Textile Structure
how cloth is put together
Depth

Series — page 4

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
A 20 tex cotton yarn and the fibre standing off it. 6 mm of a 20 tex ring-spun cotton yarn with the hair population this site computes from the yarn's own count and staple — 0.89 hairs per millimetre, every one of them drawn. The two axes are at different scales and have to be — the yarn is 167 µm across and its hairs reach past a millimetre, so a picture at one scale is either a bare line or a black rectangle. Along the yarn is 99 pixels to the millimetre and off it is 74, a 1-fold exaggeration of the vertical. Lengths are drawn from the exponential the model predicts, mean 621 µm; the rules mark one, two and three millimetres with the count a hair-counting instrument reports at each, and the hairs crossing each rule in the drawing are the ones those counts are about. At the yarn's own surface the long hairs cover 1.1% of the space beside it, which is why the picture is mostly gap. Nothing here is the short population, which carries most of the protruding length and none of the reach; and a hair reaching past the room the canvas has is drawn to the edge of it, so the very longest few are shortened in the drawing and not in the arithmetic.

Hair layer

  1. 1 A yarn's surface is a distribution
  2. 2 A yarn has a diameter for every instrument
  3. 3 Hairiness goes as the root of the count
  4. 4 Two hairiness meters read two moments
4 essays · cloth Eight fibres through one cloth, and the bracket that hides them. A muslin is 19 per cent fibre and the rest air, so its thermal conductivity is a two-phase mixture, and how the fibre and the air are arranged is not something any amount of knowing the fractions settles. What is settled is Wiener's pair of bounds: heat across a series arrangement sees the harmonic mean and along a parallel one sees the volume average, and every real arrangement lies between. Each bar here is one fibre's whole band, from the series bound at its lowest published conductivity to the parallel bound at its highest. Not one of the eight clears any other, so this model cannot tell wool from nylon in a fabric — and the same cloth at twice the thickness has twice the resistance, exactly. Air's own conductivity is marked, and every band sits within a fifth of it.

Insulation

  1. 1 Warmth is a thickness of air
  2. 2 The wind takes the air and not the cloth
  3. 3 Warmth is mostly the hairs
  4. 4 A knit is warm because of where its yarn is not
4 essays · mechanics 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.

Memory

  1. 1 A cloth gives back less than it took
  2. 2 The most a cloth can give back
  3. 3 A yarn that has been set has no torque
  4. 4 The twist a fabric gives back
4 essays · cloth What a muslin passes, against how closely it is set. A muslin's air permeability at 100 Pa as the sett is closed from 6.9 to 34.2 threads per centimetre, with the two paths separated. The channels between the threads carry 8285 mm/s at the open end and 1330 at the close one, and they go to zero when the cloth jams. The threads themselves carry 1.7 to 6.4 mm/s and never go to zero at all, because a thread is sixty per cent fibre whatever the sett is. Extended to a cloth with no channel left, that path is 8.1 mm/s — a floor set by the yarn rather than by the construction, and a specification asking for less has asked for a fabric that cannot be woven from this yarn at any sett.

Permeability

  1. 1 A cloth stops having holes before it stops passing air
  2. 2 The fourth power is a close cloth's rule
  3. 3 A windproof cloth is at its yarn's limit
  4. 4 Half the air goes through a tenth of the holes
4 essays · applied What a knitted band presses a limb with. Pressure against extension for a 20 tex cotton band at a 3.5 mm loop, wrapped round a 30 mm radius — a wrist. The pressure is the fabric's own tension per unit width divided by that radius, and the tension is the loop's bending with the relaxed shape as the yarn's natural one, so nothing here is fitted. Over the range a cuff is actually used across it runs from a twentieth of a millimetre of mercury to 0.85. The shaded bands are what a compression garment is specified at, and the curve does not reach the lowest of them until 277 per cent — which is not a cuff, it is a fabric stretched almost to the point where its yarn runs straight.

