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Keywords = terminal residual analysis (TRA)

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22 pages, 3949 KiB  
Article
Determination of Aircraft Cruise Altitude with Minimum Fuel Consumption and Time-to-Climb: An Approach with Terminal Residual Analysis
by Taehak Kang and Jaiyoung Ryu
Mathematics 2021, 9(2), 147; https://doi.org/10.3390/math9020147 - 11 Jan 2021
Cited by 2 | Viewed by 3845
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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