Developments in Theory of Bulbous Ships 



However the calculations involved are so complicated that no one seems to have 

 succeeded yet in producing a significant result from this higher order theory of 

 surface ships. 



Recently, in connection with the theory of wave cancellation in bulbous 

 bowed ships, Yim (1964) considered the Froude number effect on the ship rep- 

 resentation near the free surface, and its influence on the regular wave far be- 

 hind the ship. 



We consider a uniform source distribution whose strength 



m = a 

 o 



in 0<x<l, y = 0, -oo<z<0, in the uniform flow considered in this report. 



The y component of velocity at (x,y, z) is 



(41) 



1 



I I ^^^^'^oBT r.^^r^^^ \ [ i7 



y 



'0 "0 



ke 



k( io)- I z+n ) 



dkdf' 



(42) 



k sec - ILL sec 

 ^ . „ o ^ 



where 



r, = [(x-^)2 + y2 + (z+0^]''' (43) 



oj = (x - ^) cos + y sin . 



At a point (x,y,o) which is not on the singularity plane, the last quadruple inte- 

 gral j(x,y,o; <f), say, can be written 



J( 



x,y,o;l) -.Kx,y,o;0) = - Re j J 



(44) 



When we consider the limiting case of y^O in j^x,y,o; l) , this becomes zero 

 for any k^ since the integrand is antisymmetric in e. Now if we charge the 

 variable k -» k k 



7T 00 ikkQ(xcos0 + ysin6') 

 J(x,y,o;l) = iRe f f ^^^ ^ sin g e ^ ^^ _ (45) 



■^ J J„ k - sec^i^ - iu sec 6 



1087 



