Linearized Potential Flow Theory for ACVs in a Seaway 



*-^r dS , 



3 n 



since 



V S 2 



dG A __ 



-r — = n. vG 

 dn 



where n , the unit normal out of zL/ » i. e. into the hull, i 

 by 



s given 



VH 



VH 



we may write , 



d_G 



"dn 



dS = 



VG . VH 



IVHI 



dS 



= VG . VH d£' df ' 



dh n 



dh. 



*( 



ar 



cos0 + 



+ 5( 



dh 

 1_ 



ar' 



ar 

 ah 



cos 



dG _ dG_ + 



ar 



sin ) 



a* 



dG 



a r 



dj'df 



on the outer hull surfaces S. , and S 2 _ as discussed in Section IV. 3 

 In the case of the inner hull surfaces S 2 and S.- we replace h. 

 by h 2 . 



On linearizing with respect to 6 , 



dG 



an 



dS = 



H 



a^ 

 ar 



IF -dT + a7 +5( "a? " ^r ) aT_ 



df'df 



Now, the terms containing d have 6 as a factor and as 6 is of 

 0(5,/3,a, 5a, 0a) these terms will actually be of ( 5 2 ,5/3 , 8a). Also 



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