Pressure

  1. 1 What a cuff presses with
  2. 2 A tube of one size presses the calf harder than the ankle
  3. 3 A band presses where the limb turns
  4. 4 A stepped stocking should step most at the ankle
4 essays · applied Which knitted structures spiral, at a twist factor of 4.0. A yarn leaves the spinning frame with a torque it has not been allowed to release, and a loop knitted from it leans. The lean per unit of twist factor above balance is measured; what is counted here is the structure. A loop on the front bed and one on the back are mirror images, so their torques have opposite signs, and a fabric that knits equally on both beds nets to zero whatever the yarn is doing — which is why 1x1-rib, 2x2-rib, interlock do not spiral and plain, half-cardigan, tubular do. The count has to be made per fabric and not per structure: an interlock and a tube both knit equally on the two beds, and they are opposite cases, because an interlock's two components each straddle the beds while a tube's are each wholly on one. The integrity criterion, which asks what nothing holds together, is what tells them apart. What the bars cannot show is the tube's second face, which leans the other way.

Spirality

  1. 1 A jersey leans because its yarn still turns
  2. 2 A circular machine leans its courses whatever the yarn
  3. 3 A tuck decides whether a third of two-bed fabrics lean
  4. 4 A tuck held two courses is a second unknown
4 essays · knits A fibre's two stiffnesses, as the ratio that survives the bracket. C over B for every fibre in the table, at 20 tex, which is 2G/E and nothing else. The mark beyond each bar is the range the shear modulus is reported over. Glass is the control and is not a measurement: it is a drawn isotropic solid, so its ratio must be 1/(1+ν) and at ν = 0.2 that is 0.833, which is what the table says. Every fibre with molecules drawn out along its axis sits below the isotropic value, and the ordering is the subject rather than an accident — a fibre is stiff along its axis because its molecules are drawn out along it, and the same orientation that raises E leaves G to whatever holds one chain to the next. Aramid, the most oriented thing here, is twenty times softer in torsion relative to its bending than the glass beside it.

Torsion

  1. 1 A thread has a second stiffness
  2. 2 Twist is not torsion
  3. 3 The one fibre whose answer is known
  4. 4 Where a torsion model stops
4 essays · mechanics 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.

Beat-up

  1. 1 The blow that sets the pick
  2. 2 A pick density is a force budget
  3. 3 The half of the beat-up that is all zone
3 essays · setting Wrinkles 127 mm apart. A 300 mm width of a 120 g/m² cloth whose bending length is 20 mm, held under 5 newtons per metre across it and compressed. It cannot carry the compression in the plane, so it leaves the plane, at a wavelength the bending rigidity and the tension settle between them: 127 mm, which is 2.4 wrinkles across the width. The amplitude is drawn and is not computed — this arithmetic sets the spacing and says nothing about the depth.

Buckling

  1. 1 A cloth cannot carry a push
  2. 2 The nodes a drape test throws away
  3. 3 A stiff cloth's wrinkle is deeper and no steeper
3 essays · mechanics Where a bias cut's waste actually is. A bolt of cloth with panels placed at a stated angle, the ones that fit drawn and the rest of the cloth left shaded. Identical panels at a single angle tile the plane exactly, so the interior of the bolt loses nothing at all and the whole of the waste is at the two selvedges. The inset is the single-panel bounding box, which is the picture the usual account of bias cutting draws.

Cutting

  1. 1 The bias cut and the selvedge
  2. 2 A hemisphere costs one full turn
  3. 3 A garment is cut dry and worn wet
3 essays · applied A cloth laid over a sphere. Every thread segment is exactly one pitch and none has stretched. What has changed is the angle at each crossing, and the amount is decided by the surface — a developable one costs nothing and a curved one costs more the further the cloth goes.

Drape

  1. 1 Why clothes need darts
  2. 2 Bending stiffness and the drape coefficient
  3. 3 A drape coefficient is one number for a directional thing
3 essays · mechanics The two diameters of a 20 tex yarn. The pressure inside a twisted yarn is zero at its surface, so the outermost fibres are held by nothing but their own buried ends and some of them stand off as loops and ends. A yarn therefore has two diameters: a mass diameter of 167.1 µm, which is a volume divided by a length and is the one every other calculation of cover uses, and a contact diameter of 217.1 µm, which is what a neighbouring thread, a finger or an air stream meets. The gap is a hair layer of 25.0 µm on each side and it is measured, not computed — nothing here predicts hairiness. What is computed is the consequence, and it is 29.9% of the diameter every cover factor is built from.

