How Usain Bolt can run faster – effortlessly Can Usain Bolt cover 100 metres even quicker than his world record? Yes, says John D. Barrow; and he doesn’t even have to improve his sprinting ability to do it. © 2012 The Royal Statistical Society times) and ended up predicting a maximum future running speed for Bolt that is slower than he is now running. Unfortunately, these predictions have received quite widespread publicity in New Scientist and other publications. All the commentators have missed the three key factors that would permit Bolt to run significantly faster without any extra effort or improvement in physical conditioning. You may well ask how that could be. It sounds absurd; but it is actually relatively easy. 2010 2000 1990 1980 1970 1960 1950 1940 1930 1920 10.7 10.6 10.5 10.4 10.3 10.2 10.1 10.0 9.9 9.8 9.7 9.6 9.5 1910 Time (s) Usain Bolt may be the best human sprinter there has ever been. Yet, few would have guessed that he would run so fast over 100 metres after he started out running 400 m and 200 m races when in his mid teens. His coach decided to shift him down to running the 100 m for one season to improve his basic sprinting speed. No one expected him to shine there. Surely he is too tall to be a 100 m sprinter? (He stands 6 ft 5 in.) How wrong they were. Instead of shaving the occasional one-hundredth of a second of the world record, like his predecessors, he took big chunks out of it (see Figure 1). First, he reduced Asafa Powell’s time of 9.74 s down to 9.72 s in New York in May 2008, and then down to 9.69 s (actually 9.683 s) at the Beijing Olympics later that year, before dramatically reducing it to 9.58 s (actually 9.578 s) at the 2009 World Championships in Berlin. His progression in the 200 m was even more astounding, reducing Michael Johnson’s supposedly “unbeatable” 1996 record of 19.32 s (actually 19.313 s) to 19.30 s (actually 19.296 s) in Beijing and then to 19.19 s in Berlin. These jumps are so big that people have started to wonder about what his ultimate limits are, and attempts have been made, in particular in an article by Mark Denny1, to calculate what Bolt’s maximum possible speed might be. Denny’s analysis was not done correctly (it ignored the role of reaction Year Figure 1. Progression of men’s 100 m record. Electronic timing to one-hundredth of a second became mandatory in 1977 april2012 9 The time that a 100 m sprinter records has two parts: the reaction time to the starter’s gun and the subsequent running time over the 100 m distance: Male Table 1. Reaction and running times for the 2009 World Championship 100 m finalists Bolt Gay Powell Bailey Thompson Chambers Burns Patton 10 0.146 + 9.434 = 9.58 0.144 + 9.566 = 9.71 0.134 + 9.706 = 9.84 0.129 + 9.801 = 9.93 0.119 + 9.811 = 9.93 0.123 + 9.877 = 10.00 0.165 + 9.835 = 10.00 0.149 +10.191 = 10.34 april2012 400 400 350 350 300 300 250 250 200 200 150 150 100 100 100.0 80.0 60.0 40.0 20.0 Frequency 0 20.0 40.0 60.0 80.0 Reaction time (ms) Athletes are judged to have false-started if they react by applying foot pressure to their starting blocks within one-tenth of a second of the start gun firing. Remarkably, Bolt has one of the longest reaction times of leading sprinters – he was the second slowest of all the finalists to react in Beijing and third slowest in Berlin when he ran 9.58 s. The Berlin reaction and run times for all the finalists are shown in Table 1. (Notice how Chambers finishes ahead of Burns even though he ran slower.) In the Beijing Olympic final, where Bolt’s reaction time was 0.165s for his 9.69 s run, the other seven finalists reacted in 0.133, 0.134, 0.142, 0.145, 0.147, 0.165, and 0.169 s. Only one was slower than Bolt. Allowing for all this, Bolt’s average running speed in Beijing was 10.50 m/s and in Berlin (where he reacted faster) it was 10.60 m/s. Bolt is already running faster than the predicted ultimate maximum speed of 10.55 m/s that the Stanford biologists predicted1 for him! From these statistics it is clear what Bolt’s weakest point is: he has a very slow reaction to the gun. This is not quite the same as having a slow start. A very tall athlete has got more moving to do in order to rise upright from the starting blocks and has longer limbs, with larger moments of inertia, to get moving (top athletes take about 0.3 s to get out of the blocks). If Bolt could get his reaction time down to 0.13 s, which is very good but not exceptional, then he would reduce his 9.58 s record run to 9.56 s. If he could get it consistently down to an excellent 0.12 s then he is looking at 9.55 s, and if he responded as quickly as the rules allow, with 0.10s, then 9.53 s is the result. And he Reaction time (ms) Time recorded = Reaction time + Run time Female 100.0 Frequency Figure 2. Reaction times of 425 sprinters at the Beijing Olympics. Mean female reaction times are 23 ms slower than for men hasn’t had to run any faster! Unfortunately, in Daegu at last summer’s world championships he tried a bit too hard and started 0.104 s before the gun was fired and was disqualified. He took it all in surprisingly good heart, but Bolt has a very slow reaction to the gun. This is not quite the same as having a slow start