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Full text of "Screw propellers and estimation of power for propulsion of ships"

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SCREW PROPELLERS 

and ESTIMATION of POWER /or 
PROPULSION 0/ SHIPS. 
u4lso AIR-SHIP 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 Engineer-in-Chief, the late Rear-Admiral 
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 



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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: 

Engineer-in-Chief 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) Horse-power 18 

Indicated Horse-power 18 

Shaft Horse-power 18 

Thrust HorsQ-power 19 

Efficiency of the Propeller -, 19 

Effective (Tow-rope) Horse-power 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 Surface-friction Constants 24 

Surface-friction Constants for Painted Ships in Sea Water. ... 24 
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viii CONTENTS 

PAGE 

Estimate of Appendage Resistance 24 

Surface-friction Constants — ^Denny 25 

Surface-friction 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 
Full-sized 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 Horse-power 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 Double-ended 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 Horse-jx)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 

Three-bladed Propellers — Form for Computation 147 

Modifications of Forms for Two and Four Blades 147 

Problems of Sufficient Data — Reduced Load 148 

Three-bladed 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 

Fan-shaped and Broad-tipped Blades 178 

Tugboat 181 

Submarines 186 

Double-ended 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 
SCREW-PROPELLER 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 smoke-jack, 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 to-day 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 paddle-wheels. 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 deep-sea work and long voyages. 
The conclusion arrived at after this trial was that paddle-wheels 
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 single-threaded 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 one-sixth 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 
paddle-wheels (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 paddle-wheels, 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 horse-powers 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 horse-power required for any desired speed of any given 
hull can be obtained; more accurate instruments for the measure- 
ment of indicated and shaft horse-powers; 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 horse-power 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{ =3SXDisplacement-f-(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 after-body (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^. 
5-5-L.L.W.L.=y. 



B.C.« = 



28(i-B.C.„)+y' 



.248(i-B.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 



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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 thrust-deduction 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 54-L.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 fore-and-aft 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 v-h 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 horse-power 
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 horse-power 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 fore-and-aft 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 



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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 fore-and-aft 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 C1-C2 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 C1-C2. 

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 C3-C2. 

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 fore-and-aft 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 fore-and-aft 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 C3-C2, while the maximum values are 
reached at about 12 ft. draft and are given by the curve C-C2. 
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 C-C-C2. 

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) HORSE-POWER 

When speaking of the power required to drive any given vessel 
at a certain speed, it is usually referred to as the Indicated 
Horse-power where reciprocating engines are used for power 
development, and as Shaft Horse-power where turbines or some 
other form of rotary engine is used. 

By Indicated Horse-power 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 Horse-power 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 Horse-power — 
where Shaft Horse-power = 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 Horse-power, is measured by multiplying 
the actual thrust in poimds by the number of feet moved through 

18 



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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.-f-S.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 Horse-power, and, calling the tension on 
the tow-rope Tr, the equation for Effective Horse-power is: 

Effective Horse-power=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 horse-power 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 Horse-power is given instead of the Indi- 
cated Horse-power, 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. Horse-powers. The horse-powers of similar ships at cor- 
responding speeds are proportional to the seven-sixths 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 tow-rope 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, eddy-making, and stream-line 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- 



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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 
speed-length 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 tow-rope resistance for a paraffin model 20 ft. long 
is 12.8 lb., when towed at the speed corresponding to 25 knots 
for the full-sized vessel which has a length on load water line 
of 700 ft., then 

Vn^ : 2$ : : V20 : V700 .% »m=4-23 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; 



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ESTIMATION OF POWER 23 

therefore the frictional resistance is 

=/X5«XC=o.oo834XsS-iX4.23^-^ = 7-S4lb. 

The total frictional resistance of the full-sized 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 
tow-rope resistance of the model, gives for the residual resist- 
ance 

12.8-7.54 = 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 

horse-powers. 

(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 



B-tH 


C 


B-i-fl 


1 
C 


B-i-H 


C 


2.0 


15-63 


2.5 


15.50 


3.0 


15.62 


2.1 


15.58 


2.6 


15-51 


3-1 


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 SURFACE-FRICTION CONSTANTS 

Given by Taylor 

Surface-friction 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 


14-5 


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 
SURFACE-FRICTION 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 fac-similes of these appendages 



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ESTIMATION OF POWER 



25 



Table VI 

SURFACE-FRICTION 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 SURFACE-FRICTION CONSTANTS 

Derived from Froude's Experiments 

Surface-friction 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 horse-power curve for the 
bare hull, or the estimate of the effective horse-power 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 horse-power 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 single-screw vessels, the dead wood 
may be cut away and the propeller shaft supported by a strut. 
In some cases of twin-screw 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 v-t-Vl. 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;-5-VZ = .75 to ^;-^VZ = .83, and that a corresponding 
hump in the appendage resistance curve attains its maximum 
value 2itv-T- Vl = .75. Fig. 2 shows another hump at v-r- Vl = 1.0 
to 1.09 but the appendage curve shows no corresponding rise. 
Turning again to Fig. 2, a wide hump extending from v-t-Vl 
= 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'-t-Vl.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>-j-Vl.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;-r-yL.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, fan-tail 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 fore-and-aft 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 two-bladed 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 



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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 ttu-bine-driven center screw, x=6.$$ 
for turbine-driven 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. 



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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(V-v)X6oD AxV(V-v)Xv 

The thrust horse-power = ^^ = ^^ — . 

33,000 27s 

K E is the eflRdency of propeller and engine, 

27s £ 

Let (F— »)-^F=5=slip in per cent, then 

V-v^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 single-screw ships and for center propellers of triple- 
screw ships: 

x-.i?>Pc+Sy and C=4So. 



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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(F-t^)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 1-5 " R(i-sy 

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 foiu--bladed single screws, JIf =20; for twin, 15; 
for three-bladed single screws, M = ig; for twin, 14.3; 
for two-bladed 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 



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36 SCREW PROPELLERS 

propeller in feet per second = (PXl2)-5-6o; 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£)-5-6ot;=(LH.P.XSSoX£)-^F(i-5). 

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(i-5) ^DXV^XG] 1 DxV^{i-s)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 turbine-driven 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 fore-and-aft 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 



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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 = {AB-AC)^ABJ'^-V^^'^=^-VJ^. 

\2x / 2ir Wp 

From which the speed of advance 

V,=^'^{i-s)^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 
--CE--CD 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^(i-s ^^ 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 
co-tangent of the pitch angle of the blade tips, on integrating the 
expression for dT, is obtained. 



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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 fore-and-aft 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%as-ps^) -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(i-s)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 full-sized 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 full-sized 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 
full-l^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 
P2-PP1 =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^^lX-TT— 101.33 Z^lf^ T^ « 



PP.X^ ^^^^^^ 



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PRACTICAL METHODS OF DESIGN 47 

which, when p-r 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 horse-power 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 three-bladed 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 horse-power 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 three-bladed propellers of the built-up 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 

t-ri2Tdlk+.S{l-k)] = 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 
four-bladed propellers, but can be used for three- or two-bladed 
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 per-hour. 

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 



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PRACTICAL METHODS OF DESIGN 51 

Equation (3) is used as an aid in proportioning propellers 
which must have a given speed of revolutions. 

For three-bladed propellers the formula for Ca becomes 



^^~ LH.P. ' 



while for two-bladed 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 

A-C vtLILP: . c -3^YL 



D' ^ V 



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.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.-T-D.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; 

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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 A-B, 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 P-i-D 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 



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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, C-D. 
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. 

P-hD. 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 FULL-SIZED 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 



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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.-5-D.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- 



tionsX-X Diameter of Propeller in feet X144. 

T.S.=The tip-speeds 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. 
-5-D.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 



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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 well-designed, well-adjusted and 
well-lubricated 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. -5-D.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.-5-D.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 Horse-power of Propelling Engine on one 

propeller, without thrust deduction. 
S.H.P.,=B.H.P.p = .92 I.H.P.p = Shaft or Brake Horse-power 

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 tow-rope horse-power 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 horse-power that must be delivered by 
one propeller. 
I.H.P. = Indicated Horse-power which can be delivered by the 

propeller under Basic conditions. 
S.H.P. = B.H.P. = .92 I.H.P; = Shaft or Brake Horse-power ab- 
sorbed by the propeller under Basic conditions. 
E.H.P. = Effective (tow-rope) Horse-power 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 

1-359 
1.165 


2.0828 

1.8994 

1.7693 

1.6684 

I 58594 

1-45582 

1.3549 
1.27244 
I. 20271 

I-I715 
I . 1423 
I. 0891 


.1 
.2 
.3 
.4 
.5 
.6 

.7 
.8 

.9 

I.O 

1-05 

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 

1-25 

1-3 

1.35 

1.4 

1.45 

1-5 

1-55 

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 horse-power which would be delivered 
by the 'propeller with a total power LH-P.^ 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.= Tip-speed of Propeller in feet per minute under Basic 

conditions. 
P.A.-5-D.A. = Projected Area ratio of 3-bladed propeller. 
i(P.A. -^D.A.) = Projected Area ratio of 4-bladed propeller, 
f (P.A. -^ D. A.) = Projected Area ratio of 2-bladed 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.-5-E.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 


1-3 


.9873 


1.6 


•9843 


.OS 


1. 143 


•5 


1. 061 


1.05 


.997 


1-35 


.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 


1-45 


.9858 


I.7S 


.9828 


.2 


!i.o69 


.8 


1.022 


1.2 


.989 


1-5 


.9853 


1.8 


.9823 


.3 


1.063 


.9 


1. 019 


125 


.9884 


1-55 


.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.-7-E.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.-r-E.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 .92XPX-R 



Digitized by LjOOQ IC 



TfflRD METHOD OF DESIGN 61 

R = T.S. -i^vD = Basic revolutions. 

