The geodesic curvature terms K and K are defined, respectively, by 



de. 



% = ^ ' dT (^2a) 



de 

 • 0^ (32b) 



The derivatives in Equations (32a, 32b) can be evaluated by converting them 

 to derivatives with respect to s and using Equations (25a, 25b), 

 respectively. 



Miloh and Patel recommended the use of the orthogonal surface 

 coordinate system that consists of the cross-section curves and their 

 orthogonal trajectories on the hull surface. In terms of the surface 

 Equation (23) the cross-section curves are given by s = constant. Thus, 

 if e, in this case, is the unit tangent vector to the cross-section profile, 

 the orthogonal trajectories of the cross-sections can be computed by inte- 

 grating the differential equation 



e • dr = (33) 



which, in expanded form, and making use of Equation (29) , reads 



9r 



(34) 



de_ 



ds 



Examples of hull surface coordinate grids for the (<p,Q) system 

 described earlier and the cross-section system of Equation (34) are given 

 in the section on Computational Results and Discussion. 



17 



