Textile Structure
how cloth is put together
Concept

Appearance — where it appears

What a cloth looks like, as distinct from what it is made of, which the surface pattern and the lustre together decide. Two drafts can share an appearance and differ in every structural quantity here.

Named by 7 essays across 5 fields — each of them below, with the objects they name alongside it.

The 2/2 twill. The 2/2 twill on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.

The diagonal is not a thread

A twill's diagonal is the most looked-at feature in weaving and the most misdescribed. No thread in the cloth runs diagonally. What runs diagonally is a pattern of which thread is on top, which is a different sort of object.

pattern · Pattern Z twill, Z twist. A square of cloth with two directions on it. The broad lines are the twill, whose angle 45.0° from the warp comes from the setts alone — 24 ends and 24 picks per centimetre. The fine lines are the surface fibres of the warp ends, at 25.3° from the warp because the yarn is twisted 900 turns per metre. Between them is 19.7°, and that is the whole of the rule.

Twist and the twill line

The oldest rule of thumb in weaving says to weave a Z twill from S-twist warp for a bold line and from Z-twist warp for a subdued one. Both halves of it are geometry: the twill's angle comes from the two setts, the fibres' angle comes from the twist factor, and the rule is their difference.

setting · Twist The same error twice: scattered, and in a period. Two bands of 96 ends, drawn at spacings that differ from the reed's by the same root-mean-square amount — 6% of a dent, which is 25 µm. The upper band's errors are independent; the lower band's repeat every 8 ends, which is what one shaft set forward or one dent of the reed too wide produces. The displacement is drawn 8 times over scale, because at true scale it is half a pixel and both bands are picket fences; the arithmetic below it is at the true amplitude. The upper band reads as an even cloth with a little texture in it and the lower one has stripes, and nothing about the eye is needed to say why: at 96 ends the periodic arrangement is 7.7 times stronger at its own frequency than the scattered one is at any frequency, and over the 256 ends a buyer takes in at once it is 12.8. The ratio grows as the square root of how much cloth is looked at, which is why a fault-finding sweep is done at a distance rather than close up.

A random error hides and a periodic one shows

A warp whose threads vary by fifteen per cent looks perfectly even. One dent of the reed a tenth of a millimetre wide makes a streak that gets the piece rejected. The same amount of error, arranged two ways — and the ratio between them is √(2n/π), with nothing fitted in it.

pattern · Variation 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 same error twice: scattered, and in a period. Two bands of 96 ends, drawn at spacings that differ from the reed's by the same root-mean-square amount — 5% of a dent, which is 21 µm. The upper band's errors are independent; the lower band's repeat every 4 ends, which is what one shaft set forward or one dent of the reed too wide produces. The displacement is drawn 8 times over scale, because at true scale it is half a pixel and both bands are picket fences; the arithmetic below it is at the true amplitude. The upper band reads as an even cloth with a little texture in it and the lower one has stripes, and nothing about the eye is needed to say why: at 96 ends the periodic arrangement is 7.8 times stronger at its own frequency than the scattered one is at any frequency, and over the 256 ends a buyer takes in at once it is 12.8. The ratio grows as the square root of how much cloth is looked at, which is why a fault-finding sweep is done at a distance rather than close up.

A course is one thread and a warp is many

A woven fabric draws its warp from two thousand packages side by side, so a yarn's drift averages out across the width. A weft knit takes whole courses from one package, so the same drift becomes a band — and the standard remedy for that turns an invisible error into a visible one.

knits · Knit An operation multiplies a spread by its own log-slope. A transformation does not leave a population's spread alone: if y goes as the kth power of x then a small spread in x becomes k times that spread in y, exactly in the limit and nearly so at the CVs a yarn has. So an operation with an exponent below one narrows the population it acts on — a thickness that goes as the square root of a load comes out at half the spread it went in with — and one with an exponent of four widens it fourfold. This is the same derivative that decided every bias in this ladder, read for its magnitude rather than for its curvature, and it is why a finish can be a variance-reducing operation without anyone having chosen it for that. The straight line through the origin is the whole of the rule; the departure from it at the right-hand end is the second-order term arriving, which is where the linearisation stops being one.

A finish spends a spread before it spends a mean

Every operation on a cloth multiplies the variation it inherits by its own log-slope, so an operation with an exponent below one makes the cloth more even and one above it makes the cloth less even. Calendering, which is bought for evenness, has an exponent of 1.4.

finishing · Lustre finish The float a point fault gives a weave, over every draft there is. Every four-by-four draft that describes one cloth — 22,730 of them — laid out as 8 ends by 8 picks, with each intersection of its repeat reversed in turn and the longest float that produces kept. There are two answers and no others. 90 drafts hold the fault to a float of 3; 22,640 — 99.6% of every weave there is — hand it a float of 7. The mechanism behind the second number is that a reversal at a binding point joins the two floats on either side of it, so a weave with runs separated by single binding intersections gives a single mistake the sum of two of its own floats. The 90 that escape are the drafts whose floats are short and evenly spaced — the plain weave and the ribs — which is not the class of weave the trade recommends for hiding a fault.

Which weave hides a fault

The trade says a busy weave hides a mistake. Every four-by-four draft there is was laid out as cloth and given every wrong lift it could have, and ninety-nine in a hundred hand that single mistake a float of seven — because a reversal does not lengthen a float, it joins two.

weaves · Float

Named alongside it

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

PopulationBeatCoefficient of variationPeriodSurface patternTwill angleCalenderingCatalogueCloth thicknessCompression energyCourseCriterion

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