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New flight plan optimisation method utilising a set of alternative final point arrival time targets (RTA constraints)

Published online by Cambridge University Press:  08 July 2021

R.I. Dancila
Affiliation:
Université du Québec, École de Technologie Supérieure, Laboratory of Research in Active Control, Avionics, and Aeroservoelasticity LARCASE, Montréal, Quebec, H3C 1K3, Canada
R.M. Botez*
Affiliation:
Université du Québec, École de Technologie Supérieure, Laboratory of Research in Active Control, Avionics, and Aeroservoelasticity LARCASE, Montréal, Quebec, H3C 1K3, Canada

Abstract

This study investigates a new aircraft flight trajectory optimisation method, derived from the Non-dominated Sorting Genetic Algorithm II method used for multi-objective optimisations. The new method determines, in parallel, a set of optimal flight plan solutions for a flight. Each solution is optimal (requires minimum fuel) for a Required Time of Arrival constraint from a set of candidate time constraints selected for the final waypoint of the flight section under optimisation. The set of candidate time constraints is chosen so that their bounds are contiguous, i.e. they completely cover a selected time domain. The proposed flight trajectory optimisation method may be applied in future operational paradigms, such as Trajectory-Based Operations/free flight, where aircraft do not need to follow predetermined routes. The intended application of the proposed method is to support Decision Makers in the planning phase when there is a time constraint or a preferred crossing time at the final point of the flight section under optimisation. The Decision Makers can select, from the set of optimal flight plans, the one that best fits their criteria (minimum fuel burn or observes a selected time constraint). If the Air Traffic Management system rejects the flight plan, then they can choose the next best solution from the set without having to perform another optimisation. The method applies for optimisations performed on lateral and/or vertical flight plan components. Seven proposed method variants were evaluated, and ten test runs were performed for each variant. For five variants, the worst results yielded a fuel burn less than 90kg (0.14%) over the ‘global’ optimum. The worst variant yielded a maximum of 321kg (0.56%) over the ‘global’ optimum.

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Royal Aeronautical Society

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References

REFERENCES

Ng, H.K., Sridhar, B. and Grabbe, S. “A practical approach for optimizing aircraft trajectories in winds,” 2012 IEEE/AIAA 31st Digital Avionics Systems Conference (DASC), Williamsburg, VA, October 2012, pp 3D6-1–3D6-14. DOI: 10.1109/DASC.2012.6382319 CrossRefGoogle Scholar
Ballin, M.G., Williams, D.H., Allen, B.D. and Palmer, M.T. “Prototype flight management capabilities to explore temporal RNP concepts,” 2008 IEEE/AIAA 27th Digital Avionics Systems Conference, St. Paul, MN, October 2008, pp 3.A.6-1–3.A.6-12. DOI: 10.1109/DASC.2008.4702797 CrossRefGoogle Scholar
Patrick, N.J.M. and Sheridan, T.B. “Modeling decision-making for vertical navigation of long-haul aircraft,” SMC’98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218), San Diego, October 1998, vol.1, pp 885–890. DOI: 10.1109/ICSMC.1998.725527 CrossRefGoogle Scholar
FAA, “Title 14 – Chapter 1 – Subchapter F - Air traffic and general operating rules”, Electronic Code of Federal Regulations, Title14: Aeronautics and Space, Retrieved from https://www.ecfr.gov/cgi-bin/text-idx?SID=d478b198bb6aac8e070a37a06181eeec&mc=true&tpl=/ecfrbrowse/Title14/14CIsubchapF.tpl Google Scholar
