# Equation Determines A Person’s Speed Based On Footprints

Lee Rannals for redOrbit.com — Your Universe Online

Scientists have developed an equation that is able to estimate an individual's speed based on their footprints.

Two Spanish scientists, writing in the journal Ichnos, said they used data from professional athletes and walking and running experiments in order to develop the equation.

The team asked 14 paleontology students from the Complutense University of Madrid to run along a beach in Asturias. The scientists wanted to check how accurately an individual's speed could be calculated based on their tracks. The researchers found they could achieve an accuracy with just a ten to 15 percent margin of error.

"For humans, we are able to calculate speed based on stride length alone with a very good degree of accuracy," said Javier Ruiz, from the Complutense University of Madrid.

Ruiz and his colleague AngÃ©lica Torices from the University of Alberta applied their formula to estimate the speed at which the humans were traveling when they left the Pleistocene era fossil trackways found in the Willandra Lakes Region of Australia. This region contains hundreds of human footprints dating back to 20,000 years ago. Scientists say they were left by adults, teenagers and children walking or running across moist clay flats near Willandra Lakes.

"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.

The two compared the data obtained in the student experiments with data from professional athletes who compete in 100- and 400-meter races.  They measured the speed and stride length of the students as they ran along the beach and applied an equation developed by the British zoologist Robert McNeil Alexander in 1976. Alexander's equation was based solely on data obtained from children running.

"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 correct."

The researchers had data on speed and stride length but not limb length, so Ruiz modified the equation so this variable was not needed.

"There was a very good degree of accuracy with the new equation with a 15 percent margin of error, even better than the equation that was generally used whose margin of error was 50 percent," Ruiz said.

He said the calculation works well whether the individuals are running or walking. However Ruiz also said the equation cannot be applied in an absolute and unequivocal manner.

"Strangely, sometimes 400- and 100-meter athletes have the same stride length but run at different speeds. What the body does is try to optimize how energy is used at a given speed," he said.