Motion and Resistance of a Low-Waterplane Catamaran 



APPENDIX A - DETERMINATION OF HYDRODYNAMIC COEFFI- 

 CIENTS. 



If we assume that the fluid surrounding a catamaran has 

 irrotational motion, we can introduce a velocity potential <j) (x, y, z,t) 

 in the fluid region. The velocity potential should satisfy, in addition 

 to the Laplace equation, the following boundary conditions 



(-^" U ^) 2 4 ( x > Y. z > t) + g <j> z = on z = (57) 



where g is the gravitational acceleration, 



V<3> . n = V on S (58) 



1 — no 



where n is the unit normal vector on the body surface pointing into 

 the body, V n is the normal component of the velocity of the body 

 surface, and S is the mean position of the body, 



(j) (x, y, - <*> , t) = (59) 



z 



2 2 ± 



and a physically appropriate far-field condition for (x + y )2 — "°° 



to make the problem well posed. 



Assuming the flow disturbance to be a small perturbation 

 from uniform flow, we can express (p in the form 



$ = - Ux + (J) (x, y, z) + (J) (x, y, z) e " J W t (60) 



where U is the forward velocity of the ship; <£> s is the steady 

 potential, representing the wavemaking disturbance due to the for- 

 ward velocity; and (}) =CPoc + J ^os * s ^ e P otent i a l associated 

 with the oscillatory fluid disturbance. We can further divide (f> 

 into three distinct origins of the oscillatory fluid disturbance as 



*o = +1 + *D + *li < 61 > 



The incoming wave potential, <£) is given by 



jl Ac K (z + j x cos0 - j y sin/3 ) 



* = _^_ e ° (62) 



1 w 



where /? is the wave-heading angle with respect to the positive 



527 



