Textile Structure
how cloth is put together
Series

Insulation — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 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.

    part 1 · mechanics
  2. 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.

    part 2 · applied
  3. 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.

    part 3 · mechanics
  4. A knit's warmth is its thickness, and a rib's thickness is a machine setting. Thermal resistance in tog for a 20 tex cotton at a 3.5 mm loop, for a plain jersey and for a one-by-one rib at four bed gaps. The bar is the lower bound and the mark beyond it is the upper — Wiener's two bounds on a mixture of fibre and air at the fabric's own fibre fraction, which is 26.6% for the jersey and falls to 8.9% for the widest rib. The jersey holds 0.088 tog and the rib at five diameters 0.334 — a factor of 3.8, bought entirely by opening the beds. Every one of these is a small fraction of the still-air layer that clings to a garment's outside, which is worth about 1.2 tog on its own.

    A knit is warm because of where its yarn is not

    Warmth is a thickness of still air, and until a knitted fabric had a thickness there was nothing to compute. It has one now, and the answer is that a rib's warmth is a machine setting: opening the beds from two diameters to five nearly trebles the fabric's resistance without changing a gram of yarn.

    part 4 · applied

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