142. M. P. Tulin 
DISCUSSION 
S. F. Hoerner (Gibbs and Cox, Inc., New York) 
The Froude number is generally used in the consideration of displacement-type ships. 
As far as hydrofoil boats are concerned, it is known that such craft will be able to operate 
efficiently at higher Froude numbers. The size of hydrofoil craft is limited, accordingly, 
and to mention a number, the limit might be in the order of 500 tons. However, there is also 
an upper limit to the Froude number as far as hydrofoil craft are concerned. To explain this 
briefly, consider a craft of 200 tons operating at 50 knots, which is believed to be feasible. 
We may now put into that craft heavier machinery, propelling it at 100 knots, which is twice 
the original speed. As a consequence, to support the same weight, we will only need 1/4 
the original foil area. The size of the struts supporting the weight of the hull above the 
foils is, on the other hand, a function of the hull weight and of drag and other forces such 
as impact which are more or less proportional to that weight. In other words, the struts 
remain the same size as those of the original craft. Since struts are roughly accountable 
for half the drag of a foil system, the faster boat will have higher drag. This result can be 
said to be the consequence of high Froude number. The argument applies to plain configura- 
tions of hull plus foil system, while cavitation is not yet taken into account. 
Marshall P. Tulin 
It is certainly true that all studies of the speed and power of hydrofoil craft have 
revealed that there is a maximum practical Froude number beyond which hydrofoil craft may 
not be economically or otherwise feasible. Such studies, of course, include those made by 
Dr. Hoerner himself—which have proved very valuable to students of hydrofoil craft during 
the last few years. The actual value of a maximum Froude number depends on structural 
and power plant weights and its existence is not to be argued, but I would like to suggest 
that this Froude number may be an increasing function of time and that its estimation is 
thus not particularly easy. I might further comment on Dr. Hoemer’s remark with regard to 
the drag of struts. In particular, I don’t think I can agree that the strut drag is simply about 
half of the foil system drag; I believe that very much depends upon the configuration of the 
foil system and that the strut drag may be considerably less than half of the total for certain 
systems. 
S. F. Hoerner 
My statement that strut drag is roughly half the foil system drag applies to fully sub- 
merged foil systems at maximum speed. Generally, struts in such systems represent approxi- 
mately 1/2 the parasitic drag, which mean approximately 1/4 the total drag, at maximum- 
range speed. 
F. S. Burt (Admiralty Research Laboratory) 
I endorse the point Mr. Tulin made that there is a considerable shortage of systematic 
data of components in association with one another. It is more important that tests on these 
associated systems should be carried out at the correct cavitation number than at the correct 
Froude number. In fact you are in the usual difficulty; you want all your numbers right, 
