Sun Protection of Common Cloth, and Its Collapse When Wet and Stretched: A Post-Penalty Selection Rule

Cloth is the sun protection most outdoor workers actually use, but the protection printed or assumed for a dry, relaxed garment is not the protection delivered by a sweaty shirt stretched over working shoulders. This paper models ultraviolet transmission of common fabrics as the sum of light passing through the open fraction of the weave and light transmitted through the yarns, with yarn absorption set by material (cotton, polyester, or a blend), dye depth, and thickness, and then applies two penalties: wetting, which reduces the effective absorption (to 0.45 of its dry value for cotton, 0.60 for a blend, 0.75 for polyester), and a stated 10% area stretch, which thins the cloth and opens the weave. The white cotton T-shirt that field workers commonly wear has a dry protection factor of only 2.5, falling to 1.4 when wet and stretched. Dry ratings mislead in both directions of quality: a dark cotton denim shirt rated 85.1 dry falls to 7.9 after the penalties, and a dark blend work shirt rated 20.0 dry falls to 5.8. Of 14 common garments modelled, none retains the stated target protection factor of 15 after wetting and stretching; the best, a dark woven polyester work shirt costing a stated $12, retains 12.2 and is the least-cost garment retaining at least 10. The paper therefore states a selection rule — choose on the post-penalty protection factor, never the dry one — and specifies a construction that does meet the target: a dark woven polyester canvas shirt with open fraction at most 0.0205 and thickness at least 0.60 mm, whose reference form (open fraction 0.012, thickness 0.85 mm, stated cost $18) retains a protection factor of 16.9 after both penalties. Cotton constructions of similar dry rating do not meet the target at any modelled thickness of ordinary shirt cloth, because the wet penalty, not the dry rating, is what decides the result.