title: Gray's paradox: a fluid mechanical perspective.
abstract: Nearly eighty years ago, Gray reported that the drag power experienced by a dolphin was larger than the estimated muscle power - this is termed as Gray's paradox. We provide a fluid mechanical perspective of this paradox. The viewpoint that swimmers necessarily spend muscle energy to overcome drag in the direction of swimming needs revision. For example, in undulatory swimming most of the muscle energy is directly expended to generate lateral undulations of the body, and the drag power is balanced not by the muscle power but by the thrust power. Depending on drag model utilized, the drag power may be greater than muscle power without being paradoxical.
authors.affiliation: Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.
authors.forename: Rahul
authors.initials: R
authors.lastname: Bale
authors.affiliation: Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.
authors.forename: Max
authors.initials: M
authors.lastname: Hao
authors.affiliation: Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.
authors.forename: Amneet Pal Singh
authors.initials: AP
authors.lastname: Bhalla
authors.affiliation: Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.
authors.forename: Namrata
authors.initials: N
authors.lastname: Patel
authors.affiliation: Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA.
authors.forename: Neelesh A
authors.initials: NA
authors.lastname: Patankar
mesh_terms: D000818:Animals; D004734:Energy Metabolism; D006801:Humans; D057446:Hydrodynamics; D008962:Models, Theoretical; D053580:Muscle Strength; D018482:Muscle, Skeletal / Q000502:physiology; D013550:Swimming
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