Shoelace Study Unravels A Knotty Problem

How knot-failure happens in seconds (University of California at Berkeley/PA)

You could call it shoe string theory – scientists have finally solved the knotty problem of unravelling laces.

A pair of football boots (Richard Sellers/PA)

Press Association report continues:

Why and how firmly tied shoe laces free themselves has been a maddening mystery ever since humans first donned footwear.

Now experts have the answer. Their research suggests that a blend of two forces act like an invisible hand, first loosening the knot and then tugging until the laces trail on the ground and your securely held shoe becomes a wobbly slipper.

Using a slow-motion camera, scientists revealed how knot-failure happens in seconds, triggered by a complex interaction of forces.

Lead researcher Christopher Daily-Diamond, from the University of California at Berkeley, said: “When you talk about knotted structures, if you can start to understand the shoelace, then you can apply it to other things, like DNA or microstructures, that fail under dynamic forces.

“This is the first step toward understanding why certain knots are better than others, which no one has really done.”

The study began with co-author and graduate student Christine Gregg lacing up a pair of running shoes and jogging on a treadmill while a colleague filmed what happened next.

This is what was discovered. When running, your foot strikes the ground at seven times the force of gravity. Responding to that force, the knot stretches and then relaxes.

As the knot loosens, the swinging leg applies an inertial force on the free ends of the laces, leading to rapid unravelling in as little as two strides.

Ms Gregg said: “To untie my knots, I pull on the free end of a bow tie and it comes undone.

“The shoelace knot comes untied due to the same sort of motion. The forces that cause this are not from a person pulling on the free end but from the inertial forces of the leg swinging back and forth while the knot is loosened from the shoe repeatedly striking the ground.”

The findings, published in the journal Proceedings of the Royal Society A, revealed a high level of acceleration at the base of the knot.

To find out more, the scientists used an impacting pendulum to swing a shoelace knot and conducted tests with a variety of different laces.

While some laces might be better than others for tying knots, they all suffered from the same fundamental cause of knot failure, the study found.

Adding weights to the loose ends of a swinging knot showed that laces untied themselves more frequently as the inertial forces on their ends increased.

“You really need both the impulsive force at the base of the knot and you need the pulling forces of the free ends and the loops,” Mr Daily-Diamond explained. “You can’t seem to get knot failure without both.”

Ms Gregg added: “The interesting thing about this mechanism is that your laces can be fine for a really long time and it’s not until you get one little bit of motion to cause loosening that starts this avalanche effect leading to knot failure.”