Is there a limit to how fast a man can run ?Take a look at the
world record times for the men's 100 m sprint from 1912 to
The record is being improved in ever-decreasing changes.
Montgomery has become world record holder by improving the mark by
barely 1 part in 1000 - and you have to wonder whether the
dimensions of the track and measurement of atheletes performance is
really that accurate (particularly when the effect of wind swirls
etc.,. is considered, notwithstanding rules etc.,. relating to wind
If the data is taken at face value, the following graph shows
the reduction in speed improvements clearly...
The dark blue line connects the individual record data points. A
straight line fit to this is shown in the light blue line in Figure
1 above. This linear regression least-square error best-fit line
over 90 years shows a slope of 7.7 millisecond fall per year. The
correlation is 0.97, which is considered good for some applications
(a best fit exponential gives virtually identical results).
The data over the last 90 years does not suggest the record will
continue to fall as it did in the first 40 years to 1950. There are
noticeable mismatches in the data, and the relationship over the
first 20 years looks to have a different slope, to the middle 20 to
50 years and then the last 20 years.
A better correlation can be achieved by using a logistic
equation to fit the data.
The logistic equation is very useful for modelling processes
that reach a limit (see detailed discussion below). The correlation between the best least-square
error logistic fit and the record data is 0.99 (1 is perfect fit).
Although not a perfect match, it is a better statistical match than
the straight line. The mean square error is 0.001452 seconds - or
just 47% of that for the straight line.
The logistic equation reaches a limit : 9.48 seconds. Shown
below is the logistic model for the 250 years from 1912 to
It should be noted that in 1912, they didn't have running
spikes, they didn't have starting blocks, and they didn't have all
weather polyurethane tracks - all of which probably have
contributed to a lowering of 100 m times. Hand-timing is often
believed to have decreased recorded times (due to enthusiastic
anticipation of the finish) - although some coaches claim
professionally trained hand-timers were not susceptible to this.
Quite simply, the contribution of these factors can not be
ascertained - because we weren't there with the better
So the best that can be done is to consider the overall result
of the technological and biomechanical progress.. The assumption is
that whatever processes resulted in the improvement each would also
one day reach a limit. There is a limit to technological as well as
Australians got very interested in the 100 m Sprint in the week
ending Sat 10th May 2003, when Patrick Johnson ran an Australian
record of 9.93 secs (with 1.3 m/s wind assistance) on 6th May at
Mito, Japan, and followed up on 10th with a 10.05 sec run (-0.3 m/s
wind) in coming second to Tim Montgomery at Osaka, Japan.
What will it take for Montgomery to match his world record - and
someone like Johnson from Torres-Strait Islander and Irish stock
beat it ? See discussion below about wind effects for some clues
(Jonas Mureika's (Wind and Altitude adjustment
calculator suggests Johnson's two May efforts were equivalent to corrected times of 10.02 (Mito) and
10.03 (Osaka)), but to really know the answer to who is the faster
man you might have to look at 10 m splits for their races...
Former Canadian track coach Charlie Francis suggested that
averages of the top 10 and top 20 performances for each year since
1991 might be a
better indicator of performance trends.
Looking at the average of the top performers shows that either
performances are approaching a limit, or might have even gone
through a slight up-turn. Is this the effect of better drug-testing
? As the analysis on the Comparison of
100 m Sprinting page suggests, the limit is very near and might
have been reached. Low Sub-10 Sprints in
2003 presents a map of the sub-10 performances since 1987, and
provides further evidence of a slow-down in performances.
Other authors have predicted limits to performance. An ultimate
limit of 9.37 sec is predicted by F. Péronnet and G. Thibault
in``Mathematical analysis of running performance and world running
records'', Journal of Applied Physiology, v.67, pp. 453-465 (1989)
as cited in Jonas Mereika's paper "How
Good Can We Get? Using mathematical models to predict the future of
athletics" (published Athletics: Canada's National Track and
Field / Running Magazine (April/May 1998)). Peronnet &
Thibault's prediction of 9.73 s for Year 2000, however, has proven
optimistic by about 0.06 secs; the record is not falling as quickly
as they predicted, and the higher limit suggested above might be
According to claims on the Charlie Francis discussion forums,
Biomechanist Gideon B. Ariel Ph.D may have hypothesized in the late
'70's that .: 9.60 would be the limit of the human body
mechanically, that to exert the forces and limb velocites necesary
to exceed this would crack bones and pull tendon from connection
No Limits to Performance ?
