQ IC
XmRD METHOD OF DESIGN
65
The actual indicated horsepower or shaft horsepower re
quired to deliver E.H.P.=ii:xl.H.P. .or KxSH.F. (Basic
powers), from which at once results
K^
Actual indicated or shaft horsepower
Basic indicated or shaft horsepower
Sheet 21. The Power Corrective Factor Z.
In arriving at a satisfactory series of values of corrective
factors to use in estimating changes in power due to changes in
conditions of load from the Basic condition, many different forms
of equations were tried, using the measured mile trial data of
very long and fine vessels, tried in deep water, and where the
trials were conducted in such a manner as to give confidence in
the trial data tabxilated.
All the trials that have been used had at least three runs for
each point of the speedrevolution and speedpower curves while
the highest point plotted for each vessel was obtained as a mean of
five runs. In obtaining the mean of each set of nms, the follow
ing method of averaging was used:
For a fiverun point:
Run No. I
Run No. 2
Run No. 3
Run No. 4
Run No. 5
North
South
North
South
North
I X Power
2 X Power
2 X Power
2 X Power
iXPower
I X Revolutions
2 X Revolutions
2 X Revolutions
2 X Revolutions
I X Revolutions
Mean
2 Power
8
S Revolutions
8
For a threerun point:
Run No. I
Run No. 2
Run No. 3
North
South
North
I X Power
2 X Power
I X Power
I X Revolutions
2 X Revolutions
iXRevolutons
Mean
S Power
4
S Revolutions
4
Digitized by LjOOQ IC
66 SCREW PROPELLERS
The form of equation finally obtained was of the form
where v is any speed of vessel and I.H.P.,, the indicated horse
power for this speed. When the thrust deduction factor K
exceeds unity, the actual indicated horsepower for v becomes
ii:xI.H.P., = LH.P.tf.
Designating the effective (towrope) horsepower necessary
to obtain a speed v, by e.h.p., and taking values of v for several
trial vessels for the load ratios e.h.p. ? E.H.P. = .025, .05, .1,
.2, .3, .4, etc., up to as high a ratio as the available data would
give, and solving the equation
w = {log I.H.P.log I.H.P.,)^(log. Flog v),
I.H.P.p being the actual indicated horsepower for v in cases
where K = i and being equal to that horsepower divided by K
when K was greater than unity, a series of curves were obtained
for the different load ratios given.
Taking Z=w (log F— log z;), it was foimd that for each of
these curves of w, Z had practically a constant value which
depended upon the value of e.h.p. ^ E.H.P. These values are
given in the preceding table of Z and are also shown as a curve
on Sheet 21.
The final equation for indicated or shaft horsepower for any
other than Basic conditions becomes
I.H.P., I ^ f
S.H.P., J 1
I.H.P. I . ^
which expressed in logarithms becomes
I.H.P.
log
I.H.P.,
S.H.P.,
=log
S.H.P.
±2,
Z being subtractive when e.h.p.T E.H.P. is less than imity and
additive when greater.
The table of Z values gives two columns of values, one being
the empirical values obtained from actual trials of vessels and
Digitized by LjOOQ IC
TfflRD METHOD OF DESIGN 67
propellers, while the second are the calculated values given by
the dotted curve of Sheet 21.
The equation fitting this curve is
10'' = 
' e.h.p. \i°«^'
and the value of C is approximately 11, so that putting the equa
tion in the logarithmic form,
„ A 10 e.h.pA
Z= 1.0414 i.o4i4f log E H P /•
This equation is the fundamental equation for the estimate of
power and can be used no matter what value of effective power is
used as a base, so long as the effective thrusts do not exceed the
" Critical Thrusts, £.r." (Sheet 22). Thus, if there is avail
able for use the actual indicated or shaft horsepower, LHP.^
= K I.H.P.3, or S.H.P.tf = iS:S.H.P.p for any speed v for which
the towrope (effective) power is e.h.p., the value of the indicated
or shaft horsepower necessary for any other speed vi requiring
an effective horsepower e.h.p. 1 where the vessel is in same con
dition of hull as to displacement and condition of bottom and
where weather conditions are similar, may be computed and the
basic characteristics of the propeller used can be entirely disre
garded.
This is shown by the table on p. 68, where the basic condi
tions of design and variation of load are given and then the
changes that occur when the actual basic load is assumed as .5
of the basic design load.
The final logs of the estimated horsepower factor in
Column 9 are seen to be the same as those in Column 4.
The power corrective factors Z as given, however, only hold
for certain conditions of e.t. and of e.h.p. ~ E.H.P., and these
conditions are shown by the curve marked " Critical Thrusts,"
and aboveon Sheet 22. This curve is erected on values of e.h.p^
E.H.P. as abscissas. Should the actual value of e.t. be less than
the critical value £.7. corresponding to the value of e.h.p. ^ E.H.P.,
Digitized by LjOOQ IC
68
SCREW PROPELLERS
there may be a slight increase in the value of the propulsive coef
ficient. Should it be greater, however, the p.c. will be gradually
decreased, the decrease becoming more rapid as the value of
e.t. increases (Sheet 22). Under these conditions the power
equation becomes I.H.P.,=LH.P.mo^
I.H.P.4=LH.P.,Xii:x
(lr.)'«
T„XKXM
Table VTTT
I
2
3
4
5
6
7
8
9
Log
Log of
Log of
Z>
for
C0L6
I Z" =
Log of
of
e.h.p.
Z
I.H.P.;,
factor
iZ
I.H.Py. factor
for .5 Load
iZ«i
e.h.p.
iZZ» =
Logof I.H.P.d
I.H.P.jr
Basic
I.H.P.
E.H.P.
.SE.H.P.
factor
i=Z»
.025
1.6684
83316
9.6865
.05
1.3549
9.68651.3549
8.3316
OS
I. 3549
8.6451
9.6865
.1
I. 0414
9.6865 — 1.0414
8.6451
.1
I. 0414
8.9586
9.686s
.2
.7279
9.6865 .7279
8.9586
.2
.7279
9.2721
9.6865
•4
.4144
9.6865 .4144
9.2721
.3
.5445
94555
9.6865
.6
.231
9.6865 .231
9. 4555
.4
.4144
9 5856
9.686s
.8
.1009
9.6865— .1009
9.5856
•5
.3135
9.6865
9.686s
I.O
9.686s
9.6865
.6
.231
9.769
9.6865
1.2
.0825
9.6865 .0825
9.7690
.7
.1613
9.8387
9.6865
1.4
.1521
9.6865 .1521
9.8386
.8
.1009
9.8991
9.6865
1.6
.2126
9.6865— .2126
9.8991
Estimate of Revolutions for Other than Basic Condi
tions OF Resistance
For making the estimate of the revolutions due to the change
in conditions resulting from change in power accompanied by
corresponding change in speed, the following equations derived
by Commander S. M. Robinson, U. S. Navy, and which will here
be denoted as the " Robinson Equations for Revolutions " are
used. The forms for estimating are
I.H.P.X»"
LHRXs" io^X»"'
where all of the terms except y have the same meaning as given in
the list of terms.
Digitized byCjOOQlC
TmRD METHOD OF DESIGN 69
The values of yXlog speed, denoted by log A, are shown on
Sheet 21.
The logarithmic form is:
log of apparent slip at speed z;=log of apparent slip under Basic
condition+log of actual indicated or shaft horsepower +yiX
log of Basic Speed— log of Basic indicated or shaft horsepower—
y2Xlog of actual speed.
This in its final form becomes
log 5log 5+log K+\og Ay\og Ai^Z,
Z being subtractive for values of e.h.p.^E.H.P. less than xmity
and additive for values greater than unity.
Having the apparent slip for speed Vy the equation for revolu
tions is
» z^X 101.33 ^ ^^X 101.33
^ Pitchx(i5) PX{is)'
The values of y in the Robinson equation are given by a curve
expressed by the following equation:
2.626 ^°5i29^
tiiL .oooooi5S75(«;25)*.o4368J
9iL 28o45+(»25)*J
»
The equation for apparent slip 5i at a speed vi and indicated
horsepower I.H.P.di, in terms of the Basic conditions being,
I.H.P.^XF>
the apparent slip. $2, for a speed V2, and indicated horsepower
I.H.P.<,„wiUbe
I.H.P.^XF«>
*'"'^^LiLP3<^'
or
^ _. I.H.P.^Xi>i«"
*^~*'I.H.P.*.X»2«'
and this is titefimdatnental equation for apparent slip.
Digitized byCjOOQlC
70 SCREW PROPELLERS
The above equation for apparent slip in its final form only
holds, however, up to certain coinddent values of e.h.p.TE.H.P. ^
and e.t., that is up to fixed values of net e.t., and these values
are shown by the curve on Sheet 22, marked E.T. For any higher
value of e.t. than given by this curve for any given value of e.h.p.
■fE.H.P., the final equation for apparent slip becomes
5=5xi^^^;^;;^^
Thus, suppose i^^F = .5, e.h.p. ^ E.H.P. = 4. The value of
e.t. 5 E.T. for these values oiv^V and e.h.p. ^E.H.P. is .8.
The Critical value E,T, of e.t. ^ E.T. for e.h.p.^E.H.P. = .4,
is .627, therefore,
^,, LH.P..XF^ _ e KY^Ay I e.t. \'
and the value ( ^^ ) for \j\^ = .4 and ~ = .5, is seen from
Sheet 22, to be equal to ( — j.
Relation between Power and Revolutions when the vessel is pre
vented from advancing.
When a vessel is secured to a dock so that after the secur
ing hawsers are taut there can be no further motion of the. vessel
through the water, the conditions of operation of the propeller
become radically different from those existing when the vessel
is in free route.
Different as are the conditions there still remains a definite
relation between the actual conditions and th^ chart (Basic)
condition of the propeller so far as power and revolutions are
concerned, and this relation is expressed by the following log
arithmic equation
.. Log ^— j = .2794 log ( iHp' J +'H246 = .2794Zf. 14246,
or
/I.H.P. Y
J? /TTTP \2794
Digitized by LjOOQ IC
THIRD METHOD OF DESIGN 71
but
I.H.P. ,
/. § = 1.3882 Xl02^«*^
or
a= *
1.3882X102794^'
where R^ and I.H.P.^ are the revolutions and power for the actual
conditions and R and I.H.P. those for the Basic condition of the
propeller.
WhenI.H.P. = I.H.P.,,
i?^ = i?M.3882, and this reduction in revolutions for a power
equal to the Basic power of the propeller is due entirely to the
elimination of the effect of the Basic speed V.
Should we have two conditions of revolutions and power,
iJ^j, I.H.P.^j and R^. and I.H.P.^,, the vessel being secured to
a dock for both conditions, the relation between revolutions
and power will be expressed by
log(D...794(logji^...,<«(Z.Z,),
or
(T TT P ^ \ 2794
To find apparent slip or approximate power, power and speed
or apparent slip and speed known.
From the fimdamental equation it will be seen at once how,
having the apparent slip, speed of ship and horsepower, the
apparent slip or the horsepower for any other speed may be
obtained, provided the conditions of hull, displacement and
weather are the same, thus:
If the power and speed are known, the apparent slip can be
foimd by the fimdamental equation as already given.
Digitized by LjOOQ IC
72 SCREW PROPELLERS
To find the approximate power, the speed and apparent slip
being known :
This neglects the effect of variation of thrusts over critical thrusts.
Should IJI.P.tf,I.H.P.di,
while, should »2=»i but I.H.V.dt be greater or less than I.H.P.^
J.H.P.^
S2S1X
LH.P.1'
that is, the approximate apparent slips for constant speed but
varying power will vary almost directly as the power, or in other
words, where the speed of a vessel is constant but the power required
for that speed is variable^ the revolutions required will vary directly
as the power unless the critical thrusts are exceeded.
Effect of Variations in Mechanical Efficiency of Engine
Sheet 20, as constructed is based on a mechanical efficiency
of .92 for reciprocating engines, and the Basic values of the
propulsive coefficients as given on this sheet, only fit this mechan
ical efficiency. The relations between I.H.P., S.H.P., and E.H.P.
being expressed by
I XT Ti S.H.P. E.H.P.
.92 P.C. '
should the mechanical efficiency differ from .92, the relations
between these powers must be corrected accordingly; thus,
suppose a mechanical efficiency of only .85 is expected, then
IHP S»H.P ._ E.H.P.X.92
.85 .8SXP.C. '
Digitized by LjOOQ IC
TfflRD METHOD OF DESIGN 73
and the I.H.P. to use in the equation for diameter would be only
M Xthe actual I.H.P. of the main engines where the propeller is
being designed for Basic conditions of resistance.
Number of Blades and their Effect on Efficiency
The Design Sheet 20 has been developed from the data
of performances of threebladed propellers, and, therefore, a
correction must be applied in the calculations for diameter and
for estimated propulsive coefficients if it should be desired to use
any other number of blades.
Should a fourbladed propeller be desired, the total indicated
horsepower required for any given number of revolutions will be
the indicated horsepower required by a threebladed propeller
of the same pitch and diameter as the fourbladed one but having
only threefourths of its projected area, divided by .865, that is
LH.P.4=I.H.P.3^.86s,
while for a twobladed wheel the proportion becomes
LH.P.2 = LH.P.3X.7S.
The projected area ratio of the fourbladed propeller will be
equal to fourthirds of that of the threebladed one while that
of the twobladed one will be only twothirds of that of the three.
Thus the equations for diameter for two, three, and four
bladed propellers assume the following forms:
Twobladed:
/29i.8XLH.p!3 ^ / 29i.8XLH.p7 ^ / 389XI.H.P.2
\ LT.x>XPXiJ \.7sI.T.z>XPXiJ \I.T.x>XPXie
^'
/3.84XLH.P.2X(i5) .
LT.bXF
Threebladed:
jj^ / 29i.8Xl.H.P.3 _ /2.88Xl.H.P.3X(i5)
\ LT.dXPXR y LT.nXV
Digitized byCjOOQlC
74 SCREW PROPELLERS
Fourbladed:
^^ /29i.8XLH.rI ^ /291.8XI.H.P.4X.865
\ LT.nXPXR 'V LT.nXPXR
/252.4iXLH.P.4. _ /2.49iXLH.P.4X(i5)
V LT.pXPXi? V LT.,>XF
Now the Basic conditions of all three of the above propellers
are, in everything but propulsive coefficient, the same as those
for the threebladed propeller having only threefourths the pro
jected area of the four, and one and onehalf times the area of
the twobladed propellers, so that in using the design sheet the
values of I.T.^, i— 5, and T.S. for the projected area ratio of
the threebladed Basic propeller are taken.
In taking off the propulsive coefficient from the Sheet, how
ever, it must be taken off for the actual projected area of the
propeller whether it be two, three or fourbladed.
The usually accepted idea as to the relative propulsive
efficiencies of two, three, and fourbladed propellers is that they
stand in rank in the order given above, the twobladed propeller
being the most efficient. This is most certainly the case where
the projected area ratio of the fourbladed propeller exceeds that
of the threebladed propeller, and that of the threebladed
exceeds that of the twobladed, all being designed to deliver the
same effective horsepower at the same number of revolutions,
unless the projected area ratio of the propeller having the smaller
number of blades should become considerably less than two
tenths. In such a case the propeller of four blades might
become more efficient than that of three, and that of the
three blades than that of two. In the above statement it
is considered that the net values of e.t. are all below the
" Critical Thrusts.''
On account of the lesser number of blades, that propeller
having the fewer number of blades should, generally speaking,
have less loss due to eddying around the blades than would occur
with an increased number, hut for constant condition of pitch and
diameter, the propulsive efficiency of propellers varies with their
projected area ratio , decreasing as the projected area ratio increases y
Digitized by LjOOQ IC
THIRD METHOD OF DESIGN 75
so long as this exceeds twotenths of the disc area^ no matter what the
number of blades of the propeller.
Resume
An examination of sheets 17, 18, 19, 20, 21, 22, 22B, 23, 24, 25,
and of the forms for computation of problems which will
be given in succeeding chapters, will show at once that
they tie together, in a consistent manner, all the elements
necessary to be taken into account in the design of a propeller,
thus:
From Sheet 17 is obtained the estimate of the form of the
ship and the influence on wake of variation of location of the
propeller in relation to the hull, to act as a guide in selecting the
value of apparent slip to be used in the calculations.
From Sheet 18 is obtained an approximate estimate of the
resistance of the hull appendages to apply to the estimated bare
hull resistance.
From Sheet 19 is obtained the estimate of thrust deduction
for the type of hull and location of propeller.
From Sheet 20 is obtained the basic factors to use in the de
sign, that is factors of indicated thrust, tipspeed, i— apparent
slip, and propulsive coefficient.
From Sheet 21 are obtained factors for the estimation of
powers and revolutions for other than Basic conditions of the
propeller, while from Sheet 22 can be ascertained the position of
the propeller as regards cavitation; the correction for cavitation;
and the correction of revolutions and effective horsepower for
variation of speed with constant power on the propeller, and the
limiting values of e.t.^E.T. for safe design.
From Sheet 22B can be obtained the approximate
maximvun and minimum values of e.h.p.7E.H.P. which
should be used in calculating propellers for vessels of any
slip block coefficient and desired speed, as obtained from
actual results.
From Sheet 23 are obtained values of I.T.^^(I— 5) and
from Sheet 24, values of (P.A.^D.A.)xE.T.J„ both for different
Digitized by LjOOQ IC
76 SCREW PROPELLERS
values of P.A.^D.A. of the basic threebladed propellers, these
factors entering in the following equations
I.T..^(i5)=^^.,
and
CXE.H.P.
(P.A.^D.A.)XE.T.,=
D^XV
From Sheet 25 are obtained the standard forms of blade pro
jections which maintain the necessary constant distribution of
projected surface, and also the ratio between the values of pro
jected area ratios an/l the corresponding ratios of developed
areas.
Problems to be Encountered in the Propeller Field
These may be classified under two general heads:
1. Problems in Analysis.
2. Problems in Design.
These classes are the converse of each other as should be
expected, for according to the old saying, " It is a poor rule that
will not work both ways," so if by a set of data it is possible to
design a propeller to fit any condition, and the data is basically
correct, then this same propeller when attacked from the other
end of the problem, should return as a result, the original data.
This is what actually occurs by the use of the Basic design, Sheet
20, and which sheet thus verifies its correctness*
Digitized by LjOOQ IC
CHAPTER Vn
ANALYSIS OF PROPELLERS
By the term " analysis of a propeller '* is meant an intelli
gent criticism of the form of its blades, of its blade sections,
hub contour and an estimate of the performances of the pro
peller under varying conditions of load.
That part of the analysis relating to hub, blade form and
section will be left until a later chapter, but that relating to
the estimates of performances will be considered immediately.
Being given the form of hull, location of propeller in rela
tion to the hull, all data concerning the characteristics of the
propeller, and either the curve of towrope horsepower for the
hull or the estimated, indicated or shaft horsepower required for
any desired speed, the first step in the analysis is to obtain the
Basic condition of the propeller. The method of doing this will
now be explained:
Hull data: Slip block coefficient = .8.
Single screw and ship of deep draught, therefore thrust
deduction factor if = 1.26. (Sheet 19).
Designed speed = 11 knots and 8 knots when towing.
Eiffective (towrope) horsepower for these speeds = 1000.
There are three propellers proposed from which a choice is to
be made by analysis. It is desired to estimate the indicated
horsepower and revolutions necessary with each propeller for
the designed speeds.
The propellers are twobladed, threebladed and fourbladed,
and are of same diameter and pitch, but the projected areas and,
therefore, the projected area ratios, vary directly as the number
of blades.
77
Digitized by LjOOQ IC
78
SCREW PROPELLERS
Dekivaxion of Basic Condition
Number of blades .
P.A.^D.A
Diameter. ,
Pitch
Tip Speed (Sheet 20, for .3).
R=T.S.5irD
PXR
SlipB.C
1—5 (Sheet 20, for .3) .
,, (PXR)X(iS)
101.33
LT.x> (Sheet 20, for .3)....
TTJT> D*XI.T.dXPXR
LH.P.=
389
D*X I.T.dXPXR
291.8 •
TTJT> D*XI.T.dXPXR
252.41
P.C for actualP.A.fD.A.
E.H.P. = LH.P.XP.C
e.h.p
e.h.p.5E.H.P
Z for e.h.p.^E.H.P. (Sheet 21)
LH.P.p = I.H.P.^io^
LH.P.d=XXl.H.P., = Total Est. power for v.
Log i4Ffor 7 = 17.2 (Sheet 2i)=log (7*'), Curve x. ..
Log Av for »= II (Sheet 21) =log (t;") , Curve x
10 *"
PX(l—5)
viV
2
.2
16'
14'
6650
132.3
1852
.8
.941
17.2
374
4559
.709
3233
icoo
•3094
•534
1333
1680
II
369
312
06981
85.59
and all propellers plot on Sheet 22, as below the " Critical
Second speed V2
V2^V
e.h.p.2
(£.r.5e.t.) (Sheet 22)
Log Av for 8 knots, curve x
•6395
Thrusts.
.3
•3
16'
14'
6650
132.3
1852
.8
.941
17.2
3.74
6077
.682
4145
ICOO
.2413
.636
1405
1770
II
369
3.12
.0552
84.27
■6395
Rd.
LH.P4ifori^=LH.P.dX
p.c. at 8 knots
\E.T.) '
8
8
.465
.465
1000
1000
.57
.64
2.69
2.69
.3814
.2686
128.7
108.. 9
2947
2766
•3393
.3616
4
•4
16'
14'
6650
132.3
1852
.8
.941
17.2
'3.74
7026
.619
4349
1000
.23
.658
1544
1946
II
3 69
3."
.05247
84.03
.6395
8
46s
1000
.66
2.69
.2476
105.8
2949
3392
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
79
Now by Sheet 20, the propulsive thrusts per square inch of
projected area under Basic conditions, are for
P.A.^D.A.
I.T.D
P.O.'
P.T.i> =
I.T.z>XP.C.
P.T.p
lS
E.T.p
.3
.3
4
1.88
3.74
6.00
.709
.682
.619
1233
2.541
3714
6.16
8.47
929
.941
.941
.941
6.33
9.00
9.87
15=
F X 1 01 . 33 Speed Thrust Propulsive ThruLt
PXR Ind. Thrust
Effective Thrust per square inch
of projected area = E.T.p •
Effective Thrust '
P.T.,
iS
Allowing an increase of 15 per cent on these effective thrusts
before true cavitation begins, the values of e.t.^ at true cavita
tion become
P.A.^D.A. E.T., (Cav.)
.2 7.28
•3 • 10 35
4 11.3s
These final results show the necessity of large surface on pro
pellers where large variation in speed with constant power is
expected if a rapid falling off in propulsive efficiency at the low
speeds is to be avoided.
While, without thrust deduction, the net effective (towrope)
horsepower being delivered by the propellers is 1000, the actual
gross work being performed by the screws on the water is that
corresponding to the actual I.H.P.^ = if XLH.P.^, being expended
on the propellers.
Thus it is seen that when the vessel is so loaded that eleven
knots can be made with 1000 effective (towrope) horsepower,
any one of the three propellers will answer, that of two blades
being the most efficient, yet when the vessel is so loaded down
either by her own cargo, by the condition of her bottom or by
Digitized by LjOOQ IC
80
SCREW PROPELLERS
P.A.■^D.A.=
For II knots gross value Z=log I.H.P.log (i^XLH.P.p) =
For 8 knots gross value Z » log LH.P.
log(iS:xLH.P.px(J)') =
For II knots gross e.h.p.^E.H.P. (Sheet 21) =
For 8 knots gross e.h.p.sE.H.P. (Sheet 21) =
For II knots gross e.h.p =
For 8 knots gross e.h.p =
Gross eJ.p (11 knots) =
Gross eJ.p (8 knots) =
•43363
. 18943
.392
.662
1267
2141
6.478
10.95
•53563
•3419
.306
.472
1267
1957
4.319
6.669
.55763
.3771X
.291
.437
1267
1901
3.239
4.859
weather conditions, or by having another vessel in tow, that this
same effective horsepower will only deliver a speed of eight
knots, the twobladed propeller is entirely in adequate, as the total
gross effective thrust per square inch of projected area is far in
excess of that at the assumed cavitating point. In such a case,
therefore, the threebladed propeller might be chosen, as it is
still within the limit for cavitation and has a considerable advan
tage in efficiency when running free over the fourbladed one.
The fourbladed higharea propeller would, however, assure the
smoothest running, but at the cost of higher power, would be
well away from cavitation and would stand up better at still
higher net thrusts.
The area may, in any case, be divided among four blades in
stead of three or two, except where blades would become exceed
ingly narrow without any particular loss in efficiency, as this
latter is practically dependent upon the total projected area
ratio and not upon the number of blades.
Attention should also be called to the change in revolutions
at eight knots from those required at eleven knots, the effective
horsepower remaining constant.
Attention must also be directed to the small influence of
projected area ratio on revolutions for any given speed, where
viV corresponds approximately to " Upper E.T/' limits, as the
revolutions required at eleven knots for the twobladed propeller
of .2 projected area ratio are only 85.59^ while those required by
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
81
the fourbladed wheel of .4 projected area ratio are 84.03, a
decrease of only 2 per cent in revolutions for an increase of 100
per cent in surface, but this decrease in revolutions is accom
panied by an increase of nearly 16 per cent in power.
Number of Blades Versus Projected Area Ratio in Deter
mining Efficiency of Propulsion
As stated before, it is generally held that an increase in the
number of blades of a propeller decreases its propulsive efficiency.
This idea is held to be in error and that the propulsive efficiency
depends practically upon the projected area ratio, as long as the
blades are" sufficiently narrow to escape interference with each
other. There may, however, be a slight falling oiff in efficiency
with the higher number of blades due to the greater number of
blade edges around which eddying may occur.
To emphasize this point of efficiency depending mainly
upon projected area ratio, the fourbladed propellers of four
different vessels will be analyzed, each by reducing to f its total
projected area ratio for the Basic condition and then by using its
full projected area ratio as the Basic condition for data, and com
paring the results with those actually obtained on trial:
Vessel
Slip Block Coef.
No. of Propellers
No. of blades . . .
TotalP.A.HD.A. . .38 .38 .4 .4 2828 .2828 .391 .391
} P.A.5D.A.
D 19'. 5 19'. 5 9'. 67 9'. 67 18'. 5 i8'5 17'. 25 I7'.2S
P is' is' ii's ii'.S i8'.75 i8'75I7'.8i2S i7'.8i2S
T.S 6320 8200 6670 8600 4S40 6270 6520 8400
R 103.2 133.9 219.6 283.7 78.12 107.9 120.3 iss
PXR IS48 2008 2S25 3262 146s 2023 2143 2761
iS 94S .93s .92 .91 942 .94 .91 .90
V 14.43 18. S3 22.93 29.3 13.62 18.77 18.98 24. S2
I.T.z) 3.43 SS2 376 6.0 2.07 3.38 3.6 5.8
I.H.P 7996 14442 3S17 6247 4111 8019 18190 32660
P.C 633 .633 .62 .62 .691 .691 .626 .626
E.H.P so6i 9142 2181 3873 2841 SS4I 11384 20440
I
I
3
4
.80s
.702
.79
.6
I
]
I
I
2
4
4
4
4
4
4
4
.38
•S^
.4
.4
.2828
.2828
.391
.285
....
.3
....
.2121
....
.293
19'. 5
I9'.S
9'. 67
9'. 67
i8'.S
18'. s
17'. 2S
IS'
IS'
ii'.S
ii'.S
18'. 75
18'. 75
i7'.8i2S
6320
8200
6670
8600
4S40
6270
6520
103.2
133.9
219.6
283.7
78.12
107.9
120.3
IS48
2008
2S25
3262
146s
2023
2143
.94s
.93s
.92
.91
.942
.94
.91
14.43
18. S3
22.93
29 3
13.62
18.77
18.98
343
S.S2
3.76
6.0
2.07
3.38
3.6
7996
14442
3SI7
6247
4111
8019
18190
.633
.633
.62
.62
.691
.691
.626
So6i
9142
2181
3873
2841
SS4I
1 1384
Digitized by LjOOQ IC
82
SCREW PROPELLERS
Estimates of Performance
ti
VirV.
e.h
p.i.
c.h.p.i5E.H.P
Zi
K
LH.P.d=/rxi.H.P.p
Estimated
Actual
logi4F
logidvi..
5\ from actual power. . .
Revs.
Est. (Act. Power)
Actual
10
734
.S33
1050
(Est.)
.3696
.1895
.4S9
.746
1.24
1.24
1772
1785
1420
1420
34
3.8
2.998
2.993
05056
.06735
56.92
S7. 95
S6
S6
II. 7S
.619 .479
2295
.2016
.712
1.2
423
38S0
3.818
32
06728
71.66
69
.1123
.962
1.2
4278
3850
4 12
327
C834S
72.93
69
t>2....
e.h
p.2.
e.h.p.2HE.H.P
Z^
K
LH.P.tf=/rxLH.P.;?
Estimated
Actual
\ogAv
\ogAn
52 from actual power. . .
Revs.
Est. (Act. Power)
Actual
10.
455
11.82
11.07
15
.724 .564
.515 . 4
.813 .589
.813
IS70
456
1370 (Est.)
57
.3102
.1717
.2
.1178
.4822
.2473
.504
.535
.781
.728
.96
.342
.628
.321
1.27
1.27
1175
1. 175
1.24
1.24
1.2
2963
3037
747
805
2319
2341
10423
2755
2755
780
780
220c
2200
9950
3.47
3.783
4.045
4.285
34
3.?
3.818
3.05
3.0s
3.21
3.21
3.13
3.13
355
.0476
.06705
.1214
•1335
.0578
■07699
.09125
74.16
7571
118. 6
120.2
63.5
64.82
96.59
73
73
117. 8
117. 8
65
65
945
.629
8
.2807
•571
1.2
10524
9950
4.12
355
.1132
98.98
94. 5
rs... .
e.h
p.3.
e.h.p.3^E.H.P...
Zt
K
logi4v
log Avi
«'{S^.:
II
.12
12
.65
12
.77 .60C
•552 .432
.903
1885
545
2000
.3724
.2062
.25
.1407
.704
.457
.707
.63
.863
.167
1.27
1.27
1. 175
1. 175
1.24
3545
3601
970
1000
3470
3445
3445
990
99c
3400
347
3.783
4.045
4.285
3.4
3.15
3.15
3.3
ZZ
3.26
. 04961
.0666
.1252
.1378
.06622
79.04
80.48
127.41
129.3
70.88
78.2
78.2
128
128
74.4
3
.655
(Est.)
.3609
.468
1.24
3385
3400
35
3.26
.08821
72.9
74.4
18. 1
.953 738
10328
.9072
.048
1.2
19540
19000
3.818
3.76
.1074
115. 4
116
•5053
•32
1.2
18758
19000
4.12
3.76
•1333
I18.8
116
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS 83
The closer agreement with actual powers and revolutions
appears to rest with the method of reduction to the threeblade
condition, for values of total P.A.^D.A. above .3 and with the
other below .3, but the agreement of the two methods through
out in the results obtained is very close, considering the approxi
mations in data and in effective horsepower that must exist
where the trials of the real vessel are taken into consideration.
As the propulsive efficiency in both methods is taken as that of
the full projected area ratio, without regard to the number of
blades of the propeller, it would appear as if this latter had
very little to do with the resultant efficiency.
Taylor, in commenting on the question of the relative effi
ciencies of two, three, and fourbladed propellers states, " There
were tried a number of propellers with blades identical but differ
ing in nvunber — from two to six. It was found that efficiency
was inversely as the number of blades; that is, a propeller with
two blades was more efficient than a propeller with three identical
blades, that one with three blades was more efficient than one
with four identical blades and that one with four blades was
more efficient than one with six identical blades."
" Also while total thrust and torque increase as number of
blades is increased, the thrust and torque per blade fall off." . . .
" It should be remembered that (this) refers to propellers work
ing under identical conditions of slip, speed of advance, etc.'*
The pity of it is that Froude had covered identically the same
ground and had arrived at the same conclusions, while neither
Froude nor Taylor had atterapted to keep the projected area
constant and vary the number of blades. If they had done so
the conclusion reached would have read as follows:
The number of blades of a propeller has no effect upon its
propulsive efficiency provided each individual blade is sufficiently
narrow throughout its length to insure against blade interference
with the flow of the water through the propeller. Propulsive effi
ciency is based on projected area ratio of the propeller and that
propeller having the greater projected area ratio willy as a general
rule, have the lesser maximum propulsive efficiency, so long as the
" Critical Thrusts '* are not exceeded.
Digitized by LjOOQ IC
84 SCREW PROPELLERS
Estimates of Performance
In making estimates of expected performances of propellers
in actual service, considerable differences between the estimated
and the actual performances may be expected. These differ
ences are caused by the following:
1. Conditions under which model of ship is tried and effec
tive (towrope) horsepower obtained: Model wetted surface
in the best of condition as to smoothness; water in tank smooth;
air, still; model constrained to move in a perfectly straight course.
2. Conditions under which actual ship may be tried and the
effects on performance:
(a) Wetted surface of hull may be more or less rough, pro
ducing increased resistance to motion through the water, pro
duces increase in indicated or shaft horsepower and slight
increase in revolutions for any given speed.
(b) Weather and sea conditions may be adverse, — same effect
as (a).
(c) Strong following wind and sea, — opposite effect to (a)
and (b).
(d) Form or trim of hull or adjustment of appendages be such
as to cause a heavy wake, — this will increase the model tank
effective (towrope) horsepower required for a given speed; but
if the propeller is favorably located, a gain in propulsive effi
ciency due to wake gain will result; — the effect is to reduce power
and revolutions for the given speed, as if the actual resistance of
the hull at this speed had been reduced.
(e) Improper design of appendages producing excessive eddy
ing of the water accompanied by a reduction in pressure in the
locality in which the propeller operates; — this causes more or
less increase in power over that estimated, while the revolutions
of the propeller are considerably increased above those due to
this power; this increase in revolutions and power being accom
panied by more or less serious vibrations. The condition is
abnormal but is frequently encountered.
(/ ) Erratic steering while on trial course, — causes apparent
increase in power and revolutions for the noted speed.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS 85
(g) Errors of observations of speed.
(A) Errors of instruments for measurements of pbwVr and
revolutions of the propelling engines.
This list of handicaps against which the estimator is pitted
being very formidable, it becomes necessary, therefore, to be
satisfied with any reasonably close estimate to the actual per
formance, particularly when the estimate of power exceeds the
actual power necessary.
There is still one other source of error which may be caused
by the propeller itself, and that is —
(k) Excessive roughness of propeller surfaces or excessive
bluntness of edge, — these produce increased resistance per revo
lution, raise the power for a given speed but do not change the
revolutions for the speed from what they would be if the blades
were smooth and their edges fine.
CORKECTION OF BaSIC PROPELLER FOR VARIATION FROM STAND
ARD Form of Blade
Variations in blade form from the standard forms shown
on Sheet 23, can be divided into three general classes, as
follows:
I. Fanshaped blades having the same total projected area
as a standard form blade, whose diameter of propeller is greater
than the diameter of the actual propeller, and whose blade pro
jected area form coincides up to .7 Radius with the blade pro
jected area form of the actual blade, the amount of surface
cut off from the Basic blade by reducing the diameter to the
actual diameter being restored by adding it in to the width of
the blade between the .7 Radius of the Basic blade and the tip
of the actual blade.
Such a blade is shown in Fig. 4.
With a propeller whose blade form has been so modified from
that of the Basic propeller, the power and revolutions necessary
to deliver a given effective horsepower at a given speed of vessel
bear the following relations to these same quantities for the Basic
propeller:
Digitized by LjOOQ IC
86 SCREW PROPELLERS
Let e.h.p. = Effective (towrope) horsepower of vessel.
• » = speed of vessel corresponding to e.h.p.
I.H.P.tfj= Actual power required to deliver e.h.p. with
the Basic propeller.
I.H.P.tf,= Actual power required to deliver e.h.p. with the
actual propeller.
ii?ij = Revolutions corresponding to I.H.P.^,, e.h.p.
and V,
ii?i,= Revolutions corresponding to I.H.P.^,, e.h.p.
and?^.
Z?i = Diameter, in feet, of Basic screw.
2)2 = Diameter, in feet, of actual screw.
Then, i?2=i?ix(^) ,
D2/
LH.P.,.=LH.P.,,X^,
and the propulsive coefficients will vary directiy as the diameters.
2. Oval blades having their greatest half cords of circular arc
measurements of the projected area form at a radius greater
than .7 Radius of the propeller, as shown in Fig. 5.
3. Oval blades having their greatest half cords of circular arc
measurements of the projected area form at a radius less than
.7 Radius of the propeller.
These two cases are just the opposite of each other and the
corrections of power and efficiency for them are made in exactly
the same manner, as follows:
Let the diameter of the circular arc of greatest projected
area length
=Z)o.
2) = diameter of basic propeller.
Di = diameter of actual propeller,
e.h.p. = Effective horsepower delivered by Basic propeller.
«; = Speed corresponding to e.h.p. 1.
e.h.p.i= Effective horsepower deliver by actual propeller
at speed v.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
87
I.H.P.tf= Indicated horsepower of Basic propeller to deliver
e.h.p.i at speed v.
D
Propeller of
Reduced Diameter
Actual Projected
Area Basic ProJ. Area
with Equal Powers
, / Rad., \ i/j
' VRad.i/
For Equal e.b.p., deliveredt
I.H.P.^I.H.P.,.x(^)
Fig. 4.— Reduced Diameter
Case I.
Propeller of
Reduced Diameter
and
Correspondingly
Reduced Proj. Area
/ Rad.A 1/4
VRadi/
I.H.P.^\ /I.H.P.tfa /Radj\«
S.H.P.d,/ ^ S.H.P.rfj/ ^ VRad.iy
e.h.p.,=e.li.p.iX(^^;3;;j
Fig. 5. — Reduced Diameter
Case 2.
I.H.P.jj = Indicated horsepower of actual propeller to
deliver e.h.p.i, at speed v.
Digitized by LjOOQ IC
88 SCREW PROPELLERS
R^ and 2?^, = Revolutions of Basic and actual propellers, respec
tively, corresponding to the above conditions.
Then in the actual work of design, I.H.P.4, and e.h.p.i, and
Di are replaced by
LH.P.tf, e.h.p. and D, where
Z?=Z?o^.7,
[.H.P., = LH.P.,,x(£y,
e.h.p. = e.h.p.i,X( — ) .
Should it be desired to analyze a given propeller, it becomes
first necessary to obtain its Basic standard projected area form.
This is readily done by taking the length of the cord of the half
circular arc at diameter Do and dividing it by — , and with this
2
quotient entering the table of half cords on Sheet 23, and from
the column marked as .7 Radius, will be readily obtained the
projected area ratio corresponding to this unit half cord length.
With propellers modified as in i, 2 and 3, the modification
apparently causes but slight change in the value of the
thrust deduction factors from what these factors would be
should the Basic propellers be used, i and 2 will probably
cause a slight decrease and 3 an increase where the value of
the thrust deduction varies with the relative tip clearance.
These slight changes are due to the fact that the thrust deduc
tion does not actually vary with the tip clearance except where
blades of standard form are used. Where departures from this
form exist it would be more correct to state that the " thrust
deduction varies with the type of hull of vessel, location of pro
peller relative to the hull, and to the clearance between the
center of pressure of the propeller blades and the hull."
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
89
Problems in Estimates of Performances
In the following problems the values of Z, used in estimating
power and revolutions, are the empirical ones, the equation for Z
not having been developed at the time this work was carried out.
Also slight changes have been made in the curve of log Ay since
this work was performed, particularly for values of v below
ten knots:
Problem i
HuUData
Slip Block Coefficient = .60
Mean Referred Tip Clear. = 2'.88
Center of Propeller within limits of
Load Water Plane
Propeller — Condition i, Sheet 19
a: = 1.02
Two Propellers
Basic Condition of Propeller
No. of Blades 3
P.A.^D.A 328
D 18'. 25
^ 19'. 75
T.S. for P.A. HD.A. (Sheet 20) 7240
i2=T.S.57rZ) 126.67
PXR 2494
i5forP.A.^D.A.=.328and
SHp B.C. = .6 (Sheet 20)= .8995
V=PxRx{iS) ^101.33... 22. 14
LT.z> for P.A.^D.A.= .328
(Sheet 20) 4.35
2LH.P.= 2X(Z>2xLT.z>xP
Xi^)^29I.8= 24767
P.C. for P.A.rD.A.= .328
(Sheet 20) 665
E.H.P. = 2 XLH.P. XP.C. . . . 16420
e.h.p.4E.H.P
e.h.p
V for e.h.p
viV
Zfore.h.p.^E.H.P
K
I.H.P.d=K: I.H.P.p=ii: I.H.P
Mo^= Est. Power
Actual Power
Est. Revs, for v
Act. Revs, for v
.075
.1
.2
.3
1232
1642
3284
4926
95
10.45
1321
15 05
.429
.472
.596
.679
1. 195
1.0268
.728
•5493
1.02
1.02
1.02
1.02
1612
2373
4726
7131
1600
2200
4800
7125
52.8
58.63
74.05
84.5
52
575
73.6
84.5
4
6568
16.45
.743
.4238
9521
9300
92.68
92. 5
Digitized by LjOOQ IC
90
SCREW PROPELLERS
cJi.p.^E.H.P
c Ji.p
vfore.h.p
viV
Z£orc.h.p.^E.H.P
K
IM.T^^K I.H.P..
=ir IH.P.5io*=Est. Power
Actual Power
Est Revs, for t>
Act. Revs, for r
e.h.p.5E.H.P
e Ji.p
vfor e.h.p
viV
Zfo^e.h.p.^E.H.P
K
LH.P.tf=K: I.H.P.P
=^ LH.P.5io^=Est. Power
Actual Power
Est. Revs, for r
Act. Revs, for »
8210
17.7
.8
.3267
1.02
1 1909
11600
99.79
99. 75
.6
9852
18.92
.854
.2432
1.02
14430
14625
106.2
106.8
7
"494
19
76
892
169
I
02
17119
17200
112
112
I
8
20.33
.919
.1065
1.02
19767
19600
116
116. 2
.9
14778
20.8
.939
.0540
1.02
22307
22200
119. 8
120.2
/I.O
16420
21.24
•959
o.
1.02
25262
25200
123.4
124.8
I
05
17230
21
44
968
0225
I
.02
26605
26600
124.7
126
5
1. 10
18062
21.62
.976
.045
1.02
28020
28100
126.3
129.2
Problem 2
Hull Conditions
Slip B.C. = .627
Propeller located in Condition 2,
Sheet 19
K = 1.22 (Lower Line of K)
Twin Propellers
In Condition 2, neglect tip clear
ance
Basic Condition of Propellers
Blades 3
P.A.^D.A 304
^ 15'. 95
P i4'.436
T.S. for P.A.^D.A. = .304
(Sheet 20) 6740
i2=T.S.MrZ) 134.4
PXR 1943
(i S) for P.A. HD.A. =.304,
Slip B.C. = .627 = .904
V^{PxRX{iS)\iioi.s3 17.34
I.Tx> for P.A. HD.A. = .304. . . 3 . 85
2XLH.P 13060
PC 675
E.H.P 8815
2XS.H.P. = 2XLH.P.X.92.. 12020
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
91
ELECTRICALLY PROPELLED VESSEL
e.h.p.^E.H.P
e.h.p
V
viV
Z
K
S.H.P.d=S.H.P.pXi2:.
ActS.H.Pd.=Act.i2:x
S.H.P.P
Est. Revs
Actual Revs
.1
.2
•3
•4
882
1763
2645
3526
8.77
II. 18
12.77
14.0
.506
.645
.736
.807
1.0268
.728
.5493
.4238
1.22
1.22
1.22
1.22
1379
2743
4140
5527
1500
2780
4160
5460
67.1
85.26
97. 52
107. 5
67.3
86
98.2
108.3
•5
4408
14. 95
.862
.3267
1.22
6913
7000
114. 6
116. 2
Problem 3
Hull Conditions
4 Propellers
Slip Block Coef. = .62
Propellers located as in Condition i,
Sheet 19
Mean Referred Tip
Clearance of Blades = 2' . 24
iS: = i.i2
Basic Condition of Propellers
Blades 3
P.A.^D.A 523
D 10'
P 8'.i88
T.S moo
R 353.4
PXR 2893
15. 86
V 24.55
I.T.D 9.4
4XI.H.P 37192
PC 54
E.H.P 20084
S.H.P 34296
e.h.p.5E.H.P
e.h.p
V
viV
Z
K
S.H.P.d=i2:xS.H.P.p.
Act. S.H.P.d=Act. K:xS.H.P.p
Est. Revs
Act. Revs
Digitized by LjOOQ IC
92
SCREW PROPELLERS
c.h.p.^E.H.P
ch.p
V
v^V
Z
K
S.H.P.d=irxS.H.P.p
Act. S.H.P.d=Act. K:xS.H.P.p
Est. Revs
Act. Revs
10042
18.4s
.751
.3267
Z.12
18103
18900
271
' 266.9
.6
.7
12050
14059
19. 55
20.35
.796
.829
.2432
.169
Z.12
1. 12
21941
26929
22300
25300
287. s
300
285.5
298.9
.8
16067
20.95
.853
.1065
1. 12
30055
28800
3"5
312.2
Problem 4
Hull Conditions
Slip B.C. = .662
Propellers located in Condition 3,
Sheet 19
Neglect Tip Clearance
a: = 1.07
Two Propellers
Basic Conditions of Propellers
Blades 3
P.A.rD.A 31S
D 17'. 54
P 18'
T.S 6940
R 126
PXR 2267
^S .903
V 20.2
LT.z> 4.03
2LH.P 19265
P.C 674
E.H.P 12985
e.h.p.^E.H.P
e.h.p
V
vhV
Z
K
LH.P.ef=K:xLH.P.p....
Act. I.H.P.if=Act. KX
LH.P.P
Est. Revs
Act. Revs
.1
1299
10.4
.515
1.0268
1.07
1938
1900
63.02
62.6
2597
12.96
.641
.728
1.07
3856
4260
78.63
77.4
.3
3896
14.58
.722
•5493
1.07
5819
6150
88.76
89
.4
5194
15.55
.77
.4238
1.07
7769
7700
95.5
95.8
.5
6493
16.75
.829
.3267
1.07
9715
9900
103. 1
104.2
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
93
e.h.p.^E.H.P
e.h.p
V
viV
Z
K
LH.P^=K:xLH.P.p..
