APPENDIX A 
EVALUATION OF HYDRODYNAMIC FORCE AND MOMENT INTEGRALS 
The hydrodynamic force the craft experiences in the vertical direction as derived in the 
text is: 
‘ dm,V ; ; 
F,=-f {mV-u 9E MV iste IDV }cosoat+ J apeadt 
where U = XGG cos @ - (z-w,) sin 0 
and 
V = Xcg sin ®@ + (z-w,) cos 8 -6§ 
Another force acting in the vertical direction is the weight of the craft. 
The first two terms of the integral are evaluated by making the substitutions 
V =Xeq sin? —-@€ + Z—, cos'8-w, cos @ 
cE) ars cos 6 - ZeG sin 0) +w, 6 sin 0 
. Ow 
a = -8 - = cos 8 
A ONE) ; 
= aa 
o£ 0& 
dw ow 
aah z 
Taha he ouRE 
and noting that 
dUV 
= oe 
on Jom cine 
Using the previously described substitutions, the force becomes 
am, 
fov BE d§=-UVm, 
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