Landweber 



Finally, to determine the viscous drag, an empirical formula 

 relating the shape parameter H^ with the outer velocity U^ at the 

 tail (designated by the subscript t) and the velocity of the uniform 

 streann at infinity, U^j, 



is assumed, as well as that the equations of thin boundary-layer theory 

 may be integrated to the very tail, a dubious assumption. Since 

 this empirical relation is unlikely to be universally valid, the fore- 

 going procedure, which is that usually employed to compute viscous 

 drag, emphasizes the need for additional research on the character- 

 istics of the thick boundary layer near the stern. 



An approximate method for computing the boundary layer on 

 a ship form at a nonzero Froude nunnber has been developed and 

 applied by Webster and Huang [ 3] . Guilloton's theory of ship wave 

 resistance [12] as presented by Korvln-Kroukovsky [ 13] furnishes 

 tables from which the outer flow can be determined along three 

 streamlines on the hull. The boundary layer along these streamlines 

 Is then computed by a small cross -flow method employing streamline 

 coordinates, due to Cooke [ 14] . This method has been applied to 

 two Serles-60 forms of 0.60 and 0.80 block coefficients, over a range 

 of Froude and Reynolds numbers. Although the assumption of small 

 cross-flow is basic to the method. It was nevertheless applied to 

 estimate the locations of separation points on these streamlines on 

 the basis of Cooke's criterion that separation occurs when the cross- 

 flow Is 90°. 



Smith's comparative study of five different methods of com- 

 puting a turbulent three-dimensional boundary [ 11] indicates that a 

 method which does not assume small cross-flow, and which employs 

 a three-dlnnenslonal extension of Head's entralnment hypothesis [15] 

 for the variation of the streamwlse shape parameter gives better 

 predictions of the cross-flow than methods which assume small cross- 

 flow, and a constant value of the shape parameter. All five methods, 

 however, yielded values of the momentum thickness in poor agree- 

 ment with experimental results. Smith conjectures that this failure 

 Is probably due to the adoption of empirical relations for the shear 

 stress frorrj two-dimensional theory. 



These results of Smith Indicate that the Webster-Huang pro- 

 cedure for calculating separation points could be Innproved considerably 

 by the adoption of the best of the five methods. None of the methods, 

 however, can be used reliably to calculate the viscous drag. 



Lin and Hall [ 2] also employ streamline coordinates and the 

 small cross -flow assumption In computing the boundary layer on a 

 ship form. As In the method of Cooke [ 14] , the momentum Integral 



452 



