242 H. von Schertel 
Cp, of a V-shaped foil with an dihedral angle $ is increased to 
Cp, = Cp, /cos t 
due to the increased length of wetted surface. The third component 
Cb, = wave drag 
is negligibly small for high Froude number hydrofoil boats. The fourth component 
CD, = parasitic drag 
refers in this case to the foil struts, piercing the water surface. V-shaped foils with their 
tips above the water surface during travel permit the use of relatively narrow struts since 
the produced transverse forces can be taken up by structural elements which remain above 
the water surface when the boat is travelling in foilborne condition. Because the struts are 
only little immersed at cruising speed the parasitic drag of the foil is small. The fully- 
submerged foil however requires very long struts which in view of the existing bending 
moments must also be rather wide. Therefore a considerable parasitic drag is caused which 
offsets the more favorable hydrodynamic qualities of the straight fully-submerged foil. 
Calculation of the four drag components for the given example and on the assumptions 
stated above yields a drag/lift ratio for the surface-piercing foil of 6.9 percent and for the 
fully-submerged foil of 6.7 percent. Towing tank results obtained from two model foils of 
the two systems confirm the theoretical analysis. They both produced drag/lift ratios of 
approximately 7 percent. In conclusion, we can thus consider the two basic foil systems as 
being equally favorable in regard to resistance at design cruising speed. In travelling 
beyond cruising speed, however, the conditions change in favor of the surface-piercing foil 
system. The area of the fully-submerged foil is determined by the capacity of takeoff at the 
attainable Cy ax Value. The lift coefficient decreases then with the square of speed and 
as a rule attains an unfavorably small value at top speed. On the other hand, when speed of 
the surface-piercing foil exceeds cruising speed the wetted areas of the foil as well as that 
of the appendages (struts emerge completely) are reduced to such an extent that their fric- 
tional drag becomes less than that of the fully-submerged foil. 
Experiments carried out recently with a 1-ton test boat originally fitted with surface- 
piercing foils which were later replaced by a new system of automatically controlled sub- 
merged foils also confirmed these inherent characteristics of the two types. Figure 9 shows 
that cruising speed of the boat of about 50 km/h (27 knots) is reached with any of the two 
foils at the same engine speed whereas the top speed attained with the surface-piercing foil 
is 65 km/h (35 knots) as against 59 km/h (about 32 knots) with the fully-submerged foil. 
Behavior in Sea Waves 
The behavior of a hydrofoil vessel in sea waves is essentially the result of two func- 
tions. The first one, called the “wing characteristic Z” indicates the stabilizing variation 
(dL/dh); thus 
Z = (dL/Lo) / (dh/bo) 
