Abstract
In the absence of direct measurement, costs of locomotion to small swimming Crustacea (<10 mm) have been derived exclusively through application of the fluid dynamic theory. Results indicate very low swimming costs, and contradict experimental data on larger Crustacea (15 to 100 mm) that suggest a three-fold increase in metabolic rate with increasing swimming speed. This paper introduces a swimming model that analyzes the hydrodynamic forces acting on a crustacean swimming at non-steady velocity. The model treats separately the hydrodynamic forces acting on the body and the swimming appendages, approximating the simultaneous solution of equations quantifying the drag and added-mass forces on each by stepwise integration. Input to the model is a time-series of instantaneous swimming-appendage velocities. The model output predicts a corresponding time-series of body velocities as well as the mechanical energy required to move the swimming appendages, dissipated kinetic energy, and metabolic cost of swimming. Swimming of the calanoid copepod Pleuromamma xiphias (Calanoida) was analyzed by extrapolating model parameters from data available in the literature. The model predictions agree well with empirical observations reported for larger crustaceans, in that swimming for copepods is relatively costly. The ratio of active to standard metabolism for P. xiphias was >3. Net cost of transport was intermediate to the values found experimentally for fish and larger crustaceans. This was a consequence of the predicted mechanical efficiency (34%) of the copepod's paddle propulsion, and of increased parasitic resistance resulting from non-steady velocity swimming.
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Literature cited
Beamish, F. W. H.: Oxygen consumption of largemouth bass Micropterus salmoides, in relation to swimming speed and temperature. Can. J. Zool. 48, 1221–1228 (1970)
Beamish, F. W. H.: Swimming capacity. In: Fish physiology, Vol. 7. pp 101–187. Ed. by W. S. Hoar and D. J. Randall. London and New York: Academic Press 1978
Blake, R. W.: The mechanics of labriform locomotion. I. Labriform locomotion in the angelfish (Pterophyllum cimekei): an analysis of the power stroke. J. exp. Biol. 82, 255–271 (1979)
Blake, R. W.: The mechanics of labriform locomotion. II. An analysis of the recovery stroke and the overall fin beat cycle propulsive efficiency in the angelfish. J. exp. Biol. 85, 337–342 (1980)
Brett, J. R. and N. R. Glass: Metabolic rates and critical swimming speeds of sockeye salmon (Oncorhynchus nerka) in relation to size and temperature. J. Fish. Res. Bd Can. 30, 379–387 (1973)
Brett, J. R. and D. B., Sutherland: Respiratory metabolism of pumpkinseed (Lepomis gibbosus) in relation to swimming speed. J. Fish. Res. Bd Can. 22, 405–409 (1965)
Farmer, G. J. and F. W. H. Beamish: Oxygen consumption of Tilapia nilotica in relation to swimming speed and salinity. J. Fish. Res. Bd Can. 26, 2807–2821 (1969)
Fish, F. E.: Aerobic energetics of surface swimming in the muskrat Ondatra zibethicus. Physiol. Zoöl. 55, 180–189 (1982)
Fry, F. E. J.: The effect of environmental factors on the physiology of fish. In: Fish physiology, Vol. 6. pp 1–98. Ed. by W. S. Hoar and D. J. Randall, London and New York: Academic Press 1971
Gordon, M. S.: Animal physiology: principles and adaptations, 592 pp. New York: Macmillan 1977
Goring, D. G. and F. Raichlen: Forces on block bodies accelerating in still fluid. J. Am. Soc. civil Engrs (Waterway, Port, cstl Ocean Div.) 105 (WW2), 171–189 (1979)
Halcrow, K. and C. M. Boyd: The oxygen consumption and swimming activity of the amphipod Gammarus oceanicus at different temperatures. Comp. Biochem. Physiol. 23, 233–242 (1967)
Hill, A. V.: The dimensions of animals and their muscular dynamics. Sci. Prog., Lond. 38, 209–230 (1950)
Hoerner, S. F.: Fluid-dynamic drag, S. F. Hoerner, 2 King Lane, Greenbriar, Bricktown, N. J. 08723, USA (1965)
Hopkins, T. L.: The vertical distribution of zooplankton in the Eastern Gulf of Mexico. Deep-Sea Res. 29, 1069–1083 (1982)
Ivlev, V. S.: Energy consumption during the motion of shrimps. Zool. Zh. 42, 1465–1471 (1963)
Kils, U.: The swimming behavior, swimming performance and energy balance of antarctic krill, Euphausia superba. BIOMASS scient. Ser. 3, 1–121 (1981)
Klyashtorin, L. B. and A. A. Yarzhombek: Energy consumption in movement of planktonic organisms. Oceanology 13, 575–580 (1973)