Fanti, M.P., Pedroncelli, G., Stecco, G. and Ukovich, W. “Modeling and optimization of aircraft trajectories: a review,” 2012 7th International Conference on System of Systems Engineering (SoSE), Genova, Italy, July 2012, pp 235–240. DOI: 10.1109/SYSoSE.2012.6384209 CrossRefGoogle Scholar
Ballin, M.G., Wing, D., Hughes, M. and Conway, S. “Airborne separation assurance and traffic management: research of concepts and technology”, Guidance, Navigation, and Control Conference and Exhibit, Portland, OR, August 1999, pp 3989. DOI: 10.2514/6.1999-3989 CrossRefGoogle Scholar
Rodionova, O., Sibihi, M., Delahaye, D. and Mongeau, M. “Optimization of aircraft trajectories in North Atlantic oceanic airspace”, ICRAT 2012, 5th International Conference on Research in Air Transportation, Berkley, CA, May 2012. Retrieved from https://hal-enac.archives-ouvertes.fr/hal-00938895/ Google Scholar
Torres, S. and Delpome, K.L. “An integrated approach to air traffic management to achieve trajectory based operations,” 2012 IEEE/AIAA 31st Digital Avionics Systems Conference (DASC), Williamsburg, VA, October 2012, pp 3E6-1–3E6-16. DOI: 10.1109/DASC.2012.6382325 CrossRefGoogle Scholar
Cate, K. “Challenges in achieving trajectory-based operations.” In 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, pp 443, Grapevine, (Dallas/Ft. Worth), TX, January 2013. DOI: 10.2514/6.2013-443 CrossRefGoogle Scholar
Altus, S., “Effective flight plans can help airlines economize”, Boeing AERO Magazine, Issue 35, Quarter 03, 2009, pp 27–30. Retrieved from https://www.boeing.com/commercial/aeromagazine/articles/qtr_03_09/pdfs/AERO_Q309_article08.pdf Google Scholar
Underwood, M.C., Cotton, W.B., Hubbs, C.E., Vincent, M.J., Sagar, K.C. and Karr, D.A. “Incorporation of time of arrival constraints in a trajectory optimization technology,” NASA/TM-2020-5005117, Hampton, 2020.Google Scholar
Di Vito, V., Corraro, F., Ciniglio, U. and Verde, L.An overview on systems and algorithms for on-board 3D/4D trajectory management”. Recent Patents on Engineering, 2009, 3 (3), pp 149169. DOI: 10.2174/187221209789117744 CrossRefGoogle Scholar
Chaimatanan, S., Delahaye, D. and Mongeau, M. “A methodology for strategic planning of aircraft trajectories using simulated annealing”, ISIATM 2012, 1st International Conference on Interdisciplinary Science for Air traffic Management, Daytona Beach, FL. Retrieved from https://hal-enac.archives-ouvertes.fr/hal-00912772/ Google Scholar
Qu, Y., Zhang, Y. and Zhang, Y. “Optimal flight path planning for UAVs in 3-D threat environment.”, In 2014 International Conference on Unmanned Aircraft Systems (ICUAS), Orlando, FL, May 2014, pp 149–155. DOI: 10.1109/ICUAS.2014.6842250 CrossRefGoogle Scholar
Wickramasinghe, N.K., Harada, A. and Miyazawa, J. “Flight trajectory optimization for an efficient air transportation system”, In 28th International Congress of the Aeronautical Science (ICAS 2012), September 2012, Birsbane, Australia.Google Scholar
Rodionova, O., Delahaye, D., Sbihi, M. and Mongeau, M. “Trajectory prediction in North Atlantic oceanic airspace by wind networking,” 2014 IEEE/AIAA 33rd Digital Avionics Systems Conference (DASC), Colorado Springs, CO, October 2014, pp 7A3-1–7A3-15. DOI: 10.1109/DASC.2014.6979511 CrossRefGoogle Scholar
Chamseddine, A., Zhang, Y. and Rabbath, C.A. “Trajectory planning and re-planning for fault tolerant formation flight control of quadrotor unmanned aerial vehicles.” In 2012 American Control Conference (ACC), Montreal, QC, 2012, pp 3291–3296. DOI: 10.1109/ACC.2012.6315363 CrossRefGoogle Scholar
Woods, S., Vivona, R.A., Wing, D.J. and Burke, K.A. “Traffic aware planner for cockpit-based trajectory optimization”, 16th AIAA Aviation Technology, Integration, and Operations Conference, Washington, D.C., June 2016, DOI: 10.2514/6.2016-4067 CrossRefGoogle Scholar
