Textile Structure
how cloth is put together
Concept

Beam — where it appears

The roller a warp is wound on and let off from, whose rate decides how much thread goes into a given length of cloth. A second beam at a different rate is what makes a seersucker, a terry and every other relief made at the loom rather than in the finishing.

Named by 11 essays across 5 fields — each of them below, with the objects they name alongside it.

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 A seersucker in section. A seersucker in section across four stripes, at a feed ratio of 1.30 — the slack warp let off 30 per cent faster than the tight one — over a 6.0 mm stripe. The surplus has nowhere to go in the plane, so it buckles, and the standard small-amplitude result gives 2.09 mm of rise, which is 4.2 times the cloth's own thickness of 0.500 mm. Nothing has to relax for this to appear: unlike a honeycomb, a seersucker comes off the loom already puckered, and washing deepens it rather than creating it. What the drawing cannot show is that the buckle's shape is an assumption — a sinusoid pinned at the stripe's edges — while its amplitude follows from the surplus and the half-wavelength alone.

A seersucker is made at the loom

Every other relief weave in this collection gets its shape after the loom, from a difference of crimp between two regions of a few per cent. A seersucker's surplus is thirty per cent and is put in as the cloth is woven — an order of magnitude more, which the square root turns into a factor of four in depth and no more than that.

weaves · Texture weaves plain over 5-end satin: what each layer's warp does. A warp end of each layer of a double cloth, in section over the same span of cloth, with the length of warp each eats drawn beneath. The crimps come from Peirce's geometry asked about a thread that bends at its own average rate rather than at every crossing, and they are 14.35% for the plain and 2.03% for the 5-end satin. They are not the same, so the two layers consume warp at different rates: a hundred metres of cloth takes 114.4 m of warp from one and 102.0 m from the other. A beam delivers one rate, so the difference has nowhere to go and accumulates with the length woven — one pick spacing after 4 mm. What the sections cannot show is the yarn's thickness, which is exaggerated so the path is legible; the crimps beside them are computed at the real diameter and are not read off these drawings.

Two layers need two beams

A layer weaving a metre of cloth eats one plus its crimp metres of warp, and a beam delivers one rate. A plain face over a five-end satin back differs by twelve percentage points of crimp, which is twelve metres of warp over a hundred-metre piece and one pick spacing of slack after four millimetres of weaving. The difference has nowhere to go and does not settle — so the only double cloth that can share a beam is two layers of the same weave at the same sett.

fancy · Double cloth How many layers the repeat, the harness and the beams each allow. Three ceilings on the number of layers a double cloth can have, for five layer weaves. The repeat's bound is half its ends and is a property of the notation. The harness's is the strain budget — 13 shafts on an ordinary broad loom at a 1.0% warp strain limit — divided by the shafts one layer of that weave costs. The beams' is how many warps the loom carries, which is 2. The shortest of each three is marked, and it is the beams at the coarse end of the table and the harness at the fine end; the repeat is never the binding one except at two-end layers, where it happens to coincide with the harness. A double cloth of eight-end satin layers needs 16 shafts and the budget is 13, so it is a jacquard construction by arithmetic rather than by choice. What the bars cannot show is the pick rate: a k-layer cloth needs k times the picks per centimetre of finished cloth and takes k times as long to weave, which is a cost rather than a ceiling and is the reason four-layer cloths are rare even where they are possible.

The repeat allows four layers and the loom allows two

A repeat of eight ends can hold four separable cloths, and there is a witness that reaches the bound exactly. No loom weaves four. The harness's strain budget buys thirteen shafts and a layer costs its own weave's shaft count, so five-end satin layers stop at two and eight-end satin layers cannot be doubled on a dobby at all — and two differing layers already want a beam each. The notation's ceiling is the only one of the three that is never binding.

fancy · Double cloth A doup end crossing every pick at 1 mm. One leno pair of 0.25 mm ends over 2 crossing intervals, with picks 1 mm apart and the doup end changing sides every pick, drawn to scale in plan and in section. The standard end runs 1.00 mm per interval; the doup end, passing from 0.250 mm to one side, down 0.250 mm under its partner and up to the other side, runs 1.225 mm — 22.5% more, 11.8% of it from the sideways travel alone. Over a 100 m piece that is 22.5 m of warp, and on a shared beam a pick spacing of slack in 4.4 mm of cloth. What the drawing cannot show is the crimp both ends share over and under the picks, which the comparison cancels.

