Effects of unsteady deformation of flapping wing on its aerodynamic forces

  • Gang Du (杜刚)Email author
  • Mao Sun (孙茂)


Effects of unsteady deformation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid. Aerodynamic forces on the flapping wing are not much affected by considerable twist, but affected by camber deformation. The effect of combined camber and twist deformation is similar to that of camber deformation. With a deformation of 6% camber and 20° twist (typical values observed for wings of many insects), lift is increased by 10% ∼ 20% and lift-to-drag ratio by around 10% compared with the case of a rigid flat-plate wing. As a result, the deformation can increase the maximum lift coefficient of an insect, and reduce its power requirement for flight. For example, for a hovering bumblebee with dynamically deforming wings (6% camber and 20° twist), aerodynamic power required is reduced by about 16% compared with the case of rigid wings.

Key words

insect wing deformation unsteady aerodynamic force computational fluid dynamics 

Chinese Library Classification


2000 Mathematics Subject Classification



  1. [1]
    Dickinson M H, Götz K G. Unsteady aerodynamic performance of model wings at low Reynolds numbers[J]. J Exp Biol, 1993, 174(1):45–64.Google Scholar
  2. [2]
    Ellington C P, van den Berg C, Willmott A P. Leading edge vortices in insect flight[J]. Nature, 1996, 384(6610):626–630.CrossRefGoogle Scholar
  3. [3]
    Willmott A P, Ellington C P, Thomas A R. Flow visualization and unsteady aerodynamics in the flight of the hawkmoth, manduca sexta[J]. Phil Trans R Soc Lond B, 1997, 352(1351):303–316.CrossRefGoogle Scholar
  4. [4]
    Liu H, Ellington C P, Kawachi K, Van Den Berg C, Willmott A P. A computational fluid dynamic study of hawkmoth hovering[J]. J Exp Biol, 1998, 201(4):461–477.Google Scholar
  5. [5]
    Sun M, Tang J. Unsteady aerodynamic force generation by a model fruit fly wing in flapping motion[J]. J Exp Biol, 2002, 205(1):55–70.Google Scholar
  6. [6]
    Dickinson M H, Lehman F O, Sane S P. Wing rotation and the aerodynamic basis of insect flight[J]. Science, 1999, 284(5422):1954–1960.CrossRefGoogle Scholar
  7. [7]
    Usherwood J R, Ellington C P. The aerodynamics of revolving wings. II. Propeller force coefficients from mayfly to quail[J]. J Exp Biol, 2002, 205(11):1565–1576.Google Scholar
  8. [8]
    Ellington C P. The aerodynamics of hovering insect flight. III. Kinematics[J]. Phil Trans R Soc Lond B, 1984, 305(1122):41–78.CrossRefGoogle Scholar
  9. [9]
    Ellington C P. The aerodynamics of hovering insect flight. IV. Aerodynamic mechanisms[J]. Phil Trans R Soc Lond B, 1984, 305(1122):79–113.CrossRefGoogle Scholar
  10. [10]
    Ellington C P. The aerodynamics of hovering insect flight. VI. Lift and power requirements[J]. Phil Trans R Soc Lond B, 1984, 305(1122):145–181.CrossRefGoogle Scholar
  11. [11]
    Ennos A R. The kinematics and aerodynamics of the free flight of some Diptera[J]. J Exp Biol, 1989, 142(1):49–85.Google Scholar
  12. [12]
    Dudley R. The mechanics of forward flight in insects[D]. Ph D Dissertation. University of Cambridge, 1987.Google Scholar
  13. [13]
    Wang H, Zeng L J, Yin C Y. Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing[J]. Meas Sci Tech, 2002, 13(6):903–908.CrossRefGoogle Scholar
  14. [14]
    Ennos A R. The importance of torsion in the design of insect wings[J]. J Exp Biol, 1988, 140(1):137–160.Google Scholar
  15. [15]
    Ennos A R, Wootton R J. Functional wing morphology and aerodynamics of panorpa germanica (insecta: mecopter)[J]. J Exp Biol, 1989, 143(1):267–284.Google Scholar
  16. [16]
    Wootton R J, Herbert R C, Yong P G, Evans K E. Approaches to the structural modeling of insect wings[J]. Phil Trans R Soc Lond B, 2003, 358(1437):1577–1587.CrossRefGoogle Scholar
  17. [17]
    Vogel S. Flight in drosophila. III. Aerodynamic characteristics of fly wings and wing models[J]. J Exp Biol, 1966, 44(3):567–578.Google Scholar
  18. [18]
    Dudley R, Ellington C P. Mechanics of forward flight in bumblebees: II. Quasi-steady lift and power requirements[J]. J Exp Biol, 1990, 148(1):53–88.Google Scholar
  19. [19]
    Thomas P D, Lombard C K. Geometric conservation law and its application to flow computations on moving grids[J]. AIAA J, 1979, 17(10):1030–1037.zbMATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    Morton S A, Melville R B, Visbal M R. Accuracy and coupling issues of aeroelastic Navier-Stokes solutions on deforming meshes[J]. J. Aircraft, 1998, 35(5):798–805.CrossRefGoogle Scholar
  21. [21]
    Rogers S E, Kwak D. Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations[J]. AIAA J, 1990, 28(2):253–262.zbMATHCrossRefGoogle Scholar
  22. [22]
    Rogers S E, Kwak D, Kiris C. Steady and unsteady solutions of the incompressible Navier-Stokes equations[J]. AIAA J, 29(4):603–610.Google Scholar
  23. [23]
    Hilgenstock A. A fast method for the elliptic generation of three dimensional grid with full boundary control[M]. In: Sengupta S, Hauser J, Eiseman P R, Thompson J F (eds). Numerical Grid Generation in CFM’88, Swansea UK: Pineridge Press Ltd, 1988, 137–146.Google Scholar
  24. [24]
    Wu J H, Sun M. Unsteady aerodynamic forces of a flapping wing[J]. J Exp Biol, 2004, 207(7):1137–1150.CrossRefGoogle Scholar
  25. [25]
    Fry S N, Sayaman R, Dickinson M H. The aerodynamics of hovering flight in drosophila[J]. J Exp Biol, 2005, 208(12):2303–2318.CrossRefGoogle Scholar
  26. [26]
    Wu J H, Sun M. Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight[J]. Acta Mech Sinica, 2005, 21(3):207–217.CrossRefMathSciNetGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Aeroengine Numerical Simulation Research CenterBeijing University of Aeronautics and AstronauticsBeijingP. R. China
  2. 2.Institute of Fluid MechanicsBeijing University of Aeronautics and AstronauticsBeijingP. R. China

Personalised recommendations