Analysis of the Effect of Uncertain Average Winds on Cruise Fuel Load

Abstract

The required fuel load of an aircraft for a given cruise range with uncertain average wind (modelled by a uniform distribution) is studied in this work. The fuel mass probability density function is obtained using an approximate method previously developed by the authors. In addition, the Generalized Polynomial Chaos method is used to study the mean and typical deviation of the required fuel mass. The dynamics of mass evolution in cruise flight is defined by a nonlinear equation, which can be solved analytically to obtain the fuel mass; this exact solution is used to assess the accuracy of the proposed methods. Comparison of the numerical results with the exact analytical solutions shows an excellent agreement in all cases. The results are also compared with the Monte Carlo method, which requires a much larger computation time to obtain similar results.