# Random Fact #4

## 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 be the mass of some person, let be the radius of his foot (which we model as a circle), and let 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 , we have:

with the last step following since it is reasonable to assume

The only remaining variable is – it is reasonable to assume a small angle (i.e. , so that this adds a factor of approximately 0.1). With dynes per centimeter and kilograms, .