upper and lower sides of the mean camber of the blade, respectively; from Equations 

 (25) through (27) the tangential velocity due to the source distribution alone can 

 be written as 



" T G V £ a V s u f .... 



Y~ = - 2~^~ V~ "2 V V - ° n blade plane (28) 



s s s 



u m 



V 



u. 



T 



a s 



f 



V 



2 V 



V 



and 



on the cavity plane (29) 

 behind the blade 



When G and O are known, these two equations will form a system of Fredholm integral 

 equations of the first kind for the source distribution. 



When the propeller blade shape is given instead of the vortex distribution, the 

 problem becomes one of prediction rather than design, and the boundary condition on 

 the pressure side of the blade is 



J± = d£ (30) 



V dx 

 s 



where F is the blade ordinate with respect to the reference surface and x = ptf) sec 



Pi" 



In this case the blade reference surface must be in close agreement with the mean 



camber and the wake surfaces. Now Equations (28) through (30) become the integral 

 equations for both sources and vortices. Thus, the prediction problem becomes more 

 complicated. In this report only the design problem is considered. However, the 

 prediction problem can be solved similarly. 



SOLUTION FOR SOURCE 

 For the lifting-surface design of supercavitating propellers, the load distri- 

 bution p + O on the blade is supplied from the preliminary design computations. As 



11 



