Textile Structure
how cloth is put together
Concept

Moisture — where it appears

Water held in a fibre, whether as regain at room conditions or at saturation in a wash. Everything a fabric does in water follows from what it does to one dimension of a thread, and this site's whole account of it enters through a single multiplier on a diameter.

Named by 20 essays across 7 fields — each of them below, with the objects they name alongside it.

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 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.

cloth · Water 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.

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.

cloth · Water 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.

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.

knits · Knit 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.

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.

knits · Knit 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.

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.

fancy · Integrity 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.

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.

mechanics · Compression Shrinkage from wetting, cloth by cloth. The change in each cloth's relaxed construction when its threads swell by 20% across and 1.2% along. Both states are least-energy states of their own constant-thread-length locus, which is the only comparison the locus admits: its minimum is a state at its own sett, so it may be compared with another minimum and not with a quoted construction. Positive is smaller. Every cloth that has a wet state closes up except the cheesecloth, which opens by half a per cent because the fibre's extra hundredth of length outruns the extra crimp a thicker partner costs. What the bars cannot show is the three cloths that are missing, which have no wet state at all.

Two shrinkages, one tape measure

A cloth that comes out of a wash smaller has done two different things and the tape cannot tell them apart. One is geometric, recoverable and finished in minutes; the other is frictional, permanent and needs agitation. This collection can now compute both, and they have different signatures.

finishing · Shrinkage Shrinkage from wetting, cloth by cloth. The change in each cloth's relaxed construction when its threads swell by 20% across and 1.2% along. Both states are least-energy states of their own constant-thread-length locus, which is the only comparison the locus admits: its minimum is a state at its own sett, so it may be compared with another minimum and not with a quoted construction. Positive is smaller. Every cloth that has a wet state closes up except the cheesecloth, which opens by half a per cent because the fibre's extra hundredth of length outruns the extra crimp a thicker partner costs. What the bars cannot show is the three cloths that are missing, which have no wet state at all.

A garment is cut dry and worn wet

A cutting allowance is one number and the thing it allows for is two, in two directions. Worse: when the two directions differ, a panel cut on the bias does not merely shrink — it rotates, by half a degree for an ordinary poplin, which is nine and a half millimetres of skew across a metre and is invisible to a tape measure.

applied · Cutting Cover, dry and wetted. Warp cover for every cloth in the table when its threads swell by 20% and its spacings are held, with the dry value and the sett at which the swollen threads touch beside each bar. Cover is a diameter over a spacing and only the diameter moves, so every cover is multiplied by exactly 1.20 and every jamming sett divided by it — an identity rather than a result, and the one statement in this ladder a reader can check by hand. No cloth here reaches a cover of one, so none of them jams laterally on wetting; the closest is the sheeting at 0.628. What the bars cannot show is the through-thickness condition, which the sheeting fails at a swelling of half this one.

A wet cloth is set closer than it was woven

Cover is a diameter over a spacing. Wetting moves the diameter and does not move the spacing, so every cover factor on this site is multiplied by exactly the swelling ratio and every jamming sett divided by it — which is an identity, and the one statement in this ladder a reader can check by hand.

setting · Sett 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.

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.

mechanics · Yarn stiffness 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.

Why felting needs water

Wool felts in a wash and not in a drawer, and the usual explanation is that water lubricates the scales. It does the opposite of that. Water lowers one of wool's two friction coefficients and raises the other, so it widens the gap the ratchet rectifies — and what follows is a saturating function of the ratio, not of either coefficient.

finishing · Felting Shrinkage from wetting, cloth by cloth. The change in each cloth's relaxed construction when its threads swell by 20% across and 1.2% along. Both states are least-energy states of their own constant-thread-length locus, which is the only comparison the locus admits: its minimum is a state at its own sett, so it may be compared with another minimum and not with a quoted construction. Positive is smaller. Every cloth that has a wet state closes up except the cheesecloth, which opens by half a per cent because the fibre's extra hundredth of length outruns the extra crimp a thicker partner costs. What the bars cannot show is the three cloths that are missing, which have no wet state at all.

