Footwear Drying and the Rotation Rule: A Drying-Time Bound and the Number of Pairs a Wet Climate Requires

Wet footwear worn day after day keeps the foot damp for most of the day, and prolonged skin dampness is a recognised setting for fungal infection and skin breakdown. Advice to "rotate your shoes" is common, but it is rarely stated as a number. This paper derives such a number. Water mass in a pair after a wet working day is modelled as decaying exponentially toward an equilibrium set by ambient humidity, at a rate set by the vapour-pressure deficit, airflow, and construction. Three constructions are evaluated — a leather boot starting with 180 g of water, a canvas shoe with 120 g, and a rubber boot with 70 g in its lining zone — in four climates from warm, dry, and ventilated (30 °C, 40% relative humidity) to humid and still (28 °C, 90%). A pair is dry enough at 30 g (leather), 20 g (canvas), or 15 g (rubber), and the foot is counted as damp-exposed above 60 g, 40 g, and 30 g respectively. In temperate indoor conditions (20 °C, 65%) the leather boot needs 45.0 hours to dry enough and the rubber boot 74.4 hours, so the usual two-pair rotation, which gives each pair 38 hours of rest, is sufficient only for the canvas shoe (18.3 hours); the leather boot needs three pairs and the rubber boot needs more than three. In the humid still climate the leather boot needs 149.8 hours, the rubber boot never reaches its dry-enough level at all because its equilibrium moisture (18.0 g) sits above the 15 g target, and no rotation of two or three pairs keeps a leather or rubber pair below even the damp threshold. Worn daily as a single pair, every construction in the temperate, cool-damp, and humid climates leaves the foot above the damp threshold for 24.0 hours per day (19.9 hours for canvas in temperate conditions). Only in the warm, dry, ventilated climate does a single pair suffice for all three constructions. The rotation rule that follows is simple: count the pairs so that the rest interval, 14 hours plus 24 hours for each additional pair, exceeds the drying time for the construction and climate in question — and where it cannot, change the drying conditions, not the arithmetic.