Linearized Potential Flow Theory for ACVs in a Seaway 



f 



os k (y- r\ ) sec 6 sin 6 sec 6 d 6 / sec 6 6.6 



3 -p(z+r) cos p( x -g) cos^j C o S [ p (y_ r,) sin flj 



/ 



dp 



/ 



2 „ 

 p - k sec 6 



(6-23) 



where df indicates that the Cauchy principal value is to be taken. 



VI . 3 Wave Resistance 



The wave resistance is given by 



2 2 



R W = " b X 2000 " * X 0200 " 6 ^ X 1100 



and substituting for the longitudinal forces from (5-6), we may write 



R w = 2 >™ 2 ff*i ooo , (x ' - b - z '> B dx ' dz ' - 



2 \ x 



■ T 0Z JJ% P o P c x - V P o *010 0xx (X > '■ °)] dxd ^ + 



"//[*oioo v ,( x ' • b+ -' >:& + Vooj x, ' b -- z ')&-] 



// P o 1000 



1o 



dx'dz- +^-5f |; , 



|" ^ (6-23A) 



The first term on the RHS, is the wave resistance due to the 

 side hulls in calm water. It is assumed that the separation between 

 the side hulls is sufficiently large to avoid the necessity of evaluating 

 the potential on the two separate sides of S 1 due to possible inter- 

 ference between the two hulls. The second term gives the wave resis- 

 tance of the air cushion and the two remaining terms represent the 

 interference effects of the air cushion on the side hulls and of the si- 

 de hulls on the air cushion respectively. These terms may be evalua- 

 ted separately and then ar'ded together to give the combined wave re- 

 sistance of the entire system moving in calm water. 



149 



