Linearized Potential Flow Theory for ACVs in a Seaway 

 // G |l" dS = //r "IT f G ( x *y» ■**'■ b 'J'> + G(x,y, z;^'-b, r') + 



s 1 

 •"[j" (r ooi fc + r ioi "If-' + v %oi ff| G b + G -b 



+ i?' 1 ' t fpgiiF« Q b +0 .b) + 



V S 2 



+ r ioiif «V G .b> 



dS'di" 



(V. 17) 



We may now combine (V. 17) with (V. 16) noting that the integration 

 is to be performed on the instantaneous position of one side of the 

 longitudinal plane of one of the hulls. As the instantaneous position 

 is unknown, we will reduce the integration to the known equilibrium 

 position. 



We may write as in Appendix III 



S. = S, + S[ 



where S« is one side of the longitudinal plane immersed below the 



free surface f =0 



is the steady part of this plane below the 



load waterplane f ' = and S\ is the oscillating strip between 

 f = and f ; =0 



From the discussion in Appendix III where we 



S' 1q , the 

 correction for the first term in the integrand of (V. 17) is an additional 

 integral over the basic surface S. 



evaluated the pressure force and moment over the strip ^ « 



8V 



1K--JH 



d£ dT = 8ae 



iat \\\l- t'a \ ^ h d 



J7L o Q1 ooi pr w 



i 



G b + G -b 



ah 



_a__ 

 ar' 



G + G 

 b -b 



- e 



001 



ar 



t 



G b + °.b 



Ai'dC 



We need not correct the second term in the integrand for the integral 

 will be 0( 8 a, 80a, 8a) . 



237 



