Validation of Methodology for Estimating Aircraft Unsteady Aerodynamic Parameters from Dynamic Wind Tunnel Tests

A basic problem in flight dynamics is the mathematical formulation of the aerodynamic model for aircraft. This study is part of an ongoing effort at NASA Langley to develop a more general formulation of the aerodynamic model for aircraft that includes nonlinear unsteady aerodynamics and to develop appropriate test techniques that facilitate identification of these models. A methodology for modeling and testing using wide-band inputs to estimate the unsteady form of the aircraft aerodynamic model was developed previously but advanced test facilities were not available at that time to allow complete validation of the methodology. The new model formulation retained the conventional static and rotary dynamic terms but replaced conventional acceleration terms with more general indicial functions. In this study advanced testing techniques were utilized to validate the new methodology for modeling. Results of static, conventional forced oscillation, wide-band forced oscillation, oscillatory coning, and ramp tests are presented. Nomenclature Only the main symbols are introduced here; other symbols are defined in the paper. A, B, C numerator transfer function coefficients b wing span, m a, b1, c indicial function parameters c mean aerodynamic chord, m CL, CN lift and normal force coefficient Cm pitching moment coefficient IAR inclined-axis rolls or oscillatory coning J cost function k non-dimensional frequency, k= ω l /V l characteristic length, l = c /2 PSD power spectral density q pitch rate, rad/sec s Laplace transform variable SF single frequency t time, sec V airspeed, m/sec v measurement noise WB wide band Z vector of output measurements α angle of attack, rad β sideslip angle, rad η state variable in unsteady model θ unknown parameter vector σ 2 variance τ dummy integration variable τ1 non-dimesional time constant φ bank angle, rad ω angular frequency, rad/sec superscripts, subscripts estimate (superscript) A amplitude (subscript) Aerodynamic derivatives ( ) A A A a a C C C a ∂ ∞ ≡ = ∂ 2 2 , , ; , , , , , 2 2 2 4 qc qc c b for A L m orN a or V V V V α β α β = = * Senior Research Engineer, Associate Fellow AIAA † Professor Emeritus, Associate Fellow AIAA