A Mathematical Model for the Analysis of Jet Engine Fuel Consumption During Aircraft Climb and Descent

This paper proposes a mathematical model that studies the fuel consumption of a jet engine aircraft during the climbing and descent flight phases. Such problem is addressed by providing a closed-form formula of the aircraft's rate-of-climb and rate-of-descent, which then enables obtaining a closed-form formula of the aircraft's fuel consumption that provides the closed-form relationship between the aircraft's fuel consumption and aerodynamic, engine and design parameters. In order to validate our mathematical model, a comparison is made between our results and results provided by Piano-X software and accuracy between both is proven. Furthermore, our mathematical model is applied to the calculation of pollutant gas emissions, specifically, we present a closed-form expression that provides the dependency between the mass of pollutant gas emitted and the aircraft's aerodynamic, engine and design parameters.