Textile Structure
how cloth is put together
Concept

Pick density — where it appears

How many picks per unit length a cloth is woven at, set by the take-up gear rather than by the reed. It is limited by a force budget rather than by geometry, which is why a loom's achievable picks come in discrete steps.

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

What the two setts can be set to. Two rules on one scale from 8 to 40 threads per centimetre. The upper carries the 49 warp setts a metric reed catalogue reaches at one to four ends per dent; the lower carries the 4825 pick densities a change-wheel take-up reaches. The mean spacing is 0.656 threads per centimetre in the warp and 0.0066 in the weft, a ratio of 99. The widest gap in the reed's range is 2.10 threads per centimetre.

The setts a loom can reach

Transposing a draft gives a perfectly good draft, and every count this site takes off a matrix either is symmetric under exchanging warp and weft or has a mirror twin. The loom is not symmetric at all: over the range ordinary cloth is woven in, it can choose a pick density 99 times more finely than a warp sett — and the warp sett cannot be changed once the warp is drawn in, at any granularity whatever.

setting · Take-up The two halves of a beat-up force. The force the reed must apply per metre, for a sheeting, against the number of picks that are still sliding against the warp. The elastic half — the warp tension times the crimp's elasticity with respect to the pick spacing — is 573 N/m and does not depend on the zone at all; that cancellation is exact and is the result the rung below established. The frictional half is 1133 N/m per sliding pick and is nothing but zone. Against a reported 400–1500 N/m, that leaves room for at most 0.82 picks sliding — so the fell region a weaver can see, ten to fifty picks deep, is not the same quantity as the picks that are still moving. What the rows cannot show is that this is a static friction throughout, and a beat-up is a blow.

The half of the beat-up that is all zone

The elastic half of the beat-up force is exact and the length of the beat-up zone cancels out of it, which is this site's own result and disagrees with every practical account of weaving. The frictional half is nothing but zone — and requiring the total to match the force a loom is actually built to apply puts the number of picks still sliding at about one.

setting · Beat-up One weft fault at three periods, a fraction of a millimetre apart. A 260 mm slice of a 1500 mm cloth at 22 picks per centimetre, 220 picks deep, with a thick place recurring along the weft. Each pick takes a whole width of yarn, so the marks land 35 to a pick across the full width and step sideways by the remainder of the width divided by the fault's period. On the left that remainder is zero and every thick place in the piece falls in the same columns — a warp-way stripe made entirely by a weft fault. In the middle the period is five hundredths of a millimetre longer and the same fault draws steep diagonals. On the right it is a third of a millimetre longer again, the marks land nowhere near each other, and the fault reads as texture. Nothing about the yarn distinguishes the three; the cloth's width does. The slice is drawn rather than the whole width because thirty-five marks a pick fill a panel solid at any step but zero, which is a true picture of a dense pattern and a useless one of its structure.

A slub finds the width of the cloth

A thick place recurring along a weft yarn does not make a bar. It makes diagonals — and when the cloth's width happens to be a whole number of fault periods, it makes stripes down the piece instead, from a fault that is entirely in the weft.

pattern · Moire The magnification a cloth will carry. The largest magnification a moiré can be read at, against the irregularity of the cloth making it. The points are measured: a grating whose spacings are drawn from a seeded lognormal is laid against a perfect one, the fringes are found from the phase difference, and the gain is recorded at which their count first departs from what the ideal beat predicts. The product of the irregularity and that gain comes out at 0.82 to 0.84 across every irregularity tried, so the ceiling is 0.84 divided by the coefficient of variation — the solid curve. The dashed curve is the accumulated-wander model, in which position errors random-walk and the ceiling goes as the inverse square; it is wrong by a factor of 42 at a two per cent irregularity. What the plot cannot show is what a cloth's spacing irregularity actually is: it has not been measured, and the curve is therefore a prediction with an unmeasured input.

A moiré is a vernier, and it magnifies the error too

Two gratings a per cent apart in pitch beat at a hundred pitches, so a moiré reads a pitch difference at a hundred times — which is what a vernier is. The magnification is free and its ceiling is not: the fringes split when one thread's own spacing error reaches 0.84 of the pitch difference the beat is built on, so the usable gain is 0.84 divided by the cloth's coefficient of variation, inversely and not inverse-squarely. At an ordinary yarn's spacing irregularity, a moiré carries a magnification of five.

pattern · Moire The tucked-in edges of a 2/2 twill, 8 ends wide. A strip of 2/2 twill 8 ends wide over 8 picks, woven with tucked-in edges: every pick is cut at both edges and each tail is laid back into the next shed, so between every pair of picks there is a turn at both edges. 8 of the 16 tucked turns are caught, where the edge end is on the other face in the next shed, and 8 are not. Across all its edge placements the weave catches every tucked turn at 0 of 16. What the drawing cannot show is the tail itself, which lies alongside the next pick for the tuck's length and doubles the weft there.

A tucked-in edge asks every weave the odd repeat's question

A shuttle weft turns at one edge per pick, alternately, and that alternation is what let a 2/2 twill hold both selvedges with two ends re-entered on its own shafts. A rapier or air-jet loom cuts every pick at both edges and tucks both tails into the next shed, so every boundary between picks is a turn at both edges — the question an odd repeat always asked. Only a plain column answers it. Of the 22,874 four-by-four drafts, 10,382 can still hold their edges on their own shafts, against 13,238 under a shuttle; the 2/2 twill is among the 2,856 lost. And the tucked zone carries two picks in every shed, which lies flat only below between a half and two thirds of a weave's maximum pick density.

weaves · Firmness One warp feed, in the body and in a tucked zone of plain weave. A section along one warp end of 20 tex cotton, in plain weave woven at 70 per cent of its maximum pick density, in the body of the cloth and in the tucked zone with two picks to a shed. Both ends are fed the same length per pick, so the zone's end rises only 0.124 mm against the body's 0.161 mm, and the weft takes up the difference. The cloth is 0.341 mm thick in the body and 0.377 mm in the zone, 11 per cent thicker. The climb between crossings is drawn smooth rather than as the model's arcs and tangent.

A tucked edge stands proud because its warp goes straight

A tucked zone holds two picks in every shed, and the obvious account is that the pairs run out of room and bulge. The loom says otherwise: the warp is let off as one sheet and the cloth taken up at one speed, so the zone's ends have only the body's length to spend. They rise less. The weft takes up the height, so the edge is proud well before the pairs stop fitting, and they stand up well after the count says they must.

weaves · Firmness

Named alongside it

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

BeatCrimpJammingMeasurementMoirePeriodPlain weavePopulationReedSelvedgeTake-upAppearance

All concepts