I.T.D = I.T. -^ ( 144 X-D^ ] = 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(i-5) ■ 

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(i-5) 
\I.T.„XPXie V I.T.z>xrx (101.33) 



-^: 



2.88 XI.H.P.X (1-5) 



I.T.cXF 

This formula applies to three-bladed propellers only, and re- 
quires modifications, as follows, for four- and for two-bladed ones: 

Four-bladed 



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 



Two-bladed 



/ 389XI.H.P. ' _ /389Xl.H.P.X(i-5) 
\ 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 
horse-power, I.H.P., shaft horse-power S.H.P., with which power 
an effective (tow-rope) horse-power 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. = Tip-speed 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 Horse-power 


Constant 


Constant 


i?tf= Revolutions for E.H.P. 


Reduced 


Increased 


t.s.= Tip-speed 


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 
(tow-rope) horse-powers 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 {tow-rope) horse-power 
with a certain indicated or shaft horse-power under any given con- 
dition of resistance^ it will deliver' the same effective with the same 
indicated or shaft horse-power 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 (tow-rope) horse-power 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 horse-power or shaft horse-power 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 horse-power 
Basic indicated or shaft horse-power 



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 speed-revolution and speed-power 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 five-run 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 three-run 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 horse-power for v becomes 
ii:xI.H.P., = LH.P.tf. 

Designating the effective (tow-rope) horse-power 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. F-log v), 

I.H.P.p being the actual indicated horse-power for v in cases 
where K = i and being equal to that horse-power 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 horse-power 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 horse-power, LH-P.^ 
= K I.H.P.3, or S.H.P.tf = iS:S.H.P.p for any speed v for which 
the tow-rope (effective) power is e.h.p., the value of the indicated 
or shaft horse-power necessary for any other speed vi requiring 
an effective horse-power 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 horse-power 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 
i-Z 


I.H.Py. factor 

for .5 Load 

i-Z«i 


e.h.p. 


i-Z-Z» = 
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 


9.6865-1.3549 


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 


9-4555 


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»" 



LH-RXs" 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 horse-power +yiX 
log of Basic Speed— log of Basic indicated or shaft horse-power— 
y2Xlog of actual speed. 

This in its final form becomes 

log 5-log 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(i-5) PX{i-s)' 

The values of y in the Robinson equation are given by a curve 
expressed by the following equation: 



2.626-- ^°5i29^ 



ti-iL .oooooi5S75(«;-25)*-|-.o4368J 

9-iL 28o45+(»-25)*J 

» 

The equation for apparent slip 5i at a speed vi and indicated 
horse-power 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 horse-power 
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.-T-E.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. 
■f-E.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 = .2794Z-f-. 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= * 



1.3882X10-2794^' 

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 horse-power, the 
apparent slip or the horse-power 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.^ 



S2-S1X 



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 three-bladed 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 four-bladed propeller be desired, the total indicated 
horse-power required for any given number of revolutions will be 
the indicated horse-power required by a three-bladed propeller 
of the same pitch and diameter as the four-bladed one but having 
only three-fourths of its projected area, divided by .865, that is 

LH.P.4=I.H.P.3^.86s, 

while for a two-bladed wheel the proportion becomes 

LH.P.2 = LH.P.3X.7S. 

The projected area ratio of the four-bladed propeller will be 
equal to four-thirds of that of the three-bladed one while that 
of the two-bladed one will be only two-thirds of that of the three. 

Thus the equations for diameter for two-, three-, and four- 
bladed propellers assume the following forms: 

Two-bladed: 

/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(i-5) . 
LT.bXF 



Three-bladed: 



jj^ / 29i.8Xl.H.P.3 _ /2.88Xl.H.P.3X(i-5) 
\ LT.dXPXR y LT.nXV 



Digitized byCjOOQlC 



74 SCREW PROPELLERS 

Four-bladed: 



^^ /29i.8XLH.rI ^ /291.8XI.H.P.4X.865 
\ LT.nXPXR 'V LT.nXPXR 



/252.4iXLH.P.4. _ /2.49iXLH.P.4X(i-5) 
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 three-bladed propeller having only three-fourths the pro- 
jected area of the four, and one and one-half times the area of 
the two-bladed 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 three-bladed 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 four-bladed. 

The usually accepted idea as to the relative propulsive 
efficiencies of two-, three-, and four-bladed propellers is that they 
stand in rank in the order given above, the two-bladed propeller 
being the most efficient. This is most certainly the case where 
the projected area ratio of the four-bladed propeller exceeds that 
of the three-bladed propeller, and that of the three-bladed 
exceeds that of the two-bladed, all being designed to deliver the 
same effective horse-power 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 two-tenths 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, tip-speed, 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 horse-power 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.-7-E.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 three-bladed propellers, these 
factors entering in the following equations 

I.T..^(i-5)=^^., 

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 tow-rope horse-power for the 
hull or the estimated, indicated or shaft horse-power 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 (tow-rope) horse-power 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 
horse-power and revolutions necessary with each propeller for 
the designed speeds. 

The propellers are two-bladed, three-bladed and four-bladed, 
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.-5-irD 

PXR 



SlipB.C 

1—5 (Sheet 20, for .3) . 
,, (PXR)X(i-S) 



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.-f-D.A. 

E.H.P. = LH.P.XP.C 

e.h.p 



e.h.p.-5-E.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) 

v-i-V 



2 
.2 
16' 

14' 

6650 

132.3 
1852 

.8 
.941 
17.2 

3-74 
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.-5-e.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- 


l-S 


E.T.p 


.3 
.3 

-4 


1.88 

3.74 
6.00 


.709 
.682 
.619 


1-233 
2.541 
3-714 


6.16 
8.47 
9-29 


.941 
.941 
.941 


6.33 
9.00 
9.87 



1-5= 



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., 



i-S 



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 (tow-rope) 
horse-power 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 (tow-rope) horse-power, 
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.-s-E.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 horse-power will only deliver a speed of eight 
knots, the two-bladed 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 three-bladed 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 four-bladed one. 
The four-bladed high-area 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 
horse-power remaining constant. 

Attention must also be directed to the small influence of 
projected area ratio on revolutions for any given speed, where 
v-i-V corresponds approximately to " Upper E.T/' limits, as the 
revolutions required at eleven knots for the two-bladed propeller 
of .2 projected area ratio are only 85.59^ while those required by 



Digitized by LjOOQ IC 



ANALYSIS OF PROPELLERS 



81 



the four-bladed 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 four-bladed 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.H-D.A. . .38 .38 .4 .4 2828 .2828 .391 .391 

} P.A.-5-D.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 

i-S 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 


3-43 


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 

V-irV. 

e.h 



p.i. 



c.h.p.i-5-E.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 


3-4 


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 
3-2 

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.2H-E.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 


3-4 


3.? 


3.818 


3.05 


3.0s 


3.21 


3.21 


3.13 


3.13 


3-55 


.0476 


.06705 


.1214 


•1335 


.0578 


■07699 


.09125 


74.16 


75-71 


118. 6 


120.2 


63.5 


64.82 


96.59 


73 


73 


117. 8 


117. 8 


65 


65 


94-5 



.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 


3-47 


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 

3-5 

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 three-blade 
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 horse-power 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 four-bladed 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 (tow-rope) horse-power 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 horse-power 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 (tow-rope) horse-power 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. Fan-shaped 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 horse-power 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 (tow-rope) horse-power 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 horse-power delivered by Basic propeller. 

«; = Speed corresponding to e.h.p. 1. 
e.h.p.i= Effective horse-power deliver by actual propeller 
at speed v. 



Digitized by LjOOQ IC 



ANALYSIS OF PROPELLERS 



87 



I.H.P.tf= Indicated horse-power 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 

VRad-i/ 

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 horse-power 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. H-D.A. (Sheet 20) 7240 

i2=T.S.-5-7rZ) 126.67 

PXR 2494 

i-5forP.A.^D.A.=.328and 

SHp B.C. = .6 (Sheet 20)= .8995 
V=PxRx{i-S) ^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.4-E.H.P 

e.h.p 

V for e.h.p 

v-i-V 

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 


13-21 


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 


57-5 


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 

v-i-V 

Z£orc.h.p.-^E.H.P 

K 

IM.T^^K I.H.P.. 

=ir IH.P.-5-io*=Est. Power 

Actual Power 

Est Revs, for t> 

Act. Revs, for r 

e.h.p.-5-E.H.P 

e Ji.p 

vfor e.h.p 

v-i-V 

Zfo^e.h.p.-^E.H.P 

K 

LH.P.tf=-K: I.H.P.P 

=^ LH.P.-5-io^=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. H-D.A. =.304, 

Slip B.C. = .627 = .904 

V^{PxRX{i-S)\-i-ioi.s3 17.34 
I.Tx> for P.A. H-D.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 

v-i-V 

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 

1-5. 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.-5-E.H.P 

e.h.p 

V 

v-i-V 

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 

v-hV 

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 

v-i-V 

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 

1-5 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 

r-5-F 

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 


19-32 


.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.H-D.A 558 

D 9'.i7 

P 8'. 5 

T.S 12080 

R 419.7 

PXR 3568 

1-5 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.-5-E.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 


215-9 


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 two-shaft 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 

1-5 817 

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.-s-E.H.P 

e.h.p 

V 

V-irV 

(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.-5-E.H.P 

ch.p 

V 

V-irV 

(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 well-known naval collier type, fan-tailed 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 

~^(3-bladed) 32 -37 

T.S 7050 

PXR 2076 

S.B.C... 66s 

1-5 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 


3-8 


S'^2 


.o6s4 


72.63 


1.037 


75-3 


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 three-bladed, of manga- 
nese bronze, machined to pitch, the edges sharpened and the 
blades highly polished. 

