Cox 



Or, following Widnall, 



M 



where 



— + 1 



+ (r2 + X.2)l/2 2] 2 C„nh(r,r,-i.rjg„ 



< 5 < 



(29) 



'" ^e 



(n-i) , e^_^< 



n = 1, 2, •••, (N- 1) (30) 



gN=T^- (N-1) . ^N-l ^ ^ ^ ^N 



The use of Widnall's modes in Eq. (30), i.e., g^, provides piecewise continuity 

 in the chordwise direction and Eq. (29) could be preferable to Eq. (28) as a 

 representation of s(r,6'). However, Eq. (29) necessitates the evaluation of 

 more definite integrals than (28) for the terms associated with the unknown 

 coefficients. 



4. OUTLINE OF APPLICATION TO PROPELLER DESIGN THEORY 



Analogous to an initial design theory for subcavitating propellers [14], it is 

 necessary to obtain an estimate for the induced advance ratio k-^, and the radial 

 bound circulation r(r), to meet prescribed design conditions. 



It has to be assumed that: 



942 



