Linearized Potential Flow Theory for ACVs in a Seaway 



icrt 



andwriting r = 5r i0Q + ^ roiQ + ee ^ QQl + 



the result is 



2 p ge 



"'/( 



s z e r 



100 ' 00 



+80e f t \ _A>L 



1 010 010^ ax' 



dx' 



the integration being along the load waterline L i. e. along the 

 x 1 axis. The contribution is therefore of a much higher order. 



Similarly the contribution of the hydrostatic pressure to the 

 vertical force may be evaluated. In this case, 



2<5pg// |z + z'cos - x'sinfl - h (1 -cos0) 



dh , ^h 



cos 6 - 



o 'o r 



cos^ (h h( 



J.ff 



-- 28pg cosg (£ h(x'z') 

 C 



+ 26pg c 



z + z'cos - x' sin i 



h(x', z') dx'dz' 



— — ; sine dx 

 dx' J 



- h (l-cos0) dx' 



, S 1 +S 1 

 * o o 



+ 25p gsine^ h(x\ z') 



z + z'cos - x'sin - h (1 -cos 0) 



dz 1 



+ 25pgsi 



A //. 



5+S 

 'o 'o 



h(x',z') dx'dz' 



As before, the line integrals are each zero and the surface integrals 

 combine together to give 



1 



2« P g // h(x\ z') dx'dz' 



^ +S 1 



o 'o 



which is simply the displacement of the two hulls below z = . We 

 may write the above integral in the form 



2 5p 



JJ h(x',z' 



•! 



"lo 



) dx'dz' + 25 pgjl h(x', z') dx'dz' 



193 



