A new study hints at how skateboarders can up their half-pipe game — using math.
Tricks like kickflips and ollies require speed. As skateboarders roll along a U-shaped ramp called a half-pipe, they build speed and climb higher by pumping. To pump, they alternate between crouching and standing.
Pumping on a half-pipe is a lot like pumping on a swing, says Florian Kogelbauer. A mathematician, he works at ETH Zurich in Switzerland. On a swing, you stretch your legs while leaning backward and bend your knees while leaning forward. This motion changes how your body mass is distributed. Syncing your pumps with the back-and-forth motion of swinging gives you an energy boost that makes you go higher. This increases your potential energy. Pumping on a half-pipe does something similar for skateboarders.
Where should skateboarders change positions to get the biggest boost? Some say it’s about practice and feeling the rhythm. Kogelbauer and his colleagues instead turned to math.
They used a theoretical study. In this type, you first take a real-world problem and translate it into equations, Kogelbauer says. Then you solve these math problems and translate the answer back to the real world.
The researchers started with the equations for a simple case: a rider going back and forth on a swing. Most aspects of swinging are well understood: the forces at play, the motion and the energy involved. The scientists then modified these equations to better match the skateboard scenario. They used them to create a mathematical model. How far up the ramp a skater can go depends on how their body position changes along the half-pipe. This model captured that relationship.
Then they programmed their simple model into a computer. They added real-world details. These included things such as the size of the half-pipe and that of the skateboarder. Then this computer model calculated the…
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