BOUGHT WITH THE INCOME PROM THE SAGE ENDOWMENT FUND THE GIFT OF Hettirg M. Sage 189X A/./:7-2^-'^-Z- jLSr/(//r..f.^..^.... 5474 CORNELL UNIVERSnV LIBRARY 064 190 26 II Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924064190261 THE BESISTANCE and POWER STEAMSHIPS. W. H. ATHEKTON, M.Sc, Member of the Nm-lh-East Coast Institution of Engineers and Shipbuilders, etc.; Occasional Lecturer at the Manchester Municipal School of Technology ; AND A. L. MELLANBY, M.Sc, Late 1851 Exhibition Scholar: Member and Gold Medallist of the Nortk-East Coast Institution of Engineers and Shipbuilders, etc. ; Lecturer on Engineering at the Manchester' School of Technology. PRICE FIVE SHILLINGS NET. 1903. THE TECHNICAL PUBLISHING CO. LIMITED, 31, Whitwoeth Street, Manchester. JOHN HEYWOOD, 29 & 30, Shoe Lane, London; and Ridqefield, Manchester. And all Bookseltirg. PREFACE. The following chapters originally appeared in the form of occasional articles contributed to The- Practical Engineer, chiefly by the first- named author. Almost all the recognised methods of determining the engine power required to propel steamships are discussed in considerable detail, and examples of their application given. The subject of the fouling of ships has also been dealt with fully, because of its important influence on the actual resistance of sea-going ships. "We believe that the matter introduced and the mode of treatment adopted will appeal to most marine engineers and shipbuilders, and, in fact, to all who are interested in watching the development of steamships. As former students of the Durham College of Science, Newcastle-on- Tyne, we are glad to acknowledge our indebtedness to the lectures of Professor R. L. Weighton, M.A, vshose method of treatment we have sometimes followed. We are also under considerable obligations to Sir "W. H. White's "Manual o£ Xaval Architecture," and Mr. D. W. Taylor's " Resistance of Ships," as well as to the classical papers of Froude, Rankine, and others mentioned in the text. W. H. A., AND A. L. M. Manchester, February, 1903. CONTENTS. PAGE Introduction , 1 CHAfTER I. The Moving Body— PropeUers— Nature of the Problem— Force, Speed, and Power— Properties of Fluids 3 Chapter II. Ships and Projectiles Comrared 10 Chapter III. Tow Rope Resistance 13 Chapter IV. Factors of Resistance— Speed, Immersed Surface, Displacement, Tonnage, Angles of Eatrance and Run, Length, Shape of Bows, Breadth and Draught— Symbols and Units 16 Chapter V. Coefficient of Form— Coefficient of Fineness not a True Index— Examples — Prismatic Coefficient : Examples— Midship Section Coefficient— Relation between Coefficients— Water-plane Coefficient— Hints— Similar Ships 29 Chapter VI. Resistance of a Steamer Starting from Rest— Resistance Curves — Minor Resistances — Air Resistance — Summary 41 Chapter VII. Magnitude of Resistance— Calculation of Resistance and Power of the York- town— Inertia Effect 49 Chapter VIII. Kirk's Block Models of Ships- Calculation of Wet Surface— Examples- Hogg's Modification 57 Chapter IX. Skin Resistance— Laws of Solid and Fluid Friction— Froude's Experiments— The Index of Friction — Approximate Estimation of Skin Resistance— The Critical Speed— Tables of Frictional Coefficients— Froude's Experi- mental Apparatus 65 VI. CONTENTS. Chapter X. page The Admiralty Formula - Its Assumptions — Examples of Calculation 84 Chapter XI. The Fouling of Ships— Circumstances Favourable and Unfavourable to Fouling — Examples of Foul Ships— Barnacles— Effects of Fouling 92 Chapter X[I. Materials Used for Sheathing Ships— Eleetro-chemical Action— Application of Copper Sheathing— Cost of Sheathing— Mumford's Formula for Immersed Surface 105 Chapter XIII. Anti-fouling Compositions- Theory of the Action of Copper Sheathing and of Anti-fouliug Compositions 121 Chapter XIV,' Correspondiog Speeds — Bernouilh's Theorem— Example of Froude's Method of Comparison — Progressive Trials 131 Chapter XV. Kankine's Augmented Surface Method — Russell's Wave-line System — Examples—Comparison with Admiralty Formula- Kirk's Modification .. 141 Chapter XVI. CoiTespondiug Speeds— Examples 157 Chapter XVII. Wavesand Wave Resistance— Canal Waves 161 Chapter XVIII. Experiments with Models— Froude's Work— Colonel English's Method lt>9 Chapter XIX. Trochoidal Waves— Calculation of Wave Resistance— Examples 184 Index 196 EKRATA. Page 156, line 3 from bottom, for 43,600 read 81,210. Page 156, lines 3, 8. and 11 from bottom, for 35 read 28'5. Page 159, line 8 from top, add the index |. Page 159, line 10 from top, add the index J. INTEODUCTION. The large problem of ship propulsion, as presented to the naval architect and the marine engineer jointly, may be stated under four heads, namely : — 1. Given the weight (or displacement) and the principal dimensions of a proposed steamship, what power will be required to propel her at a specified speed ? This question leads to a study of the resistance of ships and the analysis of trial-trip records. 2. What will be the most suitable type, size, and speed of propeller, having regard to the known conditions of service ? This question involves the consideration of the action of marine propellers and of the mode of designing them. As, however, the s':reio propeller is so very much more extensively used than any other, we shall confine our attention almost entirely to that type. 3. What kind and size of engines will be best adapted to drive the chosen propeller, under the specified conditions ? Hence arises 'the consideration of the arrangement and pro- portions of the cylinders, shafting, condenser, pumps, and other important details of a marine engine. 4. What type and size of boilers should be provided to supply the requisite amount of steam to those engines? Thus we are led to a discussion of the standard types of marine boilers, and the estimation of their proportions. The present work deals with the first of these subjects only. Is THE KESISTANCE AND POWEE OF STEAMSHIPS. CHAPTER I. The Movinfi Body. — A modern steamship (also referred to hereafter as a ship, vessel, boat, or steamer indifferently) may be defined as a hollow steel structure designed for the safe conveyance on water of passengers or cargo, and so shaped as to be adapted for that rate of propulsion which the conditions of service demand. Cargo boats are so constructed that the freight is carried at the least pos- sible cost ; the interest on their first cost and the working expenses being taken into account. As will be seen from fig. 1, showing the midship section of a vessel of ordinary construction, a modern steamship is built up on a stiff cellular foundation or " bottom," the lowest part of which forms the " keel," here of the " bar " type. To this cellular bottom are riveted suitably-shaped frames, tied together by cross-beams, bulkheads, decks, and the shell, the latter being constructed of overlapping steel plates, riveted to one another and to the frames. This much constitutes the hull ; the shape and size of the immersed part being our chief concern. With the superstructure we are here little concerned, and not at all with the internal fittings, the machinery alone excepted. Propelling Instruments. — The propulsion of a steamship is usually effected by a rotating propeller, of a form adapted for continuously driving astern a stream of water, such as a paddle-wheel or a multiple-threaded screw. The function of a ship's engines is simply to rotate this propeller in either direction at sufficient speed. Ships may have more than one instrument of propulsion. The Great Eastern, for example, built in a transition age. THE EESISTANCE AND POWER OP STEAMSHIPS. Fig. 1. PEOPELLEES. had both a screw and a pair of paddle-wheels ; but this combination is never likely to be repeated. Paddles are always used in pairs, except in a few stern-wheel shallow- draught river boats. Twin screws are now quite commonly employed for driving high-powered merchant vessels, while in modern warships they are regarded as indispensable, if only to gain the utmost facility of manosuvring, apart from the additional security afforded against the total disable- ment of machinery. A few of the faster United States cruisers have been fitted with triple screws, the central screw alone being used during ordinary cruising, but all three when going into action. This arrangement, however, has not yet found favour with the British Admiralty. Further, with a view to securing great handiness, some ferry steamers on the river Mersey have been fitted with two screws at the bow and two at the stern, the screws on each side being driven by independent engines. The two bow screws act as pullers, and the others as pushers. The former, as they work in undisturbed water, are said to do the greater part of the work. This four-screw system, how- ever, has never been applied to seagoing vessels. The latest advance in multiple-screw propulsion has been made by the Hon. Charles A. Parsons, of Newcastle-on-Tyne, who has employed no less than nine small screws, running at a very high speed, to drive his experimental 100 ft. launch, the Turbinia, which has a displacement of 42 tons. Doubt- less the near future will have in store for us other important developments in this direction. Already, indeed, the Eussian Government has ordered, from the Tyneside firm of Messrs. Hawthorn, Leslie, and Co., two 38-knot torpedo boats, each equipped with turbine motors and twelve screws, three being coupled to each shaft. A similar vessel is under con- struction for the British Navy. The trials of these boats will be watched with interest. The Nature of the Problem. — Though our ultimate aim is to predict the engine power necessary to drive a given ship at a specified speed, our first object is to ascertain and b THE EESISTANCE AND POWER OF STEAMSHIPS. express the exact relation existing between the geometrical and physical features or " characteristics " of a ship's hull, and the resistance of the enveloping medium to its motion. This problem, however, admits of only approximate solution. The true nature of the resistance of water to the passage of a ship floating upon it is far from being obvious, and, indeed, could not have been discovered without the most painstaking experimental research. Of this fact the serious errors into which the earlier investigators fell afiord sufiioient evidence. For the existing knowledge of the subject of ship resistance, the profession is chiefly indebted to the labours and writings of Prof. Kankine,* Dr. Fronde,t and Mr. E. E. Froude.J In the hands of the two Frondes, at least, the science of mathematics has been useful, mainly in the way of generalising and giving concise expression to the results arrived at by systematic experiments with models about 12 ft. long, and by the progressive speed trials of full-sized steamships. As Rankine lived just before the age of experimental tanks and progressive trials, he had available, unfortunately, a far too meagre number of experimental facts to enable him to dispose of the subject in an entirely satisfactory manner. Nevertheless, he performed valuable pioneer work, which at least served to direct closer attention to the subject, and stimulated others to engage in research. Force, Speed, and Power Connected. — Before proceeding further it is necessary to point out the precise dynamical relation between the three important physical quantities — force, speed, and power. This relation is most generally expressed as Power = force x speed. * William John Macquorn Rankine, LL.D., F.R.S. ; late Professor of Engineering in the University of Glasgow. The father of engineering science. Died 1872. t William Froude, LL.D., F.R.S., M.Inst.O.E. ; late director of the Admiralty experimental tank at Torquay. The greatest experimental investigator, and the most lucid exponent of the subject of ship resistance. Died 1879. t Robert Edmund Froude, F.R.S. , M.Inst.O.E. ; son and successor of William Froude. Now director of the Admiralty experiment works, Gosport. Probably the highest living authority on the subject. FOECE, SPEED, AND POWER. 7 Hence, choosing 1 lb. as the unit of force, and 1 ft. per minute as the unit of speed, we have, in the gravitation system. Unit power = lib. x 1ft. per minute. = 1 foot-pound per minute. But as this unit of power is much too small for engineering purposes, a certain multiple of it is chosen as the practical unit. This larger unit is. sty led the horse poiver, and its value, as fixed by the celebrated founder of steam engineer- ing—James Watt— is 33,000 times the foot-pound per minute unit, or 33,000 units of work per minute. Consequently, the horse power (H. P.) required to overcome a resistance of R pounds at the rate of V feet per minute is HP =^^iT ■ ■ 33,000 This is the fundamental formula in power calculations. From it, if only we know the resistance of a vessel at any speed, we can easily calculate the effective power required to propel the vessel at that speed. The one great difficulty is to determine with accuracy the resistance in question. Still, with the aid of sufficient experimental data, it can be esti- mated approximately enough. The measurement of the speed is a comparatively simple matter. It should be carefully noticed here that by no means all the power developed by a ship's engines is usefully expended in driving the ship. As a matter of fact, only about one-half of the engine power of any ship is utilised in the direct work of propulsion ; the other half being wasted in various ways, which will be considered hereafter. The Resisting Media. — The two media which oppose the progress of a moving ship are air and water ; but the efiect of the former is comparatively insignificant. The physical properties of these fluids may be here conveniently reviewed and compared with the imaginary properties of a perfect fluid. Apart from chemical and physiological properties, the characteristic features of a given fluid are its density, inertia, elasticity, and viscosity. 8 THE RESISTANCE AND POWEE OF STEAMSHIPS. ' The density of dry air, at a temperature of 62 deg. Fah., and under the normal barometric pressure of a 30 in. column of mercury, is 534 '2 grains or 00'763 of a pound per cubic foot. The density of fresh water is usually taken as 62^ lb., and of normal sea water as 64 lb. per cubic foot. Increase of density means increase of resistance, other things being unaltered ; but there does not appear to be any simple relation between the density of diiferent media and the resistance they ofi'er. The inertia of a body, or reluctance to change of motion, is proportional to its density. Hence the inertia of a cubic foot of water is 625 -^ 00763, or 820 times as great as the inertia of a like volume of air under normal conditions. Elasticity, in reference to fluids, is the property in virtue of which a portion of fluid under pressure rapidly resumes its original bulk when the pressure is relieved. Both air and water are perfectly elastic as regards hulk^ but, unlike solids, they are quite devoid of elasticity of shape. Viscosity, or viscidity, is a peculiar and extremely import- ant property of matter. It is opposed to limpidity, mobility, or fluidity. All fluids are to some extent viscous. That is to say, their molecules do not glide over each other with perfect freedom, but with a certain amount of friction ; so that a moving thread or stream of molecules gradually sets in motion other molecules by rubbing against them. Briefly, then, by viscosity is meant molecular friction, or internal resistance of matter to change of shape, as depend- ing on the rapidity of the change of shape due to a constant stress. However hard a substance may be, if the very smallest stress, long continued, causes a constantly-increasing change of shape in it, we must regard that substance as a viscous fluid. Tar and treacle are eminently viscous liquids. Water is only slightly viscous, and alcohol is even less so. Air is less viscous than any liquid ; yet a current of air exercises a perceptible drag on adjacent matter, and when the latter is light enough it is set in motion. PKOPEETIES OF FLUIDS. \f In the kinetic theory of matter, the viscosity of a fluid is held to result from an interchange of the molecules between the different parts of the fluid, and by the collision of the molecules causing an exchange of their momentum. (See Maxwell's "Heat," Ch. xxii.) The coefficient of internal friction or viscosity of a liquid is exactly defined as the tangential force Fper square centimetre required to keep up a constant difference of speed of 1 centi- metre per second between two horizontal layers (A, B) of that liquid 1 centimetre apart (see fig. 2). Thus measured, the i Cwi PER Sec. Fig. 2. coefficient of viscosity of pure water at 10 deg. Cen. is only 013 of a dyne, while that of glycerine mixed with 6 per cent of water is 7'4 dynes. These values have been deduced from the rate of flow of the liquids through capillary tubes. Though water has so small a coefficient, yet its viscosity is the prime cause of fully 80 per cent of the resistance experi- enced by the average cargo steamer. Some resistance to the motion of a vessel arises from the viscosity of the air which rubs against the vessel's upper works. Compared with water, the viscosity of air is far greater than the relative density of air and water would suggest ; water being ordinarily 820 times denser than air, but only about 100 times more viscous. It is a curious fact, too, that the viscosity of air and other gases is increased by 10 THE EBSISTANCE AND POWEE OF STEAMSHIPS. rise of temperature, while that of -water and other liquids is diminished. A perfect, ideal, or frictionlesa fluid is a portion of matter incapable of resisting change of shape in the least degree, and therefore totally devoid of viscosity, the direction of its pressure being always normal to its surface. It has also perfect elasticity of volume. Such a fluid is a purely imaginary or unrealiaable conception of the mathematical physicist ; convenient, however, for preliminary considera- tion and as a standard of reference, like a perfectly smooth body or a perfect heat engine. No actual fluid enjoys the property of limpidity to perfection. A perfect fluid, it should be observed, is by no means with- out density. On the contrary, it may have any density one may find it convenient to assign to it, and consequently any inertia. But the perfect fluid we shall mostly have to con- sider will be supposed to have the same density as water. CHAPTER II. Ships and Pkojectiles Compaeed. In studying a difiieult subject, the comparison of allied phenomena is often helpful, as science proceeds much by analogy. We propose, therefore, on the very threshold of our inquiry . into the resistance of ships, to refer briefly to another matter of high scientific interest, which has some bearing on this subject, namely, the motion of projectiles in air. Both these subjects present great mathematical difficulty ; so much so, that neither of them could be successfully investigated in any other way than by the long but sure method of making numerous and elaborate experi- ments, or direct appeals to nature, subjecting the records of these experiments to most careful comparison and analysis, and finally deducing general conclusions for future guidance. SHIPS AND PEOJECTILES. 11 The case of a projectile moving in air differs from the case of a ship moving on water in several important respects, as stated below : — 1. In the form of the body. A projectile is a solid of revolution, usually with pointed head and flat base ; while a ship is symmetrical about a vertical plane only, and has both tapered nose and tail. 2. In the nature of the resisting medium. Water is a liquid of nearly constant density, and air a gas whose density varies at diff"erent parts of the shot's trajectory. Further, the projectile is wholly immersed in air, and yet unsupported by it ; while the ship is only partially immersed in water, and yet entirely supported by it. 3. In the rate of motion. The initial speed (say 3,000 ft. per second) of the projectile discharged from a modern gun is many times greater than the speed (say 30 ft. per second) of a modern steamship. Also the speed of the shot varies continually during the time of flight ; while that of the ship is fairly constant. 4. In the mode of progression. The shot advances and rotates in its medium, with its axis at a constantly changing inclination ; while the ship advances and oscillates with but slight variation from uniform horizontal motion. 5. In the manner of propulsion. The shot receives an initial impulse, and then continues its motion by reason of its stored energy ; while the ship moves under the influence of a constant propelling force. The effect of these differences on the magnitude and rate of variation of the resistance to motion will be alluded to hereafter, as occasion demands. Meanwhile, it suffices to state, for the sake of comparison, some of the results of the classical experiments of Bashforth* on the motion of pro- jectiles in air, made with the aid of his ingenious chronograph. * The Rev. Francis Bashfortb, B.D-, late Professor of Applied Mathematics to the AdvaDCed Class of Royal Artillery Officers, at Woolwicb, and official referee to the late Ordnance Select Committee. Experiments made from 1864 to 1881. 12 THE EESISTANCE AND POWEE OF STEAMSHIPS. 1. The resistance of the air to the motion of similarly shaped shots varies as the squares of their diameters, and therefore as the sectional areas. 2. The resistance of the air to a given shot does not vary according to any single power of bhe speed, but to a continuously varying power. 3. For a certain limited range of speed the resistance is nearly proportional to the cube of the speed, so that E = Cv", where R pounds is the resistance encountered by a shot moving at v feet per second, and C is a number, termed the " coefficient of resistance," which varies slowly with v. This cubic law of resistance is most nearly true at about 1,200 ft. per second ; for speeds much higher or much lower, the value of C varies considerably with v, this change of value being a necessary consequence of the inexact nature of the cubic law. For speeds below 100 ft. per second, the resistance of the air is negligible. This is the ordinary simple academic case, the path of the projectile being then a parabola. At speeds between 100 and 800 ft. per second, and also above 1,500 ft. per second, the resistance varies nearly as the square of the velocity of the body. At intermediate speeds, again, the cubic law approximately holds. There is thus a certain periodicity in the rate of change of the resistance of the air to the motion of projectiles, a peculiarity which also appears in respect of the resistance of water to high-speed ships, as we shall see later. It now remains to determine the actual magnitude of the resistance in a given case. From experiments made with the usual elongated ogival-headed shot, moving at not less than 1,500 ft. per second, it appears that R = cav'^, in which R pounds is the resistance of the air to a shot of section a square inches, travelling at v feet per second, and c is a small fraction which never differs much from 00000543, or 5'43 X 10 ~° in index notation. For instance, the resis- TOW-ROPE RESISTANCE. 13 tance to an elongated shot, fired from a 12 in. gun, when moving at the rate of 2,600 ft. a second, is about 5-43 X 10 -» X 113 X 2600^ = 4140 lb., or not far short of 2 tons. In the case of a spherical shot, of the same radins and nature of surface as the above-named elongated shot, the resistance was found to be about 1^ times greater ; so that the constant for this class of shot will be 1"5 x 5'43 x 10 ~ " = 8'15 x 10"°. Hence, taking a particular instance, the resistance of a 10 in. ball, moving at 2,000 ft. per second, will be something like R = constant x area x speed^, = 815 X 10-» X 78-5 X 2000^, = 2560 lb., or, say, 2^ tons. The mass of a shot, and therefore the weight, affects its motion in this way. A light shot is more rapidly set in motion than a heavy one by a given force, and hence has a higher muzzle velocity ; but the light one loses speed sooner than the heavy one, because the resistance of the former per unit mass is the greater, and therefore the loss of energy more rapid. Thus an aluminium shot would not carry so far as a steel shot of the same size and shape, if both were fired, with equal charges of powder, from the same gun set at the same elevation. CHAPTER III. Tow-rope Resistaxce. When a vessel is towed by a tugboat, the latter experiences a resistance, in dragging the former through the water, which increases with the speed. It is possible to measure this resistance in pounds, simply by making iast the tow rope to a properly-constructed spring 14 THE EESISTA.NGE AND POWER OF STEAMSHIPS. dynamometer, and taking the reading at varioas speeds. Such observations actually have been made with one or two full-sized ships ; but a much more usual and less costly method of gaining the desired information is to tow model vessels in a specially-equipped model tank, and to measure their resistance. This valuable method was worked out by the late Dr. Froude, who showed how the resistance of a full-sized ship could be correctly predicted from that of a model. The "tow-rope resistance" of a ship moving at a constant speed is equal in magnitude to the actual steady pull which would be required to tow her at that speed. In the case of a self-propelled steamship it might be supposed that the thrust of the propeller would be equal to the tow-rope resistance ; but such is not the case. Owing to the action of the screw interfering with the natural closing-in motion of the water aft, the thrust considerably exceeds the tow-rope resistance, as Froude's experiments have proved beyond a doubt. But still the actual gross resistance of a self-propelled steamship, though greater than the toiv-rope resistance, is necessarily equal to the actual thrust, since there can be no exception to the general physical law that action and reaction are equal and opposite. In the case of a paddle boat, the increase of resistance due to the disturbing action of the side wheels is comparatively slight, but not entirely absent. The following extract from a paper by Dr. William Froude, in the Transactions of the Institution of Naval Architects, vol. xv., will further elucidate this important point, and also furnish some useful data : — " In reference to the question of waste through engine friction and defective efficiency of propeller, I subjoin a comparison between the results of these (towing) experi- ments and the performance of H.M.S. Greyhound on the measured mile. TOW-EOPE EESISTANCE. 15 Speed on measured mile feet per miu. 1017 = 10 knots. 845 = 8 '3 koots, Eeaiatance from towing experiments, including' estimates of air resistance Ibs.j 10,770 Effective liorse power, or ■■^^"t. X speed 33000 Actual indicated horse power Efficiency, or E.H.P. -f- I.H.P " A perhaps more instructive way of treating the question is to compare the apparent thrust of the propeller with the actual resistance. II. Indicated horse power Speed of screw (or revs, per min. x pitch in feet) Indicated thrust = I-H-F- x 33000 j^^ speed of screw True resistance, from towing experiments . .lbs. True resistance -vindicated thrust 453 1,039 14,390 6,220 ■431 "Making the utmost allowance for engine friction,' &o., it seems from this impossible to doubt that the actual thrust delivered by the screw shaft is largely in excess of the resistance due to the ship, and that considerable extra resistance must be caused by the action of the screw, by the diminution which that action produces on the hydrostatic pressure of the water against the con- tiguous parts of the run. . . . This is corroborated by six experiments taken with the screw lowered into working position. In three of them the screw was allowed to revolve, and these show the resistance to be much higher than when it is lifted, and greater than when it is fixed." The facts of the case are best expressed in this form — Actual thrust = resistance due to ship + resistance due to screw. = tow-rope resistance + propeller augmenta- tion of resistance. 16 THE EESISTANCE AND POWER OP STEAMSHIPS, CHAPTER IV. Factoes op Resistance. The features of a ship-shaped body which influence its resistance will now be enumerated and considered in a preliminary manner. 1. The resistance of the surrounding water to a given ship in uniform motion depends on the speed at which she is driven. Experiment shows that the resistance is not proportional to any single power of the speed, but to a continuously varying power, as in the case of projectiles. For a well-designed ship, driven at ordinary speeds, however, the resistance is usually taken to vary as the square of the speed ; so that a ship when travelling at the rate of 10 miles an hour will experience four times as much resistance as when moving at five miles an hour, and will burn, about eight times as much coal. Clearly, then, high speeds are very expensive. The nautical unit of speed is the hnot, which is defined as a speed of one nautical mile (or 6,080 ft.) per hour. Many people, however, regard the knot as the nautical unit of distance, and use one knot per hour as the unit of speed ; but they very often omit the time reference — the "per hour " — and thus cause ambiguity. The other usage is preferable on the score of brevity, but there is really about as much authority for the one as the other. The context has gener- ally to decide what is meant. To express symbolically the law of variation of resistance with speed, let R pounds be the resistance and V knots the ship's speed ; then, up to a certain critical speed depending on the shape of the ship, R a V^ approximately. 2. The extent of the immersed surface is a very important factor in determining a vessel's resistance. This is measured by the number of square feet of hull and appendages in contact with the water, when the vessel is sunk to the load line in smooth water. The immersed surface is more briefly FACTORS OF RESISTANCE. 17 referred to as the " wetted " or " wet surface," or as the " wet skin." In some quarters a distinction is drawn between wetted surface and immersed surface ; the former referring to the surface in contact with the water when the ship is down to her load line, and the latter varying with the draught and trim of the ship. But this distinction is by no means universally observed. It is a simple experimental fact that the resistance of a ship is directly proportional to the extent of her wet skin — that ia, R oc S. Hence, a ship having 20,000 square feet of wet surface has twice the resistance of a ship having half of that surface, other things being the same. 3. The degree of roughness and foulness of the wet surface powerfully influences the resistance of a ship. In fact, power and speed calculations apply, with any approach to accuracy, only to newly-painted vessels, quite free from barnacles or other shell fish and marine algse ; things which form such a hindrance to economical propulsion, and lead to the expense of copper sheathing or of anti-fouling composi- tion. We shall, therefore, always assume the vessel to be perfectly clean, as on the trial trip, though this is never quite the case on the return of a ship from a long voyage. Resistance and Power Formulm. — Though we have by no means enumerated all the factors of resistance, yet we are now in a position to frame a simple formula, combining all the foregoing results, which is not without some utility. Thus, the frictional resistance of a clean ship is given roughly by the expression — wet surface x speed^ -H 140, or K = S X V2 H- 140, the units being pounds, square feet, and knots respectively, and 140 an experimental number, constant for clean painted surfaces, but varying greatly for foul surfaces. For instance, the skin resistance of a ship whose wet skin is 10,000 square feet, and speed 10 knots, is about 10000 X 102 -=- 140 = 71431b., or less than twice the air resistance of a 12 in. shot moving at 2,600 ft. per second. 2s 18 THE EESISTANCE AND POWEE OF STEAMSHIPS. Further, the horse power (H.P.) required to overcome the external frictional resistance K pounds at the speed V knots is — resistance x speed in feet per minute 33000 = R X :L^ ^ 33000. Therefore, H.P. = R x V -f- 326. In the example chosen above this becomes 7143 X 10 -^ 326 = 219 H.P. Now, the power actually developed on the trial trip of this ship was about 500 H.P., the respectable difierence of 281 having therefore been absorbed in overcoming the external resistances other than frictional, also in propeller losses and in engine friction. Later on it will be shown that, by using a variable coeifioient C, whose value is derived from the trial data of actual ships, we can employ the simple formula, LH.P. = ?^ to predict with fair accuracy the indicated horse power needed to drive proposed ships not differing greatly in type and speed from such ships as have been previously tried on the measured mile. Resistance Factors, resumed. 4. The resistance encountered by a moving body is indirectly governed by the amount of matter in motion. As the weight and the mass of a body are proportional, we may alternatively say that a ship's resistance depends partly on the weight of the ship. But, instead of the familiar word "weight," the shipbuilder invariably uses the technical term " displacement," by which he usually means the weight of water displaced by the ship. It is an experimental fact, known as the law of Archimedes, that the weight of fluid displaced by a floating body (as a ship or a balloon) is precisely equal to the weight of that body. Sometimes, however, the term displacement is used to signify the BISPLACEMENT. 