P is the pressure on the foil, and V„ is the local velocity. In designing a foil, 

 we can use the local velocity obtained during preliminary design 



2., ,2 1/2 



V £ = {(V+u a ) +(ra*u e r) (24) 



where V = V (1-w) 

 a s 



w = wake fraction 



0) = angular speed 

 When the supercavitating propeller, advancing with velocity V , is represented 

 by source and vortex distributions, the perturbation velocity component parallel to 

 the blade-reference surface can be written by a linear approximation of the Bernoulli 

 equation of flow, referring to a moving frame of reference (Appendix A), as 



(25) 



u m u m 



V 



T T 



_ £-i 



V V 



2 V 



on the pressure side of the blade, and 



m G T7 



^T + aT = 2v- (26) 



on the cavity, since 



G G r 

 U T+ " U T- = G 



G A. G 



u m . + u m = 2 u_ 

 T+ T- f 



(27) 



where u is the tangential velocity due to the vortex distribution at all points 

 except the point concerned; subscripts "plus" and "minus" indicate the values on the 



10 



