Cox 



Ap = p+ - p- , 

 Bp\ Bp^ Bp" (A5) 



iBn/ 3n Bn 



where n = n" , Eq. (A4) becomes 



From Eq. (A6) it is seen that (Bp/3n) and Ap are pressure source and doublet 

 strengths per unit area, respectively. Furthermore it is clear that the pressure 

 doublet strength is only nonzero on the blade surface s^. 



If the surface of a blade is considered to be composed of helical lines with 

 varying pitch in the r direction, the surface can be defined as 



Hence, 



where 



and 



?^Rk(r) = 



dS, = [r2 + R2x2 +(r0^>.^)2]i/2 d^^dr 



U(0 dk 



ojR '^ dr 



3 d RA. d 



r — - rd.Rk 



Bx ° ^ Br r B0^ 



d _ u 



'^"o [r2 + r2x2 + (re^R\^)2]'^' 



since the normal is defined in the n" direction. Thus, 



J \ r (x* - x) + Rkr* sin ^^ + Td^'Rk^{r - r* cos <J)q) 



\R$oi [^' + R'^' + (^^oR^r)']''' K3 



(A7) 



Now 9q = - cot, where d^ refers to axes fixed in space and d refers to a 

 rotating axes system fixed with respect to the propeller. Hence if Eq. (A3) is 

 applied to Eq. (A6) and time t is subsequently equated to zero, i.e., the time 

 at which the two axes systems are assumed to instantaneously coincide. 



952 



