and 



Lehman and Kaplan 



^1 = K^ 2^L '^■rr KL(mu,', m\) e' 



Y/ = -Im V„ 



Zi "^m* K^Cmw', m\) e 



where 



A. 



is the Theodorsen function, in which 



J(^) = Jo(^) - iJi(^) - ^ 



iNI 



-.' 



and 



C(cv') = 



K^(ioj') 



Ko(i^') + Ki(ia;') 



Forces also arise due to the induced flow field of the propeller interacting 

 with the source distribution representing the finite thickness appendage, where 

 the source distribution for that profile is given by 



M^Cx) 



U /s 



in which sg is the maximum thickness of the appendage and it is assumed that 

 the appendage profile is also parabolic. By application of Lagally's theorem (14) 

 the forces arising due to this interacting are represented by 



X, - iY, = 27TP 



J M(x) /- 



dW 

 dZ 



dx , 



where the total complex velocity induced at the appendage by the propeller is 

 given by Eq. (4). 



The nonsteady distribution of axially oriented dipoles induced within the ap- 

 pendage has a strength given by 



I ^0 



/^(x,t) = - -u(x,t) -2 



212 