Wetting moves a cloth to another locus

A cloth's constant-thread-length locus is built at a fixed thickness. Swelling changes the thickness, so a wetted cloth is not somewhere else on its own locus — it is on a different one, and the distance between the two least-energy states is the shrinkage. Five of the eight cloths here have a wet state, and one of them gets bigger.

setting · Crimp The strain at a fold against the strain each fibre breaks at. For each fibre, the surface strain at the sharpest fold a 20 tex yarn of it can make — which is √(packing × fibre tex ÷ yarn tex), with no measurement of a crease in it — beside its own measured breaking extension. cotton and flax are strained past the low end of their breaking range, so some of their fibres break at the fold, and that is what a linen crease is. The rest survive, and among them viscose and wool return less than three fifths of what they were given, which is the other way a cloth creases. Both columns are needed: viscose survives with a factor of two to spare and is among the three worst by measurement. What the bars cannot show is wool, which the census puts in the wrong column because the recovery figures are the immediate ones and wool's is the most delayed of any fibre here.

Which fibres crease, and why there are two answers

Run the sharpest fold a yarn can make against every fibre's breaking extension and its recovery, and the ranking that falls out is the trade's own — linen worst, cotton next, wool and the melt-spun filaments best. It falls out of two columns rather than one, because two fibres in the bottom three get there by different mechanisms, and a treatment that fixes one does nothing for the other.

finishing · Crease How much of a yarn has to hang before it stops snarling. The tension a 20 tex cotton needs to stay straight, at each twist level, expressed as the length of the yarn's own weight that would supply it. The two curves are the two ends of the stiffness bracket: the fibres free to slide, and the section coherent. At 800 turns a metre they are 1.9 metres and 616. Anybody who has let go of a twisted yarn knows which of those is right, which makes this one of very few places where the bracket can be closed from the everyday end. Both rise as the square of the twist, because the torque does and the criterion is quadratic in it.

A yarn that has been set has no torque

Every torque on the torsion ladder assumes a yarn is elastic in twist for ever. It is not: a steamed yarn's residual torque is gone, its twist is unchanged, and the process that removes one without the other is the trade's whole answer to liveliness.

finishing · Memory A slack twisted yarn takes a coil of one size. A 20 tex cotton at 800 turns a metre. Its own torque is 1.177 µN·mm at the free bound, and a rod under tension T is stable while its torque stays under 2·√(B·T). Below that tension the straight state stops being a minimum and the thread wraps on itself at a radius of 1.59 mm. That radius is 2B/M, which is 2/(r·ω) once the torque is written out: it depends on the twist and on the ratio of the two stiffnesses, and on neither stiffness itself.

The twist a fabric gives back

A T-shirt that hung straight in the shop has its side seam round the front after three washes. The torque was there all along, the setting had hidden it, and the water gave it back — which makes spirality a finishing failure rather than a knitting one.

finishing · Memory The flattening a knitted fabric asks for, against its own tightness. Every point is a solved fabric — 18 of them, over five loop lengths, three relaxation states and three counts — and the vertical axis is the closest its adjacent courses come, in diameters. The values run from 0.707 to 0.839 and they fall on one curve against the tightness factor, which is the model's only dimensionless group. That is what makes this a structural requirement rather than an arithmetical accident of one example: a tighter fabric demands a flatter yarn, by an amount its own tightness decides, and nothing about the fibre or the count enters except through that group.

A wet knit's yarn is flatter

A knitted fabric's own geometry demands a flattened yarn, and how flat depends on how much room the fabric leaves. A wet cotton yarn is a tenth thicker than a dry one at the same length, so a wet fabric leaves less room — and asks its yarn to be flatter by an amount the geometry gives.

finishing · State Two courses at the yarn's own width, and the place they overlap. The solved course of a 24.2 tex cotton jersey at a 3.5 mm loop, drawn in plan with the course below it, each strand at the yarn's own diameter of 0.184 mm. Where the two overlap, the fabric is occupying the same space twice. The interlacing is where the model placed them one diameter apart. The closest they come is 0.140 mm — 0.761 of a diameter — and it is not at the interlacing. A round yarn cannot occupy this arrangement; a yarn flattened to 76% of its round diameter can, and flattened is what a yarn in a fabric measurably is.

