It’s happened to all of us at some time in life. It happened to Ethan, my two-year-old grandson, at the Waikato Show in Hamilton last weekend.
One moment his sneaker was neatly and securely tied. The next, the flapping lace was threatening to trip him up. He was holding popcorn. There would have been tears.
Fortunately, a professor of mechanical engineering and several PhD students in California (no, we are not going to say, where else?) have put their collective IQs into sorting out Ethan’s sneaker distress.
In a series of experiments involving a human runner on a treadmill and a mechanical leg designed to swing and stomp, the scientists revealed that shoelace knot failure (henceforward unscientifically known as SKF) is triggered by a complex interaction of forces and happens in a matter of seconds.
Oliver O’Reilly, professor of mechanical engineering at the University of California Berkeley and the study’s senior author, said: “It’s unpredictable. But when it happens, it’s in two or three strides and it’s catastrophic. There’s no way of coming back from it.”
You don’t need a degree in mechanical engineering to understand that theory could be applied to just about anything from the Titanic triggering a complex interaction of forces with an iceberg or to … well, I’m sure you can think of something that’s all over in a matter of seconds.
The study found that the stomping of the foot gradually loosens the knot while the whipping forces produced by the swing of the foot act like hands tugging on the ends of the laces.
As the tension in the knot eases and the free ends start to slide, a runaway effect takes hold and the knot suddenly unravels.
The findings also revealed what sailors and surgeons have long suggested: the granny knot that most people use to tie their laces comes undone far quicker than an alternative method that is no more complex.
Robert Matthews, a British physicist who was not involved in the work, said: “It’s provided hard scientific backing for what many people have long suspected. The traditional way of tying shoelaces is pretty rubbish.”
Many people will be pleased to know that scientists have spent a whack of research grants to prove what many people already know.
O’Reilly said he was inspired to investigate after spending decades pondering why laces spontaneously unknot themselves. What really got him into the scientific pursuit of what we now call SKF was trying to teach his daughter how to tie her laces.
The scientist enlisted a pair of PhD students and initial tests revealed that sitting on a chair and swinging your leg or stamping your foot does not generally cause a knot to come undone. It appeared to be a combination of both motions.
Next, the scientists captured slow-motion video of a runner on a treadmill.
They found the foot strikes the ground at seven times the force of gravity. As the fabric of the shoe squashes down on impact, extra lace is freed at the top of the shoe, causing the knot to loosen slightly with each stride.
Meanwhile, the swinging leg causes the lace’s free ends to whip back and forth tugging them outwards.
As the knot loosens, the friction holding the knot tight decreases, and as the free ends lengthen, the whipping force goes up, leading to an avalanche effect.
“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,” said Christine Gregg, a graduate student at UC Berkeley and a co-author.
Ethan could probably have told her that, but his face was full of popcorn at the time he suffered SKF.
TO BE, OR KNOT TO BE
The scientists tested two basic versions of the standard knot and bow: the square knot and the weaker granny knot.
In a square knot, you start by crossing the lace in your right hand in front of the one in your left hand and then threading it under the left one.
For the bow you repeat the process, but crossing the end that’s now in your right hand behind the one in your left (with added loops to make the bow).
In a granny knot the same overhand motion is repeated for both knot and bow.
According to the data, the lace slippage rate (LSR) was cut by at least a factor of five using a square knot compared with a granny knot.
O’Reilly admits he still uses the granny knot himself through habit, but did not reveal which method he taught his daughter. Ethan’s mother tied his shoelaces in a double knot.
- The study is published in the journal Proceedings of the Royal Society A (mathematical, physical and engineering sciences).