crossflow velocity profiles. It is most often claimed by these critics 

 that an accurate representation of the boundary layer crossflow profile is 

 required for the prediction of longitudinal bilge vortices. Large-scale 

 longitudinal bilge vortices arise due to a complicated form of three- 

 dimensional separation; the vortex flow itself being the separated flow. 

 Thus, one cannot expect to be able to compute the bilge vortex flow, even 

 by the most sophisticated boundary layer methods, whether integral or 

 differential. Presently, boundary layer theory can be used only to calcu- 

 late the flow up to separation. Recently developed momentum- integral 

 methods for two-dimensional and axisymmetric boundary layers (see 

 Green et al. ) are as accurate as, yet considerably more economical than, 

 differential methods. There seems to be no reason to believe that similar 

 improvements in three-dimensional momentum- integral methods cannot be found. 



Present models of the boundary layer crossflow are primitive and 

 further experimental data and research can be expected to uncover a simple 

 crossflow velocity profile family that is adequate for calculation methods. 

 For this reason it was thought desirable to make the technical improvements 

 mentioned above in the von Kerczek method so as to accommodate easily 

 detailed improvements in the crossflow model that may come about later. 

 However, the modified surface coordinate system and the incorporation of 

 the exact double model potential flow calculations (in lieu of the slender 

 body theory potential flow calculation method) are of independent value and 

 can be used with any other boundary layer calculation method. The surface 

 coordinate system for the boundary layer calculations developed in this 

 report has some advantages over the coordinate systems recommended by 

 others (see, for example, Cebeci et al. and Miloh and Patel ). The surface 

 coordinate system used in this report is very similar to the one used by 



Cebeci et al. but it does not have the complication of being nonorthogonal. 



/I 

 The present surface coordinate system is superior to the Miloh and Patel 



coordinate system because it provides a better coordinate net coverage of 



the hull surface for uniform spacing of the coordinate parameters. 



This report is divided into six sections including the introduction. 



The second section describes the formulation of the boundary layer 



