Physics Is Untying Your Shoelaces
One of the first lessons you learn growing up is how to tie your shoe. And during that time, you also learn that your shoelaces will eventually come untied. So why do your shoes experience ‘catastrophic knot failure’ or untied shoelaces? Christine Gregg, a mechanical engineering graduate student at Berkeley, and a group of researchers investigated the different forces acting on a shoelace knot. The results were published this week in the journal Proceedings of the Royal Society. Gregg describes how the forces created by walking unties a shoelace and the difference between a ‘weak’ and ‘strong’ knot.
Christine Gregg is a graduate student in Mechanical Engineering at the University of California, Berkeley in Berkeley, California.
IRA FLATOW: One of the first lessons you’re taught in school is how to tie your shoelace. There’s the ever-popular bunny ear technique, and then there’s the one loop around method.
I hate to break it to you, but there is a wrong way and a right way to tie your shoes, or at least strong and weak way to create your shoelace knot.
But even if you know how to create a strong knot, your shoelaces eventually, well, they’re going to become untied. It’s enough to make you consider Velcro for a bit.
So why do our shoelaces become untied? That simple question has some very interesting science behind it. And a group of researchers investigated just that. The study was published this week in the journal Proceedings of the Royal Society A. Christine Gregg is one of the authors on that study. She’s also a graduate student in mechanical engineering at UC Berkeley.
Welcome to Science Friday.
CHRISTINE GREGG: Thanks for having me.
IRA FLATOW: You’re welcome. A lot of us have been tying our shoes wrong this whole time? Can you explain how you tie a strong knot versus a weak one?
CHRISTINE GREGG: Yeah, sure. So the standard bow tie knot that most people use on their shoes has a weak form and a strong form. The strong form is based on what’s called a reef knot, or a square knot, whereas the weak form is based on what most people call a granny knot.
And so it has to do with the handedness. And after you tie that first criss-cross, what you do after that determines whether you’re going to get the strong version or the weak version.
IRA FLATOW: Mm-hmm. So yeah, if you wind up with the square knot, you get a little stronger version. Does this apply to the bunny ears method too?
CHRISTINE GREGG: Yeah, you can definitely get both with the bunny ears, as well as doing the one loop and then going around.
IRA FLATOW: Now tell us about the question you wanted to answer. You want to answer the question every kindergartner and adult asks. Why do our shoelaces become untied during the day? How did you go about answering that question?
CHRISTINE GREGG: Yeah, so we had this problem, my co-authors and I, Christopher Daily-Diamond and Oliver O’Reilly We couldn’t figure out why our shoelaces were constantly becoming untied.
And so we started to look into it on Google, and we couldn’t find anyone who had actually described the mechanism of what’s happening on your shoe.
So I jumped on the treadmill, and Chris filmed me with a really nice slow motion camera, high-speed camera. And we saw this amazing dynamic interaction between the swinging of your leg that’s causing these– all sorts of inertial forces on the free ends and loops, and the impact force of your foot on the ground.
IRA FLATOW: And what did you find?
CHRISTINE GREGG: Yeah, so again, it’s that one-two punch of having these really strong inertial forces and the impact. We studied just– I would sit on a table, and I would just swing my legs back and forth to see if you could just get it by swinging your legs.
And you couldn’t. And neither could you get it to untie if you just stamped your foot. You really need both.
So as you bring your foot forward, you’re accelerating your laces, and there are inertial forces pull them forward. And at the same time, you have this impact force that’s serving to loosen the center of the knot.
And so eventually, you’re going to get loose enough so that the friction forces can’t hold on to that lace and keep it in the center of the knot. And so the inertial forces are going to start tugging on that free end of your loop, just like you if you were trying to untie it with your hand.
IRA FLATOW: So the pounding you do with your feet loosens the knot, and then the action of swinging as you swing your foot makes the knot itself move and unties it?
CHRISTINE GREGG: Right. And it’s this interesting– we noticed in the video that your knot will be fine for hundreds, thousands of cycles. And it’s only in about one or two strides that it comes undone. And that’s because you have these competing forces of the free end inertia and the loop inertia.
And so it’s this positive feedback loop of, once you get a little bit of motion, it’s all over. It just comes undone.
IRA FLATOW: I know what that’s like. But most of us, we put double knots on our shoes. Doesn’t that help?
