It’s the bane of tennis shoe wearers everywhere: No matter how tightly you tie your laces, they seem to come undone, often at the most inopportune time. Now, for the first time, scientists have untangled why shoelace knots fail. The work also reveals the best knots to tie and could have implications for everything from surgery to new cancer drugs.
“We deal with them coming untied all the time,” says Colin Adams, a mathematician at Williams College in Williamstown, Massachusetts, who was not involved with the study. “And yet, nobody’s ever taken the time to say: Why does it happen?”
Here’s one thing we do know about shoelaces: The “square knot” holds up better than the “granny knot.” Both knots appear about the same, with two bunny-ear loops, but the granny tends to rotate to its side—one loop pointing up the shoe, the other down. (Still confused? Check out this TED video.)
To find out why even the best knots fail, Oliver O’Reilly, a mechanical engineer at the University of California, Berkeley, and colleagues put a volunteer on a treadmill. The test subject tied her shoes with the weaker granny knot so that the researchers had a better chance of watching it unravel. The scientists attached accelerometers to her shoes to measure the acceleration, or g-force, the knot experienced with each stride.
Using slow-motion video, the team uncovered two stages of knot slippage: a gradual loosening with each step, and a sudden “catastrophic failure.” When the knot started to unravel, it fell apart within two strides. The researchers were surprised by the g-force the knot experienced as it bobbed up and down, which was more than any rollercoaster can generate.
Walking was key. The same knot that failed within 15 meters of walking stuck around if participants just stomped their feet on the ground or swung them while sitting on a table, the team reports today in the Proceedings of the Royal Society. Neither impact by itself—stomping or swinging—was enough to undo the knots.
“We were able to see that these two combined effects lead to shoe knots failing,” O’Reilly says. “You need both together.”
The scientists then designed an experiment to measure how long it took for knots to unravel and the rate at which the laces slipped. Working on a shoestring budget and borrowing lab equipment on weekends, the researchers designed a mechanical pendulum that smacked a plate. The pendulum’s swing approximated leg movements, and the smack the impact of shoes with the ground. The pendulum sported a shoelace with weighted ends—the added weight was needed to simulate how strongly the ends whip on runners’ shoes. The team used this controlled setup to calculate the precise slip rate of shoelaces, tied either granny or square.
The experiment confirmed the treadmill observations. Both knots initially slipped apart at a slow, gradual rate with each swing and smack of the pendulum. Eventually, though, the laces became loose enough to rapidly slip apart at a much faster rate. The study also demonstrated the superiority of the square knot. This winning knot failed about half the time (when weighted), whereas the granny knot always failed.
But though the scientists know that one knot is more resilient, they still can’t explain why. It may have something to do with how the laces press against each other within the knot and the knot’s tension, Adams says. “If you could actually predict when a knot is going to fail,” he says, “that would have implications beyond shoelaces.”
This could include knots used in surgical sutures, on boats, and in mountaineering. But knots also exist on the microscopic level: DNA knots and unknots when it creates copies of itself, for example. Scientists are already exploiting these properties to create drugs that slow tumor growth.