I^O 



NATURE 



\yune 19, 1879 



to elucidate and bring within the grasp of scientific treat- 

 ment, will naturally find a place. 



The resistance of ships and the speeds that could be 

 relied upon in practice by the application of a given 

 amount of force has aUvays been a fruitful source of 

 trouble to naval architects and engineers. The various 

 formula; that have been used for calculating the speed of 

 ships, and which were based upon what were supposed to 

 be the true laws of resistance, have always been uncertain 

 and unreliable in their application. Mr. Froude has 

 shown that this is because the approved formute " were 

 not only wrong in detail, but that the supposed cause of 

 resistance, with which alone they professed to be dealing, 

 was in reality no cause at all ; and that the real cause of 

 resistance, whatever it might be, was entirely left out." 



This supposed cause of resistance, which " was in 

 reality no cause at all," was alleged to be due to the inertia 

 of water, and the necessity for pushing those particles out 

 of the way which offer an obstruction to the progress of a 

 ship through the fluid. Thus it seems that there must be 

 an excess of pressure upon the fore part of a ship when 

 she is excavating or pushing water out of her way ; and a 

 diminution of pressure or partial vacuum on the after 

 part when she is travelling away from the particles which 

 press against her. There would therefore be a total 

 resistance caused by excess of pressure forward and 

 deficiency of pressure aft. As this resistance would 

 depend upon the volume of water that would have to be 

 pushed out of the ship's way ; it appeared obvious that it 

 must be measured by the area of the ship's cross section. 



These considerations were expressed in the following 

 formulae, which have been those chiefly used by ship- 

 builders till the last few years, and have been preferred 

 by the Admiralty to any other down to the time when 

 they placed the determination of the speeds of ships in 

 Mr. Froude's hands. The formulas are — 



V^ 



P 



c,Dy 



when V= the speed of the ship, A = the area of the 

 greatest immersed cross-section, or " the area of the ship's 

 way," D = the ship's displacement, P = a. measure of the 

 propulsive force, which stands for the indicated horse- 

 power of the engines, and C, and Cj are constants obtained 

 from the observed performances of other ships. These 

 are only formula: of comparison between different ships, 

 and were always regarded as being strictly applicable only 

 to the comparison of ships of similar form. They are 

 obviously based upon the assumption that the resistance 

 is as the square of the speed and the area of the vessel' s 

 way, or of the canal she may be supposed to cut through 

 the water in going from place to place. This is strictly 

 the assumption in the first formula, which includes the 

 exa:t area of the immersed cross-section of the vessel ; 

 but in the second formula, though the character of the 

 assumption is the same, the area is corrected to represent 

 the supposed equivalent cross-section for variations of 

 displacement. 



These formulae gave fairly accurate results when applied 

 to vessels of good form which were similar to those from 

 which the constants were derived, and when the speeds 

 were low. It was known, however, that the speeds of 

 vessels of exceptional form and dimensions could not be 

 thus calculated, and that in all ships the resistance in- 

 creased at a faster rate than the square of the speed 

 beyond certain limits, which limits were different in dif- 

 ferent ships. The development of the true laws of fluid 

 motion, or the doctrine of stream-lines, by Prof. Stokes, 

 Prof. Rankine, Sir William Thomson, and others enabled 

 the real causes of a ship's resistance to be ascertained. 

 It was then seen to be quite wrong to suppose that the 

 work done in propelling a ship is in any degree analogous 

 to excavating a canal, and spreading the water she suc- 

 cessively displaces over the surface. 



The stream-line theory showed that the reactions which 

 the inertia of the fluid would cause against the surface of 

 a ship moving through it arranged themselves quite dif- 

 ferently to vi'hat had formerly been supposed, and that 

 such methods of estimating their total effect — which was 

 supposed to constitute the resistance — as we have referred 

 to were fundamentally wrong. Indeed it shows that there 

 is nothing in nature to correspond with the old idea ot 

 head resistance, because, according to the stream-line 

 theory, a submerged body such as a fish, or a torpedo, 

 once put in motion in a frictionless fluid would continue 

 to travel with an uniform speed, and experience no resist- 

 ance. Certain particles of fluid would have to be set in 

 motion to enable such a body to pass them, but this 

 would be done in such a way as to cause no resistance in 

 the direction of motion. The backward forces acting 

 upon the body on some parts of its surface would be 

 balanced by the forward forces acting upon other parts, 

 and the inertia of the fluid would propel it forward at 

 some points with an equal force to that opposed in 

 resistance at other points. 



Mr. Froude showed most clearly and conclusively how 

 this paradoxical result came about in his presidential 

 address to the mechanical section of the British Associa- 

 tion delivered at Bristol in August, 1875,' and also in a 

 lecture delivered at the Royal Institution on May 12, 

 1876. He proves that in a perfect or frictionless fluid 

 there is no power by which any endways resistance can 

 be caused to the passage of a submerged body moving 

 uniformly through it. Substituting for the submerged 

 body moving through a stationary ocean of fluid the 

 plainly equivalent conception of a stationary submerged 

 body surrounded by a moving ocean of fluid, Mr. Froude 

 points out that at a sufficient distance ahead of the body 

 the ocean is flowing steadily on, in what may be imagined 

 to be a collection of streams of any size and cross section 

 we please. All these streams must have the same direc- 

 tion, velocity of flow, and pressure. In order to get past 

 the body these streams must alter their direction and 

 velocity, settling themselves into courses which will be 

 determined by the various reactions they exert upon each 

 other and upon the surface of the body — " yet ultimately 

 and through the reverse operation of corresponding forces, 

 they settle themselves into their original direction and 

 original velocity. Now the sole cause of the original 

 departure of each and all of these streams from, and of 

 their ultimate return to, their original direction and 

 velocity, is the submerged stationary body ; consequently 

 the body must receive the sum total of the forces necessary 

 to thus affect the streams. Conversely this sum total of 

 force is the only force which the passage of the fluid is 

 capable of administering to the body. But we know that 

 to cause a single stream, and therefore also to cause any 

 combination or system of streams to follow any courses 

 changing at various points both in direction and velocity, 

 requires the application of forces the sum total of which 

 in a longitudinal direction is nil, provided that the end 

 of each stream has the same direction and velocity as 

 the beginning. Therefore the sum total of the forces (in 

 other words, the only force) brought to bear upon the 

 body by the motion of the fluid in the direction of its 

 flow is Jtil." 



A frictionless fluid would, therefore, offer no resistance 

 to a submerged body moving through it. Mr. Froude 

 next introduced the consideration of friction, which 

 brings two causes of resistance into play. First, there is 

 the friction proper which is due to the drag of the par- 

 ticles of water upon the surface of a body as it moves 

 through it, and which is governed in amount by the area 

 of the surface, and also by its nature, whether smooth or 

 otherwise ; and secondly, there is the defect of pressure 

 at the rear end of the body caused by the stream, line 

 motions being somewhat impeded by friction between the 



1 ^ Published in Nature of November i3, December 2, 16, and 30, 1875. 



