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IHP

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Originally appearing in Volume V24, Page 949 of the 1911 Encyclopedia Britannica.
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IHP. I .H.P. (speed)3' I.H.P., The second of these is of course a curve of speed)' resistance, and the rapid rise and fall of the rate of growth of resistance manifests itself in this resistance-curve by a very marked hump between 15 and 25 knots speed. The third curve, that of LH.P.3~ (speed) is interesting as affording, by its slope at different points, a very good indication of this rate of growth. Up to about 13 knots this curve is not far from being horizontal, indicating that till then the resistance is varying about as the square of the speed. The rate of growth increases from this point till it reaches a maximum of 15 knots, and then falls, off till at about 20 -knots the resistance once more"varies as the square of the speed. From this point onward the resistance increases at a less rate, than the square of the speed. It has been previously noted that the skin friction part of the E.H.P. does not obey the law of comparison; this is on account of variation .of f , with length, and the index of the speed being different from 2. The coefficient f varies much more rapidly; at the smaller lengths, and hence for these the. skin friction correction is more important fora given change in length. For such lengths as are dealt -with in ships, e.g. too ft. and upwards, and such lengths as we should deal 'with iii applying the data that are now given, it has been found possible to express the correction for skin frictionvery accurately by the curves in fig. 38, Plate II. These indicate the absolute correction that most be applied to the .E.H.P. deduced for the. given displacement from the standard curves when interpreted by the law of comparison, and are drawn for a series of displacements on a base of speed; the correction for any odd displacement can be easily interpolated. An addition must be made for displacements under, and a deduction for displacements over, the standard t000 tons. - The following example illustrates this point and the method of using the standard curves A vessel 320' X351' X 13' X213 tons is being designed ; to construct an E.H.P. curve, for speeds 11-22i knots. The proportions Change of Speed. Corresponding Change Corresponding Index in E.H.P. of Speed. Types(i)and(6). Type (1). Type (6). Type (i). Type (6.). 14-16 knots 243 E.H.P. 273 E.H.P.. 3.1 3.0 22-23 ,, 760 „ 65o 5.3 4'9 25-26 „ 890 „ 82o „ 4.0 4'1 (Beam Draught ratio and block coefficient) of the design are most closely , approximated to by type 2, group A (32o' being the immersed length). First find the length 1 for a similar vessel of loon tons displace- 20 ment; l= (2.135) a -248.5 ft., and then from fig. 41 read off ordinate* representing E.H.P. for the given speeds of the rood-ton standard ship. These figures are converted into those appropriate for the design, by the law of comparison. If v and e are the speed and E.H.P. for the i000-ton ship, and V and E corresponding quantities for the design, then v =(2 135)*"=1.135; and a =(2.135)=2.424-using these ratios we get a table thus: In the results hitherto recorded the depth of water has been sup-posed sufficient to prevent the disturbance attending the motion of a vessel on the "surface from extending to the bottom ; in these Shallow circumstances the resistance is unaffected by a moderate water. change in, the depth. Conditions, however, frequently arise in which vessels are run at high speeds in comparatively shallow water; anda marked alteration is then observed in the resistance and power corresponding to a particular speed. An investigation of the effect of shallow water on resistance is therefore of importance and interest; and a brief account of this part of the subject is here appended. The change from' deep to shallow water modifies the shape of the stream lines, many of which in deep water are approximately in planes normal to the surface of the hull; those in shoal water tend to lie more nearly in horizontal planes, owing to the reduced space under. the bottom of the ship. In consequence, the velocity in the stream tubes in the vicinity of the ship is increased, and the changes of pressure and, the " statical " wave heights are exaggerated. This causes an increase in the frictional resistance as the depth of water becomes less; but the 'effect on the residuary resistance is more complicated. Firstly, the length ;I of the waves corresponding to a speed v is increased from that expressed by vz =$ 2r to be in accordance with the formula v2 = — tank 2ih '. which