Textile Structure
how cloth is put together
Concept

Thermal conductivity — where it appears

How readily a material passes heat, in watts per metre per kelvin. For a fabric it is a two-phase mixture of fibre and air whose value lies between Wiener's parallel and series bounds — and at a cloth's solid fraction those bounds are further apart than the difference between wool and nylon.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

Also named here as tog — the same set of essays touches all of them, so they are one junction rather than several.

Where a muslin's warmth actually is. A muslin's own thermal resistance is 0.0108 m²K/W, and the still-air layer clinging to its outside is 0.12 — so 92 per cent of what a person is wearing is air that is not in the cloth. Wind takes it: the boundary layer thins as the square root of the speed, and above a few metres per second the air is also being driven straight through the fabric, which shorts out whatever resistance the fabric had. The pair leaves 22 per cent of the still-air value at 16 m/s. Both mechanisms take away air rather than cloth, which is why a windproof layer works and a thicker weave does not, and why the fibre — which the conductivity bracket could not separate anyway — never enters this figure.

The wind takes the air and not the cloth

A shirting's own thermal resistance is eight per cent of what a person wearing it has; the other ninety-two is a still-air layer half a millimetre thick clinging to its outside. Wind destroys both, and it destroys the larger one first and by a mechanism that has nothing to do with the fabric — so a windproof layer works by keeping air still rather than by resisting heat.

applied · Insulation Eight fibres through one cloth, and the bracket that hides them. A muslin is 19 per cent fibre and the rest air, so its thermal conductivity is a two-phase mixture, and how the fibre and the air are arranged is not something any amount of knowing the fractions settles. What is settled is Wiener's pair of bounds: heat across a series arrangement sees the harmonic mean and along a parallel one sees the volume average, and every real arrangement lies between. Each bar here is one fibre's whole band, from the series bound at its lowest published conductivity to the parallel bound at its highest. Not one of the eight clears any other, so this model cannot tell wool from nylon in a fabric — and the same cloth at twice the thickness has twice the resistance, exactly. Air's own conductivity is marked, and every band sits within a fifth of it.

Warmth is a thickness of air

A fabric is a tenth fibre and the rest air, so its thermal conductivity is a mixture of the two — and the pair of bounds that any mixture must lie between comes out narrower than the difference between wool and nylon. The model cannot tell one fibre from another in a cloth. What it can tell, exactly and with no bracket at all, is that twice the thickness is twice the warmth.

mechanics · Insulation Warmth is a canopy, and a canopy grows as a logarithm. Thermal resistance of sheeting against how much its hair population has been multiplied by raising, both faces counted. The unraised cloth is given no still air at all, because its hairs cannot reach one another — n_A λ² is under one and there is no canopy to hold air still. Past the threshold the canopy's depth is λ·ln(n_A λ²), so every doubling of the hair population adds the same depth of nap and no more: the steps here are 434 µm apiece, all the way up. At 256× the nap is 3.07 mm deep and worth 39 times the cloth it grows on, which is the whole reason a flannel is warm and a poplin of the same yarn is not — a canopy is two parts in ten thousand fibre, so its conductivity is air's, while the cloth itself is a quarter fibre. What is claimed is a conduction resistance across a depth of nearly still air; whether the air is still is a question about flow and is not asked here.

Warmth is mostly the hairs

This collection established that a fabric's thermal resistance is its thickness and not its fibre, and that twice the thickness is twice the warmth. It never asked what the thickness was made of. On a raised cloth almost none of it is cloth.

mechanics · Insulation

Named alongside it

The objects these essays reach for when they reach for this one.

Fibre volume fractionThermal resistanceTogAir permeabilityBoundary layerCanopy criterionCanopy depthCloth thicknessConvectionForced convectionHair layerNap

All concepts