Turning now to the four-bladed 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 4-bladed 
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.-5-D.A.=Total Proj. 

Area Ratio 38 

P.A.^D.A 28s 

D 19'. S 

P , 15' 

T.S. for P.A. -5-D.A 6320 

R 103.2 



PXR. 
1-5.. 

v.... 

LT.D. 



^^^j,_ D^XI.T.dXPxR 
252.41 

P.C.foriP.A.-^D.A 

E.H.P 5061 



1548 

.945 

14.43 

3-43 

7996 
.633 



e.h.p 

e.h.p.-^E.H.P 

V 

v-i-V 

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. 
X-I.I7S 



Problem 10 

Basic Conditions of PropdUr 

Blades 4 

i(PA.-^DA.) .4 

PA.-5-D.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.-J-EJI.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 

1-5 

V 

I.T.D 

LH.P 4m 

P.C 691 

E.H.P 2841 



.2121 

18'. S 

18'. 75 

4540 

78.12 

146s 

.942 

13-62 

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 

v-i-V 

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.-5-E.H.P 

V 

v^V 

Z 

K 

tH.P.d-ii: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 

1-5 91 

V 18.98 

LT.D 3-6 

LH.P 18190 

P.C: 636 

E.H.P 11384 



e.h.p.-^E.H.P 

ch.p 

V 

v-i-V 

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 

v-hV 

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 
73-97 
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 
15-43 
.813 
.322 
1.2 
10400 

9950 
97-08 
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 

"5-7 
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.-5-D.A 32 

D 18'. 6s 

P 19'. 99 

T.S 7110 

R 121. 4 

PXR 2426 

1-5 899 

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.d-irxLH.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 

99-73 
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.d-irxiJi.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 rough-bottomed 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 horse-power 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 (tow-rope) horse-power 
delivered by the propeller and by comparison with the model tank curve of 
effective horse-power 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 

v-i-V 

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 

13-3 

.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 
15-45 
.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 aft-flow 
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 low-pitch 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 well-known " 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 high-speed 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 horse-power 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 horse-power (tow-rope 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 horse-power (tow-rope 
horse-power), 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 first-named 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 high-velocity 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 horse-powers 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 

1-5 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.-i-E.H.P 

e.h.p 

V (Tank) 

v-i-V 

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 
low-powered shafts hold down the revolutions of thjB higher- 
powered ones while the lower-powered 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.H-D.A 5Q5 

D 92". 5 

P 82" 

T.S 13330 

R 550.5 

PXR 3760- 

1-5 787 

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< 


v-i-V 


.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 

395-1 
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 


V-7-V 


.895 
.1613 
1 1436 
1 1500 
475.8 
476 
26.65 


Z 


S.H.P.d-S.H.P.p 

Actual Power 

Est. Revs 


Act. Revs 


Act. Speed 








c.h.p.-s-E.H.P.... 

e.h.p 

V. 

v-i-V 

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 

1-5 782 

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 


21-35 


.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.-f-D.A 6012 

D 94" 

P 81". 94 

T.S 13570 

^ 551.4 

PXR 3765 

i-S 782 

V,: 29.06 

LT.D 12 

LH.P 19003 

PC .525 

E.H.P 9076 

S.H.P 17483 



c.h.p.-5-E.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.H-E.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.-1-E.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 

577-6 
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- 
and-aft 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 horse-power 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 



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120 



SCREW PROPELLERS 



Actual S.H.P.d=S.H.P.p 

Z 

c.h.p.-i-E.H.P 

c.h.p 

• (Tank) 

Est. Revs 

• (Actual) 

»-^K (Actual) 

Actual Revs 

Actual S.H.P.d-S.H.P.p. 

Z 

e.h.p.-^E.H.P 

ch.p 

• (Tank) 

Est. Revs 

V (Actual) 

•4-7 (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 


19-45 


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. 



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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 

1-5 



... .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[=8oo-5-669.8 = i.i95 



.26025 



13.25 

385 

•4954 

.637 

.86(Sheet22) 

.314 
576 



f « 13I knots 



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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=3-93 
5= .10 
LH.P.d = 8oo 
log Av^3 3^ 

J = Apparent slips'. 2504 
Revs. = 298.5 

Problem 21. Double-ended 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 slip-block 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 horse-power 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 horse-power 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. 



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ANALYSIS OF PROPELLERS 



123 



Double-ended 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.H-D.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. -5-D.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 = 1845-1015 

1-43 

709.8 
700 (Total by two screws) 



e.h.p. aft. -5- E.H.P. 

e.h.p. aft. 

e.h.p.fd. 

v-i-V 



.194 
445.6 

254.4 = 700-445.6 

.67 



V = ^. and V^ = Ai 



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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 horse-power being developed by the 
engines and of the effective horse-power 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 = 10-5-14. 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. 
-i-E.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.-7-E.H.P. 
and (£.r.4-e.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.-5-E.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 horse-power 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 
v-i-V > 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. 


B-i-L.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 3-bladed. 



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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 



i-S... 

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 quick-running turbine-driven 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 horse-power 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 
tip-speeds 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 blade-section 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 v-i-V ior any speed v and 
load factor e.h.p.4-E.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 tow-boat or a slow-speed, 
low-powered 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, v-r- 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.-5-io», 

and the equation for apparent slip becomes 



marked *' Curves 



XH.P.,XF«' i.3Xl.H.P.Xi3.6s' 

5 = 06 = S =:z-~ ^ . 

LH-P.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 horse-power 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., 

1-5 

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 


r-j 


-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^ = i-i5 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 horse-power 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 


\ 






-ro-o»- 














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 v-rV 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 




. 










'|{>ll|i.[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: 


'Hi-e. 


^> 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 v-revolutions, 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 horse-power 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.-f-E.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, — 



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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 horse-power 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. 



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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 
(tow-rope) horse-power 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 
horse-powers 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 horse-power necessary 
for the desired speed of ships is provided. 

These two classes of problems may each be sub-divided into: 
C Problems of Basic conditions (Full Diameter). 
D. Problems of reduced load {Reduced Diameter). 

146 



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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 
Three-bladed Propeller 
(i) P. A. -^ D. A. = Different abscissa values taken from Sheet 20. 

(2) T.S. = Tip-speeds corresponding to each value of P.A.-i-D.A. 

used. Sheet 20. 

(3) Slip B.C. =Slip Block Coefficient of vessel. Obtained from Sheet 17. 

(4) 1-5 « 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 (tow-rope) horse-power for desired speed. 

Obtained from model tank curve and includes all 
appendages. 

(7) P.C. = Propulsive coefficient for P.A.-5-D.A. Sheet 20. 

(8) I.H.P. = E.H.P. -^ P.C. = Indicated horse-power 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 horse-power 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 four-bladed 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 two-bladed 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^)- 



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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.. 
1-5. 
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 
3-74 
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.-5-D.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.-5-D.A. 

Increases Eff . of Prop. 



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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.-i-D.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, 

1-5 



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 20-knot condition, but suppose the correct slip B.C. to be 
.4 instead of . 5 as used in the computation. 

P.A.4-D.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 

V-i-V 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 



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DESIGN OF THE PROPELLER 151 

Such an error produces no change in the power required for 
the speed unless the value oi v-i-V 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 full-bodied 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 deep-load 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 slip-block 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 horse-power and effective 
thrust per square inch of projected area ratio. 



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DESIGN OF THE PROPELLER 153 



These equations are 
For 2 Blades: 



„^ / 389XI.H.P. _ l 3.84Xl.H.P.X(i-5) 



>'D.A. 
For 3 Blades: 



I.T.^XF 
3.84XE.H.P. ; 
^■^•XE.T.,XF 



„^ hg8.iXl.H.P' ^ / 2.88Xl.H.P.X(i-5) 
yLT.oXPXR \ 



I.T.flXF 
/ 2.88xE.hT~ 

/^XE.T.,XF 



For 4 Blades: 

jj^ /252.4iXI.H"!r _ /2.49iXl.H.P.X(i-5) ' 

^ / 2.49IXE.H.P. . 

^|j^xe.t.,xf' 

PA ^ 

in which rr^ equals - times for the two-bladed, equals for the 
D.A. 2 ^ 

three-bladed and equals | times for the four-bladed, the pro- 
jected area ratio of the propeller, E.T.p, I.T.z>, and (i-5) 
being those corresponding to P.A.4-D.A. of the equivalent 
three-bladed 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.-5-D.A.)XE.T.p, in the second case, can be obtained: 

I.T.x,-i-(i-5)=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 -s-DA.) 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>-^(I-5) 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-(i-5) or of (P.A.-^D.A.)xE.T.p, reducing them to 
i P.A.-5-D.A. for four-bladed and to f P.A.-^D.A. for two- 
bladed propellers, the propulsive coefficient corresponding to 
these total projected area ratios, the tip-speeds 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 


1-47 


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 


3-645 


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 



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DESIGN OF THE PROPELLER 



165 











TABLE OF I.T. 


