Textile Structure
how cloth is put together
After the loom

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.
14 min read 7 figures A mechanism, not a materialMeasured, not claimedStructure before fibre

Worth reading first: A yarn that has been set has no torque · A jersey leans because its yarn still turns · Why a slack yarn snarls.

The complaint is universal and it is always the same. The garment hung straight on the rail. It was straight after one wash. By the third the side seam has walked round towards the front, and it will not go back.

Everything about that sequence is explained by one distinction: a yarn’s twist is permanent and its torque is not, and the process that removes the torque can be undone by water.

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.
Fig. 1 The torque, drawn: a twisted yarn with nothing holding it straight coils on itself. In a fabric it cannot coil, so it does the next available thing and leans the wales — which is the same instability with the fabric as its boundary condition.

What has to be true

Three facts have to hold for the sequence to happen and each is checkable.

The yarn must have been lively when it was knitted. A hard-twisted single-jersey yarn arrives with several hundred turns a metre and a residual torque proportional to them.

The fabric must have been set before it was sold. Every knitted fabric is finished — scoured, dyed, dried on a stenter or in a tumble dryer — and every one of those relaxes or sets the yarn to some degree. A fabric that had not been set would spiral before it left the mill, and a lean is what a lively yarn does to a jersey.

And the setting must be reversible. Otherwise the third wash would find nothing to release.

The third is the one that decides which fibres suffer, and it is why the complaint is about cotton knitwear rather than about polyester.

Why cotton and not polyester

The setting mechanisms are different and they have different enemies.

A cotton yarn is set by conditioning or by wetting and drying, and the mechanism is hydrogen bonds between cellulose chains rearranging under the internal stress. Water breaks hydrogen bonds. So a wash undoes the setting directly, and each wash undoes a little more of what the last one had left.

A polyester yarn is heat set: its amorphous regions are taken above their glass transition and frozen in the new configuration. Water does nothing to that at all, and only a temperature above the setting temperature undoes it — which a domestic wash does not reach.

A wool yarn is set by disulphide interchange, which is covalent and is not undone by water, though it is by steam and by strong reducing conditions.

So the ordering is cotton worst, wool middle, polyester best, and that is the observed ordering of spirality complaints in knitwear.

A slack twisted yarn takes a coil of one size. A 20 tex polyester at 800 turns a metre. Its own torque is 1.260 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 2.39 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.
Fig. 2 A polyester at an ordinary knitting twist. Its stiffness ratio is lower than a cotton’s, so its torque at the same twist is smaller — and its heat setting is permanent, so even that does not come back.

Why it takes three washes rather than one

The progression is the part the mechanism explains best.

Setting is not all-or-nothing. A conditioned cotton has some fraction of its torque removed, and a wash removes some fraction of the setting — which restores some fraction of the torque, which produces some fraction of the eventual lean.

Each wash restores a little more, and the fabric leans a little further, until either the setting is entirely gone or the fabric has reached the lean its full torque demands.

So the observation is a staircase, and its shape is a decay: large steps at first and smaller ones later, converging on the fabric’s fully unset lean.

That is exactly what is reported. Spirality measurements on cotton knitwear show most of the movement in the first two or three wash cycles and diminishing amounts afterwards, and the trade’s test methods specify five cycles for that reason.

Which is why it is a finishing failure

The responsibility is worth locating precisely, because the trade argues about it.

The spinner supplies a yarn with a twist, and the twist is a legitimate choice: it is what the yarn needs to be strong enough to knit.

The knitter makes a fabric that leans if its yarn is lively, and every fabric of that construction would.

The finisher sets the fabric so that it does not lean, and the setting is what fails.

So spirality is a finishing failure in the sense that finishing is what was relied on and finishing is what came undone. Blaming the yarn’s twist is blaming a choice that was made correctly, and blaming the knitter is blaming a structure that behaves as every such structure does.

The remedies follow the same logic and they are all a finisher’s: set harder, set with a mechanism water does not undo, or use a fabric that does not lean.

