Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-06-28T15:56:30.147Z Has data issue: false hasContentIssue false
  • English
  • Français

An unsteady lifting line theory of flapping wings with application to the forward flight of birds

Published online by Cambridge University Press:  20 April 2006

P. J. Phlips ,
R. A. East  and
N. H. Pratt
P. J. Phlips
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton, Southampton S09 5NH, U.K. Present address: Department of Aeronautics and Astronautics, MIT, Cambridge, Massachusetts.
R. A. East
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton, Southampton S09 5NH, U.K.
N. H. Pratt
Affiliation:
Department of Aeronautics and Astronautics, University of Southampton, Southampton S09 5NH, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

A lifting line theory of flapping wings in steady forward flight is presented in which the unsteady features of the flow are modelled. A detailed three-dimensional model of the vortex wake is used to evaluate the unsteadiness to first order. The method gives satisfactory agreement with well-known limiting cases. Relationships between the geometric and the kinematic parameters, and the forces and the power are predicted which are compatible with the limited experimental evidence. The theory is applied to the calculation of the power curve of specific birds. Important similarities and differences are observed between the present results and those of Pennycuick (1975) and Rayner (1979c).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 112 , November 1981 , pp. 97 - 125
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Archer, R. D., Sapuppo, J. & Betteridge, D. S. 1979 Propulsion characteristics of flapping wings. Aeronaut. J. 83, 355–371.Google Scholar
Betteridge, D. S. & Archer, R. D. 1974 A study of the mechanics of flapping flight. Aeronaut. Quart. 25, 129.Google Scholar
Bramwell, A. R. S. 1976 Helicopter Dynamics. Edward Arnold.
Brown, R. J. H. 1953 The flight of birds: II. Wing function in relation to flight speed. J. Exp. Biol. 30, 90–103.Google Scholar
Chabonat, M. 1970 Contribution à l’étude des écoulements instationnaires. L'Aéronaut. et l'Astronaut. 23, 23–37.Google Scholar
Cloupeau, M., Devillers, J. F. & Devezeaux, D. 1979 Direct measurements of instantaneous lift in desert locust; comparison with Jensen's experiments on detached wings. J. Exp. Biol. 80, 1–15.Google Scholar
Cone, C. D. 1968 The aerodynamics of flapping bird flight. Virginia Institute of Marine Science, Special Scientific Report no. 52.Google Scholar
Duncan, W. J., Thom, A. S. & Young, A. D. 1970 Mechanics of Fluids. 2nd edition. Edward Arnold.
Etkin, B. 1972 Dynamics of Atmospheric Flight. John Wiley.
Fejtek, I. & Nehera, J. 1980 Experimental study of flapping wing lift and propulsion. Aeronaut. J. 84, 28–33.Google Scholar
Filon, L. N. G. 1928 On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. Edin. 49, 38–47.Google Scholar
Goldspink, G. 1977 Mechanics and energetics of muscle in animals of different sizes, with particular reference to muscle fibre composition of vertebrate muscle. Article in Scale Effects in Animal Locomotion, pp. 37–55. Academic.
Greenewalt, C. H. 1962 Dimensional relationships for flying animals. Smithson. Misc. Colln. 144, no. 2.Google Scholar
Jones, R. T. 1940 The unsteady lift of a wing of finite aspect ratio. NACA Rep. no. 681.Google Scholar
Kokshaysky, N. V. 1979 Tracing the wake of a flying bird. Nature 279, 146–148.Google Scholar
Küchemann, D. & Weber, W. 1953 Aerodynamics of Propulsion. McGraw-Hill.
Lighthill, M. J. 1974 Aerodynamic aspects of animal flight. Bull. Inst. Math. Applics. 10, 369–393.Google Scholar
Liggthill, M. J. 1977 Introduction to the scaling of aerial locomotion. Article in Scale Effects in Animal Locomotion, pp. 365–404. Academic.
Maresca, C., Favier, D. & Rebont, J. 1979 Experiments on an aerofoil at high angle of incidence in longitudinal oscillations. J. Fluid Mech. 92, 671–690.Google Scholar
Mccroskey, W. J. 1975 Recent development in dynamic stall. Article in Proc. Univ. Arizona/USAF OSR Symposium on Unsteady Aerodynamics, vol. 1, edited by R. B. Kinney.
Mcrobert, D. M. 1980 Aerodynamic force measurements and flow visualisation of flapping wings. Univ. Southampton, Dept Aeronautics and Astronautics, B.Sc. Thesis.
Mehta, U. B. 1977 Dynamic stall of an oscillating airfoil. AGARD Fluid Dynamics Panel Symposium on Unsteady Aerodynamics, Ottawa, Canada, Sept. 1977 paper no. 23.
Moineau, R. 1939 L'aile battante autopropulsive et hypersustentatrice. Comptes Rendus, Série A, 208, 964–966.Google Scholar
Nachtigall, W. 1977 On the significance of the Reynolds number and the fluid mechanical phenomena connected to it in swimming physiology and flight biophysics. Fortschritte der Zoologie 24 (Heft 2/3).Google Scholar
Oehme, H. & Kitzler, U. 1975 Untersuchungen zur Flügbiophysik und Flügphysiologie der Vögel. II. Zur Geometrie des Vögelflügels. Zool. Jb. Physiol. 79, 402–424.English translation, NASA, Washington, Feb. 1976Google Scholar
Pennycuick, C. J. 1968 Power requirements for horizontal flight in the pigeon, Columba livia. J. Exp. Biol. 49, 527–555.Google Scholar
Pennycuick, C. J. 1975 Mechanics of flight. Article in Avian Biology V (ed. Farner and King), pp. 1–75. Academic.
Rayner, J. M. V. 1979a A vortex theory of animal flight. Part 1. The vortex wake of a hovering animal. J. Fluid Mech. 91, 697–730.Google Scholar
Rayner, J. M. V. 1979b A vortex theory of animal flight. Part 2. The forward flight of birds. J. Fluid Mech. 91, 731–763.Google Scholar
Rayner, J. M. V. 1979c A new approach to animal flight mechanics. J. Exp. Biol. 80, 17–54.Google Scholar
Robinson, A. & Laurmann, J. 1956 Wing Theory. Cambridge Univ. Press.
Tucker, V. A. 1973 Bird metabolism during flight, evaluation of a theory. J. Exp. Biol. 58, 689–709.Google Scholar
Von Holst, E. & Küchemann, D. 1942 Biological and aerodynamical problems of animal flight. J. Roy. Aero. Soc. 46, 39–56.Google Scholar
Wagner, H. 1925 Über die Entstehung des dynamischen Auftriebes von Tragflügeln. Zeit. angew. Math. Mech. 5, 17–35.Google Scholar
Weis-Fogh, T. 1973 Quick estimates of flight fitness in hovering animals including novel mechanisms for lift production. J. Exp. Biol. 59, 169–230.Google Scholar
Wilding, J. 1961 Bird flight and the aeroplane. J. Roy. Aero. Soc. 65, 796–799.Google Scholar
Wood, C. J. & Kirmani, S. F. A. 1970 Visualization of heaving aerofoil wakes including the effect of a jet flap. J. Fluid Mech. 41, 627–640.Google Scholar