Textile Structure
how cloth is put together
Generator

The channel through a muslin in 2/2 twill

The channel through a muslin in 2/2 twill
The channel through a muslin in 2/2 twill. A cut across a muslin woven 2/2 twill, at 373 µm per hundred pixels, showing one hole between two warp ends. The ends sit at different levels here, so the clear width between them is 276 µm at the waist against 250 µm straight through. The profile on the right is that width at every height in the 334 µm the threads occupy: the passage is an hourglass, its narrowest section is 274 µm across, and the band that every level contains — what a straight line of sight can use — is 250 µm. The two differ by 9.9 per cent, and the difference is the weave and nothing else.

A cut across a muslin woven 2/2 twill, at 373 µm per hundred pixels, showing one hole between two warp ends. The ends sit at different levels here, so the clear width between them is 276 µm at the waist against 250 µm straight through. The profile on the right is that width at every height in the 334 µm the threads occupy: the passage is an hourglass, its narrowest section is 274 µm across, and the band that every level contains — what a straight line of sight can use — is 250 µm. The two differ by 9.9 per cent, and the difference is the weave and nothing else.

9 essays call through-section. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the weave its essay argues about.

Where it is called

Changing this generator changes every one of these figures.

The channel through a muslin in plain. A cut across a muslin woven plain, at 373 µm per hundred pixels, showing one hole between two warp ends. The ends sit at the same level here, so the clear width between them is 250 µm at the waist against 250 µm straight through. The profile on the right is that width at every height in the 334 µm the threads occupy: the passage is an hourglass, its narrowest section is 250 µm across, and the band that every level contains — what a straight line of sight can use — is 250 µm. The two differ by 0.0 per cent, and the difference is the weave and nothing else. What cloth is

A hole is a channel, not an opening

Every hole drawn so far has been drawn from above, and the sentence underneath every one of them says the same thing: the hole between four threads is the spacing less the diameter, and every hole is the same size. That is a picture of a cloth's shadow. A cloth has a thickness, so its hole has a length, and the narrowest place along it is not the place a person looking through can see.

 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. Cloth doing a job

A cloth stops having holes before it stops passing air

Close a woven cloth up and the channels between its threads shut. What passes through it does not go to zero, because a thread is sixty per cent fibre and forty per cent air and stays that way whatever is done to the construction. So a fabric's permeability has a floor, the floor belongs to the yarn rather than to the weaver, and no sett on any loom reaches it.

 Four ways of closing a muslin, and the floor under all of them. The same muslin at four states: as woven, calendered to 3:1, wetted so its fibres swell by 20 per cent, and with the channel between its threads gone altogether. Air permeability at 100 Pa falls from 3505 mm/s to 8.1 — a factor of 434 — and stops there. The last figure is not a cloth with no holes in it: it is a cloth whose only remaining path is through the threads, which are sixty per cent fibre whatever is done to the construction. That number is the floor, it is a property of the yarn, and no sett reaches it. Note that the two middle routes are not in a fixed order: a 3:1 calender closes more than this swelling and a 2:1 calender closes less, so which is the stronger depends on how far each is taken. Cloth doing a job

A windproof cloth is at its yarn's limit

Windproof is a threshold on air permeability, and it is the only fabric specification on this site that the construction cannot settle. No weavable sett of an ordinary shirting yarn gets within two hundred times of it, layering the cloth barely helps because the resistance is inertial rather than viscous, and the floor set by the yarn's own porosity lands on the same order as the threshold with a fivefold bracket around it.

 The 14 drafts whose holes are all one size. Every four-by-four draft in which each end and each pick interlaces — 22874 of them — built and asked whether all sixteen of its holes pass the same thing. At a muslin's construction 14 of them do. Set the same yarn square and 170 do; turn the cloth over and it is 14 again. Only 2 drafts are in all three lists, and they are the plain weave and its complement, marked. The other 12 are uniform because this cloth's warp is set closer than its weft, so the gap across the ends is the smaller of the two and binds every hole whatever the picks are doing — a fact about the sett wearing a fact about the weave's clothes. Two of them carry floats of three, which is as long as this repeat allows. Weaves

Only a plain weave has one size of hole

A weave's holes come in kinds, and the kinds are read off the matrix. Asking which weaves have only one kind looks like a question with an obvious answer and a one-line proof. Every draft at four by four was built and asked instead, and the count came back fourteen — of which twelve turn out to be telling the truth about the sett rather than about the weave.

