Why Do Shoelaces Come Untied While You Walk?
― The Knot Doesn't Loosen Slowly. It Collapses in a Few Steps
A shoelace coming undone doesn't always mean you tied it badly. With every step, the knot is "hit from above" and "pulled from the side" at the same time. When both happen together, a knot that has held for hundreds of steps can come apart in just a few.
In the morning, you pull your shoelaces tight at the front door and head out. All the way to the station, you never think about them.
Then, as you climb the station stairs, the laces are flapping around your feet. You look down, and the bow you tied earlier has completely come undone.
Sitting down or just standing, laces almost never come undone. It always happens while you are walking or running.
There Are Only Two Reasons
Every time your foot hits the ground, the knot is struck with a force many times its own weight. The knot squashes and springs back, and for an instant the grip holding the laces together lets go.
On a foot swinging forward, the dangling ends and loops whip about like a lash. That motion slowly pulls the lace out of the knot.
The key point is that either one alone rarely undoes the knot. The knot is loosened by a blow, and at that moment it is pulled from the side. This combination is repeated with every step.
The Knot Is "Hit" with Every Step
Some researchers have studied this phenomenon in earnest. In 2017, a research team at the University of California, Berkeley, in the United States filmed the shoelaces of people running on a treadmill with a high-speed camera.
They reported that the impact on the knot at the moment of landing reached about 7 times the force of gravity.
Look at the left side of Figure 1. Arrow ① from above is this landing impact. The knot is squashed and then springs straight back. Each time, the grip pressing the laces together loosens for just a split second.
On the right side of Figure 1, the slider lets you change the size of the impact. If we assume the end of the lace weighs 2 grams, then in the impact of a run the end is pulled with a force equal to 14 grams.
The Swinging Foot Slowly Pulls the Lace Out
The other force arises when you swing your foot forward. Each time the foot speeds up and then stops, the dangling ends and loops are left behind and flung outward. It is the same principle as swinging a bucket of water: the water is pressed outward.
The research team made an interesting comparison here. Sitting on a chair and just swinging their feet back and forth, the laces hardly came undone. Even just stepping on the spot, the laces were still hard to undo.
At the instant the knot is loosened by the blow, the end is pulled. The lace slips out of the knot by just a tiny amount. This builds up over hundreds of steps.
Once the lace has been pulled out to a certain length, the knot suddenly collapses. In the high-speed footage, it took only a few steps from the first loosening to the knot coming completely undone.
You Can Spot a Weak Knot by Its Look
There are actually two kinds of bow. In one, the base knot is a "square knot." In the other, it is a "granny knot." They look very much alike, but the research reported that the granny knot came undone far more easily.
Telling them apart is easy. When the bow is finished, if the loops spread sideways across the foot, it is a square knot. If the loops tilt so that they line up from front to back along the foot, it is a granny knot.
If you end up with a granny knot, reverse the direction in which you first cross the laces, or reverse the direction in which you wrap the lace around the loop. That alone gives you a bow built on a square knot.
The longer and heavier the ends and loops are, the greater the pull on them when the foot swings forward, it is thought. Some people tuck overly long laces into their shoes, which may be sensible practice. The surest fix is a "double knot": tying the bow once more on top.
Summary
A shoelace comes undone because, at the moment the knot is loosened by the landing impact, the swing of the foot pulls on the ends. That small slip builds up with each step, and in the end the knot collapses within a few steps. A granny knot, with its loops lined up front to back, is an especially weak way to tie it.
What undoes the lace is your own stride.
Hit, then pull. Hundreds of times over.
Why can a rope wrapped around a post stop an enormous force? The same "friction between rope and rope" that works in a knot is covered in more detail in the article on sailors' ropes.
- Tie a bow as you usually do, and check whether the loops lie sideways or front to back. If they lie front to back, it is a granny knot.
- Sit on a chair and swing your feet back and forth 30 times. Then step on the spot 30 times. Compare how much the knot has loosened.
- Reverse the wrapping direction to make a bow on a square knot, walk the same route, and compare how far you get before it comes undone.
The lace material changes the result too. It could be fun to compare a round, slippery lace with a flat one. When you walk, watch your surroundings and your footing.
For those who want more ― Terms, Formulas, and Links to TextbooksEach part is labelled by level, from junior-high science to university courses
- Junior highCovered in junior-high science
- High schoolCovered in high-school "Basic Physics" and "Physics"
- High school+Advanced high-school material, or textbook sidebars
- UniversityUniversity-level courses not taught in high school (mechanics, mechanics of materials, mechanics of strings)
- ResearchNot yet taught as settled fact even at university; topics researchers are studying now
Junior highTerms: This Phenomenon Has Names
- Inertia: the tendency of an object to keep moving as it is. Even if the foot stops suddenly, the ends of the lace try to keep moving.
