Airfoil Theory for Non-Uniform Motion

The basic conceptions of the circulation theory of airfoils are reviewed briefly, and the mechanism by which a “wake” of vorticity is produced by an airfoil in non-uniform motion is pointed out. It is shown how the lift and moment acting upon an airfoil in the two-dimensional case may be calculated directly from simple physical considerations of momentum and moment of momentum. After a calculation of the induction effects of a wake vortex, formulae for the lift and moment are obtained which are applicable to all cases of motion of a two-dimensional thin airfoil in which the wake produced is approximately flat; i.e., in which the movement of the airfoil normal to its mean path is small. \nThe general results are applied first to the case of an oscillating airfoil and then to the problem of a plane airfoil entering a “sharp-edged” gust. In the latter case the rate of increase of the lift after the entrance of the airfoil into the gust boundary is determined, and it is shown that during the entire process the lift acts at the quarter-chord point of the airfoil. \nThe intention of the authors has been to make the airfoil theory of non-uniform motion more accessible to engineers by showing the physical significance of the various steps of the mathematical deductions, and to present the results of the theory in a form suitable for immediate application to certain flutter and gust problems.