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 (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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Pahle J, Berger D, Venti M, Duggan C, Faber J, Cardinal K (2012) An initial flight investigation of formation flight for drag reduction on the C-17 aircraft. In: AIAA atmospheric flight mechanics conference, 13–16 August 2012, Minneapolis, U.S.A., p 13
Ning SA, Flanzer TC, Kroo IM (2011) Aerodynamic performance of extended formation flight. J Aircr 48(3):855–865
Veldhuis L, Voskuijl M, Fransen B (2013) Formation flight - fine-tuning of theoretical performance prediction. In: AIAA aerospace sciences meeting, 7–10 January 2013, Grapevine, Texas, U.S.A., p 17
Ning SA, Kroo I, Aftosmis MJ, Nemec M, Kless JE (2014) Extended formation flight at transonic speeds. J Aircr 51(5):1501–1510
Bower GC, Flanzer TC, Kroo IM (2009) Formation geometries and route optimization for commercial formation flight. In: AIAA applied aerodynamics conference, 22–25 June 2009, San Antonio, Texas. U.S.A., p 18
Kent T, Richards A (2015) Analytic approach to optimal routing for commercial formation flight. J Guid Control Dyn 38(10):1872–1884
Xu J, Ning SA, Bower G, Kroo I (2014) Aircraft route optimization for formation flight. J Aircr 51(2):490–501
Xue M, Hornby GS (2012) An analysis of the potential savings from using formation flight in the NAS. In: AIAA guidance, navigation, and control conference, 13–16 August 2012, Minneapolis, U.S.A, p 12
Visser HG (2010) Airplane performance optimisation. In: Encyclopaedia of aerospace engineering. Wiley
Visser HG (2008) Environmentally optimized resolutions of in-trail separation conflicts for arrival flights. J Aircr 45(4):1198–1205
Rao AV, Benson DA, Darby CL, Patterson M, Francolin C, Sanders I, Huntington GT (2010) Algorithm 902: GPOPS, a MATLAB software for solving multiple-phase optimal control problems using the Gauss pseudospectral method. ACM Trans Math Softw 37(2), Article 22., 22.1–22.39
Francolin C, Rao AV (2012) Direct trajectory optimization and costate estimation of state inequality path-constrained optimal control problems using a radau pseudospectral method. In: AIAA guidance, navigation, and control conference, 13–16 August 2012, Minneapolis, U.S.A, p 11
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Hartjes, S., van Hellenberg Hubar, M.E.G., Visser, H.G. (2018). Multiple-Phase Trajectory Optimization for Formation Flight in Civil Aviation. In: Dołęga, B., Głębocki, R., Kordos, D., Żugaj, M. (eds) Advances in Aerospace Guidance, Navigation and Control. Springer, Cham. https://doi.org/10.1007/978-3-319-65283-2_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-65283-2_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-65282-5
Online ISBN: 978-3-319-65283-2
eBook Packages: EngineeringEngineering (R0)