Supercavitating Propeller Theory 



Q I i .^E r ."^ [x* - \.(T + 0*)] dr 



1=1 I '■'h '^L 



Q 1 '^E P< 



R. 



Mi'2 d^dr 





(2) 



1 e^ 



2 X X 2 N 1 ' 2 



1 ^ 



CO 



-J 



r ( r - r* cos \p) dr 



d^dr 



and 





q=l 



dr 



'e-e* K^ 



1^1/2 d^dr 



1 0-, 



I / 7(r,0)(r2 + X.2)i/2 



[( r* - r cos (^)dk-^ - ( X* - ^X. ) cos $] 



d^dr 



(3) 



1 (9t 



/ / 7(r,^)(r2 + \.2) 



2xX 2x1/2 



3r J 



{X.(r* - r cos .^) + [x* - >y^(T + 9*)] r sin v^} dr 



d^dr 



where 



R^ = [{x* -\.(T + 6**)}^ - 2rr* cos + r^ + r*2]i/2 ^ 

 R^ = [(X* -k.d)^ - 2rr* cos O + r^ + r*^]^''^ , 



and 0l('')j ^t(^)j ^'^'^ ^e('") define the blade leading edge, trailing edge, and 

 cavity, respectively. 



In Eqs. (2) and (3) the three contributions to the induced velocity compo- 

 nents can be recognized as due to pressure sources, bound and free vorticity, 

 respectively, i.e.. 



933 



