Stochastic analysis of fuel consumption in aircraft cruise subject to along-track wind uncertainty

The effects of along-track wind uncertainty on aircraft fuel consumption are analyzed. The case of cruise flight subject to an average constant wind is considered. The average wind is modeled as a random variable, which in this paper is assumed to follow either a uniform or a beta distribution. The probability density function (pdf) of the fuel consumption is obtained using a numerical approach that is based on the Probability Transformation Method (a method that evolves the wind pdf). The dynamics of aircraft mass evolution in cruise flight is defined by a simple nonlinear equation that can be solved analytically; this exact solution is used to assess the accuracy of the method. A general analysis is performed for arbitrary along-track winds. Comparison of the numerical results with the exact analytical solution shows an excellent agreement in all cases. A linear approximation is analyzed as well, which turns out to be very accurate for this problem. The results show that the standard deviation of the fuel mass distribution varies almost linearly with the standard deviation of the wind, whereas the mean of the fuel mass is practically independent of the wind uncertainty. They also show that, for the same along-track wind uncertainty, the uncertainty in the fuel consumption is larger in the case of headwinds than in the case of tailwinds.