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Significance Is a whale or a tuna more efficient? The answer depends on the definition of efficiency. If one uses cost of transport, defined as the energy required to move unit distance, then the tuna wins. If energy of transporting unit mass over unit distance is used then the whale wins. We address this ambiguity by rationally deriving a new efficiency measure called the energy-consumption coefficient (C E ), which is a nondimensional measure of fuel consumption.C E is a fundamental metric to quantify efficiency of self-propelled bodies analogous to the drag coefficient (C d ) to quantify aerodynamic shapes of vehicles. The analysis also leads to allometric scalings of frequency and velocity of swimming and flying organisms over more than 20 orders of magnitude of mass.

Energy efficiency and allometry of movement of swimming and flying animals