w a Axial component of perturbation velocity 



w ( Tangential component of perturbation velocity 



y Shock-free camber-offset of blade face 



Z Blade number 



a Extra angle of attack superposed to the shock-free foil 



/3j Hydrodynamic pitch angle 



7 Stagger angle of cascade 



5 Flow exit angle of cascade 



e Drag-lift ratio of a foil at the blade section 



a Local cavitation number of design propeller 



a x Cavitation number for infinite-length cavity of cascade 



H Angular speed of blade 



INTRODUCTION 



Supercavitating propellers are strong candidates for propulsors on high-speed craft' 1 '. A design 

 method for supercavitating propellers was developed first in this country by Morgan and Tachmindji' 2 ', 

 with efforts still continuing' 3 ' 7 '. 



The main problem associated with designing supercavitating propellers as opposed to subcavitating 

 propellers is the effect of three-dimensional cavities trailing from the propeller blades. In early work, 

 knowledge of an isolated two-dimensional supercavitating foil was combined with subcavitating 

 propeller-design theory I 2,3 '. However, it was soon realized that blade-cavity interference between 

 each of the supercavitating propeller blades was too large to be neglected' 3 ' 4 ' . Thus, three- 

 dimensional integrated design methods in which the cavity and the blade were considered to lie on a 

 helical surface, were formulated by several hydrodynamicists' 5,7 '. Through the medium of high- 

 speed computers' 8,9 ', these efforts have shown success in the design theory for subcavitating 

 propellers. The difficulty encountered in supercavitating propeller design is that the geometry of the 

 cavity surface is not known a priori. For two-dimensional cavity problems the complex-variable 

 theory could be efficiently utilized; but not for three dimensions. Numerical solutions using high- 

 speed computers have been contemplated' 5,7 '. However, so far, no practical, reliable, computer 

 program seems to exist. 



The hydrodynamic design method of subcavitating propellers may be divided into two steps: 

 preliminary or performance design and final or lifting surface design. Preliminary design employs 

 three-dimensional lifting-line theory' 10 ' to find the hydrodynamic pitch angle |3j and the vortex 

 distribution G along the blade span that will supply the required thrust for the design speed. The 

 hydrodynamic pitch angle is the angle of inflow velocity at the propeller plane. From this angle, the 

 angle of attack of the blade is measured. The hydrodynamic pitch angle defines a basic helical 

 surface where the vortex distribution will be located in the lifting-surface theory for the final 

 design' 8 '. Chordwise pressure and thickness distributions are obtained from two-dimensional airfoil 

 theory. In designing supercavitating propellers, it seems to be natural to consider the same two steps 

 as those for subcavitating propellers. Thus, the first problem will be preliminary design without 

 which there cannot be the final design. As previously mentioned, the preliminary design method of 

 Tachmindji and Morgan' 2 ' has not been found to be accurate enough for use in the final design. In 

 addition, since final design is extremely complicated' 5,7 ', it is to be hoped that a preliminary design 

 method will help reduce the complexity of the final design. 



To improve the existing preliminary design method for supercavitating propellers, several 

 problem areas need to be considered: 



