Biomechanics pp 106-154 | Cite as

Flying and Swimming

  • Y. C. Fung


Locomotion is, of course, an extremely interesting subject. People are forever fascinated by sports. We cheer gold medal winners. How athletes are trained is certainly a legitimate question for biomechanics. There are people who suffer impairments in locomotion and others who try to help them recover or overcome their handicaps. These people, the sports lovers, educators, patients, orthopedic surgeons, engineers, physical therapists, nurses, prosthesis manufacturers, and hospital managers, will benefit from a good understanding of the biomechanics of locomotion. Then there is the world of animals around us. We see animals walking and crawling on land, flying in air, and swimming in fluid. From man and mice to birds, fishes, and sperms, there is a tremendous variety of questions one may wish to ask about locomotion.


Reynolds Number Strouhal Number Lift Coefficient Sockeye Salmon Biharmonic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ayman, G. (1936). Bird Flight, Bodley Head, London.Google Scholar
  2. Bainbridge, R.A. (1958). The speed of swimming of fish as related to size and to the frequency and amplitude of the tail beat. J. Exp. Biol. 37: 109–133.Google Scholar
  3. Bainbridge, R. (1960). Speed and stamina in three fish. J. Exp. Biol. 37: 129–153.Google Scholar
  4. Bainbridge, R. (1963). Caudal fin and body movement in the propulsion of some fish. J. Exp. Biol. 40: 23–56.Google Scholar
  5. Berg, H.C. and Brown, D.A. (1972). Chemotaxis in Escherichia coli analyzed by three-dimensional tracking. Nature London 239: 500.Google Scholar
  6. Blake, J.R. and Sleigh, M.A. (1975). Hydromechanical aspects of ciliary propulsion. In Swimming and Flying in Nature (T.Y. Wu, C.J. Brokaw and C. Brennen, eds.), Vol. 1, Plenum Press, New York, pp. 185–209.Google Scholar
  7. Bone, Q. (1975). Muscular and energetic aspects of fish swimming. In Swimming and Flying in Nature (T.Y. Wu, C.J. Brokow and C. Brennen, eds.), Vol. 2, Plenum Press, New York, pp. 493–528.CrossRefGoogle Scholar
  8. Breder, C.M. (1926). The locomotion of fishes. Zoologica 4: 159–297.Google Scholar
  9. Brett, J.R. (1963). The energy required for swimming by young sockeye salmon with a comparison of drag force on a dead fish. Trans. Roy. Soc. Can. 1: Sec. IV, 441–457.Google Scholar
  10. Brokaw, C.J. and Gibbons, I.R. (1975). Mechanisms of movement in flagella and cillia. In Swimming and Flying in Nature (T.Y. Wu, C.J. Brokaw and C. Brennen, eds.), Vol. 1, Plenum Press, New York, pp. 89–126.Google Scholar
  11. Brown, R.H.J. (1953). The flight of birds. II. Wing function in relation to flight speed. J. Exp. Biol. 30: 90–103.Google Scholar
  12. Childress, S. (1981). Mechanics of Swimming and Flying. Cambridge Univ. Press, Cambridge.CrossRefGoogle Scholar
  13. Chwang, A.T. and Wu, T.Y. (1971). A note on the helical movement of micro-organisms. Proc. Roy. Soc. B., 178: 327–346.ADSCrossRefGoogle Scholar
  14. Chwang, A.T. and Wu, T.Y. (1974). “Hydromechanics of low-Reynolds-number flow. Part I: Rotation of axisymmetric prolate bodies. J. Fluid Mechanics 63: 607–622, 1974.MathSciNetADSMATHCrossRefGoogle Scholar
  15. Chwang, A.T. and Wu, T.Y.: Part II Singularity method for Stokes flows. ibid. 67: 787–815, 1975.MathSciNetMATHGoogle Scholar
  16. Chwang, A.T. and Wu, T.Y.: Part III (Chwang alone) Motion of spheroidal particle in quadratic flows. ibid. 72: 17–34, 1975.MATHGoogle Scholar
  17. Chwang, A.T. and Wu, T.Y.: Part IV Translation of spheroids. ibid 75: 677–689, 1976.MATHGoogle Scholar
  18. Dalton, S. (1975). Borne on the Wind, The World of Insects in Flight. E.P. Dutton and Co., New York.Google Scholar
  19. Dembo, M. and Harlow, F. (1986). Cell motion, contractile network and the physics of interpenetrating reactive flow. Biophys. J. 50: 109–121.CrossRefGoogle Scholar
