excessive grid crowding on some portion of the hull (for instance note the 



trajectories on the bilge and and those at the load waterline near the 



stern) . For these reasons the coordinate system shown in Figure 2 for 



SSPA Model 720, which consists of the lines of constant 9 and their 



orthogonal trajectories of constant <j), was chosen in preference to the 



cross-section system. Recall from the section on Calculation of the 



Surface Coordinate System that the lines of constant 6 are defined by the 



surface representation Equations (23a, 23b). Thus, it is necessary to 



always first represent the ship hull by a surface equation of the type of 



Equation (23) in order to use the coordinate system of Figure 2, whereas 



the cross-section coordinate system does not require a prior analytical 



representation of the ship hull. However, the calculation of the ship 



surface Equation (23) for a typical ship hull such as the Swedish SSPA 



Model 720 requires only about one to one and a half minutes of CDC 6700 



computer execution time. This calculation of the surface Equation (23) 



(i.e., the matrix (A )) need only be done once and then it is available for 

 mn 



several other uses. Furthermore, the computer method used to calculate 



the matrix (A ) is an old one and several modifications of this method 

 mn 



are presently under development that are expected to reduce the compu- 

 tational time by a factor of about 100. Thus, the need to calculate the 

 surface representation of the Equation (23) type is not seen as a dis- 

 advantage of the (0,(}))-coordinate system. 



The Lucy Ashton double model boundary layer was computed using the 

 earlier slender body theory potential flow method because the first test 

 of the present calculation method was to check the complete crossflow 

 formulation. It was shown previously by von Kerczek that the slender 

 body theory gives fairly accurate values of the double-body pressure 

 distribution on the Lucy Ashton. 



The boundary layer calculation method of this report is implemented 

 in terms of the (6, (|)) -coordinate system but the computed boundary layer 

 results are given in terms of the streamline momentum thickness 9-, -i » dis- 

 placement thickness 6 , shape factor H, and the stream coefficient of skin 

 friction C . This is done to facilitate the comparison of the present 



28 