D-5-(l- 


S) 








Slip B.C. 


P.A.-5-D.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 


14-47 


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 


3-141 


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 


17-39 




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 


5-709 


7-143 


8.856 


10.66 


12.79 


15-32 


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 three-blade 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.-7-D.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. -S-D.A. for ^ XE.T.P (from Sheet 24). 

f P.A.-5-D.A. for 2 blades 

t P.A.-S-D.A. for 4 blades 

P.C. for total ^ 

D.A. 

LH.P.=:E.H.P.-J-P.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. -5-D.A 

T.S. for P.A.-5-D.A 

irXZ?XFX 101.33 

T.S.X(i-5) 

Now suppose that the value oi v-i-V 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.4-E.H.P. (variable) 

e-t. __j e.h.p. 



-Ffor- 



and 



E.T. E.H.P. ;•• 

V (designed speed, knots) 

e.h.p. (designed eff. horse-power) 

V^v^iv-i-V) 

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. =Tip-speed for P.A.^D.A 

Slip B.C. (as in First Step) 

1-5 for P.A.-J-D.A. and Slip B.C 

D= Diameter (Fixed by First Step) 

ioi.33XirXyXZ> _ 3i8.3XKXZ> 
T.S. X (1-6) T.S.X(i-5)"" 

IC as in First Step 

Z for e.h.p.-5-E.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.-5-E.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. 



F-s-rfor 



E.H.P 



(above \ 
Ciit. Thr./ • * 



F=i»-5- 



{?) 



LT.i>■^(I-5) = 



CXLH.P. 



P.C. for Total • 



D'XV 

(C=3.84for 2blade, 
PA.-5-D.A. for LT.z)-^(I-5■) ] 
f P.A.-^D.A. (fora-blade) [ 
JPJ^.-5-Dj\. (for4-blad) J 
P.A. 

D.A. 

EJI.P.=LH.P.XP.C 

e.h.p.=E.H.P.x||^ 

i-5for(P.A.^D.A.) 

T.S. for (P.A.-^D.A.) 

yDXFX 101.33 
T.S.X(i-5) 



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.i-5-E.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 vi-i-V 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.4-E.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 Horse-power 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 horse-power 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 r-5-F 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 four-bladed 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 four-bladed screw being fxthat 
of the basic three-bladed one: 



I P.A.4-D.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. -s-D.A., Sheet 20. 



P.C 

LHJ».=E.H.P.-5-P.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 tip-speeds and of i —basic apparent slip are obtained 
from Sheet 20, using the basic P.A.-^D.A. values of the basic three-bladed 
propeller, the values of i — 5 being taken from the curve of i — 5 for slip 
B.C. = .80. .-. 



T.S. for 



1-5 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(i-5) • 



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 horse-power, 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 


3-21 



3.53 

3-21 



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(i-s) 



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 
horse-power. 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 horse-power 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 


lliii-jj: 




>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 


P-d 


























«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.s-E.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= 
■5-D.A... 



2.491 E.H.P. 
D'XV 



IP.A.-5-D.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 

1-5 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 


15-46 


13-93 


12.68 


13-6 


12.25 


3.38 


3-25 


321 


3.38 


3-25 


3.21 


3-21 


3-21 


321 


3-21 


.04346 


.03586 


.03616 


.04510 


.03721 


75-37 


82.98 


91.22 


85-85 


94-49 



•55 

1.0 

II 

2727 

2.137 
.256 
.34 
.659 
4139 
3808 

.27 

2045 
1.27 

2597 
5650 

• 945 

II. IS 

3.21 

3-21 

.03751 
103.9 



Digitized by LjOOQ IC 



164 



SCREW PROPELLERS 



CONSTANT 



e.h.p. 



V , 

e.h.p 

e.h-p.-s-E.HP. 

E.H.P 

v^V 

V 

g|xE.T.,.., 

P.A.-^D.A... 
1 P.A.4-D.A. 

P.C 

LH.P 



S.H.P... 

Z 

S.H.P., . 

K 

S.H.P.(f.. 

T.S 

1-5 

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 


14-65 


12.03 


10.3 


12.52 


10. 57 


338 


3.2s 


3.21 


3.38 


3-25 


3.21 


3-21 


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 

3-21 
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 horse-powers 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 horse-power. 

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 17-ft. propellers above fall approximately on the upper 
limit of well-known 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 17-ft. diameter vary from a projected area ratio of .34 
to one of .3675, while the pitch remains constant at 12.9 ft. The shaft 
horse-power 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 17-ft. diameter propeller 
having a projected ara ratio of .34 and the shaft and horse-power required 
will be approximately 2600. 



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DESIGN OF THE PROPELLER 



167 



Problem 27.— Incomplete Data 

Same vessel as in Problem 23. 9iaft horse-power 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.-r-E.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-(i-5). 
P.A.-5-D.A... 
J P.A.-^D.A. 

P.C 

E.H.P 

e.h.p 

T.S 

1-5 

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 

3-68 

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 

3-4 

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 

13-67 

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. -5-D.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 horse-power, 
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; 5-hL.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.-5-D.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 fore-and-aft, is usually taken. The 
design conditions for the foregoing vessel were: Speed, i8 knots; revolu- 
tions IIS at 8250 I.H.P. and eflfective horse-power 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.-5-E.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 

1-5 

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 

3-707 

.366 

.64 

12500 

8000 

.655 

.902 
i6'.i3 



.231 

7344 
8298 
3.98 
3-76 
.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 

3-91 
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 

3-91 

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 

3-91 

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.-5-E.H.P. = .8, »-^7 = .9I7, e.t.-^E.T. = .872. 

Maintaining constant D = i7'.25, P.A. 4-D.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.H-D.A.. 

P.C 

LH.P 



I.H.P.„.. 

K 

LH.P^.. 

V 

S.B.C... 



1-5. 



T.S. for 



P.A. 
D.A. 



logAv 

logilf. 



Rd 

LH.P.d,. 



^•-Ws 



P.d, 



P.tf 



17-25 


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 


19-75 


21'. 23 


3.94 


4.03 


4-1 


3.76 


3.76 


3-76 


.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.-4-D.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 " fan-tail," 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.-5-D.A 

P.C 

LH.P 



S.H.P 

T.S for P. A. H 
S.B.C 



D.A,. 



1-5. 
P.... 



Zfor 
I.H.P.1 



e.h.p. 
E.H.P- 



p 

S.H.P.„ 

K from C-C. (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 


17-35 


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.-s-Dj\ 304 

Laying down »-5-7 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 oiv-r-V corre- 
sponding to P.A.-^D.A. equal .304, which is found to be .802, while the 
value of e.h.p. -i-E.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.-5-E.T. 



e.h.p.-^E.H.P. 

U-5-K 

e.h.p 



E.H.P 

P.A.-5-D.A. 

P.C 

I.H.P 



S.H.P... 

Z 

S.H.Pp. . 

K 

S.H.P.d. 

T.S 

1-5.... 

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 

3-43 

.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.4-D.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.-5-D.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. 4-D.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 

v-i-V... 
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.. 
1-5. 
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.-5-D.A. and constant D and varjdng v-i-V and 
e.h.p.4-E.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. -s-D.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.h-D.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 

1-5. 

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 

33-34 

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. -s-D.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 (tow-rope) horse-power 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 horse-power 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 



FAN-SHAPED 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.i-5-E.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 

v-i-V 

V 



LT.2>-^(i-5) 

(P.A.-^DA.)XE.T.p 

3.84, 2 Blades 
Note: C= 2.88,3 Blades 

2.491, 4 Blades 
P.A.-T-D.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.i-Mo^. 
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 



i-5for^andS.B.C. 
D.A. 

ioi.33X7XtXA 

T.S.X(i-6) ••• 

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.i-5-E.H.P.i. 

E.H.P.1 

K 



LH.P.p,=LH.P.d»-5-ie^. 
Z fore.h.p.i4-E.H.P.,. 
LH.P.i=LH.P.p,Xio^ 
Designed Speed=v. . . . 

v-hV 

V 



LT.dH-(i-5) 

(P.A.-7-D.A.)XE.T.p 

Note: C as before. 

P.A.-^D.A. (Sheets 23 and 24) 

I P.A.-J-D.A. for 2 Blades 

t P.A.-5-D.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.,-T-P.C 

LH.P.p, = LH.P.i^io^ 

LH.P.rf»=LH.P.,,Xie^ 

LH.P.d-LH.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(P-s- A)'/* 

T.S. forP.A.4-D.A 

S.B.C. of Vessel 



i-5for^4^andS.B.C... 
D.A. 

ioi.33X7XxXA 

T.S.X(i-5) 

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(A-5-/?)« 
( ) ( ) ( ) 



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 four-bladed 



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 

A-M?. . . . 

(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,-5-ie^... 



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. 4-E.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.i-5-E.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.i-LogLH.P.tfi. . 
e.h,p.i-5-E.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.. 
1-5 A*XK • 



P.A.■^D.A. for 



LT.z> 
1-5* 



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.* 



x-5forS.B.C. and 



P.A. 
D.A.* 



FXioi.33XirZ) 



^ T.S.X(i-5) 

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 
3-185 
.08426 
105.1 

"3-7 



7580 

•925 
9'. 081 

3.735 

3.195 

.09501 

163 



163 



7580 

.925 
9'.838 

3.735 

3-2 

.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 


3-735 


2.845 


2.845 


.2127 


.1986 


141. 7 


"3-4 


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. 4-E.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 
horse-power 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 

(A-5-i?)^.... 

