Hydrodynamics of High Speed Hydrofoils 131 
four times the latter in value. The proximity of the free surface tends to reduce this ratio, 
however, and for the wings considered, the Cz, were in an average ratio of about two to 
one. The increase in the dynamic loads parameter for subcavitating craft between 60 and 70 
knots is entirely due to the decrease in lift coefficients demanded in order to prevent cavi- 
tation inception. For the optimized supercavitating wing families a general decrease in 
dynamic load parameter accompanies and is due to increasing speed. The family with 
thicker foil sections enjoys a smaller value of the parameter because of higher optimum 
lift coefficients. The values of 
Cre /Oni 
for three transport aircraft [12] are also shown on the vertical ordinate and are seen to be 
considerably smaller in value than for the best supercavitating wing at 85 knots; the speed 
of these aircraft range from 300 to 2,000 knots. 
The results of the calculation of the dynamic loads parameter shown in Fig. 7 and 
which have just been discussed, are combined with earlier statistical results, Fig. 3, relat- 
ing to the character of the North Atlantic and of the atmosphere, to determine the probability 
that a particular craft with passive foil system (no load alleviation) will suffer dynamic rms 
g loadings exceeding a certain level. These new results are shown in Fig. 8. The extremely 
marked effect of decreasing values of dynamic loads parameter, 
CL, /CLU 
in reducing the probability of high g loadings is to be noted. As this parameter varies from 
a value of 0.04, which is a little less than for the best supercavitating wing at 90 knots, to 
a value of 0.12 which is a little less than for the subcavitating wing at 65 knots, the prob- 
ability of exceeding an rms g loading of 0.2 increases from 4 to 70 percent. 
The results for aircraft utilizing the low-altitude gust probability curve of Fig. 3 for 
the propeller transport and the high-altitude curve for the jet are interesting in themselves, 
but they have been especially included in order to afford through comparison a striking 
illustration of the magnitude of the dynamic loads problem that must be faced by the 
designer of seagoing high-speed hydrofoil craft. 
LOAD ALLEVIATION AND FLAPS 
The results shown in Fig. 8 make it abundantly clear that extremely effective load- 
alleviating devices must be provided if the design limit of 0.15 g rms vertical acceleration 
set according to comfort criteria is to be met. These devices must counter vertical orbital 
velocities in both upward and downward directions and for 60-knot plus craft at encounter 
frequencies of the order of 2.5 radians per second and higher. If load alleviation is sought 
through tail foil trim control, then angular accelerations leading to vertical accelerations in 
excess of the design limit would, according to our calculations, seem to be implied. As an 
alternative, control of lift at the main foils without essential change of trim suggests itself 
and has the additional advantage of affording more rapid response than in the case of trim 
control. 
The use of flaps has especially been considered, and in that connection we present 
here the results of recent calculations on the behavior of two-dimensional flaps for both 
subcavitating and supercavitating foils, both operating at very high forward speeds. It must 