Act. I.H.P.d=Act.irx
LH.P.P
Est. Revs
Act. Revs
Problem 5
Hull Conditions
SUpB.C.=.62
Propeller located in G>ndItion
Sheet 19
Mean Tip Clearance =3'.$
I,
Basic Conditions of Propellers
Blades 3
P.A.^D.A SOI
D 9'.583
P 8'. 193
T.S 10580
R 351.2
PXR 2878
15 87
V 24.71
LT.i> 8.75
4XLH.P 31732
PC 554
E.H.P 17580
4XS.H.P 29196
e.h.p.^E.H.P
e.h.p
V
r5F
Z
K
S.H.Pd=/CXS.H.P.p
Act. S.H.P.d=Act. K:xS.HP.p
Est. Revs
Act. Revs
1758
10.31
.417
1.0268
I
2745
2750
148.8
153
.2
.3
3516
5274
12.96
14.81
.524
.6
.728
.5493
z
z
5461
8241
S400
8100
190.2
217.2
189.S
218
.4
7032
16.3
.66
.4238
I
11002
11050
239.6
241
Digitized by LjOOQ IC
94
SCREW PROPELLERS
cJl.p.^E.H.P
c Ji.p
V
v^V
Z
K
s.h.p^=k:xs.h.p.p
Act. S.H.P.d=Act. KXS.H.F,p
Est. Revs
Act. Revs
e.h.p.^E.H.P
e.h.p
V
v^V
Z
K
S.H.P.d=i2:xS.H.P.p
Act. S.HiP.d=Act. KXS.U.P.P
Est. Revs
Act. Revs
•5
.6
.7
8790
10548
12306
1744
18.42
1932
.706
.745
.782
.3267
.2432
.169
I
I
I
I37S9
16676
19782
13700
16300
19150
257.2
273.2
288.2
259
274 5
288.5
.8
14064
20.1
.813
.1065
I
22844
22000
303 S
302.5
•9
15822
20.7
.837
.05402
I
25779
25300
314.6
315
i.o
17580
21.13
.855
o
I
29196
28300
327.3
326
105
18459
21.3
.S62
.0225
1
30745
30000
331.5
Problem 6
HuU Conditions
Slip B.C. = . 61
No. of Propellers =4
Propellers located in Condition i,
Sheet 19
Mean T.C.
=3'.33
Basic Conditions of Propellers
Blades 3
P.A.HD.A 558
D 9'.i7
P 8'. 5
T.S 12080
R 419.7
PXR 3568
15 85
V 29.93
LT.D 10.6
4XLH.P 43596
PC 527
E.H.P 22976
4XS.H.P 40108
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
95
c.h.p.^E.H.P
ch.p
V
v^V
Z
K
S.H.P.d=^XS.H.P.p
Act. S.H.P.d=Act. A:xS.H.P.p.
Est. Revs
Act. Revs
e.h.p.5E.H.P
c.h.p
V
v^V
Z
K
S.H.P.d=lCXS.H.P.p
Act. S.H.P.if =Act. irxS.H.P.p.
Est. Revs
Act. Revs
.1
.2
.3
2298
4595
6893
12. 1
IS 05
17
.404
.503
.568
1.0268
.728
•5493
I
I
I
3771
7503
11329
3900
7800
11600
172. 1
2159
246.1
173. s
219
247 5
.4
9190
18.8
.629
.4238
I
15116
15600
272.9
273. 5
•5
.6
.7
1 1488
13786
16083
19.81
20.51
21.08
.662
.685
.704
.3267
.2432
.169
I
I
I
18903
22910
27100
19350
22900
27000
291.7
311. 6
326.8
292.5
309
325
.8
18380
21.6
.722
.1065
I
3139s
31700
341. 1
335
Problem 7
In this problem the vessel was a twoshaft destroyer with the propellers
located well aft abreast the stem post. The vessel squatted heavily at
high speeds. The squat begins approxim ately at t; 5 \/L.L. W.L. = i .48 and
is fully accomplished at »^\/L.L.W.L. =2.13, the value of log A^ in the
apparent slip equation passing slowly during the process from Curve X to
Curve Y on Sheet 21, on a straight line tangent to Y at the point of accom
plishment.
In the case in question, the propeller blades were not of standard form,
being of oval form but having the greatest circular width of projection at a
distance out from the center corresponding to .7 of 7'.3 diameter, .7 D being
the diameter of the estimated center of pressure of the standard blade form.
The cord of the half arc at this point, divided by — , corresponds to the
2
dimension of this cord given in the table on Sheet 25, for a projected area
ratio of .617, and the Basic propeller for analysis is therefore taken as
having a pitch = pitch of actual propeller, diameter = 7^.3 and projected
area ratio = .617, while the Basic S.H.P., I.H.P. and E.H.P. of the actual
/Di\^ /6 67\*
propeller are taken as those of the basic propNcller X I ^ I =1 1 .
Digitized by LjOOQ IC
96
SCREW PROPELLERS
HisU CondUions
Slip B.C. =.341
Two Screws
L.L.WX.^aSs'
V
"■7=5= = '^
V285
v« 24.99 Squat b^iDs
V
V285
v»35.96 Squat accomplished
Basic Conditions of Propellers
Acttial Basic
Blades 3 3
P.A.•^D.A 587 617
D 6'. 67 7'3
P 6'. 17 6'. 17
T.S 14250
R 632.3
PXIL 3901
15 817
V 31.45
LT.i> 12.55
2 LH.P.. .14930= \^^JX 17882
P.C 5225
E.H.P 7838
2S.H.P 13734
c.h.p.sE.H.P
e.h.p
V
VirV
(Est.Curve)Z
K
S.H.P.tf=/CXS.H.P,
Act. S.H.P^=Act. KXS.H.F.p.
Est. Revs
Act. Revs
e.h.p.5E.H.P
ch.p
V
VirV
(Est. Curve) Z
K
S.H.P.d=iS:xS.H.P.p
Act. S.H.P.tf=Act. KXS.U.F.p.
Est. Revs
Act. Revs
•05
.075
392
588
12.9
14.70
.422
.477
1. 355
1.1715
I
I
660
1060
780
1150
231.2
264.5
230
262
.1
784
16.10
.522
I. 0414
I
1358
1500
290
289
.3
.4
2352
3136
22.25
23.8s
.701
.776
5445
.4144
I
I
4262
5750
4250
5500
411
448.6
411
449
.5
3919
25.38
.823
•3135
I
7254
7250
488.9
489
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
97
c.h.p.^E.H.P
e.h.p
V
v^V
(Est. Curve) Z
K
S.H.P.tf=K:xS.H.P.p
Act. S.H.P.d Act. ITXS.H.P.p
Est. Revs
Act. Revs
.6
.7
.8
4703
5287
6271
26.77
27.6s
29.12
.867
.90s
.942
.2310
.161
.1009
I
I
I
8770
10304
1 1834
8950
99SO
1 1500
530. 2
555 9
604.1
528
555
60s
.9
7054
30.33
.978
.04770
I
13376
I29SO
642.6
648
(This problem is uncorrected for increase in efficiency due to cutting off
of blade tips, as given by equations under Case 2, change in blade form.)
Problem 8
While Problem 7 was an example of change in blade form due to cutting
of the tips of the Basic propeller with consequent reduction in projected
area as described in Case 2, change of blade form, the present problem is
one coming under Case i, where the blade tips are cut off but the total
Basic projected area is retained by broadening the ends of the blades out
side the center of pressure.
The vessel was of the wellknown naval collier type, fantailed stem,
twin screw, with the propellers located as in Position 2, Sheet 19. The
slip block coefficient is .665. The maximum diameter of propeller that
Gould be carried was 16 ft. 6 in. The tank curve of e.h.p. with all append
ages was available for use in the estimate.
From Sheet 19, the value of K for this S.B.C. and location of propeller
»1.22.
BASIC CONDITIONS OF PROPELLER
Propeller Basic Actual
D i7'.75 i6'.s
P 16'. 42 16'. 42
PA
~^(3bladed) 32 37
T.S 7050
PXR 2076
S.B.C... 66s
15 91
V 18.64
I.T.D 4.16
I.H.P 9324
P.C 67
E.H.P 6247
Digitized by LjOOQ IC
98
SCREW PROPELLERS
ESTIMATED AND ACTUAL PERFORMANCES
»
e.h.p.
e.h.p.
B.H.P.
Z
I.H.P.p
K
I.H.P.4
17.75
16.S
I.H.P.A
9
475
.076
X.X5
660
Z.22
80s
Z.076
866
10
640
.ZO24
Z.02
870
Z.22
Z086
Z.O76
zz68
xz
84s
.1353
.90s
zz6o
z.22
Z416
Z.076
1524
12
ZIOO
.Z762
.795
1495
Z.22
Z824
1.076
1964
13
1400
.224Z
.670
1994
Z.22
2432
X.O76
2617
M
1650
.264Z
.60
2342
Z.22
28S7
Z.076
3074
IS
2250
.3602
.46
3233
Z.22
3944
Z.076
4244
Revs.
Actual
I.H.P.di
LogAv
Log A.
*
Basic
Rd
(&)"
•
Est.
Act.
9
875
3.8
2.9Z
.060s
59.12
1.037
6Z.3
6z.6
JO
zz68
3.8
3.02
.0633
6S.88
1.037
68.3
68.3
IZ
ZSZ2
38
S'^2
.o6s4
72.63
1.037
753
75.x
12
1938
3.8
3.23
0654
79.24
1.037
82.2
82
13
2450
3.8
3.335
.068s
86.Z2
X.037
893
88.8
14
3109
3.8
3.43
.0647
92.37
1.037
95.8
96.2
15
3900
3.8
3. 52
.0725
99. 8z
1.037
103.5
103.8
The quantities in the estimate are for one propeller only and the powers
should be doubled for the total.
All of the foregoing propellers were threebladed, of manga
nese bronze, machined to pitch, the edges sharpened and the
blades highly polished.
Turning now to the fourbladed propellers, none of those in
the following problems were more than simply smoothed off,
there being no machining to insure pitch and no particular care
taken to sharpen blade edges.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
99
Problems in Estimates of Performances of 4bladed
Propellers
Problem 9
Hull Conditions
Slip B.C. = .80
Single Screw
Draught greater than 20 ft.
Basic Conditions of Propeller
Blades 4
i P.A.5D.A.=Total Proj.
Area Ratio 38
P.A.^D.A 28s
D 19'. S
P , 15'
T.S. for P.A. 5D.A 6320
R 103.2
PXR.
15..
v....
LT.D.
^^^j,_ D^XI.T.dXPxR
252.41
P.C.foriP.A.^D.A
E.H.P 5061
1548
.945
14.43
343
7996
.633
e.h.p
e.h.p.^E.H.P
V
viV
Z
K
I.H.P.d=irxl.H.P.p
Act. I.H.P.d=Act. /CXI.H.P.P
Est. Revs
Act. Revs
970
1570
1885
.1917
.3102
.3724
8.87
I0.4SS
II. 12
.614
.724
.77
.742
.535
.457
1.27
1.27
1.27
1839
2963
3545
1660
2755
3445
63.42.
74.63
79.15
61.63
73
78.2
Notes: Low. speed
obtained by two
runs only, one with
and one against the
tide. Shallow water
course with heavy
tide effect.
Digitized by LjOOQ IC
100
SCREW PROPELLERS
Hua Conditions
Single Screw
Slip B.C. ». 702
Draught > 12 ft.
XI.I7S
Problem 10
Basic Conditions of PropdUr
Blades 4
i(PA.^DA.) .4
PA.5D.A 3
D 9'. 67
P ii'.S
T.S 6670
R 219.6
PXR 2525
1—5. 92
V 22.93
LT.D 376
I.H.P 3517
P.C 62
E.H.P 2181
e.h.p
eJi.p.JEJI.P.
Z
if...
LH.P.d=irxLH.P.p
Act. I.H.P.d=Act.A:xl.H.P.p .
Est. Revs
Act. Revs
218
456
.1
.4822
9. 75
11.82
.425
.515
1.0268
.728
I 175
1. 175
389
747
408
780
96.53
118. 4
96
117. 8
545
.704
12.6$
.552
.63
X175
970
990
127
128
Problem 11
Hull Conditions
Single Screw
Slip B.C. = .79
Draught greater than 20 ft.
Basic Conditions of Propellers
Blades 4
4(P.A.^D.A.) . 2828
P.A.^D.A
D
P
T.S
R
PXR
15
V
I.T.D
LH.P 4m
P.C 691
E.H.P 2841
.2121
18'. S
18'. 75
4540
78.12
146s
.942
1362
2.07
Digitized by LjOOQ IC
ANALYSIS OF PROPEIXER^ '
• 101
Est.e.h.p
e.h.p.^E.H.P
V
v^V
Z
K
I.H.P.d=XXl.H.P.p
Act. I.H.P.tf=Act. /CXl.H.P.p.
Est. Revs
Act. Revs
Est. e.h.p
eJl.p.^EJ^.P
9
viV
Z
K
I.H.P.d=irxi.H.P.p
Act. I.H.P.d=Act. /CXl.H.P.p.
Est. Revs
Act. Revs
Est. e.h.p
e.h.p.5E.H.P
V
v^V
Z
K
tH.P.dii:Xl.H.P.p
Act. I.H.P.d«Act.ii:xl.H.P.p.
Est. Revs
Act. Revs
1050
.3696
1125
.396
1200
.4224
ID
.718
.46
10.27
.737
.427
10. 55
• 757
.4
1.24
1768
1420
1.24
1906
1600
2030
1800
57.73
S6
5933
08.7
60.92
61.4
1290
.4541
10.82
.777
.37
X.24
2175
2000
62.38
63.6s
1370
.4823
11.07
.795
.342
1.24
2319
2200
63.81
65
1500
.5281
II. 31
.812
.302
1.24
2543
2400
65.39
67.1
1600
.5633
"54
.83
.276
1.24
2700
2600
66.68
68.65
1725
.6073
11.76
.845
.24
1.24
2933
2800
67.92
70.15
1820
.6407
11.98
.861
.214
1.24
3"4
3000
69.36
71.65
1910
.6724
12. 18
.875
.19
1.24
3291
3200
70.5
72.9
2000
.7041
12.36
.888
.17
1.24
3447
3400
71.49
74.4
The e.h.p. 's of the foregoing vessel were estimated, and the trials were
held over a shallow water course with heavy tidal currents, one run in
each direction being made for each point.
Digitized by LjOOQ IC
102
SCREW PROPELLERS
Problem 12
Hull Conditions
Twin Screw
Slip B.C. =,655
Propellers located in Position 2,
Sheet 19
Basic Conditions of Propdlers
Blades 4
i(P.A.^D.A.) 391
P.A.^D.A 293
D 17'. 25
P 1/.812S
T.S 6520
R 120.3
PXR 2143
15 91
V 18.98
LT.D 36
LH.P 18190
P.C: 636
E.H.P 11384
e.h.p.^E.H.P
ch.p
V
viV
Z
K
LH.P.d=A:xLH.P.p....
Act. I.H.P.d=Act. KX
LH.P.P
Est. Revs
Act. Revs
e.h.p.rE.H.P
ch.p
V
vhV
Z
K
LH.P.d=/CXLH.P.^....
Act. I.H.P.if=Act. KX
LH.P.P
Est. Revs
Act. Revs
.1008
1 148
9.4
•495
1.023
1.2
2070
2000
58.33
54.5
.2016
2295
"75
.619
.719
1.2
4169
3850
7397
69
.3025
3443
134
.706
.542
1.2
6266
5940
83.53
80
.4032
4590
14.6
.77
.42
1.2
8299
8080
91.25
88.4
•5041
5738
1543
.813
.322
1.2
10400
9950
9708
94. 5
.6049
6886
16.15
.851
.24
1.2
12561
1 1 850
102.04
100
.7057
8033
16.83
.886
.168
1.2
14826
14200
106.8
105.75
.8065
9I8I
17
52
.923
.lOI
I
2
17299
16750
III
7
III
5
.9075
10328
18. 1
.954
.043
1.2
19770
19000
"57
116
There is evidently considerable wake gain with this hull at speeds
below seventeen knots, reducing power and revolutions. This excess wake
is clearly indicated by the e.h.p. curve.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
103
Problems Showing Effect of Varying Conditions
Problem 13. Smooth Versus Fair Condition of Ship's Bottom
HuU Condition
Twin Screws
Slip B.C. = .608
Propellers located, in Condition
Sheet 19
K = i for smooth bottom
Basic Conditions of Propellers
Blades 3
P.A.5D.A 32
D 18'. 6s
P 19'. 99
T.S 7110
R 121. 4
PXR 2426
15 899
V 21.52
LT.D 4.17
2I.H.P 2411S
P.C 671
E.H.P 16181
The ship with the smooth bottom was just out of dry dock when tried,
while the sister ship had been out of dock a few weeks, just sufficient to
destroy the smooth polished surface of the bottom paint. The eflfect upon
the performance will be seen to be very pronounced.
e.h.p.fE.H.P
ch.p
V
v^V
Z
K
I.H.P.d=/2:Xl.H.P.p...
Act. I.H.P.d=Act. XXI.H.P.P
(Smooth)
Act. I.H.P.d=Act. KXI.U.P.P
(Rough)
i^Xl.H.P.d (Rough) ■MCXi.H.P.d
(Smooth)
Est. Revs. (Smooth)
Act. Revs. (Smooth)
Act. Revs., (Rough)
.1
.2
.3
I6I8
3236
4854
955
12.35
14.15
.443
.574
.657
1.0268
.728
.5493
I
I
I
2267
45"
6807
2200
4450
6600
2400
4900
7300
1.09
1. 10
1. 10
54.33
68.95
79.2
52
69
79
54.5
70
80.S
.4
6472
15.51
.720
.4238
I
9089
8600
9800
1. 14
88.36
87.4
88.7
Digitized by LjOOQ IC
104
SCREW PROPELLERS
ch.p.
e.h.p.
E.H.P.
Z....
IT...
I£.P.dirxLH.P.j,
Act. I.H.P.d«Act. i^Xl.H.P.,
(Smooth)
Act. I.H.Pwi=Act. J:xLH.P.,
(Rough)
irxl.H.P.d (Rough) Virxl.H.P.fl
(Smooth)
Est. Revs. (Smooth)..
Act. Revs. (Smooth)
Act. Revs. (Rough)
•S
8090
16.7
.776
.3267
I
1 1366
mop
1 2300
1. 108
94.01
95.1
96.2
.6
9709
17.7
.822
.2432
I
I377S
13450
14900
1. 108
9973
loi.s
102.2
.7
11327
18.61
.86s
.169
I
16343
15900
17350
1.09
105.5
106.2
107.2
.8
"945
19.42
.902
.1065
I
18871
18450
1.084
iio.s
III
112
eJi.p.+E.H.P.,
ch.p
V
v+V.
Z....
iJi.p.dirxiJi.p.p
Act I.H.P4i=Act. KXl.U.^.p
(Smooth)
Act. I.H.P.d=Act. KXI.U.P.P
(Rough)
KXl.U.V^ (Rough) ^l5:Xl.H.P.tf
(Smooth)
Est. Revs. (Smooth)
Act. Revs. (Smooth)
Act. Revs. (Rough)
.9
I.O
I. OS
14563
16181
16990
20.08
20.6
20.81
.933
.957
.967
.05402
.0225
I
X
I
21295
24II5
25397
20900
23200
24500
22700
25500
27200
1.086
1. 10
I. II
"43
118. 1
"94
115. 8
120
121. 7
116. 3
120.2
122.2
1. 10
17799
21.04
.977
.045
I
26748
26200
28400
1.084
121. 3
123.9
124.4
The roughbottomed vessel is shown by this table to have required an
average of 10 per cent higher power for the same speeds than the smooth
bottomed one, and this even when the bottom was in such condition as to
be rated ** dean."
Problem 14
In this problem is given the case of a vessel whose bottom was reported
clean and in too good condition to justify docking before trial. The bottom
was painted with a grade of paint that even when newly applied was rough
and scaly. That this condition of paint had an extremely malign influ
ence was evidenced by the fact that several months after the acceptance
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
105
trial of the vessel, a service trial was reported on which the acceptance
trial was practically duplicated, the bottom being reported clean, yet the
log bore the entry "217 days out of dock."
The vessel was fitted with a single propeller driven by reduction gears,
the power delivered to the gears being measured forward of the gears.
In the estimate of periormance, a loss of 1} per cent of power has been
allowed through the gears and 2} per cent through the thrust bearing, mak
ing a total loss from the measured shaft horsepower of 4 per cent, in addi
tion to the loss by thrust deduction. This latter loss, only, is taken account
of in the estimate of revolutions.
The problem is to estimate the actual effective (towrope) horsepower
delivered by the propeller and by comparison with the model tank curve of
effective horsepower find the increase in resistance due to the roughness
of the ship's bottom.
HuU Conditions
Single Screw
SHpB.C. = .66
Draught 20 ft.
1^ = 1.07
Basic Condition of Propeller
Blades 4
i(P.A.^D.A.) 327
P.A.^DA 246
D... IS'S
P 16'
T.S.. S400
R 110.9
PXR 1774*
^s : 913
V 15.99
I.T.D 2.67
I.H.P 4509
P.C... 667
E.H.P 3008
S.H.P 4148
Total S.H.P^=Total S.U.Kp(K\K^)
K :
K^
S.H.P.P
Z=log S.H.P.log S.H.P.P
cJl.p.^E.H.P
(De.h.p. (Trial)
(5)e.h.p. (Model) .T
©i®
V
viV
Est. Revs
Act. Revs
520
1068
1635
1.07
1.07
1.07
.04
.04
.04
468
962
1473
.948
.635
.450
.117
.248
.38
352
746
1143
301
602
903
1. 17
1.239
1.266
7.5
9.8
"3
.47
.613
.706
50.79
68.36
78.91
51
67.5
78
2200
1.07
.04
1982
.321
.525
1579
1204
1.3"
12.4
.775
86.57
86
Digitized by LjOOQ IC
106
SCREW PROPELLERS
Total S.H.PHi»Total SH.V.p(K+K^y
K
K^
S.H.P.,
Z=log S.H.P.log. S.H.P.J,
c.h.p.+E.H.P
(i)e.h.p. (Trial)
(i)c.h.p. (Modd)
©+©
V
v^V
Est. Revs
Act. Revs
2770
1.07
.04
249s
.221
.641
1928
150S
1.28
133
.832
9308
92.6
3317
1.07
.04
2988
.142
.745
2241
1806
1.24
143
.894
99.81
98.2
3846
1.07
.04
3465
.078
.86
2587
2107
I;
14
103.
103
228
75
922
6
5
4341
1.07
.04
39"
,026
955
2873
2408
1. 193
1545
.966
108.3
108. s
It will be noted that at the low speeds where the resistance is mainly
frictional, the effect of the roughness of bottom on the performance is a
maximum.
Wake Gain
In the foregoing examples, particularly those in which the
maximum speed of vessel was high, there will be remarked gen
erally an excess of estimated power over the actual power at
certain speeds. This diflFerence can be attributed to what is
commonly called " wake gain," and is especially prominent in
cases where the value of K is low.
In Taylor's " Speed and Power of Ships " is shown a diagram
of the humps and hollows occurring in the resistance curves of
ships (Fig. 2). The locations of these humps and hollows depend
upon the load water line length of the ship and up on the spe ed,
but always occur at about the same values of ^;^^/L.L.W.L.
The humps are caused by increases above the normal wake
of the hull, while the hollows are caused by the wake drawing
down towards the normal wake and in some cases falling below it,
even in certain instances falling so far below it 'as to become
negative.
These humps, in the model tank, appear as abnormal in
creases in resistance and the hollows as corresponding decreases.
When, however, the vessel is propelled by its own power, with
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS 107
its screw propellers working in these wakes, these abnormally
high wakes add to the thrust of the propeller per revolution, the
power per revolution remaining constant, so that the propulsive
coefficients realized at these positions of abnormally high wake
become themselves abnormal. As the hollows fall to the normal
condition, the propulsive coefficients likewise become normal,
and finally when the actual wake falls below the normal wake
the propulsive coefficients fall below the normal ones imtil when
the wake has actually become negative the revolutions become
imduly high and this imdue increase in revolutions will be
accompanied by an excessive increase in power.
In vessels having the propellers located as shown in Condition
I, Sheet i8, the benefit of this wake gain may, however, be com
pletely lost by locating the propellers with insufficient tip clear
ance between the propeller blades and the hull. With propellers
so located, there exists with such hulls a current of high aftflow
velocity close in to the skin of the ship, and if the tip clearance
of the propeller be insufficient, the tips of the blades will penetrate
into this high velocity layer, and due to the lowpitch angle of
the propellers at the tips, the thrust per revolution will be de
creased and the velocity of flow of this malign current will be
retarded intermittently as the tip of each blade enters it. The
writer has freshly in mind the case of a destroyer, where with
propellers 8 ft. in diameter a violent pulsation of the ship's
bottom occurred at high speeds, at a location 30 ft. forward of
the propellers. Upon fitting another set of propellers having
the same pitch and projected area but with a diameter of only
7 ft. 6 in., the pulsation completely disappeared. Apparently
the additional 6 in. in diameter was sufficient to cut into this
current of high velocity of flow and produce an action similar
in all respects to that of the wellknown " water hammer.'^
Undoubtedly, some of the water in the rapid flowing skin
current will be thrown off radially by the propeller blades by this
periodic checking of flow, and when the tips of the propellers
pass in close proximity to the hull the water thus thrown off
inpinges violently on the hull plates, produces violent local
vibrations which may be of such intensity as to break in the hull
Digitized by LjOOQ IC
108 SCREW PROPELLERS
plating, and at the same time produces a loss in power which
may, and usually does, oflFset the possible " wake gain."
In highspeed vessels of normal form, such as torpedo boats
and destroyers, and in vessels having the propellers located as in
Condition i, Sheet i8, it is recommended that the relative re
ferred tip clearance of the propellers be not less than 3 ft., and
in excess of that, if possible.
In cases where large tip clearances are provided, a ^' wake
gain" may confidently be expected and, if desired, may be allowed
for in making the preliminary estimates of performance, but
where the tip clearance is small it is better to neglect the wake
gain as it may be more than offset by the exaggerated thrust
deduction occurring.
corkection of effective horsepower curve for
Expected Wake Gain
In some cases abnormal increases and decreases in wake, from
the wake usually encountered with the fullness of hull of the
vessel imder consideration, are clearly indicated by the charac
teristics of the curve of effective horsepower (towrope horse
power), obtained by towing the model of the vessel in the model
tank. This is clearly shown by the curves given in Figs. 6 and 7.
These curves are curves of eflFective horsepower (towrope
horsepower), per ton of displacement, erected on speed divided
by the square root of the length on the load water line of the
vessel imder consideration, that is, the ordinates are —^ —
Tons Disp.'
while the abscissas are z;^VL.L.W.L.
On both of these curves occur humps, more or less distinctly
shown, which indicate an increased wake over that occurring
throughout the major portions of the curves, while in Fig. 7 is
shown the characteristic change in the curve which occurs when'
a rapid decrease in wake is encoimtered.
In cases where these humps occur it is perfectly safe practice
to take a spline and follow the main character of the curve,
ignoring the humps^ in making the estimate of speeds, but in
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
109
"IdsiOjnDx T *d*i(*9 JO oiBOg
Digitized by LjOO^QIC
110
SCREW PROPELLERS
Scale for b
U
M
to
00
s
sales
)fe.h
00
i8pl.i
1 Ton
o
»»
^
So
Hi
h»
io
CO
!fk
b«
06
8C8
lefor
a
b
s
I'm
1:
r
1
pi
.;;:::
i \
■
■
iiiil;
t::: :::
titt t
7k
::::::
■■■■I
tItt t
m
::::.
1
:::,;
i;;;::;:;!
:::
LI
e
tJlllllll
:::! lili:
i
m
B
w
u
^
:::l
^
iijil
r
1:: ::
■ ■
:::::::::
fl
1
1
D
1
Ill
Npt
?
Fig. 7. — ^The Resistance Curve Showing Humps Caused by Abnormal Wake;
also Apparent Falling Off in Resistance Caused by Abnormal Decrease in
Wake.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS 111
estimating for revolutions, the speed corresponding to the power
as given by the hump must be used, the actual speed for these
revolutions being that as corrected by eliminating the hump.
For cases where an abnormal decrease in wake is indicated,
the normal character of the curve should be extended as shown
at b^y Fig. 7, the actual speeds to be expected being those cor
responding to this new curve, while the revolutions, as before,
are derived from the speeds and powers given by the actual
model tank curve.
When thrust deduction greater than unity exists it becomes
modified by these changes in wake, being increased for the humps
and decreased for the decrease. Calling the e.h.p. values of the
model tank curve, e.h.p., and those for the same speed, from the
corrected curve, e.h.p.i, and denoting the original thrust deduc
tion factor by K and the new one by Xi, then
Ki^KX^j
e.h.p.
/e.h.p.i'
but in no case should this value of Ki be taken as less than unity.
In many cases encountered the curves of e.h.p. will give no
indication of change in wake and in such cases, imless there are
performances of similar vessels at hand to use as a guide in cor
recting the estimate of performance as derived from the model
curve, this estimate, imcorrected, must be taken and the depar
tures from it caused by changes in wake accepted as something
which can not be allowed for.
Having the actual performance of such a vessel, it becomes an
easy matter to analyze and to determine whether the departure
from the estimate is due to change in wake or to errors in the
assumed curve of resistance, when there are no abnormalities
existing in the propeller itself. Using the actual powers and
speeds in the Robinson equation for apparent slip, should the
apparent slips obtained correspond closely with the actual
apparent slips, it is an indication that the curve of e.h.p. is too
high or too low, and that the vessel is obtaining her speed without
any abnormal assistance or loss from increase or decrease in
wake.
Digitized by LjOOQ IC
112 SCREW PROPELLERS
Use the actual powers and the speeds corresponding to the
e.h.p. values, as obtained from these actual powers and as given
on the resistance curve, in the Robinson equation for apparent
slips, and from these apparent slips obtain the revolutions for
these resistance curve speeds. Should the resulting revolutions
approximate closely to those actually obtained with these powers,
the difference between the estimated performance and the actual
performance will be due to wake gain or loss, depending upon
whether the actual speeds obtained are greater or less thau those
expected from the model tank curve.
Arrangebient of Strut Arms and their Influence on Wake
It has become quite the custom, at least in the United States,
in the last few years to so design the strut arms that their axes
lie in the direction of the lines of flow of the water around them
as determined from the model tank. By comparing the per
formances of vessels with struts so designed, with those of similar
vessels having the axes of the sections of the lower strut arms
parallel to the base line of the ship, one must be lead to the con
clusion that the firstnamed method is incorrect.
The performances of vessels having their strut arm sections
placed at an angle to the base line indicate that at high speeds,
such sections tend to cause the after part of the vessel to sink
deeper in the water, thus broadening out the limits of the water
plane. This produces an increased stemward velocity of both
the highvelocity current close to the hull, also broadening this
current, and of the water flowing through the propeller. This
increase in velocity of flow through the propeller increases its
revolutions for any given power so that the revolutions become
abnormally high, and when the malign skin current becomes
broad enough it enters the region of the propeller disc and
entails an increase in power while, also, vibrations of more or
less intensity occur.
With vessels having the strut arm sections parallel to the
base line, however, the stream line currents striking the lower
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS 113
sides of these arms tend to hold the after bodies up; a por
tion of the velocity of flow in these stream lines is destroyed
due to the sudden change in the direction of flow, the revolutions
are maintained more nearly normal, and where ample tip clear
ance is given the power also remains normal, or may even be
much reduced.
It should always be borne in mind that " wake gain," so far
as the action of the propeller is concerned, is equivalent to a
reduction in resistance, while " thrust deduction ^\ has exactly
the same effect as an increase in resistance. To neglect " wake
gain " produces an error which results in slightly overpowering a
vessel for a given speed, with the result that on trial, when the
designed power is developed, the speed is exceeded. This error
is one for which the designer is always forgiven if the excess
power is not too excessive. To seriously imderestimate or to
neglect the " thrust deduction," however, results in the imfor
giveable offense of imderpowering and the realization of a lower
speed than expected. The former error always delivers a ship
to a customer; the latter may throw the vessel back on the hands
of her builders. Where the thrust deduction factor K exceeds
1. 02, no account should be taken of the possible " wake gain."
Where " wake gain " is expected, the estimates of power and
revolutions should be made by using the model tank curve of
effective horsepowers and speeds, the wake gain being used only
as a correction for the speed actually expected. This expected
speed should not appear in either power or revolution calculations.
In the following problems, the data "Actual Power" is
that actually corresponding to the estimated revolutions and
"Actual Speed" is the speed which was obtained with these
revolutions.
Digitized by LjOOQ IC
114
SCREW PROPELLERS
Problems in Wake Gain
Problem 15
HuU CondUums
Mean Slip B.C. for
All Propellers = .632
Actual Tip Clearance = s'
Calculated values of Z are used in
this and the succeeding problems.
Basic Conditions of Propellers
No. of Propellers 4
Blades 3
P.A.^D.A 4247
D i2'.863
P Il'.209
T.S 9000
R 223.2
PXR 2502
15 89
V 21.97
I.T.D 6.62
I.H.P. (Total) 37404
P.C 603
E.H.P 22556
S.H.P 34412
ESTIMATE OF PERFORMANCE
c.h.p.^E.H.P
e.h.p
V (Tank)
v^V
Z
K
S.H.P.d=/i:xS.H.P.p
Actual Power
Est. Revs ,
Act. Revs
Act. Speed
e.h.p.iE.H.P
e.h.p
V (Tank)
viV
Z
K
S.H.P.d=/i:xS.H.P.p
Actual Power
Est. Revs
Act. Revs
Act. Speed
I
2256
II
501
I
0414
I
3128
3250
107
8
102
II
25
.2
4512
13.86
.631
.7279
I
6439
6550
135 9
129.6
14.00
•3
6768
IS. 75
.717
.5445
I
I
9822
13253
9850
13200
155.2
170
151.3
168
16.12
17.67
.4
9024
17.25
.784
.4144
s
II280
18.4
.838
.3135
I
I67I9
16750
182.5
181. 7
18.8
.6
.7
.8
.9
13536
15788
18048
20304
19.3
20.05
20.7
21.15
.878
.912
.942
.963
.231
.1613
.1009
.0477
I
I
I
I
20217
23736
27278
30833
20300
23700
27250
31100
192
200.9
209
215
190.6
198.6
206
213. S
19.70
20.34
20.85
21.25
I.O
22556
21.45
.976
o
I
34412
Off curve
219.8
221
21.55
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
115
In the foregoing problem the " wake gain " was abnormal,
and the problem is further complicated by the great variation in
revolutions between the different shafts due to the differences in
powers on the shafts at the various speeds. In such cases, the
lowpowered shafts hold down the revolutions of thjB higher
powered ones while the lowerpowered shafts have their revo
lutions increased, but these increases and decreases are not in
inverse proportion to each other, and this inequality produces
an inequality between estimated and actual revolutions. This
inequality is further exaggerated by differences between the
estimated and the actual powers.
Problems in Wake Gain Showing Effect of Strut Arms
^ Problem i6
In this problem the vessel is nearly similar to that of Problem 17, except
that there are two struts on each shaft, the axes of the lower strut arms being
set at an angle of 4^^ to the base line, inclined downward at the forward
edge. .
Hidl Conditions
Slip B.C. = .385
Twin Screws
•Large Tip Clearance
As already pointed out, with
struts so arranged, the stem squats
badly, the squatting beginning at
= 1.48,
VL.L.W.L. V^
©=26.06,
and being accomplished at
— r==2.I3,V = 37.S
V310
Basic Conditions of Propellers
Blades 3
P.A.HD.A 5Q5
D 92". 5
P 82"
T.S 13330
R 550.5
PXR 3760
15 787
V 29.2
I.T.D. 11.77
I.H.P 18021
P.C 525
E.H.P 9461
S.H.P 16580
Digitized by LjOOQIC
116
SCREW PROPELLERS
e.h.p.^E.H.P
e.h.p
.025
237
10.3
35
1.668
356
400
167.2
160
10.3
•OS
474
12
.41
1. 355
732
720
199.2
200
12.55
.075
711
14.3
.49
1.1715
1117
1 150
234.6
230
14.3
.1
946
15.52
.531
1. 0414
1507
1500
255.9
252
15.52
.2
1892
9
IQ.2<
viV
.66
z
.7270
S.H.P.d=S.H.P.,
Actual Power
Est. Revs
3102
3100
321. 1
317
19.45
Act. Revs
Act. Speed
e.h.p.^E.H.P
e.h.p
V
.3
2838
21. 5
.736
.5445
4732
4750
364.6
359
21.85
.4
378s
22.8
.78
.4144
6385
6300
3951
394
23.4
.5
4730
24
.822
•3135
805s
8100
422.9
425
24.65
.6
5676
25.1
.86
.231
9741
9700
449.9
453
25.7
.7
6623
26. IC
V7V
.895
.1613
1 1436
1 1500
475.8
476
26.65
Z
S.H.P.dS.H.P.p
Actual Power
Est. Revs
Act. Revs
Act. Speed
c.h.p.sE.H.P....
e.h.p
V.
viV
Z
S.H.P.d = S.H.P.p,
Actual Power
Est. Revs
Act. Revs
Act. Speed
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
117
Problem 17
This vessel is similar to that of Problem 16, except there is only one
strut on each shaft and the axes of the sections of the lower strut arms
are parallel to the base line of the vessel. Squat neglected.
Htdl Ccndition
Slip B.C. = .385
Twin Propellers
Large Tip Clearance
Propellers located at Frame 162, at
after end of knuckle of keel
Vessel 12 tons Ughter than model
at upper speeds
Causes further increase in speed and
increase in revolutions.
Basic Condition of Propellers
Blades 3
P.A.■^D.A 6013
^ 7'. 33
P 6'. 67
T.S 13570
R 589.3
PXR 3931
15 782
V 30.4s
LT.D 11.98
I.H.P. (Total) 16646
PC 525
E.H.P '.. 8739
S.H.P 15314
Act.
Actual.
e.h.p.
e.h.p.
V
(Tank)
Z
S.H.P.d
S.H.P.p
Est.
Revs.
Actual
Speed.
V
V
E.H.P.
Revs.
Power.
•335
.025
219
10
1.668
329
168.6
10.2
168
350
.407
.05
437
12.0
1. 355
676
203.8
12.4
203
675
.473
■075
656
14.3
1.1715
1032
243 I
14.4
237
1050
.515
.1
874
15.65
I. 0414
1392
267.6
15.7
259
1400
.643
.2
1748
19. 1
.7279
2866
332.6
19.6
328
2900
.716
.3
2612
2135
.5445
4371
378.3
21.8
374
4350
.775
.4
3496
22.79
.4144
5898
413.1
23.6
413
5900
.821
•5
4370
23.98
.3135
7440
444.2
25.0
446
7400
.857
.6
5044
24 83
.231
8997
469.2
26.1
474
8900
.891
.7
6118
26.16
.1613
10563
500.0
27.15
504
10550
.951
.8
6992
27.21
.1009
12139
528.3
27.95
529
1 1900
.952
.9
7866
28.19
.0477
13721
559. 4
29.0
564
13700
.983
I.O
8739
29.15
0.00
15314
586.1
29.9
592
15300
.99
I 05
9176
29.65
.0221
16114
597.2
30.15
607
15700
1. 012
I.I
9613
30.1
.0431
16910
615.8
30.81
622
16950
1.028
I. IS
10050
30.58
.0632
17713
626.1
31.3
637
17700
1.04
1.2
10487
31 03
.0825
18518
635.0
31.7
651
18500
1.054
125
10924
31.6
.1009
19320
651.0
32.1
668
19300
There does exist a certain amount of squat in this case
but not to the same extent as in the vessel of Problem 16.
Digitized by LjOOQ IC
118
SCREW PROPELLERS
Problem x8
This vessel is similar to those of Problems i6 and i7i except there is
only one strut to each shaft, the axes of the lower strut arms being inclined
6i** below the horizontal at the forward edge. The vessel was run on con
siderably higher displacement than the other two. The propellers were
located about lo ft. further aft than those of Problem 17, and slightly
forward of those of 16.
HuU Conditions
Slip B.C. = .385
Twin Screws
Large Tip Clearance
Squatting begins at 26.06 knots and
b accomplished at 37.5 knots
Basic Conditions of Propellers
Blades 3
P.A.fD.A 6012
D 94"
P 81". 94
T.S 13570
^ 551.4
PXR 3765
iS 782
V,: 29.06
LT.D 12
LH.P 19003
PC .525
E.H.P 9076
S.H.P 17483
c.h.p.5E.H.P...
c.h.p
©(Tank)
s.H.p.d=s.n.p.p.
Actual Power. . . ,
Est. Revs
Act. Speed
Act. Revs
e.h.p.HE.H.P....
ch.p
t»(Tank)
S.H.P.d=S.H.P.p.
Actual Power . . . .
Est. Revs
Act. Speed
Act. Revs
.025
249
10
376
400
163.
10
158
.05
499
12.6
772
850
205.9
12.6
198.8
.075
748
14.4
1178
1300
236.1
14.4
229.5
998
' 15.7
1589
• 2593
I 15.85
251
.2
1995
19.4
3271
3300
324.3
20.05
321
.3
2993
21.7
4990
5050
367.7
22.31
366
•4
•5
3990
4988
23.02
24.2
6733
8494
6700
8500
398.4
425.9
23.7
24.75
398
426
.6
5986
25 32
10271
10300
454.2
257
4545
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
119
c.h.p.1E.H.P....
e.h.p
t>(Tank)
S.H.P^=S.H.P.p.
Actual Power
Est. Revs
Act. Speed
Act. Revs
•7
.8
.9
6983
7981
8978
26.41
27.41
28.4
12059
13858
15662
12000
13800
15605
482.1
513. 5
544.8
26.63
27. 55
28.48
486
S18
551
I.O
9976
29.4
17483
17550
5776
29.46
583
Problem 19
This vessel was exactly similar in hull lines to those of Problems 17
and 18. It had only one strut to each shaft with the strut section axes
parallel to the base line as in 17, but the struts were located in the same fore
andaft location as those of 18. While there was undoubtedly some de
crease in resistance, particularly at the high speeds, over that of 17, the
effective horsepower curve of that vessel has been used in the analysis.
A much better agreement between actual and estimated revolutions for
equal powers will be noted in the cases of 17 and 19 than in i6 and 18,
should squat be neglected, the obliquity of the strut arm axes in these two
latter vessels apparently causing a decrease in pressure at the high speeds
at the propeller locality causing the propellers to speed up due to the in
creased velocity of flow of the water (decrease in wake) through them.
Where the tips of the propellers are located close to the hull in cases like
16 and 18, this undue increase in revolutions is accompanied by increasing
vibration and loss in power exactly as in cases of cavitation.
nuU CondUion
Slip B.C. = .385
Twin Screws
Basic CondUion of Propellers
Blades 3
P.A.^D.A 611
D 87"
P 80"
T.S 14000
R 614.7
PXR 4100
i'S' 779
V 31.52
I.T./) 12.32
I.H.P 18200
PC 525
EH.P 9553
S.H.P • 16741
Digitized by LjOOQ IC
120
SCREW PROPELLERS
Actual S.H.P.d=S.H.P.p
Z
c.h.p.iE.H.P
c.h.p
• (Tank)
Est. Revs
• (Actual)
»^K (Actual)
Actual Revs
Actual S.H.P.dS.H.P.p.
Z
e.h.p.^E.H.P
ch.p
• (Tank)
Est. Revs
V (Actual)
•47 (Actual)
Actual Revs
Actual S.H.P.d = S.H.P.p
Z
e.h.p.^E.H.P
ch.p
V (Tank)
Est. Revs
V (Actual)
i; 5 7 (Actual)
Actual Revs
1580
— 1. 025
.102
974
16. 1
276.4
16.9
•53
276
3080
4570
.735
.564
.195
.288
1863
2751
1945
21.6
339.3
382.4
20.6
22.6
.653
.717
342
382. s
6100
.438
.38
3630
23
416.6
24
.761
414
7800
9S70
1 1400
.332
.243
.167
.485
59
.695
4633
5638
6639
24.3
2S.6
26.78
4SO
483.7
515.3
25.3
26.57
27.8
.803
.843
.882
446
481
517.5
12720
.119
.77
7365
27.62
536.5
28.58
.903
541.5
14620
.059
.88
8407
28.8
570
29.7
.942
577
16680
— .0016
.99
9458
29.92
601.7
30.78
.976
611. 5
17800
+ .0266
1.065
10174
30.71
621.5
31.32
.993
628. 5
The maximum difference between estimated and actual revo
lutions is seen to not exceed 1.6 per cent while the " wake gain "
has given an increase in speed over the tank speed of from .61
to 1.02 knots.
It should be borne in mind that these vessels being of the
destroyer type, their resistance is affected very materially by
changes in load and trim, and that in trying them over the trial
course the loads are usually considerably heavier at the begin
ning of the trials than at the end. This variation in load also
has its effect on revolutions.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
121
Problem 20. Propellers for ''Tunnel" Boats
By the term " Tunnel " Boat is meant a vessel of shallow draft having
arched passages formed in the bottom of the after body and the propellers
located in these tunnels. The propeller may be so located that only a
portion of its diameter is immersed when at rest. When in motion the
propeller draws the air from the portion of the tunnel forward of it and expels
it to the rear. This produces a vacuum which is immediately filled by
water, the tunnel thus remaining full so long as the propeller is operating.
The water being constrained to move in a direction practically normal
to the disc of the propeller, the principal losses are those due to friction in the
tunnel and are therefore practically a constant percentage loss of the total
power put into the propeller, no matter what the slip block coefficient of the
ship may be.
This loss is heavy, and from the results obtained in the following problem,
appears as " thrust deduction " and amounts to K = 1.195. The problem
is an analysis of the propellers of two U. S. shallow water gimboats for which
the propellers were designed by parties who have had much experience with
this type of vessel and whose design of propeller must, therefore, be con
sidered as having been based upon actual performances.
The close agreement between the analysis results and the designed con
ditions is rather good evidence as to the correctness of the former and of the
value of K obtained.
800 (Two engines) =I.H.P.tf
PA^DA Revs. 300
Nom. B.C. = .6
5^L.W.L.=.i53
SHpB.C. = .57S
iP.A.^D.A
D
P
T.S
R
PXR
15
... .347
...4'.67
... 6'
.•• 5730
...390.6
... 2343
... .90
V 20.81
ITd 2.93
LH.P 1187
P.C 65s
E.H.P 777
V
e.h.p
e.h.p.i.E.H.P..
v^V
(£.r.^e.t.)*...
z
i.h.p.p
i.h.p.p H (£.r. ^ e.t)* . 669 . 8
ii[=8oo5669.8 = i.i95
.26025
13.25
385
•4954
.637
.86(Sheet22)
.314
576
f « 13I knots
Digitized by LjOOQ IC
122 SCREW PROPELLERS
The designed conditions of these vessels were
I.H.P^ = 800, Revs. =300, Speed = 13} knots.
The apparent sKp with these conditions « 25.41 per cent.
The computed apparent slip, from the basic condition reduced to 13}
knots and 800 1.H.P., is as follows:
log i4F=393
5= .10
LH.P.d = 8oo
log Av^3 3^
J = Apparent slips'. 2504
Revs. = 298.5
Problem 21. Doubleended Ferry Boat— Propellers
In vessels of this type the form of hull is such that the midship section
coefl&cient is usually much finer than standard for the slipblock coefficient.
No correction of slip block coefficient should, however, be made for this.
Of the two propellers, the after one is that which works in standard
propeller conditions and the analysis, therefore, applies to this propeller.
The difference between the actual horsepower of the engine and that
derived by the analysis for the after propeller is credited to the forward one.
It will be noted that the analysis indicates that the after propeller
delivers 63.66 per cent of the total effective horsepower and absorbs in doing
this about 55 per cent of the total power of the engine, while the forward
propeller only delivers 36.34 per cent of the effective power at an expense
of 45 per cent of the engine power. This inefficiency of the forward screw
would lead to the belief that the efficiency of propulsion would be greatly
increased if the forward propeller were uncoupled and allowed to revolve
freely, or, better still, if it were removed completely.
