Abstract
Winged animals such as insects are capable of flying and surviving in an unsteady and unpredictable aerial environment. They generate and control aerodynamic forces by flapping their flexible wings. While the dynamic shape changes of their flapping wings are known to enhance the efficiency of their flight, they can also affect the stability of a flapping wing flyer under unpredictable disturbances by responding to the sudden changes of aerodynamic forces on the wing. In order to test the hypothesis, the gust response of flexible flapping wings is investigated numerically with a specific focus on the passive maintenance of aerodynamic forces by the wing flexibility. The computational model is based on a dynamic flight simulator that can incorporate the realistic morphology, the kinematics, the structural dynamics, the aerodynamics and the fluid–structure interactions of a hovering hawkmoth. The longitudinal gusts are imposed against the tethered model of a hovering hawkmoth with flexible flapping wings. It is found that the aerodynamic forces on the flapping wings are affected by the gust, because of the increase or decrease in relative wingtip velocity or kinematic angle of attack. The passive shape change of flexible wings can, however, reduce the changes in the magnitude and direction of aerodynamic forces by the gusts from various directions, except for the downward gust. Such adaptive response of the flexible structure to stabilise the attitude can be classified into the mechanical feedback, which works passively with minimal delay, and is of great importance to the design of bio-inspired flapping wings for micro-air vehicles.
Similar content being viewed by others
References
Watkins, S., Milbank, J., Loxton, B.J., et al.: Atmospheric winds and their implications for micro air vehicles. AIAA J. 44, 2591–2600 (2006)
Combes, S.A., Dudley, R.: Turbulence-driven instabilities limit insect flight performance. Proc. Natl. Acad. Sci. USA 106, 9105–9108 (2009)
Ravi, S., Crall, J.D., McNeilly, L., et al.: Hummingbird flight stability and control in freestream turbulent winds. J. Exp. Biol. 218, 1444–1452 (2015)
Vance, J.T., Faruque, I., Humbert, J.S.: Kinematic strategies for mitigating gust perturbations in insects. Bioinspir. Biomim. 8, 016004 (2013)
Fuller, S.B., Straw, A.D., Peek, M.Y., et al.: Flying Drosophila stabilize their vision-based velocity controller by sensing wind with their antennae. Proc. Natl. Acad. Sci. USA 111, E1182–E1191 (2014)
Ravi, S., Crall, J.D., Fisher, A., et al.: Rolling with the flow: bumblebees flying in unsteady wakes. J. Exp. Biol. 216, 4299–4309 (2013)
Ortega-Jimenez, V.M., Greeter, J.S.M., Mittal, R., et al.: Hawkmoth flight stability in turbulent vortex streets. J. Exp. Biol. 216, 4567–4579 (2013)
Ortega-Jimenez, V.M., Sapir, N., Wolf, M., et al.: Into turbulent air: size-dependent effects of von Kármán vortex streets on hummingbird flight kinematics and energetics. Proc. R. Soc. B 281, 20140180 (2014)
Ortega-Jimenez, V.M., Mittal, R., Hedrick, T.L.: Hawkmoth flight performance in tornado-like whirlwind vortices. Bioinspir. Biomim. 9, 025003 (2014)
Ellington, C.P., van den Berg, C., Willmott, A.P., et al.: Leading-edge vortices in insect flight. Nature 384, 626–630 (1996)
Dickinson, M.H., Lehmann, F.O., Sane, S.P.: Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954–1960 (1999)
Srygley, R.B., Thomas, A.L.R.: Unconventional lift-generating mechanisms in free-flying butterflies. Nature 420, 660–664 (2002)
Bomphrey, R.J., Nakata, T., Phillips, N., et al.: Smart wing rotation and trailing-edge vortices enable high frequency mosquito flight. Nature 544, 92–95 (2017)
Engels, T., Kolomenskiy, D., Schneider, K., et al.: Bumblebee in heavy turbulence. Phys. Rev. Lett. 116, 028103 (2016)
Sun, M.: Insect flight dynamics: stability and control. Rev. Mod. Phys. 86, 615–646 (2014)
Liu, H., Ravi, S., Kolomenskiy, D., et al.: Biomechanics and biomimetics in insect-inspired flight systems. Philos. Trans. R. Soc. B371, 20150390 (2016)
