Linearized Potential Flow Theory for ACVs in a Seaway 



We may write (6-24) in the form 



^ R w '^If^ff^ dx ' dz ' ff^T^ 1 ^ ^ 



8 W hulls 2?r *V dx JJ d * 



§ 1o 



[f x (x 1 ,z' ;€', r') + f 2 (x' ,z' ;*', i") ] 



where f and f are given by (6-25) and (6-26) respectively. 



The above equation may also be written 



5 1 5 1 



[fj ( £', f'jx' fZ « ) +f 2 («\ f';x' ,z' )J 



by interchanging x' with £' and z' with f ' 



If^x' ,z' ;?', f) +f 1 ({', ?';x' ,z' ) +f 2 (x' ,z' ; {', f) + 



+ £ 2 ( {'. i";x' ,z' )] 



by the addition of the above two expressions and taking half the value, 



It will be seen that the first, second and fourth terms on the 

 RHS of (6-25) and (6-26) are odd functions of (x 1 - £* ) so that they 

 cancel respectively with each other when we take the sum 



i l (x 1 ,z' ; £', T) +f i ( f.f ;x' ,z ( ) 



and 



f 2 (x« ,«' ; t f ) + f 2 (£, f';x' ,z' ) 



but the third term is an even function and gives a contribution to the 

 sum by doubling itself in each case so that we have 



151 



