Textile Structure
how cloth is put together
Concept

Shed — where it appears

The opening made in the warp for the weft to cross, which lifts every raised end off its straight line and stretches it. Its depth sets the strain every lifted end takes, and the back shaft's ends travel furthest and work hardest.

Named by 17 essays across 4 fields — each of them below, with the objects they name alongside it.

The shed in section. A warp line 1200 mm from the fell of the cloth at the left to the back rest at the right, with 8 shafts at 300 mm and every 16 mm behind it. Each shaft lifts its ends in proportion to its own distance from the fell, which is what gives the same 30 mm clear opening at the reed from every shaft. The resulting extension is 0.460 per cent at the front shaft and 0.722 per cent at the back, a ratio of 1.57. Vertical scale exaggerated 4 times.

The shed is an extension

Every model of a finished cloth treats a thread as inextensible, and every one of them is about a fabric that has left the loom. On the loom the warp is stretched thousands of times a minute by the shed itself, and the amount is exact trigonometry with nothing fitted in it: the square of the shed's tangent, times the shaft's own distance from the fell, over twice what is left behind it.

mechanics · Shed The strain across a harness. The warp strain each shaft of a 24-shaft harness puts into its own ends, from 0.460 per cent at the front to 1.728 per cent at the back. Shafts within a budget of 1.0 per cent are drawn in one colour and those outside it in another; the budget is reached at shaft 13.

The back shaft works hardest

How hard the loom is on a warp end is the product of two numbers from different worlds — how often its column changes sides, which is a property of a binary matrix with no millimetre in it, and the strain of the shaft it happens to be on, which is a property of a machine with no weave in it. Neither knows about the other, and the threading that joins them is a decision nobody makes on structural grounds.

mechanics · Shed Flexes per end in the same check, ground a pick along. One bar per warp end above the draft of the same check, ground a pick along, each the number of times that end changes sides in one repeat — which is the number of times the shed drags it through its heddle eye. The counts run from 6 to 10, and they are the same numbers that give the cloth its interlacing rate of 0.500 per intersection.

A figure is harder on its warp

Every basic weave flexes all its ends exactly as often as each other — plain, twill, satin and sateen alike, and it is a one-line theorem. Figure one of them on another and that evenness goes, or does not, depending on where the ground weave was started relative to the figure. The same invisible offset that decides whether a fine figure holds together decides, at a coarse one, how unevenly the loom works the warp.

mechanics · Shed Heddles per shaft: stripe. The threading of a narrow satin stripe on a broad plain ground, over a warp of 1,200 ends. Each bar is one shaft and its length is the heddles on it. The draft needs 10 shafts however they are loaded; the heaviest carries 500 and the lightest 25, a factor of 20.0. Spending 20 shafts instead brings the heaviest down to 100.

Where the heddles go

A draft says how many shafts it needs and says nothing about how the ends divide between them. On a satin stripe over a plain ground the two ground shafts carry twenty times what the stripe shafts do — and the only cure is to spend shafts, which turns the threading into an allocation problem with an exact answer.

fancy · Shafts What a shed costs, in newtons. The tension the shed puts into one end at each shaft of a 24-shaft harness, for a 25 tex cotton yarn. The strain is set by the loom's geometry alone; the tension is that strain times the yarn's modulus. The front shaft holds 0.52 N and the back 1.95 N, which is 14 and 52 per cent of the yarn's breaking load. What the chart cannot show is the rest of the warp tension, which the let-off adds on top of all of these and which no geometry decides.

What the shed costs, in newtons

The shed's strain has been computed here and could not be priced: a strain is a length over a length and says nothing about how hard a thread is being pulled. A modulus turns it into a tension — and the back shaft of a twenty-four-shaft harness turns out to hold its ends at half their breaking load, all day, from the geometry alone.

mechanics · Yarn stiffness The harness a strain budget buys. How many shafts stay inside a 1.0 per cent warp-strain budget, against the clear shed opening the loom needs at the reed: 12 mm gives 43, 16 mm gives 36, 20 mm gives 28, 24 mm gives 21, 30 mm gives 13, 36 mm gives 7, 44 mm gives 1. The shed's tangent enters the strain squared, so the opening is much the strongest thing a loom builder controls.

