Textile Structure
how cloth is put together
Concept

Marker efficiency — where it appears

The fraction of a bolt that ends up in cut panels rather than in scrap, which the layout's angle and the cloth's width both decide. A bias layout costs it and a straight one does not, which is the whole of why bias-cut garments are expensive in cloth as well as in labour.

Named by 6 essays across 2 fields — each of them below, with the objects they name alongside it.

Where a bias cut's waste actually is. A bolt of cloth with panels placed at a stated angle, the ones that fit drawn and the rest of the cloth left shaded. Identical panels at a single angle tile the plane exactly, so the interior of the bolt loses nothing at all and the whole of the waste is at the two selvedges. The inset is the single-panel bounding box, which is the picture the usual account of bias cutting draws.

The bias cut and the selvedge

A bias-cut square costs exactly twice its own area, and every other shape costs more. That is an exact result about one panel — and it is not where a cutting room's waste comes from, because identical panels at one angle tile the plane. The loss is at the two selvedges, so it falls as the cloth gets wider, which no account in terms of the diagonal can explain.

applied · Cutting How much of the curvature a cloth can take without being cut. The dart angle a spherical cap still demands after the fabric's own shear has absorbed what it can, against how closely the cloth is set. The total the cap demands is fixed by Gauss–Bonnet and is the same for all of them; what changes is how much of it the trellis can supply before its threads jam. An open cloth drapes a hemisphere with no dart at all; a closely set one has to be cut from the start.

A hemisphere costs one full turn

The total angle a pattern must remove to cover a hemisphere is exactly 360 degrees, and it is the same for a hat and for a stadium dome. What changes with the fabric is how much of that the cloth can supply by shearing instead of by being cut — and that is a property of the sett, computed from the angle at which its threads jam.

applied · Cutting The same fault in the warp and in the weft. A 50 m piece 1500 mm wide, with a 3-thread fault in each direction. The width is drawn 9.3 times over scale so that the piece is a rectangle rather than a line, and the two faults are drawn as marks rather than at their own widths, which at this scale are a fifth of a pixel. They have the same cause size — 3 threads — and they condemn 0.063 m² and 0.0020 m² respectively, a ratio of 31 to one, because a warp fault runs the length of the piece and a weft fault runs its width. That ratio is the aspect ratio of the piece and nothing else, so it is a property of how cloth is made rather than of what went wrong. It is why a broken end stops the loom and a mispick often does not, and why the two faults are priced by every grading scheme as though they were different kinds of thing.

A missing end is a fault the length of the piece

A broken end and a mispick are the same size of accident — one thread — and they condemn areas that differ by a factor of thirty. The ratio is the aspect ratio of the piece and nothing else, which makes it a fact about how cloth is made rather than about what went wrong.

applied · Faults 6 tapered panels laid across a 150 cm cloth three ways. 6 panels 14 cm across the top, 32 cm across the bottom and 75 cm long, laid across a cloth 150 cm wide, drawn to scale. Turned end for end alternately, 6 fit side by side and the 6 take 75 cm of cloth. Laid all one way in lanes, 4 fit and they take 150 cm. Laid all one way with alternate columns shifted half a length, 5 columns fit and they take 150 cm. What the drawing cannot show is a real marker's other pieces, which fill the gaps these leave.

A nap is paid for by the taper of the pattern

A raised cloth's fibres lean, so a panel turned end for end shows a different amount of fibre and every piece of a garment has to lie the same way along the bolt. What that costs is not a property of the cloth. A rectangle costs nothing laid one way; a tapered panel costs (1 − r)/(1 + r) of extra cloth in lanes, where r is its narrow width over its wide one; and the best any one-way lay can do is exactly half of that, because a trapezoid's difference body is a hexagon and hexagons tile. On a real width it arrives in whole panel lengths: six skirt gores take 75 centimetres two ways and 150 one way.

finishing · Nap What the four-point system charges for a fault, and what the cutting room pays. For a single warp fault of each length: the points the four-point system scores it — one up to three inches, two to six, three to nine and four beyond — and the number of 900-millimetre panels it condemns. Below a panel's length every fault condemns exactly one panel while its points run from one to four, so the scheme charges four times as much for a fault that costs the same. Above a panel's length the panels grow without bound and the points stay at four, so the scheme stops charging exactly where the cost starts rising. A ten-metre fault scores 4 and condemns 12 panels. What the chart cannot show is the marker, which decides the panel size and therefore the whole of the second curve.

A grade charges by the length and a cutter pays by the panel

The four-point system scores a fault by how far it runs — one point to three inches, four beyond nine — and caps a linear metre at four points however many faults it holds. A cutting room pays by how many panels the fault lands in. Below a panel's length every fault costs exactly one panel while its score runs from one to four; above it the panels grow without bound and the score does not move at all. Two fifty-metre pieces built to the same 267 points a hundred square metres lose 33 per cent of their panels and 92.

applied · Faults The first 12 metres of a bolt, cut three ways. A bolt of 50 metres carrying 40 faults, with its first 12 metres drawn: the fault positions above, and below them the 900-millimetre panels a cutter gets cut blind, cut with the same rigid tiling slid to its best offset, and cut around the faults with the map in hand. Over the whole bolt the three yield 28, 30 and 40 sound panels of 55. Sliding the tiling buys 2; breaking it buys 12, which is 43 per cent more cloth from the same roll. What the strip cannot show is the width, across which the same argument runs again with a different panel dimension.

A fault map is worth most where the grade is worst

A cutter who knows where the faults are can slide the marker or break it, and only one of those is worth anything: sliding a rigid tiling to its best offset recovers two panels of fifty-five, and letting the tiling break recovers twelve — two panels in five more cloth from the same roll. The gain has a maximum in the middle of the range, because there is nothing to recover on a clean bolt and nothing to be done on a ruined one. And the prediction the grading essay made, that a map is worth most on a bolt whose faults are bunched, is false: bunching leaves clear runs for the blind cutter too.

applied · Faults

Named alongside it

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

SpecificationCondemned areaFaultMeasurementBroken endDartPoisson fieldSelvedgeBiasBias-cutCuttingDevelopable

All concepts