Formulation and System Identification of the Equations of Motion for a Dynamic Wind Tunnel Facility. - Carnduff, S. D.; Cooke, A. K. (Cranfield University, 2008)
This document describes the equations of motion of an aircraft model tested in Cranfield’s 4 degreeof- freedom (DoF) wind tunnel facility. In previous research, the equations have been derived assuming that the model’s centre of gravity (cg) is coincident with the gimbal mechanism about which the model rotates on the rig. However, in this report a general approach is taken with the cg assumed to be located away from the gimbal. The equations are developed from first principles and reduced to a linearised form where motion can be represented as small perturbations about trim. The equations are also decoupled into longitudinal and lateral/direction expressions and converted into state space form. It had been found in practice that models tested in the facility are very responsive in heave and can only be operated open-loop if movement is restricted to purely rotational motion. Therefore, the equations for this 3DoF case are also developed. Having obtained theoretical expressions, a series of wind tunnel tests were conducted on a 1/12 scale BAe Hawk model in order to establish if the theoretical relations were valid in practice. The particular technique used in testing the model was dynamic simulation and the analysis of the experimental data was performed using system identification. An established model structure determination procedure is used to determine which stability and control derivatives should be included in the equations of motion. Frequency domain, equation error parameter estimation is then employed to obtain numerical values for the stability and control derivatives. For both the longitudinal and lateral/directional examples described, the final model structure obtained from experiment matches that derived from theory. Derivatives values obtained from parameter estimation and empirical analysis are also in good agreement.