The tricky problem of why shoelaces become undone has been solved by scientists.
Walking along and then suddenly having that horrible feeling of footwear becoming loose has frustrated humans for thousands of years.
It occurs without warning – and a study now reveals the series of events that make it happen.
A double whammy of footfall and whipping forces acts like an ‘invisible hand’, loosening the knot and then tugging on the free ends of your laces until the whole thing unravels.
Using slow motion video footage and a series of experiments, researchers showed the failure happens in a matter of seconds, often without warning, and can be catastrophic.
The breakthrough goes beyond explaining a seemingly obvious problem, providing a better understanding of how knotted structures, even including DNA, fall apart.
It is a question that everyone asks, often after stopping to retie their shoes, yet one that nobody had investigated, until now.
Mechanical engineer Christopher Daily-Diamond, of 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 showed repeated impact of the shoe on the floor first serves to loosen the knot.
Then the leg swing makes the end of the laces go into a whipping motion, causing them to slip. This leads to eventual runaway untangling.
The study said there are two ways to tie the common shoelace bow tie knot, and one is stronger than the other, but no one knows why.
The strong version is based on a square knot, two lace crossings of opposite handedness on top of each other. The weak one has the same handedness, causing the knot to twist instead of lying flat when tightened.
But both fail in the same way, according to the findings published in Proceedings of the Royal Society A .
Prof Oliver O’Reilly, whose lab conducted the research, said: “We are trying to understand knots from a mechanics perspective, such as why you can take two strands and connect them in a certain way that can be very strong, but another way of connecting them is very weak.
“We were able to show the weak knot will always fail and the strong knot will fail at a certain time scale, but we still do not understand why there is a fundamental mechanical difference between those two knots.”
The researchers first recorded the process of knotted laces untying in slow motion by filming runner Christine Gregg on a treadmill while her colleagues filmed her shoes.
It showed when running the foot strikes the ground at seven times the force of gravity, causing the knot to stretch and then relax in response.
As it loosens, the swinging leg applies an inertial force on the free ends of the laces, which rapidly leads to a failure of the knot in as few as two strides.
Graduate student 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.”
Ms Gregg said: “Some laces might be better than others for tying knots, but the fundamental mechanics causing them to fail is the same, we believe.”
The researchers also tested their theory that increasing inertial forces on the free ends would trigger runaway failure of the knot.
When they added weights on swinging knots they failed at higher rates as the inertial forces on the free ends increased.
Mr Daily-Diamond, also a graduate student, explained: “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. You can’t seem to get knot failure without both.”
Of course, when a person goes walking or running, their shoelaces don’t always come untied.
Tightly tied laces can require more cycles of impact and leg swinging to fail than one may experience in a day’s worth of walking or running. More research is needed to tease apart all the variables involved in the process.
But the study does offers an answer to the annoying question of why your laces seem fine one minute and then come untied the next.
Added Ms Gregg: “The interesting thing about this mechanism is your laces can be fine for a really long time, and it is not until you get one little bit of motion to cause loosening that starts this avalanche effect leading to knot failure.”
