Textile Structure
how cloth is put together
Concept

Index of irregularity — where it appears

A yarn's measured irregularity divided by the floor its own fibre count sets, so that one is the unbeatable value. It is the only measure that compares a fine yarn with a coarse one, because a raw coefficient of variation carries the count as well as the spinning — ordinary ring-spun yarns run between 1.15 and 1.6.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

The evenness a cotton yarn cannot be better than. Lay staple fibres down at random and count how many cross a plane: the count is Poisson, its variance is its mean, and the coefficient of variation of the mass per unit length is therefore 1/√n with no material and no machine in it. The lower curve is that floor. At 20 tex there are 118 fibres in the section and the floor is 9.93 per cent; at 5 tex there are 29 and it is 19.86. The upper curve is what a yarn spun at an index of irregularity of 1.35 actually measures, which is the floor times a constant — so the whole shape belongs to the counting and none of it to the spinning. The exponent is exactly −½ and is asserted as such rather than fitted to the curve.

The spread was never free

This collection has taken a yarn's irregularity off a delivery note and used it as an input. It is not an input. Counting the fibres in a cross-section puts a floor under it that no spinner can beat, and the floor is one over the square root of the count.

cloth · Variation The evenness a cotton yarn cannot be better than. Lay staple fibres down at random and count how many cross a plane: the count is Poisson, its variance is its mean, and the coefficient of variation of the mass per unit length is therefore 1/√n with no material and no machine in it. The lower curve is that floor. At 5 tex there are 29 fibres in the section and the floor is 19.86 per cent; at 5 tex there are 29 and it is 19.86. The upper curve is what a yarn spun at an index of irregularity of 1.35 actually measures, which is the floor times a constant — so the whole shape belongs to the counting and none of it to the spinning. The exponent is exactly −½ and is asserted as such rather than fitted to the curve.

A finer yarn is a worse yarn

Fineness is the thing a yarn is priced for, and it is bought with irregularity at a fixed exchange rate. Once the spread is a function of the count, every correction this collection computes becomes a function of the count too — and the cheapest yarn on the shelf is the one the arithmetic describes best.

setting · Assembly 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.

setting · Ply

Named alongside it

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

Coefficient of variationFibre countLimit irregularitySpecificationYarn countBending rigidityConvexityCover factorFibre finenessJammingOrder statisticPly

All concepts