Sane, S.P., Dickinson, M.H.: The control of flight force by a flapping wing: lift and drag production. J. Exp. Biol. 204, 2607–2626 (2001)
Elzinga, M.J., Dickson, W.B., Dickinson, M.H.: The influence of sensory delay on the yaw dynamics of a flapping insect. J. R. Soc. Interface 9, 1685–1696 (2012)
Wootton, R.J.: Support and deformability in insect wings. J. Zool. 193, 447–468 (1981)
Combes, S.A., Daniel, T.L.: Into thin air: contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta. J. Exp. Biol. 206, 2999–3006 (2003)
Nakata, T., Liu, H.: Aerodynamic performance of a hovering hawkmoth with flexible wings: a computational approach. Proc. R. Soc. B279, 722–731 (2012)
Young, J., Walker, S.M., Bomphrey, R.J., et al.: Details of insect wing design and deformation enhance aerodynamic function and flight efficiency. Science 325, 1549–1552 (2009)
Du, G., Sun, M.: Effects of wing deformation on aerodynamic forces in hovering hoverflies. J. Exp. Biol. 213, 2273–2283 (2010)
Zheng, L., Hedrick, T.L., Mittal, R.: Time-varying wing-twist improves aerodynamic efficiency of forward flight in butterflies. PLoS ONE 8, e53060 (2012)
Le, T.Q., Truong, T.V., Park, S.H., et al.: Improvement of the aerodynamic performance by wing flexibility and elytra–hind wing interaction of a beetle during forward flight. J. R. Soc. Interface 10, 20130312 (2013)
Dickinson, M.H., Farley, C.T., Full, R.J., et al.: How animals move: an integrative view. Science 288, 100–106 (2000)
Kubow, T.M., Full, R.J.: The role of the mechanical system in control: a hypothesis of self-stabilization in hexapedal runners. Philos. Trans. R. Soc. Lond. B354, 849–861 (1999)
Carruthers, A.C., Thomas, A.L.R., Taylor, G.K.: Automatic aeroelastic devices in the wings of a steppe eagle Aquila nipalensis. J. Exp. Biol. 210, 4136–4149 (2007)
Ravi, S., Kolomenskiy, D., Engels, T., et al.: Bumblebees minimize control challenges by combining active and passive modes in unsteady winds. Sci. Rep. 6, 35043 (2016)
Mistick, E.A., Mountcastle, A.M., Combes, S.A.: Wing flexibility improves bumblebee flight stability. J. Exp. Biol. 219, 3384–3390 (2016)
Chen, J.S., Chen, J.Y., Chou, Y.F.: On the natural frequencies and mode shapes of dragonfly wings. J. Sound Vib. 313, 643–654 (2008)
Ha, N.S., Truong, Q.T., Goo, N.S., et al.: Relationship between wingbeat frequency and resonant frequency of the wing in insects. Bioinspir. Biomim. 8, 046008 (2013)
Nakata, T., Liu, H.: A fluid-structure interaction model of insect flight with flexible wings. J. Comput. Phys. 231, 1822–1847 (2012)
Liu, H.: Integrated modeling of insect flight: from morphology, kinematics to aerodynamics. J. Comput. Phys. 228, 439–459 (2009)
Willmott, A.P., Ellington, C.P.: The mechanics of flight in the hawkmoth Manduca sexta. I. kinematics of hovering and forward flight. J. Exp. Biol. 200, 2705–2722 (1997)
Nakata, T., Liu, H.: A fluid-structure interaction model of insect flight with flexible wings. J. Comput. Phys. 231, 1822–1847 (2012)
Sun, M., Xiong, Y.: Dynamic flight stability of a hovering bumblebee. J. Exp. Biol. 208, 447–459 (2005)
Taylor, G.K., Thomas, A.L.R.: Animal flight dynamics II. Longitudinal stability in flapping flight. J. Theor. Biol. 214, 351–370 (2002)
Viswanath, K., Tafti, D.K.: Effect of frontal gusts on forward flapping flight. AIAA J. 48, 2049–2062 (2010)
Acknowledgements
This work was partly supported by the Grant-in-Aid for Scientific Research on Innovative Areas, the Japan Society for the Promotion of Science (Grant 24120007), and the Japan Society for the Promotion of Science KAKENHI (Grant JP17K17638).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Nakata, T., Noda, R., Kumagai, S. et al. A simulation-based study on longitudinal gust response of flexible flapping wings. Acta Mech. Sin. 34, 1048–1060 (2018). https://doi.org/10.1007/s10409-018-0789-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-018-0789-5