Friction in rope: why knots and friction hitches hold

Friction arises when two surfaces are pressed together. The harder they are pressed and the rougher or “grippier” the material, the greater the friction force. Physicists describe grippiness with the coefficient of friction. A distinction is made between static friction, which stops something from starting to slide, and kinetic friction, which slows a part that is already sliding. Static friction is usually somewhat greater – which is why it is easier to let a sliding rope keep sliding than to stop it.

When a rope runs around a round pole, something special happens. The tension presses the rope against the pole, and this pressure creates friction that “swallows” part of the tension. On the next stretch of pole the force in the rope is already smaller, but is reduced again by the same proportion. The rope friction formula – also called the capstan equation, after the old ship's winch – therefore shows: the holding force does not grow evenly but exponentially with the wrap angle.

A picture shows what this means: if one wrap takes a certain fraction off the load, the second takes the same fraction off what is left, and so on. The effects multiply rather than simply add up. The surprising thing is that in the simple formula the diameter of the pole plays no part, only how often and how far the rope wraps around it. In reality, the stiffness and thickness of the rope change the result somewhat.

A knot is a small collection of wraps and pinch points. Where one strand runs around another, rope friction acts. Where one strand is trapped between two others or between rope and object, a “bite” is formed – experts call it a nip. The harder the load pulls, the more tightly these points are pressed together, and the better the knot holds.

That is why it is so important to dress a knot neatly and set it firmly. A neatly dressed knot has clearly defined nips. A messy, loosely set knot can “capsize” under load, that is, change its shape and slip or come undone in the process. Long tails also provide a reserve, because under varying load the rope can slowly creep through the knot.

Friction hitches such as the Prusik use the same principle cleverly. A thinner cord is wrapped several times around a thicker rope. When the cord is pulled, the wraps press it firmly onto the rope and it grips. Without tension the wraps loosen and the hitch can be slid along. If the cord is too thick in relation to the rope, it grips poorly.

The material plays its part. Smooth, stiff or very thin cords have less friction than rough natural fibres. A knot that holds securely in a hemp rope can slip in a smooth plastic cord or in modern, very slippery high-performance fibres. For such materials you choose knots with more turns or add a backup to the tail.

Wetness, ice, dirt and wear also change friction, and not always in the same direction. That is why no fixed values can be given. Theory tells you the direction of an effect – more wraps, more hold; smoother material, less hold. How well a particular knot holds in a particular rope can only be shown by trying it.

A nice practical example is the round turn: the rope goes once completely around a post before being secured with half hitches. The round turn takes up a large part of the load, so the half hitches only have to hold a little. That is why even a heavy load can be held in a controlled way and released again.

For the experiment you need a cord a few metres long, a smooth pole – such as a broomstick or a railing – and a weight such as a full water bottle or a small rucksack. Hang the weight on one end and lay the cord once over the pole. Feel how much force you need at the other end to hold it.

Then put one, two, three full wraps around the pole and compare. You will notice that just a few wraps drastically reduce the holding force needed. Also try different cords: a rough cotton cord and a smooth plastic cord behave noticeably differently.

When practising, make sure nothing heavy can fall on feet or heads, and use only small weights. The experiment is meant to show the principle – it is not a test for ropes from which people or heavy loads will hang.

You meet rope friction in many places: on bollards in the harbour, on capstans and winches, with abseiling and belay devices in climbing, and when tying up a hammock. It is always about holding a large load with little hand force, or letting it out in a controlled way.

Friction also produces heat. If a rope slides quickly over another rope or over an edge, it can get so hot that synthetic fibres begin to melt. That is why rope should never run over rope under load. More about what weakens a rope is in the rope strength entry.