Textile Structure
how cloth is put together
Concept

Reed — where it appears

A comb of fixed pitch that spaces the warp and beats each pick up, fixing the sett before the cloth takes up its crimp. It also groups the warp into dents, and where that grouping beats against the weave repeat it leaves a visible mark.

Named by 12 essays across 4 fields — each of them below, with the objects they name alongside it.

Which dentings leave a mark. Every combination of ends per dent and weave repeat, with how many ends the grouping takes to come back into step. A small number means the reed treats every repeat the same way and the grouping shows as a stripe at the dent pitch; a large one means the grouping walks across the weave and there is nothing periodic for the eye to find. The rule is one word: dent so the two share no factor.

The reed leaves its own mark

A reed does not space a warp evenly. It groups it, several ends to a dent, and the grouping beats against the weave repeat — so a denting that shares a factor with the repeat treats every repeat identically and shows as a stripe, and one that does not is invisible.

pattern · Moire The shed in section. A warp line 1200 mm from the fell of the cloth at the left to the back rest at the right, with 8 shafts at 300 mm and every 16 mm behind it. Each shaft lifts its ends in proportion to its own distance from the fell, which is what gives the same 30 mm clear opening at the reed from every shaft. The resulting extension is 0.460 per cent at the front shaft and 0.722 per cent at the back, a ratio of 1.57. Vertical scale exaggerated 4 times.

The shed is an extension

Every model of a finished cloth treats a thread as inextensible, and every one of them is about a fabric that has left the loom. On the loom the warp is stretched thousands of times a minute by the shed itself, and the amount is exact trigonometry with nothing fitted in it: the square of the shed's tangent, times the shaft's own distance from the fell, over twice what is left behind it.

mechanics · Shed The reed is not the sett. Twelve ends held at the reed's pitch above and at the cloth's pitch below, for a sheeting whose weft crimp is 14.61 per cent. The count is the same in both rows and only the spacing changes: the cloth is 12.75 per cent narrower, so a reed at 24.43 ends per centimetre produces a cloth at 28. The crimp comes from the Peirce solution at this cloth's quoted construction.

The reed is not the sett

A reed holds the warp at a pitch, and the cloth that leaves it is narrower — by exactly the weft's crimp, with nothing fitted and nothing approximated. On a close balanced sheeting that is 12.75 per cent, on an open scrim 1.87, and a weaver who allowed one figure for both would be wrong by a factor of nearly seven.

setting · Take-up What the two setts can be set to. Two rules on one scale from 8 to 40 threads per centimetre. The upper carries the 49 warp setts a metric reed catalogue reaches at one to four ends per dent; the lower carries the 4825 pick densities a change-wheel take-up reaches. The mean spacing is 0.656 threads per centimetre in the warp and 0.0066 in the weft, a ratio of 99. The widest gap in the reed's range is 2.10 threads per centimetre.

The setts a loom can reach

Transposing a draft gives a perfectly good draft, and every count this site takes off a matrix either is symmetric under exchanging warp and weft or has a mirror twin. The loom is not symmetric at all: over the range ordinary cloth is woven in, it can choose a pick density 99 times more finely than a warp sett — and the warp sett cannot be changed once the warp is drawn in, at any granularity whatever.

setting · Take-up The beat-up, at the fell. The last picks of a sheeting at 26 picks per centimetre, with the beat-up zone shaded. Driving the fell forward makes the warp take more crimp and more crimp takes more thread, which the warp can only supply by stretching — so the force is the warp tension times the crimp's elasticity with respect to the pick spacing, 0.182 here. That is 0.205 N per end and 573 N per metre of reed. What the drawing cannot show is that the shaded band's width cancels out of the derivation exactly; it is drawn because a reader needs to see what is being compressed, not because the answer depends on it.

The blow that sets the pick

The take-up gear decides how far the cloth moves between picks and says nothing about the blow that puts each pick where it goes. That blow is a force, and a virtual-work argument gives it in one line — with the length of the beat-up zone cancelling out of the answer exactly, which is the part worth having.

setting · Beat-up The harness a strain budget buys. How many shafts stay inside a 1.0 per cent warp-strain budget, against the clear shed opening the loom needs at the reed: 12 mm gives 43, 16 mm gives 36, 20 mm gives 28, 24 mm gives 21, 30 mm gives 13, 36 mm gives 7, 44 mm gives 1. The shed's tangent enters the strain squared, so the opening is much the strongest thing a loom builder controls.

The harness has a depth

Why does a dobby carry sixteen or twenty-four shafts rather than two hundred? The usual answers are about the mechanism — how many jacks a box can drive, how many hooks a dobby has — and they are real limits that are not the binding one. A stated tolerance on warp strain is a stated distance from the fell, and a stated distance is a whole number of shafts. One per cent buys thirteen.

fancy · Shafts Selectable against reachable. How far up the take-up gear's catalogue a beat-up force reaches, on a sheeting. The catalogue holds 4,825 distinct pick densities between 8 and 40 per centimetre, which is the previous rung's count of what the machine can select. At 200 N per metre only 548 of them can be woven; at 2,000 it is 4,256. The fineness of the choice is untouched by the ceiling and the top of the range is cut off entirely, so the weft direction's advantage is resolution rather than reach. What the chart cannot show is the loom's own force, which depends on the beat-up mechanism and is not a property of the cloth.

