How Long Does Proofed Cotton Stay Waterproof? A Reproofing Interval Rule and the Cost per Dry Hour

Oil- and wax-proofed cotton is sold and used on an understanding that it sheds water, with re-treatment advised in vague terms such as "from time to time" or "when water stops beading". This paper replaces the vagueness with a sizing rule. Hydrostatic resistance is modelled as decaying exponentially with wearing days, from a fresh value of 900 mm under two stated mechanisms: flexing at 10,000 flex cycles per wearing day with a decay constant of 3.0e-6 per cycle (0.030 per day), and rain wash-out at 0.008 per rain-hour at a reference intensity of 5 mm/h, scaled with intensity. Leakage is taken to begin when resistance falls below a stated threshold of 350 mm, which gives a re-treatment interval of ln(900/350) divided by the daily decay rate. The interval is 31.5 wearing days for dry wear alone, 24.9 days at 1 rain-hour per day, 17.5 days at 3 rain-hours per day, and 12.1 days at 6 rain-hours per day or at 3 rain-hours per day in 10 mm/h rain. At typical use — 3 rain-hours per day — resistance falls from 900.0 mm to 524.5 mm in 10 wearing days and crosses the threshold at 17.5 days, which is 4.4 weeks at 4 wearing days per week. Costed over a stated season of 120 wearing days and 360 rain-hours, the proofed-cloth route needs 7 treatments per season and costs $140.33 per season, or $0.390 per dry hour ($0.609 with reproofing labour valued); a stated plastic poncho at $14 replaced every 25 wearing days costs $70.00 per season, or $0.194 per dry hour — exactly half. Proofed cotton is therefore not the cheap route to staying dry on these figures; what the premium buys is durability, repairability, and a garment that remains serviceable for years, and the interval rule states how often that garment must be maintained for the waterproofing claim to remain true.