Physicists estimate how fast Usain Bolt could have run

Sep 11, 2008 By Lisa Zyga feature
This photo montage shows Usain Bolt’s position relative to the other runners, both in the real race (left Bolt) and Bolt’s projected position (right Bolt, crossing the finish line). Credit: H. K. Eriksen, et al.

(PhysOrg.com) -- By the record books, Jamaican runner Usain Bolt is the fastest human being on earth, and yet no one knows for sure exactly how fast he really is. At the Beijing 2008 Olympics, on Saturday, August 16th, Bolt broke his own world record (9.72 seconds) with a time of 9.69 seconds in the 100-meter dash. But with 20 meters remaining, the 21-year-old looked around, and, when realizing he had a strong lead, he started celebrating before he crossed the finish line.

After watching this jaw-dropping behavior, many people have wondered what Bolt’s time would have been – i.e., what the fastest time ever run by a human could have been – if he had raced the entire way.

Among the curious fans is a team of physicists from the University of Oslo led by Hans Kristian Eriksen, who has recently predicted Bolt’s hypothetical world record based on factors such as his acceleration and velocity. By extrapolating from Bolt’s speed before celebrating, the physicists estimated that the new world record would have been about 9.55 ± 0.04 seconds.

Their estimate would support the claim of Bolt’s coach, Glen Mills, who suggested at a recent press conference that the time could have been 9.52 seconds or better.

“It all started with an interview with Usain Bolt's coach published in the general media before a Golden League competition in Zurich,” Eriksen told PhysOrg.com, adding that he and his co-authors all share a general interest in sports. “He claimed that Bolt was on track for a 9.52-second record, had he not slowed down. Then it struck us that, given reasonable video footage of the race and some assumptions about his acceleration, it should be possible to ‘calculate’ what that time would have been.”

To arrive at their estimate, the Norwegian scientists analyzed different videos of the race from NBC, the BBC, and the Norwegian Broadcasting Company (NRK). A moving camera positioned on a rail along the race track served as a standard ruler, since the scientists could count the evenly spaced bolts on the rail to track the distance and align these ticks with the runners’ positions.

The scientists made two estimates based on different assumptions. The first and more conservative estimate assumed that Bolt could have maintained runner-up Richard Thompson’s acceleration during the end of the race. The second estimate assumed that Bolt could have maintained an acceleration 0.5 m/s2 faster than Thompson.

Based on their recording of Bolt’s and Thompson’s positions at the times they passed the ticks on the rail, the researchers determined an approximation of the runners’ positions as a function of time, as well as their speeds and accelerations.

By extrapolating these trajectories to 100 meters, the scientists got their results. If Bolt had maintained Thompson’s acceleration, his time would have been 9.61 ± 0.04 seconds. If Bolt had maintained an acceleration 0.5 m/s2 faster than Thompson, his time would have been 9.55 ± 0.04 seconds.

“For fun, we thought we might as well post the study on astro-ph, an archive for astrophysicists, more or less as an internal joke in the community,” Eriksen said. “However, when we started writing, we suddenly realized that this might actually be interesting and useful to more people than the originally intended audience, and we shifted to a semi-serious approach, and wrote up a ‘real’ paper. In particular, we figured this could be an interesting example of simple physics for educational and outreach purposes, and we therefore submitted the paper to the American Journal of Physics.”

As Eriksen emphasized, this study is a piece of “fun physics,” and its conclusions should not be regarded too seriously. The physicists explained that their estimates of Bolt’s potential time have a 95% error (± 0.04 seconds), but the uncertainties due to the assumptions on Bolt’s acceleration are at least as large as the statistical uncertainties. For instance, the physicists had to calibrate measurements regarding missing ticks on the rail, the precision of the screen clock, and the difference between the screen and stadium clocks.

Another potential uncertainty is the possibility that Bolt may have been tired at the end. (However, as the scientists note from an admittedly subjective perspective, “judging from his facial expressions as he crossed the finishing line, this doesn’t immediately strike us as a very plausible hypothesis.”)

Wind speed is another factor, although the measured wind speed on the track during the Beijing race was negligible. But the physicists noted that favorable wind conditions, such as a 2 m/s wind speed, could decrease the time by as much as 0.1 seconds. With these results in mind, they suggest that Bolt is capable of setting a new world record of less than 9.5 seconds in the near future – but they still reserve some scientific caution.

