Textile Structure
how cloth is put together
Concept

Agitation — where it appears

Mechanical working of a wet fabric, which supplies the cycles a frictional process needs. It multiplies a relaxation or a felting linearly and changes nothing about how much of each cycle counts, which is a separate question about the friction itself.

Named by 7 essays across 3 fields — each of them below, with the objects they name alongside it.

Stick, slip, and the ratio between the two coefficients. The force in a thread as a cloth is agitated, with a static coefficient of 0.300 and a kinetic one of 0.225 — a ratio of 0.75, which is what fibre on fibre measures. The force climbs until it reaches the static limit, the contact breaks away, and while it is sliding it resists only at the kinetic limit. So a cloth that is being shaken can be left anywhere in the narrower band, and a cloth at rest anywhere in the wider one. What the trace cannot show is how much this buys: the band does not narrow in the ratio of the coefficients, because the restoring force stiffens away from the minimum, and the real narrowing is nearer 0.87 than 0.75.

Two coefficients, not one

Every friction on this site is a single number, and the account of why a cloth relaxes better when it is agitated depends entirely on there being two. Separating static from kinetic changes what a resting state is: a cloth at rest is held by one coefficient and a cloth being shaken by the other, and the band it can be left in narrows — by less than the ratio, because a cloth's restoring force is not linear in its extension.

cloth · Friction Munden's states against the fibre swelling. What a plain knit does between its relaxation states, beside the swelling of the fibre it is made of. Going from dry-relaxed to wet-relaxed a jersey loses 5.66% along its courses and 2.44% across its wales, and going on to fully relaxed it loses 9.1% and 7.0%. The fibre swells 20%. Two things rule the swelling out as the cause: it is several times the whole change, and the change is markedly anisotropic while a swelling enters both of a loop's dimensions through the same loop length. What the bars cannot show is what does cause it, which is friction — water lets the loops move to where the yarn's own bending had been trying to put them.

A knit's change of state is not its swelling

A jersey is smaller wet-relaxed than dry-relaxed, by 5.7 per cent along its courses and 2.4 across its wales. Water is obviously involved, so the swelling is the obvious cause. Two things rule it out, and both are properties of the constants rather than measurements of a fabric.

knits · Knit A plain knit's two relaxation steps. Munden's three relaxation states are usually given as three sets of constants. Read as a path they are two steps, and the two compose to the whole exactly — which is a real check, because the three sets were measured independently. The first step is the larger in the course direction and the smaller across the wales, and the second is 0.64 of the first lengthwise. That is the shape of a laundering series and it is the same mechanism: a fully relaxed state is reached by tumbling rather than by waiting, so what the standard specifies is a quantity of agitation and not a duration. What the bars cannot show is the loop length, which cancels out of all four numbers because every dimension of a knit is a loop length times a dimensionless constant.

A knit relaxes for as long as it is allowed to

Munden's three states are usually given as three sets of constants. Read as a path they are two steps, they compose exactly, and the second is not a smaller version of the first — the fabric shrinks twice as much along its courses as across its wales on the first step and rather less than half as much on the second.

knits · Knit The resting band with two coefficients in it. The range of extensions a sheeting can be left in, at rest and while being agitated, at three ratios of kinetic to static friction. The upper bar of each pair is the stuck band, held by the static coefficient; the lower is the band a cloth being shaken can be left in, held by the kinetic one. Agitation narrows the band but by less than the ratio of the coefficients: at 0.75 the narrowing is 0.868. The restoring force is not linear in the extension, so cutting the friction by a quarter does not move the band's edges by a quarter of the way in. What the bars cannot show is where a given piece of cloth actually stops inside its band, which depends on which side it came from.

Why agitation helps a cloth relax

Every standard relaxation procedure agitates: tumble it, wash it, steam it, work it. The explanation given is that agitation lets the fabric find its own dimensions, which is true and is not a mechanism. The mechanism is that a sliding contact resists less than a stuck one — and putting a number on it shows the effect is real, is smaller than the obvious arithmetic suggests, and does not account for what a relaxation procedure achieves.

finishing · Friction Shrinkage from wetting, cloth by cloth. The change in each cloth's relaxed construction when its threads swell by 20% across and 1.2% along. Both states are least-energy states of their own constant-thread-length locus, which is the only comparison the locus admits: its minimum is a state at its own sett, so it may be compared with another minimum and not with a quoted construction. Positive is smaller. Every cloth that has a wet state closes up except the cheesecloth, which opens by half a per cent because the fibre's extra hundredth of length outruns the extra crimp a thicker partner costs. What the bars cannot show is the three cloths that are missing, which have no wet state at all.

Two shrinkages, one tape measure

A cloth that comes out of a wash smaller has done two different things and the tape cannot tell them apart. One is geometric, recoverable and finished in minutes; the other is frictional, permanent and needs agitation. This collection can now compute both, and they have different signatures.

finishing · Shrinkage The ratchet a wool fibre is. A fibre with its scales, and the two strokes of one cycle of agitation. The push is the same in both directions; the distance is not, because the scales resist tip-first motion more than root-first. Every cycle therefore nets a displacement in one direction, and no amount of further agitation undoes it.

Why felting needs water

Wool felts in a wash and not in a drawer, and the usual explanation is that water lubricates the scales. It does the opposite of that. Water lowers one of wool's two friction coefficients and raises the other, so it widens the gap the ratchet rectifies — and what follows is a saturating function of the ratio, not of either coefficient.

finishing · Felting Wash-by-wash shrinkage, reported and modelled. The shrinkage an unfinished cotton cloth shows in each of five laundering cycles, beside what a model with no rate in it predicts. The model says a wash lets every crossing whose frictional barrier is below the cloth's current excess slip to the edge of its own band, and that is a distribution rather than a rate. Two numbers are fitted — the excess the cloth came off the loom with, 7.13%, and the spread of the barriers, 37.2× — against the first two washes. Washes three, four and five are predictions with nothing left to adjust and come out at 0.506%, 0.284%, 0.179% against reported 0.50%, 0.30%, 0.20%. What the bars cannot show is the finding underneath: the reported yarn-on-yarn friction range gives a spread of only 1.34×, which would have the tail over by the third wash.

A cloth shrinks most the first time

A laundering test reports five numbers and they fall away like a geometric series. Nothing in a wash is slow — a cloth is agitated tens of thousands of times in half an hour — so a second wash that shrinks it again is direct evidence that its frictional barriers are spread, and the ratio between successive washes measures how far.

finishing · Shrinkage

Named alongside it

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

RelaxationFrictionCrimpMoistureShrinkageSwellingHysteresisKinetic frictionLoop lengthPre-shrinkingResidual shrinkageResting band

All concepts