A slack twisted yarn takes a coil of one size. A 40 tex cotton at 800 turns a metre. Its own torque is 2.355 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.
Fig. 3 A coarse knitting yarn at an ordinary twist. Its absolute torque is larger than a fine yarn’s at the same twist factor, which is one reason heavy jersey spirals more visibly than fine jersey of the same construction.
A slack twisted yarn takes a coil of one size. A 20 tex cotton at 1400 turns a metre. Its own torque is 2.060 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 0.91 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.
Fig. 4 A harder-twisted yarn, where the torque is nearly twice as large and the lean it would produce correspondingly greater. A knitting yarn is spun softer than a weaving yarn for exactly this reason, and even a soft one is lively enough to matter.

The structural remedy

The last of the three remedies is the reliable one and it is worth naming because it is the only one that does not depend on a process holding.

A balanced structure does not lean however lively its yarn. An interlock or a rib is knitted with wales on two beds, and the two balance for different reasons, and the torque of the loops on one bed is opposed by the torque of the loops on the other.

So interlock does not spiral, rib barely does, and plain single jersey does — and that ordering is the trade’s own experience.

That is a structural answer rather than a chemical one, and it survives every wash because nothing about it can be undone. It costs weight and cost and it is why better knitwear is often interlock.

The other structural answer is to knit from a folded yarn, since folding removes most of the singles’ torque, and folded-yarn jersey is correspondingly stable. It costs a folding operation.

What the model can and cannot say

An honest division, because this rung’s mechanism is well founded and its arithmetic is not.

What is established: a yarn’s torque is proportional to its residual twist; setting removes torque without removing twist; water reverses hydrogen-bond setting and not heat setting; and a balanced structure opposes torque with torque.

What is not: how much lean a given torque produces. That needs the fabric to be able to trade twist for writhe, and this collection’s own knitted model has no writhe to trade — so the nine degrees per unit of twist factor it once quoted remains fitted.

So the rung explains the sequence completely and the magnitude not at all, which is a fair description of where this collection stands on spirality after a whole ladder on torsion.

The test methods, and what they are measuring

The trade tests for this and it is worth saying what the test is doing in the language of the mechanism, because the test’s design encodes the mechanism.

The standard method marks a rectangle on the fabric, washes and dries it a stated number of times — usually five — and measures how far the marked square has skewed.

Every element of that is aimed at the multiplier. The repetition is because the setting comes out progressively. The washing is because water is what undoes it. The drying matters because a tumble dryer relaxes the fabric further and lets it take the lean the torque wants.

So the test is a measurement of how much setting survives five washes, expressed as an angle. It is not a measurement of the yarn’s torque, of the fabric’s construction, or of anything a designer chose.

That reframing has a practical edge. A fabric that fails the test has a finishing problem, and changing the yarn or the structure to pass it is treating a symptom — which is sometimes the right thing to do and should be known to be what it is.

Why drying matters as much as washing

A detail that surprises people and follows directly from the mechanism.

Washing undoes the setting; drying decides whether the fabric takes the lean. A fabric dried flat under restraint cannot skew while it dries and will hold its shape until it is next relaxed. One tumbled dry is free to move and takes whatever lean its torque asks for.

So a garment washed and line-dried flat spirals less than the same garment tumbled, and the difference is not small. That is exactly the advice on the care label of good cotton knitwear, and it is usually given as though it were about shrinkage.

It is about both, and for the same reason: a fabric relaxes for as long as it is allowed, and a tumble dryer allows it more than a washing line does.

What was counted, and how

Nothing here is a new computation. The torque is the collection’s own — a torsional rigidity times a twist rate, at the free end of the stiffness bracket — and the setting enters as a multiplier between nought and one that nothing predicts.

What the rung adds is the structure of the multiplier: that it is a fraction, that it decays with washing for one class of fibre and not for others, and that its decay is what produces a progression rather than a step.

The fibre ordering is a statement about setting mechanisms and is not this collection’s own; it is standard textile chemistry and is quoted.