“I should also say that this study is really pretty much useless for actually predicting the new world record,” said Eriksen. “Taking into account both uncertainties due to assumptions and measuring errors, a proper 95% confidence interval is something like 9.51 to 9.65 seconds – and that's something most people could have guessed very easily. However, the main point is that this is a fun example of simple physics that is interesting to many people. So its main purpose is really for popularizing physics – not to define a new world record. That being said, we do believe that the methods we use are appropriate, and with better data we could have done a lot better.”

More information: Eriksen, H. K.; Kristiansen, J. R.; Langangen, O.; and Wehus, I. K. “Velocity dispersions in a cluster of stars: How fast could Usain Bolt have run?” arxiv:0809.0209v2. Submitted for publication in the American Journal of Physics.

Copyright 2008 PhysOrg.com.
All rights reserved. This material may not be published, broadcast, rewritten or redistributed in whole or part without the express written permission of PhysOrg.com

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User comments : 10

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Duude
3.7 / 5 (6) Sep 11, 2008
Additionally, he ran his 200 meter world record which was seen by most as the least likely record to be broken, into a 1.4m headwind.
Noumenon
4.8 / 5 (49) Sep 11, 2008
What are you talking about defunct?

Doesn't seem like he cares as much as you,...

http://www.youtub...pPaCIG0g
DoctorKnowledge
3.4 / 5 (7) Sep 12, 2008
Great article. Grieves me in a new and different way. Had me thinking. Can't beat that.

People aren't machines. If the guy's goal was winning, then he accomplished his goal. His goal wasn't your goal? So what. Did anyone ask him his goal? Maybe he was enjoying the moment of being so far ahead, he could afford a gesture.

Scientists? Or sports announcers? Speculating on what if he'd had more breakfast? Whether he should have stepped slightly to the side at time 4:31?

It would be helpful if the emotional idiots in science would hand in their badges, and take up their true destiny as lead writers for "The National Enquirer".
Mayday
3.2 / 5 (5) Sep 12, 2008
I like that he goes out there and has some fun with it. I personally find his "performance" to be a very good role model. It inspires me. We should all try and enjoy life, especially while doing the very things we are good at. I'm quite tired of the down in the mouth , all serious and poutty mouthed affectations that many modern atheletes bring to the field. They should give me a break.

I laugh out loud almost every morning at the gym to watch my fellow physical aspirants dourly frowning through their workouts. I find it fun. And the endorphins make me smile. If you don't enjoy it, then find a workout or physical activity that you can enjoy.

To the real competetive atheletes: You could all learn something about life from the guy who runs, wins and loves life along the way!

To the scientists who are hoping to turn him into a machine: please strap on those golden shoes yourself and give it a try, smartguy! There are plenty of empty running tracks out their so I'm sure you can find a lane with your name on it.

Good luck with that!
Modernmystic
3.1 / 5 (8) Sep 12, 2008
Actually I think the fastest man on Earth has gone roughly mach 25.

We're creatures of the mind, not muscle. While I'm sure this is somehow interesting to some folks I honestly could care less either way.
nano999
3 / 5 (4) Sep 12, 2008
@Modernmystic - I second that.
Mayday
2 / 5 (6) Sep 12, 2008
Whoa. Pushing our physical prowess, strength and endurance will always be part of human striving. And though we may use "rocket science" to leave the planet, our body's physical abilities and limitations will not be left behind.

You might want to speak to an astronaut about it a little.
zevkirsh
2 / 5 (2) Sep 13, 2008
THEY HAVE IT ALL WRONG...he would have been at least 6 centimeters ahead of that position they calculated. my own simulations confirm this.
Sonhouse
1 / 5 (1) Sep 13, 2008
Actually I think the fastest man on Earth has gone roughly mach 25.

We're creatures of the mind, not muscle. While I'm sure this is somehow interesting to some folks I honestly could care less either way.
Actually I think the fastest man on Earth has gone roughly mach 25.

We're creatures of the mind, not muscle. While I'm sure this is somehow interesting to some folks I honestly could care less either way.
Sonhouse
1 / 5 (2) Sep 13, 2008
That would be pretty fast for him to have run at mach 25 on earth. I would have thought he would burn up a lot sooner than that. When the shuttle returns it is only doing about mach 18 or so and you saw one burn up so I am sure he didn't run mach 25 on earth. Besides how would you even measure it? His time in the 100 meter event would have been about 12 milliseconds so I am sure they couldn't measure it very well....