Shoelaces become untied due to a double whammy of whipping and stomping forces that act like an invisible hand that loosens the knot and tugs on the shoelace’s free ends until the whole thing becomes undone, says a team of mechanical engineers at the University of California, Berkeley (UC Berkeley).
“Why do my shoelaces come undone all the time?” This is a question most of us ask ourselves after stopping to do up our shoes. It is an enigma that nobody has bothered to investigate, that is, until now.
The research team says its study is much more than an example of science answering what seems to be an obvious question. A better understanding of knot mechanics is required for deeper insight into how knotted structures become untied under a range of forces.
After a series of experiments using a slow-motion camera, the study showed that shoelace ‘knot failure’ occurs rapidly – within a matter of just a few seconds – triggered by a complex interaction of different forces.
The top of the image has an illustration of the stages of the humand gait. The bottom image has the three strides after several minutes of running on a treadmill. Each row of images represents one stride – each stride lasts about one second. (Image: adapted from rspa.royalsocietypublishing.org)
The scientists wrote about their experiments and conclusions in the prestigious journal Proceedings of the Royal Society A, in an article titled: ‘The roles of impact and inertia in the failure of a shoelace knot.’
Types of knots on shoelaces
Co-author Christopher Daily-Diamond, a UC Berkeley graduate student, said regarding knots on shoelaces and other structures:
“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.”
There are two ways we can tie the common shoelace tie knot:
– Based on a Square Knot: two lace crossing of opposite handedness are placed on top of each other. This is the stronger version.
– Based on a False Knot: the two lace crossings have the same handedness, which makes the knot twist rather than lie flat when tightened. This is the weaker version.
We have always known that one is stronger than the other, but not why.
Illustration of both the False (weak) and Square (strong) knots. Each knot consists of a series of stacked trefoils, with the ‘1st trefoil’ referring to the one nearest to the shoe – it is also the first tied. According to the authors: “The difference between the knots lies in the handedness (the ordering of which lace crosses over which) of the ‘second trefoil’: that is, ‘left over right’ or ‘right over left.’ In the strong knot, the handedness of the second trefoil is different from the first.” (Image: adapted from: rspa.royalsocietypublishing.org)
The latest study showed that the two versions failed in exactly the same way. According to the authors, their findings lay the groundwork for future research into why the two structures – which are similar – have different structural integrities.
Oliver O’Reilly, a professor of mechanical engineering at UC Berkeley, whose lab carried out the research, said regarding the scientists’ understanding of knots:
“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 that 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’s a fundamental mechanical difference between those two knots.”
In the study, the researchers wanted to develop a baseline for understanding the mechanics of how bow-tie knots on shoelaces became untied under dynamic forces.
While previous studies had described how knotted structures failed under sustained loads, very few investigations had sought to show how knotted structures failed under the dynamic pressures of changing loads and forces.
Videoing knot failure in slow motion
The scientists began by recording the process of a shoelace knot becoming untied in slow motion. Co-author, graduate student Christine Gregg, who is a regular runner, put on her running shoes, tied up the shoelaces, and ran on a treadmill while team members filmed her shoes.
According to the researchers, a shoelace knot becomes unravelled in the following way:
– A runner’s foot hits the ground at seven times the force of gravity.
– In response to that force, the knot stretches and then relaxes.
– The swinging leg applies an inertial force on the free ends of the shoelaces as the knot loosens, which quickly leads to a failure of the knot.
– Shoelace knot failure can occur within two strides after inertia acts on the laces.
When the foot is stationary, the knot is nice and secure. As the leg (b) is swung backwards to impact the ground, the inertia of the loops and free ends pull open the knot’s center. Repeated impacts cause the center of the knot to loosen more and more, which reduces the frictional effects, thus loosening the knot even faster. Eventually the knocks and swinging of the leg loosen the knot completely, and we have ‘knot failure’. (Image: adapted from rspa.royalsocietypublishing.org)
Ms. Gregg, a Berkeley Chancellor’s Fellow, 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.”
Apart from the dynamic interaction of forces on the shoelace knot, the video footage also revealed that a large magnitude of acceleration occurred at the base of the knot. To get deeper insight, the scientists then used an impacting pendulum to swing a shoelace knot, and tested knot mechanics using a range of different shoelaces.
Ms. Gregg explained:
“Some laces might be better than others for tying knots, but the fundamental mechanics causing them to fail is the same, we believe.”
Weights added to ends of shoelaces
The scientists needed to test their theory that growing inertial forces on the free ends of the shoelaces would trigger runaway failure of the knot. They stuck weights to the shoelace ends on a swinging knot and observed that the knots’ fail rates rose as the inertial forces on the free ends increased.
Mr. Daily-Diamond said:
“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.”
Our shoelaces do not always become untied when we go out walking or running. Shoelaces that are tightly tied may require more cycles of impact forces and leg swinging to cause knot failure than we might experience after one day’s worth of running or walking.
The authors wrote that further studies are required to tease apart all the variables involved in the untying of knots. However, this latest study offers an answer to the shoelace mystery – “Why are my shoelaces fine one minute than then untied the next?”
Mr. Gregg said:
“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.”