SAN FRANCISCO, April 15 -- A new study shows why your shoelaces may keep coming untied. It suggests that a double whammy of stomping 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 a slow-motion camera and a series of experiments, the study by mechanical engineers at the University of California, Berkeley, and published this week in the journal Proceedings of the Royal Society A shows that shoelace knot failure happens in a matter of seconds, triggered by a complex interaction of forces.
"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 Christopher Daily-Diamond, study co-author and a graduate student at Berkeley.
"This is the first step toward understanding why certain knots are better than others."
There are two ways to tie the common shoelace bow tie knot, and one is stronger than the other.
The strong version of the knot is based on a square knot: two lace crossings of opposite handedness on top of each other. The weak version is based on a false knot; the two lace crossings have the same handedness, causing the knot to twist instead of lying flat when tightened.
Designed to develop a baseline understanding of the mechanics of how a shoelace bow tie knot comes untied under dynamic forces and claimed to be more than an example of science answering a seemingly obvious question, the study shows that both versions fail in the same way, and lays the groundwork for future investigation into why the two similar structures have different structural integrities.
The first step was to record the process of a shoelace knot untying in slow motion.
Study co-author and graduate student Christine Gregg, a runner, laced up a pair of running shoes and ran on a treadmill while her colleagues filmed her shoes.
The researchers found: when running, the foot strikes the ground at seven times the force of gravity. The knot stretches and then relaxes in response to that force.
As the knot 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 after inertia acts on the laces.
"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," said Gregg.
"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."
In addition to the dynamic interaction of forces on the knot, the footage also revealed a large magnitude of acceleration at the base of the knot.
To dig deeper, the researchers then used an impacting pendulum to swing a shoelace knot and test knot mechanics using a variety of different laces.
"Some laces might be better than others for tying knots, but the fundamental mechanics causing them to fail is the same, we believe," Gregg said in a news release from UC Berkeley.
Trying to test their theory that increasing inertial forces on the free ends would trigger runaway failure of the knot, the researchers added weights to the free ends of the laces on a swinging knot and saw that knots failed at higher rates as the inertial forces on the free 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," Daily-Diamond said. "You can't seem to get knot failure without both."
As for the fact that when a person goes walking or running, their shoelaces don't always come untied, as tightly tied laces can require more cycles of impact and leg swinging to cause knot failure than one might experience in a day's worth of walking or running, the researchers acknowledged that more research is needed to tease apart all the variables involved in the process.