The physics of the world's fastest man

The physics of the world's fastest man
Usain Bolt leaves the pack in his dust while setting a new world record for the 200-meter sprint in Bejing (Photo: jmex)
Usain Bolt leaves the pack in his dust while setting a new world record for the 200-meter sprint in Bejing (Photo: jmex)
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Usain Bolt leaves the pack in his dust while setting a new world record for the 200-meter sprint in Bejing (Photo: jmex)
Usain Bolt leaves the pack in his dust while setting a new world record for the 200-meter sprint in Bejing (Photo: jmex)
Usain Bolt leaves the field far behind as he sets the 100-meter world record for the third time (Photo: Shutterstock)
Usain Bolt leaves the field far behind as he sets the 100-meter world record for the third time (Photo: Shutterstock)
Bolt's celebratory "Lightning Bolt" stance(Photo: Shutterstock)
Bolt's celebratory "Lightning Bolt" stance(Photo: Shutterstock)
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The Honourable Usain Bolt (Order of Jamaica; Commander of the Order of Distinction) is often held out as the world's fastest man. The reigning Olympic champion in the 100-meter and 200-meter sprints as well as a member of the Olympic champion 4x100 meter relay team, Bolt is the first man to win six Olympic gold medals in sprinting, and is a five-time world champion. Long and lanky at 6 ft 5 in (2 m) tall, he towers above the (mostly) much shorter sprinters. How has he managed to come out on top for the past five years? A team of physicists from the Universidad Nacional Autonoma de Mexico (UNAM) has analyzed Bolt's past performances in the 100-meter sprint to understand what makes a record-breaker.

Beginning with the 1964 Olympics, the track and field world switched from manual to automatic timing of sprinting events, resetting the racing times so that comparison with earlier times is not consistent (From 1977, all major track events were automatically timed). In the 43 years between that time and the advent of Usain Bolt onto the major sprinting events, the 100-meter world record has fallen from 10.06 seconds (Bob Hayes) to 9.74 seconds (Asafa Powell). The record was shrinking by about 0.008 seconds per year.

Usain Bolt took his first 100-meter world record in the 2008 Reebok Grand Prix with a time of 9.72 seconds. His remarkable achievement, however, was to reduce that time to 9.58 seconds just a bit over a year later – a rate of about 0.10 seconds per year. That record stands today.

Usain Bolt leaves the field far behind as he sets the 100-meter world record for the third time (Photo: Shutterstock)
Usain Bolt leaves the field far behind as he sets the 100-meter world record for the third time (Photo: Shutterstock)

The key to sprint speed is the horizontal force the sprinter can generate. When that force is equal to drag on the runner, the runner cannot achieve a faster time. The force out of the blocks is often larger, as pushing against the blocks is more efficient than pushing against a flat surface. As a result, a sprinter can rapidly approach their top speed very shortly after a good start. The UNAM group has extracted some of these factors for Usain Bolt's 2009 IAAF record-setting run, based on times and locations every tenth of a second (supplied by the IAAF.)

First, Bolt comes out of the blocks with an acceleration of nearly one g. This is driven by a force of 817 N (184 lb). This isn't terribly surprising, as the legs are used to operating under a load of one g – it is simply a matter of training the muscles to work fully for horizontal propulsion. What is more surprising is that the UNAM analysis shows that Bolt is able to maintain that level of force for horizontal motion for the entire 100-meter event.

Maintaining a constant force implies that Bolt, at some point, will slowly approach a maximum speed. His acceleration falls essentially to zero between four and five seconds from the start of the race, and he maintains a speed of some 12.2 m/s (27.3 mph) throughout the remainder of the race.

Mechanical power is another measure of interest, which is proportional to both the velocity and the acceleration. When this is extracted for Bolt's best official run, the maximum value of power is an amazing 2600 W (3.5 HP). He achieves this less than a second after the start of the race, after which the power falls rapidly. Bolt isn't working less hard after this first peak. Rather, the air drag grows very rapidly, to the point that nearly all of Bolt's force goes into fighting drag effects after the first few seconds.

Bolt's celebratory "Lightning Bolt" stance(Photo: Shutterstock)
Bolt's celebratory "Lightning Bolt" stance(Photo: Shutterstock)

It is interesting to look at what the overall effect of drag is on a race. The total energy Bolt imparts to his motion during the 100-meter sprint is about 6.4 kJ, or 1.8 w-hr. However, using the observation that he seems to apply an essentially constant force during the sprint, the energy he delivers for the sprint is a much larger 81.6 kJ (22.7 w-hr). This represents an average power of 11.6 HP! Only about 8 percent of Bolt's effort goes into moving down the track – the remainder is totally used up in overcoming drag forces.