This expected betterment has been realized by actual experiment and
the analysis of such screws in the following problem also promises such a
result, a reductipn in total indicated power from 1845 I.H.P. to 1570 1.H.P.
being shown, a reduction in the required power of 14.9 per cent.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
123
Doubleended Ferry Boat
Hull Conditions
Slip B.C. = .76
Two propellers— one forward, one
aft
X = i.43
Draft = 13 feet
Basic Conditions of Propellers
Blades 4
iP.A.HD.A 432
P.A.rD.A 324
D 10'. 5
P 9'. 55
T.S. for P.A. ^D.A 7150
R 216.8
PX^ 2070
I 5 for P.A. ^D.A. = .324
and slip B.C. = . 76 = .93
V 19.00
I.T.^ for P.A. 5D.A 4. 25
l.U.V.^iD^Xl.T.DXPxR)
^252.41 3843
P.C.fori(P.A.^D.A.) 598
E.H.P 2298
Analysis
V 19.00
logAv 3 82
V 14 . 662 miles
V 12.73 knots
log At (Curve Y, sheet 21.) 3.15
Actual Re\'s i47 • 9
J = Apparent slip
LH.V.a=Kxl.U.F.p=s^^^^^*
Total I.H.Puf= Total Kxl.H.F.p
Power on forward screw
K
LH.P.P
e.h.p
Z 73342
.0865
1015
1845= Actual total power
830 = 18451015
143
709.8
700 (Total by two screws)
e.h.p. aft. 5 E.H.P.
e.h.p. aft.
e.h.p.fd.
viV
.194
445.6
254.4 = 700445.6
.67
V = ^. and V^ = Ai
Digitized by LjOOQ IC
124 SCREW PROPELLERS
Forward Propeller Removed
e.h.p 700
e.h.p.■^E.H.P 3046
z 5440
LH.P.tf=XxI.H.P.p 1570
v^V. .67
and the propeller plots well within the safe zone on Sheet 22 and for safe
loads on Sheet 22B.
Problem 22
Use of Sheet^ 22 in estimating power and effective power delivered.
By the aid of the curves given on this sheet it becomes possible to make
an estimate of the indicated or shaft horsepower being developed by the
engines and of the effective horsepower being delivered by the propeller,
provided the characteristics of the hidl and of the propeller together with
the revolutions necessary for any speed are known, thus:
Suppose the vessel given in Colimin i, page 81, be taken:
The slip block coefl&cient of the hull is .805.
Thrust deduction factor K is 1.27.
Basic apparent slip is .055.
By analysis of the propeller, the Basic I.H.P. is 7996 and the Basic
E.H.P. is 5061, while the Basic F« 1443 knots.
Suppose the ship be so loaded down that on account of bad weather and
head wind and sea a speed of 10 knots is made with 80 revolutions. The
pitch of the propeller being 15 ft., the apparent slip will be
(i5X8o)(ioXioi.33) . ^
i^xs^ '•^5^='
From Sheet 21, log 4 f for 14.43 knots is 3.47, while log At Curve X, for
10 knots is 3.00.
The Robinson equation for apparent slip in terms of power is
e^ LH.P.dX>4v
^"'^^LH.P.X^.'
therefore,
I.H.P..=.x?4g:^ = .i56X 7^^^ ^3^ =7864.
SxAv .055X3.47
Now the value of t>^ 7 = 10514. 43 « .693.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
125
The curve of critical thrusts, E,T,, cross the line of l•^F = .693 at e.h.p.
iE.H.P. = .6io, and this value is taken as the starting point for estimate
of e.h.p. 4 E.H.P. being delivered by the propeller.
Following along the line of .693 and taking the points where this line
crosses each curve of (E.r.^e.t.)', the following values of e.h.p.7E.H.P.
and (£.r.4e.t.)* are obtained:
e.h.p.^E.H.P.
' .610
I.O
.67
•95
.72and(£.r.^e.t.)'=
•90
.80
I .85
Turning again to the Robinson equation, but using the second form,
namely I •
KxAv ItXA*
10 xAv \E,tJ '
5=5
and using the above values of (£.^.^e.t.)*, a series of apparent slips is
obtained as follows:
s for
e.h.p. ^E.H.P. = . 610
' .1225
' .226
e.h.p.5E.H.P.= .67
•1434
' where Z= 
.18
e.h.p. ^ E.H.P. = .7 2
.1622
IS
e.h.p.^ E.H.P. = .80 ,
.1922 .
.1009
Laying down these values of apparent slips as curves having as ordi
nates values of apparent slip and as abscissas values of e.h.p. ^ E.H.P. ,
the value of e.h.p. ^ E.H.P. corresponding to an apparent slip of .156
per cent is found to be . 7035.
Therefore the effective horsepower being delivered equals
e.h.p. =E.H.P. X=rT7% = 5061 X . 7035 =3560 and the propulsive coefficient
realized equab
p.c. = e.h.p. ^I.H.P.d = 3560 4 7864 = .452 +.
The only cause of any appreciable error occurring, is the value of K
which must always remain a cause as it is dependent upon the form of hull
and location of the propeller. Errors in the value of this factor affect the
value of e.h.p. obtained and, therefore, the value of the propulsive coeffi
cient realized.
Digitized by LjOOQ IC
126
SCREW PROPELLERS
Should the propeller have fallen on or above the curve of critical thrusts,
E.T., the log LH.P.d would have equalled
log I.H.P.d =log LH.P. Z (for ^^ « .7035 is .16) +log K
» 3.90287 —.16 +.10380 = 7025 and the propulsive coefficient
«p.c. =356o^7025 = . 506+and this would have been realized where
viV > 710 which corresponds to a speed of not less than
14. 43 X. 710 = 10. 25 knots.
Problem 23. Analysis of Performance of Submarine Boat Propellers
In the following work the performances of five separate vessels are given,
three of them being of the single hull, Holland type, with the propellers
carried abaft and clear of the hull while the remaining two are of the double
hull, Lake type, the propellers being carried below and in close proximity
the hull.
HULL CHARACTERISTICS
L.L.W.L.
Vessel.
BiL.WX.
Nom.
B.C. Surf.
Cond.
SlipB.C.
Surf.
B.C.
Propeller.
Beam«B
Draft =fl
Subm.
A
153' 5
167'. 42
147
165'
155'
16'. 167
17'
15'. 25
14'. 75
14'.
13'. 5
13'.583
I2'.S
13'. 25
i2'.33
.1053
.1016
.1038
.0894
.09032
.444
.4083
.4327
.4784
.4327
•745
.73
.737
.585
.575
.745
.73
.737
.80
.79
B
c
A 1
A
A
A
A
E .
The propellers used were as follows:
A — Oval blades, broader at tip than standard;
B — Same propeller as A ;
C — Standard form of blades;
Di — Standard form of blades;
A — Di with three inches cut off diameter;
Di — Standard form of blades. Blades of cast iron, roiigh and imtrue;
A — Standard form of blades;
E — Standard form of blades.
All the above propellers were of bronze with the exception of A, were
highly polished and sharpened at the edges, and were 3bladed.
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
127
BASIC CONDITIONS OF PROPELLERS
Prop. .
Diatn.
P..
Act. . .
Basic.
P.A. f
D.A. \
Act. . .
Basic .
T.S,.
PXR
Condition.
S.B.C
iS...
V
I.T.D..
I.H.P..
P.C...
E.H.P.
S.H.P..
A
55"
63"
45"
363
S
I05S0
2399
Surf.
.745
899
21.28
8.75
1983*.
554
.837*
1390*
B
55"
63"
45"
363
5
I0S50
2399
Subm.
73
8973
21.24
8.75
1983*
• 554
837*
1390*
C
53"
53"
48". S
.297
.297
6600
1923
Subm.
.737
.926
17.59
3.7
475.8
.683
324.8
437.5
Di
63"
63"
61".!
268
268
5950
1849
Subm.
.80
.945
17.24
.323
564.1
695
392
S19
Di
60"
63"
6i".s
274
268
5950
849
Subm.
80
945
17.24
3.23
511. 7*
695
355.6*
470.7*
Dz
60"
60"
54"
.35
.35
7660
2195
Subm.
.80
.939
20.34
483
908.1
.652
592.1
835.4
Di
6b"
60"
59"
35
35
7660
2296
Subm.
.80
.939
21.28
4.83
950.1
652
619.5
874.1
E
51"!
51"!
45"
.4
.4
8600
2399
Subm.
.79
.928
21.97
Surf.
.575
.882
20.66
6.0s
910.8
.618
563 .
838.1
♦These quantities have been corrected for the reduction in diameter by multiplying
^, , . , , /Actual diameterX 2
the basic values by (5 — ; — jr 7 — I •
\ Basic diameter /
In estimating for revolutions in these cases take the values
log ^,r in all cases from the curve X, Sheet 21, while for the
Holland boats on the surface log A^ is taken from the X" curve,
it is taken from the Y curve for the submerged condition and is
taken from the same corresponding curve for both surface and
submerged conditions for the Lake boats. Where Holland type is
loaded down by the stern or of such form of hull as to produce
a heavy squat, the values of log A^ shift from X to F exactly as
occurs in the case of destroyers, which squat. At what speed
the values of log A, begin to pass from Z to F (Sheet 21), depends
entirely upon the nmning actual trim and at the present writing,
due to lack of data the approximate speed ratio due to squat
cannot be given.
With the Holland type of ves el the wake appears to be
variable in the surface condition, rapidly increasing with the
speed so that the value of log A„ :'s more nearly correct for
speeds below 9 knots when taken from the F curve, but shifts
gradually to the X curve in passing from about 8.5 to 10
knots, after which it practically remains constant.
The estimates of performance and the comparison with the
actual performance are given in the following tables.
Digitized by LjOOQ IC
128
SCREW PROPELLERS
s
B
W
CO
+
O 00
*o o
w w w CO 'O ^O
d 0« O O^ 00 M
p» «*5 op *P
r*. M ^ 00
1 5"
> «0
*^ •* O •* »o vO 00
■S 8
g O (O Q
W fO *0 *0
fill
?!
W CI *0 <*5 *0 <*>
f) 'O 'O ^O 'O *o
o o o o o o
00
00
8
lO
M
lO
«o
to
lO
M
lO
to
^
m
to
»o
^
to
M
«
w
w
w
«
«
«
f^
o
«>.
w
lO
«
o
■♦
lO
t^ 00
a
M
c«
M
M
«
«
«
8>^>g^^>g,.>8>
ro
«o
to
to
to
to
to
to
*o
to
to
to
to
to
O
o
o
o
o
o
o
M
M
M
M
M
M
M
vO O O
,<?
to «n o^
m
M
«
M
O
t
o
t^
Ok
«
lO
M
M
M
c«
lO
M
C«
M
O
s
O
t^
a
W
»o
«
•^
M
00 "^ .
't
to
a
a 00
t^
m
o
V)
S
o
t^
t«.
to
to
m
4 00
^ o
M
•^
M
"^
to
M
«
o
^
o
V) 00
t^
a
lO
to
to
»o
t^
o
lO
M
»o
M
M
w
«
a
0« 00
00
00
to
V?
>o
«?
00
•?
•*
■*
»o
»o
lO
v>
8"i2
"8
0» 00
00
M
M
M
r*.
a 00
Ov
w
>o
to
O
O
S
&
?
M
M
M
M
1
^
o
M
?
!?
to
to
M
v>
S
M
M
M
R
S
s
M to M
M
2
lO o o o o
00 a 6 M M
« to «n t>. o '^ ^o
to >o t^ 00 o^ o o
00
W « to to
« o^ o
ci lo lO
M ^ 00
« « «
to to to
« CO to
f f ^
t^ 00 0»
« w «
« « «
M M C«
t^ t^ t^
to to to
M M M
t^ t^ t^
CO to to
?f?
??f
8,<
1
00
o
o
to
to
^
1
o
M
•♦
M
M
to
UD 00
w
t>.
to NO
M
M
«
ft
cj
8,
^
to
o o
to
to
s
M
C«
w
M
M
w
>
o
00
00
o
o
to
*^ >o
vO
t^
t^
t^
^
to
M
c«
m
^
^
M
s
to
•*
m
Ifl
*?
to
c«
t^
»
o
M
s,
9
»o
to
M
f
to
M
?
f
to
M
O^ LO VO ^ NO lO
« ^ >0 On <>• ^
u) vO r« 00 On O O
Digitized by LjOOQ IC
ANALYSIS OF PROPELLERS
129
Ot
«
to 00
M
w
00
"8
^
w
M
M
^
Ov
«o
"t
«*a
f
H •«
S
■^
CO
I
lO o
00 NO
S8 ?
?8
o o
CO to
o o
00 to
M CO
t^ M
V) 00
«
«
M
M
to
«o
•8 "8
c/i t^ t^
O 00
H
U
PQ
CO
CO w lo
NO «n
to _ '^
to o» ^
to
to
^
't
^
>o
Ot
«o
«o>o
^
"^J
^
to
fO fO
u
PQ
CO
CO
i4
1
00
to
M
00
On
00
CI
O^NO
M
*"•
^
NO
«
<?
^
H
M
to
t^
"t 00
M
W
t^
o
00
t^
M
t^
t^
00
o^
•
^
*o
«>.
o
•♦
w
«
«o
M
«8
M
*?
«o
00 NO Q
to »o O
«o »o ^
t«. NO *0
ON »0 t^
fO to <*5
eo
o
NO
to
c«
«o
t^
c«
w
Ok
NO
5it
w
to
00 <»
NO NO
ON ON
to to
^"8
to 00
to NO
M to
tN. eo
t«. NO
O O
4 4
o o
•^ CO
n
u
PQ
CO
s
5
n8
c?
ii
u
PQ
CO
> «
> 00
> «*
to
to
NO 00
CO ^
« ON
2.%
ss
«• NO
H M
to
Ok
^ 00
to 00
'^ NO
%
00 t>.
M
R8>
M
!JS
00
M
00 d
00 d.
to
00 6
Digrtized by LjOOQ IC
CHAPTER Vin
CAVITATION
Taylor, in his work on " Speed and Power of Ships," states
as follows concerning this phenomenon:
" Nature of Cavitation. The phenomenon known as cavi
tation has been given much attention, of late years, in connection
with quickrunning turbinedriven propellers. It appears to
have been first identified upon the trials, in 1894, of the torpedo
boat destroyer Daring, which had reciprocating engines. When
driven at full power with the original screws this vessel showed
very serious vibration, evidently due to some irregular screw action.
The propulsive efficiency was poor, the maximum speed obtained
being 24 knots for 3700 I.H.P., and 384 revolutions per minute.
" Mr. Sidney W. Bamaby, the engineer of the Thomycrofts,
who built the Daring, came to the conclusion that at high tluiist
per square inch at which the screws were working the water was
unable to follow up the screw blades, and that ' the bad per
formance of the screws was due to the formation of the cavities
in the water forward of the screw, which cavities would prob
ably be filled with air and water vapor.* So Mr. Bamaby gave
the phenomenon the name of cavitation. The screws which
gave the poor results had a diameter of 6 ft. 2 in., a pitch of 8 ft.
7f in., and a blade area of 8.9 sq. ft. Various alternative screws
were tried, and the trouble was cured by the use of screws of
6 ft. 2 in. in diameter, 8 ft. 11 in. pitch, and 12.9 sq. ft. blade area.
With these screws 24 knots was obtained with 3050 I.H.P.,
and the maximmn speed rose from 24 knots to over 29 knots."
For the Daring cavitation appeared to begin when the screw
area was such that the thrust per square inch of projected area
was a little over 11 lb. per square inch; iij lb. is the figure given
by Mr. Bamaby. " For a time it was thought that the thrust per
square inch of projected area was a satisfactory criterion in connec
130
Digitized by LjOOQ IC
CAVITATION 131
tion with cavitation, and that the limiting thrust per square inch
of projected area found on the Daring was generally applicable.
" This, however, is not the case. Greater thrusts have been
successfully used and cavitation is liable to appear at much
lower thrusts. In one case, within the author's experience, cavi
tation appeared when the thrust was about 5 lb. per square inch
of projected area, the tip speed being about 5000 ft. per niinute,
and in another when the thrust was about 7.5 lb. and the tip
speed about 6500 ft. per minute. There is little doubt that the
prime factors involved in cavitation are: (i) The speed of the
blade through the water, which is evidentiy measured by the
tip ^)eed, and (2) the shape of the blade section."
While Chief Constructor Taylor may be correct in his state
ments as to the prime factors involved in cavitation, it would
appear that as all of the elements of the propeller, namely, pitch,
diameter, projected area and revolutions, and in addition, the
form of the afterbody of the vessel behind which the propeller is
working, each has its influence, it would be difficult, if not impossi
ble, to differentiate between them as to their relative effect. Also,
it is considered that the prime factor in regulating the thrusts that
can safely be used on any particular propeller is the form of the
afterbody of the hull. As the afterbody fines, the thrust may
be increased, and vice versa. Thus Sheet 20 is derived from the
actual performance of numerous vessels, and the values of E.T.^
derived from it for the different standard block coefficients are
considered as those which can safely be used without noticeable
cavitation occurring when no thrust deduction exists. It is
safe to exceed these Sheet 20 thrusts by 20 per cent without the
vibration from cavitation becoming excessive.
The thrusts given on Sheet 20 and on Sheet 22 are as un
affected by thrust deduction.
Where the speed is less than the Basic speed and the entire
conditions of resistance changed from the Basic conditions, the
line of equal condition of effective thrusts with those of the
Basic conditions is shown on Sheet 22. An overthrust of 20
per cent on these conditions may be allowed with safety, as
although this overload will surely put the propeller in the cavi
Digitized by LjOOQ IC
132 SCREW PROPELLERS
tating zone, the vibrations will not be serious and the loss of
power will be slight.
Should the propeller be working in conditions where " thrust
deduction " exists, however, the value of i>hF at which cavita
tion will occur will be much higher than where no " thrust
deduction " exists.
The power necessary to give a certain net e.h.p. without
" thrust deduction " has been shown to be H.P.p. Where
" thrust deduction " exists, this power becomes ir.H.P.p=H.P.j.
If no " thrust deduction " existed the power K.H.'P.p would
deliver a gross eflEective horsepower of e.h.p. i, the value, log
H.P. (Basic)— log ir.H.P.p=Z, being considerably less than log
H.P. (Basic)— log H.P.p and therefore e.h.p.i, would be consid
erably greater than e.h.p.
Now this greater power is spent on the water passing through
the propeller and requires a higher number of' revolutions (i?^),
to absorb it. This increased number of revolutions demands an
increased flow of water to the propeller over that required for any
speed V obtained with H.P.p and Rp revolutions. If this increase
in flow is not provided cavitation occurs. That is, where
" thrust deduction " exists cavitation occurs at much lower
speeds, and nominally lower effective thrusts than where no
" thrust deduction " exists.
Cavitation does not depend upon tip speed because if a vessel
is running under certain load conditions at a certain speed with
out cavitation, if she be loaded down suffidentiy to produce a
considerable diminution of speed for the same engine ix)wer,
cavitation may .ensue and yet the revolutions of the propeller
and consequently the tip speed may be considerably lower than
in the original condition. Should increase in power be met by a
corresponding increase in speed, in other words should the
apparent slip not rise abnormally for increase in power, cavita
tion, in the opinion of the writer, woxild never occur so long as the
effective thrusts were held down. Information has been received
very lately of a vessel steaming at a speed of over 39 knots, the
tipspeeds of the propellers exceeding 17,000 ft. per minute, with
no evidences of cavitation existing.
Digitized by LjOOQ IC
CAVITATION 133
As to the influence of blade section on cavitation, should the
section of the blade be so bad as to prevent the water engaging
and leaving the blade freely, false cavitation may be produced
by excessive eddying in the bladesection wake. Further,
should the section be of normal form but abnormally thick in
comparison with the blade width, the actual pitch will be in
creased very considerably above the nominal pitch, the basic V
will be increased and the speed factor viV ior any speed v and
load factor e.h.p.4E.H.P., will become smaller, thus bringing the
propeller nearer the cavitating point for any value of e.h.p. ^ E.H.P.
There is also a phenomenon encountered in the cases of vessels
subjected to great variation of resistance with practically con
stant power in the engines which is analogous in its effects to
cavitation. This condition is illustrated on Sheet 22.
On this sheet are shown two curves marked " Lower Limit of
e.t." and " Curve of Critical Thrusts, ET." This latter curve
will be called the curve of critical thrusts.
Propellers as designed for any particular resistance of ship
should usually fall between these two limiting curves, and the
curve of performance of the vessel at the hull condition corre
sponding to the resistance used in the design would then fall
between these two limits.
Now, suppose the vessel to be a towboat or a slowspeed,
lowpowered merchant ship, both of which are subject to great
variations in loading.
Suppose that the propeller be designed to deliver the neces
sary e.h.p. for 10 knots, at a load factor of e.h.p. 7 E.H.P. = .3
and at a speed factor t;7 F = .74 (See Sheet 22). This point will
then fall on the curve marked " Lower Limit of e.t.'' The cor
responding value of V will be 10^.74 = 13.65.
Assuming that the value of K=i.^, and of the basic slip
6 per cent, the LH.P. necessary for the speed will be
LH.P.< = jK: X I.H.P.P = LH.P. (Basic) ^lo^XK
= LH.P. (Basic) ^ 10 «^*«X 1.3,
and the apparent slip =
^^ I.H.P..XF' _ I.H.P..xir6?
^"'^^I.H.P.Xs'"^ ^ I.H.P.Xio' •
Digitized by LjOOQ IC
134 SCREW PROPELLERS
Now, suppose the vessel to be so loaded down or the tow
boat to take such a tow that with the same e.h.p. a speed of only
7.5 knots can be realized. As the load is gradually increased
and the speed decreases with this increase, the propulsive effi
ciency of the propeller remains practically constant while the
apparent slip increases slowly until the limit marked " Curve
of Critical Thrusts, £.r." is reached. As the load is still further
increased and the speed factor v^V falls below the value on
e.h.p.hE.H.P. = .3, corresponding to E.T., a new factor enters
into the power and slip equations due to a dispersal of the thrust
colmnn flowing from the propeller being produced. This dis
persal of the thrust column makes necessary an augmented flow
to and through the propeller and this increased demand for supply
carries with it an augment of power and of revolutions. The
inverse of these augments are shown as curves on Sheet 22,
»' m"
The new value of the power required to deliver the original
e.h.p. becomes
or
LH.P.,= 1.3 XLH.P. X (lyY ^o"^'
When V has dropped to 7.5 knots, vr 7 = .549 and the corre
sponding point on the e.h.p. 4 E.H.P. = .3 ordinate falls on the
Therefore,
I.H.P.4=i^Xl.H.P.5io»,
and the equation for apparent slip becomes
marked *' Curves
XH.P.,XF«' i.3Xl.H.P.Xi3.6s'
5 = 06 = S =:z~ ^ .
LHP.Xz;^ .8XI,H.P.X 7.3X10'^^
This new value Ki=^Kx(r=;^) =^ may be called an
\ii.i ./ .8
augmentation of the Basic thrust deduction.
Digitized by LjOOQ IC
CAVITATION
135
The new value of the propulsive coefficient, which was orig
inally
_ e.h.p.
p.c.=
has now become
KXI.H.1>.,'
e.h.p.
D.C. = =
^ ii:iXLH.P.p
e.h.p.
KX
\e.t)
XI.H.P.P
Cavitation depends upon after body, projected area ratio,
effective thrust and thrust deduction and no other conclusion
can be arrived at from the evidence at hand.
In support of this contention the cases of three identical ves
sels, identical as to hulls but fitted with different propellers, is
here given: The effective horsepower curve has been derived
from the performance of that vessel where there is absolutely
no doubt that cavitation did not exist, and the performances of
the other two vessels were then estimated from this derived
curve, although the third one of the vessels ran at lo tons heavier
displacement than the other two.
Problem 24
Ship
Propellers. .
Blades
P.A.^D.A.
D
P
T.S
R
PXR
Slip B.C.,
15
V
I.T.D
I.H.P.
P.C...
E.H.P.
Paul Jones
2
3
•43
7'.42
10'. 67
9110
390.8
4170
.31
.829
3404
.678
10668
.60
6401
Perry
2
3
.275
7'. 42
10'. 833
6100
261.7
2835
.31
.845
23.64
3.22
344S
.694
2391
Preble
2
3
.358
7'. 42
10'. 42
7800
334.6
3487
.31
.838
28.84
S.oi
6592
.647
426s
The estimates of e.h.p. and of performances, basing these upon the
values of e.h.p. derived from the performance of the Paul Jones, will
now be made.
Digitized by LjOOQ IC
136
SCREW PROPELLERS
PAUL JONES
I.H.P^I.H.P.p
i
.h.p.
.H.P.
e.h.p.
V
700
1. 183
073
467
16
1200
.949
123
787
18
3000
.727
201
1287
20
3150
.530
309
1978
22
4600
.36s
45
2881
24
S300
.304
51S
3297
25
6150
.239
S84
3738
26
6800
.196
6SS
4193
27
7350
.162
699
4474
28
7600
.147
722
4622
28.S
K^i
PERRY
2,
I.H.P.d =
= I.H.P.p
rj
V
e.h.p.
E.H.P.
Est.
Actual.
Actual.
Cavit.
e.t. = i.isE.T.
.1954
.734
636
600
.677
.1699
3293
.500
1089
995
.761
.2863
5381
.284
1791
1700
.846
.4679
.8272
.088
2813
2750
.931
•7183
205
+ .083
4171
4SOO
T.OIS
1.048
379
+ .145
481 1
5500
1.058
1. 199
564
+ .200
5460
6500
1. 100
1.36
754
+ .254
6183
7600
1. 142
1.525
871
+ .283
6610
8750
1.18s
1.627
933
+ .2981
6844
9300
1.206
1. 681
Digitized by LjOOQ IC
CAVITATION
PREBLE
137
Z
I.H.P.d =
=I.H.P.p
v + V
e.h.p.
E.H.P.
Est.
Actual.
Actual.
Cavit.
e.t. = i.isE.T.
.1095
1. 000
659
IOC»
.555
•0952
.1846
.759
1 148
1500
.624
.160S
.3015
.540
1901
2250
.694
.2622
.4638
.353
2924
3400
.763
.4033
.6754
.180
4355
4800
.832
.5873
.7729
.116
5047
5500
\867
.6721
.8765
.06
5742
6150
.902
.7622
.983
.004
+
6532
6750
.936
.8548
1.049
.022
+
693s
7200
•971
.9123
1.084
.038
7195
7400
.988
.9423
The Preble was run at a heavier displacement, with sh'ghtly
rougher bottom, and in a little worse weather conditions than the
Paid Jones and Perry j and these differences of conditions account
for the differences between estimated and actual powers for that
vessel.
Turning to Fig. 8, a curve of percentage increase in power for
the Perry is shown due to the effect of cavitation. This curve is
e t
based on values of •=^ as abscissas, e.t. being the actual values
of effective thrust, while E.T. are the Basic design conditions of
this thrust. The estimate of power given in the table is without
the effect of cavitation taken into account.
In order to estimate accurately the factor of increase to use
for cavitation, and also as a guide to prevent entering the cavita
tion range, Sheet 22 has been prepared. This sheet has as ordi
Digitized by LjOOQ IC
138
SCREW PROPELLERS
1.1 L2 1.3 1.4 1^ 1.6 1.T
Fig. 8.— Curve of M for Augment of Power Due to Cavitation.
Digitized by LjOOQ IC
CAVITATION 139
nates values of — , while the abscissas are values of J^' P* The
diagonal lines show the varying values of — and of ''%' for
e t . e t .
values of ^ttp from i to 1.75. The line of =^^==1, is that
where the actual effective thrusts are equal to the Basic effective
thrusts of the design condition. Cavitation of the suction
column, however, does not begin until E.T. equals approxi
mately 1.15.
When this condition of thrust is reached, the actual values of
Z, instead of following the mathematical curve of Z, Sheet 21,
pass off from it approximately on the tangent to the curve at this
point.
The equation to the tangent is
Tan 6= — /', \ where 6 is the angle made by the tan
/ e.h.p. \
\E.H.P./
gent with the axis of abscissas.
The new values of Z, which denote as Zi, may also be cal
culated as follows:
'Calling M the power correcter as ascertained from Fig. 8,
e t
for the value of i^ttf", ^^^ equation for power becomes
LH.P.p = M Xl.H.P.^io^ or
Log I.H.P.p = log I.H.P.+log M ±Z,
therefore Zi =logAf itZ, Z being additive when 'P* is greater
than unity.
The values of ''\1 , corresponding to these values of Zi,
should be used as abscissa values of Sheet 22, in ascertaining the
e.t.
gross values of
E.T.
Digitized by LjOOQ IC
140 SCREW PROPELLERS
Effect of Cavitation on Revolutions
In estimating the revolutions where cavitation occurs, the
effect of cavitation is exactly the same as that of " thrust deduc
tion." While the power increases, the revolutions increase with
it as in " thrust deduction " so that in the equations for apparent
slip
'^^ LH.P.Xz;^ "^^ •^lo^Xz;^'
the value of i.h.p.p corrected for cavitation =AfXi.h.p.p, and the
value Zi instead of Z must be used.
On Fig. lo, are shown the values of power and speed plotted on
revolutions as abscissas, while on Fig. 9, are shown the values of
^ plotted on '\I as abscissas, while again on Fig. 10, are
V lli.jl.ir.
e t
shown the points .where =^j equals i.o, i.i, 1.15 and 1.225.
Attention is called to the erratic character of the Perry s curves
e t
of power and speed after passing this latter value of =^.
iii.l.
e t
The indications from Fig. 9, where =7^ = ii5 coincides with
very moderate vibrations, i.i, to light vibrations, and 1.225 ^
moderately heavy vibrations were exactly realized on trial.
I I. Effect of Change of Load on Cavitation. Taking the
case of the Perry as shown on Fig. 9, it is seen that — crosses the
Ime of :^7ir=i at a value of ^ = .96 and of 5''^ =.96. Now
suppose the load on the vessel be decreased so that for the same
effective horsepower the speed be considerably increased. The
immediate effect upon the performance is to raise the curve of ^
so that it crosses the Ime of ^^ = i, at a higher value of 5.VP'
Digitized by LjOOQ IC
CAVITATION
141
\
\
\
V
A
\\
\
»•
\,
\
\
\v
A
A
U
9i
o
\
s
\
\
vj
\
. ^A
\
\
\
\l\w^
S
00
\,
\
\
m
^\
V
1^
\
\
K
Mo
V
^
\
to
\.
^
?
V
\^
L
k
\
^^
s,^\
A
Jy
\^
\
•^
^
k
\
\
V
s \
?$
.00
k
\
V
\M
\^
w
I
n
\
V
\\
w
^
^
M
w
k
vv
^
1
\
\>
^
1
1
I
■*
Kl
X
\\
^
1
\
roo»
ff\
N
k
^'
^
k
•
\\
\%
t^
$^
1
1
v
\l\
^
^
i
^
u
A
^
"^A
k\
^
^
k
'«Y
^
\
\^
^
\
^
i'
3
2
2
2
3
•A
05
r<VJ<
)OIBO
3
«2
»«.
"^
""^
^
=J
\
Fig. 9.~Curvesof vrV and e.h.p.^E.H.P. for Destroyers Paul Joms, Perry
and Preble.
Digitized by LjOOQ IC
142
SCREW PROPELLERS
29
1
1
28
10,000
1
1
27
R
'l'::.
9
^26
§
jii;
9,000
Il
1 Ih
(8 25
li
Hi
r4
24
8,000
H
■ 1
1?
i^'
s
23
■
1
1.0*
;: :;
IB
22
:g f&
• K
^^y
7,000
:
^P
■ fffH
Nff
m
81
t .
^pt
wf^
;g :;:
1
:
1^1
20
:
1
wi m
.
'{>lli.[m
4.0
^^
^^Imrmr'
H
:£>#!:
p^m::
6,000
.2
ft
f::
pp^^l
1
K
^^^^'
1
flWfjfe
P^B^
t: ^^
^ffip
^fflftffi e:
4,000
1
8
g;;ip
^ ^.t.
5
=;
i'
S^'ii
^ E.T.'
[ §
;i
i:
'Hie.
^> 11
■1 1
1^
i'
:;; E
T.' ^'^
8,000
1 1.
P
'■1
"B.t. . .1
il
e.t; ^
H ::
■' Ifiij
:: ::;
■M
i: M\
m
1,000
S^leoFB
ev J.
230 ;N0 250
270 )g80 290 300 810 320 830 840 . 850 360 870
Fig. io. — Curves of I.H.P.revolutions and vrevolutions, Destroyers Paul Jones,
Ferry and Prebk,
Digitized by LjOOQ IC
CAVITATION 143
than before and the entry into the cavitating range is delayed.
Should the ship be loaded heavier than at first, the opposite
effect occurs, cavitation is produced earlier.
" To lighten the load on a vessel with a given propeller delays
cavitation while to increase the load expedites it"
2. Effect of Chan£;e of Projected Area Ratio of the Pro
peller on Cavitation. The results accompanying change in
projected area ratio are shown very dearly by the performances
of the Paid JoneSy Perry and Preble.
The Perry with a projected area ratio of .275 is on the verge
of cavitation with 3500 I.H.P.; with a projected area ratio of
.358, the propellers of the Preble do not reach the verge imtil
6300 I.H.P. is being developed. The Paul JoneSy with a pro
jected area ratio of .43, has not even approached the verge.
" To increase the projected area ratio of a propeller, pitch and
diameter remaining constant, prodtices a delay in cavitation and in
dispersal of the thrust column while to decrease the projected area
ratio expedites them."
3. Effect of Change of Pitch, Diameter and Developed Area
of the Propeller Remaining Constant, on Production of Cavita
tion. To increase the pitch under these conditions reduces the
projected area ratio and the effect is similar to that caused by a
reduction of projected area only, although the effect is more
intensive, as it also lowers the value olv^V and brings the pro
peller much closer to cavitation. To lower the pitch produces
the opposite effect, therefore, generally speaking, —
"To increase the pitch of a given propeller tends to expedite
cavitation and dispersal of the thrust column while to decrease the
pitch tends to delay them."
4. Effect of Reduction of Diameter, the Pitch Remaining
Constant, on the Production of Cavitation. The general effect
of such a change is to lower all the Basic conditions of the pro
peller but the Basic E.H.P. will be lowered more rapidly than
V
the Basic V so that while the factor — becomes higher, the factor
'^ has increased more rapidly than — and the effect, there
Digitized by LjOOQ IC
144 SCREW PROPELLERS
fore, brings the propeller to the verge of cavitation earlier than
in its first condition, therefore, —
" To decrease the diameter of a propeller y the pitch remaining
constanty tends to produce earlier cavitationy and dispersal of the
thrust column.^^
5. Effect of ''Thrust Deduction" upon the Production of
Cavitation. It has already been pointed out that the value of
the power factor Z for any condition where " thrust deduction '*
does not exist is given by the equation
Zi = logLH.P.logLH.P.„
while should a " thrust deduction *' factor K be introduced, the
value of Z becomes
Z2 = log I.H.P.log (ii:i.H.P.p)=log LH.P..log I.H.P.^
and the value of Z2 being less than the value of Zi, the
value of the gross effective horsepower corresponding to Z2
will be greater than that corresponding to Zi and ( j\^ )
will be greater than ( ' '^ ) , while the values — will be the
\il«.ri.P./i V
same in both cases. The introduction of K, therefore, results in
shifting the curve of — horizontally to the right and causing it to
e t
intersect the line of =r7f=i> at a point corresponding to a
reduced value of — and of .^^^ below those corresponding to
the intersection when no thrust deduction existed, therefore, —
The existence of thrust deduction in addition to increasing the
power necessary for propulsioUy reduces the speed and net effective
thrust at which cavitation will occur.
6. Effect of " Wake Gain " upon the Production of Cavita
tion. The effect of " wake gain " upon speed is the same as that
of decrease in resistance. While the effective thrust e.t.fE.T.
is obtained from the model tank curve of speed, e.h.p., the actual
speed, due to the wake gain, at which this value of e.t. occurs
will be considerably higher than the tank speed, therefore, —
Digitized by LjOOQ IC
CAVITATION 145
" Where the htdl of a vessel is of such underwater form as to
produce a heavy wakey the speed at which cavitation and dispersal
of the thrust column occurs will be higher than if no wake existed, on
account of the * wake gain.^ '*
7. Effect of Insufficient Tip Clearance between Propeller
and Hull on the Production of Cavitation. Experience and the
analysis of trials of numerous vessels lead to the conclusion
that—
*' Where insufficient tip clearance exists between the propeller
and the htdl, increases in effective horsepower and speed of vessel
are accompanied by a gradual increase in the thrust deduction,
which latter increase produces earlier cavitation.^^
8. Effect of Blade Sections 09 the Production of Cavitation.
Where blade sections are very thick in proportion to their width
but their bounding lines are of such form as to give a free flow
of water around the section with no tendency to form eddies,
'* the abnormal thickness produces an acttuU pitch considerably
greater than the nominal pitch and thus tends to expedite cavitation.^*
Where blade sections are very thick and their bounding lines
of such form as to produce eddying of the water at moderate to
high revolutions, the thrust per revolution at the lower revolutions
will be increased slightly due to the higher actual pitch produced by
the thick section and the power required per revolution will increase
in greater proportion than the effective thrust. As the blade speeds
increase eddies begin to form and this formation of eddies is accom
panied by a still further exaggeration of power and all of the phe
nomena of cavitation, and this will occur at lower thrusts and speeds
than would be the case where the sections were normally fine.
Digitized by LjOOQ IC
CHAPTER DC
DESIGN OF THE PROPELLER
Computations for Pitch, Diameter, Projected Area Ratio
AND Propulsive Efficiency
In computing the prindpal characteristics of a propeller,
these being the pitch, diameter and projected area ratio, the fol
lowing factors must be considered:
1. The form of the after submerged body of the hull of the
vessel to be propelled.
2. The position of the propeller relative to the hull.
3. The effect of the hull lines and position of the propeller
in modifying propulsive eflSciency.
4. The resistance of the hull to motion through the water at
any given speed.
These four points are covered by Sheets 17, 18, and 19 and in
some cases by the model tank from which the curves of effective
(towrope) horsepower are obtained.
In other cases the model tank curves are missing, the tow
rope power is estimated and either this estimate or the estimated
I.H.P. or S.H.P. for the speed desired is supplied.
The problems facing the designers of propellers may, there
fore, be divided into two classes —
A, Problems of Sufficient Data. In such problems full data
of the hull together with the model tank curves of effective
horsepowers are provided.
B. Problems of Insufficient Data, In these problems full
hull data may be and usually is provided but either an estimate
of the effective or of the indicated or shaft horsepower necessary
for the desired speed of ships is provided.
These two classes of problems may each be subdivided into:
C Problems of Basic conditions (Full Diameter).
D. Problems of reduced load {Reduced Diameter).
146
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER 147
In Dy the reduction of load may be either positive or negative,
that is, the propeller may be designed to deliver less than the
Basic condition of E.H.P. or it may be designed to deliver a load
greater than the Basic condition of E.H.P., while the designed
speed V may be greater or less or equal to the Basic speed V.
PROBLEM A. SUBDIVISION C
Form for Computation
Threebladed Propeller
(i) P. A. ^ D. A. = Different abscissa values taken from Sheet 20.
(2) T.S. = Tipspeeds corresponding to each value of P.A.iD.A.
used. Sheet 20.
(3) Slip B.C. =Slip Block Coefficient of vessel. Obtained from Sheet 17.
(4) 15 « I Apparent slip for P.A. ^D.A. and Slip B.C. Sheet 20.
(5) I.T.i> = Indicated thrust per square inch of disc area for each
value of P.A.^D.A. Sheet 20.
(6) E.H.P. = Effective (towrope) horsepower for desired speed.
Obtained from model tank curve and includes all
appendages.
(7) P.C. = Propulsive coefficient for P.A.5D.A. Sheet 20.
(8) I.H.P. = E.H.P. ^ P.C. = Indicated horsepower required to deliver
E.H.P., without " thrust deduction."
(9) K = Thrust deduction factor for Slip B.C. and for type of
vessel and location of propeller. Sheet 19.
(10) K I.H.P. = Total indicated horsepower required.
(11) V = Desired Speed for which E.H.P. is necessary.
(12) PxR = {V (Knots) X 101.33 or V (Miles) X88) ^(i 5) =Pitch
XRevs. __^
(13) D =V(29i.8Xl.H.P.)i(I.T.z>XPXi2)=Diameter of Pro
peller.
(14) P ^(ttDxPxR) ^T.S. = Pitch of the propeller.
(15) R » T.S. ^ ttD = Revolutions of the propeller.
Should the propeller be a fourbladed one, P.A.^D.A. = ^ the total
projected area ratio. The data (2), (4), (5), are taken from Sheet 20 for
P.A.^D.A., while the value of P.C. (7) is taken for the full value of the
projected area ratio.
The value of D becomes
2> = V(252.4iXl.H.P.)5(I.T.i>xPXi2).
Should the propeller be a twobladed one the data (2), (4), (5) are taken
for f the actual projected area ratio while P.C. is, as before, taken for the
actual. The equation for diameter becomes
^ = ^/(389XLH.P.)^(I.T.I>xPXi^)
Digitized by LjOOQ IC
148
SCREW PROPELLERS
In illustrating the above type of problem, the effect of change in speed
due to change in resistance and also the effect of an error in the Slip B.C.,
will be shown.
Problem 25
Statement: Hull Slip B.C. = .5. E.H.P. = iooo. Single screw.
The vessel is so loaded at first that a speed of 20 knots an hour requires the
above value of E.H.P. Later the vessel is so lightened that a speed of 35
knots can be made with this same E.H.P. Find the diameter, projected
area ratio and pitch of the propellers for the two conditions, the desired
revolutions being assumed in each case as 600 per minute.
SOLUTION
P.A.f
T.S..
15.
I.T.i>.
D.A.
E.H.P.
P.C...
I.H.P. .
K
.2
4200
.884
1.88
1000
.709
141 1
I
.3
6650
• .88
374
1000
.682
1466
.4
8580
.869
6
1000
.619
1616
I
•5
10550
.849
8.74
1000
•554
1805
•55
1 1830
.832
10.3
1000
.526
1901
I
.6
13550
.807
"95
IOCX>
•525
1905
I
V
PXR....
D(Fett).
P(Feet).
Revs
20
2293
9.772
16.76
136.8
20
2303
7.048
7.668
300.3
20
2332
5. 804
4.956
470.5
20
2387
5.025
3.572
668.3
20
2436
4.702
3.042
800.8
20
2511
4.304
2.506
1002
v....
PXR.
D
P
R
35
401 1
7.338
22.17
181
35
4030
5.328
10.15
397.3
35
4081
4.388
6.557
622.5
35
4177
3.798
4.725
884.1
35
4263
3.555
4.024
1059
35
4395
3.253
3.315
1326
Plotting these results as shown on Fig. 11, the following propellers are
obtained for the two conditions:
V 20
D 5.25
P 392
P.A.5D.A 47
Blades 3
I.H.P.d=I.H.P.p 1743
P.C 5737
E.H.P 1000
R 600
35
4.42
6.85
.38
3
1600
.625
1000
600
E.H.P. constant,
Increase in Speed
Decreases Diameter
Increases Pitch
Decreases P.A.5D.A.
Increases Eff . of Prop.
Digitized by LjOOQ IC
DESIGN OF THE.PROPELLER
149
21
g,UQG
^
17
16
15
U
13.
\2 a
a
11 'I
ID.
\
•d R^i•tfi.
1,400
1,300
1.200
1,100
1,000
000
800
JQO
COO
JOO
JOO
goo
gou
too
Fig. II. — Curves of I.H.P., Z>, P, and i2, on P.A.iD.A. as Abscissas for
Diameter, Basic Condition Propellers at 20 Knots and at 35 Knots.
FuU
Digitized by LjOOQ IC
150 SCREW PROPELLERS
Should thrast deduction exist, that is, should K be greater than unity, the
actual power required will be
2?xLH.P.p=I.H.P.d,
while the revolutions would be obtained as follows:
Apparent Slip ==s^KS,
15
Revs.=^X
^KS'
These corrections apply both for values of K exceeding unity and below
unity, that is for " thrust deduction " and for " wake gain."
Should an error have been made in the estimate of Slip B.C., the fol
lowing analysis will indicate the effect on the actual performance of the
propeller:
Taking the 20knot condition, but suppose the correct slip B.C. to be
.4 instead of . 5 as used in the computation.
P.A.4D.A 47
Blades 3
D 5.25
P 3.92
T.S 9900 Sheet 20
R 600
PXR 2352
SlipB.C 4
I S 837 Sheet 20
V 19.43
ViV 1.029
LT.D 7.9 Sheet 20
I.H.P 1743 Sheet 20
P.C 5737
E.H.P 1000
log ^r=log (F^).. 3.85 Sheet 21
log 4t. ^log (/) 3 .89 Sheet 21
oLH.P.F^
^^•^LiLRi^ ^^^7
^^{fxh^) ^7.
I
Digitized by Lj.OOQ IC
DESIGN OF THE PROPELLER 151
Such an error produces no change in the power required for
the speed unless the value oi viV for the load factor becomes
lower than that corresponding to E,T. for this same load factor,
on Sheet 22, or the change be such as to produce a change in
the value of K, but increases the revolutions above those calcu
lated. Should the slip B.C. be higher than that used, the actual
revolutions will be lower than the estimated.
Problems A. Subdivision D
Such problems are those which are encoimtered when the
suitable propellers for vessels of low to moderate speeds, revolu
tions and power are being sought. With such conditions the
Basic conditions of design are far in excess of the actual conditions,
and the actual data of desired performance must be so handled
as to bring it up to the Basic conditions before the work of cal
culation can be xmdertaken.
Method of Design
Assumption of Diameter , Load and Speed Factors to find
Projected Area Ratio, Pitch, Revolutions , Power on and Effective
Power delivered by the Propeller.
By inspection of Sheet 22, it willl be seen that there are
shown two limiting curves of effective thrust and several curves
of thrust marked for various t3^s of vessels. The ordinates of
these curves are values oiv^V while the abscissas are values of
e.h.p.^E.H.P.
What occurs above the upper limiting curve is not known,
but between the limits the efficiency of any propeller for any
particular value of e.h.p.^E.H.P. remains practically constant
while below the lower limiting curve the efficiency falls very
rapidly as the value olv^V decreases.
The intermediate curve is derived from the performances of
some very successful vessels and is given as a guide to locate the
Digitized by LjOOQ IC
152 SCREW PROPELLERS
desired propeller for any given type of vessel. For instance,
heavy and fullbodied merchant ships should be located between
the upper curve and the second one from it in order to hold suf
ficient range to take care of deepload and adverse weather
conditions. Very fine vessels such as destroyers and speed boats
when designed for high power and speed fall in this same range.
