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

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About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at |http : //books . google . com/ ^p J^^^^* -^ !'• t • 'P' zed by Google Digitized by LjOOQ IC Digitized by LjOOQ IC 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 Digitized byCjOOQlC A^ Copyright, 1918 BY CHARLES W. DYSON Digitized by LjOOQ IC 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 382795 Digitized by Google 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 vii Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC Digitized by LjOOQIC 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. Digitized by LjOOQ IC 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- Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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- Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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, Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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, Digitized by LjOOQ IC BLOCK COEFFICIENT, THRUST DEDUCTION 11 Sheet 19. No correction should be made for variation of mid- ship section from standard. 2. Single screw ships of beam very broad as compared with length and draft of vessel. In such vessels the immersed lines of the vessel correspond to the lines below the turn of the bilge in vessels of orthodox form. No correction should be made for midship section variation. Such vessels are similar to shallow draft ferry boats. In estimating the slip block coefficient of single screw vessels, the condition of immersed hull body as to nominal Block Coefficient existing when the tips of the upper vertical blades are immersed to a depth of about 15 per cent of the diameter of the screw should be used. 3. Single or twin screw timnel boats. These vessels have the propellers so located that the only definite idea of the flow of water to the propeller that can be obtained is that of its direction and this may be considered as normal to the disc. The only thrust deduction loss that occurs is that due to friction in the tuniiel and amounts to Jir = 1.195 and this can be consid- ered as constant. Make no corrections in obtaining the slip block coefficient, but use the nominal block coefficient for the slip block coefficient. The lines X, Y and Z may be called " orthodox " for usual t)^s of hulls and location of propellers. There are, however, many departures from these " orthodox '' conditions and each of these departures produces a change in wake and, therefore, a change in revolutions of propeller for given powers of engines and speeds of vessel. These departures may be classed imder four separate heads, as follows: I. Deep draft vessels fitted with propellers of diameters bearing a ratio of less than .70 to the draft, the lower blades pass- ing close to or below the keel. In such a case, with the vessel running at light draft with the propeller diameter bearing a large ratio to the light draft, but entirely submerged, the slip block coefficient will be the normal from line Z corresponding to the L.L.W.L. or L.B.P., the beam By and the displacement at the light draft. In estimating the Digitized by LjOOQ IC 12 y SCREW PROPELLERS apparent , slip, the value Log A^ must be taken from the curve marked Xon Sheet 21. See Par. 2. As the vessel is loaded and the draft increases, conditions of wake change very slightly, and may be neglected, until after passing a ratio of diameter to draft, D : H of .75. Shortly after passing this ratio the wake rapidly reduces imtil D : H = about .70, when the wake is that corresponding to the S.B.C. as taken from line W^ Sheef 17, while the value of Log At must be taken from the ciui^e^J^heet 21. The 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC BLOCK COEFFICIENT, THRUST DEDUCTION 15 propeller for a given number of revolutions is reduced beyond a certain amount, the phenomenon being referred to later in this work as " dispersal of the thrust colimm." It is a com- rade of the phenomenon generally known as " Cavitation,'' and, like its comrade, its arrival can be retarded by increasing the projected area ratio of the propeller, which carries with it an increase in the 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. Digitized by LjOOQ IC 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: Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC ESTIMATION OF POWER 19 by the ship per minute and dividing the product by 33,ocx>. The equation is: Thrust Ho^se■powe^=T.H.P. = ^^^^^^ =(^Xy)-^326, and the Efficiency of the Propeller =£=T.H.P.-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. Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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- Digitized by LjOOQ IC 22 SCREW PROPELLERS tion to length but with fine ends, .45; freighters, .5. The value of b is also likely to be affected by speed, especially when the 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; Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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- Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 32 SCREW PROPELLERS benefit obtained by departure from the form produced by a uniform pitch was found to be very inconsiderable, if any. In all of the preceding cases the actual thrust of the propellers was measured by means of dynamometers fitted on the pro- peller shafts. In the series of tests which were made on the Pelican, while more elaborate and which appear to have been conducted with greater scientific accuracy than the British tests, no dynamometer was fitted. The experiments conducted in the Pelican in 1847 and 1848 were repeated in 1849 on board the same vessel, using propellers of larger diameter than the original, and the results obtained in the earlier experiments were corroborated. The object aimed at in the Pelican tests was the determina- tion of the specific efficiency of all kinds of screw propellers in vessels of every size, proceeding at every speed, and under all circiunstances of wind and sea, to the end that the particular species of propeller most proper for a given vessel might be readily specified. Another object in view was the determina- tion of the value of the revolving force that it was necessary to bring to act upon the propeller shaft to obtain any definite number of revolutions in a given time, supposing, of course, that the form of the vessel was known as well as the dimensions of the propeller. It is readily seen that the problem thus proposed for solution is the general problem of screw propulsion whose correct answer has been sought by many since the early days of the Pelican tests. The conclusions arrived at by these tests may be briefly sum- marized, as follows: " Not only does the efficiency of a screw increase with its diameter, or rather with the relative resistance, but the proper ratio of the pitch to the diameter, and the corre- sponding fractions of the pitch, vary with the relative resist- ance, the ratio of the pitch to the diameter diminishing when the fraction of the pitch increases, while the fraction of the pitch varies with an inverse progression." Bourne, " Treatise on Screw Propellers," states that these tests enable us, with any given diameter, to specify the best pitch and the best length of screw that can be employed, whether Digitized by LjOOQ IC f EARLY INVESTIGATIONS 33 the screw is formed with two, four, or six blades. For taking K as the resistance per square metre of immersed midship section (equal 6 kilogranmies or 13.23 lb. per square metre at a speed of I metre per second), B^ the area of immersed midship section in square metres, D the diameter of the screw in metres, and P the pitch of the screw in metres, then and Z> multiplied by the ratio of pitch to diameter, given in an empirical table obtained by the experiments, will give P. T.. ,1 PX fraction of Pitch (tabulated) ^ ^. . Fmally, . ■^, , ^= Length of screw. number of Blades For years after these experiments had been completed there was apparently no systematic attack made upon the propeller problem, engineers being apparently perfectly well satisfied with the results obtained by the use of such formulas as the following: d is the diameter of the L.P. cylinder of the engine in feet; Z is the stroke in feet; Pc is the block coefficient of vessel; Z is a multiplier = (2.4— P^) for twin screws; and = (2.7 —Pc) for single screws; 22= revolutions per minute. Ride I. D= diam. of screw in feet = Z X ^dxL, Ride II. D = diam. of screw in feet =xXPe yj ' ' ' ■, in which for single screw, nc = 7 . 25 for twin screw, nc = 6 . 55 for quadruple screw, nc = 6 . 