The doup end pays for the crossing

A leno holds its picks because its doup end crosses under its partner and comes up on the other side — half a turn at every crossing, whatever the sett. That half turn is also a length. When 0.25 mm ends cross every millimetre, the doup end travels 22.5 per cent further than its partner: twenty-two metres of extra warp over a hundred-metre piece, and a shared beam a pick short within four and a half millimetres of cloth. The extra falls with the square of the crossing interval, which is why a leno is woven from two beams and its crossings are spaced as far apart as the cloth allows.

fancy · Leno The beams a disc 12 blocks across needs, column by column. A disc 12 blocks across, 12 blocks by 12, figure shaded, with the beam feeding each column of ends written above it, for a figure floating 8 on a ground floating 1, whose warp crimps are 14.15 per cent apart, at 4 mm blocks over a 100 m piece with 1.2 mm of slack. It has 4 distinct columns and 4 distinct shares of the repeat in figure, and needs 4 beams. What the grid cannot show is the cloth's own crimp interchange, which would move tension between the columns instead.

A figured warp needs a beam for every share of its figure

Figure and ground take up warp at different rates, so a figured cloth on one beam is bounded in how long its figure may run, and a second beam is the obvious escape. It escapes only for ends that live wholly in one region. An end that crosses the figure for part of the repeat consumes warp at its own rate, and two ends can share a beam only if they spend the same share of the repeat in the figure and never drift a slack apart inside it. So a round figure twelve blocks across needs four beams, ninety-six blocks across needs twenty-nine, and any crimp difference at all — a third of a per cent will do — costs every one of them over a piece.

fancy · Jacquard What a second bar wants that the first does not. How much more yarn each guide bar needs than a tricot bar, per wale, over a 100 metre piece at 14 courses a centimetre — which is 140000 courses. A cord bar wants 111.3 metres more and a satin bar 232.3, both of which are more than the piece is long. A shared beam is one course spacing out after 0.28 courses.

Two bars cannot share a beam

Two guide bars each make one overlap a course and one underlap, and the overlap is the same object on both — the same needle, the same loop. So the difference in what they consume is exactly the difference in their underlaps, with no model of a loop in it: a cord bar wants 111 metres more yarn per wale than a tricot bar over a hundred-metre piece, and a satin bar 232. A shared beam is one course spacing of slack out after less than half a course.

knits · Warp knit What a figured warp pays in tension to share one beam. For six pairings of figure and ground, the difference in warp tension that lets their ends share one beam: the force per end that takes the take-up difference out of the ground's crimp, along that region's own constant-length locus, with the yarn's rigidity at both ends of the band two tests place it in. a damask: satin on its own complement, 0.00% apart: none needed; an eight-end satin figure on a five-end satin ground, 0.31% apart: 0.006 to 0.020 N; a five-end satin figure on a 3/1 twill ground, 0.90% apart: 0.021 to 0.069 N; an eight-end satin figure on a 2/2 twill ground, 3.02% apart: 0.304 to 0.995 N; an eight-end satin figure on a plain ground, 14.15% apart: past what the ground's crimp can give; a 2/2 twill figure on a plain ground, 11.14% apart: past what the ground's crimp can give. The loom's front shaft holds 0.52 N an end. What the chart cannot show is how uneven a warp's tension may be before it shows in the cloth.

