The Lay of a Three-Strand Rope: The Helix Angle That Carries the Most Load per Kilogram of Fibre

A rope is fibre spent along a helix, and the steepness of that helix, the lay, is the rope maker's central compromise. Lay the strands softly and they run nearly parallel to the load, which is efficient, but the rope is limp, easily damaged, and prone to unlaying; lay them hard and the rope is round, stable, and handsome, while a growing share of its fibre points sideways, where it carries nothing, and friction between strands begins to tax what remains. This paper computes the compromise for a stated three-strand rope: breaking load and fibre consumed per metre across lay angles, combined into the figure a fibre buyer cares about, load carried per unit of fibre used. In the computed results, the best angle deg is 20; the best load kn is 25.64; the best lay length mm is 104; the best merit is 24.1; the strongest angle deg is 22. Choose the lay by the figure of merit that matches the sale: maximum load for a rope sold on its rating, maximum load per fibre for a rope sold by length from bought fibre. The study is simulated, not measured; all inputs are stated assumptions, printed in the accompanying computation, which readers may replace with their own values and re-run.