Some sports physiologists are more optimistic than this. For an
intesting discussion prior to the Year 2000 Sydney Olympics, see W
G Hopkins report in Sports Science Limits to
Performance, and particularly the responses from Norway's Assoc Prof Stephen
I want to find out if we seem to be pushing the limits of human
performance. Certainly people keep breaking world records. But are
we getting to the point where training techniques are so good that
it's only a matter of time before we top out -- before performance
become essentially static, with only the occasional,
once-every-generation super athlete able to set new records? Are we
actually in a situation like that today with some sports?
What we found out when we looked at the 100 meter dash for men
was that the average performance improvement was 0.01 second per
year [~1% per decade] based on world championship and Olympic
finals performances (average time of top 6 finalists) since 56
(corrected for wind and altitude). This improvement was linear and
showed no sign of leveling off as of the end of the 20th century.
Obviously, limits are being approached, but I think we can expect
similar "steady" improvements for the next several decades. For
example, Michael Johnson's "statistical outlier" 200 meter time in
1996 demonstrates that the potential for substantial improvements
is still there (the women's data was much more complicated and I
will leave it at that for the purpose of this discussion). The
world record progression in many events is marked by these
stochastic jumps, stabilization at a new level, new jump etc.
Seiler's fit of a straight line uses data only since 1956, and
averages top performances not the peak performance (selecting
performances at particular world-class events). Unfortunately,
Seiler has not reported the goodness of fit in this discussion (
maybe he has in other publications). His method may be difficult,
if not impossible, to extend back in time due to timing and
recording inaccuracies. Other articles by Seiler at the site
suggest he may have used film or videotape of performances to
correct for hand-timing inaccuracies, and finding suitable archival
material more than 50 years old could be impossible.
Seiler's methodologies are impressively complex. Does this
complexity, however, go beyond what Occam's
Razor might caution us to seek: "Pluralitas non est ponenda
sine neccesitate" or "plurality should not be posited without
One should not increase, beyond what is necessary, the number of
entities required to explain anything. From the discussion of Occam's Razor on
Principia Cybernetica Web:
Though the principle may seem rather trivial, it is essential
for model building because of what is known as the
"underdetermination of theories by data". For a given set of
observations or data, there is always an infinite number of
possible models explaining those same data. This is because a model
normally represents an infinite number of possible cases, of which
the observed cases are only a finite subset. The non-observed cases
are inferred by postulating general rules covering both actual and
For example, through two data points in a diagram you can always
draw a straight line, and induce that all further observations will
lie on that line. However, you could also draw an infinite variety
of the most complicated curves passing through those same two
points, and these curves would fit the empirical data just as well.
Only Occam's razor would in this case guide you in choosing the
"straight" (i.e. linear) relation as best candidate model. A
similar reasoning can be made for n data points lying in any kind
...In mathematical modelling of systems, the principle can be
made more concrete in the form of the principle of uncertainty
maximization: from your data, induce that model which minimizes the
number of additional assumptions.
If Seiler's model makes subjective assumptions about what is
treated as a world class event for the purpose of constructing his
statistics and how many performances to include (top 6, why not top
4, 8, 10 etc.,.), then it might not be minimizing the number of
The discussion Hopkins reviewed includes viewpoints that there
is no limit to performance. It raises such prospects as using gene
therapy to insert the right muscle types into athletes, boosting
their capacity. At what point ligaments, cartilage and perhaps even
bones, give way and prevent a zero-second 100 m sprint is not clear
- but with rewards for elite athletes sky-rocketing the temptation
will obviously be there for some sportsmen to be willing guinea
Up until the 1968 Mexico Olympics, the 100 m sprint was
hand-measured with stop-watches calibrated in tenths of seconds.