Hydroplanes may, and usually do, plot far above the upper
curve. Vessels of nearly constant condition of loading and of
comparatively low revolutions for the power, should plot on or
near the second curve from the upper limit one, that is vessels
such as the U.S.S. Texas, Delaware, Pennsylvania, with revolu
tions from 125 to 220 for powers ranging from 25,000 on two
shafts to 30,000 on four shafts, all plot in this range, while the
Arkansas, with 330 revolutions for 28,000 S.H.P. on four shafts,
plots below the intermediate curve, and the Utah and Florida
for the same revolutions and power plot almost exactly on the
lower curve or curve of critical thrusts.
It might be inferred from Sheet 22, that any load factor
can be used in the design of the propeller without regard to
either the slipblock coefficient of the vessel or to the speed of
ship, but such is not the case. The three factors tie together
and for a vessel having a given slip block coefficient and designed
for a certain given speed there exists a load factor for design
which must not be exceeded if estimated propulsive efficiencies
are to be realized. The curves of approximate maximimi and
minimum values of e.h.p.^E.H.P. for different slip block coeffi
cients from .2 to i.o, varying by .1, are given on Sheet 22B, of
which the abscissas are speeds, v, and ordinates, e.h.p.^E.H.P.
In selecting values of e.h.p. ^E.H.P. to use in the calculations,
they should usually be taken between these maximmn and
minimum limits for the designed speed and slip block coefficient,
but the maximmn values may be exceeded by fully 25 per cent
with safety.
The equations for finding the diameter of the propeller have
already been given, but they will be given again and also an
additional one in terms of effective horsepower and effective
thrust per square inch of projected area ratio.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER 153
These equations are
For 2 Blades:
„^ / 389XI.H.P. _ l 3.84Xl.H.P.X(i5)
>'D.A.
For 3 Blades:
I.T.^XF
3.84XE.H.P. ;
^■^•XE.T.,XF
„^ hg8.iXl.H.P' ^ / 2.88Xl.H.P.X(i5)
yLT.oXPXR \
I.T.flXF
/ 2.88xE.hT~
/^XE.T.,XF
For 4 Blades:
jj^ /252.4iXI.H"!r _ /2.49iXl.H.P.X(i5) '
^ / 2.49IXE.H.P. .
^j^xe.t.,xf'
PA ^
in which rr^ equals  times for the twobladed, equals for the
D.A. 2 ^
threebladed and equals  times for the fourbladed, the pro
jected area ratio of the propeller, E.T.p, I.T.z>, and (i5)
being those corresponding to P.A.4D.A. of the equivalent
threebladed propeller.
From the above equations, Z), V and I.H.P. or D, V and
E.H.P. being known, the value of I.T.2>^(I— 5) in the first case
and of (P.A.5D.A.)XE.T.p, in the second case, can be obtained:
I.T.x,i(i5)=2^^^, 2 blades;
2.88I.H.P. , , , 2.401 1.H.P. . , ,
D^XV ' ^ ' = p2xy ' 4 blades;
Digitized byCjOOQlC
154
and
SCREW PROPELLERS
(P A sDA.) XE,T.p = 3 • p2 X f'^' > 2 blades;
_ 2.88E.H.P.
D^XV
2.491 E.H.P
D^XV
, 3 blades;
. 4 blades.
Values of I.T.l>^(I5) and of (P.A.^D.A)XE,T.p are
given in the accompanying tables for different values of slip
block coefficient and of projected area ratios and are plotted as
curves on sheets 23 and 24.
Having obtained the values of P.A.^D.A. from the values
of I.T.x>5(i5) or of (P.A.^D.A.)xE.T.p, reducing them to
i P.A.5D.A. for fourbladed and to f P.A.^D.A. for two
bladed propellers, the propulsive coefficient corresponding to
these total projected area ratios, the tipspeeds and (i— 5)
values corresponding to the basic P.A.^D.A. can all be obtained
from Design Sheet 20, and the problem solved, following the
form given on page 156:
TABLE OF ^XE.T.p
P.A.+D.A.
Slip B.C.
.3
.25
.3
.35
.4
.45
.5
.55
.6
.65
.9
1.367
2.014
2.651
3.287
3.905
4.568
5.19
5.891
/.049
8.172
85
1.383
2.037
2.682
3.322
3.951
4.621
5
263
5.969
7.146
8.249
8
1.399
2.061
2. 711
3.361
3.989
4.667
5
309
6.029
7. 211
8.368
75
1. 417
2.087
2.74
3.405
4.037
4.733
5
38
6.125
7.312
8.471
7
1.433
2. 112
2.773
3.446
i.090
4.791
5
459
6.203
7.407
8.555
65
1.452
2.138
2.806
3.488
4. 141
4.845
5
527
6.282
7.496
8.682
6
147
2.164
2.84
3.523
4.187
4.906
5
579
6.356
7.595
8.792
55
1.485
2.188
2.872
3.571
4.240
4.951
5
657
6.431
7.689
8.90s
5
1.498
2.208
2.902
3.607
4.273
5.008
5
703
6.501
7.774
9.021
45
1. 514
2.231
2.932
3645
4.319
5.067
5
764
6.58
7.846
9.127
4
1.526
2.251
2.966
3.683
4.369
5.128
5
834
6.653
7.952
9.236
35
1.549
2.28
3.OCI
3 723
4.422
5.189
5
905
6.728
8.044
9.348
3
1.565
2.31
3.037
3772
4.475
5.253
5
978
6.813
8.148
9.476
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
165
TABLE OF I.T.
D5(l
S)
Slip B.C.
P.A.5D.A.
.2
.25
.3
.35
4.
.45
.5
.55
.6
.65
9
1.928
2.865
3.888
5042
6.309
7.798
9.368
II. 2
13.43
15.57
.85
1.95
2.898
3.933
5.095
6.383
7.886
9.50
"35
13 61
15 71
.8
1.973
2.931
3.974
5. 155
6.445
7.963
9584
11.46
13 74
15 94
•75
1.998
2.969
4.017
5.222
6.522
8.077
9. 711
11.65
13.93
16.14
.7
2.022
3004
4.065
5.285
6.608
8.176
9.854
11.79
14. II
16.30
.65
2.048
3.041
4. "5
5. 349
6.689
8.268
9.977
11.94
14.28
16.54
6
2.073
3 078
4.165
5.415
6.765
8.372
10.07
12.08
1447
16.75
55
2.094
3. 112
4.212
5.476
6.849
8.448
10.21
12.23
14.65
16.96
5
2. 113
3141
4.255
5.533
6.903
8.547
10.3
12.36
14.81
17.18
45
2.135
3.173
4.299
5.59
6.977
8.647
10.41
12.51
14.95
1739
4
2.152
3.202
4.349
5649
7.059
8.75
10.53
12.65
15.15
17.59
35
2.185
3.244
4.40
5709
7143
8.856
10.66
12.79
1532
17.81
3
2.208
3.286
4 452
5.785
7.229
8.964
10.79
12.95
15.52
18.05
Suppose all revolutions obtained are higher than those
desired, while the projected area ratio has decreased to and
below .25 for the threeblade basic propeller. Investigation of
Sheet 22 reveals that so long as the ratio of e.t. to E.T. remains
constant the projected area ratio will remain constant but that
as we pass down this line of constant ratio of e.t. to E.T., with
constant diameter of propeller, the pitch of the propeller will
increase and the revolutions decrease. Therefore, taking
P.A.^D.A. constant as derived from the first step, and either
equal to .25 or to that value of P.A.7D.A. which by inspection
will result in a good ratio ol P^D without bringing the pro
peller to plot on Sheet 22, too dose to the curve of critical thrusts
as to so plot, in the cases of vessels subjected to great variation of
load conditions, might bring the thrusts greater than the critical
thrusts xmder heavy load conditions and an excessive falling off
in propulsive efficiency would result.
The form for the computation follows on page 157.
Digitized by LjOOQ IC
156
SCREW PROPELLERS
SCREW PROPELLERS
FoKM FOR Computation. e.h.p., Speed and Revolutions Fixed.
S.H.P41 Unknown.— First Step
I.H.P.d or
cJl.p.^E.H.P. (assumed).
c Ji.p
e.h.p.
E.H.P.=c.h.p.^
E.H.P.'
^'^Efet^Sr.) («»»")■
CXE.H.P.
(Pj\.^DA.)XE.T.p ^^^
Note: Values of C=3.84, 2.88, 2.491, for 2, 3, and 4 blades.
P.A. SD.A. for ^ XE.T.P (from Sheet 24).
f P.A.5D.A. for 2 blades
t P.A.SD.A. for 4 blades
P.C. for total ^
D.A.
LH.P.=:E.H.P.JP.C
Z for e.h.p.^E.H.P. (Sheet 21)
LH.P.P
SlipB.C
K for Slip B.C
I.H.P4f
S.H.P.d=LH.P.dX.92
I 5" for P. A. 5D.A
T.S. for P.A.5D.A
irXZ?XFX 101.33
T.S.X(i5)
Now suppose that the value oi viV were such as to plot on Sheet 22 for the
assumed values of e.h.p^E.H.P., below the curve of critical thrusts, then for each
of the assumed values of e.h.p.rE.H.P. we have the following values of
(E.r.^e.t.)'.
I.H.P.tf=LH.P.pX^*.
logAv
log At
A.H.P.dXAv
To Find Revolutions
s=S
LH.P.X^/
p., PX101.33
^~i>X(i.) •
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
157
FORM FOR SECOND STEP
Total Proj. Area Ratio (Constant) . .
' I Total for 2 blades
PA.^D.A.= Total for 3 blades
. f Total for 4 blades
P.C. for Total Proj. Area Ratio
e.t.■^E.T. (constant)
eJi.p.4E.H.P. (variable)
et. __j e.h.p.
Ffor
and
E.T. E.H.P. ;••
V (designed speed, knots)
e.h.p. (designed eff. horsepower)
V^v^iviV)
E.H.P.=e.h.p.^(e.h.p.^E.H.P.)
LH.P.=E.H.P.^P.C
S.H.P.=I.H.P.X.92
T.S. =Tipspeed for P.A.^D.A
Slip B.C. (as in First Step)
15 for P.A.JD.A. and Slip B.C
D= Diameter (Fixed by First Step)
ioi.33XirXyXZ> _ 3i8.3XKXZ>
T.S. X (16) T.S.X(i5)""
IC as in First Step
Z for e.h.p.5E.H.P
LH.P.p,S.H.P.p=(I.H.P.,S.H.P.)Mo^ . . .
I.H.P.d, S.H.P.d=ICX(I.H.P.p, S.H.P.p) . .
Log Ay (for V Sheet 21)
Log At (for Vf Sheet 21)
^ e IH.P.d or S.H.RdX^y
* LH.P. orS.H.P.Xi4D
** px(i.)
Constant
Constant
Constant
Digitized by LjOOQ IC
158
SCREW PROPELLERS
SCREW PROPELLERS
Lisuffident Data
FosH FOR Computation— LH.P^ or SJI.P^ and Revolutions and Speed
Fixed— e.h.p. for v Unknown
eJi.p.5E.H.P. (assumed)..
r» jj p
I.H.P.d or S.H.P.d.
SlipB.C
XforS.B.C
LH.P.P or S.H.P.P
S.H.P
IJI.P
V (Des. Speed) . . .
e.h.p.
Fsrfor
E.H.P
(above \
Ciit. Thr./ • *
F=i»5
{?)
LT.i>■^(I5) =
CXLH.P.
P.C. for Total •
D'XV
(C=3.84for 2blade,
PA.5D.A. for LT.z)^(I5■) ]
f P.A.^D.A. (forablade) [
JPJ^.5Dj\. (for4blad) J
P.A.
D.A.
EJI.P.=LH.P.XP.C
e.h.p.=E.H.P.x^
i5for(P.A.^D.A.)
T.S. for (P.A.^D.A.)
yDXFX 101.33
T.S.X(i5)
Max. Carried.
Constant
Constant
Constant
Constant
Constant
2.88 for 3 blade
Total Projected
2d— Less than
Max.
Constant
Constant
Constant
Constant
Constant
3d — Less than 2d,
Constant
Constant
Constant
Constant
Constant
and 3491 for 4
Area Ratios.
blade).
logAv
logi4e
,LH.P.dX^F
s^S
LH.P.Xi4/
P _ !>X 101.33
To Find Revolutions
Constant
Constant
Constant
Should there be a possibility of the speed being reduced to vi
while I.H.P.<, or S.H.P.4 remained constant, the value of vi being
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER 159
such that there is danger that the values e.h.p.i^E.H.P. and
^^l^F will plot below the curve of critical thrusts, it is desired
to find the value of e.h.p.i5E.H.P. and of e.h.p.i which will be
delivered under the new speed condition.
It is necessary to bear in mind that the fundamental equation
for apparent slip is
'"^^ IM.F.Xif "^^ I.Ii.F.XA/
while where viiV falls below the critical thrust curve of Sheet 22,
^ oy i^XF^ / e.t. Y_ KxAv / e.t V
Now these two values of 5 must be the same, therefore:
« yLR£XAr__ c... KxAv
•^^LH.P.XA."'^^io^>X^
.\e.tJ
LH.P. io^»^V£.r./'
log LH.P..log LH.P. = log K+x log (^^^^Zi,
Zi=logLH.P.~logLH.P.,+Iog K+x log (^^\
The value of e.h.p.i ^E.H.P. for this value of Zi will be that
delivered and
e.h.p.i = E.H.P. X (e.h.p.i ^ E.H.P.).
Should the second step be necessary to obtain the desired
revolutions, proceed as in the preceding case.
In choosing the values of e.h.p.4E.H.P. to use in the compu
tations, in no case should the values fall over 25 per cent out
side the maximum and minimum limits as given by Sheet 22B
for the slip B.C. and the designed speed.
Problem 26. — ^Full Data. Effectiye Horsepower Used
Vessel of "Tanker" type. Slip B.C. = .80.
Speed loaded 11 knots. Revs. 90; e.h.p. for designed speed = 1500.
Single screw. Draft of vessel in excess of 20 ft. Maximum diameter of
propeller that can be carried = 18 ft. Determine characteristics of four
Digitized by LjOOQ IC
160
SCREW PROPELLERS
bladed propeller and shaft horsepower necessary, the propelling engines
being of the geared turbine type.
SOLUTION
D
e.h.p.
E.H.P;
e.h.p. . .
E.H.P..
i8'
.2
1500
7500
II
18'
.3
1500
SOOQ
II
18'
.4
1500
3750
II
17'
.2
1500
7500
II
17'
1500
5000
II
17'
1500
3750
II
16'
.2
1500
7500
II
16'
.3
1500
5000
II
16'
.4
1500
3750
II
As the conditions given are for the vessel at full load, it is only necessary
to provide for sufficient leeway above the curve of critical thrusts, Sheet 22,
to take care of average rough bottom and bad weather, therefore, take the
values of r5F from the curve on Sheet 22, marked " Curve of Maximum
Efficiency."
V.,.
'SIS
19.13
.662
16.62
.73
15.07
•575
19.13
.662
16.62
.73
15.07
•575
19.13
.662
16.62
.73
15.07
Since the propeller is fourbladed and the e.h.p. is being used, the value
/^ * ^ * X X. rw, 2.491 XE.H.P.
(P.A. +D.A.) XE.T.p= j)ty^v ' •'•
P.A.
D.A.
P.A.
D.A.
XE.T.p. . .
(Sheet 24)
2.813
2.313
1. 913
3.154
2.593
2.145
3.552
2.927
.308
.27
.240
.334
.291
.256
.364
.316
2.422
278
The total projected area ratio of the fourbladed screw being fxthat
of the basic threebladed one:
I P.A.4D.A.
.412
.360
.320
.388
.340
.484
.420
.372
The basic value of the propulsive coefficient being dependent upon total
projected area ratio, we have P.C. for  P.A. sD.A., Sheet 20.
P.C
LHJ».=E.H.P.5P.C
S.H.P.«LH.P.X.92
Zfor^ (Sheet 21)..
S.H.P.p = S.H.P.Mo^...
.611
.646
.67
.59
.6275
.659
.564
.606
1 1456
7740
5597
1 1864
7968
5690
12408
8251
10540
7I2I
5149
10915
7331
5235
11416
7591
.7279
.5445
.4144
.7279
.5445
.4144
.7279
■5445
1972
2033
1983
2042
2093
2012
2136
2167
.638
5878
5408
4144
20«7
As the vessel is single screw of .80 slip block coefficient and is over 20 ft.
in draft, the value of the thrust deduction factor K is obtained from the
curve Ci—C%, Sheet 19, and is equal to 1.27. /•
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
161
S.H.P.d=ICXS.H.P.p.
1.27
2505
1.27
2581
1.27
2519
1.27
2594
1.27
2657
1.27
2561
1.27
2713
1.27
2752
1.27
2651
These values S.H.P.rf are those of the necessary designed powers for
the series of propellers obtained.
The basic values of tipspeeds and of i —basic apparent slip are obtained
from Sheet 20, using the basic P.A.^D.A. values of the basic threebladed
propeller, the values of i — 5 being taken from the curve of i — 5 for slip
B.C. = .80. ..
T.S. for
15 for
P.A.
D.A.**
P.A.
D.A.
6800
5980
5250
7330
6450
5650
7820
6990
.941
.944
.947
.939
.942
.945
.935
.940
6190
.943
Now the pitch of the propeller equals
TXDxVXioi.33
T.S.X(i5) •
P i7'i3 i6'.87 I7'.37 i5'.04 i4'.8
i5'27 i3'33 i2'.88 1$'.!$
To obtain the revolutions which may be expected from this series of
propellers when operating under the designed conditions of speed and
effective horsepower, the data is obtained from Sheet 21, where will be
found a curve of values of log 4 f and r, V being the basic speed as found
in the foregoing calculations, and v being the designed speed of 11 knots.
Logi4r .
Log Av. .
3.83
3.655
3
53
3.83
3.655
3
53
3.83
3.655
3.21
3.21
3
21
3.21
3.21
3
21
3.21
321
3.53
321
The equation for the apparent slip at the designed speed is
,S.H.P.dXi4v
^=5
S.H.P.Xi4/
IU=
t>X 101.33
PX(is)
05845
69.1
05656
70.05
05416
67.86
06043
78.87
05858
80
.0562
77.33
06439
89.4
06060
92.12
.05838
90.02
These values of Ra are the revolutions for the series of resultant propellers
at a speed of vessel of 11 knots, delivering 1500 e.h.p. with S.H.P.d shaft
PA
horsepower. The derived values of S.H.P.«i, P, J =^ and Ra can now be
plotted on cross section paper, using values of D as abscissas (Fig. 12)
and that propeller giving the desired revolutions, with its diameter, pitch
projected area ratio and necessary shaft horsepower can be taken off the
curves.
Digitized by LjOOQ IC
162
SCREW PROPELLERS
J50
V
N
Mi
g::::
:: ^
■fll
mi'
^ W
liiiiii
iWi ::
^^ Iff
litt
iiiilii
^
^.
:!ii,i
■
':i :
^1
I'^ll
m
lliiijj:
>3
ii
iHTfitu
k\\\\\
^:;;:
r ^^
fag
M\
! M
mmiii
11
.3^
irve8 >ty3%±
s
11
:!^^iiii:
: 1
Bi
o
©
"3
TlTTtTnT
Ullllill
[m
■
H
■
.30
llllllfTT
•iJ
18
2800
^
2
V
ill
"['
urvea
»f P
17
^>mjjj
^./)
>
H
• 3/
f
H
^
■
100
o 16
^i'''
[;;^!^
A
if''
■■''W^
III
1!
PI
Hii!
m
DesiK
I eU re^
.J.. ..
^ffi;
SB
muiiij
■'\
90
15
•5
dHjTTTUfjffiff
H'
j=
^
■
1
iTlttttf
.4
2
Curves
ofS.H
Pd
«M
o
80
14
n
■
fl
Immn
tft^^^^
m
^>
70
13
^
SSt
p
^^^ IttirH]
Wm
:!>
3 irves
tRa
Sea
e of Ij) in f
et
00
12
16
17
18
Fig. 12.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
163
It is seen at once that the i6 ft. diameter propeller, having a projected
area ratio of .372 and a pitch of 13.15 ft. will answer the conditions.
However, a more efficient propeller can be obtained by increasing the
diameter and the methods for doing this are illustrated in the following
calculations, taking the minimum projected area ratio propellers of 17 and 18
e.t. e.h.D.
ft. diameters and solving, first, with constant ^e^j ^^^ second, with ^ ' '
Jli. 1 . Jb.xl.ir.
constant,
CONSTANT EFFECTIVE THRUST
D
18
II
1500
•55
18
II
1500
•55
18
II
1500
•55
17
II
1500
•55
17
II
1500
.55
17
II
D
e.h.D
1500
•55
e.t.sE.T
This value of the ratio between e.t. and E.T. is that existing at the point
where e.h.p.^E.H.P. = .4, used in the previous calculations, was taken.
_ 1, _
Holding this value of e.t. 5 E.T. constant and increasing ^ ' ' ' , with the
jii.Jrl.ir.
corresponding increased values of z>r7, we have:
e.h.p.^E.H.P.
v^V
V
E.H.P
P.A
D.A
P.A.
XE.T.p=
■5D.A...
2.491 E.H.P.
D'XV
IP.A.5D.A...
P.C. for I (P.A.
I.H.P
D.A.).
S.H.P.
'<i^.
S.H.P.P
K
S.H.P.d
T.S.forP.A.!D.A
15 for PJV.^D.A. and slip B.C.
= .8
P
Logi4F.
Logilp..
s
R4
.45
•5
55
•45
•5
.82
.91
I.O
.82
.91
1342
12.09
II
13 42
12.09
3333
3000
2727
3333
3000
1. 911
1.908
1.906
2.142
2.139
.24
.24
.24
.256
.256
•32
.32
• 32
34
•34
.67
.67
• 67
659
.659
4975
4478
4071
5058
4552
4577
4120
3745
4654
4188
.36
.3135
.27
36
3153
1998
2002
201 1
2031
2035
1.27
1.27
1.27
1.27
1.27
2538
2542
2554
2580
2584
5250
5250
5250
5650
5650
.947
.947
.947
.945
.945
1546
1393
12.68
136
12.25
3.38
325
321
3.38
325
3.21
321
321
321
321
.04346
.03586
.03616
.04510
.03721
7537
82.98
91.22
8585
9449
•55
1.0
II
2727
2.137
.256
.34
.659
4139
3808
.27
2045
1.27
2597
5650
• 945
II. IS
3.21
321
.03751
103.9
Digitized by LjOOQ IC
164
SCREW PROPELLERS
CONSTANT
e.h.p.
V ,
e.h.p
e.hp.sE.HP.
E.H.P
v^V
V
gxE.T.,..,
P.A.^D.A...
1 P.A.4D.A.
P.C
LH.P
S.H.P...
Z
S.H.P., .
K
S.H.P.(f..
T.S
15
P
Log Av*
Log At..
s
Rd
i8
18
18
17
17
II
II
II
II
II
1500
1500
1500
1500
1500
.4
.4
.4
.4
.4
37SO
37SO
3750
37SO
37SO
.83
.91
I.O
.82
.91
13 42
12.09
II
13.42
12.09
2.148
2.38s
2.621
2.409
2.674
.257
.275
.293
.277
.296
.344
.368
.392
.372
.396
.656
.641
.625
.638
.622
5717
5850
6000
5878
6029
5259
5382
5520
5408
5S47
.4144
.4144
.4144
.4144
.4144
2026
2073
2126
2083
2136
1.27
1.27
1.27
1.27
1.27
2572
2633
2700
264s
2713
S550
6100
6500
6150
6570
.946
.944
.942
.943
.942
1465
12.03
10.3
12.52
10. 57
338
3.2s
3.21
3.38
325
3.21
321
3.21
3.21
3.21
.0^007
.03003
95 52
.02837
III. 4
.04124
.03111
79.2
92.41
108.8
17
II
1500
.4
3750
1.0
II
2.938
.317
.424
.604
6209
5712
.4144
2200
1.27
2794
7000
.940
9.047
321
3 21
0293s
126.9
Plotting the results obtained by these last two calculations together with
e.h.p.
the values obtained for the :
3 .4, points of the first calculations, the
E.H.P.
following propellers are obtained, all for 90 revolutions, delivering 1500
e.h.p. at II knots speed of ship.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
165
fl
■
B
d
ir «
1
1
B
1
q:
18
ii
rveso
fD.
1 ^
•veso
fP.
II
1
■
:M:
ill
II
II
12
2700
QQ
1
■
1
2000
■ :
■
1
Curv<
sofS
H.P.
I
i
■
■
■
1
2500
Sc
lie of
%pj:
.rD.
^.
■
^
.86 .96
Fig. 13.
.87
.88
Digitized by LjOOQ IC
166
SCREW PROPELLERS
CONSTANT
e.t.
E.T.
CONSTANT
e.h.p.
E.H.P.
Diam. .
Pitch..
P.A.
*D.A.'
S;H.P4
e.h.p. . .
p.c...
Rd
V
Constant =^
E.T.
Constant
16'
17'
18'
17'
13'. IS
I2'.9
12'. 87
I2'.9
.372
.34
.32
.3675
2651
2582
2550
2633
1500
1500
1500
1500
.566
.582
.627
.57
90
90
90
90
II
II
II
II
e.h.p.
eitp:
18'
12'. 87
.36
2614
1500
•574
90
II
By plotting the above characteristics and running cross curves (Fig. 13),
an innumerable number of propellers can be obtained with diameters
varying from 16 ft. to 18 ft., pitches from 13.15 to 12.87, and total pro
jected area ratios from .32 to .372. The shaft horsepowers required for
all of these propellers varies from 2550 to 2651, a difference between the best
and the poorest of only about 4 per cent or 100 shaft horsepower.
It is such peculiarities in propeller performances that create so many
different opinions as to what is the proper propeller to use for any particular
problem, the experiences of the various designers have placed no two in
exactly the same position of the zone of design.
However, as the 17ft. propellers above fall approximately on the upper
limit of wellknown propeller design territory, it would be well to confine
ourselves to this diameter and then the choice narrows to that of the pro
jected area ratio to use.
By inspection of the above table of propellers it will be seen that both
propellers given with 17ft. diameter vary from a projected area ratio of .34
to one of .3675, while the pitch remains constant at 12.9 ft. The shaft
horsepower has increased, however, from 2582 to 2633 in passing from the
lower to the higher projected area ratio, and this increase in projected area
has only resulted in a decrease in efficiency of propulsion.
Therefore, the propeller to be used should be the 17ft. diameter propeller
having a projected ara ratio of .34 and the shaft and horsepower required
will be approximately 2600.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
167
Problem 27.— Incomplete Data
Same vessel as in Problem 23. 9iaft horsepower of turbine reduction
gear engine equals 2600. Expected speed 1 1 knots. Desired revolutions 90.
Find propeller characterisitcs. Maximum diameter of propeller that can
be carried = 18 ft.
SOLUTION
Propeller 4 Bladed.
D
e.h.p.rE.H.P.
Z
S.H.P.d
K
S.H.P.P
S.H.P
I.H.P
v^rV
K^)
I.T.i>4(i5).
P.A.5D.A...
J P.A.^D.A.
P.C
E.H.P
e.h.p
T.S
15
P
Av
Av
5
Rd
18'
.2
.7279
2600
1.27
2047
10941
1 1893
II
.652
16.87
5.42
.36
.48
.567
•6743
1349
7970
.937
13' II
368
312
•05436
89.92
18'
•3
.5445
2600
1.27
2047
7173
7796
II
.74
14.87
4.031
.303
.404
.616'
4802
1441
6730
.042
13'. 44
3.51
312
.05161
87.4s
•18'
.4
.4144
2600
1.27
2047
5316
5778
II
.805
13.67
325
.267
.356
.647
3738
1495
5930
.944
13'. 99
3.4
312
05219
84.04
17'
.2
.7279
2600
1.27
2047
10941
11893
II
.652
16.87
6.076
.386
.574
545
6482
1296
8350
•933
11'. 72
3.68
3.12
05781
lOI.O
17'
.3
.5445
2600
1.27
2047
7173
7796
II
.74
14.87
4.519
.324
.432
.597
4654
1396
7150
.940
11'. 97
3. SI
3.12
S0339
98.3s
17
.4
.4144
2600
1.27
2047
5316
5778
II
.805
13.67
3 643
.284
.380
.632
3652
1461
6300
.943
I2'.45
34
3.12
.05312
94.53
16'
.2
.7279
2600
1.27
2047
10941
1 1893
II
.652
16.87
6.86
.412
.548
.527
6268
1254
8820
.930
10'. 48
3.68
3.12
.0604
113 3
16'
.3
•5445
2600
1.27
2047
7173
7796
II
.74
14.87
5.102
•347
.464
.577
4498
1349
7610
.930
10'. 61
351
312
•05517
III. 2
16'
.4
.4144
2600
1.27
2047
5316
5778
II
.80s
1367
4. "3
.306
.408
.614
3548
1419
6800
.942
10. '87
3.4
3.12
.05405
108.4
Plotting these results upon values of D as abscissas, and running cross
curves of P, J P. A. 5D.A. and e.h.p. for i? = 90 (Fig. 14), a series of propellers
will be obtained of which the following are examples:
D
i7'^4
13'. 07
.37
90
2600
1475
.567.
i7'.6
I3'.07
.39
90
3600
1455
.56
i7'.8
13'. 07
.4225
90
2600
1413
.543
17'. 97
P
l^'.07
*P.A.^D.A
j;^
.481
90
I.H.P
e.h.D
1600
1345
PC
.517
Digitized by LjOOQ IC
168
SCREW PROPELLERS
Fio. Z4.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
169
Comparing the results obtained by this latter method with those ob
tained by the previous, it will be seen that as the eflFective horsepower,
revolutions and speed of ship remain constant, the efficiency increases while
the pitch and projected area ratios slowly decrease as the diameter of the
propeller increases, while in the lattei* case, designing for constant engine or
shaft power and constant revolutions and speed of ship, the efficiency falls,
the pitch remains constant and the projected area ratio increases as the diam
eter increases.
The second case is a case of guesswork, pure and simple, depending
entirely upon the accuracy of estimate of power required for speed for any
given hull. Should this estimate be incorrect, the designer of the propeller
would be made to shoulder the blame which should in reality rest upon other
than his. In many cases care is taken to specify such an excess of engine
power as to insure the de^ed speed of vessel thus unduly increasing the
cost and weight of the machinery installation, an extravagance which could
easily be avoided by the expenditure of a few hundred dollars for the con
struction of a model of the prospective vessel and trials of it in a model
tank m order that a solid foimdation upon which to design the necessary
machinery be established.
Problem a8
Heavy vessel of intermediate speed. Showing effect of varying trim on
K. Vessel fine lined at bow and stem, full midship section.
Characteristics of vessel— L.L.W.L. =450'; H = 24'.5; B « 76.83 ;
Midship Section Cocf..i96; Nominal B.C. .66; 5hL.L.W.L = .i7i:
Slip B.C. (Twin Screw) .655; Prismatic Coef. = .787. This type of
vessel was tried over the measured mile course with four different propellers
and at four different times, as follows:
zst Propeller.
2d Propeller.
3d Propeller.
4th Propeller.
D
17'. 25
18'
3
.308
17'. 25
18'
3
.308
17'. 75
18'
3
.315
I7'.33
17.5
3
.364
P
Blades
P.A.5D.A
Displacements are all equal.
Base Line Horizontal Line tangent to lowest point of keel at 24'. 5.
Trim
Mean tip cleamace cor
rected for trim
JSTforM.T.C
31 i" by stem
25i" by stem
8" by stem
2i" by be
S'2
2'.8s
2'.05
i'.6s
1.08
1. 10
1. 19
1.31
Digitized by LjOOQ IC
170
SCREW PROPELLERS
These changes in the value of K appear abnormal and beyond the limits
of possibility and therefore are apt to be charged up against other than the
true cause, such as improper blade shape or blade section. If, however,
either of these were the cause of the diflFerence in propulsive efficiency, the
revolutions obtained by using the actual power in the equations for appar
ent slip and estimate of revolutions, would differ widely from the actual
revolutions as anything which changes the resistance of the blade to revolv
ing, dther increasing or decreasing it, would cause the estimated revolu
tions to vary widely from the actual ones.
ANALYSES
PERFORMANCE OF ABOVE PROPELLERS
PERFORMANCE AT CONTRACT SPEED OF i8 KNOTS
As a further proof of what may be called the instability of the thrust
deduction factor with this class of vessel, on the final acceptance trial of the
vessel fitted with No. 4 propeller, the vessel was displacing 660 tons more
than on the previous trial, yet the trial results obtained were:
. I.H.P. per propeller 8075
Revolutions. 118. 85
Speed 17.81
The vessel was trimmed 2 ft. 5 in. by the stem, and these results check
by analysis of power and revolutions as being produced by change in trim
only.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
171
This "instability in the value of X" existing, it becomes neces
sary to determine a standard condition of trim in order to design con
sistently. The condition of even trim foreandaft, is usually taken. The
design conditions for the foregoing vessel were: Speed, i8 knots; revolu
tions IIS at 8250 I.H.P. and eflfective horsepower 4800 on each pro
peller. Center of propeller hub 10' yj" from the stern of the ship and
q'S above base. Propellers in Position i.
DESIGN
e.h.p.5E.H.P
e.h.p
E.H.P.
(P.A.^D.A.)XE.T.p.
P.A.^D.A
P.C
LH.P
T.S
S.B.C
15
P
Hor. Tip Clear.
Im. Up. Tips . .
M.T.C
K
Z
I.H.P.,
LH.P.d.
log^v..
log Av . .
5......
Rd
17
.6
4800
8000
.837
18
21.51
3707
.366
.64
12500
8000
.655
.902
i6'.i3
.231
7344
8298
3.98
376
.lol
126.8
17
.7
4800
6857
.877
18
20.53
3.329
338
659
10405
7450
.655
•905
i6'.48
2'.I25
6'. 5
2'.5
1. 13
.i6i
7182
8116
391
3.76
.104
T23.
17
.8
4800
6000
.917
18
19.63
3.046
.318
.671
8942
7020
.655
.908
i7'.05
.1009
7088
8010
3.87
3.76
.1062
119
17 .5
.6
4800
8000
.837
18
21.51
3.498
351
.65
12307
7700
.655
.903
i7'.25
.231
7231
8402
3.98
3.76
.1099
118. 7
17'. 5
.7
4800
6857
.877
18
20.53
3.142
.335
.667
10320
7170
.655
.906
1/.6
1.875
6'. 25
2'. 32
1. 162
.161
7096
8245
391
376
.1065
116
17 .5
.8
4800
6000
.917
18
19.63
2.875
.305
.678
8850
6770
.655
.909
i7'.77
.1009
701S
8151
3.87
3.76
.108
115
18'
.6
4800
8000
.837
18
21.51
3.307
337
.66
12121
7430
.655
.905
i8'.33
.231
7121
8617
3.98
3.76
.1121
112. 1
18'
.7
4800
6857
.877
18
.2053
2.97
.312
.675
10159
6910
.655
.908
i8'.74
1.625
6.0
1.96
1. 21
.161
7012
8484
391
3.76
.1085
109.2
18'
.8
4800
6000
.917
18
19.63
2.717
.294
.685
8759
6550
.655
.910
i8'.87
.1009
6943
8401
3.87
3.76
.1112
108.8
Laying down the P, P.A. hD.A., I.H.P.d, and i^ on Z> as abscissas, and
choosing Z) = 1 7'. 2 5 as the diameter desired, arbitrarily choosing it as it was
that of the best of the propellers in the preceding analysis, we find the fol
lowing propeller:
Z) = i/.2S, P = i/.S7, P.A.^D.A.=3o8, I.H.P.(f=8ios, i2rf = ii6.4,
7 = 19.63, e.h.p.5E.H.P. = .8, »^7 = .9I7, e.t.^E.T. = .872.
Maintaining constant D = i7'.25, P.A. 4D.A. = .308, v = 18, e.h.p =4800,
and e.t.^E.T. = .872, we obtain
Digitized by LjOOQ IC
172
SCREW PROPELLERS
e.h.p
c.h.p.+E.H.P.
Z
E.H.P
P.A.HD.A..
P.C
LH.P
I.H.P.„..
K
LH.P^..
V
S.B.C...
15.
T.S. for
P.A.
D.A.
logAv
logilf.
Rd
LH.P.d,.
^•Ws
P.d,
P.tf
1725
17.2s
17.25
18
18
18
4800
4800
4800
75
.70
.65
.130
.161
.2
6400
6857
7385
.308
.308
.308
.677
.677
.677
9454
10128
10908
7008
6991
6883
1. 14
1. 14
1. 14
7989
7970
7846
.86
.803
.747
20.93
22.42
24.10
.65s
.655
.655
.91
.91
.91
6850
6850
6850
i8'.44
1975
21'. 23
3.94
4.03
41
3.76
3.76
376
.1151
.1319
.1416
III. 8
106.4
100. 1
8250
8250
8250
(Des
igned Pow
er of Engi
"3
107.6
IOI.8
8IOS
116. 4*
8250*
ne)
117. I*
* From preceding calculation.
Plotting these results on P as abscissas, the following propeller is ob
tained as filling the required conditions:
I> = i7'.35 R = ii5
P = i8' LH.P.4, = 82So
P.A.4D.A. = .3o8
while at 18 knots, the results will be i^» 114, 1.H.P.d=8o25, the differences
between revolutions and power between these results and those of the initial
analysis being caused by difference in the values of K used, and very slight
difference in the value of i —5.
Problem 29
The vessel of Problem 28 was of a type of hull whose afterbody fines
rapidly both from the keel up and from the beam in towards the center
line, the midship section being very full. The vessel in Problem 29 is, how
ever, of an entirely different type, the stem being of the type commonly
called " fantail," the diminution of beam at upper deck at the propellers
being comparatively small, while the fining of the afterbody lines occurs
chiefly in a rapid rise from the flat bottom of the middle body. The hull
of the ship above the propellers is well above the water plane. The pro
pellers are, therefore, in Position 2.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
173
Block Coef. «.72is
Coef . Mid. Sec. =.9783
Coef. L.W. Plane =.7954
Cyl. Coef. «.7375
The dimensions of the vessel are
L.L.W.L. = 52o'
5 =65' 02 H"
H = 27'6"
Displace.  19230 tons
Twin Screw
5^L.L.W.L. = .I26
Slip B.C. = .617
Des. Speed  14 knots.
Max. Diam. of Propeller = 16', Revs, at designed speed = 108, e.h.p. for
designed speed = 2550 on two screws.
For such a heavy vessel and on account of the character of her service,
which is collier, as it is desirable to carry as great a diameter of propeller
as possible in order to obtain the maximimi handling, backing and holding
power in bad weather, we, therefore, select for the first approximation, the
upper design ciu^e shown on Sheet 22, using the maximum diameter, 16',
that can be carried.
COMPUTATION
eJi.p.^E.H.P.
e.h.p
E.H.P.
V
V
D
Blades
(P.A.^DJV.)XE.Tp (Sheet 24).
P.A.5D.A
P.C
LH.P
S.H.P
T.S for P. A. H
S.B.C
D.A,.
15.
P....
Zfor
I.H.P.1
e.h.p.
E.H.P
p
S.H.P.„
K from CC. (Sheet 19).
I.H.P.tf
S.H.P.tf
Logilv.
Log .4,..
s
Rd
.3
.4
•5
.6
1775
1775
1775
1775
5917
4438
3550
2960
14
14
14
14
.742
.807
.86
.901
18.87
1735
16.28
15.54
16'
16'
16'
16'
3
3
3
3
3.464
2.819
2. 411
2.104
.347
.30
.269
.2475
.654
.682
.695
.702
9047
6508
5108
4315
8324
5987
4699
3970
7600
6660
5950
5430
.617
.617
.617
.617
.899
.903
.905
.906
14.07
14.69
IS. 4
16.09
.5445
.4144
•3135
.231
2582
2506
2482
2535
2376
2306
2283
2332
1.16s
1. 165
1. 165
1. 165
3009
2920
2891
2953
2768
2686
2660
2717
3.82
3.71
3.63
3.57
3.43
3.43
3.43
3 43
.08258
.08291
.08522
.08881
109.9
105.3
1
100.7
96.78
.7
1775
2536
.933
14
15.01
16'
3
1.867
.23
.706
3592
3305
5000
.617
.906
16.87
.161
2480
2281
1. 165
2889
2658
3.52
3 43
.093
92.71
Digitized by LjOOQ IC
174
SCREW PROPELLERS
The actual propeller fitted to this vessel and its performances, was as
follows:
Propeller
D , iS'.QS
P I4'.436
Blades 3
S.H.P(i 2730
Revs 108. s
P.A.sDj\ 304
Laying down »57 on P.A.^D.A. as abscissas from the above calcu
lations, in order to check the accuracy of the design charts by comparing
the computed performance of propellers having the same pitch and pro
jected area ratio as the actual propellers, tate off the value oivrV corre
sponding to P.A.^D.A. equal .304, which is found to be .802, while the
value of e.h.p. iE.H.P., also laid down as a curve, is found to be .39
The line drawn through this point plotted on Sheet 22, and zero, corre
sponds to a value e.t. rE.T. =49.
D
e.t.5E.T.
e.h.p.^E.H.P.
U5K
e.h.p
E.H.P
P.A.5D.A.
P.C
I.H.P
S.H.P...
Z
S.H.Pp. .
K
S.H.P.d.
T.S
15....
V
V
P
logilv..
log i4». . .
5
Rd
16'
16'
.49
.49
.4
.42s
.82
.87
1775
1775
4438
4177
.304
.304
.679
.679
653s
6151
6013
5659
.4144
.387
2316
2321
1. 165
1.165
2698
2704
6750
6750
.902
.902
14
14
17.07
16.09
14'. 28
I3'.46
3.7
3.61
3.43
3.43
.08188
.07094
108.2
"34
16'
.49
.45
.92
1775
3945
.304
.679
5809
5345
.362
2322
1. 16s
2706
6750
.902
14
15.22
12'. 73
3.54
343
.06391
119. 1
Laying down curves of P, S.H.P.d, and Ra on P.A.!D.A. as abscissas
the propeller for 108.5 revolutions is found to be, from the first set of calcu
lations:
Z)=i6',P = i5'9", P.A.4D.A.= .2S7, S.H.P.don each propeller =2700,
R4 = 108.5, » = 14 knots.
Digitized by LjOOQ IC
DESIGN OF THE PROPELIFB
175
Laying down curves of P, Ra and S.H.P.d on P as abscissas, constant
value of P.A.5D.A. =.304, from the second set of calculations, the result
ant propeller for 108.5 revolutions is found to be:
D = 16', P « 14' 3", P.A. 4D.A. = .304, S.H.P^ = 2700 on each propeller,
i2d = 108.5, v = i4 knots.
This latter propeller is foimd to agree very closely in all particulars
and in promised performance, with the actual propeller, while by comparing
it with the propeller obtained by the j&rst calculation, pitch is seen to have
been exchanged for surface while the efficiency has remained constant. Sur
face being desirable for manoeuvring power, it would be desirable to choose
the second propeller rather than the first. The weights of the two propellers
would probably be in favor of the higher pitch propeller.
Problem 30
Destroyer; Slip B.C. = .385; twin screw; designed speed =37 knots;
e.h.p. (total) of hull and appendages, for this speed = 19250; designed
revolutions not less than 495; find S.H.P.d, P, and P.A. rD.A., the diameter
that can be carried being 113 inches.
In problems of high power and speed, in order to hold the propeller
within proper and practical limits of projected area ratio and diameter it
becomes necessary to design at or near the natural speed and load limits,
the term natural here used meaning the limits imposed by Sheet 22 where
the cavitation condition is that imposed by the e.t. line e.t. = 1.225 E.T.,
and not the curve E.T.
For primary calculation use the curve on Sheet 22, marked " Safe
Limit for High Efficiency."
e.h.p.^E.H.P.
e.h.p
E.H.P.
V
viV...
V
Z>=ii3"
(P.A.^D.A.)XE.T.p(3 blades).
P.A.^D.A
P.C
LH.P
S.H.P
T.S..
15.
P....
Z...
K...
S.H.P.d=S.H.P.p.
.9
•95
I.O
1.05
9625
9625
9625
9625
10694
10132
9625
9167
37
37
37
37
952
.967
.981
.997
38.87
38.26
37.72
37."
9'. 42
9'.42
9'.42
9'. 42
8.929
8.283
8.283
8.017
.637
.624
.612
.601
.525
.525
.525
.525
20370
19298
18333
17460
18741
17755
16867
16064
15610
14550
14000
13560
.812
.822
.828
.835
9'. 195
9'. 594
9'. 757
9'. 829
.0477
— .0224
i.022I
I
I
I
I
16792
16862
16867
16902
1. 10
9625
8750
37
I. CI
36.63
9'. 42
7.752
.591
.525
16667
15334
13200
.841
9'. 896
+ .0431
I
16933
Digitized by LjOOQ IC
176
SCREW PROPELLERS
In estimating the revolutions for this type of vessel, where under high
speed there is a liability to excessive squatting of the stem, attention must be
paid to the construction of the horizontal arms of the propeller struts.
Where the long axis of the sections of these arms are parallel to the base line
of the vessel, that is, horizontal at normal trim, the tendency to squat is
much reduced and the wake conditions tend to remain normal. In such
cases the values of Log Av and of Log Av are both taken from the normal
curve X on Sheet 21.
Should the axes of the sections of the horizontal strut arms be inclined
downward at the forward ends in order to get them into the lines of flow,
the squatting of the stem is augmented, the wake rapidly decreases as the
speed increases and the revolu tions incre ase rapidly. The augmentation of
revolutions begins when v 5 \/L.L. W.L. = i .48 and at this point the values
of Log Av begin to depart from the curve X, Sheet 21, moving towards the
curve Y which they reach when »4\/l.L.W.L. = 1.75. The value of Log
i4 V is in all cases taken from the curve X, This same phenomenon will occur
where the strut arm sections are parallel to the base should the propellers
be located as far aft as the stem post.
In the case in question, let us estimate the revolutions for both condi
tions, ist, limited squat; 2d, excessive squat.
IjQgAv (X^ Sheet 21)
 . [ X, Sheet 21 .
^ ^' t F, Sheet «.
fist
\.d
4.48
4.47
4.465
4.46
4.455
4.455
4.455
4.455
4.33
4.33
4.33
4.33
.1784
.175
.176
.1756
.2656
.2457
.2347
.2342
496.3
473.7
466.3
462.7
555.2
518. 1
502.1
498.1
4.450
4. 455
4 33
.1756
.2315
459.6
493
The propellers to give 495 revolutions under the designed conditions of
speed are
A B
For Squat. For no Squat.
D 113" 113"
P n8".s iio".S
P.A.^D.A S9S .6365
Blades 3 3
S.H.P.d 16920 16800
Rd 495 495
V 37 37
Now, let us suppose that the propellers are placed as far forward on the
afterbody as possible and still retain large tip clearance, and that the axes
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
177
of the lower strut arms are parallel to the base line of the vessel. The ten
dency to squat will be much reduced, the increase in immersion of the pro
pellers due to squatting which will occur to some extent will be small and
the propellers will be in the best position for realizing the maximum bene
fit of the wake.
