Consistent Rational-Function Approximation for Unsteady Aerodynamics

An improved method is developed for the approximation of generalized, unsteady aerodynamic forces by a rational transfer function in the Laplace domain. Whereas the previous methods produce an ill-conditioned eigenvalue problem when the optimized values of two or more poles of the transfer function are close to one another, the present scheme accounts for such frequent cases consistently. Also, the new method results in a large reduction in the computational cost of an optimized aerodynamic rational approximation when compared with the previous procedures for a given accuracy. These improvements are due to the use of higher order poles (as against the simple poles of conventional methods), without increasing the total number of aerodynamic states of the system, and they make the method applicable to routine transient response calculations. The method employs a nongradient optimizing process for the selection of the nonlinear parameters of the transfer function. Approximations are presented for the three-dimensional, subsonic aerodynamics of a high aspect ratio wing.