Cox 



coefficient c^(t*), local cavitation number af , and operating angle of attack 

 (if any). If theoretical estimates are used, the work of Parkin [13] may prove 

 especially convenient for estimation of Cp(r*)p. 



Finally, having decided the chordwise distribution of bound circulation 

 r(r,(9), the lifting- surface induced velocity components can be obtained from 

 Eqs. (4), (5), and (7) of Sec. 2 (thus permitting determination of blade pressure 

 side shape). 



CONCLUSIONS 



1. Lifting- surface and lifting- line equations have been derived which 

 properly account for cavity interference effects. It should be noted that for 

 s(r,0) = 0, i.e., no cavities, the equations revert to those for the subcavitating 

 case, where blade thickness effects are neglected. 



2. Although the derived equations have been nondimensionalized on the 

 basis of uniform inflow to the propeller, only straightforward modifications 

 are necessary to account for radially varying inflow. 



3. The proposed lifting- line model is regarded as tentative and subject to 

 modification, until exploratory calculations have been carried out. In particu- 

 lar, it will be necessary to ascertain the sensitivity of the induced velocity com- 

 ponents to assumed cavity lengths, in order to formulate adequate cavity length 

 criteria. These criteria will obviously be dependent on the design choice made 

 about the nature of the blade section cavity, i.e., shock-free entry, with pre- 

 scribed cavity thickness condition, or prescribed angle of attack. 



4. Supercavitating lifting-line theory for the case of constant hydrodynamic 

 pitch ttXj, indicates dependency between axial and tangential induced velocity 

 components. When the free- stream cavitation number is zero, this dependency 

 is equivalent to that for the subcavitating case, i.e., the so-called normality 

 condition. 



ACKNOWLEDGMENTS 



Appreciation is expressed to the Hydrofoil Development Project Office 

 and the Hydromechanics Laboratory of the Naval Ship Research and Develop- 

 ment Center for encouragement in the preparation of this paper. Thanks are 

 due to Dr. W. B. Morgan, who reviewed the paper and made many helpful sug- 

 gestions. Grateful thanks are due to Shirley Childers, Mary F. Gotthardt, 

 and Terry Gilleland, for the painstaking efforts in the preparation of the 

 manuscript. 



NOTATION 



Unknown coefficients 



944 



