Rio 2016: The maths behind the fastest person on Earth

Who is the fastest man on Earth? Usain Bolt, right? Wrong. The unpopular answer is, in fact, Justin Gatlin. In 2011, he ran the 100 metres in 9.45 seconds, the fastest time a human has ever run that distance, smashing Usain Bolt’s best time by a massive 0.13 seconds.

At the time, the controversial US athlete – twice banned from competing for drug-related offences – was being pushed along the track by a huge 20 metre-per-second tail wind (the limit for a time to be ratified as a record is +2m/s). The wind was generated by a number of giant fans as part of a Japanese game show, so the “record” didn’t count. Nevertheless, no-one has ever been recorded to run faster from a stationary start on the flat – although some sub-world record times have also been clocked for people running down hill.

Wind assistance improves athletes' performances only in these short sprinting events and some of the field events, such as long jump, triple jump, which require sprints in a single direction. For most other track athletes, wind is anathema.

When Roger Banister looked out of the window on the morning of May 6 1954, for example, he almost decided to postpone his attempt to break the four-minute mile record because it was too windy. Just before the event, however, the winds dropped enough for him to want to take part and the rest is history. He knew what mathematics can prove: that if you have to do at least one lap of the track, then wind, no matter how light, will always slow you down.

Consider a wind blowing up the home straight of a standard 400 metre athletics track. When Mo Farah runs with the wind, his speed is increased by a set amount, but when he runs against it on the back straight the wind decreases his speed by the same amount. It seems reasonable that these two effects might balance each other out giving Farah the same lap time as if there were no wind at all. Strangely, however, it doesn’t work out that way.

The reason, in essence, is that because you run faster down the home straight, you derive the benefit of being pushed by the wind for only a short time. When you run down the back straight, however, you spend longer going slower, fighting against the wind. The difference in the time you spend being assisted by the wind versus the time you spend battling it ensures your lap time always slows. Imagine the extreme example of a wind so strong that it doubles your speed down the home straight. On the back straight, however, it would reduce your speed to zero meaning that you’d never finish the race.

So wind and other adverse weather conditions can act as a leveller, adding to the uncertainty about the results of individual races. Surely, though, whatever the weather, one thing we can be confident about is that the world’s fastest sprinter will always be a man? Well, perhaps not. Researchers from the University of Oxford found that, although 100 metres' times for both men and women have been decreasing linearly over the years, the women’s time was decreasing at a much faster rate than than the men’s. The team concluded that, if trends continue as they have over the last 90 years, women could be dominating the 100 metres by 2156.

However, sports scientists have been critical of the findings and have suggested that increased participation and training opportunities for women over the same time period have led to the artificially rapid reduction in their 100 metre times in comparison to the men’s. They argue that now men and women are on a roughly level playing field the decrease in women’s 100 metre times will begin to slow to a rate comparable with that of the men. Critics also cite fundamental difference in men’s and women’s physiology, including oxygen carrying capacity and body fat levels, which suggest that the “fastest person on earth” will never be a woman.

In fact, although billed as the race for the fastest person on Earth, it’s questionable whether the 100 metres always produces the fastest performance. When Bolt set two new world records for the 100 metres and 200 metres at the 2008 Bejing Olympics in the bird’s nest stadium, his 200 metres took him 19.30 seconds, less than twice the time of his 9.69 second 100 metres. This means that on average, he was running faster in the longer event.

Part of this increase, however, is due to not having to react and accelerate up to speed in the second 100 metres of the 200 metre race. Based on average speed over the whole race, the title of “fastest person on earth” has switched back and forth between 100 and 200 metre runners since the records began.

This effect is even more exaggerated in the 4x100 metre relay in which all but one of the runners begins their 100-metre stretch from a running start. In the last leg, the “anchor” doesn’t even have to worry about passing on the baton at the other end so can achieve some incredibly quick times. Several sub-nine second times have been recorded in this leg of the race including Bolt’s electronically-timed 8.65 seconds in 2014.

Despite this, the fastest human footspeed was recorded between 60 and 80 metres in Bolt’s world record 9.58-second 100 metres in Berlin. He was clocked at 44.64kph or 27.8mph.

So despite Gatlin’s “record”, the official “fastest man on Earth” title still rests with Bolt – at least for now.

Christian Yates, Lecturer in Mathematical Biology, University of Bath

This article was originally published on The Conversation. Read the original article.