9T 



mm m f anJ ^'^ + l^u sec 9) exp [-^(f -z)+1k4 i,. tqi 

 ;o a resistance 



where K , K are Bessel functions of the third kind. 



1 



Tables of wave ordlnates In the X,Z plane due to the motion of a 

 source, have been calculated by Wlgley. ^* 



B. Mlchell's Integral 



Four different methods have been used for calculating the wave re- 

 sistance of slender ship-like bodies: 



1. Mlchell's original deduction based on the concept of a wedge-like 

 ship depends upon the computation of pressure changes dp due to the wave 

 pattern. 



R = -2jjapdydz = -2||<5p || dxdz = 2pyjj^ g dxdz [11 ] 

 or 



1 



+ e k[x] 2 2 



where 



-« 



k[x] 



[131 



n U^^' '"' M^y^'^^ 



z = k[x] Is the equation of the longitudinal contour. 



Only odd terms of the hull equation contribute to the value of I. 

 For a symmetrical hull 1=0. 



Introducing dlmensionless coordinates I = y and putting 



y = y^K 



where y^ = ^—- = — - we obtain for a rectangular contour 

 2v^ 2F2 



