Aerodynamics and Energetics of Vertebrate Fliers

  • V. A. Tucker


This paper partitions the metabolic rate of an animal performing level flapping flight at constant speed into various power terms, the largest being the mean rate at which the muscles do work on the wings. This work rate (the power output) is defined by scalar products of force and velocity integrated along the wing span and over the duration of one cycle of movement. The power output is the sum of three componenets, also defined by integral equations: induced power, profile power and parasite power. Methods of evaluating the integral equations and uncertainties in the results are discussed.

The metabolic rate of the flight muscles depends not only on their power output, but also on inertial, gravitational and elastic forces. The influence of these forces on muscle efficiency (the ratio of power output to metabolic rate) is discussed.

Simple solutions to the integral equations for power output can be assumed or measured, which together with other estimates yield predictions for the energetic requirements of flying birds and bats. The predictions, when compared with measurements of metabolic rates made in wind tunnels, are accurate to better than 17% for flight at cruising speeds.


Power Output Wind Tunnel Power Input Aerodynamic Force Elastic Element 
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. Abbott, B. C., Bigland, B. and Ritchie, J. M. 1952 The physiological cost of negative work. J. Physiol. 117, 380–390.PubMedGoogle Scholar
  2. Bilo, D. 1971 Flugbiophysik von Kleinvogeln. I. Kinematik und Aerodynamik des Flugelabschlages beim Haussperling (Passer domesticus L.). Z. vergl. Physiologie, 71, 382–454.Google Scholar
  3. Bilo, D. 1972 Flugbiophysik von Kleinvogeln. II. Kinematik und Aerodynamik des Flugelaufschlages beim Haussperling (Passer domesticus L.). Z. vergl. Physiologie, 76, 426–437.Google Scholar
  4. Cavagna, G. A. 1970 Elastic bounce of the body. J. Appl. Physiol. 29, 279–282.PubMedGoogle Scholar
  5. Cavagna, G. A., Saibene, F. P. and Margaria, R. 1964 Mechanical work in running. J. Appl. Physiol. 19, 249–256.PubMedGoogle Scholar
  6. Curtin, N. A. and Davies, R. E. 1973 Chemical and mechanical changes during stretching of activated frog skeletal muscle. Cold Spring Harbor Symp. on Quantitative Biol. 37, 619–626.CrossRefGoogle Scholar
  7. Feldmann, I. F. 1944 Windkanaluntersuchung am Modell einer Möwe. Aero-revue, Zurich 19, 219–222.Google Scholar
  8. Goldstein, S. 1965 Modern Developments in Fluid Dynamics. Dover Publ., New York, New York.Google Scholar
  9. Hill, A. V. 1938 The heat of shortening and the dynamic constants of muscle. Proc. Roy. Soc. Lond., B. 126, 136–195.CrossRefGoogle Scholar
  10. Hill, A. V. 1939 The mechanical efficiency of frog muscle. Proc. Roy. Soc. Lond. B, 127, 434-451.CrossRefGoogle Scholar
  11. Jensen, M. 1956 Biology and physics of locust flight. III. The aerodynamics of locust flight. Phil. Trans. Roy. Soc. Lond., B. 239, 511–552.CrossRefGoogle Scholar
  12. Le Page, W. L. 1923 Wind channel experiments on a pariah kite. Royal. Aeron. Soc. Lond. 27, 114–115.Google Scholar
  13. Margaria, R. 1968 Positive and negative work performances and their efficiencies in human locomotion. Int. Z. angew. Physiol. ainschl. Arbeitphysiol. 25, 339–351.Google Scholar
  14. Nayler, J. L. and Simmons, L. F. G. 1921 A note relating to experiments in a wind channel with an Alsatian swift. Aeron. Res. Comm. Reports and Memoranda, No. 708.Google Scholar
  15. Oehme, H. and Kitzler, U. 1974 Über die Kinematik des Flügelschlages beim unbeschleunigten Horizontalflug. Untersuchungen zur Flugbiophysik und Flugphysiologie der Vögel. I. Zool. Jb. Physiol. 78, 461–512.Google Scholar
  16. Parrott, G. C. 1970 Aerodynamics of gliding flight of a black vulture Coragyps atratus. J. Exp. Biol. 53, 363–374.Google Scholar
  17. Pennycuick, C. J. 1968 Power requirements for horizontal flight in the pigeon Columba livia. J. Exp. Biol. 49, 527–555.Google Scholar
  18. Pennycuick, C. J. 1969 The mechanics of bird migration. Ibis, 111, 525–556.CrossRefGoogle Scholar
  19. Pennycuick, C. J. 1971a Gliding flight of the white-backed vulture Gyps africanus. J. Exp. Biol. 55, 13–38.Google Scholar
  20. Pennycuick, C. J. 197lb Gliding flight of the dog-faced bat Rousettus aegyptiacus observed in a wind tunnel. J. Exp. Biol. 55, 833–845.Google Scholar
  21. Schmidt-Nielsen, K. 1972 Locomotion: energy cost of swimming, flying and running. Science, 177, 222–228.PubMedCrossRefGoogle Scholar
  22. Schmitz, F. W. 1960 Aerodynamik des Flugmodells. Carl Lange, Duisburg, Germany.Google Scholar
  23. Shapiro, J. 1955 Principles of Helicopter Engineering. McGraw-. Hill Book Co., New York, New York.Google Scholar
  24. Stainsby, W. N. and Barclay, J. K. 1972 Oxygen uptake for brief tetanic contractions of dog skeletal muscle in situ. Am. J. Physiol. 223, 371–375.PubMedGoogle Scholar
  25. Thys, H., Faraggiana, T. and Margaria, R. 1972 Utilization of muscle elasticity in exercise. J. Appl. Physiol. 32, 491–494.PubMedGoogle Scholar
  26. Tucker, V. A. 1970 Energetic cost of locomotion in animals. Comp. Biochem. Physiol. 34, 841–846.PubMedCrossRefGoogle Scholar
  27. Tucker, V. A. 1973a Bird metabolism during flight: evaluation of a theory. J. Exp. Biol. 58, 689–709.Google Scholar
  28. Tucker, V. A. 1973b Aerial and terrestrial locomotion: a comparison of energetics. In Comparative Physiology, 63–76, L. Bolis, K. Schmidt-Nielsen and S. H. P. Maddrell, eds., North Holland Publ. Co., The Netherlands.Google Scholar
  29. Tucker, V. A. 1974 Energetics of natural avian flight. In Avian Energetics, 298–328, R. A. Paynter, Jr., ed., Publ. of the Nutall Ornith. Club, No. 15.Google Scholar
  30. Tucker, V. A. 1975 Flight energetics. Symp. Zool. Soc. Lond. No. 35, in press.Google Scholar
  31. Tucker, V.A. and Parrott, G. C. 1970 Aerodynamics of gliding flight in a falcon and other birds. J. Exp. Biol. 52, 345–367.Google Scholar
  32. Von Mises, R. 1959 Theory of Flight. Dover Publ., New York, New York.Google Scholar
  33. Weis-Fogh, T. 1972 Energetics of hovering flight in hummingbirds and in Drosophila. J. Exp. Biol. 56, 79–104.Google Scholar
  34. 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
  35. 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. Lond. B, 239, 415–458.Google Scholar
  36. Woledge, R. C. 1968 The energetics of tortoise muscle. J. Physiol. 197, 685–707.PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1975

Authors and Affiliations

  • V. A. Tucker
    • 1
  1. 1.Duke UniversityDurhamUSA

Personalised recommendations