The Heat Cost of Staying Dry: A Work-Rate Bound for Sealed Rain Garments

A waterproof garment that does not transmit water vapour keeps rain out by sealing the wearer in, and the wearer's own sweat then becomes the water problem. This paper derives a work-rate bound for that trade. Metabolic heat is computed from metabolic rate at 20% mechanical efficiency, a stated dry heat loss of 80 W is subtracted, and the remainder must be removed by evaporation at a latent heat of 2430 J/g. Each garment class is assigned a stated moisture vapour transmission rate over a covered area of 1.6 m2, giving a transmission capacity in grams per hour; sweat produced above that capacity is counted as internal accumulation. The activity ceiling — the metabolic rate at which required evaporation exactly equals transmission capacity — is 100.0 W for a sealed plastic garment (transmission 0 g/h), 167.5 W for oiled cotton (80.0 g/h), and 662.5 W for a standard breathable membrane (666.7 g/h). Ordinary work lies far above the first two ceilings: at 300 W a sealed garment accumulates 237.0 g/h of internal water and oiled cotton 157.0 g/h, while the membrane accumulates none. Above the ceiling the un-evaporated heat is stored in the body; at 400 W a sealed garment reaches a 1.5 K core-temperature rise in 27.1 minutes. Compared with the rain itself, a sealed garment in light rain at 2 mm/h makes its wearer wetter from sweat than the rain would have done above 160.7 W, and in moderate rain at 7.5 mm/h above 327.8 W; in heavy rain at 25 mm/h the crossover is at 859.4 W, outside any sustainable work rate, so there the seal still wins on wetness alone. The bound is an energy and mass balance, not a comfort prediction, and its most direct use is negative: below the stated ceilings is the only region in which a sealed garment can be worn for sustained work without the wearer supplying the water that wets them.