Skip to main content
SpringerLink
Log in

Aerodynamic Cost of Flapping

  • Published:
Journal of Bionic Engineering Aims and scope Submit manuscript

Abstract

A new modeling approach is presented for mathematically describing the drag due to wing flapping. It is shown that there is an aerodynamic cost of flapping in terms of an increase in the drag when compared with non-flapping. The drag increase concerns the induced drag which results from lift generation. There are two effects that yield the induced drag increase caused by flapping. The first effect is due to changes in the direction of the lift vectors at the left and right wings during the flapping cycle by tilting them according to the flapping angle of the wings. Because of tilting the lift vectors, more lift has to be generated than is required for the vertical force balance in flapping flight. This lift enlargement causes an increase of the induced drag. The second effect that increases the induced drag is due to changes in the magnitude of the lift vector in the course of the flapping cycle. Changes in the magnitude of the lift vector are necessary for generating thrust which is required for the longitudinal force balance. As a result, both effects of lift vector changes cause a drag increase when compared with non-flapping. Solutions on an analytical basis and as well as results using a computational fluid dynamics method are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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.

    Article  Google Scholar 

  2. Platzer M F, Jones K D, Young J, Lai J C S. Flapping-wing aerodynamics: Progress and challenges. AIAA Journal, 2008, 46, 2136–2149.

    Article  Google Scholar 

  3. Triantaflyllou M S, Techet A H, Hover F S. Review of experimental work in biomimetic foils. IEEE Journal of Oceanic Engineering, 2004, 29, 585–594.

    Article  Google Scholar 

  4. Shyy W, Berg M, Ljungqvist D. Flapping and flexible wings for biological and micro air vehicles. Progress in Aerospace Sciences, 1999, 35, 455–505.

    Article  Google Scholar 

  5. Tay W B, Bijl H, van Oudheusden, B W. Biplane and tail effects in flapping flight. AIAA Journal 2013, 51, 2133–2146.

    Article  Google Scholar 

  6. Moelyadi M A, Putra H A, Sachs G. Unsteady aerodynamics of flapping wing of a bird. Journal of Engineering and Technological Sciences, 2013, 45, 47–60.

    Article  Google Scholar 

  7. Yoon S, Kang L H, Jo S. Development of air vehicle with active flapping and twisting of wing. Journal of Bionic Engineering, 2011, 8, 1–9.

    Article  Google Scholar 

  8. Nakata T, Liu H, Tanaka Y, Nishihashi N, Wang X, Sato A. Aerodynamics of a bio-inspired flexible flapping-wing micro air vehicle. Bioinspiration & Biomimetics, 6, 1–11.

  9. Tobalske B W. Hovering and intermittent flight in birds. Bioinspiration & Biomimetics, 2010, 5, 1–10.

    Article  Google Scholar 

  10. Hedenström A. Mechanics of bird flight: The power curve of a pigeon by C. J. Pennycuick. The Journal of Experimental Biology, 2009, 212, 1421–1422.

    Article  Google Scholar 

  11. Pennycuick C J. Modelling the Flying Bird, Elsevier LTD, Oxford, UK, 2008.

    Google Scholar 

  12. Tobalske B W. Biomechanics of bird flight. The Journal of Experimental Biology, 2007, 210, 3135–3146.

    Article  Google Scholar 

  13. Askew G N, Ellerby D J. The mechanical power requirements of avian flight. Biology Letters, 2007, 3, 445–448.

    Article  Google Scholar 

  14. Tobalske B W, Hedrick T L, Dial K P, Biewener A A. Comparative power curves in bird flight. Nature, 2003, 421, 363–366.

    Article  Google Scholar 

  15. Rayner J M V, Viscardi P W, Ward S, Speakman J R. Aerodynamics and energetics of intermittent flight in birds. American Zoologist, 2001, 41, 188–204.

    Google Scholar 

  16. Rayner J M V. Estimating power curves of flying vertebrates. The Journal of Experimental Biology, 1999, 202, 3449–3461.

    Google Scholar 

  17. Rayner J M V. Bounding and undulating flight in birds. Journal of Theoretical Biology, 1985, 117, 47–77.

    Article  Google Scholar 

  18. Pennycuick C J. Power requirements for horizontal flight in the pigeon Columba livia. The Journal of Experimental Biology, 1968, 49, 527–555.

    Google Scholar 

  19. Ward-Smith A J. Aerodynamic and energetic considerations relating to undulating and bounding flight in birds. Journal of Theoretical Biology, 1984, 111, 407–417.

    Article  Google Scholar 

  20. Norberg U M. Vertebrate Flight, Springer, Berlin, Germany, 1990.

    Book  Google Scholar 

  21. Roskam J, Lan C-T E. Airplane Aerodynamics and Performance, DAR corporation, Lawrence, Kansa, USA, 1997.

    Google Scholar 

  22. Heuser H. Lehrbuch der Analysis, Teil: 1. Teubner, Stuttgart, Germany, 1990.

    MATH  Google Scholar 

  23. Muijres F T, Spedding G R, Winter Y, Hedenström A. Actuator disk model and span efficiency of flapping flight in bats based on time-resolved PIV measurements. Experiments in Fluids, 2011, 51, 511–525.

    Article  Google Scholar 

  24. Cvrlje T, Breitsamter C, Weishäupl C, Laschka B. Euler and navier-stokes simulations of two-stage hypersonic vehicle longitudinal motions. Journal of Spacecraft and Rockets, 2002, 37, 242–251.

    Article  Google Scholar 

  25. Jiang L, Moelyadi M A, Breitsamter C. Aerodynamic investigations on the unsteady stage separation of a TSTO space transport system. Forschungsbericht FLM-2003/34, Lehrstuhl für Fluidmechanik, Abteilung Aerodynamik, Technische Universität München, 2003.

    Google Scholar 

  26. Cvrlje T. Instationäre Aerodynamik des Separationsvorgangs Zwischen Träger und Orbiter. Dissertation, Technische Universität München, Germany, 2001.

    Google Scholar 

  27. Liou M S, Steffen C J. A new flux splitting scheme. Journal of Computational Physics, 1993, 107, 23–39.

    Article  MathSciNet  MATH  Google Scholar 

  28. Herzog K. Anatomie und Flugbiologie der Vögel. Gustav Fischer Verlag, Stuttgart, Germany, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Flight System Dynamics, Technische Universität München, Boltzmannstr. 15, 85748, Garching, Germany

    Gottfried Sachs

Authors
  1. Gottfried Sachs
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gottfried Sachs.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sachs, G. Aerodynamic Cost of Flapping. J Bionic Eng 12, 61–69 (2015). https://doi.org/10.1016/S1672-6529(14)60100-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1016/S1672-6529(14)60100-1

Keywords

Search

Navigation