Journal of Bionic Engineering

, Volume 15, Issue 2, pp 283–297 | Cite as

Longitudinal Flight Dynamic Analysis on Vertical Takeoff of a Tailless Flapping-Wing Micro Air Vehicle

  • Loan Thi Kim Au
  • Vu Hoang Phan
  • Hoon Cheol Park


This paper first analyzed the longitudinal dynamic behavior during vertical takeoff without control of a Flapping-Wing Micro Air Vehicle (FW-MAV). The standard linear flight dynamics based on small disturbances from trim condition was not applicable for our analysis because the initial flight condition, which was at rest on the ground, could be such a large disturbance from the trim condition that the linearization is invalid. Therefore, we derived linearized Equations of Motion (EoM) which can treat an untrimmed flight condition as a reference for disturbances. The Computational Fluid Dynamic (CFD) software ANSYS Fluent was used to compute the aerodynamic forces and pitching moments. Three flight modes were found: a fast subsidence mode, a slow subsidence mode and a divergence oscillatory mode. Due to divergence oscillatory mode, the deviation from the reference flight grew with time; the FW-MAV tumbled without control. The simulation showed for the first 0.5 second after leaving the ground (the time that is long enough for delay of feedback control), the FW-MAV flew up to a height of 6 cm with small horizontal and pitching motion, which is close to a vertical flight.


bioinspired FW-MAV flight dynamics vertical takeoff CFD linear theory 


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This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. 2013R1A2A2A01067315).