  20. Dembo, M., Harlow, F. and Alt, W. (1984). The biophysics of cell motility. In Cell Surface Dynamics: Concepts and Models. ( A.S. Perelson, C. DeLisi and F.W. Wiegel, eds.), Marcel Dekker, New York, pp. 495–541.Google Scholar
  21. Duncker, H.R. (1972). The structure and function of bird’s lung. Respiration Physiol. 14: 44–63.CrossRefGoogle Scholar
  22. Ellington, C.P. (1975). Non-steady-state aerodynamics of the flight of Encarsia formosa. In Swimming and Flying in Nature (T.Y. Wu, C. Brokow and C. Brennen, eds. ), Plenum Press, pp. 783–796.Google Scholar
  23. Fung, Y.C. (1965). Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  24. Fung, Y.C. (1977). A First Course in Continuum Mechanics, 2nd edn., Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  25. Fung, Y.C. (1981). Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York.Google Scholar
  26. Gallin, J.I. and Quie, P.G. (eds.) (1978). Leukocyte Chemotaxis: Methods, Physiology and Clinical Applications, Raven Press, New York.Google Scholar
  27. Goldman, R., Pollard, T., and Rosenbaum, J. (eds.) (1976). Cell Motility. Cold Pring Harbor Conferences on Cell Proliferation. Cold Spring Harbor Press, New York.Google Scholar
  28. Goldspink, G. (1977). Design of muscle in relation to locomotion. In Mechanics and Energetics of Animal Locomotion ( R.McN. Alexander and G. Goldspink, eds.), Chapman and Hall, London.Google Scholar
  29. Gray, J. (1939). Aspects of animal locomotion. Proc. Roy. Soc. London, B 128: 28–62.ADSCrossRefGoogle Scholar
  30. Gray, J. (1953). How Animals Move. Cambridge Univ. Press, Cambridge.Google Scholar
  31. Gray, J. (1958). The movement of the spermatozoa of the bull. J. Exp. Biol. 35: 96–108.Google Scholar
  32. Gray, J. (1968). Animal Locomotion, W.W. Norton, New York; Weidenfeld and Nicolson, London.Google Scholar
  33. Gray, J. and Hancock, G.J. (1955). The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32: 802–814.Google Scholar
  34. Gray, J. and Lissmann, H.W. (1964). The locomotion of nematodes. J. Exp. Biol. 41: 135–154.Google Scholar
  35. Hancock, G.J. (1953). The self-propulsion of microscopic organisms through liquids. Proc. Roy. Soc. A 217: 96–121.MathSciNetADSMATHCrossRefGoogle Scholar
  36. Huxley, H.E., Bray, B. and Weeds, A.G. (eds.) (1982). Molecular Biology of Cell Locomotion. Phil. Trans., Roy. Soc. London, B299: 145–327.Google Scholar
  37. Jameson, W. (1958). The Wandering Albatross. Hart-Davis, London.Google Scholar
  38. Kuethe, A.M. (1975a). On the mechanics of flight of small insects. In Swimming and Flying in Nature ( T.Y. Wu, C.J. Brokaw, and C. Brennen, eds.), Plenum Press, New York. pp. 803–813.CrossRefGoogle Scholar
  39. Kuethe, A.M. (1975b). Prototypes in nature. The carry-over into Technology. Technium, Engineering Review. 1975, Univ. of Michigan.Google Scholar
  40. Kuethe, A.M. and Chow, C.-Y. (1986). Foundations of Aerodynamics. 4th ed. John Wiley, New York.Google Scholar
  41. Lighthill, J. (1969). Hydromechanics of aquatic animal propulsion-a survey. Ann. Rev. Fluid Mech. 1: 413–446.ADSCrossRefGoogle Scholar
  42. Lighthill, J. (1975). Mathematical Biofluiddynamics, Soc. Indus. Appl. Math. Philadelphia.Google Scholar
  43. Lillienthal, O. (1889). Der Vogelflug als Grundlage der Fliegekunst. R. Oldenbourg, Berlin.Google Scholar
  44. Maxworthy, T. (1981). The fluid dynamics of bird flight. Ann. Rev. of Fluid Mechanics, (M. Van Dyke and J. V. Wehausen, eds.), Annual Reviews, Palo Alto, California.Google Scholar
  45. McAlister, K.W., Carr, L.W., and McCroskey, W.J. (1978). Dynamic stall experiments on the NACA 0012 airfoil. NASA Tech. Paper 1100.Google Scholar
  46. Nachtigall, W. (1974). Insects in Flight (Trans. by H. Oldroyd et al). McGraw-Hill, New York.Google Scholar
