Tait–Kirchhoff method for determining rotary and unsteady force derivatives

Abstract

The identification of the rotary and unsteady force derivatives through flight tests is very difficult because the sensitivity of the force coefficients with respect to spin rates and time derivatives of the aerodynamic angles is quite small in comparison with the variations of the aerodynamic coefficients caused by the angle of attack. Here, to avoid this difficulty, the estimation of these force derivatives through flight measurements is carried out using an aerodynamic model based on the Tait–Kirchhoff equations, which provide the analytical expression of each aerodynamic coefficient. The model, which exhibits several free parameters, allows to express the rotary force derivatives in terms of apparent mass tensor and of the static moment derivatives whose identifiability is verified about in nearly the entire flight envelope. The model free parameters are identified using an improved version of an identification method proposed by the author in a previous work. Thus, the main idea of the present study is that the measurements of the static moment derivatives and the knowledge of the apparent mass tensor lead to an estimation of these force derivatives. The method is here used to identify the aerodynamic coefficients of a self-launching glider. Several flight tests were accomplished, whose results are compared with those obtained by CFD simulations, using a boundary elements code. This comparison shows that the model free parameters – and the unsteady and rotary force derivatives – estimated with the proposed method, are in agreement with the results calculated by the code.