25 for 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. Digitized by LjOOQ IC 34 SCREW PROPELLERS Rule ni. A =irZ)2-^4, where Z? = diameter of propeller. The thrust of the propeller in pounds =2AxV{V—v). The work done per minute = 2^4 XV(V—v)X6ov ft. lbs. V^PXR, and t^= speed of ship in feet per minute. ^ ^, ^ , 2AxV(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. Digitized by LjOOQ IC EARLY INVESTIGATIONS 35 To determine the pitch of the propeller, using the same nota- tion as in the rules for diameter, calling the area of the propeller disc Ay the diameter D, and the pitch P, RideV. i4 =.78542)2. Thrust=2^XF(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 Digitized by LjOOQ IC 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, Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 88 SCREW PROPELLERS due to the friction of the propelling plane moving edgewise, or nearly so, through the water. In all the theories in connection with which mathematical methods are to be used, it is practically necessary to regard the blade as having no thickness. This is a serious defect in the theories, as they all use a true slip based upon true pitch and consider the designed pitch of the driving surface of the blade as this true pitch. The fact of the matter is that the face pitch of a blade with thickness, or its nominal pitch as it may be called, is very different from the true or actual pitch, and this fact causes complications in using the mathematical formulas. It would be necessary, in case these theoretical formulas were adhered to, to compare each formula with experimental results and select that one which seemed to agree more closely. Then, using this as a semi- empirical formula, with coeffi- cients and constants deduced from experiments or experi- ence, problems could be satis- factorily dealt with. When the vast niunber of various conditions for which we may be called upon to design a propeller are considered, it is readily seen how impossible it would be to tabulate the correctors which would be required to cover all, or even a large number of these con- ditions. In order to give a thorough understanding of the study that has been put on the subject of the propeller, it Fig. 3. will be well to present these in their mathematical form for the determination of thrust and torque, and in doing this Digitized by LjOOQ IC THEORETICAL TREATMENT 39 nothing better can be done than to give Naval Constructor Taylor's presentation of the theories, as set forth in '^ his work on " The Speed and Power of Ships." Fig. 3 indicates the motion of a small elementary plane blade area of radius r, breadth dr in a radial direction, and circum- ferential length dl. This element is seen with its center at O. If w is the angular velocity of rotation of the shaft, the cir- cular velocity of the element is wr. AOB is the pitch angle ^, BC the slip and BOC the slip angle 0. Now, tan ^=P^2irf. Considering Fig. 3 as a diagram of instantaneous velocities, the line OA or wr represents the circular velocity of the element. If there were no slip, the actual velocity along the helical path would be OB and AB would represent the axial velocity or the velocity of advance, and AB=OA tan e=wr tan e^wr-^^—. 2irf 2ir When there is slip the circular velocity of the element is imchanged, but the velocity of advance becomes AC^ the speed of the screw is the same as the speed of advance when the slip is zero. , Denote the percentage slip by 5, then S^BC^AB = {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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC THEORETICAL .TREATMENT 41 ^jw f^ t^[^ loge(i+g^) / loge(i+g^) 1 f \\ g 3600 2ir L2 2 \ 2 i+q^/1 "g 3600 4x L t ^ <f i+Wj Now, pq=2Trr\ f(f^/^T^f^\ ti.^^=.'^ if d is extreme 4x 4 diameter. Whence ^3600 4 L 2^ \ 5^ 1+5^/ J' and finally, r=- /<^^4-'-=^-('-^^-r^)]' I44OOJ and the torque, 2t IF. Froude's Theory. 11 I is the total 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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^ ^^^^^^ Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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- Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized byCjOOQlC PRACTICAL METHODS OF DESIGN 51 Equation (3) is used as an aid in proportioning propellers which must have a given speed of revolutions. For 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 Digitized by LjOOQ IC .g2AV^ S.H.P. ^ RD 62 SCREW PROPELLERS CORBECnON FOR VARYING VALUES OF DEVELOPED ArEA RaTIO From the Standard By assuming that the total thrust that can be delivered by any propeller of fixed pitch, diameter and revolutions will vary directly as the develop)ed area ratio, a series of curves can be laid down as shown on Sheet i6, by which the values of and can be obtained for any desired value of developed area, H.A., divided by disc area, D.A. The values of Ca are shown as ordinates on the left of the sheet, the abscissa values being increasing values of H.A.-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; Digitized by LjOOQ IC PRACTICAL METHODS OF DESIGN 63 ^ RD are obtained. Taking this value of C^ as the value of the ordinate at the abscissa value H.A.-rD.A. of the actual pro- peller, and projecting across to the ordinate erected at the abscissa whose value is that of the Cr so obtained, a point is plotted. Through this point draw a line parallel to the line 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 Digitized by LjOOQ IC 54 SCREW PROPELLERS the values of Ca and Cr corresponding to any one diameter value and plot it on the chart and through the point thus obtained draw a line parallel to the line of constant helicoidal area ratio, 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 66 SCREW PROPELLERS I.T.D, marked T.S.; the curves of i minus the apparent slip as modified by the dififerent values of slip block coefficient from unity to the phantom ship of zero block, marked i— 5; and finally the values of the propulsive coefficients wliich can be obtained at this condition of standard resistance, the hulls having the minimum losses possible due to thrust deduction; the propulsive coefficient curve is marked P.C., and the condition of Basic hull efficiency or Basic thrust deduction corresponds to the value Jf =1. These curves are laid down on values of projected area ratio, P.A.-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 Digitized by LjOOQ IC THIRD METHOD OF DESIGN 57 from unity to the zero value of the phantom ship. P.C. = Propulsive coefficient of the propeller = Basic E.H.P.-^Basic LH.P.=Basic E.H.P.-5-(Basic S.H.P.-h.92), the ratio between I.H.P. and S.H.P. for 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC ANALYSIS OF PROPELLERS 121 Problem 20. Propellers for ''Tunnel" Boats By the term " Tunnel " Boat is meant a vessel of shallow draft having arched passages formed in the bottom of the after body and the propellers located in these tunnels. The propeller may be so located that only a portion of its diameter is immersed when at rest. When in motion the propeller draws the air from the portion of the tunnel forward of it and expels it to the rear. This produces a vacuum which is immediately filled by water, the tunnel thus remaining full so long as the propeller is operating. The water being constrained to move in a direction practically normal to the disc of the propeller, the principal losses are those due to friction in the tunnel and are therefore practically a constant percentage loss of the total power put into the propeller, no matter what the slip block coefficient of the ship may be. This loss is heavy, and from the results obtained in the following problem, appears as " thrust deduction " and amounts to K = 1.195. The problem is an analysis of the propellers of two U. S. shallow water gimboats for which the propellers were designed by parties who have had much experience with this type of vessel and whose design of propeller must, therefore, be con- sidered as having been based upon actual performances. The close agreement between the analysis results and the designed con- ditions is rather good evidence as to the correctness of the former and of the value of K obtained. 800 (Two engines) =I.H.P.tf PA^DA Revs. 300 Nom. B.C. = .6 5-^L.W.L.=.i53 SHpB.C. = .57S iP.A.^D.A D P T.S R PXR 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 Digitized by LjOOQ IC 122 SCREW PROPELLERS The designed conditions of these vessels were I.H.P^ = 800, Revs. =300, Speed = 13} knots. The apparent sKp with these conditions « 25.41 per cent. The computed apparent slip, from the basic condition reduced to 13} knots and 800 1.H.P., is as follows: log i4F=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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 124 SCREW PROPELLERS Forward Propeller Removed e.h.p 700 e.h.p.