the organisers and the worldwide media were obviously devastated by this unexpected consequence of their new false-start rule. The quickest possible human reaction time that defines a false start is taken from physiological evidence to be 0.10 s, or 100 ms. This is why you are automatically signalled as false-starting if you react to the starter’s gun faster than this. Slight pressure on the starting blocks is sufficient to trigger a false start: you don’t actually have to cross the start line. Figure 2 is a chart of data on male and female reaction times prepared by Lipps et al.2 taken from 425 sprinters at the Beijing Olympics. The mean reaction time for the men was 168 ms, with 160–178 ms 95% confidence limits (CL). The mean for the women was 191 ms, with 180–205 ms 95% CL. The estimated absolute minimum for male sprinters was 124 ms, and for females was 130 ms. This data displays the systematic difference between male and female reaction times that has been present in studies of reaction times since they began. (Long ago, it was suspected that the smaller fraction of female car drivers might be the reason, but this is no longer credible.) Presumably it is related to muscular power, but I have not seen a detailed explanation provided in the biophysics literature or looked at similar data for swimmers. Intriguingly, male sprinters made 25 false starts in Beijing but females made only 4. This is consistent with female reaction times being 6 ms slower than men: their slower average reaction time makes them less likely to false-start. It has even been suggested that this difference justifies a different false-start criterion for men and women, but there would be little point in doing this as they are not competing against each other. This is the first key factor that has been missed in assessing Bolt’s future potential. But I said there were three, so what are the others? Sprinters are allowed to receive the assistance of a following wind that must not Usain Bolt crosses the finishing line of the 200m in Beijing with a world record time of 19.30 seconds. Photo: Ullsteinbild/TopFoto exceed 2 m/s in speed. Actually, wind gauge accuracy is a forgotten issue in athletics, and for all the trumpeted accuracy to a thousandth of a second in electronic timing and in wind speed limits to a tenth of a second, the accuracy of wind speed measurements may be no better than 0.2–0.5 m/s because only a single anemometer is used and wind speeds vary with position on the track3. Many world records have taken advantage of following winds. The most notorious set of world records in sprints and horizontal jumps were those set at the Mexico Olympics in 1968 where the wind gauge always seemed to record 2 m/s when a world record was broken! But this is certainly not the case for Bolt’s record runs. In Berlin his 9.58 s time benefited from only a modest 0.9 m/s tailwind and in Beijing there was nil Wind gauge accuracy is a forgotten issue in athletics holder, Maurice Greene, was not the fastest when his very advantageous following wind was taken into account. That honour fell to Frankie Fredericks. The drag force on a runner moving at speed V with wind speed W (a tailwind has a positive W and a headwind has a negative one) is D = –rcA(V – W)2(1) wind, so he has a lot more still to gain from advantageous wind conditions. Many years ago, I worked out4 how the ranking list of the best 100 m times is changed by wind. Interestingly, the then world record where r is the air density, A is the frontal area presented by the athlete in the direction of motion, and c is the drag factor (determined by what he is wearing). For a typical athlete, about 3% of his effort is expended beating wind drag and, assuming the 100 m is run at april2012 11 constant speed (it is not) the running time in seconds, T(W), achieved when the wind speed is W m/s is related to that expected when the wind speed is zero, T(0), by with their achievements (and those of their low-altitude rivals) at sea level and there was a general feeling that many of the world’s best athletes had been unfairly prevented from winning or setting best ever performances T(W = 0) by the effects of altitude. As a result there = [1.03 – 0.03(1 – WT(W)/100)2] × T(W) will never be another high-altitude Olympics A 2 m/s tailwind is worth about 0.11 s and world records in athletics cannot now be compared to a nil wind performance at a low- ratified if they are set at altitudes greater than altitude site. This means that there was 0.06 s 1000 m. assistance for Bolt’s Berlin record because of Why does altitude help the sprinters? its 0.9 m/s tailwind. So if Bolt could combine The drag on a runner moving at speed V a tough but achievable 0.12 s reaction time through air with a following wind of speed W with a maximum allowable wind assistance, is proportional to the air density, r. We can see he could transform the 9.58 s he achieved in immediately that, all other things being equal, Berlin to 9.50 s. And if he could attain the a decrease in the density of air will reduce the theoretical limiting reaction time of 0.10 s with drag and lead to more of the runner’s power the theoretical maximum wind