144 M. P. Tulin 
system where there is important effect of pitch and you have really two foils at different 
positions relative to the center, but quite different from a simple aircraft and what I have 
done was to compute some values of this gust-load factor according to the quasi-steady 
formula and then compare that with some values obtained from some experiments at the 
Model Basin. This bore out the fact that the original formulation appears to be quite pessi- 
mistic. However, the Model Basin tests were at a rather low Froude number, so perhaps 
that may cover some of the difference. Also, Mr. Tulin mentioned that he did not cover all 
of the various problems associated with the hydrodynamics of high-speed craft, and in par- 
ticular I would like to put forward the fact that in this case of high-speed and supercavitat- 
ing foils it appears that there may be a rather distinct possibility of the hydroelastic insta- 
bility, that is, flutter. Some theoretical results carried out about a year ago at Stevens 
indicated that there is a greater possibility of obtaining a hydroelastic instability, that is, 
flutter, for supercavitating foils as compared to fully wetted foils. This sort of problem 
should be looked into very carefully in the design of these craft. 
Marshall P. Tulin 
With regard to Dr. Kaplan’s question about the calculation of g loadings (which were 
admittedly based on the simplest sort of analysis), there is no question that very much more 
sophisticated calculations for hydrofoil craft should be carried out. In my paper I refer to 
several sophisticated calculations carried out for aircraft and I would suggest that these 
calculations should serve as a model with regard to hydrofoil investigations. To say that 
coupled motions are involved in such calculations is a gross understatement. In the case 
of a recent aircraft investigation, five degrees-of-freedom were considered, including torsion 
and bending of the wing, which are very important for high-speed aircraft and should cer- 
tainly be as important in the case of the hydrofoil craft with its high wing loadings. It was 
particularly this aircraft investigation which prompted me to make the remark in my paper 
that the simplest kind of analysis leads, if anything, to conservative results regarding load 
estimations. Of course, the damping of hydrofoil craft motions is not necessarily the same 
as in the case of an aircraft, and for that reason alone we cannot come to any rigorous con- 
clusions from aircraft experience. I hope that the kind of calculations, as | have indicated 
above, will be carried ‘out; I can say that we plan to make some calculations ourselves. 
Problems of hydroelastic phenomena are well-known to be important for high-speed 
supercavitating foils whether used in hydrofoil craft or in propellers. Such problems, par- 
ticularly with regard to leading edge flutter, have already been experienced, and some stop- 
gap solutions have been obtained. Certainly research on the subject of flutter and on strut 
divergence, which may be very important for high-speed craft, should be the subject of 
future investigations. 
Edward V. Lewis (Davidson Laboratory, Stevens Institute of Technology) 
Mr. Tulin has pointed out some of the serious problems of hydrofoil craft design for 
rough sea conditions. He expresses optimism regarding the possibility of solving these 
problems and suggests possible solutions. 
I should like to return to a more basic problem of the hydrofoil boat which pertains to 
fundamental limitations on this type of craft. For this purpose we may compare a hydrofoil 
boat with an airplane, in which the boat hull and airplane fuselage are comparable, but the 
hydrofoil wings are in water instead of air. At any particular speed the increased density 