■^E.H.P 3046 z 5440 LH.P.tf=XxI.H.P.p 1570 v^V. .67 and the propeller plots well within the safe zone on Sheet 22 and for safe loads on Sheet 22B. Problem 22 Use of Sheet^ 22 in estimating power and effective power delivered. By the aid of the curves given on this sheet it becomes possible to make an estimate of the indicated or shaft 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. Digitized by LjOOQ IC ANALYSIS OF PROPELLERS 127 BASIC CONDITIONS OF PROPELLERS Prop. . Diatn. P.. Act. . . Basic. P.A. f D.A. \ Act. . . Basic . T.S,. PXR Condition. S.B.C 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, — Digitized by LjOOQ IC CAVITATION 145 " Where the htdl of a vessel is of such underwater form as to produce a heavy wakey the speed at which cavitation and dispersal of the thrust column occurs will be higher than if no wake existed, on account of the * wake gain.^ '* 7. Effect of Insufficient Tip Clearance between Propeller and Hull on the Production of Cavitation. Experience and the analysis of trials of numerous vessels lead to the conclusion that— *' Where insufficient tip clearance exists between the propeller and the htdl, increases in effective 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. Digitized by LjOOQ IC CHAPTER DC DESIGN OF THE PROPELLER Computations for Pitch, Diameter, Projected Area Ratio AND Propulsive Efficiency In computing the prindpal characteristics of a propeller, these being the pitch, diameter and projected area ratio, the fol- lowing factors must be considered: 1. The form of the after submerged body of the hull of the vessel to be propelled. 2. The position of the propeller relative to the hull. 3. The effect of the hull lines and position of the propeller in modifying propulsive eflSciency. 4. The resistance of the hull to motion through the water at any given speed. These four points are covered by Sheets 17, 18, and 19 and in some cases by the model tank from which the curves of effective (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 Digitized by LjOOQ IC DESIGN OF THE PROPELLER 147 In Dy the reduction of load may be either positive or negative, that is, the propeller may be designed to deliver less than the Basic condition of E.H.P. or it may be designed to deliver a load greater than the Basic condition of E.H.P., while the designed speed V may be greater or less or equal to the Basic speed V. PROBLEM A. SUBDIVISION C Form for Computation 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^)- Digitized by LjOOQ IC 148 SCREW PROPELLERS In illustrating the above type of problem, the effect of change in speed due to change in resistance and also the effect of an error in the Slip B.C., will be shown. Problem 25 Statement: Hull Slip B.C. = .5. E.H.P. = iooo. Single screw. The vessel is so loaded at first that a speed of 20 knots an hour requires the above value of E.H.P. Later the vessel is so lightened that a speed of 35 knots can be made with this same E.H.P. Find the diameter, projected area ratio and pitch of the propellers for the two conditions, the desired revolutions being assumed in each case as 600 per minute. SOLUTION P.A.-f T.S.. 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. Digitized by LjOOQ IC DESIGN OF THE.PROPELLER 149 21 g,UQG ^ 17 16 15 U 13. \2 a a 11 'I ID-. \ •d R^i•tfi. 1,400 1,300 1.200 1,100 1,000 000 800 JQO COO JOO JOO goo gou too Fig. II. — Curves of I.H.P., Z>, P, and i2, on P.A.-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 Digitized by Lj.OOQ IC DESIGN OF THE PROPELLER 151 Such an error produces no change in the power required for the speed unless the value oi 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 208 SCREW PROPELLERS Projected area=.32 disc area Dotted lines are developments of projected areas as shown Full " ** actual developments of blades For other projected area ratios increase or decrease projected area shown proportionally on circular arcs Fig. 22. — Developments Corresponding to a Standard Projected Area Ratio of Constant Value but with Varying Values of Pitch -r Diameter. Digitized by LjOOQ IC FORMS OF PROJECTED AREAS OF BLADES 209 different values of developed area ratio are laid down, thus in both cases showing that not only the resistance of the blade, due to change of surface, and in the first case change of pitch, has been affected, but it has been still further modified by the change in the distribution of this surface and the modification in the leverage arm of the blade resistance. A distinguished educator who formerly was an advocate for the use of constant developed area form in design work, has put before the public a work on propellers in which he advo- cates the use of the projected area in place of developed area. He has adopted, in- stead of the constant ellipti- cal form of development, a constant elliptical form of projected area. Should the projected area ratio be .3 its form is that of an ellipse, and should this ratio be .6 the form is again an ellipse. The same changes in distribution of surface occur as before, and no benefit has been obtained except that of having an easy form to lay down and also one that can be mathemati- cally represented. In order to maintain as constant a distribution of blade area as possible, and thus guard against changes in resistance due to changes in distribution, there has, in this work, been adopted as a basic form of projected area the form of projection of the blades of two 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. Digitized by LjOOQ IC 210 SCREW PROPELLERS Then, with the center of the hub as a center, and different radii, circular arcs were struck crossing the axis of the projection. In obtaining the projected forms for areas differing from the basic area, the widths of the projections measured on these circular arcs were made proportional to the circular arc widths of the basic projection; that is, a .6 projected area ratio would have circular arc measurements M times as great as those for the basic .32 projection. The forms of projected area so obtained, when compared with the forms of blades of many propellers, are found to agree very closely, from the lowest to the highest values of P.A.-^D.A., with those forms which have the best records credited to them. By using these forms, for any pitch ratio the resistance arm of the blade always remains the same, no matter what the devel- oped or projected area ratio, and the only change in resistance to turning is that caused by the additional surface. The forms of projection, both on the disc and on the 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 Digitized by LjOOQ IC FORMS OF PROJECTED AREAS OF BLADES 211 order to obtain graphical or other methods of design will be easily understood by examining the following figures, 24, 25, and 26, showing forms of projected and developed areas for the Standard, the Bamaby, and the Taylor forms of blades. z o z -o I- o UJ i I Fig. 24 shows the standard form of projected area marked a, and the developed areas for pitch ratios of .8 and of 2, marked a' and a", respectively, together with the corresponding pro- jections on the fore-and-aft plane. Digitized by LjOOQ IC 212 SCREW PROPELLERS Figs. 25 and 26 show equal devel(^)ed areas with Fig. 24, and the corre^xmding projected areas on the disc and on the 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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- Digitized by LjOOQ IC FORMS OF PROJECTED AREAS OF BLADES 215 trifugal action are less. With propellers of high speed of revo- lutions, this latter point is very important, and for such screws the blades should never rake. Form of Blade Sections tor Standard Blades In the propellers designed according to the Dyson method the form of section existing in the propellers from whose data the design data curves were developed has been adhered to. In these blades, the working face of the blade forms the nominal pitch surface, the blades in all cases being made with constant pitch. The thickness of the blade is built up on the back of nominal pitch face. The form of the back is an arc of a circle and the edges are made as thin and sharp as possible without sacrificing durability to an extravagant degree. See Fig. 23. The principal forms of blade section that are met with in practice are as follows: T With a small vaflue of -— from .12 to .20 at the hub, the form W A appears, from trials, to be all that is required. Where the T value of — is higher than .20 and the fillet of the blade is also W heavier it may be advisable to slightly fine the entrance of the blade by throwing back the leading edge a small amount as shown in B, but this should not be done to any great extent, as it tends to slow the blade down by increasing the actual working pitch above the nominal more than is done by ^. Section C with the following edge of the blade thrown back, the leading edge being either similar to A or thrown back as shown, is considered to be a decided mistake, since, as the water travels along the driving face of the blade from the entering to the leaving edge, there may exist a tendency for it to break con- tact with the blade face. It was to guard against this tendency of the water to leave the blade face that axially expanding