19 volume of water displaced. As 35 cubic feet of sea water , weigh 1 ton, the displacement D, expressed in tons, multiplied by 35, gives the volume in cubic feet of the water displaced by the vessel. Thus, 35 D = volume. The displacement of a particular ship is not constant, but varies from time to time, according to the quantity of cargo and stores on board. Its greatest proper value is known as the " load displacement," which is the weight of water dis- placed by the ship when immersed to her load water line. The light displacement of a steamship is the total weight of the ship, exclusive of cargo, coal, stores, water ballast, &o. It is divided into the following three items : — (a) The net weight of the hull, known as the "structural weight.'' (5) The weight of the machinery in working order, com- prising all engines, boilers (with steam up), shafting, and propellers. (c) The weight of woodwork, outfit, and other items apart from the stores. In an interesting paper read before the Greenock Philoso- phical Society, in the year 1882, the late Mr. William Denny, of Dumbarton, drew an instructive comparison between 10 selected iron North-East Coast steamers, mostly cargo, and 9 Clyde-built steamers, chiefly passenger, some of which were constructed of iron, and others of steel. He showed that — The r.T.tio of- In Clyde steamers varied between InN.E. Coast steamers varied between Light displacement to load displacement . . . Weight of hull to load displacement Weight of machinery to load displacement . Weight of outfit to load displacement •33 and -65 ■20 and -37 ■047 and ■IS ■OSl and -n ■30 and -Si •198 and -23 ■04 and 072 ■038 and ■OSS 20 THE EESISTANCE AND POWER OF STEAMSHIPS. Though these figures cannot exactly be taken to represent modern practice, they will serve to convey some idea of the relative magnitudes of the several components of displacement. The displacement of a vessel must not be confused with the tonnage, which is an arbitrary quantity of little scientific value, employed only in the merchant service for the pur- pose of classification. The so-called " gross register tonnage " of a ship expresses her entire cubical capacity, including deck-houses, in tons of 100 cubic feet each. For instance, the gross register tonnage of the Campania is 12,600 tons, while her displacement is about 18,000 tons. " Net register tonnage " is intended to express, also in tons of 100 cubic feet, the space actually available for the conveyance of passengers or the stowage of cargo. This does not differ greatly from the gross tonnage in the case of sailing ships, but in steamships large deductions are made on account of machinery and bunker space." According to Sir W. H. White, director of naval con- struction, ordinary ocean-going steamers usually have a net register tonnage about 33 to 35 per cent less than their gross tonnage. Thus, the old White Star liner Britannic has a displacement of 8,500 tons, a gross register tonnage of 6,004 tons, and a net register tonnage of 3,162 tons. In the more modern and faster liners, the difference between gross and net tonnage is still more marked. " It may be worth notice," says Sir William White, in his excellent manual of naval architecture, " that in ocean-going steamers, both mercantile and fighting, the displacement (in tons), when fully laden, may be expected to be between once and a half and twice the gross tonnage ; and the mean of these ratios (If times) will give a fair approximation to the load displacement in most cases." The unit of displacement for British and United States ships is the ton of 2,240 lb., though the standard United States ton is now 2,0001b. The metric tonne of continental DISPLACEMENT. 21 nations contains 2,206 lb. In comparing the ships of different nations, these figures should be borne in mind. As regards the precise influence of change of displacement, it is usual to treat the resistances of two similarly-propor- tioned ships as proportional to their displacements raised to the two-thirds power, the law of variation of resistance being R oc D5 or oc yW. The reason is that the wet surface of similar ships varies as Dl, a fact which wiU be proved hereafter. Thus displace- ment serves as an indirect measure of wet surface. Taking a numerical illustration, the resistance of a 2,000- ton ship is to that of a 1,000-ton ship, as 2,000J is to l,000i = 2^ to 1 = °jTto 1 = 1-587 to 1. So that doubling the size of a ship, other things being unaltered, makes the resistance only about 1| times greater, owing to the wet surface per ton diminishing as the dis- placement increases. Evidently, then, a large increase of size makes far less difference to the coal bill than a large increase of speed. In other words, large size is favourable to economy of propulsion, a conclusion which experience has fully confirmed. Hence for many years the average size of steamships has been steadily increasing. 5. The magnitudes of the angles of entrance and run exercise an important bearing on the resistance of a high- speed ship, but are much less influential at low speeds. In the case of a high-speed ship, the problem before the ship- builder is to make the shape of the vessel so suitable for the speed at which she is to be driven that the creation of waves may be as much as possible avoided. In the case of a low-speed ship, the aim of the designer should rather be to diminish the amount of frictional resistance, by keeping down the extent of surface for a given displacement. In each case the surface should be kept as smooth as possible, but, compared with fineness, smoothness is relatively leas important at high than at low speeds in lessening resistance. 22 THE EESISTAKCE AND POWEE OF STEAMSHIPS. The angle of entrance, fig. 3, is defined as the inclination e, at the water line, of the bow to the centre line of the ship's plan view. The angle of run is the inclination e' of the stern, at the water line, to the ship's plane of symmetry. In an actual ship, however, it is impossible to measure these Sterm angles with much precision, owing to the double curvature of the surface. A coarse-lined ship, fig. 4, has an angle of entrance of about 40 deg., measured at the load- water line ; while a ^m«-lined ship has only about half that angle. These angles are quite difierent in the case of the block models to be afterwards considered. Pig. 4. The length of the tapered bow, measured parallel to the ship's plane of symmetry, is known as the "length of entrance " (E feet) ; while that of the tapering stern is styled the "length of run" (E' feet). These two lengths are not necessarily equal in actual ships, but in resistance calculations, based on the block model, are always regarded as exactly so. There should be a fixed relation between the RESISTANCE FACTORS. 23 speed of the ship V and the length E, viz., V oc ^E, for a reason to be discussed later on. Some fast vessels have no straight part, or " parallel middle body," whatever, but are all entrance and run. When the entrance angle is small the vessel is said to be fine, and when this angle is large the vessel is coarse, or Uuff. A bluff ship is suitable for slow speeds only. In fig 5 the PiQ. 5. dotted curve B shows a better form of bow line than the more convex curve A ; because, by carrying the greatest breadth farther forward, a finer entrance angle is secured without any reduction of displacement. The term fair needs some explanation. Generally speak- ing, lines are said to be "fair" when they are free from sudden changes of direction. As applied to a ship, however, " fair " means rather of fair average form — i.e., neither very sharp nor particularly bluff. 6. The length of a ship influences her resistance in two opposite ways. On the one hand, as only a long ship can have a very small angle of entrance, it follows that length, when associated with fineness, conduces to ease of propulsion. But, on the other hand, since the wet surface of similar ships varies as the squares of their lengths, it is evident that increase of length entails increased skin resistance. The length of any ship varies somewhat according to the level at which the measurement is taken. The length desired for use in resistance calculations is the mean length of the immersed part of the hull, but we have usually to be content with a rough approximation to this. As shown in 24 THE EESISTANCE AND POWER OF STEAMSHIPS. fig. 6, ships differ a good deal in the general shape of their bows, especially when extreme types are compared, such as fast passenger steamships with slowf cargo boats, and war- ships with pleasure yachts. Nevertheless, it is customary in all cases to take as the mean or effective length of the ship the so-called " length between perpendiculars " — that is to say, the distance from the after end of the stern post to the forward end of the stem, measured along the main deck, as indicated in fig. 7. This definition applies to any shape Fia. 6. of bow. Properly, however, an allowance beyond this ought to be made in favour of warships armed with large project- ing rams, but such allowance is not usual in ordinary practice. Henceforth, then, whenever the " length " of a ship is spoken of, the " length between perpendiculars " is to be understood, and not the "length over all." 7. The breadth of a ship is not a factor which enters directly into any formula of resistance, though the breadths of ships have an important indirect influence on their relative resistances. This dimension should be measured to the outside of the shell plating, and not merely to the outside of the frames, the latter measurement being known as the moulded breadth. In most ships the greatest or extreme breadth is at, or slightly below, the water line. It is a common error to suppose that great relative breadth necessarily entails great resistance. As a matter of fact, great breadth, when accompanied by fine ends, promotes ease of propulsion, at least at high speed. Costliness of construction, however, forms a serious objection to ships with broad beams, long tapering ends, and short parallel middle body. Battleships are always made relatively broad RESISTANCE FACTOKS. 26 a,nd short, compared with merchant vessels, for the sake of stability and handiness. The ratio of the length between perpendiculars to the extreme breadth varies from about 5 to 10 in difierent types of ships. Taking a few actual instances, this ratio is 450 ft. ^ 45 ft. = 10 in the old White Star liner Britannic, and 600 ft. -=- 65 ft. = 9"2 in the famous Cunarder Campania, and 500 ft. 4- 71ift. = 7 in the cruiser Terrible, and, lastly, 390 ft -i- 75 ft. = 5'2 in the battleship Magnificent. 8. The last to be considered of the principal dimensional elements of a ship is the draught, or draft. In resistance calculations by draught is meant the depth of the extreme bottom of the ship from the surface of the water, less the Fio. 7. depth of the keeL This may be termed the effective draught. Most modern ships, however, have no projecting keel, because the double bottom gives all the strength required. As a ship usually draws more water at the stern than at the bow, especially when running at a high speed, the mean draught must be taken. Choosing the breadth or " beam " of a ship as the unit of comparison with draught, as is usual, we find that the ratio of draught to breadth in the Britannic is 23'5 ft. H- 45 ft. = 0-522, in the Campania is 23 ft. -r 65 ft. = 354, in the Terrible is 27 ft. -H 71J ft. = 0'378, and in the Magnificent is 27i ft. ^ 75 ft. = 0-366. Comparing the Britannic with the Campania, both designed for the Atlantic passenger service, it appears that the largest modem vessels are considerably shallower relatively to the beam than somewhat older vessels. The 26 THE EESISTANCE AND POWER OF STEAMSHIPS. explanation of this development is that, while displace- ments are ever increasing, the depths of harbours, ship canals, and docks remain stationary ; a consideration which seriously trammels designers, and compels them to adopt shallower vessels than are known to be desirable on the score alike of structural strength, economy of construction, and seaworthiness. A very common ratio of draught to breadth in the case of moderate-sized screw cargo boats is about 055, and in modern cruisers about 0'37. The above statement scarcely applies to the latest White Star liner Oceanic, in which a bold departure has been made in adopting the unprecedented draught of 32| ft., this being 7 ft. greater than that of the Great Eastern. The following comparison between the general proportions of two recent and two older Atlantic liners is instructive : — Ship. Company. Date. L B d L a d " Oceanic ) Britaiiuic j Campania % Servia f White Star . . i Cunard < 1S99 1874 1S93 1881 Feet. 680 450 600 510 Feet. 68 45 65 62 Feet. 32-5 23-5 23 23-26 10 10 9-2 9-8 •478 •522 •364 ■448 Tons. 28,500 8,600 IS,000 9,900 A relatively smaU beam and long parallel middle body have always been characteristic of the White Star liners built by Messrs. Harland and Wolff, experience having proved that the resulting form of ship is good for speed in a seaway. On this matter of the best form of model for sea- going ships some critical remarks were expressed in a recent issue of Engineering (vol. Ixvii., page 53), which we take the liberty of quoting : — "We have no doubt that, for a given displacement, the models of the White Star steamers might be increased in width and fined at the ends, with the result that higher speed would be attained on a given power. Tank experi- ments have pointed to this result, and designers, relying on RESISTANCE FACTORS. 27 28 THE EESISTANOE AND POWER OP STEAMSHIPS. tank experiments, have accordingly gone on these lines. It must be remembered, however, that tank experiments are made in smooth water, whilst the motion of the waves introduces quite a new set of conditions. The White Star steamers are notoriously good timekeepers in stormy weather; so it would seem that the comparatively long ship, even with shorter entrance and delivery (or run), is better to drive through rough seas than the wider and finer ship, although the reverse may be true of smooth-water performances." For the accompanying interesting diagram, showing the development of Ounard steamers, we are indebted to a, hand-book published by the Cunard Steamship Company. The symbols and units of measurement of the principal quantities so far introduced are tabulated below : — Quantity Sj mbol. Unit. Abbreviation. Resistance Speed Power Wet surface Displacement Length Breadth Draught Immersed mid-area Length of entrance Angle of entrance . . R V V H.P. S D L B a M B Pound Knot Foot per second . Horse power . . . . Square foot Ton of 2,2401b. .. Foot Foot Foot I Square foot ... . Foot Degree lb. ft. / sec. pq. ft. ft. ft. ft. sq ft. ft. BLOCK COEFFICIENT. 29 CHAPTEK V. Coefficients of Form. We next proceed to explain the nature of the varions coefficients or ratios employed to define the form of a ship, and to determine their values in the case of a few well- known steamships. They are rather numerous, and need to be carefully discriminated, to prevent confusion. The following are. the names of these ratios, and the symbols we shall use in connection with them ; though, unfortunately, there is no standard notation : — (1) The coefficient of fineness of displacement (C/), also called simply the coefficient of fineness, the displacement coefficient, and the block coefficient. (2) The coefficient of water lines (Cw), also known as the cylindrical coefficient and the prismatic coefficient. (3) The midship-section coefficient (Cm). (4) The water-plane coefficient (Cwp). From a knowledge of these coefficients the experienced naval architect is able to form a good idea of the shape of the vessel to which they refer, and by their aid to readily compare halls of different types. 1. The coefficient of fineness, or block coefficient, is the form factor or characteristic oftenest used in every-day practice. It is defined as the ratio which the volume of water dis- placed by the hull, at a given mean draught, bears to the volume of a rectangular block having the same length and breadth as the ship, and also a depth equal to the ship's effective draught — i.e., the mean draught diminished by the depth of the keel. More briefly expressed, „ . ^ , ^ volume of hull below water coefficient of fineness = ^^lume of enclosing rectoid ' the term rectoid being used in place of the more cumbrous names "rectangular solid" or " parallelopipedon." Fig. 8 will serve to make the definition clearer. 30 THE EESISTANUE AND POWEE OF STEAMSHIPS, It is easy to express these volumes in terms of the princi- pal dimensions of a ship. A ton of sea water, we know, occupies practically 35 cubic feet of space, and so the number of cubic feet in the immersed part of the hull must in every case be thirty-five times the number of tons (D) of water dis- placed by the ship. Again, the volume of a box having the Fig. 8. same principal dimensions as the ship is L ft. x B ft. x d ft, see fig. 8), Hence the value of the coefficient of fineness is given by the much- used formula, ^ L X B X rf' For example, disregarding the keel correction, the coeffi- cient of fineness of the famous Atlantic liner Campania is ft. 3 35 ^^^^ X 18000 tons ton = 0702 ; 600 ft. X 65 ft, X 23 ft, and of the cruiser Terrible, the largest in existence, is (35 X 14200) cubic feet ^ ^.^^^ . 500 ft. X 71-5 ft, X 27 ft. ' and, similarly, of the first-class battleship Magnificent is 35 X 14900 390 X 75 X 27 '5 = 648 : BLOCK COEFFICIENT. 31 and, lastly, of the torpedo-boat destroyer Daring is 35 X 2 20 „.„„. These are all fine-lined high-speed vessels, the last one extremely so. It will be observed that the Campania, measured by the above index, is distinctly coarser than the warships. Merchant vessels of the better class have block coefficients lying between 056 and 75. In very full cargo boats the value is about 0"82; these boats being of the so-called "tramp" class, and not designed to travel at a greater speed than 8 or 9 knots. Eut the use of a higher block coefficient than 0"8 results in a very unsatisfactory vessel in respect of steering qualities and efficiency of pro- pulsion ; the behaviour of a vessel being adversely affected by fulness of the ends. The influence of absolute size, however, cannot be overlooked ; as it is well known to shipbuilders that, for a given speed, a very large vessel may well be given a much higher block coefficient than a small vessel. This is further exemplified by the recently-launched Oceanic, whose block coefficient is 35 X 28500 ^ „,gg^ 680 X 68 X 3-25 ^' In bad weather the advantage to a ship of good form is very noticeable. Take, for example, two ships of the same displacement and trial speed ; one of them being short, broad, and with very full ends ; the other longer, narrower, and having finer ends. In calm weather both these vessels might attain the intended low speed of 10 knots, say, with the same engine power ; but on encountering heavy seas and head winds, the full vessel would probably fall in speed to 5 knots or so, while the finer vessel would not be afiected to anything like the same extent. The latter would un- doubtedly travel faster than the full vessel with the same consumption of coal. Thus in foul weather it is possible for a slow boat, if well formed, to beat a faster smooth-water boat, if ill shaped. 32 THE RESISTANCE AND POWEK OF STEAMSHIPS. An inverse problem to that of finding the coefficient of fineness corresponding to a given displacement and leading dimensions is the determination of the displacement avail- able with a given value of C/ and given dimensions. This arises in the preliminary stages of a design, and is jnst as easily dealt with as the direct problem. It is only necessary to substitute the known values in the equation 35D = C/xLxBxc? and solve for the unknown term. For instance, the dis- placement of a proposed ship, 230 ft. x 29 ft. x 13 ft., and having a 0/ of 0'6, is D = 06 X 230 X 29 X 13 -=- 35 = 1,485 tons. Inadequacy of Of as an Index of Fineness. Although the block coefficient C/ is very useful for the purpose of general comparison, it must be used very cautiously when comparing vessels of different types, such as cargo boats with warships, since it fails to give us any exact information regarding the fineness of the water lines of the ships compared. For this reason the common name " coefficient of fineness " is rather misleading, and the name " block coefficient " is preferred by many shipbuilders. On the same displacement a long fine-ended ship and a broad full-ended ship may have the same coefficient of fine- ness. In fact, it is possible for a vessel with very fine ends and a long middle body to have a higher value of C/ than a vessel with fuller "ends and shorter parallel middle body ; C/ NOT A TRUE INDEX OF FINENESS. 33 the influence of the ends being more pronounced in the shorter vessel, because they form a greater proportion of the whole. This argument will be readily understood from fig. 9. To emphasise the inadequacy of C/ as a measure of fine- ness, when used alone, consider two ships A and B, which have the same principal dimensions and the same displace- ment, but difierent midship sections, as shown in fig. 10. Fig. 11. Here the ratio 35D-^LxBx(:^is the same in each ship ; but the hull of B has the coarser lines, since the smaller midship section can be compensated for only by fuller ends, as seen in fig. 11. Fine &h-ip. 7u//| Sh;p. Fio. 12. The most extreme comparison of types possible is that between two hypothetical hulls A and B, of like dimensions and displacement, and yet difiering in immersed midship section to the extent shown by fig. 12. 3s 34 THE RESISTANCE AND POWER OE STEAMSHIPS. The entire immersed parts of these hulls are clearly represented in the isometric views of fig. 13, a glance at which will make it plain that in each case the shaded block is one-half of the whole enclosing rectoid, and, therefore, that the block coeflScient is 0"5 in each. Nevertheless, the one hull, B, is absolutely blunt-ended, while the other, A, is very sharp. Clearly, then, C/ is not a very discriminating Fia. 13. index of fineness ; and, in fact, it is rather apt to mislead the unwary. Other coefficients are, therefore, essential to dis- tinguish completely the various forms of ships. Prismatic CoBPFtciBNT. 2. The coefficient of water lines, also known as the " pris- matic coefficient" and the "cylindrical coefficient," stands next to the coefficient of fineness in respect of generality of usaga It is defined as the ratio which the volume of the immersed part of the hull bears to that of a prism of equal length, and whose uniform sectional area is the same as the area of the immersed midship section of the vessel. Putting this statement in symbols, we have 35 D \JW L X M' where M square feet is the area of immersed midship section, or, as it is often called, the " immersed mid-area." PRISMATIC COIFFICIENT. 35 The definition will no doubt be better understood when considered in connection with fig. 14, which represents a trough of prismatic form, having a section precisely the same as the midship section of the model shown within it. The prismatic or cylindrical coefficient of the ship is the ratio — contents of model -4- contents of trough. In further illustration of the definition, the hypothetical ships A and B, shown in fig. 12 and fig. 13, may well be again referred to. The midship section of the model A is the rectangle B x d, and of the model B is J B x d ; so that, Flu. 14. from the definition, the prismatic coefficient of B is twice that of the sharp-ended model A. This coefficient, in fact, is precisely unity in the case of B, the ends of which are absolutely blunt, and, therefore, the lines of maximum coarseness. The alternative name, "cylindrical coefficient," which often appears in lieu of "prismatic coefficient," seems scarcely appropriate when the ordinary meaning of " cylin- drical " is alone considered. It should be remembered, how- ever, that the extended mathematical meaning of " cylinder'' embraces not only circular cylinders, but solids of any uniform section whatever. Still it is a pity^at so many names are applied to the same coefficient by difierent naval architects. It would be a distinct advantage if all would agree to call the same ratio by the same name. Of the two. 36 THE EESISTANCE AND POWER 0¥ STEAMSHIPS. we ourselves prefer the name "prismatic coefficient,'' the other not being at all in harmony with the average engineer's idea of a cylinder. A rough average value of the prismatic coefficient is 0'7 ; but, as it varies so much in different types of vessels, it will be advisable to apply the formula to the calculation of Cm for a few actual ships. Thus, in the case of the Cnnarder Campania, P = 35 D = (35 X 18000) cub, ft. _ „.^„„ L X M bOO f c. X 1334 sq. f c. In the old White Star liner Britannic, p _ 35 X 8500 _ „.,7, . ^"-450x 926-°^^^ In the United States cruiser Yorktown, InH.M.S. Iris, C. = II X ^6^0 = 0-603. 226 X 432 p _ 35 X 3290 _ „.. .„ *^"-300x700-*'^*^- The above are all high-speed ships. In the case of the Garonne, a 14-knot boat, p _ 35 X 46 35 „.„„3 370 X 656 Lastly, the 12-knot boat Booldana has a prismatic coeffi- cient of 35 X 4720 320 X 664 = 0778. This coefficient of water lines, or prismatic coefficient, is of a less misleading nature than the block coefficient, and gives a better notion of the fineness of the ship. The following table of values of the block coefficient (C/), and the prismatic coefficient (C™), is given on the authority of Mr. A. E. Seaton, managing director of Earle's Shipbuild- ing and Engineering Co., Hull. MIDSHIP SECTION COEFFICIENT. 37 Sort of ship. Finely-shaped Fairly-shaped Ordinary merchant steamers, 10 to 11 knots. Oargo steamers, 9 to 10 knots Modem cargo steamers of large size From the above tabulated values it will be noticed that in vessels of the same type the coefficient of water lines is about 0'06 greater than the coefficient of fineness. An inverse problem to that of finding Ow may here be mentioned. We sometimes know the length, the displace- ment, and the prismatic coefficient of a ship, and require from these data to calculate the immersed mid-area. This is readUy done by throwing the formula 35 D into the shape o« M = L X M 35 D L X (Jm and making the necessary substitutions. For instance, the immersed mid-area of the 15-knot steamship Charles V. is = (35x2478) cub ft. ^ ^ 313-5 ft. X 658 ^ 3. The midship section coefficient is the next form factor to be considered. It is defined as the ratio of the immersed 38 THE EESISTANCB AND POWER OF STEAMSHIPS. midship section of a ship to the area of the enclosing rec- tangle, as shown in fig. 15. The symbolic expression of this ratio is For example, in the case of the Campania, C™= 1^34 sq. ft. =0-893: ™ 66 ft. X 23 fc. ' and in the Britannic, and in the United States cruiser Yorktown, ^- = 36^3 = ''''■ Ships with a high "rise of floor," like yachts, have the least valne of Cm, going as low even as 0'6 ; and vessels with flat floors have the greatest. Modern steamships have much flatter floors than the older sailing vessels, in order to increase the displacement on a given length, and the space available for engines, boilers, and coal bunkers. Designers Fig. 16. now recognise that it is better to gain displacement by the use of a full midship section than by the use of bluff ends. In some very full cargo boats the midship section differs little from a rectangle, the coefficient reaching the high value of 0'98 ; while it seldom falls below 0'7 in large vessels of any type. Belation between tJie foregoing Coefficients. — Knowing any two of the form factors Cf, Cm, and Cm, the third can be found from the relation O/ = Ow X v^m, RELATION BETWEEN COEFFICIENTS. 39 the verification of which is that 35 D _ 35D ^ M LxBxrf LxM B X d' this being evidently true. Thns, in the case of the Cam- pania, we have ■703 = -787 X -893. This interdependence of the coefficients forms a useful check. Taking a final complete example, the United States gun- boat Nashville has the following dimensions : — Displacement on trial 1,335 tons. Length between perpendiculars 220 feet. Beam 38 „ Mean draught of water 11 „ Area of immersed midship section 370 sq. ft. Hence Of = 35 D ^ 35 X 1365 ^ .g,Q ^ L X B X rf 220 X 38 X 11 n - 35 D _ 35 X 1365 .^a>7 ^" ~ ir^TM ~ 220 X 370 '^ ^^^ p M 370 _ .oofi The test of correctness is that = -587 X '886 = -519. 4 The water-plane coefficient of a ship is the last form factor to be defined. It is the ratio of the area of a horizon- tal plane bounded by the water line of the ship to the area of the enclosing rectangle, as shown in fig. 16. Expressed symbolically, „ area of crater plane ^"■^■- IT^TB • Its value commonly ranges from 0'7 to 0'9. This coefficient, however, is very little used, and therefore need not concern us further. 40 THE EESISTANUE AND POWER OF STEAMSHIPS Hints. — It is possible that some readers, to whom all the above coefficients are new, may have some difficulty in dis- tinguishing and remembering them. To such, a hint or two may be helpful. The only mnemonical artifice here necessary is the very common one of recalling the various diagrams which embody the definitions, and from them writing down the several formulse. It will be observed that, as regards C/ and Cm, the numerators of the formulse are both alike, and are the volumes of ship-shaped solids, while the denominators are the volumes of the enveloping prisms. As regards the other two coefficients, the numerator of each is the area of a certain plane figure, vertical in one case and horizontal in the other ; and the denominator is the area of the enveloping rectangle. By bearing in mind these simple facts, it becomes almost impossible to confuse one ratio with another. Still it is a good plan to write down the four expressions in tabular form, and to sketch alongside of each its proper diagram, so as to keep clearly in view the physical meaning of the various ratios. Similar Ships Defined. — In the language of the naval architect, two or more ships are said to be similar when they have — (1) The same block coefficient ; (2) The same prismatic coefficient, and, therefore, also the same midship section coefficient ; (3) The same ratio of length to breadth ; (4) The same ratio of draught to breadth, and, therefore, also the same ratio of length to draught. The ships compared may be of any size. One of them may even be a model only 10 or 12 ft. long, and the other fifty times that length. Later on we shall point out an important relation between the powers required to drive similar ships at speeds related in a particular way to their lengths. Vessels that are both similar and identical in size are termed sister ships. For instance, the Campania and the Lucania, also the Powerful and the Terrible, are sister ships, RESISTANCE OF A STEAMER STARTING FROM REST. 41 It is more economical in first cost to build a number of sister ships than the same number of ships, not superior in size and quality, but each differing slightly from the other. The employment of sister ships by the same company also leads to some saving in maintenance expenses, though the saving is probably less marked than in the analogous case of sister locomotives. CHAPTER VI. Resistance of a Steamer Starting from Rest. The clearest idea of the several elements composing a vessel's resistance is afiorded by considering their successive growth in the case of a steamer starting from rest and gradually attaining a high speed. Consider, then, a large steamship, initially at rest relatively to the sea of water in which she floats. When her propeller begins to rotate, a short interval of time elapses before motion is perceptible. Daring this brief period the entire thrust of the propeller is employed in overcoming the passive resistance of the ship to change of motion, or, in other words, in overcoming the ship's inertia. The quicker the ship is set in motion the greater the thrust required to overcome this inertia ; for, by Newton's second law of motion. /the force\ _ / the mass \ /the acoeleration\ \ applied / \ set in motion/ \ produced / Consequently, no finite force, however great, will instanta- neously set a ship in motion. In a few seconds the motion of the vessel becomes quite evident ; and, as the propeller continues to rotate, the speed steadily increases. Daring the period of acceleration, or time of getting up speed, the resistance to motion consists partly of the vessel's inertia and partly of the friction of the 42 THE EESISTANCE AND POWIE OP STEAMSHIPS. water against the immersed surface of the vessel. This latter frictional drag, arising from the viscosity of water, is termed the skin resistance. At a moderate uniform speed the skin resistance constitutes fully 80 per cent of the tow- rope resistance of a well-formed ship. The energy so spent in friction is ultimately transformed into heat. Part of the energy transmitted to the propeller is used up in imparting kinetic energy to the vessel, this being stored up in much the same fashion as the energy of a flywheel, and having a similar steadying effect on the motion. In this respect, therefore, weight, or massiveness, is a great advantage to a tug boat, and, indeed, to all ships. Great length, size, and weight enable ships to maintain their speed better in a seaway. Another portion of the energy supplied to the propeller is expended in producing surface disturbance of the water — that is, in making waves ; the resistance due to the produc- tion of waves being known as the wave-making resistance. This energy also is ultimately dissipated in the form of heat, and rendered unavailable. The speed of the ship gradually increases with the rate of rotation of the propeller ; and, very soon after the engines have reached their maximum revolutions, the acceleration ceases ; or, in other words, the speed becomes constant. This is the normal state of affairs in calm weather. The inertia resistance has now completely vanished, and only re-asserts itself when the motion ceases to be uniform. Resistance Curves. — The above facts are clearly represented in fig. 17, in which the assumed speed curve shows how the speed increases from nothing to 20 knots at the end of four minutes, and then remains constant. For convenience, the acceleration is assumed to remain constant for a minute at a time, and then to change suddenly, as shown by the stepped line fig. 18. The resistance due to the inertia of the ship falls off simultaneously with the acceleration, as shown dotted in fig. 19 ; while the frictional or skin resistance in- creases in proportion to about the square of the speed, or, more accurately, as the l'83rd power. KESISTANCE CURVES. 