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Constant speed, variable ascension rate, helical trajectories for airplanes

  • Labonte, Gilles (Department of Mathematics and Computer Science, Royal Military College of Canada)
  • Received : 2017.08.25
  • Accepted : 2017.08.29
  • Published : 2018.01.25

Abstract

A particular type of constant speed helical trajectory, with variable ascension rate, is proposed. Such trajectories are candidates of choice as motion primitives in automatic airplane trajectory planning; they can also be used by airplanes taking off or landing in limited space. The equations of motion for airplanes flying on such trajectories are exactly solvable. Their solution is presented, together with an analysis of the restrictions imposed on the geometrical parameters of the helical paths by the dynamical abilities of an airplane. The physical quantities taken into account are the airplane load factor, its lift coefficient, and the thrust its engines can produce. Formulas are provided for determining all the parameters of trajectories that would be flyable by a particular airplane, the final altitude reached, and the duration of the trajectory. It is shown how to construct speed interval tables, which would appreciably reduce the calculations to be done on board the airplane. Trajectories are characterized by their angle of inclination, their radius, and the rate of change of their inclination. Sample calculations are shown for the Cessna 182, a Silver Fox like unmanned aerial vehicle, and the F-16 Fighting Falcon.

Keywords

References

  1. Aeronautics Learning Labratory for Science Technology and Research (ALLSTAR) of the Florida International University (2011), Propeller Aircraft Performance and The Bootstrap Approach.
  2. Airliners.net (2015), Santa Monica, California, U.S.A. .
  3. Ambrosino, G., Ariola, M., Ciniglio, U., Corraro, F., De Lellis, E. and Pironti, A. (2009), "Path generation and tracking in 3-D for UAVs", IEEE Trans. Contr. Syst. Technol., 17(4), 980-988. https://doi.org/10.1109/TCST.2009.2014359
  4. Anderson, J.D. Jr (2000), Introduction to Flight, 4th Edition, McGraw-Hill Series in Aeronautical and Aerospace Engineering, Toronto, Ontario, Canada.
  5. Babaei, A.R. and Mortazavi, M. (2010), "Three-dimensional curvature-constrained trajectory planning based on in-flight waypoints", J. Aircraft, 47(4), 1391-1398. https://doi.org/10.2514/1.47711
  6. Beard, R.W. and McLain, T.W. (2015), "Implementing dubins airplane paths on fixed-wing UAVs", Handbook for Unmanned Aerial Vehicles, Section XII, 1677-1701, Springer, the Netherlands.
  7. Boukraa, D., Bestaoui, Y. and Azouz, N. (2006), "A new approach to trajectories planner design for a subsonic autonomous aerial fixed wing vehicle", Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, U.S.A., June.
  8. Cavcar, M. (2004), Propeller, http://home.anadolu.edu.tr/-mcavcar/common/Propeller.pdf. Anadolu University, School of Civil Aviation, Eskisehir, Turkey.
  9. Chandler, P., Rasmussen, S. and Pachter, M. (2000), "UAV cooperative path planning", Proceedings of the AIAA Guidance, Navigation, and Control Conference, Denver, Colorado, U.S.A., August.
  10. Chitsaz, H. and LaValle, S.M. (2007), "Time-optimal paths for a dubins airplane", Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Luisiana, U.S.A., December.
  11. Commercial Aviation Safety Team (CAST), (2011), Propeller Operation and Malfunctions Basic Familiarization for Flight Crews, http://www.cast-safety.org/pdf/4_propeller_fundamentals.pdf.
  12. Cowley, W.L. and Levy, H. (1920), Aeronautics Theory and Experiment, 2nd Edition, Edward Arnold, London, U.K.
  13. Crawford, D.J. and Bowles, R.L. (1975), Automatic Guidance and Control of a Transport Aircraft During a Helical Landing Approach, NASA technical note D-7980, NASA Langley Research Center, Hampton, Va., September.
  14. Dai, R. and Cochran, J.E. (2009), "Three-dimensional trajectory optimization in constrained airspace", J. Aircr., 46(2), 627-634. https://doi.org/10.2514/1.39327
  15. Dubins, L.E. (1957), "On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents", Am. J. Math., 79, 497-516. https://doi.org/10.2307/2372560
  16. Etkin, B. (1992), Dynamics of Atmospheric Flight, John Wiley and Sons, Inc., New York, U.S.A.
  17. Filippone, A. (2000), "Data and performances of selected aircraft and rotorcraft", Prog. Aerosp. Sci., 36, 629-654. https://doi.org/10.1016/S0376-0421(00)00011-7
  18. Frazzoli, M.A., Dahleh, and Feron, E. (2005), "Maneuver-based motion planning for nonlinear systems with symmetries", IEEE Trans. Robot., 21(6), 1077-1091. https://doi.org/10.1109/TRO.2005.852260
