Surf plus a mathematician equals formula for perfection

The teenagers who catch the waves at Bondi every morning would almost certainly not approve, but a surf-mad mathematician is trying to use algebraic calculations to unlock the secrets of their sport.

Neville de Mestre, a professor at Bond University in Queensland, believes body-surfers who propel themselves towards shore on broken waves can perfect their technique by employing formulae related to fluid mechanics, turbulence and drag.

Professor de Mestre, who claims to use mathematics to give himself the edge at surf competitions, intends to reduce the sport to half a dozen definitive equations. He says that will take him five to 10 years.

"We know a lot about the art of surfing, but not the science," he said. "Mathematics can give us insights into the science of waves as they affect a body trying to ride them."

Body-surfing has been popular since at least the 18th century, when Captain Cook witnessed it with astonishment in Hawaii. Now world body-surfing competitions are set in the US and Hawaii. The sport is also popular in Australia, but Professor de Mestre, who lives and works near Surfers Paradise, believes more people should experience its peculiar thrill.

Among the questions exercising him are why body-surfers ride waves on their fronts, never on their backs, and rarely feet first. "Why shouldn't a body be able to go feet forward if it can go head forward?" he asked. "Why can we swim no faster than two metres a second? It's about power and weight ratio, about the drag on a body going through water."

The professor, a fit 65-year-old who has won international contests, knows of no other mathematicians who share his passion. "There are so few scientists who surf," he said. Five to 10 years seems a long time, but it is a complex science, he said.

"People have been studying coastal engineering for decades, and they're still trying to understand what happens when waves meet the shore." Professor de Mestre has conducted experiments with subjects including logs, Barbie dolls and "flexible humans", and has already published a preliminary paper.

In it, he notes that "water particles, beneath and on the surface of a passing deep-water wave, travel in circular orbits as the wave train passes, but for the deeper particles these circular orbits have smaller and smaller radii until the movement is essentially negligible when the depth exceeds half the wave length".

When competing, he devises a strategy while sitting on the beach. "I watch the frequency of waves coming in, to see when there might be a lull that gives me a better chance of getting out to sea. I decide on a route and ignore everyone else.

"Coming back, I put myself in the best position to catch a wave. I haven't got a slide-rule out there, but mathematics definitely helps." Testing his theories is no problem. Professor de Mestre surfs every lunchtime, between lectures. "Have you got any more questions?" he asked. "Because I need to get to the beach."

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