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Aerodynamic Analysis and Optimization of Gliding Locust Wing Using Nash Genetic Algorithm

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Natural fliers glide and minimize wing articulation to conserve energy for endured and long-range flights. Elucidating the underlying physiology of such a capability could potentially address numerous challenging problems in flight engineering. This study investigates the aerodynamic characteristics of an insect species called desert locust (Schistocerca gregaria) with extraordinary gliding skills at low Reynolds numbers. Here, locust tandem wings are subjected to a computational fluid dynamics (CFD) simulation using two-dimensional and three-dimensional (3-D) Navier–Stokes equations, revealing fore–hindwing interactions and the influence of their corrugations on aerodynamic performance. Furthermore, the obtained CFD results are mathematically parameterized using the PARSEC method and optimized based on a novel fusion of genetic algorithms and Nash game theory to achieve Nash equilibrium. It was concluded that the lift–drag (gliding) ratio of the optimized profiles were improved by at least 77% and 150% compared to the original wing and the published literature, respectively. Ultimately, the profiles are integrated and analyzed using 3-D CFD simulations that demonstrated a 14% performance improvement, validating the proposed wing models for further fabrication and rapid prototyping presented in a future study.


  • [1] Rayleigh J. W. S., “The Soaring of Birds,” Nature, Vol. 27, No. 701, 1883, pp. 534–535. CrossrefGoogle Scholar

  • [2] Walker G., “The Flapping Flight of Birds,” Royal Aeronautical Society, Vol. 29, No. 179, 1925, pp. 590–594. Google Scholar

  • [3] Ellington C. P., “The Aerodynamics of Hovering Insect Flight. 3. Kinematics,” Philosophical Transactions of the Royal Society of London B: Biological Sciences, Vol. 305, No. 1122, 1984, pp. 41–78. CrossrefGoogle Scholar

  • [4] Ellington C. P., “The Aerodynamics of Hovering Insect Flight. 4. Aeorodynamic Mechanisms,” Philosophical Transactions of the Royal Society of London B: Biological Sciences, Vol. 305, No. 1122, 1984, pp. 79–113. CrossrefGoogle Scholar

  • [5] Ellington C. P., “The Aerodynamics of Hovering Insect Flight. 6. Lift and Power Requirements,” Philosophical Transactions of the Royal Society of London B: Biological Sciences, Vol. 305, No. 1122, 1984, pp. 145–181. CrossrefGoogle Scholar

  • [6] Du G. and Sun M., “Aerodynamic Effects of Corrugation and Deformation in Flapping Wings of Hovering Hoverflies,” Journal of Theoretical Biology, Vol. 300, May 2012, pp. 19–28. CrossrefGoogle Scholar

  • [7] Henningsson P., Hedenström A. and Bomphrey R. J., “Efficiency of Lift Production in Flapping and Gliding Flight of Swifts,” PLOS One, Vol. 9, No. 2, 2014, pp. 1–7. Google Scholar

  • [8] Hou D., Yin Y., Zhong Z. and Zhao H., “A New Torsion Control Mechanism Induced by Blood Circulation in Dragonfly Wings,” Bioinspiration & Biomimetics, Vol. 10, No. 1, 2015, pp. 1–10. Google Scholar

  • [9] Kim J. K. and Han J. H., “A Multibody Approach for 6-DOF Flight Dynamics and Stability Analysis of the Hawkmoth Manduca sexta,” Bioinspiration & Biomimetics, Vol. 9, No. 1, 2014, pp. 1–22. Google Scholar

  • [10] Koehler C., Liang Z., Gaston Z., Wan H. and Dong H., “3D Reconstruction and Analysis of Wing Deformation in Free-Flying Dragonflies,” Journal of Experimental Biology, Vol. 215, No. 17, 2012, pp. 3018–3027. CrossrefGoogle Scholar

  • [11] Kesel A. B., “Aerodynamic Characteristics of Dragonfly Wing Sections Compared with Technical Aerofoils,” Journal of Experimental Biology, Vol. 203, No. 20, 2000, pp. 3125–3135. CrossrefGoogle Scholar

  • [12] Kim W. K., Ko J. H., Park H. C. and Byun D., “Effects of Corrugation of the Dragonfly Wing on Gliding Performance,” Journal of Theoretical Biology, Vol. 260, No. 4, 2009, pp. 523–530. CrossrefGoogle Scholar

