Hydrodynamics of High-Speed Hydrofoils 123 
speed versus displacement diagram the regions in which various marine vehicles, including 
semisubmerged ships in addition to those already mentioned above, would seem to offer 
optimum powering performance. This diagram is based on available data [1, 2] and powering 
calculations we have carried out at Hydronautics, Incorporated. Also shown are design 
points for various hydrofoil boats that have been constructed or are under construction. 
Study reveals that both with regard to needs and capability, the hydrofoil boat seems partic- 
ularly fated for high-speed operation, that is for speed in excess of 40 and perhaps as high 
as 120 knots. 
The engineering problems involved in the design and construction of high-speed hydro- 
foil boats are exceedingly severe with respect to power plant, transmission, structure, and 
hydrodynamic aspects. It is the purpose of the present paper to discuss some of the impor- 
tant hydrodynamic considerations involved, to underline certain problems, and generally to 
give perspective to the situation that the hydrodynamicist faces. 
3oth sub- and supercavitating craft intended for sustained operation at sea are con- 
sidered. It is emphasized that high-speed craft involve very high static foil loadings and 
additional severe seaway loadings. The hostility of the sea environment is strikingly illus- 
trated through comparison with the atmospheric environment through which the airplane 
flies. The problem of preventing cavitation on subcavitating craft is discussed and the 
effect of seaway motions on inception is predicted. The importance of flaps for loads and 
motion control is underlined and some new theoretical results relating to the effect of the 
free surface on two-dimensional flap effectiveness for both sub- and supercavitating foils 
are presented. Other new theoretical results pertaining to the effect of the free surface are 
also given and, in particular, its beneficial influence on lift-drag ratios of two-dimensional 
supercavitating foils is revealed. 
Many staff members of Hydronautics, Incorporated, have participated in the preparation 
of the results indicated above. 
WING LOADINGS 
Considering the essential similarity between the hydrofoil boat and the airplane, it is 
natural to compare the problems that have faced their development and, of course, to take 
maximum advantage of mutually useful and pertinent information and experience. This last 
statement will almost universally be translated as meaning that the naval architect should 
take advantage of the knowledge of the aeronautical engineer—as, most naturally, he often 
does. Of course, seacraft and aircraft operate in vastly different environments. Whereas 
air is so light that it is still a matter of amazement to many that anything substantial can 
support itself therein, every successful hydrodynamicist early acquires a great deal of 
respect for the weightiness of his own particular subject. A consequence of this difference 
in densities is illustrated in Fig. 2. In interpretation of this figure it is useful to recall 
that the wing or foil loading (displacement over He area) equals the wing lift coefficient 
(Cy) multiplied by the dynamic pressure 7, (QUp 2/2), and that the optimum lift coeffi- 
cient for a given design depends primarily upon hydrodynamic considerations relating to 
minimum powering requirements; practical design lift coefficients for both seacraft and air- 
craft lie in the range 0.1 to 0.35. The very much larger wing loadings experienced by high- 
speed seacraft in comparison to those for supersonic aircraft are apparent from the figure. 
It is striking that the wing loadings of 60-knot-plus seacraft are at least one and almost two 
orders of magnitude larger than for aircraft of contemplated design. At the same time, the 
hydrodynamic demands for thinness of underwater structures are just as severe as in the 
