Theory of Unsteady Propeller Forces 



(U5) 



where G^(^) is the circulation with a harmonic number n around the blade sec- 

 tion. Then referring to Eqs. (86), (69), (109), (110), (111), (113), and (96), we get 



" ( sp ) " 



'^ ( SP) 



^U' 



t> J / 5Dx " C SP1 ^-^ ^'^ 



( SP) 



(SP) 



(116) 



^Pe 



^de _ 



(SP) 



+ [v*] = y V.^ e'"^ 



'^ (SP) ^ ^" 



where 



Vxn - ^xn(^^) e + —7 J G^(^ )d^ J VrTVPLxPndv 



(117) 



We substitute Eqs. (109), (110), (111), (113), and (115) into Eq. (79), i.e., the 

 boundary condition on Sp, and multiply this equation by the weight operator 



^ / -Vf^ 



(118) 



Then, since the equation obtained in this way is to be independent of s,^, the fol- 

 lowing equation is obtained for each n similarly to Eqs. (100): 



^ ^LSPn 



where 



N 00 



k ' = 1 4) 



N CO 



k ' = 1 -d 



57 



(119) 



(120) 

 (Cont) 



