Linearized Potential Flow Theory for ACVs in a Seaway 



and equation (6-15) does not exist. We could obtain x,^^. z , _._ , and 



LOO 100 



from (6-14), (6-17) and (6-19), but there are only two remaining 



equations for solving x , z Q10 and 6 QlQ . 



We could, however, make the additional assumption that x and 



x are both zero, for the steady surge displacement is not a use- 



ful quantity and can, in any case, be absorbed in the co-ordinate 

 system. In this manner the sinkage (heave displacement) and trim 

 (pitch displacement) can be calculated. 



VI . 2 The Steady Potential 



It is shown in Appendix V that the potential in steady motion 

 can be derived in the form 



*(x,y,z) = ** 1000 +** 01 



00 



where 



and 



* 



= ^it 



1000 47rsd£' 

 1 o 



G (x, y, z; £',b, f) + G (x, y, z; £', -b, f') 



dS'dT' 



- .jl /to 



0100 47rpg JJ d£ 



/[^OlOO^^'^FS ~k G(x.y,z;«,i ? ,o) - 



G (x, y, z; £ , ij , o) d£ d v + . 



IFS 



4 7rpg 



"LaT ^oioo ^' t? '°)j^t- 

 -^ff[*oioo( £, ' b -- r )-*oioo( ? '' b+ ' r >]--- 



IFS 



EFS 



D 10 



dG (x, y, z; £', tj' , f ) 



677' 



dG (: 



V= b 



dj ?' 77' = -b J 



(6-21) 



As indicated in Appendix V, we have only derived an integral 

 equation for "$/>! nn > although $ innn has been explicitly solved in the 

 form of an integral representation on the assumption that the separa- 

 tion between the side hulls is sufficiently large for the interference 

 effects between the hulls to be considered negligible. In this case there 

 will be no "jump" in the potential between the two sides of each hull 



147 