  • [13] Meng X. and Sun M., “Aerodynamic Effects of Corrugation in Flapping Insect Wings in Forward Flight,” Journal of Bionic Engineering, Vol. 8, No. 2, 2011, pp. 140–150. CrossrefGoogle Scholar

  • [14] Xiang J., Du J., Li D. and Liu K., “Aerodynamic Performance of the Locust Wing in Gliding Mode at Low Reynolds Number,” Journal of Bionic Engineering, Vol. 13, No. 2, 2016, pp. 249–260. CrossrefGoogle Scholar

  • [15] Murphy J. T. and Hu H., “An Experimental Study of a Bio-Inspired Corrugated Airfoil for Micro Air Vehicle Applications,” Experiments in Fluids, Vol. 49, No. 2, 2010, pp. 531–546. CrossrefGoogle Scholar

  • [16] Luca M., Mintchev S., Heitz G., Noca F. and Floreano D., “Bioinspired Morphing Wings for Extended Flight Envelope and Roll Control of Small Drones,” Interface Focus, Vol. 7, No. 1, 2017, pp. 1–11. Google Scholar

  • [17] Rival D. E., Hass G. and Tropea C., “Recovery of Energy from Leading- and Trailing-Edge Vortices in Tandem-Airfoil Configurations,” Journal of Aircraft, Vol. 48, Nos. 1–2, 2011, pp. 203–211. LinkGoogle Scholar

  • [18] Broering T. M. and Lian Y. S., “The Effect of Phase Angle and Wing Spacing on Tandem Flapping Wings,” Acta Mechanica Sinica, Vol. 28, No. 6, 2012, pp. 1557–1571. CrossrefGoogle Scholar

  • [19] Broering T. M., Lian Y. and Henshaw W., “Numerical Investigation of Energy Extraction in a Tandem Flapping Wing Configuration,” AIAA Journal, Vol. 50, No. 11, 2012, pp. 2295–2307. LinkGoogle Scholar

  • [20] Levy D. E. and Seifert A., “Simplified Dragonfly Airfoil Aerodynamics at Reynolds Numbers Below 8000,” Journal of Physics of Fluids, Vol. 21, No. 7, 2009, Paper 071901. Google Scholar

  • [21] Isakhani H., Aouf N., Kechagias-Stamatis O. and Whidborne J. F., “A Furcated Visual Collision Avoidance System for an Autonomous Micro Robot,” IEEE Transactions on Cognitive and Developmental Systems, Vol. 12, No. 1, 2018, pp. 1–11. Google Scholar

  • [22] Yue S. and Rind F. C., “Redundant Neural Vision Systems—Competing for Collision Recognition Roles,” IEEE Transactions on Autonomous Mental Development, Vol. 5, No. 2, 2013, pp. 173–186. Google Scholar

  • [23] Yue S. and Rind F. C., “Near Range Path Navigation Using LGMD Visual Neural Networks,” Proceedings of International Conference Computer Science and Information Technology, Aug. 2009, pp. 105–109. Google Scholar

  • [24] Lorenz M. W., “Migration and Trans-Atlantic Flight of Locusts,” Journal of Quaternary International, Vol. 196, Nos. 1–2, 2009, pp. 4–0. Google Scholar

  • [25] Weis-Fogh T., “Biology and Physics of Locust Flight. 2. Flight Performance of the Desert Locust (Schistocerca gregaria),” Philosophical Transactions of the Royal Society of London B: Biological Sciences, Vol. 239, No. 667, 1956, pp. 459–510. CrossrefGoogle Scholar

  • [26] Jensen M., “Biology and Physics of Locust Flight. 3. The Aerodynamics of Locust Flight,” Philosophical Transactions of the Royal Society of London B: Biological Sciences, Vol. 239, No. 667, 1956, pp. 511–552. CrossrefGoogle Scholar

  • [27] Cloupeau M., Devillers J. F. and Devezeaux D., “Direct Measurements of Instantaneous Lift in Desert Locust; Comparison with Jensen’s Experiments on Detached Wings,” Journal of Experimental Biology, Vol. 80, No. 1, 1979, pp. 1–15. Google Scholar

  • [28] Shkarayev S. and Kumar R., “Instantaneous Forces in Locust Flapping Wings,” AIAA Paper 2014-2834, June 2014. Google Scholar

  • [29] Shkarayev S. and Kumar R., “Kinematics and Inertial Effects in Locust Flapping Wings,” Experimental Mechanics, Vol. 56, No. 2, 2016, pp. 245–258. CrossrefGoogle Scholar