So, as can be seen in Figure 1 above, the record fell in 0.1 second
increments. Part of the inherent inaccuracy in this was the error
due to the reaction time of the human timers. This could be between
0.1 and 0.2 seconds on starting and stopping, could vary between
starting and stopping, and could vary compared to the runner's
reaction to the gun. Measuring records in 0.1 second increments at
least recognised the limited accuracy of the process.
For the 1968 Mexico Olympics, Jim Hines had several advantages:
0.01 second timing (allowing a new record just 0.05 seconds faster
than the previous, and high altitude (equivalent to a 1.5 m/s wind
assist, added to the 1.6 m/sec actual wind assistance). It's
difficult to say how much of the improvement in his time may have
been due simply to timing artefacts. Hines record stood for 15
years until Calvin Smith beat it in 1983 by just 0.02 seconds. That
margin is so fine that if a light (eg. a LED) was flashed on for
0.02 seconds nobody would see it.
Some researchers have estimated the effect of altitude, and
wind-assistance. J.R.Mereika's paper "A
Matter of Time" (Published: Athletics: Canada's National Track
and Field / Running Magazine (December 1999)) has estimated that
the results could vary by as much as 0.18 second for the differing
extremes of wind assistance (up to 2 m/sec) and altitude effects.
The 0.18 seconds is nearly enough to cover all the improvement in
the record for the last two decades!
The difference between no wind and 2 m/sec wind assistance could
amount to around 0.1 seconds. Records that split this difference
(by measuring to better than 0.1 sec resolution) could simply be
measuring the varying contribution of wind. Tim Montgomery's 2002
record had the maximum legal wind assistance of 2 m/sec.
Don't think a 1 m/s wind can mess much with an 80 kg sprinter ?
Think about this fact: a 390,000 kg 747 takes off with a 320 km/hr
wind across its wings - that's about 90 m/s. Clearly, just being
heavy or fast doesn't mean wind has no effect.
An average sprinter is 5000 times lighter than the 747, and a
5000 times lighter wind would be 0.02 m/s.
If sprinters were as aerodynamically efficient like a jumbo
wing, they'd be literally flying at their peak speeds of close to
12 m/s (well over 0.02 m/s). Thanks to poorer aerodynamics (and
lack of smooth laminar flow), they don't fly - but aerodynamic
effects can still drag them back.
For more convincing evidence, watch TV footage showin how an
approaching hurricane can blow grown men off their feet and into
It is equally revealing to consider the effect of the start, and
particularly the reaction time of the runners. The reaction time is
the time is takes for the runner to respond to the start signal and
begin leaving the starting blocks. (see Omega and Sport -
Athletics for a good run-down of the sprint timing and start
rules). Interestingly, it is considered that there is a limit to
how fast a human can react to a start signal. As of 2002, if an
athlete left the blocks sooner than 100 mSec after the start
signal, he was deemed to have false-started.
The best athletes reaction times are usually in the range of 120
mSec to 160 mSec (see graphs). If
you track individuals performances, there is usually a spread of
0.01 to 0.03 s in their reaction times. Until someone can
consistently start in the same time (with less than 0.01 second
variatin), it's fair to question what it means when events are
timed in 0.01 second increments. At least some of the difference
between world records and world class performances might have more
to do with luck than something that can be honed by good
See Reaction Times and Sprint False Starts for
more discussion of reaction times.
Further insight can be gained by looking at the quickest 10
metre split attained by the runners - this shows the peak average
speed reached. In 1988, with 1.1 m/sec wind assistance, Carl Lewis
and the drug-fuelled Ben Johnson both hit a 0.83 sec split - or
12.08 m/sec ( = 43.37 km/hr). Lewis hit the same mark again in his
Tokyo 91 world record run with 1.2 m/sec wind assistance. Maurice
Greene's Athens 97 record, with a mere 0.2 m/sec wind assistance,
could manage only a 0.85 split. In Seville 1999, Greene managed a
0.84 with a 0.2 m/sec wind assist, as did Dwain Chambers. Tim
Montgomery's 2002 record run matched the 0.83 sec split, with
2m/sec wind assist (see
Track And Field, Nov 2002). But over nearly 14 years, the peak
speed has not been improved unless an allowance is made for wind
assistance (making Greene's 99 performance perhaps the best).. This
could be a strong signal that a limit has been reached.