What wetting does to the bending limit

A rod cannot be bent to a radius below its own. A relaxed knitted loop sits at twice that limit, and a wet yarn is a tenth thicker in the same loop — so wetting moves a fabric a tenth of the way towards a bend it cannot physically take.

finishing · State The section the fabric asks for, beside the one the model drew. A 24.2 tex cotton yarn in cross-section, at 900 times life size. The circle is what every solve in this collection has assumed: a diameter of 0.184 mm from the count and the packing factor. The ellipse has the same area and a minor axis of 76% of it, which is the closest the fabric's own adjacent courses come to one another — 0.140 mm. Nothing about that number was fitted to a fabric. It falls out of a solve that knew nothing about flattening, and it lands inside the range the trade reports for yarn in cloth, which this collection has carried as a free parameter ever since it first put a number on a sett.

The diameter that does need a state

A fabric dimension quoted without its relaxation state is not a measurement. The rule was applied to the two plan dimensions and then to the thickness, and it was never applied to the one dimension that is not the fabric's at all — the yarn's.

finishing · State Where a wet cloth keeps its water. For four cloths of this collection's own table, the share of the water a saturated cloth holds that sits inside the fibre as regain, between the fibres inside the yarn, and between the yarns in the cloth's own holes. muslin at 99 grams a square metre holds 183 per cent of its own weight, 4.6 per cent of it in the fibre; sheeting at 155 grams a square metre holds 113 per cent of its own weight, 7.5 per cent of it in the fibre; poplin at 100 grams a square metre holds 165 per cent of its own weight, 5.2 per cent of it in the fibre; duck at 207 grams a square metre holds 139 per cent of its own weight, 6.1 per cent of it in the fibre. The fibre's own water — the property cotton is sold on — is a twentieth to a thirteenth of the total, and the other nineteen twentieths are geometry. What the bars cannot show is the hair layer, which holds water outside all three of these and which this arithmetic has no place for.

A cotton's own water is a twentieth of what a cloth holds

A wet cloth keeps water in three places and only one of them is the fibre. A sheeting saturated holds 113 per cent of its own dry weight: 7.5 per cent of that inside the cotton as regain, 39 per cent in the channels between the fibres of its yarns, and 54 per cent in the holes four threads bound. The same construction in polyester, whose regain is a fortieth of cotton's, holds 105 per cent — an eight-point difference from a fortyfold one, because absorbency is a geometry with a fibre in it rather than a fibre with a geometry round it.

cloth · Water The suction water supplies, against the pressure twist supplies. The pressure pressing a yarn's fibres together, against its twist, with the suction inside the menisci of a damp yarn's own pores drawn as a level. The suction is 0.0624 newtons a square millimetre — 2γ over the pore radius of 2.3 micrometres — and it does not depend on the twist at all. The twist's pressure crosses it at about 186 turns a metre, so water is worth as much as the first 186 turns and nothing more: at 600 turns it is 11 per cent of what the twist already supplies. What the chart cannot show is the saturation, at which the suction vanishes because a full yarn has no meniscus in it.

A wet fibre is stiffer and a wet yarn is not locked

The intuitive reason a damp cloth stiffens is that water pulls the fibres together — a meniscus is curved, the pressure inside it is below atmospheric, and the suction presses the assembly exactly as twist does. Computed, that suction is worth the first 186 turns a metre of twist and nothing after them: six per cent of what an ordinary yarn's twist already supplies, and nowhere near enough to stop the fibres sliding. What wetting actually does is fatten the fibres, and a fibre's bending rigidity goes as the fourth power of its diameter — so a wet cotton fibre is 2.07 times as stiff with no contact in the argument at all.

cloth · Water

Named alongside it

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

SwellingRelaxationPacking factorCrimpFrictionYarn diameterCover factorFibre diameterJammingLoop lengthShrinkageTwist

All concepts