One for the high jump

Now that we know London is to host the 2012 Olympic Games and plans for Beijing are presumably well under way, physicists in Brazil have plenty of time to anticipate an opportunity to test their latest theories about long run-ups and vertical take-offs in events such as the high jump and long jump.

Otaviano Helene of the University of Sao Paulo and Marcelo Takeshi Yamashita of the University Estadual Paulista, in Brazil have devised a simple model based on the maximum energy that an athlete can produce in a small time interval to help them work out why a long run-up is so important to an event that is essentially all about vertical lift – the high jump and how this differs from the mechanics of the long jump. The team exploited their fundamental understanding of the conservation of angular momentum to show why athletes should run horizontally to perform a vertical jump.

Marcelo Takeshi Yamashita

For activities lasting just a few tens of seconds, our bodies break down glycogen to release energy quickly, this is anaerobic, as opposed to aerobic, energy release. The process is modulated by the conversion of energy-rich adenosine triphosphate, ATP, into the diphosphate (ADP). Helene and Yamashita explain that while a high static force can be generated by muscle contraction, ultimately the force is limited by the rate at which muscle tissue can obtain energy, which in turn is limited by ATP depletion, which occurs in just a few seconds. The researchers further explain that for both high and long jumpers, the height of the runner’s centre of mass stays roughly constant until the last stride. At this point, their centre of mass rises about 25 cm before the athlete loses contact with the ground. On the basis of published force measurements on athletes’ legs, the team used the reasonable assumption that an 80 kg runner could produce 3000 N of force with each leg), so they could add about (3000−800)N – 0.25m or 550 Joules to their kinetic energy in the vertical take off.

When the researchers fitted data on run-up and results for the high jump into their model, they found that they could predict (retrospectively, of course) the bar heights overcome by past world record results. Yamashita confessed to Spotlight that the model may not have any real application yet in the stadium: Our study does not have a direct application to improve the performance of high jumpers, he says. It just gives some explanation about the movement using a relative simple model. Nevertheless, sports coaches, always on the look out for ways to fine tune their athlete’s performance might be able to use the model to develop yet more effective training plans and tactics for high jumpers to optimise their musculature for the run-up and the subsequent conversion of the athlete’s horizontal momentum into vertical take-off.

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