pitches of blades were used. If the following edge of the blade is thrown back as in C, the face of the blade is deliberately drawn away from the water and a cavity at this edge will result, with conse- Digitized by LjOOQ IC 216 SCREW PROPELLERS quent eddying effect and resultant vibration and loss in effi- ciency. In Section D, the leading half of the back of the blade has a pitch such that its slip equals the real slip of the screw. This form is theoretically (!orrect, provided the velocity of the water meeting the propeDer is that of the vessel modified according to the wake that is equal tov—Wy but in practice, imless the blades Fig. 29. Fig. 30. — ^Variations in Blade Sections. are very wide, it gives too thick a blade and too blunt an entrance, with a consequent heavy loss in efficiency. Blades of section E, with the metal of the blade divided evenly on each side of the nominal pitch surface or plane, appear to offer less resistance to turning than any of the other sections, due probably to the fact that the real pitch of the blade is prob- ably the same as the nominal pitch, as is shown by the fact that if blades of this section, designed for zero pitch, be revolved, they will exert zero thrust, while blades of the preceding sections, Digitized by LjOOQ IC FORMS OF PROJECTED AREAS OF BLADES 217 designed for zero pitch, will, when revolved, record a decided thrust, due to the influence of the backs of the blades; the back evidently giving the blade a working pitch greater than the nominal pitch causes it to exert a thrust. While it requires less power to turn blades of section £, the resultant thrust per revolution is much lower and the apparent slip is much higher than with blades of the same nominal pitch but of different section. With blades having sections similar to F, the same results are obtained as with Section £, but in a less degree. The design curves and factors being based on the performances of blades of manganese bronze, it is desirable, when a weaker material is used, to make the thickness from the pitch plane to the back the same that it would be if the stronger material were used, and to add the additional thickness to the face, thus producing a section sim- ilar to F. Digitized by LjOOQ IC CHAPTER Xm THICKNESS OF THE BLADE AT ROOT. CENTRIFUGAL FORCE. FRICTIONAL RESISTANCE OF PROPELLER BLADES Thickness of the Blade The fiber stress to be used in determining the thickness of the blade at the root depends upon the material of which the blade is to be made and the degree of approximation of the point of design to full overload conditions. The material usually used for propeDers in the Naval Service is manganese bronze, and the specified ultimate tensile strength of the material is 60,000 lb. Where the possible overload does not exceed 10 per cent, a working stress of 10,000 lb. per square inch can be used with safety with reciprocating engines. With turbines or reduction gear this may be increased to 13,000 lb. This is the condition existing for Sheet 20 of the Design Sheets. For pro- pellers designed for about .3 load factor, ' „'^' = .3, where the power used in the calcidations may be very much lower than the maximimi power possible, this working stress should be reduced to about 6000 lb. For high speed, 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 Digitized by LjOOQ IC THICKNESS OF THE BLADE AT ROOT 219 Tr= Width of blade tangent to hub. A = (33,oooXl.H.P.d)-^ (2irXRevolutionsXNumber of blades) = 5252 LH.P.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 ! 1 1 i i 1 1 1 1 1 1 i 1 1 1 V V 1 L \ \ \ \ »k V \ \ \ \ > -> i \ v \ \ \ \ \ V \ > \ ^ \ \ V V < ^ A \ A ^^ -> ' ^' '0 I , — _j» i \ J A y \ \ t/) s! iir <! * CO LU 1— O 5) I V — 1 — Q UJ 3 z — 1 LU 8 \\ g \ \ -J D3 a. ^ \ \ ' ^ O \ t> Q. \ "S- \ {? 1 i a 1 Y 1 :p « Digitized by LjOOQ IC THICKNESS OF THE BLADE AT ROOT 221 Centrifugal Force: Increase of Stress Concerning the effect of this on blade stress, Beaton states, " Centrifugal force produces in the screw blade at all times some stress, and at high revolutions the stress becomes serious, so much so, in fact, that destruction of blades is due sometimes to this source with screws driven by turbines. "Within moderate velocities the forces set up by inertia really tend to balance those by hydraulic pressure on the blade. That is to say, that whereas the hydraulic action tends to bend the blade in a direction opposite to that of revolution, the inertia of the blade tends to make it bend the other way as well as to * throw off.' " The forces acting on a screw blade due to its velocity can be calculated from the usual formula where W is the weight of a blade in poimds, r is the distance of its center of gravity from the axis of rotation, g is gravity and taken at 32, v the velocity in feet per second: Then W v^ and the tension on the bolts=— X— , g r — being of course the accelerating force, and called usually the centrifugal force. " When a propeller is in motion on normal conditions, nm- ning at R revolutions per minute, t;=>/^tS'^+(21rr)2xi^-^6o=^\/p2+(21rr)2. "As an example take the case of a screw propeller 12 ft. diameter, 15 ft. pitch, 200 revolutions per minute; center of gravity of blade is 3.2 ft. from the center; it weighs 1600 lb. Digitized by LjOOQ IC 222 SCREW PROPELLERS Determine the bending moment on the root distance 1.8 ft. from the eg. and the tension on the screw bolts screwing it to the boss. «'=^is!+(2irX3.2)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." Digitized by LjOOQ IC THICKNESS OF THE BLADE AT ROOT 223 Frictional Resistance of Propeller Blades The following method of estimating the frictional resistance of propeller blades is given by Mr. A. E. Seaton in his work on " Screw Propellers." " Frictional resistance of a screw blade may be found by the following simple methods: Fig. 31 shows the outline of the developed surface of half a blade whose figure is symmetrical about CB. The propeller is moving at a uniform rate of revo- lution so that BC represents the velocity through the water at the tips to a convenient scale. " That is, the velocity per revolution at B and at any inter- mediate point is d being the diameter at any point taken. " If BCy etc., GK^ represents on a convenient scale the veloci- ties at By etc., G. A curve drawn through C, etc., K will per- mit of the velocity being ascertained at any intermediate points by taking the intercept between BG and CK at these points. The resistance per square foot may be calculated at three or four pomts by the rule y = i.25f — j lb. and a curve GD set up in the same way so that intercepts will give the resistance at any inter- mediate points." Now, taking narrow strips of the blades at three or four stations and multiplying by the resistance at these stations and doubling the result to allow for the blade backs, a curve HE is obtained so that intercepts again give the resistance at various stations, and the area is the measure of the total resistance of one blade. Proceed, then, to multiply the resistance of the strips as obtained above by the space moved through by them in a min- ute, and the work absorbed in turning the blade is measured by making a curve HP by means of a few of the ordinates so found as before. Digitized by LjOOQ IC 224 SCREW PROPELLERS Intercq)ts between HF and GB give the work absorbed in moving those strips through the water, and the area GBFH represents the total power in foot pounds absorbed in turning that blade through the water. Dividing it by 33,000, the 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, Digitized by LjOOQ IC THICKNESS OF THE BLADE AT ROOT 226 it being 12.33 ft- diameter with 52 sq. ft. of surface; -whereas the RatUer, of similar size and power, had a screw 10 ft. diameter with only 22.8 sq. ft. of surface, which elaborate experiments years before had shown to be sufl&cient. Moreover the Rattler had a speed coefficient (Admiralty) of 224 against that of 142 of the Greyhound, which should have opened the eyes of the authorities in 1865. With the high speed of revolution necessary for the efficient working of turbine motors, as also for the speed of revo- lution possible with modem reciprocating engines, especi- ally the enclosed variety with automatically forced lubrica- tion, propellers of small diam- eter are absolutely necessary for safe running, while to prevent cavitation the blade area must be relatively large. Hence it is found that the modem propeller is gradually getting nearer and nearer in width of blade to the common screw of sixty years ago, and differs from it now chiefly in its having nicely roimded comers instead of the rigidly square ones of that time. Fig. 33 shows one blade of H.M.S. Rattler of 1845; the dotted line is that of a blade of a modem turbine motor steamer. Now, although the difference in blade is small to look at, the action when at work is very different. The comers of the old screws caused violent vibration at high speeds; but when they were cut away there was a very marked improvement. Frictional resistance of a screw propeller may be calculated with a close approximation to the tmth by taking the velocity at the tip and the total area of acting surface, using multipliers in Fig. 32. — Estimate of Blade Resistance. Digitized by LjOOQ IC 226 SCREW PROPELLERS both cases deduced from the close calculation of it with screws of diflferent types. Let V be the velocity of the blade tips in knots per hour. Let R be the revolutions per minute. Let D be the diameter in feet. Let P be the pitch of screw in feet. Let A be the area of acting developed surface in square feet. Fig. 33. — ^Antique and Modem Propeller Blades. The resistance of a square foot is assumed to be i J lb. at 10 knots. 