  47. Newman, J.N. (1973). The force on a slender fish-like body. J. Fluid Mech. 58: 689–702.ADSMATHCrossRefGoogle Scholar
  48. Newman, J.N. and Wu, T.Y. (1973). A generalized slender-body theory for fish-like forms. J. Fluid Mech. 57: 673–693.ADSMATHCrossRefGoogle Scholar
  49. Norberg, R.A. (1975). Hovering flight of the dragoufly Aeschna Juncea L., kinematics and aerodynamics. In Swimming and Flying in Nature ( T.Y. Wu, C.J. Brokaw, and C. Brennen, eds.), Plenum Press, New York, pp. 763–781.CrossRefGoogle Scholar
  50. Nossal, R. (1988). On the elasticity of cytoskeletal networks. Biophys. J. 53: 349–359.CrossRefGoogle Scholar
  51. Oberbeck, A. (1876). Ueber stationäre Flüssigkeitsbewegungen mit Berücksichtigung der inneren Reibung. Crelle 81, 62–80.Google Scholar
  52. Oster, G.F. and Perelson, A.S. (1987). The physics of cell motility. J. Cell Sci. 8: 35–54.Google Scholar
  53. Pennycuick, C.J. (1968). A wind-tunnel study of gliding flight in the pigeon Columba livia. J. Exp. Biol. 49: 509–526.Google Scholar
  54. Pennycuick, C.J. (1972). Animal Flight. Edward Arnold, London.Google Scholar
  55. Peterson, R.T. (1963). The Birds. Time Inc., New York.Google Scholar
  56. Pollard, T.D. and Cooper, J.A. (1986). Quantitative analysis of the effect of acanthamoeba profilin on actin filament nucleation and elongation. Biochem. 23: 6631–6641.Google Scholar
  57. Prandtl, L., and Tietjens, O.G. (1934). Applied Hydro-and-Aeromechanics. McGraw-Hill, NewGoogle Scholar
  58. York. (Translated from the German edition, Springer, Berlin/Heidelberg, 1931 ).Google Scholar
  59. Pringle, J.W.S. (1975). Insect Flight. Oxford University Press, London and New York.Google Scholar
  60. Rayleigh, Lord., (J.W. Strutt). (1883). The soaring of birds. Nature 27: 534–535.Google Scholar
  61. Sato, M., Leimbach, G., Schwartz, W.H., and Pollard, T.D. (1985). Mechanical properties of actin. J. Biol. Chem. 260: 8585–8592.Google Scholar
  62. Schmid-Schönbein, G.W. and Engler, R.L. (1986). Granulocytes as active participants in acute myocardial ischemia and infarction. Am. J. Cardiovasc. Pat ho. 1: 15–30.Google Scholar
  63. Scheid, P., Slama, H., and Piiper, J. (1972). Mechanisms of unidirectional flow in parabronchi of avian lungs. Measurements in duck lung preparations. Respiration Physiol. 14: 83–95.CrossRefGoogle Scholar
  64. Sleigh, M.A. (ed.) (1974). Cilia and Flagella. Academic Press, London and New York.Google Scholar
  65. Smart, J., and Hughes, N.F. (1972). In Insect/Plant Relationships: Sympos. R. Entomol. Soc. London No. 6, pp. 143–155.Google Scholar
  66. Smith, X. (1988). Neuronal cytomechanics: the actin-based motility of growth cones. Science 242: 708–715.ADSCrossRefGoogle Scholar
  67. Stossel, T.P. (1982). The structure of the cortical cytoplasm. Phil. Trans. Roy. Soc. London B 299: 275–289.ADSCrossRefGoogle Scholar
  68. Taylor, D.L. and Condeelis, J.S. (1979). Cytoplasmic structure and contractility in amoeboid cells. Int. Rev. Cytology 56: 57–144.CrossRefGoogle Scholar
  69. Taylor, G.I. (1951). Analysis of swimming microscopic organisms. Proc. Roy. Soc. London Ser. A, 209: 447–461.MathSciNetADSMATHCrossRefGoogle Scholar
  70. Taylor, G.I. (1952). Analysis of the swimming of long and narrow animals. Proc. Roy. Soc. London, A, 214: 158–183.ADSMATHCrossRefGoogle Scholar
  71. Tucker, V.A. (1968). Respiratory exchange and evaporative water loss in the flying budgerigar. J. Exp. Biol. 48: 67–87, Company of Biologists Ltd.Google Scholar
  72. Tucker, V. and Parrott, G.C. (1970). Aerodynamics of gliding flight of falcons and other birds. J. Exp. Biol. 52: 345–368, Company of Biologists Ltd.Google Scholar
  73. Tucker, V.A. (1975). Aerodynamics and energetics of vertebrate fliers. In Swimming and Flying in Nature ( T. Wu, C. Brokaw and C. Brennen, eds). Plenum Press, New York, pp. 845–865.CrossRefGoogle Scholar
