Textile Structure
how cloth is put together
Concept

Folding twist — where it appears

The turns per metre put into a folded yarn, quoted as a fraction of the singles' twist. It is chosen to cancel the yarn's residual moment rather than to make it strong, which is possible because a folded yarn's strength barely varies across the whole range of ratios.

Named by 6 essays across 3 fields — each of them below, with the objects they name alongside it.

Folding, and what it takes out of the singles. Two 20 tex singles spun at 800 turns per metre and folded the other way at 460 — a ratio of 0.575, which is the trade's own and is a measurement rather than a derivation. A single held at its ends and wound round its neighbour turns about its own axis once for every turn of the fold, so it is left with 340 turns per metre of its own: its surface fibres lie at 10.1° to its axis rather than the 22.8° they were spun at. Folding untwists. The short strokes are drawn at that residual angle; the two long curves are centre lines and are not the yarn — each strand is itself a bundle of 118 fibres, and the residual angle is what holds them.

A sewing thread is a different animal

It is folded, balanced, lubricated and finished, and every one of those is an answer to a requirement no weaving yarn has. The lubricant is the interesting one: it makes the thread sewable by lowering the friction that was holding its own fibres together.

applied · Seams Folding, and what it takes out of the singles. Two 20 tex singles spun at 800 turns per metre and folded the other way at 540 — a ratio of 0.675, which is the trade's own and is a measurement rather than a derivation. A single held at its ends and wound round its neighbour turns about its own axis once for every turn of the fold, so it is left with 260 turns per metre of its own: its surface fibres lie at 7.8° to its axis rather than the 22.8° they were spun at. Folding untwists. The short strokes are drawn at that residual angle; the two long curves are centre lines and are not the yarn — each strand is itself a bundle of 118 fibres, and the residual angle is what holds them.

Folding is untwisting

Wind two singles round each other and each one turns about its own axis once per turn of the fold. So a folded yarn's singles are not the singles that went into it, and at a folding ratio of exactly one half the two helices cancel.

setting · Ply What the folding twist costs, which is almost nothing. Folding takes twist out of the singles, which loosens their grip on their own fibres, and puts a helix round the outside, which presses on them. The two nearly cancel. The lower curve is the singles' own contribution and it collapses as the folding twist rises; the upper is the pressure the fold supplies, in the same units; their product — the yarn's realisation — runs from 0.770 to 0.696 across the whole range, a spread of 7%. The shaded band is the folding ratio the trade uses, which is chosen for torque balance and not for strength. That the two questions can be separated is the result: a spinner is free to fold for balance precisely because strength barely notices.

The singles inside a ply are not the singles

Folding leaves each single with a fraction of its own twist, which should ruin its grip on its own fibres. It does not, because the ply's helix presses on the singles exactly as a single's helix presses on its fibres — and across the whole practical range the two very nearly cancel.

mechanics · Ply What a 2-fold yarn weighs against the sum of its singles. The count of a 2-fold cotton yarn against the sum of its singles' counts, as the folding twist runs from three tenths to nine tenths of the singles' twist, at twist factors of 3000, 3800, 4500 (turns a metre times the root of the tex). Below a ratio near two thirds the fold is lighter than the sum, above it heavier; the curves cross the sum at 0.661 at 3000, 0.658 at 3800, 0.654 at 4500, and in the small-angle limit at exactly 0.6667. The trade's folding band, 0.6 to 0.75, is shaded, and across it the fold is within −0.6% and +1.3% of its notation. What the curves cannot show is a real fibre's migration between the core and the surface of each single, which the ideal helix leaves out and which shortens the path both lengths are computed from.

Two thirds is where a fold weighs its singles

A folded yarn's count is written as its singles' count divided by the number folded, as though folding changed no length. It changes two. The fold's helix wraps each single round the yarn's axis, which puts more single into every metre, and the untwisting straightens each single's fibres, which puts less fibre into every metre of single. Each is three to seven per cent at a weaving twist. They cancel at a folding ratio that is exactly two thirds in the small-angle limit — the folder's own number — and six elevenths for three singles and two fifths for four.

setting · Count What a 2×2 cable weighs as its cable twist rises. A cotton cable of 2 folds, each of 2 singles, with the folds set at 0.707 of the singles' twist and the cable twisted the singles' way at ratios from nought to 0.60, at twist factors of 3000, 3800, 4500. A little cable twist makes the cable lighter, because it takes twist out of folds set above their own crossing; then the cable's own helix wins and the count climbs. It crosses the singles' sum at 0.260 at 3000, 0.250 at 3800, 0.239 at 4500. At the rule as quoted, a cable twist of 0.500, the cable is +2.21%, +3.54%, +4.95% heavy; at the rule read in the finished thread, 0.293, it is +0.16%, +0.32%, +0.54%. What the curves cannot show is a real cable's folds pressed out of round, which shortens the cable's helix and moves every crossing right.

A cable weighs its singles at the twists the finished thread keeps

Cabling untwists every fold and hands that twist back to the singles inside it, so beneath its own helix a cable is a fold folded at the difference of two twists — and the cable's helix is a length nothing below it can pay for. Twisted where the cabling rule is quoted, a two-by-two weighs three and a half per cent over its notation. Read in the finished thread, with every level's surface at one angle, the same rule sets the folding frame exactly where a plain fold's is and the cable at 0.293, and the cable comes back to within half a per cent.

setting · Count What a thread of twos weighs as its levels of twist are added. A two-fold, a cable of two two-folds, a cord of two such cables and a cord of two cords, all of 20 tex cotton singles, each twisted so that every level's surface sits at one angle in the finished thread, at twist factors of 3000, 3800, 4500. At 3,800 they weigh fold −1.35%, cable +0.32%, cord +2.02%, cord of cords +3.75% against the sum of their singles: a fold light, a cable on its notation, and every level after it one helix heavier than the last. Dashed, the same four twisted to the rule as quoted on the frames, +0.46%, +3.54%, +4.54%, +6.98%. What the chart cannot show is the folds' and cables' real shape, which is taken round.

The singles pay once and every level adds a helix

A cable twisted so that every level's surface sits at one angle weighs its notation, and it is tempting to read that as a law: equal angles, honest count. It is not one. With every surface at one angle the singles keep the same twist however many levels sit above them, so their saving is paid once, while every level adds a helix of the same length. A two-fold comes out light, a cable on its notation, and a cord of two such cables two per cent heavy — the cable's agreement is the walk passing through zero. For a cord to weigh its notation, everything above its singles has to sit at about half their angle.

setting · Count

Named alongside it

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

PlyHelix angleResidual twistTwist factorRetractionSpecificationYarn countContact efficiencyCritical lengthFrictionAbrasionObliquity

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