(A+i?)* 

(A-^Z))'/*.... 
(A-5-I>)^.... 
eJi.p.i= e.h.p. 

c.h.p.i=e.h.p.x(jy 

e.h.p.i-5-E.H.P.(as before) . 

E.H.P.I 

Vi (Towing) 

t>i-rF (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 

1-5 

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 

3-735 

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 

3-735 

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 

3-735 

3 26 

-07635 
131 -8 

142-3 



Case 2, Broad Tipped. 



12 

12 

II30 

I.O 

I.O 
I.O 
I.O 

1 130 

.3 
3767 

10 
.6 

16.67 
3-91 
.388 
.517 
.544 
6925 

•5445 
1977 
1.28 
2530 



2530 

8370 

.755 

.92 

8'. 268 

14 

3 735 

3-26 

.08726 

188 



188 



12' 

13' 

1 130 

1.0833 

1. 174 

1. 141 

1.02 



1289.33 

.3 

4298 

10 

.6 

16.67 

3-801 

.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 14-knot 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 



13-925 

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 horse-powers 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 

5h-L.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 three-bladed. 

Limiting e.h.p. -5-E.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.) 

v-hV 

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.. 
1-5. 
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 


3-17 


.07959 


.07472 


.1473 


.1351 


384.2 


400.5 


337 


348.1 



3 545 

3 44 

3-17 

.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. Double-ended 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.-5-E.H.P. 
e.h.p 



E.H.P. 
V 

V 



D 

Blades 

(P.A.-^D.A.)XE.T.p... 
P.A.4-D.A. (Sheet 24). 

iP.A.H-D.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 

i-5for^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 


1-933 


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 v-i-V 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. -5-E.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 f-i « 

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^ 
tJ-vO totor|-Tj-»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 



lOTj-CIMClTfOOV 

^O toto^'«i-toci 

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 h-i ^ 



Digitized by LjOOQ IC 



DESIGN OF THE PROPELLER 



191 



10 ^0 cs 
00 t^ O 
0» PO »o < 



^ »o M <0 



t-t 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 four-bladed. 

^ . . ^ 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. 

4-E.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 

v-i-V (dhovcE.T.). 
V (free) (knots) — 
V 



LHP.d. 

K* 

I.H.P.P. 



Z 

I.H.P. 



D 

LT.z>^(i-5). 
P.A.^D.A.... 



1PA.-^D.A. 

P.C 

E.H.P 



e.h.p. 
T.S... 
1-5.. 
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. -5-D.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... 
1-5.. 



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 


1-355 


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 

3-65 

2.41 

.1299 

.2364 
179.8 



* li should be i . 195. 

Curves of s cross at e.h.p. -5-E.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 
horse-power and curves of full-throttle 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 power-revolution 
curve of performance of the propeller is laid down, the curve 
of full-throttle-revolution 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 horse-power 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; 
Tip-speedi = Ri XvDi ; 

Tip-speed2 =iZ2XZ?7r2=^,XirZ)if'/«=iJiXirZ)i; 



197 



.'. Tip-speedi 


=Tip-speed2; 


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^XRiX-Dr'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 tip-speed, 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 projected-area 
ratios, and products of thrusts (effective, propulsive, and indi- 
cated), by tip-speed« 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 horse-power for Vi of existing vessel; 
I.H.P.i = Indicated horse-power for Vi of existing vessel* 
S.H.P.i = Shaft horse-power for V\ of existing vessel; 
E.H.P.2 = Effective horse-power fo*- V2 of new vessel; 
I.H.P.2 = Indicated horse-power for V2 of new vessel; 
S.H.P.2 = Shaft horse-power 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 narrow-tipped 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^ Four-shaft 
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 



















Cui-vei 


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 Four-shaft 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. Four-shaft 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. Three-shaft 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. — ^Three-shaft 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 self-propelled, 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 Shallow-draft 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 . 



9-27-1 I 
5' 6" 
4' 3" 

4 

12.92 

11.72 

III. 25 

204.3 

49 

133.78 
4-415 



lo-s-ii 
6' 2" 
3' 3" 

3 
10. o 
.942 
no 
212.9 

30.4 
149.92 

5. "7 



10- 7-1 I 

5' 9" 
3' 6" 

3 
6.58 
.60 

107. S 
210.5 

36.4 
130- 95 
4.69s 



10-13-11 
6' 3" 
3' 8" 

3 

8.58 

8.0 

115.2 

208.2 

30.8 

144.74 
S.io 



10-19-11 
6' 2" 
3' 6" 

4 

13-33 

12-13 

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* 



10-24-11 

6' 2" 
3' 6" 

4 
13.33 
12.13 

123.7 
207 . 602 
26.7 
160.0 
5.258 



11-6-11 
6' 3" 
3'o" 

3 
15.21 
14.64 
125 

228.65 
26.15 
172.67 
5.045 



1 2-20-1 1 
6' 3" 
3' 4" 

4 
20.28 
«9-52 
125 

205.95 
22.5 

175-47 
5.24 



8 



5-8-12 
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 



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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. 



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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 3-b 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. 



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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 fore-and-aft 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 low-pitch 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 projected-area 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 projected-area- 
ratio blades for any desired diameter of propeller, by means 
of which the projected-area forms can be laid down without 
the use of the diagram of forms. • 

The necessity of adhering to standard projected-area forms in 



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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 fore-and-aft plane. 



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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 
fore-and-aft 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 last-mentioned 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 



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FORMS OF PROJECTED AREAS OF BLADES 



213 



form, as in B'. This form is often met with in motor-boat 
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 



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214 SCREW PROPELLERS 

are about 3 per cent less efficient for the same projected-area 
ratio. 

Blades thrown to the side, as in i4", are used to reduce vibra- 
tion in cases where a rapid-running 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- 



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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- 



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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, 



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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. 



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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, high-powered motor 
boat propellers, the thickness with high-grade 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 



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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.d-T-(-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 X-B— 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= Fore-and-aft 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- 
and-aft 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 fore-and-aft moment normal to face 

of blade at root. 
0=Af X-E = 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.H-E.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 semi-steel, /= 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 









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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. 



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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)2X2oo4-6o=Y^iS^+(2irX3.2)2=84 feet 

per second, 
C=-4FX8i^=3S2,8oolb. 

" Tension on bolts=3S2,8oo-5-3.2 = 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." 



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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. 



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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 horse-power 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 four-bladed 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, 



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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. 



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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 



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THICKNESS OF THE BLADE AT ROOT 227 

For a common screw /= .6034 

For a fantail-shape screw /=o. 581 

For a parallel blade /=o- S5o 

For an oval /=o. 520 

For a leaf shape 7=0.450 

For a Griffiths /=o-35o 

The horse-power 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. 



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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 reciprocating-engine propellers, where the hub diam- 
eters varied from 20 per cent to 28 per cent of the diameter of 
the screw in built-up 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 
1-34 
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 built-up 
propellers. The seating of the propeller-blade 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 low-pitch 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 
tip-speeds 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 high-speed 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 left-handed thread for a right-handed screw 
propeller, and a right-handed thread for a left-handed 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 reciprocating-engined 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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niSSSS 


















w 


■ 1 






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11 

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ITMBIBKI 


















80 


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: 


» 


:::»:! 














14 




-: 


:: 






70 


;: 


is::: 




00 


:: 


::::: 


XIII 


+fH 












12 




i- 


::::: 


:ii^::: 


I:: 




III 




■■■ftii 








■■■■■ 


::::^^ 


22 




Lit 








s 

s 


SD 




&"ls 


:::::: 


Ij 

!: 


::: :::: 
■ik" :::: 










10 


« 


40 


I:: 


iiiiiiSi 


fillil 


:: 


::: ^:is 










8 




III 


lllllll 


m 


:: 


::: :: \ 


» :: 

» H 




30 




III 


ii 




:: \ 


m 






6 










::: 




:» siss: 




+m2r-- 




::: 


■SSS 




■■■ : 


:::::::![ 




20 














"'T 








nrrr 






n-ri 






i-n 




iiiiiii 11 

ml 






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■■■■ 

[til 


k 


:i: 


ill 

:s; 




: »::: 


::: :::: 




10 










iliiilli 


:: 


■■■■Sii 


li 


s:::::::::: 
^•^^::::::: 


iiiili 






!:sBSi::::sf55!! 
^:::ss:ss:ssE3 

























6 8 

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. = horse-power exerted at any instant to stop the ship; 
IT = work done (per second) by this horse-power; 
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 horse-power necessary 
to drive the ship at the given speed and the horse-power 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 


3-94 


.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) = 
13-3 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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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 model-tank 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 


95-75 


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. 



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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 










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eed. 








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_ 



-.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 




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76 Ahead 
r 


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att 


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at this 1 


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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 



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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 



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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 propeller-torque curve of Fig. 41 and 
the motor- torque curve of Fig. 43. As the ship slowed the pro- 
peller-torque 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 



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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 



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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 motor-torque 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 right-hand 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 



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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 full-power trial. The dotted 
card shows the conditions if full boiler pressure could be obtained 




Fig. 46. 

in the high-pressure valve chest. In the construction of these 
cards no account has been taken of wire-drawing 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 heavy-line card, pressure in high-pressure valve chest = 
268 lb. absolute. For dotted-line card, pressure in high-pressure 
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 full-line curve; that is to say, the engines could 
develop only 19 per cent more torque than the ahead full-power 
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 full-powfer 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 one-quarter 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 slow-speed 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 slow-speed connection 
is practically the same as when going ahead at full power on the 
high-speed connection. This shoxild give very fine backing 
results. 



