398 HYDKAULICS AND ITS APPLICATIONS 



pressure, due to eddy production is approximately proportional to v 2 , and 

 the resistance thus produced proportional to S v*. 



In general, however, skin friction accounts for the greater part of the 

 total resistance, varying from 80-90 per cent, of the total for speeds of 

 6 to 8 knots, to 50 or 60 per cent, at very high speeds this with clean 



bottoms. Eddy production, in a 



Direction of Less Resistance * . r 



well-formed ship, accounts for 

 8-10 per cent, of the total, and 

 wave-making resistance for the 

 remainder. 



The total resistance, at speeds 

 Direction of Greater Resistance up to about 10 knots, is approxi- 

 mately proportional to f 2 , while 



Sir William White 1 states that as the speed increases further, the power 

 of the velocity to which the resistance is proportional increases to a 

 maximum value of about 3, owing to the increasing magnitude of the 

 wave-making resistance, and then falls again to a value slightly below 2. 

 Thus in the case of an 80-foot boat exampled by Sir William White 

 The resistance up to 10 knots was approximately oc v^ 

 at 13 ocv 3 



17-18 oc v 1 ' 9 



while with the Iris 300 feet long, 



the resistance up to 13 knots was approximately oc v 2 . 

 at 18 a v 2 ' 8 . 



The total resistance of a ship may be deduced from that of a scale 

 model, and the skin friction alone from Froude's results, so that it 

 becomes possible to deduce the eddy and wave-making resistances 

 experimentally. 



Before proceeding to describe Mr. Froude's methods of doing this, we 

 may note that, if the relative scales of a ship and its model are as D : 1, 

 the relative wetted areas are as D 2 : 1, and if the suffix s refers to the 

 ahip and m to the model, the frictional resistances are given by 



R m = Jm S m V^\ aggmning resistance x j 



MS Js bg V s \ 



and, neglecting for the time the difference between f m and/ a , we have 

 /? o /v \2 /y \2 



^s &s / * \ r>2 / v * \ /-i\ 



o ' \ T7~ I U \ fr~ I {*) 



Km &m \ V J \VJ 



i Manual of Naval Architecture," by W. H. White, p. 466. London, John Murray. 



