“Gravity Defied: The Surprising Influence of Body Shape in Hula Hooping Mastery”

Hula hooping is so ordinary that we might neglect some intriguing inquiries it prompts: “What allows a hula hoop to defy gravity?” and “Are certain body types more beneficial for hula hooping than others?” A group of mathematicians investigated and responded to these inquiries, yielding findings that may also reveal new methods to optimize energy use and enhance robotic positioners.

The findings offer the first account of the physics and mathematics involved in hula hooping.

“We were particularly keen on understanding which types of body motions and shapes could successfully sustain the hoop and what physical prerequisites and limitations are present,” shares Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and the lead author of the study, published in the Proceedings of the National Academy of Sciences.

To address these inquiries, the researchers recreated, on a smaller scale, the act of hula hooping at NYU’s Applied Mathematics Laboratory. They examined various shapes and movements through a series of experiments involving robotic hula hoopers, utilizing 3D-printed body forms of different geometries (e.g., cylinders, cones, hourglass shapes) to model human profiles at one-tenth scale.

These forms were activated to rotate by means of a motor, emulating the actions we perform while hula hooping. Hoops approximately 6 inches in diameter were propelled on these models, with high-speed footage documenting the activities.

The findings indicated that the specific nature of the gyration motion or the cross-sectional shape of the body (circular versus elliptical) wasn’t a determinant in successful hula hooping outcomes.

“In all instances, effective twirling motions around the body were easily established without significant effort,” Ristroph clarifies.

Nonetheless, maintaining a hoop elevated against gravity for an extended duration proved to be more challenging, necessitating a particular “body type”—one featuring a slanted surface as “hips” that facilitates the correct angle for lifting the hoop, alongside a curvy contour as a “waist” to stabilize the hoop.

“Individuals possess a variety of body types—some featuring sloped and curved characteristics in their hips and waist, while others lack these traits,” Ristroph observes. “Our findings could clarify why certain individuals excel at hooping naturally, whereas others appear to exert considerable effort.”

The authors of the paper performed mathematical modeling of these dynamics to formulate equations that elucidated the findings—calculations that could be applicable for various purposes.

“We

“We were amazed that an activity as well-liked, enjoyable, and beneficial as hula hooping wasn’t comprehended even at a fundamental physics level,” states Ristroph.

“As we advanced in our research, we came to the realization that the mathematics and physics involved are quite intricate, and the insights gained could prove beneficial in motivating engineering advancements, capturing energy from vibrations, and enhancing robotic positioners and movers employed in industrial processing and manufacturing.”

The additional authors of the paper included Olivia Pomerenk, a doctoral candidate at NYU, and Xintong Zhu, an undergraduate at NYU during the course of the study.