1. Influence of neighboring cavities on cavity drag, which will affect the thrust and torque of 

 the propeller. 



2. Influence of cavities on the hydrodynamic pitch angle. 



3. Inflow retardation caused by blades and cavities. 



4. Effect of cavity on the optimum pitch distribution. 

 These problem areas will be discussed in the following sections. 



The main role of preliminary design is to supply the basic data for the final design, such as: 

 the hydrodynamic pitch angle j3j, the radial load distributions, the approximate cavity length and the 

 distribution of cavity-source strengths which will help determine the three-dimensional cavity-source 

 distribution. For this purpose the effective use of supercavitating cascade theory with lifting line 

 theory is discussed. Inputs for the preliminary design of supercavitating propellers include cavitation 

 number, leading-edge cavity thickness, and camber shape. In addition, the same information is 

 required as for subcavitating propellers. The minimum leading-edge cavity thickness is supplied from 

 a blade strength analysis. The minimum cavity length at each blade section is assumed to be 1.5 

 chord lengths. 



The computer program developed here is applied to several existing propeller models. The 

 results show that propeller efficiency is predicted well but pitch distribution is a little larger than for 

 the model. The results are analyzed and compared with the results of a lifting surface design method 

 which has been developed recently for use with the present preliminary design method. 



LIFTING LINE THEORY 



Consider the flow field of a supercavitating propeller rotating with a constant angular velocity in 

 an otherwise uniform flow. If fluid viscosity is neglected, the flow is irrotational, and can be 

 computed from appropriate vortex and source distributions. The analysis is based on linear theory in 

 which the blade angle of attack and the camber are considered to be small so that the cavity is thin. 

 The singularity distribution may be, therefore, located on a basic helical surface, near or in the blade 

 and cavity. The vortex distribution is proportional to the load distribution on the blade. Since 

 there is no load outside of the projection of the blade on the basic surface, the vortex distribution 

 for the supercavitating propeller is not different essentially from that for the subcavitating propeller. 

 Thus, the basic feature of lifting line theory for the preliminary design of a supercavitating propeller 

 is not different from that of a subcavitating propeller. The theory, developed by Lerbs' 10 ', has been 

 programmed, and is widely used. Because both cavity and blade-friction drag alter the thrust and 

 torque of the propeller due to the vortex distribution on the blades in inviscid flow, the calculation 

 has to be iterated to find the lifting line vortex distribution in the cavity flow required to produce 

 the required thrust. 



The main changes in the present lifting line program are the addition of an option for computa- 

 tion of the optimum distribution of hydrodynamic pitch, which will be discussed later, and considera- 

 tion of cavities from supercavitating cascades. These changes enable a full consideration of blade 

 cavity interferences to be incorporated while maintaining requirement on the minimum leading edge 

 cavity thickness to produce a cavity with a length 50 percent longer than the blade chord. 



BLADE CAVITY INTERFERENCE 



Results of experiments' 11,12 ' conducted on supercavitating propellers designed by the method of 

 Tachmindji and Morgan' 2 ' indicated that, in general, the propellers were underpitched. One reason 

 for this was probably inadequate treatment of blade cavity-interference effects' 2 " 4 '. Tulin' ' suggested 

 using either supercavitating cascades or a cavitating foil above a free surface in two dimensions instead 

 of an isolated two-dimensional cavitating foil, to calculate the cavity drag of the blade section of the 

 propeller. Scherer et al' 13 ' also considered a cascade model for the design of a supercavitating 



