132 M. P. Tulin 
Hydrofoil Craft (North Atlantic) 
Current Prop Transport 
Probability of Exceeding RMS "g" Loading 
fo) 0.2 0.4 06 08 1.0 1.2 
Root Mean Square “g" Loading 
Fig. 8. Statistical dynamic loading for seacraft and aircraft 
be understood that the values of flap effectiveness and hinge moments shown must be suit- 
ably modified in practice to take into account real fluid and finite aspect ratio effects; 
these results do, however, show the magnitude of the effect of near surface proximity. 
In Fig. 9 (left) are given curves of subcavitating flap effectiveness versus flap-chord 
ratio for depth-chord ratios from zero to infinity. A composite curve for a range of flap- 
chord ratios, graphically illustrating the near surface effect is also given in Fig. 9 (right). 
The important conclusion is that theory predicts about a 4-percent loss in ftap effectiveness 
relative to infinite depth at one chord submergence, and a 13-percent loss at 1/2 chord 
depth. The loss at zero submergence in the planing condition is 50 percent. These calcu- 
lations assume that no cavitation occurs on the foil in the vicinity of the hinge; such occur- 
rence would of course lead to loss in flap effectiveness. The results for surface effect on 
subcavitating flap effectiveness were obtained by my colleague C. F. Chen in a very inter- 
esting way. He determined that a particular flow reversal theorem which had previously 
been derived for flows without free surfaces [13] was applicable in the present case, and he 
was thus able to calculate the force on a flapped foil in terms of the flow about a flat plate 
at incidence under the free surface; the latter flow is exactly the flow about the lower foil 
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