Modified Exponential Series Approximation for the Theodorsen Function

An improved method is developed for the approximation of unsteady aerodynamics in the time domain by a series of decaying exponentials. The new method is different from the previous procedures in that it consistently accounts for the case when the optimum values of the lag parameters in the exponential series are close to one another. This is achieved by introducing a time-weighted exponential series for the repeated pole case. The method uses a nongradient optimizing procedure. Approximations are presented for Theodorsen's lift deficiency function and results are compared with those of a gradient-based method that was published recently.