How Usain Bolt can run faster – effortlessly

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
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.
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
Figure 1. Progression of men’s 100 m record. Electronic timing to
one-hundredth of a second became mandatory in 1977
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:
Table 1. Reaction and running times for the 2009
World Championship 100 m finalists
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
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
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
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
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
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
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!
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,
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.