What makes a knot strong? Scientists have figured out how your shoelaces untie themselves.

Well, it happened again. You were walking down the road, minding your own business, when all of a sudden you looked down, only to realize that your shoes spontaneously untied themselves again. Muttering under your breath, you kneel down, retie the laces, and go on with your day.

That scenario is familiar to anyone who has owned a pair of lace-up shoes. For many, retying one's shoes after they seemingly untie themselves is simply one of life's little inconveniences that has to be dealt with from time to time. But for a group of mechanical engineers at the University of California, Berkeley, the spontaneous unraveling of shoelaces is a scientific puzzle – one so commonplace that many would not even think it worth examining with the kind of disciplined, scientific rigor usually reserved for more arcane physical phenomena.

And on Wednesday, those researchers published a study that represents a significant first step toward understanding the physics of what causes a shoelace to unravel during day-to-day use. The new paper examines how weak and strong knots react to the application of force during sustained periods of running, shedding light onto a common problem that has troubled humans for millennia. The researchers hope that the study will provide a stepping-stone to the complex and still poorly understood physics of one of humankind's most basic tools: knots.

"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, in a statement. "This is the first step toward understanding why certain knots are better than others, which no one has really done."

It's a significant first for such an ancient technology. The oldest leather shoe ever discovered, cobbled some 5,550 years ago, has laces – and knots go even farther back in human history. But while previous scientific studies have been conducted in order to understand how knots fail under long, sustained loads, shoelaces become undone through the application of short-lived, sudden forces, which are harder for scientists to study.

In order to examine these forces, the researchers used a slow-motion camera to capture the running shoes of Christine Gregg, a graduate student and study co-author, as she ran on a treadmill. Analyzing the footage, the researchers found that the knots on her shoes were subject to extreme pressure from at least two forces, the combined effect of which was to accelerate the laces at seven times the rate of an object in free fall, subjecting them to more than twice the g-force astronauts feel during a typical rocket launch.

First, the foot striking the ground jolts the laces with a downward force. Then, the knot stretches and loosens as the swinging leg creates a forward force that pulls on the free ends of the knot, which causes it to fail suddenly. Simply stomping or swinging the leg wasn't enough to cause the knots to fail, the team found – rather, it was a combination of both that lead to the unraveling.

"In particular, there appeared to be two time scales over which untying took place: little change to the knot was observed for many strides until some untying began, after which the speed of untying was remarkable (often in less than two running strides)," the team wrote in the study, which was published in the journal Proceedings of the Royal Society A.

The team also tested the effect of different kinds of knots and types of shoelaces, with varying results. But while some knots lasted longer than others, generally the ways in which the knots failed were remarkably similar.

"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," said Oliver O'Reilly, study co-author, in the statement.

The researchers say that there is still plenty of research to do in order to determine all the variables that contribute to the stability of a tied-up shoelace, especially under the pressures of running. But their research certainly represents a significant step toward unraveling the strange physics of knots.

"It might seem like a trivial problem, but the fact remains that we are trying to understand what fundamentally makes a knot strong," Ms. Gregg told NBC.