Sears function and lifting surface theory for harmonic gust fields

Abstract

Sears' function for the lift on a two-dimensional airfoil induced by a harmonic gust field in an incompressible flow is reviewed. It is observed that a much simpler function can be defined by a transformation of the gust reference point from the airfoil midchord to its leading edge. The simplicity of the modified Sears function permits accurate interpolation for the large number of reduced frequencies required in a gust frequency response analysis. Approximations to the modified Sears function are discussed for use in preliminary analysis. The form of the transformation appropriate for interpolation of gust loads obtained from lifting surface theory for finite aspect ratio wings is then discussed. Both oneand twodimensional gust fields are considered. It is shown by example calculations for compressible subsonic flow that the transformation required by lifting surface theory is analogous to that required by the two-dimensional incompressible case. It is concluded that the computational savings permitted by interpolation makes lifting surface methods economical for gust frequency response analysis. It is also concluded that the Doublet Lattice Method for subsonic flows has the versatility required for load calculations for both oneand two-dimensional gust fields.