Linearized Potential Flow Theory for ACVs in a Seaway 

 ff + 3h l - 3h 2 



" 2 " v f <*oioo, ^ + *oioo, 7?> dx ' dz ' + 



S x' x' 



+ ZpgJ (z 01() -x'* 01() )h(x' ,o) dx' - 

 L 



- 2 ( S 100 + h G*100)i/"Po dxd y=° (6 - 10) 



S x 



O 



In the case of an arbitrary non-uniform cushion without fore- 

 and-aft symmetry and with different pressures along the front and 

 rear boundaries 



ff Po dxdy 



S 

 o 



will have a non-zero value as has just been established. In this 

 case, therefore, (6-9) gives 



x 010 + h G < 'olO = ° 



In the case of other types of cushion just discussed i. e. in the case 

 of a uniform cushion or non -uniform cushion with fore-and-aft 

 symmetry, the surface integral in (6-9) vanishes and the set of 

 three equations becomes degenerate. 



In the general case, however, we have three equations abo- 

 ve for the six unknowns determining the surge displacement, sinkage 

 and trim of the ACV during steady motion, namely 



5 ioo' W *ioo' W %o and '010 



The other three equations will be provided by the equations for the 

 moment which we shall now consider. 



Substituting for T on the left-hand side of (6-7) from (6-5) 

 and equating terms of the same order given by (5-6) and (5-8) we 

 have the three equations : 



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