'linearized Potential Flaw Theory for ACVs in a Seaway 



which becomes an integration by parts 



h (x', z') (z - x 1 0) f (x 1 , z') 

 stem 



stem 

 stern 



h(x',0)- 



c>x' 



stern 



(z - x'0) f (x 1 , z*) 

 z'zo" 



dx' 



The first term vanishes at both ends on the waterline, and the second 

 integral is taken along the + ives x' direction so that this term becomes 



/ 



Stern 



Stem 



h(x',0) 



a x - 



(z - x 1 6) f (x' 



.»■)] 



dx 1 



To this integral may be added the integral of zero value along the keel 

 from the stern back to the stem as h(x', z 1 ) is zero everywhere 

 along this line giving 



/ h(x, ' v) -b 



(z - x' e) f (x 1 



.«')] 



dx' 



which is taken around the boundary of S. 



This may be transformed by Stokes 1 theorem into 



+ if h(x, ' z,) sS^ [ 



dx'dz' + 



(z - x' 6) f (x'z') 



dx'dz 1 



The second surface integral may be written 



I 



[■ 



"'-'•■'>4f r< : -- ,, »-i? 



/ 



h(x', z') (z - x' 6) 





•fe 



(z - x'0 ) 



3f 



az- 



dx'dz 1 



dz 1 



dx'dz' 



195 



