Cox 



K the propeller is assumed to operate in uniform inflow, there appears to 

 be little advantage in not assuming x.^ independent of r. Therefore, the theory 

 will be developed for uniform inflow and constant hydrodynamic pitch, i.e., u 

 and 77\i independent of radius r. 



A major difference between subcavitating and supercavitating lifting-line 

 theory for constant induced advance ratio is that while the normality condition 

 holds for the subcavitating case provided that r {r^) = 0, i.e.. 



Ut(r*) = 



k. 



this condition no longer holds for the supercavitating case, see Fig. 1. 



Fig. 1 - Velocity and force diagram 



The mathematical model used to represent each supercavitating blade con- 

 sists of: 



(i) a lifting line at e = a^, t^^ < r < 1 with associated trailing vor- 

 ticity laid out on a helicoidal surface of pitch ratio nX.^, downstream of the 

 lifting line to represent loading; 



(ii) a pressure source distribution laid out on the trailing vortex 

 sheet at cTq < < CTq + e^ , to represent the cavity. 



\ 



938 



