Super cavitating Propeller Theory 

 \.^e^ - 2rr* cos {B ^ a^) + r^ + r*2 ^ E^_ ^ a^ + 2F^_ j a + H^_ ^ , (B8) 



where . _ 



H^_j = r2 + r*2 - 2rr* cos (e^-i + a-^) + ^i'^^-i • 



The integral with an infinite upper limit can be dealt with in a similar manner 

 after transposing it into an infinite sum of integrals, each with limits and M . 

 This is reasonable because the terms involved soon become negligible as 9 

 increases. 



By applying Eq. (28) to Eq. (21), 



f M , 



dr 



= 1 m-i -'r,_j [r2 - 2rr* cos {9* - a^) + r*2 + ^.2^*2] 



M N r ■ • 



M N 



+ 



m= 1 n= 1 



/" 



'^ __dr 



Vi [>^-^{0-d*)^ - 2rr* cos {9 - 9* ^ a^) + r^ + r*^]*''^ 



The integral associated with B^ can be integrated to give 



f r r 2 - 2r r* cos (^*-cT ) + r*2 + \.20*2] + r - r* cos {9* - a^ 



In J — — 



U^^-1 - 2r^., r* cos (0*-a ) + r*^ + K.^9*^^ + r^_,- r* cos (^* - a^ ) J 



(B9) 



The simplification of the integral associated with C^^ is similar to that already 

 discussed for Ug(r*) . 



DISCUSSION 



V. F. Bavin 



Kryloff Ship Research Institute 

 Leningrad, U.S.S.R. 



The author has indeed done a most valuable job by deriving equations for 

 supercavitating propeller design theory which take into account the cavity thick- 

 ness effect. It is fully recognized now that this is the only possible way to get 

 the correct solution of the problem. I hope we will have the first numerical 

 results in the near future. 



957 



