Problems of Commercial Hydrofoils 241 
already in existence we shall limit the discussion to the two basic foil systems which 
during recent years frequently formed the subject of discussions and led to differences of 
opinions between the experts: 
1. Surface-piercing hydrofoil systems—The surface-piercing systems consist either of 
single V-shaped foils or of a combination of smaller foils arranged one on top of the other 
like rungs of a ladder. A deviation from the equilibrium of the craft causes a change of the 
wetted lift-producing area of the foil and automatically creates restoring forces. The sys- 
tem therefore is automatically stable. 
2. Fully-submerged hydrofoil systems—Fully-submerged foils have no inherent self- 
stability. Depth of immergence must be maintained by means of mechanical, electrical, or 
other controlling devices which—measuring either the distance between the hull and the 
water surface or the foil submergence—give signals to contrivances which in turn affect the 
lift by changing the angle of incidence of the foil or of flaps at its trailing edge. - 
We shall now compare drag and compare behavior of the two basic foil systems, and 
shall consider their possible future application. 
Drag/Lift Ratio 
We shall assume equal speed (45 knots), equal aspect ratio of A = b/c = 8.3, anda 
suitable foil section for either type. An average submergence ratio of h = 1.2c is provided 
for the dihedral surface-piercing foil (lowest point & = 2c) in accordance with the boats 
which are at present in operation, and a lift coefficient of only Cy, = 0.22 with respect to 
aeration. 
The fully-submerged foil, however, requires a submergence ratio of not less than 
h = 2c in order to avoid an excessive approach to wave-troughs but it is permissible to 
apply a lift coefficient of 0.26, since this foil is not exposed to air-entrainment, and only 
cavitation by influence of orbital motion has to be considered. 
The total drag of a hydrofoil system may be expressed as 
D=Cpsg 
where S is the projected foil area and q is the dynamic pressure. The drag coefficient is 
composed of four main components: 
Oy Cp; + Cp, + Cp, + Cp 
pa°* 
The first component is Cp, = Cz,*/7A = minimum induced drag for infinite submergence. 
When approaching the water surface the second component has to be considered: 
Cp, edt CD, - = section drag. 
The frictional component Cp, is strongly dependent on roughness of foil surface. For 
smooth conditions and the applicable section thickness ratios of 0.05 to 0.10 skin friction 
drag amounts to over 90 percent of section drag, so that the pressure drag Co, is very 
small. For the determination of section drag mostly results of experiments are used. 
