Textile Structure
how cloth is put together
Concept

Thread length — where it appears

How much yarn one thread contains per unit length of cloth, which is the cloth length times one plus the crimp. Holding it fixed is what defines this collection's locus, and a swelling that changes the thickness replaces the locus rather than moving the cloth along it.

Named by 10 essays across 6 fields — each of them below, with the objects they name alongside it.

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.

Relaxation is the crimp coming back

A cloth that shrinks in the wash has not lost any thread. The thread is exactly as long as it was; more of its length is now spent going up and down rather than along, and the difference is the shrinkage, computable to the last figure from the woven geometry alone.

finishing · Shrinkage Everywhere a sheeting can go. Every state a sheeting of 28 × 26 threads per centimetre in 25 and 25 tex can reach without a yarn changing length, solved from Peirce's plain-weave geometry. The set is a curve and not a region: 4.03 per cent of extension is available along the warp, and reaching it costs 6.98 per cent of the width.

A cloth extends by moving its crimp

Everybody says the extension available along the warp is the warp's own crimp. On six of eight ordinary cloths it is not — a close sheeting has 14.61 per cent of warp crimp and reaches 4.03 per cent, because the limit lives in the weft.

mechanics · Tensile The two routes a poplin has to a strain. A poplin drawn in section at three places: as woven, at the end of what its crimp can supply, and past that. Between the first two the warp's crimp falls from 8.97% to 4.85% and the weft takes on what it gave up, and the thread length is 0.4953 mm in both — nothing has stretched, and the cloth is 3.93% longer. Between the second and the third the geometry cannot move because the weft's straight run has vanished, so the cloth's extra 2.0% is the thread's extra 2.0%. What the drawing cannot show is which of the two a piece of cloth has had: the first two states look different and the last two look the same, and it is the last two that differ in whether the cloth comes back.

A cloth gives back less than it took

Everything this collection computes about a deforming fabric is reversible, and no fabric is. The repair is not a new material property: a woven cloth has two routes to a strain, one of them costs its threads nothing and comes back in full, and where the first route runs out is a number about the sett with no fibre in it at all.

cloth · Memory A front on a thread with 8 per cent crimp. Three rows at one scale. The top row is the warp end laid out straight, with the wetted front marked at four equal quarters of its own length — which is where Washburn's law puts it at four times whose square roots are evenly spaced. The middle row is the same thread crimped at 8 per cent, so it covers 92.6 per cent of the paper the straight one did. The bottom row is the cloth, and the four fronts on it are the four above pulled back by 1.08. A coefficient is a length squared over a time, so it comes down by 1.1664 — exactly (1 + c)², with no property of the liquid or the fibre in it. The thread's thickness is not drawn and neither is the liquid: a meniscus in a 2.33 µm pore is finer than any line on this canvas.

Wicking is slower along a crimped thread

A front travelling up a warp end travels the thread's path, which is longer than the cloth by exactly the crimp. So the wicking coefficient measured on the fabric is the yarn's own divided by (1 + c)² — 14.3 per cent lost at eight per cent crimp, whatever the liquid.

applied · Wicking The poplin's two budgets as it is held stretched. What is left of a poplin's interchange in each direction as it is held at more and more warp strain. The warp's budget falls to nothing at 3.93%, which is the point of the curve; the weft's rises, because the crimp the warp gives up is crimp the weft takes on. There is one locus and one position on it, so the two are not two quantities that happen to be related — they are the two distances from one point to the two ends of one curve. The consequence is that a pre-tensioned cloth has almost no warp recovery left and more weft recovery than it started with. What the plot cannot show is that the exchange rate between them is not constant: the curve is not a straight line, and its slope is the Poisson ratio this site computes elsewhere.

A cloth has one budget for two directions

A woven cloth looks as though it carries two independent reserves of free extension, one along the warp and one across the weft. It carries one. There is a single curve of states and a single position on it, so every hundredth spent one way is refunded the other — which means a pre-tensioned cloth has not used its recovery up, it has moved it.

mechanics · Tensile How far each cloth's sett moves between the loom and the finished state. A cloth on the loom is held: the warp is under beam tension and the picks are driven up at whatever density the take-up says. Let it go and it relaxes to the least-energy state of its own locus, which is a state at a different sett. The bars are how far each sett moves, and they always move in opposite directions because there is one locus: warp ends per centimetre fall as the cloth widens and picks per centimetre rise as it shortens. Seven of the eight move a little over one per cent; the poplin, whose two counts and two setts are the only unbalanced pair in the table, moves six and ten. What the bars cannot show is what a designer does with them, which is that the two numbers a specification quotes are not two free numbers — the finished construction is a point on a one-dimensional curve.

