Linearized Potential Flow Theory for ACVs in a Seaway 



It will be noted that we have replaced the element of area 

 dxdz by dx'dz' since the Jacobian of the transformation, 



d (x, z) 

 d(x'.z') 



is unity. Also we have altered the domain of integration from the hull 

 surface to the longitudinal planes 



and we will therefore have to express the pressure in the (x^y'.z 1 ) 

 system and use its value on both sides of the longitudinal planes in 

 view of the possibility of a discontinuity across the planes. This 

 could arise because of the singularity of the potential discussed in 

 Appendix V. 



We may now replace the surface of S. by 



8=8+8, 



o+ o- 



where S. is the side of the plane y' = b facing the +ive y' - axis 



and S-| is the side facing the -ive y' - axis with a similar nota- 



tion for the other hull, 



S 2 B S 2 + S 2 



o+ o- 



It will be remembered that these surfaces which are both sides of the 



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