How hula hooping inspires robotics and energy efficiency

Hula hooping, often considered a playful pastime, raises intriguing scientific questions. What keeps a hula hoop up against gravity? Are some body types better for hula hooping than others?”

A team of mathematicians from New York University (NYU) sought answers to these questions, and uncovered findings that extend beyond hula hooping to potential engineering applications.

The study, published in the Proceedings of the National Academy of Sciences, is the first to investigate the physics and mathematics of hula hooping.

Study senior author Leif Ristroph is an associate professor at NYU’s Courant Institute of Mathematical Sciences.

“We were specifically interested in what kinds of body motions and shapes could successfully hold the hoop up and what physical requirements and restrictions are involved,” explained Ristroph.

Testing the physics of hula hooping

To investigate, the researchers created miniature robotic hula hoopers at NYU’s Applied Mathematics Laboratory.

Using 3D-printed shapes representing human forms – such as cylinders, cones, and hourglass shapes – the team tested gyrating motions that were powered by motors.

These shapes were scaled to one-tenth human size, and hoops of about six inches in diameter were set into motion. High-speed video captured the dynamics of the hoop movements.

The experiments revealed surprising results. The specific gyration motion or the body’s cross-sectional shape (e.g., circular or elliptical) didn’t significantly impact the hoop’s ability to twirl.

“In all cases, good twirling motions of the hoop around the body could be set up without any special effort,” Ristroph explained.

However, maintaining the hula hoop’s elevation against gravity required specific body features. A sloping surface, akin to hips, helped push the hoop upward, while a curvy waist provided stability.

Why some excel at hula hooping

The findings shed light on why some individuals naturally excel at hula hooping while others struggle.

“People come in many different body types – some who have these slope and curvature traits in their hips and waist and some who don’t,” noted Ristroph. “Our results might explain why some people are natural hoopers and others seem to have to work extra hard.”

This insight ties body mechanics to hula hooping ability, and offers a mathematical explanation for what many have observed anecdotally.

Practical applications of the research

The study went beyond analyzing the mechanics of hula hooping by creating mathematical models that captured the dynamics of the activity.

These models provided formulas to explain how motion, body shape, and forces interact to keep the hoop in motion. While they were developed to understand hula hooping, these equations have practical applications in other fields, particularly in engineering and industrial design.

“We were surprised that an activity as popular, fun, and healthy as hula hooping wasn’t understood even at a basic physics level,” said Ristroph.

“As we made progress on the research, we realized that the math and physics involved are very subtle, and the knowledge gained could be useful in inspiring engineering innovations, harvesting energy from vibrations, and improving in robotic positioners and movers used in industrial processing and manufacturing.”

From hula hoops to high-tech

The study initially aimed to explore the seemingly straightforward mechanics of hula hooping. However, it uncovered principles that have significant applications beyond the activity itself.

By analyzing how energy transfers and movements keep the hoop in motion, researchers identified ways to harness similar energy from vibrations. These insights could optimize energy usage in various devices.

Moreover, the findings offer potential improvements in robotic designs, particularly in enhancing the precision and efficiency of robotic movers and positioners used in manufacturing and industrial processes. This means that understanding hula hooping could help develop more effective machines and systems.

In essence, the research shows how studying a playful activity like hula hooping can lead to advances in science and technology. It demonstrates how fundamental physics can drive innovative solutions in unexpected areas, and bridge the gap between recreation and engineering progress.

The research was a collaborative effort by Ristroph, NYU doctoral student Olivia Pomerenk, and former undergraduate student Xintong Zhu.

The study is published in the journal Proceedings of the National Academy of Sciences.

Video Credit: NYU’s Applied Mathematics Lab

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