An analytical computation of aircraft’s longitudinal trimmed conditions considering its fuel mass flow rate

Abstract

The aim of this article is to give simple expressions of aircraft’s longitudinal trimmed conditions taking into account the instantaneous fuel mass flow rate, i.e. the variation of total mass. The computation of aircraft trim points is not a new problem. Nevertheless, current analytical computations are classically performed with a constant total weight of the aircraft, hence assuming that the rate of decrease of the weight due to the fuel mass flow rate has insignificant effects on the results. Thus, the goal of this study has been to assess the effect of weight variation on aircraft trimmed condition and to compute correctly “extended trimmed conditions” defined as the equilibrated conditions in flight considering the weight decrease of the aircraft. It has been demonstrated that the weight variation must have an ad-hoc form to lead to extended trimmed conditions. Moreover, extended trimmed conditions do not correspond to a perfect level flight as it is the case at constant weight, but must present a slightly positive flight path angle leading to a regular increase in altitude. And the corrected longitudinal commands including throttle and elevator positions at a given airspeed and altitude have been computed for extended trimmed conditions and compared to the basic case at constant weight. Finally, all the analytical expressions given in this article have been verified through a numerical simulation performed in the case of a twin-engine aircraft representative of the Airbus wide-body family.