6080 101.33 lb. Resistance per square foot = 1.25/ — ] Resistance of screw = 2^X1. 25/ — j X/lb Digitized by LjOOQ IC THICKNESS OF THE BLADE AT ROOT 227 For a common screw /= .6034 For a 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. Digitized by LjOOQ IC CHAPTER XIV CHANGE OF PITCH. THE HUB. LOCATION OF BIJU3E ON BLADE PAD. DIMENSIONS OF THE HUB Very often, upon the trial of a vessel, results indicate that improvement is possible if the propeller blades be set to a higher or lower pitch than that of the designed driving face. In order to provide for such a change, the bolt holes in the blade pads are made oval, so that ordinarily with large blades the blades can be twisted to mean pitches of about i ft. more and i ft. less than the designed pitch, the new pitch becoming a variable one. If the blade is set for a higher pitch than the designed, the new pitch becomes a radially expanding one, increasing from the hub towards the tips, while if the new pitch is lower than the designed, the pitch will decrease radially from the hub to the tips. The change caused by alterations in pitch may be obtained from the following table (Table X), (see Peabody's " Naval Architecture ")> by multiplying the original pitch -^ diameter by the factors given in Table X for the small angle through which the blade is twisted. The Hub In designing screw propellers it was, up to the advent of the turbine, the custom almost invariably to design propel- lers of large diameter with the blades detachable from the hub in order that injured blades might be replaced at little expense, sQid also that improvement in propulsive efficiency might be sought for by providing for slight modifications of pitch in securing the blades to the hub. Only in the smaller wheels were the blades cast solid with the hubs. With the pitch ratios ordinarily in use with the comparatively high pitch, slow- turning 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 :: niSSSS w ■ 1 :: 11 i: ■■ ITMBIBKI 80 H :?:::» : » :::»:! 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 ;:; ■■■■ [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. ::jz:: :::: :::j::: — 80 1 : : mr 170 \ :: .:: :::::X 160 :: ■.-.:::-,i::::z 18 :: (a)\i'-- ---■ ■■■■------ :g:::::;::::::::: 1(tf) V" 16 : Is ||||l||| 14 ± :::!:: -■A s — ---- u 140 :: 12 l\\\ [ 5 - - - :: 130 \[l/ -S 1^ 10 1 = ifHIIII — Ts-- : - ™^ "™^:Tmfi iff 110 8 :E ^ m:. rtn Ttll '-^rr. -■[--/ : ■■■■k': 'a [W^NIIIII .: ..dz : :;:;;!|=i;:;; 6 :: z\f'\ : ;:===?^ 100 :|:: — ^ W^ 90 -- : :::: . iH# :i^^ 4 : = \^ H 1 1 III :: ::? L<^ : = nmn :::m "■■■^'^ 80 :::_:__lsLQr'^ i "r^^w --:i|f 2 -r--H^k > ^ m¥ :: :::5:::::: [Inutea. 70 ~ =^ ili^ :: |::'s:::: :- fm- ffl lllllillrilM H4444^ 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. Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SfflPS 247 In the early part of this chapter it was shown, by experiment, that the Jupiter r.p.m. dropped to about 68 per cent. If reverse torque is now appKed to reverse the screw and is gradually increased, the r.p.m. will gradually slow till a point is reached where the propellers are making 40 per cent of the ahead r.p.m.; at this point about 95 per cent of the ahead torque will be required; from this point on down to stop less torque will be required to slow the propeller; when the propeller becomes stopped the torque has reached a minimum, and will rise again 3.50 ShlpC k>infirAI teadat 8.00 \ i;: Cod stant Si eed. 2.50 2.00 L50 ;;: j^;; ; :;:-; k 1,00 M ' " ■ % :;.-:: ^ .50 M : : « i : : =;::::;:: _ -.10 -.8 -.6 -.4 -.2 .2 A .6 .8 Per cent Normal FuU Load B.P.M. (122.2 B.P.M.) Fig. 40. XO if the screw is actually reversed. The curve given was plotted for the condition of ship going ahead at 21 knots, but it is ap- proximately correct for all speeds, as will be seen by following out the various speeds in Fig. 39. In Fig. 41 is given a similar torque curve for the Jupiter. This curve was determined by ex- periment in the following manner. With the ship going ahead at 14 knots power was suddenly thrown off; the propeller speed dropped to the point marked zero torque. The excitation of the generator was then reduced as much as possible and the backing switches thrown in; the propellers kept revolving ahead and the Digitized by LjOOQ IC 248 SCREW PROPELLERS excitation was gradually increased till the propellers just passed over the maxuniun torque point and started to reverse; the excitation was then reduced to just enough to keep the pro- peller stopped. There were two points for the stopped condi- tion, one at which the propeller would just start revolving ahead and the other at which the propeller would just back; the curve has been run between the two points. At each point the elapsed time from the beginning of the experiment was taken and, by PROPELLER TORQUE CURVE Ship vol Iff ahead itCk>n«ta It Speed 2U) y L5 mm :: :::::: Minimal 1 PropeU r Torqa< Tow netoDrJ 76 Ahead r \ ^ :::::- wl Si lie Blowi fc J! \^. A mi Pro att seller Jai lisTor^ kbacta, e — nrr ii: :::: f' 1 II :::!l i m L.4 ,...4 + ■■ Propellc at this 1 rjuatsta bivae ta ahead -S -^ -^ ^ A .6 Per cent of Full Ahead B.P3f . Fig. 41. LO means of the retardation curves in Fig. 42, all points were re- duced to the same speed. The curves in Fig. 42 were made up from " dragging " data taken at the time and from the retarda- tion curve given in Fig. 35. The torques at the two points, that is the maximimfi and minimum points, were determined by the excitation at these points and were obtained from the torque curve of the motors. Fig. 43 shows this torque curve of the motor with 245 amperes excitation; the torque for the actual excitation used at the various points was assmned to vary as the square of the excitation. It will be seen that the curves in Figs. 40 and 41 are similar, but that the actual screws have a maximum Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SfflPS .249 point (during reversing) that is lower than the model; the model shows a maximimi point of 95 per cent while the Jupiter's max- imimi point is only about 75 per cent. Trials conducted on other model screws in the model tank showed this point to vary from 80 to ICO per cent. The data obtained from the Jupiter would indicate that these values are too high. However, in REVOLUTION DECELERATION CURVE designing induction motors for backing it is not safe to have the torque on the "out of synchronism'' part of the curve drop below 100 per cent of the ahead driving torque. That will insure a safe margin for getting past this " himip " in the torque curve. The second phenomenon of the torque curves of Fig. 39 is illustrated in Fig. 44. This shows a ship backing with a con- stant nimiber of r.p.m. from any given speed till the ship is stopped. The r.p.m. assimied are those which will give 100 per Digitized by LjOOQ IC 250 SCREW PROPELLERS cent ahead driving torque at the instant of backing. This curve is approximately correct for all speeds. From it it is seen that VCDUJtoTnBT lQ9oni*9nluox the torque necessary to txim the screw at the given r.p.m. falls as the ship slows till about 22 per cent speed is reached, when the torque begins to rise and continues to rise till 5 per cent speed Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SHIPS 251 is reached, when it begins to fail again. This curve was also verified by experiment on the Jupiter. Fig. 45 shows two sets of backing trials conducted on the Jupiter, These were made with the ship going 14 knots and then suddenly reversing, using^ the resistances in the motors, and keeping the generator at a constant speed of 1950 r.p.m. and a constant excitation. Under these conditions the speed of the motors would be determined by the intersection of the 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 Digitized by LjOOQ IC 252 SCREW PROPELLERS going ahead for this test was 39.5 r.p.m., or 5 knots, and the actual r.pjn. when backing was 39.5. The curve was obtained BACKING AT 14 KNOTS. Generator Speed Oonstant, 1960 R.P.1L 1st Trial Excitation 245 Amperes. 