$. = potential representing the waves diffracted by a fixed 

 body, 



<I>r = incident wave potential. 

 Another velocity potential may be defined: 



$, = potential for total fixed-body problem, 

 so that 



Using this decomposition of the velocity potential, the boundary 

 value problems may be expressed as: 



V^$.(x,y,t) =0 for y < 0, 



and 



$. (x,0,t) + 

 tt 



lim 



for y = 0, 



V$. 



'- (x,y,t) = 0, 

 y 



(C-6) 



= V. (s) • n(s) for i = 1,2,3 



= for i = 4,6. 



These boundary value problems are solved directly using the Frank method 

 which distributes singularities over the hull surface. These singulari- 

 ties satisfy the radiation condition, Laplace's equation, the free- 

 surface boundary condition and the bottom boundary condition. To satis- 

 fy the body boundary condition requires the formulation of a set of 

 linear equations whose solution reveals the strength of each singularity 

 distributed on the body. 



Once the velocity potential is found the pressure may be found from 

 Bernoulli's equation: 



P(x,y,t) = - p$^(x,y,t). 

 The force on the body surface is: 



F = 



P(s) n(s) ds. 



(C-7) 



CC-8) 



and the moment is: 



105 