The harness has a depth

Why does a dobby carry sixteen or twenty-four shafts rather than two hundred? The usual answers are about the mechanism — how many jacks a box can drive, how many hooks a dobby has — and they are real limits that are not the binding one. A stated tolerance on warp strain is a stated distance from the fell, and a stated distance is a whole number of shafts. One per cent buys thirteen.

fancy · Shafts One pick of a 2/2 twill made in the wrong shed. Pick 2 of a 2/2 twill laid in the shed belonging to another pick. The thread is there, it is beaten up in its place, and it is simply not the pick the design asked for — so the fault is a bar the whole width of the cloth and one pick deep. This one leaves the cloth sound, with its longest float at 3. Across every four-by-four draft and every possible wrong shed — 1,372,440 substitutions — 63.2% leave a cloth that still hangs together, 36.6% leave a thread loose, and 0.25% split the cloth. The same wrong shed is harmless in one draft and destroys another, so nothing about the size of the mistake predicts the size of the fault.

A mispick is one row in the wrong place

Every four-by-four draft, with each of its picks replaced by every shed the loom could have made instead: a million and a third substitutions. Two thirds leave a cloth that still hangs together, a third leave a thread held by nothing, and the same wrong shed is harmless in one draft and fatal in another.

weaves · Derivation A jacquard harness 130 cm wide under a 150 cm fall. A jacquard harness in front elevation, to scale: hooks spread over 40 cm, cords fanning down 150 cm to a comber board 130 cm wide, and hanging straight from the board to their mails. The centre cord is vertical and lifts its mail by the whole 10 cm hook lift; the edge cord leans 16.7° and lifts its mail 9.60 cm, 96.0% as far, and its bend at the board adds 9% to the hook's load at a friction coefficient of 0.3. What the drawing cannot show is the tie that decides which hook feeds which hole, which in a real mount is not the simple spread assumed here.

A jacquard harness needs three half-spans of height

A jacquard has no front shaft and no back one, so every end takes the same shed — as long as every cord hangs straight. Across the width they cannot: the hooks sit in a machine a few tens of centimetres wide and the comber board is as wide as the cloth, so an edge cord leans and its mail rises by the difference of two hypotenuses rather than by the hook's lift. Holding the edge shed within five per cent of the centre's takes a fall of about three times the edge cord's sideways reach, and that is a height a room has to have.

fancy · Jacquard The crossed shed, with the back standard 4 shafts behind the doup. A leno's crossing end in section from the fell to the back rest of an ordinary broad loom, in the crossed shed. The doup 300 mm from the fell lifts it 50.0 mm; its back standard 64 mm further back leaves it 60.7 mm down, beneath its partner. Between the two eyes the end climbs 110.7 mm in 64 mm, and the whole path is 70.2 mm longer than the straight line, 5.85% of the free warp, of which 63.8 mm is that one climb. The same end in the open shed, lifted at its back standard, is 7.2 mm longer, and an ordinary end on the doup's shaft 5.5 mm: the crossed shed is 12.7 times the ordinary shed. Vertical scale exaggerated 3 times. What the drawing cannot show is friction at the eyes, which would keep the extra length in the short span between them.

An easer gives back the kink the crossed shed puts in

A leno loom gives its crossing ends slack at every crossed shed, and the obvious reason — the doup carrying its end sideways — is worth a hundredth of an ordinary shed. The length is one heddle further back. In the crossed shed the doup lifts the end on the far side of its partner while the end's own back heddle, a few shafts behind, holds it down, and between those two eyes the end climbs eleven centimetres in six and a half. On a loom that stretches an ordinary end 0.46 per cent, that is 5.85 per cent — nearly thirteen times as much — and no position of the back heddle takes it below four.

fancy · Leno A comber board for 60 ends a centimetre, in side elevation. A jacquard's comber board seen from the side, with the fell of the cloth at the left and the back rest at the right. The board carries one hole per end; at 60 ends a centimetre the ends are 0.167 millimetres apart and a cord with a mail on it needs 0.9, so the holes are ruled in 6 rows staggered fore and aft, 6 millimetres apart — a harness 30 millimetres deep. Each row's ends are strained by its own distance from the fell: 0.460 per cent at the front and 0.524 at the back, a spread of 0.0636. What the elevation cannot show is the sideways fan of the cords above the board, which is a separate and much larger geometry.

