subcavitating ' and supercavitating propellers. Indeed, this present study makes 

 use of many parts of the lifting-surface design programs reported by Kerwin for 

 a subcavitating propeller. The coordinate systems of the blade are the same for 

 both propeller types. 



Since the singular integral equation is a Fredholm equation of the first kind, 

 the method for its solution must be chosen with extreme care. Additionally, the 

 cavity shape is not known without examination. Thus, iteration and/or some special 

 cavity model has to be applied knowing that all the inviscid cavity models are not 

 exact; rather, they are approximate representations. The source distribution is 

 obtained from a stripwise, two-dimensional, supercavitating-cascade representation 

 developed in the preliminary design. For the procedure used at present, the source 

 distribution is multiplied by a double polynomial having unknown coefficients in 

 terms of the radial and chordwise coordinates. Since the two-dimensional cavity 

 model used in preliminary design is a linear, double spiral vortex model, the cavity 

 streamline is closed at infinity instead of at the cavity end. Thus the unknown 

 source strengths are distributed in a prefixed plane that contains the blade surface 

 and extends to the wake about 1-1/2 chord lengths. At the end of the plane is 

 attached another source line having an unknown polynomial strength that is to be 

 solved along with the double polynomial coefficients by the least squares method. 

 The solution is a function of propeller geometry, given thrust or power, blade load 

 distribution, advance coefficient, and cavitation number. 



The induced axial, radial, and tangential velocities — thus pitch and camber 

 distribution — are obtained on a blade-reference surface that allows arbitrary skew, 

 rake, and radial pitch variation. The blade cavity shape is obtained as a correction 

 to the blade cavity derived from supercavitating cascade theory. The thrust and 

 torque coefficients are obtained from the pressure on the blade surface, which is 

 converted from the lift distribution through the Kutta-Joukowsky theorem. 



If the hub boundary condition is not considered in solving for the cavity 

 source distribution, the radial velocity caused by the cavity source is not stable. 

 When the hub boundary condition is considered, the numerical results are shown to 

 have reasonable convergence in many numerical experiments. Two new supercavitating 

 propellers were designed using numerical computations derived during the present 

 program, and models were manufactured. Model test results correlate reasonably well 

 with the computed cavity shapes and powering performance. 