When you get down to looking at one part in 100 changes to split
times, it is wise to question what the wind-assistance figure
represents. This has been researched by
who reports(while with the University of Sydney School of Exercise
and Sports Science):
Accuracy of Wind Readings
In the sprint events, races are timed to the nearest 0.01
seconds and the official wind reading is a 10 second measurement
obtained from a single wind gauge placed next to the track. My wind
assistance study indicated that if athletes are to be treated
fairly when recognising world records the official wind reading
must be accurate to ±0.2 m/s. It has long been suspected that
the official wind reading does not always provide an accurate
representation of the wind affecting the athlete as they run down
A study of wind conditions at the Sydney Athletic Centre showed
that the accuracy of the official wind reading is only about
±0.9 m/s. This is equivalent to an accuracy in race time of
about 0.05 seconds. Therefore, the occasional injustice may arise
in the recognition of world records. The accuracy of the official
wind reading could be improved to the required level by using
several wind gauges placed along both sides of the 100m straight.
An instantaneous wind measurement would be taken as the runners
passed by each wind gauge. However, this approach would greatly
increase the cost and complexity of organising an event that meets
the requirements for consideration of world records.
As Linthorne suggests, gusts and swirls at fortunate parts of
the track could be affecting the results. The wind guage is
required to have an accuracy of only 1 part in 10 (relative to the
2 m/sec limit being measured) - nothing like the 1 part in 1000
reported timing accuracy. Inaccuracy of 0.05 seconds could account
for virtually all the difference between the last three world
records (9.84 to 9.78 seconds).
Most of the recent improvement in the record has been due to
improved reaction times (as shown for the Carl Lewis case above)..
Is it really a record run, or just a record start ? If the
improvement is purely due to luck or flukes in beating the gun,
then what's the record worth ? What if it's just random wind gusts
The change in the starting rules may make gambling on
fast-starts less likely and beating the records could be difficult
without this advantage. If the 100 mSec false-start limit is
reduced, and new records arise, will they be due to a genuine
improvement in performance, or just good-luck in beating the gun ?
How long will it be before anyone runs faster than Carl Lewis's
0.83 s split from 1988 ?
What effect will the April 2003 revelations of Carl Lewis and
other American athletes positive drug tests have, if any ? Lewis
was found to have tested positive to the stimulant ephedrine in the
US trials in 1988. Is that how sprinters improve reaction times
The Comparing 100 m Sprinting - Wind
& Altitude Correction page shows how correction for wind
and altitude might affect rankings, and can also be useful in
eliminating some of the variability in trends in average top
Thoroughbred Race Horses are the product of over 300 years of
selective breeding. Today, racehorse records remain much the same
as they were 100 years ago. As an example, Erica
Goode reports (New York Times 8th May 2001, "Thoroughbreds Face
Physical Limits to Improvement"):
The winning times for horses in classic races like the Kentucky
Derby have remained surprisingly static. Secretariat's
world-record-breaking Derby time of 1:59.25, for example, set in
1973, remains unsurpassed more than a quarter of a century later.
Monarchos, this year's Derby winner, clocked the second-fastest
winning time in history, running the race in 1:59.97, but still did
not break Secretariat's record.
The reasons, scientists say, may have to do both with the unique
physiology of the horse and the nature of the sport.
Horses are designed to run, their fleetness of foot having
evolved over millions of years as a strategy of escape from
predators. At one hour old, a foal is on its feet; at two hours, it
is ready to go. And the horse's natural running ability has been
nurtured and enhanced in thoroughbreds, which have been selectively
bred for racing since the 17th century.
So while people require years of training and daily practice,
thoroughbred racehorses enter the world much closer to their
performance limits, said Dr. James Rooney, an emeritus professor at
the University of Kentucky and an expert on equine
"The human is not, from the point of view of construction, a
particularly good thing to start with and be an athlete," Dr.