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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 


1-3337 


10 


13,965 


9,130 


1,400 


10,530 


8.75 


.1176 


1-4513 


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 


1-7505 


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. 



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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- 




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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 twenty-one 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 




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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 twin-screw ship, operating both propellers with one 
governor-controlled 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 


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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 lo-knottum, 
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 









Horse-power 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 horse-power readings were taken every five seconds. 
The curves obtained are all similar to those shown on the Del- 
aware's i2-knot 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 14-knot 
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 



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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. 



I 

I 
I 




2000 



f!;i;gS^3Sg^'liii»:S:::!:::::::::: 



1750 



1500 



1250 



1000 




AtMcls^e- Angle turned Tt rough 
Sli ce FuttlDfij Over Heli i. 



^1 



00** 



J20° lfiO° 

Fig. 52. 



300° 



880° 



The effect of turning on an electrically propelled ship would 
depend on the design of the motors and the turbines. In the 
case of the Jupiter the power plant of the ship is sufficient to 
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 



TiiminfiT at 14 Knots (S^Ruddei^ 
- IBO^Turn. B.P.M. Constant 1064^ . 
BhJp Oompleted IBO^'to Starb*d. in ^ Mtentei 
" " «* •* Port »*4Min.a0Seo. 



4^200 


Port, U^nottunliii to Fort 

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FiG. 54. 



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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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. 

Semi-steel 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 present-day 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 



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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 non-corrosive 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 
semi-steel for cast-iron or cast-steel propellers; of semi-steel 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 Monel-metal 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 cast-steel and cast-iron blades, however, as they are usually 
used for work where the speeds of revolution and tip-speeds 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 



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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 silver-plated. This, how- 
ever, seems of questionable expediency. It insures smooth blades 
for the trial trip, but it is doubtful if the silver-plating would 
remain on the blades for any considerable length of time. 



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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 center-lines, and also the 
outer radius of the wheel. Erect a cylindrical column on the in- 
tersection of the center-lines 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 straight-edge 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 straight-edge 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 
























- 




1 


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1 


N ^ 




P 






^ 


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p 










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1 




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Fig. 6o. 



ff 



V 






1 



^ 



r 



^ Sweep 



eLine 



Fig. 6i. 



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280 SCREW PROPELLERS 

If the straight-edge 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 base-line 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 
base-line. (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 base-line. (Lines a, b, c, 
d,f,/. Fig. 2.) 

Fig. 4 is the plan view. The center-line 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 



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GEOMETRY AND DRAUGHTING 281 

center-line project the tV of the pitch divided into 5 parts, as in 
Fig. 2. Draw lines parallel to the center-line (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 tip-line 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 base-line. 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 base-lines (see Fig. 4). 



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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 tip-line. 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 base-line along 
the center-line. The point on the center-line 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 base-line along the center-line 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. 



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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 — 3-bladed 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 center-line 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 foot-pounds. 
Z) = i2XB— Rad. of hub in inches = arm of athwartship force 

measured to root of blade = i2X5.425=6s.i" — 25,5" 

=39-6". 
£=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 inch-poimds 

=38,390X46.95 = 1,802,400. 

X= — ; — ^ = tangent of angle between face of blade and 
C.L. of hub or fore-and-aft line tangent to surface of hub 

=^=.7418. 



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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 "7-3^7 ' 

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 built-up 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 water-tight 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. 



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GEOMETRY AND DRAUGHTING 



287 



STANDARD PROPELLER HUBS 
For Solid Propelleks— Plate B 







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Di 


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37 


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* 4 




t If 


I* 


i| 


20-22 


4|. 


*i 


12 


li 


li 


15*3 


A 


^^> 


i iH 


lA 


I* 


22-24 


Si 


*i 


\ 12 


lA 


li 


17 3 


i 1 


||| £--^ 2 


I* 


i| 


I* 



Digitized by LjOOQ IC 



288 



SCREW PROPELLERS 



STANDARD PROPELLER HUBS 

For 4-Blade, Built-up, 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/ 

a-DX.34S. 

/— 4500 for manganese bronze or naval brass. 



D 


B 


C 


Di 


Dt 


Di 


F 


Fi' 


Ft 


H 


K 


L 


Z.1 


Lt 


^ 


^* . 


74 


*^ 


Til 


isH 


I3l 


r4i 


3S 


S : 


U 


qA 


ao| 


10 A 


loA 


S 


Above Si -9 incl.. 




^6J 


uf 


nk JMi 


lif^ 


jH 


6 


9H 


la 


to 
10 


8 
9 


^ yf 


7 


mI 


li Ai'sA 


28 


6 


23 


10 A 


J3 


9i-ioi 


9 


71 


i5i 


to! 


l?l 


l^f 


^a 


7 


3" 


5iii 


37 


13 


lit 


9 
iDj: 


loi- J I 


to 


S 


i6A^JtA 


2a 


7 


32 


I3l 
14 


iti 


Il-Jt J 

I1I-I2I 


10 


SJ 


17A 


23| 


ISA 


20 


28 


31 


34 


laij 


13 


II 


11 


9 


IB A 


^3H 


19 


r.p 


as 


£J 


36 


»3Als9A 


'^ * 


14A "I 


13l IJ 


12 


9l 


1^1 


as 


30 


28 


9 


h 


3H 


14A 


31 


16A 
I7t 


jj-ijI 


IJt 


fO 


20| 


26A 


3T 


23 A 


3S 


9 


H 


40 


rst 


32 t* 


15 A 


t3( 
131 


I3J t4t 


ui 


lOj 


ill 


S7l 


^ali 


^4f 


33 


10 


fl 


43 


isH 


34 A 


t8A 
i&A 


\t\ 


ui-is 


13H 


[I 


"A 


jali 


34 A 


35 H 


38 


ID 


1^ 


16 


n 


Ml 


m-17 


HA 


Hi 


J3A 


10* 


JSj 


^^1 


38 


It 


a 


17 


19 H 


'n 


IS 


ISA 


12 


2Ai\ 


jiA 


iH 


3i 


11 


4^ 


i3| 


Z9\ 


ao{ 


m 


IS* 


ISH.IJ^* 


35* 
16} 


J3 


27 A 


3QA 


38 


i2i 




Sa 


iB 


Aokl 


aiH 


191 


16I 


17 T7i 


I6A 13 


J4 


ja,^ 


30f 


as 


la 


i 


S2 


20 


AH 


3iA 


tg+i|l^i 


17t-lSi 


17 h Uk 


27i 


j.tA 


29 A 


JiH 


23 


ij 




U 


44t 


aiAaoHi-i 


J8J 19I 


11 \i 14 


aS 


Jfif 


^?U 


J3 


38 


13 




3Zl 


4^1 


a4AaiA;iSt 


15^-20 


iSi ,14* 


2?>A 


3SA 


34 A 


23 


14; 




ss 


3t 


471 


25k 22I 19 


20-2Q\ 


tg IS 


joAljgi '3^H 


35f 


23 


14 




60 


22 


49 


26 23 rof 


aoj-ii| 


t9\ \i5k 


J I 4o*i,J3i 


j&i 


2* 


IS 




6^ 


23 


sol 


26} 23i 20* 

27 34t '39} 


aij-ja 


3q| r5 
20 t6^ 


3J 42i JS 


37 H 


23 


15 




^ 


24 


52! 


22'32\ 


3j| 43 A 36 A 


381 


3B 


it 




34! 


S3H 


J 



;\^i (Vj Na Ni FD PDi PDt R 



Ti Ti Ti \ W 



Hi 
Above 81-9 mcl. 

ipj-i I 

1 i-r t J 
ir*~iJi 
I2i 13 

13 13l 
I3|-Mi 
14J 15 

15- is! 
I5l ig! 
I(3|-f7 

17-1-1 

i8J-igi 
igj 20 

ao-aol 
2oi-2il 

22-221 



13 

14 

IS 
15 
i& 
17 
i3 
I3i 



si 

10 A 

ill 



3H 

41 

sA 

s.A 

5| 

7 A 23 

7AI53 



13 

14 

IS 

17 

IQ 

21A 
2JA 
23 



2SJ 
2t\ 



'4 

10 A 



57 f 

A 30 
31 

33 

3:i 

34f 

3S 

3fi 



4! 
7 



f 



I3A 



10 

IT 

ir 
12 
124 
13 

13I 
14} 
141 



■r 



'i 
if 

if 



18 U 

3t n 

3} :^» 

jA 2it 



3J 
3! 
4A 3 

I 

i\ 



4 

■r 



I 



if 



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 


>o 


1 




l.9d 


1.2d 


i.Sd+l 


i 


t 




It 


.233d 


.766d 


.i66d 


Above 8i-9incl. 


