STABILITY, PROPULSION, AND SEA-GOING QUALITIES OF SHIPS. 17 



The following are the values of the factor and its logarithm, which give 

 the length of the forebody in feet, when the velocity is given in — 



Feet, per second 0-19518 log = 9-29045. 



Knots, per hour 0-5561 log = 9-74515. 



Statute miles, per hour . . 0-41985 log = 9-62310. 



Professor Eankine states, as the result of his own observation, that it is 

 possible to shorten the bow to two-thirds of the length given by this formula, 

 without materially increasing the resistance, but that it is very disadvanta- 

 geous to shorten the afterbody. 



In the ' Proceedings of the Institution of Civil Engineers,' vol. xxiii. (for 

 1864), p. 321, is a paper by Mr. G. II. Phipps, on the " Resistance of Bodies 

 passing through the Water." Mr. Phipps considers that the total resistance 

 may be subdivided as follows, into additive parts : — 



Head-resistance — varying directly as the midship section, and inversely 



as the square of the projection ratio of the bow. 

 Stern-resistance — a similar function for the stern. 

 Friction-resistance — varying directly as the surface immersed. 

 Adchtional Head-resistance — an empirical correction assumed to be a 

 function of the draught of water. 



The sum of these resistances is then multiplied by the square of the velo- 

 city. 



The paper was followed by a discussion in which most of the leading 

 English writers on fluid resistance took part. The paper and discussion 

 thus constitute a very fair resume of the opinions then held on the subject in 

 this country. 



Mr. Phipps considers that the coefficient of friction of water on the outer 

 surface of a vessel is less than on the inner surface of a pipe ; and this is, to 

 a certain extent, in accordance with the experiments of Darcy on the friction 

 of water in pipes, which led to the conclusion that the coefficient of friction 

 consists of two terms — one constant, and the other varying inversely as the 

 diameter of the pipe. 



Mr. John I. Thornycroft, C.E., in a paper read before the Institution of 

 Naval Architects this year, and which wiU appear in their forthcoming volume 

 of ' Transactions,' gives the following formula, the form of which is derived 

 from experiments on the flow of water in pipes : — 



I. H. P.=Y/t Js/ 3^ vr7_i_^f;in ^'+^V3'7 



{S/J^^Y- + ,S.C."^3V..}, 



where S = the wetted surface, V = the velocity in knots, I = the length, 

 h, f, n, C are constants empirically determined : 



log 7i ='3-65450, 

 log/ =2-10170, 

 log 0=2-20041, 



n=380, 

 ^S=/(sin «)2-5 ds, 



ds representing an elementary portion of the surface, S, and d the angle 

 which this portion of the surface makes with the line of motion. It will be 

 noticed that the formula involves a large number of constants, more or less 

 arbitrarily determined. 



Professor Eankine, in a paper in the ' Transactions of the Institution of 

 1869. c 



