Motion and Resistance of a Low-Waterplane Catamaran 



Integration of the pressure over the wetted surface of a 

 catamaran should yield the hydrodynamic forces and moments. Thus, 

 we have 



' 1 w -J r p»i«- 



-jjn.( jU + "£> <V V |£ 2 {ko 4> k ) d. 



s o 

 for i = 2, 3, . . . , 6, where n2 and n^ are respectively the y and z 



components of the unit normal vector and n^ = yn3 - zn2, 115 - -xn3 , 



n 6 = xn 2 . 



We can further decompose the hydrodynamic force into two 

 parts i.e. 



F (H) =F (e) + F (m) 

 i i i 



where 



(e) 

 F. = wave-excited force 



i 



= P n. (j co + U-A) (4> i + <> D ) ds (66) 



s o 



_ (m) . . , /. 



F = motion-excited force 



l 



- "g fko J^U- + «-&> * k ^ (67) 



s o 

 Applying the results of Ogilvie and Tuck (1969) to the simpli- 

 fied case in this work, we can show for any differentiable scalar 

 function (f) with the usage of Kronecker's delta function that 



and 



// 



n i * x d.= // (n 5 . 5 -n 2 s .J *ds -// n. <M (68) 



CM 

 where S is the immersed hull surface forward of the cross section 



at x, and c(x) is the line integral along the contour of the cross 



section. Utilization of Equation (68) in Equation (66) yields 



529 



