Bavin, Vashkevich, and Miniovich 



z-l 1 



j=0 -^0 ^ 



■r X + r sin \y - c - ] 



dr' , 



x2+r2+r'2-2rr' cos [j - 9 - — j 



(4) 



where \^ = -nV^/co-R^ (advance ratio) and r = r/{2Y'^/pco-R^) . 



The blade frequency content of the pressure can be determined (1) by making 

 use of the relation 



^ Vrr „=o 



where Eq = 1 and e„ = 2; Qn,-(i/2)(z) is the Legendre function of the second 

 kind, of order m - (1/2) ; and z = (x2 + r2 + r ' 2)/2rr' . 



The dimensionless circulation may be written in the form 



00 



f(r',5) = V [A^(r') cos nd + B^( r ' ) sin 6] . 



n=0 



Then for the nondimensional pressure after lengthy manipulations one obtains 



00 a> 



Pl 



4tt VT 



m=0 n=0 



y y e jf^^iMsn-ii^jsin [(m+n) e-my] 



+ Icos [(m + n) d - my] 



where 



i\ N^ xRB 



p mn mn i . r . , ^ i 



— + ]sin L(m- n) y- myj 



/ m^pNg^ xkM 



I + Jcos L(m- n) fc^ - myJ 



(5) 



r' V'-')^,r.(l/2)(^) 



dr' , 



