Textile Structure
how cloth is put together
Depth

Series — page 3

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.
The surface of a 2/2 twill, in plan. One repeat of a 2/2 twill in sheeting, drawn 2 × 2 times, with every point painted in the colour of whichever thread owns the outside of the cloth there and at an opacity set by how high it is. The range is 221.0 µm from the highest point to the lowest, the root-mean-square roughness is 74.9 µm, and 30% of the plan is hole rather than surface. The bright ribbons are the float plateaux, where a thread lies straight across the threads it passes over and its outside is a horizontal line rather than a point — which is the whole of what follows. The warp crowns at 190.8 µm and the weft at 182.8 µm, a step of 8.0 µm, so the cloth touches the world on its warp alone until anything pressing on it has sunk that far.

Surface

  1. 1 A cloth has an outside
  2. 2 The curve that says what a cloth touches with
  3. 3 Two drafts of twenty-two thousand
  4. 4 The census counted two systems and a surface has one
  5. 5 Four drafts in five have no path along their own crowns
5 essays · cloth A cotton fibre dry and wet. One cotton fibre in its dry state and saturated with water, both drawn at the same scale in both directions. It is 20% wider and 1.2% longer, so its cross-sectional area rises by 44% if the section stays similar to itself. The length difference is drawn and is nearly invisible, which is the point: a swelling that were the same in both directions would make a cloth bigger and change nothing about its structure, and this one changes every ratio of a diameter to a spacing in the cloth. What the drawing cannot show is the section: a cotton fibre is not a cylinder, and the directly measured area swelling of 40% to 42% does not agree with the square of the width change, which is a fact about the fibre.

Water

  1. 1 What water does to a thread
  2. 2 A yarn's voids are not enough
  3. 3 The hairs decide the sign of the wetting
  4. 4 A cotton's own water is a twentieth of what a cloth holds
  5. 5 A wet fibre is stiffer and a wet yarn is not locked
5 essays · cloth The plain. The plain on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.

What cloth is

  1. 1 A fabric is a structure, not a material
  2. 2 The draft is a matrix
  3. 3 Every cloth there is, at four by four
  4. 4 What the matrix cannot say
  5. 5 The third index is not a repeat
5 essays · cloth A trellis sheared 30°. The net at an angle, with every thread segment exactly the length it started at. The extension along the diagonal is the bias stretch, and it is a change of shape rather than a change of length.

Bias

  1. 1 The bias is a mechanism
  2. 2 The locking angle
  3. 3 Shear locking in a composite preform
  4. 4 The angle a hose wants
4 essays · mechanics A coating over the hole it has to bridge. Four warp ends of 40 tex seen end-on at 20 per centimetre, with a 120 micrometre PVC film over them. The film is supported everywhere it lies on a thread and unsupported over the 252 micrometre clear span between them, which is the same span at every hole in the repeat. The film's thickness is drawn to scale against that span; the bulge is exaggerated. At 20 MPa the film will hold at most 381 bar, which is a bound and not a prediction.

Coating

  1. 1 A coated cloth fails at its holes
  2. 2 Coated is a state
  3. 3 A coating fills the crowns before it bridges the holes
  4. 4 A print is as sharp as the hairs are long
4 essays · applied The tightest fold a 20 tex cotton yarn can be given. A cloth folded as sharply as it can be folded. The two yarn crowns on the inside of the fold cannot pass through one another, so the fold's radius is the yarn's own — 0.084 mm for a 20 tex cotton yarn — and there is no measurement of an iron anywhere in the argument. At that radius a fibre free to slide is strained 7.14%, which is √(packing × fibre tex ÷ yarn tex), and the whole yarn bending as a rod would be strained exactly one hundred per cent. Cotton's measured breaking extension is 6.0% to 10.0%, so the free bound does not survive and the locked one cannot. What the drawing cannot show is the fibres inside the yarn, which is exactly what the argument is about — the picture is the same either way and the strain is fourteen times different.

