Textile Structure
how cloth is put together
Concept

Retraction — where it appears

How much shorter a twisted yarn is than the fibre in it, because every fibre off the axis follows a helix. It is the secant of each fibre's angle averaged over the section, so it grows as the square of the twist and decides how much fibre a metre of yarn holds, and so its count.

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

Z twist at 800 turns per metre. A 20 tex cotton yarn, 0.167 mm across, with its surface fibres drawn as the helices they are. The angle between a surface fibre and the yarn's axis is 22.8°, and it is the only quantity in this family: the yarn is 4.1% shorter than the fibre in it and carries 85% of the strength the same fibre would give lying straight.

Twist is one angle

Every model of cloth treats a yarn as a cylinder with a diameter. It is a bundle of loose fibres, and what makes it behave like a cylinder is twist — which is a helix, so the whole subject is one angle, and the trade's twist factor turns out to be the only combination of count and turns that decides anything.

setting · Twist 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

Named alongside it

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

Helix angleTwist factorCohesionFibre migrationFolding twistObliquityPacking factorPlyResidual twistSpecificationTexYarn count

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