  19. Goman, M.G., Khramtsovsky, A.V. and Kolesnikov, E.N. (2008), "Evaluation of aircraft performance and maneuverability by computation of attainable equilibrium sets", J. Guid. Contr. Dyn., 31(2), 329-339. https://doi.org/10.2514/1.29336
  20. Granelli, F. (2007), Carl Goldberg Falcon 56, The Academy of Model Aeronautics' Sport Aviator, The E-Zine for the Newer RC Pilot, December, http://masportaviator.com/2007/12/01/carl-goldberg-falcon-56/.
  21. Horizon Hobby (2017), https://www.horizonhobby.com/product/airplanes/airplane-accessories/airplane-engines-15042--1/gt80-twin-cylinder-(488-cu-in)-zene80t.
  22. Hota, S and Ghose, D. (2010), "Optimal geometrical path in 3D with curvature constraint", Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, October.
  23. Hwangbo, M., Kuffner, J. and Kanade, T. (2007), "Efficient two-phase 3D motion planning for small fixed-wing UAVs", Proceedings of the IEEE International Conference on Robotics and Automation, Rome, Italy, April.
  24. Jia, D. and Vagners, J. (2004), "Parallel evolutionary algorithms for UAV path planning", Proceedings of the AIAA 1st Intelligent Systems Technical Conference, Chicago, Illinois, September.
  25. Judd, K.B. (2001), "Trajectory planning strategies for unmanned air vehicles", M.Sc. Dissertation, Brigham Young University, Provo, U.S.A.
  26. Labonte, G. (2012), "Formulas for the fuel of climbing propeller driven planes", Aircr. Eng. Aerosp. Technol., 84(1), 23-36. https://doi.org/10.1108/00022661211194951
  27. Labonte, G. (2015), "Simple formulas for the fuel of climbing propeller driven airplanes", Adv. Aircr. Spacecr. Sci., 2(4), 367-389. https://doi.org/10.12989/aas.2015.2.4.367
  28. Labonte, G. (2016), "Airplanes at constant speeds on inclined circular trajectories", Adv. Aircr. Spacecr. Sci., 3(4), 399-425. https://doi.org/10.12989/aas.2016.3.4.399
  29. Labonte, G. (2017), "The feasible constant speed helical trajectories for propeller driven airplanes", Adv. Aircr. Spacecr. Sci., 4(4), 371-399. https://doi.org/10.12989/AAS.2017.4.4.371
  30. Li, X., Xie, J., Cai, M., Xie, M. Wang, Z. (2009), "Path planning for UAV based on improved A* algorithm", Proceedings of the 9th International Conference on Electronic Measurement & Instruments, Beijing, China, August.
  31. Lockheed-Martin (2015), F-16 Specifications .
  32. Mair, W.A. and Birdsall, D.L. (1992), Aircraft Performance, Cambridge Aerospace Series 5, Cambridge University Press, Cambridge, G.B.
  33. McIver, J. (2003), Cessna Skyhawk II /100, Performance Assessment, Temporal Images, Melbourne, Australia, http://www.temporal.com.au/c172.pdf.
  34. Narayan, P.P., Wu, P.P. and Campbell, D.A. (2008), "Unmanning UAVs-addressing challenges in on-board planning and decision making", Proceedings of the 1st International Conference on Humans Operating Unmanned Systems, Telecom Bretagne, Brest, France, September.
  35. Nikolos, I.K., Tsourveloudis, N.C. and Valavanis, K.P. (2003), "Evolutionary algorithm based 3-D path planner for UAV navigation", IEEE Trans. Syst. Man. Cybernet. Part B: Cybernet., 33(6), 898-912. https://doi.org/10.1109/TSMCB.2002.804370
  36. Phillips, W.F. (2004), Mechanics of Flight, John Wiley & Sons, Inc., Hoboken, New Jersey, U.S.A.
  37. Roberge, V., Tarbouchi, M. and Labonte, G (2012), "Comparison of parallel genetic algorithm and particle swarm optimization for real-time UAV path planning", IEEE Trans. Industr. Informat., 9(1), 132-141. https://doi.org/10.1109/TII.2012.2198665
  38. Roud, O. and Bruckert D. (2006), Cessna 182 Training Manual, Red Sky Ventures and Memel CATS, Second Edition 2011, Windhoek, Namibia.
  39. Sadraey, M.H. (2013), Aircraft Design: A Systems Engineering Approach, Aerospace Series, John Wiley & Sons Ltd, Toronto, Ontario, Canada.
  40. Stengel, R. (2016), Problems of High Speed and Altitude. .
  41. Tsiotras, P. Bakolas, E. and Zhao, Y. (2011), "Initial guess generation for aircraft landing trajectory optimization", Proceedings of the AIAA Guidance, Navigation, and Control Conference, Portland Oregon, August.
  42. UAVGLOBAL Unmanned Systems and Manufacturers (2016), BAE Systems Silver Fox. .
  43. Von Mises, R. (1945), Theory of Flight, Dover Publications Inc., New York, U.S.A.
  44. Yang, K. and Sukkarieh, S. (2010), "An analytical continuous-curvature path-smoothing algorithm", IEEE Trans. Robot., 26, 561-568. https://doi.org/10.1109/TRO.2010.2042990
  45. Zheng, C., Ding, M. and Zhou, C. (2003), "Real-time route planning for unmanned air vehicle with an evolutionary algorithm", J. Patt. Recog. Artif. Intellig., 17(1), 63-81. https://doi.org/10.1142/S021800140300223X