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Gray's paradox: a fluid mechanical perspective.

Rahul Bale1, Max Hao1, Amneet Pal Singh Bhalla1

  • 1Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.

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Gray's paradox, concerning dolphin drag exceeding muscle power, is re-examined. Fluid mechanics reveals that muscle energy primarily generates body undulations, with thrust power balancing drag, not muscle power, resolving the paradox.

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Area of Science:

  • Fluid mechanics
  • Biomechanics
  • Animal locomotion

Background:

  • Gray's paradox (1936) highlights the discrepancy between estimated dolphin muscle power and observed drag.
  • Previous explanations often focused on direct muscle power overcoming drag, which seemed insufficient.

Purpose of the Study:

  • To provide a fluid mechanical perspective on Gray's paradox.
  • To revise the understanding of energy expenditure in undulatory swimming.

Main Methods:

  • Analysis of fluid dynamics principles applied to aquatic locomotion.
  • Examination of energy transfer during self-propelled undulatory swimming.

Main Results:

  • Muscle energy is primarily used for generating lateral body undulations, not directly for overcoming drag.
  • Drag power is balanced by thrust power, which is a consequence of body undulations.
  • The paradox is resolved by recognizing that drag power does not need to be balanced solely by muscle power.

Conclusions:

  • The traditional view of swimmers expending muscle energy solely to overcome drag requires revision.
  • Fluid mechanics offers a resolution to Gray's paradox by differentiating energy roles in undulatory swimming.
  • Drag power can exceed muscle power without presenting a paradox when thrust power is considered.