& 


1 




l.9d 


I. 2d 


i.srf+l 


A 


A 




2A 


.233d 


.766d 


.i66d 


9-9k 


1 




l.9d 


I. 2d 


i.Sd+l 


A 






2l 


.233d 


.766d 


.i66d 


9i-ioi 


^ 


1 




l,9d 


1.2d 


i.Sd+l 








2| 


.233d 


.766d 


.I66d 


IO|-II 


io 


1 




l.9d 


I. 2d 


i.Sd+t 








2t 


.a33d 


.766d 


.i66d 


IX-Ill 


s 


1 




i.9d 


I. 2d 


i.Sd + l 








2H 


.233d 


.766d 


.i66d 


Ill-lal 


!-• 


f 




l.9d 


1.2d 


i.Sd+i 


H 






2i 


.233d 


.766d 


.i66d 


I3i-I3 


P 


1 




i.gd 


I. 2d 


i.Sd + l 








3 


.233d 


.766d 


.i66d 


I3-I3i 


ji 


f 




i.9d 


I. 2d 


i.Sd+l 








3A 


.233d 


.766d 


.i66d 


I3|-I4i 


f 




i.9d 


I. 2d 


i.S^+i 








3l 


.233d 


.766d 


.i66d 


I4i-I5 


3 


f 




i.9d 


I. 2d 


i.Sd+l 


H 






3t 


.233d 


.766d 


.i66d 


IS— iSi 


"S 


i 




i.9d 


I. 2d 


i.Sd + i 




I 




31 


.233d 


.766d 


.l66d 


iSf-l6J 


i 




i.gd 


I. 2d 


i.Sd+i 




I 




3H 


.233d 


.766d 


.i66d 


I6i-17 
I7-I7i 








i.9d 
i.9d 


1. 2d 

I. 3d 


i.Sd + i 
i.Sd+i 


H 
H 


I 
I 




4 
4t 


.233d 
.233d 


.766d 
.766d 


.i66d 
.i66d 


I7i-i8i 


J 




l.9d 


I. 2d 


i.Sd + l 


I 


I 




4i 


.233d 


.766d 


.i66d 


I8i-I9i 




i 




i.gd 


I. 2d 


i.Sd + i 


I 


I 




4A 


.233d 


.766d 


.i66d 


i9i-ao 


s 


i 




i.9d 


I. 2d 


i.Sd+i 


i^ 


r It 




4A 


.233d 


.766d 


.i66d 


20-20i 


^ 


i 




i.gd 


I. 2d 


i.Sd+i 


i^ 


r It 




4i 


.233d 


.766d 


.l66d 


20i-2lJ 


g 


i 




i.9d 


I. 2d 


i.Sd + i 


1^ 


r It 




4f 


.233d 


.766d 


.i66d 


2li-22 


• 


i 


I 


i.9d 


I. 2d 


i.Sd + t 


It 


It 




SA 


.233d 


.766d 


.i66d 


22-22i 


J 


X 


i.gd 


I. 2d 


i.Sd+l 


It 


It 




St 


.233d 


.766d 


.i66d 


D 


7 


k 


*i 


k» 


/ 


m 


mi 


r 


r\ 


rt 


/ 


fi 


8i 


t| 


i 


A 


A 


H* M M 


10 


2m 


2H 


« 


A 


If 


2A 


Above8J-9incl. 


li 


i 


i 


i 


"*.'*.'*. 


i 




2H 


i 


f 


2A 


2t 


9-9* 


i| 


i 


i 


A 


Ill 


& 


. . . . 


3t 


f 


f 


2t 


2f 


9J-10J 


If 


* 


A 


A 


5 5 i 






3f 


I 


1 


2} 


2A 


loi-ii 


ij 


f 


A 


f 


1^ M 




3l 


I 


1 


2i 


2f 


ii-iij 


If 


1 


A 


1 


M N M 

J J J 


s 


. . . . 


3H 


I 


1 


2H 


2| 


Xli-I2j 


li 


1 


H 


H 


V i i 




. . . . 


4A 


It 


« 


2| 


3A 


Iat-13 


li 


! 


H 


i 


M M S 


i 




4t 


lA 


f 


3 


3t 


I3-I3i 


If 


I 


1 


i 


' 




4t 


lA 


f 


3A 


3A 


I3i-i4i 


2 


I 


1 


H 


■|i- 


m 




4J 


lA 


} 


3f 


3A 


i4t-iS 


2 


I 


H 


H 


_^ 1/) 

3 '^ 


. . . . 


5 


lA 


H 


3t 


3l 


iS-iSi 


2i 


I 


H 


i 


■«< 


ir-^ 




sA 


If 


I 


3f 


3H 


ISf-i6i 


2* 


li 


A 


H 


1 1 ^ 




. . . . 


sA 


If 


I 


3H 


4t 


i6i-i7 


2j 


li 


H 


tt 


iii 






si 


It 


lA 


4 


4i 


I7-i7i 


2i 


li 


H 


I 




•§ 


. . . . 


si 


It 


lA 


4t 


4A 


I7i-i8i 


2i 


li 


i 


I 


III 


Q 


. . . . 


6A 


If 


It 


4t 


4f 


l8J-i9i 


2f 


i| 


i 


lA 


i i 5 


:j 


. . . . 


6A 


If 


It 


4A 


41 


I9i-20 


2i 


If 


H 


i» 


« wj 


S 




6t 


iH 


It 


4A 


4H 


20-20 J 


2i 


li 


H 


li 


£j£ 


(S 


. . . . 


6i 


iH 


It 


4f 


St 


20i-2ll 


3 


li 


A 


lA 


«^o « 




. . . . 


7 


iH 


It 


4f 


SA 


2li-22 


3 


i| 


A 


It 




£ 




7l 


iH 


lA 


sA 


sA 


22-22) 


3 


It 


H 


It 


«+> 




7 A 


iH 


lA 


St 


s! 












0*3 oi 


























^•s^s 

















Digitized by LjOOQ IC 



GEOMETRY AND DRAUGHTING 



201 



STANDARD PROPELLER HUBS 
For 3-Blade, Built-up, Profelieks — ^Plate D 



D 


B 


C 


Dx 


Dt 


F 


Fi" 


Ft 


H 


K 


L 


Li 


N 


Nx 


}ft 


H 


6f 


4H 


fl2* 


IS 


16 t\ 


r 28 


7« 


26 


10 A 


20* 


10* 


8 


9* 


* 


Above 8i-9 incl. 


7J 


St 


13* 


16,^ 


18^ 


r 28 


8* 


28 


II* 


21* 


10* 


8* 


9* 


* 


9- 9\ 


8 


Si 


14* 


17* 


19* 


28 


9 


30 


12 


23 


II* 


9* 


10* 


* 


9|-I0l 


8,^ 


r 6 


IS* 


I8| 


20* 


28 


9A 


32 


12* 


24* 


12* 


9* 


II* 


* 


loj-ioi 


9\ 


61 


16* 


20 


21* 


28 


10* 


34 


13* 


26 


13 


10* 


II* 


* 


loi-iij 


9\ 


6} 


17 


21* 


23 f 


r 28 


10* 


36 


14* 


27* 


13* 


II 


12* 


* 


III-I2 


10 A 


7i 


18 


22* 


24* 


28 


II* 


38 


IS* 


29* 


14* 


II* 


13* 


* 


12 -I2f 


loi 


7i 


i8*i 


23* 


25* 


28 


12 


40 


16 


30* 


IS* 


12 


[3* 


* 


I2i-I3* 


Hi 


7J 


19* 


24* 


27 A 


r 28 


12A 


42 


16* 


32* 


16* 


12* 


14* 


1 


I3I-I4 


iiH 


8* 


20*1 


25*1 


28 A 


r 28 


13* 


44 


17* 


33* 


16* 


13* 


iSh 


* 


14 -uf 


I2| 


81 


21* 


26 H 


29*1 


28 


13* 


46 


18* 


35* 


17* 


14* 


16* 


* 


l4J-iSi 


12i 


9 


22* 


28 A 


3IA 


28 


14* 


48 


19* 


37 


18* 


14* 


16* 


I 


isi isi 


I3i 


9l 


23* 


29* 


32 A 


28 


14*4 


SO 


20 


38* 


19* 


IS* 


ilk 


I 


lSi-i6i 


13 H 


9} 


24* 


30* 


33*1 


28 


ISA 


52 


20f 


39* 


19* 


IS* 


[8 


I* 


l6J-i7i 


I4J 


10* 


25* 


31 H 


3SA 


28 


16* 


S4 


21* 


41* 


20* 


16* 


t8* 


I* 


I7i-i8 


IS 


10* 


26* 


32* 


36 A 


28 


16* 


S6 


22* 


43* 


21* 


17* 


19\ 


I* 


18 -18J 


ISA 


10* 


27 A 


34 


37 A 


28 


17 A 


58 


23* 


44* 


22* 


17* : 


»0* 


I* 


I8j-I9i 


16 A 


11* 


281 


3SA 


38* 


28 


17** 


60 


24 


46* 


23* 


18* J 


81* 


I* 


19I-19I 


i6| 


II* 


29* 


36 A 


40 A 


28 


18* 


62 


24* 


47* 


23* 


19 i 


H* 


I* 


I9l-20i 


17* 


12 


30* 


37 A 


41 A 


28 


19* 


64 


25* 


49* 


24* 


19* J 


12* 


I* 


20J-21 


17 H 


I2| 


31* 


38** 


42* 


28 


I9tt 


66 


26* 


SO* 


25* 


20* : 


«3i 


1* 


31 -2li 


18J 


12* 


32 A 


39* 


44* 


28 


20 A 


68 


27* 


52* 


26* 


20* J 


»3* 


I* 


3li-22i 


l8i 


13* 


33* 


41 A 


45* 


28 


20 tt 


70 


28 


S3l 


26* 


21* s 


>4* 


I* 


D 


Ni 


Ni 


PD 


PDi 


PDt 


R 


Ri 


Ri 


5 


T 


Ti 


Tt 


T 


1 W 


Wi 


8i 


4f 


3H 


13* 


13* 




4* 


4A 


8H 


S* 


itt 


2A 


2* 


2* 


3* 


I* 


Above 8J-9 ind. . 


