A model of vortex wake is suggested to determine the
induced power during animal hovering flight. The wake is modeled
by a series of equi-spaced rigid rectangular vortex plates, positioned
horizontally and moving vertically downwards with identical speeds;
each plate is generated during powering of the functionally wing
stroke. The vortex representation of the wake considered in the
current theory allows a considerable loss of momentum to occur. The
current approach accords well with the nature of the wingbeat since it
considers the unsteadiness in the wake as an important fluid
dynamical characteristic. Induced power in hovering is calculated as
the aerodynamic power required to generate the vortex wake system.
Specific mean induced power to mean wing tip velocity ratio is
determined by solely the normal spacing parameter (f) for a given
wing stroke amplitude. The current theory gives much higher specific
induced power estimate than anticipated by classical methods.
[1] C. Van Den Berg, and C. P. Ellington, "The vortex wake of a
hovering model hawkmoth," Philos. Trans. R. Soc. London B, vol.
352, pp. 317-328, 1997.
[2] M. H Dickinson, F. O. Lehmann, and S. P. SANE, "Wing rotation and
the aerodynamic basis of insect flight, " Science, vol. 284, pp. 1954-
1960, 1999.
[3] S. P. Sane and M. H. Dickinson, "The control of flight force by a
flapping wing: lift and drag production," J. Exp.Biol., vol. 204, pp.
2607-2626, 2001.
[4] S. P. Sane and M. H. Dickinson, "The aerodynamic effects of wing
rotation and a revised quasi-steady model of flapping flight," J.
Exp.Biol., vol. 205, pp. 1087-1096, 2002.
[5] G. R. Spedding, M. Rosén, and A. Hedenström, "A family of vortex
wakes generated by a thrush nightingale in free flight in a wind
tunnel over its entire natural range of flight speeds," J. Exp. Biol.,
vol. 206, pp. 2313-2344, 2003.
[6] M. F. M. Osborne, "Aerodynamics of flapping flight with application to
insects," J. Exp. Biol., vol. 28, pp. 221-245, 1951.
[7] C. J. Pennycuick, "A wind-tunnel study of gliding flight in the pigeon
Columba livia," J. Exp. Biol., vol. 49, pp. 509-526, 1968.
[8] C. J. Pennycuick, Mechanics of flight In Avian Biology. Vol. 5 (ed. D.
S. Farner and J. R. King), pp. 1-75. New York: Academic Press, 1975.
[9] T. Weis-Fogh, "Energetics of hovering flight in hummingbirds and in
Drosophila," J. Exp. Biol., vol. 56, pp. 79-104, 1972.
[10] T. Weis-Fogh, "Quick estimates of flight fitness in hovering animals,
including novel mechanisms for lift production," J. Exp. Biol., vol. 59,
pp. 169-230, 1973.
[11] C. D. Cone, "The aerodynamics of flapping bird flight," Spec. Sci. Rep.
Va Inst. Mar. Sci., vol. 52, 1968.
[12] J. M. V. Rayner, "Vortex theory of animal flight I. vortex wake of a
hovering animal," J. Fluid Mech., vol. 91, pp. 697-730, 1979.
[13] C. P. Ellington, "The aerodynamics of hovering insect flight," Philos.
Trans. R. Soc. London B, vol. 305, pp. 1-181, 1984.
[14] S. P. Sane, "Induced airflow in flying insects. I. A theoretical model of
the induced flow," J. Exp. Biol., vol. 209, pp. 32-42, 2006.
[15] L. M. Milne-Thompson, Theoretical Aerodynamics. Dover, New York,
1958.
[16] C. P. Ellington, "The aerodynamics of normal hovering flight," In
Comparative Physiology -Water, Ions and Fluid Mechanics (ed. K.
Schmidt-Nielsen, L. Bolis and S. H. P. Maddrell), Cambridge
University Press, pp. 327-345, 1978.
[17] M. J. Lighthill, "On the Weis-Fogh mechanism of lift generation," J.
Fluid Mech, vol. 60, pp. 1-17, 1973.
[18] T. Weis-Fogh and R. McN. Alexander, "The sustained power output
from striated muscle," In Scale Effects in Animal Locomotion (ed. T. J.
Pedley), London: Academic Press, pp. 511-525, 1977.
[19] C. J. Pennycuick and M. A. Rezende, "The specific power output of
aerobic muscle, related to the power density of mitochondria," J. Exp.
Biol., vol. 108, pp. 377-392, 1984.
[20] A. Betz and L. Prandtl, Schraubenpropeller mit geringstem
Energieverlust. Nachr. Ges. Wiss. Göttingen, pp. 193-213, 1919.
[21] I. S. Gradshteyn and I. M. Rhyzhik, Tables of Integrals, Series and
Products. Academic Press, New York, section 2.58, 1965.
[22] O. Sotavalta, "The essential factor regulating the wing stroke
frequency of insects in wing mutilation and loading experiments at
subatmospheric," Ann. Zool. Soc., vol. 15 (2), pp. 1-67, 1952.
[1] C. Van Den Berg, and C. P. Ellington, "The vortex wake of a
hovering model hawkmoth," Philos. Trans. R. Soc. London B, vol.
