Textile Structure
how cloth is put together
The collection

Every essay — page 20

Page 20 of 20, continuing through the fields in the same order.

What cloth is Weaves Setting and geometry Knits and other structures Mechanics and drape Pattern and colour Compound and figured cloths After the loom Cloth doing a job

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Compound and figured cloths

Double cloth, pile, leno, and the loom that decides what can exist. Where a fabric stops being one binary matrix — a third thread system, a warp order that changes between picks — and where the integrity criterion runs out and friction takes over.

A comber board for 60 ends a centimetre, in side elevation. A jacquard's comber board seen from the side, with the fell of the cloth at the left and the back rest at the right. The board carries one hole per end; at 60 ends a centimetre the ends are 0.167 millimetres apart and a cord with a mail on it needs 0.9, so the holes are ruled in 6 rows staggered fore and aft, 6 millimetres apart — a harness 30 millimetres deep. Each row's ends are strained by its own distance from the fell: 0.460 per cent at the front and 0.524 at the back, a spread of 0.0636. What the elevation cannot show is the sideways fan of the cords above the board, which is a separate and much larger geometry.

A jacquard's harness has a depth after all

A jacquard was said to escape the shaft loom's depth entirely, because every mail hangs at the same distance from the fell. Every mail does, if the comber board has one row of holes — and it cannot. At sixty ends a centimetre the ends are a sixth of a millimetre apart and a cord with a mail on it wants most of one, so the holes are ruled in six rows thirty millimetres deep. The escape is real and it is a factor of eight rather than a release, and it closes as the cloth is set finer.

7 figures · Jacquard What each figure-and-ground pairing costs in differential take-up. For each pairing of a figure weave with a ground weave, the difference between the two regions' warp crimps and the length of figure that difference allows before an end goes slack, taking the loom to absorb 1.2 millimetres. a damask: satin on its own complement: 0.00 per cent apart, no bound; an eight-end satin figure on a five-end satin ground: 0.31 per cent apart, a figure up to 392 millimetres; a five-end satin figure on a 3/1 twill ground: 0.90 per cent apart, a figure up to 133 millimetres; an eight-end satin figure on a 2/2 twill ground: 3.02 per cent apart, a figure up to 40 millimetres; an eight-end satin figure on a plain ground: 14.15 per cent apart, a figure up to 8 millimetres; a 2/2 twill figure on a plain ground: 11.14 per cent apart, a figure up to 11 millimetres. A damask's two regions are the same satin used two ways, so complementation leaves both float lengths where they were and the crimps are identical rather than close. What the bars cannot show is the slack, which is an input and which every length is proportional to.

A damask is the only figure that costs its beam nothing

Figure and ground consume warp at different rates, and the difference accumulates down the length of the figure. An eight-end satin figure on a plain ground puts its two regions fourteen per cent apart, which on a loom absorbing a millimetre of slack bounds the figure at eight and a half millimetres. A damask's two regions are the same satin used two ways, so complementation leaves both float lengths where they were — and their crimps are identical rather than close, to the last bit of a double.

6 figures · Jacquard The crossed shed's three spans at an eye friction of 0.3. A leno's crossing end in the crossed shed on an ordinary broad loom, back standard 4 shafts behind the doup, with both heddle eyes gripping at a coefficient of 0.3 and a background tension of 0.5 N. The end turns 69 degrees at the doup and 64 at the back standard, capstans of 1.44 and 1.40. From fell to doup it settles at 6.95 N, a strain of 5.73%; from doup to back standard it settles at 9.48 N, a strain of 7.97%; from back standard to back rest it settles at 6.78 N, a strain of 5.57%. With frictionless eyes every span would take 7.08 N; an ordinary end at the doup takes 1.02 N and the yarn breaks at 3.74 N on its initial modulus. Vertical scale exaggerated 3 times. What the drawing cannot show is the tension's fall round each eye, which happens over the eye's own few millimetres.

A heddle eye lets the kink through

A leno's crossing end is pulled up at its doup and held down at its back standard, and the length that costs was priced as if both heddle eyes were frictionless. They grip, and gripping ought to trap the kink between them at nearly a hundred per cent strain. It does not come close. A capstan bounds a ratio of tensions, not a difference, and the spans either side are already stretched, so at a coefficient of 0.3 the span between the eyes takes 9.48 newtons against 7.08 with no friction at all — a third more, not fifteen times more — and an easer has to give back 67.9 millimetres rather than 64.4. What friction changes more is when the length is wanted.

8 figures · 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.

7 figures · Jacquard What each further binder takes off a snag. How far a snag drags thread through a bouclé, in binder points, against how many binders the yarn carries: 1, 7.43 points; 2, 3.72 points; 3, 2.48 points; 4, 1.86 points; 6, 1.24 points. The relation is exactly inverse, because the grip is the exponential of the wrap angle and the reach is a logarithm of it, so the second binder removes 3.72 binder points and the third a further 1.24.

The second binder buys half of everything

A bouclé's loops are held by their binder, and a snag drags thread from one loop to the next until the thread breaks. The essay before it left that reach at seven binder points on one binder and said a second would square the grip. It does — and because the grip is exponential in the wrap and the reach is a logarithm of it, the reach is exactly inverse in the binder count: 7.43 points, then 3.72, then 2.48. Half of everything any number of binders can buy is bought by the second one, which is how many the trade uses.

6 figures · Fancy yarn What two layers of one yarn buy. For each cloth in the table here, the thickness and the thermal resistance of a two-layer cloth carrying exactly the same yarn per unit area, as ratios to the single cloth. The thickness ratio is √2 everywhere, to three figures. The warmth ratio runs from 1.588 on the openest cloth to 1.717 on the closest, because dividing the yarn also divides the fibre fraction and the mixture conducts less.

Two layers are warmer than they are thick

Six essays have taken a double cloth apart from the draft's side. None has asked what the reader gets. Divide one cloth's yarn into two layers and the fabric is 41 per cent thicker — √2, which is the account's own law — and about 70 per cent warmer, because dividing the yarn also divides the fibre fraction and the mixture conducts less. The gap widens with every further layer and never closes, and a shaft loom stops at two.

6 figures · Double cloth What the crossing end asks for, against what a cam gives it. The length a leno's crossing end needs at each fraction of the crossed shed's opening, against an easer driven in proportion to the shed. The demand is nothing for the first eighth of the opening and then rises steeply, because the kink's extra length is a hypotenuse less its run and grows as the square of the climb. The proportional easer runs ahead of it everywhere, worst at 0.375 of the way open, where it has given 16.5 millimetres more than the end can use.

A cam easer gives its slack too early

The essay before it left the crossing end with fifteen millimetres it could not use at half the shed, and three things it might do with them. All three are decidable. It cannot reach the shuttle, because the same eyes that trapped the kink keep the slack behind the harness — and the margin is negative, so that friction is not a nuisance here but the reason a leno weaves at all. It cannot snarl, because the span is under half this account's own threshold. It sags seventy-two millimetres where the easer gives it, and the repair is a cam cut to the demand rather than to the shed.

6 figures · Leno