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.

In this paper a tool is developed that optimizes the trajectories of multiple airliners that seek to join in formation to minimize overall fuel consumption or Direct Operating Cost (DOC). The developed optimization framework relies on optimal control theory to solve the multiple-phase optimization problem associated to flight formation assembly. A reduced-order point-mass formulation is employed for modelling of the aircraft dynamics within an extended flight formation, and of the solo flight legs that connect the flight formation to the origin and destination airports. When in formation, a discount factor is applied to simulate a reduction in the induced drag of the trailing aircraft. Using the developed tool a case study has been conducted pertaining to the assembly of two-aircraft formation flights across the North-Atlantic. Results are presented to illustrate the synthesis of the formation trajectories and to demonstrate the potential for reducing fuel and operating cost. The results of the various numerical experiments show that formation flight can lead to significant reductions in fuel consumption compared to flying solo, even when the original trip times are maintained. Also, the results clearly reveal how the performance and the characteristics of the flight formation mission - notably the location of rendezvous and splitting points - are affected when one aircraft seeking to join the formation suffers a departure delay.

In this paper a tool is developed that optimizes the trajectories of multiple airliners that seek to join in formation to minimize overall fuel consumption or direct operating cost. The developed optimization framework relies on optimal control theory to solve the multiple-phase optimization problem associated to flight formation assembly. A reduced-order point-mass formulation is employed for modelling of the aircraft dynamics within an extended flight formation, and of the solo flight legs that connect the flight formation to the origin and destination airports. When in formation, a discount factor is applied to simulate a reduction in the induced drag of the trailing aircraft. Using the developed tool a case study has been conducted pertaining to the assembly of two-aircraft formation flights across the North-Atlantic. Results are presented to illustrate the synthesis of the formation trajectories and to demonstrate the potential for reducing fuel and operating cost. The results of the various numerical experiments show that formation flight can lead to significant reductions in fuel consumption compared to flying solo, even when the original trip times are maintained. Additionally, the results clearly reveal how the performance and the characteristics of the flight formation mission—notably the location of rendezvous and splitting points—are affected when one aircraft seeking to join the formation suffers a departure delay.