Some Aspects of Non-Stationary Airfoil Theory and Its Practical Application

This paper consists of three notes on the theory of two-dimensional thin airfoils in non-uniform motion: 1. In the first note expressions for the lift and moment of an oscillating airfoil are collected from an earlier paper and are presented in convenient forms for practical application. 2. * In the second note the lift and moment are calculated for a rigid airfoil passing through a vertical-gust pattern having a sinusoidal distribution of intensity. The lift is determined as a function of the reduced frequency (which in this case is proportional to the ratio of the airfoil chord and the wave length of the gust pattern) and is presented in the form of a vector diagram. I t is shown that the lift acts at the quarter-chord point of the airfoil at all times. 3. In the third note the results of 1 and 2 are applied to the calculation of the amplitude of torsional oscillation of a fan blade operating in the wake of a set of pre-rotation vanes. In a numerical example the amplitude is found to be small even when the vanes are spaced so tha t the exciting frequency coincides with the natural frequency of the fan blade. 1. T H E FORCES ON AN OSCILLATING AIRFOIL T SECTION consists of a summary of the results obtained by von Karman and Sears and their application to the general case of translatory and torsional oscillations about an arbitrary axis on the chord line. The principal assumptions are that the flow can be considered two-dimensional and that the airfoil thickness and the amplitude of oscillation are small compared to the chord. In the original paper, two fundamental types of oscillatory motion were considered: ''translatory and rotational. These are characterized by different expressions for the vertical velocity w(x) of the points along the chord of the airfoil. In the translatory oscillation this velocity is constant for all points of the chord; Received September 6, 1940.