It's a pretty regular part of day-to-day life to have to stop and retie pesky shoelaces that have unraveled. But surprisingly, there has been no good science explaining why this mildly frustrating scenario repeatedly occurs. A team of graduate students at UC Berkeley set out to solve this everyday mystery and their results shed light on the mysterious mechanics of knots.

The goal of the mechanical engineers was to describe how a shoelace knot comes untied under the dynamic forces of everyday walking or running. It was initially observed that the swinging action of a leg was not enough to cause a knot to fail, and stomping ones' foot on the ground also didn't result in a shoelace untying. It turns out the interplay between the swing and stance phases involved in walking or running is what causes knot failure.

Observing slow-motion footage of a runner on a treadmill allowed the researchers to examine in detail the dynamic movements that led to a shoelace coming untied. It was discovered that as your foot hits the ground when running, the knot stretches and relaxes in response to that force. This action causes the knot to loosen and then the following swinging action creates an inertial force that pulls the laces in a way similar to how you would pull the free ends when intentionally untying a lace.

"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," explains co-author of the study Christopher Daily-Diamond. "You can't seem to get knot failure without both."

The research looked at the two common ways to tie a shoelace bow knot, and discovered that despite one knot being mildly stronger than the other, both versions did ultimately fail in the same way. It was also noted that despite some alternate lace materials holding stronger for longer, they still eventually failed due to the same mechanism.

"Some laces might be better than others for tying knots, but the fundamental mechanics causing them to fail is the same, we believe," co-author Christine Gregg added.

The most interesting part of the research showed that once loosening had been initially activated in the lace, knot failure was sudden and catastrophic. The study noted that more research is needed to further understand the variables involved in the process, but it does explain how your laces can be fine one moment and then completely untied just a few steps later.

"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," Gregg says.

Apart from simply developing an understanding of the mechanics behind this universal frustration, the research could point towards uses and applications beyond simply making a better shoelace.

"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," said Daily-Diamond.

If there is one objectively positive thing to come of this research, it is that we can now see a day in the future where the old "your shoelace is untied" joke will be a thing of the past.

The team's study was published in the journal Proceedings of the Royal Society A.

Take a closer look at the slow motion footage of a shoelace coming untied in the video below.

Source: UC Berkley