Two shrinkages, one tape measure

Put a metre of cloth in a wash, dry it, and measure it again. It is shorter. That number goes on a label, into a specification and into a cutting allowance, and it is treated as one quantity with one cause.

It is two quantities with two causes, and they behave differently in every respect that matters except the one the tape measures.

The two mechanisms #

Relaxation shrinkage is the cloth going where it always wanted to go. A fabric comes off a loom under tension, with its picks driven closer than they would sit unloaded and its warp stretched. Off the loom it is held there by friction at its own crossings, and it stays held until something helps it move — heat, water as a lubricant, and above all mechanical agitation. When it moves, the crimp comes back and the cloth contracts.

This collection computes it. It is the whole subject of relaxation being the crimp coming back, it is what pre-shrinking anticipates, and its size is set by how far the loom state is from the relaxed state.

Hygral shrinkage is different in kind. The fibres swell, the threads get thicker, and a thicker partner is a longer way round — so at constant thread length there is less thread left to span the cloth with, and the sett closes. Nothing has to slide. Nothing has to be helped. It happens in the time it takes water to get into a fibre, which is seconds to minutes.

The first is a fabric moving to a state it could already reach. The second is a fabric whose reachable states have changed.

Four ways they differ #

They run on different clocks. Swelling is complete in minutes and needs no agitation. Relaxation needs agitation and is not complete after any finite number of cycles — a much-washed garment is still relaxing, slowly.

One is recoverable and one is not. Dry the cloth and the swelling reverses exactly: the fibre gives up its water, the thread thins, the geometry returns and the cloth goes back to its dry size. Relaxation does not reverse; the crimp that came back stays back unless the cloth is stretched again, which is what a tenter frame does.

They have different signs in an open cloth. Relaxation always contracts a cloth, because the loom state is always more extended than the relaxed one. Hygral shrinkage contracts a close cloth and expands an open one, because the fibre’s extra one per cent of length beats the extra crimp below a cover factor of 0.23.

And they respond differently to construction. Relaxation shrinkage is largest where the loom tension was highest relative to the cloth’s stiffness, so it is a processing quantity. Hygral shrinkage is decided entirely by the construction — the ratio of thread length per crossing to cloth thickness — and a cloth woven twice on two looms has the same hygral shrinkage and two different relaxation shrinkages.

The same distinction in the vocabulary the trade already has #

The trade has words for both and does not always keep them apart, which is worth laying out because a reader who works with cloth will have met them.

Residual shrinkage is what a finished cloth has left to give: the relaxation part that the finishing works did not take out. It is what a specification limits and what a sanforising licence guarantees. It is a property of a piece of cloth at a moment in its life and it goes to zero as the cloth is washed.

Hygral expansion is the wool trade’s name for the other one, and the trade has it the other way up: it names the swelling, as an expansion on wetting, because in wool the effect at moderate humidity is genuinely an expansion. A worsted suiting can gain over a per cent in area between a dry room and a damp one, and it comes back, and it is a real nuisance in tailoring because a canvas and a face cloth with different hygral expansions pucker at their seams.

Progressive shrinkage is the third thing, which is the permanent part that accumulates over many launderings and is neither of the above.

So the vocabulary is there. What is missing is the connection: hygral expansion and residual shrinkage are usually discussed by different people about different fibres, and it is not obvious from either literature that they are the two halves of what a label’s number measures.

Which is which in a real wash #

Both happen at once and the tape records the sum, so separating them needs a test that exploits one of the four differences. Two are practical.

Dry it and measure again. The hygral part comes back and the relaxation part does not. A cloth measured wet, then dry, then wet again gives the hygral amplitude directly as the difference, and the residual after the first dry is the relaxation part. This is exactly the standard hygral expansion test used in the wool trade, where the effect is large enough to matter for tailoring.

Soak it without agitating it. Relaxation needs mechanical help and swelling does not, so a quiet soak gives mostly the hygral part. A soak followed by a tumble gives the rest. That the two protocols give different answers is well known in the trade and is usually reported as a nuisance rather than as a measurement.

The sizes here are comparable. This model gives two to three per cent of hygral shrinkage for an ordinary cotton, and the relaxation ladder gives a few per cent for a cloth coming off a loom. So neither dominates and a label’s number is genuinely a sum of two things of similar size.

Why pre-shrinking cannot pre-empt the second #

This is the practical consequence and it is a sharp one.

A sanforised or compressive-shrunk cloth has had its relaxation shrinkage taken out in the works: the fabric is compressed lengthwise against a rubber belt, forced into the state it would have relaxed to, and set there. What comes out has a residual shrinkage specified at under one per cent, and it is genuine.

