The Wind Shell Bound: How Much of a Loose Insulating Layer's Still-Air Value Moving Air Destroys, and the Shell Permeability That Restores It

Insulation values are quoted for still air, but people wear clothing in moving air, and a loose insulating layer can lose most of its value to wind long before the wearer judges the weather severe. This paper originates a bound on that loss. A reference garment with a still-air total resistance of 0.65 square-metre kelvins per watt (4.19 clo), of which 0.50 is a loose insulating layer, is modelled with an effective layer resistance that falls as R_ins divided by (1 plus v over v_c), where the characteristic speed v_c is set by the fabric's air permeability. For a loose knit outer with no shell (air permeability 600 millimetres per second), the whole garment falls to half its still-air value at a wind speed of only 1.84 metres per second, retains 29.5 percent of its value at 5 metres per second, and retains 20.1 percent at 10 metres per second. A woven wool outer (permeability 150) halves at 5.93 metres per second; an ordinary woven jacket cloth (permeability 40) halves at 19.71 metres per second and still retains 63.3 percent at 10 metres per second. A thin wind shell changes the result by an order of magnitude: a shell of permeability 10 keeps 79.3 percent of still-air value at 10 metres per second, and a shell of permeability 3 keeps 84.5 percent. The shell specification derived here is that keeping the total loss under 20 percent requires a permeability no greater than 23.0 millimetres per second at 5 metres per second wind, 8.5 at 10 metres per second, and 5.0 at 15 metres per second. A stricter target fails outright: a loss under 10 percent is unattainable at 5 metres per second or above at any permeability, even with a perfectly impermeable shell, because the external surface resistance alone falls by 11.3 percent at 5 metres per second. The practical bound is therefore twofold: unshelled loose insulation is a still-air product whose rating should be discounted by half in a light breeze, and a cheap thin shell of modest specification recovers most of the loss that any shell can recover.