Determination of Aircraft Cruise Altitude with Minimum Fuel Consumption and Time-to-Climb: An Approach with Terminal Residual Analysis

Taehak Kang and Jaiyoung Ryu
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Taehak Kang: Department of Mechanical Engineering, Chung-Ang University, Seoul 06974, Korea
Jaiyoung Ryu: Department of Mechanical Engineering, Chung-Ang University, Seoul 06974, Korea

Mathematics, 2021, vol. 9, issue 2, 1-22

Abstract: A pandemic situation of COVID-19 has made a cost-minimization strategy one of the utmost priorities for commercial airliners. A relevant scheme may involve the minimization of both the fuel- and time-related costs, and the climb trajectories of both objectives were optimized to determine the optimum aircraft cruise altitude. The Hermite-Simpson method among the direct collocation methods was employed to discretize the problem domain. Novel approaches of terminal residual analysis (TRA), and a modified version, m-σ TRA, were proposed to determine the goals. The multi-objective cruise altitude (MOCA) was different by 2.5%, compared to the one statistically calculated from the commercial airliner data. The present methods, TRA and m-σ TRA were powerful tools in finding a solution to this complex problem. The value σ also worked as a transition criterion between a single- and multi-objective climb path to the cruise altitude. The exemplary MOCA was determined to be 10.91 and 11.97 km at σ = 1.1 and 2.0, respectively. The cost index (CI) varied during a flight, a more realistic approach than the one with constant CI. With validated results in this study, TRA and m-σ TRA may also be effective solutions to determine the multi-objective solutions in other complex fields.

Keywords: multi-objective optimization; cruise altitude; fuel consumption; time to climb; Hermite-Simpson method; trajectory optimization; terminal residual analysis (TRA); m-? terminal residual analysis (m-? TRA) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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