N M 

 y = y(s,0) = X^ /^\n ^"''^ sin(3-2n)e 

 n=l in=l 



(23b) 



and, in the vector form, 



r = r(s,e) = x(s,e)i + y(s,e)j + sk 



(24) 



where r is the vector from the origin of the (x,y,s) coordinate system to a 

 point on the hull surface, and (i>j>k) are unit tangent vectors to the 

 (x,y,s) coordinates, respectively. 



The surface coordinate lines 6 = constant, run along the length of the 

 hull surface, and the coordinate lines (J) = constant, are nearly parallel to 

 the hull cross-sections. The arclength increments along the (}) and 9 

 coordinates are d£, and d£n, respectively, and are given by 



1/2 

 d£, = (dr-dr)^'^ ^ ^ 

 (b - - H=constant 



= [(i 



-,1/2 



8s / \ ds 



ds 



(25a) 



and 



d£„ = (dr-dr) 



1/2 

 d)=constant 



jx _3x d_s 

 36 8s d0 



' 19 9s de 



ds 



1/2 



(25b) 



where (ds/d9| ,) denotes the evaluation of the derivative ds/d9 along the 

 d) = constant line. 



15 



