Motion and Resistance of a Low-Waterplane Catamaran 



In the previously given equations, M is the mass of the catamaran; 

 I, .15 and I & are mass moments of inertia about the Ox, Oy 

 and Oz axes, respectively; z„ is the z coordinate of the center 

 of mass; and the restoring constants C33 , C35 , C55 , C53 and C44 

 are given by 



C 33 = " gA w 



C J5 = C 53 = - PgM 



w 



C__ = M (GM) 

 55 g 'e 



C 44 = ^8V ( GM) t 



Here A is the waterplane area at the mean position of the catama- 

 ran, M the area moment of the waterplane about the Oy axis, 

 (GM) e and (GM) t the restoring moment arm in pitch and roll respec- 

 tively. 



The major task in solving the equations of motion shown 

 previously lies in determining the hydrodynamic coefficients, A jk 

 B jk and Fj ,e) ; i, k = 2, 3, . . . , 6. They are functions of hull 

 geometry, wave frequency, and forward speed. The method of deter- 

 mining these coefficients is described in Appendix A, and the results 

 are presented in Table 1. The lowercase letters a ik and b ik shown 

 in Table 1 are sectional added mass and damping, and U is the for- 

 ward velocity. These are obtained by solving two-dimensional boun- 

 dary-value problems for velocity potentials representing the fluid 

 motion generated by an oscillation of infinitely long twin cylinders. 

 The cylinders are semisubmerged horizontally, have a certain sepa- 

 ration distance between, and are rigidly connected together from 

 above. The twin cylinders have a uniform cross section which is 

 identical to the cross section at any given location along the length 

 of the catamaran. 



The method of distribution of pulsating sources along the 

 sumberged contours of the cylinders is employed in solving the velo- 

 city potential; see Lee, Jones, and Bedel (1971). The method used is 

 similar to the one developed by Frank (1967) for single cylinders. 



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