43 V i 25^ UiwiTlSi Fio. IS. ""i ^ % J» MiiwlK. 's Fig. 20. 44 THE EESISTANCB AND POWER OP STEAMSHIPS. The curve marked t«(i?;« represents the resistance due to surface disturbance, or the formation of waves. This is negligible at low speeds in finely-formed ships, but it increases very rapidly at high speeds, and may even con- stitute the greater part of the resistance. Wave-making resistance varies approximately as the square of the speed at low speeds, but the index ot variation increases as the speed rises, even passing beyond the value 4. The curve of combined resistance is arrived at by adding together the ordinates of the inertia, skin, and wave resistance curves at the end of each minute. The "power curve, fig. 20, is drawn by setting up ordinates proportional to the products of the heights of the corres- ponding speed and resistance ordinates, and drawing a fair curve through their summits. The enormous increase of power required to produce a small gain of speed, during the fourth minute from rest, is very noticeable. The curves drawn are about correct for the United States warship Yorktown, to which further reference will be made. Mince Resistances. In addition to the above-named principal sources of resist- ance, there are still some of rather less importance. One of these is due to the formation of little whirlpools, eddies, or broken water, arising from abrupt changes of form. The irregular motion of the water aft causes a diminution of pressure on the stern, which becomes manifest as an increase of resistance. The production of eddies occurs chiefly at the stern, a defective shape of stern causing largely increased eddy making ; but in well-formed ships the eddy-making resistance is only about 6 per cent of the skin resistance. Its magnitude varies as the square of the speed. Another species of resistance, of importance in screw vessels, is known after Bankine as the propeller augment of resistance, or the propeller suction. Mr. Fronde calls it the "thrust deduction.'' This arises from the suction of the water from the stern of the ship by the action of the screw ; AIE RESISTANCE. 45 thus diminiahing the forward pressure on the stern, due to the closing in of the displaced water. It is most marked in bluff ships. The precise action will be better understood after we have considered the theory of stream lines, as -will also the reason why the use of twin screws has the effect of reducing the propeller suction. From some experiments of the late Dr. William Froude, it appeared that, in single- screw ships, the propeller augment was equivalent to an increase of from 40 to 50 per cent upon the tow-rope resistance at the same speed. Mr. R. E. Froude, however, has since pointed out that this high estimate includes the resistance of thick square stern posts and appendages to the propeller, and that the augmentation proper varies from 8 to 18 per cent only, the lower value referring to twin- screw vessels with fine lines. Air Bedstance. — The last source of resistance requiring mention is that arising from the immersion of the above- water portion of a ship in an ocean of air, viz., the wind resistance. This is partly f rictional in character, and partly a direct head resistance. Its magnitude varies as the square of the wind's speed relatively to the vessel. Dr. Froude, in his classical experiments with the Grey- hound, when unrigged, found that a force of 330 lb. repre- sented the effect on her hull of the wind blowing past the ship at a speed of 15 knots. Had she been masted and rigged, the resistance would have been about double, the increase being due to the opposition of the masts and rigging to the passage of the air. Some figures given by Sir W. H. White are interesting. When the Greyhound is moving at a speed of 10 knots through still air, the total air resistance of the hull, masts, rigging, and funnel is about 300 lb., the corresponding total of water resistance being about 10,2001b. Thus the air resistance at 10 knots is about a^ of the water resistance. Farther, if the same ship were to steam head to wind at a speed of 8 knots, the actual speed of the wind being 7 knots, the air would pass the ship with a 46 THE EESISTANCE AND POWER OF STEAMSHIPS. relative speed of 15 knots. At that speed the air resistance would probably amount to about 650 lb., and the total water resistance at 8 knots would be about 5,6001b., assuming the water to be smooth. Thus the ratio of the two resistances is about 1 to 9. The above figures, though not exact, are sufficiently cor- rect for the purpose of illustration, and they serve to explain the considerable decrease in the speed of a ship when steam- ing head to wind, especially if rigged. Froude's Eule for Air Resistance. — The late Dr. Froude suggested a rale for calculating the air resistance of a ship's hull, which is given by Sir W. H. White in the following words : " If the above- water portions of the hull are pro- jected back upon the midship section of a ship, and the total area (A) enclosing these projections is determined, then the air resistance on that area (A) will approximately equal the air resistance on the hull for any assumed speed." Unfortunately this rule, as it stands, is incomplete and scarcely intelligible ; but it is made rather clearer by refer- ence to a particular example. In the case of H.M.S. Grey- hound, the projected area (A) was rather less than 400 square feet, the displacement of the ship being 1,160 tons. Now, Froude found by experiment that the air resistance per square foot, on a plane area, was about 0017 of a pound, at a speed of 1 ft. per second. Consequently, since the speed of 15 knots is about 25 '3 ft. a second, and the air resistance varies as the square of the speed, the pressure per square foot of area at 15 knots should be about 25-32 X 00017 lb. = 1-09 lb. By the present rule, then, the pressure on the hull of the Greyhound of air passing the ship at a relative speed of 15 knots should be about 436 lb. ; but actual experiment gave only 3301b. The agreement between the calculated and the observed resistances is therefore not very close, the former resistance being 32 per cent too high. Nevertheless, this approximate rule is useful in comparing different types Taylor's rule. 47 of ships ; and, when applied to mastless ships, it gives a rough estimate of the total air resistance at any assigned relative speed of wind and ship. As an extreme case, it will be instructive to calculate the approximate air resistance at the highest speed of wind that the ship in question can possibly encounter. A hurricane blows at a rate approaching 100 miles per hour, or 147 ft. per second. This corresponds to a pressure per square foot of about 147^ X 00017 lb. = 36-7 lb. Hence the resistance on 400 square feet of projected area wiU be something of the order of 400 X 36-7 lb. = 14680 lb. This force is equal to the total water resistance on the same ship at a speed of about 11 knots. Taylor's Rule for Air Resistance. — Mr. D. W. Taylor, of the United States navy, states that, for a rough approxima- tion, the resistance of the air in pounds may be expressed by the formula, Ra= -005 A V2, where A is the area in square feet of the upper works rigging, &c., opposing the air, and V is the speed in knots of the air past the ship. Presumably the actual and not the projected area is meant, but as no examples of the application of the rule are given, this point is doubtful. Mr. Taylor summarily dismisses the subject in the words, "the air resistance is so small, comparatively, that it may be neg- lected, except for a type that is obsolete — or nearly so — the full-rigged steamer." Summary of Ship Resistances.— The various elements com- posing the resistance of a steamship may now be tabulated as under : — 1. Inertia resistance, due to the reluctance of the ship to change of momentum. Absent at constant speed. 2. Skin resistance, caused by the friction between the water and the immersed surface. 48» THE EESISTANCE AND POWER OF STEAMSHIPS. 3. Wave resistance, arising from the surface disturbance of the water and the consequent formation of waves. 4. Eddy resistance, resulting from bluntness of shape and the consequent production of eddies. 5. Propeller augment of resistance, or the thrust deduc- tion, caused by the suction of the screw. 6. Wind resistance, due to the resistance of the ship's superstructure to air in motion. The more important of these will receive detailed con- sideration hereafter. The name residuary resistance, we may here point out, has been given by the Froudes to the difference between the tow-rope resistance of a ship, at a given constant speed, and the skin resistance. It is therefore equal to the sum of the wave and eddy resistances, and differs little from the wave-making resistance alone. Waste Work. — It must not be forgotten that the combined resistances to the motion of a vessel do not constitute the entire load on its engines. There is, in addition, the internal friction of the mechanism, the pump loads, the friction of the shaft bearings and thrust block, as well as the frictional resistance of the propeller blades. But these, though im- portant, scarcely come under the head of ship resistances, the entire ship resistance being a force external to the vessel. They must rather be debited to the mechanism of propulsion. These losses, in the aggregate, represent a large but unavoid- able waste of energy. In fact, not much more than one-half of the indicated power of the engines is usefully employed in overcoming the external resistance. The frictional resis- tance of the screw itself, according to Froude, is somewhere about 10 per cent of the tow-rope resistance of the whole ship. MAGNITUDE OF RESISTANCE. 49 CHAPTER VII. Magnitude of Resistance. Unfoetunately very few fall-sized ships have been system- atically towed at various speeds with the express object of measuring their actual resistances. Many years ago, however, the late Dr. Froude carried out some careful experiments Merkara. Grej hound. Service Merchant, for steam only. Warship, for sail or steam. Fairly fine. 3,9S0 BluEf. Displacement tons 1,160 Length ....feet 360 172^5 ....feet 144 75 Breadth (extreme) ....feet 37-2 S3 •a 9-7 4^8 Draught (mean) ....feet 16-.5 I 13-75 Block coefficient •64 •515 Immersed surface , square feel 18,660 7,540 Maximum speed under ateam .. . ..,lalot^ 13 10 Tow-rope resistance— ....lbs. 2,240 5,150 8,740 13,440 20,160 25,760 1,344 ....lbs. 3,140 ....lbs. 5,600 ....lbs. 10,630 ....lbs. 20,150 ....lbs. Ratio ^^^^°^^^ resistance total resistance at 8 knots •85 ■70 •80 ■35 Ratio of resistance to weight of ship at 1 to 442 1 to 12D 4s 50 THE EE&ISTANCE AND POWER OF STEAMSHIPS, with two vessels of different types, viz., the Greyhound, placed at his disposal by the Admiralty, and the Merkara, by Messrs. Denny Brothers, of Dumbarton. Particulars of these ships, as well as the valuable results arrived at, are given on page 49. In fig. 21 the above results have been plotted, and the resistance curves drawn. The Greyhound, herself a slow ship, was towed by another steamer at various speeds up to 13 knots, or 3 knots higher than could be attained by her own engines. Owing to her bluff form, the wave-making 26,OQQ. LBS. .aoiOOii r < 1- in S) ui DC ui lO.OQQ 0. o i -\ T— T— c-r '5 • I'o SpE-ED IN Knots \'5 resistance was excessive at the higher speeds. Thus, at a speed of 8 knots the skin or frictioual resistance was 70 per cent of the whole, while at 12 knots it amounted to only 35 per cent, the remaining 65 per cent representing the wave and eddy resistances. In the case of the Merkara, a finer ship, the proportion of the skin resistance changed only from SPEED TRIALS. 51 85 to 80 per cent of the whole as the speed rose from 8 to 12 knots. We therefore conclude that the length of entrance and run in the Greyhound was insufficient for a speed of 12 knots. From the above figures, the approximate law, that the resistance of a ship varies as the square of the speed, is seen to hold fairly well only so long as the skin resistance forms the greater part of the total resistance. Thus, for the Merkara we have E at 12 knots : R at 6 knots = 20160 : 5150 = 4 to 1, nearly. Again, in the case of the Greyhound, E at 8 knots : E at 4 knots = 5600 : 1344 =- 4 to 1, nearly. But if we compare the resistance of the Greyhound at 12 knots with that at 6 knots, we have 20150 -r- 3140 = 6-4, instead of 4 ; so that the resistance no longer varies as the square of the speed. In fact, at 10 knots E '^ V^, nearly ; and at 12 knots E X V*, nearly. Not long after the speed trials of the Greyhound, Sir W. H. White wrote as follows : " Considerable lengths of entrance and run are advantageous, not merely in adapting vessels for high speeds, but in keeping down the law of increase, in terms of the velocity, for more moderate speeds. If economical performance under steam were the sole or principal condition to be fulfilled in the Greyhound, it would undoubtedly have been preferable to adopt greater propor- tions of length to breadth, and finer forms at the extremities. Then, with the same lengths of entrance and ran, associated perhaps with a certain length of middle body, there would probably be somewhat greater frictionil resistance than in the actual ship, but a very considerable decrease in the wave- making resistance ; and on the whole a less resistance would have to be overcome in obtaining the designed speed. S loh 52 THE EESISTANCE AND POWEE OF STEAMSHIPS. latitude of choice in forms and proportions was not, however, possible in the design of the Greyhound. She was intended to be efScient under sail, as well as to have moderate speed under steam ; hence moderate proportions of length to breadth became necessary, in order to secure sufficient 'stiffness' and handiness. Greater fulness of form at the extremities, accompanying these moderate proportions, in- volved an increase in the wave-making resistance. And here we have an illustration of the fact that, in designing ships, the naval architect frequently has to put into a subor- dinate place considerations of diminished resistance and economical performance." Estimated Resistance and Power or the Yoektown. We now proceed to calculate the resistance and power curves for an actual ship of modem type, selecting as an example the United States warship Yorktown. The for- mulse made use of will be discussed later. The following are the particulars of this ship : — Displacement 1,680 tons Length 226 feet Breadth (extreme) 36 feet Length -^ breadth 628 Draught (mean) 13 feet Block coefficient '555 Immersed surf ace 10,840 sq. ft. Greatest speed on trial 17 knots. 1. The combined skin and eddy resistance = coefficient of friction x wet surface x (speed)i'** = / X S X Vl-83. Wiien the speed is 4 knots, this becomes •0094 X 10840 X 4183 = 1280 lb. Similarly, using a table of logarithms, the resistances at other speeds are calculated, and tabulated as follow : — THE YOEKTOWN. 53 Speed V. yi'ss Skin and eddy resistance. Wave resistance. Total resistance. Knots. lbs. lbs. lbs. 4 12-6 1,280 72 1,362 8 45 4,580 1,147 5,727 12 94 9,550 5,800 16,350 16 160 16,270 18,350 34,620 20 240 24,400 44.800 69,200. 2. The wave resistance for such a ship is approximately 28 V*, by -which we calculate the values given in the table. For instance, at 4 knots we have wave resistance = "28 x 256 = 72 lb. Comparison of the Calculated Probable Indicated Horse Power with the Actual. — At 16 knots, or 1,621ft. per minute, 34620 X 1621 useful H.P. = 1700. 33000 Assuming an efficiency of propulsion, at this speed, of '55, probable I.aP. = 1700 -h -55 = 3100. The actual indicated horse power was 2,950. At 8 knots, or 810 ft. per minute. useful H.P. = 5727 X 810 = 140. 33000 Assume a low efficiency at low speeds, say '5 ; then probable I.H.P. = 140 -^ -5 = 280. The actual was 286. 3. Inertia Effect. — We have still to consider how the inertia resistance is calculated when the speed is increasing. Assuming the ship to start from rest and attain a constant speed of 20 knots in four minutes, as represented by the series of curves, figs. 17 to 20, page 43, we have : — 54 THE RESISTANCE AND POWEK OF STEAMSHIPS. luc •ease of speed. Average acceleration. In 1st minute .... S knots S knots per min. = ■2256ft./sec.-' 2nd „ 6 „ „ = -1692 3rd i 1, 4 „ „ = -1128 4th „ 2 2 „ „ = '0564 The acceleration in knots per minute is reduced to the more convenient units feet per second per second, or ft./sec.^, as follows : — 1 knot per minute = 6080 ft. per hour per min. 6080 60 X 60 6080 -^ ft. per sec. per min. ft./sec.2 = -0282ft./sec.' uu X 60 X 60 . ■. 8 knots per minute = 8 X -0282 ft. /sec. 2 = '2256 ft. /sec. ^- Now, applying the general dynamical law that resistance due to inertia = mass x acceleration, we have, in the present case — Inertia resistance of ship ^ displacement of ship ^ acceleration of ship, acceleration due to gravity For the first minute this becomes — Inertia resistance = oot^°^°°%x -2256 ft/sec.^ 32 2to./sec.'' = 11-76 tons = 26320 lb. Similarly, assuming the acceleration to remain constant during each minute, though really varying, we find the other values given in the following table : — THE YOBKTOWN. Interval of time. Inertia resistance. 11-76 tons = 26,3201b. 8-82 „ =19,740 lb. 5-88 „ =13,160 lb. 2-94 „ = 6,680 lb. 2nd , Srd , 4th , Allowing for the inertia resistance, the effective power of the Yorktown, at the end of each minute daring the period of getting up a speed of 20 knots, works out as follows :— Time. Speed. Resistance. Fffective horse power. At end of— Knots.; Feet/min. Lbs. 1st minutt . . 8 810 26,000 638 2nd ,, 14 1,420 36,000 1,650 3rd „ IS 1,825 52,000 2,880 4th „ 20 2,030 69,000 4,250 The curves given in jBga. 19 and 20 were plotted from these figures. But although these powers at increasing speeds are interesting scientifically, only the powers at various uniform speeds are of much practical use; and accordingly the estimated efiective horse powers, disregarding inertia, have been calculated and plotted in fig. 22 on a speed base, from t he values tabulated below : — Speed. Estimated resistance. Effective horse pi>wer. Assumed efBciency. Eptimat'd LH.P. Actual I.H.P. LH.P. per ton. Knots Ft./min. Lbs. 4 403 1,352 16-6 •25 60 Not taktn 8 810 5,727 140 •50 280 286 0-17 12 1,215 15,350 565 •55 1,026 986 0^58V 16 1,620 34,620 1,700 •58 2,940 2,952 1^75 20 2,030 69,200 4,250 •60 7,080 fi (?) 56 THE KESISTANCB AND POWER OP STEAMSHIPS. In the same figure the actual recorded indicated horse powers of the Yorktown have also been plotted, and the curve extended beyond the actual maximum power of 3,694 units at 17 knots to an estimated power of 7,080 units at 20 knots. It is important to notice, from the table, how the eflBciency of propulsion, or the ratio of the effective to the indicated horse power, increases as the speed goes up ; the rate of 70QO -1 1 1 1 1 r- '5- „ to |'5 o ptED IN Knots. Pig. 22. increase of efficiency being greatest at low speeds. The last column of the table gives the indicated horse power required to propel 1 ton of displacement at various speeds, a figure of great service in comparing the economy of propulsion of different ships. KIRK'S BLOCK MODELS OF SHIPS 57 CHAPTER VIII. Kiek's Block Models of Ships. IiT prervioas chapters it has been shown that the important factors of a vessel's resistance are the area of wet surface and the lengths, as well as the angles, of entrance and rnn ; so that a simple approximate method of arriving at these particulars is a desideratum. Dr. A. C. Kirk, of Qlasgow, has solved the problem in a very neat and satisfactory manner, as we shall now proceed to show. In the year 1880 Dr. Kirk read an important, though short, paper before the Institution of Naval Architects, entitled " A Method of Analysing the Forms of Ships, and Determining the Lengths and Angles of Entrance." (See vol. xxi. of the Transactions.) In tabulating the results of progressive trials, Kirk, in this paper, emphasised the necessity of analysing the shapes of the ships tried, and also pointed out how difficult and tedious it was to find, from ^ 83-8 — the working plans of any vessel, the actual lengths and the mean angles of entrance and run. He had therefore devised a method of reducing the form of any ship to that of a remarkably simple geometrical solid ; so that the general shapes of different vessels could be readily compared, and the approximate wet surfaces calculated with the utmost 58 THE RESISTANCE AND POWER OP STEAMSHIPS. Fig. 23 will serve to give a general idea of the so-called Kirk's block model. The top of the block is supposed to float level -with the surface of smooth water. The total length AB represents the length of the ship between perpendiculars, and the depth of the block G L is the same as the mean draught of the ship, excluding the keel. The sectional area through the parallel part H K is equal to the immersed midship section of the vessel ; and, lastly, the total volume of the model is the same as the cubic displace- ment of the ship. The width of the block model, however, is less than that of the ship. Example. — A numerical example will best illustrate the mode of constructing a Kirk's block model, and we therefore Pig. 24. proceed to calculate the dimensions of the block model for a ship of the following size : — Length L = 240 ft. Breadth B = SIS ft. Draught d = 13-5 ft. Immersed mid-area M = 386 square feet. Displacement D = 1723 tons. Keferring again to fig. 23, on which the dimensions have been marked, we have — kiek's block models of ships. 59 Breadth of block x draught = immersed mid-area ; .-. 6 X 13-5 ft. = 386 square feet ; .-. 6 = 386-M35 = 286 ft. It is most important to notice that the block model is narrower than the actual ship, the amount of difference between them deppnding on the shape of the midship section of the ship. A glance at fig. 24 will make this clear. The shaded rectangle represents the section of the block model, and the figure N O F IS* the midship section of the ship. For both figares to have the same area and depth, evidently N P must be greater than G C. {i.28-6 — Fia. 25b. In every block model it is assumed that the length of entrance, or "forebody," is equal to the length of run, or " after-body." Hence, for the purpose of finding the volume of the model, we may reduce it to the more simple geometrical form indicated by fig. 25. Here the triangular pieces from 60 THE EESISTAJSTCE AND POWEE OF STEAMSHIPS. one end have been fitted to the other end, so as to make a rectangular block of the same capacity as the block model. Volume of block = A K x immersed mid-area, = (A K X 386) cubic feet. Also Cubic displacement of ship = 1723 x 35 cubic feet. Equating these values, we have AK X 386 = 1723 x 35. From which we find that AK, or L - E, is 156'2ft. Hence the lengths of entrance and run of the ship in question are each 240ft. - 156-2 ft. = 838 ft. To Calculate the Wet Sukfacb of a Kiek's Block. As a block model is in every case supposed to float with its top surface on a level with the water, it is evident that the surface immersed is the sum of the area of the base, the two parallel sides and the four sloping sides forming the entrance and run. Referring to fig. 23, we have, in the present case, Area of base = AK x GC = 156'2 x 28-6 = 4467 sq. ft. Area of two parallel sides = 2 (F G x G L) = 2 x 72-4 X 13'5 = 1955 square feet. Area of four end pieces = 4 (G B x G L) ; GB = VGK-' + KB'' = ^A 14-32 +83-82 = 84-8 ; .-. area of end pieces = 4 x 84-8 x 135 = 4579 square feet. The total wet surface of block is the sum of these areas = 11001 square feet. The actual wet surface of this ship was 9,680 square feet, so that the ratio wet surface of ship _ „.„„ wet surface of model To Find a Ship's Mean Angle of Entrance and Run. — The angle HAD, fig. 23, is the half angle of entrance and run, and its tangent is the ratio HP ^ 14-3 _ . „ A H 83^ - ^^°^' KIKK S BLOCK MODELS OF SHIPS. 61 Oa referring to a table of tangents, we find that the angle HAD = 9° - 41'. The following table, taken from Dr. Kirk's paper, shows the relation between the actual wet surface of the ship and the wet surface of the model, for some difierent types of vessels. L B D 0/ Ship surface IVloael aurface Feet. Feet. Tons. 342 38 4,500 •658 •92S 320 40 2,335 •522 ■955 2S0 60 7,555 •663 ■96 210 32 1,693 •647 •963 190 25-5 1,115 ■694 •945 Relation between the Prismatic Coefficients of a Ship and the Length of Entrance of a Kirk's Block, — The fundamental equation connecting a Kirk's block with its ship is — Volume of block = immersed volume of ship. Referring to fig. 28, and using M for immersed mid-area, this equation becomes (L - E; M = 35 D (1) Again, by definition of the prismatic coefficient, we have cubic displacement of ship (jw — volume 01 a prism ot length L and section M 35 D ~ L X M ■ ■ Combining equations (1) and (2), there results P, _ ( L - E) M _ L - E . ^" TTVM IT" ' which readily transposes to E = L (1 - C»). (2) 62 THE RESISTANCE AND POWEE OF STEAMSHIPS. From this interesting result, knowing the prismatic coefficient Cm of a ship of given length L, we can easily "B :iX! F Fig. 26.— Modern Cargo Steamer. calculate the length of entrance E. Thus, in the case of the Campania, fig. 28, we have E = 600 (1 - -787) = 127-8 ft. The block models for three different types of vessels are shown in figs. 26 to 28. Fig. 26 shows a modern cargo boat with a block coefficient of '78, designed for speeds of from Fig. 27. — Combined Passenger and Cargo Steamer. 9 to 10 knots. Fig. 27 illustrates a type of boat which has lately become very popular with shipowners, and has proved to be very successful. Boats of this class are designed to >U— -E— 3« Fig. 28. — Atlantic Liner Campania. carry large cargoes and a fair number of passengers, and to steam at about 13 knots. Fig. 28 shows the model of the well-known Campania, a 21-knot boat. The par- KIRKS BLOCK MODELS OF SHIPS. 63 tieulars of these ships and their block models are given below : — Ship Paeticulaes. Modern cargo. Passenger and cargo. Atlantic liner Campania. L 352 ft. 476 ft. 600 ft. B 49 ft. 52-25 ft. 65 ft. d 22-61 ft. 27^25 ft. 23 ft. D 8,704 tons 13,810 tons isiooo tons. M 1,076 sq. ft. 1,320 sq. ft. 1,334 sq. ft. C/ •78 •716 ■702 Cm •805 •772 •787 Paeticulaes F Block Models. Modem cargo. Passenger and cargo. Atlantic liner Campania. AB 852 ft. 475 ft. 600 ft. GO 47^6 ft. 48^44 ft. 68 ft. GL 22^61ft. 27 •25 ft. 23 ft. AH 69 ft. 109 ft. 127-8 ft. e 19 deg. 12^6 deg. 12-8 deg. Hogg's Modification of Kirh's Block.— In. an interesting and valuable paper* read before the North-East Coast Institution of Engineers and Shipbuilders in the year 1897, Mr. Archibald Hogg proposed a modification of Kirk's method of making block models. For a ship with perpen- dicular sides and the usual angular bottom, he reduces the * " Comparison and Construction of Ship Lines," by Archibald Hogg. Trans- actions of the North-East Coast Institution of Engineers and Shipbuilders, vol. xiv. 64 THE RESISTANCE AND POWER OF STEAMSHIPS. draught of the model, in order to get the mid-area of the block equal to that of the ship, as shown in fig. 29, leaving the beam unaltered. This method, we may mention, was Pig. 29. first used by Kirk, but was rejected by him as not being so suitable as that above described. For a ship whose sides have a "lie out," as in fig. 30, Mr. Hogg reduces both the draught and the beam ; the block beam being a mean between the breadths at the upper turn of the bilge and at the load water-line. The draught of the block is then made so as to enclose the mid-area. It is not probable, however, that this method will come into general use. SKIN RESISTANCE. 65 CHAPTER IX. Skin Resistance. In the present chapter we propose to consider, in greater detail than hitherto, the frictional or skin resistance experienced by ships in motion. Although the frictional resistance between the surface of a solid and a fluid is primarily due to the viscosity of the fluid, yet the laws governing it are found to be quite different from those of simple viscous resistance. This difference is due to the complicated motions that are set up in the vicinity of the solid, as will be seen from what follows. Let us consider the case of water flowing slowly and regularly through a tube of small diameter. We might at first imagine that the rate of movement of each particle at a given cross-section would be the same. But such is not the case. As a matter of fact, the layer of water next to the wall of the tube adheres to it, and successive layers slide over each other, the result being that the central thread of water has the greatest velocity. If water were to flow in a similar manner — i.e., slowly and regularly, through a large pipe of uniform bore, investiga- tion shows that the neighbouring layers would acquire very great relative velocities, especially those near the sides, and the resistance to the motion of the water — as calculated from the known value of the coefficient of viscosity of water at a given temperature — would be very small. Experiment, however, shows that, at velocities like those met with in practice, the character of the motion of the water changes altogether. It becomes turhvlent; that is to say, instead of the comparatively simple gliding of one layer of water over another, motion in parallel layers becomes unstable, and parts of the fluid are detached from the sides of the pipe. These detached portions of the fluid are set revolving, so as to form eddies, which traverse the fluid in all directions. 5s 66 THE RESISTANCE AND POWEE OF STEAMSHIPS. An exactly similar motion to the above occurs when a solid body, as a ship, moves through water. Owing to the roughness of its surface, rotating eddies are formed, unless the speed of the body is very low indeed. The particles of 11 aid near to the solid communicate their rotary motion to more remote particles, and so the energy expended in . producing eddies is gradually dissipated. The frictional resistance to the motion of a ship is theoretically measured by the rate of change of momentum of the "skin" of water adjacent to the frictional surface. For, by Newton's second law of motion, force = mass x acceleration, or /resistance\ _ /mass of water set\ /increase of speed per\ Vto motion/ \in motion per sec./ Vsecond of the water/ Hence, if it were possible in any way to find the mass of water set in motion per second, and also its increase of velocity per second, it would be easy to calculate from fundamental principles the frictional resistance of a given ship. Bat as this is manifestly impossible, we must have recourse to direct experiment. The motion of the particles of water is so complicated that it is not possible to frame, from reasoning alone, any formula for calculating the frictional resistance of actual ships. On a few points, however, theory is clear, viz. : — 1. The particles of water close to the ship's skin move in frictional eddies, owing to the adhesion between the skin or frictional surface and the particles of water that glide over it. 2. Energy is expended in the production of these frictional eddies. The number of foot-pounds of work done on the particles of water while the ship advances through 1 ft. is equal to the number of pounds of frictional resistance. 3. The distance from the hull to which the frictional disturbance extends depends on the roughness of the surface and the speed. SKIN RESISTANCE. 67 4. The frictional current thus created is continually left behind by the moving ship, and a so-called "frictional wake " is formed, which follows the ship. 5. The forward motion of this wake is gradually imparted to larger masses of water. Hence its speed diminishes, and fiaally the motion ceases to be perceptible. 6. The momentum imparted per second to the neigh- bouring water by a surface moving at a given speed is independent of the depth of immersion. In other words, the frictional resistance between a solid and a fluid is independent of the pressure of the fluid. Professor John Perry, in his " Applied Mechanics," page 83, has an interesting paragraph bearing on the question in hand, which is worth quoting. It reads as follows : — " The mathematical investigation of the resistance to the passage of a bo^T through a viscous fluid ia so diflioult that we have almost no results which may be relied upon. With- out viscosity there would be no resistance to steady motion, whatever the shape of the object. It is difficult to imagine that there would be no propelling force on a sailing boat if the air were frictionless, and yet this is so.* Even in the case of a ship, experiments on which have been going on continuously since ships were first built, our knowledge is very incomplete. Roughly, we may take it that resistance is generally proportional to the square of the speed. In the case of shot this law holds probably up to speeds of 300 ft. per second ; from 400 to 1,000 ft. per second the resistance is possibly proportional to the 2 J power of the speed. B3yond 1,100 ft. per second we may take — F being in pounds, d the diameter of a shot in feet, v the velocity in feet per second — ^ =fd^ {v - 800), where / = 3 for spherical and 2 for elongated shots with ogee-shaped heads. The velocity is greater than that of * The statement 5s too sweeping. A body moving in a perfect fluid' would experience no resistance if the conditions — ag to shape of body, mode of present- ment, and velocity — were such that the stream-line motion remained continuous : but not otherwise. — W. H. A. 68 THE EESrSTANCE AND POAVEK OF STEAMSHIPS. sound, and probably it is to this that the change of law is due. The fact that even in the steadiest winds there is pulsation, causes scientific speculation about wind pressure to be difficult." Comparison op the Laws of Solid and Fluid Friction. That fluid friction is fundamentally different in nature from solid friction is clearly shown by the following parallel statements : — Friction between two solids. Friction between a solid and a fluid. 