Foil Drag

Resistance of a hydrofoil can be found by equation(1), where 'rho' is the liquid density, V is the speed, C is the resistance coefficient, and S is the area of the hydrofoil. Resistance coefficient is the sum of profile, induced, and wave drag coefficients (2). Profile drag appears due to the liquid viscosity and includes friction and form resistance. For small positive attack angles of flat-convex profiles, it can be computed by equation (3), where 'ksi' is the resistance coefficient of an equivalent plate determined by Prandtl-Shlihting-Nikuradze diagram, m is depended on C and (varies from 0.4 to 0.7), 'fi' is the relative decompression on the upper side of a foil, and k is taken from expression (4) of the Lift section. In the flow around a foil with a finite span, upward leak of the fluid occurs around the side ends of a foil, accompanied by a fomration of free vorteces. The reason for the appearance of these vorteces is the pressure difference between two foil sides. The vortices force the flow downward, so that the hydrodynamic force deviates backward, and the actual attack angle decreases. The induced resistance coefficient can be calculated by equation (4), where 'delta' (5) is the correction for a rectangular foil (in comparison with an elliptic foil), 'lambda' is the aspect ratio, and 'dzetta' is taken from expression (7) of Lift section. When a foil is moving in the vicinity of a free surface, a wave system appears downstream. For practical calculation of the wave resistance coefficient, one can use the simplest formula (6), where Fr is the Froude number based on a foil chord.

Note that the wave drag can be calculted for high speed only, otherwise expression (6) will give negative values. Note that this method is applicable only for a single foil in calm waters.