Textile Structure
how cloth is put together
Concept

Doup — where it appears

The heddle arrangement that carries one warp end to the other side of its partner between picks, which is what makes a leno's crossing possible. It is a mechanism rather than a draft, which is why leno is the clearest case of a fabric this site's central notation cannot hold.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

A leno and the open plain weave it is not. Two warp ends and the picks they hold. On the left the doup end passes under its partner between picks and comes up the other side; on the right it never crosses, which is an open plain weave at the same sett. The layer count under each panel is computed by the same criterion that decides every other draft, and it returns the same verdict for both.

Leno is not a matrix

A doup end crosses under its partner between picks and comes up on the other side, so the end at position three on pick two is a different end on pick three. The entry W[i][j] does not name anything. The encoding is not wrong about leno; it is undefined for it.

fancy · Leno Mock leno, 3 threads to a bundle. Threads that interlace identically have no weft passing between them, so nothing holds them apart and they lie touching. The reed still sets the average spacing, so the space they leave collects at the bundle's edge — a hole 0.60 by 0.60 mm, made without one thread crossing another. Drawn to scale on a fixed 9 mm square of cloth at 20 threads per centimetre and a 0.3 mm yarn.

A hole with nothing crossing

A real leno holds its holes open by crossing one thread over another, which is a topological arrangement and cannot come undone. A mock leno makes the same holes by grouping threads that nothing separates, and everything about it is friction.

weaves · Texture weaves 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 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 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.

LenoCapstanEaserGauzeFrictionShedWarp strainBack restBeamBraidCloth integrityConnectivity

All concepts