1. Frictional resistance is propor- tional to the total ■pressure between the two aurfaces. 2. Frictional resistance is indepen- dent of the area of the rubbing surfaces. 3. Frictional resistance does not much depend on the relative speed of sliding, taut it is certainly greatest at low speeds. 4. Frictional resistance depends very much on the nature of the rub- bing surfaces, as to their roughness, texture, hardness, &c. In other words, the coefficient of friction for different surfaces varies greatly. 1. Frictional resistance does not at all depend on the pressure between the solid and the fluid. 2. Frictional resistance ia directly proportional to the area of the wetted surface. 3. Frictional resistance very much depends on the relative speed of glid- ing, and it is certainly extremely small at low speeds. 4. Frictional resistance, though not independent of the natiLre of the wetted surface, is not greatly influenced by it at moderate speeds, provided the sur- face ia fairly smooth and long. In other words, the coefficient of fluid friction for different surfaces does not vary very much. The law that fluid friction does not depend on the pressure between the solid and the fluid, has been proved to be strictly true for a small range of pressure. The first experimenter who investigated this matter was the French physicist, Coulomb. He suspended a circular disc by means of a wire, and caused it to oscillate axially whilst fully immersed in water. A pointer, working over a fixed scale, was attached to the wire, so that the angle through which it turned might be read off! Owing 'to the friction between the disc and the water, the amplitude of the oscillations gradually diminishes, the diminution enabling the experi- menter to determine the frictional resistance. Coulomb LAWS OF SOLID AND FLUID FRICTION. 69 fonnd that, whether the surface of the water was exposed to the pressure of the atmosphere, or whether there was a vacuum in the vessel, the rate of " stilling " was the same, from which Coulomb inferred that f rictional resistance was independent of pressure. It would have been more satisfactory and convincing, however, if a greater range of pressure had been tried, say from atmospheric pressure up to 2 tons per square inch. It thus appears that the skin friction per square foot of a ship's hull is the same at the keel as near the water line, the increase of pressure due to the greater depth producing no increase of friction. The law that the friction between a solid and a fluid is directly proportional to the area of the surface in contact with the fluid is of very great importance, and forms a remarkable contrast to the law governing the friction between solids. Undoubtedly, the most valuable experi- ments on the influence of surface on frictional resistance were those made by Dr. Froude ; but, before dealing with these, mention should be made of the earlier experiments of Colonel Beaufoy, on the resistance of bodies moving through water, which furnished some of the most useful data avail- able up to the time of Fronde's labours. Beaufoy 's definition of fluid friction is interesting, and reads as follows : " By friction is meant that sort of resistance to a body moved throagh a fluid which arises either from the adhesion of the particles of the fluid to the surface of the moving body, or from the roughness of the body, or from both these causes united." Beaufoy's experiments were carried out, towards the close of the 18th century, in the Greenland Dock at Deptford, and were published in 1834 under the title of " Nautical and Hydraulic Experiments." Beaufoy did not investigate the resistances of thin boards moved normally or obliquely, but devoted his attention chiefly to the resistances of solids with wedge-shaped ends, the fineness of the angle of the wedge being varied. None of the bodies were of ship- shaped form. 70 THE EESISTANCE AND POWEE OF STEAMSHIPS. Some of Beaufoy's results are stated in White's "Naval Architecture." At a i^peed of 8 miles per hour, a flat-ended body experienced a resistance of 1481 lb. ; while the resistances of other bodies with wedge ends were as follow : Angle of wedge. Resistance. Degrees. Lbs. n 307 lU- 35-8 m 41-7 so 61-4 It is quite evident that, at the high speed (for a model) of 8 miles an hour, or 11'7 ft. a second, the angle of entrance has a very marked influence on the resistance. Further reference will be made to these experiments under the head of " Wave Eesistance." Professor Cotterill, in his "Applied Mechanic?," remarks that Beaufoy employed the formula K = / X S X V« to represent the results of his experiments on surface friction, and that for the index n he obtained the values 1'66, 1 71, and 19 in three series of experiments. Fkoude's Experiments. About 30 years ago, the late Dr. William Fronde carried out a valuable series of experiments on the frictional resistance of plane surfaces of various lengths and materials, moving at various speeds. He used boards A in. thick, 19 in. deep, and of lengths from 1 ft. to 50 ft. The extremities were sharpened, to get rid of eddy-making resistance. These boards were coated with various sub- stances, and towed lengthwise, below the surface of still water at Torquay. Apparatus was arranged so that, in any experiment, the speed and the resistance to towing were automatically recorded. FKOUDi's EXPERIMENTS. 71 The extreme interest of these experiments on flat surfaces, which at first seem to have little to do with the curved surfaces of ships, results from Fronde's startling experi- mental discovery that the skin resistance of a ship is practically the same as that of a plane rectangular surface of equal wetted area, length, and condition, when moving at the same speed. This discovery simplifies enormously the estimation of the skin resistance of a given ship ; for we need take no account whatever of the shape of the hull, but consider only its wetted surface, its roughness, and its speed. Thus, it appears that two ships, difiering greatly in form and proportion, but of equal wetted area, like quality of surface, and the same length, will have the same friniional resistance at the same speed ; though they will probably have quite diflFerent total resistances, especially if the chosen speed be high. The chief results of Fronde's experiments have been rearranged in the table on page 72, the resistance of each surface being expressed in pounds per square foot, when moving at a standard speed of 10 ft. per second. The index of the speed, according to which the friction was found to vary, is also stated, from which the resistance at other speeds can be easily calculated. In comparing the resistances of a small model, say 12 ft. long, and of a full-sized ship, perhaps 400 ft. long, the correc- tion for the variation of / with length is very important, especially at high speeds. From a careful inspection of these results, it will be noticed that — 1. The coefficient of fluid friction varies with the character of the surface in contact with the fluid. 2. The resistance per square foot of wetted surface near the following end of the plane or board is in all cases less than the mean resistance per square foot. The explanation of this peculiarity is that the after part of the board is in contact with water which has already been set in motion by the friction of the forward part, so that the relative speed of gliding is least at points nearest the tail. 72 THE EESISTANCE AND POWER OF STEAMSHIPS. 3. The average resistance per square foot is greater for short than for long boards. This fact is emphasised by the Material of surface. Length of surface. L Coefficient of fluid friction. / Index of variation of x-esistance with speed. n Mean resistance per sq. fc. of surface, at 10 ft. per second. r Resistance per. sq. ft. at L ft. from cutwater. I'eet. Lb. Lb. Varnish, smooth paint, or compositions. 2 S •011- ■0121 2-00 1^£5 ■410 •325 ■890 ■264 20 ■0104 1-S'j ■278 ■240 to •0097 1-83 ■250 ■226 Paraffin. 2- ■0119 1 '.i:. ■380 ■370 8 ■0100 1^04 •314 ■260 20 ■ooss 1-93 ■271 ■237 50 Tinfoil. 2 ■0064 2^16 ■soo ■296 8 ■0031 1 99 ■278 •263 20 ■00S9 1^90 ■262 •244 60 ■0095 1^S3 ■246 •232 Calico. 2 ■0281 1-S3 ■S70 ■725 8 ■0206 102 ■f26 ■604 20 ■01S4 1-89 ■631 ■447 60 ■0170 1-67 ■474 ■423 Medium sand. 2 ■0J67 2^00 ■900 •730 S ■0178 2^00 ■025 •488 20 ■0152 2-00 •534 •465 60 0139 2^C0 •438 •456 curves in fig. 31, from which the rate of diminution of resistance per square foot is clearly seen to be very small as FROUDE S EXPERIMENTS. 73 the boards advance in length, and negligible beyond a length of 50 ft. No longer boards were tried, however, owing to practical difficulties. It is evident that there is a certain 20 30 Length of surface in feet. * Fig. 31. length of board beyond which any increase of length makes very little difference to the mean resistance per square foot of surface. The general formula expressing the results of the experi- ments on frictional resistance is K=/.S.V», where R pounds is the skin resistance of the surface in question ; / is the coefficient of friction — that is, the mean resistance per square foot of surface at a speed of 1 knot, or 1'69 ft. a second ; S square feet is the wetted surface ; V knots is the speed of advance of the surface ; n is the index of variation of E, with V. 74 THE EESISTANCE AND POWER OF STEAMSHIPS. The surface friction of a newly-painted ship differs little from the friction of a varnished surface of like extent ; s» that, for this important case, the formula becomes E = -01 X S X Vi-83. I'or example, the skin resistance of a surface 10,000 square feet in area, and moving at the rate of 10 knots, -will be something like •01 X 10000 X 67-6 = 67601b. The value of the coefficient /, though independent of the fluid pressure, depends on the nature of the fluid in which the body is immersed ; and, for small changes of density, / varies as the density of the fluid. Consequently, as Fronde's experiments were made in fresh water, it will be necessary, in adapting the values obtained to salt water conditions, to multiply by the correcting factor 64 -r 62 4 = 1'025. A further refinement, of theoretical interest only, is that the value of / for a given surface and fluid will diminish slightly as the temperature rises, owing to decrease of both density and viscosity. Derivation of f — The values of / given in the second column of table are derived from the values of n and )■ given in the next two columns, in the following manner : — By definition of the coefficient of fluid friction, we have jr ( 1 knot \-" f = r y. [ 5 — ■ I \10tt. per sec./ since the experiments were made with boards moving at 10 ft. per second. Thus, taking the case of a varnished surface 2 ft. long, /=-411b. X (l-69ft.perseay V 10 re. per sec. / = -41 X 169- = -41 X ■02g0 = -0117 lb. per square foot. Again, taking the case of a similar surface 50 ft. long, / = -25 X ICfli-ss FKOUDE S EXPERIMENTS. 7^ Now, log -leoiss = 183 log -169 = 1-83 X 1-2279 (by tables) = - 1-83 + -417 = 2-587 to -which the corresponding number is '0386. Hence, / = '25 x -0386 = -00965 lb. per square foot. The case of a tin/oil surface calls for special notice. For this particular material it is remarkable that the value of / increases as the length of the board increases, as the above method of derivation will show ; whereas, for all the other materials tried, the value of / diminishes with length of surface. The Index of Friction. — Before Froude's experiments were published, it was customary to assume that the skin friction always varied precisely as the square of the speed, an assumption which was shown to be incorrect for smooth surfaces equal in length to ships. The value 183 of the frictional index, correct for long smooth surfaces, gives results differing to a much greater extent than is commonly supposed, from the results arrived at by taking n = 2. This difierence becomes relatively greater as the speed increases, as seen by the following table : — V V = VI sa V=H- V'-'*" Knots. 5 25 19-0 1-316 10 100 67 6 1-480 15 220 142-0 1-6 85 20 400 340 4 1-663 26 025 361-6 1-728 30 90O 604 S 1-783 35 1225 669-3 1-832 The diminution of the frictional index n with increase of length is probably due to the same cause as the diminution V6 THE RESISTANCE AND POWEE OF STEAMSHIPS. of the mean resistance per square foot, namely, the reduction of the relative velocity of the plane and the water in passing from the nose to the tail of the board. Froude explains the latter diminution in the following words : " The portion of surface that goes first in the line of motion, in experiencing resistance from the water, must in turn communicate motion to the water in the direction in which it is itself travelling. Consequently, the portion of the surface which succeeds the first will be rubbing, not against stationary water, but against water partially moving in its own direction, and cannot, therefore, experience as much resistance from it.'' Approximate Estimation of Shin Resistance, — For rough estimates at low speeds, frictional resistance is still usually taken to vary as the square of the speed, for the sake of convenience of calculation. On this hypothesis we may frame a simple approximate formula. Froude's experiments show that a surface 50 ft. or more long, fully immersed, painted like a new ship, and moving at the rate of 10 ft. a second, or 592 knots, experiences a mean frictional resist- ance of '25 lb. per square foot. Hence, if r lb. be the mean resistance per square foot at any other low speed, V knots we must have •25 V592/ • r = '^°^ = ^ '35 " 140' Thus, the frictional resistance per square foot of wet sur- face at a speed of 1 knot is tIt of a pound, on the assumption that resistance varies as the square of the speed. And if S square feet be the total frictional surface, then the total skin friction will be R = ^^. 140 For a speed of 10 knots or higher, however, the more correct formula should be used, namely^ ^ ^ S X Yi-83 100 ■ FilOtTDE's EXPEEIMBNTS. 77 Since, at comparatively low speeds, the shin resistance of a well-formed ship is from 80 to 90 per cent of the total resistance, many estimators consider that this item is alone worth considering. At these low speeds they take wave and eddy resistances to vary as the first power of the speed, and allow for them by the use of a lower constant than 140— say 110 to 120, according to the speed and type of ship. Example.— The shin resistance of the U.S. warship York- town when clean, at a speed of 8 knots (or 810 ft. per minnte), will be about 10810-^^^=4950 lb. 14U And if we assume that the frictional resistance at this speed is 85 per cent of the total resistance, we have total resistance = ^^ = 5820 ib.* "85 Hence the effective horse power required to drive the ship will be 58201b. X 810 ft. per minute ,.„ 33000 = 1*^- So that, assuming a combined efficiency of 50 per cent, the estimated indicated horse power of the engines is 286. Curiously, this was precisely the power observed on the measured mile trials. The Critical Speed. — The limit of speed up to which the total resistance of a ship may be taken without much error, as proportional to the shin resistance alone, is shown, by the theory of wave resistance, to be given by the formula — where V knots is the required limit of speed, and E feet is the length of entrance or run of the ship's block model. * Since '85 X 140 = 119, this calculation gives practically the same result as the formula T5 ,S X V2 =i- 12U 78 THE EESISTANCB AND POWEE OF STEAMSHIPS. An expression for E, in terms of the better known quanti- ties, displacement D, length of ship L, and immersed mid- area M, is 35 D E M the units being the ton and the foot. The term 35 D represents the cubic feet of sea water displaced. For instance, taking the case of the Yorktown, 35 X 1680 E = 226 = 226 432 136 = 90 ft. Consequently, the critical speed V is ^ 90 = 95 knots. Above this speed wave-making resistance becomes important. The following table gives the values of the coefficient of friction used by Mr. R, E. Froude. It has been calculated Froude's Feictional Coefficients foe Paeaffin oe Smoothly-painted Suefaces Moving in Salt Watee. Length of vessel Coe or model. fi L ficient of lotion. / Length of vessel Coe or model. f L fficient of lotion. / Feet. Feet. S 01197 SO 00933 9 01177 90 00i*28 10 01161 100 00923 12 01131 120 00916 14 01106 140 00911 16 01083 160 00907 IS 01069 ISO 00904 20 01055 200 00902 25 01029 250 00S97 30 01010 \ 300 00S92 35 00993 350 00SS9 40 009S1 40O 008S6 45 00971 450 00SS3 60 00963 500 008SO 60 00950 650 00S77 70 00940 600 C0874 FKOUDES EXPERIMENTS. 79 by Mr. D. W. Taylor, from data contained in a paper read before the Institution of Naval Architects, in 1888. The index n of variation of friction with speed is taken through- out as 1"825, when calculating the resistance at any speed. From the point of view of friction alone, the ship of least resistance, for a given displacement, is that of least surface. This consideration, therefore, dictates a spherical form ; which, however, is quite out of the question, for constructive and other reasons. A brick-shaped solid also has a small surface for a given volume, and this form is approximated to by some very full-lined cargo boats. Long fine-lined ships present a large surface for a given displacement, and are therefore to be avoided for slow-speed vessels. Expe- rience and theory alike show that the bluff 8 or 9-knot tramps are the most economical purely cargo boats. The next table gives the frictional coefficients for paraffin models moving in fresh water, the index n being throughout taken as 1'94. Feictiox of Paraffin Models in Fresh Water. Independently of William and E. E. Froude, a prominent DntL-h naval architect, Dr. Tideman, has experimentally 80 THE RESISTANCE AND POWER OF STEAMSHIPS. investigated the subject of the frictional resistance of ships ; and the following table contains the values of / and n, ascer- tained by him for various surfaces, including those of copper and zinc sheathing. Surface Friction Constants for Ships in Salt Water OP 1026 Density. Iron b( an and w Copper or zinc sheathed. Length cie of ehip. ttom. jllpainted. s ano beathing smooth, in good condition. Sheathing rough, and in bad condition. f ,. / n / ,. Feet. 10 01124 1-35:; 0100 1-9175 -0140 i-sro 20 O10T5 1-849 0099 1-900O 0136 1-861 30 OIOIS 1-844 0O903 1-865 -0131 1-863 40 00998 1-S397 00978 1-840 -01273 1-S47 50 00991 1-8367 00970 1830 0120 1-843 100 00070 1-820 00966 i-s-:7 -0120 160 00957 ,, 00963 „ ■01183 200 00944 ,, 009 i 3 ,, ■01170 250 00933 „ 00936 ,, ■one. 1 300 00923 ,, 00630 ,, ■OU.vj 350 00916 , 00927 ,, -01 H ■) 400 00910 ,, 00926 ,, -ouj;) 460 00906 „ ,, ■0HS7 600 00904 '■ " •■ •01136 These values should be used in preference to those given by Froude, -when no separate calculation is made for eddy resistance, as Tideman's values are about 5 per cent greater than Froude's. This extra 5 per cent is a sufficient allow- ance for eddy resistance in the case of well-formed ships. fb.oudes expeeimbntal apparatus. 81 Feoude's Expeeimental Apparatus. The dynamometric apparatus used by the late W. Froude, in his " Experiments on the Surface Friction Experienced by a Plane Moving through Water," is of considerable scientific interest, and worthy of attentive study. The original account of this apparatus is given in the Report of the British Association for 1872. The planes experimented upon were formed of thin pointed boards, A in. thick, 19 in. broad, and from 1ft. to 50 ft. long, these being bodies of such a form as to possess the least possible displacement and sectional area for a given wetted surface, and at the same time capable of being made stable in the water, though entirely submerged. The experimental boards were towed through the water (fresh) contained in a parallel-sided tank, 278 ft. long, 36 ft. broad at the top, and about 9 ft. deep. This first experi- mental tank was roofed from end to end, and a light railway, carried by the framing of the roof, traversed its entire length. The dynamometric, or measuring, apparatus was carried by a four-wheeled wooden truck, which was moved along the railway by an endless wire rope. This hauling rope was coiled in a spiral groove on an accurately-turned barrel, driven by a small double-cylinder engine, fitted with a heavy high-speed flywheel and a chronometric governor of very exact action. Any required speed between 100 ft. per per minute (about 1 knot) and 1,000 ft. per minute could be given to the truck. A diagram of the apparatus is shown in fig . 32. A is the bed of the truck, B one of the planes whose resistance was to be measured, the upper edge being l^in. below the surface of the water. To overcome the buoyancy of the wood, the lower edge consisted of a lead keel of the same thickness as the board. Although this ensured stability, it was necessary to keep the plane resolutely vertical, and the line of its length horizontal. Perfect liberty in the line of 6s 82 THE RESISTANCE AND POWBE OF STEAMSHIPS. motion was also required, so that the wholo towing force might be accurately delivered to the dynamometer. A light, stifi wooden beam C was therefore hung below the truck, just clear of the water, and to this beam the experimental boards were attached. The beam was carried at each end by light rocking frames E, E, which formed a parallel motion perfectly free longitudinally, and unyielding transversely. One of the frames was extended above the point of suspen- sion to carry a weight F, adjusted so as to counterbalance the weight of the beam C, together with any sinking or floating force that the board B might exert. Otherwise the frame would not have been in equilibrium in the line of motion, except in one position, and in any other position would have exerted a pull or a push on the dynamometer. The rigid connection between the board and the beam C was made by fastening the upper end of the cutwater D to an upright on the swinging bar by means of bolts. The board was rebated to receive the sheath, so that the surface was flash at the junction. The towing lever O was attached to the front end of the spring H. Through this spring and the connecting line h the towing force, or resistance offered by the plane B, was transmitted to the trussed beam C. Thus the deflection of the spring would be proportional to the plane's resistance. As the spring extended, it moved the lever M, which in turn moved the index arm K by means of a short connecting link N. The upper end of K moved through a distance much greater than the extension of the spring, owing to its greater distance from the fulcrum, and to it was attached a pen, which registered its motion on a sheet of paper wound round the revolving drum U. This drum or barrel was rotated by means of a band connected to the axle of the truck and the gearing g. Its circumferential motion was therefore proportional to the distance travelled by the truck. The action was as follows : The pen having been set in the zero position while the apparatus was at rest, when the board was dragged through the water the frictional resist- frotjde's experimental appaeattjs. 83 since caused the spring to extend. The link N was therefore pulled to the left, and the pen moved through a much greater distance to the right, the extent of movement being a measure of the resistance between the surface of the board 84; THE EESISTANCE AND POWBE OF STEAMSHIPS. and the -water. Thus the pen traced on the paper a line, more or less ■vfavy according to the degree of variation of the resistance, whose ordinates, measured from the zero base, represented resistances, and whose abscissse represented distances moved by the truck. Hence the skin resistance at any point of the run could be found. In order to record the speed at which the board was travelling, another pen V was added. This was connected to a clock, and marked equal intervals of time upon the paper. Thus the two pens together gave the resistance at any speed up to 1,000 ft. a minute. The function of the levers G, G, fig. 32, was to take the stress before uniform speed was acquired, thus relieving the spring H. The bell crank K E was used to test or calibrate the spring H by means of weights hung from the hook shown. Unfortunately, with the apparatus described, it was not - possible to determine the resistance of planes greater than 50 ft. in length, and it was the intention of the experimenter to devise some other arrangement, by which greater lengths could be tried in open water. Apparently, however, the intended experiments were never carried out. CHAPTER X. The Admiealty Foemula. The expression almost universally used to calculate the horse-power required to drive a ship at a given speed is known as the Admiralty formula, and is of the form LHP. = V^xD« where V is the speed in knots, D is the displacement in tons, and C is an experimental co-efficient. THE ADMIRALTY FOEMULA. 85 The formula may be transposed thus — ■ ^ _ V3 X dS ^~ LH.P. C is then called the coe^cient of performance. Few formulse have been more abused than this latter one, for until a comparatively recent date it was a common custom to make use of it in comparing the performances ' of ships widely differing in type ; the ship -with the highest O being called the most efficient. If we consider how the formula is obtained, and examine the assumptions upon which it is based, we shall see how liinited must be its application, and thereby be enabled to avoid the error made by early engineers of attaching to it undue importance. Assumptions made to obtain the Admiralty Formula. 1. That the resistance to motion of a vessel varies as the square of the speed, or K oc V^. 2. That the resistance to motion of a vessel varies as the wetted surface, or R oo S. 3. That the indicated horse power of the engines varies as the effective horse power, or.I.H.P. qc E.H.P. The manner in which the Admiralty formula is obtained from these assumptions will now be shown. Since R oc V^ and R x S, 1st and 2nd assumptions — .-.Roc V^ X S. Multiplying by Y we get — R X V oc V^ X S (1) Now, R X V measures the work done in unit time, hence, R X V oc E.H.P. .-. V^ X S also oc E.H.P f rom (1) Introducing the third assumption that LH.P. x E.H.P., we obtain the result V^ x S oc I.H.P (2) This result may also be put in the form I.H.P. = ^ — ■ where C is a constant, and we have a formula for indicated 86 THE EESISTANCE AND POWER OF STEAMSHIPS. horse-power in terms of speed and wetted surface, which may be used if the latter is known. This, however, is not usually the case, and it is therefore convenient to modify the formula so as to express the wetted surface in terms of the displacement. The following considerations will show how to make the change. In all prismatic bodies the contents vary as the cube of the linear dimensions, and the surfaces vary as the square of the linear dimensions. This may readily be seen from the following simple illustration. Consider two rectangular blocks, one of them being 2 ft. x 1 ft. x 1 ft. and the other 4 ft. X 2 ft. X 2 ft. The linear dimensions of the second block are twice those of the first, and according to our state- ment the contents of the second should be 2^ = 8 times, and the surface 2^ = 4 times, that of the first. On calculating these quantities we find this to be the case ; the small block contains 2 cubic feet and has a surface of 10 square feet, the larger one contains 16 cubic feet, and its surface is 40 square feet. If we apply this to the comparison of similar ships, the same statements are true. Thus, if there are two exactly similar vessels, one 100 ft. and the other 400 ft. long, the linear dimensions of the larger are 4 times those of the smaller vessel. The cubic contents and consequently the displace- ment of the 400 ft. vessel are 4^ = 64 times, and the wet surface 4^ = 16 times as great as those quantities in the 100ft. vessel. Patting this into algebraic form we have the important relations D x L^ and S oc L'-=. Since L^ oc D, .-. L cc »^or dJ; also since L^ oc S, Combining the last two results we have si oc D^, ■■. Soc Di, or S = c X dI THE ADMIRALTY FOEMULA. 87 Inserting this valae of S in the formula previously obtained, viz., P X S I.H.P. C and introducing a new constant, we get the well-known formula — I.H.P = ILgJDl. On transposing this we again obtain the expression for the coe£B.cient of performance Lti.lf. ■ We are now in a position to make an extremely important statement, the truth of which will be readily seen. The coefficients of performance are not constant numbers, but are different for dif event ships and vary with the speed even in the same ship. This statement we will now proceed to verify by closely examining the assumptions upon which the formula just obtained is based, and by pointing out to what a limited extent these assumptions are true. Consider the 1st assumption, that the resistance varies as the square of the speed. In a former article we showed that for low speeds the resistance of water to a moving body varies approximately as the square of the speed, or more correctly as the (speed) ^■^^. This, however, is only true with a speed so low that the total resistance is frictional. At higher speeds wave-making resistance comes into play, the law connecting resistance and speed changes altogether, and consequently our assumption becomes false. We must therefore remember that the 1st assumption is only approximately true for any vessel up to that speed below which the resistance is chiefly frictional. The 2nd assumption that K oc S is no longer true when the speed involves wave-making resistance. So far as friction is concerned, a coarse, full-lined boat will experience approximately the same resistance as a finer boat of equal 88 THE EESISTANCB AND POWER OF STEAMSHIPS. surface at the same speed. But at higher speeds we know that the fine boat has the advantage. It should be noted then that the deduction we made, namely, R oc V^ x S does not hold for all cases, and consequently the later step 160 150 140 130 120 110 100 90 SO 70 60 60 « 30 20 10 ,/ / / / / < 1 t •J / .^ ^ o .5^ *• tt) 'O aii^ 1 1 f_[ qjL ■1^— y-^ •^ .-> y ■5 / / ' .<" c F / / > / 1 1 / k / - g. 80 a 60 50 40 SO 20 10 10 20 30 40 60 60 70 SO < Brake horse power, KiG. 36. 100 110 120 130 140 V'^ X S oc E.H.P. is only true when V is below that speed at which wave-making resistance becomes measurable. The third assumption, that the indicated .horse power varies as the effective horse power, is also true for only a TEE ADMIKALTY FORMULA. 89 limited range of power in any engine. This is well illustrated by fig. 85, which shows the relation between the indicated horse power and the brake or effective horse power of a quadruple-expansion engine of the marine type.* The I.H.P was in each trial obtained from the indicator diagrams, and the B.H.P. was measured by means of a self-recording hydraulic brake on the engine shaft. Full particulars of these engines with accounts of trials made upon them will be found in the Proceedings of the North-East Coast Insti- tution of Engineers and Shipbuilders, volumes 13, 14, and 16. In the series of trials illustrated by fig. 35, the power of the engines was altered by varying the boiler pressure, which ranged from 2101b. per square inch in the highest trial to about 70 lb. in the lowest ; the points of cut-off in all the cylinders remained constant throughout the whole of the experiments. By altering the resistance of the brake, the revolutions were maintained at about 140 per minute in all the trials. In an actual marine engine if the power were reduced the revolutions would become fewer, so that the trials shown are not quite an exact illustration of what occurs in everyday practice. In all probability, however, the curve connecting I.H.P. and B.H.P. would have the same general form. The important point to notice on the diagram is that the full line does not cut the base line when the B.H.P. is zero. The ordinate corresponding to zero B.H.P. represents the I.H.P. that would be expended in simply running the engine when no external work was being done, and gives an idea of the amount of work wasted by friction. It will be found that the law connecting the indicated and brake horse powers is given by the formula I.H.P. =10-1- 1-06 B.H.P. The dotted curve marked efficiency, on the same diagram, shows T> TT p the value of the ratio ^ u t^ ^°^ difierent horse powers. If I.H.P. * The experimental engine in the engineering laboratory of the Durham College of Science, Newcastle-upon-Tyne. 90 THE KBSISTANCE AND POWER OF STEAMSHIPS. the asaumption we made that I.H.P. varies as B.H.P. were true for all cases, it would mean that the efficiency of the engine was a constant quantity, and the curve denoting its value would be therefore a straight line parallel to the base. The efficiency in this case, however, varies from to "89, but it is worthy of note that its value for a considerable range is practically constant. Consequently for small differences of power we may practically consider the effisctive horse power of an engine to vary as its indicated horse power unless the engine is running very light. It is interesting to note that if we assume the formula given above I.H.P. = 10 + 1'06 B.H.P'. to hold for all horse powers of the particular soo 250 200 \ ■."^o \X)£ i. s °> if* "Wilj la. H- -■-" x - "— 1 ' 10 11 12 13 14 15 IS 17 18 Speed in knots. Fin. 36. engine, the maximum efficiency that could be attained is •94. Changes of efficiency due to variations in the propeller losses at different powers must also be taken into account when we are considering to what extent we may assume the 3rd assumption to be true. Examples of the Calculation of C from Trial Data.— Fig. 36 graphically shows how the value of the Admiralty coefficient of performance varies for two ships at progressive speeds. The particulars of one of these ships, the U.S. cruiser Yorktown, have already been given ; those of the other, the Italian battleship Lepanto, are as follow : — THE ADMIEALTY FORMULA, 91 Displacement on full-power trial 14,860 tons. Length between perpendiculars 400^ ft. Breadth 72ft. 9in. Mean draught 30ft. 4in. Immersed midship section 2,000 sq. ft. Speed on trial 18 38 knots. Indicated horse power 16,150 The ship has four main engines, driving twin screws . These data will enable us to calculate the value of C for the Lepanto at the speed stated, thus : — C = ^^ xDi ^ 18-38^ X 14860§ i.H.P. 1615U .