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.
Hartjes, S., van Hellenberg Hubar, M., & Visser, H. G. (2018). Multiple-phase trajectory optimization for formation flight in civil aviation. CEAS Aeronautical Journal, 10 (2019)(2), 453-462. https://doi.org/10.1007/s13272-018-0329-9