  1. [1]
    Jansen M. Biology and physics of locust flight III: The aerodynamics of locust flight. Philosophical Transactions of the Royal Society B, 1956, 239, 511–552.CrossRefGoogle Scholar
  2. [2]
    Rayner J M V. A new approach to animal flight mechanics. Journal of Experimental Biology, 1979, 80, 17–54.Google Scholar
  3. [3]
    Dickinson M H, Lehman F O, Sane S P. Wing rotation and the aerodynamics basis of insect flight. Science, 1999, 284 1954–1960.CrossRefGoogle Scholar
  4. [4]
    Sane S P. The aerodynamics of insect flight. Journal of Experimental Biology, 2003, 206, 4191–4208.CrossRefGoogle Scholar
  5. [5]
    Nguyen T T, Byun D. Two-dimensional aerodynamic models of insect flight for robotic flapping wing mechanisms of maximum efficiency. Journal of Bionic Engineering, 2008, 5, 1–11.CrossRefGoogle Scholar
  6. [6]
    Nguyen Q V, Truong Q T, Park H C, Goo N S, Byun D. Measurement of force produced by an insect-mimicking flapping-wing system. Journal of Bionic Engineering, 2010, 7, S94–S102.CrossRefGoogle Scholar
  7. [7]
    Truong Q T, Phan H V, Park H C, Ko J H. Effect of wing twisting on aerodynamic performance of flapping wing system. AIAA Journal, 2013, 51, 1612–1620.CrossRefGoogle Scholar
  8. [8]
    Ma K Y, Chirarattananon P, Fuller S B, Wood R J. Controlled flight of a biologically inspired, insect-scale robot. Science, 2013, 340, 603–607.CrossRefGoogle Scholar
  9. [9]
    Taylor G K, Thomas A L R. Dynamic flight stability in the desert locust Schistocerca gregaria. Journal of Experimental Biology, 2003, 206, 2803–2829.CrossRefGoogle Scholar
  10. [10]
    Sun M, Xiong Y. Dynamic flight stability of a hovering bumblebee. Journal of Experimental Biology, 2005, 208, 447–459.CrossRefGoogle Scholar
  11. [11]
    Sun M, Wang J, Xiong Y. Dynamic flight stability of hovering insects. Acta Mechanica Sinica, 2007, 23, 231–246.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Gao N, Aono H, Liu H. A numerical analysis of dynamic flight stability of hawkmoth hovering. Journal of Biomechanical Science and Engineering, 2009, 4, 105–116.CrossRefGoogle Scholar
  13. [13]
    Faruque I, Humbert J S. Dipteran insect flight dynamics Part 1: Longitudinal motion about hover. Journal of Theoretical Biology, 2010, 264, 538–552.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Cheng B, Deng X. Translational and rotational damping of flapping flight and its dynamics and stability at hovering. IEEE Transactions on Robotics, 2011, 27, 849–864.CrossRefGoogle Scholar
  15. [15]
    Liang B, Sun M. Dynamic flight stability of a hovering model dragonfly. Acta Mechanica Sinica, 2014, 348, 100–112.MathSciNetGoogle Scholar
  16. [16]
    Zhang Y, Sun M. Dynamic flight stability of a hovering model insect: Lateral motion. Acta Mechanica Sinica, 2010, 26, 175–190.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Faruque I, Humbert J S. Dipteran insect flight dynamics part 2: Lateral–directional motion about hover. Journal of Theoretical Biology, 2010, 265, 306–313.CrossRefGoogle Scholar
  18. [18]
    Xu N, Sun M. Lateral dynamic flight stability of a model bumblebee in hovering and forward flight. Journal of Theoretical Biology, 2013, 319, 102–115.CrossRefGoogle Scholar
  19. [19]
    Xu N, Sun M. Lateral dynamic flight stability of a model hoverfly in normal and inclined stroke-plane hovering. Bioinspiration & Biomimetics, 2014, 9, 036019.CrossRefGoogle Scholar
  20. [20]
    Kim J K, Han J H. A multibody approach for 6-DOF flight dynamics and stability analysis of the hawkmoth Manduca sexta. Bioinspiration & Biomimetics, 2014, 9, 016011.CrossRefGoogle Scholar
  21. [21]
    Xiong Y, Sun M. Dynamic flight stability of a bumblebee in forward flight. Acta Mechanica Sinica, 2008, 24, 25–36.CrossRefzbMATHGoogle Scholar
  22. [22]
    Kim J K, Han J S, Lee J S, Han J H. Hovering and forward flight of the hawkmoth Manduca sexta: Trim search and 6-DOF dynamic stability characterization. Bioinspiration & Biomimetics, 2015, 10, 056012.CrossRefGoogle Scholar
  23. [23]
    Etkin B, Reid L D. Dynamics of Flight: Stability and Control, John Wiley & Sons, New York, USA, 1996.Google Scholar
  24. [24]
    Bimbard G, Kolomenskiy D, Bouteleus O, Casas J, Godoy-Diana R. Force balance in the takeoff of a pierid butterfly: Relative importance and timing of leg impulsion and aerodynamic forces. Journal of Experimental Biology, 2013, 216, 3551–3563.CrossRefGoogle Scholar
  25. [25]
    Chen M W, Sun M. Wing/body kinematics measurement and force and moment analyses of the takeoff flight of fruitflies. Acta Mechanica Sinica, 2014, 30, 495–506.CrossRefGoogle Scholar
  26. [26]
    Chen M W, Zhang Y L, Sun M. Wing and body motion and aerodynamic and leg forces during take-off in droneflies. Journal of the Royal Society Interface, 2013, 10, 20130808.CrossRefGoogle Scholar
  27. [27]
    Kolomenskiy D, Maeda M, Engels T, Liu H, Schneider K, Nave J C. Aerodynamic ground effect in fruitfly sized insect takeoff. PLOS One, 2016, 11, e0152072.CrossRefGoogle Scholar
  28. [28]
    Liang B, Sun M. Nonlinear flight dynamics and stability of hovering model insects. Journal of the Royal Society Interface, 2013, 10, 20130269.CrossRefGoogle Scholar
  29. [29]
    Phan H V, Kang T, Park H C. Design and stable flight of a 21 g insect-like tailless flapping wing micro air vehicle with angular rates feedback control. Bioinspiration & Biomimetics, 2017, 12, 1–17.Google Scholar
  30. [30]
    Hedrick T. Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & Biomimetics, 2008, 3, 034001.CrossRefGoogle Scholar
  31. [31]
    Truong Q T, Nguyen Q V, Truong V T, Park H C, Byun D Y, Goo N S. A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system. Bioinspiration & Biomimetics, 2011, 6, 036008.CrossRefGoogle Scholar
  32. [32]
    Meng X G, Sun M. Aerodynamics and vortical structures in hovering fruitflies. Physics of Fluids, 2015, 27, 031901.CrossRefGoogle Scholar
  33. [33]
    Atkinson K E. An Introduction to Numerical Analysis, John Wiley & Sons, New York, USA, 1989.zbMATHGoogle Scholar
  34. [34]
    Taylor G K, Thomas A L R. Animal flight dynamics. II. Longitudinal stability in flapping flight. Journal of Theoretical Biology, 2002, 214, 351–370.CrossRefGoogle Scholar

Copyright information

© Jilin University 2018

Authors and Affiliations

  • Loan Thi Kim Au
    • 1
  • Vu Hoang Phan
    • 1
  • Hoon Cheol Park
    • 1
  1. 1.Department of Advanced Technology Fusion and Artificial Muscle Research CenterKonkuk UniversitySeoulKorea

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