Two Spanish scientists have designed an equation that provides a highly accurate estimate of an individual's speed based on stride length.
They used data from professional athletes and walking and
running experiments on a beach in order to come up with the equation. The
result has applications in the study of fossil track ways of human footprints.
In the spring of 2008, 14 palaeontology students from the
Complutense University of Madrid ran along a beach in Asturias (Spain) at the
request of a planetary geologist who was a friend of their fieldwork director.
Javier Ruiz, from the Complutense University of Madrid (Spain), and his
colleague Angélica Torices, from the University of Alberta (Canada), just out
of curiosity, wanted to check how accurately an individual's speed could be
calculated based on their tracks.
The results, published in 2013 in the journal 'Ichnos', show that, without needing any
other data such as leg length, they were able to achieve quite a high degree of
accuracy, with a margin of error of 10 to 15%.
"For humans, we are able to calculate speed based on
stride length alone with a very good degree of accuracy," Javier Ruiz told
How the study was
The authors applied their formula to estimate the speed at
which the humans were travelling who left the Pleistocene era fossil track ways
found in the Willandra Lakes Region of Australia.
"A previous study had made a very elaborate calculation
of their speed but the results were as high as if they had been professional
athletes" Ruiz explained. His results show a reasonable sprint pace.
In order to come up with their equation, Ruiz and Torices
compared the data obtained in the experiments with the students with data from
professional athletes who compete in 100 and 400-metre races.
Up to now, the individual's leg length or at least an
estimate of the length was required to calculate speed based on tracks. An
equation formulated by the British zoologist Robert McNeil Alexander in 1976
was used which he based solely on data obtained from his children running.
Ruiz and Torices measured the speed and stride length of the
students as they ran along the beach and applied Alexander's equation.
"The data fit with the equation very well", Ruiz explained,
"Alexander did a good job with very little statistical data but with a
large mathematical basis and we have seen empirically that his equation is
The speed of elite
In the case of the athletes, the researchers had data on
speed and stride length but not limb length, which led Ruiz to modify the
equation so that this piece of data was not needed. "There was a very good
degree of accuracy with the new equation with a 15% margin of error, even
better than the equation that was generally used whose margin of error was
In addition, the calculation works perfectly well both
whether the individuals are running or walking and this was very surprising
according to Ruiz. "There is a little more variability in running but even
so it works very well."
Despite that fact that the speed calculation is very
accurate, Ruiz admits that it cannot be applied in an absolute and unequivocal
manner but rather statistically. "Strangely, sometimes 400 and 100-metre
athletes have the same stride length but run at different speeds. What the body
does is try to optimise how energy is used at a given speed."