-. log C = 3 log 18-38 4- i log 14860 - log 16150, = 3 X 1-2644 + I X 4-1720 - 4-2082, = 3-7932 + 2 7813 - 42082, = 2-3663. Hence C = 2324. To take another example, the bluff cargo boat Booldana has a displacement of 4,720 tons, and requires 1,788 I.H.P. to drive her at 11-8 knots. Hence, q = H'S^ x 4720? _ 258-6 1788 Lastly, the Italian cruiser Piemonte, built at Elswick, has a displacement of 2,500 tons, and requires 12,980 I.H.P. to propel her at 223 knots, the engines being four-crank triples. Hence, log C = 3 log 22-3 -1- f log 2500 - log 12980, and C = 157-3. The above typical values of C may be used in estimating the power required to propel other ships of similar type at corresponding speeds. They may also be used, with fair accuracy, for ships which differ slightly from the required relationship between shape, length, and speed. 92 THE EKSISTAXCE AXD POWER OF STEAMSHIPS. CHAPTER XL The Fouling of Ships. Nature and Importance of Fouling. — The adhesion of grass, sea-weed, barnacles, mussels, oysters, and other low- forms of vegetable and animal life to the under-water portion or bottom of a ship is technically known as the fouling of the ship. The prevention of the serious fouling of a steamship ia a matter of great practical importance, because the resistance, and therefore the speed, of a ship is greatly influenced by the state of her bottom. It is also of high scientific interest. The subject leads to a discussion of the respective merits and theory of action of different sheathing materials and anti-fonling compositions, and it involves a great variety of biological, chemical, electrical, and mechanical questions. On account, then, both of its scientific interest and of its important bearing on the resis- tance of ships, we shall not hesitate to treat the subject of fouling at considerable length. At the time of the introduction of iron for shipbuilding purposes, some 40 years ago, the question of fouling excited much attention, and some of the opinions then expressed are not without interest to-day. Thus, in an enumeration of the drawbacks of iron ships, by Rear-Admiral Robinson, at that time Controller of the Navy, this great objection was stated::* "The rapidity with which the bottom of an iron ship gets foul, and the immense loss of all the ship's qualities that follows from the adhesion of marine zoophytes. No practical remedy has been found for this serious disadvan- tage ; repeated docking and cleaning is the only palliative." Hence arose the advocacy of the composite system of con- struction and the use of copper sheathing nailed to the timber planking. ^ Trans. Inst. Naval Architects, 1864. THE FOULING OF SHIPS. 93 Though the evil of foaling was long ago recognised by- shipbuilders and owners, the subject was never investigated with that thoroughness which its importance merited. Shipbuilders, instead of looking closely into the matter themselves, preferred to shirk it, and tell the chemist it was his business to find out a remedy for fouling. Thus, that pioneer of iron shipbuilding. Sir William Fairbairn, in his "Treatise on Iron Shipbuilding," published in 1865, says on page 92 : "I have not attempted any inquiry into the laws of oxidation, the adhesion of barnacles and marine vegeta- tion, and the means necessary to prevent such evils. This is a subject which does not come within the province of the present inquiry, and more properly belongs to that of the chemist." So that our statement is literally correct. Again, recurring to the subject on page 235, Fairbairn says : " We are sensibly alive to the objections that may be urged against iron as a material of construction for ships, and amongst them as the most prominent is that of fouling, and the adhesion of shells and marine growths to the immersed surface of the ship. This is a serious drawback to the application of this useful material, but we have reason to believe that some antidote for this evil — causing the retar- dation of speed — will, in the hands of our chemical friends, receive that attention which the importance of the subject demands, and that the time is fast approaching when immersed iron may become the repulsive instead of the attractive surface of adhesion.'' In these later days, however, even Sir W. H. White is not so hopeful of success. He has come to the conclusion that no cure for fouling has yet been devised, nor is ever likely to be, the best compositions in use being only palliatives. As for the chemist, hip words are hardly more encouraging. No English chemist, we believe, has given more attention to the question of fouling than Professor V. B. Lewes,, of the Koyal Naval College, and he candidly admits that the problem of the prevention of fouling is by no means easy of 94 THE EESISTANCE AND POWEE OF STEAMSHIPS. solution, saying:* "Fouling is no new trouble born with the advent of our present' iron monsters. It has been the one trouble that the combined engineering and scientific skill of many centuries has been unable to overcome. ... It must be clearly borne in mind that there is no anti-fouling com- position which has ever been made, or probably ever will be made, that will answer for all cases, and that until this is clearly recognised, the present unsatisfactory condition of the question will exist." Circumstances Favourable to Fouling. 1. Lying at anchor in shallow water. Fouling probably always begins when the ship is at rest, and not when in motion on the open sea. But the growth of the fouling matter goes on continuously after it has become securely attached. 2. High temperature of the water. During the spring and summer, marine life grows apace, while winter is a period of comparative inactivity. In the harbours of tropical climes fouling goes on with special rapidity. 3. Kough corroded surfaces foul more quickly than smooth surfaces. Hence, if only for this reason, it is wise to take every precaution against the corrosion of ships' bottoms. The smoothest bodies, however, even glass, will roughen and foul in course of time. . 4 The prevalence of the germs of fouling matter, owing to certain local peculiarities. The waters of the East Indian Archipelago are notoriously favourable to fouling, those of Java in particular. It is said that vessels lying for a week at Surabaya, a port of Java, at almost any time of the year, will get foul in spite of the best composition ever invented, and that even copper-bottomed vessels discharging or load- ing at this port come home covered with shells 4 to 6 in. long. During about eight months of the year the ports of Southern India and Ceylon cause rapid fouling. Kurrachee * "The Corrosion and Fouling of Iron and Steel Ships." Trans. Inst. Naval Architects, 1889J THE FOULING OP SHIPS. 95 and Bombay are also bad. The mail steamers running to the island of Mauritius seldom return clean, although they dock and paint three or four times a year. The waters of the West Coast of Africa, the West Indies, and the coast of Brazil are likewise noted for their fouling properties. On the other hand, comparatively little fouling goes on at the Chinese fresh-water ports, at Calcutta, at the Anti- podes, at the North Atlantic ports, and at European ports generally, save those on the Mediterranean. Conditions Unfavourable to Fouling. 1. Cold. Fouling, we believe, is little complained of in the Arctic regions. 2. Rapid motion, especially when accompanied by vibration. 3. A hard, smooth surface of the ship's skin. 4 The presence of fresh and brackish water, as in the estuary of a river, unless sewage matter is present. On this point Sir W. Fairbairn long ago made the following remarks and suggestion : — " The subject of fouling and the adhesion of barnacles to the hulls of iron vessels has been, since their first introduc- tion, a source of trouble and difficulty for which no effectual remedy has been applied. On inquiry at Liverpool as to the effect of fouling of iron vessels trading between that port and Calcutta, I was informed by Captain Campbell that he had no trouble with his ship, as the plates were left perfectly clean after being a short time in the fresh water of the Hooghly. If this be the case, why not have docks or basins filled with fresh watef at the different ports, into which vessels covered with moUusca might be floated, for the purpose of cleansing and removing the obstructions to which they are subject when built of iron ? It is an easy mode of getting quit of the nuisance, and that without injury to the plates."* 6. The presence of a poisonous zone around a ship is generally thought to be unfavourable to fouling, though the * *'Iron Shipbuilding," page 3C4. \ 96 THE EESISTANUB AND POWER OF STEAMSHIPS. point has been much disputed. Poisons, in this connection, are probably efiective in e?ther killing or repelling the germs or infantile life, but useless in their effect on adult life. Examples of Foul Ships. — The following examples* of bad fouling will serve to convey some idea of the nature and extent of the fouling nuisance : — 1. When the Koyal Oak, an old sailing man-of-war, was broken up at Bermuda, the layers of oysters were so thick that their weight was estimated at over 80 tons. 2. Owing to the length of time the Achilles has been lying in the river Thames, her bottom has become exceedingly foul, and the examination of her by a diver has resulted in the discovery that the whole of her bottom is covered with marine insects, barnacles, and seaweed, some of the last being as much as two feet in length. The bottom of the Achilles was coated with Hay's anti-fouling composition before the frigate was undocked. As she has been lying some nine months in Chatham Harbour, a pretty correct estimate may be formed of the state of our ironclads if detained only for a very short time in tropical waters.^ — (The Times, September 23rd, 1864.) 3. Captain Fishbourne stated that when he was on the coast of Africa an iron whaler came out from England ; and though she had left only six months ago, and had been cleaned every month as well as possible at sea with long brooms and ropes under her bottom, yet she had long grass and barnacles of immense size attached to her, in consequence of which she would neither sail nor steer, and was therefore neither manageable nor safe. 4. The bottom of the Koyal Oak, though sheathed with Muntz's metal, was found to be foul beyond all conception. Immense quantities of zoophytes, weed, and coralline flourished in the wildest profusion ; and so hard had the little insects (?) formed their habitations that nothing short -• Selected from Young's " Fouling and Corrosion of Iron Ships ". (now out of print), and other sources; THE FO0LING OF SHIPS. 97 of a general scraping with short scrapers would remove the incrustations, the result of barely six months' accumulation. (The Times, January 25th, 1865.) 5. One iron ship of nearly 800 tons register, which had been eight months in a warm latitude, had 30 cartloads of barnacles removed from her bottom ; an encumbrance which could by no means have improved her sea-going qualities. 6. The inspector of machinery to the East India Company, at Bombay, stated that when the Indus steamer was docked at that port he took off her bottom barnacles 12 in. thick and 18 in. long ! 7. When the French iron-cased frigate Invincible was docked, after 10 months of service, her copper-sheathed bottom was in a surprisingly dirty state. The copper was covered with a thick mass of marine vegetation ; a sort of white coral, and many kinds of shell fish formed a stratum which completely hid the sheathing, and was nearly 2 in. thick over certain parts. There were also, in certain places, patches of oysters, which firmly adhered to the sheathing. Not less than 10 tons of fouling were removed from the bottom. When this vessel was tried, after her completion, in 1862, she attained a speed of 13'5 knots under full steam with 53 to 54 revolutions per minute of the engines. In April, 10 months after being undocked, she was tried under full, steam, the weather being calm and the water smooth. Her greatest speed was then 9 8 knots with 51 '5 revolutions per minute. After her bottom had been cleaned she was again tried, when a speed of 13"2 knots at 53 revolutions per minute was attained. 8. The Pekin, which left England in February, 1847, was docked at Bombay, in October. She then resembled a half- tide rock. The barnacles were 9 in. long, the second stratum being complete, with a feathering coral formation sprouting from cluster to cluster. The stench from the animal matter was so great that no one could remain on board at night. The Pekin, though a fast-sailing ship, had her speed reduced by the fouling to 6J knots. 7s 98 THE RESISTANCE AND POWER OF STEAMSHIPS. 9. In February, 1865, H.M.S. Valiant was docked at Portsmouth, and one side was coated with a poisoning anti-fouling composition, of whioh mercury was the basis. The inventor of this composition asserted that it not only prevented the least accumulation of animal or vegetable matter, but at the same time preserved the iron from corrosion. To the other side of the ship was applied one of the preparations of copper. Five months later both sides were found to be thickly covered with barnacles, weeds, and the like- 10.' A Dundee ship was thoroughly cleaned and painted before she sailed for India. In spite of this her return passage, which was expected to be done in 100 days, occupied fully five months, on account of the bottom being covered with barnacles. Many of them were 3 in. long, though the vessel had been only four or five months in eastern waters. The Natural History of Barnacles. — A few notes on the zoology of barnacles, as the chief offenders or obstructionists, will not be out of place here, in view of the erroneous views concerning them prevalent. The barnacle is a crustacean animal, allied to the crab, the lobster, and the shrimp. It used to be considered a mollusk allied to the oyster and the mussel, even by professional naturalists, and most people still speak of it as such. The error has been clearly pointed out by Agassiz in the follow- ing interesting passage : " Cuvier divided the mollusks into a larger number of classes than are now admitted. He placed the barnacles with them on account of their shells, and it is only since an investigation of the germs born from these animals has shown them to be articulates that their true position is understood. They give birth to little shrimps that afterwards become attached to the rocks, and then assume the shelly covering that has misled naturalists about them. They ought therefore to be referred to the class of Crustacea, in which they are now generally included." * * Metliods of Study in Natural History," Boston, 1870. THE FOULING OF SHIPS. 99 A characteristic feature of the order of Crustacea to which the barnacle belongs is the possession of curled jointed feet, for which reason the order is styled Cirripedia, a term derived from the Latin cirrus, a curl, and pes, pedis, a foot. In their infancy barnacles are free-swimming little creatures, resembling tiny shrimps, but they early fix themselves to some solid body, such as a rock, a log of timber, or, unfortunately, the bottom of a ship. Otherwise they perish. When in this fixed condition the internal organs become protected by a calcareous shell, composed of five pieces. The only parts of the animal remaining movable are the legs, which are continually employed in searching for food (see fig. 33). The anterior part of the body forms a kind of long stalk, by means of which the animal anchors itself to any convenient object. When once detached from its resting place the adult bar- nacle cannot again attach itself, but perishes. It is believed that barnacles inhabit only shallow waters, in common with most other crustaceans, and they do not thrive in 100 THE EESISTANCE AND POWEK OF STKAMSHIPS. cold water. On dying, barnacles leave their shells tirmly attached to the ship on which they have taken up their abode, and these remains are not removed without some difficulty. Besides the stalked barnacle, there is the so-called acorn barnacle, or Balanus, which has no stalk (see fig. 34). The shell is built up of six segments, forming the body cavity. One end of the shell is fixed to some solid object, while the other end is protected by a movable roof or lid, in at least two pieces, between which the animal thrusts out its curled legs like a net, in search of food. This is the animal that is so abundant on rocks below high-water mark, and which accumulates on ships bottoms in such objectionable clusters. Both of the kinds of barnacles described are hermaphrodites; i.e., each individual unites in itself the functions of both sexes. In the Manchester Museum (Owens College) there is a large specimen, fully 15 in. long, of the common stalked barnacle (Lepas hillii), the stalk of which tapers in thickness from about fin. at the root to j,-in. at the junction with the shell. The latter is llattened, and measures about 11 in. by 1 in. The museum also contains a curious piece of whale's skin, to which are tirmly clinging several large acorn THE EFFECTS OF FOULING. 101 barnacles, these in their turn carrying a heavy burden of stalked barnacles.* The museum of Greenwich Hospital contains an interest- ing collection of fouling matter, which has been taken from the bottoms of British warships. The Effects of Fouling. The chief eflfect of the fouling of a steamship is a great increase of skin resistance. This means considerable loss of speed, and much waste of time and fuel. Owning to fouling, it is not unusual for the coefficient of friction to be doubled, and ships do occasionally become so foul, through neglect of known precautions, that the akin friction mounts up to four times its proper value for a clean bottom. The wave-making resistance of a ship at a given speed is probably not materially altered by reason of fouling. Increase of frictional resistance causes a reduction of revolutions per minute, for a given mean effective pressure referred to the low-pressure piston. Hence, unless the mean pressure can be increased when the ship becomes foul, the indicated horse power of the engines will necessarily fall off in proportion to the revolutions. Thus the speed of the ship will be reduced both by the increase of resistance and by the diminution of the power developed. In exceptional cases the reduction of speed of a ship, due to fouling, is known to have amounted to as much as 50 per cent, after passing a few months in tropical waters. A rough calculation will serve to give some idea of the waste of fuel caused by fouling. Take the moderate case of a cargo boat capable, when clean, of steaming at 12 knots, with engines indicating 2,000 horse power at 80 revolutions per minute ; and suppose the amount of fouling to be such that she can actually do only 9 knots. On the assumption that speed is proportional to revolutions, which is nearly true, the revolutions per minute corresponding to 9 knots * A standard work on the Cirripedia. or barnacles, was written by Charles Darwin. Vol. i. was published by the Ray Society in 1851, and vol. ii. in 1854. 102 THE RESISTANCE AND POWEE OF STEAMSHIPS. will be A of 80, or 60, and therefore the power developed will be reduced to | of 2,000, or 1,500 horse power. Now, if the power required to drive the ship varies as the cube of the speed, throughout the range of speed considered, then we shall have (^Vx 2000 = 844I.H.P. 10 11 12 Speed in knots. FiG. 87. as the power needed to drive the ship at 9 knots when clean. Thus the horse power wasted in overcoming the extra skin friction of the foul bottom is 1500 - 844 = 656. This is no less than 44 per cent of the entire power developed at the lower speed. Further, if the coal consumption is IJ lb. per I.H.P. per hour, the waste of coal per day caused by fouling will be 656 X 24 X 1-5 lb. = 10-55 tons, THE EFFECTS OF FOULING. 103 or 316 tons per month. With coal at 12a. a ton, this represents a dead loss of about £190 per month for fuel alone. But in addition to the increased coal bill, the delay arising from fouling and the extra wages to be paid per mile are also important commercial considerations. It is interesting to observe the effect of fouling on the indicated horse power curve of a steamship tried at pro- gressive speeds. The effect is seen in fig. 37, where the highest full curve shows the actual indicated horse power required to drive the United States cruiser Manning at all speeds between 5 and 16 knots, and the dotted curve shows the horse power required to drive the same ship when moderately foul — i.e., on the assumption that the actual coefficient of friction is doubled. The leading particulars of the United States steamship Manning are as follow : — Displacement 1,000 tons. Length between perpendiculars 188 ft. in. Extreme beam 32ft. lOin. Mean draught on trial 12 ft. 4 in. Wetted surface 7,270 sq. ft. Cylinders of engine (25, 37^, 56^) 30 in. Diameter of propeller lift. Oin. Pitch of propeller 12 ft. 1 in. Revolutions at 16 knots 152 per min. Mean pressure referred to L.P 38 lb. per sq. in. The series of full curves in fig. 37 show the distribution of indicated horse power amongst its six components, viz. : 1. The power (Rw) expended in overcoming the wave-making resistance. 2. The power (Rs) due to the skin resistance of the ship. 3. The power (R() accounted for by the thrust deduction or the propeller augment of resistance. 4. The power (R^) lost in propeller friction, which is a large item. Lastly, there is the power lost in engine friction, ijvhich is subdivided into the initial friction (ri) or the friction of the unloaded engine, and the load friction (r2). 104 THE RESISTANCE AND POAVBR OF STEAMSHIPS. The dotted curve has been arrived at simply by doubling the skin resistance power (Es) at each ordinate, the other components being unaltered. The power required to drive the ship at 10 knots is increased, by fouling, from 350 horse power to 500 horse power, an increase of 43 per cent. At 15 knots the power is increased from 1,640 to 2,130 horse power, or 30 per cent. Again, 500 horse power will drive the foul ship at 10 knots only, in place of 11 '2 knots when clean ; and 2,000 horse power will drive the foul ship at 14'7 knots only, instead of at 15 6 knots when clean. These are merely round numbers, measured from the curves. All the effects of fouling that occur to us, including those of minor importance, may be conveniently tabulated as under : — 1. Loss of speed, and, consequently, delay. 2. Waste of fuel. 3. Waste of labour. 4. The trouble and expense of frequent docking, scraping, and painting. When carelessly done, scraping tends to shorten the life of a ship, and many anti-fouling paints certainly do, by their destructive action on the ship's plates. The alternative is the still greater expense of copper sheathing. 5. A slight increase of displacement. 6. Some loss of steering power. THE SHEATHING OF SHIPS. 105 CHAPTER XII. The Sheathing of Ships. Materials Used for Sheathing Ships. — The practice of covering ships with an outer sheath of thin sheet metal is very old. It is even said that the Romans employed lead and copper sheathing on the immersed parts of their ships.* Without doubt copper sheathing has long been applied to ■wooden ships with the double object of preserving a clean bottom and of protecting the timbers from the ravages of the ship-worm (Teredo navalis), a curious mollusc which can perforate the hardest timber, and so riddle it with holes that its substance is entirely destroyed. An alloy of copper and zinc, known as muntz or yellow metal, has also been used for a long time on wooden ships with fair success. The proportions of the constituent metals in this alloy are not well defined. Most authorities give 3 of copper and 2 of zinc ; others give 2 of copper, 1 of zinc, and a little lead. On the introduction of iron ships the bottoms fouled so rapidly that copper sheathing was tried as a preventive. The difficulty was to devise a satisfactory method of attach- ment. As the immersion in salt water of iron and copper in metallic contact leads to powerful galvanic action and the rapid destruction of the more electro-positive element, iron, it was soon found requisite to carefully insulate the copper sheathing from the iron hull by means of wood backing. This, of course, meant great expense and increased beam. In order to reduce the expense and danger attending the use of copper, the attempt was made to utilise zinc sheets placed in metallic contact with the iron hull. As zinc is only about one-third the price of copper, and does not need insulating from the iron, the economy is obvious. A notable * See a paper on " Anti-fouling Compositions," by Mr. M. Holzapfel, read before the British Association in 1889. 106 THE RESISTANCE AND POWER OF STEAMSHIPS. example of a zinc-sheathed ship is the Italian battleship Italia, of about 14,500 tons displacement. From a theoretical point of viesr, zinc undoubtedly possesses great advantages over copper as an anti-fouling material, since zinc is electropositive to iron, and therefore protects the latter from corrosion. Hence in the past its use has been strongly advocated by various writers, and several modes of attaching zinc sheets to iron hulls have been patented. One of these plans is shown in fig. 38, which represents Mr. T. B. Daft'a method. A space about fin. wide is left between the edges of the plates, and filled up with compressed teak. The zinc sheets are nailed to the teak caulking by their edges, and the zinc nails, being longer that the thickness of the teak, are turned over when driven against the iron strap, thus preventing the nails working out. A paper describing this historically interesting method was read by Mr. Daft before the Institution of Naval Architects in 1866, and entitled " The Jointing of Plates in Shipbuilding." In actual practice zinc sheathing seems to have proved a complete failure. The fact is, when zinc and iron are kept in good metallic connection the zinc is fairly effective as an anti-fouler so long as it lasts, but it rapidly wastes away. On the other hand, when the two metals are not in close metallic connection the zinc lasts some years, but is of little use as an anti-fouler. It has also been found that zinc THE SHEATHING OF SHIPS. 107 becomes so rough after no great service as to increase the skin resistance of the ship very materially. Other objections ■which have been raised to zinc sheathing are that it wastes away in a very uneven fashion, and that it becomes so brittle after a short period of service as to break off in patches. Even copper sheathing is not by any means a perfect preventive of fouling. An experienced shipbuilder reports that he used to dock and re-copper the Tees floating light- ship every three years, when he found it necessary to scrape off tons of mussels, ilr. H. van Meerten, late chief con- structor of the Dutch navy, in a private communication, also says : "From time to time I have docked copper-sheathed ships badly fouled, without having discovered any reason for this fouling. And, curiously enough, copper which has lost its anti-fouling properties seems not to be able to recover them. Copper once fouled, either by electro-nega- tiving it zinc, or through other unknown reasons, however well cleaned in dock, soon becomes again fouled. Some permanent setting of the molecules must be the cause of this strange circumstance.'' The metals lead and tin do not appear to have been used for sheathing iron ships. Like copper, they are ordinarily electro-negative to iron, though to a less degree ; and therefore, if used at all, they would have to be insulated from the iron or steel work of the hull. Tin is higher in price than copper, but lead is much less costly. Electro-chemical Action. — As many people have rather vague ideas on the subject of galvanic action, a few elemen- tary explanations may be useful. The complete theory of electro-chemical action, however, is very complex, and, indeed, has scarcely yet been fully worked out. 1. It is well known that when a strip of zinc is placed in a glass or porcelain vessel containing dilute acid, as sulphuric, chemical action goes on. Bubbles of gas (hydrogen) collect on the zinc, and rise to the surface of the liquid. The zinc also wastes away — that is, passes into solution in the form 108 THE EESISTANCE AND POWER OF STEAMSHIPS. of a salt of zinc, the chemical reaction being represented by the equation — Zn + H2SO4 = ZaSOi + H2. On repeating this experiment with a atrip of iron, a similar reaction takes place, hydrogen being evolved, and the iron slowly dissolved; but the action is less vigorous than before. On trying the same experiment with copper, however, no action can be observed. Bence there is a gradation in the chemical activity of zinc, iron, and copper. The action so far considered is purely chemical. 2. When a plate of either pure or amalgamated zinc and a plate of iron are together placed in a slighly acid bath, and allowed to touch each other outside of the liquid, a vigorous action is seen to proceed. Hydrogen is given off at the iron plate, and the zinc rapidly wastes away. This action is not purely chemical. It is the simplest case of electro-chemical, or so-called galvanic action. As soon as the plates are separated the action ceases, or nearly so. On repeating the experiment with copper and iron, a similar galvanic action goes on, but with this important diflference : the gas is now given off from the copper plate, while the iron wastes away, and is deposited on the copper. Thus, compared with the iron-zinc couple, there is a distinct reversal of efiect. 3. If, nextly, we attach a copper wire or other conductor to the nnimmersed parts of both the zinc and the iron plates under consideration, bubbles of hydrogen will escape from the iron plate, and the zinc will waste away. Further, the connecting wire will acquire the power of deflecting a magnetised needle placed near to and parallel with it, and of producing other marked electrical and thermal effects. On repeating the last experiment with an iron-copper couple, the deflection of the needle is seen to be in the oppoaito direction. The efiect described is best observed by the aid of a galvanometer. If we substitute a saline solution, as sea water, in place of THE SHEATHING OF SHIPS. 109 the dilute acid, then the efiecta will be similar in kind, bnt feebler in intensity. 4. We are thus led to the important conclusion that, when two metals diSering in chemical activity are immersed in a conducting liquid, and connected by a conductor outside of the liquid, a current of electricity is established, the direc- tion of which depends on the comparative ease of solution of the two metals. Conventionally speaking, the current starts within the liquid at the surface of that metal which is the more easily dissolved, and which is styled the electro- positive element. After traversing the outer circuit, the current re enters the liquid by the electro-positive plate. The famous Swedish chemist, Berzelius, framed an elec- trical theory of chemistry, according to which the chemical union of any two substances is held to be an electrical act. During contact, immediately before union, one of the sub- stances is relatively positive and the other relatively negative ; and the act of union is the result of these states. During the act of union the two electric states neutralise each other, producing heat and current. The author of this theory arranged the elements in a series, beginning with the most electro-positive, and ending with the most electro-negative element. From this instruc- tive electro-chemical series, the following selection of 16 well-known elements has been made : — ■ + 1. Sodium. 9. Mercury. 2. Magnesium. 10. Silver. 3. Aluminium. 11. Gold. 4. Zinc. 12. Platinum. 5. Iron. 13. Hydrogen. 6. Lead. 14- Carbon. 7. Tin. 16. Sulphur. 8. Copper. 16. Oxygen. For a given exciting liquid, the further apart in this series that the elements of a voltaic couple are separated. 110 THE RESISTANCE AND POWBE 01' STEAMSHIPS. the greater will be the difFerence between the chemical action on the elements (usually metals), and the higher will be the electro-motive force of the resulting current. Hence the list is sometimes termed the electro-motive series. It will be noticed that zinc is feebly electro-positive to iron, and copper moderately electro-negative to iron. A word of caution is here necessary. The direction of the current set up does not depend solely on the nature of the elements composing the couple. It is influenced also by the nature of the exciting liquid. So far as can be gathered the above order is true only when the liquid is water slightly acidulated with sulphuric acid. When other liquids are used the order is rather different. Thus, taking hydro- chloric acid as the exciting liquid, and comparing six common metals, we have the following order — zinc, tin, lead, iron, copper, silver. In potassium sulphate the order becomes — zinc, copper, tin, silver, lead, iron. These facts explain the wide variation of the electro-motive force of different voltaic cells. In Ganot's " Treatise on Physics'' the following interest- ing passage occurs : " A metal which is acted upon by a liquid can be protected from solution by placing in contact with it a more electro-positive metal, and thus forming a simple voltaic circuit. This principle is the basis of Davy's proposal to protect the copper sheathing of ships, which is rapidly acted upon by sea water. If zinc or iron be con- nected with the copper, these metals are dissolved, and the copper protected. Davy found that a piece of zinc the size of a nail was sufficient to protect a surface of 40 or 50 square inches. Unfortunately, the proposal has not been of practical value, for the copper must be attacked, to a certain extent, to prevent the adherence of marine plants and shellfish." The Application of Copper Sheathing. — For the protection of warships against fouling during long periods afloat, it is believed that no composition is equal to properly-insulated copper sheathing. Yef so expensive is sheathing, that THE SHEATHING OF SHIPS. Ill opinions differ greatly as to the advisability of its use. In its favour, we find that Chief-constructor Hichborn, of the United States Navy, in his annual report for 1899, strongly urged the importance of sheathing all warships intended for distant service. It was, therefore, decided to sheathe the new U.S. battleships. Further, six second-class cruisers for the same navy are to be sheathed with pine up to 30 in. above the water line, and then coppered. It is stated that the anti-fouling virtues of this method were amply demonstrated during the late Spanish-American War. On the other hand, Constructor Bowles, of the U.S. Navy, recently* said : " I am not an advocate of wood sheathing on ft Naral Brass Scre» I^OPP "- -^ Shea thing Bottom Fio. 39. steel ships. I have always been against it. It may be necessary, now that a number of our ships are in the Philippines, but only until a dry dock is built there." Again, in The Practical Engineer, of 2nd March, 1900, page 215, this important note appeared : " The sheathing of war- ships has been voted against by the United States Board of Construction. It was shown that expensive wood and copper sheathing put upon the Chesapeake was not only a failure, but menaced the life of the metal [vessel ?]