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.

Aerodynamic Characterizations of Asymmetric and Maneuvering 105mm, 120mm, and 155mm Fin-Stabilized Projectiles Derived from Telemetry Experiments

“…This analysis is conducted within the Extending Telemetry Reduction to Aerodynamic Coefficients and Trajectory Reconstruction (EXTRACTR) software. The EXTRACTR methodology, its validation, and past applications have been documented previously (3)(4)(5)(6).…”

High-order iterative learning identification of projectile's aerodynamic drag coefficient curve from radar measured velocity data

“…The Doppler tracking radar such as TERMA's OPOS DR-582 has become a common equipment in proving grounds. Many efforts have been made to extract the accurately and rapidly based on a parameter identification [1], [2] framework [3]- [9]. By combining the ballistic model into a Newton-Raphson-like iteration scheme, the differential correction method is proposed in [3] for searching aerodynamic parameters, which was applied to determine the aerodynamic drag from radar data in [4].…”

Inflatable Re-entry Vehicle Experiment (IRVE) Design Overview

“…A pressure transducer downstream of the differential regulator set and another transducer measuring ambient pressure inside the centerbody will be used to verify regulator performance and will also confirm that the pyrovalves successfully opened. 21 The calculated aerodynamics of the vehicle are then tabulated in a database for use within POST trajectory predictions. Figure 25 shows a shadowgraph of the IRVE model during a ballistic range shot.…”