A Warp Tension Bound for the Hand Loom: The Highest Setting That Keeps Expected Breaks Below Two per Thousand Picks

Warp tension on a hand loom is usually set by feel and defended by results: if the cloth weaves well and the ends hold, the tension was right. That method fails silently in one direction. A weaver can run a warp considerably tighter than necessary for months, paying for it in a slow drip of breaks that is blamed on the yarn, because nothing in the feel of the loom announces that the last quarter-turn of the ratchet doubled the expected break rate. This paper computes that relationship directly, from stated distributions for yarn strength and for per-end load, and draws the bound a tension setting should not cross. In the computed results, the bound tension cn is 85; the bound breaks is 0.2; the bound pct strength is 28.3; the next step breaks is 2.1; the high tension breaks is 487.7. Set working tension by the break criterion, not by a fraction of breaking strength quoted without a distribution. 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.