Textile Structure
how cloth is put together
Concept

Double cloth — where it appears

Two complete fabrics woven at once on one loom, which one matrix describes and the layer count reports as two. The layer count reporting two where one was intended, or one where two were, is the accident this site's criterion exists to catch.

Named by 12 essays across 3 fields — each of them below, with the objects they name alongside it.

Whether the cloth is one cloth. Two drafts. Both interlace everywhere, both have short floats, and both look like perfectly ordinary weaves. One is a single fabric and the other is two fabrics lying on each other, and the bars beside each strand say which layer it belongs to.

Does it hang together

A draft can interlace everywhere, have short floats, and describe two fabrics lying on each other rather than one. Nothing about the drawing says so, and the test that does is exact.

cloth · Integrity A double cloth. Two complete fabrics woven in one repeat, and what happens when a single intersection is turned over. The layer count beside the draft is computed from the matrix drawn, and the census below it is every single-square change tried in turn.

Backed and stitched constructions

A double cloth is two fabrics woven at once, and the check that verifies it says exactly two. Turn one intersection over and it says one — which means one mistake is enough to destroy the construction, and the enumeration says half of them would do it.

weaves · Integrity 3 cloths on 6 ends. A repeat of 6 ends and 6 picks holding 3 complete cloths, each with 2 ends and 2 picks of its own. The bars beside the strands say which cloth each belongs to; the ceiling at this size is 3, and the longest float is 5 because the face warp passes over every pick below it.

How many layers a draft can have

Of the 22,874 four-by-four drafts this site sweeps, 22,730 are one cloth and 144 are two. None is three, and none can be — a repeat of n ends holds at most n halved cloths, because every cloth needs two ends and two picks of its own before it interlaces at all.

cloth · Integrity One cloth, before the knife. Double plush: two ground cloths woven face to face with a pile warp shuttling between them. Uncut, the pile is the only thing either ground touches the other through, and the integrity criterion says one cloth. Cut down the middle, every pile end is severed and the same criterion says two. The whole manufacture is the deliberate destruction of an integrity the criterion otherwise exists to confirm.

Velvet is cut apart

Two ground cloths are woven face to face with a pile warp shuttling between them, and while it does the whole thing is one cloth — the criterion says so, and the pile is the only reason it is true. Then a knife runs down the middle and the same criterion says two. The manufacture is the deliberate destruction of cloth integrity.

fancy · Pile A tube. A two-layer fabric 6 ends wide in each layer, with the weft's path drawn across the section below the draft. 1 piece of cloth, 0 free selvedges, 1 shuttle, and a developed width of 12 ends however the edges are joined. The connectivity of the infinite repeat is 2 for this draft and cannot tell this construction from the others.

A tube and two cloths are the same draft

Two separate fabrics, a cloth twice the width of the loom and a seamless tube are the same draft to the last square. The check this site is built on reports two layers for all three and is right every time — because the thing that separates them is four free selvedges, or two, or none, and a repeat has no selvedges in it.

fancy · Double cloth Where a stitch can hide on a 5-end satin face. The face weave on point paper, with a mark on every gap between two ends at which a stitch would be covered. 15 of the 25 positions in the repeat pass the cover rule, which is 60 per cent of them, and 5 of those can be used at once without two stitches sharing a pick or a gap.

Where a stitch can hide

One reversed intersection turns two cloths into one, and half the intersections in the repeat would do it. Almost none of them may be used — a plain-faced double cloth has nowhere at all to put a stitch, a five-end satin has fifteen places or none depending on which rule is asked, and two satins of the same order differ by a factor of two.

fancy · Double cloth A two-layer interchange, 1 block by 2. A two-layer cloth whose layers change places from block to block, drawn as the draft and as the section a weaver would draw. Each block is one repeat of the stack, 4 picks by 4 ends, and the design has 2 boundaries in it. Every strand in the draft is coloured by the cloth this site's criterion puts it in, and there is one colour, because there is one cloth — with no intersection reversed anywhere in the repeat. A stitch joins two layers at a point; an interchange joins them along a line, and the line is the design's own block boundary rather than anything added to it. The section below is schematic: it draws each ply as a line rather than as its threads, because what has to be seen is that the two lines cross, and a section at thread level over 2 blocks is a picture nobody can count.

An interchange joins what a stitch would have had to

The rung below spent a whole essay on where a stitch may be put in a double cloth, and found face weaves with nowhere to put one at all. A design in which the two layers change places from block to block needs no stitch anywhere: the boundary is the join. Two blocks side by side make one cloth with not a single intersection reversed, and the same two blocks with no boundary between them make two.

fancy · Double cloth plain over 5-end satin: what each layer's warp does. A warp end of each layer of a double cloth, in section over the same span of cloth, with the length of warp each eats drawn beneath. The crimps come from Peirce's geometry asked about a thread that bends at its own average rate rather than at every crossing, and they are 14.35% for the plain and 2.03% for the 5-end satin. They are not the same, so the two layers consume warp at different rates: a hundred metres of cloth takes 114.4 m of warp from one and 102.0 m from the other. A beam delivers one rate, so the difference has nowhere to go and accumulates with the length woven — one pick spacing after 4 mm. What the sections cannot show is the yarn's thickness, which is exaggerated so the path is legible; the crimps beside them are computed at the real diameter and are not read off these drawings.