- Friction: the force that resists sliding between surfaces in contact. A knot stays tied only because of friction between lace and lace.
- Square knot and granny knot: two knots made with the same steps, differing only in the direction of the crossing. The square knot tightens when pulled; the granny knot is said to twist and roll easily.
Junior highHigh schoolChecking with a Formula: The Force on the Lace End at Landing
Think of the end of the lace as a small weight. When the foot stops suddenly on landing, the end is stopped in the same way. We estimate the force on the end with the basic equation of motion.
| In symbols | F ＝ m × a 、 a ＝ n × g |
| In words | Force on the end ＝ weight of the end (mass) × acceleration. The acceleration is expressed as "how many times gravity" |
| Where it comes from | Newton's second law of motion. To change an object's motion suddenly takes a force equal to mass times acceleration |
| Symbol | Meaning and unit |
|---|---|
| F | Force on the lace end (newtons) |
| m | Mass of the lace end and loop (kilograms) |
| a | Acceleration at landing (metres per second squared) |
| n | How many times gravity the acceleration is (no unit) |
| g | Gravitational acceleration, 9.8 metres per second squared |
| Landing impact (running, reported in the experiment) | About 7 times gravity |
| Mass of the lace end and loop (assumed) | 2 grams ＝ 0.002 kg |
| Gravitational acceleration | 9.8 m/s² |
| Length of one step (typical adult) | About 0.75 m |
| Acceleration at landing | 7 × 9.8 ＝ 68.6 m/s² |
| Force on the end | 0.002 × 68.6 ≒ 0.137 N |
| Converted to weight | 0.137 ÷ 9.8 ≒ 0.014 kg (14 grams' worth) |
| Steps in 1 km | 1000 ÷ 0.75 ≒ 1333 steps |
| Landings per foot | 1333 ÷ 2 ≒ 667 times |
The end is yanked with 7 times its own weight, a force equal to 14 grams. Each pull is small, but over just 1 km it is repeated about 670 times per foot. That is plenty of repetitions for a tiny slip to build up.
High schoolHigh school+Why Does It Collapse "All at Once in a Few Steps"?
High schoolFrom the point of view of something moving with the foot, when the foot suddenly stops or speeds up, an apparent force (an inertial force) acts on the end of the lace. Its size is the same "mass × acceleration" as in the formula above, and its direction is opposite to the foot's acceleration.
High school+The friction on a lace that is not moving (static friction) is usually larger than the friction once it starts to slide (kinetic friction). Once sliding begins, the grip weakens, and so it slides further. The looser the knot gets, the weaker its squeeze becomes, so the slip is thought to accelerate like an avalanche.
UniversityRope Friction and What Decides a Knot's Strength
The friction when a rope wraps around a curved surface grows exponentially with the angle of wrap. This is described by the capstan equation (Euler's belt friction equation). Inside a knot, the laces wrap around one another, so the same mechanism works many times over. In 2020, a study was reported that made the forces inside knots visible using fibres that change colour when pressed, and compared knot strength by the number of crossings and the direction of twist.
📖 Derivation of the formula and further reading: Capstan equation (Wikipedia) ／ Friction (Wikipedia)
ResearchWhat Is Still Not Clear
- The real reason granny knots come undone more easily The difference between the square knot and the granny knot has been confirmed, but the full picture of how force is divided inside the knot is still being studied.
- What triggers the loosening Which step is the one where a knot that has lasted hundreds of steps begins to loosen? The trigger is still not well understood.
- Lace material and shape How the ease of untying changes with the material and cross-section, such as round laces, flat laces and waxed laces, is said not to have been studied systematically yet.
So the contents of this article are also "an explanation of what is known so far." There are still questions left at our feet that were too familiar for anyone to study.
Links to Textbooks (by Level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Junior high | Science: force and motion (inertia, friction) | The ends of the lace are flung outward by the swinging foot |
| High school | Basic Physics: laws of motion | Estimating the force on the end with F ＝ m × a |
| High school+ | Physics: inertial force, static and kinetic friction | Why it collapses all at once in a few steps |
| University | Mechanics and mechanics of materials (capstan equation) | Friction between laces and knot strength |
| Research | Mechanics of knots | Why granny knots come undone, the effect of material |
| ― | Link to daily life | Spot a granny knot by the loop direction and retie it |
※This article is a general-audience science explainer. The numbers given are rough guides for understanding the mechanism. The weight of the lace end is an assumption made for the calculation; the real value varies with the shoe and the lace.