Where a Loaded Rope Breaks: Coils, Weight and the Pulley
The multiplying grip of wrapped turns and why a cord fails at its weakest, most-loaded point
Written in two columns around an arched frame diagram, the folio continues Leonardo's study of ropes. He observes that a cord wound in many turns grips ever more tightly, each successive turn adding a pound of holding power so that a hundred turns hold as with a hundred pounds. Under the heading 'Conception' he reasons that a uniform cord breaks where it is weakest, which is where it feels the most weight, and that such a cord snaps at the middle of its length when its two ends are equally fastened. A further passage explains why the part of a rope bending over a pulley becomes the point of least resistance, its outer fibres stretched longer than its central line.
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Coiled turns multiply a rope's grip
A thing is bound more tightly by a cord wrapped in many turns, one over another. A continuous force of one pound gives, at the first turn, a grip of one pound; at the second, two pounds; at the hundredth, a hundred, like a hundred weights stacked one upon another all pressing on the support of the first.
A uniform cord breaks where it feels most weight
'Conception': a cord of uniform strength breaks where it becomes weakest, and it is weakest where it feels the greater gravity, that is where its whole weight bears rather than a part. When broken at the point of equality, with ends of equal resistance and density, it parts at the middle of its length.
Why the rope thins where it bends over the pulley
The part of the cord that curves and rests on the pulley becomes least resistant: from the middle of its thickness up, its outer edge stretches longer than its central line, while the inner side shortens. The stretched outer part gains more weight than the compressed inner part loses. A cord broken at the point of equality between unequal fastenings parts at its stronger anchor, like a rope snapped by hand.
Arched frame diagram accompanying the rope study
An arched, hatched frame is drawn at the head of the left column, of the kind Leonardo uses to mount a pulley for testing a loaded cord. Its lettered labels are not included in the transcription and are not read here.