Motion and Resistance of a Low-Wat erp lane Catamaran 



" Z m' ( * OA - x * + y- * J (38) 



2 



M' = - co m' 

 1 



f 3 ■ -■ «W « 30 " X *50 + ?' *40 



''{ ^30 -^-V *2()} 



- " 2 [ r + m' I (z- - h Q ) 2 + (y 1 ) 2 }] (39) 



where m' is the mass of the half section, I'« is the mass moment 

 of inertia of roll about the center of mass of the half cross section, 

 and (y 1 , z"' ) is the coordinate of the mass center of the half section. 

 The restoring forces and moment are given by 



RJ = -2p gab( f 30 -x « 50 ). PgS' A GM' (^ (4Q) 



where b and a are as shown in figure 2, S'^ is one-half of the 

 immersed total sectional area, and GM 1 is the transverse metacen- 

 tric height from the mass center. 



R^ = (41) 



R' = - 2oga( « 30 -x « 5Q + b i 40 ) (42) 



The pressure p at any point on the immersed contour of the 

 right half section is given by 



p= p(jco + U^-H<() T+ 6 + £ * <b) (43) 



dx' T I T D ^ 2 s ko 



Then 



/p n. di = i P co / (J> T n. dJt + j 9 co / (t>_n 

 °1 ll J c D 



+ j'» E * ko \ n i dl 



(44) 



'c 



for i = 2,3,4, where n2 and n^ are respectively the y and z compo 

 nents of the unit normal vector on the body surface and n^ = yn-j-z^. 



Note that we can no longer apply Haskind's relation (1957) to 

 express the diffracted wave force for a half cross section in terms of 

 (]) t and (h^ as shown in Appendix A. This means that we 



4 To be strictly true, the application of Haskind's relation in strip 

 approximation is incorrect. Faltinsen (1971) has shown a three-dimen- 

 sional diffraction effect. 



485 



