since it is assumed small in comparison with the forward speed arae The velocities U and V 
may then be written as 
U= Xog Cos 6 - (Z¢g-Wz) sin 0 
V = Xcq sin @ - bg + (Z6g-Wz) cos 9 
The depth of submergence h of the body at any point P(£,¢) may be determined by 
h = Zceg - & sin @ + § cos @ -r 
where r is the instantaneous value of the wave elevation directly above the point. 
For regular head waves the wave elevation for a linear deepwater wave is 
TS atcOs k(x+ct) 
where r, is the wave amplitude 
k is the wave number 
c is the wave celerity. 
At point P(é,¢) 
X = Xo, t Ecos 8 +§ sin 8 
(9) 
(10) 
(11) 
(12) 
The hydrodynamic moment Fg about CG is obtained in a similar manner by integrating 
over the wetted length the product of the normal force per unit length and the corresponding 
moment arm. 