It still swells. Every time that cloth is wetted, its fibres get twenty per cent wider and it contracts by the geometric amount, and every time it dries it comes back. A pre-shrunk shirt is a shirt that is a stable size dry, and it is smaller wet — by two or three per cent, forever.

That is why a shirt feels tight straight out of a wash and normal once it is dry and pressed, and why the effect never goes away no matter how many times it is laundered. It is not residual shrinkage that has failed to be taken out. It is a different quantity that a pre-shrinking process has no way to address, because there is nothing to take out: the cloth is not somewhere it does not want to be.

A treatment can only remove a shrinkage that is a departure from equilibrium. Hygral shrinkage is not one.

What would remove it #

Two things would, and both are used.

Change the fibre. Polyester swells by a thousandth of a per cent, so a polyester cloth has essentially no hygral shrinkage at all. That is the largest single reason polyester-cotton blends took over shirting, and it is a much more precise statement than “polyester is stable”: a blend’s hygral shrinkage is roughly the cotton fraction’s, so a 65/35 polyester-cotton shirting has about a third of an all-cotton one’s.

Or resin-treat the cellulose. A cross-linked cotton — the durable-press treatments — has its cellulose chains bridged, which physically prevents the amorphous regions from taking up as much water. That reduces the swelling itself rather than its consequences, at a well-known cost in tear strength and abrasion resistance, and it is why an easy-care cotton shirt wears out sooner.

Both act on the same place: the twenty per cent. Nothing acts on the geometry, because the geometry is not doing anything wrong.

A blend does not merely dilute the effect #

The claim that a 65/35 polyester–cotton shirting has about a third of an all-cotton one’s hygral shrinkage is worth checking, because it turns out to be right for the reason given and wrong about what else changes.

The transverse half dilutes exactly as expected. In an intimate blend the yarn’s swelling is the volume-weighted mean of its components’, and thirty-five per cent cotton by mass is 32.8 per cent by volume against polyester’s lower density. So the yarn swells 20 × 0.328 = 6.6 per cent rather than twenty, and the geometric shrinkage — very nearly proportional to the swelling at these sizes — comes down by the same third.

The axial half does not dilute; it is suppressed. Along a fibre’s own length the components of a blended yarn are in parallel and share a strain, so the yarn’s axial swelling is weighted by stiffness rather than by volume, and polyester is several times stiffer than wet cotton. Taking three gigapascals against ten, the composite’s axial swelling is

0.15 per cent, against 0.39 if it had merely diluted.

A further factor of two and a half down, on top of the dilution.

That matters because the axial term is the one that pushes the other way. It is what makes an open cloth expand on wetting, and it is what puts the sign-change boundary at a cover of 0.230 for cotton at all. Weakening it while merely diluting the transverse term moves the balance between them: the ratio of axial to transverse swelling falls from 0.060 for cotton to 0.023 for the blend.

So, scaling the threshold with that ratio — which is a scaling rather than a solve, and should be read as one —

a polyester–cotton blend’s sign-change cover is somewhere near 0.09.

Below a tenth of a cover is not a cloth. Essentially every blended construction is on the shrinking side, where an all-cotton scrim at a cover of 0.2 would have been on the expanding side.

Which is a small correction with a clean consequence #

The practical upshot is not that the blend shrinks more than a third — it shrinks very slightly more, and the difference is well inside everything else this model does not know.

It is that a blend loses the expanding regime altogether, and with it the one construction in which hygral movement can be arranged to cancel rather than accumulate. An all-cotton fabric near its own threshold is hygrally neutral: wet it and it does not move, because the two terms balance. That is a genuinely useful construction and it exists at a cover of about a quarter, which is an open shirting or a voile.

No blend has one, because its threshold has moved below any weavable cover. A blended cloth is always on the shrinking side, always moves the same way, and the only lever left is how far.

That is a fair description of what the two fibres are used for. An all-cotton voile is stable in changing humidity in a way its cover factor, and nothing else on its specification, would explain; a polyester–cotton shirting is stable because its movement is small rather than because it is balanced.

And it sharpens what the blend actually buys. Polyester does not make a cloth hygrally neutral. It makes it hygrally quiet — a third of the movement, all in one direction, at every construction. The two are different kinds of stability, and only one of them survives being cut into a garment whose panels have different covers.

The residual that is neither #

There is a third contribution and it is worth naming so it is not swept into either.

