Textile Structure
how cloth is put together
Generator

Warp strain against shaft position

Warp strain against shaft position
Warp strain against shaft position. The warp strain a shed puts into an end, against the distance of its shaft from the fell, for 40 shafts on a warp line of 1200 mm at a half-shed tangent of 0.1667. The exact trigonometry and the leading-order form t² a / 2(L − a) are drawn separately and agree to within 5.67 per cent over the whole harness.

The warp strain a shed puts into an end, against the distance of its shaft from the fell, for 40 shafts on a warp line of 1200 mm at a half-shed tangent of 0.1667. The exact trigonometry and the leading-order form t² a / 2(L − a) are drawn separately and agree to within 5.67 per cent over the whole harness.

11 essays call loom-curve. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

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. Mechanics and drape

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.

 The strain across a harness. The warp strain each shaft of a 24-shaft harness puts into its own ends, from 0.460 per cent at the front to 1.728 per cent at the back. Shafts within a budget of 1.0 per cent are drawn in one colour and those outside it in another; the budget is reached at shaft 13. Mechanics and drape

The back shaft works hardest

How hard the loom is on a warp end is the product of two numbers from different worlds — how often its column changes sides, which is a property of a binary matrix with no millimetre in it, and the strain of the shaft it happens to be on, which is a property of a machine with no weave in it. Neither knows about the other, and the threading that joins them is a decision nobody makes on structural grounds.

 Flexes per end in the same check, ground a pick along. One bar per warp end above the draft of the same check, ground a pick along, each the number of times that end changes sides in one repeat — which is the number of times the shed drags it through its heddle eye. The counts run from 6 to 10, and they are the same numbers that give the cloth its interlacing rate of 0.500 per intersection. Mechanics and drape

A figure is harder on its warp

Every basic weave flexes all its ends exactly as often as each other — plain, twill, satin and sateen alike, and it is a one-line theorem. Figure one of them on another and that evenness goes, or does not, depending on where the ground weave was started relative to the figure. The same invisible offset that decides whether a fine figure holds together decides, at a coarse one, how unevenly the loom works the warp.

 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. Setting and geometry

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.

 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. Setting and geometry

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.

 What a shed costs, in newtons. The tension the shed puts into one end at each shaft of a 24-shaft harness, for a 25 tex cotton yarn. The strain is set by the loom's geometry alone; the tension is that strain times the yarn's modulus. The front shaft holds 0.52 N and the back 1.95 N, which is 14 and 52 per cent of the yarn's breaking load. What the chart cannot show is the rest of the warp tension, which the let-off adds on top of all of these and which no geometry decides. Mechanics and drape

What the shed costs, in newtons

The shed's strain has been computed here and could not be priced: a strain is a length over a length and says nothing about how hard a thread is being pulled. A modulus turns it into a tension — and the back shaft of a twenty-four-shaft harness turns out to hold its ends at half their breaking load, all day, from the geometry alone.

 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. Compound and figured cloths

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.

 A repeat across a 1800-end warp. Four repeat widths laid across the same 1800-end warp, drawn at the warp's own scale. The pale bands at the two ends are the selvedge threading, 24 ends each, which weaves its own firmer weave and is not part of the design. Between them the body is ruled into whole repeats, alternating so they can be counted, and the marked bands at the two sides are the remainder — the part of a repeat that did not fit, split between the two selvedges because the trade centres the pattern. None of these four repeats divides the body exactly, and the leftovers run from 2 to 24 ends. What the drawing cannot show is what the break looks like: a quarter of a repeat at the selvedge reads as a border and half of one reads as a mistake, and where the line between those falls is a judgement. What cloth is

A repeat has to fit the width

A repeat tiles the plane and a warp has two edges, so somewhere between them a repeat is cut through. The set of repeat widths that divide a warp exactly is the set of divisors of its body, and a body of a few thousand ends has a few dozen — two to eight per cent of the candidates. So a designer choosing a repeat for any reason except the width chooses one that does not fit, and the leftover averages half a repeat, split between the two selvedges.

 What matching a pattern costs a cutting room. The cloth a matched panel needs beyond its own length, against the pattern repeat, for 6 panels of 70 cm. Every panel of a patterned cloth must start at the same phase of the repeat or the pattern breaks at the seams, so a panel's cut length is rounded up to a whole number of repeats. The bar is the allowance a cutting room budgets — a whole repeat a panel, because a panel's length is not a multiple of anything — and the mark is the waste actually expected, which is half a repeat. The two differ by (L + r)/(2L + r), which is between a half and two thirds and is nearer two thirds the larger the repeat. The rows marked in the second colour are the repeats that happen to divide the panel exactly and waste nothing at all, which is what makes the real cost jagged rather than smooth. What the bars cannot show is nesting: a cutting room lays many panels on one length and a short panel can sometimes be taken from another's waste. What cloth is

A repeat has to fit the panel, and the panel is cut

The warp's width is fixed at warping and a piece's length is not, so the fitting problem in the two directions is not the same problem. Along the length a repeat has to fit a *panel*, because every panel of a patterned cloth must start at the same phase or the pattern breaks at the seams — and the allowance is a whole repeat per panel. A ten-centimetre repeat costs a seventy-centimetre panel twelve and a half per cent and a sixty-four-centimetre repeat costs it forty-eight.

 Two lots of one cloth matched at the top over a 250 cm drop. Two lengths of the same patterned cloth, woven with the warp at tensions of 0.6 and 0.7, which relax by 6.80% and 7.94% along the length, hung side by side over a 250 cm drop and matched at the top, with a mark at every 32 cm repeat. The whole drop is drawn to scale on the left and the last mark at six times the scale on the right: lot B's repeat is 31.61 cm, and 7 repeats down its mark is 27.3 mm from lot A's. A 3 mm match holds for the first 25 cm. What the drawing cannot show is how large an offset an eye accepts across a seam, which the tolerance stands in for. What cloth is

Two lots of one cloth drift apart down a drop

A pattern repeat is a count of picks, and its length in the finished cloth is whatever that count's loom length became after the cloth gave back its crimp. Two lots woven with the warp held a tenth harder give back 1.13 points more of their length — so matched at the top, two lengths from the two lots are thirty millimetres apart at a 250 cm hem, and visibly apart a quarter of a metre down. The size of the repeat does not enter, and no cutting allowance can take it out.

 3 widths of cloth at 2% skew and 0% bow, hung level. 3 widths of a 140 cm patterned cloth hung side by side and joined at their selvedges, with three of its pattern rows drawn across each. The cloth's weft is skewed by 2% of the width and bowed by 0%. Hung level, every width starts its rows at the same height, so each seam shows the skew's 28 mm step. The rows' displacement is drawn 8 times its true size against the width. What the drawing cannot show is the ceiling, pole and hem a real hanging is seen against, which is what a tilt is read by. What cloth is

A skew steps at every seam and a bow at none

A finished cloth's weft rows are seldom square to its selvedges, and on a patterned cloth the weft rows are the pattern rows. A skew — rows straight but slanting — puts its whole rise across every seam where two widths meet: two per cent on a 140 cm width is a 28 mm step, and matching the steps out tips the whole hanging instead, 112 mm across four widths. A bow — rows curving between level selvedges — matches perfectly at every seam and scallops each width in between. A three-millimetre match needs a skew under a quarter of a per cent, and down the seam a lot difference overtakes it.

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