applies to shallow-water waves for. a depth It. When the depth his' equal to 99-2, the length of wave is infinite, and the wave becomes of the type investigated by Scott Russell in canals, and termed a " solitary wave " or a " wave of translation." When the z depth of water is less than v no permanent wave system of speed v can exist. These changes in the wave length considerably affect the wave pattern and alter the speeds at which interference between the bow and stern systems has a favourable or unfavourable effect on the efficiency of propulsion. In the second place the amount by which the speed of; travel of the energy of the wave falls short of the speed of the ship is expressed by v 4A/l sinh4lh The curve shown in fig. 39, Plate II. results from plotting col. (6) to a base of speed given by col. (3). Since the propulsive coefficient varies with the speed, it is preferable to take the E.H.P. from the curve and convert to I.H.P., using an appropriate coefficient, than to use a common coefficient by plotting a curve of I.H.P. In deep water this difference of. speed_i.sz; in shallow water it diminishes, becoming zero at the critical depth producing Is wave of translation. Thirdly, the local disturbance immediately surrounding the ship is increased in,shallow water, theoretical investigation showing that, at the critical” depth above-referred to, it becomes indefinite or is only limited .by its own viscosity and eddying-resistance. ,in still shallower water, the amount of disturbance is reduced as the departure from the critical depth becomes greater. Finally, the increase of ` the frictional resistance due to the higher velocity of rubbing is further modified by the large 'dimensions of the wave' accompanying the ship; the particles of a wave in ' very shallow water are moving appreciably in the direction of travel, which might lead to a reduction in the frictional resistance. From these considerations it appears impossible to obtain, a priori, the net effect of shallow water on the resistance, owing to the divergent character of the component effects producing the final result. This difficulty is confirmed by the inconsistency of the readings frequently obtained during experiments in shallow water, pointing to instability in the conditions then existing. A ' number of experiments have been carried out in shallow water with both ships and models; the most important are those by Constructor Paulus (Schleswig-Holstein District Club, 1904), Captain°Rasmussen, Mr Yarrow, Herr Popper and Major Rota, many of which are recorded in the I.N.A. Transactions. A summary of the conclusions drawn from them is appended: 1. The minimum depth of water that has no appreciable influence on the resistance increases with the speed and, in some degree, with the dimensions of the ship. 2. At constant speed the resistance is, in general, greatest z at the critical depth of water (v) . It is concluded, there-, g fdre; that the increase of resistance due to the enhanced dimensions of the wave then accompanying the ship is more than sufficient to counteract the gain resulting from the diminished &a n oL energy from the wave system astern. 3. At high speeds, when a considerable portionof the resistance is due tq wave-making, the total resistance diminishes at depths lower than the critical depth, and is frequently less in very shallow water than in deep water. 4. The " humps " in the curves of resistance on a base of As read from As converted by Correction to Co1.4-Co1.5 the Standard Law of Compari- 'Col.4 for Skin son for 2135-Tons Curves at a Design. ' Fri on: =E.H.P. Length = 'read. Corrected. 248.5 Ft. V E' Figure. Col. IX(:'135=v) Col. 2X12'424= T) Knots. E.H.P. Knots. E.H.P. E.H,P. E.H.P. io 15o 11.35 364 i6 348 12 275. — 43.62- 667 29 .638 . 14 `' 475 15.89 1151 42 1109 16 740 18.16 1794 55 1739 17 940 19.30 2278 61 2217 t8 1285 20'43 3115 67 , 3048 19 1825 21.56 4423 74 4349 20 2590 22.70 6278 8o 6191i speed occur at lower speeds in shallow water, and are more pronounced; the resistance is occasionally reduced when the speed is increased. 