Malavard 



simple analogically, since it amounts to imposing on the plane of the wing, and 

 outside the wing, the cavity, and the wake, a zero normal derivative condition 

 for an even function, or a constant potential condition for an odd function. These 

 three potentials are defined by their boundary conditions so that their sum on 

 each boundary is equal to the condition of the potential (p. Thus, for example, 

 on the lower surface of the wing and cavity we will have 



^El = A(y) , 



C,(y) 



g(x- X8 ,y) , 



g(x-x,y)] , 



The constants A(y) and B(y) are connected according to the above expressions 

 by 



A(y) + B(y) = <^o(y) + -^ ■ 



Figures 15 and 16 show the shape of two supercavitating wings: one of 

 rectangular planform with a span ratio of 4, and the other having an elliptical 

 leading edge and a straight trailing edge, with a span ratio of 4.5, The chosen 

 pressure distribution following the chord of each section is of the Tulin-Burkart 

 type; that of the span circulation is elliptical. The maximum length of the 

 cavity, in the median section, is three times the chord. Especially notable are 

 the difference between the sections of the two hydrofoils and the thickening of the 

 rectangular wing at the wingtip. 



Supercavitating Hydrofoils with Zero Cavitation Number 



In the case of high Froude numbers the flow around the wing is similar to 

 that already studied for two-dimensional bodies in the subsection on Infinite 

 Froude Number. However, the solution of the optimum distribution of span cir- 

 culation should precede the design of supercavitating wings. 



Luu (3) has shown that this problem is reducible to that of the optimum 

 vortex distribution of the finite span biplane, i.e., constant induced velocity 

 over the span, as treated in (43) and (44). In these publications are found only 

 global results concerning the lift-drag ratio, and not the vortex distribution on 

 the span which is the most interesting feature. Although it is possible to obtain 

 a solution to this problem by analytical methods, it is appropriate to indicate 

 that the rheoelectric method can be utilized advantageously. Consider the flow 

 observed in the Trefftz plan. The potential 0p, which is the harmonic function 

 in y, z, is defined by the following boundary conditions: 



388 



