Rapoport’s mathematical formula, published online Oct. 21 in PLoS Computational Biology, shows the speediest pace any marathoner can sustain for the entire race.

“A 10-second difference in pace per mile could make the difference between success and a dramatic failure,” says Rapoport, of Harvard Medical School and MIT, who experienced his own traumatic wall splat in the 2005 New York City Marathon. He started out pushing too hard, he says, and was out of steam by the last few miles. Rapoport finished, but with a slower time than he wanted.

To avoid this scenario, a runner has to maintain a pace that conserves carbohydrates, the body’s main source of quick-burn energy, all the way to mile 26.2. Rapoport calculates the ideal pace from a measure of aerobic capacity called VO_2max, along with a few other variables. VO_2max indicates how efficiently a body consumes oxygen.

“This is a unique area that hadn’t been addressed in the medical literature in any substantial way,” says Mark Cucuzzella, a physician and running coach based in Harpers Ferry, W.Va. “He’s lending some hard numbers to what experienced runners and coaches have been doing.”

A man with a VO_2max of 60 — which, after training, is attainable by only the top 10 percent of male runners — can achieve a 3:10 marathon finish time, according to the model. This time happens to be the cutoff for 18- to 34-year-old men to qualify for the Boston Marathon.

Elite male marathoners clock in with a VO_2max in the high 70s. The average untrained young man’s number is in the 40s. (Incidentally, Rapoport, who has run 18 marathons, has a VO_2max above 70 and breezes through marathons in less than three hours.)

VO_2max is usually measured with specialized equipment while someone exercises at maximum exertion, but the value can also be estimated by measuring heart rate while running at a constant pace.

Rapoport’s model also shows that a slightly faster pace can be maintained by consuming a midrace snack.

This carb-eating strategy can help, but it can’t win races, since the body can store only so much fuel, says Cucuzzella, chief medical consultant for the Air Force Marathon and a marathoner himself. “It’s not about how much sugar or spaghetti you eat the night before a race,” he says. “There’s a critical pace.”

Rapoport plans to put an easy-to-use version of his formula on the Internet to help runners calculate their ideal pace. “My primary goal is to give any marathon runner a qualitative plan for their training,” he says.

Image: Flickr/Stijn Bokhove

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Authors: Laura Sanders

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