2nd Trial Excitation 225 Amperes. ERiip Stopped in About 4 Min. 45 Sec in Each Oaae Resistance Kept In AU the Time. by taking H.P. and r.p.m. readings every five seconds and reduc- ing the H.P. to torque. The curve obtained from the Jupiter is similar in oil respects to that obtained from the Ddamxre's Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SHIPS 253 model. The minimum torque comes at 65 per cent for the Jupiter and 60 per cent for the Delaware; the maximum point comes at 12 per cent for the Jupiter and 15 per cent for the Del- aware, The maximum and minimum torques, however, are much lower in the case of the actual screw than in the case of the model. From an inspection of Fig. 39 it will be seen that the condi- tions of (i) ship going ahead and propeller going from ahead to astern and (2) ship going astern and propeller going from astern to ahead are similar and should give similar torque curves when plotted. Also that the conditions of (i) ship backing at con- stant r.p.m. from any speed ahead to speed astern corresponding to the given r.p.m. and (2) ship going astern at any speed and propellers going ahead at a constant r.p.m. till ship is stopped and brought to speed ahead corresponding to the given r.p.m. are similar. To illustrate these points Fig. 57 has been plotted. This curve or set of curves takes the screw through the entire cycle of conditions. It is made up of the various curves that have already been considered. Starting with the ship going ahead, the screw is suddenly reversed and brought up to revolutions which will give the same torque as was used when going ahead; holding these revolutions constant, the ship is backed till she stops; this is further continued till the ship picks Xip speed astern corresponding to the revolutions; the screw is then suddenly reversed and revolutions brought up to those which the problem started with (the latter part of this curve is taken beyond prac- tical limits of actual screws as it runs the torque up too high, but it was chosen so as to make a complete cycle and end up at the starting point); these revolutions are maintained till the ship stops; they are continued further till the ship picks up speed corresponding to these revolutions, which brings conditions back to the starting point. Part i shows the cycle through which the torque passes while the screw is being reversed. Part 2 shows the change in torque while the ship is slowing down, backing at constant r.p.m. Part 3 shows the ship picking up stemboard with screw going at same r.p.m. Part 4 shows the Digitized by LjOOQ IC 254 SCREW PROPELLERS torque cycle of the screw when it is suddenly reversed to go ahead, ship still going astern. Part 5 shows the torque cycle while the ship is slowing down, propeller going ahead at constant r.p.m. Part 6 shows the torque cycle of the propeller while ship is picking up speed ahead, propeller turning ahead at same revolutions as before. From inspection it will be seen that parts I and 4 are similar curves, parts 2 and 5 are similar and parts 3 and 6 are similar. Part 5 was taken so far over on the chart that it does not show the drop in the torque before the rise comes, in other words, it is part 2 beginning to the left of the minimmn point. Parts i, 2, and 3 have already been verified by test on the actual screws of the Jupiter, and to make the veri- fication complete Fig. 58 is given. The curves obtained here were obtained imder the same conditions as those in Fig. 45, that is, the generator was kept at constant speed and excitation and the motors were nm with resistances in; under these con- ditions the speed of the motors would be determined by the inter- section of the propeller torque and the 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 Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SHIPS 255 till the ship is stopped, some cases of actual backing will be taken up. As previously stated, the power any engine is capable of delivering while backing is limited by the maximimi torque of the engine. To make this plainer the engines of the Delaware are taken as an example, and two theoretical indicator cards have been constructed and are shown in Fig. 46. The heavy- line curve shows the card when going at full power, the data for the card being taken from the 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. Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SfflPS 257 Fig. 47. Digitized by LjOOQ IC 258 SCREW PROPELLERS Table XIV "DELAWARE," BACKING Knott. I.H.P. I.H.P.X P.C. E.H.P. (aUapp.) Total H.P. a Interval Time in Minutes. Total Time. 31 19 12,500 8,170 9,900 18,070 7.9 .2925 .2925 x8 12,66s 8,275 8.500 16,775 7.7s .1276 .4201 17 12,825 8,400 7,225 15,625 7,65 .1299 .5500 x6 12,990 8,500 6,000 14,500 7. S3 .1315 .6815 IS 13*150 8,600 4,900 13,500 7.48 .1331 .8146 14 I3»3i5 8,720 3,900 12,620 7.49 •1335 .9481 13 13^75 8,820 3,100 11,920 7.62 .1322 1.0803 12 13,640 8,920 2.430 ",350 7.85 .1292 I. 2095 IZ 13,800 9,030 1,880 10,910 8.24 .1242 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. Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SHIPS 259 From the values of a given on this curve a retardation curve has been plotted on Fig. 49. This curve shows the total time to stop the ship to be two minutes three seconds. The actual 18 - IP - 11 " lO - ::::::::: ;.±::::: -5 -4k'-~-'.Z --JI 1 10 - Ul4l- :-|;e;e • ---.: _: j::::. .-.±::: _: i::: g - 1 ::":::"j ■ A - V :_: 5 : ::: 4 - l nJl L. .::::::::: : ":: — -,-.- ,.... 2- --- = '-::■- ;::=:=;;;:;;;:;::![:i:;==;:;;;;::;: _.| - III III III 1 II IIIL1II III II II III II II U 24 34 44 54 a Knots per Hour j;>er Minute Fig. 48. 64 U 84 time as measured was two minutes 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 : .: rFKi ill ;::-: ■ 4 1 i|;:;;;;; 2 WM m 10 15 Minutes Fig. 49. 20 due to the large maximum torque of the induction motor. It has also been assumed that the ship drops in speed to 20 knots during the act of reversal. The values of a have been plotted on Fig. 50 and from these values the retardation curve has been plotted on Fig. 51. This curve shows the time necessary to Digitized by LjOOQ IC STOPPING, BACKING AND TURNING SHIPS 261 bring the ship to a stop to be i mmute 50.4 seconds. It is realized, of course, that this condition may not be entirely 20 40 eo 80 100 €C Knots per Hour per Minute Fig. so. 120 liO W reached, as some reason (such as propeller vibration) which has nothing to do with the engines may make it imdesirable to use this much power in backing. Digitized by LjOOQ IC 262 SCREW PROPELLERS Table XV "NEW MEXICO," BACKING E.H.P. B.H.P.(all) S.H.P.X Total Mins. 1 ^ixne in Knots. (Bare Hull) 14,9 per C«nt. App. P.C. H.P. a (Interval). Mins. ai 16,300 18,740 0,000 20 13,400 15,400 18,740* 34,140 8.87 .232 .232 19 11,200 12,880 18,740 31,620 8.65 .114 .346 18 9,400 10,800 18,740 29,540 8.53 .1165 .4625 17 7,800 8,960 18,740 27,700 8.45 .1178 .5803 x6 6^50 7,300 18,740 26,040 8.45 .1182 .6985 IS S,ioo 5,860 18,740 24,600 8.52 .1178 .8163 14 4,100 4,710 18,740 23,450 8.70 .1162 9325 13 3,250 3,730 18,740 22,470 8.97 .1132 I 04S7 xa 2^50 2,930 18,740 21,670 9.38 .109 I 1547 XI i,9SO 2,240 18,740 20,980 9.90 . 1036 I 2583 xo 1,500 1,720 18,740 20,460 10.62 .0975 I 3558 9 X,10O 1,260 18,740 20,000 "•55 .0843 I 4401 8 775 890 18,740 19,630 12.75 .0823 I 5224 7 525 600 18,740 19,340 14.35 .0738 I 5962 6 325 375 18,740 19,115 16.55 .0647 I 6609 5 175 200 18,740 18,940 19.70 ■0551 I 7160 4 75 86 18,740 18,826 24.40 .0453 I 7613 3 50 S8 18,740 18,798 32.55 .0351 I- 7964 2 25 29 18,740 18,769 48.75 .0246 I. 8210 I 10 12 18,740 18,752 97.50 .0137 I. 8347 18,740 18,740 .00530 I. 8400 Turning It has always been known that when a ship turns, the mboard screw slows down if the throttle is not touched during the turn, as is the rule ordinarily followed. In the case of an electrically propelled 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 FU 1 ifi -s 10 16 14 — 1 — — ^ — Mlllllllll 12 iKI """'" -^-■■^■-■iiiiiiiii — » — — s — ^... :::::::S:: . -^ . ... — ^ 11 "5 X.L :z::\::z:: ^ - 1 ::::z::\:: o ':::;::;:: n ::::::::: JS& .50 .75 1.0 Minutes. Fig. 51. 1.25 L50 1.75 2. that, for speeds above lo knots the tactical diameter is prac- tically the same, whether the turn is made with r.p.m. constant or whether the inboard screw is allowed to slow down. In the turn at 12 knots, with i6° rudder and r.p.m. constant, it will be Digitized by LjOOQ IC 261 SCREW PROPELLERS seen that the I.H.P. of the inboard screw rose steadily as the turn progressed, and that the I.H.P. of the outboard screw first dropped and then rose steadily as the turn progressed. This latter peculiarity is not observed in the curves given on the 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 I < 00 ^ 9 -8 *)s«inajoj »« r- pajns«9ax 9i8u« %jup p»n|ji ^ •^ ^ N w> <* •ttinj uo poodB |BUi^ « t^ 00 o M Ok r^ so S "ro so ^ « 00 'Sunun) joj axuix ^ •o Vi « lO o Vi M O so t* H Q 1 M •^ 'ja^auzBTp iBuij 1 o o 1 1 o o M M i >* & •VOd « ;§ t S •pjBOqjB^S so s 5 S »o •^ r« o M m Q •Suiuan; joj acaix lO O *o M O lO l/» o •* w> ^ f*J ua^auxBip iB3i;3«x 1 o o ^ 1 o o M M •^ «« •»JOd lO Vi o « ^ = ^ Vi o O •o pEi H •pjBoqjB^s o J « ^ = 5 S t^ O »* ^ 00 o \i •Suiium JOJ auxix o ro w> o o Q >0 n fO w w « w» tfi o „ o o •jajsuBJX § •^ ^ '33n«Apv s o o o M 00 SI -s ■o ■s e 1 •^roj d :3 1 1 1 -a II <J 1 1 1 C o 9 Ji s •pjBoqjB^s 5 "S iS "S 5 o i g i 8 > ^ & H S p§ 1 uaAo ^nd o^ auiix 5> « « « o « •ai8uv o M M M ^ •uoi;oaj|a I ■s 5 ■§ d d !e :i •pjBoqjB^s s « S :§ ;s ^1 'M9J3S pjBoqjB^s s ;§ s s |S •pwds o o M M >4 •UIU JO jaqinnu iBuag 1 - «« ro ^ WJ « 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 ill!;:::! A nnn i-rM iiiiiiiiiLHii #fl ^ : ; r : : :: : : Starb'd. 1^ Enoltanil icrtoStarb^ 8,800 I ^:::::::::itHftttt ::::::z:: in — ^ — /I :::;!:::::: 3,fl00 - ' ■ HHIIIII ^ — W TT /f ::::::::j:::::^:::: : 3,400 !