How Long Should a Warp Be? Setup Time, Loom Waste and Fault Risk in One Balance

Every warp begins with hours of work that produce no cloth: winding, beaming, threading, sleying. Every warp also ends with a length of yarn that was threaded, tensioned, and never woven. Both costs are charged per warp, so both argue for long warps; yet every experienced weaver also knows the long warp's counter-argument, the slow accumulation of tension drift, sticky ends, and faults that a short warp never lives to meet. This paper puts all three effects into one seasonal account for a stated schedule of orders, and finds the warp length at which their sum is least. In the computed results, the best length m is 60; the best warps is 4; the best cost index is 1026; the short cost index is 1279; the short warps is 16. Dress the loom for the computed middle length, and re-derive it when the construction changes. 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.