Watching the Olympics over the weekend gave me the wonderful opportunity of not only being a spectator, but, as an engineer, thinking about how to improve the races for the athletes.

I watched parts of the 10,000 meter race for both the women and the men. That distance equates to 6.2 miles, so this is no sprint. The athletes run around the 400-meter track 25 times. That’s a lot of running, and almost made me want to exercise.

So, I am watching these races and the lead runner often has a shadow, the runner in second place, running right off his or her shoulder, for many of the laps. It made me think, which is a good thing for an engineer to do. I wondered how much longer that second-place runner had to run every time around the track. The lead runner is running about a half meter off the inside line of the track and the second-place runner about a half meter outside of that. This means that the second place runner must be running further as he or she runs half the circumference of the curve of the track.

I looked it up. The track dimensions are laid out with a curve of radius 36.500 meters. Therefore, the distance around the curved end of the track is explained by the equation:

d = (1/2) * 2πr

where,

d = the distance along the curve

r = the radius of the circle

It is 1/2 of the full circumference of 2πr because the curve is 1/2 of a circle. Simple enough.

Considering we know the radius, and note that the first runner is 0.5 meters outside of the inside track line, and second runner, in same lane (the lanes being 1.17 meters wide), right off the first runner’s shoulder, is 0.5 meters outside of the first runner, we end up with a table like this:

Line Radius (m) Distance around curve (m)

inside lane line 36.500 114.668

first runner 37.000 116.239

second runner 37.500 117.810

We have found out that the second runner runs 117.810-116.239 = 1.571 meters further as he or she runs just off the first runner’s shoulder, and this happens every time around one curve of the track. For a full lap, this is doubled to 3.142 meters. When I was watching, a second place runner would easily hang out there for up to 10 laps, meaning that runner would run 31.42 meters longer! 10,000 meters is a long race, but the difference between first and second is often under 30 meters. I don’t know if it was over the weekend. I was busy doing calculations. But I was able to run the numbers and, if I had their cell numbers, would have texted the coaches of the second runners and tell them to back off and run right behind or go ahead and run in front of the other runner. Save the distance. It could mean the distance between silver and gold.

The engineer helps improve the Olympics once again.

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