The math behind cords getting tangled.


I’m curious if there is some grand equation, or if it is compounding complexity as the cord gets more and more tangled toward a “tangle equilibrium,” where it can’t get tangled anymore? Thanks!

In: 11

There’s only a few possible ways cords can be laid so they are untangled. In contrast, there are many ways cords can tangle and knot themselves.

When you stuff cords somewhere, there’s a higher probability they’ll end up tangled rather than untangled.

Stiffer cords and slicker surfaces help reduce tangling. Your hair is one example where its stiffness and slickness helps prevent it from tangling.

There is actually quite a bit of mathematics behind this and it even touches on physics as a model for a thermodynamic system reaching equilibrium. Every time the cord moves and crosses itself it can either start a new knot or it can untie an existing knot. The probability for each depend on the length of the cord, how stiff it is and how many knots are already on it. If there are no knots then any change will start a new knot. However over time there will be more knots and the movement of the chord will have an equal chance of creating a new knot or untying an existing knot. At that point the cord will not get any more tangled.

I can help fixing it, I let the “why/how” to others:

There are 2 main causes of tangling, and both have to do with the wire-cord-cable-rope tendency to twist.

1 for electric wires, the conductor inside is made of many copper wires twisted. If you pull the cable often enough, the core untwists itself and applies a twisting force to the cable. Aka, don’t pull electric cables if not necessary.

2 for everything: storing something is the cause of the twisting. If you wind up a wire in a circle, you are also twisting it. You let it rest twisted, it “memorize” the shape and when you use it again it will twist on himself.

This can be prevented by:

A: store the thing in a 8 shape instead of a circle. Perfect for long things.

B: grab both ends of the cable, put them together, then wind the cable in a circle, around something, as you like. Because you are doing a circle with both half of the cable, the result will be the cable memorize the twist 50% one way and 50% the other way. When used again the two twisting will counter each other. Works wonders with short things like phone chargers, headsets, audio cables.