Approximate transfer functions for large aspect ratio wings in turbulent flow

TLDR: In this article, the authors derived approximate closed form expressions for the gust transfer functions relating the lift and moments to the upwash in such a wave, and suggested simple scaling laws, based on these results, are then suggested for flight through large scale turbulence.

Abstract: The fundamental aerodynamic problem associated with flight through atmospheric turbulence is calculation of the response of a wing flying through a single sinusoidal wave of upwash with lines of constant phase arbitrarily inclined to the flight path. Approximate closed form expressions for the gust transfer functions" relating the lift and moments to the upwash in such a wave are derived for large aspect ratio rectangular wings in incompressible flow. The lift transfer function is expressed as the usual two-dimensional Sears function multiplied by a factor to correct for finite span and a further factor to account for the span wise gust wave number. Multiplying this expression by the chordwise (or spanwise) center of pressure leads to the pitching (or rolling) moment transfer function. Some simple scaling laws, based on these results, are then suggested for flight through large-scale turbulence.