GEOMETRY OF THE BLADE 



The geometry of the blade of a supercavitating propeller is almost the same as 

 that of a subcavitating propeller. The blade is represented in the flow by singu- 

 larity distributions of vortices and sources on the blade-reference surface in the 

 linear version. Thus, the blade-reference surface has to be known approximately, 

 although the blade shape has to be obtained as a solution. As in the theory for sub- 

 cavitating propellers, the reference surface will be close to the helical surface of 

 the hydrodynamic pitch angle (3. obtained in the preliminary design. Although the 

 reference surface could be determined more accurately by an iterative procedure, in 

 the present program B. is used once without iteration, which is considered to be a 

 reasonable approximation. The pitch angle of the reference surface of the wake can 

 be set differently from that of the blade. 



A cylindrical coordinate system (x,r,0), seen in Figure 1, is defined; the x- 

 axis is coincident with the axis of rotation of the propeller and is positive when 

 facing downstream. Thus, the reference surface can be represented by 



x = A0 + C(r), r„ < r < 1, 9_-< < » (1) 



n L 



X = r tan £. (2) 



i 



where C(r) depends on rake and skew, and A is in general close to a constant. If a 

 Cartesian coordinate is defined as in Figure 1, the parametric representation of the 

 reference surface x(r,9) = xi + yj + zk is 



x(r,6) = A6 + £(r) 



y(r,9) = r cos 6 (3) 



z(r,8) = r sin 



Then the area element is 



