State — the series · Textile Structure

The same thread, on the loom and off it. One warp end in section over eight picks, drawn twice at the same scale. The thread is the same length in both panels; in the lower one more of that length is in the bends, so the cloth it spans is shorter. Nothing has been lost — the length has moved into the crimp. The thread's thickness and the height of its bends are drawn larger than scale so the interlacing is legible; the two panels' spacings are not.

What comes off the loom is not the cloth

Every number on this site so far describes a fabric in one particular condition — held under tension, stretched to the reed width, never wetted — and none of them says so. That condition lasts until the cloth is taken off the machine, which is the first thing that happens to it.

part 1 · finishing

The cloth gains weight by losing size

Mass per unit area is the number a fabric is bought by, and it rises by eleven per cent when a cloth relaxes — with nothing added, nothing removed and no thread changed. The quantity is a ratio, and finishing moves its denominator.

part 2 · finishing

How much a cloth can give back. Relaxation shrinkage against how much of the warp crimp the loom took out, with the area shrinkage above it and the ceiling drawn across. The ceiling is the crimp itself, read as c/(1+c): it is all the length there is to give, and no tension reaches past it.

A dimension without a state

Every essay in this field turned on the same omission, and collecting them produces a result none of them had on its own — the quantities a cloth's geometry determines divide cleanly into those a finishing works can move and those it cannot, and the division is not the one the vocabulary suggests.

part 3 · finishing

The resting band, not the resting point. The bending energy of a sheeting along its own constant-thread-length locus, with the band in which friction can hold it shaded. The minimum is a single state; the band is 10.9 per cent of length wide, because the cloth stops sliding as soon as the energy it can release falls below the 0.0756 N friction takes to move a crossing. What the drawing cannot show is which end of the band a given piece of cloth stops at, which depends on the direction it arrived from and is what makes relaxation hysteretic.

A cloth relaxes until its threads stop pushing

The finishing field treats the relaxed state as a place a cloth arrives at. With an energy along its own locus and a friction at its crossings it is not a place but a band — and which point of the band a piece of cloth stops at depends on which side it came from, which is why washing it twice gives two answers.

part 4 · finishing

A knitted loop is a plane curve in a plane that is not the fabric's. A relaxed 20 tex jersey at a 3.5 mm loop, seen from the end of a course. Each course is a straight line because it is one: a half period leaves and arrives along the course direction, so the plane it bends in contains that direction, and a plane curve seen along a line in its own plane projects to a segment. The upper panel expands the thickness 3× so the arrangement can be seen and no angle may be measured off it; the lower panel is the same fabric at one scale, where the tilt is what it really is. The angle is 11.75°: a climb of one yarn diameter, 0.167 mm, against a drop of a course spacing and a diameter, 0.803 mm. Successive courses overlap by exactly one diameter, which is the interlacing, and the fabric is therefore 0.334 mm thick — two yarn diameters, with nothing fitted.

A state is a thickness too

This collection's rule is that a fabric dimension quoted without its relaxation state is not a measurement. A knitted fabric has three dimensions and only two of them obey the rule: its thickness is the same in every state, because the interlacing that sets it does not relax.

part 5 · finishing

The flattening a knitted fabric asks for, against its own tightness. Every point is a solved fabric — 18 of them, over five loop lengths, three relaxation states and three counts — and the vertical axis is the closest its adjacent courses come, in diameters. The values run from 0.707 to 0.839 and they fall on one curve against the tightness factor, which is the model's only dimensionless group. That is what makes this a structural requirement rather than an arithmetical accident of one example: a tighter fabric demands a flatter yarn, by an amount its own tightness decides, and nothing about the fibre or the count enters except through that group.

A wet knit's yarn is flatter

A knitted fabric's own geometry demands a flattened yarn, and how flat depends on how much room the fabric leaves. A wet cotton yarn is a tenth thicker than a dry one at the same length, so a wet fabric leaves less room — and asks its yarn to be flatter by an amount the geometry gives.

part 6 · finishing

Two courses at the yarn's own width, and the place they overlap. The solved course of a 24.2 tex cotton jersey at a 3.5 mm loop, drawn in plan with the course below it, each strand at the yarn's own diameter of 0.184 mm. Where the two overlap, the fabric is occupying the same space twice. The interlacing is where the model placed them one diameter apart. The closest they come is 0.140 mm — 0.761 of a diameter — and it is not at the interlacing. A round yarn cannot occupy this arrangement; a yarn flattened to 76% of its round diameter can, and flattened is what a yarn in a fabric measurably is.

What wetting does to the bending limit

A rod cannot be bent to a radius below its own. A relaxed knitted loop sits at twice that limit, and a wet yarn is a tenth thicker in the same loop — so wetting moves a fabric a tenth of the way towards a bend it cannot physically take.

part 7 · finishing

The section the fabric asks for, beside the one the model drew. A 24.2 tex cotton yarn in cross-section, at 900 times life size. The circle is what every solve in this collection has assumed: a diameter of 0.184 mm from the count and the packing factor. The ellipse has the same area and a minor axis of 76% of it, which is the closest the fabric's own adjacent courses come to one another — 0.140 mm. Nothing about that number was fitted to a fabric. It falls out of a solve that knew nothing about flattening, and it lands inside the range the trade reports for yarn in cloth, which this collection has carried as a free parameter ever since it first put a number on a sett.

The diameter that does need a state

A fabric dimension quoted without its relaxation state is not a measurement. The rule was applied to the two plan dimensions and then to the thickness, and it was never applied to the one dimension that is not the fabric's at all — the yarn's.

part 8 · finishing