CHRISTINE GREGG: It certainly helps. Oliver complains that even his double knotted laces still come untied. So we didn’t specifically study those, so I can only offer limited commentary.
IRA FLATOW: I’m Ira Flatow. This is Science Friday from PRI, Public Radio International. Talking with Christine Gregg, a graduate student at UC Berkeley who has studied shoelace science.
So the average lifespan of a shoelace knot– we don’t know. It could just come apart with the right bang on the ground?
CHRISTINE GREGG: There are so many factors. There’s what size your laces are. What they’re made out of. How tightly did you tie it in the first place?
But I can tell you that the strong knot will last you at least twice as long as the weak one.
IRA FLATOW: And actually the shape of the shoelace. I remember when back in the day when I had fancy shoes. I don’t wear them much anymore. They used to have these very skinny, round shoelaces that never stayed closed.
CHRISTINE GREGG: Yeah, we actually–
IRA FLATOW: They’re like strings, they’re stringy things, you know?
CHRISTINE GREGG: Absolutely. So those are the ones that we actually used in the study, because if you’re trying to study shoelaces coming untied, you better choose laces that want to come untied. But we definitely want to look into, are different shapes going to serve you better? And all the different variables that go into it.
IRA FLATOW: Now, I know there are people– and you sit down, and you’re having a beer sometime, you’re talking– believe me, I’ve gotten around to talking about shoelace knots before– and people have commented about the knot. Where the knot is placed on the shoe.
Some people say, look, you have your knot tied all the way to the side. Other people have it tied straight in the middle. Is there a difference in the strength or the durability of that spot?
CHRISTINE GREGG: We didn’t study that specifically. Again, we were trying to just describe the basic mechanism and control just the thousands of variables that could go into it.
But keep in mind that it depends on what your inertial forces are and how those forces are acting. So I imagine that the placement can at least have a subtle effect on that.
IRA FLATOW: Is there any application in real life for this? Understanding your shoelace knot science?
CHRISTINE GREGG: Well it’s I’d say it’s primarily applicable in real life. I use it every day.
IRA FLATOW: So what do you do? OK, now you have the knowledge. How do you keep you shoelaces from untying?
CHRISTINE GREGG: My life has been changed by the strong version of the knot. I’ll tell you that much. But really, to your actual question, what makes a certain knot stronger than another and better able to withstand forces is still an open question in science. At this point, we can’t look at just any given knot and say, oh, the structure of this one has these characteristics, and so it should be better at resisting force than another.
And so we see our work as an open invitation for collaboration in the field and trying to make progress on understanding what is it about knots that makes them strong. And if you understand that, you can start to do anything from understanding surgical sutures to understanding how, perhaps, other entangled structures like DNA self-interact.
IRA FLATOW: Interesting. Because I know, as a former Boy Scout doing a lot of knots, I know there were some knots that actually get tighter as you try to loosen them. And they’re better at that.
CHRISTINE GREGG: Absolutely. Right. And so right now, we have hundreds of years to work with of heuristic data of, well, we know this one performs a lot better. And so we’re trying to dig into being able, from a scientific standpoint, to predict the behavior of certain knots based only on their structure.
IRA FLATOW: All right, let me see if I can get a quick call from Mimi in Birmingham, Alabama. Hi Mimi. Quickly.
MIMI: Hey, how are you?
IRA FLATOW: Fine.
MIMI: Well, someone taught me years ago when my kids were little, if I would tie them up and make one loop with the string around them, not that you’re holding, and another loop. In other words, two loops to tie it, and then push it through and pull it. That it would never come undone.
And I have found that to be true. And my kids are now 58 and 56.
IRA FLATOW: Thank you, thank you, Mimi. I got to go.
I’ve seen this also– push back on the internet. You make two loops instead of that one round around the loop. Have you thought of that one?
CHRISTINE GREGG: Sure. Absolutely. That’s just another knot that we’re looking to understand. We stuck with the basic knot that most people are tying, but again, we think the mechanism that those forces that are pulling on it are going to be the same, no matter what that knot is.
But again, it’s still an open question of, what is it about that extra loop that’s making it so much stronger?
IRA FLATOW: Well, the forces are with us, even when we tie our shoes. Thank you, Christine. Christine Gregg, graduate student, mechanical engineering, UC Berkeley.