  74. Von Holst, E. and Küchemann, D. (1974). Motion of animals in fluids. J. Royal Aeronautical Soc. 43: 39–56.Google Scholar
  75. Von Kármán, T. and Gabrielli, G. (1950). What price speed? Specific power required for propulsion of vehicles. Mech. Eng. 72: 775–781.Google Scholar
  76. Wang, Y.-L. (1985). Exchange of actin subunits at the leading edge of living fibroblasts: possible role of treadmilling. J. Cell Biol. 101: 597–602.CrossRefGoogle Scholar
  77. Webb, P.W. (1975). Hydrodynamics and energetics of fish propulsion. Bull. Fish Res. Bd. Can. 190: 1–158.Google Scholar
  78. Weis-Fogh, T. and Jensen, M. (1956). Biology and physics of locust flight. I. Basic principles in insect flight. A critical review. Phil. Trans., Roy. Soc. London, B 239: 415–458.CrossRefGoogle Scholar
  79. Weis-Fogh, T. (1956). Biology and physics of locust flight. II. Flight performance of desert locust (Schistocera gregaria). Phil. Trans. Roy. Soc. London B, 239: 459–510.ADSCrossRefGoogle Scholar
  80. Weis-Fogh, T. (1960). J. Exp. Biol. 37: 889–907.Google Scholar
  81. Weis-Fogh, T. (1960). J. Exp. Biol. 59: 169–230.Google Scholar
  82. Weis-Fogh, T. (1964). VIII. Lift and metabolic rate of flying locusts. J. Exp. Biol. 41: 257–271.Google Scholar
  83. Weis-Fogh, T. (1967). Energetics of hovering flight in hummingbirds and in Drosophila. J. Exp. Biol. 56: 79–104.Google Scholar
  84. Weis-Fogh, T. (1973). Quick estimates of flight fitness in hovering animals, including novel mechanisms for lift production. J. Exp. Biol. 59: 169–230, Company of Biologists Ltd.Google Scholar
  85. Weis-Fogh, T. (1975). Flapping flight and power in birds and insects, conventional and novel mechanisms. In Swimming and Flying in Nature ( T.Y. Wu, C.J. Brokaw, and C. Brennen, eds.), Plenum Press, New York, pp. 729–762.CrossRefGoogle Scholar
  86. Wilkinson, P.C. (1974). Chemotaxis and Inflammation, Churchill Livingstone, Edinburgh and London.Google Scholar
  87. Wu, T.Y. (1971). Hydromechanics of swimming fishes and cetaceans. In Advances in Applied Mechanics (C.S. Yih, ed.), 11: Academic Press, New York. pp. 1–63.Google Scholar
  88. Wu, T.Y. (1971). Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins. J. Fluid Mech. 46: 545–568.ADSCrossRefGoogle Scholar
  89. Wu, T.Y. and Newman, J.N. (1972). Unsteady flow around a slender flish-like body. Proc. International Symp. on Directional Stability and Control of Bodies Moving in Water. Institution of Mechanical Engineers, London.Google Scholar
  90. Wu, T.Y., Brokaw, C.J. and Brennen, C. (eds.) (1975). Swimming and Flying in Nature. Vols. 1 and 2, Plenum Press, New York.Google Scholar
  91. Wu, T.Y. (1976). Introduction to the scaling of aquatic animal locomotion. In Scale Effects of Animal Locomotion. ( M.J. Lighthill and T.J. Pedley, eds.), Academic Press, London, pp. 753–766.Google Scholar
  92. Wu, T.Y. and Yates, G.T. (1978). A comparative mechanophysiological study of fish locomotion with implications for tuna-like swimming mode. In Physiological Ecology of Tuna ( G.D. Sharp and A.E. Dizon, eds.), Academic Press, New York.Google Scholar
  93. Yates, G.T. (1983). Hydromechanics of body and caudal fin propulsion. Chapter 6 in Fish Biomechanics. (P.W. Webb and D. Weihs, eds.), Praeger Scientific, New York.Google Scholar
  94. Zhu, C., Skalak, R., and Schmid-Schönbein, G.W. (1988). One-dimensional steady continuum model of retraction of pseudopod in leukocytes. J. Biomech. Eng. 111: 69–77.CrossRefGoogle Scholar
  95. Zigmoid, S.H. (1978). Chemotaxis by polymorphonuclear leukocytes. (review) J. Cell Biol. 77: 269–287.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Y. C. Fung
    • 1
  1. 1.Department of Applied Mechanics and Engineering Science/BioengineeringUniversity of California, San DiegoLa JollaUSA

Personalised recommendations