Abstract
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.
Highlights
The potential to significantly reduce aircraft induced drag in extended formation flight has been clearly demonstrated in a range of numerical and experimental studies [1–4]
The results of the delay scenario reveal that the fuel burn for the formation mission with one delayed aircraft is still lower than that for the corresponding solo flights, while the total flight time increased only marginally compared to the no-delay case
When the value of α is increased, Fig. 8 shows that the total flight time decreases while the total fuel burn increases
Summary
The potential to significantly reduce aircraft induced drag in extended formation flight has been clearly demonstrated in a range of numerical and experimental studies [1–4]. The primary reason for resorting to a multi-phase trajectory optimization formulation for the mission design problem is that it allows the concurrent optimization of the single two-aircraft formation flight leg, and the four solo flights legs connecting, respectively, the two origin airports to the rendezvous point and the two destination airports to the splitting point of the formation. In a case study, involving the Transatlantic crossing of two Boeing B747-400 aircraft, the developed multiple-phase optimization tool is deployed to optimize the trajectories of the aircraft that join in formation and experiments are conducted to investigate what the general characteristics and the potential benefits of formation flight are It is explored whether fuel savings can still be obtained if no increase in trip time is permitted relative to flying solo. The take-off and landing phases are not considered in this study and, the initial and final points of the mission are, respectively, the entry and exit points of the Terminal Manoeuvring Area (TMA), located at an altitude of 10,000 ft AGL
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