Physics confirms the best way to make a playground swing go higher

Whether the back-and-forth arc of a playground swing becomes bigger over time depends on how the person sitting on it moves against the swing – a phenomenon many children seem to understand intuitively. Now, physicists have determined exactly when you should lean back while riding a swing to make it go higher.

“Children don’t know the laws of physics, but they somehow embody them nevertheless and swing very well,” says Chiaki Hirata at Jumonji University in Japan. He and his colleagues used the laws of physics and observations of swingers to determine some rules for how to make a swing go higher.

The researchers worked out equations for the swing’s motion that accounted for the person on it being able to lean backwards or forwards at any point in the swing’s arc. They then solved these equations for different sizes of swings and various sequences of the person’s upper body motions, and determined which combination made the swing gain the most altitude from one back-and-forth oscillation to the next.

The researchers found that the best time to lean back depends on how high the swing is going already. When the arc is small, as it is when you first start swinging, the person should move their upper body backwards when the swing is at the bottom of the arc and moving forward. After doing this a few times, the swing will start gaining height and the person should start leaning back earlier, when the swing is at the furthest part of the backswing.

Hirata and his colleagues then wanted to see how their model stacked up against real-world playground swinging, so they built a swing in the lab and recruited 10 college students to try it. All of them said they had played on swings before but were never explicitly taught how to move to get the swing to go higher.

The researchers attached a total of 10 special markers to both the swing and the participant, and then recorded their swinging with a camera for about a minute at a time. When they analysed the footage, the researchers saw that what the students were doing matched the rules derived from their mathematical model.

Hirata says that this agreement leads to more questions. “How do the swingers shift their body so well? It is hard to believe that they are moving intentionally because they must adjust their body as quickly as in 10 milliseconds,” he says.

The researchers’ current hypothesis is that swingers are subconsciously reacting to some centrifugal-like force that is pushing them back. They want to test this idea by having students use a playground swing in virtual reality where those forces may not exist.