arbitrary three-dimensional bodies. In the method of Hess and Smith, ' 

 the body surface is approximated by planar quadrilateral elements and the 



solution is derived in terms of simple source distributions. A recently 



12 

 developed computer code based on this approach is employed in the present 



work. Briefly, the formulation is as follows. 



The body is assumed to be deeply submerged and advancing at a constant 

 velocity, V , in an incompressible, inviscid fluid. By considering only the 

 time-averaged propeller disturbance field, the flow is steady relative to a 

 Cartesian coordinate system r = (x,y,z) advancing with the body. Outside the 

 propeller blade row and slipstream the flow is irrotational. Thus, a velo- 

 city potential (t)(r) exists such that V(^) = V(})(r) and 



V^ (!)(r) = (1) 



where r is outside the body and the propeller slipstream. The boundary 

 conditions are that the velocity must be tangent to the body surface, 



n(rg) • V(|>(rg) = (2) 



and approach the free stream value at a large distance from the body- 

 propeller system 



V(J>(r) -> V^, as |r| -> - (3) 



A solution for (|>(r) which satisfies equations (1) and (3) may be written in 



ibutic 



terms of a surface source distribution, a(r ), as 



h 1^ - ^bI 



Hess, J.L. and A.M.O. Smith, "Calculation of Nonlifting Potential Flow 

 About Arbitrary Three-Dimensional Bodies," Journal of Ship Research (Sep 

 1964). 



Hess, J.L. and A.M.O. Smith, "Calculation of Potential Flow About Arbi- 

 trary Bodies," Pergamon Press, Progress in Aeronautical Sciences , Vol. 8 

 (1966). 



12 



Dawson, C.W. and J.S. Dean, "The XYZ Potential Flow Program," NSRDC 



Report 3892 (Jun 1972). 



