How Math Helps Skateboarders Shred on the Half-Pipe

By Mark Miller

Professional and accomplished amateur skateboarders do amazing tricks on half-pipes, grabbing massive air and performing spins and other maneuvers. But how do they build up enough speed and height to pull off these moves? They use a technique called “pumping”—lowering and raising their bodies as they roll back and forth. A Science News Explores article, “Math reveals how skateboarders can ramp up their half-pipe power,” explains how researchers used mathematical equations to show skaters how they could pump more efficiently.

A Theoretical Approach

According to the article, mathematician Florian Kogelbauer of ETH Zurich in Switzerland and his fellow researchers used a theoretical study to examine how skateboarders gain speed and height on the half-pipe. This type of study translates real-world phenomena into equations, solves those equations, then compares the answers with reality.

The team used the basic motion of somebody riding a swing and modified the equations associated with swinging to fit a skateboarding scenario. The modified equations helped them build a mathematical model that showed a relationship between how a skater changed their body position and how high they could go on the half-pipe. Based on the model, the key to effective pumping is to crouch low when descending, move to a standing position as the pipe flattens out, then crouch low and stand again as you approach the transition and ascend the other side.

Back to Reality

To review the output from the model, the team enlisted two skateboarders—one more experienced than the other. They asked each to reach a certain height on the ramp as fast as they could. The more experienced rider pumped the way the mathematical model suggested and outpaced the less-experienced rider, whose body position didn’t align well with the model.

To Kogelbauer, this meant that the model accurately found a more optimized way for skaters to improve their pumping efficiency. To be a better half-pipe rider, “try to crouch and stand just as the model shows,” he said in Science News Explores.

Ramps to Robots

The research carried out by Kogelbauer and team may have ramifications beyond the ramp. “Discover How Math Helps Skateboarders Optimise Half-Pipe Speed and Height,” an article published in Gadgets 360, reports that the type of model used in the skateboard study could also be applied to making robots more efficient. According to Sorina Lupu, an engineer at the California Institute of Technology, the research shows that the straightforward models used in the skateboard study may provide alternatives to more complex machine-learning models commonly applied to robotics.