Model for Estimating Unsteady Force Derivatives

The estimation of the unsteady force derivatives through flight measurements is difficult to perform because the sensitivity of the force coefficients with respect to spin rate and time derivatives of the aerodynamic angles is smaller than the static variations of the aerodynamic coefficients. Thus, an analysis that uses flight measurements can be insufficient to adequately identify these derivatives. A new model for calculating the aerodynamic coefficients in the incompressible regime is proposed, which is based on the linear property of the continuity equation. From this, all the coefficients are linked with each other because these arise from the pressure distribution over the wetted surface. The model provides the analytical expressions of the aerodynamic coefficients, which include free parameters that have to be identified. The model, based on the Lagrange equations method, allows the unsteady force derivatives to be analytically expressed in terms of the vehicle apparent mass tensor and of the static moment derivatives for which the identifiability is verified in nearly the entire flight envelope. The model was applied to the calculation of the aerodynamic coefficients and of the force derivatives of a glider. The obtained results show that the proposed model is able to perform an excellent fitting of these unsteady force derivatives in function of the steady moment derivatives and of the apparent mass tensor.