_.-.?_.:_: - : = = : = = ::::. ^: = ::: = : : f w j- -, . 8^::::^f::(:::::::::: :|MMm|^|||j||| H 3,000 y^M ILf ...,«: Port, l4Ki ottnrnlDK o8tarb*d. — Mm ----- ittit KmWff mmijiii4m- 1 ft:::::::::):::::: ::::;<?!.:: starb*d.l^ Knotturnl tgtoPort, 2,800 *:::::::::>:::::: |::::::::^:::::! ; E ) ^ - \ / yf f IN / LK ■ : 8.000 E^::::!::::;!::::: : :(:-::::::(:::::: : :: "" S" " " ;z ■" :: — ... 2i«0 - -- 2 3 4 Minutes 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 ent JOX1 1193 J» J 2 ~¥ pl !? o 1 fl ^ 1 n H L M^ Hi II 1 11 n 1 P4 1 + 5 1 «a II I *-! m HI 1 1 1 A ■ 1 1 1 , 91 O s ,,a» o ■ rA 1 1 JO. _ 1 1 CO ■ ■ li + 1 -I- 1 1 + a 5 1 1 & I 1 1 o jaj 1 r 9 T h 9t bJox luaD 19^ 1 1 § s § S g § s. 2 ^f^ ¥ "S. ? 8. s Digitized by LjOOQ IC 272 SCREW PROPELLERS 1 1 1 II 1 1 ^m jjUjj^ 5 «•« I i a o m I £ ^ _iPi^ 3 E"' .-T*"'*'"^ n fe^^n.j^r^iiE m ps^n -'' ,:J «? ' p ' "■! 1 If * • J / ! ' 1 ? — -' • 1 1 J^ 2^ ! 1 ■ S I " 1 1 I \i ■ ■ . \i ■ ■ 1 1 1 1 iN|.-; i f 1 ,1 H ' i — • ,- ^ — ^ %:^ 1 ^5 : >^435« i 9 1 iSlFI 1 £ 1 r !^. •tf ' ' .>ftv\4V>' •^h^.f-'^ "^ ^ J ^: %" _i«. ii. ^: ^. •^ ^ i^ * * "^ t 1 Digitized byCjOOQlC STOPPING, BACKING AND TURNING SHIPS 273 ^ I g 8 s s g a^n iIW* dsnci A.aH a ■ ■ II 1 1 1 1 1 ■ 1 I 1 fjjjijjl ^M 5 , —5— 1 n.8 I muni ^ffi 1 H 1 mijUji H[i[IHI g a- mm ^R ijlHIJI jjljlljl I ■ mm ii[i|iiii lllM Wn i Ttttnti B B B Hi B 1\ I mm mm ■ w »o f-4 ■ II ap I I s s _S s 5 s 5 k1su< 8 8 a S lO "W— ^ Digitized by LjOOQ IC 272 SCREW PROPELLERS "*""^ UMtitf^n "i ilJflllHllIU * . in? 4 J "g [^lllllll ^m m o , ^M ^1- iiiiiffli . L 1 -^.t *9- £ 1 Ti 1 1 .1 1 1 1 fij — 1 ^^ ♦ e -«8- tk 8 -^1 m P4 m aibjc .,»n8 : joa s_ f I 1 s \ I 1 a ! ! « 1 S «? ? 8 " _ to I Digitized byCjOOQlC STOPPING, BACKING AND TURNING SfflPS 273 J2 g s S !? 9)111 ^9 9 is SI I « 8 ■ ■ 1 1 g 1 mm ^Bi mm Hi ■{fflf 1 ^H|| 11 |l|Ht[|[|||||| 11 1 |H 1 J s llllll s imlllllllll 5 j 1 -—5— ■1 1 1 H 1 i ^L »!? ■ II ■ ■ B WM WM 1 d ■tttt ffi ii 1 fl n H llljlllH m Unttllttttlll mTTIT inimii jlljijUl 1 J a- "5 1 ■B 1 H I'll 1 ^'^ III 1 «^,— H II P9 1-3 iS s ¥ ? s 8 5 Kl8U( l^nioAa !3 8 JS s lO I Digitized by LjOOQ IC CHAPTER XVI liATERIALS FOR CONSTRUCTION OF AND GENERAL REQUIREMENTS FOR SCREW PROPELLERS Material of Blades. The materials of which propeller blades are made are cast iron, cast steel, forged steel, manganese or some other strong bronze, and Monel metal. Cast iron is used for the blades of propellers which work mider conditions rendering them very liable to strike against obstructions. When so striking, the cast iron being weak, the blade breaks and, by so breaking, saves the shafting or th?engine. Its disadvantages are extreme corrosion in sea water, heavy blade sections, and blimt edges 'due to the weakness of the metal. 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 Digitized by LjOOQ IC MATERIALS FOR CONSTRUCTION 275 Monel metal is extremely strong and tough, pennits of very light blade sections and sharp edges, takes a very high polish, and is practically 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 Digitized by LjOOQ IC 276 SCREW PROPELLERS balance will produce excessive vibration when the speeds of revolution are high. In some cases, in order to insure a smooth blade surface, bronze blades have been 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. Digitized by LjOOQ IC CHAPTER XVII GEOMETRY AND DRAUGHTING OF THE SCREW PROPELLER Geometery of the Screw Propeller The geometrical construction of the screw propeller forms one of the most interesting problems for the engineer and the draughts- man; it is also of equal interest to the patternmaker and the foundryman, who are called upon to produce the structure itself from the plans. Therefore, a thorough imderstanding of the methods employed to generate its construction should be useful to all concerned. The screw propeller of uniform pitch is the one which is gener- ally accepted by engineers for the propulsion of ships, and this is divided into two distinct types, viz.: propellers having the verti- cal generatrix, and propellers having the inclined generatrix, the vertical generatrix being preferable for twin or other multiple screws where ample clearance between blade tips and hull, and between leading edges of the blades and the after edges of stmts exists, while the inclined generatrix has advantages on single- screw vessels where the propeller is working behind the usual stem post. In order to make the constmction of the various types referred to as clear as possible, diagrams have been prepared which show the methods involved. Also, drawings of various propeller giveels have been made which conform to those diagrams, thus whing a very definite idea of the whole subject. One of the simplest methods of making a screw propeller, viz.: that of sweeping up in the foundry, will probably afiford a good illustration as to how a tme screw may be generated. Suppose, as an example, a propeller of 12 ft. diameter and 12 ft. pitch be taken, which means that the propeller must make one complete 277 Digitized by LjOOQ IC 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 <* 1 N ^ P ^ .^ p > 1 < Ci« im. j^l 2 IT Fig. 6o. ff V 1 ^ r ^ Sweep eLine Fig. 6i. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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). Digitized by LjOOQ IC 282 SCREW PROPELLERS The radial lines a, b, c, d, e, /, in the plan must correspond to radial lines a, h, c, d, e, /, in Figs, i and 2. Project from the intersection of the arc of the full radius with lines a, by Cy d, ty /, Fig. I, to the corresponding lines a, 6, c, rf, Cy /, Fig. 4 laid oflf from the 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. Digitized by LjOOQ IC GEOMETRY AND DRAUGHTING 283 Number of blades 3 Diameter . 17' 6" Pitch 18' o" R.P.M 117 I.H.Ptf 14,700 — total 2 engines I.H.Pd 7350 — one shaft P.A. The geometrical construction is laid down for the vertical generatrix, and on this plot the form of projected surface. Sheet 32 is the sheet to which the following work applies: P.A. D.A. From Sheet 25 — ^Determine the chords of half arcs for = .32 — 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. Digitized by LjOOQ IC GEOMETRY AND DRAUGHTING 285 Zr = Sine of arc whose tangent is 1^=36®— 34' = Sine .5958. Jlf = Cosine of arc whose tangent is -^=36°— 34' = cosine .8032. N=LXJ = component of fore and aft moment normal to face of blade at root = .5958X1, 802 ,400 =1,009,100. 0=JlfX£=same for athwartship moment =.8032X802,800 =644,800. P = N+0 = total moment at root of blade in inch poimds = 1,009,100+644,800 = 1,653,900. /'=Fibre stress = 10,000 as e.h.p.-=-E.H.P. = i.o. r- J^ X^3>i25 _ J i,653,900Xi3,i25 _^ .^//. ^"■\"irx7 ^ 40x10,000 "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. Digitized by LjOOQ IC GEOMETRY AND DRAUGHTING 287 STANDARD PROPELLER HUBS For Solid Propelleks— Plate B r }J ^l.-^ L-T 4*- tr J ^ D Di Dt H L Li L2 Li Li Li AT Ni Nt Ni Ni PD R 5 Above 3- 4" inch 4~ S 7f 4* 6i 61 8i 9* 12 4l 5l 3i 4l 5i 6* 4i 5i 61 7* iH 2A 3 3* I* 2A 2| 3A 2 2* 3 3* 4* Ti 2A 3A 4 S- 6 o| 7* lOj 13J 14J i8i 6J 81 Ti "- 6- 8 II* lOi I* 3A li 4A i 8-10 isi I3i 17J 24 iiA IJ 4l I* 5* 8* 10* 5* 4* Q 5A 6 10-12 18* i6i 21J 29 I3i 2 sA itt 5« lof 12* 6* 5 1 61 7* 12-14 22J 20 2Si 34i i6i 2i 61 2A 6f I2| 14* 7* 5l 7* 8* 14-16 2Si 22^ 29 39* i8| 2i 7i 2* 71 I4I 16* 8* 6H s 8* 10 16-18 28* 26 33 45 21 A 2| 8A 2« 8A i6| 18* 9* 7H V 1 11* 18-20 32i 29i 37 SOj 24 2i 9A 3A 9A i8i 20* lOf 81 lA 12* 20-22 3Si 32i ♦oj ssl 261 2j loA 3* loA 20J 23* iij 9tt 2A 14 22-24 38J 3Si 44* 61 29 A 2| II* 3H 11* 22i 25* 13 10* 3* 15* D T di a 2 No. of di d. d» / ; ki / m r n rt n Above 3- 4" incl. i 1 6 A 1 3i i i t555?55H* 3 «o 1 fV * 1 4- 5 i i 6 1 A 4i f A \\ II II II II II li II ^-Q * 1 A 5- 6 1 1 6 i i Si * A iv'i" 4 1 A 6- 8 lA 2 1 1 1 6 * 8 A A f 7 I 8ii A * * ^ggggggg •l> ^ i 1 i i 4 1 1 8-10 55t?iiii * 10-12 12-14 2j 3 f 1 I 8 I 10 i * f * 9jl 10* I * A * 1 M M M M CI C^ ' 'JJJJJJ I * lA * i * I 14-16 3l * I 10 H I 12 2 A "to U5 r- w U5 1^ 1^ : § «9 J I 1 lA H I* 16-18 3* ii 10 tt I i3i2 ii* M M M W W 4 1* lA I* 18 20 4i *i 10 I I 14*2 * 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* lSi-i5i 8} 7* 26* 26 A 9* 8H 17A 10* 3* 4* 4tt 4f *6A 3* iSi-i6| 9i 7A 27* 27* % 9* 9* 18* 10* 3* 4A 4* 5 6tt 3* I6i-I7i 9i 7« 28 H 28 A 10 9* 18 tt II* 4 4A sA 51^ r7* 3* I7i-i8 10 8* 30 29* 2 io| 10 19* II* 4A 4* 5* S* 7* 3l X8 -18} lOf 8* 31A 30* i 10* lOl 20 A 12* 4A -4tt sA 5^ r7» 3* I8i-I9i 10! 