A Formula to Help Marathoners Avoid Hitting the Wall

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When the weather turns crisp and farmer’s markets are lousy with pumpkins and apples, there’s a bounty of another sort: marathon runners. Everywhere. Right now, weekends in New York City’s Central Park mean droves of marathoners diligently completing their 10- or 12-mile training runs in advance of the big event (on Nov. 7). But for all their training, perhaps 40% of runners will “hit the wall,” the dreaded moment, usually around mile 21, when the body depletes its available carbohydrate stores and starts burning fat instead — which causes pain, dizziness and extreme fatigue. (More on Time.com: Video: Understanding the Heart Hazards of Marathon Running)

New Scientist explains:

Carbohydrates release energy faster than does fat, but we can carry only limited supplies, stored in the liver and muscles. Once they reach critical levels our bodies switch to fat reserves, which are more energy-dense but a less efficient power source. When this happens, by-products from the fat metabolism build up in the body, often causing the excruciating pain of hitting the wall.

Endurance runners try to avoid this transition by loading up on carbs before a race, but until now individual athletes have relied on intuition to gauge how much they need to complete a marathon.

Some never make it: the wall keeps maybe 1% to 2% of marathoners from crossing the finish line. For the rest, it can shave valuable seconds or minutes off their time. But Benjamin Rapoport, a graduate student in the Harvard-MIT Health Sciences and Technology department, says he’s figured out a formula that can tell runners how much energy they need and at what pace they can run without hitting the wall — a phenomenon with which he is well acquainted. (More on Time.com: Wii = Ouch. Video Games Can Be Hazardous to Your Health).

An experienced marathoner, Rapoport hit the wall during the 2005 New York City Marathon, he says because he pushed himself a little too hard at the beginning of the race. Since too much energy expended during the first few miles can have such a dramatic effect near the finish line, Rapoport realized he would need to be more precise (and less enthusiastic).

He set out to calculate the maximum pace he could achieve with enough power left to finish strong. Since the body has a maximum amount of carbs it can store at a given time, the trick is to maintain enough energy to last the 26.2 miles of a marathon by calibrating running pace and intake of mid-race snacks or drinks. (More on Time.com: Fitness Tech: 10 Cool Ways to Get in Shape)

The result of Rapoport’s efforts is a study in PLoS Computational Biology and this online calculator, which offers a rough estimate of the carb intake necessary to achieve a certain finish time, based on an athlete’s age, weight, goal time and something called the VO2max — a measure of aerobic capacity. The last metric, which is a bit tricky to calculate, is the most useful: it is a measure of the rate at which oxygen is delivered to the muscles, and it helps determine your best possible running time.

The White Coat Notes blog on the Boston Globe‘s website has a nice explanation:

Don’t know what your VO2max is? You can find out by running a constant pace on a treadmill with a heart rate monitor. A man not training for a marathon might have a VO2max of 45, but an elite male marathoner might have a VO2max of 75 or above. For women, the VO2max range runs from 28 to 52. It measures how much oxygen your body can bring to your muscles.

Leg muscle mass also matters, because that’s where carbs are stored. For men, levels typically range from 14 to 27.5 percent of body mass, and for women, they range from 18 to 22.5 percent.

A man in his 30s trying to hit the Boston Marathon qualifying time of 3:10 who has a VO2max of 50 should consume 10 calories of carbohydrate per kilogram of body weight (about 700 calories for a runner who weighs about 155 pounds), assuming that his legs make up at least 15 percent of his body mass, Rapoport said.

Rapoport’s next project is to create an online VO 2max calculator. He told Wired: “My primary goal is to give any marathon runner a qualitative plan for their training.”

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