S 


4 


IS 


14* 




sA 


5 


9* 


5* 


3* 


2* 


2* 


2* 


*3tt 


I* 


9- 9\ 


5l 


4A 


16 


IS* 




sA 


5l 


10 A 


6* 


2* 


2A 


2tt 


2* 


3« 


2 


9J-I01 


s! 


4H 


17* 


16 H 




si* 


S^ 


II* 


6* 


2* 


2tt 


3 


3^ 


UA 


2* 


lOl-ioi 


61 


4* 


18* 


17* 


■«• 


6A 


6A 


iiH 


7 


2A 


2* 


3A 


3* 


4* 


2* 


loi-iii 


61 


sA 


19* 


18 H 


1 


6* 


6A 


12* 


7* 


2tt 


3A 


3* 


3* 


4* 


2A 


Ili-I2 


6i 


sA 


20* 


20 




7 


6* 


13* 


8 


2tt 


3* 


3A 


3* 


5 


2A 


12 -12} 


7 


sH 


21 A 


21 A 


1 


7* 


7* 


13 tt 


8* 


3 


3* 


3* 


3* 


S* 


2tt 


I2l-l3i 


7* 


6A 


22* 


22* 


7* 


7* 


14* 


8* 


3* 


3A 


3tt 


41' 


ks* 


2tt 


I3J-I4 


71 


6* 


23 A 


23* 


1 


8* 


7* 


ISA 


9* 


3A 


3* 


4* 


4* 


Stt 


2tt 


14 -14} 


8i 


6* 


24* 


24A 


8* 


8A 


16 


9l 


3A 


3* 


4A 


41" 


k6A 


3A 


i4i-iSi 


8i 


6H 


2sH 


2S* 


8* 


8A 


16* 


10 


3A 


4A 


4* 


4* 


6A 


3* 


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Digitized by LjOOQ IC 



282 



SCREW PROPELLERS 







H '<^ 4 



Plated 



Digitized byCjOOQlC 



GEOMETRY AND DRAUGHTING 



293 



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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, one-sixth to one-fourth of its weight, or 

P Gross weight 



The effective horse-power, 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 horse-power 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 up-wind to a down-wind 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 horse-power 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 horse-power 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 full-throttle variable brake ciuve of shaft 
horse-power 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, tip-speed 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 tip-speed, 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.-4-D.A. 

The Design Sheet as shown is for three-bladed propellers, the 
same method of correction for two- and four-bladed 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.-5-D.A. and 
varying values of e.h.p.-5-E.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. -5-D.A. 
has been ascertained, this value of e.h.p. -7-E.H.P. is retained con- 
stant and the problem solved for varying values of P.A.-4-D.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 three-bladed 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 4-bladed 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.-S-DA (assumed) 

|P.A,-5-D.A 

eh.p.-5-E.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(i-5) 

»rZ>X88 

1-5 

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 

^" pxd-i) 



.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 


5-231 


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.-f-D.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 





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7 




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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.-f-E.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.-5-D.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 



i-5for(P.A.^D.A.).. 
F={PXT.S.X(i-5)}- 

(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 
5-231 

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.4-D.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.-5-D.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.-5-D.A. = .12. 



/P.A.y" 



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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 four-bladed propellers. 

Where three-bladed propellers are desired, and it is always 
preferable to use them, rather than two-bladed, 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.-5-D.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 four-bladed 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.-T-D.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. 



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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 three-bladed propeller: 



P.A.-^D.A 

T.S 

1-5 

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 


99-7 


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 

99-7 



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>-^(i-5) for I.T.2>-^(i-5) and S.H.P.dfor 
I.H.P^, and a problem worked out by this method is now 
given. 

Shaft horse-power, 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 horse-power of engine = S.H.P.tf = 400. 

Maximimoi diameter of propeller that can be carried =8' 4" 

=8'.33. 

Propeller to be f our-bladed. 



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304 



SCREW PROPELLERS 



Power expended in climbing =^ ^5— =61.46 e.h.p. 

10X330CX) 

Estimated propulsive efficiency (assumed) = .70. 

Shaft horse-power expended in climbing = — ^=88. 

.70 

Shaft horse-power 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.-J-E.H.P. (assumed). 

Z (Sheet 21) 

S.H.P.d 



S.H.P. = S.H.PHfXio^ 

v^VioT^^(Sheet22).... 

V (knots) 

S.T.tf-5-(i-S) (Sheet 26) 

P.A.^D.A. for S.T.tf^(i-5) 
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, 

1-5 for ^ (Sheet 26) 

7rXDXioi.33XF 

T.S.X(i-5) 

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 

93-54 
.2224 

.134 
.179 

.767 

444-5 
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 

4-95 
4.88 

.3213 
1798 



8'.o 

95 

82.5 

.6 

.231 

400 

680.9 

.838 

98.45 
.2692 

.150 
.200 

.77 

524-3 
315 
293 

62064 

.655 
6'. 168 

5-03 
4.88 

.2863 
1899 



8'.o 

95 

82.5 

.7 

.161 

400 

579.5 

.882 

93-54 

.2411 

.1436 

.191 

.77 

446.2 

312 

293 

591 10 
.65s 

6'. 153 

4.985 
4.88 

.3033 
1950 



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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.d-i-(i-S) (Sheet 26). .. . 
P.A.-5-D.A. for S.T.d-5-(i-5) 
|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(i-5^ 

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 
504-6 


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 


4-95 
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: 



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306 



SCREW PROPELLERS 



e.t+E.T 

e.h.p.-i-E.H.P 

S.H.Pm 

Z 

S.H.P #. 

P.A.-8-D.A. (as before). . 
1P.A.+D.A 

^•^•^-♦5X 

E.H.P 

eJi.p 

. T7 1 c-t- J e.h.p. 

t-r y for and ^— 

E.T. E.H.P. 

r (knots) 

y 

T.S.for^ (Sheet 26). 

i-5for^ (Sheet 26). 
Jj.A. 

XXDX101.35XF 

T.S.X(i-5) ••*• 

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 


5-215 


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 six-tenths to 
seven-tenths of its radius. The maximum width of the devel- 
oped arc, measured for zero pitch and on the circular arc, 
averages about one-twelfth the diameter of the screw. The 
thickness of blade near the hub is very great but diminishes 
rapidly to about half-blade 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 mid-radius 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 one-third 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 semi-ellipse, 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- 



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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 tkree-bladed propellers) and their hub 



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310 SCREW PROPELLERS 

ends securely glued together in highly efficient joints of very 
large glue-contact 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 twenty-four 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 high-powered 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 three-bladed screw, even though 
having less diameter, shows marked superiority over the two- 
bladed in every particular. The three-bladed 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 screwed-on covers 



Digitized by LjOOQ IC 



312 SCREW PROPELLERS 

and heavy battens and iron-bound ends. A center bolt clamps 
the propeller between battens in the top and bottom of the box 
and felt-lined 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 helicoidal-area 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 slip-block 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 horse-power 
was originally given. They also include the propulsive coeffi- 
cient on the bare hull, the appendage multiplier as obtained from 

313 



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314 SCREW PROPELLERS 

Sheet i8, and the resultant propulsive coefficient on the hull with 
all appendages. 

13. A large number of cuts showing one-half 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 center-line 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 tip-speeds 
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. 



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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 73-83 

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 

Broad-tipped blades, design 180 

, estimate of performance 95 

Brown, Samuel, mention 3 

Buchanan, Robert 2 

Bushnell, mention 2 



Cavitation 130 

, effect of blade section 133-145 

" 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 46-196 

, 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 46-196 

, 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 62-73-153 

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 

Double-ended 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 horse-power, definition and formula 19 

thrust, formula 61-79 

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 

Fan-shaped blades, design 179 

, estimate of performance 97 

Ferry boat, double-ended, 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 trans-Atlantic ship 4 

Greenhill's theoretical assumptions for propellers 37 

theory developed 42 

Gross effective horse-power 132 



H 

Hooke, Robert, mention 1 

Horse-Power, 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 horse-power, 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. -5-P.C., tables of values 59 



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INDEX 321 

PACK 

Pitch, effect of excess 200 

, formula for 63 

Position of propeller, 4-shaft 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 4-sliaft 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, 3-blade, 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, broad-tipped blades 95 

'* , double-ended ferry boat 122 

** , f an shaped 97 

" , 2, 3 and 4 blades 77 

, estimate of power and effective power 124 

Problems, estimates of performances, 3-blades 89 

'' 89 

4-blades 99 

, effect of rough bottom 103-105 

, 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 

* * double-ended 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 33-36 

, factors in design 146-294 

, 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 horse-power, 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. h-E.H.P 59 

Z S8 

Theories, final formulas of 44 

of design of propellers 37 

'* * * , Taylor's presentation of 39 

Thickness of blades 218-284 

Three-shaft 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 

horse-power, 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 

Tow-boat 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 screw-propelled American 4 

Weddell, fits propeller to ship 4 

Wetted surface, approximate formula 22 

Z 

Z, determination of values of 65 

, equation of 66-67 

, tables of values 58 

, use in correction of power 66 



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