Motion and Resistance of a Low-Watevplane Catamaran 



£.(.) = - " 2 m (■><«,« -3 {_„) (26; 



R 2 ■ ° 



/, 



R, • - Pg / b(s) ( { 3Q - s ( 50 )d= (27; 



! <, 



where m (s) is the sectional mass; z (s) is the vertical coordinate 

 of the sectional mass center; b (s) is the sectional beam at x = s; 

 - X.y is the x coordinate of the aft perpendicular of the ship; and 

 c (s) implies a contour integral in the counterlockwise direction 

 over the immersed portion of the section. The hydrodynamic pres- 

 sure p is obtained from the Bernoulli equation by 



6 



p = ,(i" i " &> < *! + * D ♦ lS 2 £ ko K » 



where ($),- is the velocity potential for the incoming waves; (J) q , 

 for the diffracted waves; and (J) k , for the motion-generated distur- 

 bance in the fluid; see Appendix A for a more detailed explanation 

 for these potentials. Employing procedures similar to those used 

 in deriving Equations (72) and (73) in Appendix A, we can show that 



ds pndl = P I ds / (ju> n. + 0. JL) (b 



dl 



- -^ /"(D f <t> di - P £{. /"ds (28) 



c(s) ,/ c(s) 



for i = 2, 3 



where Qj n , for instance, means — and the last term corresponds 

 to the last term of Equation (68) . 



If we let 



V s I 



rvc 



is I <k (t>. df=o> A., (x) + jw B, (x) (29) 



k in lk ik 



'C(S) 

 for i = 2, 3, and substitute this expression into Equation (28), we get 



481 



