Estimation of Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Testing

Improved aerodynamic mathematical models, for use in aircraft simulation or flight control design, are required when representing nonlinear unsteady aerodynamics. A key limitation of conventional aerodynamic models is the inability to map frequency and amplitude dependent data into the equations of motion directly. In an effort to obtain a more general formulation of the aerodynamic model, researchers have been led to a parallel requirement for more general testing methods. Testing for a more comprehensive model can lead to a very time consuming number of tests especially if traditional single frequency harmonic testing is attempted. This paper presents an alternative to traditional singlefrequency forced-oscillation testing by utilizing Schroeder sweeps to efficiently obtain the frequency response of the unsteady aerodynamic model. Schroeder inputs provide signals with a flat power spectrum over a specified frequency band. For comparison, experimental results using the traditional single-frequency inputs are also considered. A method for data analysis to determine an adequate unsteady aerodynamic model is presented. Discussion of associated issues that arise during this type of analysis and comparison of results using traditional single frequency analysis are provided. * Senior Research Engineer, Senior Member AIAA † Professor Emeritus, Associate Fellow AIAA Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The U.S. Government has a royaltyfree license to exercise all rights under the copyright claimed herein for Governmental purposes. All other rights are reserved by the copyright owner. Nomenclature A, B, C numerator transfer function coefficients a, b1 indicial function parameters c mean aerodynamic chord, m CL lift coefficient Cm pitching moment coefficient J cost function k non-dimensional frequency, k= ω l /V l characteristic length, l = c /2 N number of frequencies PSD power spectral density q pitch rate, rad/sec s Laplace transform variable t time, sec V airspeed, m/sec v measurement noise Z output measurement vector α angle of attack, rad θ unknown parameter vector σ 2 variance τ dummy integration variable ω angular frequency, rad/sec