Linearized Potential Flow Theory for ACVs in a Seaway 



where the operator <5 stands for the Dirac delta -function. 

 Similarly, in the case of S , the normal derivative is of 0(6) or 



-^(4" )L * - 27r<5 ( x -o 5( z - r ) + 0{ 6 ) 



and results for S y _ and S could also be written down in the same 



manner. 



We may therefore write, neglecting the 0( 8 ) terms. 



iG 



// H?- « =JNi? 



+ 2*6 (x - $.)« ( z - r )>+ 



V S 2 



S 1 + S 2 

 o *o 



>? = b + 



) a 7 ? 



+ i?=-b^- — 



^b 



- 2x* ( x - l)8(z - D 



+ 2tt5 (x - £ )5 (z - f)J + 



+* 



»? = -b 



\^G 



■n=- b -)bv 



-I 



h -* 



7, = -b_ 



ac 



2tt 6 (x - Z)8(z - f ) 



d£cir j 



o o 



b- b + | )b-V 



+/^-b - * - b 



- 2x8 (x - £ ) (z -f )(+ 



ac 



a*? i 



+ 2x8 (x - e) 5 (z - f) 



df'df' 



where S^ and S 2 denote one side each of the immersed part of 

 the longitudinal planes of the hulls. We have assumed here that G 

 and G^ are continuous across the longitudinal planes, but allowed 

 for a discontinuity in the value of the potential across the planes. The 

 values of G^ at v = b and v = - b will, of course, be different. 



233 



