Hydrofoil is a specially designed hydrodynamic body that creates significant lift at minimum drag. On a hydrofoil boat this lift support the weight of the ship. Resistance is greatly reduced since only foils and struts are in the water.
Hydrofoil lift can be calculated using equation (1), where 'rho' is the water density, V is the speed, C is the lift coefficient, S is the area of a hydrofoil.
Lift coefficient is determined by expression (2).
For practical calculations in real viscous liquid, the derivative of lift coefficient on the attack angle and the zero-angle are taken according to expression (3), where f is the profile camber. Reduced values (wirh overbars) are normalized by a foil chord. Angles are in radians.
The influence of the free water surface is accounted by function (4), where c is the largest thickness of the foil and h is the foil depth.
Modification of zero-angle due to the free surface proximity is calculated using equation (5).
The influence of the foil shape on downwash and induction resistance is approximated by expression (6). The aspect ratio 'lambda' equals to the span divided by the chord for rectangular foils.
Function 'dzetta' accounts for the influence of the foil depth on downwash. This function can be calculated by equation(7) at condition (8).
Expression (2) may be applied for planar foils. In the case of inclined foils, special diagrams are applied for calculation of additional decrement or strip-wise integration is carried out.
Lift of the foils with stabilizers crossing the water surface is calculated by taking a horizontal projection instead of the actual foil area, and the depth is substituted by its average value.
Lift formula in Excel
(implementation by Harry Larsen)
More detailed description of engineering formulae (sufficiently simple and reliable) for hydrofoil hydrodynamics will be given in my new book.