5. The changes of resistance produced by shallowness are accompanied by corresponding changes in the speed of revolution of the engines and in the trim of the vessel. These are illustrated by the curves in fig. 52, Plate VI., which are taken from a paper read before the I.N.A. by the writer in 1909, giving the results of some trials on H.M. torpedo-boat destroyer " Cossack." The data obtained from the various shallow water experiments are capable of extension to ships of similar types by the application of the law of comparison at corresponding depths :(proportional to the linear dimensions) and at corresponding speeds. The influence of shallow water on the speed of a large number of ships can be thus obtained; but the data at present available are insufficient to enable a general law, if any exists, to be determined. A further modification in the conditions arises when a ship proceeds along a channel of limited breadth and depth. Some interesting experiments were made in this connexion by Scott Russell on the resistance of barges towed in a narrow canal. He obtained (by measuring the pull in the tow rope) the resistance of a barge of about 6 tons displacement, for a mean depth of the canal of about 4; ft., as follows: Speed in miles per hour 6.19 7.57 8.52 9'04 Resistance in pounds 250 500 At the critical speed (8.2 M. per hour) corresponding to the depth, the resistance was in this case reduced; and at a higher speed a further reduction of resistance was observed. It is stated that the boat was then situated on a wave of translation extending to the sides of the canal, and which was capable of travelling unchanged for a considerable distance; the resistance of the boat was then almost entirely due to skin friction. When the speed of a ship is not uniform, the resistance is altered by an amount depending on the acceleration, the inertia of the ship Aacelera~ and the motion of the surrounding water. In the ideal AcQ conditions of a vessel wholly submerged in a perfect fluid, the force producing acceleration is the product of the acceleration with the " virtual mass," which is the mass of the vessel increased by a proportion of the displacement; e.g. for a sphere, one half the displacement added to the mass is equal to the virtual mass. The effect of acceleration on a ship under actual conditions is less simple; and the virtual mass, defined as the increase of resistance divided by the acceleration of the ship, varies considerably with the circumstances of the previous motion.. The mean value of the virtual mass of the " Greyhound," obtained by Froude from the resistance experiments, was about 20% in excess of the displacement. This value is probably approximately correct for all ships of ordinary form, and is of use in estimating the time and distance required to make a moderate alteration in speed; the conditions during the stopping, starting and reversing of ships are generally, however, such as to make this method inapplicable. Propulsion. The action of a marine propeller consists fundamentally of the sternward projection of a column of water termed the propeller race; the change of momentum per unit time of this water is equal to the thrust of the propeller, which during steady motion is balanced by the resistance of the ship. Assuming in the first place that the passage of the ship does not affect and is uninfluenced by the working of the propeller, let V be the speed of the ship, v „that of the propeller race ,relative to the ship, and m the mass of water added to the propeller race per second. The thrust T is then equal to nr (v–V), and the. rate at which useful work is done is TV or mV (v–V). Loss of energy is caused by (a) shock or disturbance at the propeller, (b) friction at the propeller surface, (e) rotational motions of the water in the race, and (d) the astern motion of the race. Of these (a), (b) and (c) are capable of variation and reduction by suitable propeller design; though unavoidable in practice, they may be disregarded for the purpose of obtaining the theoretical maximum efficiency of a perfect propeller. The remaining loss, due to the sternward race, is equal to 1m(v-V)2; whence the whole energy supplied to the propeller in unit time is expressed by 1-m(v2–V2) and the efficiency by V+ v. The quantity v–V is commonly termed the slip, and vV the slip ratio ; the latter expression being denoted by s, the theoretical maximum efficiency obtained on this basis becomes— jS It appears, therefore, that the maximum efficiency should be obtained with minimum slip; actually, however, with screw propellers the losses here disregarded entirely modify this result, which is true only to the extent that very large slip is accompanied by a low efficiency. The foregoing considerations show that, with a given thrust, the larger m the quantity of water acted upon (and the smaller, therefore, the slip), the higher is the efficiency generally obtained. The type of propeller most nearly conforming to the fundamental assumption is the jet propeller in which water is drawn into the ship through a pipe, accelerated by a pump, and discharged aft. The " Waterwitch " and a few other vessels have been propelled in. this manner; since, however, the quantity of water dealt with is limited for practical reasons, a considerable sternward velocity in the jet is required