Rooney said. "But the horse is born to be an athlete. And the more
they learn about horse physiology, the more people begin to realize
that this animal has evolved to a certain point and you can't
change it very much."
Lest you gather from this that Thoroughbreds have reached
perfection, Loren Bolinger's 1998 article On the Manipulation of the Gene
Pool What's Best for the Thoroughbred?
-A Human Conceit, (once at
"http://www.sunshow.com/pool.html"), gone by 2004)"
raises a number of shortfalls in the history
of thoroughbred breeding. This include a reluctance to incorporate
female bloodlines until recent times, and disastrous destructive
inbreeding. These mistakes and shortfalls lead to Loren's question
on the wisdom of genetic manipulation:
The altruistic or otherwise tampering with the breed by
latter-day well-meaning horsemen with that most noble of mankind's
biological creations, the Thoroughbred horse, has largely been
ill-advised, ill-conceived, and fortunately, historically
relatively meaningless... Even with current advancements in
molecular cyto-genetics, can we be sure we are as wise as Mother
Nature? It would be a naive arrogance and a conceit to respond too
quickly with an all-knowing yes. Be assured there are plenty of
mysteries left to confound us. Are we so sure of ourselves or so
smart to want to attempt to manipulate the gene pool of the
Thoroughbred on any large scale? If such were the case, for what
factors would we select - would we be wise enough to know beyond
reasonable doubt the correctness of our decisions for the future of
It does not seem reasonable to expect human performance to
improve forever and ever, when it's clear that human efforts -
including selective breeding over hundreds of years - has not been
able to achieve that for racehorses - does it ? Have we learned
enough from the mistakes in thoroughbred selective breeding to not
make even more disastrous mistakes with human athletic inbreeding ?
Today's panacea, Genetic manipulation, may turn out to be hi-tech
Interestingly, thoroughbreds continue to be raced while records
no longer fall. Financial support for genetic manipulation of
horses was so little that researchers have had great difficulty in
funding the Horse Genome
Project. The horse racing industry is not convinced of its
Racing is about competition - which is beating the other horse,
not necessarily winning world records. Thoroughbread racing is also
a lot about gambling, and that doesn't require record-breaking.
Eventually, the human 100 m sprint will get to that !
Mathematics of Logistic Equation
For there to be a performance limit, we need the Performance
P(t) function to reach a limit at some future time - with no
further change. The objective function is then:
dP/dt = 0 ...(1)
There clearly has to be a limit - even if it is the no-time-flat
value of Plimit(t®¥) = 0.
We don't know what sort of function to use for dP/dt. Let's
postulate that it might be some function of the current performance
level (so that we can use current performance to predict future
dP/dt = f(P) = 0 ...(2)
The Taylor series expansion of any function f(P) gives:
dP/dt = bP + dP2 + gP3 + .... ...(3)
Let's take to equation 3 with Occam's Razor. Using one term of
the taylor series expansion for f(P) gives an exponentially
increasing performance - and can't satisfy the objective (1) of
reaching a limit (except for the trivial case of b = 0, which implies no change at all)
Taking the first two terms of the taylor series expansion is the
simplest approximation to f(P) that will permit a non-trivial
solution to (1).
dP/dt = bP + dP2 ...(4)
Solving (2) and (4) gives
0 = Plimit ( b + dPlimit )
b + dPlimit= 0
Plimit = - b /d ...(5a)
Plimit >= 0
we would expect that b >= 0 and d <= 0 in equation (9).
The solution to the differential equation in (4) is given is
Summary: The logistic equation is the simplest
mathematical model that captures a process of change that reaches a
Applications of Logistic
The Solver feature of Microsoft Excel can be used to to fit data
to the solution to (4). Instructions for this can be found on
further discussion of the Logistic
Equation, which includes application to fitting Australia's
population growth and links to applications to airport growth
Airport Growth for Sydney Airports shows how well the logistic
model has predicted growth at Sydney's KSA airport (in comparison
with exponential estimates and experts' guesses).
An in depth discussion of modelling the growth of foot and mouth
disease with a logistic equation can be found here. For
application of logistic equations to the 2003 SARS epidemics in
Hong Kong, Singapore and Canada see Forecasting