. The practice has been abandoned in England after a fair trial. * See E'/igimermg, 29tli December, 1899. 112 THE EESISTANCE AND POWER OF STEAMSHIPS. The copper does not prevent fouling ; and it is believed that some kind of paint, or substitute for paint, will better protect the bottom of the ship." It is not always safe, however, to place implicit reliance on isolated statements. In attempting to arrive at the truth, in any subject of scientific inquiry, it is needful to compare many facts and opinions by balancing the state- ments of one writer against those of another ; and also, wherever feasible, by carrying out independent experimental investigation. It appears that an important discussion has taken place, amongst the American naval experts, in regard to the propriety of sheathing the new warships. From a recent issue of the American Marine Bevieiu we learn that the Board of Naval Construction originally recommended that the ships should be sheathed, but afterwards changed its mind on the ground of expense. The Congressional Naval Committee thereupon decided to leave the matter to the discretion of the Secretary to the Navy. Admiral Hichborn (the Chief-constructor) still holds out for the use of copper sheathing, pointing out that, amongst other advantages, the bottom of a sheathed vessel is materially strengthened, since the wood acts as a cushion, and distributes any blow over a wider area. Hence, in the British Navy it is found possible to make the steel shell- plating ^u in. thinner when the bottom is sheathed. One thing at least has been made clear, viz., that, as regards the best means of preventing the fouling of war- ships, there is no unanimity of opinion and of practice, even amongst those presumably the best qualified to judge. According to some naval architects, copper sheathing is an excellent thing ; according to others, it is useless, and even dangerous. Certainly the costliness of copper sheathing has resulted in its omission in by far the greater number of ships afloat, including the finest Atlantic liners. But, according to Sir W. H. White's "Manual of Naval Archi- tecture," a very large number of sheathed ships are employed THE SHEATHING OF SHIPS. 113 in the Royal Navy and in foreign navies. The extra cost and weight of the wood and copper sheathing, and of the bronze stems, stern posts, and rudders (required in order to avoid destructive galvanic action), must be regarded as the price paid for securing the maintenance of speed during long periods afloat, and the avoidance of frequent dockings and re-coatings, such as are necessary in unsheathed ships. Speaking before the Institution of Naval Architects, in 1896, Sir W. H. White said, in reference to the sheathed frigate Inconstant : " This ship has now been afloat for 27 years, and has performed much trying service under steam and sail Her sheathing has never given serious trouble, and the anti- fouling properties of her copper bottom have been well secured." So well has copper sheathing been found to answer its purpose, that all British first-class cruisers built since 1802 have been sheathed, as well as several battleship?. It is incredible to suppose that the Chilians, Japanese, and others would pay for the sheathing of their latest cruisers unless they were perfectly convinced of the superiority of that mode of preventing fouling in the case of high-speed ships of war, often stationed in tropical waters. Of course, the initial cost of copper sheathing renders its use quite out of the question in the case of ordinary merchant ships. Fig. 39 shows a method of insulating copper sheathing from an iron hull which has been used in the Royal Navy. Each of the wrought-iron bolts is screwed through the plating, and further secured by a thin washer and a nut resting on a hemp packing ring, steeped in red lead. The head of each bolt also rests on a hemp packing ring, or so- called "grummet." The outer planking is fixed to the inner by naval- brass* screw boltp, fin. diameter, packed in a similar way. The surfaces of the planking in contact, also the outer surface, are well painted with a mixture of red and white lead. The edges are caulked with oakum. Lastly, sheets of tarred brown paper are inserted between * Naval brass consists of 62 per cent copper, 37 per cent zinc, and 1 per cent tin. 8s 114 THE RESISTANCE AND POAVER OF STEAMSHIPS. the copper sheathing and the planking, to -which it is fastened by copper nails. Almost as much care is thus taken with the insulation as in the case of electrical machinery. In spite of all these precautions the insulation is not perfect, though the electrical resistance is sufficiently great to render the current comparatively feeble. In fact, in recent ships a single thickness of planking, well caulked and fastened with bolts, has been found to suffice. In ships so sheathed there exists the danger that, should any damage to the insulating material take place — as by grounding — the small exposed area of iron bottom plating, and the large area of copper immersed in sea water, would together form a voltaic couple, the inevitable result being rapid corrosion of the iron or steel plates. The American practice of insulating copper sheathing was described in detail by Chief-constructor Hichborn, in a paper read in December, 1894, before the American Society of Naval Architects and Marine Engineers. A plank of teak is worked in 12 in. strakes, from 3Jin. to 4 in. thick. The bolts are of fin. naval brass, the heads being l|in. diameter, and sunk to about fin. below the surface. They are well tightened up, so as to compress the wood under the heads about g in. Each nut bears on a thin iron washer, and the thread is centre-punched to check it. Hempen grum- mets, saturated with red and white lead, are fitted under both the head and washer of each bolt, the recess over the head being filled with Portland cement. The bolts are spaced about. 15 in. pitch, except at the butt, each butt having four bolts. After the fastening is completed, in order to fill up all spaces between the plank and the ship's skin, holes are bored in the centre of each strake of plank, about 6 ft. apart, and a mixture of red and white lead is cautiously pumped in, until it comes out at the adjoining holes. Finally, the holes are plugged. A recent example of a sheathed ship is the U.S. cruiser Denver, of 3,200 tons displacement, shown in figs. 40 and 41. THE SHEATHING OF SHIPS. 115 116 THE RESISTANCE AND POWER OF STEAMSHIPS. The length on load water line is 292 ft., the extreme beam 44ft., and the mean draught 15 ft. 9 in. The hull ia sheathed with 4 in. pine, covered with copper weighing from 28 to 32 ounces per square foot, which represents a thickness of nearly aVin. The stem, stern post, shaft struts, and rudder are of manganese bronze. By way of comparison, the method of attaching zinc sheathing, formerly in use in the British Navy, is not without interest. A single thickness of 3 in. to 4 in. planks was bolted outside the skin plating, and to this the zinc sheets were nailed. The strakes of planking were not caulked, but the water which found its way under the sheathing could pass freely through the seams to the iron skin. Iron stems and stern-posts were used, and a certain amount of metallic connection was made between the zinc sheets and the iron hull, in order to keep the surface of the zinc freer from incrustation. It was found difficult, how- ever, to adjust the relative amounts of the surfaces of iron and zinc, so as to prevent too rapid or too local wearing of zinc, without interfering with its anti-fouling properties. Sir W. H. White says that, on some merchant ships where the zinc was laid almost directly on the iron skin, with felt or some similar material interposed, its rate of wear was so quickened that a single voyage sufficed to destroy it. In other exceptional cases zinc sheets, ^in. thick, have been worn through in the course of 12 months. The usual life of either yellow metal or copper sheathing is about five years, by which time it is usually found to be wasted so thin as to require renewal. The Cost of Sheathing. — A simple calculation will serve to give a rough idea of the cost of the raw material required to sheathe a given ship, leaving out of account the expensive bronze castings needed for the stem, stern-post, &c. Taking the case of the Denver, above cited, the immersed surface will first be approximately found ; then some allowance will be made for the sheathing which extends above the water- line, and the cost of so many square feet of timber and sheet THE SHEATHING OF SHIPS. 117 J3 O Fia. 41. L^^f-: 118 THE EESISTANCB AND POWER OF STEAMSHIPS. copper estimated according to the market rates. The cost of bolts and of drilling, shaping, and other labour -will not, however, be gone into. The most convenient method of finding the approximate immersed surface of a ship is to use Mumford's formula, as given by Mr. Archibald Denny, in a paper read before the Institution of Naval Architects in 1894, as follows : where S = {L xd X 1-7) + (L X B X C) S sq. ft. = wetted surface, L feet = length between perpendiculars, d feet = mean draught, B feet = beam, C = block coefficient. On substituting = = ^ in place of C, and simplifying, Ij X x5 X a Mumford's formula takes the somewhat handier form, S = 1-7 cZ L + ?!?, D being the displacement in tons. Mr. Denny says that the formula gives very close results for ships of medium draught, beam, and fineness. In the case of twin-screw ships, having projecting shaft casings, an addition must be made for these projections, as also for any bilge or other projecting keels that may be fitted. The approximate wetted surface of the Denver will, therefore, be 1-7 X 15-75 ft. X 292 ft. + 35 x 3200 tons id 75 ft. = 7830 + 7120 = 14950 sq. ft. Adding 10 per cent for the sheathing above water, brings the total sheathed surface up to about 16,500 square feet. Now, pine " deals," of a quality good enough for sheathing, cost in England about 2d. per square foot per inch of thick- ness, up to 11 in. wide — or say 8d. per square foot for 4 in. THE SHEATHING OF SHIPS. 119 plankd. Hence, the coat of timber alone for sheathing the Dcjnver will be about 16500 X -i-£ = £550, 240 ' allowing nothing for waste. The price of copper sheets varies a good deal from time to time, but we may take £85 per ton as near enough for our present purpose. The sheets used for sheathing weigh about 2 lb. per square foot, so that the weight of 16,500 square feet will be 33,000 lb., and the coat about 33000 2240 X £85 = £1250. Thus the total coat of wood and copper is £1,800. Of course, this estimated co-st of the raw material is much less than the actual cost of sheathing such a ship. A few figures as to the percentage gross cost of sheathing warships may be of interest. In the Marine Review for March 22, 1900, it was stated that the sheathing of the Marietta, a composite gunboat of 1,000 tons displacement, cost 7^ per cent of the cost of the hull and engines. Admiral Hichborn, however, points out that it is fairer to calculate the percentage upon the whole cost of the completed vessel, in which case it would be reduced to 559 per cent. For the Chesapeake the percentage was 4'65 of the total cost of construction. These are American ships. The expense of sheathing is relatively much greater for small than for large vessels, since the wetted surface of similar ships varies as the square of the length, while the displacement varies as the cube. Two sheathed cruisers of the Royal Arthur class, built in the Royal dockyards in 1891-2, only exceeded the cost of two similar unsheathed ships by 1'87 per cent, while for contract-built ships the excess was but 1'53 per cent. Two and a half per cent of the cost of a £400,000 cruiser means the sum of £10,000. The Electro-coppering of Ships. — On the subject of the electro-deposition of copper on the bottoms of steel ships, 120 THE RESISTANCE AND POWER OF STEAMSHIPS. the accounts of experiments are singularly contradictory, some stating that the process is a success, and others an utter failure. It appears that a few years ago a syndicate was started in the United States to deposit copper by electrolysis on the bottoms of steel ships. As it was not practicable to fill the entire dry dock with a copper solution, coffer dams were fitted round various sections of the ship and filled with the electrolyte. A dynamo supplied the electric current required to decompose the solution of copper salt which formed the electrolyte. In this way the entire bottom of a ship could be covered, bit by bit, with a deposit of copper to any desired thickness. The syndicate bought a tug, to which they applied the system, after carefully cleaning the bottom by the sand-blast process. The tug was then put into service, but in two years the bottom was found to be in such a bad state, owing to galvanic action between the copper and the iron, that the vessel had to be condemned, and the system of electro-plating ships' bottoms pronounced a total failure. Some years ago also the enterprising firm of Messrs. Denny Bros , of Dumbarton, tried the experiment of electro- coppering the bottom of their steam tender. After the vessel had been again in use for a few months she was taken out of the water and examined, but the condition of the shell-plating proved to be so unsatisfactory that the copper coating was forthwith removed. Notwithstanding these unpleasant experiences, the follow- ing statement has been going the rounds of the press : " After trials lasting four years a favourable report has been made to the United States Government on Crane's system of copper-plating the hulls of ships, in order to prevent fouling by marine growths. The whole bottom of a ship, 400 ft. long and drawing 20 ft. of water, can be plated in eight or nine days with a thickness of copper of -^ in. or more. Some 55,000 lb. of copper would be required for a vessel of that size. On the other hand, £4,000 a year is ANTI-fOULING COMPOSITIONS. 121 expended by some trans-atlantic boats in overcoming the resistance due to fouling, and to this must be added the cost of docking for cleansing the bottom." We are unable to give the name of the author of the report, or to state on what grounds the conclusion is based. CHAPTER XIII. Anti-fguling Compositions. The great majority of steamships are not sheathed, but have their bottoms covered ■with a special anti-fouling paint or composition, which is laid over one or two coatings of an anti-corrosive or protective paint. Such ships are docked once or twice a year for a general inspection of the bottom, and also for cleaning and repainting the fame. The cost of docking a vessel of about 4,000 tons deadweight, in the dry dock of one shipbuilding yard on the North-East Coast, is about £20. This sum includes shoring, pumping out the dock, laying on two coats of paint — which is supplied by tV e owners — and undocking. The work is undertaken at that moderate price, however, in expectation of other work in the way of repairs being, in many cases, found neccessary. The manufacture of ship^' compositions is not a small industry, no less than 42 firms appearing in the Post-office Directory of London alone under the head of " makers of compositions for preventing fouling on ships' bottoms." One firm alone turns out over 2O0 tons of ships' paints per month. Many so-called anti-fouling compositions, however, are almost valueless in preventing fouling. At the same time there are some well-known compositions on the market which have undoubted anti-fouling properties. They also dry more rapidly than the ordinary red oxide of iron paint, thus enabling two or three coats to be applied in one day. This property of quick drying is very important, owing to the time and dock dues thereby saved. 122 TBB EISISTANCK AND POWEE OF STEAMSHIPS. The comparative cost of ships' paints is a matter of some interest and commercial importance. Red oxide of iron protective paint costs 20a. per cwt., and common anti-fouling paint 403., one coat of the former and three coats of the latter being applied. Messrs. Holzapfel's "International" composition, for quick-fouling waters, costs 70s. per cwt. for No. I (protective), and 120s. for No. II (anti-fouling). Their "National" composition, for coasting trades and waters where the fouling is slow, is sold at 383. per cwt. for No. I, and 653. for No. II. The price quoted by Messrs. Ripolin for their " Rieps " compositions is 71s. per cwt. for anti-corrosive, and 100s. for anti-fouling paint. The compositions named are all largely used, and may be regarded as sufficiently representative. The requirements of a satisfactory anti-fouling com- position are the following : — 1. It must dry quickly. 2. When dry, it should have a hard, smooth surface. 3. It must adhere well. 4. It must prevent serious fouling for from nine to twelve months. 5. When properly applied, it must not act injuriously on the ship's plates. It is not possible to make a single anti-f onling composition which shall be equally satisfactory in all waters. The constituents must be varied to suit the particular trade in which the vessel to be protected is engaged. It is not the duty of an anti-fouling composition to preserve the plates from rusting, that being the function of the preparatory anti-corrosive or protective coatings, which consist of either a slow-drying oil paint or a quick-drying varnish paint. Most anti-fouling paints are divisible into two classes : — (a.) Grease paints, which consist of either tallow or soap mixed with compounds of copper, zinc, or lead. Tallow and zinc white (ZnO), also called Chinese white, form a well- known mixture, which has been much used. It answers best when the tallow is rancid. Such mixtures have the dis- ANTI-FOULING COMPOSITIONS 123 advantage of requiring to be heated before application, and the surface produced by them ia neither hard nor very smooth. Hence the coating ia not durable, and the skin resistance of the ship is considerable. (6.) Varnish Paints— These are prepared either by dis- solving certain gums in cold spirits of wine (dilute alcohol), or by boiling them with oil and turpentine. Shellac, for example, ia a gum soluble in spirits of wine, and resin is soluble in either spirits of wine or naphtha. The harder gums however (such as cowrie, manilla, copal, and amber), will not dissolve in the cold state, and boiling must be resorted to. After the varnish thus prepared has been coloured with a strong pigment, such as Venetian red (chiefly Fe203), the metallic salt forming the anti-fouling ingredient is added in the physical form of a dry powder, and the mixture kept well stirred for some days. Finally, the paint is diluted to the desired consistency, when necessary, by the addition of turpentine, and run out into drums containing 1 cwt. The drums are strongly made of sheet steel, from which the mill scale has been removed by an acid bath, bnd then coated with molten lead by the process of '' dipping,'' the superfluous lead being wiped off'. The principal salts used in the preparation of varnish paints appear to be copper sulphide (CuS), copper oxy- chloride (CuClsSCaO+iHaO), mercuric chloride (HgClg) and, perhaps, mercuric nitrate (HgNOs), all of which are soluble in water. Of course, they are not all used in the same composition. Manufacturers are rather reticent as to the precise proportions of the several constituents of their anti-fouling mixtures, apparently regarding this informa- tion in the light of a trade secret, which it would be against their interests to disclose. The original Rahtjen'a paint consists, in general terms, of a shellac solution or varnish, poisoned by the addition of arsenic and mercuric oxide (HgO), the latter alone being effective. The object aimed at in the manufacture of these anti-fouling paints is to combine the metallic salts with a varnish sufficiently soluble 124 THE EESISTANCB AND POWER OF STEAMSHIPS. to admit of these salts being slowly acted upon by sea water for a period of nearly a year. A paint said to give good results in the home trades, as the Baltic, consists of black varnish covered with a coat of blacklead mixed with beer ! Hundreds of patents have been taken out for anti-fouling compositions, many of them being quite useless. One patent composition consists of linseed oil, corrosive sublimate (HgCi2), litharge (PbO), red lead {Pb304), bitumen, pitch, and sufficient turpentine to form a workable paint. Another specification gives orange shellac, white and red lead, vegetable pitch, marine driers, linseed oil, and turpentine. A recent patent specifies a mixture of resin, varnish, and alnm, together with a pigment and a naphtha drier. Arsenical and phosphoric soaps have been tried, but with small success. Paints containing copper powder, though effective in preventing serious fouling, should on no account be used on steel ships, owing to the rapid corrosion induced by the galvanic action which is sure to go on. Paints containing copper sulphide are also very risky. Mr. M. Holzapfel informs us that if an unlimited amount of copper preparation could be safely used in the manufacture of composition for iron and steel vessels, the question of preventing fouling would be a comparatively easy one to solve. " The time is, perhaps, not far distant when anti-fouling compositions will become a general staple trade article, sold according to analysis, the same as soda, potash, and other chemicals. At present there is much prejudice in respect of brands, as well as general ignorance of the subject among consumers. They may pay a high price to one firm for the identical article which is offered to them by another firm at a much lower price. By analysing the various articles submitted to them, shipowners might save thousands of pounds per annum in their composition account.'' This suggestion was made ten years ago by Mr. A. C. Holzapfel in the Shipping World, but it does not yet appear to have borne fruit. Compositions are still bought on faith, in much ANTI-rOULING COMPOSITIONS. 125 the same way as pills and patent medicines generally ; and not in accordance with the requirements of a scientific specification, corresponding to the medical man's prescription. For the production of a satisfactory anti-fouling paint, however, it is not sufficient to know merely the proper ingredients to be used. The nature of the various chemical processes involved, and the order of the mechanical operations must also be carefully considered. For dealing expeditiously with large quantities of paint, special chemical plant is needful, as well as pulverising, mixing, and trans- porting machinery. It is very important to get the metallic salts quite free from water before mixing ihem with the varnish ; and this involves the use of special presses and drying stoves. By the courtesy of Messrs. Holzapfel's Compositions Company Limited, of Newcastle-on-Tyne, we have had the opportuity of observing the processes of manufacture, as carried on at their works, and also of inspecting a number of badly fouled iron plates, which had been sunk in various harbours of the world, and then preserved in a mixture of glycerine and water. Similar interesting collections of fouling matter were on view at the Paris Exhibition of 1900. The precautions necessary to be observed for efficiently coating a steel ship are the following : — 1. When the first protective paint is applied, the ship's plates must be dry, not " sweating." 2. All foreign matter, rust and unsound old paint must be scraped ofi the bottom. 3. In the case of new ships two coats of "priming" (or protective paint) must be applied and allowed to dry. In subsequent dockings it may suffice, in many cases, to simply touch up the bad parts with the priming, leaving the sound paint undisturbed. 4. The anti-fouling composition must be kept well stirred, to prevent the metallic salts separating out, and applied uniformly in one coat over the entire bottom. 5. Soon after the composition is dry, the ship should be 126 THE RESISTANCE AND POWER OF STEAMSHIPS. floated ; for anti-fouling paint rapidly deteriorates on exposure to the atmosphere. Should the mill-scale or "bloom" be removed from the ship's plates before any paint is applied 1 This is an unsettled question. Some people consider it best to launch a steel vessel before painting the hull at all, and, after allowing the plates to rust superficially for a few months, to dry- dock the ship, thoroughly scrape and clean her, and then apply a coat of zinc oxi de paint. O thers advise the removal of of the mill scale from the plates by the process of " pickling " in an acid bath ; and others, again, say that the best course to pursue is to leave the mill scale alone, and paint it over with white lead. Theoe,y op the Action of Copper Sheathing and of Anti-fouling Compositions. The explanation of the anti-fouling properties of sheathing and compositions is a difficult and vexed question, the various causes assigned by difierent writers being mechanical, chemical, and biological. Perhaps the most generally held view is that concisely given by Prof. V. B. Lewes, on page 58 of his "Service Chemistry," viz., that uopper acts in preventing fouling by reason of its forming, in contact with salt water, oxy-chloride of copper, which being poisonous, helps to retard the growth of certain forms of animal and vegetable life ; whilst the wasting away of its surface from this cause throws off barnacles and such forms of fouling as obtain hold, in spite of the poisonous character of the copper salts. So far as barnacles are concerned the true explanation of the anti-fouling properties of copper sheathing appears to be the following : The copper oxy-chloride, formed by the action of sea water on the sheathing, slowly dissolves and exerts a chemical action on the albuminous cementing material, by means of which all young barnacles seek to attach themselves, which has the effect of coagulating this substance and depriving it of its cementing properties, so ANTI-FOULING COMPOSITIONS. 127 that they fail to secure attachment so long as the copper remains in proper condition. It is clearly misleading to say that copper sheathing acts by exfoliation, for exfolia- tion means " to come off in scales," and not to slowly pass into solution, which is an essential feature of the actual process. In the case of compositions the first stage is the gradual loosening and setting free of the active anti-fonling substance from the inert varnish in which it is embedded. The next step consists in the dissolving of the particles of that substance in sea water, accompanied by a chemical action, which usually results in the formation of either oxy- chloride of copper, or chloride of mercury (HgCla). The slow solution of these chlorides leads to the coagulation or curdling of the albuminous coating of such juvenile barnacles as come in dangerous proximity to the ship's hull, and the consequent failure of their attack. We are indebted to Mr. M. Holzapfel for the interesting fact that a solution of chloride of mercury or of oxy- chloride of copper will at once coagulate any albuminous substance, and quite spoil its cementiag properties. The same authority maintains that no anti-fouling composition exists that is based on the theory of exfoliation, and, indeed, cannot exist ; because cirripedia, after once getting a hold on a ship's bottom, grow very rapidly, and in doing so, penetrate with their base through the paint, and find attach- ment to the metal surface. If the theory of exfoliation were tenable, animal life would have to find attachment to the paint only, and their shells would fall off when their occupants were killed in fresh water, which, he asserts, is not the case . Farther, experiments prove that all metallic salts capable of forming chlorides with the salts and oxygen contained in sea water are anti-fouling in their efiect, though not equally so, while compounds which do not form chlorides in this way have no anti-fouling effect at all, however poisonous they may be. The number of graias of the various solids dissolved iu 128 THE RESISTANCE AND POWER OF STEAMSHIPS. one gallon of sea water is given below, and compared with the composition of river water and also of spring water. Sodic chloride Magnesic chloride . Magaesic sulphate . Calcic sulphate . . . Calcic carbonate . . . Magnesic carbonate Silica, alumni'i, 'KINES POWER RULE. 149 Thus Eankine'a power rule is — AS. X V3 ~ 20000 ■ I.H.P. Hence the probable speed of a given ship, with a specified power, is given by the formula — V = 3/I.fl.P. X 20000 J- A.ti. In order to show the apparent remarkable accuracy of the augmented surface method, Rankine gave the following example of its application to an actual ship, which had been tried on the measured mile. The calculation is not likely to be repeated, but the figures will serve better than mere words to give some idea of the labour involved, as well as the great amount of information necessary to be known about the ship, before the method can be applied at all. Example. — To calculate the probable speed of H.M.S. Warrior, given : displacement on trial, 8,997 tons ; draught of water— forward 25 83 ft., aft 26-75 ft. :— Water-lines. Sine o£ obliquity. Square of sine. Fourth power of sine. L 2 3 1 5 6 Keel •S70 •315 ■290 •265 •235 •165 ■000 •1369 •0992 •0S41 •0702 ■0052 •0272 ■0000 •01S74 ■009S1 •00707 •00492 •00304 •00074 ■ooooo Means ■0074 ■00583 150 THE EESISTANCE AND POWER OF STEAMSHIPS. Therefore the coefficient of augmentation = 1 + (4 X -0,674) + -0058 = 1-275. Half girths from body-plan. Sim son's multipliers. Prodx^cts. Feet. 21 1 21-0 27-2 4 lOS-S SO-8 2 ei-6 84-8 4 13S'4 3S-S 2 77-C 41-5 4 160-0 42-6 2 85-2 44 4 176-0 44 2 8S-0 44 4 176-0 4S-.ll 2 S6-G 42-1 4 16S-4 40-8 2 SO-6 3S-1 ' 4 162-4 36 2 72-0 35 4 140-0 32 1 32-0 Divide by 3 ) 1830-6 sum Divide by half number of intervals.. S ) 610-2 Mean immersed girth X length . Product X coefficient of augmentation Augmented surface . . 70-3 3S0 28994 1-275 36,979 sq. feet. eamkine's method. 151 Indicated horse power, on trial . X coefficient of propulsion 5,471 20,000 Divide by augmented surface... 36,970 ) 109,420,000 product. Cube of probable speed Probable speed, computed Actual speed, on trial 2,959 Knots, 14-356 14-354 Difference -002 This is certainly a very close agreement between calcula- tion and experiment. Had the speed been 20 knots, however, instead of 14, the method would probably have told a very diSisrent tale. Example S. — To compute the coefficient of propulsion for a copper-sheathed vessel, Eankine examined the case of the Royal yacht Victoria and Albert, a wooden vessel of 1,980 tons trial displacement, 13-8 ft. draught forward and 14 ft. aft:— Water-lines. Sine of obliquily. Square of sine. Fourth power of eine. L WL •19 ■0361 •0013 2 WL ■IS'i •0342 •0O12 3 WL •17 •O'^sn ■ooos 4 WL •14 •0198 ■0001 Keel Means ^^ •0252 •ooos Coefficient of augmentation. Length of water-line X mean immersed girth (measured with an instrument) X coefficient of augmentation Augmented surface = 1-K4X 0252) -H 0008 = 1102. 300 ft. 40 ft. 1102 13224 sq. ft. 152 THE RESISTANCE AND POWER OF STEAMSHIPS. AS. X V3 Now, since I H.P. = C therefore C = ^'^^-^-^ ^ 13224 X n^ = 21802. Had the probable speed been computed with the coefficient ' of propulsion 20,000, the result would have been 1653 knots, instead of 17. Comparison with the Admiralty Formula. — In point of convenience of application, Eankine's augmented surface method is far inferior to the Admiralty formula. Witness, for example, the ease with which the Admiralty coefficient is found from few data in the case of the famous Hamburg- American liner Deutschlaud, whose displacement is 23,600 tons ; length, 663 ft. between perpendiculars ; breadth, 67 ft. ; moulded depth, 44 ft. ; and draught, 29 ft. The speed is rather over 23 knots, with 35,000 horse power. Since LHP. = ^'xl^^ C = U ' ys X DS I.H.P. 233 X 23600S = 286. 35000 Eankine's power formula, on the contrary, could not be applied to this ship without knowing a great deal more about her. The formula was roundly attacked by the late William Denny, of Dumbarton, in his paper on "The Difficulties of Speed Calculations," the object of which was " to prove the uselessness of Kankine's formula, and to urge the desirability of having all steamers tried progressively." The method in its original form has now become quite obsolete, but in a modified form it is still used by some estimators for ships of slow or moderate speed. In thi modification the augmented surface of a Kirk's block-model kirk's method. 