Propagation of Initial Mass Uncertainty in Aircraft Cruise Flight

Abstract

The propagation of initial mass uncertainty in cruise flight is studied. Two cruise conditions are analyzed: one with given cruise fuel load and the other with given cruise range. Two different distributions of initial mass are considered: uniform and gamma type. The generalized polynomial chaos method is used to study the evolution of mean and variance of the aircraft mass. To compute the mass distribution function as a function of time, two approximate methods are developed. These methods are also applied to study the distribution functions of the flight time (in the case of given fuel load) and of the fuel consumption (in the case of given range). The dynamics of mass evolution in cruise flight is defined by a nonlinear equation, which can be solved analytically; 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, hence verifying the methods developed in this work.