Theory of Airfoil Response in a Gusty Atmosphere. Part I - Aerodynamic Transfer Function

摘要

An approximate closed form expression is derived for the loading on a two-dimensional airfoil passing through an inclined sinusoidal gust. This expression is the basic transfer function required for the construction of the response to any arbitrary localized gust or continuous turbulence by Fourier superposition. The expression, based on linearized impressible lifting surface theory, is asympototically exact in the limiting cases where the reduced frequency (which is proportional to the ratio of airfoil chord to gust wavelength) is either very large. When the gust inclination is such that the nodal lines are perpendicular to the flight path, the resulting special case is a well-known problem of unsteady airfoil theory (Sears' problem). The loading obtained for this case has the form predicted by classical theory. The value for the lift, while not exactly identical to the Sears function, differs from it only slightly in the range of reduced frequency of order unity. It is demonstrated that the accuracy for the general case is of the same order. (Author)