Wave Forces on a Restratned Ship tn Head-Sea Waves 
THE FORWARD-SPEED PROBLEM 
We write the total potential @¢ as follows 
is, ¥o2,t) = Ux + Ud, (x,y,z) + or (seaar,t) (50) 
where U®@, is the perturbation velocity potential in the steady motion 
problem. It can easily be shown that $7 satisfies 
= 10 on Sot ple (ony) (52) 
By combining (3) and (4) and using the assumption about linearity, 
it can be shown that oT satisfies the free-surface condition 
Since the time dependence of the incident wave is given by ead: : 
(see (5)), it is expected that the time dependence for the potential 
¢y is also given by e 1@t This implies that we can write equa - 
tion (52) as 
Eroo 