By doing this, the propeller A is eliminated and propeller B may be
chosen, although not necessarily, as we may extend our choice, as follows:
Take e.t.+E.T. for _.' '^ and zz (Sheet 22), corresponding to above
computations. Draw lines through zero and these points on Sheet 22,
and with constant P.A.5D.A. and constant D and varjdng viV and
e.h.p.4E.H.P., taken from each of these lines of e.t.^E.T., obtain a
series of propellers for each of the values of P. A. sD.A. obtained in the
first calculations, and obtain from each series that propeller giving 495
revolutions. This will allow a cross curve of propellers of constant
diameter but of varying P.A.hD.A. varying pitch and varying S.H.P.d,
but all of constant revolutions, 495, for constant speed, 37 knots, from
which we may make our choice.
SOLUnON
e.h.p
eIlF* •
v^V
P.A.^D.A
e.h.p
E.H.P....
P.C
I.H.P
S.H.P
Z.
S.H.P.tf . . .
V
V
T.S
15.
P
Logilv...
Logi4o....
s
Rd
I.O
1.05
I.I
I.I5
1. 15
1.02
1. 07s
I OS
I.I
1.06
.624
.624
.601
.601
.591
9625
9625
962s
9625
9625
9625
9167
8750
8370
8370
.525
.525
.525
.525
.525
18333
17460
16667
15943
15943
16867
16064
15334
14668
14668
0.00
I.0221
+ .0431
+ .0632
+ .0632
16867
1690;
16934
16965
1696s
37
37
37
37
37
36.28
34.42
35.24
33.64
34.91
14550
14550
13560
13560
13200
.822
.822
.835
.835
.841
9'. 095
8'. 63
9'. 333
8'.909
9.429
4.445
4.415
4.43
4.395
4.42
4.455
4.455
4.455
4.455
4.455
.174
.1708
.1720
.1662
.1697
499.1
523.9
485.2
504. 8
478.9
1.20
I. II
591
9625
8021
.525
15728
14470
+ .082S
17497
37
3334
13200
.841
9.004
4.39
4. 455
.1655
499
Laying down these results on values of
e.h.p.
as abscissas, a series of
E.H.P.
curves P, P.A. sD.A. and of S.H.P.d are obtained for the constant diameter
Digitized by LjOOQ IC
178
SCREW PROPELLERS
113 in., constant revolutions, 495, and constant e.h.p.) 9625 on each pro
peller, from which the following table of propellers may be prepared:
D
P.A. + D.A.
P
Ra
Total
S.H.P.d
e.h.p.
p.c.
V
113"
•59
no"
495
34700
19250
5547
37
113"
•S9S
iio"i
495
. 34050
19250
5653
37
U3"
.600
III"
495
33900
19250
5678
37
U3"
.60s
III"!
495
338S0
19250
5682
37
X13"
.610
in"!
495
33850
19250
5687
37
113"
.6IS
112"
495
33800
19250
5695
37
"3"
.620
II2"i
495
33780
19250
5698
37
113"
.625
II2"i
495
33760
19250
5700
37
In selecting the propeller to use it will be advisable to take one of the
heavier projected area ratios as they not only promise slightly higher pro
pulsive efficiencies but have the added advantage of greater range before
cavitation is encountered.
Should squatting occur to any great extent, the revolutions will speed
up until a sufficient degree of squat has been obtained to shift the factor
Log At from the X to the Y curve, Sheet 21, when no further increase will
occur. To cover this contingency it may be considered desirable to design
the propeller for conditions of wake at the des'gned speed corresponding
to a position intermediate to curve X and Y so that the decrease or increase
in revolutions will not be excessive.
Design of Propellers having blades not of Standard Form,
It has already been pointed out how such propellers may be
divided into three cases for analysis. The same distinction
can be made as to design and the forms for computation mod
ified accordingly.
In the first forms the resultant propeller is designed to
deliver the same effective (towrope) horsepower as the basic
propeller of diameter Z?i, but does so at an increase in power
and revolutions over those of the basic. In the second form,
the eflfective horsepower delivered varies directly as the f
power of the ratio between the actual and basic diameters, and
the powers vary according to the square ojf the same ratio,
the revolutions increase inversely as the \ power of the diam
eter ratios. The propulsive coefficient of the actual propeller
will be to that of the basic propeller as the square root of the
inverse ratio of the diameters.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
179
FANSHAPED BLADES: FORMS FOR CASE i: REVOLUTIONS
LESS THAN STANDARD FOR POWER, DIAMETER AND SPEED
Condition
Diameter possible
Diameter (Basic Prop., assumed) .
Basic Power
e.h.p.i5E.H.P.i..
E.H.P.1
K
I.H.P.„,=I.H.P.d,^A'
Z for e.h.p.i^E.H.P.i
LH.P.i=I.H.P.,,iXio^
Designed speed
viV
V
LT.2>^(i5)
(P.A.^DA.)XE.T.p
3.84, 2 Blades
Note: C= 2.88,3 Blades
2.491, 4 Blades
P.A.TD.A. (Sheets 23 and 24).
iP.A.^D.A. (2 Blades)
tP.A.^D.A.(4 Blades)
P.C. for total proj. area ratio..
E.H.P.=I.H.P.iXP.C
Constant I.H.P.d
D (constant).
A
I.H.P.d; = I.H.P.dX
( ) ( ) ( )
Constant
Constant
( ) ( ) ( )
( ) ( ) ( )
V = Constant
( ) ( ) ( )
( ) ( ) ( )
(Cxl.H.P.i)^(A«XF)
e.h.p.i=E.H.P.
e.h.p.=e.h.p.i
I.H.P.= E.H.P.1 H P.C.
I.H.P.^,=I.H.P.iMo^.
I.H.P.d,=I.HP.p,Xi<:.
.A
^^(^5?^)
D'
LH.P.d= I.H.P.diX
T.S. forP.A.^D.A...
S.B.C. of vessel
i5for^andS.B.C.
D.A.
ioi.33X7XtXA
T.S.X(i6) •••
Log. i4yfor F (Sheet 21).
Log. At for V (Sheet 21). .
,I.H.P.rf,X^F
5i = 5
I.H.P.,X.4/
z>Xioi. 33
^^""Pxd.O •
iJ<(=Revs. of Actual Screw.
Proj. Area Ratio (Actual) = Total P
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( )
Constant
( ) ( ) ( )
(0 ( ) ( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( )
( ) ( ) ( )
roj. Area Ratio of Bas
Constant e.h.p.
D (constant)
e.h.p.i=e.h.p.
( ) ( ) ( )
( ) ( ) ( )
Constant
( ) ( ) ( )
v= Constant
( ) ( ) ( )
( ) ( ) ( )
(CxEi^P.l)^(Z),«XF)
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Constant
( )
( )
( )
( )
( )
( ) ( ) ( )
( ) ( ) ( )
( )
( )
( )
( )
( )
( )
( ) ( ) ( )
( ) ( )
icPropellerX(A^/>)*
Digitized by LjOOQ IC
180
SCREW PROPELLERS
OVAL BLADES BROADER OR NARROWER AT TIPS THAN STAND
ARD. FORMS FOR CASES 2 AND 3. REVOLUTIONS GREATER
OR LESS THAN STANDARD FOR POWER, DLVMETER, AND
SPEED
Condition
Diameter possible
Diameter (Basic, assumed) .
Basic Power
e.h.p.i5E.H.P.i.
E.H.P.1
K
LH.P.p,=LH.P.d»5ie^.
Z fore.h.p.i4E.H.P.,.
LH.P.i=LH.P.p,Xio^
Designed Speed=v. . . .
vhV
V
LT.dH(i5)
(P.A.7D.A.)XE.T.p
Note: C as before.
P.A.^D.A. (Sheets 23 and 24)
I P.A.JD.A. for 2 Blades
t P.A.5D.A. for 4 Blades
P.C. for Total Proj. Area Ratio. . .
E.H.P.i=LH.P.iXP.C
LH.P.i = E.H.P.,TP.C
LH.P.p, = LH.P.i^io^
LH.P.rf»=LH.P.,,Xie^
LH.P.dLH.P.tfiX (^y
e.h.p.i= E.H.P.1 x(e.h.p.i^E.H.P.i)
e.h.p.=e.h.p.iX(Ps A)'/*
T.S. forP.A.4D.A
S.B.C. of Vessel
i5for^4^andS.B.C...
D.A.
ioi.33X7XxXA
T.S.X(i5)
LogiiF
Logi4»
i2di
LH.P.iX^.
101.33XP
PX(i^)**'
Constant I.H.P.«i
D (constant)
A
I.H.P.di=LH.P.d
X(A5/?)«
( ) ( ) ( )
Constant
Constant
( ) ( )
( ) ( )
z>= Constant
( ) ( )
( ) ( )
( )
( )
( )
( )
(CxI.H.P.,)5(D,»xF)
( )
{ )
( )
( )
( )
( )
( )
( )
( )
( )
) ( )
) ( )
) ( )
Constant
) ( )
) ( )
( )
( )
) ( )
) ( )
) ( )
( )
( )
( )
( )
( )
Constant e.h.p.
D (constant)
e.h.p.i=e.h.p.
X(A^J
( )
( ) (
( )
( ) (
Constant
( )
( ) (
0= Constant
( )
( ) (
( )
( ) (
(CXEJI.P.,)^(Pi»
( )
( )
( )
( )
( )
( )
( )
( )
( ) (
( )
( ) (
Constant
( )
( )
( )
( )
( )
( )
( )
)
)
'XV)
)
)
)
)
)
)
)
Digitized byCjOOQlC
DESIGN OF THE PROPELLER
181
The limit that can be put to this change in diameter is not
known, but it is believed that a difference not exceeding from 15
to 20 per cent between the actual and the basic diameters can
be used without any material error being introduced.
Problem 31
In order to illustrate the foregoing methods of design, let the case of
a tow boat be taken for which the data are as follows:
Hull Conditions
Displ. = ii47 tons
L.L.W.L. = i85'2''
5=34' li"
iy = i2'6"
5^L.L.W.L. = .i84 .
Nominal B.C. = .531
Coef. Mid. Sec. =875
Slip B.C. (single screw) = .755
K (curve C— C— C2, Sheet 21)'
Propeller to be fourbladed
Power and Propeller
Designed I.H.P. = 1800
Designed Revs. = 1 20
Max. Diam. of Prop. = 12'
Expected sea speed = 14 knots
To tow efl&ciently at 10 knots, engine
assumed to be able to develop
full power at this speed.
i.28
e.h.p. for 14 knots =1130
In solving this problem, solve for both Case i and Case 2, using designed
full power of the engine and then solve in Problem 32 again for both cases
of diameter reduction, using the e.h.p. for 14 knots.
FULL POWER OF ENGINE
Case.
I.H.P.tf.
D
A
AM?. . . .
(A^I>)^..
1800
12'
12'
i.o
i.o
1.0
1.0
I.H.P.d,=I.H.P.<iH^...
I.H.P.d,=I.H.P.tfx(^y
K
I.H.P.j„=I.H.P.d,5ie^...
1800
1.28
1406
i8cx>
12'
13'
I 0833
1. 041
1662
1.28
1298
i8cx)
12'
14'
I . 1667
1.080
1543
1.28
1205
1800
12'
12'
1.0
1.0
1.0
1.0
1.0
1800
1.28
1406
1800
12'
13'
1.0833
1. 174
1. 141
1.02
1.28
1650
1800
12'
14'
: . 1667
1. 361
1.26
1033
2450
1.28
1914
•Digitized by LjOOQ IC
182
SCREW PROPELLERS
In selecting the value of e.h.p. 4E.H.P. to use, as the vessel is required
to tow efficiently at lo knots when developing full power of the engine, the
maximum value of e.h.p. ^E.H.P. for the slip block coefficient of the vessel
and for lo knots, obtained from Sheet 22B, should be used. This is seen
to be, by interpolation, .3. /.
e.h.p.i5E.H.P.i.
Z
LH.P.
•3
•3
.3
•3
.3
5445
5445
•5445
5445
.5445
4927
4548
4223
4927
5782
.3
.5445
6706
To find the value of »i ^ 7 from which to obtain the value of 7, Vx being
the towing speed, proceed:
Z»=LogLH.P.iLogLH.P.tfi. .
e.h,p.i5E.H.P.i for 71
43729
.382
43729
.382
43229
.382
43729
.382
43729
.382
43729
.382
e.h.p,
e.t.
Vx^V for JJ,^ =.382 and ^r^ = i,o is only .283. .*. no danger of
Jii.Jtl.i^.i iLA .
cavitation. To avoid dispersion of thrust column for
Vx
a value r^ well above critical thrusts, say =.6
e.h.p,
eIlr
= .3, take
Vx
Vx¥V,
V..,.
I.T.z> _ 2.491 LH.P..
15 A*XK •
P.A.■^D.A. for
LT.z>
15*
tP.A.^D.A...
P.Cforl^^
'D.A.
E.H.P.,
e.h.p.i
e.h.p.=e.h.p.iX f^j
e.h.p.=e.h.pi
«fore.h.p.*
i>\'/«
10
10
10
10
10
.6
.6
.6
.6
.6
16.67
16.67
16.67
16.67
16.67
5. "3
4.021
3.219
5. "3
5. "3
.346
.30
.26
.346
.346
.460
.40
.347
.460
.460
.58
.62
.654
.58
.58
2858
2820
2762
2858
3354
857
846
829
857
857
1006
882
857
846
829
13.22
13.2
13.15
13.22
13.3
10
.6
16.67
5. "3
.346
.460
.58
3890
1 167
926
13.43
♦Taken from model tank e.h.p. curve.
Digitized by LjOOQIC
DESIGN OF THE PROPELLER
183
Vessel, therefore, can not make 14 knots with i8cx) I.H.P.d. In
fact, the two sister ships built on these lines made 13.32 and 13.54 knots,
respectively, with this power.
T.S. for
P.A.
D.A.*
x5forS.B.C. and
P.A.
D.A.*
FXioi.33XirZ)
^ T.S.X(i5)
Log Af (Curve X, Sheet 21).
Log Ab (Curve F, Sheet 21) .
U.
7580
.925
9'. 081
3.735
3.195
.09501
163
163
6650 5740
.93
11'. 14
3.735
3.198
.0897
131. 8
137. 1
•935
I3'.84
3.735
3185
.08426
105.1
"37
7580
•925
9'. 081
3.735
3.195
.09501
163
163
7580
.925
9'.838
3.735
32
.09611
151. 6
154.6
7580
.925
10'. 6
3.735
3.21
.09722
142.3
147.9
By inspection it is at once seen that the propeller designed under Case 2
will not do, as their revolutions are all too high. From those designed by
Case I a propeller giving the desired revolutions can be obtained, therefore,
laying down these Case i propellers on A values as abscissas, we obtain:
Propeller. Basic.
D 13'. 725
P i3'.o6
P.A.^D.A .27
JP.A.^D.A 36.
LH.P.d*
e.h.p •
P.C
V
Rd
Actual.
12'
13'. 06
•3532
.4709 (Fan Shaped)
1800
834
.463
13 16
120
To find the revolutions at 10 knots, supposing the engine, to be able to
develop its full power at this speed of vessel, proceed as follows:
Log Av (Curve X, Sheet 21).
Log Av (Curve F, Sheet 21) .
Rdi.
'A\^
IU^R..X{^)
3.735
3735
2.845
2.845
.2127
.1986
141. 7
"34
141. 7
II3.I
3.735
2.84s
.1844
89.77
96.9s
Digitized by LjOOQ IC
184 SCREW PROPELLERS
Laying down these values of Raon DiBs abscissas it will be found that
the revolutions of the propeller selected will be 102.4 at 10 knots speed and
with the engine developing 1800 I.H.P.d.
Comparing the two methods of diameter reduction it will be seen that
for constant values of e.h.p. 4E.H.P. and oi v^V and constant power, as
the diameter reduction is increased,
Case I Case 2
Proj. Area Ratio Decreases Constant
Revolutions Decrease rapidly Decrease slowly
Pitch Increases rapidly Increases slowly
Propulsive efficiency Decreases slowly Increases slowly
Where the desired revolutions are much below those which would be
obtained with the desired diameter and power without diameter reduction,
Case I is to be preferred. Where the reduction of revolutions and diameter
are small Case 2 should be always used.
Problem 32
Same hull and speed requirements as in Problem 31. The effective
horsepower for 14 knots equals 1130, as before. To obtain propeller
characteristics, revolutions and I.H.P.d necessary for a sea speed, light, of
14 knots; and revolutions with this power for a towing speed of 10 knots.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
185
Shape of Blade.
'/J
D
A
e.h.p
D.i'D
(A5i?)^....
(A+i?)*
(A^Z))'/*....
(A5I>)^....
eJi.p.i= e.h.p.
c.h.p.i=e.h.p.x(jy
e.h.p.i5E.H.P.(as before) .
E.H.P.I
Vi (Towing)
t>irF (as before)
V
(P.A.^D.A,)XE.T.p
P.A.^D.A
^P.A.^D.A.....
P.C
I.H.P.i=E.H.P.i^P.C....
Z
I.H.P.P,
K .,
I.H.P.di
I.H.P.d=LH.P.d,X (g^)
I.H.P.d=I.H.P.d^^(gi)'
T.S
S.B.C
15
P
V
Log Ay (Curve X, Sheet 21).
Log i4p (Curve F, Sheet 21) .
S\
Case I, Pan.
12
12
1 130
I.O
I.O
1 130
•3
3767
10
.6
16.67
391
.388
.517
544
6925
•5445
1977
1.28
2530
2530
8370
•755
.92
8'. 268
14
3735
3.26
.08726
188
188
12
13
1 130
1.0833
1. 041
1 130
.3
3767
10
.6
16.67
3 332
.344
.457
.582
6473
•5445
1848
1.28
2365
2562
7520
.755
.926
9'. 905
14
3735
3 26
.08071
155.8
162.2
12'
14'
1 130
I . 1667
1.08
1 130
.3
3767
10
.6
16.67
2.873
•31
.413
.61
6176
5445
1763
1.28
2256
2632
6850
.755
.93
11'. 66
14
3735
3 26
07635
131 8
1423
Case 2, Broad Tipped.
12
12
II30
I.O
I.O
I.O
I.O
1 130
.3
3767
10
.6
16.67
391
.388
.517
.544
6925
•5445
1977
1.28
2530
2530
8370
.755
.92
8'. 268
14
3 735
326
.08726
188
188
12'
13'
1 130
1.0833
1. 174
1. 141
1.02
1289.33
.3
4298
10
.6
16.67
3801
.38
.505
.551
7801
• 5445
2227
1.28
2850
2428
8220
.755
.922
9'.ioi
14
3.735
. 3 26
.08508
170.4
12'
14'
1 130
.1667
1. 361
1.26
1.033
1423.8
.3
4746
10
.6
16.67
3.619
.366
.488
.561
8460
.5445
2415
1.28
3091
2271
8000
755
.923
10'. 06
14
3. 735
3.26
.08399
154
173.8
159
Digitized by LjOOQ IC
186
SCREW PROPELLERS
In order to arrive at 120 revohitioiis a still greater diameter reduction
would be required, therefore, in order to shc^oi the work, let us suppose
the desired revolutions under the 14knot condition are 160, then laying
down both Case i and Case 2 on A as abscissas we obtain the following
propellers:
Condition.
Case :
Basic.
Actual.
Cask 2
Base.
Actual.
Diameter
Pitch
P.A.+D.A...
P.A.^.D.A.
Blades
I.H.P^,
LH.P^
iZ*
Rd
e.h.p.i
13M
io'.o6
•34
452
4
2352
153
1 130
e.h.D
P.C.=
e.hp.
LH.Pd
14
12'
io'.o6
.5387
4
2567
160
1 130
.44
14
13925
9' 99
.3675
.490
4
3780
155
1415
14
12'
9'99
4
2288
160
1 130
•494
14
The revolutions for 10 knots with these same values of I.H.P.d can now
be calculated, using Log Av from Curve F, Sheet 21, and using the values
of I.H.P.i, I.H.P.<(t, as obtained in the foregoing calculations.
It will be noted that where the desired revolutions can be obtained by
the use of Case 2, without excessive reduction in diameter, this method
should always be used as the propeller so obtained is considerably more
efficient than the corresponding one from Case i.
Problem 33
Submarine of the double hull (Lake) t)T)e, the propellers being carried
under the hull but being given large tip clearances bewteen each other
and from the hull. The surface speed to be 16 knots and the submerged
speed 13 knots. The effective horsepowers for these speeds being 1030
and 954, total on two shafts.
Hull dimensions:
L.L.W.L.=22i'
Beam = 23'.s
H (Surface) 1 2'. s
DiBpl.«83o
Nominal B.C.= .4475
Twin Screws
5hL.L.W.L=.io63
Slip B.C. (Surf, and Subm.) =.817 (Line V, Sheet 17).
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
187
Surface triak to be run on even trim. Find propeller characteristics,
revolutions and power both surface and submerged.
The maximum diameter of propeller possible = s ft. g in. Maximum
surface revolutions not to exceed 375 per minute and minimum submerged
revolutions at full submerged power of 1300 S.H.P. (total on both shafts)
not to be less than 300 per minute. Propellers threebladed.
Limiting e.h.p. 5E.H.P. (Sheet 22B) for S.B.C.=.8i7 and »i=i3, is
approximately .9.
Q54 . „ 954 .
E.H.P.^ •• "^•^•^ V ••
Subm. Condition
1030
E,H.P.
1030 X. 9 927 e.h.p.
SUBMERGED CONDITION
e.h.p.^E.H.P
V
vi (subm.)
vhV
V
e.h.p. (one screw)
E.H.P
D
(P.A.^D.A.)XE.T.p
P.A.^DA. (Sheet 24)
P.C
I.H.P
Z
I.H.P.P
K
I.H.P.d
(Subm.) S.H.P.d=I.H.P.dX.92
.900
.900
.900
16
16
16
13
13
13
8 (Min.)
.825
.85
16.25
15.76
15.3
477
477
477
530
530
530
S'.75
5'. 75
5'. 75
2.841
2.929
3.018
3"
.317
.324
.67s
.672
.669
785.2
788.7
792.2
.0477
.0477
.0477
703.5
706.7
709.8
I
I
I
703.5
706.7
709.8
647.3
650.1
653.1
POWER— SURFACE
V
c.h.p.^E.H.P
Z
IJIP.,
K
I.H.P.tf
Surf. S.H.P.d.
16
16
16
.972
.972
.972
.035
.035
.035
724.4
727.6
730.9
I
I
I
724 4
727.6
730.9
666.5
669.4
672.4
Digitized by LjOOQ IC
188
SCREW PROPELLERS
TO FIND PITCH
T.S..
15.
P....
6880
7000
.943
.942
4'. 585
4'. 375
7130
.941
4' 174
ESTIMATE OF REVOLUTION
Log Av (Curve X, Sheet 21)
r (Sufr. Curve F, Sheet, 21).
Log Av \ (5^^^ ^^^^ Y^ Sheet 21)
r Surface
I Submerged
r Surface
I Submerged
3.63
3.585
3.44
3.44
317
317
.07959
.07472
.1473
.1351
384.2
400.5
337
348.1
3 545
3 44
317
.06932
.1254
417.3
360.8
These results show that the diameter is too small for straight chart
conditions of design and it therefore becomes necessary to resort to either
Case I or 2 of diameter reduction as in the preceding problem. In solving
by these methods use e.h.p.^E.H.P. = .9 for the submerged condition and
t>^F for that same condition equal .8.
Problem 33. Doubleended Ferry Boat
Hull Conditions:
Slip B.C. for after propeller =.76
A: = i.29
Total e.h.p. = ii22
Per cent e.h.p. delivered by
after propeller = 63!
Draft = 13'
Revolutions = 125
v = is knots
e.h.p. delivered by after propeller
= 1122X631 = 714
LH.P.d on after propeller = 55 per
cent of total power
Maximum D = ii' —Propellers four
bladed
Approximate Limits of e.h.p.^ E.H.P. for S.B.C. = .76 and r = i2,
assuming that when in actual service, the vessel may be slowed down to this
speed by increased resistance due to overloading and to wind resistance,
equal, from Sheet 22B, .36 and .57. Use from .3 to .6.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
189
e.h.p.5E.H.P.
e.h.p
E.H.P.
V
V
D
Blades
(P.A.^D.A.)XE.T.p...
P.A.4D.A. (Sheet 24).
iP.A.HD.A
P A
D,A.
I.H.P.
Z
LH.P.P
K (Line C—C, Sheet 19) ... .
LH.P.d
Total Power =LH.P.d^ .55.
T.S. for P.A.^D.A
i5for^andS.B.C...
D.A.
Log Av (Cu ve X, Sheet 21).
Vi
Log A VI (Curve F, Sheet 21) .
s
Rd
•3
.4
S
.6
714
714
714
714
2380
178s
1428
1 190
12
12
12
12
.662
.733
.789
.838
18.13
16.37
15.21
M.32
11'
11'
11'
11'
4
4
4
4
2.703
2.24s
1933
1. 711
.298
.264
•24
.223
.397
•352
.32
.297
.622
.651
.67
.682
3826
2742
2131
1745
5445
.4144
•3135
•231
1092
1056
1036
1025
1.29
1.29
1.29
1.29
1409
1362
1336
1322
2562
2476
2430
2404
6610
5820
5250
4830
.933
.936
.938
.94
10'. 29
10'. 52
10'. 82
11'. 05
3.77
3.63
354
3.46
13
13
13
13
3.17
3.17
3.17
3.17
.09821
.0917
.09109
.08866
139
137.8
134
130.9
These revolutions are all too high. In order to obtain the proper number
we may proceed in four ways; ist, by decreasing the values oi viV until
the critical thrusts are reached, values of e.h.p. ^ E.H.P. constant; 2d, by de
creasing the values of ©4 7 until the critical thrusts are reached, e.t. 5E.T.
constant; 3d, by Case i, diameter reduction; 4th, by Case 2, diameter
reductions. These methods have already been explained, but in order to
obtain a comparison of results from these different methods, we will take one
of the above conditions, say the .4 e.h.p. 4 E.H.P. propeller as a base and
depart from it in each of the above ways, as follows:
Digitized by LjOOQ IC
190
SCREW PROPELLERS
J
3"
lO t> 't fi «
M P M
lo O oo "«*■ >
n
M r^ 00
O >0 to
M g M
M lO O^ ^ <^ Ok
o\ 0> OO ^ oo ct
C( O c« M woo
ro t^ '<t .
to lO
to vO
CI ^ M M
»o
^
"<<•
*.
00
»^
^
to
C*
fO
t<N.
■rt
»>.
to OO
r^
OO
r*
M
O
lO
M
M
. oo
CO
«o
»o
1
o
M
OO
OO
O
•f
8
CI
<>*
00 •
• o
. t^
r^
t^
vO
M
CI
VO
»o
M
1
M
• M
M
V3
M
M
•
•
CI
'«*•
M
M
8^
<0 vO vO fO CI
.00 «o w »^ »o
5 OO M «0 ^O O
(X4 M
tJ lO W «0 «^ 't'
( <^ W M W Tf O
• O to to '<t ^ »o
. . . e* Tj M
CO
'* . 00
CO
to M o^
• to M
O •
Clt^Mlt .OV'^CIMtOtOClO*
CO
CI CI ro vO O^ • b
Tj to W ro t^ "*
lO^CiMCiitvOO^
tJvO totorTj»oci
CiCl«OOt>MO.
CO
fO tp '"t .
O O 73
■^ I
CO
Ov '^ O «^ "^
c* c* CI o >0
0\ . «o • vO
CI CI
M O
rf lo CI fN. M It
M 00 M O OV
CI Ok CI «o CI ^
O
Tj Pp CI
M O
Tj to CI
M OO M
rO t^ '<t .
J2 *? o
I
CO
lOTjCIMClTfOOV
^O toto^'«itoci
CI CI CO vO *^ M O
. CI ^ M M
PL4
w
•I
d
4J ,d .n
•I
q c^ cS"
> :i! :5?
•I I I H
i^ri^rj,::!. <u w
CO . •!• I '. . •?
^.p
N hi ^
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
191
10 ^0 cs
00 t^ O
0» PO »o <
^ »o M <0
tt t^i Tt t» O^ ' . to M
?
w
CI
vO
w
to
«o
t^
t^ 00
00
vO
t^ «
«o »o
M
«o
t^
Tj 00
•
«o
t>.
M
M
w to
' "0
M
ro
to
ro
• M
M
M
vO
^
'<t
ro
fO
fN.
t^ o^
•*
o«
w
r^ w
Tj ^0
M
M
«o
C4
to
t^ VO
10 •
8
M
M
M ♦
' ^O
to
«o
^ s,
00 00 o o o» «0 fO
M ro t^ »0 «0 O^ M .
to ^ VO M O^ •
fO t^ O O VO
'^
W MvO O^O ^1 to«Ot^t^OOOO
>0<Ot^MfO»OMVOM»H
«O«O^00OV' .Qst^l^
MMW10«>j tO«00«OfO
vOO TfOvOO tOQvt^O l>»t^
tO»OvO««O00M00Mt^ •
«O«O^00O\« .rOOOOO
MMWlO'Vl fOfOMMM
t^t^t^O^O M t0»0t^»^0000
10«OOC*«0»0»HOVMVO
«O«O^00OV' O •t>vOvO
rj fo o M M
M wo 0"0 « tO«Ot^
«0 »0 "* 00 Ov •
M M M 10 • Vt »0 <0
8
M M POO t^lOtOfOt^tOM
«WO»OtO»OMOOMO
to «o ^ « o* • • ^ «o
M M CI 10 • "V» <0 <0 M M
00
00
N
VO Tj
to
»o
t^
2 ^
to
s?
s
?5
fO w
Ov •
M
s
M
6
6
M
M
W lO
M
to
M CI
CI
to
• M
M
«
W
VO
VO w
to
to
t^
C^ 00
00
VO
t^ «
to «o
M
"O
M
fO
»o
r* 00
Ov •
to
• M
t>.
« to
•
M
to
to
to
M
O
CO
HH HH H H M Al »■
3^
ft^ ft^
' \tii o
a* to
X g
M Ov
^ „ . ^ vO »0
r« O ro
00 10 ^f
. 10 '^
t^ CI M
M l> 00
t^ vO »0
t^ VO W
■ ^ vO
Ai H Pk ;?;
Digitized by LjOOQ IC
192
SCREW PROPELLERS
An examination of the resultant wheels reveals
very small differences between Nos. i, 2 and 3,
except in surface, the power required increasing
as the surface increases so that No. 3 promises
as the wheel of lowest efficiency. In wheel No.
4, surface has been replaced by pitch and the
efficiency is again high. It must be remem
bered, howevfer, that in the case of twin screw
vessels where the propellers are so located that
the thrust deduction varies with tip clearance
for standard formed blades, but really as clear
ance of the center of pressure, the thrust de
duction to be expected with blades of the
forms of No. 3 and No. 4 will be considerably
higher than those experienced with standard
formed blades, and therefore the efficiency will
be less than promised when standard thrust
deduction values are used. With single screw
vessels it is doubtful whether this augmentation
of thrust deduction occurs unless the propeller
is roofed over by immersed hull.
Problem 34
Twin screw tunnel boat. Propellers located
as shown in Fig. 15. Tip clearance between
blades and tunnel roof should not exceed i in.
Nominal B.C. and Slip B.C. are taken equal
to each other = .8. K is constant for type and
equals 1.195. I.H.P.d per propeller = 150 =300
total. Rd running free without tow = 225. Speed
running free = 8 statute miles per hour. Speed
when towing = 6 statute miles per hour. Maxi
mum diameter of propellers = 5 f t. 6 in. Propel
lers to be fourbladed.
^ . . ^ e.h.p.
Lmuts of T^ TT p 2ire for
f S.B.C.= .8 1
8X88
101.33
v=
=6.95
= .087,
and
S.B.C. = .8
for { 6X88
101.33
/ !!
pq
4
p4
o
s
a
I
i
v=
= 5.21
=.057.
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER
193
As the speeds are very low it will be necessary in order to obtain a prac
tical propeller, to use the free speed and to use a somewhat higher e.h.p.
4E.H.P. than the lowest limit for the S.B .C. and speed. Let us take .g^' ' '
= .i and take what can be realized for towing ability, then
e.h.p.^E.H.P
viV (dhovcE.T.).
V (free) (knots) —
V
LHP.d.
K*
I.H.P.P.
Z
I.H.P.
D
LT.z>^(i5).
P.A.^D.A....
1PA.^D.A.
P.C
E.H.P
e.h.p.
T.S...
15..
P....
V (free)
Log i4v (Curve X, Sheet 21).
Log Av (Curve X, Sheet 21 . .
s '.
Ra
.1
.1
.1
.36
.4
.44
6.9s
6.9s
6.9s
19.3
17.37
15.79
ISO
ISO
150
1.0973
1.0973
1.0973
136.7
136.7
136.7
I. 0414
I. 0414
I. 0414
1504
1504
1504
S'^S
S'S
5'.5
6.416
7.129
7.842
.398
.422
.446
.531
.563
.595
•535
.525
.525
804.5
789.5
789.5
80.4s
78.95
78.95
8580
9000
9470
.93
.927
.923
4'. 23s
3'.645
3'. 163
6.95
6.95
6.95
3.84
3.71
3.585
2.655
2.655
2.655
.1069
.08265
.06538
182.6
210.5
238.2
.1
.48
6.95
14.48
150
1.0973
136.7
1. 0414
1504
5.5
8.555
.468
.624
.525
789.5
78.95
9890
.919
2 .788
6.95
3.475
2.655
.05339
266.7
* The proper value to use for K is 1.195.
Laying down PjRdoni (P.A. 5D.A.) as abscissas, the propeller to meet
the free route condition is foimd to be as follows:
D=s' 6"
P=3'4l"
4 PA. ■
Blades =4
I'H P. =300 Total on two screws
»=8 statute miles
i2d=225
e.h.p. = 1 5 7 . 9 by two screws
PC. = .526.
Digitized by LjOOQ IC
194
SCREW PROPELLERS
To analyze for the towing condition, proceed as follows:
D.
P..
RA,
*D.A.
P.C...
PA.
D.A. •
T.S...
15..
IT.D..
I.H.P. .
E.H.P.
V (kncts).
v^V
ch.p.
K*
Log Av
Log Av
^l.U.F.dXAv
s=S
5=5
LH.P.Xilr
icy^XA
;^ \E.t)
R4.
s's
3' 375
.581
.525
.436
9250
.925
16.49
6.95
1505
790
5. 211
5. 211
5. 211
.3159
•3159
.3159
.05
.07
.09
I.O
.70
.60
1355
1.2
1.09
I 0973
I .0973
I .0973
365
3.6s
3.65
2.41
2.41
.241
.1299
.1299
.1299
.06315
.1289
.1938
179.8
179.8
179.8
5. 211
.3159
•55
I. 0414
I .0973
365
2.41
.1299
.2364
179.8
* li should be i . 195.
Curves of s cross at e.h.p. 5E.H.P. = .0705.
/. e.h.p. delivered per propeller in towing with 150 I.H.P. per engine,
at 6 statute miles = 790 X.o7os = 55.7, total = iii.4.
The problem may be solved by using Cases i and 2, " Diameter Reduc
tion " with some possible gain for the towing condition. The broadening
of the bfade tips will, however, undoubtedly injure the performance in free
route due to the increase in thrust deduction.
Motor Boats
In the design of propellers for motor boats, curves of effective
horsepower and curves of fullthrottle engine power, when the
engine carries a varying brake load, plotted on revolutions,
Digitized by LjOOQ IC
DESIGN OF THE PROPELLER 195
should be furnished as if when the estimated powerrevolution
curve of performance of the propeller is laid down, the curve
of fullthrottlerevolution curve of the engine should fall below it
at any point, the engine would not be able to carry the revolu
tions above this point and disappointment in speed would result.
Also in boats of this class where the speed is so great that the
vessel planes, the point where this planing begins will be shown
on the effective horsepower curve by a decided hump in the
curve. The standard block coefficient should be found in the
ordinary manner by Sheet 17, up to the vertex of the hump.
From this point on the slip block coefficient rapidly decreases,
until at a speed equal to about t times the speed at the hump the
slip block coefficient will equal about 50 per cent of the standard
slip block coefficient.
Digitized by LjOOQ IC
CHAPTER X
DESIGN OF PROPELLERS BY COMPARISON
Sometimes, in designing the propellers for a vessel, it is
desired to obtain propellers which will give an equal propulsive
efficiency with those fitted to an earlier vessel of similar form but
of different size, and whose performance has been regarded as
excellent.
In the method of comparison here proposed, the formulas
take the following forms:
Li = Length of original vessel;
£2 = Length of new vessel ;
(Both on L.W.L.)
Xi'
2?2=Z?ir'/';
V2 = Vir^;
Apparent sUpx= P^X^';°^33Fx .
Apparent slip2 =
//2
196
Digitized by LjOOQ IC
DESIGN OF PROPELLERS BY COMPARISON
Apparent slipi = Apparent slip2;
Tipspeedi = Ri XvDi ;
Tipspeed2 =iZ2XZ?7r2=^,XirZ)if'/«=iJiXirZ)i;
197
.'. Tipspeedi
=Tipspeed2;
Again,
I.H.P.2
=I.H.P.i/^;
Disc area2
4
Disc areai
im
P2XiJ2
'Fo'Xw.'
I.T. per square inch disc area2
^ LH.P.iX//'X33>ooo ^ IH.P.iXi32,ooo ,
Pir^XRiXDr'r^ PiXiJiXirZJi^ '
4
I.T. per square inch disc areai
LH.P.iX 132,000
PiXRiXirDi^ '
.'. I.T.i=I.T.2, and for the model screw the tipspeed, apparent
slip, and thrust per square inch of disc area are identical with
those of the original screw.
The equations for Diameter, Pitch and Revolutions may also
be put in the following forms:
To obtain such propellers, it is possible to work directly with
the Chart formulas, always remembering that, according to the
Charts, for equal propulsive efficiencies the projectedarea
ratios, and products of thrusts (effective, propulsive, and indi
cated), by tipspeed« must remain equal. Bearing this in mind,
Digitized by LjOOQ IC
198 SCREW PROPELLERS
and obtaining the ratios between the equations for diameter,
pitch, and revolutions of the existing propellers, and those of the
propellers that are being designed, the following equations
result:
^ ^ / E.H.R2XF1 ^ / lH.P,2XFi ^ / S.H.R2XF1 ,
^' =^We.H.P.i X V, =^WlH.P., X V, =^Ws.H.P.x X F2'
p / E.H.P.2XF2 _p / LH.R2XF2 ^p / S.H.P.2XF2 .
^ We.H.P.iXFi ^^LH.P.iXFi ^^S.H.P.iXFi'
^ ^ /E.H,RiXF2 J. / LH,RiXF2 ^ / S.H.R1XF2
^' =^We.H.R2XFi ""^WlH.P.2XFi ^Ws.H.P.2XFi'
Where
Z7i = Diameter of existing propeller;
£>2 = Diameter of propeller for new ship;
Pi = Pitch of existing propeller;
P2 = Pitch of propeller for new ship;
iJi = Revolutions of existing propeller;
lf2 = Revolutions of propeller for new ship;
Vi = Speed of existing vessel;
F2 = Speed of new ship;
E.H.P.i = Effective horsepower for Vi of existing vessel;
I.H.P.i = Indicated horsepower for Vi of existing vessel*
S.H.P.i = Shaft horsepower for V\ of existing vessel;
E.H.P.2 = Effective horsepower fo* V2 of new vessel;
I.H.P.2 = Indicated horsepower for V2 of new vessel;
S.H.P.2 = Shaft horsepower for V2 of new vessel.
The speeds used in the above should be the corresponding
speeds by Froude's Law of Comparison, where
V V / P^splacement2 \ ^^'
\Displacementi/ '
Power.=H.P..=H.P.xfg!?2^^^^)'",
\Displacementi/
Digitized by LjOOQ IC
and
DESIGN OF PROPELLERS BY COMPARISON 199
the following forms will obtain:
^^. / Displacement ,„JL,\"'.Dm)'
\Displacementi/ \Li/ \Vi/
"•^s^.
2XF1
IXF2'
\Displacementi/ \Li/ \Vi/
p i H.P.zXFa .
\Displacement2/ \Z.2/ \V2/
"^'^'H.p.2XFl'
where Li and Z2 are the load water line lengths of the old and the
new vessel respectively.
According to these formulas it appears that the "Law of
Mechanical Similitude " does not apply to screw propellers, as
the diameters are seen to vary approximately as the cubes of the
speeds, while the pitches vary, with the same degree of approxi
mation, as. the fourth power.
Digitized by LjOOQ IC
CHAPTER XI
EFFECT ON PERFORMANCE OF THE PROPELLER CAUSED
BY VARYING ANY OF ITS ELEMENTS
Epfect of Change of Blade Form on Performance
Should the forms of projected areas here advocated not be
adhered to, the following results may be confidently looked for:
1. Broadening the Blades at the Tips. Revolutions will be
decreased, apparent slip will be decreased, and thrusts will be
increased and efficiency slightly decreased.
2. Narrowing the Blades at the Tips. Revolutions will be
increased, apparent slip increased, and thrusts decreased.
In the matter of relative weights for equal blade strengths
the narrowtipped blade has the advantage.
It should be distinctly understood that no claim is made that
the forms advocated in this work are necessarily those giving the
maximmn efficiency. It is believed that equal efficiencies can
be obtained with all shapes, if for each shape the proper diameter,
pitch, and surface have been provided for the absorption of the
delivered power under the ccaiditions in which the screw is
operating. Each series of forms must, however, have its own
particular factors of design if results in conformity with the
computed performance are to be expected.
Some Points Governing Propulsr'e EFFiciENcy
1. Effect of Excess Pitch. Shown by Fig. i6. — Gain in pro
pulsive coefficient at low powers. Loss in propulsive coefficient
at high powers. Both sets of propellers having blades exactly
alike, but projected area ratio decreasing as pitch increases.
2. Effect of Variation of Blade Surface. Least surface:
Greatest efficiency at low powers; rapid loss of efficiency as
200
Digitized by LjOOQ IC
EFFECT OF VARYING PROPELLER ELEMENTS
201
power increases; least efficiency and earlier cavitation at high
powers. Blades all of same form, which was the standard form.
Maximum surface: Greatest efficiency and smoothest nmning
28000
/
27000
'96000
25000
Biono
N
Dimensions of PropcUer
Developed
Diam. Pitch Area
Montana 18'0* Sl'«' 100/
North CaroUna 18'0' 22'6' 100#
/
/
/
//
1
7
^nnn
/
P oormn
/
S210OO
/
/
H 20000
/
19000
y
'/
—^
p^isooo
A
§17000
'f 16000
A
'i
y
/a
P
(215000
/
14000
Y
13000
*A
12000
11000
/
/
/
/
10000
/
/
9nnn
/
/
V
i
1
7
1
3
1
9
2
2
1
2S
I
23
Speed in Knots
Fig. 16. — Influence of Projected Area Ratio on EflSciency.
at high powers; lowest efficiency at low powers.* Lowest tip
speeds for equal indicated thrusts per square inch of disc area
with the other screws. See Fig. 17.
Digitized by LjOOQ IC
202
SCREW PROPELLERS
3. Effect of Variation of Power Distribution oi^ Fourshaft
Installation. One H.P. ahead turbine on each outboard (wing)
shaft. One L.P. ahead, one backing and one M.P. cruising
230 ^40 250 2G0 270 280 290 300 310 320 830 S40 350 3U0 370 380
Scale of Revolutions
Fig. 17. — Power and Revolutions as Affected by Projected Area Ratio.
turbine on one inboard shaft. One L.P. ahead, one backing
and one H.P. cruising turbine on other inboard shaft. See
Fig. 18. These variations will vary with the distribution of
power on the shafts.
Digitized by LjOOQ IC
EFFECT OF VARYING PROPELLER ELEMENTS
203
s
0.60
Cuivei
of
p^
polsiv
> CoeiB
cie
Its.
"*«^
^
^
K
V
s,
f^
^
\
V
=
=7"
^
^
s
\
_
—
"^S
s.
S"
—
—
—
—
—
—
u
—
—
_
/
7
—
—
—
—
i
s"
—
—
— ^
«S
"V
=
—
—
rTTI^

/
N
k
V
rv
\
V
"^H


5 Turbine
6T
url
ine
i
• 10 11 12 13 14 15 16 17 18 19 20 21 22 23 IM 25
Speed in Knots
Fig. 1 8. — Effect of Varying Distribution of Power on Fourshaft Arrangement.
7000
f
/

J
/
/
f
/
6000
A
/
/
/i
fe
}
/
s
/
f
/
/
^
/
/
5000 O
/
/

d
/
/
1^
s
/
/
'/
*
i
/
1
^
£
■
s
fA
A
4000 o
^
'
x
f
a
/
A
¥
1
€*
A
.^'
/
y^
o
^
V
r
r
5
^.
y\/
f
3000 1
f
/
'

/
/
•
/
^
y
/<
^
'
Power for Inboard Screw at 610
2000
^
^
4:
»
4
10
4
50
4i
iO
5(
X)
5'^
iO
54
K)
fA
M)
5i
K)
6(
K)
6:
10
ft
K)
6C
K)
6£
to
7(
Scale of RevolatioQS
Fig. iq.— Effect of Position of Propellers on Power and Revolutions, Four
shaft Arrangement.
Digitized by LjOOQ IC
204
SCREW PROPELLERS
4. Fourshaft Arrangement. All propellers of the same
dimensions. Effect of position of propellers in relation to the
hull on the power and revolutions. See Fig. 19.
5. Cases A and B. Threeshaft arrangements.
Case A. Dead wood cut away. Center propeller working
in locality well clear of hull.
r
/
^
/
^
"
/
^
V
^
,•
y
^
c
f
^
^
^
^
^
y*
r^
V
^
^
rf"
^
»*V
r
.'^
sv
i^
y
f^C
b'
^
y
,<^
^
c
f\
r
r
4
r1
t^^
^.«
^
si
\
■r^
Wl
<"^
^
■A
»;
>
>
^
^
>•
k
^v
>
/
y
^
\<
r
^
/
z'
f.
^
y*
\
'y*
>A
/
y^
y
^
X
n
/i
X
^'
^
y
/
>
^^
y
h
y
/
k. Power reqiUred for Center Screw at 800 rev8.=1.18
that required for the wing screws
\ Power required for Center Screw at 800 reT8;=1.27
that required for the wing screws
^
^
\
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Propellers nearly Identical In the two cases
Sllerhtly more Surface in B, than in A. Center screws same as
wlnfiT ones. Case B, vessel displacing about 15 tons more
than In case A
..
1
eooo
5000
I
400o
o
n
3000»S
aooo
700 730 740 760 780 800 8% 810 860 880 900 920 910 960 960 1000
Scale of revolutions
Fig. 2o. — ^Threeshaft Arrangement. Influence of Character of Afterbody on
Power and Revolutions.
Case B, Dead wood carried well aft. Center propeller
working immediately in wake of stem post.
Center propellers of same dimensions as wing ones and
propeller of Case A almost identical in dimensions with Case B.
See Fig. 20.
6. Effect on Propulsive Efficiency of Location of Propeller
When Operating in the Wake of a Full Afterbody. An in
teresting problem of the above conditions has recently arisen
Digitized by LjOOQ IC
EFFECT OF VARYING PROPELLER ELEMENTS
205
in the case of a selfpropelled, barge constructed for the Navy
Department. The block coeflBicient of the hull was .9, the
afterbody being very full.
