Hydrodynamics of High-Speed Hydrofoils 133 
Flap Effectiveness, C, Je 
050 1.00 
Flap-Chord Ratio, f/¢ Depth-Chord Ratio, hy 
Fig. 9. Free surface effect on two-dimensional subcavitating flap effectiveness 
of a two-dimensional biplane and has been known for decades [14]. This calculation con- 
stituted the first application to my knowledge of flow reversal theorems for flows with a 
free surface. 
The flap effectiveness of supercavitating flaps at a given depth and for a particular 
flap-chord ratio is less than that of subcavitating flaps, but the difference in effectiveness 
decreases with depth and finally disappears at zero submergence. This situation corresponds 
to the fact that subcavitating flap effectiveness decreases as the free surface is approached 
whereas supercavitating flaps become more effective. J. Auslaender [15] has recently devel- 
oped pertinent theory and calculated the performance of supercavitating flaps including the 
effect of the free surface. In Fig. 10 are presented curves of flap effectiveness versus flap- 
chord ratio for depth-chord ratios of 0, 1, and infinity. The results for infinite submergence 
had been obtained previously [16], at which time it was observed that supercavitating flaps 
at infinite depth reached a maximum value of flap effectiveness for flap-chord ratios less 
than one. It will be observed in Fig. 10 that for a flap-chord ratio of 0.25, the supercavitat- 
ing flap gains 17 percent in effectiveness at 1 chord submergence (relative to infinite depth) 
and 47 percent at 0 submergence in the planing condition. Also, presented as Fig. 11 are 
hinge moment coefficients for supercavitating foils composed of a forward flat section oper- 
ating at various angles of incidence 4, followed by a 25-percent flap, all operating at a 
depth of 1 chord. These results and many more of the same nature have been obtained by 
Auslaender using linearized theory for zero cavitation number [16-19]. Itis presumed that 
practical foils will be ventilated to the atmosphere and thus operate at a cavitation number 
close to zero, so that the present results are meaningful practically. 
The action of flaps or other load alleviation devices must, of course, be supervised by 
a suitable sensing and control system. Such systems, involving acoustic wave sensors and 
similarly sophisticated devices—plus the ubiquitous black box or two—are apparently under 
active development. I will not dare to say anything about these things, but it is perhaps 
worth speculating in the present context that high-speed boats must mainly plow through 
rather than respond to the sea, and that the alleviation of dynamic loads, rather than the 
