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How Do Track Runners Use Math?

By Ian Linton

Track runners use math in their racing and training programs. Track running is a competitive sport. The emphasis for the track runner is on performance, and math plays an important part in determining performance levels. For elite athletes, where fractions of a second matter, the math in sports science can be vital to success.

  1. Get the pace right or finish with a poor result. In track races from 400 meters/440 yards or more, pace judgment is vital. Runners who run very fast in the early stages tend to slow badly as they near the finish. In longer races, fatigue makes it difficult to match a competitor's finishing sprint. As an example, runners with a best 5,000 meter/3-mile time of 15 minutes would have problems if they completed the first two laps in less than two minutes.

  2. Use pace judgment to determine race tactics. In longer track races, competitors use a variety of tactics from steady pace on each lap, mid-race surges or slow start and fast finish. Understanding competitors' likely tactics can help a runner plan a race strategy. An article in the Math Forum, Go for Gold, illustrates how coaches can analyze racing statistics for a range of competitors to prepare tactics for their own runners (reference 1).

  3. Make allowance for conditions on the track. "Peak Performance" magazine reported the findings of Dr L.G.C.E. Pugh on wind resistance when running. Pugh calculated that the energy cost of overcoming air resistance at a pace of 67 seconds per 400 meters was about eight percent of the total energy cost (reference 2). A school math website, Motivate, described a range of conditions affecting track and field athletes where students could use math to calculate changes in performance. Among the issues were the impact of altitude on performance and the use of streamlined hoods to overcome air resistance (reference 3).

  4. Train for your target performance using math to calculate session speeds. Interval training is a popular way to increase speed endurance for events from 1,500 meters/1 mile to 10,000 meters/6 miles. Athletes work out their average pace for a target finishing time and run a series of intervals at race pace. For a 1,500 meter event where the runner is aiming at a time under four minutes, the session might be six times 400 meters at 60 seconds for each training lap.

  5. Use sports science to optimize training programs. Runners can use heart rate monitors to achieve different training effects. Running in a certain heart rate zone for a specified period of time can help runners improve lactate tolerance -- an important factor in distance racing. The Polar website describes training zones (reference 4). Elite endurance athletes use sports science to calculate and improve competitive factors such as the proportion of maximum oxygen uptake, as Dean Hebert explains in "The Running World According to Dean" (reference 5).

  6. Calculate age-related performance. Older runners whose performances decline naturally with age can compare their times with younger runners using a system developed for World Masters Athletics (reference 6). Enter the best times and age, and the system uses math to calculate age-related times. A 65-year-old male running 5 minutes for the 1,500 meters is running the equivalent of 3 minutes 46 seconds, an elite time that represents 91 percent of his age group performance.

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