In previous investigations, the thrust deduction has been derived by 

 applying the Lagally steady-flow theorem to the propeller sink-disk singu- 

 larities. In the present formulation, it is more convenient to consider 

 the body flow directly. Thus, time-averaged propeller induced velocities 

 and modified hull pressure distributions are computed, including appropriate 

 corrections to the body singularity strengths. The force is then calculated 

 by integrating the pressure and also by applying Lagally' s theorem to the 

 body singularities. It is assumed, as before, that for a given representa- 

 tion of the propeller, the added hull resistance arises entirely from the 

 reduction in afterbody pressure and that this pressure distribution may be 

 derived solely from potential flow considerations. Although it is recog- 

 nized that the boundary layer at the stern is relatively thick, the poten- 

 tial flow formulation has been widely accepted on the basis of agreement 

 between predicted and measured thrust deduction. Recently, wind-tunnel 



experiments were conducted on streamlined bodies of revolution with and 



9 

 without a propeller in operation. The results show that while the theory 



cannot satisfactorily predict the absolute pressure distributions near the 

 stern, the difference in pressure due to the action of the propeller is 

 predicted remarkably well. It was also found that increases in wall shear 

 stress contribute less than 5 percent of the integrated pressure force. 

 For these reasons, it appears that the Douglas-Neumann potential-flow calcu- 

 lation is a sound approach, at least for nonseparating hull forms. Moreover, 

 the calculation of the detailed pressure distribution will serve as a 

 necessary first step in future treatments of the viscous flow problem. 



In this report, the theoretical basis and numerical techniques for 

 predicting the thrust deduction are presented. The analysis is restricted 

 to deeply submerged bodies, for which the hull potential flow calculation 

 is only briefly reviewed, being extensively documented in the cited 

 literature. (The theory can, in principle, be extended to surface ship 

 applications; the free-surface would be approximately represented by 



Huang, T. et al., "Propeller/Stern/Boundary-Layer Interaction on 

 Axisymmetric Bodies: Theory and Experiment," DTNSRDC Report 76-0113 

 (Dec 1976). 



