strength is represented by the normal velocities of two-dimensional cascade results 

 solved in the preliminary design program; see Appendix B. 



For convenience, short cavity effects of the super cavitating cascade are com- 

 puted in the lifting-surface theory, when the two-dimensional cascade is used as an 

 approximate solution to be corrected. 



After computing all the B coefficients of Equation (37), the simultaneous 

 Equations (38) are solved by a subroutine which uses a Gaussian elimination method. 

 The accuracy of the solution obtained by the least-squares method is approximately 

 checked by a comparison of the left-hand and right-hand sides of Equation (28). Then 

 the total source strength on the blade is obtained from Equation (31). The velocity 

 component due to sources is obtained from all the velocity component functions 

 created for A in Equation (36). 



pq 



Because many existing supercavitating-propeller models have chord lengths 

 smaller near the blade tip than near the hub, angular intervals near the tip are too 

 small. Thus, the present program allows intervals of all the even degrees, such as 

 2, 4, etc. In addition, a 1-deg interval is tested for a six-bladed propeller. This 

 feature is supplied by using the addition rule of trigonometry, making use of data 

 stored for cosine and sine functions. 



When the rake and skew are present in the reference surface, the correct area 

 element Hdpd<f> in all the area integrals has to be taken into account instead of 

 H dpd<j>. 



The collocation points can be taken to be 10 points on the blade and 5 points 

 on the cavity wake. However, if four points are selected on the blade this will be 

 exactly the same as the collocation points for the subcavitating case, except for 

 the extra points on the cavity wake. 



In addition to other preliminary data, the P and Q in Equation (44) are pre- 

 pared in the preliminary design and are conveyed through an input tape. As in the 

 subcavitating case, friction is taken into account, but only on the pressure side. 



The output routine is created in a format similar to that of Kerwin by con- 

 sidering data taken from the super cavitating cascade of the preliminary design for 

 the blade-section and the cavity shapes. 



The input to the computer program includes the same information as is used for 

 the subcavitating propeller design, such as rpm; ship speed; propeller diameter; hub 

 diameter; helical distance from an arbitrarily fixed reference plane, distance from 



24 



