Lung-Jieh Yang This email address is being protected from spambots. You need JavaScript enabled to view it.1, Balasubramanian Esakki2 and Reshmi Waikhom1

1Department of Mechanical and Electromechanical Engineering, Tamkang University, 25137, Tamsui, Taiwan, R.O.C.
2Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, 600062, Tamil Nadu, India


Received: November 17, 2019
Accepted: January 9, 2020
Publication Date: June 1, 2020

Download Citation: ||  


This note presents the time-averaged inertial force which relates to the velocity difference between the final and initial states of a flapping wing motion. For the periodic flapping motion with identical final and initial velocities, there are no inertial force contribution to the time-averaged lift. Therefore, the wake capture mechanism proposed by Dickinson justifies more convincing than Sunada’s added mass or Sun’s rapid acceleration at the stroke onset of hovering. The vanishing inertial force to the time-averaged lift is also beneficial to the concise signal processing of lift data from the wind tunnel test.

Keywords: Flapping Wing, Inertial Force, Hovering, Wake Capture



  1. [1] Dickinson, M.H., F.O. Lehmann, and S.P. Sane (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284, 1954-1960.
  2. [2] Chin, D. D. and D. Lentink (2016) Flapping wing aerodynamics: from insects to vertebrates. Journal of Experimental Biology 219, 920-932.
  3. [3] Shyy, W., H. Aono, C.K. Kang, and H. Liu (2013) An Introduction to Flapping Wing Aerodynamics, Cambridge University Press, New York, chapters 1 and 3.
  4. [4] Sunada, S. and C.P. Ellington (2000) Approximate added-mass method for estimating induced power for flapping flight. AIAA Journal 38, 1313-1321.
  5. [5] Sun, M. and J. Tang (2002) Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion. The Journal of Experimental Biology 205, 55-70.
  6. [6] Lua, K., T. Lim, K. Yeo (2011) Effect of wing-wake interaction on aerodynamic force generation on a 2D flapping wing. Experiments in Fluids 51(1) 177-95.
  7. [7] Shkarayev, S. and R. Kumar (2016) Kinematics and inertial effects in locust flapping wings. Experimental Mechanics 56(2) 245-258.
  8. [8] Hu, H., A.-G. Kumar, G. Abate, and R. Albertani (2010) An experimental investigation on the aerodynamic performances of flexible membrane wings in flapping flight. Aerospace Science and Technology 14(8), 575-586.
  9. [9] Yang, L.-J., F.-Y. Hsiao, W.-T. Tang, and I.-C. Huang (2013) 3D flapping trajectory of a micro-air-vehicle and its application to unsteady flow simulation. International Journal of Advanced Robotic Systems 10, paper no. 264.
  10. [10] Yang, L. J. (2012) The micro-air-vehicle Golden Snitch and its figure-of-8 flapping. Journal of Applied Science and Engineering 15, 192-212.