Wave Forces on a Restrained Shtp tn Head-Sea Waves 
‘taped ; , 
[¥, r. a oil w vx) : oil wt - vx) |. cekZ 
: 2 + A Uy ee | eZ 
mVw, (aera f2)) Ci ¥s 
4k u(s, k) = (s) ds 
+ | ky (ack) [(G(eY, RZ;ce (5)-. kn (Ga) Gtk eee =k Ss (py), 
EG) kn (s) )] es a 
2 
V. NUMERICAL CALCULATIONS 
V.1. Theoretical background 
It would be time consuming to evaluate the solutions we have 
found (see (48) and (92) ) for a ship with arbitrary cross-sections. 
But if the ship had circular cross-sections, there is a faster way to 
find the solutions. We can use the solution given by Ursell (1968 b) 
for a circular cross-section. Ursell has used a different coordinate 
system that we have used earlier, and I find it convenient using 
Ursell's coordinate system when talking about Ursell's solution. The 
coordinate system is shown in Figure 2. 
free surface 
Figure 2 Ursell's coordinate system 
The two-dimensional problem which Ursell solves is given by the 
Helmholtz equation 
Fe 2 
z 
| ae - ¥ |e = 0 (93) 
