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Many swimming and flying animals are observed to cruise in a narrow range ofStrouhal numbers, where the Strouhal number ${St = 2fA/U}$ is a dimensionlessparameter that relates stroke frequency $f$, amplitude $A$, and forward speed$U$. Dolphins, sharks, bony fish, birds, bats, and insects typically cruise inthe range $0.2 < St < 0.4$, which coincides with the Strouhal number range formaximum efficiency as found by experiments on heaving and pitching airfoils. Ithas therefore been postulated that natural selection has tuned animals to usethis range of Strouhal numbers because it confers high efficiency, but thereason why this is so is still unclear. Here, by using simple scalingarguments, we argue that the Strouhal number for peak efficiency is largelydetermined by fluid drag on the fins and wings.

Efficient cruising for swimming and flying animals is dictated by fluid drag