Lunate-Tail Swimming Propulsion

  • M. G. Chopra


The non-uniform motion of a thin wing of finite-aspect ratio, with rounded leading edge and sharp trailing edge, executing heaving and pitching oscillations at zero mean lift, characterizing the horizontal lunate tail of a cetacean mammal, has been investigated. These very oscillations turned through 90° to become horizontal motions of sideslip and yaw characterize the vertical lunate tails of the fast swimming Percomorphi fishes. An oscillating vortex sheet consisting of streamwise and spanwise components is shed to trail behind the wing and it is the streamwise component resulting from the finiteness of the wing that makes this study a generalization of the two-dimensional treatment of lunate-tail propulsion by Lighthill (1970). Dependence of the forward thrust and hydromechanical propulsive efficiency on the aspect ratio, reduced frequency, feathering parameter, and the position of the pitching axis has been studied. The possibility of the use of this analysis to the study of the wing making finite amplitude motion has also been discussed.


Vortex Wake Suction Force Thrust Coefficient Pitching Axis Propulsive Efficiency 
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  1. Breder, C. M. 1926 Locomotion of fishes. Zoologica, 4, 159–297.Google Scholar
  2. Chopra, M. G. 1974 Hydromechanics of lunate-tail swimming propulsion. J. Fluid Mech. 64, 375.Google Scholar
  3. Karman, T. Von 1935 Neue Darstellung der Tragflügel Theorie. Z. Angew. Math. Mech. 15, 56.Google Scholar
  4. Karman, T. Von and Burgers, J. M. 1934 General aerodynamic theory-perfect fluids. In Aerodynamic Theory Vol. II, Div. E, 304–310, W. F. Durand, ed., Springer, Berlin.Google Scholar
  5. Karman, T. Von and Sears, W. R. 1938 Aerofoil theory for nonuniform motion. J. Aero. Sci. 5, 379.Google Scholar
  6. Lighthill, M. J. 1960 Note on the swimming of slender fish. J. Fluid Mech. 9, 305.Google Scholar
  7. Lighthill, M. J. 1969 Hydromechanics of aquatic animal propulsion. Ann. Rev. Fluid Mech. 1, 413.Google Scholar
  8. Lighthill, M. J. 1970 Aquatic animal propulsion of high hydro-mechanical efficiency. J. Fluid Mech. 44, 265.Google Scholar
  9. Lighthill, M. J. 1971 Large-amplitude elongated-body theory of fish locomotion. Proc. Roy. Soc. B, 179, 125.Google Scholar
  10. Lighthill, M. J. 1973 Aquatic animal locomotion. Proc. of 13th Int. Cong. Theoretical and Applied Mechanics. Springer, Berlin, 29.Google Scholar
  11. Munk, M. 1922 General theory of thin wing sections. N. A. C. A. Report No. 142.Google Scholar
  12. Munk, M. 1924 Elements of the wing section theory and of the wing theory. N. A. C. A. Report No. 191.Google Scholar
  13. Possio, C. 1938 Aerodynamic forces acting on an oscillating wing at supersonic speeds. L’Aerotecnica, 18, 441.Google Scholar
  14. Prandtl, L. and Betz, A. 1927 Vier Abhandlungen zur Hydrodynamik,Im selbstverlag des Kaiser Wilhem-Instituts für Strömungs forschung, Göttingen.Google Scholar
  15. Sears, W. R. 1938 A contribution to the aerofoil theory for nonuniform motion, Proc. of fifth Intern. Congress for Applied Mechanics. London, 483Google Scholar
  16. Wu, T. Y. 1961 Swimming of a waving plate. J. Fluid Mech. 10, 321.Google Scholar
  17. Wu, T. Y. 1971 Hydromechanics of swimming of fishes and cetaceans. Adv. in Appl. Mech. 11, 1.Google Scholar

Copyright information

© Springer Science+Business Media New York 1975

Authors and Affiliations

  • M. G. Chopra
    • 1
  1. 1.University of CambridgeCambridgeEngland

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