A figured warp pays in tension before it needs a beam

Figure and ground take up warp at different rates, and counted against a fixed slack, any difference at all — a third of a per cent — made a round figure need four beams. A real let-off holds tension, not length. Ends that consume more pull harder, and an end pulled harder gives up crimp, until every end consumes alike. For an eight-end satin figure on a five-end satin ground that costs a hundredth of a newton an end, and one beam serves. For a satin on plain it costs more crimp than the ground has, and no tension will do.

fancy · Jacquard A disc woven on one beam, as it catches a lamp. A disc of 5-float satin on a ground of float 3, twelve blocks square, woven on one beam so that every column is pulled to the tension that makes it consume what the others do, and drawn as its blocks catch a lamp. A block is lit when its warp's crossings still reflect into the eye; outlined blocks are figure. At the mirror every block is lit. Tilted by 10.8° along the warp, the ground in the columns that carry most ground — the tightest — has gone dark, while the ground in line with the figure's widest part, pulled least, still shines: a band as wide as the figure runs down the ground above and below it. What the drawing cannot show is the diffuse light every block also returns, which dilutes the contrast and does not reverse it.

A figure woven on one beam shows its columns off the mirror

A figured warp shares one beam by letting the columns that want more yarn pull tighter until every column consumes alike. With the figure allowed to give crimp as well as the ground, the tightest column of a satin disc on a twill needs 0.013 to 0.042 newtons, under a tenth of the working tension. Its warp lies tens of micrometres lower, a relief too small to see. At the mirror it shines exactly as a slack column does. A few degrees off the mirror, along the warp, its crossings stop reflecting before a slack column's do, and the figure's own columns appear as bands in the ground. Only a damask has none.

fancy · Jacquard Where an air arch first wrinkles under snow over the whole span. A semicircular air arch 4 m across, pinned at both feet, of a tube 200 mm across at 50 kPa, under snow over the whole span; beside it, unrolled from the left foot to the right, the share of the tube's wrinkling budget πpr³/2 spent at each section when the first wrinkle forms, with the thrust's part, N·r/2, shaded darker. The first wrinkle forms 25° above the right foot, at 167 N per metre of span, where the moment of 60.2 N·m compresses the inside of the curve and the thrust is 336 N; there the thrust has taken 21 per cent of the budget. Judged by its moment alone the arch would carry 218.

An air arch pays for its thrust out of its pressure

An inflated tube bent into an arch was expected to start with its inside wall pulled differently from its outside, and to wrinkle where that difference and the load's moment combined worst. It does not: a curved tube is pulled along its length at exactly the straight tube's pr/2, all the way round. What the arch spends its pressure on instead is the thing every arch exists to make — its own thrust — which takes a fifth of the wrinkling budget at the haunch of a shelter arch under snow and more than half on a tight one.

applied · Membrane A patterning bar's thread through one repeat. One guide-bar thread followed through a 12-course repeat, needle places across and courses down, with each course's underlap drawn beside it as a bar against the beam's steady delivery, the repeat's mean of 1.984 mm. The shogs are 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3: 6 of 1 space (1.155 mm) and 6 of 3 spaces (2.814 mm), at 28 gauge and 14 courses a centimetre. The overlaps, the same on every course, are not drawn. What the drawing cannot show is the tension: a course whose bar runs past the mean is a course the beam has not yet paid for.

A patterned warp knit needs a stroke as long as its stripe

A guide bar that changes its shog from course to course takes yarn at a changing rate from a beam that delivers at one. The overlap is the same on every course, so it cancels again, and the running shortfall is the sum of each course's underlap less the mean — exact, with no loop in it. It returns to nought every repeat and strays inside it by a stroke that something must absorb. For a stripe the stroke is about the stripe's own height in the cloth, whatever the machine's gauge. The same twelve courses of tricot and satin need six times the stroke in two blocks as alternating, and of all 924 orderings exactly one pattern needs the least.

knits · Warp knit

Named alongside it

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

Take-upCrimpWarp tensionJacquardDamaskBucklingDouble clothEaserLappingSettThread lengthWarp knitting

All concepts