Experimental Mechanics

, Volume 50, Issue 8, pp 1183–1197 | Cite as

An Experimental and Numerical Study of Calliphora Wing Structure

  • R. GanguliEmail author
  • S. Gorb
  • F.-O. Lehmann
  • S. Mukherjee
  • S. Mukherjee


Experiments are performed to determine the mass and stiffness variations along the wing of the blowfly Calliphora. The results are obtained for a pairs of wings of 10 male flies and fresh wings are used. The wing is divided into nine locations along the span and seven locations along the chord based on venation patterns. The length and mass of the sections is measured and the mass per unit length is calculated. The bending stiffness measurements are taken at three locations, basal (near root), medial and distal (near tip) of the fly wing. Torsional stiffness measurements are also made and the elastic axis of the wing is approximately located. The experimental data is then used for structural modeling of the wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Inertial values of nine sections are found to approximately vary according to an exponentially decreasing law over the nine sections from root to tip and it is used to calculate an approximate value of Young’s modulus of the wing biomaterial. Shear modulus is obtained assuming the wing biomaterial to be isotropic. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. The results provide a complete analysis of Calliphora wing structure and also provide guidelines for the biomimetic structural design of insect-scale flapping wings.


Micro air vehicle Calliphora Mass per unit length Flexural rigidity Torsional rigidity Natural frequency Finite element method 



The first author thanks the Alexander von Humboldt foundation for providing a fellowship for conducting part of this work.


