14 REPORT 1869. 



speed, the jiressure needed to attain this speed increases more slowly than 

 the sui'face of the greatest transverse section. It is near the truth to say 

 that, for similar forms, the resistance per square metre of midship section, at 

 the same speed, decreases as the vessel increases, in the ratio of the square 

 roots of the radii of curvature of its lines, these radii being themselves pro- 

 portional to the linear dimensions of the ships ; it is therefore wrong to 

 compare the resistance of different ships by means of experiments made on 

 models to reduced scales*. 



" 2°. If the same vessel be driven at different speeds, the force needed to 

 obtain these velocities increases less rapidly than the square of the speed, 

 while that is small. The force increases as the square for ordinary rates of 

 3 to 5 metres per second, according to the condition of the surface in respect 

 of smoothness. Beyond that speed it increases faster than the square f. 



" 3°. The diminution of the angle of entrance, and the lengthening of the 

 radius of curvature of the lines wliich the water has to follow, especiallj' in 

 the replacement in wake of the stern bj^ the water coming up from below, are 

 the principal means of diminishing the resistance. This has the greater in- 

 fluence the greater the driving-power. For very slow motion, the influence 

 of form is less than that of surface friction. 



" 4". The sharpness of the bow, both above and below the water-line, 

 which has in calm water the effect just mentioned, has more marked advan- 

 tages in a heavy sea-way. 



" 5°. The smoothness of the wetted surface plays a considerable part in 

 the resistance ; and this part, due to friction, varies but little with the speed. 



" I add that the resistance of the hull increases markedly in narrow chan- 

 nels, and still moi-c where the depth of water does not much exceed the 

 draught of the sliip ; so that experiments ought to be made in deep water. 



" Finally, my numerous observations on the resistance of ships, in calm 

 weather and open sea, agree, with a close approach to exactness, with the 

 following formula, which I have since adopted as the measure of the resis- 

 tance : — 



E=KS(V^ + 0-145V')-FK'S^ W. 



" In this formula, I call — 



S, the area of midship section in square inches. 



S', the product of the mean girth (wetted), into the extreme length, 

 also in square metres. 



V, the speed in metres per second. 



K, a coefficient varying with the form, diminishing inversely as the 

 square root of the radii of the curvature of the longitudinal sections, and 

 also diminishing with the mean angle of entrance. This second reduc- 

 tion amounts to about 15 per cent., as the mean angle of entrance comes 

 clown from 45° to 15°. It is therefore about g per cent, for each degree 

 between those limits. 



K^, a coefficient independent of the fonn, and varying only with the 

 smoothness of the wet sldu. This coefficient may increase in the ratio 

 of 1 to 10, from 0-3 for bottoms very smoothly covered with good copper, 



* M. Eeecli, Director of the Ecole d'Application du Genie Maritime, Las long since 

 pointed out in liis lectures the error frequently made of comparing the resistance of vessels 

 of various forms by means of experiments upon models driven at the speed proper to the 

 vessels themselves. — Kofe b// ihe French author. 



t I am here speaking of vessels only partially immersed, not of vessels vhieh are en- 

 tirely imder water. — Note hy the French author. 