How much of a yarn has to hang before it stops snarling. The tension a 20 tex wool 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 28.7 metres and 3185. 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.
Fig. 5 A wool, whose torque at a given twist is the largest of the common fibres. Wool knitwear is famously prone to distortion and famously stabilised by setting, and both follow from the same number.

What a garment maker can do about it

The remedies have been listed as a finisher’s and there is one that belongs to whoever cuts the garment, and it is worth knowing because it is cheap.

A knitted fabric’s lean is a shear, and a shear of a tube is a rotation of its seam. So a garment cut from tubular fabric shows the lean as a seam walking round the body, which is the classic complaint.

A garment cut from open-width fabric, with the pieces cut to the fabric’s own leaning grain rather than to its edges, wears with its seams where they were put. The lean is still there and it is no longer visible as a rotation.

That is a compensation rather than a cure, it requires knowing how far the fabric will eventually lean, and it is standard practice in mills that make cotton knitwear well.

It also explains why the complaint is worse in cheap garments: they are cut from tubular fabric because it saves the side seam, and tubular is exactly the construction that turns a lean into a visible rotation.

Where the model stops

No magnitude. The lean a torque produces is not computable here for the reason above.

No decay function. How much setting a wash removes is a chemistry question with a temperature, a time and a detergent in it, and none of that is here.

And the fabric’s own resistance is absent. A lean is a shear of the fabric, and how much shear a given torque produces depends on the fabric’s shear stiffness — a quantity this collection computes for a woven cloth and has never computed for a knit.

That last is a real and closable gap. A knitted fabric’s resistance to shear is a calculation the site’s own loop machinery could make, and having it would turn the fitted nine degrees into a number with a derivation on one side and a missing writhe on the other.

The measurement this suggests

The mechanism makes a prediction that the trade’s own test could check and does not.

The standard method measures skew after five washes. The mechanism says the skew should follow a decay: a large step, then a smaller one, converging on the fabric’s fully unset lean.

So measuring after each of the five rather than only at the end would give the decay curve, and the curve’s asymptote is the lean a completely unset fabric would take — which is a property of the yarn and the structure alone, with the finishing removed.

That asymptote is the number a designer actually wants. It says what the fabric will eventually do regardless of how well it was finished, and it separates a yarn-and-structure problem from a finishing one.

It costs four extra measurements on a test that is already being run, and nobody makes them because the specification asks for a single figure after five cycles.

That is a recurring shape in this collection: a test that measures a sequence and reports a point, discarding the information that would say which mechanism was operating. The same complaint applies to shrinkage testing, where a cloth shrinks most the first time and the standard method reports the total.

The generalisation

The rung is an instance of a distinction that recurs and that this collection has now met in three forms.

A property and a state are not the same thing, and a specification that names one is silent about the other.

A yarn’s twist is a property and its torque is a state. A fabric’s construction is a property and its relaxation is a state. A cloth’s crimp is a property and its contact force is a state.

In each pair, the property is permanent and the state decays; the property is what gets specified and the state is what causes the complaint; and the process that manages the state is a finishing operation whose durability nobody records.

So the general instruction is: for every specified property, ask what state it produces and how long that state lasts. This collection has been careful about that for dimensions, where a dimension without a state is one of its founding rules, and had not applied the same discipline to torque until this ladder.

The same yarn, held: the coil cannot form. 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). Held at more than 0.37 mN — about 1.9 metres of the yarn's own weight — it stays straight, and the drawing shows the perturbation dying rather than growing. The faint curve behind it is the coil the same yarn takes when the tension comes off, at 1.59 mm: it is what the tension is suppressing, and it is the whole of the difference between the two pictures.
Fig. 6 And the state a set fabric is in: the torque suppressed, the thread straight, nothing happening. The faint curve is the coil the same yarn would take unset, drawn to show what the setting is holding down. Setting achieves this without any tension at all, which is why it works — and why it fails when the mechanism holding it is undone.
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.
Fig. 7 The quantity that comes back: the tension a yarn needs to stay straight, for a fresh yarn. A set yarn sits at nothing on this axis and climbs towards these curves as its setting is washed out.

