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Marine Biology

, Volume 86, Issue 3, pp 283–295 | Cite as

Propulsion efficiency and cost of transport for copepods: a hydromechanical model of crustacean swimming

  • M. J. Morris
  • G. Gust
  • J. J. Torres
Article

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.

Keywords

Swimming Speed Hydrodynamic Force Metabolic Cost Parasitic Resistance Simultaneous Solution 
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.

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Literature cited

  1. 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)Google Scholar
  2. 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 1978Google Scholar
  3. 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)Google Scholar
  4. 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)Google Scholar
  5. 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)Google Scholar
  6. 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)Google Scholar
  7. 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)Google Scholar
  8. Fish, F. E.: Aerobic energetics of surface swimming in the muskrat Ondatra zibethicus. Physiol. Zoöl. 55, 180–189 (1982)Google Scholar
  9. 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 1971Google Scholar
  10. Gordon, M. S.: Animal physiology: principles and adaptations, 592 pp. New York: Macmillan 1977Google Scholar
  11. 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)Google Scholar
  12. 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)Google Scholar
  13. Hill, A. V.: The dimensions of animals and their muscular dynamics. Sci. Prog., Lond. 38, 209–230 (1950)Google Scholar
  14. Hoerner, S. F.: Fluid-dynamic drag, S. F. Hoerner, 2 King Lane, Greenbriar, Bricktown, N. J. 08723, USA (1965)Google Scholar
  15. Hopkins, T. L.: The vertical distribution of zooplankton in the Eastern Gulf of Mexico. Deep-Sea Res. 29, 1069–1083 (1982)Google Scholar
  16. Ivlev, V. S.: Energy consumption during the motion of shrimps. Zool. Zh. 42, 1465–1471 (1963)Google Scholar
  17. Kils, U.: The swimming behavior, swimming performance and energy balance of antarctic krill, Euphausia superba. BIOMASS scient. Ser. 3, 1–121 (1981)Google Scholar
  18. Klyashtorin, L. B. and A. A. Yarzhombek: Energy consumption in movement of planktonic organisms. Oceanology 13, 575–580 (1973)Google Scholar
  19. Kutty, M. N.: Oxygen consumption in the mullet Liza macrolepis with special reference to swimming velocity. Mar Biol. 4, 239–242 (1969)Google Scholar
  20. Lehman, J. T.: On calculating drag characteristics for decelerating zooplankton. Limnol. Oceanogr. 22, 170–172 (1977)Google Scholar
  21. Lighthill, M. J.: Aquatic animal propulsion of high hydrodynamic efficiency. J. Fluid Mech. 44, 265–301 (1970)Google Scholar
  22. Lighthill, M. J.: Aquatic animal propulsion. Int. Congr. appl. Mech. (Moscow) 13, 29–46 (1972)Google Scholar
  23. Minkina, N. I. and E. V. Pavlova: Hydrodynamic drag and power at variable swimming in Calanus helgolandicus (Claus). Ekol. Morila 7, 63–75 (1981)Google Scholar
  24. 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)Google Scholar
  25. 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 1974Google Scholar
  26. 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 1977Google Scholar
  27. O'Dor, R. K.: Respiratory metabolism and swimming performance of the squid, Loligo opalescens. Can. J. Fish. aquat. Sciences 39, 580–587 (1982)Google Scholar
  28. Petipa, T. S.: Trophic dynamics of copepods in marine planktonic systems, 245 pp. [In Russ.] Kiev: Naukowa Dumka 1981Google Scholar
  29. Prange, H. D. Energetics of swimming of a sea turtle. J. exp. Biol. 64, 1–12 (1976)Google Scholar
  30. 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)Google Scholar
  31. Schmidt-Nielsen, K.: Locomotion: energy cost of swimming, flying, and running. Science, N.Y. 177, 222–228 (1972)Google Scholar
  32. 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)Google Scholar
  33. 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 1975Google Scholar
  34. 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)Google Scholar
  35. 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)Google Scholar
  36. Thom, A. and P. Swart: The forces on an aerofoil at very low speeds. Jl.R. aeronaut. Soc. 44, 761–770 (1940)Google Scholar
  37. 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)Google Scholar
  38. 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)Google Scholar
  39. 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)Google Scholar
  40. Tucker, V. A.: Energetic cost of locomotion in animals. Comp. Biochem. Physiol. 34, 841–846 (1970)Google Scholar
  41. Vlymen, W. J.: Energy expenditure of swimming copepods. Limnol. Oceanogr. 15, 348–356 (1970)Google Scholar
  42. Webb, P. W.: The swimming energetics of trout. (1) Oxygen consumption and swimming efficiency. J. exp. Biol. 55, 521–540 (1971)Google Scholar
  43. 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 1975Google Scholar
  44. White, F. M.: Viscous fluid flow, 640 pp. New York: McGraw-Hill 1974Google Scholar
  45. 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)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • M. J. Morris
    • 1
  • G. Gust
    • 1
  • J. J. Torres
    • 1
  1. 1.Department of Marine ScienceUniversity of South FloridaSt. PetersburgUSA

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