result is the boundary layer on the Lucy Ashton model for which experi- 



20 

 mental boundary layer data are given by Joubert and Matheson and which 



von Kerczek computed using the small crossflow approximation. The second 

 sample computational result described below is the boundary layer develop- 

 ment on the Swedish SSPA Model 720 for which boundary layer experimental 



21 

 data and calculations are provided by Larsson. 



It is first necessary to describe some details of the calculation of 

 the surface coordinate system before embarking on a description of the 

 results of the boundary layer calculation. There are many different surface 

 coordinate systems that one can use for three-dimensional boundary layer 

 calculation methods. The most prevalent coordinate systems used for ship 

 boundary layers are the streamline coordinate system and the coordinate 

 system made up of the cross-sectional curves and their orthogonal tra- 

 jectories on the hull surface; henceforth referred to simply as the cross- 

 section system. The streamline coordinate system has the advantage of 

 yielding the simplest form of the boundary layer equations, but it may be 

 difficult and costly to generate this system when flows about a ship hull 

 at nonzero Froude number are considered. Thus it is worthwhile to consider 

 coordinate systems that only depend on the ship hull geometry and not on 

 the inviscid flow. 



Figure 1 shows a sample of the cross-section coordinate system recom- 

 mended by Miloh and Patel on the Swedish SSPA Model 720. The calculation 

 of the network of coordinate lines shown in Figure 1 is described in the 

 previous section of this report. Calculation of the Surface Coordinate 

 System and Potential Flow. The main feature of the cross-sectional co- 

 ordinate system that has been found to be objectionable is that the length- 

 wise running coordinate lines seem to diverge on certain portions of the 

 hull (at keel near the bow and stern) where the opposite, i.e., convergence 

 of these lines, is desirable. Another, minor, annoyance of this coordinate 

 system is that it is difficult to find the set of starting values at any 

 particular station for the coordinate lines along the length (the orthogonal 

 trajectories of the cross-sections) that will result in a suitable surface 

 coordinate grid. Such a grid should not have large grid intervals or 



26 



