Hydrodynamics of High-Speed Hydrofoils 125 
case of aircraft; for either a supercavitating or supersonic foil of given length, drags are 
incurred proportional to the square of the foil thickness. It is rather difficult to put this 
comparison on a quantitative basis, but suffice it to say that a 5 percent diamond-shaped 
strut has the same drag coefficient (about 0.1 based on thickness) operating at mach number 
2.3 in air, as when operating at 60 knots and 5 feet submergence in water while ventilated 
to the atmosphere. 
Similarly, for subsonic or subcavitating foils a great premium is placed on structural 
slenderness, since the speeds which may be attained in either case without impairment in 
operation increase with thinness of structure. An attempt is made to illustrate this fact in 
Fig. 2 (bottom) where the critical pressure coefficient for aircraft and inception cavitation 
number for seacraft are plotted, together with the minimum pressure coefficient for a wing of 
about 7 percent thickness ratio and 0.1 lift coefficient. Such a wing would encounter, 
according to Fig. 2, drag rise and buffeting difficulties at 500 knots plus in air and 65 knots 
plus in calm water. However, a wing of 4 percent thickness and 0.1 lift coefficient could 
probably achieve about 530 knots in air and 80 knots in calm water before impairment of 
operation. The crucial observation to be made is that the seacraft structural designer must 
thin his wings at design dynamic pressures and wing loadings some 20 to 50 times greater 
than would exist in the case of an aircraft. 
It is interesting, having put the static loading problem in some perspective, to note 
some analogies between propulsion and hydrodynamic problems for the airplane and hydro- 
foil boat. In these analogies, which it will be immediately recognized cannot be taken too 
literally, high-speed problems incurred in air due to the finite speed of sound become 
equivalent to difficulties caused by cavitation in water. In both media, screw propellers 
are commonly used at low speeds, with their use being finally impaired unless radical 
change in form is made at speeds of the order of 400 knots in air and 40 knots in water. 
The propulsion barriers that existed as a consequence, have both been successfully hur- 
dled at this time, by the introduction of jet propulsion in one case, and of the supercavitat- 
ing propeller in the other [3, 4]. It is taken for granted that high-speed hydrofoil craft 
will utilize supercavitating propellers with efficiencies at design in the range 0.65 to 0.72. 
At speeds somewhat higher than those at which the low-speed screw propeller runs 
afoul of efficiency loss and severe vibration, the supporting foils of vehicles in both media 
begin to suffer those same difficulties, and at speeds in excess of 750 knots in air and 75 
knots in water, it is almost essential that the design of wings and foils be based on entirely 
different principles than for low speeds. As is indicated in Fig. 2, the first hydrofoil craft 
utilizing supercavitating foils is being test flown this year (1960); it has been designed and 
constructed by Dynamic Developments, Inc., of Babylon, New York, under contract to the 
Office of Naval Research of the U.S. Navy. The cavities attached to these foils are not, 
of course, filled with water vapor, but are ventilated through the free surface to the 
atmosphere. 
THE HOSTILE SEA 
In a very important respect and in addition to considerations of static wing loading, the 
sea is a much more difficult, even hostile, environment in which to fly than the atmosphere. 
Most naval designers and ship’s passengers have acquired an appreciation for the severity 
of the wind-driven motions which must statistically be expected to exist near and on the 
ocean’s surface; and all of us who allow ourselves to be transported from place to place in 
aircraft have awareness of the turbulence in the atmosphere—we may even have observed 
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