Unsteady thin-airfoil theory for subsonic flow.

An approximate theory has been developed for the unsteady motion of a two-dimensional thin airfoil in subsonic flow. The basic theory is restricted by the condition that (s//?2)2 <^ 1, where e is i/(2n) times the product of the Mach number M and the conventional reduced frequency CM, and ft2 = 1 —M 2. Closed-form expressions are presented for the forces on, the circulation about, and the strength of the vortex wake emanating from a two-dimensional thin airfoil that is subjected to the general class of oscillating upwash distribution whose A dependence may be expanded in a cosine series. Expressions are also set down for three particularly important examples of this upwash distribution, namely the Kemp-type upwash, the convected sinusoidal gust, and the flutter case. Some preliminary comparisons of the present method with the few existing theories for the sinusoidal-gust case reveals good agreement up to at least M = 0.6 and for relatively large values of e.