ABSTRACT 



An analytical method is presented for predicting the added 

 resistance (thrust deduction) arising from propeller-hull in- 

 teraction. The theory is formulated in terms of the potential 

 flow about the hull and appendages which are represented by 

 surface singularity distributions. The influence of the pro- 

 peller is derived from lifting-surface theory including the 

 effects of blade number, thickness, skew, rake, and radial and 

 chordwise load distribution. In order to determine the inter- 

 action force, propeller-induced velocities and the modified hull 

 pressure distribution are computed with appropriate corrections 

 to the hull singularities. The axial force is then derived by 

 integration of the pressure on the hull and also by application 

 of the steady-flow Lagally theorem. 



The usefulness of this technique is illustrated by its appli- 

 cation to several stern propeller-body-of-revolution configura- 

 tions. It is shown that stern appendages contribute up to 25 

 percent of the total thrust deduction. The relative contribu- 

 tions of propeller loading and thickness are examined. It is 

 found that the lifting-surface representation predicts 10 to 20 

 percent lower thrust deduction than the classical lifting-line 

 (sink disk) approximation. Calculations for a series of four 

 raked propellers illustrate the significant (over 50 percent) 

 attenuation of the interaction force as rake is increased. It 

 is concluded that the method is useful for both the analysis of 

 a given design and for parametric investigations of higher 

 efficiency propeller-afterbody configurations. The method may 

 also be extended to treat contrarotating and ducted propellers. 



ADMINISTRATIVE INFORMATION 

 This work was performed under the in-house independent research and 

 exploratory development program of the David W. Taylor Naval Ship Research 

 and Development Center (DTNSRDC) (Work Unit No. 1552-119) and the High 

 Speed Submarine Direct Laboratory Funding Program (Work Unit No. 1520-004 

 and 1500-200) , 



INTRODUCTION 

 The interaction force arising from propellers operating in close proxi- 

 mity to the ship's stern is a familiar concept to naval architects. The 

 propeller accelerates the flow over the hull afterbody. For sufficiently 

 fine ship forms where flow separation effects are minimal, the velocity 

 increase and accompanying reduction in pressure increases the hull pressure 

 drag. The higher velocity also increases the wall shear stress, and hence. 