352, pp. 317-328, 1997.
[2] M. H Dickinson, F. O. Lehmann, and S. P. SANE, "Wing rotation and
the aerodynamic basis of insect flight, " Science, vol. 284, pp. 1954-
1960, 1999.
[3] S. P. Sane and M. H. Dickinson, "The control of flight force by a
flapping wing: lift and drag production," J. Exp.Biol., vol. 204, pp.
2607-2626, 2001.
[4] S. P. Sane and M. H. Dickinson, "The aerodynamic effects of wing
rotation and a revised quasi-steady model of flapping flight," J.
Exp.Biol., vol. 205, pp. 1087-1096, 2002.
[5] G. R. Spedding, M. Rosén, and A. Hedenström, "A family of vortex
wakes generated by a thrush nightingale in free flight in a wind
tunnel over its entire natural range of flight speeds," J. Exp. Biol.,
vol. 206, pp. 2313-2344, 2003.
[6] M. F. M. Osborne, "Aerodynamics of flapping flight with application to
insects," J. Exp. Biol., vol. 28, pp. 221-245, 1951.
[7] C. J. Pennycuick, "A wind-tunnel study of gliding flight in the pigeon
Columba livia," J. Exp. Biol., vol. 49, pp. 509-526, 1968.
[8] C. J. Pennycuick, Mechanics of flight In Avian Biology. Vol. 5 (ed. D.
S. Farner and J. R. King), pp. 1-75. New York: Academic Press, 1975.
[9] T. Weis-Fogh, "Energetics of hovering flight in hummingbirds and in
Drosophila," J. Exp. Biol., vol. 56, pp. 79-104, 1972.
[10] T. Weis-Fogh, "Quick estimates of flight fitness in hovering animals,
including novel mechanisms for lift production," J. Exp. Biol., vol. 59,
pp. 169-230, 1973.
[11] C. D. Cone, "The aerodynamics of flapping bird flight," Spec. Sci. Rep.
Va Inst. Mar. Sci., vol. 52, 1968.
[12] J. M. V. Rayner, "Vortex theory of animal flight I. vortex wake of a
hovering animal," J. Fluid Mech., vol. 91, pp. 697-730, 1979.
[13] C. P. Ellington, "The aerodynamics of hovering insect flight," Philos.
Trans. R. Soc. London B, vol. 305, pp. 1-181, 1984.
[14] S. P. Sane, "Induced airflow in flying insects. I. A theoretical model of
the induced flow," J. Exp. Biol., vol. 209, pp. 32-42, 2006.
[15] L. M. Milne-Thompson, Theoretical Aerodynamics. Dover, New York,
1958.
[16] C. P. Ellington, "The aerodynamics of normal hovering flight," In
Comparative Physiology -Water, Ions and Fluid Mechanics (ed. K.
Schmidt-Nielsen, L. Bolis and S. H. P. Maddrell), Cambridge
University Press, pp. 327-345, 1978.
[17] M. J. Lighthill, "On the Weis-Fogh mechanism of lift generation," J.
Fluid Mech, vol. 60, pp. 1-17, 1973.
[18] T. Weis-Fogh and R. McN. Alexander, "The sustained power output
from striated muscle," In Scale Effects in Animal Locomotion (ed. T. J.
Pedley), London: Academic Press, pp. 511-525, 1977.
[19] C. J. Pennycuick and M. A. Rezende, "The specific power output of
aerobic muscle, related to the power density of mitochondria," J. Exp.
Biol., vol. 108, pp. 377-392, 1984.
[20] A. Betz and L. Prandtl, Schraubenpropeller mit geringstem
Energieverlust. Nachr. Ges. Wiss. Göttingen, pp. 193-213, 1919.
[21] I. S. Gradshteyn and I. M. Rhyzhik, Tables of Integrals, Series and
Products. Academic Press, New York, section 2.58, 1965.
[22] O. Sotavalta, "The essential factor regulating the wing stroke
frequency of insects in wing mutilation and loading experiments at
subatmospheric," Ann. Zool. Soc., vol. 15 (2), pp. 1-67, 1952.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49799", author = "Khaled. M. Faqih", title = "A Vortex Plate Theory of Hovering Animal Flight", abstract = "A model of vortex wake is suggested to determine the
induced power during animal hovering flight. The wake is modeled
by a series of equi-spaced rigid rectangular vortex plates, positioned
horizontally and moving vertically downwards with identical speeds;
each plate is generated during powering of the functionally wing
stroke. The vortex representation of the wake considered in the
current theory allows a considerable loss of momentum to occur. The
current approach accords well with the nature of the wingbeat since it
considers the unsteadiness in the wake as an important fluid
dynamical characteristic. Induced power in hovering is calculated as
the aerodynamic power required to generate the vortex wake system.
Specific mean induced power to mean wing tip velocity ratio is
determined by solely the normal spacing parameter (f) for a given
wing stroke amplitude. The current theory gives much higher specific
induced power estimate than anticipated by classical methods.", keywords = "vortex theory, hovering flight, induced power,Prandlt's tip theory.", volume = "4", number = "9", pages = "784-12", }