  • [30] Simmons P. J., Rind F. C. and Santer R. D., “Escapes with and Without Preparation: The Neuroethology of Visual Startle in Locusts,” Journal of Insect Physiology, Vol. 56, No. 8, 2010, pp. 876–883. Google Scholar

  • [31] Walker S. M., Thomas A. L. R. and Taylor G. K., “Deformable Wing Kinematics in the Desert Locust: How and Why Do Camber, Twist and Topography Vary Through the Stroke?Journal of the Royal Society Interface, Vol. 6, No. 38, 2009, pp. 735–747. CrossrefGoogle Scholar

  • [32] Kovač M., Fauria O., Zufferey J. and Floreano D., “The EPFL Jumpglider: A Hybrid Jumping and Gliding Robot with Rigid or Folding Wings,” IEEE International Conference Robotics and Biomimetics, Dec. 2011, pp. 1503–1508. Google Scholar

  • [33] Henningsson P., Michaelis D., Nakata T., Schanz D., Geisler R., Schröder A. and Bomphrey R. J., “The Complex Aerodynamic Footprint of Desert Locusts Revealed by Large-Volume Tomographic Particle Image Velocimetry,” Journal of the Royal Society Interface, Vol. 12, No. 108, 2015, pp. 1–11. Google Scholar

  • [34] Henningsson P. and Bomphrey R. J., “Time-Varying Span Efficiency Through the Wingbeat of Desert Locusts,” Journal of the Royal Society Interface, Vol. 9, No. 71, 2012, pp. 1177–1186. CrossrefGoogle Scholar

  • [35] Le T. Q., Truong T. V., Park S. H., Truong T. Q., Ko J. H., Park H. C. and Byun D., “Improvement of the Aerodynamic Performance by Wing Flexibility and Elytra-Hind Wing Interaction of a Beetle During Forward Flight,” Journal of the Royal Society Interface, Vol. 10, No. 85, 2013, pp. 1–15. Google Scholar

  • [36] Samareh J. A., “A Survey of Shape Parameterization Techniques,” CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics, 1999, pp. 333–344. Google Scholar

  • [37] Sobieczky H., “Geometry Generator for CFD and Applied Aerodynamics,” New Design Concepts for High Speed Air Transport, edited by Sobieczky H., Vol. 366, International Centre for Mechanical Sciences (Courses and Lectures), Springer, Vienna, 1997, pp. 137–158. Google Scholar

  • [38] Sobieczky H., “Parametric Airfoils and Wings,” Recent Development of Aerodynamic Design Methodologies, edited by Fujii K. and Dulikravich G. S., Notes on Numerical Fluid Mechanics (NNFM), Vol. 65, Springer, 1998, pp. 71–88. Google Scholar

  • [39] Kennedy J. and Eberhart R., “Particle Swarm Optimization,” Proceedings of IEEE International Conference Neural Networks, Vol. 4, 1995, pp. 1942–1948. Google Scholar

  • [40] Boggs P. T. and Tolle J. W., “Sequential Quadratic Programming,” Acta Numerica, Vol. 4, Jan. 1996, pp. 1–51. CrossrefGoogle Scholar

  • [41] Goldberg D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1989, pp. 211–372. Google Scholar

  • [42] Srinivas N. and Deb K., “Multiobjective Optimisation Using Non-Dominated Sorting in Genetic Algorithms,” Evolutionary Computation, Vol. 2, No. 3, 1994, pp. 221–248. CrossrefGoogle Scholar

  • [43] Nash J., “Non-Cooperative Games,” Annals of Mathematics, Vol. 54, No. 2, 1951, pp. 286–295. CrossrefGoogle Scholar

  • [44] Taylor G. K. and Thomas A. L. R., “Dynamic Flight Stability in the Desert Locust Schistocerca gregaria,” Journal of Experimental Biology, Vol. 206, No. 16, 2003, pp. 2803–2829. CrossrefGoogle Scholar

  • [45] Kesel A. B., Philippi U. and Nachtigall W., “Biomechanical Aspects of the Insect Wing: An Analysis Using the Finite Element Method,” Journal of Computers in Biology and Medicine, Vol. 28, No. 4, 1998, pp. 423–437. CrossrefGoogle Scholar

  • [46] Chen Y. H. and Skote M., “Gliding Performance of 3-D Corrugated Dragonfly Wing with Spanwise Variation,” Journal of Fluids and Structures, Vol. 62, April 2016, pp. 1–13. CrossrefGoogle Scholar

