Abstract
In this paper we propose a mathematical model for the fuel consumption analysis during aircraft cruise. A closed-form formula that expresses the aircraft’s weight variation over time, and hence, the fuel flow rate, is obtained as a result. Furthermore, a closed-form expression of the aircraft’s main performance parameters is also obtained. We compare the values of such parameters computed by using the Piano-X software and computed by using our mathematical model. Simulation results confirm that our mathematical model provides results very close to reality. Finally, the closed-form formula of the fuel flow rate provided by our model is used to improve the calculation of the carbon dioxide emissions for four example routes, which, unlike here, are usually obtained under the assumption of a constant value of the fuel flow rate.
Highlights
IntroductionFlight dynamics is a discipline that studies the performance of an aircraft flying
Mathematical Model for the AnalysisFlight dynamics is a discipline that studies the performance of an aircraft flying.Among other topics, it studies the influence of aerodynamic, propulsive and gravitational forces on an aircraft
Flight planning is concerned with the estimation of the trip fuel required for a certain mission profile and the fulfillment of the standards established by safety and regulatory agencies (EASA, FAA, ICAO, etc.), along with the requirements of Air Traffic Control (ATC) in order to guarantee the optimal and safest route to the destination airport
Summary
Flight dynamics is a discipline that studies the performance of an aircraft flying. Among other topics, it studies the influence of aerodynamic, propulsive and gravitational forces on an aircraft. One of its main purposes is to provide mathematical models of the aircraft’s state variables as a function of time during the different flight phases, with applications such as fuel consumption analysis. Common methods for the fuel economy analysis of an aircraft include the study of parameters such as fuel burn and fuel efficiency per seat, both of them determined by the interior configuration of the aircraft and the trip distance. The Boeing 767-300ER has an average fuel burn of 5.51 kg/km and a fuel efficiency of 2.56 L/100 km per passenger for a trip distance of 3000 nautical miles (nmi) and a 269-passenger configuration [2]
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