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
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, .