A jacquard's harness has a depth after all

A jacquard was said to escape the shaft loom's depth entirely, because every mail hangs at the same distance from the fell. Every mail does, if the comber board has one row of holes — and it cannot. At sixty ends a centimetre the ends are a sixth of a millimetre apart and a cord with a mail on it wants most of one, so the holes are ruled in six rows thirty millimetres deep. The escape is real and it is a factor of eight rather than a release, and it closes as the cloth is set finer.

fancy · Jacquard The crossed shed's three spans at an eye friction of 0.3. A leno's crossing end in the crossed shed on an ordinary broad loom, back standard 4 shafts behind the doup, with both heddle eyes gripping at a coefficient of 0.3 and a background tension of 0.5 N. The end turns 69 degrees at the doup and 64 at the back standard, capstans of 1.44 and 1.40. From fell to doup it settles at 6.95 N, a strain of 5.73%; from doup to back standard it settles at 9.48 N, a strain of 7.97%; from back standard to back rest it settles at 6.78 N, a strain of 5.57%. With frictionless eyes every span would take 7.08 N; an ordinary end at the doup takes 1.02 N and the yarn breaks at 3.74 N on its initial modulus. Vertical scale exaggerated 3 times. What the drawing cannot show is the tension's fall round each eye, which happens over the eye's own few millimetres.

A heddle eye lets the kink through

A leno's crossing end is pulled up at its doup and held down at its back standard, and the length that costs was priced as if both heddle eyes were frictionless. They grip, and gripping ought to trap the kink between them at nearly a hundred per cent strain. It does not come close. A capstan bounds a ratio of tensions, not a difference, and the spans either side are already stretched, so at a coefficient of 0.3 the span between the eyes takes 9.48 newtons against 7.08 with no friction at all — a third more, not fifteen times more — and an easer has to give back 67.9 millimetres rather than 64.4. What friction changes more is when the length is wanted.

fancy · Leno What the crossing end asks for, against what a cam gives it. The length a leno's crossing end needs at each fraction of the crossed shed's opening, against an easer driven in proportion to the shed. The demand is nothing for the first eighth of the opening and then rises steeply, because the kink's extra length is a hypotenuse less its run and grows as the square of the climb. The proportional easer runs ahead of it everywhere, worst at 0.375 of the way open, where it has given 16.5 millimetres more than the end can use.

A cam easer gives its slack too early

The essay before it left the crossing end with fifteen millimetres it could not use at half the shed, and three things it might do with them. All three are decidable. It cannot reach the shuttle, because the same eyes that trapped the kink keep the slack behind the harness — and the margin is negative, so that friction is not a nuisance here but the reason a leno weaves at all. It cannot snarl, because the span is under half this account's own threshold. It sags seventy-two millimetres where the easer gives it, and the repair is a cam cut to the demand rather than to the shed.

fancy · Leno The springs a leno easer can be. The stiffest spring, per end, that an easer can carry without any span of the crossing end rising above an ordinary end's working tension at any fraction of the crossed shed, against how far its preload sits above the warp's resting tension of 0.5 N. Behind the harness, where an easing bar acts, it is 1.1 N/m at a preload equal to the resting tension and falls to nothing by 15 per cent above it; in front of the harness it is 4.8 N/m. Everything under a curve works and nothing above it does. The window is a corner: a spring barely stiffer than a dead weight, with a preload matched to the warp's own tension. What the chart cannot show is the bar's mass, which the loom's speed makes matter and which the next views take up.

A leno easer should be a light weight

A spring easer gives length when the crossing end pulls, so it cannot give it too early, which was the fault in a cam driven off the shed. The question left was its rate. The answer is that it hardly has one. Behind the harness the easer feels the back span, and two gripping eyes keep that span within fifteen per cent of its resting tension while the kink carries its load. So the spring must hold its span almost constant over a sixty-eight-millimetre stroke: at most 1.1 newtons a metre per end, a dead weight in all but name. At speed the bar's own mass is what limits it, and it falls with the square of the loom's speed: 2.3 grams an end at a hundred picks a minute, 0.6 at two hundred.

fancy · Leno How likely one staple length of yarn is to be weaker than a tension, under three laws. The probability that one independent try — a staple length of a 20 tex cotton yarn — is weaker than a tension, on a logarithmic scale, with the tension as a fraction of the yarn's 500 mm breaking load. Three laws are drawn, a normal, a lognormal and a Weibull, each fitted to reproduce the same two tensile tests at 100 and 500 mm exactly. Near the breaking load, where a tensile test samples at about one chance in 18, they lie together. At one chance in 1.4×10⁸, where a warp of 4,000 ends by 1,000 metres samples, they are far apart: at the back shaft's 52 per cent the three give normal 1.3×10⁻⁷, lognormal 1.1×10⁻¹¹, Weibull 4.0×10⁻⁶ per try. What the chart cannot show is which of the three a real yarn follows, which no tensile test can decide.

