Linearized Potential Flow Theory for ACVs in a Seaway 



-( 



3 h l 



+ P 



5 h 2 



sin0 



dx'dz' 



(III. 1) 



where we have combined all the four sides of the two longitudinal 

 planes whose immersed parts are geometrically similar, except that 

 the profile of the disturbed water surface will be dissimilar on the 

 inner and outer sides of each plane. This wave elevation, however, 

 introduces a very high order correction, as will be seen presently, and for 

 our present purposes we may indeed consider that all the four sides 

 are equivalent. The integration is now over one side of a longitudinal 

 plane, but the different pressures on the two sides are to be taken 

 into account. 



We will now have to express the pressure on both sides of 

 the longitudinal plane of a hull in the (x'.y 1 , z 1 ) system. The pressure 

 is given in the (x, y, z) system in terms of the potential in the form 



p (x, y, z;t) = - p 



**. - v4> .. +Hr(v*) - gz 



t x 2 



and inserting the expansion for <f> 



$ = 5$ + 



1000 



0* + 50$ +e iat I*"* 



M *oioo p iioo y 1010 



M 9 0110 f *0001 *1001 0101J 



we have 



p(x.y..;t) = *PV* 1000 + ft>V* 0100 + Mp(v» uoo 



X X V X 



- v *iooo ■ v *oioo) " * ■ "T^oioo • V *0100 



iff t > 



oape (i(T<i> - V$ ) - 



p V 1010 1010 ; 



x 



P K T 0110 0110 ; 



x 



i°"t /. ,,- \ 



cpe (i<r$ - V$ ) - 



v 0001 ^0001 ' 



187 