A cotton garment shrinks most in its first wash and much less afterwards, and the usual explanation is that the relaxation was mostly taken then. That is true and it is not the whole of it: repeated wet-dry cycling permanently changes a cotton fabric. Fibres that have been swollen and dried under the loads their neighbours impose do not return to exactly the same section, and the yarn compacts a little each time.

This collection cannot compute that. Everything here is recoverable — dry the cloth and the model puts it back exactly — and the real process is not. This collection can say what pressure a wetting generates, and it is megapascals in a close cloth; what it cannot say is what fraction of that is spent permanently.

So a real wash has three parts and this collection can compute two of them. That is stated here rather than left implicit, because a label’s number is the sum of all three and quoting the model’s two against it would be quoting an incomplete sum as a prediction.

Why wool’s is large and cotton’s is not #

Wool swells sixteen per cent transversely against cotton’s twenty, so it is not the swelling that makes wool’s hygral behaviour the famous one.

It is the construction. Worsted suitings are woven open and relatively slackly by the standards of a cotton shirting — cover factors well under a half — and they are made of a fibre whose axial swelling is the same one and two tenths per cent as cotton’s while its transverse swelling is smaller. Run the crossing-cover arithmetic on wool and it changes sign at a cover of 0.259 rather than cotton’s 0.230, so a wider band of ordinary wool constructions sits on the expanding side of the boundary.

That is the geometric half of why the wool trade talks about hygral expansion and the cotton trade about shrinkage: the two fibres’ cloths sit on opposite sides of a boundary whose position each fibre sets for itself.

The other half is that wool is tailored. A cotton shirt that moves two per cent between a damp day and a dry one is a shirt; a jacket whose face cloth and interlining move different amounts is a jacket with a rippled lapel, and it is visible from across a room. The effect is not larger in wool so much as it is more expensive.

What was counted, and how #

The two mechanisms are computed by different machinery and that separation is itself the check.

The relaxation half goes through the loom-state solver, which is handed a relaxed spacing and works out what loom state implies it. Its inputs are two tensions.

The hygral half goes through the constant-thread-length locus at two thicknesses. Its inputs are a swelling and an axial swelling. It contains no tension at all.

There is no shared code and no shared parameter, so the two answers cannot be accidentally the same computation twice. That is worth more than an assertion here, because the failure this rung most needs to avoid is a model that reports one mechanism under two names.

Three assertions cover the hygral half. The closure margin and its closed form agree; the wet minimum is geometric for a balanced cloth; and suppressing the axial swelling must make every cloth shrink while restoring it must make at least one grow. That last is the one that distinguishes the two terms of the mechanism rather than checking the total.

Where the model stops #

No plasticity, as above, and it is the largest gap.

The relaxation half’s loom tensions are chosen rather than measured. They always have been in this collection, and the numbers here inherit that: the hygral part is a prediction from construction and the relaxation part is a prediction from two numbers somebody picked.

Neither half has temperature in it. A hot wash relaxes far more than a cold one, because heat softens the fibre and lets crossings slip. It also swells slightly more. Both effects go the same way and neither is modelled.

And the anisotropy is only computed for the hygral half. Warp and weft shrink by different amounts and this ladder computes that too; nothing here combines the two anisotropies, which do not have to point the same way.

The generalisation #

Two mechanisms that share a unit will be reported as one quantity until somebody finds a test that separates them.

A per cent of shrinkage is a per cent of shrinkage, and a tape measure is a very old and very reliable instrument. That is precisely why the merger has lasted: the measurement is good, the number is useful, and nothing about it announces that it is a sum.

What separated them here was not a better measurement. It was two models with disjoint inputs that both produced a per cent, and then asking which of their predictions differed. They differ in sign for an open cloth, in recoverability, in their response to agitation and in their dependence on construction — four tests, of which two are practical and one is already a standard method for a different fibre.

The habit is to be suspicious of a number that everybody agrees about and nobody can decompose.

Who found it, and when #

Both mechanisms are old. Relaxation shrinkage and its cure by compressive shrinking are Sanford Cluett’s, patented in 1930, which is where the word sanforised comes from. Hygral expansion in wool was named and measured in the 1950s and is a standard quantity in worsted tailoring, where it causes seam pucker and is a genuine nuisance.

That the same mechanism operates in cotton is not in doubt and is much less discussed, mostly because in cotton it is smaller than the relaxation part and in wool it is not.

What is this collection’s is computing the hygral part from the same locus machinery the tensile ladder uses, and the list of four ways the two differ — of which the sign reversal in an open cloth is the one nobody would look for.

Where the ladder goes next #

Into the other place water changes a fabric permanently, which is felting — where water’s job turns out not to be lubrication at all.