June 19, 1879] 



NATURE 



171 



particles. This is very obvious in blunt-ended bodies 

 where the stream-lines, instead of closing in round the 

 rear end and exerting their due pressure in the direction 

 of motion, force themselves into eddies and whirls. Mr. 

 Froude calls this element of resistance "eddy-making 

 resistance." It is imperceptible in ships of fairly easy 

 shape, but is of large amounts in ships with very full 

 stems. He shows that a submerged body of good easy 

 shape would practically experience no resistance except 

 that due to surface friction, and the amount of resistance 

 would be practically the same as that of a thin plane 

 moving edgeways, which has the same area of wetted 

 surface. 



Mr. Froude next shows that when we come to the case of 

 a ship or a body travelling at the surface, a new cause of 

 resistance is introduced, due to the system of surface- 

 waves which is generated. The variation of pressure in 

 the stream-lines formed at the sides of a ship relieves 

 itself at the surface by raising or lowering the level, and 

 thus a bow and stem wave with a depression amidships 

 are formed and carried along as the ship progresses. 

 These waves once made, however, require little force for 

 their maintenance, so long as they are not swollen to 

 abnormal dimensions by the increased wave-making ten- 

 dency a ship possesses at high speeds. Other systems of 

 waves are also generated and driven off from the ship in 

 various directions by features of form that interfere with 

 the natural courses of the stream-lines. There are, there- 

 fore, three great causes of resistance to a ship ; i, sur- 

 face friction ; 2, eddy making ; and 3, wave genesis. 

 Mr. Froude shows that the first, viz., surface friction, 

 practically agrees with the resistance experienced by a 

 plane of the same wetted surface drawn longitudinally 

 through the water at high speeds, and that the eddy- 

 making resistance is practically nothing in well-formed 

 ships having fine ends ; but that the wave-making resist- 

 ance is so indeterminate in its character as to be inca- 

 pable at present of direct calculation. 



Mr. Froude estimated the total amount of a ship's 

 resistance by means of careful experiments with a model 

 made to her exact form. The method of doing this with 

 accuracy is one of Mr. Froude' s greatest and most useful 

 discoveries. Model experiments of this nature that had 

 previously been made were so misleading that it was 

 generally believed to be impossible to infer the resistance 

 of a ship from that of a small scale model. Mr. Froude 

 saw, however, that all three elements of resistance fol- 

 lowed the same laws in similar bodies, whatever the 

 differences of size might be, and that all that was required 

 to make experiments with models reliable was to discover 

 the true scale of comparison. This scale, or law of com- 

 parison, he discovered, and stated as follows ; — "If the 

 ship be D times the ' dimension ' (as it is termed) of the 

 model, and if at the speeds Fj, V^ V^. . . . the measured 

 resistances_of the model are ^1, R^, R^. . . ., then for 

 speeds >J D F„ V5 V^, 'Ju K, .... of the ship the re- 

 sistances will be ly /?i, Z)3 R^, D^R^. . . . To the speeds 

 of model and ship thus related it is convenient to apply 

 the term 'corresponding speeds'"; the special feature of 

 this " correspondence " being the fact that at such speeds 

 precisely similar wave systems are generated by ship and 

 model. 



Mr. Froude tried in 1867 a large number of resistance 

 experiments with models of various forms p.nd dimensions, 

 by towing them from the ends of lo-foot scale beams, 

 connected with self-recording dynamometric apparatus, 

 and mounted on booms projecting sideways from the bow 

 of a steam-launch. Soiie of the results were in glaring 

 contravention to the ordinary principles current at the 

 time, and Mr. Froude invited Mr. E. J. Reed, C.B., M.P., 

 who was then Chief Constructor of the Navy, to witness 

 the experiments. Mr. Reed saw the necessity for fresh 

 investigation, and by his recommendation a further series 

 of experiments was sanctioned by the Admiralty. 



These experiments were brought into further promin- 

 ence by the action which was taken upon a report of a 

 committee of the British Association in 1869, upon the 

 stability, propulsion, and sea-going qualities of ships. 

 On the recommendation of this committee an application 

 was made to the Government for carrying out experiments 

 upon resistance with actual ships of considerable size. 

 Mr. Froude, who was a member of the committee, dis- 

 sented from this report on the ground that the various 

 elements of resistance and the laws of their operation 

 " could be discovered with far greater facility and com- 

 pleteness by small-scale than by full-size experiments." 

 The Admiralty requested Mr. Froude to conduct an ex- 

 tensive series of experiments with models ; this he under- 

 took and continued up to the time of his death with the 

 greatest skill and success. The results thus obtained 

 furnished data for determining the resistance of ships of 

 various forms and dimensions to a considerable degree 

 of exactness, and also showed what circumstances were 

 favourable to speed and what were not. 



This subject had an important bearing upon some of 

 the inquiries instituted by the Committee on Designs for 

 Ships of War, in 1871, and they requested the Admiralty 

 to determine experimentally the actual resistance of a full- 

 sized ship. The Admiralty accordingly ordered the re- 

 quisite experiments to be made upon H.M.S. Greyhound, 

 a vessel of about 1,150 tons displacement. The experi- 

 ments were made under Mr. Froude's superintendence. 

 The Greyhound was towed by H.M.S. Active, and the 

 resistance at various speeds recorded by means of a deli- 

 cate dynamometric apparatus. She was towed from the 

 end of a long outrigged boom, so as to be clear of the 

 wake of disturbance, and every possible precaution was 

 adopted to eliminate all the various sources of error. The 

 experiments verified to a remarkable degree the law of 

 comparison propounded by Mr. Froude as governing the 

 relation between ships and their models, and perfectly 

 justified the reliance he had placed upon his method of 

 investigating the effects of variation of form by trials with 

 varied models, a method which, as Mr. Froude afterwards 

 remarked, "if trastworthy, is equally serviceable for 

 testing abstract formulas, or for feeling the way towards 

 perfection by a strictly inductive process." 



The value of Mr. Froude's method of calculating the 

 speeds of ships from those of their models, became so 

 obvious, that the Admiralty discarded their old methods, 

 and referred their designs to Mr. Froude for his estimate 

 of. their speeds. Besides the elaborate series of experi- 

 ments which Mr. Froude has had in course of procedure 

 at his experimental tank at Torquay for determining the 

 best form and proportion for various classes of ships, 

 designed for various speeds, most of the new Admiralty 

 designs have been experimented upon and modified forms 

 suggested where improvement could be made. The 

 results of his work, and especially of the recent trials of 

 H.M.S- Tris, whose lines were determined by Mr. Froude 

 for the high speed of 17^ knots— have borne striking tes- 

 timony to the correctness of his work. 



Mr. Froude has, however, done much more than show 

 how to calculate with accuracy the speed of a ship from 

 that of her model. He has shown how the various 

 elements of resistance act upon a ship at given speeds, 

 and the laws upon which they depend. In well-formed 

 steamers the resistance at low speeds consists almost 

 entirely of surface-friction. This was the case in H.M.S. 

 Greyhound at a speed of eight knots. If a curve of total 

 resistance be made from experiments with a ship or 

 model, and a curve of frictional resistance be also 

 placed on the same base line, they will be found almost 

 identical at their low speeds. The resistance due to the 

 formation of eddies is so small in well formed ships 

 as to be hardly appreciable. When a ship of tolerably 

 fine lines is moving at a moderate speed, the whole resist- 

 ance, therefore, consists of surface-friction. As the speed 



