Hula hooping is a well-known activity, but it prompts fascinating questions like, “What allows a hula hoop to defy gravity?” and “Do certain body types excel at hula hooping?” A group of mathematicians has examined these queries, leading to discoveries that could enhance energy utilization and improve robotic positioning systems.
Hula hooping is a well-known activity, but it prompts fascinating questions like, “What allows a hula hoop to defy gravity?” and “Do certain body types excel at hula hooping?” A group of mathematicians has examined these queries, leading to discoveries that could enhance energy utilization and improve robotic positioning systems.
These findings represent the first comprehensive analysis of the physics and mathematics behind hula hooping.
“Our interest focused on the types of body movements and shapes that can effectively maintain the hoop’s elevation, as well as the physical demands and limitations involved,” says Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and the primary author of the research published in the Proceedings of the National Academy of Sciences.
To delve into these questions, the team created miniaturized hula hooping simulations in NYU’s Applied Mathematics Laboratory. They explored various shapes and motions through experiments involving robotic hula hoopers outfitted with 3D-printed forms representing human shapes at one-tenth their size (like cylinders, cones, and hourglass figures). These robotic forms were made to spin using a motor, mimicking the movements of an actual hula hooper. Hoops measuring around 6 inches in diameter were set into motion on these bodies, with high-speed cameras recording the action.
The findings revealed that neither the specific gyration pattern nor the body’s cross-sectional shape (circular or elliptical) significantly influenced the effectiveness of hula hooping.
“In every instance, effective twirling motions could be achieved without any particular effort,” Ristroph notes.
Nonetheless, maintaining a hoop in an elevated position against gravity for an extended period proved more challenging and demanded a specific “body type,” characterized by a sloping surface for the “hips” to create the correct angle to elevate the hoop, along with a curvy “waist” to secure the hoop in place.
“Humans exhibit a variety of body types; some possess the sloping and curvy features necessary for hooping, while others may not,” Ristroph explains. “Our findings could clarify why some individuals excel at hula hooping naturally, while others may find it more difficult.”
The authors employed mathematical modeling to develop formulas illustrating these dynamics, which may have applications in various fields.
“We were astonished that such a widespread, enjoyable, and healthful activity like hula hooping was not thoroughly understood from a physics perspective,” Ristroph remarks. “As our research advanced, we discovered that the mathematics and physics involved were quite intricate, and the insights gained could be pivotal in driving engineering innovations, capturing energy from vibrations, and enhancing robotic positioners and transporters used in manufacturing and industrial processes.”
The other contributors to the paper are Olivia Pomerenk, a doctoral student at NYU, and Xintong Zhu, an undergraduate at the time of the research.
This project was funded by a National Science Foundation grant (DMS-1847955).
