Textile Structure
how cloth is put together
Series

Ply — the series

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

    part 1 · setting
  2. 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.

    part 2 · setting
  3. 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.

    part 3 · mechanics
  4. 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.

    part 4 · setting
  5. 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.

    part 5 · setting
  6. 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.

    part 6 · setting
  7. 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.

    part 7 · setting

All series