The force and moment on an oscillating aerofoil

In an interesting paper1, published early in 1925 in the Zeitschrift fur angewandte Mathematik und Mechanik, Dr. H. Wagner has developed a method of calculating the lift and pitching moment of an aerofoil in accelerated motion. Dr. Wagner’s paper is confined mainly to linear motion at a constant angle of incidence, but towards the end of the paper the analysis is extended to include the effects of an angular velocity also. Towards the end of last year I became interested in the problem of an oscillating aerofoil and wished to calculate the aerodynamic damping moment experienced by the aerofoil, since certain wind tunnel experiments had suggested that this damping moment increased with the frequency of the oscillation. If the amplitude of the oscillation is small, Dr. Wagner’s equations may by applied directly to the problem of the oscillating aerofoil, and the following paper is a brief account of my calculations, full details of which are contained in two reports2 of the R. and M. Series. In passing I may mention that I derived the expressions for the force and moment on the aerofoil by suitable transformations of the fundamental hydrodynamical equations on lines differing from those followed by Dr. Wagner, and so obtained an independent check on his equations.