The Found-Rope Problem: A Derating Schedule for the Safe Working Load of Used Rope

A rope found beside a well, in a barn, or on a building site arrives without a history, yet people routinely trust it with a full bucket, a load of blocks, or a piece of machinery. This paper constructs a multiplicative derating schedule that starts from stated new-rope breaking strengths for manila, nylon, polyester, and polypropylene at diameters of 6 mm, 8 mm, 10 mm, 12 mm, 16 mm, and 20 mm, and then applies separate factors for age, abrasion, ultraviolet exposure, wetness, and a knot in the line. With a design factor of 5 applied after derating, a pristine 12 mm nylon rope with a new breaking strength of 27.0 kN has a safe working load of 5.4 kN, or 550.5 kg, whereas the same rope in a heavily degraded found condition — product factor 0.0862 — has a derated breaking strength of only 2.327 kN and a safe working load of 0.465 kN, or 47.4 kg. A single blanket rule that divides new breaking strength by 10 gives 2.7 kN, or 275.2 kg, for that rope in every condition: it discards half the justified capacity of a pristine rope, it roughly matches a lightly used rope, and in the heavily degraded case it exceeds the derated breaking strength itself, with a ratio of 1.16 to that derated strength, so a load permitted by the blanket rule could break the rope before any design factor is reached. The schedule therefore replaces a single divisor with an inspection-based product of factors, tabulated here for common sizes and for conditions ranging from pristine to heavily degraded.