Lift Force on a Circular Arc Wing

Abstract

The lift force is calculated for a gliding wing with a circular arc top and a flat bottom in a uniform fluid. It is: const ρ U 2 / R 0 , where is the constant fluid density, U is the uniform flow speed far from the wing and is the radius of curvature of the wing’s top surface. To obtain this result two non-linear differential equations in pressure and velocity are combined into one linear governing equation for velocity, which contains a non-constant coefficient, R ( z ), the radius of curvature of the streamlines above the wing as a function of the vertical coordinate z . Bernoulli’s principle along a streamline and the force balance across a streamline (pressure gradient equals centrifugal force) are the starting equations. A solution to the governing equation is derived by providing an algebraic function for R ( z ) that is consistent with observations, and the order of magnitude one constant in the lift force is worked out. It is believed that the present approach to understanding the lift force on a wing has not been tried before. More theoretical and observational work are needed to better specify R ( z ) .