Textile Structure
how cloth is put together
Concept

Stitching — where it appears

Threads that tie two layers of a compound cloth together, which is what stops a double cloth being two cloths. This collection's criterion is what says whether a stitch plan works, and where a stitch may hide without showing on either face.

Named by 8 essays across 3 fields — each of them below, with the objects they name alongside it.

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 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 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 A 4-layer stack round a 180° fold. 4 layers of 260 µm cloth taken round a 180 degree fold, drawn as concentric arcs at their own separation. The outer layer runs round a larger radius than the inner one, so it must be longer — by the angle times the separation, which is 2.45 mm here and 0.82 mm at every interface. In a loose stack that length is found by the layers sliding over one another at the fold. In a stitched seam they cannot: the stitches pin them every 3 mm, so the slip a fold needs is 82 per cent of the distance between two stitches and has nowhere to come from. What the arcs cannot show is what happens instead, which is that the fold opens out to a radius the stack can manage.

A crease cannot cross a seam

The outer layer of a folded stack has further to go than the inner, by the fold's angle times the stack's own thickness. A four-layer seam of quarter-millimetre cloth taken through a half turn needs its outer layer to be 2.45 millimetres longer than its inner — and a stitch line every three millimetres has pinned them. So the fold opens out where it crosses the seam, which is what a trouser crease visibly does, and the arithmetic gives the radius it opens to.

finishing · Crease 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.

Double clothCloth integrityConnectivityBacked clothCloth thicknessPoint paperStitching planTubeBending rigidityBlockCantileverCovering rule

All concepts