Textile Structure
how cloth is put together
Concept

Ply — where it appears

A yarn made of two or more singles twisted together, usually the other way. The folding removes its own twist from each single exactly, so a folded yarn's singles are softer than the singles that went into it — and the ply's own helix supplies the grip that softness gave up.

Named by 13 essays across 4 fields — each of them below, with the objects they name alongside it.

The same thread count, twice. Two cloths with identical thread counts and different yarn. The count is the same number in both; the fraction of the surface the threads actually occupy is not, and that fraction is what thread count is usually taken to mean.

Thread count is not quality

It counts threads. It says nothing about how much of the cloth they cover, it can be inflated by counting plies, and it ranks fabrics in nearly the wrong order. The quantity it is mistaken for is cover factor, and that one is computable.

setting · Cover 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 Folding improves the evenness and not the yarn. Two independent singles of 15% give a fold of 10.61%, because independent errors add in quadrature: an improvement of exactly √2. The floor falls by exactly √2 as well, from 9.93 per cent to 7.02, because the fibre count is 2 times what it was. So the index of irregularity is unchanged — 1.511 before and 1.511 after, equal to twelve figures, not merely close. Folding does not make a better yarn; it makes a bigger one, and every part of the improvement is the part the count was going to give anyway. What folding does buy is elsewhere: the torque, the surface, and where the grip comes from.

A two-fold yarn is not twice a single

Folding halves nothing. It improves a yarn's evenness by exactly √2 and lowers the floor that evenness is measured against by exactly √2, so the index of irregularity comes out identical — folding does not make a better yarn, it makes a bigger one.

setting · Ply A bouclé at an overfeed of 0.80. A core of 20 tex running straight, an effect thread of 30 tex delivered 80 per cent faster than it, and a binder of 15 tex over the top. The surplus effect thread has nowhere to go but into loops, and their size is not a free choice: a semicircular loop of radius r consumes r(π − 2) of surplus, so at one loop every 3 mm the radius is 2.10 mm — 0.70 of the spacing. The yarn's resultant count is 89 tex and the sum of its three components is 65, because the effect enters multiplied by its own overfeed. What the drawing cannot show is the load path: the core and the binder are at the yarn's own length and the effect thread is longer than the yarn, so a pull on the yarn is carried by 39 per cent of its mass and the loops stay slack.

A fancy yarn has its crimp in the wrong thread

A bouclé is made by feeding an effect thread eighty per cent faster than the core it wraps, so the yarn contains more thread than it is long — which is crimp by this collection's own definition. A cloth's crimp is in the thread that carries the load, so removing it is the cloth's first extension. A bouclé's surplus is in a thread that carries nothing, so pulling the yarn stretches the core at once and the loops never straighten. Thirty-nine per cent of the yarn's mass is on the load path, and the other sixty-one is decoration.

fancy · Fancy yarn Where a fold's two moments cancel, and where the trade folds. The two moments about a fold's own axis, for 2 singles of 20 tex cotton at 800 turns a metre. The falling curve is what the singles' own residual twist supplies, which the folding takes out of them; the rising one is what bending each single onto its helix costs. They cross at 161 turns a metre, a ratio of 0.201, and the closed form for that crossing is C/(B+C) — the ratio of the two stiffnesses and nothing else. The shaded band is where the trade actually folds, 0.6 to 0.75 of the singles twist. The balance point is nowhere near it, by a factor of three.

The folding rule is not a torque balance

Fold a two-fold yarn at about two thirds of its singles twist. This collection has carried that as a bracket copied from the trade and derived nowhere. It is now derivable, the derivation gives a fifth rather than two thirds, and reaching two thirds would need a fibre stiffer in torsion than in bending.

setting · Ply Three rules for how hard to fold a yarn, and which one the trade uses. For 2, 3, 4 folds of 20 tex cotton at 800 turns a metre: the ratio that makes the fold's surface helix angle equal its singles', the ratio that sets the fold's net moment to zero, and the ratio the trade actually folds at. The surface rule is 1/√n exactly, because a fold of n singles is √n times the diameter. The torque balance is C/(B+C), which for this fibre is 0.201 and is the same at every count, every twist and every number of folds. The trade's brackets contain the surface rule in all three rows and the torque balance in none of them.

The folding rule is a surface angle

Fold at two thirds for two singles, six tenths for three, a half for four. Those are one over the square root of the fold count, they are what makes a fold's surface twist angle equal its singles', and all three of the trade's brackets contain the number exactly.

setting · Ply The fold the trade actually makes. 2 singles of 20 tex cotton at 800 turns a metre, folded at 566 — a ratio of 0.707. That is 1/√2, the ratio at which the fold's surface helix angle equals its singles' — 22.8° — because a fold of 2 singles is √2 times the diameter. The trade's own bracket for 2 folds is 0.6 to 0.75, and it contains this number.

What a balanced yarn is balanced about

A specification that says a yarn is balanced does not say which of two conditions it means, and the two have different numbers, different dependences and different consequences. One of them is what folding achieves and the other is what folding is said to achieve.

setting · Ply Three rules for how hard to fold a yarn, and which one the trade uses. For 2, 3, 4 folds of 20 tex cotton at 800 turns a metre: the ratio that makes the fold's surface helix angle equal its singles', the ratio that sets the fold's net moment to zero, and the ratio the trade actually folds at. The surface rule is 1/√n exactly, because a fold of n singles is √n times the diameter. The torque balance is C/(B+C), which for this fibre is 0.201 and is the same at every count, every twist and every number of folds. The trade's brackets contain the surface rule in all three rows and the torque balance in none of them.

A cabled yarn is a fold of folds

The rule that sets a fold's twist is one over the square root of the number of components. Apply it twice and a cabled yarn's three twist levels are fixed by two integers — which is a prediction with no free constants, about a class of yarn the trade quotes no rule for at all.

setting · 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.

Helix angleTwist factorYarn countFolding twistSpecificationResidual twistBalanceTwistPacking factorRetractionYarn diameterContact efficiency

All concepts