Textile Structure
how cloth is put together
Generator

What the folding twist costs, which is almost nothing

What the folding twist costs, which is almost nothing
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.

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.

3 essays call ply-curve. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

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. Setting and geometry

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.

 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. Mechanics and drape

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.

 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. Setting and geometry

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.

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