Textile Structure
how cloth is put together
Concept

Tensile locus — where it appears

Every state a cloth can reach without any thread changing length, which is a set rather than a point. It is built at a fixed thread thickness, so anything that changes the thickness replaces the set rather than moving the cloth within it.

Named by 11 essays across 6 fields — each of them below, with the objects they name alongside it.

The two routes a poplin has to a strain. A poplin drawn in section at three places: as woven, at the end of what its crimp can supply, and past that. Between the first two the warp's crimp falls from 8.97% to 4.85% and the weft takes on what it gave up, and the thread length is 0.4953 mm in both — nothing has stretched, and the cloth is 3.93% longer. Between the second and the third the geometry cannot move because the weft's straight run has vanished, so the cloth's extra 2.0% is the thread's extra 2.0%. What the drawing cannot show is which of the two a piece of cloth has had: the first two states look different and the last two look the same, and it is the last two that differ in whether the cloth comes back.

A cloth gives back less than it took

Everything this collection computes about a deforming fabric is reversible, and no fabric is. The repair is not a new material property: a woven cloth has two routes to a strain, one of them costs its threads nothing and comes back in full, and where the first route runs out is a number about the sett with no fibre in it at all.

cloth · Memory The energy well, and where the cloth sits in it. The bending energy of a sheeting at every state on its own constant-thread-length locus, plotted against how the crimp divides between the two systems. The minimum is at 1.22 and the value every Peirce solution here is drawn at is 1.00, marked. The well's depth decides how firmly the ratio is settled, which is why an open scrim's measured crimp scatters and a close sheeting's does not. What the plot cannot show is the friction that stops a cloth reaching the bottom, which turns the minimum into a band.

The crimp ratio is not a measurement

Peirce's geometry is two thread systems, four unknowns and three equations. It cannot say how the crimp divides between warp and weft, so every cloth solved so far has been drawn at a ratio somebody chose. Give the threads a stiffness and the missing equation arrives — and for six of the eight cloths in the table it arrives with no material constant in it at all.

setting · Crimp The load–extension curve, computed from a stiffness. The tension in one end of a sheeting against how far the cloth has been extended, computed as the slope of its bending energy along its own constant-thread-length locus. The curve passes through zero at the state of least energy, which is where an unloaded cloth sits, and rises either side of it. What the curve cannot show is what happens after the crimp runs out: past the end of the locus the load is carried by stretching yarn rather than by straightening it, and that is a modulus three orders of magnitude higher and a different figure.

The locus gets a force

This site has drawn the set of states a cloth can reach without stretching any yarn, and has never been able to say which of them it is in or what it would cost to move. Both questions are one derivative of a bending energy — and the answer explains the flat start every fabric's load–extension curve has, which is not slack yarn but a symmetry.

mechanics · Tensile The interchange budget against cover, at three yarn counts. The extension a plain cloth can reach with no thread stretching, plotted against its warp cover factor, for 10, 20, 40 tex yarn. The three curves coincide, because every length in Peirce's geometry is a multiple of the yarn diameter and a spacing measured in diameters is a cover factor — so the count divides out exactly and the maximum is at 0.407782 for all of them, at a budget of 7.2857%. That the curve has a maximum at all is the finding: crimp is what a cloth spends, so more of it should be better, and past this cover the weft has nowhere to put what the warp gives up. What the plot cannot show is the balance, which moves the height of the maximum a long way and its position hardly at all.

The most a cloth can give back

The extension a cloth can find without stretching a thread comes from crimp, so setting a cloth closer ought to give it more. It does, up to a point, and then takes it away again — and the point is a cover factor of 0.4078 at a budget of 7.2857 per cent, identical to six figures for every yarn count from five tex to a hundred.

cloth · Memory 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.

finishing · State A 40-by-40 motif on a poplin, drawn and finished. A motif 40 ends wide and 40 picks tall, at the setts the reed and the take-up were set to, and the same motif measured on the finished cloth. Point paper has one cell per end and per pick, so a motif's proportions are the ratio of the two setts — and both setts move in the finishing, in opposite directions. On the poplin the aspect changes by a factor of 0.8429, so a circle drawn as a circle at the loom's numbers comes back 15.7% out of round and a designer who wants a circle must draw an ellipse of 1.1863. What the drawing cannot show is that the correction is not a property of the design: it belongs to the cloth, so the same card woven on a different construction is a different shape.

