Murthy 



so that 



( dH-_ v J^H . 

 d$ at tfx' 



V H 



> h 



a 1 



an 



=5|<— cos6 -— sinG + (z' - z) 6 + V cos6 >-r— 7 

 Ll x z G J dx 1 



■u 



-K-sine +— cose - x'e + Vsine >^ — - 



[■ '•■<&)■ .■■&)']'-■ 



- 1/2 



(4-10) 



This applies to the surface S 1+ . On the surface S_ the hull func- 

 tion h is the same, but ^H/dy 1 will be + 1 instead of -1. The 

 expression P$/on will be unaltered for I ^H I will be the same. 



Thus (4-10) expresses the normal velocity for the two outer 

 hull surfaces S and S 



In the case of the two inner hull surfaces S and S we 



simply replace the hull function h by h . 



V. THE FORCES AND MOMENTS 



It is shown in the earlier work (Appendix III of Reference 1) 

 that the forces and moments acting on the ACV as a rigid body may 

 be written in the form 



F = X A i + Yj + Zk = Fp + F^ 



and 



M = Li + Mj + Mk = M + M 



where, taking into account the side hulls in addition to the cushion 

 hull which was the subject of the previous study, we may write for 

 the pressure force 



f p xF p +f p 



C 



= - /jfp s ndS - /YphdS (5-1) 



S l +S 2 



130 



