Aerodynamics and Energetics of Vertebrate Fliers
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.
KeywordsPower Output Wind Tunnel Power Input Aerodynamic Force Elastic Element
Unable to display preview. Download preview PDF.
- 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
- 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
- Feldmann, I. F. 1944 Windkanaluntersuchung am Modell einer Möwe. Aero-revue, Zurich 19, 219–222.Google Scholar
- Goldstein, S. 1965 Modern Developments in Fluid Dynamics. Dover Publ., New York, New York.Google Scholar
- Le Page, W. L. 1923 Wind channel experiments on a pariah kite. Royal. Aeron. Soc. Lond. 27, 114–115.Google Scholar
- 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
- 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
- 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
- Parrott, G. C. 1970 Aerodynamics of gliding flight of a black vulture Coragyps atratus. J. Exp. Biol. 53, 363–374.Google 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. 1971a Gliding flight of the white-backed vulture Gyps africanus. J. Exp. Biol. 55, 13–38.Google Scholar
- 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
- Schmitz, F. W. 1960 Aerodynamik des Flugmodells. Carl Lange, Duisburg, Germany.Google Scholar
- Shapiro, J. 1955 Principles of Helicopter Engineering. McGraw-. Hill Book Co., New York, New York.Google Scholar
- Tucker, V. A. 1973a Bird metabolism during flight: evaluation of a theory. J. Exp. Biol. 58, 689–709.Google Scholar
- 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
- 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
- Tucker, V. A. 1975 Flight energetics. Symp. Zool. Soc. Lond. No. 35, in press.Google Scholar
- 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
- Von Mises, R. 1959 Theory of Flight. Dover Publ., New York, New York.Google Scholar
- Weis-Fogh, T. 1972 Energetics of hovering flight in hummingbirds and in Drosophila. J. Exp. Biol. 56, 79–104.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
- 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