 Where Poiseuille's rule starts being true of a cloth. Every account of a fabric's air permeability quotes the fourth power: flow down a channel goes as the fourth power of its width, so a small change of sett is a large change of flow. That is Poiseuille's result and it is about the viscous drop. A channel through a cloth is about as long as it is wide and the air in it is moving fast, so most of the pressure goes on giving that air its kinetic energy instead — and the inertial term does not depend on the hole's size at all. Plotted against cover, the viscous share of the drop runs from 1.0 per cent in an open muslin to 61.6 in a close one, passing half at a cover of 0.571. Quoting the fourth power alone below that is wrong by a factor rather than by a correction: at the open end it overstates the flow 98-fold. Setting and geometry

The fourth power is a close cloth's rule

Every account of a fabric's air permeability quotes the same thing: flow down a channel goes as the fourth power of its width, so a small change of sett is a large change of flow. That is Poiseuille's result, it is about the viscous drop, and in an open cloth the viscous drop is two per cent of the pressure. The rule becomes true as the cloth closes, and where it starts being true is a number.

 How open a muslin is, against where the light is. One minus the cover is a cloth's openness to a light directly behind it, and for this muslin it is 37.9 per cent. Move off the normal and a line of sight has to clear the hole at the top of the cloth and the same hole one thickness below, so what it can use falls as t·tan α is taken off each side — reaching nothing at 36.1° across the ends. Averaged over the whole sky with Lambert's cosine weighting, the cloth is 5.36 per cent open — 7.1 times less than the covering rule says, and the whole of the difference is the thickness. One minus the cover is the openness of a cloth with no thickness, and no cloth has none. Setting and geometry

One minus the cover is a cloth with no thickness

The covering rule says a cloth's openness is one minus its cover factor, and this collection derived it and has used it ever since. It is the answer for a light directly behind the cloth. Move the light and a line of sight has to clear the hole at the top of the fabric and the same hole one thickness below, so the openness falls, and it reaches nothing at thirty-six degrees. Averaged over the whole sky a muslin is a seventh as open as the rule says.

 The coarsest pore and the finest, in one muslin. A muslin's two pore systems asked the same question. Water at a contact angle of 120° is held back by a pore of radius r at a head of 2γ|cos θ|/ρgr, so the hole between four threads — hydraulic radius 134 µm — holds 56 mm of water, and the space between the fibres inside a thread — 2.50 µm — holds 2975 mm. Water takes the cheapest path, so the cloth leaks at the first of them and the second is never asked. Turn the contact angle round to a wetting one and the same two radii give a rise instead, and now it is the finest that decides, because that is the one that lifts highest: 5950 mm. One expression, two ends of a distribution, and the fabric's two properties read opposite ends of it. After the loom

The pore that wicks is the pore that leaks

A cloth's water resistance and a cloth's wicking are one expression, read at the two ends of a contact angle. The geometry cannot be chosen to give both, because it is the same geometry; the only thing that decides which a fabric does is a finish. And the two questions do not even read the same pore — a rise is set by the finest and a leak by the coarsest, so the same cloth lifts water three metres and holds it back at fifty-six millimetres.

 Where a muslin's warmth actually is. A muslin's own thermal resistance is 0.0108 m²K/W, and the still-air layer clinging to its outside is 0.12 — so 92 per cent of what a person is wearing is air that is not in the cloth. Wind takes it: the boundary layer thins as the square root of the speed, and above a few metres per second the air is also being driven straight through the fabric, which shorts out whatever resistance the fabric had. The pair leaves 22 per cent of the still-air value at 16 m/s. Both mechanisms take away air rather than cloth, which is why a windproof layer works and a thicker weave does not, and why the fibre — which the conductivity bracket could not separate anyway — never enters this figure. Cloth doing a job

The wind takes the air and not the cloth

A shirting's own thermal resistance is eight per cent of what a person wearing it has; the other ninety-two is a still-air layer half a millimetre thick clinging to its outside. Wind destroys both, and it destroys the larger one first and by a mechanism that has nothing to do with the fabric — so a windproof layer works by keeping air still rather than by resisting heat.

 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. Mechanics and drape

Warmth is a thickness of air

A fabric is a tenth fibre and the rest air, so its thermal conductivity is a mixture of the two — and the pair of bounds that any mixture must lie between comes out narrower than the difference between wool and nylon. The model cannot tell one fibre from another in a cloth. What it can tell, exactly and with no bracket at all, is that twice the thickness is twice the warmth.

The whole library · All essays