Textile Structure
how cloth is put together
Concept

Closure condition — where it appears

The requirement that a woven cloth's two thread systems supply its whole thickness between them. It is one equation with no slack in it, and past a certain swelling of the threads there is no state that satisfies it at all.

Named by 4 essays across 4 fields — each of them below, with the objects they name alongside it.

A loop's cell, dry and wetted. One stitch of a 20 tex cotton jersey at a 3.50 mm loop, drawn inside the rectangle of one wale by one course that its own dimensions give. The thread is drawn at its own width, and it already fills 1.129 of the cell dry — more than the whole of it, which is what an opaque jersey looks like from above. Wetting takes it to 1.355. So the reason a knit does not build a swelling pressure is not that it has room; it is that its dimensions are a loop length times a constant with no yarn diameter in them, so there is no closure condition to fail. What the drawing cannot show is the third dimension: the legs lie over one another rather than overlapping in the plane, which is exactly why an occupancy above one is possible.

A loop has no closure condition

A woven cloth can run out of room: its two systems must supply its whole thickness between them, and past a certain swelling they cannot. A knit has no such equation, so no critical swelling and no pressure. The obvious explanation — that a knit is open and has somewhere to put the swelling — is false, and the arithmetic refuses it.

knits · Knit A sheeting's crossing, dry and wetted. One crossing of a sheeting in section at three swellings: dry, at the swelling where its geometry has its last state, and fully wetted at 20%. The closure condition is that the two systems' crimp heights add to the cloth's thickness, and each can supply at most the height it reaches when its straight portion has just vanished. Swelling raises the demand in proportion and the supply more slowly, so the margin closes and then goes negative — at 9.29% for this cloth against cotton's 20%. The bottom panel is drawn as far as the threads reach and no further, because there is no state to draw. What the drawing cannot show is what happens instead, which is that the yarn is compacted.

The swelling a cloth cannot take

Three of the eight cloths in this collection's table have no wet state at all. A thread of fixed length cannot wrap a partner that has grown by a fifth, so the closure condition fails and the geometry has nothing to offer. What happens instead costs megapascals, and the alternative route is not merely dearer but unavailable — the thread would break first.

mechanics · Compression The surface of a 2/2 twill, in plan. One repeat of a 2/2 twill in sheeting, drawn 2 × 2 times, with every point painted in the colour of whichever thread owns the outside of the cloth there and at an opacity set by how high it is. The range is 221.0 µm from the highest point to the lowest, the root-mean-square roughness is 74.9 µm, and 30% of the plan is hole rather than surface. The bright ribbons are the float plateaux, where a thread lies straight across the threads it passes over and its outside is a horizontal line rather than a point — which is the whole of what follows. The warp crowns at 190.8 µm and the weft at 182.8 µm, a step of 8.0 µm, so the cloth touches the world on its warp alone until anything pressing on it has sunk that far.

A cloth has an outside

Every quantity in this collection is a property of the inside of a fabric — a crimp, a cover, a hole, a fibre count. None of them says where the cloth stops. The outside is a height field the draft computes, its crowns stand at two different levels, and which of the two is higher decides what the cloth touches the world with.

cloth · Surface The sett sets the pitch of the relief and not its height. A 2/2 twill in sheeting set from 14 to 29 ends per centimetre. The spacing of the crowns falls from 714 µm to 345 µm — in exact proportion to the sett, because it is the sett — while the height the surface swings through moves from 381 µm to 381 µm, which is not at all. The reason is the closure condition: the two crimp heights must add to the sum of the two diameters whatever the spacing, so the amplitude of the surface is pinned by the yarn and only its wavelength is free. The third curve is the root-mean-square roughness measured off the sampled surface, which wanders by a few per cent because it depends on where the sample grid falls relative to the crowns — it is drawn to show that it has no trend, not to be read off. A closer sett therefore makes a finer-grained cloth and not a smoother one, and the two are confused in every description of fabric handle. At 32 ends per centimetre the geometry refuses altogether: the cloth is close enough that its crimp can no longer divide equally, which is the jam arriving as a loss of symmetry rather than as a loss of room.

The sett owns the pitch and the yarn owns the height

Set a cloth twice as close and its surface does not get smoother. The crowns come twice as often, because that is what a sett is, and they stand at very nearly the same height, because the closure condition pins the amplitude to the yarn — so a fine cloth is finer-grained rather than flatter, and the two are confused in every description of handle.

setting · Sett

Named alongside it

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

JammingCover factorCrimp heightCrown heightMoistureSurface heightSwellingBreaking strainCloth thicknessCompactionContact forceCrimp

All concepts