Multiple-phase trajectory optimization for formation flight in civil aviation

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.

Trajectory Optimization of Extended Formation Flights for Commercial Aviation

“…Similar to [18], an induced drag coefficient reduction of 25% (ε = 0.25) is assumed as a baseline for the trailing aircraft within a two-aircraft formation. In a three-ship formation, the second trailing aircraft in the formation typically enjoys a larger induced drag reduction than the first trailing aircraft (flying in the middle) of the string, as it is essentially able to benefit from two wake vortex generators.…”

“…The DOC criterion is essentially a weighted combination of time and fuel costs. DOC-optimized formation flight trajectories have been extensively studied in [18]. In this study, the focus is more environmentally oriented, and the minimum fuel-burn criterion considered herein is assumed to be a good proxy for minimum CO 2 emission.…”

“…Surprisingly, the development of higher-fidelity mission design optimization models-capable of handling real-world complications-has received very little attention within the research community to date. Only recently a study appeared that describes the development of a multi-phase optimal control (MOC) framework for the synthesis of two-ship formation flight missions, based on a high-fidelity point-mass model [18]. The main benefit of using a MOC formulation for the two-ship mission design problem is that it allows the simultaneous optimization of the single two-ship formation flight leg, and the four solo flights legs that link the origin airports to the joining point and the destination airports to the splitting point.…”

“…The main benefit of using a MOC formulation for the two-ship mission design problem is that it allows the simultaneous optimization of the single two-ship formation flight leg, and the four solo flights legs that link the origin airports to the joining point and the destination airports to the splitting point. In [18], the effectiveness of a multi-phase trajectory optimization (formation flight mission design) tool is demonstrated in a case study related to the assembly of two-ship formation flights across the North-Atlantic Ocean in the absence of wind. The results presented in this study not only confirm that formation flight can indeed result in appreciable fuel burn savings, but additionally reveals some very interesting characteristic features of the resulting formation flight trajectories that were not identified before.…”

“…In this study, the original MOC framework conceived in [18] is extended to permit the assembly of three-ship flight formations. As in [18], the effectiveness of the enhanced optimization framework is demonstrated in a transatlantic traversing scenario. An additional aspect addressed in the current study is the assessment of the influence of wind fields on formation flight performance and trajectory shaping.…”