Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 111, Issue 21, Pages 7517-7521Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1310544111
Keywords
cost of transport; Froude efficiency
Categories
Funding
- National Science Foundation (NSF) [CBET-0828749, CMMI-0941674, CBET-1066575]
- NSF's TeraGrid Project [CTS-070056T, CTS-090006]
- Div Of Chem, Bioeng, Env, & Transp Sys
- Directorate For Engineering [1066575] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0941674] Funding Source: National Science Foundation
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Which animals use their energy better during movement? One metric to answer this question is the energy cost per unit distance per unit weight. Prior data show that this metric decreases with mass, which is considered to imply that massive animals are more efficient. Although useful, this metric also implies that two dynamically equivalent animals of different sizes will not be considered equally efficient. We resolve this longstanding issue by first determining the scaling of energy cost per unit distance traveled. The scale is found to be M-2/3 or M-1/2, where M is the animal mass. Second, we introduce an energy-consumption coefficient (C-E) defined as energy per unit distance traveled divided by this scale. C-E is a measure of efficiency of swimming and flying, analogous to how drag coefficient quantifies aerodynamic drag on vehicles. Derivation of the energy-cost scale reveals that the assumption that undulatory swimmers spend energy to overcome drag in the direction of swimming is inappropriate. We derive allometric scalings that capture trends in data of swimming and flying animals over 10-20 orders of magnitude by mass. The energy-consumption coefficient reveals that swimmers beyond a critical mass, and most fliers are almost equally efficient as if they are dynamically equivalent; increasingly massive animals are not more efficient according to the proposed metric. Distinct allometric scalings are discovered for large and small swimmers. Flying animals are found to require relatively more energy compared with swimmers.
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