where 



Y*(r,V) = Y (r,«^) V, < ¥> < <ft 

 S S Jj, tc 



k 



= y^(r,^)-.f^ '^>\ 



(32) 



The induced velocity due to a distribution of sources over the blade 

 surfaces is given by 



<;<' (p) 



^ 1 f^ n ? r^ 1 



u'(x,r,(P) = - ^ -i- I Jx:(p)+p^ J a(p,a) V -^ dp da (33) 



k=l ^^ \ >/ ^ •'^^(P) |dJ 



k 



where a(r,<?') is the source strength density. 



It follows that the lifting surface induced velocity may be considered 

 as the sum of four terms 



f^ (P ) 



Z y-R px r (* k e X D 



-ii(x,r,^) =-ll'(x,r,<P) + E -b / J^i(P)+P J Y*(P.<^) -^TTI^ 



^ k=i '^^\>' ^ \(P) ^ IdJ-' 



k 

 ® © (34) 



+ [u^(x,r,^)]^.^^.^g^.^^ + u;(x,r,<^) 



® © 



where 



(T) = velocity due to a distribution of bound vorticity on the blade 

 surface (equation (28)) 



(2) = velocity due to a distribution of free vorticity on the blade 



surface 



(3) = velocity due to the lifting line free-vortex sheet (equation (12)) 



21 