A pick density is a force budget

The take-up ladder counted what a change-wheel take-up can select: 4,825 distinct pick densities between eight and forty threads per centimetre, against forty-nine warp setts a reed catalogue offers over the same range. That count assumed every setting is available. A beat-up force says otherwise, and cuts the top off the range without touching the fineness of the choice.

setting · Beat-up The same error twice: scattered, and in a period. Two bands of 96 ends, drawn at spacings that differ from the reed's by the same root-mean-square amount — 6% of a dent, which is 25 µm. The upper band's errors are independent; the lower band's repeat every 8 ends, which is what one shaft set forward or one dent of the reed too wide produces. The displacement is drawn 8 times over scale, because at true scale it is half a pixel and both bands are picket fences; the arithmetic below it is at the true amplitude. The upper band reads as an even cloth with a little texture in it and the lower one has stripes, and nothing about the eye is needed to say why: at 96 ends the periodic arrangement is 7.7 times stronger at its own frequency than the scattered one is at any frequency, and over the 256 ends a buyer takes in at once it is 12.8. The ratio grows as the square root of how much cloth is looked at, which is why a fault-finding sweep is done at a distance rather than close up.

A random error hides and a periodic one shows

A warp whose threads vary by fifteen per cent looks perfectly even. One dent of the reed a tenth of a millimetre wide makes a streak that gets the piece rejected. The same amount of error, arranged two ways — and the ratio between them is √(2n/π), with nothing fitted in it.

pattern · Variation The two halves of a beat-up force. The force the reed must apply per metre, for a sheeting, against the number of picks that are still sliding against the warp. The elastic half — the warp tension times the crimp's elasticity with respect to the pick spacing — is 573 N/m and does not depend on the zone at all; that cancellation is exact and is the result the rung below established. The frictional half is 1133 N/m per sliding pick and is nothing but zone. Against a reported 400–1500 N/m, that leaves room for at most 0.82 picks sliding — so the fell region a weaver can see, ten to fifty picks deep, is not the same quantity as the picks that are still moving. What the rows cannot show is that this is a static friction throughout, and a beat-up is a blow.

The half of the beat-up that is all zone

The elastic half of the beat-up force is exact and the length of the beat-up zone cancels out of it, which is this site's own result and disagrees with every practical account of weaving. The frictional half is nothing but zone — and requiring the total to match the force a loom is actually built to apply puts the number of picks still sliding at about one.

setting · Beat-up 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 Where a muslin's warp jams, over 40 ends. 40 ends drawn at their own diameters, with every neighbouring pair's combined width plotted beneath. A cloth cannot be set closer than its threads will lie, and the pair that decides that is not the average pair — it is the widest one anywhere across the warp, which here is ends 8 and 9 at 205 µm apiece against a mean of 167 µm. Over the 2000 ends of a real warp rather than the 40 drawn here the worst pair is 42% above the mean, and it goes on growing with the width of the cloth: the same yarn in a wider loom jams sooner. The naive estimate that treats every window as an independent try overstates it by 0.48%, which is small enough to say that the overlap between neighbouring windows is not what is going on here.

A warp jams where its threads are thickest

The closest a cloth can be set is decided by its worst pair of neighbours, not its average thread — and the worst pair depends on how many pairs there are. The same yarn in a wider loom jams sooner, which makes a jammed sett a property of the machine as well as of the yarn.

setting · Sett A colour order against a 2/2 twill. The visible face of a 2/2 twill under 2 colour orders, drawn at the repeat the divisor arithmetic allows and outlined at the repeat the surface has. A filled cell is a dark thread on the face, which is the warp's colour where the warp is up and the weft's where it is not — so none of these patterns is in the draft, and the draft is the same in all of them. The colour period and the weave repeat beat exactly as a reed's grouping beats against a weave: the surface repeats on the least common multiple of the two, which here is 8×8 and 4×4. What the panels cannot show is colour: the two threads are drawn as filled and empty, and two colours of similar value make a pattern far weaker than this.

A colour order beats the weave it is threaded on

The reed's grouping beats against the weave repeat and the arithmetic is a least common multiple. A colour order is a second grouping of the same warp and the arithmetic is identical — but where the reed's beat is a fault to be dented out of a cloth, the colour order's beat is the pattern the cloth is sold for. Across 472 colour orders on four weaves the divisor bound is the surface's exact repeat in 470 or more, and the handful that beat it have no pattern left at all.

pattern · Moire

Named alongside it

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

SettDentingLoomTake-upContractionBeatBeat-upCrimpJammingPeriodBack restCoefficient of variation

All concepts