A motif is drawn at the wrong shape on purpose

Point paper has one cell per end and per pick, so a design's proportions on the cloth are the ratio of the two setts. Both setts move in the finishing and they move in opposite directions, so a circle drawn as a circle comes back out of round — by three per cent on a balanced cloth and by sixteen on a warp-dense one.

pattern · Pattern The poplin's two budgets as it is held stretched. What is left of a poplin's interchange in each direction as it is held at more and more warp strain. The warp's budget falls to nothing at 3.93%, which is the point of the curve; the weft's rises, because the crimp the warp gives up is crimp the weft takes on. There is one locus and one position on it, so the two are not two quantities that happen to be related — they are the two distances from one point to the two ends of one curve. The consequence is that a pre-tensioned cloth has almost no warp recovery left and more weft recovery than it started with. What the plot cannot show is that the exchange rate between them is not constant: the curve is not a straight line, and its slope is the Poisson ratio this site computes elsewhere.

A cloth has one budget for two directions

A woven cloth looks as though it carries two independent reserves of free extension, one along the warp and one across the weft. It carries one. There is a single curve of states and a single position on it, so every hundredth spent one way is refunded the other — which means a pre-tensioned cloth has not used its recovery up, it has moved it.

mechanics · Tensile 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 How far each cloth's sett moves between the loom and the finished state. A cloth on the loom is held: the warp is under beam tension and the picks are driven up at whatever density the take-up says. Let it go and it relaxes to the least-energy state of its own locus, which is a state at a different sett. The bars are how far each sett moves, and they always move in opposite directions because there is one locus: warp ends per centimetre fall as the cloth widens and picks per centimetre rise as it shortens. Seven of the eight move a little over one per cent; the poplin, whose two counts and two setts are the only unbalanced pair in the table, moves six and ten. What the bars cannot show is what a designer does with them, which is that the two numbers a specification quotes are not two free numbers — the finished construction is a point on a one-dimensional curve.

The construction a loom must be set to

A specification quotes ends and picks per centimetre in the finished cloth, and a loom is set to neither of them. The cloth relaxes to the least-energy state of its own locus, which is a state at a different sett — and because the locus is one curve, the two numbers a specification quotes are not two free numbers.

setting · Take-up What a tensioned sheeting has left of its load. A sheeting pulled to a strain, clamped at that length and left. Its length does not change, and its load does: crossings rearrange locally until the load has fallen to what friction alone can hold, which is 0.0756 N per end and is the same number whatever the cloth was pulled to. So the fraction retained is that floor over the load applied, and it falls — a cloth tensioned to 4.94 per cent keeps 29 per cent of what it was given. Below the resting band's own edge nothing is lost at all, because the cloth was never outside what friction could hold. What the plot cannot show is time: nothing here says how long the rearrangement takes, only where it stops.

A tensioned cloth loses its load

Clamp a fabric at a fixed length and its tension falls overnight. Nothing crept and nothing flowed: the crossings rearranged locally until the load had dropped to what friction alone can hold, and that level is the same number whatever the cloth was pulled to — so the harder it was tensioned, the smaller the share it keeps.

mechanics · Set The extension ceiling, with the yarn given a thickness. As a jersey is pulled along its courses the wale spacing grows and the course spacing has to fall, because the yarn between two interlacings is a fixed length. The upper curve is how small the course spacing may be before the yarn runs out; the lower is how small it may be before two adjacent courses occupy the same space. The geometric ceiling is 322% and the contact one 299% — 7% lower. That is the result and it is a negative one: a measured jersey extends by about a hundred per cent, so contact between courses is not what puts the computed ceiling three times beyond a real one. The candidate this ladder was written to test is ruled out.

Contact is not why a jersey stops

The model says a jersey can be pulled to three hundred and twenty per cent along its courses. Real ones stop at about a hundred. The recorded diagnosis was that nothing stops adjacent courses passing through one another — and giving the yarn a thickness closes seven per cent of a gap of two thirds.

knits · Elastica

Named alongside it

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

Crimp interchangeCrimpJammingInterchange budgetSettBending rigidityPermanent setRelaxationPeirce's geometrySpecificationThread lengthYarn diameter

All concepts