Random Generation of Aerodynamic Derivatives for Monte Carlo Evaluation

Monte Carlo simulation (MCS) has been widely applied in the preflight evaluation of flight systems because of advantages such as its ability to evaluate nonlinear systems with uncertain parameters, which are incorporated into MCS randomly and simultaneously. Some aerodynamic and control derivatives can have significant effects on flight control and vehicle performance, so it is important to evaluate the influences of their uncertainties. However, it has not been easy to incorporate uncertainties of derivatives into MCS appropriately. A derivative is the slope of a curve, such as the Cm–α curve. To randomly vary it for use in MCS, the rotation point on the curve must be determined. However, the deviation from the nominal curve becomes greater as the flight condition, such as α, moves further from the rotation point, which can result in excessive variance of the aerodynamic coefficient. This paper presents a new method to generate derivative and bias uncertainties randomly using a covariance matrix of uncertain parameters. The method is applied to the MCS of an existing experimental flight system, and the MCS results are compared with a result that excludes derivative uncertainties to show how to apply the presented method.