Denny's paradox

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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.

If capillary waves are assumed to generate the momentum transfer to the water, the animal's legs must move faster than the phase speed cm 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.

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