reflecting the hull and propeller (Images) in the waterline plane.) The 

 propeller representation and field point velocity calculations are dis- 

 cussed in some detail. The further analysis considers the determination of 

 the modified hull pressure and solution for the interaction force by 

 pressure integration and by application of Lagally's theorem. 



Comparisons between theoretical and experimental thrust deduction are 

 given for deeply submerged stern propeller body-of-revolution configura- 

 tions both with and without stern appendages. These configurations were 

 chosen for initial calculations because the body geometry characteristics 

 afford easier computation. However, it is noted that in application to 

 submarines and torpedoes, the thrust deduction is of great practical im- 

 portance in selecting propeller characteristics (e.g., diameter) for maxi- 

 mum propulsive efficiency. In the examples presented, it is shown that 

 stern appendages develop as much as 25 percent of the thrust deduction. 

 The relative contributions of propeller loading and thickness are examined 

 and compared with the classical lifting-line sink-disk results. It is 

 found that lifting-surface effects reduce the thrust deduction by 10 to 20 

 percent. Calculations for a series of four rakes illustrate the significant 

 (over 50 percent) attenuation of the interaction force as rake is increased. 

 Based on these examples, it is concluded that the theory provides a useful 

 technique for both the analysis of a given design and for parametric 

 studies of higher efficiency propeller-hull configurations. 



PROPELLER-HULL INTERACTION IN POTENTIAL FLOW 



SINGULARITIES REPRESENTING THE HULL AND APPENDAGES 



The propeller-hull interaction analysis rests on the computation of 

 the potential flow about the hull in the presence of the propeller. A 

 great deal of effort has been devoted in the past to developing accurate 

 and computationally efficient techniques for calculating the flow about 