Two layers need two beams

A layer weaving a metre of cloth eats one plus its crimp metres of warp, and a beam delivers one rate. A plain face over a five-end satin back differs by twelve percentage points of crimp, which is twelve metres of warp over a hundred-metre piece and one pick spacing of slack after four millimetres of weaving. The difference has nowhere to go and does not settle — so the only double cloth that can share a beam is two layers of the same weave at the same sett.

fancy · Double cloth How many layers the repeat, the harness and the beams each allow. Three ceilings on the number of layers a double cloth can have, for five layer weaves. The repeat's bound is half its ends and is a property of the notation. The harness's is the strain budget — 13 shafts on an ordinary broad loom at a 1.0% warp strain limit — divided by the shafts one layer of that weave costs. The beams' is how many warps the loom carries, which is 2. The shortest of each three is marked, and it is the beams at the coarse end of the table and the harness at the fine end; the repeat is never the binding one except at two-end layers, where it happens to coincide with the harness. A double cloth of eight-end satin layers needs 16 shafts and the budget is 13, so it is a jacquard construction by arithmetic rather than by choice. What the bars cannot show is the pick rate: a k-layer cloth needs k times the picks per centimetre of finished cloth and takes k times as long to weave, which is a cost rather than a ceiling and is the reason four-layer cloths are rare even where they are possible.

The repeat allows four layers and the loom allows two

A repeat of eight ends can hold four separable cloths, and there is a witness that reaches the bound exactly. No loom weaves four. The harness's strain budget buys thirteen shafts and a layer costs its own weave's shaft count, so five-end satin layers stop at two and eight-end satin layers cannot be doubled on a dobby at all — and two differing layers already want a beam each. The notation's ceiling is the only one of the three that is never binding.

fancy · Double cloth 20 tex yarn in one layer and in 2. Sections across the width, to scale, of a cloth of 20 tex cotton at a cover of 0.8, and of the same yarn per area divided into 2 layers two ways: by count, 10.0 tex at the same sett, and by sett, 20 tex at 1/2 of the ends. Divided by count the cloth is 1.41 times as thick with a cover of 0.57 in each layer; divided by sett it is 2.00 times as thick with a cover of 0.40. At the free end of the yarn's stiffness bracket both are exactly as stiff as the single cloth; at the coherent end the first is 0.50 times as stiff and the second 1.00. What the sections cannot show is crimp, which thickens every layer by an amount the weave decides.

A double cloth is only softer if its yarn is set

A double cloth is sold as weight without stiffness: two light cloths in place of one heavy one. Divide the same yarn into two layers and the cloth is √2 or twice as thick, but at the free end of a yarn's stiffness bracket — where an unset yarn sits — its bending rigidity does not move at all, because it is the number of fibres across the width times the stiffness of one. Only a set yarn makes the double cloth the softer, and stitching the layers together pushes it the other way.

fancy · Double cloth What two layers of one yarn buy. For each cloth in the table here, the thickness and the thermal resistance of a two-layer cloth carrying exactly the same yarn per unit area, as ratios to the single cloth. The thickness ratio is √2 everywhere, to three figures. The warmth ratio runs from 1.588 on the openest cloth to 1.717 on the closest, because dividing the yarn also divides the fibre fraction and the mixture conducts less.

Two layers are warmer than they are thick

Six essays have taken a double cloth apart from the draft's side. None has asked what the reader gets. Divide one cloth's yarn into two layers and the fabric is 41 per cent thicker — √2, which is the account's own law — and about 70 per cent warmer, because dividing the yarn also divides the fibre fraction and the mixture conducts less. The gap widens with every further layer and never closes, and a shaft loom stops at two.

fancy · Double cloth What stitching takes back from a double muslin. The warmth a two-layer muslin of the same yarn gains beyond its √2 thickness, against the share of a layer's intersections that carry a stitch, with a 5-end satin face. Under the parallel rule the bonus is 18.8 per cent whatever the stitching, because that rule already treats every fibre as running through the cloth. Under Maxwell's rule for fibres lying across the heat's path the bare bonus is 8.4 per cent and each stitch takes some back: one stitch a repeat (4% of intersections) leaves 7.6, one a pick, scattered (20% of intersections) leaves 4.7, every hidden position (60% of intersections) leaves -1.5.

A stitch takes back what the parallel rule cannot see

Dividing a cloth's yarn into two layers makes it warmer than its thickness, and the essay that found it computed the warmth by the one mixing rule that cannot see a stitch — the one that treats every fibre as though it ran straight through the cloth. That rule gives the largest bonus there is. Yarn in a cloth lies in its plane, and by the rule for fibres lying across the heat's path a double muslin's bonus is 8.4 per cent, not 18.8. A stitch is the one fibre that does run through the cloth, and at half the intersections it takes the whole bonus back.

fancy · Double cloth

Named alongside it

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

Cloth integrityStitchingConnectivityBacked clothFloatPoint paperRepeatBeamCloth thicknessHanging togetherInsulationLoose end

All concepts