Hula hooping may be literal child's play, but as it turns out, the physics behind the gym-class staple is so complicated that scientists have spent decades trying to understand how the hula hoop defies gravity.
Multiple scientific papers have been devoted to this minor mystery: How do one's hips and legs collude with friction and centrifugal forces to keep a simple toy spinning in midair? The still-unresolved question led a team of UC Berkeley-affiliated engineers to tackle the problem by using an innovative method to analyze motion-tracking data.
Their results, recently published in the journal Nonlinear Dynamics, challenge 20 years of conventional wisdom about hula hooping - and suggest a better way to model complex mechanical systems like the hula hoop's twirl, which could be useful in fields like physical rehabilitation and robotics.
Previous studies had concluded that two distinct sets of movements, one back-and-forth and the other a vertical bounce, separately controlled the hoop's orbit around the body and its up-down wobble. To reach these findings, these studies used a mathematical method called principal component analysis to distill a vast quantity of data into its clearest patterns. But the Berkeley team's analysis revealed that the orbit and wobble were inextricably connected - they couldn't be divided into two clean categories because one set of movements impacted the other.
UC Berkeley
Led by Oliver O'Reilly, a professor of mechanical engineering and vice provost for undergraduate education, the Berkeley researchers initially intended to build on previous studies by tracking the motion of the hoop itself with a specialized sensor that gathered 120 snapshots a second of rotational velocity, acceleration, gravitational force and magnetic fields. When a principal component analysis of the additional data they'd gathered led them to starkly different findings than past teams, they changed tacks and employed a non-linear mathematical method to process their data, which revealed that the thigh, shin and feet bones work together to keep the hoop circling, while thigh movement is responsible for the toy's vertical wobble. Unlike previous studies, they showed that the hoop's rotation and wobble were fundamentally linked.
Upending the physics of hula hooping wasn't the study's primary goal. O'Reilly - who has previously dissected the physics of how shoelaces become untied and Star Wars' spherical droid BB-8 rolls - started by trying to pinpoint which body motions were essential for hula hooping. His collaborators, structural engineering postdoctoral researcher Chrystal Chern and recent Berkeley Ph.D. Theresa Honein, now an assistant professor at the American University of Beirut, devised a way to rig high-tech sensors, the kind Chern normally used to track how model buildings would react to simulated earthquakes, to the hoop, right leg and foot. (The hips didn't get tracked, since the sensor would have hit the hoop.) Then Chern, an erstwhile gymnast, hooped as the sensors gathered a massive trove of data.
When they tried to replicate others' results with their data, the researchers found that the numbers didn't add up. Those previous studies had used principal component analysis, which relies on linear math - in which the relationships among variables are driven by addition and subtraction, and when mapped, become straight lines - to distill a morass of data into the strongest and most consistent patterns.
"We were really surprised," said O'Reilly. "The dominant results…show that the motion of the body did not influence the hula hoop at all and vice versa." But logically, that couldn't be the case.
They checked their work repeatedly and realized it would make sense to try an approach called functional network analysis. This technique is based in nonlinear math, or the kind of math behind curved lines such as quadratics and exponential equations. Building on a fairly new method Honein had learned about from a researcher at Hamburg University of Technology, they analyzed the data once more. This time, the results made sense.
Courtesy of Oliver O'Reilly
They determined that the hula hoop's orbit around Chern's waist was a joint project of the femur, or thigh bone; tibia, or shin bone; and the metatarsals, or the long bones of the mid-foot. The femur and tibia twisted like faucet knobs, the tibia moved up and down as she bent and straightened her legs, and her metatarsals shifted as she rocked her weight from the inner to outer edge of her foot. The crucial role that the ankle and foot played surprised the researchers, O'Reilly said.
When hula hooping, the hoop doesn't stay perfectly parallel to the floor but tilts up and down; Chern's thigh bones were influencing that wobble as they rotated in their sockets. Because you can't move the femur like this without also twisting the tibia, you can't separate the actions that account for the hoop's rotation from those that drive its wobble.
While it centers on a 1950s toy, the research's implications are far from trivial. The findings could lead to better models of how people take steps with the aid of a walker, for example, which would help physical therapists focus on rehabilitating the most essential movements. This kind of motion analysis could also prove useful in prosthetic design or robotics, Honein added.
O'Reilly confessed to feeling a bit disappointed their project was over; bringing a hula hoop to work and drilling down on the complex math that made it whirl had been genuinely fun. O'Reilly's officemates had even picked up on a "spirit and spark" in the air of California Hall when the trio was meeting.
"This was just a wonderful collaboration that started out with curiosity and became far more interesting than we ever imagined," he said.
