Hydrofoils Running Near a Free Surface 159 
Below F,’ = 1, i.e., in the subcritical speed range, the depth of submergence of any 
foil plays a similar part for the circulation as the water depth does for the orbital velocity 
of waves in shallow water. Thus correspond the C, reduction on the upper side and the 
wave speed reduction 
Crh ad ee 
Lo re) 
Hence 
2 
F, = 
follows. 
To be sure, this can be seen exactly only at small depths, for example for h/c = 0.37 
as in Fig. 13. For larger depths the transition is smoothed at F, = 1 and disappears gradu- 
ally in the same manner as it does in deep water. Above F, = 2 no dependency of the Froude 
depth number exists. Hydrofoil boats generally run by dynamic lift at a speed more than 25 
knots and at a submergence less than 2 m. This corresponds to a smallest Froude depth 
number of about 3. 
Summing up, the results of examination of the state of flow are as follows: 
1. The hydrofoil is susceptible to the shallow water effect. For operating conditions 
of hydrofoil boats the flow pattern is a supercritical one. For theoretical considerations by 
analogy from wave theory, rapid flow is presumed in the direct neighborhood of the hydrofoil 
in place of orbital motion for waves. 
2. For individual hydrofoils no critical speed barrier can exist as it does for displace- 
ment ships in shallow water, given by speed and depth. But for the complete craft fitted 
with several hydrofoils such a barrier, of course, can exist, since the wave formation behind 
the hydraulic jump follows the Froude depth number given by the water depth and changes 
the flow against the next hydrofoil in line. 
3. The only significant quantity for the influence of the water surface on the circulation 
around a hydrofoil in the supercritical range is the relative depth of submergence of the foil 
element, h=h/c. It is independent of the configuration and speed of the hydrofoil. 
FLOW FORCES MEASUREMENT 
In 1941 six component tests on hydrofoils already had been made in the circulating water 
tunnel of the firm Gebr. Sachsenberg AG., Berlin, under the direction of G. Weinblum. The 
results were published at that time only fs a restricted number of persons. 
In one case a model of a dihedral foil with a constant circle segment profile of a con- 
stant length { =.96 mm and a thickness t = 6.4 mm was used [6]. The dihedral angle could 
