where A = waterplane area 

 wp 



M = moment 

 wp 



X = longitudinal center of gravity 



X = longitudinal center of flotation 



I = moment of inertia of A with respect to the longitudinal 

 center of flotation 



KG = distance between the keel and vertical center of gravity 



KB = distance between the keel and vertical center of buoyancy 



A = displacement of the ship 



With substitution of F„ = F.^ e and F = Fj.,. e , 

 expressed as complex algebraic equations: 



Equation (96) can be 



- CO (M+A^^) + "^33 " ^^^33 



- ^^ S3 + S3 - i^S3 



- (,\^ + C33 - 10.633 



Od (I+A ) + C - iojB 



33 



55 



(98) 



RELATION OF TWO-DIMENSIONAL SOURCE STRENGTHS BETWEEN THE FRANK CLOSE-FIT 

 METHOD AND MULTIPOLE EXPANSION METHOD 



The potential function given in Equation (50) is the solution obtained by the 

 multipole expansion method. If we apply the Frank close-fit method to solve the 

 two-dimensional potential, we should have some relationship between the two methods. 

 That means we should have a correspondence between the sources located at the origin 

 in the multipole expansion method and those around the ship's contour in the Frank 

 close-fit method. 



Because the radiation condition states that far away from the disturbance, the 

 wave is outgoing, we should have the same potential from these two methods at a 

 distance far from the body. For the multipole expansion method, the potential of 

 the outgoing wave is given by Equation (34) 



Kz+iK I y I 



(99) 



where a is the source strength at the origin. 



25 