Slight changes in the air drag will clearly change this balance to a more effective run. This is why many past records have been set at altitude, and why such records are usually taken with a grain of salt. It is also fascinating that virtually all sprinters run in a totally upright position, which one would think would increase air drag. It would also seem that Bolt's great height would increase air drag, but it does not appear to be a problem for him. Could a simple change in the running outfit, to make it fit more tightly or present a smoother surface to the air, result in less drag, and faster times? Such matters are largely regulated to keep competitors on an even playing field, but there could be changes in response to the advent of new materials.

Despite the analysis, none of this explains why Usain Bolt dominates the shorter track events so thoroughly. If anything, it appears that he may have handicaps concerning excess air drag. However, like so many highly successful people, he goes ahead and does what he wants, instead of what the numbers tell him he can do. This is the Olympic spirit, and the reason he has been called the world's greatest athlete.

Source: European Journal of Physics

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Mike Hagley
9.58 is ridiculous. will it ever be beaten?
The new york times did a writeup of past 100 meter times that offers some perspective here:
The olympic gold medal time in 1896 was 12.6 seconds. In 1906 it was 11.3 and it wasn't until the 1920's that someone posted a time under 11 seconds in the olympics. I have a slightly over 11 second 100m time that would have qualified me for gold in the olympics ~100 years ago and I outweigh the early 1900s sprinters by a decent amount. There are kids in high school close to breaking under 10 seconds now.
Progress will slow but his 9.58 time will fall.
I would be quietly curious as to what the highest possible speed is for a biologically enhanced human being. Thinking 5 seconds flat wold be a nice goal.
Not mechanically assisted by any means, so no leg extensions, or external power sources or external energy storage-release tech.
What I'm talking about here is free use of any performance enhancing chemical or process including DNA augmentation, for any length of time in preparation for the one event. Like a Bane (batman reference) if you will, minus external pumps.
Athletes are not allowed to take anything one hour before the event as the object is to test to some degree the athlete, not the ability of the chemicals to do all the work.
The athlete would of course have to consider options in preparing his body so as not to do any long term damage to his organs and ligaments. The stakes can be a lot higher. Rather then the paltry amount athletes receive now, give then half a mill or more for their winnings.
Bob Stuart
I can't wait for the explanation of how he maintains a constant force against the ground while his feet are in the air. All this article did was make me wonder what someone else could have done with the source information.
What is this nonsense about a taller man incurring more air drag? Its clearly not a factor and, after a proper analysis, it will become clear that longer legs (well muscled and trained to use fast-twitch energy) are a key component of success in the sprinting game. After all, you wouldn't expect a Shetland Pony to win at the Kentucky Derby...despite the fact that a larger thoroughbred might require more force to counter whatever actual differential in air drag.
Not to take away from his incredible accomplishments, but those figures are a little exaggerated. For instance, the terminal velocity of a human body is ~60m/S He s running at 12m/S, eg. his drag would be (12 / 60) ^ 2 * 900N (weight), or approximately 40N
At 12m/S his power would be ~480W, a bit under 1HP These figures are more in line with typical bicycle riding as well. A horse power on a bicycle goes a bit faster.
I think the final limit to going faster is how fast can ones legs reciprocate? Thats where most of the power gets wasted.
Fritz Menzel
As a tall athletic person this is very interesting to me. I'm an elder now, but as a kid I could NEVER run the 100 in less than 12 seconds - in other words, I was slow. Therefore I always theorized it was because of my ability to 'horizontalize' my strong vertical jump that I could outrun anybody in the opening seconds, e.g., from home plate to first base in softball, where the only infield hit I couldn't beat out was a hard one-bouncer to the pitcher. This seems to support my theory. But Bolt's ability to sustain that is otherworldly and I just love watching him run!
re; Alzie
Bicycles are more efficient than walking or running because the energy you expend just resisting gravity gets converted to forward motion.
re; Alzie part 2
Also the energy used to lift the leg can be turned into forward motion as well. There are also mechanical advantages to using the lower leg muscles rather than thigh muscles That can not be matched while on foot.
We are not far off the time when no human being will be prepared to live the life of isolation from humanity that will be necessary to be an unaugmented human athlete. Its already the case that any athlete that takes a common cold cure will be hounded out of their profession as a filthy scum drug cheat. Frankly you are watching the last days of a quaint human activity. Primitive human athletics.
Thats not to say that Bolt isn't a supremely admirable human being which he is, but he is one of the last of a kind.
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