How Berkeley researchers decoded the loopy physics of hula hooping.

A team of UC Berkeley-affiliated engineers has reported that the leg movements that keep a hula hoop circling and the ones that make it wobble cannot be separated. Their results, published in the journal Nonlinear Dynamics, challenge about 20 years of conventional wisdom, according to the university.

Earlier 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-and-down wobble. Those studies used principal component analysis, a mathematical method that relies on linear math to distill large amounts of data into clear patterns.

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The Berkeley team was led by Oliver O'Reilly, a professor of mechanical engineering and vice provost for undergraduate education. With collaborators Chrystal Chern, a structural engineering postdoctoral researcher, and Theresa Honein, a recent Berkeley Ph.D. now at the American University of Beirut, he set out to pinpoint which body motions are essential to hula hooping. They attached sensors, of the kind Chern normally used to study how model buildings react to simulated earthquakes, to the hoop, her right leg and her foot. The sensor on the hoop recorded 120 snapshots a second, and Chern hooped while the data were gathered.

When the team ran a principal component analysis on its data, the results did not match earlier work. "We were really surprised," O'Reilly said. They then turned to functional network analysis, a nonlinear method Honein had learned about from a researcher at Hamburg University of Technology.

That analysis indicated that the thigh bone, shin bone and the long bones of the mid-foot work together to keep the hoop circling. The thigh and shin twisted, the shin moved up and down as the legs bent and straightened, and the foot bones shifted as weight rocked from the inner to the outer edge of the foot. Thigh rotation was responsible for the wobble. Because the femur cannot rotate without twisting the tibia, the researchers concluded the two kinds of motion are fundamentally linked. The role of the ankle and foot surprised them, O'Reilly said. The hips were not tracked because a sensor there would have hit the hoop.

The researchers suggest the approach could improve models of complex mechanical systems. Examples they cite include how people walk with a walker, which could help physical therapists focus on the most essential movements, as well as prosthetic design and robotics.