The construction a loom must be set to

A specification quotes ends and picks per centimetre in the finished cloth, and a loom is set to neither of them. The cloth relaxes to the least-energy state of its own locus, which is a state at a different sett — and because the locus is one curve, the two numbers a specification quotes are not two free numbers.

setting · Take-up What a second bar wants that the first does not. How much more yarn each guide bar needs than a tricot bar, per wale, over a 100 metre piece at 14 courses a centimetre — which is 140000 courses. A cord bar wants 111.3 metres more and a satin bar 232.3, both of which are more than the piece is long. A shared beam is one course spacing out after 0.28 courses.

Two bars cannot share a beam

Two guide bars each make one overlap a course and one underlap, and the overlap is the same object on both — the same needle, the same loop. So the difference in what they consume is exactly the difference in their underlaps, with no model of a loop in it: a cord bar wants 111 metres more yarn per wale than a tricot bar over a hundred-metre piece, and a satin bar 232. A shared beam is one course spacing of slack out after less than half a course.

knits · Warp knit The locus a warp knit's underlaps put it on. Width against length for each shog, at 28 needles an inch and 14 courses a centimetre. An underlap keeps its own length, so the two spacings lie on a circle and every fabric moves along an arc of it. A tricot can be pulled 27.3 per cent wider and 62 per cent longer; a cord 7.5 and 173. The shog decides which.

The shog is the anisotropy

An underlap is a straight run from one needle to another on the next course, so it is a hypotenuse — and its length is fixed while the two spacings are not. Pulling the fabric wider turns it towards the horizontal and pulls the courses together, on a circle. Every state a warp knit's underlaps allow lies on that circle, its as-knitted point sits where the shog puts it, and the ratio of the length it can give to the width it can give runs from 2.3 at a tricot to 218 at four needle spaces.

knits · Warp knit A patterning bar's thread through one repeat. One guide-bar thread followed through a 12-course repeat, needle places across and courses down, with each course's underlap drawn beside it as a bar against the beam's steady delivery, the repeat's mean of 1.984 mm. The shogs are 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3: 6 of 1 space (1.155 mm) and 6 of 3 spaces (2.814 mm), at 28 gauge and 14 courses a centimetre. The overlaps, the same on every course, are not drawn. What the drawing cannot show is the tension: a course whose bar runs past the mean is a course the beam has not yet paid for.

A patterned warp knit needs a stroke as long as its stripe

A guide bar that changes its shog from course to course takes yarn at a changing rate from a beam that delivers at one. The overlap is the same on every course, so it cancels again, and the running shortfall is the sum of each course's underlap less the mean — exact, with no loop in it. It returns to nought every repeat and strays inside it by a stroke that something must absorb. For a stripe the stroke is about the stripe's own height in the cloth, whatever the machine's gauge. The same twelve courses of tricot and satin need six times the stroke in two blocks as alternating, and of all 924 orderings exactly one pattern needs the least.

knits · Warp knit One repeat of two patterned fabrics, pulled two ways. One twelve-course repeat of a two-bar warp knit, each band a course drawn at its spacing and its kind: two tricot underlaps, two satin, or one of each. With the bars coincident the repeat is two bands, and narrowed to four fifths of its width the satin band opens to +150% while the tricot band opens to +26%; widened a fiftieth the satin band closes by −36% and the tricot band by −3%. Opposed, every course is the mixed kind and every course moves alike, by the smaller opening and the larger closing. The bands are drawn at the fabric's width to scale. What the drawing cannot show is the loops, held fixed here.

Opposed bars even a warp knit by locking it

Two patterning bars knitting the same stripe can be set so that each bar's long underlaps fall where the other's are short. Neither bar's stroke changes, and every course then carries the same total yarn — but that is not why the cloth comes out even. Every course pairs a long underlap with a short one, the long one stops the width and the short one stops the length, and so every course gives like the stiffer bar in both directions. The evenness is bought with the stripe's give.

knits · Warp knit

Named alongside it

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

Crimp interchangeCrimpTensile locusLappingSettWarp knittingAnisotropyInterchange budgetJammingBeamElastic recoveryPeirce's geometry

All concepts