Textile Structure
how cloth is put together
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A cotton fibre dry and wet

A cotton fibre dry and wet
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.

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.

7 essays call wet-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.

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. What cloth is

What water does to a thread

A cotton fibre in water is a fifth wider and a hundredth longer. If it grew equally in both directions a wet cloth would simply be a bigger cloth and nothing structural would follow; because it does not, every ratio of a diameter to a spacing in a cloth moves, and they all move the same way.

 A yarn's voids against its fibres' swelling. One cotton yarn's cross-section at a packing factor of 0.60, drawn dry and with every fibre swollen by 20% while the yarn's own outline is held. The fibres now occupy 0.864 of the section, which is above the 0.75 a heavily compacted assembly reaches and above the 0.65 of a spun yarn, so the yarn cannot stay this size: it must grow by at least 7.3%. What the drawing cannot show is disorder — the fibres are laid on a lattice here to make the areas exact, and a real yarn's fibres are neither round nor evenly spaced, which is why the bound is quoted over three packing limits rather than at one. What cloth is

A yarn's voids are not enough

A ring-spun cotton yarn is sixty per cent fibre and forty per cent air, and its fibres gain forty-four per cent of area in water. The obvious thought is that the air takes it. The arithmetic says the air cannot, and gives a floor on how far the yarn itself must grow with no measurement of a yarn in it anywhere.

 A loop's cell, dry and wetted. One stitch of a 20 tex cotton jersey at a 3.50 mm loop, drawn inside the rectangle of one wale by one course that its own dimensions give. The thread is drawn at its own width, and it already fills 1.129 of the cell dry — more than the whole of it, which is what an opaque jersey looks like from above. Wetting takes it to 1.355. So the reason a knit does not build a swelling pressure is not that it has room; it is that its dimensions are a loop length times a constant with no yarn diameter in them, so there is no closure condition to fail. What the drawing cannot show is the third dimension: the legs lie over one another rather than overlapping in the plane, which is exactly why an occupancy above one is possible. Knits and other structures

A loop has no closure condition

A woven cloth can run out of room: its two systems must supply its whole thickness between them, and past a certain swelling they cannot. A knit has no such equation, so no critical swelling and no pressure. The obvious explanation — that a knit is open and has somewhere to put the swelling — is false, and the arithmetic refuses it.

 Munden's states against the fibre swelling. What a plain knit does between its relaxation states, beside the swelling of the fibre it is made of. Going from dry-relaxed to wet-relaxed a jersey loses 5.66% along its courses and 2.44% across its wales, and going on to fully relaxed it loses 9.1% and 7.0%. The fibre swells 20%. Two things rule the swelling out as the cause: it is several times the whole change, and the change is markedly anisotropic while a swelling enters both of a loop's dimensions through the same loop length. What the bars cannot show is what does cause it, which is friction — water lets the loops move to where the yarn's own bending had been trying to put them. Knits and other structures

A knit's change of state is not its swelling

A jersey is smaller wet-relaxed than dry-relaxed, by 5.7 per cent along its courses and 2.4 across its wales. Water is obviously involved, so the swelling is the obvious cause. Two things rule it out, and both are properties of the constants rather than measurements of a fabric.

 The pressure a wetting generates in a close cloth. The pressure a sheeting's yarn is compacted at, against how far its fibres have swollen. Below 9.29% the cloth accommodates the swelling as a shape change and the pressure is nothing; above it there is no state at constant thread length, so the yarn must be compacted back to a diameter the geometry can hold and van Wyk's cube law prices it. At cotton's 20% it is 7.80 MPa. The other route out — stretching the threads until they are long enough to wrap the swollen partner — needs 9.1% of strain against a breaking strain of 6.6% computed from the site's own tenacity and modulus, so the thread would break first and there is one route rather than two. What the curve cannot show is its own uncertainty: van Wyk's constant runs from 0.003 to 0.011, so the height of this curve is known to a factor of nearly four and its shape is not. Compound and figured cloths

A wetting supplies the force the criterion needs

This collection's criterion decides whether a cloth is one cloth, exactly, and cannot see friction — so pricing what it misses needed a contact force, and the only one available had a measured fabric thickness inside it. A wetted close cloth generates one from geometry alone, and it lands within seven per cent of the measured route's answer.

 A sheeting's crossing, dry and wetted. One crossing of a sheeting in section at three swellings: dry, at the swelling where its geometry has its last state, and fully wetted at 20%. The closure condition is that the two systems' crimp heights add to the cloth's thickness, and each can supply at most the height it reaches when its straight portion has just vanished. Swelling raises the demand in proportion and the supply more slowly, so the margin closes and then goes negative — at 9.29% for this cloth against cotton's 20%. The bottom panel is drawn as far as the threads reach and no further, because there is no state to draw. What the drawing cannot show is what happens instead, which is that the yarn is compacted. Mechanics and drape

The swelling a cloth cannot take

Three of the eight cloths in this collection's table have no wet state at all. A thread of fixed length cannot wrap a partner that has grown by a fifth, so the closure condition fails and the geometry has nothing to offer. What happens instead costs megapascals, and the alternative route is not merely dearer but unavailable — the thread would break first.

 Cotton and viscose in every column this site carries. The two cellulosic fibres compared across every constant on this site. Both are cellulose at 1.52 g/cm³, both are given a modulus of 8 GPa and a fineness of 1.7 dtex, so a 20 tex yarn of either has the same diameter to the last figure — and therefore the same crimp, the same cover, the same jamming sett and the same bending bracket. Every geometric result on this site is the same number for the two fibres. Water separates them twice: viscose swells 1.75 times as far across and loses half its strength where cotton gains a tenth. What the table cannot show is why, which is a question about how cellulose is arranged inside a fibre and is not in this collection. Mechanics and drape

Water tells two fibres apart

Cotton and viscose are the same material by every constant this collection carries. Same density, same modulus, same fineness, so the same diameter at every count and the same crimp, cover, jamming sett and bending bracket. A wash separates them by a factor of two, and it is the only thing here that can.

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