Owing to the periodicity of the motion 



dE 



dt 



= 



(253) 



we have the relation 





dS = 



r 27T r l 



+U cos 9 dz = 



(254) 



The velocity potential is the sum of the incident wave, the steady forward 

 motion, and the periodical disturbances, so we can write 



+ U <j> + <\> ± 



(255) 



Now we consider that the direction of the wave propagation which makes an 

 angle a with the direction of the forward motion of the ship, namely the 

 negative direction of x. The incident wave potential is 



= c h exp(Kz+iKx cos a+iKy sin a+itot) 



(256) 



The contribution of <}>_ to D is the wave resistance in calm water. The 

 periodical disturbance potential has, on the other hand, an asymptotic 

 expression 



= - 2 i e 



iwt 



- e-ir/2 



- -tt/2 



r - j 



e+iT/2- 



tt/2 



a.. exp[a.. z+ia,R cos(a-6)] 

 H(a 1 ,a) ■ — ■ — da 



Jl^ti 



(257) 

 (cont . ) 



91 



