APPENDIX A 

 Leading-Edge Cavity Thickness for a Given Cavity Length 



According to Reference 17 the solution for an finite-cavity cascade can be obtained by super- 

 position of the infinite cavity solution 



(Al) 



and the finite cavity correction 



u 2 -iv 2 (A2) 



That is, the solution is 



u - iv = u ( + u 2 -i(v t +v 2 ) (A3) 



The value at infinity downstream is represented as 



u, = a cos 7 C L /(4wK) 



v, = -(a 2 C M +asin7C M )/(47rK) (A4) 



where C L and C M represent the lift and moment coefficients, respectively, in the transformed plane; 



a is the transformation constant' 17 '; and K = (a 2 d cos 7)/(27r). 



The values at infinity downstream for the finite cavity correction are 



u =-i(a/2-u 3 ) ftan-' - C ° S . 7 -tan'' _Z£2iI_U _ U(ff/u _ u ) 

 2 7r 3 V aja-sin7 -a 3 a-sin7y ' 



i a. 2 a 2 - 2a. a sin 7 + 1 



v 2 = - 7- (a/2 - u 3 ) log ! = - V(a/2 - u 3 ) ( A5) 



277 a 3 2 a 2 + 2a 3 a sin 7 + 1 



where 



Uj = Uj +u 2 

 v 3 = v, + v 2 

 u 3 = v 3 tan 7 (A6) 



and a x and a 3 are the corresponding values of the upper and lower cavity lengths in the transformed 



plane. 



Therefore, C L /C M can be represented in terms of the given finite cavity parameters a, a,, and a 3 . 



17 