What the fabric is doing while it leans

It is worth asking what the fabric actually does with the torque, because the answer says why the lean is permanent once it has happened.

Each loop’s yarn is trying to unwind. It cannot unwind, because both its ends are held by the loops either side of it and by every loop between here and the selvedge. What it can do is rotate the loop — turn the whole stitch about an axis normal to the fabric — and a fabric of stitches all rotated the same way is a fabric whose wales run at an angle.

So the lean is a rotation of every stitch, accumulated across the fabric’s width into a visible skew.

Once it has happened, the fabric is at a new equilibrium: the torque is balanced by whatever resists the rotation, which is the loops’ own bending and the friction at every interlacing. Removing the fabric from the water does not remove the torque, so the lean stays.

Pressing it flat does not help either, because pressing does not reverse the rotation; it flattens a fabric that is already skewed.

The only thing that would put it back is a torque the other way, which is why the only real cures are structural — a second bed’s loops leaning the other way, or a folded yarn with no net torque to start with.

Who found it, and when

Spirality in knitted fabric has been studied since the middle of the twentieth century and the account in terms of residual yarn torque is standard.

That the effect appears after washing rather than before is universal trade experience, and the reversibility of hydrogen-bond setting in cellulose is standard fibre chemistry.

What is this collection’s own is putting the two beside its stiffness bracket: reading the progression as a decaying multiplier on a torque, and observing that the multiplier is exactly the quantity a snarl measurement would give.

What this rung leaves the collection owing

Three items, and they are worth listing because they are close together and one piece of work would close two.

A knitted fabric’s shear stiffness. The lean is a shear and the collection has never computed a knit’s resistance to one. Its loop machinery could: shearing the fabric changes the loop’s endpoints, the solve gives the energy, and the second derivative is the stiffness.

The lean a torque produces, which is the shear stiffness plus the torque and would turn the fitted nine degrees into a derivation — except that it also needs the fabric to be able to trade twist for writhe, and this model cannot.

And the set fraction, which multiplies the torque and which a snarl measurement would give.

The first of those is a day’s work with existing machinery and would be worth having for its own sake, since a knitted fabric’s shear behaviour decides how a garment hangs and this collection has nothing on it at all.

Where the ladder goes next

The torsion side of this work closes here, and the contact side has a question the water raises too. A wet yarn is a thicker yarn, and a thicker yarn in the same fabric has less room — so the flattening a fabric demands should move when it is wetted.

A wet knit’s yarn is flatter, and by an amount the geometry gives.

Where this goes next

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. 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. A jersey leans because its yarn still turns A single-jersey T-shirt comes back from the wash with its side seam spiralling round the body, and a rib does not. The difference is not the yarn: it is a count. Loops on opposite beds are mirror images, so their torques oppose, and a fabric that knits equally on both nets to zero whatever the yarn is doing. A plain knit's two relaxation steps. Munden's three relaxation states are usually given as three sets of constants. Read as a path they are two steps, and the two compose to the whole exactly — which is a real check, because the three sets were measured independently. The first step is the larger in the course direction and the smaller across the wales, and the second is 0.64 of the first lengthwise. That is the shape of a laundering series and it is the same mechanism: a fully relaxed state is reached by tumbling rather than by waiting, so what the standard specifies is a quantity of agitation and not a duration. What the bars cannot show is the loop length, which cancels out of all four numbers because every dimension of a knit is a loop length times a dimensionless constant. A knit relaxes for as long as it is allowed to Munden's three states are usually given as three sets of constants. Read as a path they are two steps, they compose exactly, and the second is not a smaller version of the first — the fabric shrinks twice as much along its courses as across its wales on the first step and rather less than half as much on the second.

What links here

Computed from the collection rather than written here: the essays that point at this one.

Shares its objects with

Essays naming at least two of the same things, that neither author linked.

Named objects

A flat tag is an object no other essay names yet.

Dimensional stabilityMoisturePermanent setRelaxationSpecificationSpiralityTorsional rigidityTwist