8H 32* 31A iiA 10 H w* 12* 4* sA 5* 5*^ \1\ 4 I9i-I9} II* 9 33* 32* iiA iiA "A 13 4* 5* stt 6 8A 4* I9f 20§ Ili 9* 34* 33** iiH iiA 22* 13* 4tt sA 6 6* 8A 4* 20|-2I III 9H 35* 34* 12A II* 23 14 4tt s» 5A 6* Stt 4A 21 -2li I2i 9* 36 A 3SH 12A 12* 13 tt 14* SA 5* 3* 6A r8tt 4A 21I-22I 12} 10* 37* 36* 12H 12* 24* IS S* Stt6A 6* 9A 4tt Digitized by LjOOQ IC 282 SCREW PROPELLERS H '<^ 4 Plated Digitized byCjOOQlC GEOMETRY AND DRAUGHTING 293 STANDARD PROPELLER HVBS-CotUinued Si 9i-iOl lol Ilj 1 1 i- t J 14 -Mt Mi -IS* iSi-i64 i6i-i7i I7i-1K 2ot-ai 31 ^3Ti da ifi di 714^ 714^ 7i4ii 7t4^ 714'^ Tiid ?I4^ 7M^ 714^ 7:4^ 714*^ 7i4fi 7i4ii 7M^ 7141J 714*^ 7M^ 7UJ 714^ 714^ . i4J^ . M3rf .i4Jrf . I4jif .14,1(1 . I4jd . MJd , i4Jt^ -143d 143^ ^14^1*^ . 14.W . t43d .143*^ . 143d 143 J .I43£' ► 3 43^ .143*^ 143^ aR6d :iE6d 2 SO J aS6J aS6J!/ 2&6d 2EGd 3^6d 2&6d 2Md .2»6d 2&6d . 3S6fJ 2»6rf .2&6d 386d ,2S6cf ,286(1 ,386ff (fT ii jii / /i ik Jki J Jt A ♦ * 1} h3S7<^ .64Jrf i^ iV A A lA JS7rf .64J'' i| 1 A lA 357d .643rf 1} I i iH 357^ .64J(i i| i I ij 357^ .<i4jd li A t ti ,3S7d .fi43'^ 1 j A H J 357d .64a£i ^1 ^k !i :| 2* 357*^ M^d tj * 1 2A 357-^ .fi^sd i| J i 2A .357*^ .&43J 2 i H =! 357^ .643d 2 i\ fl 2i 3S7d ,643^ it\ A i 2l 357^ .643*' 3| A * 3t 357d .tjA^d jj A H Zi 357^^ .t43d ij H ^n .357^ .643(f ^i r 3 357*' .04J^ ^t I 3i 3S7*' ,64Jii ^t lA 3i 357^i .&43d 3} tA 3} .357d ,64Jd 2| li 3A ► 3S7tf .64jcf J It jX 3A '3S7'' .&43'^ 3 lA a 3t .357d H 043 if 3 D h Jbj J^ ki fe ki i m r n fs ( ii Ji H U A t| A SS7^ .2&6d "^ ^ H* 3A f] A It A 1 8i-9 H i It 4 ■ SsTrf .2iifjd It 1 l[ ifl 3t i li i 1 9- 9\ I i lA t .BS7J . 2&(id 'J d u J3 33 1 It 4 t gi-ioi I A It A 8S7J .2a6d K) 4l I t* A A loi-ioj a A i| A 8nJ . aftfir; t^ s ei > 4l r a A A loi-iii U i lA 1 ^SS7J .2&bd J "j ■0 4! I iH A A Ill-15 il I iH 1 .8s7J .28f^(/ ^ ^" 4 4J 1 It H 3 A ti A 12 'I2| il ti It H .RS7*^ .3B^d « H^n 1-^ Si li it 2A h A 121-13 J Tf I it t .857rf .2&6d ^ 5l lA 2l } A I3I-I4 IlV 1 iH 1 .857^ .28^d £n Si lA 51 1 A 14 'I4i iJ H 2 » .857^ .3RfiJ S« 6 lA M 2t ii A i4l-lSi tA i 3t 1 857^ .a86d CTj = t 6A lA it aA it A iji-ui M i at 1 .Bs7d .286 J ^L^ E^ 6A ti I ^H A A isM&i tH t* ^A tt .357J -fl86d II ir B £ 6ti li I 2it it A i6i-i7i ^ tl 3 j tt .857^ . 286d J iJ U in 6H ! i\ lA 3{ H I ni-ia It* I ^A t ,es7rf , ^BOd 5:5 ^S 7i i| lA 3 1 t 18 -tg| ti t 3A r .Ss7rf . 3a6d ^ \i" a 7i a n 3t i t 18*-I9i lU lA 2| I A ,8S7ii . 2Sfid on"? 4 7l a ' a 3i H i ipi^ioi 2 tA 2| lA .SS7d .2Sbd J ;l J g 8 lit li 3l A A iSpi-aoj a il 2U It .857^ .2f^d ^0 r% 8i lit It 3^1 A A »oi-2i 3t lA 2i I A .857*^ .2%tid S 8i lil lA 3A i» A 2t ~Jl4 jA lA 3 lA .8S7'' . 2^(td ^^^ 8i iH <A At H A aH-33S 3t It 3A a .857 J .286ei pt, fj U M 3t t A 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 m 11 1 1 II 1 %000 I 95 •tt d R<|. 6 1 S ' \:: VMO 1 90 B liitiiiiii IB II i:::il 1 II II 1.000 1 4 i I < } 7 fi s > li 9 1 I Scale of I>itoh in Feet. Fig. 62. Should it be desired to increase the projected area ratio of the propeller in an attempt to obtain a higher propulsive effi- ciency, any load factor lower than that corresponding to the above propeller, whose load factor is somewhere between '\' = .5 and = .6, may be taken and used as constant and the second step undertaken, as follows: Digitized by LjOOQ IC AEROPLANE PROPELLERS 301 SECOND STEP e.h.p.-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" Digitized by LjOOQ IC 302 SCREW PROPELLERS Log Av^ for values beyond i8o miles is found by means of the equations given for the same purpose under hydraulic propellers. VariaUans in the computations produced by the change from two- to three- or 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. Digitized by LjOOQ IC AEROPLANE PROPELLERS 303 Such problems are denoted as problems of " full diameter," and the method of procedure will be shown by the following computation for a full diameter 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. Digitized by LjOOQ IC 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 Digitized by LjOOQ IC AEROPLANE PROPELLERS 305 D (assumed) , V (stat. miles) V (knots) e.h.p.-^E.H.P. (assimied). . . . Z (Sheet 2i) S.H.P.d S.H.P.=S.H.P.dXio^ v-^ for 1^ (Sheet 22).. V (knots) S.T.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: Digitized by LjOOQ IC 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- Digitized by LjOOQ IC AEROPLANE PROPELLERS 309 menting the pitch. This gives the blade a sort of unstable pitch which may introduce heavy strains and resistances to the turning of the propeller at the moment when highest turning speed is required. In order that the pitch may remain imaflfected by bending or deflection of the blades under load or increase of load it is necessary to dispose the centers of pressure of the sections farthest from the hub on a line curving somewhat rearwardly in the direction of the trailing edge. Variable pitch propellers are designed by so far extending the. rearward curvature of the blades that the application of working blade pressure will institute a torsional action on the entire blade causing its pitch to increase or diminish in response to variation in pressure. In this torsion design for variable pitch the portion of wood em- ployed in the curved trailing edge of the blade is steamed and bent so that the grain of wood parallels the curved edge of blade. In this process a slight compression is given to the fibres which greatly increases the endurance of the thin edge portions of the blade. Nearly every kind of wood has been used in propellers. Walnut and mahogany have long been favorite in Europe. The experience of one noted builder rules out all wood that was not quarter sawed and points to American quartered white oak as the surpassing material from every standpoint, the particulars of which need not be detailed here. It is almost needless to say that the wood for air propellers should be selected and treated with utmost care. The boards are sawn to i in., rough dressed to | and finish dressed to ^ or |-inch thickness. The propellers are built up by five or ten laminations accord- ing to size. The laminations are laid out on the boards and sawed to outline, care being taken to avoid all defects in wood and to have the grain and density of wood as nearly similar as may be at opposite ends of the same piece. In the better and preferred practice, however, the laminations for each single blade are laid out separately and carefully weighed, matched and balanced against each other. They are then selected in pairs (or in trios for tkree-bladed propellers) and their hub Digitized by.LjOOQlC 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 Digitized by LjOOQ IC 314 SCREW PROPELLERS Sheet i8, and the resultant propulsive coefficient on the hull with all appendages. 13. A large number of cuts showing 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. Digitized by LjOOQ IC INDEX .A PAGB Admiralty coefficient 19 Aeroplane propellers 294 , construction 307 , correction for number of blades 302 , design, Basic conditions 302 , design sheet, description 296 , estimate of power \ 294 , first method of design 298 , limits of P.A. -^D.A 298 , second method of design 303 Alleghney, U. S. S., fitted with screw propellers 4 Analysis, illustrative problem in 2, 3 and 4 blades \ 77 of performance of submarine boat screws 126 of propellers 77 Appendage resistance, curve for merchant ships 30 , description sheet 18 27 , estimate 24 Appendages, hull, list of 26 Archimedes, propeller fitted on 4 Arrangement of strut arms 112 Atlas, contents of 313 B Backing of ships 243 Baddeley, mention 4 Bare hull resistance, formula 22 Bamaby's method of design 49 Basic condition for design 55 Blades and blade sections 207 , corrections for variations from standard form 85 , effect of number on efficiency 73-83 316 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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( Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 Digitized by LjOOQ IC 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 FINTS Digitized by LjOOQ IC Digitized by Google Digitized by LjOOQ IC THIS BOOK 18 DT7E ON THE ULST DATE STAMPED BELOW AN INITIAL FINE OF 25 GENTS WILL BK ASSKSSED FOR FAILURE TO RmJRN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO BO CENTS ON THE FOURTH DAY AND TO $1.00 ON THE SEVENTH DAY OVERDUE. Tt^ X5A9^ T9P6SFel>i8 OCT 191934 OEC 3 ig:- ^^ no. \^ MAff Uim/i^ ^ ^ ^ 7^ FJAHX L OAN Au£6*5^'t lyOof S THj MMM'ftlBT f^^C'D I n ^PR 1 I9G7 LD 21-100111-7/33 Digitized by LjOOQ IC YC 1 06953 3S2t95 Vd. T UNIVEPSnY OF CALIFORNIA UBRARY f^*nS!:iV Google * 1 •