153 of the ship is made use of instead of the augmented surface of the ship itself, the latter being too troublesome to calculate. The expression 1 + 4 sin^ ^ is termed the coeflGlcient of augmentation, 6 being the half-angle of entrance of the block-model. It is a factor which takes account of the fine- ness of the ship, being greater for full than for fine ships. The so-called augmented block surface is the product of this factor and the actual block surface. The following example will serve to explain the method. Example of Kirk's Modification.— Given a ship 315 ft. by 38 ft. by 14 ft. 7 in. draught (ex keel), displacement 3,327 tons, immersed mid-area 512 sq. ft, and whose engines indicate 2,000 horse power at 13 knots speed. 1. E,eqnired a block-model of the ship, its wetted surface, its augmented surface, and the half-angle of entrance ; also the ship's coefficient of fineness and the prismatic coefficient. 2. In the case of a similar proposed ship, 420 ft. long, to find the displacement, the speed corresponding to 13 knots of the model ship, and the power required to drive her at that speed, assuming equal efficiency of engines and propeller in each case. Referring to fig. 47, since volume of block = volume of ship, (L-E)M = 35D or (315 - E) 512 = 35 x 3327 315 - E = 227 5 E = 87-5 ft. Again, bd = "M 6 X 14 58 = 512, or 6 = 35 1 feet. Length of slope s = JWTIJW = Jslb' + 17'5^ = 89-2 ft. Hence e = IV 22' 154 THE EESISTANCB AND POWER OF STEAMSHIPS, The block-model can now be drawn to scale, as in fig. 48, and its wetted surface calculated as follows : — Perimeter = 4 s + 2 m = (4 X 89-2) + (2 X 140) = 636 8 ft. Wetted surface of sides = perimeter and draught = 036-8 X 14o8 = 9300 sq. ft. Wetted surface of bottom = 6 (E + »i) = 351 (87-5 + 140) = 7980 sq. ft. The total wetted surface of the block is the sum of these, or 17,280 sq. ft. — A — r.- FiG. 47. Coefficient of augmentation = 1 = 1 = 1 Augmented surface = wetted augmentation = 17280 X 11548 = 19950 sq. ft The coefficient of fineness of the ship is — 35 J)^ = 35 X 332 LBc< + 4 sin^ e + 4 X -197- + 4 X 0387 = 1-1548. surface x coefficient ■667. of 316 X 38 X 1458 The prismatic coefficient of the ship is — 35 D ^ 35 X 33 27 ^ .^g., LM 315 X 5i2 '""' 2. In dealing with the second part of the problem, the following relations are required :— (1) Length ratio = length of proposed ship or r = — length of model ship THE METHOD OF COMPARISON. 155 (2) Corresponding speed of proposed ship = speed of model x »yiengtn ratio, or Vc^ = Vc X Jr. (3) Power of proposed ship = power of model ship X ri or pi P X the ships being exactly similar in shape. (4) Displacement of proposed ship = (displacement of model ship) x r^, or D'^ = D X 7-^- FlG. 48. A tabular form is prepared, and the quantities filled in as soon as calculated, thus : — Model ship. Proposed ship. L 316 ft. 420 ft. D 3,327 tons Di 7,930 tons r 1 1-335 v^ 1 1-155 ri 1 2-74 Vc 13 knots .. Vc^ 15 knots P 2,000 H.P. pi 6,480 H.P. 156 THE EESISTASrCE AND POWEE OP STEAMSHIPS. For similar ships at corresponding speeds- Vc .-. Vfli = 13 X 1155 = 15 knots. If X = rl = J'r = ^^ log x: = '- log 1-335 = ^ X 125 = •4375. .-. X = 2-74. Hence the power required to drive the proposed ship at 15 knots will be — Pi = Pr? = 2000 X 274 = 5480 horse power. Lastly, since the displacement of similar ships varies as the cube of the length, we have — .-. D^ = 3327 X 1-3353 = 7930 tons. This, then, is the displacement of a ship to steam at 15 knots with an engine power of 5,480 I.H.P. i-i-5 A S^-hnot Atlantic Liner. — The method just described has been used to calculate the power required to drive a similar ship to the Deutschland, but 1,000 ft. long between perpen- diculars, at a speed corresponding to 232 knots, viz.rSS knots. The results are tabulated below :— ■**'■*' Vv Deutschland England Feet. C68 Tons. 23,600 Knots. 23-2 H.P. 35,000 148,000 Such a ship is not, however, at present commercially practicable. COEEESPO^DING SPEEDS. 157 CHAPTER XVI. Corresponding Speeds. In addition to the methods already described in previons chapters, two others are sometimes employed to calculate the horse power required for any proposed ship from the trials of a similar ship. They avoid the use of the Admiralty coefficient, and are based upon the following equations : — I.H.K, Li5 VLi/ ■ ^ ■ • ■ ■ W I HP. ^ Di ^ /JD y. ,2) I.H.P.J Di? VDi/ ^ ' Proof of equation (1). In a previous chapter it was shown that I.H.P. V^ X wfit.ted surface of A I.H.P.i Vi^ X wetted snrtace of B But, from the lato of corresponding speeds, V jn u therefore But (a) 11 = !■'-- wetted surface of A L^ wetted surface of B L^'^ Therefore, substituting in equation (a), we get I.H.F. = L3 y ^ L? _ /L\i I.H.P.1 LJ Li^ Li5 \lJ • The proof of equation (2) is very similar. By the Admiralty formula we know that LHP. Y" X Di I.H.P.1 Vi^ X DJ (b) 158 THE EESISTANCE AND POWER OP STEAMSHIPS. But ^1 = Il Vi^ L, L ^m Z! = Di If, therefore, we substitute in equation (6), we get- I.H.P. Di X D5 and also BO that and Iflp.l Di* X Di I.H.P., (B'- The proof of equation (2) may also be derived directly from equation (1) as follows : — T.H.P. U 1.H.P.1 w and since ^ J TJ p therefore ^^=^4=-^ ~(P\ v = r£V. — I.H.P.1 KB^iJ VDi/ If either of these equations are used to calculate the horse power, the calculations are, perhaps, rather simpler than those involved by the use of the Admiralty coefficient method. In making actual calculations it will be well to adopt the following order : — 1. Find the corresponding speed of the type or model ship. 2. Find the I. H. P. of the model ship at that speed. 3. Find the I.H.P. of the proposed ship by using equations (1) or (2). Example. — As an illustration of these methods, take the example given on page 137, where it was required to find EXAMPLES. 159 the I.H.P. necessary to drive a ship 600 ft. long at 17 knots from progressive trial data of a similar ship, 475 ft. long. The corresponding speed of the model was shown to be 15-2 knots. (See page 138.) From the curves given in fig. 44 the value of the I.H.P. of the model ship is seen to be about 6000. Therefore, if we use equation (1), the power required for the proposed ship is — 6000 X (^S^ 13500 I.H.P. If we use equation (2), the power works out to— 6000 X ( ^^''^^.\K= 13500 I.H.P. \ 9764 / In the previous example the calculated power was 13,300 I.H.P. The difference in the two cases arises partly from the difficulty of reading the I.H.P. correctly where the curve is so steep. It shows, however, the degree of accuracy that may be expected when the slide rule is used in conjunction with experimental curves. Examples of Every-day Practice. — For ordinary oases, where there are no data from progressive trials, it is customary to use the Admiralty formula, by selecting a coefficient, according to experience, for the type of boat proposed. The following three examples are from common types of cargo vessels, and illustrate the methods generally adopted in practice. Example of a Rather Fine Cargo Boat. — It is required to find the I.H.P. necessary to drive the following ship at eleven knots : — L = 380. B = 50-25. cZ = 23 83. D = 10018. D| = 464-7. M = 1158-4 (square feet). C = 35 X 10018 ^ .^^ ■'^ 380 X 50i!5 X 23 8 J (-, ^ 35 X 10^18 _ .H,g^ " 380xTl58 4 Half block angle = 17° 31'. 160 THE RESISTANCE AND POWBE OF STEAMSHIP.?. The Admiralty coeflScient at 11 knots would be about 263, so that, using the equation — I.H.P. = Vi_x^ the necessary power is lii-^i^ = 2350 I.H.P. 263 Example of a Medium Coarse Cargo Boat. — Find the I.H P. necessary for the following ship at 9i knots : — L = 340 B = 45-5 d = 21-64 D = 7585 Dii = 386 jM = 964 5 (square feet) p ^ 35 X 7585 ^ .^ ■' 340 X 45-5 X 21-64 P, _ 35 X 7585 _ .„, ^" " 340 X 964 5 ~ "^ Half block angle = 18° 55' Admiralty coefficient at 9^ knots would be about 245 ; there- fore I.H.P. = ^^' ^ ^^^ = 1350. 245 Example of a Very Coarse Cargo Boat. — Find the I.H. P. necessary for the following ship at 9 knots : — L = 310 B = 44 d = 2104 D = 6600 Di = 351-86 M = 887-7 (square feet) C/= 35 X 6600 ^ . ■' 310 X 44 X 2104 n 35 X 6600 .„.„ ^"- = 310 X 887-7 = ^*° Half block angle = 22' 51' Admiralty coefficient at 9 knots will be about 233 ; therefore the I.H.P. = '^^^^- = 1100. WAVES AKD WAVE EESISTAXCE. 161 CHAPTER XVI I. Waves and Wave Eesistaxce. In preceding articles we have discussed the various methods of finding the engine power necessary to drive a steamship which are commonly used in practice. In the present and following articles we shall deal with the theory and pheno- mena of waves and wave resistance, a subject of great scientific interest, especially in relation to very high-speed ships. Lord Kelvin's definitiont of a wave is " the progression through matter of a state of motion," or "a wave is the progression of a displacement." This rather abstract defioi- tion applies both to transverse waves, as those of water, and to longitudinal waves, as those of an organ pipe. In the case of a water wave, that which travels or progresses is an elevation of the water at the crest and a depression in the hollow. The water itself does not travel, but moves in a closed curve. In other words, only the wave form advances, and not the water composing the wave. The progression of a wave, apart from that of the matter composing the wave, may be studied by fixing one end of a light rope, and then agitating the other end. The wave form is seen to travel along the rope, although the particles of the rope only swing to and fro. A wind-swept field of corn farther illustrates the same important physical fact. Similarly, a block of wood floating in water agitated by the wind does not progress, unless in a current, but merely oscillates about a fixed mean position. In defining a wave. Prof. Gr. M. Minchin, in his " Hydro- statics and Hydrokineticp," page 396, says : " Any disturbance •which is communicated from point to point of a body, t See Lord Kelvin's lecture on Sbip Waves, delivered bef oi e the Institution of Mechanical Engineers at Edinburgh, August, 1SS7. lis 162 THE RESISTANCE AND POWER OF STEAMSHIPS. whereby each particle is displaced from its position of rest, and the relative distances and directions of the particles are altered, is called a wave. As a rule, in such disturbances the displacement of each particle from its position of rest in the body is small. The motions of the individual particles may be very complicated, or may be simple oscillatory motions in small circles or other closed curves." In all cases the dis- turbance which travels by communication from particle to particle throughout the medium is correctly described as a wave, though the terms " tremor " and " vibration " are also used in this connection. There are at least five magnitudes relating to simple waves, namely : — 1. Wave-length, or distance from crest to crest (see fig. 48). 2. Period, or interval of time between the passage past a fixed point of successive wave crests. Wove LPtiq>h 3. Velocity of propagation, or rate of advance ; comniDnly called simply the speed of the wave. The term velocity properly includes the idea of direction, the term speed does not. 4. Distance from the place of propagation or origin. 5. Amplitude, or amount of displacement of a moving particle in the wave. In the case of a water wave, this is termed the height of the wave, or vertical distance from hollow to crest. The hydrostatic pressure increases from crest to hoUoWj'the difference of head being equal to the height of the wave. The relation between the first three quantities is — velocity = ^^X?:l?Bg^, period WAVES AND WAVE EESISTANCE. 163 the wave-length being usually expressed in feet, the period in seconds, and the velocity in feet per second, or else in knots. Common large storm -waves have periods varying from six to nine seconds, the corresponding lengths varying from 200 ft. to 400 ft. ; but considerably larger -waves are on record. Thus the velocity or speed of advance of a 500 ft. -wave of ten seconds period -would be 500 -=- 10, or 50 ft. per second. The following table, compiled from "White's Manual of Naval Architecture," gives the lengths and speeds of tro- choidal -waves of known periods. Such -waves are a close mathematical approximation to actual regular deep-sea Pel iod. Leugth. apeed of ad -auce. Seconds. Feet. Feet per second. Knots. 1 yu 5-12 3-03 2 ■JO -49 10-24 6-07 4.;-[] lv37 9-10 4 Sl-il7 20-49 12-14 6 iL'S 1 2; -6 J 15-17 6 1S4-1 30-74 lS-21 r 251-0 35-S6 21-24 s 3 27 40-99 24-2S 4150 46-11 27-31 10 512 3 51-23 30-35 11 6J0-0 56-36 33-38 12 7.7-S 61-48 36-42 13 Sflj-S 66-00 i 39-43 It 1004 71-73 42-49 i; 1163 7r)-So 42-62 Great -waves -will travel at sea for days, -with but little loss of energy ; though there is necessarily some loss, owing 164 THE EESISTANCE AND POWER OF STEAMSHIPS. to the viscosity of water. As a rule, waves are caused by the action of the wind, but an earthquake is sometimes the exciting cause of a very large wave. Canal Waves. Before passing to the detailed consideration of deep-sea waves, let us first consider the motion of a wave confined in a canal of limited width and depth, assuming water to be a perfect fluid— i.e., non-viscous. A canal wave naturally travels at a certain speed, which depends on the depth of the canal, and the shorter the wave the slower is its speed. When the length of a wave is many times the depth of the canal, as 50 times, the wave is termed a long ivave, and its velocity is the same as that acquired by a body in falling freely from a height equal to hat/ the depth of the canal. Thus, the natural velocity of a long wave travelling in a canal 8ft. deep is J 2gh, or, say, 8 V 4 = 16 ft. per second, which is the highest speed of any wave moving in a canal 8 ft. deep. If the canal were only 4 ft. deep, the natural speed of the long wave would be 5 J 2 — 11 3 ft. per second, and no wave could exceed this speed. Fig. 49. BoqV ljtKmdrticWa« cession or \" Bool on vhe Wave Fig. 60. Scott Kussell experimented on the genesis or formation of waves in canals, and observed that when a boat is dragged along a canal at any speed below the natural speed of the long wave proper to the canal, the boat leaves behind it a CANAL WAVES. 165 train of shorter waves, such that their speed of propagation is equal to the speed of the boat. Fig. 49 shows the position of the boat on the rear slope of the wave. If the water surface in fig. 49 were drawn far enough backwards, it would show an end to the procession of waves in the rear of the boat, at a distance depending on the time the boat had been moving, assuming water to be a perfect fluid. In reality, however, water has sufficient viscosity to stop the wave procession at a certain distance astern of the ship. In a canal the inflaence of this viscosity in extinguishing waves is very marked ; because the water has to flow, to some extent, across the bottom and up and down by the banks. The rear of the procession of waves travels onward at half the boat's speed, when the water is . very deep. The expression "very deep" here means a depth equal to at least one wave-length ; but without much error we may here speak of water as very deep when the depth is greater than three-quarters of the length of a wave. Thus, if the wave-length were 100 ft., then 75 ft. of water would be considered very deep. The length of the wave generated by a ship commonly lies between 50 ft. and 250 ft., according to the speed of the ship. Still neglecting viscosity, the work done in dragging a boat along a canal is equal to the energy required to generate the ever-lengthening procession of waves astern of the boat- The number of foot-pounds of work so done per minute, divided by the number of feet travelled by the boat in one minute, is the wave-making resistance expressed in pounds. Critical Speed. — We have said above that the speed of the fastest long wave which can possibly travel in a canal is the satie as the speed gained by a body falling freely through a height equal to half the depth of the canal. Consequently, a boat dragged along the canal at a higher rate than this critical speed will be unable to make a regular procession of waves at all, for no wave could keep up to the boat. The 166 THE RESISTANCE AND POWEK OF STEAMSHIPS. boat can only make a hump or hillock, travelling along with it, as shown in fig. 50. Further, since no waves are continuously produced above this critical speed, no energy will be expended in their production ; in other words, the wave-making resistance of the boat will be nil. In fact, if we neglect the viscosity of water, the skin resistance of the boat will also be nothing, and no energy at all will be needed to keep the boat in motion. Once started, it would go on for ever, as a curling stone projected along the ice would go on for ever were it not for the friction of the ice. In John Scott Kussell's paper,* entitled "Experimental Researches into the Laws of Certain Hydro-dynamical Phenomena that accompany the Motion of Floating Bodies," there is an interesting account of how a horse discovered the existence of the critical speed above which the resistance is less than at lower speeds. The account reads as follows : — "It is to the diminished anterior section of displacement, produced by raising a vessel with a sudden impulse to the summit of the progressive wave, that a very great improve- ment recently introduced into c»nal transports owes its existence. As far as I am able to learn, the isolated fact was discovered accidentally on the Glasgo w and Ardroasdn Canal. A spirited horse in the boat of William Houston, Esq., one of the proprietors of the works, took fright and ran off, dragging the boat with it, and it was then observed, to Mr. Houston's astonishment, that the foaming stern surge which used to devastate the banks had ceased, and the vessel was carried on through water comparatively smooth, with a resist- ance very greatly diminished. Mr. Houston had the tact to perceive the mercantile value of this fact to the canal com- pany, and devoted himself to introducing on that canal vessels moving with this high velocity. The result of this improvement was so valuable, in a mercantile point of view, as to bring a large increase of revenue to the canal pro- * Trausactious of thtj Koyai Society of Ediaburgh, 1840. CAXAL WAVES. 1G7 prietors. The passengers and luggage are conveyed in light boats, about 60 ft. long and 6 ft. wide, made of thin sheet iron, and drawn by a pair of horses. The boat starts at a low velocity behind the wave, and at a given signal it is by a sadden jerk of the horses drawn up on the top of the wave, where it moves with diminished resistance at the rate of 7, 8, or 9 miles an hour.'' The old fly-boats, however, had but a short life, as they were soon supplanted by the speedier railway train. It is noteworthy that iron canal boats were in use so early as 1837. Scott Rassell carried out an elaborate experimental inves- tigation into the resistance of canal boats at various speeds on the Forth and Clyde Canal, some of the results being tabulated below. The depth of water was 4 ft. to 5 ft., and the natural speed of the long wave about 12 ft. a second, or 8 miles an hour. Boat's displacement. Speed. Tow-rO(je resistance. Pound c. Miles per hour. Pound-. 4-72 11-.' 5-92 261 No. 1.-10,240 / 6-19 275 9-04 250 I 10-48 26S-5 / 0-19 260 No. 2.— 12,580 1 7-57 S-62 600 400 9-04 280 Fig. 51 shows the same results plotted on a speed base. Had water been a perfect fluid, the resistances at the lower speeds would have been rather less than those given, and at all speeds above the critical speed of eight miles an hour the 108 THE RESISTANCE AND POWER OF STEAMSHIPS. resistance would have been nothing. Once started, the boat would then have gone on without being dragged until stopped by some obstacle. Actually, however, the viscosity of water is very much in evidence at the higher speeds, so that, afcer the wave resistance has vanished, considerable skin resistance still remains. We may profitably summarise the above remarks on the resistance to motion of boats in canals in the following words of Lord Kelvin, taken from his lecture on Ship Waves, already referred to : — " The conclusion at which we have arrived is this : Sup- posing at first the velocity of the boat to be such as to make 4« .V 7^ \ LCfl /- Boof: \ k CTO y^ /^ ^ ISO / '' 4 s 6. 7 a. 9. o. 1 . Mi ed per hour. Fig. 61. the waves behind it of wave-length short in comparison with the depth of water in the canal : let the boat go a little falter, and give it time until steady waves are formed behind it ; these waves will be of longer wave-length. The greater the speed of the boat the longer will be the wave-length, uatil we reach a certain limit; and as the wave-length begins to be equal to the depth, to twice the depth, or three times the depth, we approach a wonderful and critical condition of affairs — we approach the case of constant wave velocity. There will still be a procession of waves behind the boat, but it will be a shorter procession and of higher waves; and this procession will not now EXPEEIMENTS WITH MODELS. 160 lengthen astern at half the speed of the boat, but will lengthen perhaps at a third, or a fourth, or perhaps at a tenth of the speed of the boat. We are approaching the critical condition : the rear of the procession of waves is going forward nearly as fast as the boat. This looks as if we were coming to a diminished resistance ; but it is not really so. Though the procession is lengthening less rapidly relatively to the boat than when the speed was smaller, the waves are very much higher, and we approach almost in a tumultuous manner to a certain critical velocity. Once that crisis has been reached, away the boat goes merrily, leaving no wave behind it, and experiencing no resistance whatever if the water be free from viscosity, but in reality «xperiencing a very large resistance, because now the vis- cosity of the water begins to tell largely on the phenomena." CHAPTER XVIII. Experiments with Models. Eeoii the former articles it ought to be. evident that, to calculate the horse power required to drive proposed vessels at very high speeds, experiments with similar vessels must be made. The method of using small models of vessels to find the resistance, and thereby the power required to drive actual ships, is associated with the name of the late Mr. W. Froude. Although at first his proposals met with some opposition, at the present time all naval architects are agreed that this class of experiment affords the most exact method of fixing the horse power required for any high-speed vessel. In a piper read before the Institution of Naval Architects, 1874, Mr. Froude describes his method of determining the resistance offered to a ship as deduced from model experi- ments. The paper is extremely interesting, as it also shows how correct the deductions made from such experiments are when carried out in a scientific manner. In this paper 170 THK EESISTANCE AND POWBE OF STEAMSHIPS. aa account is given of towing trials made upon H.M.S, Greyhound, to determine its resistance at various speeds. These resistances were measured by a recording dyna- mometer, and readers are referred to the actual papers for fail details of the modes of experiment. After these trials a model was made one-sixteenth of the size of the Greyhound, and a set of experiments carried out ia the experimental tank at Torquay to determine the laws of its resistance. The actual resistances of the Greyhouad could, therefore, be compared with the resistances as calcu- lated from the model experiments, and the result went far to support Mr. Fronde's theory. The principle involved in making the calculation is almost exactly the same as that shown in the chapter upon the use of progressive trials to determine the horse power of similar ships. A diflerence, however, arises owing to the great disparity in the lengths and speeds of the vessel and model, which makes the calculation somewhat complicated. Briefly, the manner of making the experiments is as follows : The model is towed through the tank at the speed corresponding to that at which the proposed vessel has to travel, its resistance being automatically recorded. The towing and recording apparatus used for the model of the Greyhound are the same as shown in fig. 32 for finding the friction of boards. It might be thought that the law of comparison could be at once applied to determine the resistance that would be offered to the proposed ship. This would be the case if the surface-friction resistance varied as the square of the speed, as we have generally assumed. It was, however, shown in the chapter dealing with the experi- ments upon the resistance due to surface friction of boards, that the resistance was not exactly proportional to the square of the speed, but that it depended somewhat upon the length of the board and the actual speed at which it was moving. On account of the great differences in length and speed that exist between the surface of a model and of a ship these variations must be taken into account^ EXPERIME>'TS WITH MODELS. 171 although, when comparing vessels of approximately the same size, it may be assumed, without any great error being introduced, that the surface-friction resistance varies as the square of the speed. It therefore becomes necessary to distinguish between the three resistances, viz., surface friction, wave making, and eddy making. The two last may be taken to follow the law of comparison exactly, and from the experiments that have been made upon surface SPEED or MODEL SPEED or SHIP =1= 000 FEET PER MINUTE 1000 friction of boards it is easy to calculate the skin resistance of the model, and to thereby separate it from the wave and eddy making resistances. By the law of comparison the amount of the residuary resistances can then be found for the proposed ship. Next, the surface friction of the ship can be calculated, and added to the resistance just deter- mined. The sum will give the total retarding forces acting upon the vessel. The following curves are taken from Mr. Froude's paper, and serve to elucidate the manner in which the actual calculations are made. In fig. 52 the curve marked 1 shows the resistance of the model at various speeds, the numbers being an average of several runs. The immersed skin of 172 THE RESISTANCE AND POWER OF STEAMSHIPS. the model was carefully measured, and Lts friction resistance determined on the assumption that it -was equal to that of a rectangular surface moving at the same speed, of equal area and of equal length to that of the model. Mr, Froude states in reference to this assumption : " I am confident that no sensible error arises from thus disregarding the small alternate motions in the surrounding water due to stream-line action.'' These surface-friction resistances are shown by the curve 2. The lengths of the ordinates, therefore, between 1 and 2 sho^the remaining resistances due to wave and eddy making. Oq some scale, therefore, these represent the resistances of the ship without surface friction. The scales are obtained very easily. The model was one-sixteenth of the size of the Greyhound, and remembering that corresponding speeds are proportional to the square roots of the lengths of the ships to be com- pared, the scale of speeds for model and ship must be as ^ 1 : J 16, or 1 to 4 — that is to say, a speed of 100 ft. per minute of the model corresponds to 400 ft. per minute of the ship. The resistances of similar ships have been shown to vary as the cubes of their lengths at similar speeds, so that the scile for resistances must be in the proportion of 1'^ to 16'^, or 1 to 4,096. This means that a resistance of 1 lb. on the model indicates a resistance of 4,096 lb. on the ship at the corresponding speed. A slight correction has also to be made owing to the fact that the model experiments were made in fresh water, whilst we require the resistance of the ship when sailing in salt water. It h»s been shown that the resistance varies as the density of the water, so that the scale of the ship's resistance has been altered to correspond. It now remains to calculate the friction resistance of the ship. It will be seen that this presents some difficulty, on account of a lack of knowledge as to the exact state of the ship's surface. Assuming that the quality of the surface of the Greyhound was the same as that of a varnished surface, the calculated resistance would be shown by the curve 3. If, therefore, ordinates of this curve are added to those EXPERIMENTS WITH MODELS. 173 included between curves 1 and 2, their sum will represent the total resistance of the ^hip on the assumption that its surface is of the same quality as a varnished surface. Carve 2, in fig. 53, shows the sums of the resistances calculated on this assumption, and curve 1 represents the actual values of the resistances obtained from the trials of the Greyhound at the various speeds. As a matter of fact the Greyhound was covered with copper that was no longer new. The CO sooon / I50m , y/- ^-,-\-\ ^^ 1 ^^ / 500 £00 rcn ^0 aoo loca 120O SPEED OF SHIP (feet PER MINUTe) Fig. 53, surface, therefore, must certainly have been worse than a varnished surface, and consequently the skin resistance higher than shown by carve 3, fig. 52. To obtain a nearer approximation to the truth Mr. Fronde assumed that one-third of the Greyhound's surface had a resistance equal to that of unbleached calico, and the remaining two-thirds equal to that of a varnished surface. On this assumption the total resistance curve practically coincides with 1, in fig. 53. The effect that the state of the surface has upon the resistance it offers (mentioned in the chapter on the fouling 174: THE RESISTANCE AND POWER OF STEAMSHIPS. of ships) will be again brought to mind. Had the Grey- hound been a nesv ship with fresh copper, its resistance would have been more nearly that shown by curve 2 instead of curve 1, dsr. 53 ; and it ought to be remembered that all vessels after they have been even slightly fouled will require more power to drive them than when new. The nearness of the calculated result? to the actual ones confirms most markedly the " L^w of Comparison " for wave resistance, and is a most convincing argument in favour of model trials. It is worth while to examine fig. 52 somewhat closely. At low speeds the skin resistancs of the model is seen to be practically the whole of the retardiug force, whilst at higher speeds the wave-making resistance becomes of more importance. This confirms our previous statement, that for the ordinary slow-speed cargo boat the chief resistance to be considered is that of skin friction. The fineness of its lines will have little effect upon the speed of a vessel of this type, provided that it is at all ship-shape. On the other hand, the passenger boat built for speed requires great care to be taken in its design, so that the shape with least wave-making resistance may be obtained. It is interesting to note that in the discussion on Mr. Fronde's paper, Mr. J. Scott Eussell remarked that he had commenced to make experiments on models and actual ships some 30 years before, and was delighted to find his results confirmed by Mr. Fronde. For a full description of the processes of making and cutting the models to their correct shapes', the reader is referred to a paper read by the late Mr. W. Froude before the Institution of Mechanical Engineers, in July, 1874. It may be here mentioned that the models are made of hard paraffine, about 14 ft. long, and slightly more than lin. thick. They are cast in moulds, with about J in. allowance for cutting to the accurate shape. This shaping is done by means of a most ingenious copying machine, which cuts grooves in the models along different water lines to the depths of the finished surface. Fig. 54 shows a cross section EXPERIMESTS WITH MODELS. 175 of the model with some of the grooves cut in. After leaving the machine the wax left between the grooves is trimmed off by hand, and the surface finished to the proper curved shape by the eye. After many years experimental work at Torquay, the Admiralty were so satisfied with the result of the experience that they decided to erect a new experimental establishment at Haslar, which was opened in 1886. A full description of this tank will be found in a paper read by Mr. R. E. Froude, son of the late Mr. W. Froude, before the Institute of Mechanical Eagineers, in 1893. The object of this paper was chiefly to describe improvements made upon the various mechanical appliances that had been used at Fio. 54. Torquay. In &g. 55 is shown a longitudinal and cross sectiou of the tank. The water way is nearly 400 ft. long, about twice the length of the old tank at Torquay, the other principal difference being that the dynamometer truck runs along rails in the side walls of the tank, instead of being suspended from the roof, as in the old arrangement. An interesting point about the carriage is that instead of being an iron or steel structure, it is composed of wood, and is altogether a most remarkable construction. Other countries are now following the example set by our Admiralty, and similar experimental establishments have been erected by the Dutch, French, Italian, and United States Grovernments. At the present time only one private firm of shipbuilders in this country, Messsrs. W. Denny and Sons, of Dambarton, 170 THE EISISTAKCB AND POWER OF STEAMSHIPS. ~ "if I ft- m) li ■i!ii,ii £ EXPERIMENTS WITH MODELS. 177 possess a similar tank. The late Mr. W. Denny was per- haps, among practical shipbuilders, the most enthusiastic admirer of Mr. Froude's methods. He often spoke in support of them before the various scientific societies, and vigorously protested, when other shipbuilders advanced the opinion that model trials were of no practical value.. In 1882 he commenced the erection of the tank at Dumbarton on almost exactly similar lines to the Government one at Torquay. The Denny tank is 300ft. long, 22ft. broad, and about 9 ft. deep. Colonel English's Method. — An altogether different method of model experimenting has been suggested by Lieutenant- Colonel Thomas English, in a paper read before the Institu- tion of Mechanical Engineers.