## Today’s Fact: Foot On Water

Andi came up with an insane question: How wide does a human foot have to be for a human to stand on water? Of course, he came up with something insane, reproduced here.

## Foot On Water, Andi Gu

### Relevant Parameters

Let $m$ be the mass of some person, let $R$ be the radius of his foot (which we model as a circle), and let $\gamma$ be the surface energy of water (i.e. surface tension).

We make a simplistic model in which the water deforms in a circularly symmetric pattern around the foot, that when viewed at a cross-section appears as follows:

### Derivation of Foot Size

The increase in the water surface area is

Since $\Delta E=\gamma \Delta A$, we have:

with the last step following since it is reasonable to assume $R \gg h$

The only remaining variable is $\theta$ – it is reasonable to assume a small angle $\theta$ (i.e. $\theta \approx \frac{\pi}{10}$, so that this adds a factor of approximately 0.1). With $\gamma=72.8$ dynes per centimeter and $m=80$ kilograms, $R \approx 13 \text{km}$.