Pien and Lee 



M^y) = M^O) - V 5 (0) y 



m» (i,)(y - n)( ^ 3Q -x f 50+ , « 40 )d, (51) 

 o 



Let us proceed to derive the expressions for the torsion 

 moments T 2 and T 3 We assume that the twist center is loca- 



ted at the center of mass of the catamaran. The torque T 2 and T 3 

 are induced by out-of -phase hydrodynamic moments of yaw and pitch 

 acting on the two hulls of a catamaran. From the equilibrium law, 

 each hull should exercise equal magnitude but opposite torque load 

 on the cross-deck structure. Thus, we can determine T-> and T 3 

 by considering the yaw and pitch moment contributed by dynamic 

 effects on one hull. 



Utilizing the expressions derived earlier, we can write 

 T z = -j- I ' l x f (x) dx - / xdx p n 2 dl (52) 



and 



T 3 = ~ I *T 3 Wd« + I xdx pn 3 



50 



d* 

 ) dx (53) 



where - X . and JL are the locations of the aft and fore perpendicu- 

 lars; f 2 (x) and fj (x) are given by Equations (25) and (26), respecti- 

 vely; c R is the contour integral of a half cross section; p the 

 hydrodynamic pressure and the expressions for Jr p njd^. for 

 i = 2, 3 are given by Equation (44); and b (x) is the half beam of the 

 cross section at x. 



1.4- Results and Discussion. 



Numerical results from the theory developed in the preceed- 

 ing sections are compared with available experimental results. The 

 presentation of the results is made in the following order. The first 

 part deals with the two-dimensional hydrodynamic coefficients. The 

 second part deals with the three-dimensional hydrodynamic coeffi- 

 cients. The third part deals with the heave and pitch motions of three 

 catamaran models. Two of the models are of conventional-catamaran 

 configuration and the other one is of a SWATHS configuration* Thedes 

 cription of these three catamarans is given in Table 2 and figure 5 



488 



