Supercavitating Propeller Theory 



(a) Thrust loading coefficient Cj (or power coefficient Cp), advance 

 ratio k, free- stream cavitation number cr, and number of blades Q are known. 



(b) The design conditions for the propeller are such that it can operate 

 effectively as a supercavitating propeller. 



In an actual theoretical design procedure, it is necessary to solve the Eqs. 

 (12) or (13) and (14) of Sec. 3 for prescribed values of induced advance ratio k^ 

 to determine the bound circulation r (r*) and hence lift coefficient CL(r*), using 



CrCr*) 



c(r*) 277r(r*) cos /3.(r*) 



(31) 



where cos /3.^{v*) = r*/(r*2 + \.2)i/2 andc(r*)/D are assumed known. Once 

 drag-to-lift ratios e(r*) have been assessed, it is possible to calculate the 

 thrust loading coefficient Cj, or power coefficient Cp, from 



4Q 



1 



r(r*) 



- + u,(r*) 



L k 



Te(r*) 



(32) 



4Q 



1 



J 



r*r(r*) [1 + u rr*)] 



1 + — e (r*) 

 k. 



dr* 



(33) 



see Fig. 1. 



An iteration or interpolation process is necessary to meet the desired de- 

 sign value of Cy or Cp. Once this has been achieved, it is possible to estimate 

 propeller efficiency v from 



(34) 



For the purposes of design it appears easier to account for section cavity 

 pressure-drag coefficient Cj)(r*)p along with viscous drag coefficient Ci3(r*)f, 

 i.e.. 



CpCr*) = CpCr*) + CD(r*)f 



(35) 



when considering section drag-to- lift ratios e(r*) = CD(r*)/cL(r*). Hence, both 

 drag contributions are accounted for on a strip-theory basis when determining 

 thrust loading coefficient c^ and power coefficient Cp. Hence, c^{t*) is ob- 

 tained from experimental or theoretical two-dimensional data. This data, 

 especially for cavity pressure drag, should conform as closely as possible to 

 the propeller-blade- section design details such as chordwise loading, lift 



943 



