How do earphones tangle

With a cord longer than that, the probability of a knot forming reaches a plateau of 50 percent. It turns out that the odds of getting a knot do not go higher because a longer cord gets wedged inside the shape of the box and that prevents further tangles from forming. Raymer and Smith performed 3, trials to demonstrate this. Apple's iPhone earbuds are centimetres 55 inches long and thus right at the 50 percent tangle-rate-sweet-spot, at the top of the curve.

In other words, if you place your earbuds in a bag the odds of them tangling into a knot as you carry them around are 50 percent, at least. Raymer and Smith didn't look at strings with more than one branch, but anecdotally I can confirm that the tangle-rate is pretty high. Finally, here is a schematic showing how a cord that starts off neatly coiled - you don't just stuff them in there, do you?

Raymer and Smith also classified the types of knots they found, using the Jones polynomials developed by mathematicians. After each tumble, they took a picture of the string and fed the image into a computer algorithm that could categorize the knots. Knot theory has shown that there are 14 kinds of primary knots, which involve seven or fewer crosses. Raymer and Smith found that all 14 types formed, with higher odds of forming simpler ones.

They also saw more complicated knots, some with up to 11 crossings. The researchers created a model to explain their observations. Basically, in order to fit inside a box, a string has to be coiled up. This means the end of the string lies parallel to different segments along the length of the string. As the box spins, the string end has a certain chance of falling over and around one of these middle segments.

If it moves enough times, the end will essentially braid itself around some part in the middle, tangling up the string and creating different knots. The most important question from these experiments is what can be done to keep my cables from getting all screwy. One method that decreased the chances of knot formation was placing stiffer strings into the tumbling boxes. Perhaps this is what motivated Apple to make the power cables for more recent generations of laptops less flexible.

It also helps explain why your long, thin Christmas tree lights are always a tangled mess while your shorter and stockier surge protector cable stays relatively smooth. A smaller container size also helped keep the knots away.

Longer strings pressed against the walls of a small box, preventing the cord from falling over itself and braiding up. This has been proposed as the reason why umbilical cord knots are rare happening in about 1 percent of births : The womb is too small to allow for the organ to tangle around itself. Unless they're on that plastic spindle that came with the box — and no one ever keeps that — those headphone wires will knot themselves on a daily basis. It turns out that there is a reason this happens, and it has been the subject of scientific research.

When the two are plotted against each other — length versus agitation — the rate of knots and tangles obeys a statistical pattern that describes a curve. A paper titled " Spontaneous knotting of an agitated string " by Dorian M. Raymer and Douglas E. Smith of the University of California at San Diego Department of Physics demonstrated this phenomenon: It revealed that a cord of less than 46 centimeters in length about 1 foot six inches will almost never tangle itself when sealed inside a rotating box for a period.

But between 46 centimeters and centimeters about five feet , the probability of a knot forming rises dramatically. It turns out that the odds of getting a knot do not go higher because the cord wedges itself inside the shape of the box and that prevents further tangles from forming. Raymer and Smith performed 3, trials to demonstrate this. Raymer and Smith didn't look at strings with more than one branch, but anecdotally I can confirm that the tangle-rate is pretty high.

Finally, here is a schematic showing how a cord that starts off neatly coiled — you don't just stuff them in there, do you? It shows that one end of a wire only has to cross another part of the wire twice in order to start spontaneously knotting itself:.