semi-gliding and gliding boats. Because of difficulties in experimenting they were seldom 

 conducted in a following sea. 



We mention first an elementary investigation on the behavior of hydrofoil 

 systems in heave and pitch motion [57]. Assuming that we have at least two foil sys- 

 tems (at the bow and at the stern) we easily see that the coupling of heave and pitch 

 is an essential feature of the problem involved. Expressions for the natural periods 

 and the damping are readily obtained; the latter can be made much stronger than 

 with displacement ships. This has to be considered an advantage of the hydrofoil 

 principle. Conditions are in general less favorable in a following sea, the main reason 

 being the direction of the orbital velocities. 



Transverse stability of piercing foil systems so far has not caused much trouble. 

 Experience has shown that it is easy to cope with the problem of roll; so little has 

 been done in this direction. 



At present a thesis is being prepared which deals with all six degrees of freedom, 

 the hydrodynamic part of the investigation being kept as elementary as possible. 



One can expect that such theories may serve at least as guide for planning 

 experiments. Investigations of this character may be linked with those on displacement 

 vessels with fins, and may yield a valuable extension of our knowledge on future lines 

 of development of high-speed seaworthy vessels. Another important sideline is the 

 connection with seaplane research. 



Quite recently an important step forward in the field of hydrofoil theory has 

 been made by P. Kaplan [58]. The theory developed by him refers to unsteady motions 

 of a completely submerged foil of infinite span near a free surface. Explicit results are 

 given for the lift force and mean wave drag for two important special cases, assuming 

 a constant speed of advance : 



1. foil performing harmonic heaving oscillations in calm water. 



2. foil advancing rectilinearly, head-on under sinusoidal waves. 



The amplitude of lift force is rather frequency dependent. Values obtained by 

 quasi-steady considerations grossly overestimate the actual conditions even at moderate 

 Strouhal numbers. 



It is to be expected that this theory, notwithstanding its limitations, will prove 

 extremely useful in promoting hydrofoil boat development. 



By far the largest part of our scientific knowledge concerning planing vessels 

 (hydro gliders) is due to investigations on seaplane performance. 



So far no theory exists of the behavior of hydrogliders in a seaway and literature 

 on experiments is extremely meager also. It is imaginable that useful results can be 

 developed from the impact theory due to Wagner, and such a theory supported by 

 experiments should enable us to reach conclusions as to advisable dead rise angles, 

 L/B ratios etc. 



The present writer does not consider this task especially important since it is 

 obvious that planing vessels must remain much inferior to hydrofoils with respect to 

 seaworthiness. It is recommended, however, that the hydroglider problem be treated as 

 a byproduct of research on hydrofoil and Archimedean vessels. 



II. The Significance of Research Results for Design 

 /. General Remarks 



Recently in a technical journal engineers were described as people toiling over 

 meager problems left over by physicists and mathematicians and frequently suffering 

 from an inferiority complex. 



Because physics is developing with increased speed in its '"central" part, many 

 classical problems like hydrodynamics and theory of elasticity, are left aside and taken 

 over by engineering sciences. In addition, however, engineers have to fulfill other tasks, 

 for example, to consider and coordinate the multitude of problems arising in a tech- 



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