to produce the thrust, and the slip being necessarily large, only a very low efficiency is obtained. A second type of propeller is the paddle, or stern-wheel which operates by means of floats mounted radially on a circular frame, and which project a race similar to that of the jet propeller. Certain practical difficulties inherent to this form of propulsion render it unsuitable or inefficient for general use, although it is of service in some ships of moderate speed which require large manoeuvring powers, e.g. tugs and pleasure steamers, or in vessels that have to run in very shallow water. The screw, which is the staple form of steamship propeller, has an action similar in effect to the propellers already considered. ''Before proceeding to discuss the action of screw propellers, it is desirable to define some of the' terms employed. The product of the revolutions and pitch is often called the speed of the propeller; it represents what the speed, would be; in the absence of slip. Speed of advance, on the other hand, is applied to the forward movement of the propeller without reference to its rotation; and is equal to the speed of the ship or body carrying the propeller. The difference between the speed of the propeller and the -speed of advance is termed the slip; and if the two former speeds be denoted by v and V respectively, the slip is v–V and the slip ratio (or properly the apparent slip ratio) . This notation,corresponds to that previously used, v-V being then defined • as the absolute velocity of the race; it is found with propellers of the usual type, that zero thrust is obtained when v = V, provided that the " conventional " pitch, which for large screws is approximately 1.02 times the pitch of the driving surface, is used in estimating v. The pitch divided' by the diameter is termed the pitch ratio.. ` The theories formulated to explain the action of the screw propeller are divisible into two classes—(i.) those in which the action of the screw as a whole is considered with reference to the change of motion produced in the water which it encounters, the blade friction being, however, deduced from experiments on planes; and (ii) those in which the action of each elementary portion of the blade surface is separately estimated from the known forces on planes moved through water with various speeds and at diffei-ent angles of obliqui'ty'; the force on any element being assumed uninfluenced by the surrounding elements, and being resolved axially and circumferentially, the thrust, turning moment, and efficiency are given by suinniation:' Professor Rankine in Trans. Inst. Nev. Archs., 1865, assumed that the propeller impressed change of. motion upon the water withbutchange of pressure except such as is caused by the rotation of the race. In Sir George Greenhill's investigation (Trans. Inst. Nat. Ardis., 1888) it is assumed conversely that the thrust is obtained by change'of pressure, the only changes of motion being the necessary circumferential velocity due to the rotation of the screw, and a sufficient sternward momentum to equalize the radial and axialpressuresr These two theories are both illustrative of class (i.); and this idea Wm further developed by Mr R. E. Froude in 1889, who concluded that, the screw probably obtained its thrust by momentarily impressing an increase of pressure on the water' which eventually resulted in' an increase of velocity about one-half of which 'was'obtained `before and one-half abaft the screw. A lateral contraction of the race necessarily accompanies each process of acceleration. These general conclusions have been in' some degree confirmed by experiments: carried Out by Mr D. W. Taylor; Proceedings of the (American) Society of Naval Architects, &c., 1906, and by Professor Flamm, who obtained photo-graphs of a screw race in a glass tank, air being drawn in to show-he spiral path of the wake. In Trans. Inst. Nate Archs., 1878, Froude propounded a theory. of the screw propeller illustrative of the second class above mentioned, the normal and tangential pressures on an elementary area being deduced from the results of his own previous experiment's on obliquely moving planes. He was led to the following conclusions regarding maximum efficiency:e–(1) The slip angle (obliquity of surface bathe direction of its motion) should have a particular value (proportional to the square root of the coefficient of friction) ; and..