SUPERCAVITATING PROPELLER THEORY- 

 THE DERIVATION OF INDUCED VELOCITY 



Geoffrey G. Cox 

 Naval Ship Research and Development Center 



Washington, D.C. . •■ - . 



ABSTRACT _ ' ■ ' 



The determination of induced velocity components is the central prob- 

 lem of propeller design theory. Induced velocity equations — together 

 with a pressure equation — are derived for a lifting- surface representa- 

 tion of a supercavitating propeller, where blade loading is represented 

 by bound and free vorticity, and blade cavities by pressure-source dis- 

 tributions. Particular attention is paid to a tentative lifting- line model 

 analogous to previous development of subcavitating propeller design 

 theory. 



1. INTRODUCTION 



The increasing availability of digital computers during recent years has 

 provided the necessary stimulus to improve propeller design methods. It is 

 now relatively straightforward to perform the extensive numerical calculations 

 based upon adequate mathematical models, to represent the complicated hydro- 

 dynamic action of subcavitating propellers. Although further efforts continue 

 to be necessary with regard to refinement and improved accuracy of numerical 

 calculation procedures, contemporary design theories for the propulsion per- 

 formance of light to moderately loaded subcavitating propellers in inviscid flow 

 can be considered satisfactory. The same situation however, does not apply to 

 the case of supercavitating propeller design theory. Tulin, in an excellent 

 paper presented at the Fourth ONR Symposium on Naval Hydrodynamics [1] 

 drew attention to the work carried out in several countries, which led to an 

 understanding of the operating characteristics and mechanism of operation for 

 supercavitating propellers. He emphasized that the effects of the blade cavities 

 must be recognized at all stages of the design process. Prior to this time, pub- 

 lished design methods [2,3j had ~ paraphrasing Tulin — "essentially grafted two- 

 dimensional supercavitating section theory or experimental data onto subcavi- 

 tating design theory." 



Recently, English formulated a supercavitating propeller theory [4], based 

 on an extension of Goldstein's work for a subcavitating finite-bladed propeller 

 [5j, and modified the boundary conditions to allow for the effect of the cavities. 

 Also Malavard and Sulmont devised a rheoelectric analogy method for perform- 

 ing supercavitating propeller design calculations [6j. 



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