The propeller, as first fitted, was located as shown by the
dotted lines in Fig. 21, the hull lines shown being those of the
actual vessel.
The contract speed of the barge was six knots, but, although
Fig. 21. — ^Positions of Maximum and Minimum Efficiency Positions of Propeller
in the Case of Very Full Afterbodied Shallowdraft Vessel.
a series of seven propellers was tried, the maximum speed ob
tained was only approximately 5J knots.
After, thoroughly considering the conditions, it was deter
mined that the best chance of success, at the least expense, was
offered by relocating the propeller so that a better flow of water
to it from forward would occur. This idea was adopted, and the
propeller was located as shown by the full lines of Fig. 21, the
shaft being given a very heavy inclination.
Digitized by LjOOQ IC
206
SCREW PROPELLERS
After this change had been made, the vessel was again tried
and a speed of approximately 6j knots was realized with about
the same power and revolutions that had given si knots mider
the original conditions.
The results of the various trials and the data of the propellers
used are given in Table IX, the trial marked No. 8 being the
final successful one. The major part of improvement in per
formance in this case was caused by the change in location of
the propeller, the second position permitting a much freer and
more direct flow of water to the propeller, a much reduced
thrust deduction factor resulting therefrom.
Table IX
U.S.N. OIL BARGES NOS. 2 AND 3, COURSE ON CHESAPEAKE BAY
Prop. Nos .
Date
Diameter of wheels . . .
Pitch
Number of blades ....
Dev. area square feet .
Proj. area square feet
Average steam
R.P.M
Slip per cent
I.H.P
Speed knots .
9271 I
5' 6"
4' 3"
4
12.92
11.72
III. 25
204.3
49
133.78
4415
losii
6' 2"
3' 3"
3
10. o
.942
no
212.9
30.4
149.92
5. "7
10 71 I
5' 9"
3' 6"
3
6.58
.60
107. S
210.5
36.4
130 95
4.69s
101311
6' 3"
3' 8"
3
8.58
8.0
115.2
208.2
30.8
144.74
S.io
101911
6' 2"
3' 6"
4
1333
1213
122.6
200.7s
23.8
152.24
Prop. Nos...
Date
Diameter of wheels. . .
Pitch
Number of blades . . . .
Dev. area square eet .
Proj. area square feet .
Average steam
R.P.M
Slip per cent.
I.H.P. ......
Speed knots .
5*
102411
6' 2"
3' 6"
4
13.33
12.13
123.7
207 . 602
26.7
160.0
5.258
11611
6' 3"
3'o"
3
15.21
14.64
125
228.65
26.15
172.67
5.045
1 2201 1
6' 3"
3' 4"
4
20.28
«952
125
205.95
22.5
17547
5.24
8
5812
6' 9"
3' 6"
3
14
13.2
129 S3
206.27
12.56
177.64
6.235
Propeller number marked * is Official Trial.
No. 8. Line of shaft so modified as to bring lower blades of propeller well below
keel of vessel.
Digitized by LjOOQ IC
CHAPTER XII
STANDARD FORMS OF PROJECTED AREAS OF BLADES
FOR USE WITH THE CHARTS OF DESIGN
Forms of Blades and Blade Sections
Returning to the Bamaby presentation of Froude's results,
the constants obtained by Mr. Bamaby are only correct so long
as the ratio of developed area to disc area and the elliptical form
of this developed area used by him are adhered to. There is
no way of allowing for the effect of increase or decrease in this
developed area except the rough one of estimating that the total
thrust that can be delivered by the propeller will vary directly
as the developed area.
By investigation of what occurs when the standard elliptical
blade used by Bamaby in his experiments is broadened or nar
rowed, it is readily seen that this method ef correcting for varia
tions in developed area ratio is incorrect, for as the blade widens,
for any one pitch ratio, the length of its resistance arm increases
above that of the standard widtJi blade, and as it narrows the
length of this arm decreases. In the first case, the resistance
of the blade to turning is increased not only by the increased
surface friction of the larger bJade, but also by the increase in
the length of the radius to the center of pressure of the blade.
Should the blade be narrowed below standard, the opposite
effect will be produced.
If elliptical blades of varying pitch ratios, but having the
same area of projection on the disc, be laid down, it will be noted
that the form of projection, not only on the disc but also on the
plane of the axis of the propeller, changes in passing from the
lower to the higher pitch ratios. This same change in form of
projected area also occurs if blades of the same pitch ratio but of
207
Digitized by LjOOQ IC
208
SCREW PROPELLERS
Projected area=.32 disc area
Dotted lines are developments of projected areas as shown
Full " ** actual developments of blades
For other projected area ratios increase or decrease projected
area shown proportionally on circular arcs
Fig. 22. — Developments Corresponding to a Standard Projected Area Ratio of
Constant Value but with Varying Values of Pitch r Diameter.
Digitized by LjOOQ IC
FORMS OF PROJECTED AREAS OF BLADES
209
different values of developed area ratio are laid down, thus in
both cases showing that not only the resistance of the blade,
due to change of surface, and in the first case change of pitch,
has been affected, but it has been still further modified by the
change in the distribution of this surface and the modification in
the leverage arm of the blade resistance.
A distinguished educator who formerly was an advocate for
the use of constant developed area form in design work, has put
before the public a work on
propellers in which he advo
cates the use of the projected
area in place of developed
area. He has adopted, in
stead of the constant ellipti
cal form of development, a
constant elliptical form of
projected area. Should the
projected area ratio be .3 its
form is that of an ellipse, and
should this ratio be .6 the
form is again an ellipse. The
same changes in distribution
of surface occur as before, and
no benefit has been obtained
except that of having an easy
form to lay down and also
one that can be mathemati
cally represented.
In order to maintain as constant a distribution of blade area
as possible, and thus guard against changes in resistance due to
changes in distribution, there has, in this work, been adopted as a
basic form of projected area the form of projection of the blades
of two 3b laded propellers having approximately a projected
area ratio of .32. These two propellers had most excellent
records, which could hardly be bettered.
Using a standard hub diameter equal to .2 of the diameter of
the propeller, this standard basic form of projection was drawn.
Fig.
23.
Projected Area Standard Form
and Blade Sections.
Digitized by LjOOQ IC
210 SCREW PROPELLERS
Then, with the center of the hub as a center, and different radii,
circular arcs were struck crossing the axis of the projection. In
obtaining the projected forms for areas differing from the basic
area, the widths of the projections measured on these circular
arcs were made proportional to the circular arc widths of the basic
projection; that is, a .6 projected area ratio would have circular
arc measurements M times as great as those for the basic .32
projection.
The forms of projected area so obtained, when compared with
the forms of blades of many propellers, are found to agree very
closely, from the lowest to the highest values of P.A.^D.A., with
those forms which have the best records credited to them.
By using these forms, for any pitch ratio the resistance arm
of the blade always remains the same, no matter what the devel
oped or projected area ratio, and the only change in resistance to
turning is that caused by the additional surface. The forms of
projection, both on the disc and on the foreandaft plane, remain
constant for all pitch ratios.
Naval Constructor D. W. Taylor, in writing on the effect of
blade form as deduced from model tank experiments, stated " A
good practical rule would seem to be to make the blades broader
at the tips for lowpitch ratios and narrow them for high ones."
The blades here advocated follow this rule automatically, as the
broadest part of the developed blade, measured on the elliptical
development of the circular projected arc, moves slowly in
towards the hub as the pitch ratio increases, thus gradually
narrowing the tips of the blade for the higher pitch ratios.
The derived projected forms are shown on Sheet 25 (Atlas),
where is also shown a diagram by which the developed area ratio
can be obtained for standard propellers of any pitch ratio and
any given projectedarea ratio, and vice versa. On this same
sheet is given a table of multipliers for obtaining the lengths of
chords for half circular arc widths for different projectedarea
ratio blades for any desired diameter of propeller, by means
of which the projectedarea forms can be laid down without
the use of the diagram of forms. •
The necessity of adhering to standard projectedarea forms in
Digitized by LjOOQ IC
FORMS OF PROJECTED AREAS OF BLADES
211
order to obtain graphical or other methods of design will be easily
understood by examining the following figures, 24, 25, and 26,
showing forms of projected and developed areas for the Standard,
the Bamaby, and the Taylor forms of blades.
z
o
z
o
I
o
UJ
i
I
Fig. 24 shows the standard form of projected area marked a,
and the developed areas for pitch ratios of .8 and of 2, marked
a' and a", respectively, together with the corresponding pro
jections on the foreandaft plane.
Digitized by LjOOQ IC
212 SCREW PROPELLERS
Figs. 25 and 26 show equal devel(^)ed areas with Fig. 24,
and the corre^xmding projected areas on the disc and on the
foreandaft plane, for Bamaby's and for Taylor's blades, re
spectxvefy.
The dotted forms shown on Figs* 25 and 26 are the projected
area forms of Fig. 24.
Attention is called to the great variation in distribution of
blade surface, as the pitch ratio changes, in blades of the forms
given in Figs. 25 and 26, and the rational and gradual change of
form that occurs in Fig. 24.
The standard form need not be adhered to rigidly, but may
be modified between the greatest width and the hub in order to
decrease the resbtance of the sections of the blade in this region
by allowing the blade to be made wider, thinner, and sharper
edged.
Variations from the Standard Form
With the exception of the lastmentioned case there are but
two cases where departures from the standard form are justified,
after such form has been adopted and the method of design been
. based upon it. These cases occur when ]imitations of draught or
conditions of design make it impossible to fit a propeUer of as
large a diameter as is indicated by the calculations to be neces
sary to obtain the desired revolutions with the maximum pos
sible efficiency.
Such cases are shown by projected areas shown in Figs 4 and
5, and as A and B in Fig. 27, having a diameter of screw of 2R,
With case A, the allowable radius is R', so, while retaining the
pitch of the greater diameter propeller, it becomes necessary to
broaden the tip of the blade which takes the form shown by A\
the area of the projection A' being equal to the projected area A .
This area A^ may be as shown, or may be greatly modified in
appearance, as in A'\ provided the circular arc measurements of
width at equal radial distances remain equal.
Where the difference between the calculated and the allowed
dltttneters is large, the resultant blade would have an abnormal
Digitized by LjOOQ IC
FORMS OF PROJECTED AREAS OF BLADES
213
form, as in B'. This form is often met with in motorboat
propellers, disguised as B'\ Patents have been allowed on this
form, and great claims are made for it on the grounds of high
efl&ciency, when in reality its greater efl&dency over a blade of
ordinary form is caused by its approximation in amount and
Fig. 27. — ^Variations in Projected Area Fonns.
distribution of area to those of a propeller having the proper
dimensions for the work which it is called on to do. In place of
this tip broadening, however, the problem may be solved for
the diameter that can be carried, and the standard form of
projected area be adhered to. Blades having the greatest
width thrown well out beyond its location in the standard form
Digitized by LjOOQ IC
214 SCREW PROPELLERS
are about 3 per cent less efficient for the same projectedarea
ratio.
Blades thrown to the side, as in i4", are used to reduce vibra
tion in cases where a rapidrunning screw operates close to the
strut or stem post. As a general rule, though, they are unde
sirable, as the form is weak and the blade must be made extra
heavy at the root in order to provide the necessary rigidity to
insure against change of pitch, due to springing of the blade
when subjected to heavy thrusts.
Rake of Blades. It is a very common practice to rake the
blades aft to a more or less degree, and this practice was gener
ally followed in the United States Navy until a few years ago.
There was a generally accepted idea that centrifugal action of
the screw was decreased and that efficiency was increased by so
doing.
An examination of the performances of actual screws in
service, and of model screws in the tank, shows that there is no
solid ground for either belief. In the cases of the actual screws,
no difference in the propulsive efficiencies of screws with and
screws without rake can be noticed, and the models gave prac
tically identical results. As to centrifugal action, nimierous
tank experiments have shown the propeller race to be almost
cylindrical, and that so far from there being centrifugal action,
there appears to be a slight convergence abaft the propeller as
shown by Fig. i A.
An actual advantage gained by raking the blades aft is that
the blade tips of wing screws are given greater clearance from
hulls of usual form than if the blades were radial; also, for the
same blade clearance, the strut arms may be made shorter.
Another advantage which the rake may have is in giving greater
clearance between the leading edges of the blades and the after
side of the stem post and struts, this additional clearance allow
ing the water a chance to enter the disc at a better angle.
Radial blades, in addition to being as efficient as those with
rake, are more easily machined, have less total developed area
for equal projected area, and therefore less surface friction, are
stiff er and lighter; also, the stresses in the blades due to cen
Digitized by LjOOQ IC
FORMS OF PROJECTED AREAS OF BLADES 215
trifugal action are less. With propellers of high speed of revo
lutions, this latter point is very important, and for such screws
the blades should never rake.
Form of Blade Sections tor Standard Blades
In the propellers designed according to the Dyson method
the form of section existing in the propellers from whose data
the design data curves were developed has been adhered to.
In these blades, the working face of the blade forms the nominal
pitch surface, the blades in all cases being made with constant
pitch. The thickness of the blade is built up on the back of
nominal pitch face. The form of the back is an arc of a circle
and the edges are made as thin and sharp as possible without
sacrificing durability to an extravagant degree. See Fig. 23.
The principal forms of blade section that are met with in
practice are as follows:
T
With a small vaflue of — from .12 to .20 at the hub, the form
W
A appears, from trials, to be all that is required. Where the
T
value of — is higher than .20 and the fillet of the blade is also
W
heavier it may be advisable to slightly fine the entrance of the
blade by throwing back the leading edge a small amount as
shown in B, but this should not be done to any great extent, as
it tends to slow the blade down by increasing the actual working
pitch above the nominal more than is done by ^.
Section C with the following edge of the blade thrown back,
the leading edge being either similar to A or thrown back as
shown, is considered to be a decided mistake, since, as the water
travels along the driving face of the blade from the entering to
the leaving edge, there may exist a tendency for it to break con
tact with the blade face. It was to guard against this tendency
of the water to leave the blade face that axially expanding pitches
of blades were used. If the following edge of the blade is thrown
back as in C, the face of the blade is deliberately drawn away
from the water and a cavity at this edge will result, with conse
Digitized by LjOOQ IC
216
SCREW PROPELLERS
quent eddying effect and resultant vibration and loss in effi
ciency.
In Section D, the leading half of the back of the blade has a
pitch such that its slip equals the real slip of the screw. This
form is theoretically (!orrect, provided the velocity of the water
meeting the propeDer is that of the vessel modified according to
the wake that is equal tov—Wy but in practice, imless the blades
Fig. 29.
Fig. 30. — ^Variations in Blade Sections.
are very wide, it gives too thick a blade and too blunt an entrance,
with a consequent heavy loss in efficiency.
Blades of section E, with the metal of the blade divided
evenly on each side of the nominal pitch surface or plane, appear
to offer less resistance to turning than any of the other sections,
due probably to the fact that the real pitch of the blade is prob
ably the same as the nominal pitch, as is shown by the fact that
if blades of this section, designed for zero pitch, be revolved,
they will exert zero thrust, while blades of the preceding sections,
Digitized by LjOOQ IC
FORMS OF PROJECTED AREAS OF BLADES 217
designed for zero pitch, will, when revolved, record a decided
thrust, due to the influence of the backs of the blades; the
back evidently giving the blade a working pitch greater than
the nominal pitch causes it to exert a thrust. While it requires
less power to turn blades of section £, the resultant thrust per
revolution is much lower and the apparent slip is much higher
than with blades of the same nominal pitch but of different
section.
With blades having sections similar to F, the same results are
obtained as with Section £, but in a less degree. The design
curves and factors being based on the performances of blades of
manganese bronze, it is desirable, when a weaker material is used,
to make the thickness from the pitch plane to the back the same
that it would be if the stronger material were used, and to add the
additional thickness to the face, thus producing a section sim
ilar to F.
Digitized by LjOOQ IC
CHAPTER Xm
THICKNESS OF THE BLADE AT ROOT. CENTRIFUGAL
FORCE. FRICTIONAL RESISTANCE OF PROPELLER
BLADES
Thickness of the Blade
The fiber stress to be used in determining the thickness of
the blade at the root depends upon the material of which the
blade is to be made and the degree of approximation of the point
of design to full overload conditions. The material usually
used for propeDers in the Naval Service is manganese bronze,
and the specified ultimate tensile strength of the material is
60,000 lb. Where the possible overload does not exceed 10
per cent, a working stress of 10,000 lb. per square inch can be
used with safety with reciprocating engines. With turbines or
reduction gear this may be increased to 13,000 lb. This is the
condition existing for Sheet 20 of the Design Sheets. For pro
pellers designed for about .3 load factor, ' „'^' = .3, where the
power used in the calcidations may be very much lower than
the maximimi power possible, this working stress should be
reduced to about 6000 lb. For high speed, highpowered motor
boat propellers, the thickness with highgrade material may be
made f in. for each foot radius of propeller. Plate A.
The formula used for the determination of blade thickness
has been derived from Naval Constructor D. W. Taylor's work
on " Resistance of Ships and Screw Propulsion," and is an
adaptation of the formula proposed by him. The nomenclature
and formulas are as follows:
r= Thickness of blade at and tangent to hub, additional thick
ness due to fillets being neglected. T should not exceed
.2W.
218
Digitized by LjOOQ IC
THICKNESS OF THE BLADE AT ROOT 219
Tr= Width of blade tangent to hub.
A = (33,oooXl.H.P.d)^ (2irXRevolutionsXNumber of blades)
= 5252 LH.P.dT(RXiV)= Maximum indicated torque
per blade, in foot pounds.
B.^i XDiameter of screw, in feet = Mean arm.
C= 4^5= Resultant athwartship force on one blade, in foot
pounds.
Z?= 12 XB— Radius of hub, in inches = Arm of athwartship
force measured to root of blade.
jE=CxZ?=Athwartship moment at root of blade, in inch
poimds.
F= (33,000 Xl.H.P.d)^ (Pitch, in feet X Revolutions XNum
ber of blades) = Indicated thrust per blade, in pounds.
G=. 345 XDiameter of propeller, in inches = Mean arm of
thrust, in inches.
£r=G— Radius of hub, in inches = Arm of thrust measured to
root of blade, in inches.
/=FXJ7= Foreandaft moment at root of blade, m inch
poimds.
^= Circumference of hub, in feet ^ Pitch, in feet = Tangent of
angle between face of blade and center line of hub or fore
andaft line tangent to surface of hub.
L == Sine of arc whose tangent is K.
Af= Cosine of arc whose tangent is K.
iV=Z»X/= Component of foreandaft moment normal to face
of blade at root.
0=Af XE = Same for athwartship moment.
P=i\^^0= Total moment at root of blade in inch poimds.
/= Fiber stress = as per values of e.h.p.HE.H.P. given on
Plate i4.
^^ /PXi3£25
^""V wxf •
Fixing th e maximu m thickness at T=.2W, T should never
exceed T=\j j^ for the strong bronzes.
For cast iron and semisteel, /= from 2500 to 4000, for values
of e.h.p.^E.H.P. not in excess of .4.
Digitized by LjOOQ IC
220
SCREW PROPELLERS
!
1
1
i i 1 1 1 1
1
1
i
1
1
1
V
V
1
L
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\
\
\
»k
V
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\
\
\
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i
\
v
\
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\
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V
\
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\
^
\
\
V
V
<
^
A
\
A
^^
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'
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'0
I ,
—
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LU
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Q
UJ
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8
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Digitized by LjOOQ IC
THICKNESS OF THE BLADE AT ROOT 221
Centrifugal Force: Increase of Stress
Concerning the effect of this on blade stress, Beaton states,
" Centrifugal force produces in the screw blade at all times some
stress, and at high revolutions the stress becomes serious, so
much so, in fact, that destruction of blades is due sometimes to
this source with screws driven by turbines.
"Within moderate velocities the forces set up by inertia
really tend to balance those by hydraulic pressure on the blade.
That is to say, that whereas the hydraulic action tends to bend
the blade in a direction opposite to that of revolution, the inertia
of the blade tends to make it bend the other way as well as to
* throw off.'
" The forces acting on a screw blade due to its velocity can be
calculated from the usual formula where W is the weight of a
blade in poimds, r is the distance of its center of gravity from the
axis of rotation, g is gravity and taken at 32, v the velocity in
feet per second:
Then
W v^
and the tension on the bolts=— X— ,
g r
— being of course the accelerating force, and called usually the
centrifugal force.
" When a propeller is in motion on normal conditions, nm
ning at R revolutions per minute,
t;=>/^tS'^+(21rr)2xi^^6o=^\/p2+(21rr)2.
"As an example take the case of a screw propeller 12 ft.
diameter, 15 ft. pitch, 200 revolutions per minute; center of
gravity of blade is 3.2 ft. from the center; it weighs 1600 lb.
Digitized by LjOOQ IC
222 SCREW PROPELLERS
Determine the bending moment on the root distance 1.8 ft. from
the eg. and the tension on the screw bolts screwing it to the boss.
«'=^is!+(2irX3.2)2X2oo46o=Y^iS^+(2irX3.2)2=84 feet
per second,
C=4FX8i^=3S2,8oolb.
" Tension on bolts=3S2,8oo53.2 = 110,125 lb.
" If seven bolts, tension on each = 15,732 lb.
" Bending moment due to 0=352,800X1.8=635,040 ft.lb.
This is, however, in a plane through the face at the eg, and
therefore is resisted by the section at the root longitudinally.
" Taking circular motion and no advance of the screw,
r=21rX3.2X2oo^6o=67 ft.
Then _
C=4FX67^ = 224,5oo lb.
" The bending moment on a plane at right angles to axis=
224,500X1.8=404,100 ft. lb.
" Taking an extreme case of an Atlantic steamer driven by
turbines so that each screw receives 18,000 I.H.P. at 180 revo
lutions, the diameter being 16 ft. 6 in., the pitch 18 ft., the
weight of each blade 11,200 lb., its e.g. being 4.5 ft. from the axis
and 2.0 ft. from the root.
" Here velocity = —Vi&^+iirg)^ = 1 1 1 f t. per second.
00
^ 11,200^^111^
C= —  — X = 1925 tons.
32 2240
" Taking circular velocity only,
^ 11,200^^ 85^ .
C= —  — X^ = ii2o tons.
32 2240
" Tension on bolts = — ^ = 251 tons.
4.5 ^
"If thirteen bolts to each blade, the load on each =19.3
tons in addition to that due to the pressure on the blade."
Digitized by LjOOQ IC
THICKNESS OF THE BLADE AT ROOT 223
Frictional Resistance of Propeller Blades
The following method of estimating the frictional resistance
of propeller blades is given by Mr. A. E. Seaton in his work on
" Screw Propellers."
" Frictional resistance of a screw blade may be found by the
following simple methods: Fig. 31 shows the outline of the
developed surface of half a blade whose figure is symmetrical
about CB. The propeller is moving at a uniform rate of revo
lution so that BC represents the velocity through the water at
the tips to a convenient scale.
" That is, the velocity per revolution at B and at any inter
mediate point is
d being the diameter at any point taken.
" If BCy etc., GK^ represents on a convenient scale the veloci
ties at By etc., G. A curve drawn through C, etc., K will per
mit of the velocity being ascertained at any intermediate points
by taking the intercept between BG and CK at these points.
The resistance per square foot may be calculated at three or four
pomts by the rule y = i.25f — j lb. and a curve GD set up in the
same way so that intercepts will give the resistance at any inter
mediate points."
Now, taking narrow strips of the blades at three or four
stations and multiplying by the resistance at these stations and
doubling the result to allow for the blade backs, a curve HE is
obtained so that intercepts again give the resistance at various
stations, and the area is the measure of the total resistance of
one blade.
Proceed, then, to multiply the resistance of the strips as
obtained above by the space moved through by them in a min
ute, and the work absorbed in turning the blade is measured
by making a curve HP by means of a few of the ordinates so
found as before.
Digitized by LjOOQ IC
224
SCREW PROPELLERS
Intercq)ts between HF and GB give the work absorbed in
moving those strips through the water, and the area GBFH
represents the total power in foot pounds absorbed in turning
that blade through the water.
Dividing it by 33,000, the horsepower required to overcome
h is obtained.
Fig. 31 represents the equivalent resistance of two of the
four blades of H.M.S. Amazon, and Fig. 32 is that of one of the
Fig. 31. — Estimate of Blade Resistance.
two of the Griffiths screw which replaced it and gave so much
better results.
The ill effect of the broad tip is seen at a glance, as are also
the losses arising from excessive diameter, for, by taking 6 in. off
each tip, the resistance is in both cases very much reduced, espe
cially so in the case of the fourbladed screw. Froude found
the efficiency of the Greyhound^ s machinery to be exceedingly
low, and attributed it chiefly to engine resistance, whereas it
was largely due to the absurdly large diameter of the screw,
Digitized by LjOOQ IC
THICKNESS OF THE BLADE AT ROOT
226
it being 12.33 ft diameter with 52 sq. ft. of surface; whereas
the RatUer, of similar size and power, had a screw 10 ft. diameter
with only 22.8 sq. ft. of surface, which elaborate experiments
years before had shown to be sufl&cient. Moreover the Rattler
had a speed coefficient (Admiralty) of 224 against that of 142
of the Greyhound, which should have opened the eyes of the
authorities in 1865.
With the high speed of revolution necessary for the efficient
working of turbine motors,
as also for the speed of revo
lution possible with modem
reciprocating engines, especi
ally the enclosed variety with
automatically forced lubrica
tion, propellers of small diam
eter are absolutely necessary
for safe running, while to
prevent cavitation the blade
area must be relatively large.
Hence it is found that the
modem propeller is gradually
getting nearer and nearer in
width of blade to the common
screw of sixty years ago, and
differs from it now chiefly in
its having nicely roimded
comers instead of the rigidly square ones of that time.
Fig. 33 shows one blade of H.M.S. Rattler of 1845; the
dotted line is that of a blade of a modem turbine motor
steamer. Now, although the difference in blade is small to
look at, the action when at work is very different. The
comers of the old screws caused violent vibration at high
speeds; but when they were cut away there was a very
marked improvement.
Frictional resistance of a screw propeller may be calculated
with a close approximation to the tmth by taking the velocity at
the tip and the total area of acting surface, using multipliers in
Fig. 32. — Estimate of Blade Resistance.
Digitized by LjOOQ IC
226
SCREW PROPELLERS
both cases deduced from the close calculation of it with screws of
diflferent types.
Let V be the velocity of the blade tips in knots per hour.
Let R be the revolutions per minute.
Let D be the diameter in feet.
Let P be the pitch of screw in feet.
Let A be the area of acting developed surface in square feet.
Fig. 33. — ^Antique and Modem Propeller Blades.
The resistance of a square foot is assumed to be i J lb. at 10
knots.
6080 101.33
lb.
Resistance per square foot = 1.25/ — ]
Resistance of screw = 2^X1. 25/ — j X/lb
Digitized by LjOOQ IC
THICKNESS OF THE BLADE AT ROOT 227
For a common screw /= .6034
For a fantailshape screw /=o. 581
For a parallel blade /=o S5o
For an oval /=o. 520
For a leaf shape 7=0.450
For a Griffiths /=o35o
The horsepower absorbed in overconduig the frictional resist
ance may be found now by multiplsdng the resistance by the
space in feet moved through in a minute and dividing by 33,000.
The mean space moved through by the blade surface from tip
to boss of an ordinary propeller'=o. 7 X distance moved through
by the tip.
TT FX0.7X6080 ^ ,,
Hence mean space = ^ = 70.97.
00
Then I.H.P. expended = 2^ Xi.2s(— j X/X 70.987 ^ 33,000
^ AxV^Xf
18,612 •
Edge resistance =iVX 5 per centXi.H.P. expended where
N= number of blades.
Total resistance of screw =I.H.P. expended +Edge resistance.
Example. A screw 12 ft. diameter, 15 ft. pitch, has 42
sq. ft. of surface and moves at 130 revolutions per ndnute (three
leaf blades).
♦ Here 7=^i3o_^^^^:p^^4olXi3^
101.33 101.3
Frictional resistance screw H.P. = ^^^^f '^ Xo.515 ^ ^^^g
18,612
Edge resistance here will be 3X5 per cent or 15 per cent of
166.8 = 25 H.P.
Then total resistance of screw = 166.8+25 = 191.8 H.P.
* »■• is here taken = 10.
Digitized by LjOOQ IC
CHAPTER XIV
CHANGE OF PITCH. THE HUB. LOCATION OF BIJU3E ON
BLADE PAD. DIMENSIONS OF THE HUB
Very often, upon the trial of a vessel, results indicate that
improvement is possible if the propeller blades be set to a higher
or lower pitch than that of the designed driving face. In order
to provide for such a change, the bolt holes in the blade pads are
made oval, so that ordinarily with large blades the blades can be
twisted to mean pitches of about i ft. more and i ft. less than
the designed pitch, the new pitch becoming a variable one. If
the blade is set for a higher pitch than the designed, the new
pitch becomes a radially expanding one, increasing from the hub
towards the tips, while if the new pitch is lower than the designed,
the pitch will decrease radially from the hub to the tips.
The change caused by alterations in pitch may be obtained
from the following table (Table X), (see Peabody's " Naval
Architecture ")> by multiplying the original pitch ^ diameter by
the factors given in Table X for the small angle through which
the blade is twisted.
The Hub
In designing screw propellers it was, up to the advent
of the turbine, the custom almost invariably to design propel
lers of large diameter with the blades detachable from the
hub in order that injured blades might be replaced at little
expense, sQid also that improvement in propulsive efficiency
might be sought for by providing for slight modifications of
pitch in securing the blades to the hub. Only in the smaller
wheels were the blades cast solid with the hubs. With the pitch
ratios ordinarily in use with the comparatively high pitch, slow
turning reciprocatingengine propellers, where the hub diam
eters varied from 20 per cent to 28 per cent of the diameter of
the screw in builtup wheels, the pitch angles at the hub ranged
228
Digitized by LjOOQ IC
CHANGE OF PITCH
229
from about 50® to 58®, while with solid propellers with hubs
var3dng in diameter from 14! per cent to 18 J per cent of the
diameter of the propeller, the pitch angle varied from 67° to
76° at the hub.
Table X
Angle the
Blade is
Twisted.
5^
Q
0.8
0.9
i.o
Z.I
1.2
1.3
1.4
IS
Z.6
1.25
I. II
1. 00
0.90
0.83
0.77
0.71
0.66
0.62
1.70.59
1. 80.55
1.90.52
2.0
2,1
2.2
0.50
0.47
0.45
2.30.43
a. 4
0.42
2.5 0.40
070.93
0.94
0.94
0.94
0.94
0.9s
0.95
0.96
.040.96
040.96
040.96
040.96
040.96
040.96
040.96
030.96
030.96
03
0.96
15
14
12
II
10
10
09
09
1.09
1.08
1.08
1.08
1.08
1.08
1.07
1.07
1.07
1.07
0.85
0.87
0.88
0.89
0.89
0.90
0.91
0.91
0.91
0.92
0.92
0.92
0.92
0.92
0.93
0.93
0.93
0.93
.22
.20
.19
.17
.16
•IS
.14
.14
•13
.13
.13
.12
.12
.12
.11
.11
.11
.11
0.78
0.81
0.82
0.84
0.84
0.86
0.86
0.87
0.87
0.88
0.88
0.88
0.88
0.88
0.89
0.89
0.89
0.90
0.71
0.75
0.76
0.78
0.79
0.81
0.82
0.83
0.83
0.84
0.84
0.85
0.85
0.85
0.85
0.86
0.86
0.86
1.37
134
1.31
1.29
1.27
1.26
1.24
1.24
1.22
1.22
1. 21
1.20
1.20
1.20
1.20
1. 19
1. 19
1. 19
0.64
0.68
0.70
0.73
0.74
0.76
0.77
0.78
0.79
0.80
0.81
0.81
0.81
0.82
0.82
0.83
0.83
0.83
45
41
.38
35
32
31
30
,29
.28
1.27
26
25
25
24
24
24
24
23
0.57
0.61
0.65
0.68
0.70
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.78
0.79
0.79
0.79
0.80
0.80
Desirable as it is to reduce the diameter of the hub to that
of the strut boss in order to avoid eddying between the boss and
strut, it is not always possible to do this with the hubs of builtup
propellers. The seating of the propellerblade pad in the hub
must be circular to permit of pitch adjustments, the hub must be
spherical to maintain its symmetry of outline when variations
of pitch are made, and the seating must be of sufficient diameter
to accommodate a proper niunber of holding bolts of sufficient
strength; finally, the blade pad must be of sufficient width to
Digitized by LjOOQ IC
230
SCREW PROPELLERS
accommodate a blade having such a ratio of thickness to width
as will prevent excessive blade resistance.
The effect of the above requirements, when met for turbine
driven propellers of large diameter and lowpitch ratio, was to
throw the effective blade areas too far out from the axis of the
hub, thus leading to serious increase in blade friction at the
tipspeeds employed, and also to bring the 45° pitch angle
of the helical surface well within the surface of the hub. In
the few cases coming to notice, in which detachable blades were
used for these highspeed turbine screws, the results obtained
were poor, but there were other conditions existing in these
cases which may have been responsible for the poor propulsive
eflSciency realized.
Location of Blade on Blade Pad
In order to provide sufficient space for the blade bolts to pass
through the pad without cutting into the true working face or
Fig. 34. — Correct Method of Changing Blade Position to Permit Bolting to Hub.
the working section of the blade, disregarding the fillet, it is
very often necessary to shift the blade on the pad so that the
blade axis does not coincide with the axis of the pad. To do
this, the blade axis may be shifted forward or aft of the pad
axis along the axis of the hub, or it may be swimg aroimd the
hub to an angular position with the axis of the pad, or the two
shifts may be combined (Fig. 34).
Digitized by LjOOQ IC
CHANGE OF PITCH 231
Whatever is done in this way, care must be taken that the
axis of the generatrix shall always remain coincident with the axis
of the hub. Many cases are encoimtered where, in order to give
sufficient space for the blade bolts, the blade has been moved to
one side or the other of the pad axis, the axis of the blade remain
ing parallel to the axis of the pad, but the axis of the generatrix
becoming transferred several inches to one side of the hub axis
to which it remains parallel
Dimensions of the Hub
The following rules for hub dimensions are abstracted from
Bauer's " Marine Machinery " and are on the lines of accepted
good practice:
Diameter of shaft =d.
Propeller Hub. i. In smaller propellers the hub and blades
are cast in one. Length of hub, ^=2.3 to 2.6d. Maximtmi
diameter of hub Ai=^.o to.2.3J. Slope of cone of the propeller
shaft I in 10 to I in 16.
As a rule the center part of the hub aroimd the shaft is cut
away, firstly, to effect a saving of weight, secondly, to facilitate
the fitting of the propeller on to the conical end of the shaft. In
order that the turning moment of the shaft may be transmitted
to hub at its thickest part, the latter must, especially at the
thicker end of the cone, fit accurately on to the shaft. The hub
is prevented from turning on the shaft by one or two strong keys.
Key: Breadth of the i=T+ hich. Thickness of key 0.5
o
to o.6i, d being the diameter of the propeller shaft. If there are
two keys, only o.8i instead of b is required. The keys must fit
both hub and coned shaft accurately at the sides, but a little
clearance may be allowed in the hub at the top. The hub is
first fitted on to the shaft without the keys, then removed, and
the keys fitted to the shaft in coimtersunk keyways. The hub
is replaced, and it should be possible to push it as far up the cone
as before the keys were fitted.
Digitized by LjOOQ IC
232 SCREW PROPELLERS
The keys almost always extend the whole length of the hub;
but sometimes, if the propeller is small, they occupy only the
front half. The propeller nut has a fine thread, and may be
made with either indentations or projections.
Diameter of the nut ^1 = 1.4 to i.sda. Thickness of nut
Ai=o.75 to o.&sday da being the diameter over the thread. The
smaller values may be used for larger nuts. These values hold
for nuts where the shaft has a diameter measured outside the
thread of over sJ in., otherwise di is taken from the table of
dimensions of bolts and nuts, and equals the width across the
flats of a hexagonal nut. To prevent the nut slacking back, it is
usually made with a lefthanded thread for a righthanded screw
propeller, and a righthanded thread for a lefthanded screw
propeller, but this rule is often departed from. Some method
of locking the nut is also usually provided. To screw on the nut
easily, the shaft is continued for a short distance beyond the nut,
and given a diameter slightly less than that at the bottom of
the thread.
2. Hubs with Blades Bolted on. In merchant vessels with
propellers over 10 to 13 ft. diameter, and in warships with pro
pellers over 6 ft. 6 in. to 8 ft. 6 in. diameter, the blades may be
bolted on to the hub.
In the best practice, the flanges of the blades are very care
fully fitted to the surfaces on the hub, to prevent the water get
ting imdemeath them, and sometimes a rubber ring is inserted,
and screwed up against the hub.
Thickness of flange of blade /i =0.18 to o.22d for bronze or
cast steel.
Diameter of flange of blade Di = 1.9 to 2. 3 J.
Corresponding to this diameter of flange, the external diam
eter of the hub is:
dn 2.6 to 3d for large screws;
dn 3.0 to 3.5^ for small screws.
Length of hub with blades bolted on, £ = 2.1 to 2,6d (higher
values are for smaller hubs).
Thickness of hub round the cone:
Ci=o.i9 to 0.22J for bronze;
Digitized by LjOOQ IC
CHANGE OF PITCH 233
Ci =o.i8 to o.2id for cast steel;
ci =0.22 to 0.24J for cast iron.
Thickness of metal at front and back ends of hub:
wi = o.22d for bronze;
Wi=o,2od for cast steel:
Wi =0.24^ for cast iron.
In all these formulae d is the diameter of the propeller shaft.
Digitized by LjOOQ IC
CHAPTER XV
STOPPING, BACKING AND TURNING SHIPS
The data* given in this chapter were principally obtained and
the text prepared by Commander S. M. Robinson, U. S. N., in
connection with the development of electric drive for ships. The
performance of an induction motor is vitally affected by the per
formance of the ship so that in addition to the normal "steaming
ahead " condition there are three others that must be consid
ered. These are (i) stopping (that is motors nmning free with
no power on them), (2) backing (with ship going ahead), (3)
turning. In the past, little attention seems to have been paid
to these points, so it was necessary to do considerable experi
menting in order to determine what actual]^' happens in each
of these cases.
Stopping
In the case of a ship fitted with reciprocating engines, when
the signal " stop *' is received the engines are held stopped; if
it is necessary, the links are thrown over and enough steam
admitted on the backing side to hold the engines. In this case
the screws act as a powerful brake, and stop the ship rapidly.
In the case of turbine ships, some engineers shut steam off of the
ahead turbines and let the propellers keep revolving ahead while
others admit steam to the backing turbines to hold the screws
stopped; however, it is not believed that the latter practice is
much used. An electrically propelled ship is similar to the tur
bine ship when the latter uses no steam in the backing turbine.
The retardation of the speed of a reciprocatingengined ship
will therefore be considerably more rapid than that of either a
turbine ship or an electrically propelled ship when the engines
are stopped.
234
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
235
For the purpose of determining what this retardation is,
experiments were conducted on the U.S.S. Jupiter by running
over a measured course with power off and propellers running
freely. Observations were taken on shore and also on board ship,
and from these were plotted speed and r.p.m. retardation curves.
100
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^:::ss:ss:ssE3
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Jlinutes.
Fig. 35.
10
12
14
16
These are shown in Fig. 35. Curve a represents the actual speed
of the ship at any time interval, curve h represents actual revolu
tions per minute of the screws at any time interval, and curve c
represents the revolutions per ndbute necessary to drive the ship
at the speeds represented by curve a. From curve b it will be
Digitized by LjOOQ IC
236 SCREW PROPELLERS
seen that the apparent slip of the screws, when dragging, is
about 28 per cent and from curve c that it is about 9 per cent
when going ahead. Apparent slip when going ahead is taken
to be,
_ (PXJg)(z;Xioi.33)
^" PXi?
Slip when draggmg is taken to be
^_ (z;Xioi.33)(i^XiZ)
»Xioi.33 '
where 5 = per cent slip ;
1;= speed of ship, in knots;
P= pitch of screw, in feet;
R = revolutions per minute of screw.
This retardation curve shows that the zero torque point oh
the propeller occurs at about 68 per cent of the r.p.m. necessary
to drive the ship; that is to say, the propellers, when dragging,
will turn at about 68 per cent of the r.p.m. necessary to drive
ahead. Later on it will be seen that this agrees fairly well with
results obtained in the model tank, where the zero torque point
on the propeller was foimd to be between 70 per cent and 78 per
cent of the r.p.m. necessary to drive the ship.
This retardation curve is necessary for properly working out
a reteirdation curve when applying backing power. As it is not
always feasible to actually determine this curve by actual experi
ment, a method has been worked out for calculating it, and it is
believed that it will be accurate enough for all practical pur
poses.
By this method the retardation ciu^e can be obtained
whether the ship is running with engines stopped or backing.
The following is the method used:
Let H.P. = horsepower exerted at any instant to stop the ship;
IT = work done (per second) by this horsepower;
F= force in pounds acting on the ship to stop it;
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS 237
ilf= mass of the ship;
a = retardation in knots per hour per minute;
a' = retardation in feet per second per second;
g = force of gravity =32.16;
»= speed of the ship, in knots;
A = displacement, in tons.
Then
also
or
„^_ H.P.X33,ooo
^^ 60
W^Fx^^^""^
60X60'
But
then
H.P.X33,ooo _ /^Xz^X6o8o ,
60 60X60 '
. p. H.P.X33,oooX6o
z;X6o8o
32.16
H.P.X33,oooX6o _ AX224oXa'
i;X6o8o 32.16 '
. ,_ H.P.X33,oooX6oX32.i6
z;XAX 2240X6080 '
^_ H.P.X33^oooX6o^X32.i6
t;XAX224oX6o8o2
For the Jupiter A was 16,670 tons at the time of the experi
ment, so for that ship
H.P.X. 009964
V
Digitized by LjOOQ IC
238 SCREW PROPELLERS
To calculate the H.P. acting to stop the ship at any speed v,
there must be added together the effective horsepower necessary
to drive the ship at the given speed and the horsepower due to
the braking effect of the screw if the ship is running with power
shut off or the power delivered by the engines if she is backing.
If the ship is nmning without power it is believed that the fol
lowing method of estimating the braking effect of the screw will
be accurate enough. Consider the action of the screw (while
revolving freely) to be similar to that of the struts. This seems
a reasonable assumption, as the screws will at all times have
water back of them if they are revolving. As an example of this
method take the Jupiter:
Strut area (one) 8.96 sq. ft.
Propeller hub area (one) 7.92 sq. ft.
Total area covered by strut and propeller
hub 16.88 sq. ft.
Projected area of propeller (one) 60.56 sq. ft.
From Sheet 18, Atlas, the strut resistance is found to be 9.3
per cent of the resistance of the bare hull.
.'. Propeller resistance = — ^X9.3=33.7 per cent of bare
hull resistance.
From Sheet 18, the total appendage resistance is found to be
1 1.3 per cent of bare hull resistance.
Total added resistance will be
11.3 per cent+33.7 per cent=45 per cent.
/• Total H.P. = 1.45 X effective horse power (bare hull).
In Table XI the values of a have been calculated by substi
tuting these values of H.P. in the equation previously derived.
The derived values of a are shown in Fig. 36. In this figure it
will be seen that the curve between any two speeds differing by
only one knot is nearly a straight line, so that the average
retardation, while the ship is dropping one knot, can be taken as
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
239
the average of the retardation at the two speeds. Using this
method, the time for the ship to drop to any speed has been cal
culated in Table XI. This gives a retardation curve which has
6 8 10
Knots per Hour per Minute.
Fig. 36.
U
U
16
been plotted on Fig. 37. The actual retardation curve (ob
tained by experiment) is also shown in this figure. This curve
can be represented very closely by an equation of the form —
Digitized by LjOOQ IC
240
SCREW PROPELLERS
v(t+b)=a.
In this case the equation is of the form v= ^^^ '^ ,
/+2.S2'
where v = speed of the ship and / = time intervals. It will be seen
that the calculated, actual and equation curves all agree very
closely. It will be noted that at the high speeds the change of
speed is much more rapid than at the low speeds.
Table XI
"JUPITER," STOPPING
Knots.
E.H.P. (Bare
H.P.
Time to Decel
Total Time
Hull).
1.4S E.H.P.
a
erate I Knot.
from 21 Knots.
21
*i4.o
♦ii.o
♦.0
♦.0
SO
♦.0800
♦.08
19
11,800
17,100
9.0
.1000
.18
18
8,950
12,970
7.21
.1235
•303s
17
6,52s
9,450
5.56
.1565
.4601
16
5,150
7,470
4.67
.i860
.6461
IS
4,07s
5,910
394
.2320
.8781
14
3,200
4,640
331
.2755
I. 1536
13
2,500
3,630
2.79
.3280
I. 4816
12
1,950
2,830
2.36
.3878
1.8694
ZI
1,500
. 2,17s
1.98
.4560
2.3254
ZO
I,I2S
1,630
1.63
.556
2.8814
9
82s
1,195
1.33
.676
3 5574
8
575
834
1.04
.840
4.3974
7
425
616
.88
1.042
5.4394
6
25s
370
.616
1.338
6.7747
S
170
246. s
.493
1.8
8.5774
4
98
142
.355
2.36
10.9374
3
50
72.4
.242
334
14.2774
2
25
36.3
.181
4.94
19.2174
1
10
14.5
.145
6.14
25.3574
* Obtained by extending the curve.
Following the above method, the retardation curves for the
U.S.S. New Mexico have been determined, and these will be
used later on in the chapter when the subject of " backing "
is treated.
The New Mexico's strut area (two on one side of the ship) =
133 sq.ft.
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
241
Area of two propeller hubs = 11.94 sq.ft.
Total strut area = 13.3+1 1.95 = 25.24 sq.ft.
Projected area of two propellers = 107.7 sq.^t.
Strut resistance = 9.4 per cent.
Fig. 37.
Propeller resistance = . 4 X — — = 40. 2 per cent.
25.24
Appendage resistance = 14.9 per cent.
Total added resistance (to bare hull) = 14.9+40. 2 = 55.1
per cent.
Digitized by LjOOQ IC
242
SCREW PROPELLERS
Substituting A=32,cxx) tons in the a equation previously
reduced, we have
H.P.X. 005101
a= .
V
Table XII
"NEW MEXICO," STOPPING
Knots.
E.H.P. (Bare Hull).
H.P.«E.H.P.Xi.SSi.
a
32
21,200
32,900
7.77
21
16,300
25,300
6.2s
20
I3i400
20,800
5.40
19
11,200
17,400
4.75
18
9,400
14,600
4.21
17
7,800
12,100
3.69
16
6,350
9,850
3.19
IS
S,ioo
7,920
2.74
14
4,100
6,370
2.36
13
3,250
5,050
2.02
12
2.550
3,960
1. 71
II
1.950
3,030
1.43
10
1,500
2,330
I. 21
9
1,100
1,710
.986
8
775
1,20s
.781
Table XII gives the calculations for a and the curve is plotted
in Fig. 38. From this curve the knots retardation curve can
be plotted as in the case of the Jupiter. The curve of r.p.m.
to drive at these speeds can next be plotted, and taking 70 per
cent of this as the dragging r.p.m. this curve also can be plotted.
