Trajectory optimization of extended formation flights for commercial aviation

Sander Hartjes, Hendrikus G. Visser, Marco E.G.van Hellenberg Hubar

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
42 Downloads (Pure)


This paper presents a trajectory optimization study that has been conducted using a recently developed tool for the synthesis and analysis of extended flight formations of long-haul commercial aircraft, with the aim to minimize overall fuel consumption. In extended flight formations, trailing aircraft can attain an appreciable reduction in induced drag and associated reduction in fuel burn by flying in the upwash of the lead aircraft's wake. In the present study, a previously developed multi-phase optimal control (MOC) framework for the synthesis of two-ship flight formations has been extended to include the assembly of three-ship flight formations. Using the extended tool, various numerical experiments have been conducted in relation to the assembly of two-ship and three-ship flight formations in long-haul operations across the North-Atlantic Ocean. Additionally, numerical experiments have been carried out to examine the impact of wind fields on the synthesis and performance of flight formations. Additionally, a parametric investigation has been conducted to assess the sensitivity of the solutions with respect to the degree of the induced drag reduction that might be attained by the trailing aircraft in a formation. The results of the various numerical experiments reveal that formation flight can result in appreciable reductions in fuel burn in comparison to flying solo-particularly when larger formation strings are permitted.

Original languageEnglish
Article number100
Number of pages20
Issue number9
Publication statusPublished - 1 Sep 2019


  • Flight formations
  • Fuel burn
  • Trajectory optimization
  • Wind fields

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