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Denny's paradox

In the study of animal locomotion, Denny's paradox refers to the apparent impossibility of surface-dwelling animals such as the water strider generating enough propulsive force to move. It is named for Mark Denny.

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If capillary waves are assumed to generate the momentum transfer to the water, the animal's legs must move faster than the phase speed $c m$ of the waves, given by

$c_m=\left(4g\sigma/\rho\right)^{1/4}$

where $g$ is the acceleration due to gravity, $σ$ is the strength of surface tension, and $ρ$ the density of water. For standard conditions, this works out to be about 0.23 m/s.

Infant water striders' legs move at speeds much less than this and, according to this physical picture, cannot move. For a resolution of Denny's paradox, see water strider.

Category: Locomotion