Hairiness

  1. 1 The hairs are what touch
  2. 2 Singeing is the cheapest change to a surface
  3. 3 A hair layer is a balance, not a stock
3 essays · cloth What a balanced cloth wastes under pressure. The fraction of a balanced fabric's fibre that is along for the ride, in a stress field of each ratio. A closed cylinder is exactly two to one — the ratio of the two areas the pressure acts on — so a balanced cloth reaches its limit around the circumference with the axial system at half its capacity, and a quarter of the fibre is doing nothing.

Membrane

  1. 1 An inflated cylinder wants an unbalanced cloth
  2. 2 An inflated beam wrinkles at a moment with no cloth in it
  3. 3 An air arch pays for its thrust out of its pressure
3 essays · applied A filter cloth has two jobs. Opening size against sett for a woven filter cloth, with the two limits that specify one: the soil is retained below the retention line, and the water passes above the open-area floor. They pull opposite ways, so the answer is an interval in the sett — and for a fine enough soil there is no interval at all.

Openings

  1. 1 A filter cloth has two jobs
  2. 2 A hole is a channel, not an opening
  3. 3 Only a plain weave has one size of hole
3 essays · applied The strong fibre is the one that pills. Standing pills per unit area by fibre, relative to wool, at one and the same fuzz supply — every row is the same cloth raised the same amount, so the only thing varying is how long a pill survives once it exists. A pill is not made, it is kept: rubbing generates it and rubbing breaks the fibres that tie it down, and a tie survives in proportion to how much force it takes to break. So polyester carries 18 times wool's standing population from the same generation rate, and the ordering here is exactly the ordering of tenacity and nothing else. Wool sheds its pills because wool's ties break. No two real fabrics have the same fuzz supply, which is why a wool knit still pills more than a cotton shirting in practice — the comparison drawn here isolates the tie and says nothing about the generation, and reading it as a ranking of fabrics would be wrong.

Pilling

  1. 1 A pill is anchored, not made
  2. 2 The strong fibre is the one that pills
  3. 3 The knitted pilling criterion gets its number
3 essays · applied 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.

Shed

  1. 1 The shed is an extension
  2. 2 The back shaft works hardest
  3. 3 A figure is harder on its warp
3 essays · mechanics half-cardigan as an array. One cell per needle per course, over 2 repeats each way. K knits a new loop and casts the old one off, T tucks the yarn into the loop below without casting off, M misses the needle and floats past it. The margins carry the two conditions: a wale with no K in it never casts off, and a course with no K in it is never caught by anything. Both hold here.

Stitch notation

  1. 1 Knit, tuck and miss
  2. 2 What a tuck costs
  3. 3 A tuck is the one stitch that links twice
3 essays · knits 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.

Take-up

  1. 1 The reed is not the sett
  2. 2 The setts a loom can reach
  3. 3 The construction a loom must be set to
3 essays · setting Seven weaves at one construction, and what each of them really passes. Every weave here is drawn at the same filter — the same yarn, the same sett, the same cover and therefore the same open area, equal to twelve decimal places. Each one shows an opening of 263.7 µm to anybody looking straight through it, and that is the number a specification quotes. The bar is what each will actually let past, which is the narrowest section anywhere along the channel rather than the narrowest view down it. The plain weave passes exactly what it shows and it is the only weave here that does: its ends transit at every gap, so the four threads round every hole are level in pairs and the waist is at the middle. A float leaves two ends together at the top of the cloth, their neighbours at the bottom, and a passage between them that is wider than its own mouth — up to 12.8 per cent over the rating, for the basket.

Filtration

  1. 1 A filter is rated by the hole it does not show
  2. 2 A woven filter beats its own rating
2 essays · applied Where the strain goes, at a 25° twist. Extend a twisted yarn and the fibres in it are not all strained alike. If each stays at its own radius — the affine model — a fibre at helix angle θ takes cos²θ of the yarn's strain, so the fibre on the axis takes all of it and the fibre at the surface takes 82.1% of it. The core reaches its breaking extension first and the yarn cannot realise its own fibres. If instead every fibre migrates between the core and the surface, every fibre has the same mean strain and they all break together. The two are exactly computable — 0.8214 against 0.9509 of what the fibres could give — and the ratio between them, 2/(cos α(1 + cos α)) = 1.158, is what migration is worth. The shading is that arithmetic and the two panels use the same scale.

Migration

  1. 1 A straight fibre cannot share the load
  2. 2 What grips the end of a fibre
2 essays · mechanics

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