assistance, he being used for fast forward motion than would be looking at around 9.48 s. overcoming resistance. At sea level, the air The third factor that can help Bolt record density is 1.23 kg/m3 – at Berlin’s 34 m above faster times is the possibility of reducing the sea level, and Beijing’s 44 m, it is practically the density of air that enters into the drag formula same – but at the 2240 m altitude of Mexico in equation (1). The simplest way to achieve City it is down to 0.98 kg/m3, at a moderate this is to run at high altitude. As an aside, we temperature of about 20°C. This means that the drag on runners in Mexico City because of air resistance was smaller by a factor 0.98/1.23 = 0.80 than at sea level. This leads to a time improvement of about 0.08% in events like It can be argued that Usain 100, 200 m and 400 m. This is significant Bolt is not the world’s fastest although it is not large enough to explain the improvements displayed by male and human any more – and the 1.5–2% female athletes in those events at the Mexico 100 metres is not the race in Olympic Games5. The first use of an allwhich humans run fastest weather artificial track surface at an Olympics, rather than cinders, was undoubtedly another very helpful factor. What could this mean for Bolt? Every 1000 m of altitude will decrease his 100 m might mention that the cyclists in the Olympic running time by about 0.03 s because of the velodrome in London are being aided in this fall in air density. If he were to run at a highrespect by the heating of the air at track level altitude site like Mexico City, then he will go so as to lower its local air density, reduce drag faster and effortlessly shave off another 0.07 s from his 100 m time. However, if he wants his and produce faster times. The choice of Mexico City to host the performance to be valid for record purposes 1968 Olympic Games first brought the word he can only go to 1000 m and reduce it by “altitude” into the vocabulary of athletics. 0.03s. In summary, what advice can I offer Usain Mexico City sits at an altitude of 2240 m above sea level. The effects were twofold. For the Bolt? At the moment his world record stands distance running events above 800 m, it was at 9.58 s. By improving his poor reaction time much harder to run at altitude because oxygen to the gun he can realistically reduce it to absorption by the body was diminished by 9.55 s. By making use of the maximum allowed 10–15% for unacclimatised runners. Athletes following wind assistance of 2 m/s (instead of who lived at altitude, notably Africans, were the 0.9 m/s tailwind that he actually had) he significantly advantaged and won all the can reduce it further to 9.50 s. And by running distance running events. However, their in the thinner air at an altitude of 1000 m he winning times were generally poor compared can bring it down to 9.47 s (although he could 12 april2012 get it down to 9.43 s in Mexico City). With the theoretical limit reaction time of 0.10 s, these times become 9.48 s with best wind, 9.45 s with best legal altitude, and 9.41 s in Mexico. These are amazing improvements but they can all happen without Bolt becoming a better sprinter. They serve to illustrate how far we are from any type of “ultimate” sprinting speed in the men’s 100 m and the scale of improvements that are possible without appealing to any statistical extreme occurring in the future. Finally, as a postscript, I think it could be argued that Usain is not the fastest human any more. At the end of last season his training partner, Yohan Blake, who won the 100 m in Daegu after Bolt’s disqualification, ran the second fastest 200 m ever in a time of 19.26 s with a +0.7 m/s following wind. However, I pointed out6 soon afterwards that the most remarkable thing about this completely unexpected performance was Blake’s reaction time to the starter’s gun. It was an extraordinarily lethargic 0.269 s. Blake’s 200 m running time was therefore 18.99 s against Bolt’s 19.06 s. If you halve these times you get 9.495 s for Blake versus 9.530 s for Bolt – and they are faster than the 100 m record, because of the advantage of the rolling start. Despite all the hype about the men’s 100 m final at London 2012, it’s the 200 m you really want to see! References 1. Denny, M.W. (2008) Limits to running speed in dogs, horses and humans. Journal of Experimental Biology, 211, 3836–3849. 2. Lipps, D. B., Eckner, J. T., Richardson, J. K., Galecki, A. and Ashton-Miller, J. A. (2009) On gender differences in the reaction times of sprinters at the 2008 Beijing Olympics. American Society of Biomechanics Annual Assembly, State College, Pennsylvania, August. 3. Linthorne, N. (2000) Accuracy of wind measurements in athletics. Sports Engineering, 3, 241. 4. Barrow, J.D. (1997) Frankie’s fastest. Athletics Weekly, August 6th. 5. Pritchard, W.G. (1993) Mathematical models of running. SIAM Review, 35, 359–379. 6. Barrow, J.D. (2011) Slow off the mark, Athletics Weekly, September 29th. John D. Barrow FRS is Professor of Mathematical Sciences and Director of the Millennium Mathematics Project at Cambridge University, and the current Gresham Professor of Geometry at Gresham College, London.