Woods, S., Vivona, R.A., Roscoe, R., LeFebvre, B.C., Wing, D.J. and Ballin, M.G. “A Cockpit-based application for traffic aware trajectory optimization”, AIAA Guidance, Navigation, and Control (GNC) Conference, Boston, MA, August 2013, DOI: 10.2514/6.2013-4967 CrossRefGoogle Scholar
Nuic, A., Poles, D. and Mouillet, V.BADA: an advanced aircraft performance model for present and future ATM systems”. International Journal of Adaptive Control and Signal Processing, 2010, 24 (10), pp 850866. DOI: 10.1002/acs.1176 CrossRefGoogle Scholar
Eurocontrol, “BADA: aircraft performance model,” Retrieved from https://simulations.eurocontrol.int/solutions/bada-aircraft-performance-model/ Google Scholar
Nuic, A. “User manual for base of aircraft data (BADA) revision 3.8”, Eurocontrol Experimental Centre, EEC Technical/Scientific Report No. 2010-003, April 2010, Retrieved from https://www.eurocontrol.int/sites/default/files/library/007_BADA_User_Manual.pdf Google Scholar
Eurocontrol, “Documents for BADA Version 3.7”, Retrieved from https://www.eurocontrol.int/eec/public/standard_page/proj_BADA_documents_37.html Google Scholar
Murrieta-Mendoza, A. and Botez, R. “Aircraft vertical route optimization deterministic algorithm for a flight management system,” SAE Technical Paper 2015-01-2541, 2015. DOI: 10.4271/2015-01-2541 CrossRefGoogle Scholar
Sibin, Z., Guixian, L. and Junwei, H. “Research and modelling on performance database of flight management system,” In 2010 2nd International Asia Conference on Informatics in Control, Automation and Robotics (CAR), Wuhan, China, March 2010, pp 295–298. DOI: 10.1109/CAR.2010.5456841 CrossRefGoogle Scholar
Ramasamy, S., Sabatini, R., Gardi, A. and Liu, Y. “Novel flight management system for real-time 4-dimensional trajectory based operations”, In proceedings of AIAA Guidance, Navigation, and Control conference 2013 (GNC 2013), Boston, MA, USA, 2013. DOI: 10.2514/6.2013-4763 CrossRefGoogle Scholar
Ramasamy, S., Sabatini, R., Gardi, A. and Kistan, T.Next generation flight management system for real-time trajectory based operations”. Applied Mechanics and Materials, 2014, 629, pp 344349, . DOI: 10.4028/www.scientific.net/AMM.629.344 CrossRefGoogle Scholar
Ghazi, G. and Botez, R. Development of a high-fidelity simulation model for a research environment, SAE Technical Paper 2015-01- 2569, 2015. DOI: 10.4271/2015-01-2569 CrossRefGoogle Scholar
Ghazi, G., Botez, R. and Achigui, J.M.Cessna citation X engine model identification from flight tests.SAE International Journal of Aerospace, 2015, 8 (2), pp 203213. DOI: 10.4271/2015-01-2390 CrossRefGoogle Scholar
Murrieta-Mendoza, A., Demange, S., George, F. and Botez, R. “Performance DataBase creation using a level D simulator for Cessna Citation X aircraft in cruise regime.” In IASTED Modeling, Identification and Control Conference, Innsbruck, Austria. 2015. DOI: 10.2316/P.2015.826-028 CrossRefGoogle Scholar
Ghazi, G., Botez, R.M. and Tudor, M. “Performance database creation for Cessna Citation X aircraft in climb regime using an aero-propulsive model developed from flight tests.” In Sustainability 2015: Environmental Sustainability in Design and Operations of Aircraft, Montreal, QC, Canada, Sept. 22–24, 2015, American Helicopter Society.Google Scholar
Dancila, B.D., Botez, R. and Labour, D.Fuel burn prediction algorithm for cruise, constant speed and level flight segments.The Aeronautical Journal, 2013, 117 (1191), pp 491504. DOI: 10.1017/S0001924000008149 CrossRefGoogle Scholar
NOAA, “NCEP WMO GRIB2 documentation”, Retrieved from http://www.nco.ncep.noaa.gov/pmb/docs/grib2/grib2_doc/ Google Scholar
