Textile Structure
how cloth is put together
Series

Coating — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. A coating over the hole it has to bridge. Four warp ends of 40 tex seen end-on at 20 per centimetre, with a 120 micrometre PVC film over them. The film is supported everywhere it lies on a thread and unsupported over the 252 micrometre clear span between them, which is the same span at every hole in the repeat. The film's thickness is drawn to scale against that span; the bulge is exaggerated. At 20 MPa the film will hold at most 381 bar, which is a bound and not a prediction.

    A coated cloth fails at its holes

    Spread a film over a fabric and it is supported everywhere it lies on a thread and unsupported over every hole. A woven cloth's holes are all the same size — exactly, because a repeat is a repeat — so the film has one span to bridge and the fabric has a burst pressure rather than a distribution. A nonwoven gives it a distribution, and a membrane fails at the largest hole it meets.

    part 1 · applied
  2. What a coating does to the rest of the site. Seven quantities this site computes for uncoated fabric, with what each becomes once a film bonds the crossings: the shear a cloth will take — changed in kind; tear strength — changed in kind; the loss from a hole — reversed; wicking — halved; air permeability — reversed; the sett's effect on strength — unchanged in sign; areal weight — added to. Two of the seven reverse outright. The table is a collection rather than a computation, and each row points at the essay whose result it qualifies.

    Coated is a state

    Every mechanism on this site assumes threads that can move relative to one another — the bias is a mechanism because the crossings rotate, a tear runs because threads gather, a cloth takes a hole without minding because the neighbours pick the load up. A film bonds the crossings. Two of those results reverse outright, the rest change in kind, and no number on this site has ever said which state it belongs to.

    part 2 · finishing
  3. What it takes to bury a cloth's crowns. The film needed to fill a fabric's surface to a stated level, for plain, 2/2 twill, satin 8 in sheeting, at a film density of 1.2 g/cm³. Burying the crowns entirely takes 187 g/m² on the plain, 186 g/m² on the 2/2 twill, 183 g/m² on the satin 8 — and the ordering is not the ordering of roughness. A weave with plateaux presents a wide flat top that a thin film covers, and a weave with points presents crowns with valleys between them that the film has to fill before it is continuous anywhere. Every gram spent filling a valley is a gram that is not bridging a hole, which is where a coated cloth fails.

    A coating fills the crowns before it bridges the holes

    A film does not sit on a cloth, it fills it — and the volume it has to supply to reach a level is the integral of one minus the bearing area. Burying an ordinary sheeting's crowns takes 185 grams a square metre, which is more than the cloth weighs, and the whole of the weave's influence is spent in the first ten of them.

    part 3 · finishing
  4. A print is as sharp as the hairs are long. How far ink carried on a hair reaches past a printed edge into the unprinted cloth, for sheeting in three states. A hair lying near the edge bridges as far as its own length, and the number bridging at least a distance x is (n_A λ/2)e^(−x/λ) — an exponential with the population's own decay length — so the visible feather is a quantile rather than a mean, taken here at one hair per 50 millimetres of edge. As woven the feather is 1911 µm, which is a fifteenth of an inch and coarser than any screen worth engraving: the cloth cannot hold better than 7 lines to the inch whatever the printer does. Singeing caps it at the flame's own reach of 200 µm and takes the cloth to 63 lines — a factor of 10, bought by burning off a fraction of one per cent of the cloth's mass. That is why singeing comes before printing and why nobody prints a fine figure on a raised cloth.

    A print is as sharp as the hairs are long

    Singeing comes before printing in every finishing route ever written down and the reason given is that the cloth must be smooth. The reason is sharper than that: ink carried on a fibre end reaches as far as the fibre is long, so the feather on a printed edge is a quantile of a hair population and nothing else.

    part 4 · finishing

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