On Optimal Routing For Commercial Formation Flight

Abstract

Commercial aviation is constantly looking for ways to cope with predicted increases to future demand1 whilst simultaneously trying to mitigate the resulting impact on the environment. This paper explores the possibility of flying in formation, as an alternative to the way commercial flight operates today, in an attempt to optimize current routes and decrease overall fuel burn. One of the immediate benefits of formation flight, over other proposed fuel saving methods,2–4 is the relatively minimal change to the current infrastructure. The majority of today’s commercial airliners can fundamentally observe a reduction in drag from formation flight.5 Although the possibility of designing new aircraft in the future to take advantage of the aerodynamic benefits of this scenario would be a long term goal, in the short term it would not be a necessity. Studies into areas of biomimicry such as geese flying in a ‘V’ formation6,7 have always interested scientists, while the military have long flown in formation for communicative and defensive purposes. More recent studies assessing the aerodynamic possibility of flying in close proximity in order to reduce drag8 coupled with real time flight tests9,10 shows promise that flying in formation can reduce fuel burn and in turn improve performance factors such as range and speed. While some studies show a positive trade o↵ between deviating routes, in order to fly in formation and the reduction in drag it produces,11–15 few have tackled the substantial fleet-assignment problem when routing for formation flight. The massively combinatorial nature of this task means that in order to assess sizeable problems a smart approach is needed. Both centralized and decentralized approaches are explored in Ref. 16, wherein a small case study for the two-aircraft problem is covered. The incorporation of ‘proposal-marriage’ type algorithm explores the idea of joining formation in an ad-hoc fashion. Route optimization studied in Ref. 5, along with a case study, shows significant cost saving potential, while using a more in-depth optimizer, solutions obtained retain many of the restrictions imposed by today’s infrastructure. Although there is a clear interest in harnessing formation flight to improve aircraft performance,5,11–16 little work has been done on the large scale allocation problem. That is, given a set of possible solo flights, how to go about assigning them to particular formation ‘fleets’. The problem in question is highly combinatorial and therefore as the number of flights or size of the fleets increase the possible ways of joining them together grows dramatically. This paper proposes a time-free possible solution method through the use of a FermatToricelli approach which precedes the route assignment problem. Section II begins by first reviewing this fast geometric approach to finding time-free optimal routes with few constraints (previously introduced by the authors in Ref. 17). Then sections III and IV make an extension to this framework to include an increasing level of detail arising from aircraft specific performance factors and di↵erential rates of fuel burn.