Counting Swing Cycles

par Eva

A curious thing about the physics of a swing is that the amount of time it takes to swing a full cycle is independent of your mass or of how high you are swinging. People can synchronize and get melodic rewards ♫♫ on our swings, even if one person swings dangerously high and the other timidly low. Their swing cycle times are theoretically the same because a swing acts as a simple pendulum – a mass attached to a pivot – and all you need to calculate a pendulum’s cycle time is the length of the pendulum and the local acceleration of gravity.

Every single swing from The Swings, which were recently presented in high altitude Colorado, have a distance of 255 cm (100 inches) between the structure’s pivot point and the center of the swings’ seat. The Simple Pendulum Calculator estimates that a swing period here is 3.2 seconds long. The animated GIF below shows 3.2 seconds of a video of The Swings, which demonstrates that the math might just be right.

A looped full swing cycle

So that’s 3.2 seconds to make a swing move completely back ♪ and forth ♪. Interpolated, that’s 19 potential cycles per minute, 1,123 cycles per hour, and 13,478 cycles per 12-hour day. But those stats are all based on theoretical physics. In real life, the cycle time is obviously also affected by friction, air drag, and however much you push, move, or fidget on your swing. (Interesting side fact: The 21 Balançoires in Montréal are shorter and therefore have a shorter cycle time of about 2.7 seconds.)

To get a better understanding of how much and at what times people used the swings, we incorporated a simple logging procedure into the installation’s software (using the SQLite object in Max/MSP). For each swing, we counted the number of cycles completed every hour. Here are the results for Colorado:

Duration 21 days (June 23-July 13)

Open hours 12 hours (9am to 9pm)
Total measured cycles 1,919,066 cycles
Average Cycles per Swing 191,907 cycles
Average Cycles per Swing per Day 9,138 cycles
Average Cycles per Swing per Hour 761 cycles

When comparing the average cycle count to the maximum possible cycle count, we can then know that the swings were in use 68% of the time. (Contrary to early call-outs of 75%. We blame our quick math.)

Amazingly, that’s an incredibly high usage count. We love it that the locals and visitors of the Green Box Arts Festival kept our swings so busy. And the only reason we can think of for not having reached higher usage, is the rain:

Swing Cycles and rainfall in Colorado

[graph done with Google Spreadsheets, precipitation values via]