(2),whenthis is-so, the pitch angle should be 45°. The maximum efficiency obtained from this investigation was 77%. This theoretical investigation, though of importance and interest; does not exactly represent the attt{al conditions, inasmuch as the deductions' from a small element are applied to the whole blade, and, further, the considerable disturbance of the water when a blade reaches it, owing to the passage of the preceding blade, is ignored. The most complete information respecting the properties of screw propellers has been obtained from model experiments, tlie. ; es law of comparison which has been shown to hold for Ei F! ship resistance being assumed to apply equally to screw , ro#t>t, propellers. No frictional correction is made in obtain= mg the values for large screws from the model ones; as stated by 28o 94.8 Mr R. E. Froude in 1908, it is probable that the effect of friction would be in the direction of giving higher efficiencies for large screws than for small. The results obtained with ships' propellers are in general accordance with those deduced from model propellers, although the difficulties inherent to carrying out experiments with full-sized screws have hitherto prevented as exact a comparison being made as was done with resistance in the trials of the " Greyhound " and her model. Results of model experiments have been given by Mr R. E. Froude, Mr D. W. Taylor, Sir John Thornycroft and others; of these a very complete series was made by Mr R. E. Froude, an account of which appears in Trans. Inst. Nay. Archs., 1908. Propellers of three and four blades, of pitch ratios varying from o-8 to 1.5, and with blades of various widths and forms were successively tried, the slip ratio varying from zero to about 0.45. In each case the screw advanced through undisturbed water; the diameter was uniformly 0-8 ft., the immersion to centre of shaft 0.64 ft., and the speed of advance 300 ft. per minute. Curves are given in the paper which express the results in a form convenient for application. Assuming as in Froude's theory that the normal pressure on a blade element varies with the area, the angle of incidence, and the square of the speed, the thrust T would be given by a formula such as T=a R2—bR where R is the number of revolutions per unit time. On rationalising the dimensions, and substituting for R in terms of the slip ratio s, the " conventional " pitch ratio p, the diameter D, and the speed of advance V, this relation becomes: 'I'= DaV9 (I S 5)2. From the experiments the coefficient a was determined, and the final empirical formula below was obtained— . T=D'V2XB p2IX1•o2((1—)O85) I—S2 orH=•003216DZV'XB• ' p21Xs((I_0)2) where H is the thrust horse-power, R the revolutions in hundreds per minute, V is in knots, and D in feet. The " blade factor " B depends only on the type and number of blades; its value for various " disk area ratios," i.e. ratio of total blade area (assuming the blade to extend to the centre of shaft) to the area of a circle of diameter D is given in the following table: Disk area ratio . . -30 •40 •50 •6o .70 •8o B for 3 blades elliptical .0978 •1050 •1085 •1112 .1135 •I157 B for 3 blades, wide tip •1045 •1126 •1166 •1195 •1218 •1242 B for 4 blades, elliptical . 1040 •1159 •1227 •1268 ;• I294 •1318 The ratio of the ordinates of the wide tip blades to those of the elliptical blades varies as i +D, where r is the radius from centre of shaft. Curves of propeller efficiency on a base of slip ratio are drawn in fig. 53, these are correct for a 3-bladed elliptical. screw of disk area ratio 0.45 ; a uniform deduction from the efficiency obtained by the curves of •02 for a 3-bladed wide tip and •012 for a 4-bladed elliptical screw must be made. Efficiency correc- tions for different disk area ratios have also to be applied; for a disk ratio of 0.70 the deductions are -o6, .035, -02 and •oi with pitch ratios of o•8, 1-o,1.2 and 1.4 respectively; for other disk ratios, the deduction is roughly proportional to (disk ratio-o-45), a slight increase in efficiency disk ratio. A skew- back of the blades to an angle of 15° was found to make no material difference to the results. [PROPULSION Hitherto, the theoretical and experimental considerations of the screw have been made under the convention that the propeller is advanced into undisturbed or " open " water, which conditions are very different from those existing Inter-behind the ship, The vessel is followed by a body of action water in complex motion and the assumption usually between made is that the " wake," as it is termed, can be con- ship and sidered to have a uniform forward velocity V' over the screw. propeller disk. If V be the speed of the ship, the velocity of the propeller relative to the water in which it works, i.e. the speed of advance of the propeller is V-V'. The value of the wake velocity is given by the ratio V' V—V'=w, which is termed the wake value. The propeller behaves generally the same as a screw advancing into " open " water at speed V —V' instead of at speed V and the real slip is v—(V—V')=v—I+w The real slip is greater than the apparent slip v-V, since in general w is a positive fraction; and the real slip must be taken into account in the design of propeller dimensions. On the other hand the influence of the screw extends sufficiently far forward to cause a diminution of pressure on the after part of the ship, thereby causing an increase in resistance. The thrust T, given by the screw working behind the ship, must be sufficient to balance the tow-rope resistance R and the resistance caused by the diminution in pressure. If this diminution of pressure be expressed as a fraction t of the thrust exerted by the screw then T(i-t) = R. The power exerted by the propeller or the thrust horse-power is proportional to T X (V-V') ; the effective or tow rope horse-power is R XV, and the ratio of these two powers (V VV,) _ (1—t) -1)(1 +w) is termed the hull efficiency. It is evident that the first factor (1+w) represents the power regained from the wake, which is itself due to the resistance of the ship. As the wake velocity is usually a maximum close to the stern, the increase of w obtained through placing the screw in a favourable position is generally accompanied by an increase in t; for this reason the hull efficiency does not differ greatly from unity with different positions of the screw. Model screw experiments with and without a ship are frequently made to determine the values of w, t, and the hull efficiency for new designs; a number of results for different ships, together with an account of some interesting experiments on the effect of varying the speed, position of screw, pitch ratio, direction of rotation, &c., are given in a paper read at the Institution of Naval Architects in 1910 by Mr W. J. Luke. The total propelling efficiency or propulsive coefficient (p) is the ratio of the effective horse-power (RV) to the indicated horse-power,' or in turbine-driven ships to the shaft horse-power as determined from the torque on the shaft. In addition to the factor " hull efficiency," it includes the losses due to engine friction, shaft friction, and the propeller. Its value is generally about o•5, the efficiencies of the propeller and of the engine and shafting being about 65 and 8o % respectively. The engine losses are eliminated in the propulsive coefficient as measured in a ship with steam turbines; but the higher rate of revolutions there adopted causes a reduction in the propeller efficiency usually sufficient to keep the value of the pro pulsive coefficient about the same as in ships with reciprocating engines. The table on the following page gives approximate values of w, t, and p in some ships of various types. The action of a screw propeller is believed to involve the acceleration of the water in the race before reaching the screw, which is necessarily accompanied by a diminution of pressure; cavitation. and it is quite conceivable that the pressure may be reduced below the amount which would preserve the natural flow of water to the screw. This would occur at small depths of immersion where the original pressure is low, and with relatively small blade-areas in relation to the thrust, when the acceleration is rapid; and it is in conjunction with these circumstances that so-called " cavitation " is generally experienced. It is accompanied by excessive slip, and a reduction in thrust; experiments on the torpedo-boat destroyer " Daring," made by Mr S. W. Barnaby in 1894,1 showed that'cavitation occurred when the thrust per square inch of projected blade area exceeded a certain amount (Hi ib). Further trials have shown that the conditions under which cavitation is produced depend upon the depth of immersion and other factors, the critical pressure causing cavitation varying to some extent with the type of ship and with the details of the propeller; the phenomenon, however, provides a lower limit to the area of the screw below which irregularity in thrust may be expected, and the data for other screws (whether model or full-size) become inapplicable. i Trans. I.N.A. 1897 (vol. xxxix.). U. 4. .o w= and F=, The conditions of equilibrium, viz. (a) that the total weight and buoyancy are equal, and (b) that the centre of gravity and the The above figures refer to full speed and are affected by alteration of speed. centre of buoyancy are 1 Higher values have been obtained for the propulsive coefficients of the most recent turbine-driven ships. in the same vertical transverse section, en- sure that the end ordinates of the shearing force and bending The forces tending to strain a ship's structure include (I) the These curves are usually constructed for three standard conditions of a ship, viz. (i.) in still water; (ii.) on a trochoidal wave of length equal to that of the ship - amidships; and (iii.) on a similar wave with the trough amidships. The curve of weight is obtained by distributing each item of weight over the length of the ship occupied by it and sum- Such a condition of the ship as regards stores, coal cargo, &c., is select- FIG. 55.