The Physics of Footwear

Erica P. Johnson

To bring scientific concepts into the mainstream, sometimes explaining popular culture helps. Inspired by TV's Sex and the City and its heroine, Carrie, who often wobbles around in designer shoes, Paul Stevenson at the UK-based Institute of Physics developed a formula to determine the maximum "safe" height for such footwear. Stevenson, of the University of Surrey, wanted to see just how high Carrie could go. "As you get up in a high heel," Stevenson says, "your base of support is shortened, so you are trying to balance your weight over a shorter distance."

Applying Pythagoras' Theorem, he found that the maximum heel height (h, in cm) is h = Q(12 + 3s/8), where s is the UK shoe size and Q is a sociological factor between 0 and 1. Stevenson says he added Q, at his wife's urging, because shoe selection reflects more than physics, such as...