Textile Structure
how cloth is put together
Series

Hairiness — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. The two diameters of a 20 tex yarn. The pressure inside a twisted yarn is zero at its surface, so the outermost fibres are held by nothing but their own buried ends and some of them stand off as loops and ends. A yarn therefore has two diameters: a mass diameter of 167.1 µm, which is a volume divided by a length and is the one every other calculation on this site uses, and a contact diameter of 217.1 µm, which is what a neighbouring thread, a finger or an air stream meets. The gap is a hair layer of 25.0 µm on each side and it is measured, not computed — nothing here predicts hairiness. What is computed is the consequence, and it is 29.9% of the diameter every cover factor on this site was built from.

    The hairs are what touch

    The pressure inside a twisted yarn falls to exactly zero at its surface, so the outermost fibres are held by nothing and some of them stand off. A yarn therefore has two diameters — the one its mass gives and the one a neighbour meets — and only the first is in the arithmetic.

    part 1 · cloth
  2. The two diameters of a 20 tex yarn. The pressure inside a twisted yarn is zero at its surface, so the outermost fibres are held by nothing but their own buried ends and some of them stand off as loops and ends. A yarn therefore has two diameters: a mass diameter of 167.1 µm, which is a volume divided by a length and is the one every other calculation on this site uses, and a contact diameter of 217.1 µm, which is what a neighbouring thread, a finger or an air stream meets. The gap is a hair layer of 25.0 µm on each side and it is measured, not computed — nothing here predicts hairiness. What is computed is the consequence, and it is 29.9% of the diameter every cover factor on this site was built from.

    Singeing is the cheapest change to a surface

    Pass a cloth through a flame fast enough and it loses under one per cent of its mass. What it loses is the part of itself that was doing most of the touching, and lustre, friction, printability, pilling and measured cover all move at once.

    part 2 · finishing
  3. A hair layer is a balance, so singeing does not stay done. The hair population of a 20 tex cotton yarn under rubbing, started from a singed cloth and from an unusually fuzzy one. Abrasion does two opposite things: it frees ends that spinning left buried, from a supply of 2.23 per millimetre in the surface shell, and it removes hairs that are long enough to be caught. Where the two meet is a fixed point at 1.43 per millimetre, and the cloth goes there from either side with the same time constant — 248 cycles to halve the distance, whichever direction it is travelling. A singeing is therefore undone in a few hundred rubs, because the flame changed the stock and not the balance. What is predicted here is that a fixed point exists, that it does not remember the starting state, and that one rate serves both directions; where it sits relative to the spun level needs two rates the model does not supply, and it is set to reproduce the one thing everyone has noticed, which is that fabrics get fuzzier as they are worn.

    A hair layer is a balance, not a stock

    Singeing takes under one per cent of a cloth's mass and changes its lustre, its friction, its printability and its pilling. It also does not stay done, because rubbing frees fibre ends as fast as it breaks them off, and a flame changes the stock while leaving the balance exactly where it was.

    part 3 · finishing

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