—Cruiser of 14,000 Tons on ed, which will produce Wave Crest. the greatest bending moment in each case. The ordinates of the curve of buoyancy are calculated from•the areas of the immersed sections, the ship being balanced longitudinally on the wave in the second and third conditions. The shearing force and bending moment' curves are then are shown in figs. 55 to 59 for a first-class cruiser on wave crest, a torpedo-boat destroyer on wave crest (bunkers empty) down the g and in trough (bunkers full), and a cargo vessel on wave crest (hold and bunkers empty) and in trough (hold and bunkers full). From these curves FIG. 56.—Torpedo Boat Destroyer on . it is seen that the maxi- Wave Crest. occurs- near amidships ; its effect in figs. 55, 56 and 58 is to cause distribution of the weight and the buoyancy. Let WWW the ends to fall relatively to the middle, such a moment being termed hogging "; the reverse or a " sagging " moment is illustrated in figs. ndlag. per foot run of a ship plotted along the length the over ill-water cond Curves of a similar character are obtained in the s ition, but the bending moments and hea ing fo ces The maximum bending moment is frequently expressed as a ratio of the product of the ship's length and the displacement; average I • f '1 d d s t values for various types of ships are tabulated below: Class of Ship. W Whether Hogging XI (on Wave Crest) or sagging (in Wave Hollow). Maximum B.M. Mail steamer From 25 to 30 H" Cargo vessel . . . From 30 to 35 H Battleship (modern) About 3o H Battleship (older types) About 40 H First-class cruiser . About 32 H Second-class cruiser About 25 S Scout 'About 22 H Torpedo-boat destroyer , ) About 22 H Torpedo boat • . . From 17 to 25 S S About 23 H j About 23 S Propulsive Thrust Type of Ship. of Coefficient, Wake Value, Deduction, Hull Remarks. p' Screws. — p w t Efficiency. Battleship (turbine driven) 4 471 t5 •I2 1•o1 Inner screws •20 16 1•oI Outer screws Battleship (older types) 2 •47 '14 •17 '95 First-class cruiser 2 •53 .to •I0 •99 .. Second „ 2 •48 •o6 •IO •95 •. Third „ 2 •48 •o5 •o8 •97 Torpedo-boat destroyer 2 •62 •oI •02 •97 Mail steamer (turbine) 30 .17 1.o8 Inner screws 4 46 •22 20 .98 Outer screws Cargo vessel 2 • . •20 •14 I.03 Sloop I •45 •2I .17 I•oo •. Submarine (on surface) 2 .. .16 •10 I•o4 (diving) 2 .. •20 •12 1.05 M M Mis obtained which gives. the bending moment at any section. Symbolically, if w, F, M represent the load, shearing force, and bending moment, and x the co-ordinate of length, static forces arising from the distribution of the weight and buoyancy when inertia of the ship and its lading under the accelerations experi enced in the various motions to which the ship rolling pr operation of the various mechanica carries. the of the ship of the strength of the structure which can be considered theoretically reactions with assumptions have always to be made in order to enable them to be calculated. strength an actually theoretical in mastrength, on the one hand, and of keeping th es is roughly structure and dependent the total available displacement and proportions are subject, are due to inequalities in the longitudinal Longitudinal be ancy ; while from a to b ordinates are equal to the differences b 0etween oa those ose of of s an repre en and Is liable such as and pitching in a sea way; and (3) local forces and water essures incidental to (¢) propulsion and steering, and (b) the l contrivances which it weight and buoyancy of the ship at rest and to the inertia any generality; the character of the internal calculations with the results of experience forms anvaluable guide to the proper distribution of material. In kng such a comparison the necessity of providing sufficient e other hand, has to be borne in mind; the latter point being pecially important in a ship, since its economical performance on the difference between the weight of the , c to d, e tof, it is in defect. A curve LLL, whose WWW ed a , s the net load of the ship regarded as a beam subject to longitudinal bending. Shearing forces are produced whose resultant at any trans-verse section is equal to the total net load on either side of the section; they are represented by the " shearing force " curve FFF ... , whose ordinate at any trans-verse section is pro- of the loads " curve
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