Environment Canada, “What is GRIB?” Retrieved from https://weather.gc.ca/grib/what_is_GRIB_e.html Google Scholar
Environment Canada, “Global deterministic prediction system”, Retrieved from http://data.ec.gc.ca/data/weather/products/global-deterministic-prediction-system/?lang=en Google Scholar
Buehner, M., McTaggart-Cowan, R., Beaulne, A., Charette, C., Garand, L., Heilliette, S., Lapalme, E., Laroche, S., Macpherson, S.R., Morneau, J. and Zadra, A.Implementation of deterministic weather forecasting systems based on ensemble variational data assimilation at Environment Canada. Part I: The global system.Monthly Weather Review, 2015, 143 (7), pp 25322559. DOI: 10.1175/MWR-D-14-00354.1 CrossRefGoogle Scholar
Environment Canada, “Regional deterministic prediction system”, Retrieved from http://data.ec.gc.ca/data/weather/products/regional-deterministic-prediction-system/?lang=en Google Scholar
Caron, J.F., Milewski, T., Buehner, M., Fillion, L., Reszka, M., Macpherson, S. and St-James, J.Implementation of deterministic weather forecasting systems based on ensemble–variational data assimilation at environment Canada. Part II: the regional system.Monthly Weather Review, 2015, 143 (7), pp 25602580. DOI: 10.1175/MWR-D-14-00353.1 CrossRefGoogle Scholar
Cole, R.E., Green, S., Jardin, M., Schwartz, B. and Benjamin, S. “Wind prediction accuracy for air traffic management decision support tools.”, In 3rd USA/Europe Air Traffic Management R&D Seminar, Napoli, Italy, June 2000.Google Scholar
Wynnyk, C.M. “Wind analysis in aviation applications”, In 2012 IEEE/AIAA 31st Digital Avionics Systems Conference (DASC), Williamsburg, VA, October 2012, pp 5C2-1–5C2-10. DOI: 10.1109/DASC.2012.6382366 CrossRefGoogle Scholar
Bronsvoort, J., McDonald, G., Potts, R. and Gutt, E. “Enhanced descent wind forecast for aircraft.” In 9th USA/Europe Air Traffic Management Research and Development Seminar (ATM2011), Berlin, Germany, June 2011. Retrieved from http://atmseminar.org/seminarContent/seminar9/papers/25-Bronsvoort-Final-Paper-4-6-11.pdf Google Scholar
Stohl, A., Wotawa, G., Seibert, P. and Kromp-Kolb, H.Interpolation errors in wind fields as a function of spatial and temporal resolution and their impact on different types of kinematic trajectories.Journal of Applied Meteorology, 1995, 34 (10), pp 21492165. DOI: 10.1175/1520-0450(1995)034<2149:IEIWFA>2.0.CO;2 2.0.CO;2>CrossRefGoogle Scholar
Stohl, A.Computation, accuracy and applications of trajectories - a review and bibliography.Atmospheric Environment, 1998, 32 (6), pp 947966. DOI: 10.1016/S1352-2310(97)00457-3 CrossRefGoogle Scholar
Lewis, T.A., Burke, K.A., Underwood, M.C. and Wing, D.J. “Weather design considerations for the TASAR traffic aware planner”, AIAA Aviation 2019 Forum, Dallas, Texas, June 2019, DOI: 10.2514/6.2019-3616 CrossRefGoogle Scholar
Stell, L. “Predictability of top of descent location for operational idle-thrust descents”, In 10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Fort Worth, Texas, September 2010, pp 9116. DOI: 10.2514/6.2010-9116 CrossRefGoogle Scholar
Stell, L. “Analysis of flight management system predictions of idle-thrust descents”, In 29th Digital Avionics Systems Conference, Salt Lake City, UT, October 2010, pp 1.E.2-1–1.E.2-13. DOI: 10.1109/DASC.2010.5655506 CrossRefGoogle Scholar
De Smedt, D. and Berz, G. “Study of the required time of arrival function of current FMS in an ATM context”, IEEE/AIAA 26th Digital Avionics Systems Conference, DASC’07, Dallas, TX, October 2007, pp 1.D.5-1–1.D.5-10. DOI: 10.1109/DASC.2007.4391837 CrossRefGoogle Scholar
