Wednesday, April 14, 2010

Mathematics Reveal Universal Properties Of Old Rope

 For 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
Mathematicians prove that a three-stranded rope is always 68% the length of its component strands, regardless of the material from which it is made.

Despite rope's obvious geometric properties, the art of rope making has been strangely neglected by mathematicians over the centuries. Today, Jakob Bohr and Kasper Olsen at the Technical University of Denmark put that right by proving the remarkable property that ropes cannot have more than a certain number of turns per unit length, a number which depends on the diameter of the component strands.

And that's just the start. They go on to show that a rope with a smaller number turns than this maximum will always twist in one direction or another under tension. So they call this maximum number of turns the zero-twist configuration.


Via: Technology Review

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