Maths and Olympics: How fast could Usain Bolt run?

[1]

Usain Bolt, already the world's fastest man, could lop another 0.18 seconds off his 100 metre sprint world record even without running any faster. It's just a question of getting a few conditions right - and doing the maths.

Luckily for the top Jamaican sprinter, John Barrow, a professor of mathematical sciences at Britain's Cambridge University, has done the calculations for him.

He's also done some serious sums on the triathlon - an event he describes as "crazily constructed" and "ridiculously biased" - and on high jumping, archery, rowing and 100 or so other sports he feels could do with a little more number crunching.

His mission, he says, is to enrich understanding of sport and enliven appreciation of maths. All at the same time.

"It's about getting some perspective on how far there is to go," Barrow told Reuters ahead of a series of talks on the maths behind the Olympics in Cambridge and in London, host city for the 2012 Games.

NEW RECORD COULD BE 9.40 SECONDS

With Bolt, the distance is set - at 100 metres - but there's a lot that could be done with the timing, according to Barrow.

Having analysed Bolt's reaction times to the starting gun - which are generally slower than other leading sprinters and often much slower than the 0.1 seconds allowed - the mathematician says that's where the first gain could be.

"The time that people record in the 100 metre sprint is the sum of two parts -- one is the reaction time to the starting gun and the other is the actual running time," Barrow said.

"So if Bolt could get his reaction time down to say 0.13 seconds, which is good but not exceptional, he'd make some improvement on his overall record time of 9.58. It may only be few hundredths of a second, but it's certainly room for improvement."

Barrow has also worked out the top wind speed Bolt would be allowed within Olympic rules to have helping him along - a maximum of 2 metres per second - and the optimum altitude at which he could race in thinner, and hence less resistant, air.

Adding them all together, Bolt could be looking at a new 100-metre world record of 9.4 seconds, without actually running any faster, Barrow said.

"The point I'm trying to make is that we're not going to be reaching the limits of human speed anytime soon," he said. "And there's no reason to assume Bolt is going to be just shaving fractions of hundredths of seconds off each time. There's scope for some quite big improvements."

Besides Bolt, Barrow has also turned his mathematical mind to scores of others sports and is publishing his musings in a new book due out this week called "100 Essential Things You Didn't Know You Didn't Know About Sport".

REDUCING ROWERS' WIGGLE

For rowing he has devised a funky equation to help coaches place crew members in fours or eights in the best possible combination to minimise the boat's "wiggle", which Barrow says results form the boat being subjected to alternating sideways forces.

The equation is M = sF-(s+r)F-(S+2r)F+(s +3r)F = 0, and Barrow concludes that in a coxless four, the rowers at front and back should be have their oars to the right, while the two in the middle should have theirs to the left.

For an eight, he suggests the rowers sit in a pattern from stern to bow with their oars stuck out to the right, left, left, right, left, right, right, left to reduce the wiggle, and says he hopes one of the Olympic crews will put his theory into practice at London 2012.

Barrow also turns his attentions to the newest sport in the Olympic Games - the triathlon - which consists of a swim, a bike ride and a distance run.

Barrow wonders whether the relative lengths of the swim, ride and run stages are really fair. And after analysing the results of women's and men's triathlon medal winners at the Beijing Olympics, he thinks not.

"As the rules stand, the winning man spent a mere 16.7 percent of this total time swimming, 28.3 percent of it running, 0.8 percent of it in transition (going from one sport to the next) and a whopping 54.2 percent of it cycling," the mathematician writes in his book, concluding that this shows there is far too much emphasis put on cycling performance.

Asked what should be done about it, Barrow proposes what he calls an "equitempered triathlon".

"If it was sensibly constructed there would be an equal amount of time on each of three sports," he told Reuters. "That would be much fairer."