A warp breaks in a tail no tensile test reaches

A 500 mm tensile test is the weakest of about eighteen staple lengths of yarn. A warp of four thousand ends by a thousand metres is the weakest of a hundred and forty million, and an end breaks wherever one of them is weaker than the shed's tension. Three strength laws fitted to the same two tensile tests agree within five per cent at every gauge a tester can clamp, and disagree by a factor of 375,000 on how many ends a warp will break at the back shaft.

setting · Assembly Where the weight on a shared leno easer comes to rest. The tension in the back span of each end of a leno pair — the length between its last heddle and the back rest, where an easing bar acts — at each fraction of the crossed shed, with one bar under both ends weighted at 1.0 N a pair, twice the warp's resting tension, so that it rests on its stop with the shed closed. The two back spans always sum to the weight. Closed, they share it equally. The partner, an ordinary end lying in the bottom of the shed, can take only 11 mm of the bar's travel before it goes slack, which it does at 37.5% of the opening; from there the crossing end's back span carries the whole 1.0 N. On a bar of its own, dashed, the same span stays at 0.50 N. What the chart cannot show is what the crossing end's other spans do with the extra tension, which the next views take up.

One weight under a leno pair ends on one end

A leno's crossing end wants about seventy millimetres eased to it at every crossed shed; its partner lies in the bottom of the shed as an ordinary end and wants none. One weighted bar under both is set where the closed shed shares its weight between them, but the partner can take only eleven millimetres before it hangs, and it is slack by three eighths of the shed. From there the crossing end carries the whole weight, twice the rest its own bar would hold it at, and its tightest span ends forty per cent over the working tension while the partner hangs thirteen centimetres behind the harness. No weight serves both, because a bar gives every end it carries one length.

fancy · Leno A leno partner lifted by its doup's loop. The tension in each span of a leno's partner end at the full crossed shed, against how far the doup's loop lifts it above its own straight line 6 mm in front of its heddle on the doup's shaft. The partner is then three spans: fell to loop, loop to heddle, heddle to back rest. With the loop clear it is an ordinary end, 1.07 N in its front span. At a 4 mm lift the front span carries 1.48 N, +38% on the untouched partner, the span between loop and heddle 1.26 and the back span 1.00; with nothing gripping, dotted, all three would carry 1.12. At 8 mm the front span reaches 1.90 N. What the chart cannot show is how far a real loop lifts its partner, which the doup's standard decides and which is swept here rather than computed.

A leno's slackener eases the partner, not the doup

In a bottom-doup leno the doup's loop passes beneath the partner, and if it lifts the partner on its way up it puts a second turn six millimetres in front of the partner's heddle. A four-millimetre lift bends the partner through 74 degrees in two places, and its front span goes from 1.07 newtons to 1.48 — a tenth of that from the bend and the rest from grip. The back span, which is all an easing bar can feel, does not move. A slackener that drops the doup's standard four millimetres clears the partner exactly, gives the crossing end six per cent of its easing, and costs the shuttle nothing.

fancy · Leno The partner's peak against how late a slackener starts. The largest tension the partner's front span reaches, against the share of the shed opened when the slackener starts to drop, at a 4 mm rise. It stays at 1.07 N for any start up to 0.748 of the shed, where the partner with no slackener passes that tension. Later than that, the peak is the touched tension at the moment it starts, up to 1.39 N at 0.95, against 1.48 N for no slackener at all.

A leno's slackener only has to arrive

A slackener that lets the doup down in step with the loop keeps a leno's partner clear at every moment of the shed, and it looked as though a real one would have to track that closely. It does not. A partner's tension only rises as the shed opens, so a slackener can leave its whole drop until three quarters of the way up and the peak does not move at all. Lateness is paid for elsewhere: starting later than 0.58 of the shed rubs the loop more than having no slackener, and above 234 picks a minute a falling weight cannot start as late as the partner would let it.

fancy · Leno

Named alongside it

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

CapstanLoomWarp strainDoupEaserHarnessLenoWarp tensionHeddleJacquardThreadingBack rest

All concepts