* The object of the author was to show that by using the ordinary appliances of a shipyard, results could be obtained equal to those hitherto only obtained by model trials in an experimental tank. The method is extremely simple and ingenious, and deserves to be widely known. The case to which it is applicable is the following : Given the indicated horse power and the speed of a ship at sea, to find the horse power necessary to drive another ship at any other speed. The manner in which this is accomplished is to make two models on such scales that, if they are both towed at the same speed, the speed for one model will correspond with that of the ship tried at sea, and for the other with that of the proposed ship. The following table shows the symbols used : — Wave I Skin ! Dlsplace- reaiatance. ' resistance. mont. Speed. Actual ship '^i. S^ Di I Vj. Proposed ship ^2 < ^2 ^2 V^ Model of actual ship Ki j si ] d^ vx Model of proposed ship w, s^ d.2 ♦Calculation of Horse Power lor Marine Propulsion. Proceedings Institution of Mechanical Engineers, January, 1896. 12s 178 THE RESISTANCE AND POAVEE OF STEAMSHIPS. If v^ and Vi are corresponding speeds, from previous chapters it is known that Therefore „ c _ v « '^i Similarly, if Wg ^^^ ^2 are to be corresponding speeds— therefore ^^ ^ ^^ (^v^y If the models are to be towed at the same speed, then therefore therefore d^ ^ {YiY ^ d„ \yJ ' D, ■• (5;) - ^'' (&) and the speed of the models is equal to ^. (& The total resistance of each model is the sum of the skin and the wave-making resistances. So that the ratio of the total resistances of the model of the proposed ship to that of the model of the actual ship will be V'2 + S2 which may be called n. Then W2 + S2 = n{wi + Sj^) (1) The skin resistances s^ and $2 can be calculated in the manner similar to that adopted by Fronde by measuring the wetted surfaces. EXPEKIMBNTS WITH MODELS. 179 Remembering that the wave resiscance of similar ships at corresponding speeds varies as the cubes of their lengths, and also that their displacements are proportional to the cubes of their lengths, it follows that therefore _ w (^i Wi - W, ^^. Substituting this value of lo^ in (1), we obtain the following — iWa = » Wi =^ + M Si - Sg (2) Wi can be found in a manner similar to that adopted when separating the resistances of the Greyhound. Thus the indicated horse power is known from the trial and by means of a coefficient for the ratio thrust horse nower indicated horse power the total resistance, Wi + Sj, is thereby found. Sj can be calculated when the particulars of the wetted surface are known, and thus Wi may be obtained. All the terms on the right-hand side of equation (2) are now known, so that Wj, the wave resistance of the model of the proposed ship, can be determined. To find W2, the wave resistance of the proposed ship, it has to be remembered that therefore w„ = i«2 5^ (3) 0,2 The skin resistance S2 of the proposed ship will then be calculated, which enables the total resistance W2 + S2 to be fixed. By means of the coefficient thrust horse power indicated horse power 180 THE RESISTANCE AND POWER OF STEAMSHIPS. the indicated horse power of the proposed ship can be found. It will be seen that the only result to be found by actual experiment is the ratio of the total resistances experienced by the two models. This is obtained by Colonel English in the following simple manner : The models are attached to the two arms of a horizontal lever, and towed from the fulcrum at the required speed. The relative lengths of the levers are adjusted until the models tow abreast, and the ratio of these lengths gives the required value n. Fig. 56 shows the arrangement. Pia. 56. The following example is given by Colonel English, and serves to make the method clear : — Actual ship . . . Proposed ship , Displacement in tons. 247 300 Speed in knots. ,, J°'*'°„*„t'^ ^ horse power. 27-85 80 8915 If the ships are similar, then the length of the proposed ship will be \^t^) = 1'067 times that of the actual ship. EXPERIMENTS WITH MODELS. 181 The model of the actual ship was on a scale of ^th, so that the ratio^f the^ speed of ship to that of the model would be as ^^20 : Jl, which gives the speed of the model 27-85 *^ 720 ^ ^^^ knots. Since the model of the proposed ship has to be towed at the same speed, its size must be so proportioned that its 6-23 knots will correspond with the 30 knots of the proposed ship. The scale of this model will therefore be as 6-232 : 302 = 1 : 232. Since the wetted surfaces vary as the squares of the lengths, and as the surface of the actual ship is 3796 the wetted surface of proposed ship is 3796 x 1 •067'^ = 4321 the wetted surface of model of actual ship is 3796 X J_ = 9-4!) •jn2 iO" the wetted surface of model of proposed ship is 3796 X = S'02 23-21= From tables the following values of the skin resistance are obtained : — Actual ship Si = 0-OU94 X 3790 X 27-85"^-='= = 167201b. Proposed ship S^ = 0-0094 X 4321 X SO-OQi-s^ = 205001b. Model of actual ship «i = 0-01124 x 9-49 x 6-231-" = 3-15 lb.' Model of proposed ship »3 = 0-01124 x 8-02 x 6-23^-^= = 2-661b. The co-efficient thrust horse power indicated borse power was taken at 0'6 ; this makes the thrust horse power of the actual ship equal to 6 x 3915 = 2349. To obtain the actual resistance opposed to the ship, we must remember that the thrust horse power _ resistance in pounds x speed per minute ~ 33000 ' so that the actual resistance offered to the ship is 2349 X 33000 x 60 _ 97467 lbs 27-85 X e080 182 THE RESISTANCE AND POAVEK OP STEAMSHIPS. From this we see that Wi + Si = 27467, and we have shown that Si = 15720. therefore Wi = 27467 - 15720 = 11747 lbs. From the trial it was found that the ratio n = ^^ + ^^ was O'Sll. Wl + Si From equation (2) Wo = 0-811 X 11747 X ^ + 'Sll X 3-15 - 266 2 L>i = 1-19 + 2-55 - 266 =- 108. From equation (3) = 108 X •00008 = 13500. Therefore the total resistance of the proposed ship.is Wg + Sa = 13500 + 20500 = 34000. Thus speed per minute 30 X 6080 60 Therefore thrust horse power ^ 34000 X 30 X 6080 ^ gj^gg 60 X 33000 Using the same coefficient for thrust horse power indicated horse power EXPERIMENTS WITH MODELS. 183 as before, namely '6, we find the indicated horse power to be ?i5? = 5220. 0-6 The simplicity of the experimental work necessary to obtain this result should be especially noticed. The models used were cut out by the shipyard model maker and were of yellow pine, ballasted with lead to the required draught. No elaborated measurements of the towing resistance were needed. A small electric motor furnished the power necessary to tow the models, and when the levers had been adjusted so that the models towed abreast, the only measurement to be made was the ratio of the levers. It ought to be recognised that in model experiments, what is obtained is the resistance of the ship. So far as the engine builder is concerned, what is required is the indicated horse power, and, as has been shown, it is necessary to employ coefficients to obtain this. This again emphasises the need for experience in deciding upon the engines for any ship. Mr. E. E. Froude states, as his opinion, that the engine and propeller losses are the following : — Percentages Friction of engine 26 Work expended on air pumps, feed pumps, &o., worked by main engines 69 Loss due to slip 91 Loss due to friction of propeller 3'8 Loss due to propeller augmentation of resistance ... 15 -5 Effective horse power 38"7 Total 1000 It is evident, however, that there must be some difference between the many types of engines and styles of propellers now used. In Colonel English's method the result does not depend so much upon the actual value of thrust horse pow er indicated horse power 184 THE RESISTANCE AND POAVER OF STEAMSHIPS. as in Froude's method, where only the actual resistance of the model is obtained. If the two ships are to be similar and the engines to be worked at the same revolutions and mean pressure, then by using the same coeflacient for both ships the estimated horse power will be probably quite correct. If the ships are not exactly similar and different coefficients are used, then the result depends upon the ratio these coefficients bear to one another, and not upon the actual values assumed for them. It seems therefore, that the chief use of model experiments is to find, not so much the actual powers required to drive proposed ships, but the shapes of least resistance. CHAPTER XIX. Trochoidal Waves. Rankine's trochoidal wave theory assumes that every particle of water in a regular deep-sea wave revolves in a circular orbit, situated in a vertical plane normal to the wave ridge, and completes a revolution during the period in which the wave advances through its own length. This is the best working theory of wave motion yet proposed, and fairly well represents the actual phenomena of deep-sea waves. As such it has been generally adopted by naval architects in studying the wave resistance and the oscilla- tions of ships. A trochoid may be simply defined as the curve traced on a vertical wall by a pencil fixed in one of the spokes of a wheel when the rim is made to run along level ground at the foot of the wall. As thus described, however, the curve would be inverted. In fig. 57 A B is a straight line under which is made to roll the large circle of radius O A. The distance A B is half the circumference of this rolling circle, which will therefore TEOCHOIDAL WAVES. 185 complete half a revolution during its motion from A to B. A tracing point P is taken on the radius of the rolling circle. As the circle rolls P will trace out the trochoid shown, which is the theoretical wave profile from the hollow P to the crest S. The length of this wave is twice AB, and the height twice O P. Fig. When the tracing point lies on the circumference of the rolling circle the curve traced is a cycloid, and corresponds to a wave on the point of breaking, the crest being quite sharp, while the hollow is very flat, as shown dotted. DirecCia/t of /lclvcuit:.a Fig. 5S. In fig. 58 the points P represent particles of water at the surface of a wave, their orbits being the equal dotted circles. The radii of the orbits are shown by O P, while the arrows give the direction Of rotation. The long arrow below the wave profile indicates its direction of advance from right to left. At the wave crest the particle P is moving in the same direction as the wave, while at the hollow it is moving opposite to the direction of advance. 186 THE RESISTANCE AND POWER OF STEAMSHIPS. In a fraction of a second later the wave profile has passed to the position dotted, but the orbits of the particles have not moved. The particles themselves have continued their revolutions, and the tracing arms have advanced to the series of new positions marked O p. The motion of the particles in the direction of advance is limited by the diameter of their orbits, and therefore they simply sway to and fro about the centres of the orbits. This affords a reasonable explanation of the fact that a log of wood, floating in the open sea, is not carried bodily along by the wave, but merely rises and falls with the passage of the wave. The disturbance caused by the passage of a wave extends some distance below the surface of the water, but at a certain depth the disturbance practically ceases, and still 777777777; FiG. 69. water is reached. The disturbance decreases according to some law which the trochoidal theory indicates, enabling the whole internal structure of a wave to be represented. Diagrams such as fig. 59 can be drawn to show exactly how the orbits of the water particles diminish from the surface downwards, the trochoids becoming flatter and flatter until their curvature ceases to be sensible. Wave Resistance. In Chapter XVII. we described the phenomena of waves produced by a boat moving in a narrow canal, and saw that the boat's resistance increases with the speed up to a certain WAVE RESISTANCE. 187 critical speed, when it suddenly falls off as the boat rises upon a wave. We shall now consider the phenomena of waves produced by ships moving in the open sea. Fig. 60 shows the wave profile of a ship 250 ft. long, moving at a speed of 18'4 knots, the wave-length being 183"5 ft. The water rises to a maximum height close to the Fig. 60. bow, sinks to a minimum amidships, and flows away past the stern slightly above still water level. The stream-line theory affords a reasonable explanation of this phenomenon. At the bow, where the stream-lines broaden out and the particles of water move more slowly PerspecUte, vieM' of Echelon-- Mtyes. Pia. 61. relatively to the ship, a wave crest is formed ; because the retardation to the motion of the particles, or the reduction of speed, is accompanied by an increase of stream-line 188 THE EESISTANCB AND POWER OF STEAMSHIPS. pressure, which appears as an elevation of the water above the normal level, i.e., as a wave crest. Amidships the speed of the water is increased, because of the closing in of the stream-lines, and this acceleration results in a reduction of pressure. Consequently the surface of the water falls below the Stillwater level. At the stern another wave crest is formed, due to the opening out of the streamlines, being accompanied by a reduction of velocity and increase of head. The perspective diagram (fig. 61) shows, in an exaggerated manner, the oblique diverging or echelon waves set up by a hypothetical ship with an abnormally long parallel middle body, against which the wave profile is also well seen. Figs. 62 and 63 show diagrammatically the wave systems made by an 83 ft. launch and by a 333 ft. ship, when steaming at a speed of 18 knots. The positions of the wave crests are indicated by the transverse shading. In practice the wave systems of actual ships are not so clearly defined as these diagrams show, except in the case of very high speed ships. The transverse and diverging wave systems are perhaps best shown by a high-speed paddle steamer. We have seen that a ship or other large body moving rapidly on the surface of open water produces two systems of waves, one at the front and another at the rear, which WAVE EESISTANCE. 189 spread out into undisturbed water. Each of these wave systems represents a certain dissipation of energy, which is derived from the ship's engines. The total energy thus lost per minute in foot-pounds is equal to the wave resistance in pounds multiplied by the movement of the ship in feet per minute. This drain of energy due to surface disturbance would still occur even if the ship were moving at the surface of a perfect fluid, or, in other words, if the water had no viscosity. To get rid of wave resistance the body must be wholly immersed, as a submarine boat, the resistance to motion of which is almost entirely due to skin resistance. Theory undoubtedly points in the direction of submarine ships for economical propulsion at very high speeds, since the skin resistance increases roughly as the square of the speed only, while the wave resistance increases about as the fourth power of the speed. But it is questionable whether, by the employment of compressed air, liquid air, or oil fuel, submarine Atlantic liners will ever be possible. For short runs, of course, submarine ships are practicable, though in some respects objectionable. A fish is certainly more economically propelled than a duck ; for the latter, when going at full speed, wastes a great part of its energy in 190 THE RESISTANCE AND POWER OF STEAMSHIPS. producing surface disturbance of the water, while the resistance of the fish is nearly all due to skin friction. Below are given the values of the skin and wave resis- tance of three different ships at two speeds : — Reference. Length. Beam. Displace- ment. Speed. Skin Resistance. Wave Resistance. Total. A B Yorktown . Feet. 300 300 226 Feet. 31-5 46-3 3S Tons. 2,634 3,636 1,680 Knots. {11 {11 {11 Tons. 6-8 6-6 6 95 8 4-26 7-26 Tons. J -20 6 15 2-46 3-15 2-69 S-20 Tons. 9 12-75 9-40 11-16 6-85 15-46 The vessel A had some parallel middle body, and B had not. The influence of the finer ends in reducing wave resistance is marked. In respect of wave resistance, the most favourable speed for a ship of given size and shape is that in which the stern- wave system annuls the bow-wave system. And, on the other hand, when the crest of a wave astern due to the action of the ship's entrance coincides with the crest of a wave astern due to the action of the ship's run, then the speed is unfavourable for that particular size of ship. Thus a certain amount of parallel middle body may sometimes be advantageously introduced with the object of preventing the superposition of two systems of waves. As a rule, however, a ship which is all entrance and run offers the least wave resistance for a given displacement, because the smaller the angle of entrance and ran the better. Thus, for example, the old experimenter Beanfoy found that the resistance of a wedge-shaped body having an entrance angle of 9| deg. was 30'7 lb., while that of a wedge of 30 deg. angle was 51°41b., at the same speed. In the case of such over-driven ships as torpedo craft, there is noticed at very high speeds a phenomenon similar to that which occurs with canal boats towed at a good speed. WAVE RESISTANCE. 191 The boat rises partly out of the water at the bow, and travels on the back of a transverse wave moving at the same speed, the change of trim being very marked. The speed at which a torpedo boat thus begins to rise is given approximately by the formula — E,ising speed in knots = 9 V (displacement). The following are values of this rising speed for various displacements : — Tons. Knots. Tons. Knots. 25 15-4 200 21-8 50 17-3 300 23-3 100 19-4 400 24-4 150 SO- 7 500 26-4 According to Taylor's " flesistance of Ships " the following is the best working formula for calculating the wave resistance of a vessel, being applicable to nine-tenths of the cases that occur in practice : — R=V^ X ^ X b. Li R is the wave resistance in pounds. V is the speed in knots. D is the displacement in tons. L is the length in feet. 6 is a coefficient varying in value with the type of ship. The value of 6 is usually about "4 for fast vessels, rising to •5 for full and slow vessels. In the case of ships which are broad in proportion to their length, with fine extremities, b is about "45. For ships which are exceptionally long in relation to their beam, and also moderately fine, as modern Atlantic liners, b is about "35. The value of the coefficient would probably be still less in the case of torpedo boats and destroyers, perhaps not exceed- 192 THE RESISTANCE AND POWEE OF STEAMSHIPS. ing "3 ; but the law of resistance of such vessels varies so rapidly as the speed goes up that the above formula does not apply to them at extreme speeds. As an example of the use of this formula we may calculate the wave-making resistance of the Yorktown at a speed of 16 knots : — R = 16* X ^^^^ - X -45 = 18,400 pounds. 226 This approx;imate formula is considered safEoiently correct when applied to ships in which the ratio of the speed in knots to the square root of the length in feet does not exceed the value 1°2. In the case of a ship 100 ft. long this means that the highest speed for which the rule is applicable is 1'2 J 100 = 12 knots. Similarly in the case of a ship 400 ft. long the limiting speed is 1-2 ^^400 = 24 knots. For calculating the wave resistance of the few exceptional vessels that lie outside the limits of applicability of the above simple formula, Mr. D. W. Taylor has proposed the following more comprehensive formula, which is applicable to ships of any speed whatever — K = V* (A^ + B^ + 2 /c A B cos ^646 deg.). Although this formula involves too many coefficients of uncertain value to permit of practical use, it is still of much scientific interest, and worthy of attentive examination. V knots is the speed of the ship. »i is a coefficient, usually ranging in value between 1 and I'l. The latter is a fairly safe value for ships of ordinary form and speeds. The first crests of the bow and stern wave systems of a ship change in position and height with the speed, but at a given speed there is a fixed distance between them which is called the wave-making length. This is equal to m times the length of the ship, m varying slightly as the speed alters. The law of wave resistance which we are examining is deduced from the assumption that the actual bow wave set WAVE EESISTANCE. 193 op by a ship can be replaced by an imaginary trochoidal •wave, whose height is equal to the mean height of the actual wave. c is the ratio of V to the square root of the length of the ship in feet, and is styled the speed length ratio. Its value is unity for a 100 ft. boat travelling at 10 knots, and for a 900 ft. vessel at 30 knots. For a 100 ft. boat at 30 knots its value is 3, while in the case of a 400 ft. ship at 10 knots it reaches the value '5. A and B are coefficients which diminish as the speed rises. At low speeds they are nearly constant in value. Taylor states that the values of A and B can only be found by making experiments with model ships, and unfortunately he gives no actual values for any ship. A^ V* is the mean resistance due to the natural how wave. B^ V* is the mean resistance due to the natural stern wave. The last term in the formula is a periodic function of an angle, being sometimes positive and sometimes negative for a given ship, according to the speed. At some speeds, there- fore, this term will increase the mean resistance, and at other speeds diminish it, thus producing humps and hollows on the curve of wave resistance. ^ is a coefficient whose value is quite small for the speeds attained in practice by ships of ordinary size and speed. In a given ship h increases as the speed goes up, and for a constant speed h diminishes as the length increases. At low speeds, i.e., when c is less than °6, k is practically zero, and therefore the last term vanishes. The extreme range in the value of h is from to "5 A curve of residuary resistance (which is chiefly wave resistance), as deduced from model experiments, is shown in fig. 64 for a ship 400ft. long between perpendiculars, 382 ft. broad, 19 95 ft. effective draught, and, 5,930 tons displace- ment. The humps and hollows above referred to are well shown. Example.— As a final example of the manner of calculating the engine power required to propel a ship, by the indepen- 13s 194 THE EESISTANCE AND POWER OF STEAMSHIPS. dent estimate method, let us assume the case of an Atlantic liner on the model of the Oceanic, increased to 1,000 ft. long between perpendiculars, and designed for a speed of 35 knots. The speed length ratio Jh x/lOOO so that the approximate wave resistance formula will apply. The displacement of the supposed ship is first calculated from the known relation that the volumes of similar bodies vary as the cubes of their lengths, thus — Eequired displacement _ /1000\^ _ -i.^bs Displacement of Oceanic V 680 ) .-. Displacement = 28,500 x 318 = 91,000 tons. Next assume a value of 6, say "35. Then the luave re- sistance is — V* X D^ X & L = 1,062,000 lb. To estimate the shin resistance we must first calculate the wetted surface of the hull. This will be C^^^V or 217 N 680 / times that of the Oceanic, but as we do not know the wetted surface of the latter, we will make use of the approximate formula — s = 15-5 jux: from which we have Wetted surface = 15-5 ^91,000 x 1000 = 15-5 X 9540 = 148,000 square feet. WAVE RESISTANCE, 195 Now, the skin resistance equals / X S X Yi-83 = '009 X 148,000 X 351 83 lb. = 1332 X 675 = 900,000 lb. Adding 5 per cent to this, to allow for eddy resistance, we have Wave resistance = 1,062,000 lb. Skin resistance = 900,000 lb. Eddy resistance = 45,0001b. Total 2,007,0001b. Lbp. 180,000 160,000 140,000 120,000 100,000 80,000 60,000 40,000 20,000 10 11 12 13 U 15 10 17 IS 19 20 21 22 24 knots. Fig. 64. The effective horse power required to overcome this resistance is Resistanc e x s peed in feet pe r minute 33,000 _ 2.007,000 X 35 X 6080 33,000 X 60 = 216,000 H.P. 196 THE RESISTANCE AND POWEE OF STEAMSHIPS. Assuming an efficiency of propulsion of 6, the estimated power of the engines will be 216,000 -^ '6 = 360,000 I.H.P., which is a surprisingly large power. Exactly the saipe method applied to the Deutschland gives the following results : — Wave resistance = 122,000 lb. 8kin resistance = 171,000 lb. Eddy resistance = 8,550 lb. 301,550 lb. I H P = 301,560 X 23 X 6080 ^ og kqo ■ ' ■ 33,000 X 60 X -6 ' ' The stated power is 35,000 I.H.P. This agreement between the calculated and the actual power is closer than any method of calculation may be expected to give in most cases. INDEX. Acceleration, 41, 54. Acorn Barnacle, 100. Action of Sheathing and Compositions, 126. Admiralty Formula, S4, 152. Admiralty Coefficient for Similar Ships, 135. Air Resistance, 45. Amplitude Defined, 162. Angles of Entrance and Run, 22. Angle of Obliquity of Stream Line, 146. Anti-fouUng Conpositione, 121. Apparent Thrust of Propeller, 15. Assumptions of the Admiralty Formula, 85. Atacamite, the Mineral, 129. Atlantic Liners, Comparison of, 26. Augmentation, Coefficient of, 145, 150. Augmented Surface, 144. Bad "Weather Steaming, 31. Italanus, or Acorn Barnacle, 100, Barnacles, 92. 98. liaahforth, F., on the Motion of Pro- iectiles, 11. Beaufoy's Experiments, 69, 100. HernouilU's Theorem, 133. Beraelius' Theory, 109, Block Coefficient Defined, 29. Block Models, 57, 154. BluflE Form, Effect of, 31, 50. Kooldana, 12-knot Cargo Boat, 36,91. Bowles, Constructor, on Sbeathiog, 111. Bows, Various Forms of, 24. Breadth of a Ship, its influence on Resistance, 24. Britannic, old Atlantic Liner, 25, 26, 36, Campania, Atlantic Liner, 25, 26, 30, 36, 38. Canal Waves, 162. Charles V., 15-knot Boat, 37. Circumstances Favourable to Fouling, 9i^ Cii'ripedia, or Barnacles, 99. Coefficient of Augmentation, 145. Coefficient of Fineness, 29. Coefficient of Fluid Friction, 72, Coefficient of Performance, 85. Coefficient of Resistance of Projectiles, 12. Coefficient of Viscosity, 9. Coefficient of Water Liaes, 29. Coefficients of Form, 29. Colonel English's Method of Experiment- ing, 177. Comparison of Laws of Solid and Fluid Friction, 68. Components of Power. 103. Conditions Unfavourable to Fouling, 95.. Constituents of Varnish Paints, 123, Copper Chloride and Oxychioride, 129. Copper Sheathing, 105, 107, 110. Corresponding Speeds. 131, 155, 157, 17&. Cost of Anti-touiing Paints, 12l'. Cost of Sheathing, 116. Coulomb's Experiment, 68. Critical Speed of Canal Boats, 165. Critical Speed of Ships, 77. Crustacea, 99. Cunard Steamers, Development of, 27. Cycloid Curve, l^'j. Cylindrical Coefficient, 29. Daring, H.M.S., 31. Davy, Sir ti., on Action of Copper Sheathing, 128. Davy's Propo.-al, 110. Denny, AVilliam, 19. 140, 152. Denny, Archibald, 118, Denny Brothers, 50, 120. Denny Tank, 177. Density of Air and of Water, 8. Denver, U.S. Cruiser, Sbeathing of, 114. Derivation of Coefficient of Friction (f),. 74. Deutschland, Atlantic Liner, 152, 156^ 196. .198 JNDEX. Displacement Defined, 18. Draught, its Influence on Resistance, 25. Duck and Fish Compared, 189. iiurham College of Science Engines, 89. Dynamometric Apparatus of troude, 81. Echelon "Waves, 188. Kddies in Pipes, 65. Eddy-making Resistance, 44, 80, 195. Effects of Fouling, 101. Effective Horse Power, 7, 77. Elasticity Defined, 8. Electro-Chemical Action, 107. 'Electro-Coppering of Ships, 119. Electro-Positive and Electro-Negative Elements, 109. English Colonel, on Model Experiments, 177. Entrance, Angle of and Length of, 22. Entrance and Run, Effect of, 51. Examples of Foul Ships, 96. Examples of Everyday Practice, 159. Exfoliation Theory of Anti-Pouling, 129, 130. Experimental Apparatus, 81. Experimental Engine at Newcastle, 89. Experiments with Models, 169. Factors of Resistance, 16. Fairbairn, Sir William, on Fouling, 93, 95. Fineness, Coefficient of, 29. Fish and Duck Compared, 189, Fluid Friction, C' efficient of, 72. Force, Speed and Power Connected, 6. Form Factors, 38. Formula for Frictional Resistance, 73. P'orthand Clyde Canal Experiments, 167. Fouling of Ships, 92, Foul Ships, 96. Foulness of Wet Surface, its Effect, 17. Frictional Resistance, 17, 65. Frictional Wake, 67. Froude, W. and R. E., 6. Fronde's Experiments. 14. Fronde's Experiments on Friction of Planes, 70, 81. Froude's Method of Comparison, 137, 155. Fronde's Model Experiments, 169. Froude's Rule for Air Resistance, 46. G i^alvanic Action, 105, 107. "Garonne, 14-knot Boat, 36. General Formula for Wave Resistance, 192. -Glasgow and Ardropsan Canal. 166. Grease Paint?, Composition of, 123. Great Eastern, 26. Greenland Dock Experiments, 69. Greyhound Experiments, 14, 45, 49, 170. Gums for Paints, 123. ' H Harland and Wolff, 26. Hichborn, Chief-Constructor, on Sheath- ing, 111, 114. Hints respecting CoefBcients of Form, 40. Hogg's Modification of Kirk's Block, 63. Holzapfel, A, C, on Anti-Fouling Com- positions, 124. Holzupfel, M., on the Theory of Anti- Fouling, 127. Holzapfel's Compositions Co., 125. Horse Power Defined, 7. Horse Power to Overcome Friction, 18, Hull of a Ship, 3, Humps and Hollows in Curve of Resistance, 193. I Immersed Surface as a Factor of Resistance, 16. Independent Estimate Method, 194. Index of Friction, 75. Indicated Horse Power, 15, 88, 179, 183. Indicated Thrust of Propeller, 5. Inertia Defined, 8. Inertia Resistance, 41, 53, Insulating Copper Sheathing, 113. Investigators on Ship Resistance, 6. Iris, H.M.S.. 36. Italia, Italian Battleship, 106, K Keel, 3. Kelvin, Lnrd, on Waves, 168. Kirk's Block Model, 57, 154. Kirk's Modification of Rankine's Method, 153. Knot Defi.ned, 16, 148. Laws of Resistance of Projectiles in Air, 12. Laws of Solid and Fluid Friction, 68, Length of a Ship, its Influe:ice on Resistance, 23, Length between Perpendiculars, 24. Lepanto, Italian Battleship, 90. Lewes, Professor V. B., on Fouling, 93. Lewes, Professor V. B., on Sheathing, 126, 130. 199 Life of Sheathing, 116. Light Displacement Defined, 19. Load Displacement Defined, 19. Losses due to Engine and Propeller, 1S3. M Magnificent, H.M.S., 25, 30. Magnitude of Resistance, 49. Manning, U.S. Warship, 103. Mass. 18, 41. Materials Used for Sheathing, 105. Mean Angle of Entrance and Run, 60. Measured Mile Course. 140. Meerten, H. Van, on Sheathing, 107. Merkara, Particulars of, 49. Method of Comparison, 137, 155. Midship Section Coefficient, 29, 37. Minor Resistances, 44. Model Ships, 136, 177. Motion of Projectiles in Air, 11. Multiple Screw Propulsion, 5. Mumford's Formula for Wet Surface, 118. Muntz Metal Sheathing, 105. N Xashville, U.S. Gunboat, Particulars of, 30. Natural History of Barnacles, 93. Newton's Second Law of Motion, 41, 66. o Obliquity of Stream Lines 146. Oceanic, Atlantic Liner, 26, 31, 194. Orbits of Water Particles, 186. Parallel Middle-body, 190. Paddle Wheels, 3, 14. Paints, Anti-fouling, 121, Parson's Use of Multiple Screws, 5. Perfect Fluid Defined, 10. Performance, Coefficient of, 85. Period of a Wave Defined, 162. Perpendiculars, Length between, 25. Perry, Professor J'-hn, on Resistauce, 67. Piemonte, Italian Cruiser, 91. Pipes, Flow of Water through, 65. Poisons, Effect on Germs, 95. Power, Components of, 103. Power Curve, 44, 102. Power Rule of Ranbine, 147. Prismatic Coefficient, 34, 37, 61. Precautions necessary in Coating Ships. 125. Progressive Trials, 139. Projectiles, Resistance of, 11. Propellers, 3. Propeller Augment of Resistance, 44, 103. Properties of Air and Water, 7. Quick Drying in Paints, Importance of,. 121. Rahtjen's Anti-fouling Paint, 123. Kankine, Professor W. J. M., 6, 141, 14^, Rankine's Augmented Surface Method, 141. Rectoid, Meaning of, 29. Relation between I.H.P. and B.H.P., 89. Resisting Media, Air and Water, 7. Resistance of a Steamer Starting from Rest, 41. Resistance Curves, 42. Resistance, Skin, 65. Resistance, Rankine's Rule for, 10. Residuary Resistance Detjned, 48. Residuary Resistance, Curve of, 193. Rise of Floor, 33. Rising Speed of a Boat. 191. Roughness of Wet Surface, its EfEeot, 17. Bun, Angle and Length of, 22. Run, Effect of, 51. Scott-Ruasell, 141, 164, 166, 174. Seatou, Mr. A. E., 36. Sea-water, Composition of, 128. Servia, Atlantic Liner, Particulars of, 26.- Sheathing, Friction of, 80. Sheathing of Ships, 105. Shellac, 123. Ship Defined, 3. bhip Worm, 105. Similar Ships, 40, 132, 135. Sister Ships, 40. Skin Resistance, 42, 65. 76, 195. Slide Rule Calculation, 139. Slip Loss, ] 83. Speed as a Factor of Resistance, 16. Speed of Screw, Ift. Speed Length Ratio 193. Steady Motion Formula. 134. Stems, Various Forms of, 24. Stream Lines, 132, 187. Submarine Vessels, 189. Summary of Ship Resistances, 47. Surfaces, Friction of, 72. Symbols used, 28, Table of Co-eflBcients of Fluid Friction,, 72, 78, 79. Table of Functions of V, 75. Table of Tideman's Constants, 80. Tank, Fronde's Experimental, 81, 175. Tank, Denny's Experimental, 177. Taylor's Rule for Air Resistance, 47. Taylor's Rule for Wave Resistance, 191.- 200 INDEX. Teredo Navalis, or Ship Worm, 105. Terrible, H.M.S., 25, 80. Thrust Ueductlon, 44, 103. Thrust of Propeller, 14. Thrust Horse- power, 179,181. Tinfoil Surface, Friction of, 75. Tonnage Explained, 20. Torpedo Craft, 191. Tow-rope Resistance, 13. Trochoid Defined, 145. Trochoidal Hiband, 145. Trochoidal Waves, Length and Period of, 163. Trochoidal Wave Theory, 184. u Units of Measurement, 28. V Varnish Paints, 123. "Vibration, 162. Victoria and Albert Yacht, 151. Viscosity Defined, 8. Viscosity the Cause of Skin Resistance, 66. w Wake, Frictional, 67. "Waste Work, 48. Warrior, H.M.S., 149. Water, Composition of. 128. Water-plane CoefBcient, 39. Waves, 161. Wave-line System (Scott-Russell's), 142. Wave Resistance, 161. Wave-length Defined, 162. Wave Profile of a Ship, 187. Weight of Ship, 18. Weight of Machinery and Outfit, 19. Wetted Surface Defined, 17. Wetted Surface, Calculation of, 118, 181, 194. Wetted Surface of a Kirk's Block, 00. White, Sir W. H., 20, 45, 51, 93. White, Sir W. H., on Sheathing of Ships, 113. White Star Steamers, Forms of, 26. Yachts, 38. Yorktown, U.S. Warship, 36, 38, 44, 52, 66, 77, 90, 192. Zinc Sheathing, 105. Zinc White Paint, 122i John HaYwooo, txcelsior Printing and iiookbindiug Works, Manchester. i////i//////////MA