The study is published today in Significance, the magazine of the Royal Statistical Society and the American Statistical Association. In it Professor Barrow illustrates how, based on concrete mathematical evidence, Bolt could cut his world record from 9.58 seconds to 9.44.
It is part of the Millennium Maths Project’s Maths and Sport programme which highlights the hidden maths behind the 2012 Olympic and Paralympic Games.
Usain Bolt holds the current 100m world record, at 9.58s, and has been described as the best sprinter there has ever been, dramatically reducing his running times since he first won the world record in 2008. Previous scientific studies have been carried out aiming to predict his maximum speed, yet have failed to take all the relevant factors into account, and Bolt has already surpassed the speeds they predicted.
Today’s Significance study highlights the three key factors instrumental in improving Bolt’s performance, which combined produce an improvement of 0.14s.
Firstly Bolt’s reaction time is surprisingly poor, in fact one of the longest of leading sprinters. By responding to the gun as quickly as possible without triggering a false start, with 0.10s, he would shave 0.05s off his world record to 9.53s.
Secondly, advantageous wind conditions can help an athlete improve their time, although this is supposedly taken into account. According to Professor Barrow, “the accuracy of wind speed measurements is currently much lower than is generally believed because only a single anemometer is used, and wind speeds vary with position on track”. Bolt’s Berlin record of 9.58s benefited from a modest 0.9m/s tailwind. If he were to benefit from a maximum permissible tailwind of 2m/s, he would expend less effort on beating wind drag and reduce this record further by 0.06s to 9.47s.
Thirdly, running at altitude reduces the air density in the wind drag calculation, as was witnessed at the 1968 Olympic Games in Mexico City (2240m above sea level), where significant improvements over short distances were displayed. As a result, athletics world records are only permitted at altitudes of up to 1000m, but this still allows Bolt to reduce his time by a further 0.03s to 9.44s if he runs at this altitude.
“With the relatively big chunks we’ve seen Bolt take out of world records, we are still a long way from understanding the limits of his, and others’, sprinting speeds” said Professor Barrow. “What this study serves to illustrate is the insight maths can give into sports performance, which has not been done previously to such a degree of accuracy.”
The Maths and Sport: Countdown to the Games programme, which has been awarded the Inspire Mark, the badge of the London 2012 Inspire programme, forms part of the education legacy of the London Games. It features in the Practical Learning strand of Get Set +, the London 2012 education programme and includes online maths resources for teachers and students as well as a Maths and Sport roadshow.