Pop-up tents and tennis balls

tennis ball

A bent ring made from two loops of slinky looks very similar to the line on a tennis ball.

Have you ever noticed the wiggly line on a tennis ball? A group of Belgian scientists was researching buckling and folding of ring shapes. They noticed that many bent rings, from those in pop-up tents to broken bicycle wheels, had similar shapes. They all looked a bit like a line on a tennis ball.

The researchers devised an experiment to investigate these rings. They cut lengths off a slinky spring and joined the two ends together. If they used exactly one loop of the spring, then the result lay flat. When they took more than one loop, the shape twisted into interesting forms. Intrigued, the researchers used different materials such as wood and paper to check their results. They found the same shapes using big loops a metre across and tiny ones less than half a millimetre wide.

The researchers now had to describe the shapes they found. There were two important features they noticed. Firstly, the rings curved constantly along the entire length – there were no sharp corners. Secondly, they noticed that every shape they made could be drawn on the surface of a sphere. They did some reading and found that mathematicians had already described similar shapes and that their rings were made up of ‘Salkowski curves’.

The researchers found that they could predict the shape of any of their experiments using only one quantity: the number (including fractions) of extra loops of slinky or other material that were used. This simple formula has many uses. It will help people to manufacture folding systems, and could help with scientific research on micro-devices and particular DNA structures. As part of their research, the team found the best way to fold a pop-up tent and this research could lead to increasingly compact tents in the future!

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