Dancila, R.I. and Botez, R.M. “New atmospheric data model for constant altitude accelerated flight performance prediction calculations and flight trajectory optimization algorithms”, Proceedings of the Institution of Mechanical Engineers Part G: Journal of Aerospace Engineering, 2020. DOI: 10.1177/0954410020945555 CrossRefGoogle Scholar
Schreur, J.M. “B737 Flight management computer flight plan trajectory computation and analysis”. In Proceedings of the 1995 American Control Conference ACC’95, 1995, Vol.5, pp 3419–3424. DOI: 10.1109/ACC.1995.532246 CrossRefGoogle Scholar
Karr, D.A., Vivona, R.A., Woods, S. and Wing, D.J. “Point-mass aircraft trajectory prediction using a hierarchical, highly-adaptable software design”, AIAA Modeling and Simulation Technologies Conference, Denver, Colorado, June 2017, DOI: 10.2514/6.2017-3336 CrossRefGoogle Scholar
Dancila, B.D. and Botez, R. “Construction of an aircraft’s VNAV flight envelope for in-FMS flight trajectory computation and optimization”, In 14th AIAA Aviation Technology, Integration, and Operations Conference pp 2291, 2014. DOI: 10.2514/6.2014-2291 CrossRefGoogle Scholar
Dancila, B.D., Beulze, B. and Botez, R.M.Geometrical vertical trajectory optimization – comparative performance evaluation of phase versus phase and altitude-dependent preferred gradient selection”. IFAC-PapersOnLine, 2016, 49 (17) pp 1722, DOI: 10.1016/j.ifacol.2016.09.004.CrossRefGoogle Scholar
Dancila, B.D., Beulze, B. and Botez, R.M.Flight phase and altitude-dependent geometrical vertical flight plan optimization minimizing the total number of vertical plan segments.” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2019, 233 (13) pp 48254838. DOI: 10.1177/0954410019832127 CrossRefGoogle Scholar
Yu, X. and Zhang, Y.Sense and avoid technologies with applications to unmanned aircraft systems: review and prospects.Progress in Aerospace Sciences, 2015, 74, pp 152166. DOI: 10.1016/j.paerosci.2015.01.001 CrossRefGoogle Scholar
Ceruti, A. and Marzocca, P.Heuristic optimization of Bezier curves based trajectories for unconventional airships docking”. Aircraft Engineering and Aerospace Technology, 2017, 89 (1), pp 7686. DOI: 10.1108/AEAT-11-2014-0200 CrossRefGoogle Scholar
Liden, S. “Optimum 4D guidance for long flights,” In IEEE/AIAA 11th Digital Avionics Systems Conference, Seattle, WA, October 1992, pp 262–267. DOI: 10.1109/DASC.1992.282146 CrossRefGoogle Scholar
Hagelauer, P. and Mora-Camino, F.A soft dynamic programming approach for on-line aircraft 4D-trajectory optimization”. European Journal of Operational Research, 1998, 107 (1), pp 8795. DOI: 10.1016/S0377-2217(97)00221-X CrossRefGoogle Scholar
Murrieta Mendoza, A., Bunel, A. and Botez, R.M. “Aircraft vertical reference trajectory optimization with a RTA constraint using the ABC algorithm.”, In 16th AIAA Aviation Technology, Integration, and Operations Conference, Washington, D.C., June 2016, pp 4208. DOI: 10.2514/6.2016-4208 CrossRefGoogle Scholar
Gardi, A., Sabatini, R. and Ramasamy, S. Multi-objective optimisation of aircraft flight trajectories in the ATM and avionics context. Progress in Aerospace Sciences, 2016, 83, pp 136. DOI: 10.1016/j.paerosci.2015.11.006 CrossRefGoogle Scholar
Diaz-Mercado, Y., Lee, S.G., Egerstedt, M. and Young, S. “Optimal trajectory generation for next generation flight management systems,” In 2013 IEEE/AIAA 32nd Digital Avionics Systems Conference (DASC), East Syracuse, NY, October 2013, pp 3C5-1–3C5-10. DOI: 10.1109/DASC.2013.6712566 CrossRefGoogle Scholar
Ceruti, A., Voloshin, V. and Marzocca, P.Heuristic algorithms applied to multidisciplinary design optimization of unconventional airship configuration.Journal of Aircraft, 2014, 51 (6), pp 17581772. DOI: 10.2514/1.C032439 CrossRefGoogle Scholar
