Textile Structure
how cloth is put together
Concept

Loom — where it appears

The machine that holds a warp under tension, opens a shed in it, passes a weft through and beats each pick up to the cloth. Every dimension it has — the shed's depth, the reed's pitch, the beam's diameter — decides something about what cloth can exist.

Named by 12 essays across 3 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 The reed is not the sett. Twelve ends held at the reed's pitch above and at the cloth's pitch below, for a sheeting whose weft crimp is 14.61 per cent. The count is the same in both rows and only the spacing changes: the cloth is 12.75 per cent narrower, so a reed at 24.43 ends per centimetre produces a cloth at 28. The crimp comes from the Peirce solution at this cloth's quoted construction.

The reed is not the sett

A reed holds the warp at a pitch, and the cloth that leaves it is narrower — by exactly the weft's crimp, with nothing fitted and nothing approximated. On a close balanced sheeting that is 12.75 per cent, on an open scrim 1.87, and a weaver who allowed one figure for both would be wrong by a factor of nearly seven.

setting · Take-up 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 the two setts can be set to. Two rules on one scale from 8 to 40 threads per centimetre. The upper carries the 49 warp setts a metric reed catalogue reaches at one to four ends per dent; the lower carries the 4825 pick densities a change-wheel take-up reaches. The mean spacing is 0.656 threads per centimetre in the warp and 0.0066 in the weft, a ratio of 99. The widest gap in the reed's range is 2.10 threads per centimetre.

The setts a loom can reach

Transposing a draft gives a perfectly good draft, and every count this site takes off a matrix either is symmetric under exchanging warp and weft or has a mirror twin. The loom is not symmetric at all: over the range ordinary cloth is woven in, it can choose a pick density 99 times more finely than a warp sett — and the warp sett cannot be changed once the warp is drawn in, at any granularity whatever.

setting · Take-up 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 beat-up, at the fell. The last picks of a sheeting at 26 picks per centimetre, with the beat-up zone shaded. Driving the fell forward makes the warp take more crimp and more crimp takes more thread, which the warp can only supply by stretching — so the force is the warp tension times the crimp's elasticity with respect to the pick spacing, 0.182 here. That is 0.205 N per end and 573 N per metre of reed. What the drawing cannot show is that the shaded band's width cancels out of the derivation exactly; it is drawn because a reader needs to see what is being compressed, not because the answer depends on it.

The blow that sets the pick

The take-up gear decides how far the cloth moves between picks and says nothing about the blow that puts each pick where it goes. That blow is a force, and a virtual-work argument gives it in one line — with the length of the beat-up zone cancelling out of the answer exactly, which is the part worth having.

setting · Beat-up 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 Selectable against reachable. How far up the take-up gear's catalogue a beat-up force reaches, on a sheeting. The catalogue holds 4,825 distinct pick densities between 8 and 40 per centimetre, which is the previous rung's count of what the machine can select. At 200 N per metre only 548 of them can be woven; at 2,000 it is 4,256. The fineness of the choice is untouched by the ceiling and the top of the range is cut off entirely, so the weft direction's advantage is resolution rather than reach. What the chart cannot show is the loom's own force, which depends on the beat-up mechanism and is not a property of the cloth.

A pick density is a force budget

The take-up ladder counted what a change-wheel take-up can select: 4,825 distinct pick densities between eight and forty threads per centimetre, against forty-nine warp setts a reed catalogue offers over the same range. That count assumed every setting is available. A beat-up force says otherwise, and cuts the top off the range without touching the fineness of the choice.

setting · Beat-up 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 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

Named alongside it

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

ShedHarnessReedWarp strainSettHeddleJacquardThreadingContractionShaftSpecificationTake-up

All concepts