A method for extracting aerodynamic coefficients from free-flight data

Abstract

Methods now used to obtain aerodynamic coefficients from free-flight data introduce assumptions and limitations into the equations of motion (e.g., linear aerodynamics, small amplitudes of oscillation, constant roll rate, etc.) so that closed-form solutions can be obtained. Experimental free-flight data are then “fit” by adjusting coefficients and initial conditions in these expressions. A method described herein eliminates the need for closed-form solutions by employing numerical solutions to the equations of motion. This makes possible a far more general treatment. A least-squares technique employing differential corrections must be used; for this, partial derivatives of each dependent variable with respect to each unknown coefficient, including all initial conditions, must be known accurately at every data station. Application of the method of parametric differentiation yields the required accuracy in these partial derivatives and rapid convergence of the solution is usually obtained. Four cases are presented to illustrate specific points: 1) linear aerodynamics, duplication of existing methods; 2) nonlinear aerodynamics, simultaneous analysis of four ballistic-range flights of models of the Gemini capsule; 3) varying freestream density along a trajectory; and 4) large amplitude (to 40° resultant angle of attack) rolling motion of a trimmed Apollo Command Capsule model. © 1970, American Institute of Aeronautics and Astronautics, Inc., All rights reserved.