Textile Structure
how cloth is put together
Concept

Warp strain — where it appears

The extension a warp end takes when the shed opens, which is the extra length of a path that goes up and comes back down. It is what limits how many shafts a loom can carry, because a deeper harness makes a longer path for the back shaft's ends.

Named by 9 essays across 2 fields — each of them below, with the objects they name alongside it.

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 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.

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.

mechanics · Shed 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.

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.

mechanics · Shed 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 A jacquard harness 130 cm wide under a 150 cm fall. A jacquard harness in front elevation, to scale: hooks spread over 40 cm, cords fanning down 150 cm to a comber board 130 cm wide, and hanging straight from the board to their mails. The centre cord is vertical and lifts its mail by the whole 10 cm hook lift; the edge cord leans 16.7° and lifts its mail 9.60 cm, 96.0% as far, and its bend at the board adds 9% to the hook's load at a friction coefficient of 0.3. What the drawing cannot show is the tie that decides which hook feeds which hole, which in a real mount is not the simple spread assumed here.

A jacquard harness needs three half-spans of height

A jacquard has no front shaft and no back one, so every end takes the same shed — as long as every cord hangs straight. Across the width they cannot: the hooks sit in a machine a few tens of centimetres wide and the comber board is as wide as the cloth, so an edge cord leans and its mail rises by the difference of two hypotenuses rather than by the hook's lift. Holding the edge shed within five per cent of the centre's takes a fall of about three times the edge cord's sideways reach, and that is a height a room has to have.

fancy · Jacquard The crossed shed, with the back standard 4 shafts behind the doup. A leno's crossing end in section from the fell to the back rest of an ordinary broad loom, in the crossed shed. The doup 300 mm from the fell lifts it 50.0 mm; its back standard 64 mm further back leaves it 60.7 mm down, beneath its partner. Between the two eyes the end climbs 110.7 mm in 64 mm, and the whole path is 70.2 mm longer than the straight line, 5.85% of the free warp, of which 63.8 mm is that one climb. The same end in the open shed, lifted at its back standard, is 7.2 mm longer, and an ordinary end on the doup's shaft 5.5 mm: the crossed shed is 12.7 times the ordinary shed. Vertical scale exaggerated 3 times. What the drawing cannot show is friction at the eyes, which would keep the extra length in the short span between them.

An easer gives back the kink the crossed shed puts in

A leno loom gives its crossing ends slack at every crossed shed, and the obvious reason — the doup carrying its end sideways — is worth a hundredth of an ordinary shed. The length is one heddle further back. In the crossed shed the doup lifts the end on the far side of its partner while the end's own back heddle, a few shafts behind, holds it down, and between those two eyes the end climbs eleven centimetres in six and a half. On a loom that stretches an ordinary end 0.46 per cent, that is 5.85 per cent — nearly thirteen times as much — and no position of the back heddle takes it below four.

fancy · Leno 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.

fancy · 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.

fancy · 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.

fancy · Leno

Named alongside it

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

ShedLoomHarnessJacquardBack restCapstanHeddleShaftDamaskDoupEaserInterlacing

All concepts