  • [47] Anderson J. D., “Aerodynamics: Some Introductory Thoughts,” Fundamentals of Aerodynamics, 5th ed., McGraw-Hill, New York, 2011, pp. 3–102. Google Scholar

  • [48] Hu H. and Tamai M., “Bioinspired Corrugated Airfoil at Low Reynolds Numbers,” Journal of Aircraft, Vol. 45, No. 6, 2008, pp. 2068–2077. LinkGoogle Scholar

  • [49] Spalart P. and Allmaras S., “A One-Equation Turbulence Model for Aerodynamic Flows,” Recherche Aerospatiale, Vol. 1, Jan. 1992, pp. 5–21. Google Scholar

  • [50] Isakhani H., Xiong C., Yue S. and Chen W., “A Bioinspired Airfoil Optimization Technique Using Nash Genetic Algorithm,” Proceedings of International Conference on Ubiquitous Robots (UR), 2020, pp. 506–513. Google Scholar

  • [51] Della Vecchia P., Daniele E. and D’Amato E., “An Airfoil Shape Optimization Technique Coupling PARSEC Parameterization and Evolutionary Algorithm,” Journal of Aerospace Science and Technology, Vol. 32, No. 1, 2014, pp. 103–110. CrossrefGoogle Scholar

  • [52] Basar T. and Olsder G. J., “Noncooperative Finite Games: N-Person Nonzero-Sum,” Dynamic Noncooperative Game Theory, Vol. 23, Academic Press, New York, 1995, pp. 77–160. Google Scholar

  • [53] Haupt R. L. and Haupt S. E., Practical Genetic Algorithms, Wiley, Hoboken, NJ, 1998, pp. 105–272. Google Scholar

  • [54] D’Amato E., Daniele E., Mallozzi L. and Petrone G., “Equilibrium Strategies via GA to Stackelberg Games Under Multiple Follower’s Best Reply,” International Journal of Intelligent Systems, Vol. 27, No. 2, 2012, pp. 74–85. Google Scholar

  • [55] D’Amato E., Daniele E., Mallozzi L., Petrone G. and Tancredi S., “A Hierarchical Multimodal Hybrid Stackelberg–Nash GA for a Leader with Multiple Followers Game,” Dynamics of Information Systems: Mathematical Foundations, Vol. 20, Springer, New York, 2012, pp. 267–280. Google Scholar

  • [56] Fudenberg D. and Tirole J., Game Theory, MIT Press, Cambridge, MA, 1991, pp. 43–604. Google Scholar

  • [57] Drela M. and Youngren H., “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils,” Low Reynolds Number Aerodynamics. Lecture Notes in Engineering, edited by Mueller T. J., Springer, Berlin, 1989, pp. 1–0. Google Scholar

  • [58] Deng J., Zhang L., Liu Z. and Mao X., “Numerical Prediction of Aerodynamic Performance for a Flying Fish During Gliding Flight,” Bioinspiration & Biomimetics, Vol. 14, No. 4, 2019, pp. 1–13. Google Scholar

  • [59] Okamoto M., Yasuka K. and Azuma A., “Aerodynamic Characteristics of the Wings and Body of a Dragonfly,” Journal of Experimental Biology, Vol. 199, No. 2, 1996, pp. 281–294. CrossrefGoogle Scholar

  • [60] Isakhani H., Yue S., Xiong C., Chen W., Sun X. and Liu T., “Fabrication and Mechanical Analysis of Bioinspired Gliding-Optimized Wing Prototypes for Micro Aerial Vehicles,” Proceedings of IEEE International Conference Advanced Robotics and Mechatronics (ARM), 2020, pp. 602–608. Google Scholar

  • [61] Baker P. S. and Cooter R. J., “The Natural Flight of the Migratory Locust, Locusta migratoria L. 2. Gliding,” Journal of Comparative Physiology, Vol. 131, March 1979, pp. 89–94. Google Scholar

  • [62] Menter F., Kuntz M. and Langtry R. B., “Ten Years of Industrial Experience with the SST Turbulence Model,” Turbulence, Heat and Mass Transfer, Vol. 4, No. 1, 2003, pp. 625–632. Google Scholar

  • [63] Jeong J. and Hussain F., “On the Identification of a Vortex,” Journal of Fluid Mechanics, Vol. 332, No. 1, 1995, pp. 339–363. Google Scholar