# The Physics of Footwear

Erica P. JohnsonTo 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, "

By | April 26, 2004

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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 cost and fashion, not to mention how much one drinks. A sober Carrie can wear a 12.54-cm heel. Jane Andersen, of the American Podiatry Medical Association, says that higher heels exact more pressure on the ball of the foot than do flat shoes. This increased pressure, plus the unsteadiness these shoes cause, can lead to problems such as shortening of the Achilles tendon, ankle strains, and fractures.

But Stevenson expects women to continue shopping sans calculator: "Most women are much better able to just look at a pair of shoes and tell if they could walk in them without falling over." As to why these shoes appeal to women, George Malkemus, a Manolo Blahnik spokesman, says simply, "It's all about fashion."

- Caryn Evilia

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