Kutty, M. N.: Oxygen consumption in the mullet Liza macrolepis with special reference to swimming velocity. Mar Biol. 4, 239–242 (1969)
Lehman, J. T.: On calculating drag characteristics for decelerating zooplankton. Limnol. Oceanogr. 22, 170–172 (1977)
Lighthill, M. J.: Aquatic animal propulsion of high hydrodynamic efficiency. J. Fluid Mech. 44, 265–301 (1970)
Lighthill, M. J.: Aquatic animal propulsion. Int. Congr. appl. Mech. (Moscow) 13, 29–46 (1972)
Minkina, N. I. and E. V. Pavlova: Hydrodynamic drag and power at variable swimming in Calanus helgolandicus (Claus). Ekol. Morila 7, 63–75 (1981)
Morrison, J. R., M. P. O'Brien, J. W. Johnson and S. A. Schaat: The forces exerted by surface waves on piles. J. Petrol. Technol. 189 (TP2846), 149–189 (1950)
Nachtigall, W.: Locomotion mechanics and hydrodynamics of swimming in aquatic insects. In: The physiology of insects, Vol. 3. pp 381–432. Ed. by M. Rockstein, New York: Academic Press 1974
Nachtigall, W.: Swimming mechanics and energetics of locomotion of variously sized water beetles — Dytiscidae, body lengths 2 to 35 mm. In: Scale effects in animal locomotion, pp 269–283. Ed. by T. J. Pedley London: Academic Press 1977
O'Dor, R. K.: Respiratory metabolism and swimming performance of the squid, Loligo opalescens. Can. J. Fish. aquat. Sciences 39, 580–587 (1982)
Petipa, T. S.: Trophic dynamics of copepods in marine planktonic systems, 245 pp. [In Russ.] Kiev: Naukowa Dumka 1981
Prange, H. D. Energetics of swimming of a sea turtle. J. exp. Biol. 64, 1–12 (1976)
Quetin, L. B., T. J. Mickel and J. J. Childress: A method for simultaneously measuring the oxygen consumption and activity of pelagic crustaceans. Comp. Biochem. Physiol. 59A, 263–266 (1978)
Schmidt-Nielsen, K.: Locomotion: energy cost of swimming, flying, and running. Science, N.Y. 177, 222–228 (1972)
Smith, H., J. M. Amelink-Koutstall, J. Vijverberg, and J. C. von Vaupel-Klein. Oxygen consumption and efficiency of swimming goldfish. Comp. Biochem. Physiol. 39A, 1–28 (1971)
Strickler, J. R.: Swimming of planktonic Cyclops species (Copepoda, Crustacea): pattern, movements, and their control. In: Swimming and flying in nature, Vol. 2. pp 599–613. Ed. by T. Y. T. Wu, C. J. Brokaw and C. Brennan, New York: Plenum Press 1975
Strickler, J. R. and A. K. Bal: Setae on the first antennae of the copepod Cyclops scutifer (Sars): their structure and importance. Proc. natn. Acad. Sci. U.S.A. 70, 2656–2659 (1973)
Svetlichnyi, L. S., Yu. A. Zagorodnyaya and V. N. Stepanov: Bioenergetics of copepods Pseudocalanus elongatus during migration. Soviet J mar Biol. 3, 430–436 (1977)
Thom, A. and P. Swart: The forces on an aerofoil at very low speeds. Jl.R. aeronaut. Soc. 44, 761–770 (1940)
Torres, J. J.: Relationship of oxygen consumption to swimming speed in Euphausia pacifica. II. Drag, efficiency and a comparison with other swimming organisms. Mar. Biol. 78, 231–237 (1984)
Torres, J. J. and J. J. Childress: Relationship of oxygen consumption to swimming speed in Euphausia pacifica. 1. Effects of temperature and pressure. Mar. Biol. 74, 79–86 (1983)
Torres, J. J., J. J. Childress and L. B. Quetin: A pressure vessel for the simultaneous determination of oxygen consumption and swimming speed in zooplankton. Deep-Sea Res. 29, 631–639 (1982)
Tucker, V. A.: Energetic cost of locomotion in animals. Comp. Biochem. Physiol. 34, 841–846 (1970)
Vlymen, W. J.: Energy expenditure of swimming copepods. Limnol. Oceanogr. 15, 348–356 (1970)
Webb, P. W.: The swimming energetics of trout. (1) Oxygen consumption and swimming efficiency. J. exp. Biol. 55, 521–540 (1971)
Webb, P. W.: Efficiency of pectoral-fin propulsion of Cymatogaster aggregata. In: Swimming and flying in nature, pp 573–584. Ed. by T. Y. T. Wu, C. J. Brokaw and C. Brennen New York: Plenum Press 1975
White, F. M.: Viscous fluid flow, 640 pp. New York: McGraw-Hill 1974
Wohlschlag, E. E., J. N. Cameron and J. J. Cech, Jr.: Seasonal changes in the respiratory metabolism of the pinfish (Lagodon rhomboides). Contr. mar. Sci. Univ. Tex. 13, 89–104 (1968)
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Communicated by J. M. Lawrence, Tampa
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Morris, M.J., Gust, G. & Torres, J.J. Propulsion efficiency and cost of transport for copepods: a hydromechanical model of crustacean swimming. Mar. Biol. 86, 283–295 (1985). https://doi.org/10.1007/BF00397515
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DOI: https://doi.org/10.1007/BF00397515