Crease

  1. 1 A crease is a fold the crimp cannot supply
  2. 2 Which fibres crease, and why there are two answers
  3. 3 A wrinkle cannot settle what a crease settles
  4. 4 A crease cannot cross a seam
4 essays · finishing The ratchet a wool fibre is. A fibre with its scales, and the two strokes of one cycle of agitation. The push is the same in both directions; the distance is not, because the scales resist tip-first motion more than root-first. Every cycle therefore nets a displacement in one direction, and no amount of further agitation undoes it.

Felting

  1. 1 The ratchet that makes wool felt
  2. 2 Milling holds the cloth a second time
  3. 3 Shrink-resist is one number
  4. 4 Why felting needs water
4 essays · finishing The 5-end satin. The 5-end satin on point paper, a filled square meaning the warp is on the face. Its longest float, its interlacing count and the number of separable cloths it describes were all counted from the matrix that drew it.

Foundation weaves

  1. 1 Plain, twill and satin
  2. 2 Twill direction, and how it is named
  3. 3 Broken and herringbone twills
  4. 4 How many twills a repeat admits
4 essays · weaves Stick, slip, and the ratio between the two coefficients. The force in a thread as a cloth is agitated, with a static coefficient of 0.300 and a kinetic one of 0.225 — a ratio of 0.75, which is what fibre on fibre measures. The force climbs until it reaches the static limit, the contact breaks away, and while it is sliding it resists only at the kinetic limit. So a cloth that is being shaken can be left anywhere in the narrower band, and a cloth at rest anywhere in the wider one. What the trace cannot show is how much this buys: the band does not narrow in the ratio of the coefficients, because the restoring force stiffens away from the minimum, and the real narrowing is nearer 0.87 than 0.75.

Friction

  1. 1 Two coefficients, not one
  2. 2 Why agitation helps a cloth relax
  3. 3 Friction is two surfaces, not one
  4. 4 What friction has to hold in a relaxed knit
4 essays · cloth 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 same yarn, flattened. One yarn's cross-section at five degrees of flattening, all drawn at one scale and all of the same area. Nothing is added: the yarn is wider because it is thinner. The cover rises for that reason alone, which is why a calendered cloth is more opaque than the cloth that went into the machine.

Lustre finish

  1. 1 Calendering is the cloth arriving at the other model
  2. 2 Mercerising is a packing factor
  3. 3 A calender spends the compression for good
  4. 4 A finish spends a spread before it spends a mean
4 essays · finishing 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 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 20 tex, counted. The cross-section of a 20 tex cotton yarn, with every fibre in it drawn. The count is a division and nothing else: a 20 tex yarn spun from 0.17 tex fibre has 117.6 fibres crossing any plane through it, and the yarn is 14.0 fibre diameters across because n fibres packed at 0.6 fill a circle √(n/φ) times as wide. The arrangement is drawn on a lattice and is not claimed: real fibres are not on one, they migrate between the core and the surface as they run, and everything this collection says about a yarn's strength turns on their doing so.

Assembly

  1. 1 How many fibres make a thread
  2. 2 A finer yarn is a worse yarn
  3. 3 A yarn breaks at its thinnest place
3 essays · setting 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 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 same fault in the warp and in the weft. A 50 m piece 1500 mm wide, with a 3-thread fault in each direction. The width is drawn 9.3 times over scale so that the piece is a rectangle rather than a line, and the two faults are drawn as marks rather than at their own widths, which at this scale are a fifth of a pixel. They have the same cause size — 3 threads — and they condemn 0.063 m² and 0.0020 m² respectively, a ratio of 31 to one, because a warp fault runs the length of the piece and a weft fault runs its width. That ratio is the aspect ratio of the piece and nothing else, so it is a property of how cloth is made rather than of what went wrong. It is why a broken end stops the loom and a mispick often does not, and why the two faults are priced by every grading scheme as though they were different kinds of thing.

Faults

  1. 1 A missing end is a fault the length of the piece
  2. 2 A grade charges by the length and a cutter pays by the panel
  3. 3 A fault map is worth most where the grade is worst
3 essays · applied

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