They are all shown in Fig. 38.
The equation for the knots retardation curve is
v=
81.4
^+3.87'
The sudden drop in the r.p.m. when power is taken off, from
175 to about 122, corresponds to results obtained by experiment
on the Jupiter and also to results obtained in the model tank.
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
243
This sudden large drop is a very material help to the induction
motor when backing as it makes a larger torque available for the
reversal of the screw.
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=^ ili^
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ffl lllllillrilM
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2 3 4 5
Knots Per Hour Per Minute.
Fig. 38.
Backing
The subject of "backing'' seems to have been very little
considered in the past. The main reason for this probably was
that with reciprocating engines the backing power was ample
Digitized by LjOOQ IC
244 SCREW PROPELLERS .
and was fixed by the design of the engine itself. When the marine
turbine first entered the field of marine propulsion the subject
of " backing" became a very live one. The first backing tur
bines built were wholly inadequate for the purpose, and this has
resulted in more stringent requirements in this particular; but
the term " backing power " is very vague and does not really
define anything.' In order to properly specify what the backing
power of any ship should be, the speed at which the ship is mov
ing through the water when she develops this power should be
specified, as the latter limits the former, as will be seen later on.
The limit of the power of any engine when backing is defined
by the maximum attainable torque of the engine. This will be
better understood after a study of Fig. 39. These curves were
obtained by trials in the model tank, using a model of the U.S.S.
Delaware's screws. The speeds of the ship are plotted both
ahead (+) and astern (— ) as well as the r.p.m. when turning
ahead (+) and the r.p.m. when backing (— ). From these
exudes the torque of the propeller can be taken off for any given
condition of speed and r.p.m. These trials were run with the
screw free of the model, so that it was running in imdisturbed
water, and consequently a wake factor will have to be appb'ed
to obtain actual ship conditions. In this case a factor of 14.5
per cent has been used, as this brings the actual torque of the
ship, when driving ahead, into fairly close accord with the model
results. For example, 122.2 r.p.m. corresponds to 21 knots
speed; to find the speed on the curves corresponding to 21
21
knots, take = 18. .35 knots. The torque, from the curves
i«i4S
corresponding to 122.2 r.p.m. and 18.35 knots is 465,000 Ib.ft
and the actual torque developed by the engine was 464,500
Ib.ft. Using this same method for all speeds Table XIII has
been prepared, and this shows fairly close accord between actual
engine torque and propeller torque. However, it is not intended
to use this modeltank curve for actual values but only for com
parative ones.
There are two very striking phenomena to be noticed about
these curves. The first is that, with speed of ship constant,
Digitized by'VjOOQlC
STOPPING, BACKING AND TURNING SfflPS
245
^ s s
^^ ^^ r^
•o^nufW aad snonnioAo^ joj arBog
_i . ,. I ._ I I T^ '7*
Digitized by LjOOQ IC
246
SCREW PROPELLERS
the torque of the propeller, as its revolutions per minute are
reduced, passes through a high maximiun torque before it reaches
zero r.p.m. In other words, it requires a greater torque to
bring the screw to rest than it does to hold it at rest. The second
is that in backing, with constant r.p.m., the torque of the screw
decreases as the ship slows down until a certain speed is reached,
when the torque begins to increase; it reaches a maximum
and then decreases again before the ship becomes stopped.
Both of these phenomena have been verified by actual experi
ments on the Jupiter. They will each be taken up and con
sidered in detail.
Table XIII
" DELAWARE "
Knots.
R.p.m.
I.H.P.
Actual Torque.
Curve Torque
(14.S Factor).
21
122.2
23450
464,500
465,000
20
113. 75
18,100
385,000
380 000
19
107.3
14,700
331,500
332,000
18
loi.s
12,200
290,500
292,000
17
9575
10,250
258,800
255,000
16
90.0
8,600
231,000
230,000
IS
84.2s
7,050
202,300
201,500
14
78.2s
5,700
176,300
175,500
13
72.50
4,550
151,800
145,500
12
66.60
3,550
129,000
125,000
II
60.75
2,650
105,400
100,000
10
55.00
1,880
82,700
83,000
To illustrate the first point Fig. 40 has been plotted from
the curves in Fig. 39. The ordinates of this curve represent
per cent of the normal ahead driving torque and the abscissas
represent per cent of ahead r.p.m. corresponding to the speed
which it is assiuned the ship is making. The ship is assiuned
to be making a constant speed ahead at all points represented
on this curve. Starting at the right of the curve, it is seen that
when power is taken off the engines, leaving the propellers free,
the r.p.m. drop to about 76 per cent of the previous revolutions.
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS
247
In the early part of this chapter it was shown, by experiment,
that the Jupiter r.p.m. dropped to about 68 per cent. If reverse
torque is now appKed to reverse the screw and is gradually
increased, the r.p.m. will gradually slow till a point is reached
where the propellers are making 40 per cent of the ahead r.p.m.;
at this point about 95 per cent of the ahead torque will be
required; from this point on down to stop less torque will
be required to slow the propeller; when the propeller becomes
stopped the torque has reached a minimum, and will rise again
3.50
ShlpC
k>infirAI
teadat
8.00
\
i;:
Cod
stant Si
eed.
2.50
2.00
L50
;;: j^;; ;
:;:;
k
1,00
M '
" ■ %
:;.::
^
.50
M
: :
«
i : :
=;::::;::
_
.10 .8 .6 .4 .2 .2 A .6 .8
Per cent Normal FuU Load B.P.M. (122.2 B.P.M.)
Fig. 40.
XO
if the screw is actually reversed. The curve given was plotted
for the condition of ship going ahead at 21 knots, but it is ap
proximately correct for all speeds, as will be seen by following
out the various speeds in Fig. 39. In Fig. 41 is given a similar
torque curve for the Jupiter. This curve was determined by ex
periment in the following manner. With the ship going ahead at
14 knots power was suddenly thrown off; the propeller speed
dropped to the point marked zero torque. The excitation of the
generator was then reduced as much as possible and the backing
switches thrown in; the propellers kept revolving ahead and the
Digitized by LjOOQ IC
248
SCREW PROPELLERS
excitation was gradually increased till the propellers just passed
over the maxuniun torque point and started to reverse; the
excitation was then reduced to just enough to keep the pro
peller stopped. There were two points for the stopped condi
tion, one at which the propeller would just start revolving ahead
and the other at which the propeller would just back; the curve
has been run between the two points. At each point the elapsed
time from the beginning of the experiment was taken and, by
PROPELLER TORQUE CURVE
Ship vol
Iff ahead
itCk>n«ta
It Speed
2U)
y
L5
mm
:: ::::::
Minimal
1 PropeU
r Torqa<
Tow
netoDrJ
76 Ahead
r
\ ^
:::::
wl
Si
lie Blowi
fc
J!
\^.
A
mi
Pro
att
seller Jai
lisTor^
kbacta,
e —
nrr
ii:
::::
f'
1 II
:::!l
i
m
L.4
,...4
+ ■■
Propellc
at this 1
rjuatsta
bivae
ta ahead
S ^ ^ ^ A .6
Per cent of Full Ahead B.P3f .
Fig. 41.
LO
means of the retardation curves in Fig. 42, all points were re
duced to the same speed. The curves in Fig. 42 were made up
from " dragging " data taken at the time and from the retarda
tion curve given in Fig. 35. The torques at the two points, that
is the maximimfi and minimum points, were determined by the
excitation at these points and were obtained from the torque
curve of the motors. Fig. 43 shows this torque curve of the
motor with 245 amperes excitation; the torque for the actual
excitation used at the various points was assmned to vary as the
square of the excitation. It will be seen that the curves in Figs.
40 and 41 are similar, but that the actual screws have a maximum
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS
.249
point (during reversing) that is lower than the model; the model
shows a maximimi point of 95 per cent while the Jupiter's max
imimi point is only about 75 per cent. Trials conducted on
other model screws in the model tank showed this point to vary
from 80 to ICO per cent. The data obtained from the Jupiter
would indicate that these values are too high. However, in
REVOLUTION DECELERATION CURVE
designing induction motors for backing it is not safe to have the
torque on the "out of synchronism'' part of the curve drop below
100 per cent of the ahead driving torque. That will insure a
safe margin for getting past this " himip " in the torque curve.
The second phenomenon of the torque curves of Fig. 39 is
illustrated in Fig. 44. This shows a ship backing with a con
stant nimiber of r.p.m. from any given speed till the ship is
stopped. The r.p.m. assimied are those which will give 100 per
Digitized by LjOOQ IC
250
SCREW PROPELLERS
cent ahead driving torque at the instant of backing. This curve
is approximately correct for all speeds. From it it is seen that
VCDUJtoTnBT
lQ9oni*9nluox
the torque necessary to txim the screw at the given r.p.m. falls
as the ship slows till about 22 per cent speed is reached, when the
torque begins to rise and continues to rise till 5 per cent speed
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
251
is reached, when it begins to fail again. This curve was also
verified by experiment on the Jupiter. Fig. 45 shows two sets
of backing trials conducted on the Jupiter, These were made
with the ship going 14 knots and then suddenly reversing, using^
the resistances in the motors, and keeping the generator at a
constant speed of 1950 r.p.m. and a constant excitation. Under
these conditions the speed of the motors would be determined
by the intersection of the propellertorque curve of Fig. 41 and
the motor torque curve of Fig. 43. As the ship slowed the pro
pellertorque curve dropped lower so that the motors speeded up,
but a maximum point was finally reached and the motor speed
1.00
.75
.60
.25
2.?
Ship backing atconatanjt B«P.M..beginniDg witb ship eroln?
ahead at any speed and osinff backini; torque equal to the
ahead driving torque at beginning of backing.
.4 .5 .6
Per cent Speed Ahead
Fig. 44.
began to decrease, showing that the necessary driving torque
had begim to go up. The motors dropped to a minimum and
then speeded up again as the torque began to drop again. This
follows the conditions of Fig. 44 exactly.
To explain this point further Figs. 55 and 56 are given. Fig.
55 is plotted from the model tank data given on Fig. 39, and
Fig. 56 was obtained by actual experiment on the Jupiter. In
these figures, as in Fig. 44, the ship is backing with constant
revolutions till the ship is stopped; however, the revolutions
chosen are the same as were used in going ahead, at the given
speed, and this requires about three times as much torque
as when going ahead. The actual speed of the Jupiter when
Digitized by LjOOQ IC
252
SCREW PROPELLERS
going ahead for this test was 39.5 r.p.m., or 5 knots, and the
actual r.pjn. when backing was 39.5. The curve was obtained
BACKING AT 14 KNOTS.
Generator Speed Oonstant, 1960 R.P.1L
1st Trial Excitation 245 Amperes.
2nd Trial Excitation 225 Amperes.
ERiip Stopped in About 4 Min. 45 Sec in Each Oaae
Resistance Kept In AU the Time.
by taking H.P. and r.p.m. readings every five seconds and reduc
ing the H.P. to torque. The curve obtained from the Jupiter
is similar in oil respects to that obtained from the Ddamxre's
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS 253
model. The minimum torque comes at 65 per cent for the
Jupiter and 60 per cent for the Delaware; the maximum point
comes at 12 per cent for the Jupiter and 15 per cent for the Del
aware, The maximum and minimum torques, however, are
much lower in the case of the actual screw than in the case of
the model.
From an inspection of Fig. 39 it will be seen that the condi
tions of (i) ship going ahead and propeller going from ahead to
astern and (2) ship going astern and propeller going from astern
to ahead are similar and should give similar torque curves when
plotted. Also that the conditions of (i) ship backing at con
stant r.p.m. from any speed ahead to speed astern corresponding
to the given r.p.m. and (2) ship going astern at any speed and
propellers going ahead at a constant r.p.m. till ship is stopped
and brought to speed ahead corresponding to the given r.p.m.
are similar.
To illustrate these points Fig. 57 has been plotted. This
curve or set of curves takes the screw through the entire cycle of
conditions. It is made up of the various curves that have
already been considered. Starting with the ship going ahead,
the screw is suddenly reversed and brought up to revolutions
which will give the same torque as was used when going ahead;
holding these revolutions constant, the ship is backed till she
stops; this is further continued till the ship picks Xip speed astern
corresponding to the revolutions; the screw is then suddenly
reversed and revolutions brought up to those which the problem
started with (the latter part of this curve is taken beyond prac
tical limits of actual screws as it runs the torque up too high, but
it was chosen so as to make a complete cycle and end up at the
starting point); these revolutions are maintained till the ship
stops; they are continued further till the ship picks up speed
corresponding to these revolutions, which brings conditions
back to the starting point. Part i shows the cycle through which
the torque passes while the screw is being reversed. Part 2
shows the change in torque while the ship is slowing down,
backing at constant r.p.m. Part 3 shows the ship picking up
stemboard with screw going at same r.p.m. Part 4 shows the
Digitized by LjOOQ IC
254 SCREW PROPELLERS
torque cycle of the screw when it is suddenly reversed to go
ahead, ship still going astern. Part 5 shows the torque cycle
while the ship is slowing down, propeller going ahead at constant
r.p.m. Part 6 shows the torque cycle of the propeller while ship
is picking up speed ahead, propeller turning ahead at same
revolutions as before. From inspection it will be seen that
parts I and 4 are similar curves, parts 2 and 5 are similar and
parts 3 and 6 are similar. Part 5 was taken so far over on the
chart that it does not show the drop in the torque before the rise
comes, in other words, it is part 2 beginning to the left of the
minimmn point. Parts i, 2, and 3 have already been verified
by test on the actual screws of the Jupiter, and to make the veri
fication complete Fig. 58 is given. The curves obtained here
were obtained imder the same conditions as those in Fig. 45,
that is, the generator was kept at constant speed and excitation
and the motors were nm with resistances in; under these con
ditions the speed of the motors would be determined by the inter
section of the propeller torque and the motortorque curve given
in Fig. 43. The Jupiter is carried through the same cycle in
Fig. 58 that the model screw is in Fig. 57, that is, the ship was
going ahead 12 knots and the screws suddenly reversed; the
ship then backed till she had full stemboard; the screws were
again reversed and kept going ahead till the ship had full ahead
speed. The points where the ship stopped are noted. From an
inspection of Fig. 43 it will be seen that on the righthand side
the torque curve of the motor is practically a straight line, so
that revolutions vary directly as the torque. The curves plotted
in Fig. 58 are revolutions of the screw, but they may also be
taken as torque on the motor shaft simply by reversing the
curves, that is when r.p.m. are increasing torque is decreasing,
when r.p.m. reaches a maximimi torque reaches a minimum, and
so on. It will be seen that the curves are similar to parts 2, 3, 5
and 6 of Fig. 57; also the two parts of Fig. 58 are similar. This
confirms the correctness of the shape of all the curves given in
Kg. 57.
Now that it has been shown how a propeller acts during the
entire cycle of backing, from the instant the power is removed
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
255
till the ship is stopped, some cases of actual backing will be
taken up. As previously stated, the power any engine is capable
of delivering while backing is limited by the maximimi torque
of the engine. To make this plainer the engines of the Delaware
are taken as an example, and two theoretical indicator cards
have been constructed and are shown in Fig. 46. The heavy
line curve shows the card when going at full power, the data for
the card being taken from the fullpower trial. The dotted
card shows the conditions if full boiler pressure could be obtained
Fig. 46.
in the highpressure valve chest. In the construction of these
cards no account has been taken of wiredrawing or clearances,
as they are only for the purpose of illustration. The data used
in the construction of the cards are as follows:
Diameter H.P. cyl. = 38 . 5 in.
Diameter LP. cyl. = 57 . o in.
Diameter L.P. cyl. (2) = 76.0 in.
Stroke =48 in.
H.P. cutoff =.86 in.
LP. cutoff =.8 in.
L.P cut off = .62 in.
Digitized by LjOOQ IC
256 SCREW PROPELLERS
For heavyline card, pressure in highpressure valve chest =
268 lb. absolute. For dottedline card, pressure in highpressure
valve chest =315 lb. absolute. Back pressure = 5 lb. absolute in
both cases.
The area of each card represents work per stroke, and since
the stroke is the same for each card, the areas can also be used
to represent torque. The area of the dotted curve is 19 per cent
greater than the fullline curve; that is to say, the engines could
develop only 19 per cent more torque than the ahead fullpower
torque if full boiler pressure could be obtained in the high
pressure valve chest. Actually, on backing trials, the highest
torque attained was about 9 per cent greater than the torque
developed on the fullpowfer ahead trial. By reference to Figs.
40 and 41 it will be seen that this torque is reached when backing
at about 40 per cent of the revolutions necessary to drive ahead,
if the ship is going ahead full speed and the engines are backing.
This means that about 43.6 per cent (1.09X40) of full ahead
power will be developed when the ship first begins to back.
This amount will, of course, be increased as the ship slows. In
the case of turbine ships the torque is far less than in the case of
reciprocating engines, probably not more than half, so that they
probably do not develop more than onequarter of full ahead
power at beginning of their backing. An induction motor can
be designed to give a much greater maximum torque than the
normal driving torque; also, since induction motors for ship
propulsion will have two sets of pole connections, the motors
can be arranged to back on the slowspeed connection. This
will allow the turbine to nm at nearly full speed while backing
at a low niunber of propeller r.p.m. This condition is ideal for
getting high power while backing; the motor is capable of pro
ducing large torque and the turbine is nmning at a sufficiently
high speed to enable it to develop full power. In other words,
the turbine condition when backing on the slowspeed connection
is practically the same as when going ahead at full power on the
highspeed connection. This shoxild give very fine backing
results.
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS 257
Fig. 47.
Digitized by LjOOQ IC
258
SCREW PROPELLERS
Table XIV
"DELAWARE," BACKING
Knott.
I.H.P.
I.H.P.X
P.C.
E.H.P.
(aUapp.)
Total
H.P.
a
Interval
Time in
Minutes.
Total
Time.
31
19
12,500
8,170
9,900
18,070
7.9
.2925
.2925
x8
12,66s
8,275
8.500
16,775
7.7s
.1276
.4201
17
12,825
8,400
7,225
15,625
7,65
.1299
.5500
x6
12,990
8,500
6,000
14,500
7. S3
.1315
.6815
IS
13*150
8,600
4,900
13,500
7.48
.1331
.8146
14
I3»3i5
8,720
3,900
12,620
7.49
•1335
.9481
13
13^75
8,820
3,100
11,920
7.62
.1322
1.0803
12
13,640
8,920
2.430
",350
7.85
.1292
I. 2095
IZ
13,800
9,030
1,880
10,910
8.24
.1242
13337
10
13,965
9,130
1,400
10,530
8.75
.1176
14513
9
14,125
9,250
1,050
10,300
9 50
.1095
1.5608
8
14,290
9,350
750
10,100
10.50
.1000
1.6608
7
14,450
9,450
500
9,950
11.82
.0897
17505
6
14,615
9,560
300
9,860
13.65
.0784
1.9289
5
14,775
9,660
190
9,850
16.35
.0667
1.8956
4
14,940
9,770
120
9,890
20.55
.0542
1.9498
3
15,100
9,880
60
9,940
27.50
.0416
I. 9914
2
15,265
9,980
20
10,000
41.50
.0290
2.0204
I
15,430
10,100
10
10,110
84.00
.0160
2.0364
15,600
10,200
10,200
.0076
2.0440
To show what this means a comparison has been made with
the Delaware when going ahead at 21 knots and the engines
were suddenly reversed. Fig. 47 gives the data obtained on this
trial. At the beginning she developed 12,500 I.H.P., which is
43.8 per cent of her ahead full power, and at stop she developed
15,600 I.H.P., which is 54.6 per cent of her full power. The
Delaware's displacement is 20,000 tons. Substituting this value
of A in the a equation, there results,
H.P. X. 00831
V
Substituting the data given by Fig. 47 in this equation. Table
XrV has been calculated for the backing condition. The values
of a obtained have been plotted on Fig. 48.
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
259
From the values of a given on this curve a retardation curve
has been plotted on Fig. 49. This curve shows the total time
to stop the ship to be two minutes three seconds. The actual
18 
IP 
11 "
lO 
:::::::::
;.±:::::
5
4k'~'.Z
JI
1
10 
Ul4l
:;e;e
•
.:
_: j::::.
..±:::
_: i:::
g 
1
::":::"j ■
A 
V
:_: 5 : :::
4 
l nJl
L. .:::::::::
: ":: — ,.
,....
2
 = '::■
;::=:=;;;:;;;:;::![:i:;==;:;;;;::;:
_.

III III III 1 II IIIL1II III II II III II II
U 24 34 44 54
a Knots per Hour j;>er Minute
Fig. 48.
64
U
84
time as measured was two minutes twentyone seconds. The
results are considered to be very close, as it is difficult to deter
mine the exact instant a ship becomes dead in the water. The
same method of calculation has been followed for the New
Digitized by LjOOQ IC
260
SCREW PROPELLERS
Mexico. In her case A =32,000, so
^_ H.RX.oo59i
V
Table XV shows the results of the calculations for a. It has
been assumed that full power is developed aU the way through
^
20
m '■■■
miM
1 ■ ■
18
U
U
12
Sio
8
e
: .:
rFKi
ill
;:::
■
4
1
i;:;;;;;
2
WM
m
10 15
Minutes
Fig. 49.
20
due to the large maximum torque of the induction motor. It
has also been assumed that the ship drops in speed to 20 knots
during the act of reversal. The values of a have been plotted
on Fig. 50 and from these values the retardation curve has been
plotted on Fig. 51. This curve shows the time necessary to
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
261
bring the ship to a stop to be i mmute 50.4 seconds. It is
realized, of course, that this condition may not be entirely
20
40
eo 80 100
€C Knots per Hour per Minute
Fig. so.
120
liO
W
reached, as some reason (such as propeller vibration) which has
nothing to do with the engines may make it imdesirable to use
this much power in backing.
Digitized by LjOOQ IC
262
SCREW PROPELLERS
Table XV
"NEW MEXICO," BACKING
E.H.P.
B.H.P.(all)
S.H.P.X
Total
Mins. 1
^ixne in
Knots.
(Bare Hull)
14,9 per
C«nt. App.
P.C.
H.P.
a
(Interval).
Mins.
ai
16,300
18,740
0,000
20
13,400
15,400
18,740*
34,140
8.87
.232
.232
19
11,200
12,880
18,740
31,620
8.65
.114
.346
18
9,400
10,800
18,740
29,540
8.53
.1165
.4625
17
7,800
8,960
18,740
27,700
8.45
.1178
.5803
x6
6^50
7,300
18,740
26,040
8.45
.1182
.6985
IS
S,ioo
5,860
18,740
24,600
8.52
.1178
.8163
14
4,100
4,710
18,740
23,450
8.70
.1162
9325
13
3,250
3,730
18,740
22,470
8.97
.1132 I
04S7
xa
2^50
2,930
18,740
21,670
9.38
.109 I
1547
XI
i,9SO
2,240
18,740
20,980
9.90
. 1036 I
2583
xo
1,500
1,720
18,740
20,460
10.62
.0975 I
3558
9
X,10O
1,260
18,740
20,000
"•55
.0843 I
4401
8
775
890
18,740
19,630
12.75
.0823 I
5224
7
525
600
18,740
19,340
14.35
.0738 I
5962
6
325
375
18,740
19,115
16.55
.0647 I
6609
5
175
200
18,740
18,940
19.70
■0551 I
7160
4
75
86
18,740
18,826
24.40
.0453 I
7613
3
50
S8
18,740
18,798
32.55
.0351 I
7964
2
25
29
18,740
18,769
48.75
.0246 I.
8210
I
10
12
18,740
18,752
97.50
.0137 I.
8347
18,740
18,740
.00530 I.
8400
Turning
It has always been known that when a ship turns, the mboard
screw slows down if the throttle is not touched during the turn,
as is the rule ordinarily followed. In the case of an electrically
propelled twinscrew ship, operating both propellers with one
governorcontrolled turbine, the r.p.m. of the two screws are
maintained the same as they were before the turn. In order to
determine exactly what effect this would produce, turning trials
were carried out on the Delaware and the Jupiter. Six turns of
360° were made on the Delaware, two at 10 knots with 16° right
rudder, two at 12 knots with 16° right rudder, two at 12 knots
with 27° rudder. The first four turns are shown as curves in
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS
263
Fig. SI. The data obtained on the last two turns are given in
Table XVI. The data on tactical diameter, etc., for all six
turns are given in Table XVII. It will be seen from Table XVII
20
FU 1
ifi
s
10
16
14
— 1 — — ^ —
Mlllllllll
12
iKI
"""'" ^■■^■■iiiiiiiii
— » —
— s
— ^...
:::::::S::
. ^ .
... — ^
11
"5
X.L
:z::\::z::
^ 
1
::::z::\::
o
':::;::;::
n
:::::::::
JS&
.50
.75
1.0
Minutes.
Fig. 51.
1.25
L50
1.75
2.
that, for speeds above lo knots the tactical diameter is prac
tically the same, whether the turn is made with r.p.m. constant
or whether the inboard screw is allowed to slow down. In the
turn at 12 knots, with i6° rudder and r.p.m. constant, it will be
Digitized by LjOOQ IC
261
SCREW PROPELLERS
seen that the I.H.P. of the inboard screw rose steadily as the turn
progressed, and that the I.H.P. of the outboard screw first
dropped and then rose steadily as the turn progressed. This latter
peculiarity is not observed in the curves given on the loknottum,
probably on account of inability to indicate power frequently
enough, but it is present in all of the turns made by the Jupiter
as will be seen later on. The reason for the shape of the horse
power curves when turning is that the inboard screw is main
taining a constant r.p.m. at a much lower virtual speed of
the ship than these r.p.m. would give if driving ahead, so, of
course, the power goes up; the condition is still more exaggerated
as the ship slows during the turn. The outboard screw, at the
beginning of the turn, is maintaining a constant r.p.m. at a con
siderably higher virtual speed of the ship than these r.p.m.
would give if driving ahead, so the power required drops; but
as the ship slows during the turn a point is soon reached where
this excess speed is lost, and as the speed of the ship falls lower
the power commences to rise. From Table XVI, on the turn at
12 knots with 27® rudder, the greatest increase of power on the
inboard screw was 73.5 per cent of the normal driving power;
the greatest increase on the outboard screw was 4.2 per cent of
the normal driving power, and the total increase of power was
39 per cent of the total driving power.
Table XVI
U. S. S. " DELAWARE," FEBRUARY 12, 1914.— TURNING TRIALS
Turn at 12 knots speed. 27° helm. Throttle tmtouched.
Run No. 5.
I.H.P.
Pressures.
H.P. Valve
Chest.
I St
Receiver.
2d
Receiver.
Revolu
tions.
Starboard,
1880
76
75
30
24
3
X
54
66
Port,
22^S
Total,
4124
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
265
Turn at 12 knots speed. 27° helm. Maintaining same revo
lutions during turn. Run No. 6.
Pressures.
I.H.P.
H.P. Valve
I St
2d
Revolu
tions.
Chest.
Receiver.
Receiver.
Starboard.
xa6q
170
75
60
10
66
Port
204.7
22
— I
66
Total,
5516
Horsepower on straight run. From former records.
10 knots speed
12 knots speed
{
Starboard engine
Port engine
Starboard engine
Port engine
H7S I.H.P.
11S0I.H.P.
2000 I.H.P.
1965 I H.P.
1 55 turns
1 66 turns
In Figs. 52 and 53 are shown the results of turning trials
on the Jupiter, Two turns were made at 12 knots and two at
14 knots; one turn was made to starboard and one to port in
each case; the turn was made through 180° in each case using 25°
rudder. It was possible to get very accurate results on these
trials as the r.p.m. were maintained exactly constant by the gov
ernor, and horsepower readings were taken every five seconds.
The curves obtained are all similar to those shown on the Del
aware's i2knot turn in Fig. 52. The reason for the shape of
these ciurves has already been given imder the explauation of
the Delaware's curves. The difference in the curves obtained
when turning to starboard and port are due, partly to the fact
that the rudder angles were probably not exactly the same, and
partly to the difference in the effect of wind and sea on the two
sides. The greatest increase of power occurred on the 14knot
turn to port. The inboard screw increased in power 53.5 per
cent, the outboard screw increased 4.5 per cent, and the total
increase of power was 29 per cent. These percentages are con
siderably lower than those obtained on the Delaware, but the
Digitized by LjOOQ IC
266
SCREW PROPELLERS
I
<
00 ^
9 8
*)s«inajoj »«
r
pajns«9ax 9i8u« %jup p»nji
^
•^
^
N
w> <*
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Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SHIPS
267
Delaware's rudder is 50 per cent larger than that of the Jupiter ^
so that she turns and slows faster than the Jupiter and conse
quently takes a larger increase of power.
U.S.S. DELAWARE.
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The effect of turning on an electrically propelled ship would
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maintain constant r.p.m. at all speeds during a turn; also the
maximimi torque of the motors is sufficient to insure that they
Digitized by LjOOQ IC
268
SCREW PROPELLERS
Fig ss
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS 269
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 IBO^Turn. B.P.M. Constant 1064^ .
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Digitized by LjOOQ IC
270
SCREW PROPELLERS
will stay in step during a turn if the proper excitation is main
tained. In the case of the New Mexico, however, when turning
at high speeds, either at i8 knots with one tiurbine or at 21 knots
with two turbines, the boilers and turbines are not capable of
giving a 39 per cent overload, and consequently the turbines will
.4 A .6
Per cent Full Speed
Fig. 55.
.4 .5 .6
Per cent Full Speed
Fig. 56
simply slow during the turn, provided that the maximum torque
of the motors is greater than that of the turbine. In other words,
the New Mexico will turn without any reduction of r.p.m. at all
low speeds, say below 16 knots, and will slow her r.p.m. during
the turn at all speeds above this.
Digitized by LjOOQ IC
STOPPING, BACKING AND TURNING SfflPS
271
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STOPPING, BACKING AND TURNING SHIPS
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Digitized by LjOOQ IC
CHAPTER XVI
liATERIALS FOR CONSTRUCTION OF AND GENERAL
REQUIREMENTS FOR SCREW PROPELLERS
Material of Blades. The materials of which propeller blades
are made are cast iron, cast steel, forged steel, manganese or some
other strong bronze, and Monel metal.
Cast iron is used for the blades of propellers which work
mider conditions rendering them very liable to strike against
obstructions. When so striking, the cast iron being weak, the
blade breaks and, by so breaking, saves the shafting or th?engine.
Its disadvantages are extreme corrosion in sea water, heavy
blade sections, and blimt edges 'due to the weakness of the metal.
Semisteel is the name given to cast iron when a percentage
of steel scrap has been added to the pig iron in the cupola. While
stronger than cast iron, it is liable to carry flaws and is imre
liable. Its use for propeller blades is not recommended.
Cast steel is stronger than cast iron, but has the same dis
advantages although in a lesser degree.
Forged steel was formerly used in some instances for torpedo
boat propellers, but is not met with in presentday practice. It
also possessed the disadvantage of excessive corrosion with conse
quent roughening and weakening of blade.
Manganese bronze and other strong bronzes appear to be all
that may be wished for in propeller material. They are of
high strength, permitting a low ratio of thickness to width of
blade, can be brought to a sharp edge, and can be highly polished,
while the corrosion to which they are subject is comparatively
slight. They also cast without difficxilty, giving blades free from
porosity and blow holes. They may exercise a strong corrosive
action on a steel hull if care is not taken to protect the hull in
their vicinity by zinc plates.
274
Digitized by LjOOQ IC
MATERIALS FOR CONSTRUCTION 275
Monel metal is extremely strong and tough, pennits of very
light blade sections and sharp edges, takes a very high polish,
and is practically noncorrosive in sea water. These qualifi
cations are all very desirable in a propeller metal. It has, how
ever, the imdesirable qualities of heavy and irregular warping
of the blades when cooling in the mould, and a tendency to po
rosity aroimd the tips and blade edges. On account of the ten
dency to warp, it is very difficult to insure the desired pitch imless
the blade be cast with a large amoimt of waste metal which will
permit of pitch correction in machining.
Material of the Hub. Hubs are usually made of cast iron or
semisteel for castiron or caststeel propellers; of semisteel for
the poorer classes of work, and of manganese bronze for the
better class, with manganese bronze blades; of manganese
bronze or of Monel metal for Monelmetal blades. Where the
propeller is cast solid, of course, the hub is of the same material
as the blades.
General Requirements for Propellers
For all propellers except those made of cast iron or cast steel,
the blades should be polished in order to reduce surface friction.
With caststeel and castiron blades, however, as they are usually
used for work where the speeds of revolution and tipspeeds are
low, the loss due to roughness of surface is not very high and it
is preferable to retain the hard skin of the casting as a guard
against corrosion than to sacrifice it in order to gain an advantage
which would be only temporary.
Where blades and hub are made of one of the strong bronzes
or of Monel metal, both blades and hub should be polished, the
blades be made as thin as is consistent with strength, and the
blade edges sharpened.
For work of the highest class and where the speeds of revo
lutions are high, the blades should be machined to true pitch, the
backs of the blades finished to template and the blades polished
to as smooth a surface as possible. The propeller should then
be swung upon a mandrel and accurately balanced, as lack of
Digitized by LjOOQ IC
276 SCREW PROPELLERS
balance will produce excessive vibration when the speeds of
revolution are high. In some cases, in order to insure a smooth
blade surface, bronze blades have been silverplated. This, how
ever, seems of questionable expediency. It insures smooth blades
for the trial trip, but it is doubtful if the silverplating would
remain on the blades for any considerable length of time.
Digitized by LjOOQ IC
CHAPTER XVII
GEOMETRY AND DRAUGHTING OF THE SCREW PROPELLER
Geometery of the Screw Propeller
The geometrical construction of the screw propeller forms one
of the most interesting problems for the engineer and the draughts
man; it is also of equal interest to the patternmaker and the
foundryman, who are called upon to produce the structure itself
from the plans. Therefore, a thorough imderstanding of the
methods employed to generate its construction should be useful
to all concerned.
The screw propeller of uniform pitch is the one which is gener
ally accepted by engineers for the propulsion of ships, and this is
divided into two distinct types, viz.: propellers having the verti
cal generatrix, and propellers having the inclined generatrix, the
vertical generatrix being preferable for twin or other multiple
screws where ample clearance between blade tips and hull, and
between leading edges of the blades and the after edges of stmts
exists, while the inclined generatrix has advantages on single
screw vessels where the propeller is working behind the usual
stem post.
In order to make the constmction of the various types referred
to as clear as possible, diagrams have been prepared which show
the methods involved. Also, drawings of various propeller
giveels have been made which conform to those diagrams, thus
whing a very definite idea of the whole subject.
One of the simplest methods of making a screw propeller, viz.:
that of sweeping up in the foundry, will probably afiford a good
illustration as to how a tme screw may be generated. Suppose,
as an example, a propeller of 12 ft. diameter and 12 ft. pitch be
taken, which means that the propeller must make one complete
277
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278
SCREW PROPELLERS
revolution in order to advance 12 ft. when no slip occurs. If a
piece of paper be cut so that the base represents the circumfer
ence of the propeller, and the perpendicular represents its pitch,
and this paper be wrapped around a cylinder whose diameter is
12 ft., the hypothenuse will generate the true helical line, Fig. 59.
Fig. 59.
In a screw propeller, a fractional part only of the helix is
dealt with, and this is used as the upper or guiding edge of an
angle board from which to generate the working surface of one
blade.
Instructions for Sweeping up the Helical Surface of a
Screw Propeller
Make a level surface and lay off the centerlines, and also the
outer radius of the wheel. Erect a cylindrical column on the in
tersection of the centerlines of this surface in a vertical position,
then erect the angle board on this same surface at its proper
radial distance out from the center of the column and parallel
with the column. Construct a straightedge having one end
arranged to fit aroimd and slide up and down this coliunn, of*
sufiident length to extend beyond the angle board and provide
means for keeping this straightedge at an angle of 90® with the
column at all times.
The surface of a screw propeller blade having a vertical
generatrix can now be developed by simply causing the straight
edge to follow the helical edge of the angle board while passing
through the arc AB, Fig. 60 and Fig. 61.
Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING
279

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Digitized by LjOOQ IC
280 SCREW PROPELLERS
If the straightedge be inclined at any angle other than 90^
and the same operation be carried out, a screw having an in
clined generatrix will be developed.
Geometry of a Screw Propeller having a Vertical Genesa
TBDc. Sheet 28
Lay down a baseline and erect a perpendicular to it. Where
they intersect will be the axis on which the blade is generated.
On each side of this perpendicular draw lines, at an angle to
suit the form and area of the projected surface, passing through
the axis. ^
An angle of any magnitude may be used, but in this case 30^
has been chosen, as this angle will cover any ordinary condition.
Through these 30° angles, draw an arc with a radius equal to
the radius of the propeller. Divide this radius into ten equal
parts, and draw in arcs through each of these division points.
(See Fig. i.) Divide the angles into five equal parts and draw
lines passing through the axis. (Lines a, b, c, J, e, /, Fig. i.)
Where the arcs intersect the 30° angles draw lines parallel to the
baseline. (Lines i to 10, Fig. i.)
Now, to the right or left of this figure, erect another perpen
dicular to the base. This perpendicular becomes the generatrix
on which the blade is developed.
The helix that the tip of the screw develops has already been
explained. As 30°, or A of the whole drciunference, has been
used to develop the blade, so A of the pitch must be used. (If
any angle other than 30° is used, the same proportion of the
pitch must be used, and as iV of the circumference has been
divided into five equal parts, so the A pitch must also be divided.)
On each side of the generatrix lay off A of the pitch, and
divide this into 5 equal parts, and through these points erect
perpendiculars passing through the baseline. (Lines a, b, c,
d,f,/. Fig. 2.)
Fig. 4 is the plan view. The centerline in this view repre
sents the plane through which the generatrix would move if
rotated around its axis without any pitch. On each side of this
Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING 281
centerline project the tV of the pitch divided into 5 parts, as in
Fig. 2. Draw lines parallel to the centerline (Lines a, 6, c, d, e,/),
which become the radial lines. Project up from Fig. i, through
the intersection of the line, a, 6, c, d, e, f, with the arc of the full
radius, to the lines a, J, c, d, e,/, respectively (Fig. 4), and draw
in the curve passing through these intersections. This forms
the helix.
The curves i, 2, 3, 4, 5, 6, 7, 8, 9, Fig. 4, are formed by pro
jecting up from the intersections of lines i, 2, 3, 4, etc., Fig. i,
with the radial lines a, J, c, etc., Fig. i, to the corresponding lines,
a, b, c, dy etc.. Fig. 4. The ciurves thus formed are true curves of
the driving face at sections passed through lines i, 2, 3, 4, etc.,
Fig. I.
Geometry of a Screw Propeller having an Inclined Gen
eratrix. Sheet 29
The surface having an inclined generatrix is developed simi
larly to the one having a vertical generatrix, except that, looking
at the plan the sections will not pass through the same center
on account of the inclination.
Draw the construction lines in Fig. i, as for the vertical gen
eratrix. Draw the generatrix at some predetermined angle
(Fig. 2). Lay off the 1^ pitch, divided into 5 parts, each side of
the generatrix at the tip and at the base. (Fig. 2, lines a, b, c, d
Cjf.) Draw perpendiculars to the tipline passing through these
points. Project from Fig. i the intersections of the arc of the
full radius with lines a, J, c, d, e, /, to the corresponding lines,
fl, J, c, dy e, /, Fig. 2. Through these intersections draw in the
curve. Now, from these intersections draw lines passing through
points a, b, c, d, e, /, on the baseline. Then project the arcs of
the tenths of the radius (Fig. i), from where they intersect
lines fl, by c, d, e,/, to the corresponding lines a, J, c, d, e,f,
Fig. 2.
Lay down two lines parallel with each other at the distance
" A " apart, and project around the points a, by c, d, e, /, from
Fig. 2, on both the tip and baselines (see Fig. 4).
Digitized by LjOOQ IC
282 SCREW PROPELLERS
The radial lines a, b, c, d, e, /, in the plan must correspond
to radial lines a, h, c, d, e, /, in Figs, i and 2. Project from the
intersection of the arc of the full radius with lines a, by Cy d, ty /,
Fig. I, to the corresponding lines a, 6, c, rf, Cy /, Fig. 4 laid oflf
from the tipline. A curve drawn through these points will form
the helix. Through these points on the helix draw lines passing
through the points a, 6, c, i, e, /, laid off from the baseline along
the centerline. The point on the centerline through which each
of the sections, i, 2, 3, 4, 5, 6, 7, 8, 9, 10, will pass will be the dis
tance apart caused by the inclination.
These distances are obtained by projecting lines, i, 2, 3, 4,
etc.. Fig. I, through the generatrix, Fig. 2. Then the sine of the
angle, formed by the generatrix and a perpendicular to the base
passing through this intersection will be the distance to lay off
from the baseline along the centerline in Fig. 4, and the point
through which each of the sections, i, 2, 3, 4, etc., will pass.
The sections are then formed by passing curves through the
intersections of lines a, J, c, d, Cy /, Fig. 4, with the projections
from the corresponding lines a, 6, c, rf, e, /, Fig. i, where they
intersect the lines i, 2, 3, 4, etc.. Fig. i.
The Draughting of the Propeller
Sheet 30 shows a propeller of the type used on merchant
vessels with a single screw working behind the stem post, and,
in order to give a good clearance, it is made with an inclined
generatrix which throws the tips of the blades further away from
the post.
Sheet 31 shows a tj'pe of propeDer used on torpedo boat
destroyers, driven by turbines directly, where a high nmnber of
revolutions is necessary. The propeller shown is built with a
vertical generatrix.
Sheet 32 shows a type of propeller used on battleships where
the revolutions are comparatively low.
The following are the calculations and points of design, which
are practically the same for any type of wheel, the principal
dimensions for design having been calculated from Sheet 20.
Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING
283
Number of blades 3
Diameter . 17' 6"
Pitch 18' o"
R.P.M 117
I.H.Ptf 14,700 — total 2 engines
I.H.Pd 7350 — one shaft
P.A.
The geometrical construction is laid down for the vertical
generatrix, and on this plot the form of projected surface. Sheet
32 is the sheet to which the following work applies:
P.A.
D.A.
From Sheet 25 — ^Determine the chords of half arcs for
= .32 — 3bladed wheel. As no multipliers are given for ratio. 32
in the list interpolate by direct proportion, as follows:
Take the multipKer given for ratio .30 and increase it by the
proportion '^ for each chord of the several half arcs; this gives
the following:
^ X multiplier X rad. in inches = — XmultiplierXioq''
.30 .30
= 1 1 2 X multiplier ; then
2 i2 = ii2X.o82 = 9.i84 in.
3 22 = 112 X.i28 = 14.336 in.
4 i2 = ii2X. 170 = 19.04 in.
5 i2=ii2X. 207 = 23. 184 in.
6 i? = 112 X.236 = 26.432 in.
7 i? = ii2X.253 = 28.336in.
8 i? = ii2X.25o = 28.ooin.
9 i? = ii2X. 210 = 23.52 in.
925i? = n2X. 190 = 21. 28 in.
95 i? = 112 X.i6i = 18.032 in.
97Si? = 112 X. 120 = 13.44 in.
Lay down these chords on each side of the centerline on the
half arcs of the tenths of the radius and draw in the curve passing
Digitized by LjOOQ IC
284 SCREW PROPELLERS
through these points. Now, project the intersections of this
curve with the lines i, 2, 3, 4, etc., in the front elevation, Fig. i,
to the corresponding lines i, 2, 3, 4, in the plan. Fig. 3, and side
elevation, Fig. 2, and draw in the curve in these other two views.
Figs. 2 and 3.
Determine the thickness of the blade at the root by the method
described in chapter on Blade Thickness, as follows:
Blade, manganese bronze, 60,000 T.S.
Design based on Sheet 20.
T = Thickness of blade at root.
TF=Width of blade tangent to hub = 3' 4"=4o".
^33,ocx)XLHP. ^ 33^X7350 ^^ f, .lb.
2TXRXN 6.2832X117X3
B = .3iXdiam. in feet= mean ann = .3iX 17.5 = 5.425 ft.
C = — = —  — = 20,270= resultant athwartship force on one
B 5.425
blade in footpounds.
Z) = i2XB— Rad. of hub in inches = arm of athwartship force
measured to root of blade = i2X5.425=6s.i" — 25,5"
=396".
£=CXZ?= athwartship moment at root of blade in inch
poimds = 20,270X39.6 = 802,800.
F = 33>QQQ ' ' ' ^ indicated thrust per blade in pounds
PitchXiexNo. blades ^ ^
^ 33,000X7350 ^ 8,390 lb.
18X117X3
G^ = 34SXdiam. in inches=mean arm of thrust =345X2 10
= 72.45 in.
£r=G— Rad. hub in inches = arm of thrust measured to the root
of blade = 72.45 25.5 =46.95.
/=FxH=fore and aft moment at root of blade, in inchpoimds
=38,390X46.95 = 1,802,400.
X= — ; — ^ = tangent of angle between face of blade and
C.L. of hub or foreandaft line tangent to surface of hub
=^=.7418.
Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING 285
Zr = Sine of arc whose tangent is 1^=36®— 34' = Sine .5958.
Jlf = Cosine of arc whose tangent is ^=36°— 34' = cosine .8032.
N=LXJ = component of fore and aft moment normal to face of
blade at root = .5958X1, 802 ,400 =1,009,100.
0=JlfX£=same for athwartship moment =.8032X802,800
=644,800.
P = N+0 = total moment at root of blade in inch poimds
= 1,009,100+644,800 = 1,653,900.
/'=Fibre stress = 10,000 as e.h.p.=E.H.P. = i.o.
r J^ X^3>i25 _ J i,653,900Xi3,i25 _^ .^//.
^"■\"irx7 ^ 40x10,000 "73^7 '
say 7I" for safety.
Draw in the shape of the back of the blade, as in the section
shown on Fig. 2, Sheet 32, using 7.5 in. at the root and a thick
ness of f in. at the tip. The tip is then fined down to a very
small radius, about i in. at the tip and faired back to about 5 in.
from the edge of the blade. Now, determine and draw in the
flange of the blade. This is determined from the plan view,
Fig. 3, and must be of a diameter large enough to take the blade
and the blade bolts. The diameter of the hub can now be deter
mined by drawing in the flange in the front elevation. Fig. i,
and drawing a circle, with the axis of the blade as the center and
the radius of the hub forming the top of the flange.
The hubs of builtup propellers are usually spherical, as in
this case.
The niunber and size of the bolts holding the flange to the
hub must now be determined.
The niunber used is dependent upon the space on the flange
to accommodate them, but either 7 or 9 is the most common
practice. Nine have been used in this case, and are spaced 5
on the driving side of the blade, and 4 on the backing side
The area of the bolts is determined in the following manner:
A =area in square inches of one bolt.
n= Niunber of bolts on driving side of one blade = 5.
r=Rad. of pitch circle (as the leverage is different for each
bolt, the radius is taken as the mean) = 14".
Digitized by LjOOQ IC
286 SCREW PROPELLERS
L=arm of thrust measured from face of flange = . 345 Xdiam.
—distance from C.L. of hub to face of flange = (.345
X 210) 13^ = 58.95 in.
iV= Number of blades =3.
IZ=Revs. per minute = 117.
P= Pitch in feet =18.
