normalized by the lift coefficient, for example) one finds the shock-free angle at 

 each station of a supercavitating propeller blade by considering a supercavitating 

 cascade of infinite cavity length at each blade section. The angle of attack and 

 the point drag are combined with the basic shock-free camber to supply the given 

 leading-edge thickness, the minimum cavity length, and the required load distribu- 

 tion. In this process there are two options: either the camber or the angle of 

 attack per unit lift coefficient is preset, where the former is Case 1 and the 

 latter is Case 2. 



The hydrodynamic advance angle 3. can be determined by either of two ways: any 



form of tan 3. may be preset, such as tan 3. = c/r, or the optimum pitch condition 



1 17 1 



for the supercavitating propeller may be preset 



I 1/2 I I -1/2 



f tan 3. = c(l-t)- (e+G ||) j\ (l-w) 1/2 l+c(l-t)- (e+G |§) £ (46) 



where e is the drag-lift ratio, and t is the thrust deduction. 



Since the local cavitation number is fixed according to the design conditions, 

 and the lift coefficient varies for each iteration, the cavity length may also vary. 

 Therefore, the sectional supercavitating cascade problem must be solved for each 

 section and for each iteration. This requires a great deal of computer time. We 

 resolved this difficulty by conveniently treating the cavity problem as a foil 

 having infinite cavity length with a correction for the finite cavity effect. The 

 former needs to be calculated only once at each blade section, regardless of the 

 number of iterations. Only the finite cavity effect is computed for each iteration, 

 assuming the same load distribution as for infinite cavity length. Thus, the finite 

 cavity effect appears as a reduction of angle of attack and camber. 



The output of the preliminary design program consists of the thrust and power 



coefficients, circulation and lift distribution, tan 3., pitch distribution, 



l 



efficiency, etc. Normal velocity distribution on the cavity and foil, foil cavity 

 shape, load distribution, and other necessary data are stored on a tape to be fed 

 into the lifting-surface design. 



22 



