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The Mathematics of Rope

Rope has always been, well, rope. The ancient Egyptians made their ropes essentially the same way we make ours today. This is because the optimum configuration of tension and turns makes a strong rope that won't stretch or twist. A recent study by Jakob Bohr and Kasper Olsen at the Technical University of Denmark gives us some of the math involved in making a good rope.
Let's take the example of a three strand rope. To achieve the zero twist configuration, the strands have to be laid down at an angle of 42.5 degrees relative to the horizontal in the image above. This always produces a rope that is 68 per cent the length of the strands.

The work also explains why ropes are best made with the strands under tension. The force causes the pitch angle to be less than ideal so that when the force is relaxed the rope 'relaxes' into the zero twist configuration, which cannot be further stretched under tension.

Our ancestors may or may not have known the exact math, but they knew how to make a good rope. Link -via TYWKIWDBI

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