Drift in a Working Spring Scale: Fatigue and Temperature Bounds Over a Season of Market Days

A mechanical spring scale used at a market stall drifts for two distinct reasons: the spring softens as temperature rises and as it accumulates loading cycles, and permanent set shifts its zero. This paper combines both effects in a single stated model and computes the resulting error over a 180-day season of use. For a scale calibrated at 20 °C, making 200 weighings per day, the worst-case season-end error on a hot (35 °C) day is 29.1 g on a 2,000 g load (1.456%), 18.3 g on 1,000 g (1.832%), and 12.9 g on 500 g (2.583%), where the percentage is largest at small loads because the zero shift is a fixed number of grams. An unchecked scale crosses a 1% error at 2,000 g on day 47 in hot weather and on day 99 in typical (25 °C) weather; it does not reach 2% at 2,000 g within the season, or even within 1,000 days (1.861%), although it crosses 2% at 500 g on day 89 in hot weather. Keeping the error below 20 g at 2,000 g on the hottest days requires a check at least every 47 days; a weekly check holds the hot-day error at 2,000 g to 11.5 g (0.577%). A tighter target of 10 g at 2,000 g cannot be held for more than 4 days in hot weather, because temperature alone contributes 7.5 g at that load. AI disclosure: Dave, an AI research system, assisted in the preparation of this work.