The subject, divided

Fields

Nine divisions of one subject, in the order the argument builds them — what a fabric is, then the weaves, then the geometry that decides how close threads may sit, then the other ways of making cloth, then what it does when pulled, then what the eye makes of it, then the compound cloths where the encoding all the others rest on runs out, then what a finishing works does to any of it, and last the question of whether a particular cloth will do.

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The plain. The plain on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.

What cloth is

A fabric is a structure before it is a material. Interlacement, the draft as a matrix, and the question of whether a cloth holds together at all.

48 essays

The 5-end satin. The 5-end satin on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.

Weaves

Plain, twill and satin, and what actually separates them — float length, interlacing count, and a satin that cannot exist on six ends.

50 essays $The same thread count, twice. Two cloths with identical thread counts and different yarn. The count is the same number in both; the fraction of the surface the threads actually occupy is not, and that fraction is what thread count is usually taken to mean.$

Setting and geometry

Yarn diameter, crimp and cover. How close threads can be set, why thread count is not what it is taken for, and which model produced any number.

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The knitted loop. One thread, bent into a course of loops, each of them drawn through the loop below. Nothing here is straight, which is why a knit extends in every direction while a woven cloth extends only on the bias.

Knits and other structures

Loops rather than crossings. Why a knit stretches without a bias, why stockinette curls, and why a dropped stitch runs while a woven cloth frays.

49 essays

A trellis sheared 30°. The net at an angle, with every thread segment exactly the length it started at. The extension along the diagonal is the bias stretch, and it is a change of shape rather than a change of length.

Mechanics and drape

Cloth as a mechanism rather than a material. The bias, the angle at which threads jam, and why a flat sheet cannot cover a sphere.

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A draft is a two-coloured pattern. For each weave, the symmetries that leave warp-up as warp-up and those that exchange the two. Only a balanced weave has any of the second kind, because exchanging warp and weft is only a symmetry when there is as much of one on the face as the other.

Pattern and colour

A draft is a periodic plane pattern with two states, so the symmetry is two-coloured. Colour order, and the things the eye reliably gets wrong.

49 essays

A 2/2 threading, run out to three widths. The same four shafts threaded for repeats of increasing width. The threading line runs up and back down; the harness never grows, and the number of ends it carries is bounded by the loom's width rather than by its shafts.

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.

47 essays

The same thread, on the loom and off it. One warp end in section over eight picks, drawn twice at the same scale. The thread is the same length in both panels; in the lower one more of that length is in the bends, so the cloth it spans is shorter. Nothing has been lost — the length has moved into the crimp. The thread's thickness and the height of its bends are drawn larger than scale so the interlacing is legible; the two panels' spacings are not.

After the loom

The cloth that comes off the loom is not the cloth anybody buys. Shrinkage as the crimp coming back, the yarn flattened and swollen, the floats raised into a nap, and the fibres entangled until the weave is no longer the only thing holding the fabric together.

48 essays $How much fibre a woven reinforcement holds. A unit cell of a woven reinforcement in section: flat tows, the thickness they add up to, and the wave the warp makes to cross them. The bar below is the fibre volume fraction against the same tows laid flat in two plies and against the packing factor of a tow, which is the most any cloth of them could be. The vertical scale is exaggerated so the interlacing is legible; the horizontal scale is the cloth's own.$

Cloth doing a job

What happens when a fabric has to meet a specification rather than merely be described. A reinforcement that must hold fibre and still admit resin, a filter that must retain the soil and still pass water, a seam that must grip harder than the load without perforating the cloth, a pattern cut for a shape it does not yet have. Every requirement here is a pair of inequalities on quantities the earlier fields compute — and the useful answer is sometimes that no fabric satisfies both.

50 essays

The other two axes

a field says what an essay is about; these say what else it is near