Ceruti, A., Fiorini, T., Boggi, S. and Mischi, L.Engineering optimization based on dynamic technique for order preference by similarity to ideal solution fitness: Application to unmanned aerial vehicle wing airfoil geometry definition.Journal of Multi-Criteria Decision Analysis, 2018, 25, (34), pp 88100. DOI: 10.1002/mcda.1637 CrossRefGoogle Scholar
Marler, R. and Arora, J.Survey of multi-objective optimization methods for engineering”, Structural and Multidisciplinary Optimization, 2004, 26, pp 369395. DOI: 10.1007/s00158-003-0368-6 CrossRefGoogle Scholar
Miettinen, K.Some methods for nonlinear multi-objective optimization.” In: Zitzler, E., Thiele, L., Deb, K., Coello Coello, C.A., & Corne, D. (Eds), Evolutionary Multi-Criterion Optimization. EMO 2001. Lecture Notes in Computer Science, vol 1993, pp 120, 2001, Springer, Berlin, Heidelberg. DOI: 10.1007/3-540-44719-9_1 Google Scholar
Fonseca, C.M. and Fleming, P.J. “Genetic algorithms for multiobjective optimization: formulation, discussion and generalization.” In Proceedings of the 5th International Conference on Genetic Algorithms, 1993, Vol. 93, pp 416–423. DOI: 10.5555/645513.657757 CrossRefGoogle Scholar
Murata, T. and Ishibuchi, H. “MOGA: multi-objective genetic algorithms.” In IEEE International Conference on Evolutionary Computation, 1995, Vol. 1, pp 289–294. DOI: 10.1109/ICEC.1995.489161 CrossRefGoogle Scholar
Ishibuchi, H. and Murata, T. “Multi-objective genetic local search algorithm,” In Proceedings of IEEE International Conference on Evolutionary Computation, 1996, pp 119–124. DOI: 10.1109/ICEC.1996.542345 CrossRefGoogle Scholar
Ishibuchi, H. and Murata, T.A multi-objective genetic local search algorithm and its application to flowshop scheduling.In IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 1998, 28 (3), pp 392403. DOI: 10.1109/5326.704576 CrossRefGoogle Scholar
Fonseca, C.M. and Fleming, P.J.Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation.” In IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 1998, 28 (1), pp 2637. DOI: 10.1109/3468.650319 CrossRefGoogle Scholar
Fonseca, C.M. and Fleming, P.J.Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example.” In IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 1998, 28 (1), pp 3847. DOI: 10.1109/3468.650320 CrossRefGoogle Scholar
Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T.A fast and elitist multiobjective genetic algorithm: NSGA-II.In IEEE Transactions on Evolutionary Computation, 2002, 6 (2), pp 182197. DOI: 10.1109/4235.996017 CrossRefGoogle Scholar
Jensen, M.T., “Reducing the run-time complexity of multiobjective EAs: the NSGA-II and other algorithms.In IEEE Transactions on Evolutionary Computation, 2003, 7 (5), pp 503515. DOI: 10.1109/TEVC.2003.817234 CrossRefGoogle Scholar
Lenart, A.S.Orthodrome and loxodromes in marine navigation.Journal of Navigation, 2017, 70 (2), pp 432439. DOI: 10.1017/s0373463316000552 CrossRefGoogle Scholar
Janssen, V.Understanding coordinate reference systems, datums and transformations”. International Journal of Geoinformatics, 2009, 5 (4), pp 4153. Retrieved from: https://eprints.utas.edu.au/9575/ Google Scholar
Carlton-Wippern, K.C.On loxodromic navigation”. Journal of Navigation, 1992, 45 (2), pp 292297. DOI: 10.1017/s0373463300010791 CrossRefGoogle Scholar
Karney, C.F.Algorithms for geodesics”. Journal of Geodesy, 2013, 87 (1), pp 4355. DOI: 10.1007/s00190-012-0578-z CrossRefGoogle Scholar
Dancila, R.I. and Botez, R.M. “New flight trajectory optimization method using genetic algorithms”, paper accepted for publication in the April issue of The Aeronautical Journal, DOI: 10.1017/aer.2020.138 CrossRefGoogle Scholar
FlightAware, American Airlines 107, 2019, [Online], Retrieved from https://flightaware.com/live/flight/AAL107/history/20190225/1715ZZ/EGLL/KJFK Google Scholar