Textile Structure
how cloth is put together
Concept

Evenness — where it appears

How little a yarn's mass per unit length varies along it, quoted as a coefficient of variation. It has a floor set by the number of fibres in a section, and it describes the middle of the strength distribution rather than the rare weak places a loom breaks at.

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

How much of a 20 tex yarn's unevenness survives being woven. Weaving averages, and the averaging is a square root. A patch of cloth 3 mm across contains 7.2 warp threads and as many picks, each contributing its own mass independently, so the patch's coefficient of variation is 3.53% against the yarn's 13.4% — a reduction of 3.8-fold. The rule at the top is the yarn's own figure. The curve steepens past the staple length, where a patch starts to contain independent samples along each thread as well as across them, and the second regime is the one a large area of cloth is judged in.

A cloth cannot be more even than its yarn

It can be very much more even than its yarn, and by exactly the square root of the threads in view. Which raises a question the fineness argument left open — and the answer is that at a fixed cloth weight the count cancels out entirely.

pattern · Variation Where a 20 tex yarn breaks, against how much was clamped. A tensile test clamps a length of yarn and pulls until the thinnest section between the clamps gives. So a yarn's strength is a minimum, and a minimum depends on how many independent tries the sample contains. The tries are not sections — a plane can be taken anywhere — but staple lengths, because two planes closer together than one fibre share most of their fibres. At 28 mm staple a 100 mm specimen holds 3.6 independent tries and a 500 mm one holds 17.9, and the longer test reads 11% lower. The spread is not fitted either: it is the evenness floor at 118 fibres times an index of 1.35, which is 13.4%.

A yarn breaks at its thinnest place

A tensile test does not measure a yarn. It measures the worst section between the clamps — so evenness and strength are one measurement taken twice, and the number of independent tries in a specimen is set by the length of a fibre.

mechanics · Assembly How likely one staple length of yarn is to be weaker than a tension, under three laws. The probability that one independent try — a staple length of a 20 tex cotton yarn — is weaker than a tension, on a logarithmic scale, with the tension as a fraction of the yarn's 500 mm breaking load. Three laws are drawn, a normal, a lognormal and a Weibull, each fitted to reproduce the same two tensile tests at 100 and 500 mm exactly. Near the breaking load, where a tensile test samples at about one chance in 18, they lie together. At one chance in 1.4×10⁸, where a warp of 4,000 ends by 1,000 metres samples, they are far apart: at the back shaft's 52 per cent the three give normal 1.3×10⁻⁷, lognormal 1.1×10⁻¹¹, Weibull 4.0×10⁻⁶ per try. What the chart cannot show is which of the three a real yarn follows, which no tensile test can decide.

A warp breaks in a tail no tensile test reaches

A 500 mm tensile test is the weakest of about eighteen staple lengths of yarn. A warp of four thousand ends by a thousand metres is the weakest of a hundred and forty million, and an end breaks wherever one of them is weaker than the shed's tension. Three strength laws fitted to the same two tensile tests agree within five per cent at every gauge a tester can clamp, and disagree by a factor of 375,000 on how many ends a warp will break at the back shaft.

setting · Assembly

Named alongside it

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

Fibre countGauge lengthLimit irregularityPopulationSpecificationStaple lengthAreal densityBundle strengthCoefficient of variationHarnessOrder statisticSett

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