Hydrofoil Size and Seaworthiness 203 
[7] Berentzik, H., “Vergleich der theoretisch errechneten Beschleunigungen eines Trag- 
fliigelbootes im Seegang mit den experimentell ermittelten Werten,” Schiffbautechnik, 10 
Jahrgang, Heft 7, Berlin, 1960 
[8] Heer, C.C., “Ergebnisse von Beschleunigungsmessungen an einem 10-m—Tragfliigelboot- 
Groszmodell im natiirlichen Seegang der Ostsee,” Schiffbautechnik, 9 Jahrgang, Heft 11 
and 12, Berlin, 1959 
[9] Abkowitz, M.A., “The Effect of Antipitching Fins on Ship Motions,” Trans. of the Soc. 
of Naval Arch. and Marine Eng., New York, 1959 
DISCUSSION 
P. Kaplan (Technical Research Group, Inc., Syosset, New York) 
I want to know if the results just depend upon the assumption that the system is a 
simple spring-mass system. It appears that hydrofoils alone as simple spring-mass systems 
are overdamped in free motion as a single-degree-of-freedom. You have no such thing as a 
natural frequency in many cases. Also, I would like to know if the result that vertical 
accelerations are maximum at ratios of wavelength to craft length equal to two-thirds and 
three-halves is true for all cases or just for the particular designs chosen for illustration. 
A. Hadjidakis 
I said at the beginning of my lecture that what I have done was done in a very general 
way and in a very simple way, because, otherwise, one would need a computer and would 
have to go into very difficult calculations. I have chosen this very simple spring and mass 
system to get some quick results and to make it clear that in any case the seaworthiness 
of bigger craft would be better than that of small craft. I meant, indeed, in all cases, 
except fully submerged foil systems. 
I might say now concerning what one should take for the characteristic length of the 
craft; one had perhaps better take the distance of the extreme foils, or something like that, 
to obtain better results. I do not pretend the diagrams I have shown are very accurate, but 
the main thing I wanted to prove is the direction wherein we are going if we make craft 
bigger. What you said about the damping ratios, that hydrofoil craft are overdamped, I do 
not agree. Damping, as far as heave is concerned, is very high indeed, but damping on 
pitch depends on what sort of hydrofoil system you have. With our one-foil system, on very 
small craft we find damping ratios as small as 0.4, so in that case one can feel on different 
wavelengths what is approximately the critical frequency of the craft. If you look at Fig. 
4 it will be clear that this critical frequency is not a well-defined thing; you cannot measure 
it very exactly. 
P. Kaplan 
You said that in following seas the important characteristic of seaworthiness is pitch- 
ing. I think that heave is rather important, and that you get large possibilities of settling 
in the water just due to that motion as well. - 
