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Physics Demonstrates How to Maximize Swing Height on a Playground

This setup in the lab helped researchers track motion using markers attached to the swinger and the swing

Chiaki Hirata et al./APS 2023

The back-and-forth motion of a playground swing can become bigger over time if the person sitting on it moves in a certain way. This phenomenon, often understood intuitively by many children, has now been explored by physicists who have determined the ideal technique to make a swing go higher.

According to Chiaki Hirata, a researcher at Jumonji University in Japan, children seem to naturally embody the laws of physics when swinging, even though they may not fully understand them. Inspired by this observation, Hirata and his colleagues used physics principles to uncover the rules for maximizing swing height.

The researchers developed equations that described the motion of the swing, taking into account the ability of the person on the swing to lean forward or backward at any point in the swing’s arc. By solving these equations for various swing sizes and sequences of upper body movements, they were able to determine the combination that allowed the swing to gain the most altitude from one oscillation to the next.

The study revealed that the optimal time to lean back on the swing depends on its current height. When the swing’s arc is small, such as at the beginning of swinging, it is ideal to lean back when the swing is at the bottom of the arc and moving forward. As the swing gains height, the person should start leaning back earlier, when the swing is at the furthest point of its backswing.

To examine the real-world application of their findings, Hirata and his team built a swing in the lab and had 10 college students try it out. These students had previous experience with swings but were not taught the specific techniques for maximizing swing height. Using markers attached to both the swing and the participants, the researchers recorded the swinging movements and analyzed the footage.

The analysis showed that the students’ swinging motions aligned with the rules derived from the researchers’ mathematical model, confirming the validity of their findings.

Hirata is fascinated by how well individuals instinctively adjust their bodies while swinging. He believes that swingers may subconsciously respond to a centrifugal-like force pushing them backward. To test this hypothesis, the researchers plan to have students use a virtual reality swing where such forces can be manipulated.

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