  1. 1.
    Templin RJ (2000) The spectrum of animal flight: insects to pterosaurs. Prog Aerosp Sci 36:393–436CrossRefGoogle Scholar
  2. 2.
    Shyy W, Berg M, Ljungqvist D (1999) Flapping and flexible wings for biological and micro air vehicles. Prog Aerosp Sci 35:455–505CrossRefGoogle Scholar
  3. 3.
    Dickinson MH, Lehmann FO, Sane SP (1999) Wing rotation and the aerodynamic basis of insect flight. Science 284:1954–1960CrossRefGoogle Scholar
  4. 4.
    Maybury WJ, Lehmann FO (2004) The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings. J Exp Biol 207:4707–4726CrossRefGoogle Scholar
  5. 5.
    Ellington CP (1999) The novel aerodynamics of insect flight: applications to micro-air vehicles. J Exp Biol 202:3439–3448Google Scholar
  6. 6.
    Ansari SA, Zbikowski R, Knowles K (2006) Aerodynamic modelling of insect-like flapping flight for micro air vehicles. Prog Aerosp Sci 42:129–172CrossRefGoogle Scholar
  7. 7.
    Szmelter J, Zbikowski R (2002) A study of flow arising from insect wing flapping motion. Int J Numer Methods Fluids 40:497–505zbMATHCrossRefGoogle Scholar
  8. 8.
    Delauriar JD, Harris JM (1982) Experimental-study of oscillating-wing propulsion. J Aircr 19:368–373CrossRefGoogle Scholar
  9. 9.
    Wang ZJ (2000) Vortex shedding and frequency selection in flapping wing flight. J Fluid Mech 410:323–341zbMATHCrossRefGoogle Scholar
  10. 10.
    Hall KC, Hall SR (1996) Minimum induced power requirements for flapping flight. J Fluid Mech 323:285–315zbMATHCrossRefGoogle Scholar
  11. 11.
    Okamoto M, Yasuda K, Azuma A (1996) Aerodynamics characteristics of the wings and body of a dragonfly. J Exp Biol 199:281–294Google Scholar
  12. 12.
    Wang ZJ (2005) Dissecting insect flight. Annu Rev Fluid Mech 37:183–210CrossRefGoogle Scholar
  13. 13.
    Meyers MA, Chen PY, Lin AYM, Seki Y (2008) Biological materials: structure and mechanical properties. Prog Mater Sci 53:1–206CrossRefGoogle Scholar
  14. 14.
    Wang XS, Li Y, Shi YF (2008) Effects of sandwich microstructures on mechanical behavior of dragonfly wing vein. Compos Sci Technol 68:186–192CrossRefGoogle Scholar
  15. 15.
    Machida K, Oikawa T (2007) Structure analysis of the wings of anotogaster sieboldii and hybris subjacens. Key Eng Mater 345–346:1237–1240CrossRefGoogle Scholar
  16. 16.
    Smith MJC (1996) Simulating moth wing aerodynamics: towards the development of flapping wing technology. AIAA J 34:1348–1355zbMATHCrossRefGoogle Scholar
  17. 17.
    Wootton RJ, Herbert RC, Young PG, Evans KE (2003) Approaches to the structural modelling of insect wings. Philos Trans R Soc Lond B Biol Sci 358:1577–1587CrossRefGoogle Scholar
  18. 18.
    Combes SA, Daniel TL (2003a) Flexural stiffness in insect wings I. scaling and the influence of wing venation. J Exp Biol 206:2979–2987CrossRefGoogle Scholar
  19. 19.
    Combes SA, Daniel TL (2003b) Flexural stiffness in insect wings II. spatial distribution and dynamic wing bending. J Exp Biol 206:2989–2997CrossRefGoogle Scholar
  20. 20.
    Ennos AR (1988) The importance of torsion in the design of insect wings. J Exp Biol 140:137–160Google Scholar
  21. 21.
    Ennos AR (1988) The inertial cause of wing rotation in diptera. J Exp Biol 140:161–169Google Scholar
  22. 22.
    Ennos AR (1995) Mechanical behaviour in torsion of insect wings, blades of grass and other canbered structures. Proc R Soc Lond B Biol Sci 140:161–169Google Scholar
  23. 23.
    Sunada S, Zeng LJ, Kawachi K (1998) The relationship between dragonfly wing structure and torsional deformation. J Theor Biol 193:39–45CrossRefGoogle Scholar
  24. 24.
    Rosenfeld NC, Wereley NM (2009) Time-periodic stability of a flapping insect wing structure in hover. J Aircr 46:450–464CrossRefGoogle Scholar
  25. 25.
    Barbakadze N, Enders S, Gorb S, Arzt E (2006) Local mechanical properties of the head articulation cuticle in the beetle Pachnoda marginata (Coleoptera, Scarabaeidae). J Exp Biol 209:722–730CrossRefGoogle Scholar
  26. 26.
    Langer MG, Ruppersberg JP, Gorb S (2004) Adhesion forces measured at the level of a terminal plate of the fly’s seta. Proc R Soc Lond B Biol Sci 271:2209–2215CrossRefGoogle Scholar
  27. 27.
    Deng XY, Schenato L, Wu WC, Sastry SS (2006a) Flapping flight for biomimetic robotic insects: part I—System modeling. IEEE Trans Robot 22:776–788CrossRefGoogle Scholar
  28. 28.
    Deng XY, Schenato L, Sastry SS (2006b) Flapping flight for biomimetic robotic insects: part II—Flight control design. IEEE Trans Robot 22:789–803CrossRefGoogle Scholar
  29. 29.
    Gorb SN, Popov VL (2002) Probabilistic fasteners with parabolic elements: biological system, artificial model and theoretical considerations. Philos Trans R Soc Lond Ser A Math Phys Eng Sci 360:211–225CrossRefGoogle Scholar
  30. 30.
    Matushkina N, Gorb S (2007) Mechanical peoperties of the endophytic ovipositor in damselflies (Zygopetra, Odonata) and their oviposition substrates. Zoology 110:167–175CrossRefGoogle Scholar
  31. 31.
    Rao SS (2004) Mechanical vibrations, 4th edn. Pearson Education (Singapore) Pte. Ltd., Indian Branch, DelhiGoogle Scholar
  32. 32.
    Bao L, Hu JS, Yu YL, Cheng P, Xu BQ, Tong BG (2006) Viscoelastic constitutive model related to deformation of insect wing under loading in flapping motion. Appl Math Mech 27:741–748zbMATHCrossRefGoogle Scholar
  33. 33.
    Vincent JFV, Wegst UGK (2004) Design and mechanical properties of insect cuticle. Arthropod Struct Develop 33:187–199CrossRefGoogle Scholar
  34. 34.
    Watson GS, Watson JA (2004) Natural nano-structures on insects—possible functions of ordered arrays characterized by atomic force microscopy. Appl Surf Sci 235:139–144CrossRefGoogle Scholar
  35. 35.
    Cook RD, Malkus RD, Plesha ME, Witt RJ (2005) Concepts and applications of finite element analysis. Wiley, SingaporeGoogle Scholar
  36. 36.
    Gere JM, Timoshenko SP (1999) Mechanics of materials. Stanley Thrones, Kingston upon ThamesGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2009

Authors and Affiliations

  • R. Ganguli
    • 1
    Email author
  • S. Gorb
    • 2
  • F.-O. Lehmann
    • 3
  • S. Mukherjee
    • 4
  • S. Mukherjee
    • 1
  1. 1.Department of Aerospace EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Evolutionary BiomaterialsMax Planck Institute for Metal ResearchStuttgartGermany
  3. 3.Biofuture Research Group, Institute of NeurobiologyUniversity of UlmUlmGermany
  4. 4.Department of Civil EngineeringNational Institute of TechnologyTiruchirappalliIndia

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