/= Stress — ^manganese bronze or naval brass =6,000 lb.
.^ LH.P.X33,oooXZ: _ 7350X33,000X58.95 .. ^qqo^
NxPXRXnXrXf 3X18X117X5X14
5.388 sq. in. ^ 2I in. diameter.
•
(As 6000 lb. is max. stress to be used, — ^bolts have been made
3 in. diameter = area 7.0686, and the stress is:
73SoX33>oooX58.95 ^,„ . .u
3X18X117XSX14X7.0686 ^^ ^ *
•
Care must be taken in spacing the bolts in the flange that the
section of the blade where it joins the hub, fillets being neglected,
is not decreased in area. This can easily be avoided by pro
jecting, in the plan view. Fig. 3, the line of intersection of the
driving face and the back of the blade, with the surface of the
hub, as shown by the dashed lines.
The blade shown on Sheet 32 has the bolt holes slotted to
allow for an adjustment of the pitch 9 in. either way, but this
practice is, while allowable, incorrect, as the propeller is no
longer a true screw if the pitch be altered from the designed
pitch.
The practice in the U. S. Navy is to provide a cover over
the bolts and nuts, flush with the surface of the flange, and
having a watertight joint with the flange.
The bolts are locked in place by locking pieces, which fit
between the heads and are held in place by a tap bolt screwed
into the flange between the bolts.
Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING
287
STANDARD PROPELLER HUBS
For Solid Propelleks— Plate B
r }J ^l.^ LT 4* tr J
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Digitized by LjOOQ IC
288
SCREW PROPELLERS
STANDARD PROPELLER HUBS
For 4Blade, Builtup, Propellers — Plate C
Formulas for obtainin« d.
*A *net area. sq. in., one bolt, a — distance from center of sbaft to center of thrust,
in inches, fr— distance from center of shaft to face of blade flange. D — diameter of
propeller in inches, / — allowed stress in lbs. per sq. in. of bolt section. G — arm of thrust
measured from face of flange, in inches. iV — number of blades, n — number of bolts on
driving ride of one blade. P pitch in feet. K  revolutions per minute, r —radius of
pilch circle in inches.
 S.H.P. X33000 XG
iVXPX/JXnXrX/
aDX.34S.
/— 4500 for manganese bronze or naval brass.
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Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING
289
Plate C
Digitized by LjOOQ IC
290
SCREW PROPELLERS
STANDARD PROPELLER KUBS^otUinued
D
d
di
dt
da
dt
di
d.
d»
/
/I
h
hi
ht
8i
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1
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Digitized by LjOOQ IC
GEOMETRY AND DRAUGHTING
201
STANDARD PROPELLER HUBS
For 3Blade, Builtup, Profelieks — ^Plate D
D
B
C
Dx
Dt
F
Fi"
Ft
H
K
L
Li
N
Nx
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Digitized by LjOOQ IC
282
SCREW PROPELLERS
H '<^ 4
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GEOMETRY AND DRAUGHTING
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Digitized by LjOOQ IC
CHAPTER XVm
AEROPLANE PROPELLERS. DESIGN, MATERIALS AND
CONSTRUCTION
In designing aeroplane propellers, as in the design of those
for the propulsion of ships, there are six variables to be taken
into account. These variables are
1. The speed of flight;
2. The power required;
3. The number of revolutions of the propeller;
4. The allowable diameter of the propeller;
5. The pitch of the propeller, whidi is dependent on i, 2, 3, 4;
6. The projected area ratio of the propeller.
In determining these variables, i is arbitrarily fixed. To
obtain 2, the mean gross flying weight of the machine must be
furnished. Having given this flying weight, which should
include all weights on board, the machine, when flying at the
designed speed, experiences a total resistance to its horizontal
motion of approximately, onesixth to onefourth of its weight, or
P Gross weight
The effective horsepower, e.h.p., necessary to overcome this
resistance is
, PXi^XS28o PXv
e.n.p. = '^ — = ,
.60X33,000 375
where v equals the speed of flight in miles per hour.
The effective horsepower thus obtained is that which is
necessary for horizontal flight only, at the designed speed. For
climbing purposes and for rapid turning purposes when turning
from an upwind to a downwind direction of flight when the
294
Digitized by LjOOQ IC
AEROPLANE PROPELLERS 295
wind is high, an excess of power over that necessary to deliver
the effective horsepower as obtained above, must be provided.
This excess power should amount to approximately 35 per cent
above that required for the normal speed of flight.
Suppose the gross fl3dng weight of a machine = 1800 lb. and
the normal speed of flight be seventy miles per hour, then
^ 1800
C=^=3oo,
e.h.p.=32^><7o^ 6^
375
The factor 6 is variable, however, and for very high speeds
should be taken as low as 4.
Suppose that a propeller delivering a propulsive eflSdency of
70 per cent on shaft horsepower can be fitted, then using the
same notation as for hydraulic propellers vdth the exception of
the propulsive coefficient which with aeroplane propellers equals
e.h.p.
S.H.P.tf'
S.H.P.,=— =80 and the total power to be provided =
S.H.P.tfM«. = 80X 1.3s = 108.
Number 3 of the variable elements is usually fixed by the
the design of the engine and by the amount of speed reduction
that is desired to be installed between engine speed of revolu
tions and the propeller speed.
Number 4 is limited by conditions of necessary clearances
fixed by the aeroplane itself.
To obtain the necessary power, the e.h.p. being known or
estimated, the proper pitch and projected area ratio, a sheet of
design curves of the same general character as those used in
hydraulic propeller design, has been prepared. These curves
have been derived from the performances of four aeroplane pro
pellers tested out at the United States Aviation School at Pen
sacola, Florida. They can not claim the same amount of
accuracy, however, as can those for hydraulic propulsion as
Digitized by LjOOQ IC
296 SCREW PROPELLERS
unfortunately up to the present date there have not been devel
oped any means of accurately measuring the power of the engine
and the actual thrust of the propeller while the aeroplane is
in actual flight.
In designing aeroplane propellers the designer should always
be provided with a fullthrottle variable brake ciuve of shaft
horsepower and revolutions, in order to insure the ability of
the engine to turn the propeDer at the desired revolutions
under any conditions of resistance that may occur.
Description of the Design Sheet, No. 26
On this Sheet are shown:
i.CurveofS.T..= S.H.RX33,ooo
PX^X^!— X144
4
2. Curve of T.S.=irZ)Xi2.
3. Curve of i— 5.
4. Curve of P.C. = g ^'p 
5. Curve of Log A where A = Speed'.
6. Curve of S.T.i>■^ (i 5).
7. Curve of Log A — o to no knots.
8. Curve of Log A — no to 180 knots.
The nomenclature is similar to that used in the computation
forms for hydraulic propellers and for lack of evidence to the
contrary, it is assumed that the laws governing variations of
power and revolutions for hydraulic propellers apply equally as
well to those operating in air.
There is a radical difference, however, between hydraulic and
aeroplane propellers due to the difference in the projected area
ratios which are used for the two types. While with hydraulic
propellers the projected area ratios used range from about .2 to
.6 and have a propulsive efficiency decreasing as the projected
area ratio, tipspeed and indicated thrust increase, the aeroplane
propeller has its projected area ratio between zero and .2; it is
Digitized by LjOOQ IC
AEROPLANE PROPELLERS 297
thus located in the portion of the propeller range wherein the
propulsive coefficient increases with the tipspeed, thrust and
projected area ratio, referring always to the Basic Condition of
Design as given by the Design Sheet. With hydraulic pro
pellers as the projected area ratio increases the apparent slip also
increases for the basic condition, and this same variation of
apparent slip is seen to occur with aeroplane propellers.
With aeroplane propellers there is no such correction for slip
block coefficient in the estimate of apparent slip as exists with
hydraulic propellers. In other words, the air ship is treated as
a phantom ship and the value of i *5 remains at a constant value
for the basic condition of each value of P.A.4D.A.
The Design Sheet as shown is for threebladed propellers, the
same method of correction for two and fourbladed propellers
being used as in the cases of hydraulic propellers of like niunber
of blades.
In the application of the Design Sheet, the same method of
computation may be employed as in the case of hydraulic pro
pellers. In the example here given an alternate method is
used. In the first step a constant value of P.A.5D.A. and
varying values of e.h.p.5E.H.P. are used, while in the second
step when that value of e.h.p.^E.H.P. giving the nearest value
to the desired revolutions with the maximum value of P.A. 5D.A.
has been ascertained, this value of e.h.p. 7E.H.P. is retained con
stant and the problem solved for varying values of P.A.4D.A.
Care must be taken that the projected area ratio does not
become too large in order that the blade widths do not become
excessive and deform easily under thrust. The Design Sheet
carries the projected area ratio of the threebladed propeller to
.12, the table on the same sheet extending it to .17, and the lim
itation of these values is given in Table XVIII.
Digitized by LjOOQ IC
298
SCREW PROPELLERS
Table XVIII
Constant P.A.fD.A.=>.3
•
P.A.+D.A.
P+D.
3 Blades.
2 Blades.
4 Blades.
.0
. .2
.133
.266
.1
.198
.132
.264
.2
.196
.131
.262
3
.194
.1293
.2586
.4
.1915
.1277
.2554
S
.189
.126
.252
.6
.186
.124
.248
.7
.1826
.1217
.2434
8
•1793
"95
.2390
9
.1755
.117
.2340
.172
.1146
.2292
I
.1677
.1118
.2236
2
.1635
.109
.218
3
.1592
.1061
.2122
4
.1548
.1032
.2064
5
.1502
.1002
.2004
6
.146
.0972
.1944
7
.141
.0940
.1880
8
.1362
.0908
.1816
9
.1315
.0876
.1752
2.
.127
.0846
.1692
For a 4bladed wheel, for maximum efficiency, the total projected area ratio
of the projected surface outside the .2/) circle should never exceed .2.
Problem
Aeroplane fitted with an engine to give 125 S.H.P. at 1300
revolutions when flying at a speed of 90 miles an hour. The
maximum diameter of propeller that can be carried is 8 ft.
Determine pitch, projected area ratio and propulsive efficiency
of a propeller to meet these conditions, the propeller to be two
bladed.
Digitized by LjOOQ IC
AEROPLANE PROPELLERS
299
FIRST STEP
P.A.SDA (assumed)
P.A,5D.A
eh.p.5E.H.P
S.H.P.p = S.H.P.tf
Z (Sheet 21)
S.H.P. = S.H.P.iXio^
P.C.foj:fP.A.rD.A
E.H,P
e.h.p
V
»>yn, ^XS.H.P.X389
S.T.dXT.S.
S.T.D. (Sheet 26)
T.S (Sheet 26)
D
P
PXT.S.X(i5)
»rZ>X88
15
Fmknots= — , ^
6080
,inknots=22^
LogAv(Vm Knots). (Curve X,
Sheet 21)
Log Av (vin knots). (Curve X,
Sheet 21)
_ S.H.P.dXi4v
* S.H.P.X^i4r
« » (Miles) X 88
^" pxdi)
.Ill
.III,
.III
.074
.074
.074
.4
.6
.8
125
125
125
.4144
.231
• .1009
32s
213
158
.70
.70
.70
227.5
149. 1
no. 6
91
89.46
88.48
90
90
90
85.26
55.88
41.45
.1048
.1048
.1048
444SO
44450
44450
8'
8'
8'
10.66
6.985
5. 181
140. 1
91.81
68.1
.654
.654
.654
121. 7
79.73
59.14
78.34
78.34
78.34
5231
4.85
4.67
4.84
4.84
4.84
.3274
.2078
1851
1 105
1431
1876
.III
.074
I.O
125
o
125
.70
87.5
87.5
po
32.79
.1048
44450
8'
4.099
53.88
.654
46.79
78.34
4.62
4.84
.2085
2441
Plotting these results, using Pitch for abscissas and e.h.p.
and Ra as ordinates, curves are obtained (Fig. 62), from which
the propeller characteristics are obtained. They are
Diameter =8';
Pitch =8'. 25;
P.A.fD.A. (2Blades) =.074;
S.H.P. =125;
Total S.H.P. =125X1.35 = 168.75;
9 =90 miles;
Digitized by LjOOQ IC
300
SCREW PROPELLERS
R
= 1300;
e.h.p.
=90;
P.C.
_e.li.p._
125
m
11
1
1
II
1
%000
I
95
•tt
d
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6
1
S
'
\::
VMO
1
90
B
liitiiiiii
IB
II
i:::il
1
II
II
1.000
1
4
i
I
<
}
7
fi
s
>
li
9
1
I
Scale of I>itoh in Feet.
Fig. 62.
Should it be desired to increase the projected area ratio of
the propeller in an attempt to obtain a higher propulsive effi
ciency, any load factor lower than that corresponding to the
above propeller, whose load factor is somewhere between '\'
= .5 and = .6, may be taken and used as constant and the second
step undertaken, as follows:
Digitized by LjOOQ IC
AEROPLANE PROPELLERS
301
SECOND STEP
e.h.p.fE.H.P
P.A.^D.A
P.A.hDJV
SJI.P.p=S.H.P,d..
Z
S.H.P
P.C. (for{P.A.5D.A.).
E.H.P
e.h.p
D
PXD=
XS.H.P.X389
'' S.T.DXT.S. *
T.S.s.S..8o(^)
S.T.D
i5for(P.A.^D.A.)..
F={PXT.S.X(i5)}
(xDX88)
F(knots^
V (knots) . . .
Ay (knots).
Av (knots). .
5
^
.4
.III
.74
125
,4144
.70
227. s
91
8
85.26
10.66
444SO
.1048
.654
140. 1
121. 7
90
78.34
5231
4.84
.3274
1 105
•4
.4
.114
.117
.76
.78
125
125
.4144
.4144
325
325
.702
.704
228.48
229.94
91.4
91.98
8
8
79.33
73.69
9.916
9. 211
45680
46992
.1096
.1147
6545
.655
134 OS
128.19
116. 4
III. 3
90
90
78.34
78.34
5.187
5.143
4.84
4.84
.2958
.267
1 134
"73
.4
.12
.8
I2S
.4144
325
.706
231.08
92.43
8
68.47
8.558
48343
.12
.6555
122.62
104. 1
90
78.34
5.077
4.84
.229
1200
The increase in P.A.4D.A. has not been sufficient to. carry
the revolutions to 1300 as required, and it would be necessary to
go to still wider blades of lower pitch to reach those revolutions
unless it were decided to try a load factor e.h.p. ^E.H.P. between
that of the first step propeller and the second step.
Should the value of P.A.5D.A. be such as to be beyond the
limits of the Design Sheet, then the various factors can be found
as follows:
^•T»4^(5X)"
T.S. =519,580
I —Sis of same value as at P.A.5D.A. = .12.
/P.A.y"
Digitized by LjOOQ IC
302 SCREW PROPELLERS
Log Av^ for values beyond i8o miles is found by means of
the equations given for the same purpose under hydraulic
propellers.
VariaUans in the computations produced by the change from
two to three or fourbladed propellers.
Where threebladed propellers are desired, and it is always
preferable to use them, rather than twobladed, on accoimt of
their smaller diameter and smoother nmning, the P.A.^D.A.
as taken from the Design Sheet will be those of the propellers
derived, and all the data including the P.C. must be taken for
those values of P.A.5D.A
The only change in formulas which occurs is in that for
PXD, which becomes
pv>7._ ^XS.H.P.X29i.8
^^^" S.T.i>XT.S. '
In the case of fourbladed propellers, this latter formula
becomes
i>yn^ ^XS.H.RX2524i
S.T.z>XT.S. '
while all of the data with the exception of P.C. are taken for the
various values of P.A.^D.A. used, the actual projected area
ratio of the propeller will be i (P.A.TD.A.) and the P.C. cor
responding to this' full projected area ratio must be used.
Case of Full Load and Full Diameter
In the foregoing cases, the propeller would have a large
amoimt of reserve power and the full power of the engine could
be put into it without any trouble being experienced. A pro
peller can be obtained directly from the design chart which will
fit the full power of the engines at the revolutions and speed of
flight expected and will have a very much reduced reserve capac
ity. In computing such a propeller, no diameter need be
assiuned, as the computation determines not only the pitch,
projected area ratio and the propulsive efficiency but also the
diameter.
Digitized by LjOOQ IC
AEROPLANE PROPELLERS
303
Such problems are denoted as problems of " full diameter,"
and the method of procedure will be shown by the following
computation for a full diameter threebladed propeller:
P.A.^D.A
T.S
15
S.T.D
V (Estimated Speed). (Miles)
S.H.P. (Power of Eng.)
P.C
E.H.P .
n,^/ g9i 8XS.H.P.
^s.t.dxpxr
PXRXtD
T.S.
p T.S.
•7
.8
.9
I.O
I.I
26500
30900
35150
39400
43800
.834
.757
.696
.6645
.654
.0476
.06
.0737
.088
.1032
99.7
99.7
997
99.7
99.7
170
170
170
170
170
.694
.706
.717
.726
.735
118
120
122
123
125
9'. 953
8'.446
7'.307
6'. 534
5'.986
12'. 41
9'. 952
8'. 233
6'.879
5'.69i
847. S
1165
1530
1919
2357
1.2
48340
•6S5S
.12
997
170
•744
126
5'. 558
5'.424
2468
In all of these problems, however, the work may follow the
same forms as are used for hydraulic propellers, substituting
S.T.2> for LT.2>, S.T.i>^(i5) for I.T.2>^(i5) and S.H.P.dfor
I.H.P^, and a problem worked out by this method is now
given.
Shaft horsepower, revolutions and expected speed, (S.H.P.d,
R41 and v) given, to find propeller.
Data Gi\^n
Gross load of plane = 5200 lb.
Useful load on plane = 1460 lb.
Estimated speed = 95 statute miles = 82.5 knots.
Required climb = 3900' in ten minutes.
Revolutions =i2d = 1625.
Shaft horsepower of engine = S.H.P.tf = 400.
Maximimoi diameter of propeller that can be carried =8' 4"
=8'.33.
Propeller to be f ourbladed.
Digitized by LjOOQ IC
304
SCREW PROPELLERS
Power expended in climbing =^ ^5— =61.46 e.h.p.
10X330CX)
Estimated propulsive efficiency (assumed) = .70.
Shaft horsepower expended in climbing = — ^=88.
.70
Shaft horsepower available for speed of advance while climb
ing=4oo— 88=312.
Speed of advance while climbing =i;i.
^1^ • 9S^"3i2 : 400.
1^1=87.38 statute miles.
COMPUTATION FOR PROPELLER
D (assumed)
V (stat. miles)
V (knots)
e.h.p.JE.H.P. (assumed).
Z (Sheet 21)
S.H.P.d
S.H.P. = S.H.PHfXio^
v^VioT^^(Sheet22)....
V (knots)
S.T.tf5(iS) (Sheet 26)
P.A.^D.A. for S.T.tf^(i5)
JP.A.hD.A
p.C. for t^ (Sheet 26)....
U.A.
E.H.P.'
e.h.p. . .
=S.H.P.XP.C.
♦ e.h.p. (estimated necessary) .
T.S. for ZA (Sheet 26)
U.A,
15 for ^ (Sheet 26)
7rXDXioi.33XF
T.S.X(i5)
Log Av (Sheet 21)
Log Aj, (Sheet 21, Line .X")
„ S.U.^.aXAv
5=0
S.H.P.X^^
_ ioi.33Xp
^pxo^
♦ e.h.p.=?^^?^^^^^.
4.5X60X33000*
8'. 33
95
82.5
.6
.231
400
680.9
.838
98.45
.2483
•14375
.192
.77
524.3
315
293
59180
.655
6'. 735
5 03
4.88
.2863
1739
8'. 33
95
82.5
.7
.161
400
579. 5
.882
9354
.2224
.134
.179
.767
4445
3"
293
54 700
.655
6'. 923
4.985
4.88
.3033
1733
8'.33
95
82.5
.8
.1009
400
504.6
.92
89.68
.202
.130
.170
.766
386.5
309
293
52998
.655
6', 85
495
4.88
.3213
1798
8'.o
95
82.5
.6
.231
400
680.9
.838
98.45
.2692
.150
.200
.77
5243
315
293
62064
.655
6'. 168
503
4.88
.2863
1899
8'.o
95
82.5
.7
.161
400
579.5
.882
9354
.2411
.1436
.191
.77
446.2
312
293
591 10
.65s
6'. 153
4.985
4.88
.3033
1950
Digitized by LjOOQ IC
AEROPLANE PROPELLERS
305
D (assumed) ,
V (stat. miles)
V (knots)
e.h.p.^E.H.P. (assimied). . . .
Z (Sheet 2i)
S.H.P.d
S.H.P.=S.H.P.dXio^
v^ for 1^ (Sheet 22)..
V (knots)
S.T.di(iS) (Sheet 26). .. .
P.A.5D.A. for S.T.d5(i5)
P.A.^D.A
P.C. for i^' (Sheet 26)...
iJ.A.
E.H.P.=S.H.P.XP.C
e Ji.p
* e.h.p, (estimated necessary)
T.S. for ^' (Sheet 26)
Jj.A.
i_5for^ (Sheet 26)
D.A.
7rXl>X 101.33 XF
T.S.X(i5^
Log Av (Sheet 21)
Log At (Sheet 21, line X
_ S.H.P.dXi4v
^ S.H.P.Xi4r
_ 101.33 Xp
^"PXO^
♦ e h p. , 95X5280X5209
4.5X60X33000*
S'.o
7'. 75
/.75
95
82.S
.8
95
82.5
.6
95
82.5
.7
.1009
.231
m6i
400
5046
400
680.9
400
579. 5
.92
.838
.882
89.68
.219
98.45
.2868
93.54
.257
.134
.155
.145
.179
.207
.193
.767
.77
.77
387.1
524.3
444.5
310
315
312
293
293
293
.'>'t7oo
64390
. 59756
.655
.655
.655
6'. 374
5' 759
5'.883
495
4.88
5.03
4.88
4.985
4.88
.3213
.2863
•3033
1933
2034
2040
7.7s
95
82.5
.8
.1009
400
504.6
.92
89.68
.2334
.140
.187
.768
387.6
310
293
57454
.655
5'. 879
4.95
4.88
.3213
2091
All revolutions obtained are too high. To reduce them hold
the value of e.t.: E.T. corresponding to any chosen condition of
'^^^ and , in this case .55 and 838 as the propeller obtained
for those conditions and with a diameter of 8' 4", had low revo
lutions combined with maximum efficiency, constant and reduce
the values of ' '^ and ~ by coming down along the line of this
e.t.
E.T.
on Sheet 22. as follows:
Digitized by LjOOQ IC
306
SCREW PROPELLERS
e.t+E.T
e.h.p.iE.H.P
S.H.Pm
Z
S.H.P #.
P.A.8D.A. (as before). .
1P.A.+D.A
^•^•^♦5X
E.H.P
eJi.p
. T7 1 ct J e.h.p.
tr y for and ^—
E.T. E.H.P.
r (knots)
y
T.S.for^ (Sheet 26).
i5for^ (Sheet 26).
Jj.A.
XXDX101.35XF
T.S.X(i5) ••*•
LogAr
Log A,
_ S.HJP.dXi4y
* S.H.P.Xi4.
_ioi.33X!'
^px(I^
.715
.715
.55
.5
400
400
.27
.3135
780
823.2
.144
.144
.192
.192
.77
.77
600.6
634
315 4
317
.768
.698
82.5
82.S
108.7
118. 2
59180
59180
.655
.655
7'. 434
8'. 086
5.12
5215
4.88
4.88
.322
.3625
1659
1622
.715
.47
400
.342
879.2
.144
.192
.77
676.9
318.2
.655
82.5
126
59180
.655
8'. 61 7
5.28
4.88
•3943
1602
Take that propeller promising 1622 revolutions as the one
to be used. Its characteristics are as follows:
Blades 4
Diameter 8' 4''
Pitch 8'i''
Total projected area ratio outside of .2 radius of propeller .192.
P A
Standard — ^ form 144
S.H.P 400
R 1625
V 95 statute miles.
Digitized by LjOOQ IC
AEROPLANE PROPELLERS 307
Construction of Aeroplane Propellers
Material furnished by Mr. Spencer Heath, American Propeller Co.
The aeronautical screw propeller or air screw, strange as it
may seem, was in point of theory and conception, at least, the
forenmner of the hydraulic screw.
Like nearly all things aeronautic, in its own day this invention
was scorned and neglected, particularly by the man of science,
and afterwards virtually forgotten, so much so that when the
same device many years later was employed for marine propulsion
it was hailed and received as wholly new.
In their basic principle all screws are the same for whatever
purpose used. They differ only in their proportions, form and
material. These differences are due to the different nature of
materials through which the screws act. A machine screw acting
through a previously prepared nut is a special case of a member
progressing along an inclined plane, the movement of the member
being along a helical curve instead of a straight line. A wood
screw and a corkscrew, however, make their own " nut " through
the cork or wood in which they act. These screws, in common
with the machine screw, have an axial advance in one revolution
substantially equal to the distance between turns of the " thread,"
known as the pitch of the screw. The air and hydraulic screw
propellers are like the cork and wood screw in that they form their
own " nut " through the air or water, but they differ markedly in
that the fluid mediimi through which they pass has no great sta
bility and yields to the screw in such manner that commonly it
does not advance its full pitch in one revolution. This yielding
of fluid is entirely analogous to the yielding of the water to the
bending of an oar or paddle. The resistance with which the
fluid yields in the stemward direction creates a fulcnmi for the
oar and measures the propulsive impulse of oar or screw. The
magnitude of this impulse depends upon the density of the fluid
medium and the stemward velocity with which it is caused to
move.
The differences between air and hydraulic screw propellers
may be said to be the reflex of the differences between air and
Digitized by LjOOQ IC
I
306 SCREW PROPELLERS i
I
water. Air is thinner, lighter, larger, swifter than water. Air
propellers are longer and thinner of blade, lighter in weight of ,
material, larger in proportion to duty and swifter in velocity of i
rotation and of flight I
Almost all air propellers are made of wood. In general 
appearance, except for width of blade, they resemble hydraulic i
propellers. The number of blades may be two, three or four.
The widest part of the blade is usually at about sixtenths to
seventenths of its radius. The maximum width of the devel
oped arc, measured for zero pitch and on the circular arc,
averages about onetwelfth the diameter of the screw. The
thickness of blade near the hub is very great but diminishes
rapidly to about halfblade length and then gradually to the
end. The side of the blade facing rearwardly (the driving
face), is of true and constant pitch and may be slightly
concave in its wider and midradius portions and flat or
slightly convex at its narrowed end and near the hub. The
forward facing side of the blade (the back of the blade), is
convex in all parts and the greatest thickness of any section is
about onethird the distance from the entering to the trailing
edge. Nearly all air propellers have the general characteristics
already mentioned. In blade outline, however, there is wide
diversity. Some designers prefer to approximate a slender
ellipse; others prefer the slender ellipse with squared ends on
the blades; others approximate a semiellipse, the axis of the
ellipse proceeding radially from the axis of rotation and forming
the trailing edge of the blade. Among these various forms no
special preference is known. Some of them are laid out with a
view to placing the centers of gravity of all the blade sections in
one radial line; some with the aim of having the center of pres
sure on each blade section lie in the same straight line.
As in hydraulic propellers, it is desirable to adhere to a
standard form of blade if a rapid solution of the propeller prob
lem is to be obtained.
In all the above forms of blade a common property obtains:
The deflection of the blade under load is accompanied by more
or less increase of angle in its most effective parts, thus aug
Digitized by LjOOQ IC
AEROPLANE PROPELLERS 309
menting the pitch. This gives the blade a sort of unstable pitch
which may introduce heavy strains and resistances to the turning
of the propeller at the moment when highest turning speed is
required. In order that the pitch may remain imaflfected by
bending or deflection of the blades under load or increase of load
it is necessary to dispose the centers of pressure of the sections
farthest from the hub on a line curving somewhat rearwardly
in the direction of the trailing edge. Variable pitch propellers
are designed by so far extending the. rearward curvature of
the blades that the application of working blade pressure will
institute a torsional action on the entire blade causing its pitch
to increase or diminish in response to variation in pressure. In
this torsion design for variable pitch the portion of wood em
ployed in the curved trailing edge of the blade is steamed and
bent so that the grain of wood parallels the curved edge of blade.
In this process a slight compression is given to the fibres which
greatly increases the endurance of the thin edge portions of the
blade.
Nearly every kind of wood has been used in propellers.
Walnut and mahogany have long been favorite in Europe. The
experience of one noted builder rules out all wood that was not
quarter sawed and points to American quartered white oak as
the surpassing material from every standpoint, the particulars
of which need not be detailed here.
It is almost needless to say that the wood for air propellers
should be selected and treated with utmost care. The boards
are sawn to i in., rough dressed to  and finish dressed to ^
or inch thickness.
The propellers are built up by five or ten laminations accord
ing to size. The laminations are laid out on the boards and
sawed to outline, care being taken to avoid all defects in wood
and to have the grain and density of wood as nearly similar as
may be at opposite ends of the same piece. In the better and
preferred practice, however, the laminations for each single
blade are laid out separately and carefully weighed, matched
and balanced against each other. They are then selected in
pairs (or in trios for tkreebladed propellers) and their hub
Digitized by.LjOOQlC
310 SCREW PROPELLERS
ends securely glued together in highly efficient joints of very
large gluecontact area. Only by this method is it possible to
make the blades of the same propeller uniform in respect to
weight, grain texture and yielding of the wood under stress.
When the separate laminations have been prepared and
surfaced to required thickness they are slightly roughened by
tooth planing, warmed over steam coils and assembled together
with the best of hide stock glue and firmly clamped. The entire
gluing process is carried on in a room kept at ioo° F. After
eighteen to twentyfour hours the clamps are removed and
center hole in hub bored roughly to size. The propeller is now
himg for about ten days to dry. It is then put through a machine
which at one operation faces both sides of the hub and bores out
the center hole to finish size. After being faced and bored the
propeller is " outlined " in a machine that profiles the hub and
edges of the blades all to exact size and shape by means of a
rotary cutter following a form which has the precise outline of
the blades.
From the outlining machine the propeller progresses to one
of the duplicators. In this machine the work is clamped in
definite relation to a rigid fixed form having the same shape as
the blades. On the carriage of the machine there is a roller which
traverses the surface of the form and guides a high speed cutter
in a manner to remove nearly all surplus wood from the rough
propeller. The carriage is self feeding and self reversing and the
bed and other parts of the machine, including the form, are made
duplex in order to secure continuous operation of the cutter,
the work being removed and renewed at each end of the machine
in turn while the carriage is operating iminterruptedly at the
other end.
After the duplicating process the propeller again dries for a
few days after which it is carefully surfaced and balanced by
hand and then forwarded to the sanding machine. After sanding
there is careful inspection before proceeding further, and careful
examination of balance, pitch and tracking of blades, hub dimen
sions, etc. The inspection itself is an elaborate process requir
ing special appliances, etc., of various kinds.
Digitized by LjOOQ IC
AEROPLANE PROPELLERS 511
From inspection the propeller passes to the finishing depart
ment. Here it is first treated with silex filler, then with primer,
and lastly with various coats of high test waterproof spar var
nish. This is the usual finish. For certain United States Army
work five applications of hot linseed oil and a final rubbing with
prepared wax are required. During the entire varnishing proc
ess the propeller is kept carefully balanced on a steel mandrel
resting on sensitive parallel ways. Without this very few pro
pellers could pass final inspection.
On final inspection the utmost attention is given to every
detail. Balance must be absolutely perfect in all positions;
the blades must track, that is must follow each other in the
same path, within .03 in.; the pitch of the blades checked at
three points must not vary from the standard by more than 2 per
cent nor from each other more than i per cent. These limits are
only to allow for possible changes in the wood during the finishing
process after the first inspection.
A few words should be said as to the number of blades: For
training work and all ordinary work, provided a suflSdent diam
eter can be swung, two blades are usually preferred. For expert
flying and for highpowered machines in which there is a restricted
diameter of propeller in proportion to power applied, three and
four blades are required. As to the relative merits of three and
four blades there are no conclusive data. It is known, however,
that in nmnerous instances the threebladed screw, even though
having less diameter, shows marked superiority over the two
bladed in every particular. The threebladed propeller is also
noted for its peculiar jointing and fitting of the ends of the
laminations together where they form the hub. This hub is
trebly laminated over its entire area with the material so disposed
as to direction of grain, etc., that it makes without doubt the
strongest hub that can be built in any propeller regardless of
the number of blades. In repeated cases of wreck and accident
all the blades of these propellers have been wholly demolished
leaving the hubs always intact.
After final inspection the propellers are usually packed in
standardized pine or white cypress boxes with screwedon covers
Digitized by LjOOQ IC
312 SCREW PROPELLERS
and heavy battens and ironbound ends. A center bolt clamps
the propeller between battens in the top and bottom of the box
and feltlined pillow blocks formed to the shape of the screw
secure it firmly in place.
Digitized by LjOOQ IC
CHAPTER XIX
CONTENTS OF ATLAS
In the Atlas accompanying this text will be found:
1. Bamaby Chart of Propeller Efficiencies. Sheet i6.
2. Chart for correction of Block Coefficients. Sheet 17.
3. Chart for estimation of Appendage Resistance, Sheet 18.
4. Chart for thrust deduction. Sheet 19.
5. Chart of Design, maximimi thrust, Basic Conditions.
Sheet 20.
6. Chart of Design, Estimate of Revolutions and of Z for
power. Sheet 21.
7. Chart of Load Limitation. Sheet 22B.
8. Chart of Thrusts. Sheet 22,
9. Chart of values LT.2>^ (i —5). Sheet 23.
10. Chart of values of (P.A.^D.A.)XE.T.,. Sheet 24.
11. Chart of Standard Forms of Projected Area Ratios, curves
showing relation between projected — and helicoidalarea ratios,
and table of multipliers to use in laying down standard forms.
Sheet 25.
12. Table of Hull and Propeller Characteristics for a large
number of vessels, giving the nominal block coefficients, the
standard block coefficients as corrected by line X and the co
efficient of immersed amidship section, and the slipblock coeffi
cient as corrected for location of propeller. Sheets 12, 13, 14, 15.
These tables also include the performance of the different
propellers, including indicated thrusts per square inch of disc
and per square inch of projected area, the indicated thrust being
taken as equal to the shaft thrust 5 .92, where shaft horsepower
was originally given. They also include the propulsive coeffi
cient on the bare hull, the appendage multiplier as obtained from
313
Digitized by LjOOQ IC
314 SCREW PROPELLERS
Sheet i8, and the resultant propulsive coefficient on the hull with
all appendages.
13. A large number of cuts showing onehalf of the projected
areas of many of the blades studied and whose p>erf ormance is
given in the foregoing tables; also the blade sections tangent to
the hubs. In order to compare these forms more readily, all
propellers have been reduced to a common diameter, the sections
being reduced in the same scale, and all the projected areas are
arranged symmetricaUy aroimd the centerline of the blade nor
mal to the axis of the hub. Sheets i to 11.
Upon these projected areas are shown, in dotted lines, the
standard form of blade projection, Sheet 25, having approximately
the same area.
A comparison of these forms will show that the majority of
the most successful propellers have projected area forms approx
imating very closely to the proposed standard forms of projection,
while of those not having the standard form, the most successful
are slightly broader at the tips of the blades. Those which are
narrower at the tips than the standard show higher tipspeeds
and higher slips than the charts will give.
Sheet 26. Design Sheet for Aeroplane Propellers.
Sheet 27. Blade Form Sheet for Aeroplane Propellers.
Sheets 28, 29, 30, 31, 32. Examples in geometry and draught
ing of the hydraulic propeller.
Digitized by LjOOQ IC
INDEX
.A PAGB
Admiralty coefficient 19
Aeroplane propellers 294
, construction 307
, correction for number of blades 302
, design, Basic conditions 302
, design sheet, description 296
, estimate of power \ 294
, first method of design 298
, limits of P.A. ^D.A 298
, second method of design 303
Alleghney, U. S. S., fitted with screw propellers 4
Analysis, illustrative problem in 2, 3 and 4 blades \ 77
of performance of submarine boat screws 126
of propellers 77
Appendage resistance, curve for merchant ships 30
, description sheet 18 27
, estimate 24
Appendages, hull, list of 26
Archimedes, propeller fitted on 4
Arrangement of strut arms 112
Atlas, contents of 313
B
Backing of ships 243
Baddeley, mention 4
Bare hull resistance, formula 22
Bamaby's method of design 49
Basic condition for design 55
Blades and blade sections 207
, corrections for variations from standard form 85
, effect of number on efficiency 7383
316
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316
INDEX
PAGE
Blades, form, constant, objections. 207
'* , effect of change 200
'' , standard, advantages 209
' ' , variations from standard 212
, materiab of 274
on blade pad, location of 230
, rake of 214
sections, form of 215
, thickness of 218
versus projected area, effect on efficiency 81
Block coefficient 7
, departures from orthodox slip 11
, effect on revolutions 150
, nominal, formula for 7
, reduction to standard slip 8
, sheet 17, use of 8
, standard slip, derivation 7
Bolts, number and size of blade 285
Bougner, mention 2
Bourne, formulas for propeller 33
, John, mention i
Bramah, mention 2
Broadtipped blades, design 180
, estimate of performance 95
Brown, Samuel, mention 3
Buchanan, Robert 2
Bushnell, mention 2
Cavitation 130
, effect of blade section 133145
" change in pitch 143
" " " projected area i3S~i43
" " " load 140
" insufficient tip clearance 145
" a: on. 132
on power 139
" reduction of diameter 143
" revolutions 140
" thrust deduction 144
" tip speed ^132
" wake gain 144
u
it
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INDEX 317
Cavitation, power corrector ,. . .' 139
, remedy for 15
Centrifugal force on propellers 221
Change from Basic to other conditions of resistance 63
Clearance, relative tip, determination 17
Coefficient, Admiralty, equation 19
, block 7
" , correction from nominal to standard 8
" , nominal, formula 7
" , submarines 12
" , variations from orthodox 11
, slip block, formulas for 10
, standard slip block, derivation 7
" " " , departures from 10
Comparison, design by 46196
, rules of law 20
Conditions governing performances 84
Construction of air ship propellers 307
Contents of atlas 313
Corrections for wake, propulsive coefficient, blade width 51
Corresponding speeds, laws of 20
Critical thrusts 133
, effect on K^ 17
C, values of, for wetted surface 23
Deduction, causeof thrust 13
chart, description of thrust 16
, thrust 7
, " , for tunnel boats 11
Definitions of terms and abbreviations, Dyson method 56
Denny's surface friction coefficients 25
Design, Bamaby's method ^ 49
, by comparison 46196
, Dyson method 55
, reduced load 151
, of air ship propellers, first method 298
, of propellers, factors entering m 146
, " " not of standard form 178
, " the propeller, hydraulic 146
, practical methods of 45
, sheet for air ship propellers 296
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318 INDEX
PAGB
Design, Taylor's method 48
Diameter of propeller, formulas for 6273153
Dispersal of thrust column 134
« " " ^remedyfor 15
Dbplacement, Law of comparison 20
, variation of power with 21
DoUman, mention 3
Doncaster, transport, trials of Shorter's propeller 4
Doubleended ferry boat propellers, analysis 122
" " " " " design 188
Z>ra;<7n, H.B. M.S., trials with Shorter's propeller 4
Draughting of propeller 282
Du Quet, mention 2
Dwarf, experiments with 31
Dyson method of design 55
£
Early experiments on screw propulsion 31
Effective horsepower, definition and formula 19
thrust, formula 6179
Efficiency, effect of number of blades 83
, law of , 64
of engines, variations in mechanical 72
of propeller, formula 19
" ,lawof 74
of 2, 3, and 4 blades, Taylor's statement 83
Equation for p. c *. 60
Ericsson, John, first successful propeller 4
, patents propeller 3
Estimate of appendage resistance 24
performance 84
" , problems 89
resistance, independent 21
" , methods for 19
revolutions for variations from Basic 68
Experiments on screw propulsion, early 31
F
Factors in design of air ship propellers 294
hydraulic propellers 146
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INDEX 319
PAGB
Fanshaped blades, design 179
, estimate of performance 97
Ferry boat, doubleended, design of propeller 188
Flow of water from screw propeller 13
Form of blade section 215
, effect of change in 200
, variations from standard 211
Formulas for Basic conditions, derivation of 61
Friction of propeller blades 223
Froude's constants for surface friction of hulls 24
theoretical assumptions for propellers 37
theory developed 41
G
Generatrix, inclined 281
, vertical 280
Geometry of screw propeller 277
Great Britain, first screw propelled transAtlantic ship 4
Greenhill's theoretical assumptions for propellers 37
theory developed 42
Gross effective horsepower 132
H
Hooke, Robert, mention 1
HorsePower, I.H.P., S.H.P., definitions and formulas 18
, law of comparison 20
, thrust and effective, definitions, formulas 19
Hub, dimensions 231
, materials 275
propeller 228
, standard 287
Himter, Lieutenant, mention 5
I
Inclined generatrix 281
Independent estimate of resistance 21
Indicated horsepower, definition and formula 18
thrust, formula 61
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320 INDEX
K
PAGE
K, control of valueof 15
, efiFect of critical thrusts on 17
, method of obtaining 65
, in terms of thrust deduction and wake gain 15
E
Law of comparison, rules 20
efficiency 64
Location of propeller blades in blade pads 230
L3rttleton, William, mention 2
M
Material of blades 274
hub 275
Mechanical efficiency of engine, effect of variation 72
Merchant ships, appendage resistance 30
Method of design, Bamaby's 49
, Dyson's 55
, Taylor's 48
MinXj experiments on 31
Model experiments, estimate of resistance 22
tank, appearance in field of design 5
Motor boats, propellers for 194
Mystery of propdler, factors in 5
N
Number of blades^ effect on efficiency 73
P
Pancton, mention 2
Pelican J experiments on 31
Performances, conditions governing 84
, estimates of 84
, * ' *' problems 89
Perkins, mention 3
P.c, equation of 60
P.C. 5P.C., tables of values 59
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INDEX 321
PACK
Pitch, effect of excess 200
, formula for 63
Position of propeller, 4shaft arrangement, effect of 204
Power correction by use of Z 66
, correction for wake gain , 108
corrective factor Z, derivation of 65
, effect of distribution on 4sliaft arrangement 202
and revolutions, vessel stationary 70
Power, estimate when apparent slip and speed given 71
, variation with displacement , 21
, '* ** speed : 21
, ** '* revolutions 72
Practical methods of design 45
Problem, analysis of tunnel boat propellers 121
, Basic conditions, 3blade, form for 147
, design, full data, reduced load . ; 159
, incomplete data, reduced load 167
, effect of change in speed and block coefficient 148
varying trim 169
, estimate of performance, broadtipped blades 95
'* , doubleended ferry boat 122
** , f an shaped 97
" , 2, 3 and 4 blades 77
, estimate of power and effective power 124
Problems, estimates of performances, 3blades 89
'' 89
4blades 99
, effect of rough bottom 103105
, effect of varying conditions 103
in propeller field 76
, insufficient data 146
in wake gain 114
of Basic conditions 146
of reduced load 146
, reduced load, design 151
, sufficient data 146
, wake gain and effect of strut arms 115
Projected area ratios, air ship propellers, limits of . 298
** " '* versus number of blades, effect 81
Propellers, airship 294
, analysis of 77
* * doubleended ferry boat 122
" tunnel boat 121
t(
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322 INDEX
PAGB
Propellers, Bourne's formulas $$
, design by comparison 196
, *' of 146
, efficiency of, formula 19
, empirical formulas 3336
, factors in design 146294
, field, problems In 76
, formulas for diameter 73
, geometry of the screw 277
, law of efficiency 74
, materials 274
, mystery of, factors in 5
, propulsive efficiency, formula 19
, screw, flow of water from 13
, Shorter's trials 4
, theories of design 37
Propulsive efficiency, effect of position of screw 204
, formula 19
R
Rake of blades 214
Rankine's theoretical assumptions 37
theory developed , . 40
Rattier, experiments in 31
, success of 4
Reduced load, insufficient data, form 158
, problems in 151
, sufficient data, form 156
Relation between power and revolution, vessel stationary 70
Relative tip clearance, determination of 17
Resistance, appendage, description of sheet 18 27
, estimate of 24
, independent estimate si
, merchant ships 30
, methods of estimating 19
, model experiments for estimate of 22
, total bare hull 22
R6sum6 of design sheets 75
Revolutions for other than Basic conditions, est'mate 68
, relation between power and, vessel r>tationafy 70
, Robinson's equation for 69
, with power, variation of 72
Robinson's equations for slip and revolutions 68
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INDEX 423
Seaton, A. E., mention * i
Sections, form of blade 215
Shaft horsepower, definition and formula 18
Sheets of design, r6sum6 of 75
Shorter invents propeller 4
Slip, apparent, fundamental equation 69
, to find when power and speed are given 71
, block coefficient, derivation of standard 7
, formulas for 10
, Robinson's equation of 68
Smith, first successful application of propeller 4
Sopley, Josiah, mention 3
Speed, Basic, formula for 63
, corresponding, law of 20
, effect on revolutions and efficiency 148
, thrust, equation 61
, variation with power 21
Squatting of ships, effect of 12
Standard hubs 287
slip block coefficients, departures from 10
Stopping, formulas for 236
of ships 234
, problem 238
Strut arms, influence on wake 112
, problems showing effect of 115
Submarines, block coefficients of 12
, design of propeller 186
, estimate of performance 126
Superb J H. M. S., trials with Shorter's propeller 4
Surface, effect of varying blade 200
, friction constants for painted ships 24
, wetted, formula for 22
Sweeping up 278
Tank, model, appearance in field of design 5
Taylor's method of design 48
presentation of design theories •. 39
statement as to relative efficiencies of 2, 3 and 4 blades 83
Tables of factors for estimating hull resistance 23, 24, 25
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324 INDEX
PAGB
Tables of values of p.c. +P.C. for values of e.h.p. hE.H.P 59
Z S8
Theories, final formulas of 44
of design of propellers 37
'* * * , Taylor's presentation of 39
Thickness of blades 218284
Threeshaft arrangements, effect 204
Thrust column, disposal of 134
deduction 7
, cause of 13
chart, description of 16
, effect of variation of hull form 88
, in terms of thrust deduction and wake gain 15
in tunnel boats 11
, method of deriving factor 65
, effective, formula 79
horsepower, definition and formula 19
, I.T.D, V.T., E.T 61
Thrusts, critical 133
effect on X 17
Tideman's hull constants 25
Tip clearance, relative 17
Towboat propeller, design , 181
Tredgold suggests expanding pitch 3
Trim, effect of varying 169
Tunnel boats, design of propellers 192
, problem in analysis of screws 121
, thrust deduction 11
Turning of ships 262
V
Variations from standard blade forms, correction 85
in conditions of resistance, method of change 63
wake, etc., correction for 51
of power with displacement 21
'' '' '' speed 21
Vertical generatrix 280
W
Wake gain, cause of 13
, correction for 108
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INDEX 325
PAGE
Wake gain, negative, indication and correction in
" , problems 114
Watenvitchj U. S. S., first screwpropelled American 4
Weddell, fits propeller to ship 4
Wetted surface, approximate formula 22
Z
Z, determination of values of 65
, equation of 6667
, tables of values 58
, use in correction of power 66
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