Lehman and Kaplan 



I 

 where R^ is the effective radius of the propeller, assumed to be 0.7R, and the 

 angle ap = tan"^ (VAJ). 



With the definition >v. 



p I 'p^ P'^ p 



'- c 



and making the substitution Xp = c cos e , the vorticity distribution is 



'a ( 1 - COS 6) 



7 = 2V 

 ^p p 



+ 2Aj sin 6 



(2) 



where 



Vp = U COS ap + V sin ctp = v^U^ + V^ . 



This choice of steady propeller vorticity distribution includes the effect of angle 

 of attack on a flat plate airfoil (represented by the A^ term) and a circular arc 

 camber (represented by the A^ term). 



Using the definition a- - 2c/d , which is the blade solidity, where the pro- 

 peller blade spacing d = 277R^/N, with N the number of propeller blades, the com- 

 plex velocity induced at the appendage is 



dw^ 



dZ 



11 ^^ r 



_ P V G^ e 



where v^ - Nw and 



^ _ a-nl -<T77m[(Xo/c)-i sin a ^] /gx 



in which 



- la . 



u- .T -Tx ^1 (2ie 



where the argument of the Bessel functions is 



-i[(T7/2)-a ] 

 CTTTme ^ 



The velocity field induced by the propeller blade thickness can be accounted 

 for by a source distribution along the chord line of each propeller blade, given by 



V 

 M(Xp) = -f f'(Xp) , 



210 



