Hydrodynamics of High-Speed Hydrofoils 139 
For foils of optimum design, the sum of induced and cavity drags seems to be con- 
siderably greater than the friction drag. The division of induced and cavity drag depends 
very much on the wing aspect ratio, the cavity drag being generally larger and thus more 
important for aspect ratios of 2 or 3 and higher. 
Theoretical studies [16, 17], now confirmed by experiments [18, 22], have led to the 
design of low-drag supercavitating foils such as are used in propeller design. We have 
recently developed a theory and made calculations to reveal the effect of near-surface 
proximity on the shape of optimized low-drag foils, and on the resulting lift-cavity drag 
(L/D ,) ratios. It may be recalled that I had some time ago shown that, according to linear- 
ized theory, there exist for supercavitating foils at infinite submergence, optimum values of 
L/D, inversely proportional to the foil lift coefficient. These ideal optimum ratios are not 
realized in practice partly because of the necessity to design foils of sufficient strength, 
and thus develop lift from incidence as well as camber; nevertheless, these ratios do pro- 
vide information as to the efficiency with which lift can be developed through camber. In 
Fig. 16 are shown together with previous results for infinite submergence, theoretical two- 
dimensional foil efficiencies at a submergence of one chord. The optimum ratios of L/D, 
are seen to be almost four times higher at this moderately shallow submergence than for 
deep submergences, but for various reasons these same ratios for practical foils and lift 
coefficients are reduced to about 1.5. As a caution against any undue optimism that might 
be generated by this finding, it should be recalled that active load-alleviation devices such 
as the supercavitating flaps earlier discussed will, it seems safe to predict, inevitably 
extract their own penalty in terms of increased cavity drag. 
Theoretical Lift-Drag (Cavity) Ratios, Lp, 
40 Practical" Two Term’ 
Foils 
asian 
zeae 
10 
0 0.1 0.2 03 
Lift Coefficient, C, 
Fig. 16. Theoretical two-dimensional lift-drag (cavity) ratios 
